%------------------------------------------------------------------------------
% File     : SCT003-1 : TPTP v8.2.0. Released v4.1.0.
% Domain   : Social Choice Theory
% Problem  : Arrow Order 048_1
% 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-048_1 [Nip10]

% Status   : Unsatisfiable
% Rating   : 1.00 v7.3.0, 0.92 v7.0.0, 0.93 v6.3.0, 0.91 v6.2.0, 0.90 v6.1.0, 0.93 v6.0.0, 0.90 v5.5.0, 0.95 v5.3.0, 0.94 v5.0.0, 0.93 v4.1.0
% Syntax   : Number of clauses     :  491 ( 158 unt;  34 nHn; 229 RR)
%            Number of literals    :  973 ( 273 equ; 460 neg)
%            Maximal clause size   :    6 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :   22 (  21 usr;   0 prp; 1-9 aty)
%            Number of functors    :   55 (  55 usr;   4 con; 0-5 aty)
%            Number of variables   : 1802 ( 220 sgn)
% SPC      : CNF_UNS_RFO_SEQ_NHN

% Comments :
%------------------------------------------------------------------------------
cnf(cls_Image__iff_2,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),V_b),c_Relation_OImage(V_r,V_A,T_b,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_b,T_a)),c_Pair(V_x,V_b,T_b,T_a)),V_r))
    | ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A)) ) ).

cnf(cls_rev__ImageI_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_b),V_b),c_Relation_OImage(V_r,V_A,T_a,T_b)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_b)),c_Pair(V_a,V_b,T_a,T_b)),V_r))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)) ) ).

cnf(cls_Image__Id_0,axiom,
    c_Relation_OImage(c_Relation_OId(T_a),V_A,T_a,T_a) = V_A ).

cnf(cls_Image__Un_0,axiom,
    c_Relation_OImage(V_R,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(V_R,V_A,T_b,T_a),c_Relation_OImage(V_R,V_B,T_b,T_a),tc_fun(T_a,tc_bool)) ).

cnf(cls_rel__comp__empty1_0,axiom,
    c_Relation_Orel__comp(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_c),tc_bool)),V_R,T_a,T_c,T_b) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_bool)) ).

cnf(cls_rel__comp__empty2_0,axiom,
    c_Relation_Orel__comp(V_R,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_bool)),T_a,T_c,T_b) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_bool)) ).

cnf(cls_Image__empty_0,axiom,
    c_Relation_OImage(V_R,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_antisym__empty_0,axiom,
    c_Relation_Oantisym(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) ).

cnf(cls_trancl__empty_0,axiom,
    c_Transitive__Closure_Otrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_bool)) ).

cnf(cls_Field__empty_0,axiom,
    c_Relation_OField(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).

cnf(cls_Un__Image_0,axiom,
    c_Relation_OImage(c_Lattices_Oupper__semilattice__class_Osup(V_R,V_S,tc_fun(tc_prod(T_b,T_a),tc_bool)),V_A,T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OImage(V_R,V_A,T_b,T_a),c_Relation_OImage(V_S,V_A,T_b,T_a),tc_fun(T_a,tc_bool)) ).

cnf(cls_refl__on__empty_0,axiom,
    c_Relation_Orefl__on(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) ).

cnf(cls_rtrancl__empty_0,axiom,
    c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) = c_Relation_OId(T_a) ).

cnf(cls_union__comp__emptyL_0,axiom,
    ( c_Relation_Orel__comp(V_B,V_C,T_a,T_a,T_a) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_bool))
    | c_Relation_Orel__comp(V_A,V_C,T_a,T_a,T_a) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_bool))
    | c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(tc_prod(T_a,T_a),tc_bool)),V_C,T_a,T_a,T_a) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_bool)) ) ).

cnf(cls_union__comp__emptyR_0,axiom,
    ( c_Relation_Orel__comp(V_A,V_C,T_a,T_a,T_a) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_bool))
    | c_Relation_Orel__comp(V_A,V_B,T_a,T_a,T_a) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_bool))
    | c_Relation_Orel__comp(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a,T_a,T_a) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_bool)) ) ).

cnf(cls_Id__on__empty_0,axiom,
    c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_bool)) ).

cnf(cls_partial__order__on__empty_0,axiom,
    c_Order__Relation_Opartial__order__on(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) ).

cnf(cls_preorder__on__empty_0,axiom,
    c_Order__Relation_Opreorder__on(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) ).

cnf(cls_Image__Id__on_0,axiom,
    c_Relation_OImage(c_Relation_OId__on(V_A,T_a),V_B,T_a,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) ).

cnf(cls_lnear__order__on__empty_0,axiom,
    c_Order__Relation_Olinear__order__on(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) ).

cnf(cls_Image__singleton__iff_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_b,T_a)),c_Pair(V_a,V_b,T_b,T_a)),V_r))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_b),c_Relation_OImage(V_r,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b),T_b,T_a))) ) ).

cnf(cls_Image__singleton__iff_1,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),V_b),c_Relation_OImage(V_r,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b),T_b,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_b,T_a)),c_Pair(V_a,V_b,T_b,T_a)),V_r)) ) ).

cnf(cls_quotientI_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),c_Relation_OImage(V_r,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a)),c_Equiv__Relations_Oquotient(V_A,V_r,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).

cnf(cls_Partial__order__eq__Image1__Image1__iff_0,axiom,
    ( c_Relation_OImage(V_r,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a) != c_Relation_OImage(V_r,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a)
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_b),c_Relation_OField(V_r,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Relation_OField(V_r,T_a)))
    | ~ c_Order__Relation_Opartial__order__on(c_Relation_OField(V_r,T_a),V_r,T_a)
    | V_a = V_b ) ).

cnf(cls_finite__trancl_0,axiom,
    ( c_Finite__Set_Ofinite(V_r,tc_prod(T_a,T_a))
    | ~ c_Finite__Set_Ofinite(c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a)) ) ).

cnf(cls_Diff__triv_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
    | c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)) = V_A ) ).

cnf(cls_Int__Un__distrib2_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_B,V_A,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).

cnf(cls_Int__Un__distrib_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).

cnf(cls_inf__sup__distrib1_0,axiom,
    ( ~ class_Lattices_Odistrib__lattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a) ) ).

cnf(cls_inf__sup__distrib2_0,axiom,
    ( ~ class_Lattices_Odistrib__lattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),V_x,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a),c_Lattices_Olower__semilattice__class_Oinf(V_z,V_x,T_a),T_a) ) ).

cnf(cls_Int__Collect_1,axiom,
    ( hBOOL(hAPP(V_P,V_x))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Collect(V_P,T_a),tc_fun(T_a,tc_bool)))) ) ).

cnf(cls_linear__order__on__def_2,axiom,
    ( c_Order__Relation_Olinear__order__on(V_A,V_r,T_a)
    | ~ c_Relation_Ototal__on(V_A,V_r,T_a)
    | ~ c_Order__Relation_Opartial__order__on(V_A,V_r,T_a) ) ).

cnf(cls_Un__absorb_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(V_A,V_A,tc_fun(T_a,tc_bool)) = V_A ).

cnf(cls_sup__idem_0,axiom,
    ( ~ class_Lattices_Oupper__semilattice(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(V_x,V_x,T_a) = V_x ) ).

cnf(cls_trans__trancl_0,axiom,
    c_Relation_Otrans(c_Transitive__Closure_Otrancl(V_r,T_a),T_a) ).

cnf(cls_inj__on__insert_2,axiom,
    ( c_Fun_Oinj__on(V_f,c_Set_Oinsert(V_a,V_A,T_a),T_a,T_b)
    | hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),c_Set_Oimage(V_f,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a,T_b)))
    | ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).

cnf(cls_Nitpick_Ortrancl__def_0,axiom,
    c_Transitive__Closure_Ortrancl(V_r,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(V_r,T_a),c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) ).

cnf(cls_UnionE_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),V_A),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(V_A,V_C,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_A),c_Complete__Lattice_OSup__class_OSup(V_C,tc_fun(T_a,tc_bool)))) ) ).

cnf(cls_total__on__def_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_xa,V_x,T_a,T_a)),V_r))
    | hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_xa,T_a,T_a)),V_r))
    | V_x = 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_Relation_Ototal__on(V_A,V_r,T_a) ) ).

cnf(cls_insert__commute_0,axiom,
    c_Set_Oinsert(V_x,c_Set_Oinsert(V_y,V_A,T_a),T_a) = c_Set_Oinsert(V_y,c_Set_Oinsert(V_x,V_A,T_a),T_a) ).

cnf(cls_INT__extend__simps_I4_J_0,axiom,
    c_HOL_Ominus__class_Ominus(V_A,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_B,T_b,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A ).

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_inj__on__Un_3,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(V_f,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a,T_b),c_Set_Oimage(V_f,c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool)),T_a,T_b),tc_fun(T_b,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))
    | ~ c_Fun_Oinj__on(V_f,V_B,T_a,T_b)
    | ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
    | c_Fun_Oinj__on(V_f,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a,T_b) ) ).

cnf(cls_inj__on__Un_2,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(V_f,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a,T_b),c_Set_Oimage(V_f,c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool)),T_a,T_b),tc_fun(T_b,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))
    | ~ c_Fun_Oinj__on(V_f,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a,T_b) ) ).

cnf(cls_Diff__idemp_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)) ).

cnf(cls_in__rtrancl__UnI_1,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),V_x),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(V_R,V_S,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),V_x),c_Transitive__Closure_Ortrancl(V_S,T_a))) ) ).

cnf(cls_in__rtrancl__UnI_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),V_x),c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(V_R,V_S,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),V_x),c_Transitive__Closure_Ortrancl(V_R,T_a))) ) ).

cnf(cls_doubleton__eq__iff_4,axiom,
    c_Set_Oinsert(V_xa,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = c_Set_Oinsert(V_x,c_Set_Oinsert(V_xa,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) ).

cnf(cls_eq__eqI_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_xa,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)
    | V_xa = V_y ) ).

cnf(cls_eq__eqI_0,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
    | V_x_H = V_y_H ) ).

