TPTP Problem File: SCT082-1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SCT082-1 : TPTP v9.0.0. Released v4.1.0.
% Domain : Social Choice Theory
% Problem : Arrow Order 270_7
% Version : Especial.
% English : Formalization of two proofs of Arrow's impossibility theorem. One
% formalization is based on utility functions, the other one on
% strict partial orders.
% Refs : [Nip09] Nipkow (2009), Social Choice Theory in HOL: Arrow and
% : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe
% : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% Source : [Nip10]
% Names : Arrow_Order-270_7 [Nip10]
% Status : Unsatisfiable
% Rating : 0.95 v7.4.0, 0.94 v7.3.0, 0.92 v7.0.0, 1.00 v4.1.0
% Syntax : Number of clauses : 885 ( 183 unt; 83 nHn; 498 RR)
% Number of literals : 2084 ( 511 equ;1156 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 15 ( 2 avg)
% Number of predicates : 59 ( 58 usr; 0 prp; 1-9 aty)
% Number of functors : 58 ( 58 usr; 14 con; 0-5 aty)
% Number of variables : 2993 ( 551 sgn)
% SPC : CNF_UNS_RFO_SEQ_NHN
% Comments :
%------------------------------------------------------------------------------
cnf(cls_INT__constant_1,axiom,
( c_Complete__Lattice_Ocomplete__lattice__class_OINFI(V_A,c_COMBK(V_c,tc_fun(T_a,tc_bool),T_b),T_b,tc_fun(T_a,tc_bool)) = V_c
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)) ) ).
cnf(cls_INF__const_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_b)
| c_Complete__Lattice_Ocomplete__lattice__class_OINFI(V_A,c_COMBK(V_M,T_b,T_a),T_a,T_b) = V_M
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_double__eq__0__iff_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_add__is__0_2,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) ).
cnf(cls_add__nonneg__eq__0__iff_2,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(T_a)))
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_inv__into__image__cancel_0,axiom,
( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_a,T_b),c_Set_Oimage(V_f,V_S,T_a,T_b),T_b,T_a) = V_S
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_S),V_A))
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
cnf(cls_add__sup__distrib__left_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add__join(T_a)
| c_HOL_Oplus__class_Oplus(V_a,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_b),V_c),T_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a)),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)) ) ).
cnf(cls_add__sup__distrib__right_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add__join(T_a)
| c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b),V_c,T_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a)) ) ).
cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_HOL_Oplus__class_Oplus(V_a,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_b),V_c),T_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a)),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)) ) ).
cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b),V_c,T_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a)) ) ).
cnf(cls_order_Oless__le_1,axiom,
( ~ hBOOL(hAPP(hAPP(V_less,V_x),V_x))
| ~ c_Orderings_Oorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_order_Ole__less_1,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,V_x),V_y))
| ~ hBOOL(hAPP(hAPP(V_less,V_x),V_y))
| ~ c_Orderings_Oorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_add__nonneg__nonneg_0,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)) ) ).
cnf(cls_finite__vimageI_0,axiom,
( c_Finite__Set_Ofinite(c_Set_Ovimage(V_h,V_F,T_b,T_a),T_b)
| ~ c_Fun_Oinj__on(V_h,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_a)
| ~ c_Finite__Set_Ofinite(V_F,T_a) ) ).
cnf(cls_Un__absorb_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_A) = V_A ).
cnf(cls_sup__idem_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_x) = V_x ) ).
cnf(cls_psubset__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_C))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_psubsetD_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_Nitpick_OEps__psimp_0,axiom,
( hBOOL(hAPP(V_P,c_Hilbert__Choice_OEps(V_P,T_a)))
| ~ hBOOL(hAPP(V_P,V_x))
| c_Hilbert__Choice_OEps(V_P,T_a) = V_x ) ).
cnf(cls_boolean__algebra_Ocompl__eq__compl__iff_0,axiom,
( hAPP(V_uminus,V_x) != hAPP(V_uminus,V_y)
| ~ c_Lattices_Oboolean__algebra(V_minus,V_uminus,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a)
| V_x = V_y ) ).
cnf(cls_inf__sup__distrib2_0,axiom,
( ~ class_Lattices_Odistrib__lattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_z),V_x)) ) ).
cnf(cls_inf__sup__distrib1_0,axiom,
( ~ class_Lattices_Odistrib__lattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_z)) ) ).
cnf(cls_Int__Un__distrib_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C)) ).
cnf(cls_Int__Un__distrib2_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)),V_A) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A)) ).
cnf(cls_sup__fun__eq_0,axiom,
( ~ class_Lattices_Olattice(T_b)
| hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,T_b)),V_f),V_g),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_b),hAPP(V_f,v_x)),hAPP(V_g,v_x)) ) ).
cnf(cls_add__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_c),V_d))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b)) ) ).
cnf(cls_image__subset__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_x)),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Set_Oimage(V_f,V_A,T_b,T_a)),V_B)) ) ).
cnf(cls_finite__surj_0,axiom,
( c_Finite__Set_Ofinite(V_B,T_b)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_b,tc_bool)),V_B),c_Set_Oimage(V_f,V_A,T_a,T_b)))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_inj__on__image__Int_0,axiom,
( c_Set_Oimage(V_f,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_b,tc_bool)),c_Set_Oimage(V_f,V_A,T_a,T_b)),c_Set_Oimage(V_f,V_B,T_a,T_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_C))
| ~ c_Fun_Oinj__on(V_f,V_C,T_a,T_b) ) ).
cnf(cls_inj__image__subset__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_b,tc_bool)),c_Set_Oimage(V_f,V_A,T_a,T_b)),c_Set_Oimage(V_f,V_B,T_a,T_b)))
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_inj__image__subset__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_b,tc_bool)),c_Set_Oimage(V_f,V_A,T_a,T_b)),c_Set_Oimage(V_f,V_B,T_a,T_b)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_sup__eq__if_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)) = hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))) ) ).
cnf(cls_funcset__mem_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b))) ) ).
cnf(cls_inf__0__imp__0_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)) != c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_ivl__disj__int_I11_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_m,T_a)),c_SetInterval_Oord__class_OatLeastLessThan(V_m,V_u,T_a)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_zero__le__double__add__iff__zero__le__single__add_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)) ) ).
cnf(cls_zero__le__double__add__iff__zero__le__single__add_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a))) ) ).
cnf(cls_less__Suc0_0,axiom,
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))) ) ).
cnf(cls_neg__less__0__iff__less_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),c_HOL_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)) ) ).
cnf(cls_neg__less__0__iff__less_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),c_HOL_Ozero__class_Ozero(T_a))) ) ).
cnf(cls_add__is__1_4,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)) ).
cnf(cls_add__strict__increasing_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_c))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)) ) ).
cnf(cls_PiE_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),hAPP(V_B,V_x)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,V_B,T_a,T_b))) ) ).
cnf(cls_Pi__mem_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),hAPP(V_B,V_x)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,V_B,T_a,T_b))) ) ).
cnf(cls_Times__eq__cancel2_0,axiom,
( c_Product__Type_OSigma(V_A,c_COMBK(V_C,tc_fun(T_a,tc_bool),T_b),T_b,T_a) != c_Product__Type_OSigma(V_B,c_COMBK(V_C,tc_fun(T_a,tc_bool),T_b),T_b,T_a)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_C))
| V_A = V_B ) ).
cnf(cls_bot__fun__eq_0,axiom,
( ~ class_Orderings_Obot(T_b)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,T_b)),v_x) = c_Orderings_Obot__class_Obot(T_b) ) ).
cnf(cls_ComplD_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A))) ) ).
cnf(cls_ComplI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A)))
| hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A)) ) ).
cnf(cls_inf__compl__bot_0,axiom,
( ~ class_Lattices_Oboolean__algebra(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Obot__class_Obot(T_a) ) ).
cnf(cls_compl__inf__bot_0,axiom,
( ~ class_Lattices_Oboolean__algebra(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Obot__class_Obot(T_a) ) ).
cnf(cls_Compl__disjoint_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_Compl__disjoint2_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A)),V_A) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_zero__le__power_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_Power_Opower__class_Opower(V_a,V_n,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)) ) ).
cnf(cls_neg__less__eq__nonneg_1,axiom,
( ~ class_OrderedGroup_Oordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),V_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)) ) ).
cnf(cls_neg__less__eq__nonneg_0,axiom,
( ~ class_OrderedGroup_Oordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),V_a)) ) ).
cnf(cls_less__eq__neg__nonpos_1,axiom,
( ~ class_OrderedGroup_Oordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))) ) ).
cnf(cls_less__eq__neg__nonpos_0,axiom,
( ~ class_OrderedGroup_Oordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a))) ) ).
cnf(cls_minus__le__self__iff_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),V_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)) ) ).
cnf(cls_minus__le__self__iff_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),V_a)) ) ).
cnf(cls_le__minus__self__iff_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))) ) ).
cnf(cls_le__minus__self__iff_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a))) ) ).
cnf(cls_empty__is__image_0,axiom,
( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Set_Oimage(V_f,V_A,T_b,T_a)
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)) ) ).
cnf(cls_power__0__Suc_0,axiom,
( ~ class_Ring__and__Field_Osemiring__0(T_a)
| ~ class_Power_Opower(T_a)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Suc(V_n),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_add__Suc__right_0,axiom,
c_HOL_Oplus__class_Oplus(V_m,c_Suc(V_n),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)) ).
cnf(cls_add__Suc_0,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)) ).
cnf(cls_notin__Lin__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin)) ) ).
cnf(cls_notin__Lin__iff_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin)) ) ).
cnf(cls_neg__le__iff__le_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a))) ) ).
cnf(cls_le__imp__neg__le_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b)) ) ).
cnf(cls_Compl__anti__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_Compl__subset__Compl__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_A))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B))) ) ).
cnf(cls_Compl__subset__Compl__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_A)) ) ).
cnf(cls_nat_Osimps_I2_J_0,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) ).
cnf(cls_Zero__neq__Suc_0,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m) ).
cnf(cls_image__vimage__subset_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Set_Oimage(V_f,c_Set_Ovimage(V_f,V_A,T_b,T_a),T_b,T_a)),V_A)) ).
cnf(cls_less__add__Suc1_0,axiom,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_i),c_Suc(c_HOL_Oplus__class_Oplus(V_i,V_m,tc_nat)))) ).
cnf(cls_less__add__Suc2_0,axiom,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_i),c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_i,tc_nat)))) ).
cnf(cls_less__iff__Suc__add_1,axiom,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_x,tc_nat)))) ).
cnf(cls_inj__vimage__image__eq_0,axiom,
( c_Set_Ovimage(V_f,c_Set_Oimage(V_f,V_A,T_a,T_b),T_a,T_b) = V_A
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_empty__subsetI_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),V_A)) ).
cnf(cls_bot__least_0,axiom,
( ~ class_Orderings_Obot(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ).
cnf(cls_add__increasing_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_c))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)) ) ).
cnf(cls_add__increasing2_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_c)) ) ).
cnf(cls_add__eq__inf__sup_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b),T_a) ) ).
cnf(cls_subset__Compl__self__eq_1,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))) ).
cnf(cls_inj__on__Un__image__eq__iff_0,axiom,
( c_Set_Oimage(V_f,V_A,T_a,T_b) != c_Set_Oimage(V_f,V_B,T_a,T_b)
| ~ c_Fun_Oinj__on(V_f,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b)
| V_A = V_B ) ).
cnf(cls_INT__subset__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),hAPP(V_A,V_i)))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_i),V_I))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(V_I,V_A,T_b,tc_fun(T_a,tc_bool)))) ) ).
cnf(cls_inv__into__f__f_0,axiom,
( hAPP(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_a,T_b),hAPP(V_f,V_x)) = V_x
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
cnf(cls_inv__into__f__eq_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_aa),V_x),V_A))
| ~ c_Fun_Oinj__on(V_f,V_A,T_aa,T_a)
| hAPP(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_aa,T_a),hAPP(V_f,V_x)) = V_x ) ).
cnf(cls_inf__bot__right_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
cnf(cls_inf__bot__left_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = c_Orderings_Obot__class_Obot(T_a) ) ).
cnf(cls_Int__empty__left_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),V_B) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_Int__empty__right_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) ).
cnf(cls_comm__monoid__add_Omult__commute_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) ).
cnf(cls_nat__add__commute_0,axiom,
c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat) ).
cnf(cls_class__semiring_Oadd__c_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) = c_HOL_Oplus__class_Oplus(V_y,V_x,T_a) ) ).
cnf(cls_INT__D_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_b),hAPP(V_B,V_a)))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_a),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_b),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(V_A,V_B,T_b,tc_fun(T_a,tc_bool)))) ) ).
cnf(cls_INT__E_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_b),V_a),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_b),hAPP(V_B,V_a)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_b),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(V_A,V_B,T_b,tc_fun(T_a,tc_bool)))) ) ).
cnf(cls_INT__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_b),hAPP(V_B,V_x)))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_b),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(V_A,V_B,T_b,tc_fun(T_a,tc_bool)))) ) ).
cnf(cls_finite_OemptyI_0,axiom,
c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ).
cnf(cls_of__nat__eq__iff_0,axiom,
( ~ class_Nat_Osemiring__char__0(T_a)
| c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a) != c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)
| V_m = V_n ) ).
cnf(cls_INT__extend__simps_I1_J_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_A,T_b,tc_fun(T_a,tc_bool))),V_B) = V_B ).
cnf(cls_INT__extend__simps_I2_J_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_B,T_b,tc_fun(T_a,tc_bool))) = V_A ).
cnf(cls_class__ringb_Oadd__r0__iff_0,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_add__eq__self__zero_0,axiom,
( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != V_m
| V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
cnf(cls_natgb_Oadd__r0__iff_0,axiom,
( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,tc_nat)
| V_a = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
cnf(cls_image__Int_0,axiom,
( c_Set_Oimage(V_f,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_b,tc_bool)),c_Set_Oimage(V_f,V_A,T_a,T_b)),c_Set_Oimage(V_f,V_B,T_a,T_b))
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_Sup__empty_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) = c_Orderings_Obot__class_Obot(T_a) ) ).
cnf(cls_image__Int__subset_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Set_Oimage(V_f,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_b,tc_bool)),V_A),V_B),T_b,T_a)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Oimage(V_f,V_A,T_b,T_a)),c_Set_Oimage(V_f,V_B,T_b,T_a)))) ).
cnf(cls_finite__Un_2,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_F),V_G),T_a)
| ~ c_Finite__Set_Ofinite(V_G,T_a)
| ~ c_Finite__Set_Ofinite(V_F,T_a) ) ).
