%------------------------------------------------------------------------------
% File     : SWV978-1 : TPTP v9.0.0. Released v4.1.0.
% Domain   : Software Verification
% Problem  : Java type soundness 501_5
% Version  : Especial.
% English  :

% Refs     : [vON99] von Oheimb & Nipkow (1999), Machine-Checking the Java
%          : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe
%          : [BN10]  Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% Source   : [Nip10]
% Names    : TypeSafe-501_5 [Nip10]

% Status   : Unsatisfiable
% Rating   : 1.00 v7.4.0, 0.94 v7.3.0, 0.92 v7.0.0, 1.00 v6.2.0, 0.90 v6.1.0, 1.00 v4.1.0
% Syntax   : Number of clauses     :  368 ( 132 unt;  58 nHn; 169 RR)
%            Number of literals    :  725 ( 347 equ; 316 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    8 (   1 avg)
%            Number of predicates  :   24 (  23 usr;   0 prp; 1-5 aty)
%            Number of functors    :   77 (  77 usr;  22 con; 0-6 aty)
%            Number of variables   : 1560 ( 273 sgn)
% SPC      : CNF_UNS_RFO_SEQ_NHN

% Comments :
%------------------------------------------------------------------------------
cnf(cls_dom__fun__upd_0,axiom,
    c_Map_Odom(c_Fun_Ofun__upd(V_f,V_x,c_Option_Ooption_ONone(T_b),T_a,tc_Option_Ooption(T_b)),T_a,T_b) = c_HOL_Ominus__class_Ominus(c_Map_Odom(V_f,T_a,T_b),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)) ).

cnf(cls_restrict__fun__upd_0,axiom,
    ( c_Map_Orestrict__map(c_Fun_Ofun__upd(V_m,V_x,V_y,T_a,tc_Option_Ooption(T_b)),V_D,T_a,T_b) = c_Fun_Ofun__upd(c_Map_Orestrict__map(V_m,c_HOL_Ominus__class_Ominus(V_D,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a,T_b),V_x,V_y,T_a,tc_Option_Ooption(T_b))
    | ~ hBOOL(c_in(V_x,V_D,T_a)) ) ).

cnf(cls_fun__upd__restrict__conv_0,axiom,
    ( c_Fun_Ofun__upd(c_Map_Orestrict__map(V_m,V_D,T_a,T_b),V_x,V_y,T_a,tc_Option_Ooption(T_b)) = c_Fun_Ofun__upd(c_Map_Orestrict__map(V_m,c_HOL_Ominus__class_Ominus(V_D,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a,T_b),V_x,V_y,T_a,tc_Option_Ooption(T_b))
    | ~ hBOOL(c_in(V_x,V_D,T_a)) ) ).

cnf(cls_fun__upd__image_0,axiom,
    ( c_Set_Oimage(c_Fun_Ofun__upd(V_f,V_x,V_y,T_b,T_a),V_A,T_b,T_a) = c_Set_Oinsert(V_y,c_Set_Oimage(V_f,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b),tc_fun(T_b,tc_bool)),T_b,T_a),T_a)
    | ~ hBOOL(c_in(V_x,V_A,T_b)) ) ).

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(c_in(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),T_b))
    | ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).

cnf(cls_inj__on__insert_1,axiom,
    ( ~ hBOOL(c_in(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),T_b))
    | ~ c_Fun_Oinj__on(V_f,c_Set_Oinsert(V_a,V_A,T_a),T_a,T_b) ) ).

cnf(cls_fun__upd__restrict_0,axiom,
    c_Fun_Ofun__upd(c_Map_Orestrict__map(V_m,V_D,T_a,T_b),V_x,V_y,T_a,tc_Option_Ooption(T_b)) = c_Fun_Ofun__upd(c_Map_Orestrict__map(V_m,c_HOL_Ominus__class_Ominus(V_D,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a,T_b),V_x,V_y,T_a,tc_Option_Ooption(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(c_in(V_x,V_B,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(c_in(V_x,V_B,T_a)) ) ).

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(c_in(V_a,V_A,T_a)) ) ).

cnf(cls_Compl__empty__eq_0,axiom,
    c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) ).

cnf(cls_compl__bot__eq_0,axiom,
    ( ~ class_Lattices_Oboolean__algebra(T_a)
    | c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(T_a),T_a) = c_Orderings_Otop__class_Otop(T_a) ) ).

cnf(cls_fun__Compl__def_0,axiom,
    ( ~ class_HOL_Ouminus(T_b)
    | hAPP(c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(t_a,T_b)),v_x) = c_HOL_Ouminus__class_Ouminus(hAPP(V_A,v_x),T_b) ) ).

cnf(cls_Diff__UNIV_0,axiom,
    c_HOL_Ominus__class_Ominus(V_A,c_Orderings_Otop__class_Otop(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_Compl__eq__Compl__iff_0,axiom,
    ( c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool)) != c_HOL_Ouminus__class_Ouminus(V_B,tc_fun(T_a,tc_bool))
    | V_A = V_B ) ).

cnf(cls_neg__equal__iff__equal_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != c_HOL_Ouminus__class_Ouminus(V_b,T_a)
    | V_a = V_b ) ).

cnf(cls_compl__eq__compl__iff_0,axiom,
    ( ~ class_Lattices_Oboolean__algebra(T_a)
    | c_HOL_Ouminus__class_Ouminus(V_x,T_a) != c_HOL_Ouminus__class_Ouminus(V_y,T_a)
    | V_x = V_y ) ).

cnf(cls_Compl__UNIV__eq_0,axiom,
    c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(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_compl__top__eq_0,axiom,
    ( ~ class_Lattices_Oboolean__algebra(T_a)
    | c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(T_a),T_a) = c_Orderings_Obot__class_Obot(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_Compl__eq__Diff__UNIV_0,axiom,
    c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) ).

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_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_DiffE_1,axiom,
    ( ~ hBOOL(c_in(V_c,V_B,T_a))
    | ~ hBOOL(c_in(V_c,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)) ) ).

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

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_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_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_ComplI_0,axiom,
    ( hBOOL(c_in(V_c,c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool)),T_a))
    | hBOOL(c_in(V_c,V_A,T_a)) ) ).

cnf(cls_ComplD_0,axiom,
    ( ~ hBOOL(c_in(V_c,V_A,T_a))
    | ~ hBOOL(c_in(V_c,c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool)),T_a)) ) ).

cnf(cls_dom__minus_0,axiom,
    ( hAPP(V_f,V_x) != c_Option_Ooption_ONone(T_a)
    | c_HOL_Ominus__class_Ominus(c_Map_Odom(V_f,T_b,T_a),c_Set_Oinsert(V_x,V_A,T_b),tc_fun(T_b,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Map_Odom(V_f,T_b,T_a),V_A,tc_fun(T_b,tc_bool)) ) ).

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_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_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_Diff__iff_2,axiom,
    ( hBOOL(c_in(V_c,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a))
    | hBOOL(c_in(V_c,V_B,T_a))
    | ~ hBOOL(c_in(V_c,V_A,T_a)) ) ).

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

cnf(cls_image__set__diff_0,axiom,
    ( 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_HOL_Ominus__class_Ominus(c_Set_Oimage(V_f,V_A,T_a,T_b),c_Set_Oimage(V_f,V_B,T_a,T_b),tc_fun(T_b,tc_bool))
    | ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).

cnf(cls_fun__diff__def_0,axiom,
    ( ~ class_HOL_Ominus(T_b)
    | hAPP(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(t_a,T_b)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(V_A,v_x),hAPP(V_B,v_x),T_b) ) ).

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(c_in(V_x,V_A,T_a)) ) ).

cnf(cls_double__complement_0,axiom,
    c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A ).

cnf(cls_minus__minus_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = V_a ) ).

cnf(cls_double__compl_0,axiom,
    ( ~ class_Lattices_Oboolean__algebra(T_a)
    | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = V_x ) ).

cnf(cls_equation__minus__iff_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | V_b = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ).

cnf(cls_equation__minus__iff_1,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | V_a = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ).

cnf(cls_minus__equation__iff_1,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = V_b ) ).

cnf(cls_minus__diff__eq_0,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Ominus__class_Ominus(V_b,V_a,T_a) ) ).

cnf(cls_restrict__upd__same_0,axiom,
    c_Map_Orestrict__map(c_Fun_Ofun__upd(V_m,V_x,hAPP(c_Option_Ooption_OSome(T_b),V_y),T_a,tc_Option_Ooption(T_b)),c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a,T_b) = c_Map_Orestrict__map(V_m,c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a,T_b) ).

cnf(cls_fun__upd__None__restrict_0,axiom,
    ( c_Fun_Ofun__upd(c_Map_Orestrict__map(V_m,V_D,T_a,T_b),V_x,c_Option_Ooption_ONone(T_b),T_a,tc_Option_Ooption(T_b)) = c_Map_Orestrict__map(V_m,c_HOL_Ominus__class_Ominus(V_D,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a,T_b)
    | ~ hBOOL(c_in(V_x,V_D,T_a)) ) ).

cnf(cls_dom__eq__singleton__conv_0,axiom,
    ( c_Map_Odom(V_f,T_a,T_b) != c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)
    | V_f = c_Fun_Ofun__upd(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_x,hAPP(c_Option_Ooption_OSome(T_b),c_Map_Osko__Map__Xdom__eq__singleton__conv__1__1(V_f,V_x,T_a,T_b)),T_a,tc_Option_Ooption(T_b)) ) ).

cnf(cls_override__on__emptyset_0,axiom,
    c_Fun_Ooverride__on(V_f,V_g,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a,T_b) = V_f ).

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_image__inv__f__f_0,axiom,
    ( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_f,T_a,T_b),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b,T_a) = V_A
    | ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).

cnf(cls_inv__image__comp_0,axiom,
    ( c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_f,T_a,T_b),c_Set_Oimage(V_f,V_X,T_a,T_b),T_b,T_a) = V_X
    | ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).

cnf(cls_option_Osplit_5,axiom,
    ( hBOOL(hAPP(V_P,c_Option_Ooption_Ooption__case(V_f1,V_f2,V_x,t_a,t_b)))
    | ~ hBOOL(hAPP(V_P,hAPP(V_f2,v_sko__Option__Xoption__Xsplit__1(V_P,V_f2,V_x))))
    | ~ hBOOL(hAPP(V_P,V_f1)) ) ).

cnf(cls_the__inv__f__f_0,axiom,
    ( hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_f,T_a,T_b),hAPP(V_f,V_x)) = V_x
    | ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).

cnf(cls_inj__on__image__iff_4,axiom,
    ( c_Fun_Oinj__on(V_g,V_A,T_a,T_b)
    | ~ c_Fun_Oinj__on(V_g,c_Set_Oimage(V_f,V_A,T_a,T_a),T_a,T_b)
    | ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_a)
    | hAPP(V_g,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(V_A,V_f,V_g,T_a,T_b)) = hAPP(V_g,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(V_A,V_f,V_g,T_a,T_b))
    | hAPP(V_g,hAPP(V_f,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(V_A,V_f,V_g,T_a,T_b))) = hAPP(V_g,hAPP(V_f,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(V_A,V_f,V_g,T_a,T_b))) ) ).

cnf(cls_inj__on__image__iff_5,axiom,
    ( c_Fun_Oinj__on(V_g,c_Set_Oimage(V_f,V_A,T_a,T_a),T_a,T_b)
    | ~ c_Fun_Oinj__on(V_g,V_A,T_a,T_b)
    | ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_a)
    | hAPP(V_g,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(V_A,V_f,V_g,T_a,T_b)) = hAPP(V_g,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(V_A,V_f,V_g,T_a,T_b))
    | hAPP(V_g,hAPP(V_f,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(V_A,V_f,V_g,T_a,T_b))) = hAPP(V_g,hAPP(V_f,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(V_A,V_f,V_g,T_a,T_b))) ) ).