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_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,
    c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).

cnf(cls_Un__assoc_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).

cnf(cls_sup__assoc_0,axiom,
    ( ~ class_Lattices_Oupper__semilattice(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) ) ).

cnf(cls_sup__left__commute_0,axiom,
    ( ~ class_Lattices_Oupper__semilattice(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a) ) ).

cnf(cls_inf__sup__aci_I7_J_0,axiom,
    ( ~ class_Lattices_Olattice(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a) ) ).

cnf(cls_inf__sup__aci_I6_J_0,axiom,
    ( ~ class_Lattices_Olattice(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) ) ).

cnf(cls_rtrancl__reflcl__absorb_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(V_R,T_a),c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) = c_Transitive__Closure_Ortrancl(V_R,T_a) ).

cnf(cls_Int__commute_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_B,V_A,tc_fun(T_a,tc_bool)) ).

cnf(cls_inf__commute_0,axiom,
    ( ~ class_Lattices_Olower__semilattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a) ) ).

cnf(cls_inf__sup__aci_I1_J_0,axiom,
    ( ~ class_Lattices_Olattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,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_sym__rtrancl_0,axiom,
    ( c_Relation_Osym(c_Transitive__Closure_Ortrancl(V_r,T_a),T_a)
    | ~ c_Relation_Osym(V_r,T_a) ) ).

cnf(cls_insert__Diff__single_0,axiom,
    c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = c_Set_Oinsert(V_a,V_A,T_a) ).

cnf(cls_partial__order__on__def_2,axiom,
    ( c_Order__Relation_Opartial__order__on(V_A,V_r,T_a)
    | ~ c_Relation_Oantisym(V_r,T_a)
    | ~ c_Order__Relation_Opreorder__on(V_A,V_r,T_a) ) ).

cnf(cls_singleton__inject_0,axiom,
    ( c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) != c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)
    | V_a = V_b ) ).

cnf(cls_Un__Int__crazy_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).

cnf(cls_irrefl__tranclI_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(V_r,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_bool))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_x,T_a,T_a)),c_Transitive__Closure_Otrancl(V_r,T_a))) ) ).

cnf(cls_Refl__antisym__eq__Image1__Image1__iff_0,axiom,
    ( c_Relation_OImage(V_r,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a) != c_Relation_OImage(V_r,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a)
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_b),c_Relation_OField(V_r,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Relation_OField(V_r,T_a)))
    | ~ c_Relation_Oantisym(V_r,T_a)
    | ~ c_Relation_Orefl__on(c_Relation_OField(V_r,T_a),V_r,T_a)
    | V_a = V_b ) ).

cnf(cls_quotientE_0,axiom,
    ( V_X = c_Relation_OImage(V_r,c_Set_Oinsert(c_List_Osko__Equiv__Relations__XquotientE__1__1(V_A,V_X,V_r,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a,T_a)
    | ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),V_X),c_Equiv__Relations_Oquotient(V_A,V_r,T_a))) ) ).

cnf(cls_finite__trancl_1,axiom,
    ( c_Finite__Set_Ofinite(c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a))
    | ~ c_Finite__Set_Ofinite(V_r,tc_prod(T_a,T_a)) ) ).

cnf(cls_singletonE_0,axiom,
    ( V_b = V_a
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_b),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a))) ) ).

cnf(cls_InterI_1,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),V_A),c_Complete__Lattice_OInf__class_OInf(V_C,tc_fun(T_a,tc_bool))))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_A),c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(V_A,V_C,T_a))) ) ).

cnf(cls_image__constant_0,axiom,
    ( c_Set_Oimage(c_COMBK(V_c,T_b,T_a),V_A,T_a,T_b) = c_Set_Oinsert(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b)
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).

cnf(cls_sym__Id__on_0,axiom,
    c_Relation_Osym(c_Relation_OId__on(V_A,T_a),T_a) ).

cnf(cls_trancl__reflcl_0,axiom,
    c_Transitive__Closure_Otrancl(c_Lattices_Oupper__semilattice__class_Osup(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) = c_Transitive__Closure_Ortrancl(V_r,T_a) ).

cnf(cls_inj__on__insert_0,axiom,
    ( c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
    | ~ c_Fun_Oinj__on(V_f,c_Set_Oinsert(V_a,V_A,T_a),T_a,T_b) ) ).

cnf(cls_insert__Diff1_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B)) ) ).

cnf(cls_refl__on__Id__on_0,axiom,
    c_Relation_Orefl__on(V_A,c_Relation_OId__on(V_A,T_a),T_a) ).

cnf(cls_r__comp__rtrancl__eq_0,axiom,
    c_Relation_Orel__comp(V_r,c_Transitive__Closure_Ortrancl(V_r,T_a),T_a,T_a,T_a) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(V_r,T_a),V_r,T_a,T_a,T_a) ).

cnf(cls_antisym__reflcl_0,axiom,
    ( c_Relation_Oantisym(V_r,T_a)
    | ~ c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) ) ).

cnf(cls_antisym__reflcl_1,axiom,
    ( c_Relation_Oantisym(c_Lattices_Oupper__semilattice__class_Osup(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a)
    | ~ c_Relation_Oantisym(V_r,T_a) ) ).

cnf(cls_rtrancl__reflcl_0,axiom,
    c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(V_R,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) = c_Transitive__Closure_Ortrancl(V_R,T_a) ).

cnf(cls_sym__inv__image_0,axiom,
    ( c_Relation_Osym(c_Relation_Oinv__image(V_r,V_f,T_a,T_b),T_b)
    | ~ c_Relation_Osym(V_r,T_a) ) ).

cnf(cls_finite__Diff_0,axiom,
    ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
    | ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).

cnf(cls_inj__on__diff_0,axiom,
    ( c_Fun_Oinj__on(V_f,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a,T_b)
    | ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).

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_Inf__insert_0,axiom,
    ( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
    | c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(V_a,V_A,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_a,c_Complete__Lattice_OInf__class_OInf(V_A,T_a),T_a) ) ).

cnf(cls_rtrancl__trancl__absorb_0,axiom,
    c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(V_R,T_a),T_a) = c_Transitive__Closure_Ortrancl(V_R,T_a) ).

cnf(cls_reflcl__trancl_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Otrancl(V_r,T_a),c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) = c_Transitive__Closure_Ortrancl(V_r,T_a) ).

cnf(cls_Un__insert__left_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,V_B,T_a),V_C,tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),T_a) ).

cnf(cls_Un__insert__right_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ).

cnf(cls_vimage__Diff_0,axiom,
    c_Set_Ovimage(V_f,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_b,tc_bool)),T_a,T_b) = c_HOL_Ominus__class_Ominus(c_Set_Ovimage(V_f,V_A,T_a,T_b),c_Set_Ovimage(V_f,V_B,T_a,T_b),tc_fun(T_a,tc_bool)) ).

cnf(cls_trans__rtrancl_0,axiom,
    c_Relation_Otrans(c_Transitive__Closure_Ortrancl(V_r,T_a),T_a) ).

cnf(cls_Collect__def_0,axiom,
    c_Collect(V_P,T_a) = V_P ).

cnf(cls_Sup__insert_0,axiom,
    ( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
    | c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(V_a,V_A,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_a,c_Complete__Lattice_OSup__class_OSup(V_A,T_a),T_a) ) ).

cnf(cls_Diff__insert_0,axiom,
    c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)) ).

cnf(cls_Diff__insert2_0,axiom,
    c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) ).

cnf(cls_finite__Diff2_0,axiom,
    ( c_Finite__Set_Ofinite(V_A,T_a)
    | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
    | ~ c_Finite__Set_Ofinite(V_B,T_a) ) ).

cnf(cls_finite__Diff2_1,axiom,
    ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
    | ~ c_Finite__Set_Ofinite(V_A,T_a)
    | ~ c_Finite__Set_Ofinite(V_B,T_a) ) ).

cnf(cls_insert__not__empty_0,axiom,
    c_Set_Oinsert(V_a,V_A,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).

cnf(cls_vimage__singleton__eq_1,axiom,
    hBOOL(hAPP(hAPP(c_in(T_aa),V_a),c_Set_Ovimage(V_f,c_Set_Oinsert(hAPP(V_f,V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_aa,T_a))) ).

cnf(cls_insert__inter__insert_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(V_a,V_A,T_a),c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ).

cnf(cls_insert__absorb2_0,axiom,
    c_Set_Oinsert(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Set_Oinsert(V_x,V_A,T_a) ).

cnf(cls_O__assoc_0,axiom,
    c_Relation_Orel__comp(c_Relation_Orel__comp(V_R,V_S,T_a,T_d,T_c),V_T,T_a,T_c,T_b) = c_Relation_Orel__comp(V_R,c_Relation_Orel__comp(V_S,V_T,T_d,T_c,T_b),T_a,T_d,T_b) ).

cnf(cls_finite__UN_0,axiom,
    ( c_Finite__Set_Ofinite(hAPP(V_B,V_x),T_b)
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
    | ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_bool)),T_b)
    | ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).

cnf(cls_insert__code_0,axiom,
    ( hBOOL(hAPP(V_A,V_x))
    | V_y = V_x
    | ~ hBOOL(hAPP(c_Set_Oinsert(V_y,V_A,T_a),V_x)) ) ).

cnf(cls_UNION__empty__conv_I2_J_0,axiom,
    ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_b,tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
    | hAPP(V_B,V_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
    | ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A)) ) ).

cnf(cls_sym__Un_0,axiom,
    ( c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(V_r,V_s,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a)
    | ~ c_Relation_Osym(V_s,T_a)
    | ~ c_Relation_Osym(V_r,T_a) ) ).