cnf(cls_finite__UnI_0,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_F),V_G),T_a)
| ~ c_Finite__Set_Ofinite(V_G,T_a)
| ~ c_Finite__Set_Ofinite(V_F,T_a) ) ).
cnf(cls_Un__Int__assoc__eq_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),V_A)) ) ).
cnf(cls_Un__Int__assoc__eq_1,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),V_A)) ) ).
cnf(cls_finite__INT_0,axiom,
( c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(V_I,V_A,T_a,tc_fun(T_b,tc_bool)),T_b)
| ~ c_Finite__Set_Ofinite(hAPP(V_A,V_x),T_b)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_I)) ) ).
cnf(cls_INT__simps_I10_J_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Set_Oimage(V_f,V_A,T_c,T_b),V_B,T_b,tc_fun(T_a,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(V_A,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_a,tc_bool),T_c),V_B),V_f),T_c,tc_fun(T_a,tc_bool)) ).
cnf(cls_inj__image__mem__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),c_Set_Oimage(V_f,V_A,T_a,T_b)))
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_inj__image__mem__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),c_Set_Oimage(V_f,V_A,T_a,T_b)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_add__nonneg__eq__0__iff_1,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
| c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_y))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_x))
| V_y = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_add__nonneg__eq__0__iff_0,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
| c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_y))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_x))
| V_x = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_class__semiring_Oadd__a_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_z,T_a) ) ).
cnf(cls_add__cancel__21_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_y,c_HOL_Oplus__class_Oplus(V_x,V_z,T_a),T_a) ) ).
cnf(cls_nat__add__left__commute_0,axiom,
c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(V_y,c_HOL_Oplus__class_Oplus(V_x,V_z,tc_nat),tc_nat) ).
cnf(cls_nat__add__assoc_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Oplus__class_Oplus(V_m,c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat) ).
cnf(cls_comm__monoid__add_Omult__assoc_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ).
cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) ).
cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom,
( ~ class_OrderedGroup_Oab__semigroup__add(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_d,T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_b,T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oplus__class_Oplus(V_a,V_d,T_a),T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ).
cnf(cls_add__gr__0_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_m))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat))) ) ).
cnf(cls_neg__0__equal__iff__equal_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Ozero__class_Ozero(T_a) != hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)
| c_HOL_Ozero__class_Ozero(T_a) = V_a ) ).
cnf(cls_power__eq__0__iff_1,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Power_Opower(T_a)
| c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_dual__lattice_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_Lattices_Olattice(c_COMBC(c_lessequals(T_a),T_a,T_a,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(T_a),T_a,T_a,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(T_a),c_Lattices_Olower__semilattice__class_Oinf(T_a),T_a) ) ).
cnf(cls_SigmaD2_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_b),V_b),hAPP(V_B,V_a)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_b)),c_Pair(V_a,V_b,T_a,T_b)),c_Product__Type_OSigma(V_A,V_B,T_a,T_b))) ) ).
cnf(cls_SigmaD1_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_b)),c_Pair(V_a,V_b,T_a,T_b)),c_Product__Type_OSigma(V_A,V_B,T_a,T_b))) ) ).
cnf(cls_inv__into__injective_0,axiom,
( hAPP(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_a,T_b),V_x) != hAPP(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_a,T_b),V_y)
| V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_y),c_Set_Oimage(V_f,V_A,T_a,T_b)))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),c_Set_Oimage(V_f,V_A,T_a,T_b))) ) ).
cnf(cls_add__cancel__21_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) != c_HOL_Oplus__class_Oplus(V_y,V_u,T_a)
| c_HOL_Oplus__class_Oplus(V_x,V_z,T_a) = V_u ) ).
cnf(cls_inv__into__into_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_b),hAPP(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_b,T_a),V_x)),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Set_Oimage(V_f,V_A,T_b,T_a))) ) ).
cnf(cls_mem__def_1,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_S))
| ~ hBOOL(hAPP(V_S,V_x)) ) ).
cnf(cls_mem__def_0,axiom,
( hBOOL(hAPP(V_S,V_x))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_S)) ) ).
cnf(cls_COMBS__def_0,axiom,
hAPP(c_COMBS(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),hAPP(V_Q,V_R)) ).
cnf(cls_less__fun__def_1,axiom,
( ~ class_HOL_Oord(T_b)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,T_b)),V_g),V_f))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,T_b)),V_f),V_g)) ) ).
cnf(cls_preorder_Oless__le__not__le_2,axiom,
( hBOOL(hAPP(hAPP(V_less,V_x),V_y))
| hBOOL(hAPP(hAPP(V_less__eq,V_y),V_x))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_x),V_y))
| ~ c_Orderings_Opreorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_preorder_Oless__irrefl_0,axiom,
( ~ hBOOL(hAPP(hAPP(V_less,V_x),V_x))
| ~ c_Orderings_Opreorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_preorder_Oless__imp__le_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,V_x),V_y))
| ~ hBOOL(hAPP(hAPP(V_less,V_x),V_y))
| ~ c_Orderings_Opreorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_neg__0__le__iff__le_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a))) ) ).
cnf(cls_neg__0__le__iff__le_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))) ) ).
cnf(cls_rangeI_0,axiom,
hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_x)),c_Set_Oimage(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_a))) ).
cnf(cls_add__inf__distrib__left_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(T_a)
| c_HOL_Oplus__class_Oplus(V_a,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_b),V_c),T_a) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a)),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)) ) ).
cnf(cls_add__inf__distrib__right_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(T_a)
| c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b),V_c,T_a) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a)) ) ).
cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_HOL_Oplus__class_Oplus(V_a,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_b),V_c),T_a) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a)),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)) ) ).
cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_HOL_Oplus__class_Oplus(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b),V_c,T_a) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a)) ) ).
cnf(cls_one__is__add_5,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) ).
cnf(cls_add__strict__increasing2_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_c))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)) ) ).
cnf(cls_power__mono_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a)),c_Power_Opower__class_Opower(V_b,V_n,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b)) ) ).
cnf(cls_one__is__add_3,axiom,
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)
| V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
cnf(cls_one__is__add_0,axiom,
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)
| V_m = c_HOL_Ozero__class_Ozero(tc_nat)
| V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ).
cnf(cls_image__empty_0,axiom,
c_Set_Oimage(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_linorder_Oneq__iff_1,axiom,
( ~ hBOOL(hAPP(hAPP(V_less,V_x),V_x))
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_linorder_Onot__less__iff__gr__or__eq_2,axiom,
( ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a)
| ~ hBOOL(hAPP(hAPP(V_less,V_x),V_x)) ) ).
cnf(cls_add__Suc__shift_0,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_m,c_Suc(V_n),tc_nat) ).
cnf(cls_inj__on__empty_0,axiom,
c_Fun_Oinj__on(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a,T_b) ).
cnf(cls_Un__left__commute_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_C)) ).
cnf(cls_Un__assoc_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)) ).
cnf(cls_sup__assoc_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z)) ) ).
cnf(cls_sup__left__commute_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_z)) ) ).
cnf(cls_inf__sup__aci_I7_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_z)) ) ).
cnf(cls_inf__sup__aci_I6_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z)) ) ).
cnf(cls_IntE_1,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B))) ) ).
cnf(cls_IntE_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B))) ) ).
cnf(cls_inj__on__contraD_0,axiom,
( hAPP(V_f,V_x) != hAPP(V_f,V_y)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_y),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| V_x = V_y
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
cnf(cls_inj__on__iff_0,axiom,
( hAPP(V_f,V_x) != hAPP(V_f,V_y)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_y),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| V_x = V_y ) ).
cnf(cls_inj__on__def_0,axiom,
( hAPP(V_f,V_x) != hAPP(V_f,V_xa)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xa),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| V_x = V_xa ) ).
cnf(cls_inj__onD_0,axiom,
( hAPP(V_f,V_x) != hAPP(V_f,V_y)
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_y),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_funcset__image_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_b,tc_bool)),c_Set_Oimage(V_f,V_A,T_a,T_b)),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b))) ) ).
cnf(cls_Int__absorb2_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_A
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_Int__absorb1_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_B
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_A)) ) ).
cnf(cls_le__iff__inf_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) = V_x
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_le__iff__inf_1,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) != V_x
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_inf__absorb2_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) = V_y
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x)) ) ).
cnf(cls_zero__less__Suc_0,axiom,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(V_n))) ).
cnf(cls_gr0__conv__Suc_1,axiom,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(V_x))) ).
cnf(cls_Un__subset__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_C)) ) ).
cnf(cls_Un__upper2_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B))) ).
cnf(cls_Un__upper1_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B))) ).
cnf(cls_Un__least_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_C)) ) ).
cnf(cls_le__supI_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b)),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_x)) ) ).
cnf(cls_sup__ge1_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y))) ) ).
cnf(cls_sup__ge2_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y))) ) ).
cnf(cls_sup__least_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z)),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_z),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x)) ) ).
cnf(cls_le__sup__iff_2,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_z)) ) ).
cnf(cls_inf__sup__ord_I4_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y))) ) ).
cnf(cls_inf__sup__ord_I3_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y))) ) ).
cnf(cls_Int__commute_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_A) ).
cnf(cls_inf__commute_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_x) ) ).
cnf(cls_inf__sup__aci_I1_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_x) ) ).
cnf(cls_dual__boolean__algebra_0,axiom,
( ~ class_Lattices_Oboolean__algebra(T_a)
| c_Lattices_Oboolean__algebra(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(T_a,T_a),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,T_a)),T_a),c_COMBB(T_a,T_a,T_a)),c_Lattices_Oupper__semilattice__class_Osup(T_a)),T_a,tc_fun(T_a,T_a),tc_fun(T_a,T_a)),c_HOL_Ouminus__class_Ouminus(T_a)),c_HOL_Ouminus__class_Ouminus(T_a),c_COMBC(c_lessequals(T_a),T_a,T_a,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(T_a),T_a,T_a,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(T_a),c_Lattices_Olower__semilattice__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a),c_Orderings_Obot__class_Obot(T_a),T_a) ) ).
cnf(cls_Lin__irrefl_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_b,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin)) ) ).
cnf(cls_distrib__inf__le_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_z))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z)))) ) ).
cnf(cls_of__nat__0_0,axiom,
( ~ class_Ring__and__Field_Osemiring__1(T_a)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_left__minus_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_right__minus_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Oplus__class_Oplus(V_a,hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_ab__left__minus_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_eq__neg__iff__add__eq__0_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_compl__unique_0,axiom,
( ~ class_Lattices_Oboolean__algebra(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) != c_Orderings_Otop__class_Otop(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) != c_Orderings_Obot__class_Obot(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ).
cnf(cls_Un__Int__crazy_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_C),V_A)) ).
cnf(cls_bex__empty_0,axiom,
( ~ hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) ) ).
cnf(cls_add__neg__neg_0,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a)),c_HOL_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),c_HOL_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))) ) ).
cnf(cls_power__strict__mono_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a)),c_Power_Opower__class_Opower(V_b,V_n,T_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)) ) ).
cnf(cls_distrib__lattice_Oinf__sup__distrib1_0,axiom,
( hAPP(hAPP(V_inf,V_x),hAPP(hAPP(V_sup,V_y),V_z)) = hAPP(hAPP(V_sup,hAPP(hAPP(V_inf,V_x),V_y)),hAPP(hAPP(V_inf,V_x),V_z))
| ~ c_Lattices_Odistrib__lattice(V_less__eq,V_less,V_inf,V_sup,T_a) ) ).
cnf(cls_distrib__lattice_Oinf__sup__distrib2_0,axiom,
( hAPP(hAPP(V_inf,hAPP(hAPP(V_sup,V_y),V_z)),V_x) = hAPP(hAPP(V_sup,hAPP(hAPP(V_inf,V_y),V_x)),hAPP(hAPP(V_inf,V_z),V_x))
| ~ c_Lattices_Odistrib__lattice(V_less__eq,V_less,V_inf,V_sup,T_a) ) ).
cnf(cls_distrib__lattice_Osup__inf__distrib1_0,axiom,
( hAPP(hAPP(V_sup,V_x),hAPP(hAPP(V_inf,V_y),V_z)) = hAPP(hAPP(V_inf,hAPP(hAPP(V_sup,V_x),V_y)),hAPP(hAPP(V_sup,V_x),V_z))
| ~ c_Lattices_Odistrib__lattice(V_less__eq,V_less,V_inf,V_sup,T_a) ) ).
cnf(cls_distrib__lattice_Osup__inf__distrib2_0,axiom,
( hAPP(hAPP(V_sup,hAPP(hAPP(V_inf,V_y),V_z)),V_x) = hAPP(hAPP(V_inf,hAPP(hAPP(V_sup,V_y),V_x)),hAPP(hAPP(V_sup,V_z),V_x))
| ~ c_Lattices_Odistrib__lattice(V_less__eq,V_less,V_inf,V_sup,T_a) ) ).
cnf(cls_pred__equals__eq_0,axiom,
( hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_R) != hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_S)
| V_R = V_S ) ).
cnf(cls_exE__some_0,axiom,
( ~ hBOOL(hAPP(V_P,V_x))
| hBOOL(hAPP(V_P,c_Hilbert__Choice_OEps(V_P,T_a))) ) ).
cnf(cls_someI_0,axiom,
( hBOOL(hAPP(V_P,c_Hilbert__Choice_OEps(V_P,T_a)))
| ~ hBOOL(hAPP(V_P,V_x)) ) ).
cnf(cls_image__constant__conv_0,axiom,
c_Set_Oimage(c_COMBK(V_c,T_a,T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_Compl__partition2_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A)),V_A) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) ).
cnf(cls_add__is__0_0,axiom,
( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
cnf(cls_add__is__0_1,axiom,
( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
cnf(cls_double__eq__0__iff_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_HOL_Oplus__class_Oplus(V_a,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_Suc__inject_0,axiom,
( c_Suc(V_x) != c_Suc(V_y)
| V_x = V_y ) ).
cnf(cls_nat_Oinject_0,axiom,
( c_Suc(V_nat) != c_Suc(V_nat_H)
| V_nat = V_nat_H ) ).
cnf(cls_infinite__descent__measure_0,axiom,
( hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Nat__Xinfinite__descent__measure__1__1(V_P,V_V,T_a))) ) ).
cnf(cls_not__psubset__empty_0,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) ).
cnf(cls_less__Suc0_1,axiom,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))) ).
cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a)),c_HOL_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))) ) ).
cnf(cls_double__add__less__zero__iff__single__less__zero_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a)),c_HOL_Ozero__class_Ozero(T_a))) ) ).