cnf(cls_inj__on__image__iff_6,axiom,
    ( hAPP(V_g,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(V_A,V_f,V_g,T_a,T_b)) != hAPP(V_g,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(V_A,V_f,V_g,T_a,T_b))
    | hAPP(V_g,hAPP(V_f,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(V_A,V_f,V_g,T_a,T_b))) != hAPP(V_g,hAPP(V_f,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(V_A,V_f,V_g,T_a,T_b)))
    | c_Fun_Oinj__on(V_g,V_A,T_a,T_b)
    | ~ c_Fun_Oinj__on(V_g,c_Set_Oimage(V_f,V_A,T_a,T_a),T_a,T_b)
    | ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_a) ) ).

cnf(cls_inj__on__image__iff_7,axiom,
    ( hAPP(V_g,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(V_A,V_f,V_g,T_a,T_b)) != hAPP(V_g,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(V_A,V_f,V_g,T_a,T_b))
    | hAPP(V_g,hAPP(V_f,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(V_A,V_f,V_g,T_a,T_b))) != hAPP(V_g,hAPP(V_f,c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(V_A,V_f,V_g,T_a,T_b)))
    | c_Fun_Oinj__on(V_g,c_Set_Oimage(V_f,V_A,T_a,T_a),T_a,T_b)
    | ~ c_Fun_Oinj__on(V_g,V_A,T_a,T_b)
    | ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_a) ) ).

cnf(cls_set__empty__eq_1,axiom,
    c_Option_Oset(c_Option_Ooption_ONone(T_a),T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).

cnf(cls_bex__empty_0,axiom,
    ( ~ hBOOL(hAPP(V_P,V_x))
    | ~ hBOOL(c_in(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),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_conf__widen_0,axiom,
    ( c_Conform_Oconf(V_P,V_h,V_v,V_T_H,T_a)
    | ~ c_TypeRel_Owiden(V_P,V_T,V_T_H,T_a)
    | ~ c_Conform_Oconf(V_P,V_h,V_v,V_T,T_a) ) ).

cnf(cls_widen__trans_0,axiom,
    ( c_TypeRel_Owiden(V_P,V_S,V_T,T_a)
    | ~ c_TypeRel_Owiden(V_P,V_U,V_T,T_a)
    | ~ c_TypeRel_Owiden(V_P,V_S,V_U,T_a) ) ).

cnf(cls_widen__refl_0,axiom,
    c_TypeRel_Owiden(V_P,V_T,V_T,T_a) ).

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_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_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_dom__empty_0,axiom,
    c_Map_Odom(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),T_a,T_b) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).

cnf(cls_bot__fun__eq_0,axiom,
    ( ~ class_Orderings_Obot(T_b)
    | hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,T_b)),v_x) = c_Orderings_Obot__class_Obot(T_b) ) ).

cnf(cls_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_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_UNIV__I_0,axiom,
    hBOOL(c_in(V_x,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a)) ).

cnf(cls_injD_0,axiom,
    ( hAPP(V_f,V_x) != hAPP(V_f,V_y)
    | ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b)
    | V_x = V_y ) ).

cnf(cls_restrict__map__empty_0,axiom,
    hAPP(c_Map_Orestrict__map(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),t_a),V_D,t_a,T_b),v_x) = c_Option_Ooption_ONone(T_b) ).

cnf(cls_option_Ocase__cong_3,axiom,
    ( hAPP(V_f2,c_ATP__Linkup_Osko__Option__Xoption__Xcase__cong__1__1(V_xa,V_f2,V_g2,T_aa,T_a)) != hAPP(V_g2,c_ATP__Linkup_Osko__Option__Xoption__Xcase__cong__1__1(V_xa,V_f2,V_g2,T_aa,T_a))
    | c_Option_Ooption_Ooption__case(V_x,V_f2,V_xa,T_a,T_aa) = c_Option_Ooption_Ooption__case(V_x,V_g2,V_xa,T_a,T_aa) ) ).

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

cnf(cls_UNIV__not__empty_0,axiom,
    c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).

cnf(cls_option_Osplit__asm_5,axiom,
    ( hBOOL(hAPP(V_P,c_Option_Ooption_Ooption__case(V_f1,V_f2,V_x,t_a,t_b)))
    | ~ hBOOL(hAPP(V_P,hAPP(V_f2,v_sko__Option__Xoption__Xsplit__asm__1(V_P,V_f2,V_x))))
    | ~ hBOOL(hAPP(V_P,V_f1)) ) ).

cnf(cls_top1I_0,axiom,
    hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_x)) ).

cnf(cls_top__fun__eq_0,axiom,
    ( ~ class_Orderings_Otop(T_b)
    | hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,T_b)),v_x) = c_Orderings_Otop__class_Otop(T_b) ) ).

cnf(cls_set__empty__eq_0,axiom,
    ( c_Option_Oset(V_xo,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
    | V_xo = c_Option_Ooption_ONone(T_a) ) ).

cnf(cls_restrict__in_0,axiom,
    ( hAPP(c_Map_Orestrict__map(V_m,V_A,T_a,T_b),V_x) = hAPP(V_m,V_x)
    | ~ hBOOL(c_in(V_x,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_bot__empty__eq_0,axiom,
    hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) ).

cnf(cls_dom__eq__empty__conv_0,axiom,
    ( c_Map_Odom(V_f,T_a,T_b) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
    | V_f = c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),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_ran__empty_0,axiom,
    c_Map_Oran(c_COMBK(c_Option_Ooption_ONone(T_a),tc_Option_Ooption(T_a),T_b),T_b,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).

cnf(cls_emptyE_0,axiom,
    ~ hBOOL(c_in(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) ).

cnf(cls_empty__iff_0,axiom,
    ~ hBOOL(c_in(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) ).

cnf(cls_ball__empty_0,axiom,
    ( hBOOL(hAPP(V_P,V_x))
    | ~ hBOOL(c_in(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) ) ).

cnf(cls_ex__in__conv_0,axiom,
    ~ hBOOL(c_in(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) ).

cnf(cls_o__def_0,axiom,
    hAPP(c_Fun_Ocomp(V_f,V_g,T_c,T_b,t_a),v_x) = hAPP(V_f,hAPP(V_g,v_x)) ).

cnf(cls_Option_Oset_Osimps_I2_J_0,axiom,
    c_Option_Oset(hAPP(c_Option_Ooption_OSome(T_a),V_x),T_a) = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ).

cnf(cls_dom__const_0,axiom,
    c_Map_Odom(c_COMBK(hAPP(c_Option_Ooption_OSome(T_b),V_y),tc_Option_Ooption(T_b),T_a),T_a,T_b) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) ).

cnf(cls_inv__f__f_0,axiom,
    ( hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_f,T_a,T_b),hAPP(V_f,V_x)) = V_x
    | ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).

cnf(cls_inv__f__eq_0,axiom,
    ( ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_aa,tc_bool)),T_aa,T_a)
    | hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(T_aa,tc_bool)),V_f,T_aa,T_a),hAPP(V_f,V_x)) = V_x ) ).

cnf(cls_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_restrict__map__to__empty_0,axiom,
    hAPP(c_Map_Orestrict__map(V_m,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a,T_b),v_x) = c_Option_Ooption_ONone(T_b) ).

cnf(cls_o__inv__o__cancel_0,axiom,
    ( c_Fun_Ocomp(c_Fun_Ocomp(V_g,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_f,T_a,T_b),T_a,T_c,T_b),V_f,T_b,T_c,T_a) = V_g
    | ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).

cnf(cls_set__ConsD_0,axiom,
    ( hBOOL(c_in(V_y,c_List_Oset(V_xs,T_a),T_a))
    | V_y = V_x
    | ~ hBOOL(c_in(V_y,c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a),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(c_in(V_x,V_xa,T_a)) ) ).

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

cnf(cls_singleton__iff_1,axiom,
    hBOOL(c_in(V_x,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)) ).

cnf(cls_ranI_0,axiom,
    ( hAPP(V_m,V_a) != hAPP(c_Option_Ooption_OSome(T_a),V_b)
    | hBOOL(c_in(V_b,c_Map_Oran(V_m,T_b,T_a),T_a)) ) ).

cnf(cls_elem__set_0,axiom,
    ( V_xo = hAPP(c_Option_Ooption_OSome(T_a),V_x)
    | ~ hBOOL(c_in(V_x,c_Option_Oset(V_xo,T_a),T_a)) ) ).

cnf(cls_domI_0,axiom,
    ( hAPP(V_m,V_a) != hAPP(c_Option_Ooption_OSome(T_a),V_b)
    | hBOOL(c_in(V_a,c_Map_Odom(V_m,T_b,T_a),T_b)) ) ).

cnf(cls_elem__set_1,axiom,
    hBOOL(c_in(V_x,c_Option_Oset(hAPP(c_Option_Ooption_OSome(T_a),V_x),T_a),T_a)) ).

cnf(cls_rangeI_0,axiom,
    hBOOL(c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_a),T_a)) ).

cnf(cls_inv__into__into_0,axiom,
    ( hBOOL(c_in(hAPP(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_b,T_a),V_x),V_A,T_b))
    | ~ hBOOL(c_in(V_x,c_Set_Oimage(V_f,V_A,T_b,T_a),T_a)) ) ).

cnf(cls_inv__into__injective_0,axiom,
    ( hAPP(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_a,T_b),V_x) != hAPP(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_a,T_b),V_y)
    | V_x = V_y
    | ~ hBOOL(c_in(V_y,c_Set_Oimage(V_f,V_A,T_a,T_b),T_b))
    | ~ hBOOL(c_in(V_x,c_Set_Oimage(V_f,V_A,T_a,T_b),T_b)) ) ).

cnf(cls_f__inv__into__f_0,axiom,
    ( hAPP(V_f,hAPP(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_b,T_a),V_y)) = V_y
    | ~ hBOOL(c_in(V_y,c_Set_Oimage(V_f,V_A,T_b,T_a),T_a)) ) ).

cnf(cls_List_Oset_Osimps_I2_J_0,axiom,
    c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_Set_Oinsert(V_x,c_List_Oset(V_xs,T_a),T_a) ).

cnf(cls_inv__into__f__f_0,axiom,
    ( hAPP(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_a,T_b),hAPP(V_f,V_x)) = V_x
    | ~ hBOOL(c_in(V_x,V_A,T_a))
    | ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).

cnf(cls_inv__into__f__eq_0,axiom,
    ( ~ hBOOL(c_in(V_x,V_A,T_aa))
    | ~ c_Fun_Oinj__on(V_f,V_A,T_aa,T_a)
    | hAPP(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_aa,T_a),hAPP(V_f,V_x)) = V_x ) ).

cnf(cls_the__inv__into__f__f_0,axiom,
    ( hAPP(c_Fun_Othe__inv__into(V_A,V_f,T_a,T_b),hAPP(V_f,V_x)) = V_x
    | ~ hBOOL(c_in(V_x,V_A,T_a))
    | ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).

cnf(cls_the__inv__into__f__eq_0,axiom,
    ( ~ c_Fun_Oinj__on(V_f,V_A,T_aa,T_a)
    | hAPP(c_Fun_Othe__inv__into(V_A,V_f,T_aa,T_a),hAPP(V_f,V_x)) = V_x
    | ~ hBOOL(c_in(V_x,V_A,T_aa)) ) ).