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,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a,T_b)
    | V_A = V_B ) ).

cnf(cls_inf__bot__right_0,axiom,
    ( ~ class_Lattices_Obounded__lattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Orderings_Obot__class_Obot(T_a),T_a) = c_Orderings_Obot__class_Obot(T_a) ) ).

cnf(cls_inf__bot__left_0,axiom,
    ( ~ class_Lattices_Obounded__lattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(T_a),V_x,T_a) = c_Orderings_Obot__class_Obot(T_a) ) ).

cnf(cls_Int__empty__left_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).

cnf(cls_Int__empty__right_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).

cnf(cls_acyclic__def_0,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_x,T_a,T_a)),c_Transitive__Closure_Otrancl(V_r,T_a)))
    | ~ c_Wellfounded_Oacyclic(V_r,T_a) ) ).

cnf(cls_finite__insert_0,axiom,
    ( c_Finite__Set_Ofinite(V_A,T_a)
    | ~ c_Finite__Set_Ofinite(c_Set_Oinsert(V_a,V_A,T_a),T_a) ) ).

cnf(cls_finite__insert_1,axiom,
    ( c_Finite__Set_Ofinite(c_Set_Oinsert(V_a,V_A,T_a),T_a)
    | ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).

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_trans__inv__image_0,axiom,
    ( c_Relation_Otrans(c_Relation_Oinv__image(V_r,V_f,T_a,T_b),T_b)
    | ~ c_Relation_Otrans(V_r,T_a) ) ).

cnf(cls_UN__absorb_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(hAPP(V_A,V_k),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_I,V_A,T_a,tc_fun(T_b,tc_bool)),tc_fun(T_b,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(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_complete__lattice_OSup__binary_0,axiom,
    ( hAPP(V_Sup,c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)) = hAPP(hAPP(V_sup,V_a),V_b)
    | ~ 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__binary_0,axiom,
    ( hAPP(V_Inf,c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)) = hAPP(hAPP(V_inf,V_a),V_b)
    | ~ 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_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_finite__Un_2,axiom,
    ( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(V_F,V_G,tc_fun(T_a,tc_bool)),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(c_Lattices_Oupper__semilattice__class_Osup(V_F,V_G,tc_fun(T_a,tc_bool)),T_a)
    | ~ c_Finite__Set_Ofinite(V_G,T_a)
    | ~ c_Finite__Set_Ofinite(V_F,T_a) ) ).

cnf(cls_rtrancl__eq__or__trancl_2,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),c_Transitive__Closure_Ortrancl(V_R,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),c_Transitive__Closure_Otrancl(V_R,T_a)))
    | V_x = V_y ) ).

cnf(cls_rtrancl__eq__or__trancl_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),c_Transitive__Closure_Otrancl(V_R,T_a)))
    | V_x = V_y
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),c_Transitive__Closure_Ortrancl(V_R,T_a))) ) ).

cnf(cls_rtranclD_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_b,T_a,T_a)),c_Transitive__Closure_Otrancl(V_R,T_a)))
    | V_a = V_b
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_b,T_a,T_a)),c_Transitive__Closure_Ortrancl(V_R,T_a))) ) ).

cnf(cls_rtrancl__converseI_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(V_r,T_a,T_a),T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_y,V_x,T_a,T_a)),c_Transitive__Closure_Ortrancl(V_r,T_a))) ) ).

cnf(cls_rtrancl__converseD_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_y,V_x,T_a,T_a)),c_Transitive__Closure_Ortrancl(V_r,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(V_r,T_a,T_a),T_a))) ) ).

cnf(cls_antisym__Id_0,axiom,
    c_Relation_Oantisym(c_Relation_OId(T_a),T_a) ).

cnf(cls_Diff__empty_0,axiom,
    c_HOL_Ominus__class_Ominus(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A ).

cnf(cls_Diff__cancel_0,axiom,
    c_HOL_Ominus__class_Ominus(V_A,V_A,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).

cnf(cls_trans__reflclI_0,axiom,
    ( c_Relation_Otrans(c_Lattices_Oupper__semilattice__class_Osup(V_r,c_Relation_OId(T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a)
    | ~ c_Relation_Otrans(V_r,T_a) ) ).

cnf(cls_sup1E_0,axiom,
    ( hBOOL(hAPP(V_B,V_x))
    | hBOOL(hAPP(V_A,V_x))
    | ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_x)) ) ).

cnf(cls_sup1CI_0,axiom,
    ( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_x))
    | ~ hBOOL(hAPP(V_B,V_x)) ) ).

cnf(cls_sup1CI_1,axiom,
    ( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_x))
    | ~ hBOOL(hAPP(V_A,V_x)) ) ).

cnf(cls_rtrancl__unfold_0,axiom,
    c_Transitive__Closure_Ortrancl(V_r,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OId(T_a),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(V_r,T_a),V_r,T_a,T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) ).

cnf(cls_partial__order__on__def_1,axiom,
    ( c_Relation_Oantisym(V_r,T_a)
    | ~ c_Order__Relation_Opartial__order__on(V_A,V_r,T_a) ) ).

cnf(cls_refl__on__Un_0,axiom,
    ( c_Relation_Orefl__on(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_r,V_s,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a)
    | ~ c_Relation_Orefl__on(V_B,V_s,T_a)
    | ~ c_Relation_Orefl__on(V_A,V_r,T_a) ) ).

cnf(cls_inf__sup__aci_I2_J_0,axiom,
    ( ~ class_Lattices_Olattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ).

cnf(cls_inf__sup__aci_I3_J_0,axiom,
    ( ~ class_Lattices_Olattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a) ) ).

cnf(cls_inf__left__commute_0,axiom,
    ( ~ class_Lattices_Olower__semilattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a) ) ).

cnf(cls_inf__assoc_0,axiom,
    ( ~ class_Lattices_Olower__semilattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ).

cnf(cls_Int__assoc_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).

cnf(cls_Int__left__commute_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_B,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).

cnf(cls_finite__Inter_0,axiom,
    ( c_Finite__Set_Ofinite(c_Complete__Lattice_OInf__class_OInf(V_M,tc_fun(T_a,tc_bool)),T_a)
    | ~ c_Finite__Set_Ofinite(V_x,T_a)
    | ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),V_x),V_M)) ) ).

cnf(cls_UNION__empty__conv_I1_J_0,axiom,
    ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_b,tc_fun(T_a,tc_bool))
    | hAPP(V_B,V_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
    | ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A)) ) ).

cnf(cls_finite__Un_0,axiom,
    ( c_Finite__Set_Ofinite(V_F,T_a)
    | ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(V_F,V_G,tc_fun(T_a,tc_bool)),T_a) ) ).

cnf(cls_finite__Un_1,axiom,
    ( c_Finite__Set_Ofinite(V_G,T_a)
    | ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(V_F,V_G,tc_fun(T_a,tc_bool)),T_a) ) ).

cnf(cls_sup__bot__right_0,axiom,
    ( ~ class_Lattices_Obounded__lattice(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Orderings_Obot__class_Obot(T_a),T_a) = V_x ) ).

cnf(cls_sup__bot__left_0,axiom,
    ( ~ class_Lattices_Obounded__lattice(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(T_a),V_x,T_a) = V_x ) ).

cnf(cls_Un__empty__left_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = V_B ).

cnf(cls_Un__empty__right_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A ).

cnf(cls_trans__Id_0,axiom,
    c_Relation_Otrans(c_Relation_OId(T_a),T_a) ).

cnf(cls_empty__Diff_0,axiom,
    c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).

cnf(cls_UN__extend__simps_I2_J_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_A,T_b,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = V_B ).

cnf(cls_UN__extend__simps_I3_J_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_B,T_b,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A ).

cnf(cls_rtrancl__idemp__self__comp_0,axiom,
    c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(V_R,T_a),c_Transitive__Closure_Ortrancl(V_R,T_a),T_a,T_a,T_a) = c_Transitive__Closure_Ortrancl(V_R,T_a) ).

cnf(cls_bot1E_0,axiom,
    ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x)) ).

cnf(cls_Diff__Int__distrib_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(V_C,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_C,V_A,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_C,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).

cnf(cls_Diff__Int__distrib2_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).

cnf(cls_image__constant__conv_1,axiom,
    ( c_Set_Oimage(c_COMBK(V_c,T_a,T_b),V_A,T_b,T_a) = c_Set_Oinsert(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)
    | V_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)) ) ).