cnf(cls_even__less__0__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a)),c_HOL_Ozero__class_Ozero(T_a))) ) ).
cnf(cls_even__less__0__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a)),c_HOL_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))) ) ).
cnf(cls_one__is__add_1,axiom,
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)
| V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ).
cnf(cls_one__is__add_2,axiom,
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)
| V_m = c_HOL_Ozero__class_Ozero(tc_nat)
| V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
cnf(cls_power__less__imp__less__base_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a)),c_Power_Opower__class_Opower(V_b,V_n,T_a))) ) ).
cnf(cls_card__psubset_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(V_A,T_a)),c_Finite__Set_Ocard(V_B,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ c_Finite__Set_Ofinite(V_B,T_a) ) ).
cnf(cls_zero__less__power_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_Power_Opower__class_Opower(V_a,V_n,T_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)) ) ).
cnf(cls_sup1E_0,axiom,
( hBOOL(hAPP(V_B,V_x))
| hBOOL(hAPP(V_A,V_x))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),V_x)) ) ).
cnf(cls_sup1CI_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),V_x))
| ~ hBOOL(hAPP(V_B,V_x)) ) ).
cnf(cls_sup1CI_1,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),V_x))
| ~ hBOOL(hAPP(V_A,V_x)) ) ).
cnf(cls_endo__inj__surj_0,axiom,
( c_Set_Oimage(V_f,V_A,T_a,T_a) = V_A
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Set_Oimage(V_f,V_A,T_a,T_a)),V_A))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_UnE_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
| hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B))) ) ).
cnf(cls_eq__neg__iff__add__eq__0_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_a = hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b) ) ).
cnf(cls_minus__unique_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ).
cnf(cls_inf__sup__aci_I2_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z)) ) ).
cnf(cls_inf__sup__aci_I3_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_z)) ) ).
cnf(cls_inf__left__commute_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_z)) ) ).
cnf(cls_inf__assoc_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z)) ) ).
cnf(cls_Int__assoc_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)) ).
cnf(cls_Int__left__commute_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C)) ).
cnf(cls_ivl__disj__un_I17_J_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_m,T_a)),c_SetInterval_Oord__class_OatLeastLessThan(V_m,V_u,T_a)) = c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_u,T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_m),V_u))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_l),V_m)) ) ).
cnf(cls_const__Lin__Prof_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBK(V_L,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin)) ) ).
cnf(cls_finite__Un_0,axiom,
( c_Finite__Set_Ofinite(V_F,T_a)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_F),V_G),T_a) ) ).
cnf(cls_finite__Un_1,axiom,
( c_Finite__Set_Ofinite(V_G,T_a)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_F),V_G),T_a) ) ).
cnf(cls_INF__leI_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_b)
| hBOOL(hAPP(hAPP(c_lessequals(T_b),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(V_A,V_M,T_a,T_b)),hAPP(V_M,V_i)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_i),V_A)) ) ).
cnf(cls_INT__lower_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_b,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(V_A,V_B,T_a,tc_fun(T_b,tc_bool))),hAPP(V_B,V_a)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)) ) ).
cnf(cls_sup__bot__right_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ).
cnf(cls_sup__bot__left_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ).
cnf(cls_Un__empty__left_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),V_B) = V_B ).
cnf(cls_Un__empty__right_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = V_A ).
cnf(cls_sup__Un__eq_0,axiom,
hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),V_R)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),V_S)),v_x) = hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),V_R),V_S)) ).
cnf(cls_card__Un__disjoint_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Ocard(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),T_a) = c_HOL_Oplus__class_Oplus(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_a),tc_nat) ) ).
cnf(cls_bij__betw__def_2,axiom,
( ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| c_Fun_Obij__betw(V_f,V_A,c_Set_Oimage(V_f,V_A,T_a,T_b),T_a,T_b) ) ).
cnf(cls_inj__image__eq__iff_0,axiom,
( c_Set_Oimage(V_f,V_A,T_a,T_b) != c_Set_Oimage(V_f,V_B,T_a,T_b)
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b)
| V_A = V_B ) ).
cnf(cls_add__nonpos__neg_0,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a)),c_HOL_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),c_HOL_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))) ) ).
cnf(cls_add__neg__nonpos_0,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a)),c_HOL_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),c_HOL_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))) ) ).
cnf(cls_inj__on__inv__into_0,axiom,
( c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_b,T_a),V_B,T_a,T_b)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),c_Set_Oimage(V_f,V_A,T_b,T_a))) ) ).
cnf(cls_INTER__UNIV__conv_I1_J_0,axiom,
( c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OINFI(V_A,V_B,T_b,tc_fun(T_a,tc_bool))
| hAPP(V_B,V_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A)) ) ).
cnf(cls_sup__0__imp__0_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)) != c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_neg__equal__0__iff__equal_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_compl__top__eq_0,axiom,
( ~ class_Lattices_Oboolean__algebra(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
cnf(cls_Compl__UNIV__eq_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_setprod__constant_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__mult(T_b)
| c_Finite__Set_Osetprod(c_COMBK(V_y,T_b,T_a),V_A,T_a,T_b) = c_Power_Opower__class_Opower(V_y,c_Finite__Set_Ocard(V_A,T_a),T_b)
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_bot1E_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x)) ).
cnf(cls_disjoint__iff__not__equal_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_image__vimage__eq_0,axiom,
c_Set_Oimage(V_f,c_Set_Ovimage(V_f,V_A,T_b,T_a),T_b,T_a) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_Set_Oimage(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_a)) ).
cnf(cls_distrib__sup__le_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_z)))) ) ).
cnf(cls_order_Oeq__iff_0,axiom,
( ~ c_Orderings_Oorder(V_less__eq,V_less,T_a)
| hBOOL(hAPP(hAPP(V_less__eq,V_x),V_x)) ) ).
cnf(cls_atLeastLessThan__empty_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_SetInterval_Oord__class_OatLeastLessThan(V_a,V_b,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_a)) ) ).
cnf(cls_one__is__add_4,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) ).
cnf(cls_psubset__eq_1,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_x),V_x)) ).
cnf(cls_less__fun__def_2,axiom,
( ~ class_HOL_Oord(T_b)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,T_b)),V_f),V_g))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,T_b)),V_g),V_f))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,T_b)),V_f),V_g)) ) ).
cnf(cls_sup__inf__absorb_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)) = V_x ) ).
cnf(cls_add__pos__pos_0,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)) ) ).
cnf(cls_card__eq__0__iff_2,axiom,
( c_Finite__Set_Ocard(V_A,T_a) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_INT__extend__simps_I10_J_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OINFI(V_A,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_a,tc_bool),T_b),V_B),V_f),T_b,tc_fun(T_a,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Set_Oimage(V_f,V_A,T_b,T_c),V_B,T_c,tc_fun(T_a,tc_bool)) ).
cnf(cls_measure__induct_1,axiom,
( hBOOL(hAPP(V_P,V_a))
| ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Nat__Xmeasure__induct__1__1(V_P,V_f,T_a))) ) ).
cnf(cls_compl__eq__compl__iff_0,axiom,
( ~ class_Lattices_Oboolean__algebra(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_x) != hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_y)
| V_x = V_y ) ).
cnf(cls_neg__equal__iff__equal_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a) != hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)
| V_a = V_b ) ).
cnf(cls_Compl__eq__Compl__iff_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B)
| V_A = V_B ) ).
cnf(cls_pred__subset__eq_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_R),V_S))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_R)),hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_S))) ) ).
cnf(cls_pred__subset__eq_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_R)),hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_S)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_R),V_S)) ) ).
cnf(cls_equalityI_0,axiom,
( V_A = V_B
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_A))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_set__eq__subset_2,axiom,
( V_A = V_B
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_A))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_order__eq__iff_2,axiom,
( ~ class_Orderings_Oorder(T_a)
| V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_order__antisym_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_order__antisym__conv_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x)) ) ).
cnf(cls_inf__sup__absorb_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)) = V_x ) ).
cnf(cls_psubset__eq_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_less__fun__def_0,axiom,
( ~ class_HOL_Oord(T_b)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,T_b)),V_f),V_g))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,T_b)),V_f),V_g)) ) ).
cnf(cls_sup__absorb1_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) = V_x
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x)) ) ).
cnf(cls_le__iff__sup_1,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) != V_y
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_le__iff__sup_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) = V_y
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_Un__absorb1_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B) = V_B
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_Un__absorb2_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B) = V_A
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_A)) ) ).
cnf(cls_subset__Un__eq_1,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B) != V_B
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_minus__add__cancel_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) = V_b ) ).
cnf(cls_add__cancel__end_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_z),c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = V_y ) ).
cnf(cls_preorder_Oeq__refl_0,axiom,
( ~ c_Orderings_Opreorder(V_less__eq,V_less,T_a)
| hBOOL(hAPP(hAPP(V_less__eq,V_x),V_x)) ) ).
cnf(cls_preorder_Oless__asym_0,axiom,
( ~ hBOOL(hAPP(hAPP(V_less,V_y),V_x))
| ~ hBOOL(hAPP(hAPP(V_less,V_x),V_y))
| ~ c_Orderings_Opreorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_preorder_Oless__asym_H_0,axiom,
( ~ hBOOL(hAPP(hAPP(V_less,V_b),V_a))
| ~ hBOOL(hAPP(hAPP(V_less,V_a),V_b))
| ~ c_Orderings_Opreorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_preorder_Oless__trans_0,axiom,
( hBOOL(hAPP(hAPP(V_less,V_x),V_z))
| ~ hBOOL(hAPP(hAPP(V_less,V_y),V_z))
| ~ hBOOL(hAPP(hAPP(V_less,V_x),V_y))
| ~ c_Orderings_Opreorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_preorder_Oorder__refl_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,V_x),V_x))
| ~ c_Orderings_Opreorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_preorder_Oorder__trans_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,V_x),V_z))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_y),V_z))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_x),V_y))
| ~ c_Orderings_Opreorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_preorder_Ole__less__trans_0,axiom,
( hBOOL(hAPP(hAPP(V_less,V_x),V_z))
| ~ hBOOL(hAPP(hAPP(V_less,V_y),V_z))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_x),V_y))
| ~ c_Orderings_Opreorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_preorder_Oless__le__trans_0,axiom,
( hBOOL(hAPP(hAPP(V_less,V_x),V_z))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_y),V_z))
| ~ hBOOL(hAPP(hAPP(V_less,V_x),V_y))
| ~ c_Orderings_Opreorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_preorder_Oless__le__not__le_1,axiom,
( ~ hBOOL(hAPP(hAPP(V_less__eq,V_y),V_x))
| ~ hBOOL(hAPP(hAPP(V_less,V_x),V_y))
| ~ c_Orderings_Opreorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_finite__imageI_0,axiom,
( c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b)
| ~ c_Finite__Set_Ofinite(V_F,T_a) ) ).
cnf(cls_inf__Int__eq_0,axiom,
hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),V_R)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),V_S)),v_x) = hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),V_R),V_S)) ).
cnf(cls_nat_Osimps_I3_J_0,axiom,
c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat) ).
cnf(cls_Compl__partition_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) ).
cnf(cls_compl__sup__top_0,axiom,
( ~ class_Lattices_Oboolean__algebra(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Otop__class_Otop(T_a) ) ).
cnf(cls_sup__compl__top_0,axiom,
( ~ class_Lattices_Oboolean__algebra(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Otop__class_Otop(T_a) ) ).
cnf(cls_atLeastLessThan__subset__iff_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_c),V_a))
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(V_a,V_b,T_a)),c_SetInterval_Oord__class_OatLeastLessThan(V_c,V_d,T_a))) ) ).
cnf(cls_atLeastLessThan__subset__iff_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_d))
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(V_a,V_b,T_a)),c_SetInterval_Oord__class_OatLeastLessThan(V_c,V_d,T_a))) ) ).
cnf(cls_add__nonneg__pos_0,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)) ) ).
cnf(cls_add__pos__nonneg_0,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)) ) ).
cnf(cls_vimage__Compl_0,axiom,
c_Set_Ovimage(V_f,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_b,tc_bool)),V_A),T_a,T_b) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),c_Set_Ovimage(V_f,V_A,T_a,T_b)) ).
cnf(cls_natgb_Oadd__cancel_0,axiom,
( c_HOL_Oplus__class_Oplus(V_x,V_y,tc_nat) != c_HOL_Oplus__class_Oplus(V_x,V_z,tc_nat)
| V_y = V_z ) ).
cnf(cls_nat__add__right__cancel_0,axiom,
( c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat) != c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat)
| V_m = V_n ) ).
cnf(cls_nat__add__left__cancel_0,axiom,
( c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat)
| V_m = V_n ) ).
cnf(cls_class__ringb_Oadd__cancel_0,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Oplus__class_Oplus(V_x,V_z,T_a)
| V_y = V_z ) ).
cnf(cls_add__imp__eq_0,axiom,
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(T_a)
| c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)
| V_b = V_c ) ).
cnf(cls_add__left__cancel_0,axiom,
( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a)
| c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)
| V_b = V_c ) ).
cnf(cls_add__right__cancel_0,axiom,
( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a)
| c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) != c_HOL_Oplus__class_Oplus(V_c,V_a,T_a)
| V_b = V_c ) ).
cnf(cls_preorder__class_Oaxioms_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_Orderings_Opreorder(c_lessequals(T_a),c_HOL_Oord__class_Oless(T_a),T_a) ) ).
cnf(cls_vimage__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_b,tc_bool)),c_Set_Ovimage(V_f,V_A,T_b,T_a)),c_Set_Ovimage(V_f,V_B,T_b,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_Un__empty_1,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| V_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Un__empty_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_sup__eq__bot__eq1_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_A),V_B) != c_Orderings_Obot__class_Obot(T_a)
| V_A = c_Orderings_Obot__class_Obot(T_a) ) ).
cnf(cls_sup__eq__bot__eq2_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_A),V_B) != c_Orderings_Obot__class_Obot(T_a)
| V_B = c_Orderings_Obot__class_Obot(T_a) ) ).
cnf(cls_bij__betw__inv__into_0,axiom,
( c_Fun_Obij__betw(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_a,T_b),V_B,V_A,T_b,T_a)
| ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b) ) ).
cnf(cls_Int__subset__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),V_B))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B))) ) ).
cnf(cls_Int__subset__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),V_A))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B))) ) ).
cnf(cls_le__infE_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b))) ) ).
cnf(cls_le__infE_1,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b))) ) ).
cnf(cls_le__infI1_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b)),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_x)) ) ).
cnf(cls_le__infI2_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b)),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_x)) ) ).