cnf(cls_restrict__out_0,axiom,
    ( hAPP(c_Map_Orestrict__map(V_m,V_A,T_a,T_b),V_x) = c_Option_Ooption_ONone(T_b)
    | hBOOL(c_in(V_x,V_A,T_a)) ) ).

cnf(cls_domIff_0,axiom,
    ( hAPP(V_m,V_a) != c_Option_Ooption_ONone(T_b)
    | ~ hBOOL(c_in(V_a,c_Map_Odom(V_m,T_a,T_b),T_a)) ) ).

cnf(cls_domIff_1,axiom,
    ( hBOOL(c_in(V_a,c_Map_Odom(V_m,T_a,T_b),T_a))
    | hAPP(V_m,V_a) = c_Option_Ooption_ONone(T_b) ) ).

cnf(cls_restrict__fun__upd_1,axiom,
    ( c_Map_Orestrict__map(c_Fun_Ofun__upd(V_m,V_x,V_y,T_a,tc_Option_Ooption(T_b)),V_D,T_a,T_b) = c_Map_Orestrict__map(V_m,V_D,T_a,T_b)
    | hBOOL(c_in(V_x,V_D,T_a)) ) ).

cnf(cls_insert__dom_0,axiom,
    ( hAPP(V_f,V_x) != hAPP(c_Option_Ooption_OSome(T_a),V_y)
    | c_Set_Oinsert(V_x,c_Map_Odom(V_f,T_b,T_a),T_b) = c_Map_Odom(V_f,T_b,T_a) ) ).

cnf(cls_inj__on__the__inv__into_0,axiom,
    ( c_Fun_Oinj__on(c_Fun_Othe__inv__into(V_A,V_f,T_a,T_b),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b,T_a)
    | ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).

cnf(cls_inj__image__eq__iff_0,axiom,
    ( c_Set_Oimage(V_f,V_A,T_a,T_b) != c_Set_Oimage(V_f,V_B,T_a,T_b)
    | ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b)
    | V_A = V_B ) ).

cnf(cls_the__inv__into__onto_0,axiom,
    ( c_Set_Oimage(c_Fun_Othe__inv__into(V_A,V_f,T_a,T_b),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b,T_a) = V_A
    | ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).

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_restrict__map__insert_0,axiom,
    c_Map_Orestrict__map(V_f,c_Set_Oinsert(V_a,V_A,T_a),T_a,T_b) = c_Fun_Ofun__upd(c_Map_Orestrict__map(V_f,V_A,T_a,T_b),V_a,hAPP(V_f,V_a),T_a,tc_Option_Ooption(T_b)) ).

cnf(cls_map__add__dom__app__simps_I1_J_0,axiom,
    ( hAPP(c_Map_Omap__add(V_l1,V_l2,T_a,T_b),V_m) = hAPP(V_l2,V_m)
    | ~ hBOOL(c_in(V_m,c_Map_Odom(V_l2,T_a,T_b),T_a)) ) ).

cnf(cls_map__add__dom__app__simps_I2_J_0,axiom,
    ( hAPP(c_Map_Omap__add(V_l1,V_l2,T_a,T_b),V_m) = hAPP(V_l2,V_m)
    | hBOOL(c_in(V_m,c_Map_Odom(V_l1,T_a,T_b),T_a)) ) ).

cnf(cls_map__add__dom__app__simps_I3_J_0,axiom,
    ( hAPP(c_Map_Omap__add(V_l1,V_l2,T_a,T_b),V_m) = hAPP(V_l1,V_m)
    | hBOOL(c_in(V_m,c_Map_Odom(V_l2,T_a,T_b),T_a)) ) ).

cnf(cls_K__record__comp_0,axiom,
    hAPP(c_Fun_Ocomp(c_COMBK(V_c,T_b,T_c),V_f,T_c,T_b,t_a),v_x) = V_c ).

cnf(cls_map__upds__apply__nontin_0,axiom,
    ( hAPP(c_Map_Omap__upds(V_f,V_xs,V_ys,T_a,T_b),V_x) = hAPP(V_f,V_x)
    | hBOOL(c_in(V_x,c_List_Oset(V_xs,T_a),T_a)) ) ).

cnf(cls_map__le__def_0,axiom,
    ( hAPP(V_m_092_060_094isub_0621,V_x) = hAPP(V_m_092_060_094isub_0622,V_x)
    | ~ hBOOL(c_in(V_x,c_Map_Odom(V_m_092_060_094isub_0621,T_a,T_b),T_a))
    | ~ c_Map_Omap__le(V_m_092_060_094isub_0621,V_m_092_060_094isub_0622,T_a,T_b) ) ).

cnf(cls_option_Ocase__cong_2,axiom,
    ( c_Option_Ooption_Ooption__case(V_x,V_f2,V_xa,T_a,T_aa) = c_Option_Ooption_Ooption__case(V_x,V_g2,V_xa,T_a,T_aa)
    | V_xa = hAPP(c_Option_Ooption_OSome(T_aa),c_ATP__Linkup_Osko__Option__Xoption__Xcase__cong__1__1(V_xa,V_f2,V_g2,T_aa,T_a)) ) ).

cnf(cls_option_Osplit__asm_4,axiom,
    ( hBOOL(hAPP(V_P,c_Option_Ooption_Ooption__case(V_f1,V_f2,V_x,t_a,t_b)))
    | V_x = hAPP(c_Option_Ooption_OSome(t_b),v_sko__Option__Xoption__Xsplit__asm__1(V_P,V_f2,V_x))
    | ~ hBOOL(hAPP(V_P,V_f1)) ) ).

cnf(cls_option_Osplit_4,axiom,
    ( hBOOL(hAPP(V_P,c_Option_Ooption_Ooption__case(V_f1,V_f2,V_x,t_a,t_b)))
    | V_x = hAPP(c_Option_Ooption_OSome(t_b),v_sko__Option__Xoption__Xsplit__1(V_P,V_f2,V_x))
    | ~ hBOOL(hAPP(V_P,V_f1)) ) ).

cnf(cls_option_Osplit_3,axiom,
    ( hBOOL(hAPP(V_P,c_Option_Ooption_Ooption__case(V_f1,V_f2,V_x,t_a,t_b)))
    | ~ hBOOL(hAPP(V_P,hAPP(V_f2,v_sko__Option__Xoption__Xsplit__1(V_P,V_f2,V_x))))
    | V_x = c_Option_Ooption_ONone(t_b) ) ).

cnf(cls_option_Ocase__cong_1,axiom,
    ( hAPP(V_f2,c_ATP__Linkup_Osko__Option__Xoption__Xcase__cong__1__1(V_x,V_f2,V_g2,T_a,T_b)) != hAPP(V_g2,c_ATP__Linkup_Osko__Option__Xoption__Xcase__cong__1__1(V_x,V_f2,V_g2,T_a,T_b))
    | V_x = c_Option_Ooption_ONone(T_a)
    | c_Option_Ooption_Ooption__case(V_f1,V_f2,V_x,T_b,T_a) = c_Option_Ooption_Ooption__case(V_g1,V_g2,V_x,T_b,T_a) ) ).

cnf(cls_option_Osplit__asm_3,axiom,
    ( hBOOL(hAPP(V_P,c_Option_Ooption_Ooption__case(V_f1,V_f2,V_x,t_a,t_b)))
    | ~ hBOOL(hAPP(V_P,hAPP(V_f2,v_sko__Option__Xoption__Xsplit__asm__1(V_P,V_f2,V_x))))
    | V_x = c_Option_Ooption_ONone(t_b) ) ).

cnf(cls_WT__elim__cases_I5_J_2,axiom,
    ( c_Decl_Ois__class(V_P,V_C,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
    | ~ c_WellType_OWT(V_P,V_E,c_Expr_Oexp_OTryCatch(V_e_092_060_094isub_0621,V_C,V_V,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),V_T) ) ).

cnf(cls_is__type__simps_4,axiom,
    ( c_Decl_Ois__class(V_P,V_C,T_a)
    | ~ c_Decl_Ois__type(V_P,c_Type_Oty_OClass(V_C),T_a) ) ).

cnf(cls_is__type__simps_5,axiom,
    ( c_Decl_Ois__type(V_P,c_Type_Oty_OClass(V_C),T_a)
    | ~ c_Decl_Ois__class(V_P,V_C,T_a) ) ).

cnf(cls_map__comp__None__iff_1,axiom,
    ( c_Map_Omap__comp(V_m1,V_m2,V_k,T_b,T_a,T_c) != c_Option_Ooption_ONone(T_a)
    | hAPP(V_m1,c_Map_Osko__Map__Xmap__comp__None__iff__1__1(V_k,V_m1,V_m2,T_c,T_b,T_a)) = c_Option_Ooption_ONone(T_a)
    | hAPP(V_m2,V_k) = c_Option_Ooption_ONone(T_b) ) ).

cnf(cls_rev__image__eqI_0,axiom,
    ( ~ hBOOL(c_in(V_x,V_A,T_aa))
    | hBOOL(c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_aa,T_a),T_a)) ) ).

cnf(cls_image__iff_2,axiom,
    ( ~ hBOOL(c_in(V_x,V_A,T_b))
    | hBOOL(c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_b,T_a),T_a)) ) ).

cnf(cls_image__eqI_0,axiom,
    ( hBOOL(c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_b,T_a),T_a))
    | ~ hBOOL(c_in(V_x,V_A,T_b)) ) ).

cnf(cls_imageI_0,axiom,
    ( hBOOL(c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b))
    | ~ hBOOL(c_in(V_x,V_A,T_a)) ) ).

cnf(cls_comp__swap_0,axiom,
    c_Fun_Ocomp(V_f,c_Fun_Oswap(V_a,V_b,V_g,T_a,T_c),T_c,T_b,T_a) = c_Fun_Oswap(V_a,V_b,c_Fun_Ocomp(V_f,V_g,T_c,T_b,T_a),T_a,T_b) ).

cnf(cls_map__add__le__mapI_0,axiom,
    ( c_Map_Omap__le(c_Map_Omap__add(V_f,V_g,T_a,T_b),V_h,T_a,T_b)
    | ~ c_Map_Omap__le(V_f,c_Map_Omap__add(V_f,V_g,T_a,T_b),T_a,T_b)
    | ~ c_Map_Omap__le(V_g,V_h,T_a,T_b)
    | ~ c_Map_Omap__le(V_f,V_h,T_a,T_b) ) ).

cnf(cls_WTrt_H__WTrts_H_Ointros_I22_J_0,axiom,
    ( c_Progress_OWTrt_H(V_P,V_h,V_E,c_Expr_Oexp_OTryCatch(V_e_092_060_094isub_0621,V_C,V_V,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),V_T_092_060_094isub_0622)
    | ~ c_TypeRel_Owiden(V_P,V_T_092_060_094isub_0621,V_T_092_060_094isub_0622,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
    | ~ c_Progress_OWTrt_H(V_P,V_h,c_Fun_Ofun__upd(V_E,V_V,hAPP(c_Option_Ooption_OSome(tc_Type_Oty),c_Type_Oty_OClass(V_C)),tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Type_Oty)),V_e_092_060_094isub_0622,V_T_092_060_094isub_0622)
    | ~ c_Progress_OWTrt_H(V_P,V_h,V_E,V_e_092_060_094isub_0621,V_T_092_060_094isub_0621) ) ).