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))
    | c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).

cnf(cls_trans__Int_0,axiom,
    ( c_Relation_Otrans(c_Lattices_Olower__semilattice__class_Oinf(V_r,V_s,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a)
    | ~ c_Relation_Otrans(V_s,T_a)
    | ~ c_Relation_Otrans(V_r,T_a) ) ).

cnf(cls_Pow__bottom_0,axiom,
    hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),c_Set_OPow(V_B,T_a))) ).

cnf(cls_Diff__Int2_0,axiom,
    c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) ).

cnf(cls_acyclic__impl__antisym__rtrancl_0,axiom,
    ( c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(V_r,T_a),T_a)
    | ~ c_Wellfounded_Oacyclic(V_r,T_a) ) ).

cnf(cls_linear__order__on__def_0,axiom,
    ( c_Order__Relation_Opartial__order__on(V_A,V_r,T_a)
    | ~ c_Order__Relation_Olinear__order__on(V_A,V_r,T_a) ) ).

cnf(cls_sup__inf__absorb_0,axiom,
    ( ~ class_Lattices_Olattice(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = 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_refl__on__def_1,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_x,T_a,T_a)),V_r))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
    | ~ c_Relation_Orefl__on(V_A,V_r,T_a) ) ).

cnf(cls_refl__onD2_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),V_y),V_A))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),V_r))
    | ~ c_Relation_Orefl__on(V_A,V_r,T_a) ) ).

cnf(cls_refl__onD1_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),V_r))
    | ~ c_Relation_Orefl__on(V_A,V_r,T_a) ) ).

cnf(cls_refl__onD_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_a,T_a,T_a)),V_r))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
    | ~ c_Relation_Orefl__on(V_A,V_r,T_a) ) ).

cnf(cls_in__inv__image_1,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),c_Relation_Oinv__image(V_r,V_f,T_b,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_b,T_b)),c_Pair(hAPP(V_f,V_x),hAPP(V_f,V_y),T_b,T_b)),V_r)) ) ).

cnf(cls_in__inv__image_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_b,T_b)),c_Pair(hAPP(V_f,V_x),hAPP(V_f,V_y),T_b,T_b)),V_r))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),c_Relation_Oinv__image(V_r,V_f,T_b,T_a))) ) ).

cnf(cls_partial__order__on__def_0,axiom,
    ( c_Order__Relation_Opreorder__on(V_A,V_r,T_a)
    | ~ c_Order__Relation_Opartial__order__on(V_A,V_r,T_a) ) ).

cnf(cls_comm__monoid__add_Ononempty__iff_2,axiom,
    ( c_Set_Oinsert(V_x,V_xa,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
    | hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_xa)) ) ).

cnf(cls_UN__constant_1,axiom,
    ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(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_SUP__const_0,axiom,
    ( ~ class_Complete__Lattice_Ocomplete__lattice(T_b)
    | c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(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_insert__code_2,axiom,
    ( hBOOL(hAPP(c_Set_Oinsert(V_y,V_A,T_a),V_x))
    | ~ hBOOL(hAPP(V_A,V_x)) ) ).

cnf(cls_antisym__Id__on_0,axiom,
    c_Relation_Oantisym(c_Relation_OId__on(V_A,T_a),T_a) ).

cnf(cls_R__O__Id_0,axiom,
    c_Relation_Orel__comp(V_R,c_Relation_OId(T_b),T_a,T_b,T_b) = V_R ).

cnf(cls_Id__O__R_0,axiom,
    c_Relation_Orel__comp(c_Relation_OId(T_a),V_R,T_a,T_a,T_b) = V_R ).

cnf(cls_insert__image_0,axiom,
    ( c_Set_Oinsert(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) = c_Set_Oimage(V_f,V_A,T_a,T_b)
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).

cnf(cls_finite__Field_0,axiom,
    ( c_Finite__Set_Ofinite(c_Relation_OField(V_r,T_a),T_a)
    | ~ c_Finite__Set_Ofinite(V_r,tc_prod(T_a,T_a)) ) ).

cnf(cls_Int__insert__right_1,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool))
    | hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)) ) ).

cnf(cls_Int__insert__left_1,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(V_a,V_B,T_a),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool))
    | hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_C)) ) ).

cnf(cls_Un__empty_1,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,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_Un__empty_0,axiom,
    ( c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) != 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)
    | c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,T_a) != 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)
    | c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,T_a) != c_Orderings_Obot__class_Obot(T_a)
    | V_B = c_Orderings_Obot__class_Obot(T_a) ) ).

cnf(cls_Un__Diff__cancel2_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool)) ).

cnf(cls_Un__Diff__cancel_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(V_A,c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) ).

cnf(cls_rel__comp__distrib2_0,axiom,
    c_Relation_Orel__comp(c_Lattices_Oupper__semilattice__class_Osup(V_S,V_T,tc_fun(tc_prod(T_a,T_c),tc_bool)),V_R,T_a,T_c,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(V_S,V_R,T_a,T_c,T_b),c_Relation_Orel__comp(V_T,V_R,T_a,T_c,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool)) ).

cnf(cls_rel__comp__distrib_0,axiom,
    c_Relation_Orel__comp(V_R,c_Lattices_Oupper__semilattice__class_Osup(V_S,V_T,tc_fun(tc_prod(T_c,T_b),tc_bool)),T_a,T_c,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Orel__comp(V_R,V_S,T_a,T_c,T_b),c_Relation_Orel__comp(V_R,V_T,T_a,T_c,T_b),tc_fun(tc_prod(T_a,T_b),tc_bool)) ).

cnf(cls_trans__Id__on_0,axiom,
    c_Relation_Otrans(c_Relation_OId__on(V_A,T_a),T_a) ).

cnf(cls_UN__constant_0,axiom,
    c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(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_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).

cnf(cls_Field__Un_0,axiom,
    c_Relation_OField(c_Lattices_Oupper__semilattice__class_Osup(V_r,V_s,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_OField(V_r,T_a),c_Relation_OField(V_s,T_a),tc_fun(T_a,tc_bool)) ).

cnf(cls_Un__Diff_0,axiom,
    c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(V_A,V_C,tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).

cnf(cls_sym__Id_0,axiom,
    c_Relation_Osym(c_Relation_OId(T_a),T_a) ).

cnf(cls_insert__def_0,axiom,
    c_Set_Oinsert(V_a,V_B,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(T_a),T_a,T_a,tc_bool),V_a),T_a),V_B,tc_fun(T_a,tc_bool)) ).

cnf(cls_Un__commute_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool)) ).

cnf(cls_sup__commute_0,axiom,
    ( ~ class_Lattices_Oupper__semilattice(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,V_x,T_a) ) ).

cnf(cls_inf__sup__aci_I5_J_0,axiom,
    ( ~ class_Lattices_Olattice(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,V_x,T_a) ) ).

cnf(cls_sym__def_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_y,V_x,T_a,T_a)),V_r))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),V_r))
    | ~ c_Relation_Osym(V_r,T_a) ) ).

cnf(cls_symD_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_b,V_a,T_a,T_a)),V_r))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_b,T_a,T_a)),V_r))
    | ~ c_Relation_Osym(V_r,T_a) ) ).

cnf(cls_rel__compI_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_c)),c_Pair(V_a,V_c,T_a,T_c)),c_Relation_Orel__comp(V_r,V_s,T_a,T_b,T_c)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_b,T_c)),c_Pair(V_b,V_c,T_b,T_c)),V_s))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_b)),c_Pair(V_a,V_b,T_a,T_b)),V_r)) ) ).

cnf(cls_insert__is__Un_0,axiom,
    c_Set_Oinsert(V_a,V_A,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_A,tc_fun(T_a,tc_bool)) ).

cnf(cls_Un__left__absorb_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) ).

cnf(cls_sup__left__idem_0,axiom,
    ( ~ class_Lattices_Oupper__semilattice(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) ) ).

cnf(cls_inf__sup__aci_I8_J_0,axiom,
    ( ~ class_Lattices_Olattice(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) ) ).

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_Diff__disjoint_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(V_A,c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).

cnf(cls_Inf__singleton_0,axiom,
    ( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
    | c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = V_a ) ).

cnf(cls_sym__Un__converse_0,axiom,
    c_Relation_Osym(c_Lattices_Oupper__semilattice__class_Osup(V_r,c_Relation_Oconverse(V_r,T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) ).

cnf(cls_finite_0,axiom,
    ( ~ class_Finite__Set_Ofinite_Ofinite(T_a)
    | c_Finite__Set_Ofinite(V_A,T_a) ) ).

cnf(cls_Int__Collect_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Collect(V_P,T_a),tc_fun(T_a,tc_bool)))) ) ).

cnf(cls_vimage__Un_0,axiom,
    c_Set_Ovimage(V_f,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_b,tc_bool)),T_a,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(V_f,V_A,T_a,T_b),c_Set_Ovimage(V_f,V_B,T_a,T_b),tc_fun(T_a,tc_bool)) ).

cnf(cls_Sup__binary_0,axiom,
    ( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
    | c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a) ) ).

cnf(cls_inj__on__insert_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),c_Set_Oimage(V_f,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a,T_b)))
    | ~ c_Fun_Oinj__on(V_f,c_Set_Oinsert(V_a,V_A,T_a),T_a,T_b) ) ).

cnf(cls_Union__disjoint_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Complete__Lattice_OSup__class_OSup(V_C,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
    | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_A,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),V_x),V_C)) ) ).

cnf(cls_rtrancl__Un__rtrancl_0,axiom,
    c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(c_Transitive__Closure_Ortrancl(V_R,T_a),c_Transitive__Closure_Ortrancl(V_S,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) = c_Transitive__Closure_Ortrancl(c_Lattices_Oupper__semilattice__class_Osup(V_R,V_S,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) ).

cnf(cls_insert__Diff__if_1,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_x,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
    | hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B)) ) ).

cnf(cls_inf1E_1,axiom,
    ( hBOOL(hAPP(V_B,V_x))
    | ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_x)) ) ).

cnf(cls_inf1E_0,axiom,
    ( hBOOL(hAPP(V_A,V_x))
    | ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_x)) ) ).