cnf(cls_le__inf__iff_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z))) ) ).
cnf(cls_le__inf__iff_1,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z))) ) ).
cnf(cls_add__is__1_3,axiom,
( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
cnf(cls_add__is__1_0,axiom,
( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| V_m = c_HOL_Ozero__class_Ozero(tc_nat)
| V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ).
cnf(cls_bij__betw__imp__funcset_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b)))
| ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b) ) ).
cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a) ) ).
cnf(cls_vimage__eq_1,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Set_Ovimage(V_f,V_B,T_a,T_b)))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),V_B)) ) ).
cnf(cls_vimageI2_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_b),V_a),c_Set_Ovimage(V_f,V_A,T_b,T_a)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_a)),V_A)) ) ).
cnf(cls_vimageI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_b),V_a),c_Set_Ovimage(V_f,V_B,T_b,T_a)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_a)),V_B)) ) ).
cnf(cls_vimageE_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Set_Ovimage(V_f,V_B,T_a,T_b))) ) ).
cnf(cls_vimageD_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Set_Ovimage(V_f,V_A,T_a,T_b))) ) ).
cnf(cls_INTER__UNIV__conv_I2_J_0,axiom,
( c_Complete__Lattice_Ocomplete__lattice__class_OINFI(V_A,V_B,T_b,tc_fun(T_a,tc_bool)) != c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))
| hAPP(V_B,V_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A)) ) ).
cnf(cls_complete__lattice_OInf__lower_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,hAPP(V_Inf,V_A)),V_x))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_complete__lattice_OSup__upper_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,V_x),hAPP(V_Sup,V_A)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_inf__eq__neg__sup_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b) = hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b))) ) ).
cnf(cls_Un__commute_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_A) ).
cnf(cls_sup__commute_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_x) ) ).
cnf(cls_inf__sup__aci_I5_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_x) ) ).
cnf(cls_Compl__Int_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B)) ).
cnf(cls_compl__inf_0,axiom,
( ~ class_Lattices_Oboolean__algebra(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_y)) ) ).
cnf(cls_neg__inf__eq__sup_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)) ) ).
cnf(cls_of__nat__less__0__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)),c_HOL_Ozero__class_Ozero(T_a))) ) ).
cnf(cls_setprod__zero__iff_2,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(T_b)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_b)
| hAPP(V_f,V_x) != c_HOL_Ozero__class_Ozero(T_b)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Osetprod(V_f,V_A,T_a,T_b) = c_HOL_Ozero__class_Ozero(T_b) ) ).
cnf(cls_setprod__zero_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_b)
| hAPP(V_f,V_x) != c_HOL_Ozero__class_Ozero(T_b)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Osetprod(V_f,V_A,T_a,T_b) = c_HOL_Ozero__class_Ozero(T_b) ) ).
cnf(cls_power__eq__imp__eq__base_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_Power_Opower__class_Opower(V_b,V_n,T_a)
| V_a = V_b
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)) ) ).
cnf(cls_nat__less__induct_1,axiom,
( hBOOL(hAPP(V_P,V_n))
| ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Nat__Xnat__less__induct__1__1(V_P))) ) ).
cnf(cls_atLeastLessThan__empty__iff2_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_SetInterval_Oord__class_OatLeastLessThan(V_a,V_b,T_a)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)) ) ).
cnf(cls_atLeastLessThan__empty__iff2_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(V_a,V_b,T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)) ) ).
cnf(cls_add__cancel__end_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) != V_y
| V_x = hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_z) ) ).
cnf(cls_dual__bounded__lattice_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| c_Lattices_Obounded__lattice(c_COMBC(c_lessequals(T_a),T_a,T_a,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(T_a),T_a,T_a,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(T_a),c_Lattices_Olower__semilattice__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a),c_Orderings_Obot__class_Obot(T_a),T_a) ) ).
cnf(cls_Un__left__absorb_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B) ).
cnf(cls_sup__left__idem_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) ) ).
cnf(cls_inf__sup__aci_I8_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) ) ).
cnf(cls_inv__image__comp_0,axiom,
( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_f,T_a,T_b),c_Set_Oimage(V_f,V_X,T_a,T_b),T_b,T_a) = V_X
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_image__inv__f__f_0,axiom,
( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_f,T_a,T_b),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b,T_a) = V_A
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_empty__is__image_1,axiom,
c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) = c_Set_Oimage(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a) ).
cnf(cls_order_Oneq__le__trans_0,axiom,
( hBOOL(hAPP(hAPP(V_less,V_a),V_b))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_a),V_b))
| V_a = V_b
| ~ c_Orderings_Oorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_order_Ole__neq__trans_0,axiom,
( hBOOL(hAPP(hAPP(V_less,V_a),V_b))
| V_a = V_b
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_a),V_b))
| ~ c_Orderings_Oorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_order_Oless__le_2,axiom,
( hBOOL(hAPP(hAPP(V_less,V_x),V_y))
| V_x = V_y
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_x),V_y))
| ~ c_Orderings_Oorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_order_Ole__less_0,axiom,
( V_x = V_y
| hBOOL(hAPP(hAPP(V_less,V_x),V_y))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_x),V_y))
| ~ c_Orderings_Oorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_Compl__Un_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B)) ).
cnf(cls_compl__sup_0,axiom,
( ~ class_Lattices_Oboolean__algebra(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_y)) ) ).
cnf(cls_neg__sup__eq__inf_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)) ) ).
cnf(cls_finite_0,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(T_a)
| c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_vimage__Un_0,axiom,
c_Set_Ovimage(V_f,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_b,tc_bool)),V_A),V_B),T_a,T_b) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Set_Ovimage(V_f,V_A,T_a,T_b)),c_Set_Ovimage(V_f,V_B,T_a,T_b)) ).
cnf(cls_bounded__lattice_Oinf__bot__left_0,axiom,
( hAPP(hAPP(V_inf,V_bot),V_x) = V_bot
| ~ c_Lattices_Obounded__lattice(V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_bounded__lattice_Oinf__top__left_0,axiom,
( hAPP(hAPP(V_inf,V_top),V_x) = V_x
| ~ c_Lattices_Obounded__lattice(V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_bounded__lattice_Osup__bot__left_0,axiom,
( hAPP(hAPP(V_sup,V_bot),V_x) = V_x
| ~ c_Lattices_Obounded__lattice(V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_bounded__lattice_Osup__top__left_0,axiom,
( hAPP(hAPP(V_sup,V_top),V_x) = V_top
| ~ c_Lattices_Obounded__lattice(V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_bounded__lattice_Oinf__bot__right_0,axiom,
( hAPP(hAPP(V_inf,V_x),V_bot) = V_bot
| ~ c_Lattices_Obounded__lattice(V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_bounded__lattice_Oinf__top__right_0,axiom,
( hAPP(hAPP(V_inf,V_x),V_top) = V_x
| ~ c_Lattices_Obounded__lattice(V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_bounded__lattice_Osup__bot__right_0,axiom,
( hAPP(hAPP(V_sup,V_x),V_bot) = V_x
| ~ c_Lattices_Obounded__lattice(V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_bounded__lattice_Osup__top__right_0,axiom,
( hAPP(hAPP(V_sup,V_x),V_top) = V_top
| ~ c_Lattices_Obounded__lattice(V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_bounded__lattice_Oinf__eq__top__eq1_0,axiom,
( ~ c_Lattices_Obounded__lattice(V_less__eq,V_less,V_inf,V_sup,V_bot,hAPP(hAPP(V_inf,V_A),V_B),T_a)
| V_A = hAPP(hAPP(V_inf,V_A),V_B) ) ).
cnf(cls_bounded__lattice_Oinf__eq__top__eq2_0,axiom,
( ~ c_Lattices_Obounded__lattice(V_less__eq,V_less,V_inf,V_sup,V_bot,hAPP(hAPP(V_inf,V_A),V_B),T_a)
| V_B = hAPP(hAPP(V_inf,V_A),V_B) ) ).
cnf(cls_bounded__lattice_Osup__eq__bot__eq1_0,axiom,
( ~ c_Lattices_Obounded__lattice(V_less__eq,V_less,V_inf,V_sup,hAPP(hAPP(V_sup,V_A),V_B),V_top,T_a)
| V_A = hAPP(hAPP(V_sup,V_A),V_B) ) ).
cnf(cls_bounded__lattice_Osup__eq__bot__eq2_0,axiom,
( ~ c_Lattices_Obounded__lattice(V_less__eq,V_less,V_inf,V_sup,hAPP(hAPP(V_sup,V_A),V_B),V_top,T_a)
| V_B = hAPP(hAPP(V_sup,V_A),V_B) ) ).
cnf(cls_card__empty_0,axiom,
c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) = c_HOL_Ozero__class_Ozero(tc_nat) ).
cnf(cls_linorder_Oantisym__conv2_0,axiom,
( V_x = V_y
| hBOOL(hAPP(hAPP(V_less,V_x),V_y))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_x),V_y))
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_linorder_Oantisym__conv1_0,axiom,
( V_x = V_y
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_x),V_y))
| hBOOL(hAPP(hAPP(V_less,V_x),V_y))
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_power__inject__base_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) != c_Power_Opower__class_Opower(V_b,c_Suc(V_n),T_a)
| V_a = V_b
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)) ) ).
cnf(cls_card__gt__0__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Ocard(V_A,T_a)))
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_inf1E_1,axiom,
( hBOOL(hAPP(V_B,V_x))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),V_x)) ) ).
cnf(cls_inf1E_0,axiom,
( hBOOL(hAPP(V_A,V_x))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),V_x)) ) ).
cnf(cls_finite__surj__inj_0,axiom,
( c_Fun_Oinj__on(V_f,V_A,T_a,T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),c_Set_Oimage(V_f,V_A,T_a,T_a)))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_inj__on__Un_1,axiom,
( c_Fun_Oinj__on(V_f,V_B,T_a,T_b)
| ~ c_Fun_Oinj__on(V_f,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b) ) ).
cnf(cls_inj__on__Un_0,axiom,
( c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| ~ c_Fun_Oinj__on(V_f,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b) ) ).
cnf(cls_disjoint__eq__subset__Compl_1,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B))) ) ).
cnf(cls_disjoint__eq__subset__Compl_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B))) ) ).
cnf(cls_of__nat__0__le__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a))) ) ).
cnf(cls_zero__le__imp__of__nat_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a))) ) ).
cnf(cls_vimage__subsetI_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Set_Ovimage(V_f,V_B,T_a,T_b)),V_A))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_b,tc_bool)),V_B),c_Set_Oimage(V_f,V_A,T_a,T_b)))
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_Suc__neq__Zero_0,axiom,
c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat) ).
cnf(cls_dual__distrib__lattice_0,axiom,
( ~ class_Lattices_Odistrib__lattice(T_a)
| c_Lattices_Odistrib__lattice(c_COMBC(c_lessequals(T_a),T_a,T_a,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(T_a),T_a,T_a,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(T_a),c_Lattices_Olower__semilattice__class_Oinf(T_a),T_a) ) ).
cnf(cls_add__le__cancel__right_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b)) ) ).
cnf(cls_add__le__cancel__right_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a))) ) ).
cnf(cls_add__le__cancel__left_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Oplus__class_Oplus(V_c,V_a,T_a)),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b)) ) ).
cnf(cls_add__le__cancel__left_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Oplus__class_Oplus(V_c,V_a,T_a)),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a))) ) ).
cnf(cls_add__right__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b)) ) ).
cnf(cls_add__left__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Oplus__class_Oplus(V_c,V_a,T_a)),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b)) ) ).
cnf(cls_bot__empty__eq_0,axiom,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = hAPP(hAPP(c_in(t_a),v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))) ).
cnf(cls_linorder_Onot__less__iff__gr__or__eq_1,axiom,
( ~ hBOOL(hAPP(hAPP(V_less,V_x),V_y))
| ~ hBOOL(hAPP(hAPP(V_less,V_y),V_x))
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_linorder_OleD_0,axiom,
( ~ hBOOL(hAPP(hAPP(V_less,V_x),V_y))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_y),V_x))
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_linorder_OleI_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,V_y),V_x))
| hBOOL(hAPP(hAPP(V_less,V_x),V_y))
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_linorder_Olinear_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,V_y),V_x))
| hBOOL(hAPP(hAPP(V_less__eq,V_x),V_y))
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_linorder_Onot__le_0,axiom,
( hBOOL(hAPP(hAPP(V_less,V_y),V_x))
| hBOOL(hAPP(hAPP(V_less__eq,V_x),V_y))
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_linorder_Onot__le_1,axiom,
( ~ hBOOL(hAPP(hAPP(V_less__eq,V_x),V_y))
| ~ hBOOL(hAPP(hAPP(V_less,V_y),V_x))
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_linorder_Onot__leE_0,axiom,
( hBOOL(hAPP(hAPP(V_less,V_x),V_y))
| hBOOL(hAPP(hAPP(V_less__eq,V_y),V_x))
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_linorder_Oantisym__conv1_1,axiom,
( hBOOL(hAPP(hAPP(V_less,V_x),V_x))
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a)
| hBOOL(hAPP(hAPP(V_less__eq,V_x),V_x)) ) ).
cnf(cls_linorder_Oantisym__conv2_1,axiom,
( ~ hBOOL(hAPP(hAPP(V_less__eq,V_x),V_x))
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a)
| ~ hBOOL(hAPP(hAPP(V_less,V_x),V_x)) ) ).
cnf(cls_lattice_Oinf__sup__aci_I1_J_0,axiom,
( hAPP(hAPP(V_inf,V_x),V_y) = hAPP(hAPP(V_inf,V_y),V_x)
| ~ c_Lattices_Olattice(V_less__eq,V_less,V_inf,V_sup,T_a) ) ).
cnf(cls_lattice_Oinf__sup__aci_I2_J_0,axiom,
( hAPP(hAPP(V_inf,hAPP(hAPP(V_inf,V_x),V_y)),V_z) = hAPP(hAPP(V_inf,V_x),hAPP(hAPP(V_inf,V_y),V_z))
| ~ c_Lattices_Olattice(V_less__eq,V_less,V_inf,V_sup,T_a) ) ).
cnf(cls_lattice_Oinf__sup__aci_I3_J_0,axiom,
( hAPP(hAPP(V_inf,V_x),hAPP(hAPP(V_inf,V_y),V_z)) = hAPP(hAPP(V_inf,V_y),hAPP(hAPP(V_inf,V_x),V_z))
| ~ c_Lattices_Olattice(V_less__eq,V_less,V_inf,V_sup,T_a) ) ).