cnf(cls_WTTry_0,axiom,
    ( c_WellType_OWT(V_P,V_E,c_Expr_Oexp_OTryCatch(V_e_092_060_094isub_0621,V_C,V_V,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),V_T)
    | ~ c_Decl_Ois__class(V_P,V_C,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
    | ~ c_WellType_OWT(V_P,c_Fun_Ofun__upd(V_E,V_V,hAPP(c_Option_Ooption_OSome(tc_Type_Oty),c_Type_Oty_OClass(V_C)),tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Type_Oty)),V_e_092_060_094isub_0622,V_T)
    | ~ c_WellType_OWT(V_P,V_E,V_e_092_060_094isub_0621,V_T) ) ).

cnf(cls_WTrtTry_0,axiom,
    ( c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OTryCatch(V_e_092_060_094isub_0621,V_C,V_V,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),V_T_092_060_094isub_0622)
    | ~ c_TypeRel_Owiden(V_P,V_T_092_060_094isub_0621,V_T_092_060_094isub_0622,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar))))
    | ~ c_WellTypeRT_OWTrt(V_P,V_h,c_Fun_Ofun__upd(V_E,V_V,hAPP(c_Option_Ooption_OSome(tc_Type_Oty),c_Type_Oty_OClass(V_C)),tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Type_Oty)),V_e_092_060_094isub_0622,V_T_092_060_094isub_0622)
    | ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e_092_060_094isub_0621,V_T_092_060_094isub_0621) ) ).

cnf(cls_IH_H_1,axiom,
    c_TypeRel_Owiden(v_P,v_Te_H____,v_Te____,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))) ).

cnf(cls_option__map__o__empty_0,axiom,
    hAPP(c_Fun_Ocomp(c_Option_Omap(V_f,T_c,T_b),c_COMBK(c_Option_Ooption_ONone(T_c),tc_Option_Ooption(T_c),t_a),tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),t_a),v_x) = c_Option_Ooption_ONone(T_b) ).

cnf(cls_map__upds__twist_0,axiom,
    ( c_Map_Omap__upds(c_Fun_Ofun__upd(V_m,V_a,hAPP(c_Option_Ooption_OSome(T_b),V_b),T_a,tc_Option_Ooption(T_b)),V_as,V_bs,T_a,T_b) = c_Fun_Ofun__upd(c_Map_Omap__upds(V_m,V_as,V_bs,T_a,T_b),V_a,hAPP(c_Option_Ooption_OSome(T_b),V_b),T_a,tc_Option_Ooption(T_b))
    | hBOOL(c_in(V_a,c_List_Oset(V_as,T_a),T_a)) ) ).

cnf(cls_map__add__upd__left_0,axiom,
    ( c_Map_Omap__add(c_Fun_Ofun__upd(V_e1,V_m,hAPP(c_Option_Ooption_OSome(T_b),V_u1),T_a,tc_Option_Ooption(T_b)),V_e2,T_a,T_b) = c_Fun_Ofun__upd(c_Map_Omap__add(V_e1,V_e2,T_a,T_b),V_m,hAPP(c_Option_Ooption_OSome(T_b),V_u1),T_a,tc_Option_Ooption(T_b))
    | hBOOL(c_in(V_m,c_Map_Odom(V_e2,T_a,T_b),T_a)) ) ).

cnf(cls_ran__map__upd_0,axiom,
    ( hAPP(V_m,V_a) != c_Option_Ooption_ONone(T_a)
    | c_Map_Oran(c_Fun_Ofun__upd(V_m,V_a,hAPP(c_Option_Ooption_OSome(T_a),V_b),T_b,tc_Option_Ooption(T_a)),T_b,T_a) = c_Set_Oinsert(V_b,c_Map_Oran(V_m,T_b,T_a),T_a) ) ).

cnf(cls_ospec_0,axiom,
    ( hBOOL(c_in(c_ATP__Linkup_Osko__Option__Xospec__1__1(hAPP(c_Option_Ooption_OSome(T_a),V_x),V_P,T_a),c_Option_Oset(hAPP(c_Option_Ooption_OSome(T_a),V_x),T_a),T_a))
    | hBOOL(hAPP(V_P,V_x)) ) ).

cnf(cls_the__inv__into__comp_0,axiom,
    ( hAPP(c_Fun_Othe__inv__into(V_A,c_Fun_Ocomp(V_f,V_g,T_a,T_b,T_c),T_c,T_b),V_x) = hAPP(c_Fun_Ocomp(c_Fun_Othe__inv__into(V_A,V_g,T_c,T_a),c_Fun_Othe__inv__into(c_Set_Oimage(V_g,V_A,T_c,T_a),V_f,T_a,T_b),T_a,T_c,T_b),V_x)
    | ~ hBOOL(c_in(V_x,c_Set_Oimage(V_f,c_Set_Oimage(V_g,V_A,T_c,T_a),T_a,T_b),T_b))
    | ~ c_Fun_Oinj__on(V_g,V_A,T_c,T_a)
    | ~ c_Fun_Oinj__on(V_f,c_Set_Oimage(V_g,V_A,T_c,T_a),T_a,T_b) ) ).

cnf(cls_inv__into__comp_0,axiom,
    ( hAPP(c_Hilbert__Choice_Oinv__into(V_A,c_Fun_Ocomp(V_f,V_g,T_a,T_b,T_c),T_c,T_b),V_x) = hAPP(c_Fun_Ocomp(c_Hilbert__Choice_Oinv__into(V_A,V_g,T_c,T_a),c_Hilbert__Choice_Oinv__into(c_Set_Oimage(V_g,V_A,T_c,T_a),V_f,T_a,T_b),T_a,T_c,T_b),V_x)
    | ~ hBOOL(c_in(V_x,c_Set_Oimage(V_f,c_Set_Oimage(V_g,V_A,T_c,T_a),T_a,T_b),T_b))
    | ~ c_Fun_Oinj__on(V_g,V_A,T_c,T_a)
    | ~ c_Fun_Oinj__on(V_f,c_Set_Oimage(V_g,V_A,T_c,T_a),T_a,T_b) ) ).

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(c_in(V_x,V_A,T_a)) ) ).

cnf(cls_map__comp__empty_I2_J_0,axiom,
    c_Map_Omap__comp(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_c),V_m,v_x,T_c,T_b,t_a) = c_Option_Ooption_ONone(T_b) ).

cnf(cls_map__comp__empty_I1_J_0,axiom,
    c_Map_Omap__comp(V_m,c_COMBK(c_Option_Ooption_ONone(T_c),tc_Option_Ooption(T_c),t_a),v_x,T_c,T_b,t_a) = c_Option_Ooption_ONone(T_b) ).

cnf(cls_map__comp__None__iff_0,axiom,
    ( c_Map_Omap__comp(V_m1,V_m2,V_k,T_b,T_a,T_c) != c_Option_Ooption_ONone(T_a)
    | hAPP(V_m2,V_k) = hAPP(c_Option_Ooption_OSome(T_b),c_Map_Osko__Map__Xmap__comp__None__iff__1__1(V_k,V_m1,V_m2,T_c,T_b,T_a))
    | hAPP(V_m2,V_k) = c_Option_Ooption_ONone(T_b) ) ).

cnf(cls_empty__upd__none_0,axiom,
    hAPP(c_Fun_Ofun__upd(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),t_a),V_x,c_Option_Ooption_ONone(T_b),t_a,tc_Option_Ooption(T_b)),v_xa) = c_Option_Ooption_ONone(T_b) ).

cnf(cls_option_Osplit_2,axiom,
    ( hBOOL(hAPP(V_P,c_Option_Ooption_Ooption__case(V_f1,V_f2,V_x,t_a,t_b)))
    | V_x = hAPP(c_Option_Ooption_OSome(t_b),v_sko__Option__Xoption__Xsplit__1(V_P,V_f2,V_x))
    | V_x = c_Option_Ooption_ONone(t_b) ) ).

cnf(cls_option_Ocase__cong_0,axiom,
    ( c_Option_Ooption_Ooption__case(V_f1,V_f2,V_x,T_b,T_a) = c_Option_Ooption_Ooption__case(V_g1,V_g2,V_x,T_b,T_a)
    | V_x = hAPP(c_Option_Ooption_OSome(T_a),c_ATP__Linkup_Osko__Option__Xoption__Xcase__cong__1__1(V_x,V_f2,V_g2,T_a,T_b))
    | V_x = c_Option_Ooption_ONone(T_a) ) ).

cnf(cls_option_Osplit__asm_2,axiom,
    ( hBOOL(hAPP(V_P,c_Option_Ooption_Ooption__case(V_f1,V_f2,V_x,t_a,t_b)))
    | V_x = hAPP(c_Option_Ooption_OSome(t_b),v_sko__Option__Xoption__Xsplit__asm__1(V_P,V_f2,V_x))
    | V_x = c_Option_Ooption_ONone(t_b) ) ).

cnf(cls_dom__fun__upd_1,axiom,
    ( c_Map_Odom(c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,tc_Option_Ooption(T_b)),T_a,T_b) = c_Set_Oinsert(V_x,c_Map_Odom(V_f,T_a,T_b),T_a)
    | V_y = c_Option_Ooption_ONone(T_b) ) ).

cnf(cls_setprod__reindex__cong_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__mult(T_c)
    | ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
    | c_Finite__Set_Osetprod(V_h,c_Set_Oimage(V_f,V_A,T_a,T_b),T_b,T_c) = c_Finite__Set_Osetprod(c_Fun_Ocomp(V_h,V_f,T_b,T_c,T_a),V_A,T_a,T_c) ) ).

cnf(cls_setprod__reindex_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__mult(T_c)
    | c_Finite__Set_Osetprod(V_h,c_Set_Oimage(V_f,V_B,T_a,T_b),T_b,T_c) = c_Finite__Set_Osetprod(c_Fun_Ocomp(V_h,V_f,T_b,T_c,T_a),V_B,T_a,T_c)
    | ~ c_Fun_Oinj__on(V_f,V_B,T_a,T_b) ) ).

cnf(cls_setsum__reindex_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_c)
    | c_Finite__Set_Osetsum(V_h,c_Set_Oimage(V_f,V_B,T_a,T_b),T_b,T_c) = c_Finite__Set_Osetsum(c_Fun_Ocomp(V_h,V_f,T_b,T_c,T_a),V_B,T_a,T_c)
    | ~ c_Fun_Oinj__on(V_f,V_B,T_a,T_b) ) ).

cnf(cls_fun__upd__None__restrict_1,axiom,
    ( c_Fun_Ofun__upd(c_Map_Orestrict__map(V_m,V_D,T_a,T_b),V_x,c_Option_Ooption_ONone(T_b),T_a,tc_Option_Ooption(T_b)) = c_Map_Orestrict__map(V_m,V_D,T_a,T_b)
    | hBOOL(c_in(V_x,V_D,T_a)) ) ).