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,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),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,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a,T_b) ) ).

cnf(cls_sym__Int_0,axiom,
    ( c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(V_r,V_s,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a)
    | ~ c_Relation_Osym(V_s,T_a)
    | ~ c_Relation_Osym(V_r,T_a) ) ).

cnf(cls_trancl__id_0,axiom,
    ( c_Transitive__Closure_Otrancl(V_r,T_a) = V_r
    | ~ c_Relation_Otrans(V_r,T_a) ) ).

cnf(cls_sym__trancl_0,axiom,
    ( c_Relation_Osym(c_Transitive__Closure_Otrancl(V_r,T_a),T_a)
    | ~ c_Relation_Osym(V_r,T_a) ) ).

cnf(cls_rtrancl__into__trancl1_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_c,T_a,T_a)),c_Transitive__Closure_Otrancl(V_r,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_b,V_c,T_a,T_a)),V_r))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_b,T_a,T_a)),c_Transitive__Closure_Ortrancl(V_r,T_a))) ) ).

cnf(cls_rtrancl__into__trancl2_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_c,T_a,T_a)),c_Transitive__Closure_Otrancl(V_r,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_b,V_c,T_a,T_a)),c_Transitive__Closure_Ortrancl(V_r,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_b,T_a,T_a)),V_r)) ) ).

cnf(cls_Diff__insert__absorb_0,axiom,
    ( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(V_x,V_A,T_a),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)) = V_A
    | hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).

cnf(cls_trancl__unfold_0,axiom,
    c_Transitive__Closure_Otrancl(V_r,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_r,c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(V_r,T_a),V_r,T_a,T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) ).

cnf(cls_r__r__into__trancl_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_c,T_a,T_a)),c_Transitive__Closure_Otrancl(V_R,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_b,V_c,T_a,T_a)),V_R))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_b,T_a,T_a)),V_R)) ) ).

cnf(cls_trancl__trans_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_c,T_a,T_a)),c_Transitive__Closure_Otrancl(V_r,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_b,V_c,T_a,T_a)),c_Transitive__Closure_Otrancl(V_r,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_b,T_a,T_a)),c_Transitive__Closure_Otrancl(V_r,T_a))) ) ).

cnf(cls_vimage__Int_0,axiom,
    c_Set_Ovimage(V_f,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_b,tc_bool)),T_a,T_b) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Ovimage(V_f,V_A,T_a,T_b),c_Set_Ovimage(V_f,V_B,T_a,T_b),tc_fun(T_a,tc_bool)) ).

cnf(cls_pair__in__Id__conv_1,axiom,
    hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_x,T_a,T_a)),c_Relation_OId(T_a))) ).

cnf(cls_IdI_0,axiom,
    hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_a,T_a,T_a)),c_Relation_OId(T_a))) ).

cnf(cls_finite__Int_1,axiom,
    ( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(V_F,V_G,tc_fun(T_a,tc_bool)),T_a)
    | ~ c_Finite__Set_Ofinite(V_G,T_a) ) ).

cnf(cls_finite__Int_0,axiom,
    ( c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(V_F,V_G,tc_fun(T_a,tc_bool)),T_a)
    | ~ c_Finite__Set_Ofinite(V_F,T_a) ) ).

cnf(cls_Inf__binary_0,axiom,
    ( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
    | c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a) ) ).

cnf(cls_Int__iff_2,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool))))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A)) ) ).

cnf(cls_IntI_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool))))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A)) ) ).

cnf(cls_ord_OatLeastLessThan__iff_2,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OatLeastLessThan(V_less__eq,V_less,V_l,V_u,T_a)))
    | ~ hBOOL(hAPP(hAPP(V_less,V_i),V_u))
    | ~ hBOOL(hAPP(hAPP(V_less__eq,V_l),V_i)) ) ).

cnf(cls_insert__iff_2,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Set_Oinsert(V_b,V_A,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)) ) ).

cnf(cls_insertCI_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Set_Oinsert(V_b,V_B,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_B)) ) ).

cnf(cls_ord_OatLeastAtMost__iff_2,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OatLeastAtMost(V_less__eq,V_l,V_u,T_a)))
    | ~ hBOOL(hAPP(hAPP(V_less__eq,V_i),V_u))
    | ~ hBOOL(hAPP(hAPP(V_less__eq,V_l),V_i)) ) ).

cnf(cls_UnCI_1,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool))))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A)) ) ).

cnf(cls_UnCI_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool))))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B)) ) ).

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_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_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_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_insertE_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
    | V_a = V_b
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Set_Oinsert(V_b,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),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)))) ) ).

cnf(cls_DiffE_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)))) ) ).

cnf(cls_DiffE_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)))) ) ).

cnf(cls_bexI_1,axiom,
    ( hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__XbexI__1__1(V_A,V_P,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
    | ~ hBOOL(hAPP(V_P,V_x)) ) ).

cnf(cls_bexE_1,axiom,
    ( hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__XbexE__1__1(V_A,V_P,T_a)))
    | ~ hBOOL(hAPP(V_P,V_x))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).

cnf(cls_insert__iff_1,axiom,
    hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Set_Oinsert(V_x,V_A,T_a))) ).

cnf(cls_insertI1_0,axiom,
    hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Set_Oinsert(V_a,V_B,T_a))) ).

cnf(cls_insertCI_1,axiom,
    hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Set_Oinsert(V_x,V_B,T_a))) ).

cnf(cls_ball__conj__distrib_3,axiom,
    ( hBOOL(hAPP(V_Q,V_xf))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xf),V_A))
    | ~ hBOOL(hAPP(V_Q,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(V_A,V_P,V_Q,T_a)))
    | ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(V_A,V_P,V_Q,T_a))) ) ).

cnf(cls_ball__conj__distrib_2,axiom,
    ( hBOOL(hAPP(V_P,V_xg))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xg),V_A))
    | ~ hBOOL(hAPP(V_Q,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(V_A,V_P,V_Q,T_a)))
    | ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(V_A,V_P,V_Q,T_a))) ) ).

cnf(cls_ballE_0,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
    | hBOOL(hAPP(V_P,V_x))
    | hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__XballE__1__1(V_A,V_P,T_a)),V_A)) ) ).

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),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)))) ) ).

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),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)))) ) ).

cnf(cls_extensionalityI_1,axiom,
    ( hAPP(V_f,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(V_A,V_f,V_g,T_a,T_b)) != hAPP(V_g,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(V_A,V_f,V_g,T_a,T_b))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_g),c_FuncSet_Oextensional(V_A,T_a,T_b)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_Oextensional(V_A,T_a,T_b)))
    | V_f = V_g ) ).

cnf(cls_Collect__empty__eq_0,axiom,
    ( c_Collect(V_P,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
    | ~ hBOOL(hAPP(V_P,V_x)) ) ).

cnf(cls_pair__in__Id__conv_0,axiom,
    ( V_a = V_b
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_b,T_a,T_a)),c_Relation_OId(T_a))) ) ).

cnf(cls_inf__sup__absorb_0,axiom,
    ( ~ class_Lattices_Olattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = V_x ) ).

cnf(cls_Un__Diff__Int_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A ).

cnf(cls_refl__on__Int_0,axiom,
    ( c_Relation_Orefl__on(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_r,V_s,tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a)
    | ~ c_Relation_Orefl__on(V_B,V_s,T_a)
    | ~ c_Relation_Orefl__on(V_A,V_r,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_Id__on__iff_0,axiom,
    ( V_x = V_y
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),c_Relation_OId__on(V_A,T_a))) ) ).

cnf(cls_Id__on__eqI_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_x,T_a,T_a)),c_Relation_OId__on(V_A,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).

cnf(cls_Id__on__iff_1,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),c_Relation_OId__on(V_A,T_a))) ) ).

cnf(cls_doubleton__eq__iff_0,axiom,
    ( c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) != c_Set_Oinsert(V_c,c_Set_Oinsert(V_d,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)
    | V_a = V_d
    | V_a = V_c ) ).

cnf(cls_doubleton__eq__iff_1,axiom,
    ( c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) != c_Set_Oinsert(V_c,c_Set_Oinsert(V_d,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)
    | V_b = V_c
    | V_a = V_c ) ).

cnf(cls_doubleton__eq__iff_2,axiom,
    ( c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) != c_Set_Oinsert(V_c,c_Set_Oinsert(V_d,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)
    | V_a = V_d
    | V_b = V_d ) ).

cnf(cls_doubleton__eq__iff_3,axiom,
    ( c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) != c_Set_Oinsert(V_c,c_Set_Oinsert(V_d,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)
    | V_b = V_c
    | V_b = V_d ) ).

cnf(cls_r__into__rtrancl_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),V_p),c_Transitive__Closure_Ortrancl(V_r,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),V_p),V_r)) ) ).

cnf(cls_antisymD_0,axiom,
    ( V_a = V_b
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_b,V_a,T_a,T_a)),V_r))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_b,T_a,T_a)),V_r))
    | ~ c_Relation_Oantisym(V_r,T_a) ) ).

cnf(cls_antisym__def_0,axiom,
    ( V_x = V_y
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_y,V_x,T_a,T_a)),V_r))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),V_r))
    | ~ c_Relation_Oantisym(V_r,T_a) ) ).

cnf(cls_preorder__on__def_1,axiom,
    ( c_Relation_Otrans(V_r,T_a)
    | ~ c_Order__Relation_Opreorder__on(V_A,V_r,T_a) ) ).

cnf(cls_UN__insert_0,axiom,
    c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(V_a,V_A,T_b),V_B,T_b,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(V_B,V_a),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_b,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).