cnf(cls_lattice_Oinf__sup__aci_I4_J_0,axiom,
( hAPP(hAPP(V_inf,V_x),hAPP(hAPP(V_inf,V_x),V_y)) = hAPP(hAPP(V_inf,V_x),V_y)
| ~ c_Lattices_Olattice(V_less__eq,V_less,V_inf,V_sup,T_a) ) ).
cnf(cls_lattice_Oinf__sup__aci_I5_J_0,axiom,
( hAPP(hAPP(V_sup,V_x),V_y) = hAPP(hAPP(V_sup,V_y),V_x)
| ~ c_Lattices_Olattice(V_less__eq,V_less,V_inf,V_sup,T_a) ) ).
cnf(cls_lattice_Oinf__sup__aci_I6_J_0,axiom,
( hAPP(hAPP(V_sup,hAPP(hAPP(V_sup,V_x),V_y)),V_z) = hAPP(hAPP(V_sup,V_x),hAPP(hAPP(V_sup,V_y),V_z))
| ~ c_Lattices_Olattice(V_less__eq,V_less,V_inf,V_sup,T_a) ) ).
cnf(cls_lattice_Oinf__sup__aci_I7_J_0,axiom,
( hAPP(hAPP(V_sup,V_x),hAPP(hAPP(V_sup,V_y),V_z)) = hAPP(hAPP(V_sup,V_y),hAPP(hAPP(V_sup,V_x),V_z))
| ~ c_Lattices_Olattice(V_less__eq,V_less,V_inf,V_sup,T_a) ) ).
cnf(cls_lattice_Oinf__sup__aci_I8_J_0,axiom,
( hAPP(hAPP(V_sup,V_x),hAPP(hAPP(V_sup,V_x),V_y)) = hAPP(hAPP(V_sup,V_x),V_y)
| ~ c_Lattices_Olattice(V_less__eq,V_less,V_inf,V_sup,T_a) ) ).
cnf(cls_lattice_Oinf__sup__absorb_0,axiom,
( hAPP(hAPP(V_inf,V_x),hAPP(hAPP(V_sup,V_x),V_y)) = V_x
| ~ c_Lattices_Olattice(V_less__eq,V_less,V_inf,V_sup,T_a) ) ).
cnf(cls_lattice_Osup__inf__absorb_0,axiom,
( hAPP(hAPP(V_sup,V_x),hAPP(hAPP(V_inf,V_x),V_y)) = V_x
| ~ c_Lattices_Olattice(V_less__eq,V_less,V_inf,V_sup,T_a) ) ).
cnf(cls_vimage__const_1,axiom,
( c_Set_Ovimage(c_COMBK(V_c,T_b,T_a),V_A,T_a,T_b) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| hBOOL(hAPP(hAPP(c_in(T_b),V_c),V_A)) ) ).
cnf(cls_le__eq__neg_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a)),c_HOL_Ozero__class_Ozero(T_a))) ) ).
cnf(cls_le__eq__neg_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a)),c_HOL_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b))) ) ).
cnf(cls_finite__compl_0,axiom,
( c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a)
| ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A),T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_finite__compl_1,axiom,
( c_Finite__Set_Ofinite(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A),T_a)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_subset__empty_0,axiom,
( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) ) ).
cnf(cls_subset__empty_1,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) ).
cnf(cls_neg__0__equal__iff__equal_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Ozero__class_Ozero(T_a) = hAPP(c_HOL_Ouminus__class_Ouminus(T_a),c_HOL_Ozero__class_Ozero(T_a)) ) ).
cnf(cls_power__le__imp__le__base_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a)),c_Power_Opower__class_Opower(V_b,c_Suc(V_n),T_a))) ) ).
cnf(cls_card__bij_0,axiom,
( c_Finite__Set_Ocard(V_A,T_a) = c_Finite__Set_Ocard(V_B,T_b)
| ~ c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Fun_Oinj__on(V_g,V_B,T_b,T_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_b,T_a)),V_g),c_FuncSet_OPi(V_B,c_COMBK(V_A,tc_fun(T_a,tc_bool),T_b),T_b,T_a)))
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b))) ) ).
cnf(cls_card__bij__eq_0,axiom,
( c_Finite__Set_Ocard(V_A,T_a) = c_Finite__Set_Ocard(V_B,T_b)
| ~ c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Set_Oimage(V_g,V_B,T_b,T_a)),V_A))
| ~ c_Fun_Oinj__on(V_g,V_B,T_b,T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_b,tc_bool)),c_Set_Oimage(V_f,V_A,T_a,T_b)),V_B))
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
cnf(cls_field__power__not__zero_0,axiom,
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(T_a)
| c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_power__eq__0__iff_0,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Power_Opower(T_a)
| c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_neg__le__0__iff__le_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),c_HOL_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)) ) ).
cnf(cls_neg__le__0__iff__le_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),c_HOL_Ozero__class_Ozero(T_a))) ) ).
cnf(cls_of__nat__0__less__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n)) ) ).
cnf(cls_of__nat__0__less__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a))) ) ).
cnf(cls_f__inv__into__f_0,axiom,
( hAPP(V_f,hAPP(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_b,T_a),V_y)) = V_y
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_y),c_Set_Oimage(V_f,V_A,T_b,T_a))) ) ).
cnf(cls_update__accessor__congruence__foldE_0,axiom,
( hAPP(V_f,hAPP(V_acc,V_x)) != hAPP(V_f_H,hAPP(V_acc,V_x))
| ~ c_Record_Oiso__tuple__update__accessor__cong__assist(V_upd,V_acc,T_a,T_aa)
| hAPP(hAPP(V_upd,V_f),V_x) = hAPP(hAPP(V_upd,V_f_H),V_x) ) ).
cnf(cls_update__accessor__noopE_0,axiom,
( hAPP(V_f,hAPP(V_acc,V_x)) != hAPP(V_acc,V_x)
| ~ c_Record_Oiso__tuple__update__accessor__cong__assist(V_upd,V_acc,T_a,T_b)
| hAPP(hAPP(V_upd,V_f),V_x) = V_x ) ).
cnf(cls_emptyE_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) ).
cnf(cls_empty__iff_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) ).
cnf(cls_ball__empty_0,axiom,
( hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) ) ).
cnf(cls_ex__in__conv_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) ).
cnf(cls_Un__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_C),V_D)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_D))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_C)) ) ).
cnf(cls_power__0__left_1,axiom,
( ~ class_Ring__and__Field_Osemiring__0(T_a)
| ~ class_Power_Opower(T_a)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
cnf(cls_power__eq__0__iff_2,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Power_Opower(T_a)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
cnf(cls_inf__sup__ord_I1_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)),V_x)) ) ).
cnf(cls_inf__sup__ord_I2_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)),V_y)) ) ).
cnf(cls_inf__greatest_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_le__inf__iff_2,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_le__infI_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_a)) ) ).
cnf(cls_inf__le2_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)),V_y)) ) ).
cnf(cls_inf__le1_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)),V_x)) ) ).
cnf(cls_Int__lower1_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),V_A)) ).
cnf(cls_Int__lower2_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),V_B)) ).
cnf(cls_Int__greatest_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),V_B))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),V_A)) ) ).
cnf(cls_Int__subset__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),V_B))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),V_A)) ) ).
cnf(cls_INT__empty_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_B,T_b,tc_fun(T_a,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) ).
cnf(cls_fun__Compl__def_0,axiom,
( ~ class_HOL_Ouminus(T_b)
| hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(t_a,T_b)),V_A),v_x) = hAPP(c_HOL_Ouminus__class_Ouminus(T_b),hAPP(V_A,v_x)) ) ).
cnf(cls_neg__equal__zero_1,axiom,
( ~ class_OrderedGroup_Oordered__ab__group__add(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),c_HOL_Ozero__class_Ozero(T_a)) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_add__minus__cancel_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a),V_b,T_a),T_a) = V_b ) ).
cnf(cls_minus__zero_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),c_HOL_Ozero__class_Ozero(T_a)) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_sup__inf__distrib2_0,axiom,
( ~ class_Lattices_Odistrib__lattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_z),V_x)) ) ).
cnf(cls_sup__inf__distrib1_0,axiom,
( ~ class_Lattices_Odistrib__lattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_z)) ) ).
cnf(cls_Un__Int__distrib_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_C)) ).
cnf(cls_Un__Int__distrib2_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)),V_A) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_A)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_C),V_A)) ).
cnf(cls_compl__bot__eq_0,axiom,
( ~ class_Lattices_Oboolean__algebra(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
cnf(cls_Compl__empty__eq_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) ).
cnf(cls_pos__add__strict_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_c))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)) ) ).
cnf(cls_inf__sup__aci_I4_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) ) ).
cnf(cls_inf__left__idem_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) ) ).
cnf(cls_Int__left__absorb_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) ).
cnf(cls_double__add__le__zero__iff__single__add__le__zero_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a)),c_HOL_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))) ) ).
cnf(cls_double__add__le__zero__iff__single__add__le__zero_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a)),c_HOL_Ozero__class_Ozero(T_a))) ) ).
cnf(cls_bij__betw__def_1,axiom,
( c_Set_Oimage(V_f,V_A,T_a,T_b) = V_B
| ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b) ) ).
cnf(cls_sup__eq__if_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)) = V_a
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))) ) ).
cnf(cls_complete__lattice_OSup__empty_0,axiom,
( hAPP(V_Sup,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = V_bot
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_complete__lattice_OInf__empty_0,axiom,
( hAPP(V_Inf,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = V_top
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_UnCI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B)) ) ).
cnf(cls_UnCI_1,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A)) ) ).
cnf(cls_Suc__n__not__n_0,axiom,
c_Suc(V_n) != V_n ).
cnf(cls_n__not__Suc__n_0,axiom,
V_n != c_Suc(V_n) ).
cnf(cls_inf__idem_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_x) = V_x ) ).
cnf(cls_Int__absorb_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_A) = V_A ).
cnf(cls_le__sup__iff_1,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)),V_z)) ) ).
cnf(cls_le__sup__iff_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)),V_z)) ) ).
cnf(cls_le__supI2_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_b)) ) ).
cnf(cls_le__supI1_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_a)) ) ).
cnf(cls_le__supE_1,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b)),V_x)) ) ).
cnf(cls_le__supE_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b)),V_x)) ) ).
cnf(cls_Un__subset__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C)) ) ).
cnf(cls_class__semiring_Oadd__0_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = V_x ) ).
cnf(cls_comm__monoid__add_Omult__1_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ).
cnf(cls_natgb_Oadd__r0__iff_1,axiom,
V_x = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
cnf(cls_plus__nat_Oadd__0_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n ).
cnf(cls_Nat_Oadd__0__right_0,axiom,
c_HOL_Oplus__class_Oplus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ).
cnf(cls_class__ringb_Oadd__r0__iff_1,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| V_x = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_comm__monoid__add_Omult__1__right_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ).
cnf(cls_add__0__left_0,axiom,
( ~ class_OrderedGroup_Omonoid__add(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ).
cnf(cls_monoid__add__class_Oadd__0__right_0,axiom,
( ~ class_OrderedGroup_Omonoid__add(T_a)
| c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ).
cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ).
cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ).
cnf(cls_neg__equal__zero_0,axiom,
( ~ class_OrderedGroup_Oordered__ab__group__add(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a) != V_a
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_rev__image__eqI_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_aa),V_x),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_x)),c_Set_Oimage(V_f,V_A,T_aa,T_a))) ) ).
cnf(cls_image__iff_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_x)),c_Set_Oimage(V_f,V_A,T_b,T_a))) ) ).
cnf(cls_image__eqI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_x)),c_Set_Oimage(V_f,V_A,T_b,T_a)))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A)) ) ).
cnf(cls_imageI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),c_Set_Oimage(V_f,V_A,T_a,T_b)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_bij__betw__def_0,axiom,
( c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b) ) ).
cnf(cls_double__complement_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A)) = V_A ).
cnf(cls_minus__minus_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ).
cnf(cls_double__compl_0,axiom,
( ~ class_Lattices_Oboolean__algebra(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ).
cnf(cls_equation__minus__iff_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| V_b = hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)) ) ).
cnf(cls_equation__minus__iff_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| V_a = hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)) ) ).
cnf(cls_minus__equation__iff_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)) = V_b ) ).
cnf(cls_add__le__less__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_c),V_d))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b)) ) ).
cnf(cls_add__less__le__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_c),V_d))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)) ) ).
cnf(cls_vimage__Int_0,axiom,
c_Set_Ovimage(V_f,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_b,tc_bool)),V_A),V_B),T_a,T_b) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Ovimage(V_f,V_A,T_a,T_b)),c_Set_Ovimage(V_f,V_B,T_a,T_b)) ).
cnf(cls_add__gr__0_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n)) ) ).
cnf(cls_add__gr__0_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_m)) ) ).
cnf(cls_zero__less__double__add__iff__zero__less__single__add_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a))) ) ).
cnf(cls_zero__less__double__add__iff__zero__less__single__add_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)) ) ).
cnf(cls_finite__Int_1,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_F),V_G),T_a)
| ~ c_Finite__Set_Ofinite(V_G,T_a) ) ).
cnf(cls_finite__Int_0,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_F),V_G),T_a)
| ~ c_Finite__Set_Ofinite(V_F,T_a) ) ).
cnf(cls_le__funD_0,axiom,
( ~ class_HOL_Oord(T_b)
| hBOOL(hAPP(hAPP(c_lessequals(T_b),hAPP(V_f,V_x)),hAPP(V_g,V_x)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,T_b)),V_f),V_g)) ) ).
cnf(cls_le__minus__iff_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b))) ) ).
cnf(cls_le__minus__iff_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a))) ) ).
cnf(cls_minus__le__iff_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)),V_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ).
cnf(cls_minus__le__iff_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),V_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)),V_a)) ) ).
cnf(cls_linorder__antisym__conv2_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| V_x = V_y
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_linorder__antisym__conv1_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_order__neq__le__trans_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b))
| V_a = V_b ) ).
cnf(cls_order__le__neq__trans_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b))
| V_a = V_b
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b)) ) ).
cnf(cls_order__less__le_2,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_order__le__less_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| V_x = V_y
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_xt1_I12_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_a))
| V_a = V_b ) ).
cnf(cls_xt1_I11_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_a))
| V_a = V_b
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_a)) ) ).
cnf(cls_order__less__le__trans_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_z))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_order__le__less__trans_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_xt1_I8_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_z),V_x))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_z),V_y))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x)) ) ).
cnf(cls_xt1_I7_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_z),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_z),V_y))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x)) ) ).