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_inj__on__image__iff_1,axiom,
    ( c_Fun_Oinj__on(V_g,c_Set_Oimage(V_f,V_A,T_a,T_a),T_a,T_b)
    | ~ c_Fun_Oinj__on(V_g,V_A,T_a,T_b)
    | ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_a)
    | hBOOL(c_in(c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(V_A,V_f,V_g,T_a,T_b),V_A,T_a)) ) ).

cnf(cls_inj__on__image__iff_0,axiom,
    ( c_Fun_Oinj__on(V_g,V_A,T_a,T_b)
    | ~ c_Fun_Oinj__on(V_g,c_Set_Oimage(V_f,V_A,T_a,T_a),T_a,T_b)
    | ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_a)
    | hBOOL(c_in(c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(V_A,V_f,V_g,T_a,T_b),V_A,T_a)) ) ).

cnf(cls_inj__on__image__iff_3,axiom,
    ( c_Fun_Oinj__on(V_g,c_Set_Oimage(V_f,V_A,T_a,T_a),T_a,T_b)
    | ~ c_Fun_Oinj__on(V_g,V_A,T_a,T_b)
    | ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_a)
    | hBOOL(c_in(c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(V_A,V_f,V_g,T_a,T_b),V_A,T_a)) ) ).

cnf(cls_inj__on__image__iff_2,axiom,
    ( c_Fun_Oinj__on(V_g,V_A,T_a,T_b)
    | ~ c_Fun_Oinj__on(V_g,c_Set_Oimage(V_f,V_A,T_a,T_a),T_a,T_b)
    | ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_a)
    | hBOOL(c_in(c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(V_A,V_f,V_g,T_a,T_b),V_A,T_a)) ) ).

cnf(cls_f__the__inv__into__f_0,axiom,
    ( hAPP(V_f,hAPP(c_Fun_Othe__inv__into(V_A,V_f,T_a,T_b),V_y)) = V_y
    | ~ hBOOL(c_in(V_y,c_Set_Oimage(V_f,V_A,T_a,T_b),T_b))
    | ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).

cnf(cls_inj__image__mem__iff_1,axiom,
    ( hBOOL(c_in(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b))
    | ~ hBOOL(c_in(V_a,V_A,T_a))
    | ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).

cnf(cls_inj__image__mem__iff_0,axiom,
    ( hBOOL(c_in(V_a,V_A,T_a))
    | ~ hBOOL(c_in(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b))
    | ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).

cnf(cls_is__none__def__raw_0,axiom,
    c_Option_Ois__none(v_x,t_a) = c_fequal(v_x,c_Option_Ooption_ONone(t_a),tc_Option_Ooption(t_a)) ).

cnf(cls_inj__on__map__add__dom_1,axiom,
    ( c_Fun_Oinj__on(c_Map_Omap__add(V_m,V_m_H,T_a,T_b),c_Map_Odom(V_m_H,T_a,T_b),T_a,tc_Option_Ooption(T_b))
    | ~ c_Fun_Oinj__on(V_m_H,c_Map_Odom(V_m_H,T_a,T_b),T_a,tc_Option_Ooption(T_b)) ) ).

cnf(cls_inj__on__map__add__dom_0,axiom,
    ( c_Fun_Oinj__on(V_m_H,c_Map_Odom(V_m_H,T_a,T_b),T_a,tc_Option_Ooption(T_b))
    | ~ c_Fun_Oinj__on(c_Map_Omap__add(V_m,V_m_H,T_a,T_b),c_Map_Odom(V_m_H,T_a,T_b),T_a,tc_Option_Ooption(T_b)) ) ).

cnf(cls_dom__eq__singleton__conv_1,axiom,
    c_Map_Odom(c_Fun_Ofun__upd(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_x,hAPP(c_Option_Ooption_OSome(T_b),V_xa),T_a,tc_Option_Ooption(T_b)),T_a,T_b) = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ).

cnf(cls_map__le__map__add_0,axiom,
    c_Map_Omap__le(V_f,c_Map_Omap__add(V_g,V_f,T_a,T_b),T_a,T_b) ).

cnf(cls_map__comp__simps_I1_J_0,axiom,
    ( hAPP(V_m2,V_k) != c_Option_Ooption_ONone(T_a)
    | c_Map_Omap__comp(V_m1,V_m2,V_k,T_a,T_c,T_b) = c_Option_Ooption_ONone(T_c) ) ).

cnf(cls_map__comp__None__iff_2,axiom,
    ( hAPP(V_m2,V_k) != c_Option_Ooption_ONone(T_b)
    | c_Map_Omap__comp(V_m1,V_m2,V_k,T_b,T_a,T_c) = c_Option_Ooption_ONone(T_a) ) ).

cnf(cls_lconf__def_1,axiom,
    ( hAPP(V_l,V_V) != hAPP(c_Option_Ooption_OSome(tc_Value_Oval),V_v)
    | ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a)
    | c_Conform_Oconf(V_P,V_h,V_v,c_Conform_Osko__Conform__Xlconf__def__1__1(V_E,V_P,V_V,V_h,V_v,T_a),T_a) ) ).

cnf(cls_not__Cons__self_0,axiom,
    V_xs != c_List_Olist_OCons(V_x,V_xs,T_a) ).

cnf(cls_not__Cons__self2_0,axiom,
    c_List_Olist_OCons(V_x,V_t,T_a) != V_t ).

cnf(cls_map__add__None_2,axiom,
    ( hAPP(V_m,V_k) != c_Option_Ooption_ONone(T_a)
    | hAPP(V_n,V_k) != c_Option_Ooption_ONone(T_a)
    | hAPP(c_Map_Omap__add(V_m,V_n,T_b,T_a),V_k) = c_Option_Ooption_ONone(T_a) ) ).

cnf(cls_inj__on__swap__iff_0,axiom,
    ( c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
    | ~ c_Fun_Oinj__on(c_Fun_Oswap(V_a,V_b,V_f,T_a,T_b),V_A,T_a,T_b)
    | ~ hBOOL(c_in(V_b,V_A,T_a))
    | ~ hBOOL(c_in(V_a,V_A,T_a)) ) ).

cnf(cls_inj__on__swap__iff_1,axiom,
    ( c_Fun_Oinj__on(c_Fun_Oswap(V_a,V_b,V_f,T_a,T_b),V_A,T_a,T_b)
    | ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
    | ~ hBOOL(c_in(V_b,V_A,T_a))
    | ~ hBOOL(c_in(V_a,V_A,T_a)) ) ).

cnf(cls_inj__on__imp__inj__on__swap_0,axiom,
    ( c_Fun_Oinj__on(c_Fun_Oswap(V_a,V_b,V_f,T_a,T_b),V_A,T_a,T_b)
    | ~ hBOOL(c_in(V_b,V_A,T_a))
    | ~ hBOOL(c_in(V_a,V_A,T_a))
    | ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).

cnf(cls_comp__inj__on_0,axiom,
    ( c_Fun_Oinj__on(c_Fun_Ocomp(V_g,V_f,T_b,T_c,T_a),V_A,T_a,T_c)
    | ~ c_Fun_Oinj__on(V_g,c_Set_Oimage(V_f,V_A,T_a,T_b),T_b,T_c)
    | ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).

cnf(cls_option__map__None_0,axiom,
    hAPP(c_Option_Omap(V_f,T_b,T_a),c_Option_Ooption_ONone(T_b)) = c_Option_Ooption_ONone(T_a) ).

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

cnf(cls_is__none__def_0,axiom,
    ( V_x = c_Option_Ooption_ONone(T_a)
    | ~ hBOOL(c_Option_Ois__none(V_x,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(c_in(V_x,V_B,T_a))
    | hBOOL(c_in(V_x,V_A,T_a))
    | V_A = V_B ) ).

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(c_in(V_x,V_A,T_a)) ) ).

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_conf__hext_0,axiom,
    ( c_Conform_Oconf(V_P,V_h_H,V_v,V_T,T_a)
    | ~ c_Conform_Oconf(V_P,V_h,V_v,V_T,T_a)
    | ~ c_Objects_Ohext(V_h,V_h_H) ) ).

cnf(cls_hext__refl_0,axiom,
    c_Objects_Ohext(V_h,V_h) ).

cnf(cls_hext__trans_0,axiom,
    ( c_Objects_Ohext(V_h,V_h_H_H)
    | ~ c_Objects_Ohext(V_h_H,V_h_H_H)
    | ~ c_Objects_Ohext(V_h,V_h_H) ) ).

cnf(cls_WTrt__hext__mono_0,axiom,
    ( c_WellTypeRT_OWTrt(V_P,V_h_H,V_E,V_e,V_T)
    | ~ c_Objects_Ohext(V_h,V_h_H)
    | ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T) ) ).

cnf(cls_WT__implies__WTrt_0,axiom,
    ( c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T)
    | ~ c_WellType_OWT(V_P,V_E,V_e,V_T) ) ).

cnf(cls_map__add__None_0,axiom,
    ( hAPP(c_Map_Omap__add(V_m,V_n,T_b,T_a),V_k) != c_Option_Ooption_ONone(T_a)
    | hAPP(V_n,V_k) = c_Option_Ooption_ONone(T_a) ) ).

cnf(cls_map__add__None_1,axiom,
    ( hAPP(c_Map_Omap__add(V_m,V_n,T_b,T_a),V_k) != c_Option_Ooption_ONone(T_a)
    | hAPP(V_m,V_k) = c_Option_Ooption_ONone(T_a) ) ).

cnf(cls_map__add__Some__iff_3,axiom,
    ( hAPP(V_m,V_k) != hAPP(c_Option_Ooption_OSome(T_a),V_x)
    | hAPP(V_n,V_k) != c_Option_Ooption_ONone(T_a)
    | hAPP(c_Map_Omap__add(V_m,V_n,T_b,T_a),V_k) = hAPP(c_Option_Ooption_OSome(T_a),V_x) ) ).

cnf(cls_swap__triple_0,axiom,
    ( c_Fun_Oswap(V_a,V_b,c_Fun_Oswap(V_b,V_c,c_Fun_Oswap(V_a,V_b,V_f,T_a,T_b),T_a,T_b),T_a,T_b) = c_Fun_Oswap(V_a,V_c,V_f,T_a,T_b)
    | V_b = V_c
    | V_a = V_c ) ).

cnf(cls_BlockRedSome_I4_J_0,axiom,
    ~ c_SmallStep_Oassigned(v_V____,v_ea____) ).

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(c_in(V_y,V_A,T_a))
    | ~ hBOOL(c_in(V_x,V_A,T_a)) ) ).

cnf(cls_inj__on__def_0,axiom,
    ( hAPP(V_f,V_x) != hAPP(V_f,V_xa)
    | ~ hBOOL(c_in(V_xa,V_A,T_a))
    | ~ hBOOL(c_in(V_x,V_A,T_a))
    | ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
    | V_x = V_xa ) ).

cnf(cls_inj__on__iff_0,axiom,
    ( hAPP(V_f,V_x) != hAPP(V_f,V_y)
    | ~ hBOOL(c_in(V_y,V_A,T_a))
    | ~ hBOOL(c_in(V_x,V_A,T_a))
    | ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
    | V_x = V_y ) ).

cnf(cls_inj__on__contraD_0,axiom,
    ( hAPP(V_f,V_x) != hAPP(V_f,V_y)
    | ~ hBOOL(c_in(V_y,V_A,T_a))
    | ~ hBOOL(c_in(V_x,V_A,T_a))
    | V_x = V_y
    | ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).

cnf(cls_option_Orecs_I1_J_0,axiom,
    c_Option_Ooption_Ooption__rec(V_f1,V_f2,c_Option_Ooption_ONone(T_b),T_a,T_b) = V_f1 ).

cnf(cls_empty__map__add_0,axiom,
    c_Map_Omap__add(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_m,T_a,T_b) = V_m ).

cnf(cls_map__add__empty_0,axiom,
    c_Map_Omap__add(V_m,c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),T_a,T_b) = V_m ).

cnf(cls_option_Osplit_0,axiom,
    ( ~ hBOOL(hAPP(V_P,c_Option_Ooption_Ooption__case(V_f1,V_f2,c_Option_Ooption_ONone(t_b),t_a,t_b)))
    | hBOOL(hAPP(V_P,V_f1)) ) ).

cnf(cls_COMBK__def_0,axiom,
    hAPP(c_COMBK(V_P,T_a,T_b),V_Q) = V_P ).

cnf(cls_COMBI__def_0,axiom,
    hAPP(c_COMBI(T_a),V_P) = V_P ).

cnf(cls_mem__def_0,axiom,
    ( hBOOL(hAPP(V_S,V_x))
    | ~ hBOOL(c_in(V_x,V_S,T_a)) ) ).

cnf(cls_mem__def_1,axiom,
    ( hBOOL(c_in(V_x,V_S,T_a))
    | ~ hBOOL(hAPP(V_S,V_x)) ) ).