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_bex__Un_4,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(V_A,V_B,V_P,T_a)),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool))))
    | ~ hBOOL(hAPP(V_P,V_xa))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xa),V_A)) ) ).

cnf(cls_bex__Un_6,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(V_A,V_B,V_P,T_a)),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool))))
    | ~ hBOOL(hAPP(V_P,V_x))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B)) ) ).

cnf(cls_linear__order__on__def_1,axiom,
    ( c_Relation_Ototal__on(V_A,V_r,T_a)
    | ~ c_Order__Relation_Olinear__order__on(V_A,V_r,T_a) ) ).

cnf(cls_trancl__into__rtrancl_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_b,T_a,T_a)),c_Transitive__Closure_Ortrancl(V_r,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_b,T_a,T_a)),c_Transitive__Closure_Otrancl(V_r,T_a))) ) ).

cnf(cls_complete__lattice_OSup__insert_0,axiom,
    ( hAPP(V_Sup,c_Set_Oinsert(V_a,V_A,T_a)) = hAPP(hAPP(V_sup,V_a),hAPP(V_Sup,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_OInf__insert_0,axiom,
    ( hAPP(V_Inf,c_Set_Oinsert(V_a,V_A,T_a)) = hAPP(hAPP(V_inf,V_a),hAPP(V_Inf,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_bex__UN_3,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3(V_A,V_B,V_P,T_b,T_a)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_b,tc_fun(T_a,tc_bool))))
    | ~ hBOOL(hAPP(V_P,V_xa))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xa),hAPP(V_B,V_x)))
    | ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A)) ) ).

cnf(cls_trancl__rtrancl__trancl_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_c,T_a,T_a)),c_Transitive__Closure_Otrancl(V_r,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_b,V_c,T_a,T_a)),c_Transitive__Closure_Ortrancl(V_r,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_b,T_a,T_a)),c_Transitive__Closure_Otrancl(V_r,T_a))) ) ).

cnf(cls_rtrancl__trancl__trancl_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_z,T_a,T_a)),c_Transitive__Closure_Otrancl(V_r,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_y,V_z,T_a,T_a)),c_Transitive__Closure_Otrancl(V_r,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),c_Transitive__Closure_Ortrancl(V_r,T_a))) ) ).

cnf(cls_rtrancl__eq__or__trancl_1,axiom,
    hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_x,T_a,T_a)),c_Transitive__Closure_Ortrancl(V_R,T_a))) ).

cnf(cls_rtrancl_Ortrancl__refl_0,axiom,
    hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_a,T_a,T_a)),c_Transitive__Closure_Ortrancl(V_r,T_a))) ).

cnf(cls_rtrancl__trans_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_c,T_a,T_a)),c_Transitive__Closure_Ortrancl(V_r,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_b,V_c,T_a,T_a)),c_Transitive__Closure_Ortrancl(V_r,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_b,T_a,T_a)),c_Transitive__Closure_Ortrancl(V_r,T_a))) ) ).

cnf(cls_empty__not__insert_0,axiom,
    c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Set_Oinsert(V_a,V_A,T_a) ).

cnf(cls_trancl_Or__into__trancl_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_b,T_a,T_a)),c_Transitive__Closure_Otrancl(V_r,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_b,T_a,T_a)),V_r)) ) ).

cnf(cls_Int__insert__left_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(V_a,V_B,T_a),V_C,tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),T_a)
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_C)) ) ).

cnf(cls_Int__insert__right_0,axiom,
    ( c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)) ) ).

cnf(cls_converse__rtrancl__into__rtrancl_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_c,T_a,T_a)),c_Transitive__Closure_Ortrancl(V_r,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_b,V_c,T_a,T_a)),c_Transitive__Closure_Ortrancl(V_r,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_b,T_a,T_a)),V_r)) ) ).

cnf(cls_rtrancl_Ortrancl__into__rtrancl_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_c,T_a,T_a)),c_Transitive__Closure_Ortrancl(V_r,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_b,V_c,T_a,T_a)),V_r))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_b,T_a,T_a)),c_Transitive__Closure_Ortrancl(V_r,T_a))) ) ).

cnf(cls_trancl__into__trancl2_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_c,T_a,T_a)),c_Transitive__Closure_Otrancl(V_r,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_b,V_c,T_a,T_a)),c_Transitive__Closure_Otrancl(V_r,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_b,T_a,T_a)),V_r)) ) ).

cnf(cls_Transitive__Closure_Otrancl__into__trancl_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_c,T_a,T_a)),c_Transitive__Closure_Otrancl(V_r,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_b,V_c,T_a,T_a)),V_r))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_b,T_a,T_a)),c_Transitive__Closure_Otrancl(V_r,T_a))) ) ).

cnf(cls_image__insert_0,axiom,
    c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a) ).

cnf(cls_total__on__empty_0,axiom,
    c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_r,T_a) ).

cnf(cls_vimage__singleton__eq_0,axiom,
    ( hAPP(V_f,V_a) = V_b
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Set_Ovimage(V_f,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b),T_a,T_b))) ) ).

cnf(cls_UN__extend__simps_I1_J_0,axiom,
    c_Set_Oinsert(V_a,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_B,T_b,tc_fun(T_a,tc_bool)),T_a) = c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ).

cnf(cls_sup__inf__distrib2_0,axiom,
    ( ~ class_Lattices_Odistrib__lattice(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),V_x,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_y,V_x,T_a),c_Lattices_Oupper__semilattice__class_Osup(V_z,V_x,T_a),T_a) ) ).

cnf(cls_sup__inf__distrib1_0,axiom,
    ( ~ class_Lattices_Odistrib__lattice(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a) ) ).

cnf(cls_Un__Int__distrib_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).

cnf(cls_Un__Int__distrib2_0,axiom,
    c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).

cnf(cls_empty__Collect__eq_0,axiom,
    ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Collect(V_P,T_a)
    | ~ hBOOL(hAPP(V_P,V_x)) ) ).

cnf(cls_insert__code_1,axiom,
    hBOOL(hAPP(c_Set_Oinsert(V_x,V_A,T_a),V_x)) ).

cnf(cls_inf__sup__aci_I4_J_0,axiom,
    ( ~ class_Lattices_Olattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) ) ).

cnf(cls_inf__left__idem_0,axiom,
    ( ~ class_Lattices_Olower__semilattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) ) ).

cnf(cls_Int__left__absorb_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) ).

cnf(cls_r__into__trancl_H_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),V_p),c_Transitive__Closure_Otrancl(V_r,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),V_p),V_r)) ) ).

cnf(cls_finite__Diff__insert_0,axiom,
    ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
    | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)),T_a) ) ).

cnf(cls_finite__Diff__insert_1,axiom,
    ( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)),T_a)
    | ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ) ).

cnf(cls_converseD_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_b,T_a)),c_Pair(V_b,V_a,T_b,T_a)),V_r))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_b)),c_Pair(V_a,V_b,T_a,T_b)),c_Relation_Oconverse(V_r,T_b,T_a))) ) ).

cnf(cls_converseI_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_b,T_a)),c_Pair(V_b,V_a,T_b,T_a)),c_Relation_Oconverse(V_r,T_a,T_b)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_b)),c_Pair(V_a,V_b,T_a,T_b)),V_r)) ) ).

cnf(cls_converse__iff_1,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_b)),c_Pair(V_a,V_b,T_a,T_b)),c_Relation_Oconverse(V_r,T_b,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_b,T_a)),c_Pair(V_b,V_a,T_b,T_a)),V_r)) ) ).

cnf(cls_transD_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_c,T_a,T_a)),V_r))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_b,V_c,T_a,T_a)),V_r))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_b,T_a,T_a)),V_r))
    | ~ c_Relation_Otrans(V_r,T_a) ) ).

cnf(cls_trans__def_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_z,T_a,T_a)),V_r))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_y,V_z,T_a,T_a)),V_r))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),V_r))
    | ~ c_Relation_Otrans(V_r,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_UN__empty2_0,axiom,
    c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool),T_b),T_b,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).

cnf(cls_insert__Diff_0,axiom,
    ( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)) ) ).

cnf(cls_inf__idem_0,axiom,
    ( ~ class_Lattices_Olower__semilattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_x,T_a) = V_x ) ).

cnf(cls_Int__absorb_0,axiom,
    c_Lattices_Olower__semilattice__class_Oinf(V_A,V_A,tc_fun(T_a,tc_bool)) = V_A ).

cnf(cls_preorder__on__def_0,axiom,
    ( c_Relation_Orefl__on(V_A,V_r,T_a)
    | ~ c_Order__Relation_Opreorder__on(V_A,V_r,T_a) ) ).

cnf(cls_Sup__singleton_0,axiom,
    ( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
    | c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = V_a ) ).

cnf(cls_trancl__unfold__right_0,axiom,
    c_Transitive__Closure_Otrancl(V_r,T_a) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(V_r,T_a),V_r,T_a,T_a,T_a) ).

cnf(cls_trancl__unfold__left_0,axiom,
    c_Transitive__Closure_Otrancl(V_r,T_a) = c_Relation_Orel__comp(V_r,c_Transitive__Closure_Ortrancl(V_r,T_a),T_a,T_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_Diff__Un_0,axiom,
    c_HOL_Ominus__class_Ominus(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).

cnf(cls_singleton__conv_0,axiom,
    c_Collect(hAPP(c_COMBC(c_fequal(T_a),T_a,T_a,tc_bool),V_a),T_a) = c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ).

cnf(cls_Int__Diff_0,axiom,
    c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_HOL_Ominus__class_Ominus(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).

cnf(cls_complete__lattice_OSup__singleton_0,axiom,
    ( hAPP(V_Sup,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) = 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_OInf__singleton_0,axiom,
    ( hAPP(V_Inf,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) = 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_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_singleton__iff_1,axiom,
    hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a))) ).

cnf(cls_Int__Collect_2,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Collect(V_P,T_a),tc_fun(T_a,tc_bool))))
    | ~ hBOOL(hAPP(V_P,V_x))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).

cnf(cls_vimage__insert_0,axiom,
    c_Set_Ovimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_a,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(V_f,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b),T_a,T_b),c_Set_Ovimage(V_f,V_B,T_a,T_b),tc_fun(T_a,tc_bool)) ).

cnf(cls_Diff__Int_0,axiom,
    c_HOL_Ominus__class_Ominus(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).

cnf(cls_Union__Pow__eq_0,axiom,
    c_Complete__Lattice_OSup__class_OSup(c_Set_OPow(V_A,T_a),tc_fun(T_a,tc_bool)) = V_A ).

cnf(cls_UN__Un_0,axiom,
    c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_b,tc_bool)),V_M,T_b,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_M,T_b,tc_fun(T_a,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_B,V_M,T_b,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).

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_inf1I_0,axiom,
    ( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_x))
    | ~ hBOOL(hAPP(V_B,V_x))
    | ~ hBOOL(hAPP(V_A,V_x)) ) ).

cnf(cls_singleton__conv2_0,axiom,
    c_Collect(hAPP(c_fequal(T_a),V_a),T_a) = c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_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,
    c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).

cnf(cls_sym__Int__converse_0,axiom,
    c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(V_r,c_Relation_Oconverse(V_r,T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)),T_a) ).

cnf(cls_image__Un_0,axiom,
    c_Set_Oimage(V_f,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(V_f,V_A,T_b,T_a),c_Set_Oimage(V_f,V_B,T_b,T_a),tc_fun(T_a,tc_bool)) ).