cnf(cls_add__less__cancel__left_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Oplus__class_Oplus(V_c,V_a,T_a)),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a))) ) ).
cnf(cls_add__less__cancel__left_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Oplus__class_Oplus(V_c,V_a,T_a)),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)) ) ).
cnf(cls_add__strict__left__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Oplus__class_Oplus(V_c,V_a,T_a)),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)) ) ).
cnf(cls_add__less__cancel__right_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a))) ) ).
cnf(cls_add__less__cancel__right_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)) ) ).
cnf(cls_add__strict__right__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)) ) ).
cnf(cls_order__less__imp__le_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_order__le__less_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_less__infI1_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b)),V_x))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_x)) ) ).
cnf(cls_less__infI2_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b)),V_x))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_x)) ) ).
cnf(cls_add__strict__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_c),V_d))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)) ) ).
cnf(cls_less__le__not__le_2,axiom,
( ~ class_Orderings_Opreorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_neg__less__iff__less_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a))) ) ).
cnf(cls_neg__less__iff__less_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)) ) ).
cnf(cls_not__leE_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x)) ) ).
cnf(cls_linorder__antisym__conv2_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_x))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_x)) ) ).
cnf(cls_linorder__antisym__conv1_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_x))
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_x)) ) ).
cnf(cls_linorder__not__less_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x)) ) ).
cnf(cls_linorder__not__less_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_linorder__not__le_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x)) ) ).
cnf(cls_linorder__not__le_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x))
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_less__le__not__le_1,axiom,
( ~ class_Orderings_Opreorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_less__supI1_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_a)) ) ).
cnf(cls_less__supI2_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_b)) ) ).
cnf(cls_less__minus__iff_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b))) ) ).
cnf(cls_less__minus__iff_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a))) ) ).
cnf(cls_minus__less__iff_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)),V_a))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ).
cnf(cls_minus__less__iff_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),V_b))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)),V_a)) ) ).
cnf(cls_image__image_0,axiom,
c_Set_Oimage(V_f,c_Set_Oimage(V_g,V_A,T_c,T_b),T_b,T_a) = c_Set_Oimage(hAPP(hAPP(c_COMBB(T_b,T_a,T_c),V_f),V_g),V_A,T_c,T_a) ).
cnf(cls_dual__linorder_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_Orderings_Olinorder(c_COMBC(c_lessequals(T_a),T_a,T_a,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(T_a),T_a,T_a,tc_bool),T_a) ) ).
cnf(cls_dual__order_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_Orderings_Oorder(c_COMBC(c_lessequals(T_a),T_a,T_a,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(T_a),T_a,T_a,tc_bool),T_a) ) ).
cnf(cls_dual__preorder_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_Orderings_Opreorder(c_COMBC(c_lessequals(T_a),T_a,T_a,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(T_a),T_a,T_a,tc_bool),T_a) ) ).
cnf(cls_finite__range__imageI_0,axiom,
( c_Finite__Set_Ofinite(c_Set_Oimage(hAPP(hAPP(c_COMBB(T_a,T_c,T_b),V_f),V_g),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_c),T_c)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(V_g,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_a),T_a) ) ).
cnf(cls_less__SucI_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),c_Suc(V_n)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n)) ) ).
cnf(cls_Suc__lessD_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(V_m)),V_n)) ) ).
cnf(cls_nat__add__left__cancel__less_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat)),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n)) ) ).
cnf(cls_nat__add__left__cancel__less_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat)),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat))) ) ).
cnf(cls_add__less__mono1_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat)),c_HOL_Oplus__class_Oplus(V_j,V_k,tc_nat)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_i),V_j)) ) ).
cnf(cls_not__add__less2_0,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_i,tc_nat)),V_i)) ).
cnf(cls_not__add__less1_0,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat)),V_i)) ).
cnf(cls_neq0__conv_1,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))) ).
cnf(cls_gr0I_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n))
| V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
cnf(cls_less__trans__Suc_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(V_i)),V_k))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_j),V_k))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_i),V_j)) ) ).
cnf(cls_less__Suc__eq_2,axiom,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),c_Suc(V_x))) ).
cnf(cls_lessI_0,axiom,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),c_Suc(V_n))) ).
cnf(cls_add__less__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat)),c_HOL_Oplus__class_Oplus(V_j,V_l,tc_nat)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_k),V_l))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_i),V_j)) ) ).
cnf(cls_not__less__less__Suc__eq_0,axiom,
( V_n = V_m
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),c_Suc(V_m)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),V_m)) ) ).
cnf(cls_less__antisym_0,axiom,
( V_m = V_n
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),c_Suc(V_m)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),V_m)) ) ).
cnf(cls_less__SucE_0,axiom,
( V_m = V_n
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),c_Suc(V_n))) ) ).
cnf(cls_less__add__eq__less_0,axiom,
( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_k),V_l))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n)) ) ).
cnf(cls_trans__less__add2_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_i),c_HOL_Oplus__class_Oplus(V_m,V_j,tc_nat)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_i),V_j)) ) ).
cnf(cls_Un__subset__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C)) ) ).
cnf(cls_boolean__algebra_Osup__compl__top_0,axiom,
( hAPP(hAPP(V_sup,V_x),hAPP(V_uminus,V_x)) = V_top
| ~ c_Lattices_Oboolean__algebra(V_minus,V_uminus,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_boolean__algebra_Oinf__compl__bot_0,axiom,
( hAPP(hAPP(V_inf,V_x),hAPP(V_uminus,V_x)) = V_bot
| ~ c_Lattices_Oboolean__algebra(V_minus,V_uminus,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_boolean__algebra_Ocompl__sup__top_0,axiom,
( hAPP(hAPP(V_sup,hAPP(V_uminus,V_x)),V_x) = V_top
| ~ c_Lattices_Oboolean__algebra(V_minus,V_uminus,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_boolean__algebra_Ocompl__inf__bot_0,axiom,
( hAPP(hAPP(V_inf,hAPP(V_uminus,V_x)),V_x) = V_bot
| ~ c_Lattices_Oboolean__algebra(V_minus,V_uminus,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_boolean__algebra_Odouble__compl_0,axiom,
( hAPP(V_uminus,hAPP(V_uminus,V_x)) = V_x
| ~ c_Lattices_Oboolean__algebra(V_minus,V_uminus,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_boolean__algebra_Ocompl__unique_0,axiom,
( ~ c_Lattices_Oboolean__algebra(V_minus,V_uminus,V_less__eq,V_less,V_inf,V_sup,hAPP(hAPP(V_inf,V_x),V_y),hAPP(hAPP(V_sup,V_x),V_y),T_a)
| hAPP(V_uminus,V_x) = V_y ) ).
cnf(cls_boolean__algebra_Ocompl__top__eq_0,axiom,
( hAPP(V_uminus,V_top) = V_bot
| ~ c_Lattices_Oboolean__algebra(V_minus,V_uminus,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_boolean__algebra_Ocompl__bot__eq_0,axiom,
( hAPP(V_uminus,V_bot) = V_top
| ~ c_Lattices_Oboolean__algebra(V_minus,V_uminus,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_boolean__algebra_Odiff__eq_0,axiom,
( hAPP(hAPP(V_minus,V_x),V_y) = hAPP(hAPP(V_inf,V_x),hAPP(V_uminus,V_y))
| ~ c_Lattices_Oboolean__algebra(V_minus,V_uminus,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_boolean__algebra_Ocompl__inf_0,axiom,
( hAPP(V_uminus,hAPP(hAPP(V_inf,V_x),V_y)) = hAPP(hAPP(V_sup,hAPP(V_uminus,V_x)),hAPP(V_uminus,V_y))
| ~ c_Lattices_Oboolean__algebra(V_minus,V_uminus,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_boolean__algebra_Ocompl__sup_0,axiom,
( hAPP(V_uminus,hAPP(hAPP(V_sup,V_x),V_y)) = hAPP(hAPP(V_inf,hAPP(V_uminus,V_x)),hAPP(V_uminus,V_y))
| ~ c_Lattices_Oboolean__algebra(V_minus,V_uminus,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_inf__fun__eq_0,axiom,
( ~ class_Lattices_Olattice(T_b)
| hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,T_b)),V_f),V_g),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_b),hAPP(V_f,v_x)),hAPP(V_g,v_x)) ) ).
cnf(cls_xt1_I6_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_z),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_z),V_y))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x)) ) ).
cnf(cls_add__nonpos__nonpos_0,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a)),c_HOL_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),c_HOL_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))) ) ).
cnf(cls_order__trans_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_set__mp_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_subsetD_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_equalityE_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_x),V_x)) ).
cnf(cls_set__rev__mp_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_subset__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_subset__refl_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_A)) ).
cnf(cls_subset__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_subset__inj__on_0,axiom,
( c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ c_Fun_Oinj__on(V_f,V_B,T_a,T_b) ) ).
cnf(cls_predicate1D_0,axiom,
( hBOOL(hAPP(V_Q,V_x))
| ~ hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_P),V_Q)) ) ).
cnf(cls_order__eq__iff_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_x)) ) ).
cnf(cls_order__eq__refl_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_x)) ) ).
cnf(cls_finite__subset_0,axiom,
( c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_psubset__subset__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_subset__psubset__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_C))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_rev__predicate1D_0,axiom,
( hBOOL(hAPP(V_Q,V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_P),V_Q))
| ~ hBOOL(hAPP(V_P,V_x)) ) ).
cnf(cls_rev__finite__subset_0,axiom,
( c_Finite__Set_Ofinite(V_A,T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ c_Finite__Set_Ofinite(V_B,T_a) ) ).
cnf(cls_le__add__right__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_c),V_d))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a))) ) ).
cnf(cls_atLeastLessThan__empty__iff_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_SetInterval_Oord__class_OatLeastLessThan(V_a,V_b,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)) ) ).
cnf(cls_atLeastLessThan__empty__iff_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_SetInterval_Oord__class_OatLeastLessThan(V_a,V_b,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)) ) ).
cnf(cls_measure__induct__rule_1,axiom,
( hBOOL(hAPP(V_P,V_a))
| ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Nat__Xmeasure__induct__rule__1__1(V_P,V_f,T_a))) ) ).
cnf(cls_inv__f__f_0,axiom,
( hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_f,T_a,T_b),hAPP(V_f,V_x)) = V_x
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_inv__f__eq_0,axiom,
( ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_aa,tc_bool)),T_aa,T_a)
| hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(T_aa,tc_bool)),V_f,T_aa,T_a),hAPP(V_f,V_x)) = V_x ) ).
cnf(cls_SigmaI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_b)),c_Pair(V_a,V_b,T_a,T_b)),c_Product__Type_OSigma(V_A,V_B,T_a,T_b)))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_b),hAPP(V_B,V_a)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)) ) ).
cnf(cls_mem__Sigma__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_b)),c_Pair(V_a,V_b,T_a,T_b)),c_Product__Type_OSigma(V_A,V_B,T_a,T_b)))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_b),hAPP(V_B,V_a)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)) ) ).
cnf(cls_INF1__D_0,axiom,
( hBOOL(hAPP(hAPP(V_B,V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| ~ hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(V_A,V_B,T_a,tc_fun(T_b,tc_bool)),V_b)) ) ).
cnf(cls_INF1__E_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| hBOOL(hAPP(hAPP(V_B,V_a),V_b))
| ~ hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(V_A,V_B,T_a,tc_fun(T_b,tc_bool)),V_b)) ) ).
cnf(cls_INF1__iff_0,axiom,
( hBOOL(hAPP(hAPP(V_B,V_x),V_b))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(V_A,V_B,T_a,tc_fun(T_b,tc_bool)),V_b)) ) ).
cnf(cls_card__Un__Int_0,axiom,
( c_HOL_Oplus__class_Oplus(c_Finite__Set_Ocard(V_A,T_a),c_Finite__Set_Ocard(V_B,T_a),tc_nat) = c_HOL_Oplus__class_Oplus(c_Finite__Set_Ocard(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),T_a),c_Finite__Set_Ocard(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),T_a),tc_nat)
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_image__is__empty_0,axiom,
( c_Set_Oimage(V_f,V_A,T_b,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)) ) ).
cnf(cls_card__eq__0__iff_0,axiom,
( c_Finite__Set_Ocard(V_A,T_a) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Int__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_D)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_D))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_C)) ) ).
cnf(cls_add__is__1_5,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)) ).
cnf(cls_eq__card__imp__inj__on_0,axiom,
( c_Finite__Set_Ocard(c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) != c_Finite__Set_Ocard(V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
cnf(cls_inj__on__iff__eq__card_0,axiom,
( c_Finite__Set_Ocard(c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) = c_Finite__Set_Ocard(V_A,T_a)
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_order_Oeq__iff_2,axiom,
( V_x = V_y
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_y),V_x))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_x),V_y))
| ~ c_Orderings_Oorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_order_Oantisym_0,axiom,
( V_x = V_y
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_y),V_x))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_x),V_y))
| ~ c_Orderings_Oorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_order_Oantisym__conv_0,axiom,
( V_x = V_y
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_x),V_y))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_y),V_x))
| ~ c_Orderings_Oorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_lfp__lowerbound_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),c_Inductive_Ocomplete__lattice__class_Olfp(V_f,T_a)),V_A))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(V_f,V_A)),V_A)) ) ).
cnf(cls_INT__Un_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OINFI(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_b,tc_bool)),V_A),V_B),V_M,T_b,tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(V_A,V_M,T_b,tc_fun(T_a,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(V_B,V_M,T_b,tc_fun(T_a,tc_bool))) ).
cnf(cls_some__sym__eq__trivial_0,axiom,
c_Hilbert__Choice_OEps(hAPP(c_fequal(T_a),V_x),T_a) = V_x ).
cnf(cls_inj__image__Compl__subset_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_b,tc_bool)),c_Set_Oimage(V_f,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A),T_a,T_b)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_b,tc_bool)),c_Set_Oimage(V_f,V_A,T_a,T_b))))
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_Pair__eq_0,axiom,
( c_Pair(V_a,V_b,T_a,T_b) != c_Pair(V_a_H,V_b_H,T_a,T_b)
| V_a = V_a_H ) ).
cnf(cls_Pair__eq_1,axiom,
( c_Pair(V_a,V_b,T_a,T_b) != c_Pair(V_a_H,V_b_H,T_a,T_b)
| V_b = V_b_H ) ).
cnf(cls_subset__Compl__self__eq_0,axiom,
( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A))) ) ).
cnf(cls_INT__absorb_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_b,tc_bool)),hAPP(V_A,V_k)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(V_I,V_A,T_a,tc_fun(T_b,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(V_I,V_A,T_a,tc_fun(T_b,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_k),V_I)) ) ).