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_insertCI_1,axiom,
    hBOOL(c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a)) ).

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

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

cnf(cls_swap__commute_0,axiom,
    c_Fun_Oswap(V_a,V_b,V_f,T_a,T_b) = c_Fun_Oswap(V_b,V_a,V_f,T_a,T_b) ).

cnf(cls_swap__nilpotent_0,axiom,
    c_Fun_Oswap(V_a,V_b,c_Fun_Oswap(V_a,V_b,V_f,T_a,T_b),T_a,T_b) = V_f ).

cnf(cls_inj__on__imageI_0,axiom,
    ( c_Fun_Oinj__on(V_g,c_Set_Oimage(V_f,V_A,T_a,T_c),T_c,T_b)
    | ~ c_Fun_Oinj__on(c_Fun_Ocomp(V_g,V_f,T_c,T_b,T_a),V_A,T_a,T_b) ) ).

cnf(cls_map__le__upds_0,axiom,
    ( c_Map_Omap__le(c_Map_Omap__upds(V_f,V_as,V_bs,T_a,T_b),c_Map_Omap__upds(V_g,V_as,V_bs,T_a,T_b),T_a,T_b)
    | ~ c_Map_Omap__le(V_f,V_g,T_a,T_b) ) ).

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_wt_H__wt_0,axiom,
    ( c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T)
    | ~ c_Progress_OWTrt_H(V_P,V_h,V_E,V_e,V_T) ) ).

cnf(cls_wt__wt_H_0,axiom,
    ( c_Progress_OWTrt_H(V_P,V_h,V_E,V_e,V_T)
    | ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,V_e,V_T) ) ).

cnf(cls_image__ident_0,axiom,
    c_Set_Oimage(c_COMBI(T_a),V_Y,T_a,T_a) = V_Y ).

cnf(cls_override__on__apply__notin_0,axiom,
    ( hAPP(c_Fun_Ooverride__on(V_f,V_g,V_A,T_a,T_b),V_a) = hAPP(V_f,V_a)
    | hBOOL(c_in(V_a,V_A,T_a)) ) ).

cnf(cls_inj__on__id2_0,axiom,
    c_Fun_Oinj__on(c_COMBI(T_a),V_A,T_a,T_a) ).

cnf(cls_map__add__le__mapE_0,axiom,
    ( c_Map_Omap__le(V_g,V_h,T_a,T_b)
    | ~ c_Map_Omap__le(c_Map_Omap__add(V_f,V_g,T_a,T_b),V_h,T_a,T_b) ) ).

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_swap__self_0,axiom,
    c_Fun_Oswap(V_a,V_a,V_f,T_a,T_b) = V_f ).

cnf(cls_map__le__refl_0,axiom,
    c_Map_Omap__le(V_f,V_f,T_a,T_b) ).

cnf(cls_map__le__trans_0,axiom,
    ( c_Map_Omap__le(V_m1,V_m3,T_a,T_b)
    | ~ c_Map_Omap__le(V_m2,V_m3,T_a,T_b)
    | ~ c_Map_Omap__le(V_m1,V_m2,T_a,T_b) ) ).

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_lconf__def_2,axiom,
    ( c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a)
    | hAPP(V_l,c_Conform_Osko__Conform__Xlconf__def__1__2(V_E,V_P,V_h,V_l,T_a)) = hAPP(c_Option_Ooption_OSome(tc_Value_Oval),c_Conform_Osko__Conform__Xlconf__def__1__3(V_E,V_P,V_h,V_l,T_a)) ) ).

cnf(cls_ty_Oinject_0,axiom,
    ( c_Type_Oty_OClass(V_list) != c_Type_Oty_OClass(V_list_H)
    | V_list = V_list_H ) ).

cnf(cls_o__apply_0,axiom,
    hAPP(c_Fun_Ocomp(V_f,V_g,T_b,T_a,T_c),V_x) = hAPP(V_f,hAPP(V_g,V_x)) ).

cnf(cls_o__eq__dest__lhs_0,axiom,
    hAPP(V_a,hAPP(V_b,V_v)) = hAPP(c_Fun_Ocomp(V_a,V_b,T_c,T_b,T_a),V_v) ).

cnf(cls_override__on__apply__in_0,axiom,
    ( hAPP(c_Fun_Ooverride__on(V_f,V_g,V_A,T_a,T_b),V_a) = hAPP(V_g,V_a)
    | ~ hBOOL(c_in(V_a,V_A,T_a)) ) ).

cnf(cls_WT__elim__cases_I5_J_0,axiom,
    ( c_WellType_OWT(V_P,V_E,V_e_092_060_094isub_0621,V_T)
    | ~ c_WellType_OWT(V_P,V_E,c_Expr_Oexp_OTryCatch(V_e_092_060_094isub_0621,V_C,V_V,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),V_T) ) ).

cnf(cls_map__add__assoc_0,axiom,
    c_Map_Omap__add(V_m1,c_Map_Omap__add(V_m2,V_m3,T_a,T_b),T_a,T_b) = c_Map_Omap__add(c_Map_Omap__add(V_m1,V_m2,T_a,T_b),V_m3,T_a,T_b) ).

cnf(cls_map__add__upds_0,axiom,
    c_Map_Omap__add(V_m1,c_Map_Omap__upds(V_m2,V_xs,V_ys,T_a,T_b),T_a,T_b) = c_Map_Omap__upds(c_Map_Omap__add(V_m1,V_m2,T_a,T_b),V_xs,V_ys,T_a,T_b) ).

cnf(cls_option__map__is__None_0,axiom,
    ( hAPP(c_Option_Omap(V_f,T_b,T_a),V_opt) != c_Option_Ooption_ONone(T_a)
    | V_opt = c_Option_Ooption_ONone(T_b) ) ).

cnf(cls_map__le__iff__map__add__commute_0,axiom,
    ( c_Map_Omap__add(V_f,V_g,T_a,T_b) = c_Map_Omap__add(V_g,V_f,T_a,T_b)
    | ~ c_Map_Omap__le(V_f,c_Map_Omap__add(V_f,V_g,T_a,T_b),T_a,T_b) ) ).

cnf(cls_map__le__iff__map__add__commute_1,axiom,
    ( c_Map_Omap__add(V_f,V_g,T_a,T_b) != c_Map_Omap__add(V_g,V_f,T_a,T_b)
    | c_Map_Omap__le(V_f,c_Map_Omap__add(V_f,V_g,T_a,T_b),T_a,T_b) ) ).

cnf(cls_option__map__comp_0,axiom,
    hAPP(c_Option_Omap(V_f,T_b,T_a),hAPP(c_Option_Omap(V_g,T_c,T_b),V_opt)) = hAPP(c_Option_Omap(c_Fun_Ocomp(V_f,V_g,T_b,T_a,T_c),T_c,T_a),V_opt) ).

cnf(cls_insertE_0,axiom,
    ( hBOOL(c_in(V_a,V_A,T_a))
    | V_a = V_b
    | ~ hBOOL(c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a)) ) ).

cnf(cls_upd__None__map__le_0,axiom,
    c_Map_Omap__le(c_Fun_Ofun__upd(V_f,V_x,c_Option_Ooption_ONone(T_b),T_a,tc_Option_Ooption(T_b)),V_f,T_a,T_b) ).

cnf(cls_map__le__antisym_0,axiom,
    ( V_f = V_g
    | ~ c_Map_Omap__le(V_g,V_f,T_a,T_b)
    | ~ c_Map_Omap__le(V_f,V_g,T_a,T_b) ) ).

cnf(cls_is__none__def_1,axiom,
    hBOOL(c_Option_Ois__none(c_Option_Ooption_ONone(T_a),T_a)) ).

cnf(cls_option_Osimps_I4_J_0,axiom,
    c_Option_Ooption_Ooption__case(V_f1,V_f2,c_Option_Ooption_ONone(T_b),T_a,T_b) = V_f1 ).

cnf(cls_exp_Osimps_I205_J_0,axiom,
    c_Expr_Oexp_OTryCatch(V_exp1_H,V_list_H,V_a_H,V_exp2_H,T_a) != c_Expr_Oexp_OBlock(V_a,V_ty,V_exp,T_a) ).

cnf(cls_map__le__empty_0,axiom,
    c_Map_Omap__le(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_g,T_a,T_b) ).

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_map__add__SomeD_0,axiom,
    ( hAPP(c_Map_Omap__add(V_m,V_n,T_b,T_a),V_k) != hAPP(c_Option_Ooption_OSome(T_a),V_x)
    | hAPP(V_n,V_k) = c_Option_Ooption_ONone(T_a)
    | hAPP(V_n,V_k) = hAPP(c_Option_Ooption_OSome(T_a),V_x) ) ).

cnf(cls_inj__on__fun__updI_0,axiom,
    ( c_Fun_Oinj__on(c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_b),V_A,T_a,T_b)
    | hBOOL(c_in(V_y,c_Set_Oimage(V_f,V_A,T_a,T_b),T_b))
    | ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).

cnf(cls_fun__upd__image_1,axiom,
    ( c_Set_Oimage(c_Fun_Ofun__upd(V_f,V_x,V_y,T_b,T_a),V_A,T_b,T_a) = c_Set_Oimage(V_f,V_A,T_b,T_a)
    | hBOOL(c_in(V_x,V_A,T_b)) ) ).

cnf(cls_o__assoc_0,axiom,
    c_Fun_Ocomp(V_f,c_Fun_Ocomp(V_g,V_h,T_d,T_c,T_a),T_c,T_b,T_a) = c_Fun_Ocomp(c_Fun_Ocomp(V_f,V_g,T_c,T_b,T_d),V_h,T_d,T_b,T_a) ).

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

cnf(cls_image__compose_0,axiom,
    c_Set_Oimage(c_Fun_Ocomp(V_f,V_g,T_c,T_a,T_b),V_r,T_b,T_a) = c_Set_Oimage(V_f,c_Set_Oimage(V_g,V_r,T_b,T_c),T_c,T_a) ).

cnf(cls_map__comp__None__iff_3,axiom,
    ( hAPP(V_m1,V_x) != c_Option_Ooption_ONone(T_a)
    | hAPP(V_m2,V_k) != hAPP(c_Option_Ooption_OSome(T_b),V_x)
    | c_Map_Omap__comp(V_m1,V_m2,V_k,T_b,T_a,T_c) = c_Option_Ooption_ONone(T_a) ) ).

cnf(cls_list_Oinject_0,axiom,
    ( c_List_Olist_OCons(V_a,V_list,T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a)
    | V_a = V_a_H ) ).

cnf(cls_list_Oinject_1,axiom,
    ( c_List_Olist_OCons(V_a,V_list,T_a) != c_List_Olist_OCons(V_a_H,V_list_H,T_a)
    | V_list = V_list_H ) ).