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_trancl__converseD_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),c_Relation_Oconverse(c_Transitive__Closure_Otrancl(V_r,T_a),T_a,T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(V_r,T_a,T_a),T_a))) ) ).

cnf(cls_trancl__converseI_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),c_Transitive__Closure_Otrancl(c_Relation_Oconverse(V_r,T_a,T_a),T_a)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),c_Relation_Oconverse(c_Transitive__Closure_Otrancl(V_r,T_a),T_a,T_a))) ) ).

cnf(cls_Collect__mem__eq_0,axiom,
    c_Collect(hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_A),T_a) = V_A ).

cnf(cls_trancl__rtrancl__absorb_0,axiom,
    c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(V_R,T_a),T_a) = c_Transitive__Closure_Ortrancl(V_R,T_a) ).

cnf(cls_preorder__on__def_2,axiom,
    ( c_Order__Relation_Opreorder__on(V_A,V_r,T_a)
    | ~ c_Relation_Otrans(V_r,T_a)
    | ~ c_Relation_Orefl__on(V_A,V_r,T_a) ) ).

cnf(cls_rtrancl__idemp_0,axiom,
    c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(V_r,T_a),T_a) = c_Transitive__Closure_Ortrancl(V_r,T_a) ).

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_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_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_CollectI_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Collect(V_P,T_a)))
    | ~ hBOOL(hAPP(V_P,V_a)) ) ).

cnf(cls_CollectD_0,axiom,
    ( hBOOL(hAPP(V_P,V_a))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Collect(V_P,T_a))) ) ).

cnf(cls_ord_OatMost__iff_1,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OatMost(V_less__eq,V_k,T_a)))
    | ~ hBOOL(hAPP(hAPP(V_less__eq,V_i),V_k)) ) ).

cnf(cls_ord_OatMost__iff_0,axiom,
    ( hBOOL(hAPP(hAPP(V_less__eq,V_i),V_k))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OatMost(V_less__eq,V_k,T_a))) ) ).

cnf(cls_Diff__iff_2,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))))
    | hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A)) ) ).

cnf(cls_DiffI_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))))
    | hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A)) ) ).

cnf(cls_ball__conj__distrib_1,axiom,
    ( hBOOL(hAPP(V_Q,V_xd))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xd),V_A))
    | hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(V_A,V_P,V_Q,T_a)),V_A)) ) ).

cnf(cls_ball__conj__distrib_0,axiom,
    ( hBOOL(hAPP(V_P,V_xe))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xe),V_A))
    | hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(V_A,V_P,V_Q,T_a)),V_A)) ) ).

cnf(cls_ballE_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
    | hBOOL(hAPP(V_P,V_x))
    | ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__XballE__1__1(V_A,V_P,T_a))) ) ).

cnf(cls_insert__ident_0,axiom,
    ( c_Set_Oinsert(V_x,V_A,T_a) != c_Set_Oinsert(V_x,V_B,T_a)
    | hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))
    | hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
    | V_A = V_B ) ).

cnf(cls_bexI_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__XbexI__1__1(V_A,V_P,T_a)),V_A))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
    | ~ hBOOL(hAPP(V_P,V_x)) ) ).

cnf(cls_UN__iff_2,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),V_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_b,tc_fun(T_a,tc_bool))))
    | ~ 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)) ) ).

cnf(cls_UN__I_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_b),V_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_bool))))
    | ~ 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_ord_OgreaterThan__iff_1,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OgreaterThan(V_less,V_k,T_a)))
    | ~ hBOOL(hAPP(hAPP(V_less,V_k),V_i)) ) ).

cnf(cls_ord_OgreaterThan__iff_0,axiom,
    ( hBOOL(hAPP(hAPP(V_less,V_k),V_i))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OgreaterThan(V_less,V_k,T_a))) ) ).

cnf(cls_bex__UN_4,axiom,
    ( hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3(V_A,V_B,V_P,T_b,T_a)))
    | ~ hBOOL(hAPP(V_P,V_xa))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xa),hAPP(V_B,V_x)))
    | ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_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_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_ord_OatLeastAtMost__iff_1,axiom,
    ( hBOOL(hAPP(hAPP(V_less__eq,V_i),V_u))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OatLeastAtMost(V_less__eq,V_l,V_u,T_a))) ) ).

cnf(cls_ord_OatLeastAtMost__iff_0,axiom,
    ( hBOOL(hAPP(hAPP(V_less__eq,V_l),V_i))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OatLeastAtMost(V_less__eq,V_l,V_u,T_a))) ) ).

cnf(cls_bex__Un_7,axiom,
    ( hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(V_A,V_B,V_P,T_a)))
    | ~ hBOOL(hAPP(V_P,V_x))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B)) ) ).

cnf(cls_bex__Un_5,axiom,
    ( hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(V_A,V_B,V_P,T_a)))
    | ~ hBOOL(hAPP(V_P,V_xa))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xa),V_A)) ) ).

cnf(cls_bexE_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__XbexE__1__1(V_A,V_P,T_a)),V_A))
    | ~ hBOOL(hAPP(V_P,V_x))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).

cnf(cls_insert__absorb_0,axiom,
    ( c_Set_Oinsert(V_a,V_A,T_a) = V_A
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)) ) ).

cnf(cls_ord_OlessThan__iff_1,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OlessThan(V_less,V_k,T_a)))
    | ~ hBOOL(hAPP(hAPP(V_less,V_i),V_k)) ) ).

cnf(cls_ord_OlessThan__iff_0,axiom,
    ( hBOOL(hAPP(hAPP(V_less,V_i),V_k))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OlessThan(V_less,V_k,T_a))) ) ).

cnf(cls_SUP2__iff_2,axiom,
    ( hBOOL(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_fun(T_c,tc_bool))),V_b),V_c))
    | ~ hBOOL(hAPP(hAPP(hAPP(V_B,V_x),V_b),V_c))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).

cnf(cls_SUP1__iff_2,axiom,
    ( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_bool)),V_b))
    | ~ hBOOL(hAPP(hAPP(V_B,V_x),V_b))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).

cnf(cls_SUP2__I_0,axiom,
    ( hBOOL(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_fun(T_c,tc_bool))),V_b),V_c))
    | ~ hBOOL(hAPP(hAPP(hAPP(V_B,V_a),V_b),V_c))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)) ) ).

cnf(cls_SUP1__I_0,axiom,
    ( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_bool)),V_b))
    | ~ hBOOL(hAPP(hAPP(V_B,V_a),V_b))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)) ) ).

cnf(cls_ord_OatLeastLessThan__iff_1,axiom,
    ( hBOOL(hAPP(hAPP(V_less,V_i),V_u))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OatLeastLessThan(V_less__eq,V_less,V_l,V_u,T_a))) ) ).

cnf(cls_ord_OatLeastLessThan__iff_0,axiom,
    ( hBOOL(hAPP(hAPP(V_less__eq,V_l),V_i))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OatLeastLessThan(V_less__eq,V_less,V_l,V_u,T_a))) ) ).

cnf(cls_rev__bexI_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(V_A,V_P,T_a)),V_A))
    | ~ hBOOL(hAPP(V_P,V_x))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).

cnf(cls_rev__bexI_1,axiom,
    ( hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(V_A,V_P,T_a)))
    | ~ hBOOL(hAPP(V_P,V_x))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_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_Pi__I_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,V_B,T_a,T_b)))
    | hBOOL(hAPP(hAPP(c_in(T_a),c_FuncSet_Osko__FuncSet__XPi__I__1__1(V_A,V_B,V_f,T_a,T_b)),V_A)) ) ).

cnf(cls_Pi__I_H_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,V_B,T_a,T_b)))
    | hBOOL(hAPP(hAPP(c_in(T_a),c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(V_A,V_B,V_f,T_a,T_b)),V_A)) ) ).

cnf(cls_extensional__arb_0,axiom,
    ( hAPP(V_f,V_x) = c_HOL_Oundefined(T_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_Oextensional(V_A,T_a,T_b))) ) ).

cnf(cls_Pi__I_1,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,V_B,T_a,T_b)))
    | ~ hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,c_FuncSet_Osko__FuncSet__XPi__I__1__1(V_A,V_B,V_f,T_a,T_b))),hAPP(V_B,c_FuncSet_Osko__FuncSet__XPi__I__1__1(V_A,V_B,V_f,T_a,T_b)))) ) ).

cnf(cls_extensionalityI_0,axiom,
    ( V_f = V_g
    | hBOOL(hAPP(hAPP(c_in(T_a),c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(V_A,V_f,V_g,T_a,T_b)),V_A))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_g),c_FuncSet_Oextensional(V_A,T_a,T_b)))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_Oextensional(V_A,T_a,T_b))) ) ).