cnf(cls_vimage__code_0,axiom,
( hBOOL(hAPP(V_A,hAPP(V_f,V_x)))
| ~ hBOOL(hAPP(c_Set_Ovimage(V_f,V_A,T_a,T_b),V_x)) ) ).
cnf(cls_vimage__code_1,axiom,
( hBOOL(hAPP(c_Set_Ovimage(V_f,V_A,T_a,T_b),V_x))
| ~ hBOOL(hAPP(V_A,hAPP(V_f,V_x))) ) ).
cnf(cls_the__sym__eq__trivial_0,axiom,
c_The(hAPP(c_fequal(T_a),V_x),T_a) = V_x ).
cnf(cls_linorder_Onot__less__iff__gr__or__eq_0,axiom,
( V_x = V_y
| hBOOL(hAPP(hAPP(V_less,V_y),V_x))
| hBOOL(hAPP(hAPP(V_less,V_x),V_y))
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_linorder_OneqE_0,axiom,
( hBOOL(hAPP(hAPP(V_less,V_y),V_x))
| hBOOL(hAPP(hAPP(V_less,V_x),V_y))
| V_x = V_y
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_linorder_Oless__linear_0,axiom,
( hBOOL(hAPP(hAPP(V_less,V_y),V_x))
| V_x = V_y
| hBOOL(hAPP(hAPP(V_less,V_x),V_y))
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_linorder_Oantisym__conv3_0,axiom,
( V_x = V_y
| hBOOL(hAPP(hAPP(V_less,V_x),V_y))
| hBOOL(hAPP(hAPP(V_less,V_y),V_x))
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_lattice_Oinf__sup__ord_I1_J_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,hAPP(hAPP(V_inf,V_x),V_y)),V_x))
| ~ c_Lattices_Olattice(V_less__eq,V_less,V_inf,V_sup,T_a) ) ).
cnf(cls_lattice_Oinf__sup__ord_I2_J_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,hAPP(hAPP(V_inf,V_x),V_y)),V_y))
| ~ c_Lattices_Olattice(V_less__eq,V_less,V_inf,V_sup,T_a) ) ).
cnf(cls_lattice_Oinf__sup__ord_I3_J_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,V_x),hAPP(hAPP(V_sup,V_x),V_y)))
| ~ c_Lattices_Olattice(V_less__eq,V_less,V_inf,V_sup,T_a) ) ).
cnf(cls_lattice_Oinf__sup__ord_I4_J_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,V_y),hAPP(hAPP(V_sup,V_x),V_y)))
| ~ c_Lattices_Olattice(V_less__eq,V_less,V_inf,V_sup,T_a) ) ).
cnf(cls_lattice_Odistrib__inf__le_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,hAPP(hAPP(V_sup,hAPP(hAPP(V_inf,V_x),V_y)),hAPP(hAPP(V_inf,V_x),V_z))),hAPP(hAPP(V_inf,V_x),hAPP(hAPP(V_sup,V_y),V_z))))
| ~ c_Lattices_Olattice(V_less__eq,V_less,V_inf,V_sup,T_a) ) ).
cnf(cls_lattice_Odistrib__sup__le_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,hAPP(hAPP(V_sup,V_x),hAPP(hAPP(V_inf,V_y),V_z))),hAPP(hAPP(V_inf,hAPP(hAPP(V_sup,V_x),V_y)),hAPP(hAPP(V_sup,V_x),V_z))))
| ~ c_Lattices_Olattice(V_less__eq,V_less,V_inf,V_sup,T_a) ) ).
cnf(cls_IntI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A)) ) ).
cnf(cls_Int__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A)) ) ).
cnf(cls_card__image_0,axiom,
( c_Finite__Set_Ocard(c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) = c_Finite__Set_Ocard(V_A,T_a)
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
cnf(cls_of__nat__add_0,axiom,
( ~ class_Ring__and__Field_Osemiring__1(T_a)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),T_a) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ).
cnf(cls_inf1I_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),V_x))
| ~ hBOOL(hAPP(V_B,V_x))
| ~ hBOOL(hAPP(V_A,V_x)) ) ).
cnf(cls_sup__eq__neg__inf_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b) = hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b))) ) ).
cnf(cls_Pi__empty_0,axiom,
c_FuncSet_OPi(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_B,T_a,T_b) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_bool)) ).
cnf(cls_image__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_b,tc_bool)),c_Set_Oimage(V_f,V_A,T_a,T_b)),c_Set_Oimage(V_f,V_B,T_a,T_b)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_subset__image__iff_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_b,tc_bool)),V_x),V_A))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Set_Oimage(V_f,V_x,T_b,T_a)),c_Set_Oimage(V_f,V_A,T_b,T_a))) ) ).
cnf(cls_neg__0__less__iff__less_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))) ) ).
cnf(cls_neg__0__less__iff__less_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a))) ) ).
cnf(cls_finite__imageD_0,axiom,
( c_Finite__Set_Ofinite(V_A,T_b)
| ~ c_Fun_Oinj__on(V_f,V_A,T_b,T_a)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(V_f,V_A,T_b,T_a),T_a) ) ).
cnf(cls_Un__empty_2,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_add__is__1_1,axiom,
( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ).
cnf(cls_add__is__1_2,axiom,
( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| V_m = c_HOL_Ozero__class_Ozero(tc_nat)
| V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
cnf(cls_psubset__eq_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B))
| V_A = V_B
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_subset__iff__psubset__eq_0,axiom,
( V_A = V_B
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_image__Un_0,axiom,
c_Set_Oimage(V_f,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_b,tc_bool)),V_A),V_B),T_b,T_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Set_Oimage(V_f,V_A,T_b,T_a)),c_Set_Oimage(V_f,V_B,T_b,T_a)) ).
cnf(cls_vimage__empty_0,axiom,
c_Set_Ovimage(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_a,T_b) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_less__minus__self__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a))) ) ).
cnf(cls_less__minus__self__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))) ) ).
cnf(cls_Sup__upper_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),c_Complete__Lattice_OSup__class_OSup(V_A,T_a)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_infinite__descent_0,axiom,
( hBOOL(hAPP(V_P,V_n))
| ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Nat__Xinfinite__descent__1__1(V_P))) ) ).
cnf(cls_minus__add__distrib_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a)) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b),T_a) ) ).
cnf(cls_minus__add_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a)) = c_HOL_Oplus__class_Oplus(hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a),T_a) ) ).
cnf(cls_linorder__linear_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x))
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_trans__less__add1_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_i),c_HOL_Oplus__class_Oplus(V_j,V_m,tc_nat)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_i),V_j)) ) ).
cnf(cls_add__lessD1_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_i),V_k))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat)),V_k)) ) ).
cnf(cls_termination__basic__simps_I2_J_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),V_z)) ) ).
cnf(cls_termination__basic__simps_I1_J_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),V_y)) ) ).
cnf(cls_nat__less__induct_0,axiom,
( hBOOL(hAPP(V_P,V_n))
| hBOOL(hAPP(V_P,V_m))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),c_ATP__Linkup_Osko__Nat__Xnat__less__induct__1__1(V_P))) ) ).
cnf(cls_measure__induct_0,axiom,
( hBOOL(hAPP(V_P,V_a))
| hBOOL(hAPP(V_P,V_y))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(V_f,V_y)),hAPP(V_f,c_ATP__Linkup_Osko__Nat__Xmeasure__induct__1__1(V_P,V_f,T_a)))) ) ).
cnf(cls_gr__implies__not0_0,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),c_HOL_Ozero__class_Ozero(tc_nat))) ).
cnf(cls_not__less0_0,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),c_HOL_Ozero__class_Ozero(tc_nat))) ).
cnf(cls_infinite__descent_1,axiom,
( hBOOL(hAPP(V_P,V_n))
| hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),c_ATP__Linkup_Osko__Nat__Xinfinite__descent__1__1(V_P))) ) ).
cnf(cls_Suc__lessI_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(V_m)),V_n))
| c_Suc(V_m) = V_n
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n)) ) ).
cnf(cls_infinite__descent__measure_1,axiom,
( hBOOL(hAPP(V_P,V_x))
| hBOOL(hAPP(V_P,V_xa))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(V_V,V_xa)),hAPP(V_V,c_ATP__Linkup_Osko__Nat__Xinfinite__descent__measure__1__1(V_P,V_V,T_a)))) ) ).
cnf(cls_not__less__less__Suc__eq_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),V_x))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),c_Suc(V_x))) ) ).
cnf(cls_not__less__eq_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),c_Suc(V_m))) ) ).
cnf(cls_not__less__eq_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),c_Suc(V_m)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n)) ) ).
cnf(cls_ex__nat__less__eq_1,axiom,
( hBOOL(hAPP(V_P,c_List_Osko__List__Xex__nat__less__eq__1__1(V_P,V_n)))
| ~ hBOOL(hAPP(V_P,V_xa))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_xa),V_n)) ) ).
cnf(cls_measure__induct__rule_0,axiom,
( hBOOL(hAPP(V_P,V_a))
| hBOOL(hAPP(V_P,V_y))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(V_f,V_y)),hAPP(V_f,c_ATP__Linkup_Osko__Nat__Xmeasure__induct__rule__1__1(V_P,V_f,T_a)))) ) ).
cnf(cls_less__Suc__eq__0__disj_3,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(V_x)),c_Suc(V_n)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),V_n)) ) ).
cnf(cls_Suc__less__eq_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(V_m)),c_Suc(V_n))) ) ).
cnf(cls_Suc__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(V_m)),c_Suc(V_n)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n)) ) ).
cnf(cls_preorder_Odual__preorder_0,axiom,
( c_Orderings_Opreorder(c_COMBC(V_less__eq,T_a,T_a,tc_bool),c_COMBC(V_less,T_a,T_a,tc_bool),T_a)
| ~ c_Orderings_Opreorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_lattice_Odual__lattice_0,axiom,
( c_Lattices_Olattice(c_COMBC(V_less__eq,T_a,T_a,tc_bool),c_COMBC(V_less,T_a,T_a,tc_bool),V_sup,V_inf,T_a)
| ~ c_Lattices_Olattice(V_less__eq,V_less,V_inf,V_sup,T_a) ) ).
cnf(cls_some__eq__trivial_0,axiom,
c_Hilbert__Choice_OEps(hAPP(c_COMBC(c_fequal(T_a),T_a,T_a,tc_bool),V_x),T_a) = V_x ).
cnf(cls_linorder_Odual__linorder_0,axiom,
( c_Orderings_Olinorder(c_COMBC(V_less__eq,T_a,T_a,tc_bool),c_COMBC(V_less,T_a,T_a,tc_bool),T_a)
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_the__eq__trivial_0,axiom,
c_The(hAPP(c_COMBC(c_fequal(T_a),T_a,T_a,tc_bool),V_a),T_a) = V_a ).
cnf(cls_distrib__lattice_Odual__distrib__lattice_0,axiom,
( c_Lattices_Odistrib__lattice(c_COMBC(V_less__eq,T_a,T_a,tc_bool),c_COMBC(V_less,T_a,T_a,tc_bool),V_sup,V_inf,T_a)
| ~ c_Lattices_Odistrib__lattice(V_less__eq,V_less,V_inf,V_sup,T_a) ) ).
cnf(cls_bounded__lattice_Odual__bounded__lattice_0,axiom,
( c_Lattices_Obounded__lattice(c_COMBC(V_less__eq,T_a,T_a,tc_bool),c_COMBC(V_less,T_a,T_a,tc_bool),V_sup,V_inf,V_top,V_bot,T_a)
| ~ c_Lattices_Obounded__lattice(V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_complete__lattice_Odual__complete__lattice_0,axiom,
( c_Complete__Lattice_Ocomplete__lattice(V_Sup,V_Inf,c_COMBC(V_less__eq,T_a,T_a,tc_bool),c_COMBC(V_less,T_a,T_a,tc_bool),V_sup,V_inf,V_top,V_bot,T_a)
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_order_Odual__order_0,axiom,
( c_Orderings_Oorder(c_COMBC(V_less__eq,T_a,T_a,tc_bool),c_COMBC(V_less,T_a,T_a,tc_bool),T_a)
| ~ c_Orderings_Oorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_inv__def_0,axiom,
hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),V_f,T_b,t_a),v_y) = c_Hilbert__Choice_OEps(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(t_a,tc_fun(t_a,tc_bool),T_b),c_fequal(t_a)),V_f),T_b,t_a,tc_bool),v_y),T_b) ).
cnf(cls_psubset__card__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(V_A,T_a)),c_Finite__Set_Ocard(V_B,T_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ c_Finite__Set_Ofinite(V_B,T_a) ) ).
cnf(cls_card__gt__0__iff_1,axiom,
( c_Finite__Set_Ofinite(V_A,T_a)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Ocard(V_A,T_a))) ) ).
cnf(cls_card__gt__0__iff_0,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a))) ).
cnf(cls_top__greatest_0,axiom,
( ~ class_Orderings_Otop(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ).
cnf(cls_inf__top__left_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ).
cnf(cls_inf__top__right_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ).
cnf(cls_inf__eq__top__eq1_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_A),V_B) != c_Orderings_Otop__class_Otop(T_a)
| V_A = c_Orderings_Otop__class_Otop(T_a) ) ).
cnf(cls_inf__eq__top__eq2_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_A),V_B) != c_Orderings_Otop__class_Otop(T_a)
| V_B = c_Orderings_Otop__class_Otop(T_a) ) ).
cnf(cls_sup__top__left_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = c_Orderings_Otop__class_Otop(T_a) ) ).
cnf(cls_sup__top__right_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
cnf(cls_finite__UNIV_0,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(T_a)
| c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a) ) ).
cnf(cls_subset__UNIV_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)))) ).
cnf(cls_Int__UNIV__right_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))) = V_A ).
cnf(cls_Int__UNIV__left_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))),V_B) = V_B ).
cnf(cls_UNIV__not__empty_0,axiom,
c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_injD_0,axiom,
( hAPP(V_f,V_x) != hAPP(V_f,V_y)
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b)
| V_x = V_y ) ).
cnf(cls_UNIV__I_0,axiom,
hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)))) ).
cnf(cls_Un__UNIV__right_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) ).
cnf(cls_Un__UNIV__left_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))),V_B) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) ).
cnf(cls_vimage__UNIV_0,axiom,
c_Set_Ovimage(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_a,T_b) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) ).