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

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

cnf(cls_o__eq__dest_0,axiom,
    ( c_Fun_Ocomp(V_a,V_b,T_c,T_b,T_a) != c_Fun_Ocomp(V_c,V_d,T_d,T_b,T_a)
    | hAPP(V_a,hAPP(V_b,V_v)) = hAPP(V_c,hAPP(V_d,V_v)) ) ).

cnf(cls_comp__cong_0,axiom,
    ( hAPP(V_f,hAPP(V_g,V_x)) != hAPP(V_f_H,hAPP(V_g_H,V_x_H))
    | hAPP(c_Fun_Ocomp(V_f,V_g,T_b,T_a,T_c),V_x) = hAPP(c_Fun_Ocomp(V_f_H,V_g_H,T_d,T_a,T_e),V_x_H) ) ).

cnf(cls_exp_Osimps_I10_J_2,axiom,
    ( c_Expr_Oexp_OBlock(V_a,V_ty,V_exp,T_a) != c_Expr_Oexp_OBlock(V_a_H,V_ty_H,V_exp_H,T_a)
    | V_exp = V_exp_H ) ).

cnf(cls_exp_Osimps_I10_J_1,axiom,
    ( c_Expr_Oexp_OBlock(V_a,V_ty,V_exp,T_a) != c_Expr_Oexp_OBlock(V_a_H,V_ty_H,V_exp_H,T_a)
    | V_ty = V_ty_H ) ).

cnf(cls_exp_Osimps_I10_J_0,axiom,
    ( c_Expr_Oexp_OBlock(V_a,V_ty,V_exp,T_a) != c_Expr_Oexp_OBlock(V_a_H,V_ty_H,V_exp_H,T_a)
    | V_a = V_a_H ) ).

cnf(cls_exp_Osimps_I204_J_0,axiom,
    c_Expr_Oexp_OBlock(V_a,V_ty,V_exp,T_a) != c_Expr_Oexp_OTryCatch(V_exp1_H,V_list_H,V_a_H,V_exp2_H,T_a) ).

cnf(cls_exp_Osimps_I15_J_3,axiom,
    ( c_Expr_Oexp_OTryCatch(V_exp1,V_list,V_a,V_exp2,T_a) != c_Expr_Oexp_OTryCatch(V_exp1_H,V_list_H,V_a_H,V_exp2_H,T_a)
    | V_exp2 = V_exp2_H ) ).

cnf(cls_exp_Osimps_I15_J_2,axiom,
    ( c_Expr_Oexp_OTryCatch(V_exp1,V_list,V_a,V_exp2,T_a) != c_Expr_Oexp_OTryCatch(V_exp1_H,V_list_H,V_a_H,V_exp2_H,T_a)
    | V_a = V_a_H ) ).

cnf(cls_exp_Osimps_I15_J_1,axiom,
    ( c_Expr_Oexp_OTryCatch(V_exp1,V_list,V_a,V_exp2,T_a) != c_Expr_Oexp_OTryCatch(V_exp1_H,V_list_H,V_a_H,V_exp2_H,T_a)
    | V_list = V_list_H ) ).

cnf(cls_exp_Osimps_I15_J_0,axiom,
    ( c_Expr_Oexp_OTryCatch(V_exp1,V_list,V_a,V_exp2,T_a) != c_Expr_Oexp_OTryCatch(V_exp1_H,V_list_H,V_a_H,V_exp2_H,T_a)
    | V_exp1 = V_exp1_H ) ).

cnf(cls_map__upd__eqD1_0,axiom,
    ( c_Fun_Ofun__upd(V_m,V_a,hAPP(c_Option_Ooption_OSome(T_b),V_x),T_a,tc_Option_Ooption(T_b)) != c_Fun_Ofun__upd(V_n,V_a,hAPP(c_Option_Ooption_OSome(T_b),V_y),T_a,tc_Option_Ooption(T_b))
    | V_x = V_y ) ).

cnf(cls_the_Osimps_0,axiom,
    c_Option_Othe(hAPP(c_Option_Ooption_OSome(T_a),V_x),T_a) = V_x ).

cnf(cls_option_Orecs_I2_J_0,axiom,
    c_Option_Ooption_Ooption__rec(V_f1,V_f2,hAPP(c_Option_Ooption_OSome(T_b),V_a),T_a,T_b) = hAPP(V_f2,V_a) ).

cnf(cls_fun__upd__other_0,axiom,
    ( hAPP(c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_b),V_z) = hAPP(V_f,V_z)
    | V_z = V_x ) ).

cnf(cls_fun__upd__apply_1,axiom,
    ( hAPP(c_Fun_Ofun__upd(V_f,V_x,V_y,T_b,T_a),V_z) = hAPP(V_f,V_z)
    | V_z = V_x ) ).

cnf(cls_map__upd__triv_0,axiom,
    ( hAPP(V_t,V_k) != hAPP(c_Option_Ooption_OSome(T_a),V_x)
    | c_Fun_Ofun__upd(V_t,V_k,hAPP(c_Option_Ooption_OSome(T_a),V_x),T_b,tc_Option_Ooption(T_a)) = V_t ) ).

cnf(cls_map__upd__Some__unfold_3,axiom,
    hAPP(c_Fun_Ofun__upd(V_m,V_xa,hAPP(c_Option_Ooption_OSome(T_a),V_x),T_aa,tc_Option_Ooption(T_a)),V_xa) = hAPP(c_Option_Ooption_OSome(T_a),V_x) ).

cnf(cls_map__comp__Some__iff_2,axiom,
    ( hAPP(V_m1,V_x) != hAPP(c_Option_Ooption_OSome(T_a),V_v)
    | hAPP(V_m2,V_k) != hAPP(c_Option_Ooption_OSome(T_b),V_x)
    | c_Map_Omap__comp(V_m1,V_m2,V_k,T_b,T_a,T_c) = hAPP(c_Option_Ooption_OSome(T_a),V_v) ) ).

cnf(cls_map__add__upd_0,axiom,
    c_Map_Omap__add(V_f,c_Fun_Ofun__upd(V_g,V_x,hAPP(c_Option_Ooption_OSome(T_b),V_y),T_a,tc_Option_Ooption(T_b)),T_a,T_b) = c_Fun_Ofun__upd(c_Map_Omap__add(V_f,V_g,T_a,T_b),V_x,hAPP(c_Option_Ooption_OSome(T_b),V_y),T_a,tc_Option_Ooption(T_b)) ).

cnf(cls_fun__upd__idem__iff_1,axiom,
    c_Fun_Ofun__upd(V_f,V_x,hAPP(V_f,V_x),T_aa,T_a) = V_f ).

cnf(cls_fun__upd__apply_0,axiom,
    hAPP(c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_aa),V_x) = V_y ).

cnf(cls_fun__upd__triv_0,axiom,
    c_Fun_Ofun__upd(V_f,V_x,hAPP(V_f,V_x),T_a,T_b) = V_f ).

cnf(cls_fun__upd__same_0,axiom,
    hAPP(c_Fun_Ofun__upd(V_f,V_x,V_y,T_b,T_a),V_x) = V_y ).

cnf(cls_fun__upd__idem_0,axiom,
    c_Fun_Ofun__upd(V_f,V_x,hAPP(V_f,V_x),T_b,T_a) = V_f ).

cnf(cls_swap__def_0,axiom,
    c_Fun_Oswap(V_a,V_b,V_f,T_a,T_b) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(V_f,V_a,hAPP(V_f,V_b),T_a,T_b),V_b,hAPP(V_f,V_a),T_a,T_b) ).

cnf(cls_fun__upd__upd_0,axiom,
    c_Fun_Ofun__upd(c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_b),V_x,V_z,T_a,T_b) = c_Fun_Ofun__upd(V_f,V_x,V_z,T_a,T_b) ).

cnf(cls_lconf__upd2_0,axiom,
    ( c_Conform_Olconf(V_P,V_h,c_Fun_Ofun__upd(V_l,V_V,hAPP(c_Option_Ooption_OSome(tc_Value_Oval),V_v),tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)),c_Fun_Ofun__upd(V_E,V_V,hAPP(c_Option_Ooption_OSome(tc_Type_Oty),V_T),tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Type_Oty)),T_a)
    | ~ c_Conform_Oconf(V_P,V_h,V_v,V_T,T_a)
    | ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a) ) ).

cnf(cls_override__on__upd__lemma_0,axiom,
    c_Fun_Ofun__upd(c_Fun_Ooverride__on(V_f,c_Fun_Ofun__upd(V_g,V_a,hAPP(c_Option_Ooption_OSome(T_b),V_b),T_a,tc_Option_Ooption(T_b)),V_A,T_a,tc_Option_Ooption(T_b)),V_a,hAPP(V_g,V_a),T_a,tc_Option_Ooption(T_b)) = c_Fun_Ooverride__on(V_f,V_g,c_Set_Oinsert(V_a,V_A,T_a),T_a,tc_Option_Ooption(T_b)) ).

cnf(cls_IH_H_0,axiom,
    c_WellTypeRT_OWTrt(v_P,v_h_Ha____,c_Fun_Ofun__upd(v_E____,v_V____,hAPP(c_Option_Ooption_OSome(tc_Type_Oty),v_T____),tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Type_Oty)),v_e_Ha____,v_Te_H____) ).

cnf(cls_WTrtBlock_0,axiom,
    ( c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OBlock(V_V,V_T,V_e,tc_List_Olist(tc_String_Ochar)),V_T_H)
    | ~ c_WellTypeRT_OWTrt(V_P,V_h,c_Fun_Ofun__upd(V_E,V_V,hAPP(c_Option_Ooption_OSome(tc_Type_Oty),V_T),tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Type_Oty)),V_e,V_T_H) ) ).

cnf(cls_option_Osplit__asm_1,axiom,
    ( ~ hBOOL(hAPP(V_P,c_Option_Ooption_Ooption__case(V_f1,V_f2,hAPP(c_Option_Ooption_OSome(t_b),V_xa),t_a,t_b)))
    | hBOOL(hAPP(V_P,hAPP(V_f2,V_xa))) ) ).

cnf(cls_option_Osplit_1,axiom,
    ( ~ hBOOL(hAPP(V_P,c_Option_Ooption_Ooption__case(V_f1,V_f2,hAPP(c_Option_Ooption_OSome(t_b),V_a),t_a,t_b)))
    | hBOOL(hAPP(V_P,hAPP(V_f2,V_a))) ) ).

cnf(cls_inj__Some_0,axiom,
    c_Fun_Oinj__on(c_Option_Ooption_OSome(T_a),V_A,T_a,tc_Option_Ooption(T_a)) ).

cnf(cls_is__none__code_I2_J_0,axiom,
    ~ hBOOL(c_Option_Ois__none(hAPP(c_Option_Ooption_OSome(T_a),V_x),T_a)) ).

cnf(cls_fun__upd__twist_0,axiom,
    ( c_Fun_Ofun__upd(c_Fun_Ofun__upd(V_m,V_a,V_b,T_a,T_b),V_c,V_d,T_a,T_b) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(V_m,V_c,V_d,T_a,T_b),V_a,V_b,T_a,T_b)
    | V_a = V_c ) ).

cnf(cls_WTBlock_0,axiom,
    ( c_WellType_OWT(V_P,V_E,c_Expr_Oexp_OBlock(V_V,V_T,V_e,tc_List_Olist(tc_String_Ochar)),V_T_H)
    | ~ c_WellType_OWT(V_P,c_Fun_Ofun__upd(V_E,V_V,hAPP(c_Option_Ooption_OSome(tc_Type_Oty),V_T),tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Type_Oty)),V_e,V_T_H)
    | ~ c_Decl_Ois__type(V_P,V_T,tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))) ) ).

cnf(cls_option_Oinject_0,axiom,
    ( hAPP(c_Option_Ooption_OSome(T_a),V_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H)
    | V_a = V_a_H ) ).

cnf(cls_not__None__eq_1,axiom,
    hAPP(c_Option_Ooption_OSome(T_a),V_xa) != c_Option_Ooption_ONone(T_a) ).