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_Pi__I_H_1,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,T_b)),V_f),c_FuncSet_OPi(V_A,V_B,T_a,T_b)))
    | ~ hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(V_A,V_B,V_f,T_a,T_b))),hAPP(V_B,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(V_A,V_B,V_f,T_a,T_b)))) ) ).

cnf(cls_InterI_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),V_A),c_Complete__Lattice_OInf__class_OInf(V_C,tc_fun(T_a,tc_bool))))
    | hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(V_A,V_C,T_a)),V_C)) ) ).

cnf(cls_UnionE_1,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1(V_A,V_C,T_a)),V_C))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_A),c_Complete__Lattice_OSup__class_OSup(V_C,tc_fun(T_a,tc_bool)))) ) ).

cnf(cls_quotientE_1,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),c_List_Osko__Equiv__Relations__XquotientE__1__1(V_A,V_X,V_r,T_a)),V_A))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),V_X),c_Equiv__Relations_Oquotient(V_A,V_r,T_a))) ) ).

cnf(cls_Pow__top_0,axiom,
    hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),V_A),c_Set_OPow(V_A,T_a))) ).

cnf(cls_partial__order__on__converse_0,axiom,
    ( c_Order__Relation_Opartial__order__on(V_A,V_r,T_a)
    | ~ c_Order__Relation_Opartial__order__on(V_A,c_Relation_Oconverse(V_r,T_a,T_a),T_a) ) ).

cnf(cls_partial__order__on__converse_1,axiom,
    ( c_Order__Relation_Opartial__order__on(V_A,c_Relation_Oconverse(V_r,T_a,T_a),T_a)
    | ~ c_Order__Relation_Opartial__order__on(V_A,V_r,T_a) ) ).

cnf(cls_total__on__converse_1,axiom,
    ( c_Relation_Ototal__on(V_A,c_Relation_Oconverse(V_r,T_a,T_a),T_a)
    | ~ c_Relation_Ototal__on(V_A,V_r,T_a) ) ).

cnf(cls_total__on__converse_0,axiom,
    ( c_Relation_Ototal__on(V_A,V_r,T_a)
    | ~ c_Relation_Ototal__on(V_A,c_Relation_Oconverse(V_r,T_a,T_a),T_a) ) ).

cnf(cls_linear__order__on__converse_0,axiom,
    ( c_Order__Relation_Olinear__order__on(V_A,V_r,T_a)
    | ~ c_Order__Relation_Olinear__order__on(V_A,c_Relation_Oconverse(V_r,T_a,T_a),T_a) ) ).

cnf(cls_linear__order__on__converse_1,axiom,
    ( c_Order__Relation_Olinear__order__on(V_A,c_Relation_Oconverse(V_r,T_a,T_a),T_a)
    | ~ c_Order__Relation_Olinear__order__on(V_A,V_r,T_a) ) ).

cnf(cls_converse__Un_0,axiom,
    c_Relation_Oconverse(c_Lattices_Oupper__semilattice__class_Osup(V_r,V_s,tc_fun(tc_prod(T_b,T_a),tc_bool)),T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Relation_Oconverse(V_r,T_b,T_a),c_Relation_Oconverse(V_s,T_b,T_a),tc_fun(tc_prod(T_a,T_b),tc_bool)) ).

cnf(cls_preorder__on__converse_1,axiom,
    ( c_Order__Relation_Opreorder__on(V_A,c_Relation_Oconverse(V_r,T_a,T_a),T_a)
    | ~ c_Order__Relation_Opreorder__on(V_A,V_r,T_a) ) ).

cnf(cls_preorder__on__converse_0,axiom,
    ( c_Order__Relation_Opreorder__on(V_A,V_r,T_a)
    | ~ c_Order__Relation_Opreorder__on(V_A,c_Relation_Oconverse(V_r,T_a,T_a),T_a) ) ).

cnf(cls_rtrancl__converse_0,axiom,
    c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(V_r,T_a,T_a),T_a) = c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(V_r,T_a),T_a,T_a) ).

cnf(cls_acyclic__converse_1,axiom,
    ( c_Wellfounded_Oacyclic(c_Relation_Oconverse(V_r,T_a,T_a),T_a)
    | ~ c_Wellfounded_Oacyclic(V_r,T_a) ) ).

cnf(cls_acyclic__converse_0,axiom,
    ( c_Wellfounded_Oacyclic(V_r,T_a)
    | ~ c_Wellfounded_Oacyclic(c_Relation_Oconverse(V_r,T_a,T_a),T_a) ) ).

cnf(cls_antisym__converse_1,axiom,
    ( c_Relation_Oantisym(c_Relation_Oconverse(V_r,T_a,T_a),T_a)
    | ~ c_Relation_Oantisym(V_r,T_a) ) ).

cnf(cls_antisym__converse_0,axiom,
    ( c_Relation_Oantisym(V_r,T_a)
    | ~ c_Relation_Oantisym(c_Relation_Oconverse(V_r,T_a,T_a),T_a) ) ).

cnf(cls_converse__Id__on_0,axiom,
    c_Relation_Oconverse(c_Relation_OId__on(V_A,T_a),T_a,T_a) = c_Relation_OId__on(V_A,T_a) ).

cnf(cls_trancl__converse_0,axiom,
    c_Transitive__Closure_Otrancl(c_Relation_Oconverse(V_r,T_a,T_a),T_a) = c_Relation_Oconverse(c_Transitive__Closure_Otrancl(V_r,T_a),T_a,T_a) ).

cnf(cls_converse__inv__image_0,axiom,
    c_Relation_Oconverse(c_Relation_Oinv__image(V_R,V_f,T_b,T_a),T_a,T_a) = c_Relation_Oinv__image(c_Relation_Oconverse(V_R,T_b,T_b),V_f,T_b,T_a) ).

cnf(cls_converse__Id_0,axiom,
    c_Relation_Oconverse(c_Relation_OId(T_a),T_a,T_a) = c_Relation_OId(T_a) ).

cnf(cls_trans__converse_1,axiom,
    ( c_Relation_Otrans(c_Relation_Oconverse(V_r,T_a,T_a),T_a)
    | ~ c_Relation_Otrans(V_r,T_a) ) ).

cnf(cls_trans__converse_0,axiom,
    ( c_Relation_Otrans(V_r,T_a)
    | ~ c_Relation_Otrans(c_Relation_Oconverse(V_r,T_a,T_a),T_a) ) ).

cnf(cls_converse__rel__comp_0,axiom,
    c_Relation_Oconverse(c_Relation_Orel__comp(V_r,V_s,T_b,T_c,T_a),T_b,T_a) = c_Relation_Orel__comp(c_Relation_Oconverse(V_s,T_c,T_a),c_Relation_Oconverse(V_r,T_b,T_c),T_a,T_c,T_b) ).

cnf(cls_sym__conv__converse__eq_1,axiom,
    ( c_Relation_Oconverse(V_r,T_a,T_a) != V_r
    | c_Relation_Osym(V_r,T_a) ) ).

cnf(cls_sym__conv__converse__eq_0,axiom,
    ( c_Relation_Oconverse(V_r,T_a,T_a) = V_r
    | ~ c_Relation_Osym(V_r,T_a) ) ).

cnf(cls_refl__on__converse_1,axiom,
    ( c_Relation_Orefl__on(V_A,c_Relation_Oconverse(V_r,T_a,T_a),T_a)
    | ~ c_Relation_Orefl__on(V_A,V_r,T_a) ) ).

cnf(cls_refl__on__converse_0,axiom,
    ( c_Relation_Orefl__on(V_A,V_r,T_a)
    | ~ c_Relation_Orefl__on(V_A,c_Relation_Oconverse(V_r,T_a,T_a),T_a) ) ).

cnf(cls_Field__converse_0,axiom,
    c_Relation_OField(c_Relation_Oconverse(V_r,T_a,T_a),T_a) = c_Relation_OField(V_r,T_a) ).

cnf(cls_converse__Int_0,axiom,
    c_Relation_Oconverse(c_Lattices_Olower__semilattice__class_Oinf(V_r,V_s,tc_fun(tc_prod(T_b,T_a),tc_bool)),T_b,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Relation_Oconverse(V_r,T_b,T_a),c_Relation_Oconverse(V_s,T_b,T_a),tc_fun(tc_prod(T_a,T_b),tc_bool)) ).

cnf(cls_finite__converse_1,axiom,
    ( c_Finite__Set_Ofinite(c_Relation_Oconverse(V_r,T_b,T_a),tc_prod(T_a,T_b))
    | ~ c_Finite__Set_Ofinite(V_r,tc_prod(T_b,T_a)) ) ).

cnf(cls_finite__converse_0,axiom,
    ( c_Finite__Set_Ofinite(V_r,tc_prod(T_b,T_a))
    | ~ c_Finite__Set_Ofinite(c_Relation_Oconverse(V_r,T_b,T_a),tc_prod(T_a,T_b)) ) ).

cnf(cls_sym__converse_1,axiom,
    ( c_Relation_Osym(c_Relation_Oconverse(V_r,T_a,T_a),T_a)
    | ~ c_Relation_Osym(V_r,T_a) ) ).

cnf(cls_sym__converse_0,axiom,
    ( c_Relation_Osym(V_r,T_a)
    | ~ c_Relation_Osym(c_Relation_Oconverse(V_r,T_a,T_a),T_a) ) ).

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_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_InterD_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),V_A),V_X))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),V_X),V_C))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_A),c_Complete__Lattice_OInf__class_OInf(V_C,tc_fun(T_a,tc_bool)))) ) ).

cnf(cls_UnionI_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(T_a),V_A),c_Complete__Lattice_OSup__class_OSup(V_C,tc_fun(T_a,tc_bool))))
    | ~ hBOOL(hAPP(hAPP(c_in(T_a),V_A),V_X))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_fun(T_a,tc_bool)),V_X),V_C)) ) ).

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_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_converse__converse_0,axiom,
    c_Relation_Oconverse(c_Relation_Oconverse(V_r,T_a,T_b),T_b,T_a) = V_r ).

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_conjecture_0,negated_conjecture,
    ( ~ 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))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Relation_Oconverse(v_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_OLin)) ) ).

cnf(cls_conjecture_1,negated_conjecture,
    ( hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Relation_Oconverse(v_L,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_OLin))
    | 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(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__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__Lattices_Olattice,axiom,
    ( class_Lattices_Olattice(tc_fun(T_2,T_1))
    | ~ class_Lattices_Olattice(T_1) ) ).

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__Finite__Set_Ofinite_Ofinite,axiom,
    class_Finite__Set_Ofinite_Ofinite(tc_bool) ).

cnf(clsarity_bool__Lattices_Olattice,axiom,
    class_Lattices_Olattice(tc_bool) ).

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)) ) ).

%------------------------------------------------------------------------------