cnf(cls_complete__lattice_OInf__UNIV_0,axiom,
( hAPP(V_Inf,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))) = V_bot
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_complete__lattice_OSup__UNIV_0,axiom,
( hAPP(V_Sup,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))) = V_top
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_vimage__const_0,axiom,
( c_Set_Ovimage(c_COMBK(V_c,T_b,T_a),V_A,T_a,T_b) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_c),V_A)) ) ).
cnf(cls_bij__betw__same__card_0,axiom,
( c_Finite__Set_Ocard(V_A,T_a) = c_Finite__Set_Ocard(V_B,T_b)
| ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b) ) ).
cnf(cls_lfp__const_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| c_Inductive_Ocomplete__lattice__class_Olfp(c_COMBK(V_t,T_a,T_a),T_a) = V_t ) ).
cnf(cls_iso__tuple__update__accessor__cong__assist__def_0,axiom,
( hAPP(hAPP(V_upd,c_COMBK(hAPP(V_f,hAPP(V_acc,V_va)),T_a,T_a)),V_va) = hAPP(hAPP(V_upd,V_f),V_va)
| ~ c_Record_Oiso__tuple__update__accessor__cong__assist(V_upd,V_acc,T_a,T_b) ) ).
cnf(cls_INT__constant_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OINFI(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),c_COMBK(V_c,tc_fun(T_a,tc_bool),T_b),T_b,tc_fun(T_a,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) ).
cnf(cls_Pi__UNIV_0,axiom,
c_FuncSet_OPi(V_A,c_COMBK(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),tc_fun(T_b,tc_bool),T_a),T_a,T_b) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_bool)) ).
cnf(cls_UNIV__Times__UNIV_0,axiom,
c_Product__Type_OSigma(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),c_COMBK(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),tc_fun(T_b,tc_bool),T_a),T_a,T_b) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_a,T_b),tc_bool)) ).
cnf(cls_setprod__gen__delta_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__mult(T_b)
| c_Finite__Set_Osetprod(hAPP(c_COMBC(c_COMBS(hAPP(hAPP(c_COMBB(tc_bool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_HOL_OIf(T_b)),hAPP(c_COMBC(c_fequal(T_a),T_a,T_a,tc_bool),V_a)),V_b,T_a,T_b,tc_fun(T_b,T_b)),T_a,T_b,T_b),V_c),V_S,T_a,T_b) = c_Power_Opower__class_Opower(V_c,c_Finite__Set_Ocard(V_S,T_a),T_b)
| hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_S))
| ~ c_Finite__Set_Ofinite(V_S,T_a) ) ).
cnf(cls_vimage__if_2,axiom,
( c_Set_Ovimage(hAPP(c_COMBC(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_bool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_HOL_OIf(T_b)),hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_B)),T_a,T_b,tc_fun(T_b,T_b)),V_c),T_a,T_b,T_b),V_d),V_A,T_a,T_b) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B)
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_d),V_A))
| hBOOL(hAPP(hAPP(c_in(T_b),V_c),V_A)) ) ).
cnf(cls_vimage__if_3,axiom,
( c_Set_Ovimage(hAPP(c_COMBC(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_bool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_HOL_OIf(T_b)),hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_B)),T_a,T_b,tc_fun(T_b,T_b)),V_c),T_a,T_b,T_b),V_d),V_A,T_a,T_b) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| hBOOL(hAPP(hAPP(c_in(T_b),V_d),V_A))
| hBOOL(hAPP(hAPP(c_in(T_b),V_c),V_A)) ) ).
cnf(cls_vimage__if_1,axiom,
( c_Set_Ovimage(hAPP(c_COMBC(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_bool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_HOL_OIf(T_b)),hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_B)),T_a,T_b,tc_fun(T_b,T_b)),V_c),T_a,T_b,T_b),V_d),V_A,T_a,T_b) = V_B
| hBOOL(hAPP(hAPP(c_in(T_b),V_d),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_c),V_A)) ) ).
cnf(cls_boolean__algebra_Odual__boolean__algebra_0,axiom,
( c_Lattices_Oboolean__algebra(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(T_a,T_a),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,T_a)),T_a),c_COMBB(T_a,T_a,T_a)),V_sup),T_a,tc_fun(T_a,T_a),tc_fun(T_a,T_a)),V_uminus),V_uminus,c_COMBC(V_less__eq,T_a,T_a,tc_bool),c_COMBC(V_less,T_a,T_a,tc_bool),V_sup,V_inf,V_top,V_bot,T_a)
| ~ c_Lattices_Oboolean__algebra(V_minus,V_uminus,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_finite__UNIV__card__ge__0_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a)))
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a) ) ).
cnf(cls_finite__indi_0,axiom,
c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi) ).
cnf(cls_vimage__if_0,axiom,
( c_Set_Ovimage(hAPP(c_COMBC(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_bool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_HOL_OIf(T_b)),hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_B)),T_a,T_b,tc_fun(T_b,T_b)),V_c),T_a,T_b,T_b),V_d),V_A,T_a,T_b) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_d),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_c),V_A)) ) ).
cnf(cls_of__nat__less__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a))) ) ).
cnf(cls_of__nat__less__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n)) ) ).
cnf(cls_range__composition_0,axiom,
c_Set_Oimage(hAPP(hAPP(c_COMBB(T_c,T_a,T_b),V_f),V_g),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_a) = c_Set_Oimage(V_f,c_Set_Oimage(V_g,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_c),T_c,T_a) ).
cnf(cls_top__fun__eq_0,axiom,
( ~ class_Orderings_Otop(T_b)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,T_b)),v_x) = c_Orderings_Otop__class_Otop(T_b) ) ).
cnf(cls_Sup__UNIV_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| c_Complete__Lattice_OSup__class_OSup(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a) = c_Orderings_Otop__class_Otop(T_a) ) ).
cnf(cls_surjh_0,axiom,
c_Set_Oimage(v_h____,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) = c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) ).
cnf(cls_card__eq__UNIV__imp__eq__UNIV_0,axiom,
( c_Finite__Set_Ocard(V_A,T_a) != c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a)
| V_A = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_1_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(hAPP(c_COMBC(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),c_HOL_Oord__class_Oless(tc_nat)),v_h____),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),c_HOL_Ozero__class_Ozero(tc_nat))),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____)))) ).
cnf(cls_injh_0,axiom,
c_Fun_Oinj__on(v_h____,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) ).
cnf(cls_0_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_F(hAPP(c_COMBC(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),c_HOL_Oord__class_Oless(tc_nat)),v_h____),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),V_n)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____))),c_Arrow__Order__Mirabelle_OLin)) ).
cnf(cls_PiProf_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),c_HOL_Oord__class_Oless(tc_nat)),v_h____),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),V_n)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____)),c_Arrow__Order__Mirabelle_OProf)) ).
cnf(cls_order__less__asym_H_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_a))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)) ) ).
cnf(cls_order__less__asym_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_not__less__iff__gr__or__eq_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x)) ) ).
cnf(cls_xt1_I9_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_a)) ) ).
cnf(cls_linorder__antisym__conv3_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| V_x = V_y
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x)) ) ).
cnf(cls_linorder__less__linear_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x))
| V_x = V_y
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_linorder__neqE_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| V_x = V_y ) ).
cnf(cls_linorder__neqE__nat_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_y),V_x))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),V_y))
| V_x = V_y ) ).
cnf(cls_nat__less__cases_0,axiom,
( hBOOL(hAPP(hAPP(V_P,V_n),V_m))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),V_m))
| V_m = V_n
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n)) ) ).
cnf(cls_nat__neq__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),V_m))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))
| V_m = V_n ) ).
cnf(cls_not__less__iff__gr__or__eq_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| V_x = V_y
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_linorder__neqE__ordered__idom_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| V_x = V_y ) ).
cnf(cls_top1I_0,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_x)) ).
cnf(cls_order__less__irrefl_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_x)) ) ).
cnf(cls_linorder__neq__iff_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_x)) ) ).
cnf(cls_order__less__le_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_x)) ) ).
cnf(cls_less__not__refl_0,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),V_n)) ).
cnf(cls_nat__less__le_1,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),V_x)) ).
cnf(cls_order__less__trans_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_z))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_xt1_I10_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_z),V_x))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_z),V_y))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x)) ) ).
cnf(cls_COMBB__def_0,axiom,
hAPP(hAPP(hAPP(c_COMBB(T_b,T_a,T_c),V_P),V_Q),V_R) = hAPP(V_P,hAPP(V_Q,V_R)) ).
cnf(cls_COMBC__def_0,axiom,
hAPP(hAPP(c_COMBC(V_P,T_b,T_c,T_a),V_Q),V_R) = hAPP(hAPP(V_P,V_R),V_Q) ).
cnf(cls_COMBK__def_0,axiom,
hAPP(c_COMBK(V_P,T_a,T_b),V_Q) = V_P ).
cnf(cls_CHAINED_0,axiom,
c_Set_Oimage(v_h____,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_nat) = c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_nat) ).
cnf(cls_conjecture_0,negated_conjecture,
hAPP(c_COMBC(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),c_HOL_Oord__class_Oless(tc_nat)),v_h____),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),tc_Arrow__Order__Mirabelle_Oindi))),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____) != c_COMBK(v_Lab____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi) ).
cnf(clsarity_prod__Finite__Set_Ofinite_Ofinite,axiom,
( class_Finite__Set_Ofinite_Ofinite(tc_prod(T_2,T_1))
| ~ class_Finite__Set_Ofinite_Ofinite(T_1)
| ~ class_Finite__Set_Ofinite_Ofinite(T_2) ) ).
cnf(clsarity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_1) ) ).
cnf(clsarity_fun__Lattices_Oupper__semilattice,axiom,
( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ) ).
cnf(clsarity_fun__Lattices_Olower__semilattice,axiom,
( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ) ).
cnf(clsarity_fun__Lattices_Odistrib__lattice,axiom,
( class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Odistrib__lattice(T_1) ) ).
cnf(clsarity_fun__Lattices_Obounded__lattice,axiom,
( class_Lattices_Obounded__lattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Obounded__lattice(T_1) ) ).
cnf(clsarity_fun__Lattices_Oboolean__algebra,axiom,
( class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))
| ~ class_Lattices_Oboolean__algebra(T_1) ) ).
cnf(clsarity_fun__Finite__Set_Ofinite_Ofinite,axiom,
( class_Finite__Set_Ofinite_Ofinite(tc_fun(T_2,T_1))
| ~ class_Finite__Set_Ofinite_Ofinite(T_1)
| ~ class_Finite__Set_Ofinite_Ofinite(T_2) ) ).
cnf(clsarity_fun__Orderings_Opreorder,axiom,
( class_Orderings_Opreorder(tc_fun(T_2,T_1))
| ~ class_Orderings_Opreorder(T_1) ) ).
cnf(clsarity_fun__Lattices_Olattice,axiom,
( class_Lattices_Olattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ) ).
cnf(clsarity_fun__Orderings_Oorder,axiom,
( class_Orderings_Oorder(tc_fun(T_2,T_1))
| ~ class_Orderings_Oorder(T_1) ) ).
cnf(clsarity_fun__Orderings_Otop,axiom,
( class_Orderings_Otop(tc_fun(T_2,T_1))
| ~ class_Orderings_Otop(T_1) ) ).
cnf(clsarity_fun__Orderings_Obot,axiom,
( class_Orderings_Obot(tc_fun(T_2,T_1))
| ~ class_Orderings_Obot(T_1) ) ).
cnf(clsarity_fun__HOL_Ouminus,axiom,
( class_HOL_Ouminus(tc_fun(T_2,T_1))
| ~ class_HOL_Ouminus(T_1) ) ).
cnf(clsarity_fun__HOL_Oord,axiom,
( class_HOL_Oord(tc_fun(T_2,T_1))
| ~ class_HOL_Oord(T_1) ) ).
cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Ono__zero__divisors,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__mult,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat) ).
cnf(clsarity_nat__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_nat) ).
cnf(clsarity_nat__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring__0,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_nat) ).
cnf(clsarity_nat__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_nat) ).
cnf(clsarity_nat__Nat_Osemiring__char__0,axiom,
class_Nat_Osemiring__char__0(tc_nat) ).
cnf(clsarity_nat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_nat) ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat) ).
cnf(clsarity_nat__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_nat) ).
cnf(clsarity_nat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_nat) ).
cnf(clsarity_nat__Orderings_Obot,axiom,
class_Orderings_Obot(tc_nat) ).
cnf(clsarity_nat__Power_Opower,axiom,
class_Power_Opower(tc_nat) ).
cnf(clsarity_nat__HOL_Oord,axiom,
class_HOL_Oord(tc_nat) ).
cnf(clsarity_bool__Complete__Lattice_Ocomplete__lattice,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool) ).
cnf(clsarity_bool__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_bool) ).
cnf(clsarity_bool__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_bool) ).
cnf(clsarity_bool__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_bool) ).
cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_bool) ).
cnf(clsarity_bool__Lattices_Oboolean__algebra,axiom,
class_Lattices_Oboolean__algebra(tc_bool) ).
cnf(clsarity_bool__Finite__Set_Ofinite_Ofinite,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool) ).
cnf(clsarity_bool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_bool) ).
cnf(clsarity_bool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_bool) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool) ).
cnf(clsarity_bool__Orderings_Otop,axiom,
class_Orderings_Otop(tc_bool) ).
cnf(clsarity_bool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_bool) ).
cnf(clsarity_bool__HOL_Ouminus,axiom,
class_HOL_Ouminus(tc_bool) ).
cnf(clsarity_bool__HOL_Oord,axiom,
class_HOL_Oord(tc_bool) ).
cnf(cls_ATP__Linkup_OCOMBC__def_0,axiom,
hAPP(hAPP(c_COMBC(V_P,T_b,T_c,T_a),V_Q),V_R) = hAPP(hAPP(V_P,V_R),V_Q) ).
cnf(cls_ATP__Linkup_OCOMBB__def_0,axiom,
hAPP(hAPP(hAPP(c_COMBB(T_b,T_a,T_c),V_P),V_Q),V_R) = hAPP(V_P,hAPP(V_Q,V_R)) ).
cnf(cls_ATP__Linkup_OCOMBK__def_0,axiom,
hAPP(c_COMBK(V_P,T_a,T_b),V_Q) = V_P ).
cnf(cls_ATP__Linkup_OCOMBI__def_0,axiom,
c_COMBI(V_P,T_a) = V_P ).
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
hBOOL(hAPP(hAPP(c_fequal(T_a),V_x),V_x)) ).
cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom,
( V_X = V_Y
| ~ hBOOL(hAPP(hAPP(c_fequal(T_a),V_X),V_Y)) ) ).
%------------------------------------------------------------------------------