cnf(cls_option_Osimps_I3_J_0,axiom,
    hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ).

cnf(cls_map__le__upd_0,axiom,
    ( c_Map_Omap__le(c_Fun_Ofun__upd(V_f,V_a,V_b,T_a,tc_Option_Ooption(T_b)),c_Fun_Ofun__upd(V_g,V_a,V_b,T_a,tc_Option_Ooption(T_b)),T_a,T_b)
    | ~ c_Map_Omap__le(V_f,V_g,T_a,T_b) ) ).

cnf(cls_WTrt_H__WTrts_H_Ointros_I17_J_0,axiom,
    ( c_Progress_OWTrt_H(V_P,V_h,V_E,c_Expr_Oexp_OBlock(V_V,V_T,V_e,tc_List_Olist(tc_String_Ochar)),V_T_H)
    | c_SmallStep_Oassigned(V_V,V_e)
    | ~ c_Progress_OWTrt_H(V_P,V_h,c_Fun_Ofun__upd(V_E,V_V,hAPP(c_Option_Ooption_OSome(tc_Type_Oty),V_T),tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Type_Oty)),V_e,V_T_H) ) ).

cnf(cls_map__le__imp__upd__le_0,axiom,
    ( c_Map_Omap__le(c_Fun_Ofun__upd(V_m1,V_x,c_Option_Ooption_ONone(T_b),T_a,tc_Option_Ooption(T_b)),c_Fun_Ofun__upd(V_m2,V_x,hAPP(c_Option_Ooption_OSome(T_b),V_y),T_a,tc_Option_Ooption(T_b)),T_a,T_b)
    | ~ c_Map_Omap__le(V_m1,V_m2,T_a,T_b) ) ).

cnf(cls_WT__elim__cases_I5_J_1,axiom,
    ( c_WellType_OWT(V_P,c_Fun_Ofun__upd(V_E,V_V,hAPP(c_Option_Ooption_OSome(tc_Type_Oty),c_Type_Oty_OClass(V_C)),tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Type_Oty)),V_e_092_060_094isub_0622,V_T)
    | ~ c_WellType_OWT(V_P,V_E,c_Expr_Oexp_OTryCatch(V_e_092_060_094isub_0621,V_C,V_V,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),V_T) ) ).

cnf(cls_lconf__def_3,axiom,
    ( hAPP(V_E,c_Conform_Osko__Conform__Xlconf__def__1__2(V_E,V_P,V_h,V_l,T_a)) != hAPP(c_Option_Ooption_OSome(tc_Type_Oty),V_x)
    | c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a)
    | ~ c_Conform_Oconf(V_P,V_h,c_Conform_Osko__Conform__Xlconf__def__1__3(V_E,V_P,V_h,V_l,T_a),V_x,T_a) ) ).

cnf(cls_map__upd__Some__unfold_4,axiom,
    ( hAPP(V_m,V_x) != hAPP(c_Option_Ooption_OSome(T_a),V_y)
    | V_x = V_a
    | hAPP(c_Fun_Ofun__upd(V_m,V_a,hAPP(c_Option_Ooption_OSome(T_a),V_b),T_b,tc_Option_Ooption(T_a)),V_x) = hAPP(c_Option_Ooption_OSome(T_a),V_y) ) ).

cnf(cls_map__upd__Some__unfold_2,axiom,
    ( hAPP(c_Fun_Ofun__upd(V_m,V_a,hAPP(c_Option_Ooption_OSome(T_a),V_b),T_b,tc_Option_Ooption(T_a)),V_x) != hAPP(c_Option_Ooption_OSome(T_a),V_y)
    | hAPP(V_m,V_x) = hAPP(c_Option_Ooption_OSome(T_a),V_y)
    | V_b = V_y ) ).

cnf(cls_map__upd__Some__unfold_0,axiom,
    ( hAPP(c_Fun_Ofun__upd(V_m,V_a,hAPP(c_Option_Ooption_OSome(T_a),V_b),T_b,tc_Option_Ooption(T_a)),V_x) != hAPP(c_Option_Ooption_OSome(T_a),V_y)
    | hAPP(V_m,V_x) = hAPP(c_Option_Ooption_OSome(T_a),V_y)
    | V_x = V_a ) ).

cnf(cls_map__upd__nonempty_0,axiom,
    c_Fun_Ofun__upd(V_t,V_k,hAPP(c_Option_Ooption_OSome(T_b),V_x),T_a,tc_Option_Ooption(T_b)) != c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a) ).

cnf(cls_lconf__upd_0,axiom,
    ( hAPP(V_E,V_V) != hAPP(c_Option_Ooption_OSome(tc_Type_Oty),V_T)
    | ~ c_Conform_Oconf(V_P,V_h,V_v,V_T,T_a)
    | ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a)
    | c_Conform_Olconf(V_P,V_h,c_Fun_Ofun__upd(V_l,V_V,hAPP(c_Option_Ooption_OSome(tc_Value_Oval),V_v),tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)),V_E,T_a) ) ).

cnf(cls_lconf__def_0,axiom,
    ( hAPP(V_l,V_V) != hAPP(c_Option_Ooption_OSome(tc_Value_Oval),V_v)
    | ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a)
    | hAPP(V_E,V_V) = hAPP(c_Option_Ooption_OSome(tc_Type_Oty),c_Conform_Osko__Conform__Xlconf__def__1__1(V_E,V_P,V_V,V_h,V_v,T_a)) ) ).

cnf(cls_option_Osimps_I5_J_0,axiom,
    c_Option_Ooption_Ooption__case(V_f1,V_f2,hAPP(c_Option_Ooption_OSome(T_b),V_a),T_a,T_b) = hAPP(V_f2,V_a) ).

cnf(cls_option__map__o__map__upd_0,axiom,
    c_Fun_Ocomp(c_Option_Omap(V_f,T_c,T_b),c_Fun_Ofun__upd(V_m,V_a,hAPP(c_Option_Ooption_OSome(T_c),V_b),T_a,tc_Option_Ooption(T_c)),tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_a) = c_Fun_Ofun__upd(c_Fun_Ocomp(c_Option_Omap(V_f,T_c,T_b),V_m,tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_a),V_a,hAPP(c_Option_Ooption_OSome(T_b),hAPP(V_f,V_b)),T_a,tc_Option_Ooption(T_b)) ).

cnf(cls_Some_0,axiom,
    hAPP(v_l_Ha____,v_V____) = hAPP(c_Option_Ooption_OSome(tc_Value_Oval),v_v____) ).

cnf(cls_map__upds__Cons_0,axiom,
    c_Map_Omap__upds(V_m,c_List_Olist_OCons(V_a,V_as,T_a),c_List_Olist_OCons(V_b,V_bs,T_b),T_a,T_b) = c_Map_Omap__upds(c_Fun_Ofun__upd(V_m,V_a,hAPP(c_Option_Ooption_OSome(T_b),V_b),T_a,tc_Option_Ooption(T_b)),V_as,V_bs,T_a,T_b) ).

cnf(cls_map__upd__Some__unfold_1,axiom,
    ( V_b = V_y
    | hAPP(c_Fun_Ofun__upd(V_m,V_x,hAPP(c_Option_Ooption_OSome(T_aa),V_b),T_a,tc_Option_Ooption(T_aa)),V_x) != hAPP(c_Option_Ooption_OSome(T_aa),V_y) ) ).

cnf(cls_fun__upd__comp_0,axiom,
    c_Fun_Ocomp(V_f,c_Fun_Ofun__upd(V_g,V_x,V_y,T_a,T_c),T_c,T_b,T_a) = c_Fun_Ofun__upd(c_Fun_Ocomp(V_f,V_g,T_c,T_b,T_a),V_x,hAPP(V_f,V_y),T_a,T_b) ).

cnf(cls_not__Some__eq_1,axiom,
    c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_y) ).

cnf(cls_option_Osimps_I2_J_0,axiom,
    c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ).

cnf(cls_wt_0,axiom,
    c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_Expr_Oexp_OBlock(v_V____,v_T____,v_ea____,tc_List_Olist(tc_String_Ochar)),v_Te____) ).

cnf(cls_image__map__upd_0,axiom,
    ( c_Set_Oimage(c_Fun_Ofun__upd(V_m,V_x,hAPP(c_Option_Ooption_OSome(T_b),V_y),T_a,tc_Option_Ooption(T_b)),V_A,T_a,tc_Option_Ooption(T_b)) = c_Set_Oimage(V_m,V_A,T_a,tc_Option_Ooption(T_b))
    | hBOOL(c_in(V_x,V_A,T_a)) ) ).

cnf(cls_map__add__SomeD_1,axiom,
    ( hAPP(c_Map_Omap__add(V_m,V_n,T_b,T_a),V_k) != hAPP(c_Option_Ooption_OSome(T_a),V_x)
    | hAPP(V_m,V_k) = hAPP(c_Option_Ooption_OSome(T_a),V_x)
    | hAPP(V_n,V_k) = hAPP(c_Option_Ooption_OSome(T_a),V_x) ) ).

cnf(cls_option__map__Some_0,axiom,
    hAPP(c_Option_Omap(V_f,T_b,T_a),hAPP(c_Option_Ooption_OSome(T_b),V_x)) = hAPP(c_Option_Ooption_OSome(T_a),hAPP(V_f,V_x)) ).

cnf(cls_WTrt__elim__cases_I5_J_1,axiom,
    ( c_WellTypeRT_OWTrt(V_P,V_h,c_Fun_Ofun__upd(V_E,V_V,hAPP(c_Option_Ooption_OSome(tc_Type_Oty),c_Type_Oty_OClass(V_C)),tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Type_Oty)),V_e_092_060_094isub_0622,V_T)
    | ~ c_WellTypeRT_OWTrt(V_P,V_h,V_E,c_Expr_Oexp_OTryCatch(V_e_092_060_094isub_0621,V_C,V_V,V_e_092_060_094isub_0622,tc_List_Olist(tc_String_Ochar)),V_T) ) ).

cnf(cls_lconf__hext_0,axiom,
    ( c_Conform_Olconf(V_P,V_h_H,V_l,V_E,T_a)
    | ~ c_Objects_Ohext(V_h,V_h_H)
    | ~ c_Conform_Olconf(V_P,V_h,V_l,V_E,T_a) ) ).

cnf(cls_map__comp__simps_I2_J_0,axiom,
    ( hAPP(V_m2,V_k) != hAPP(c_Option_Ooption_OSome(T_a),V_k_H)
    | c_Map_Omap__comp(V_m1,V_m2,V_k,T_a,T_c,T_b) = hAPP(V_m1,V_k_H) ) ).

cnf(cls_ospec_1,axiom,
    ( ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Option__Xospec__1__1(hAPP(c_Option_Ooption_OSome(T_a),V_x),V_P,T_a)))
    | hBOOL(hAPP(V_P,V_x)) ) ).

cnf(cls_COMBI__def__raw_0,axiom,
    hAPP(c_COMBI(t_a),v_P) = v_P ).

cnf(cls_map__add__find__right_0,axiom,
    ( hAPP(V_n,V_k) != hAPP(c_Option_Ooption_OSome(T_a),V_xx)
    | hAPP(c_Map_Omap__add(V_m,V_n,T_b,T_a),V_k) = hAPP(c_Option_Ooption_OSome(T_a),V_xx) ) ).

cnf(cls_map__add__Some__iff_2,axiom,
    ( hAPP(V_n,V_k) != hAPP(c_Option_Ooption_OSome(T_a),V_x)
    | hAPP(c_Map_Omap__add(V_m,V_n,T_b,T_a),V_k) = hAPP(c_Option_Ooption_OSome(T_a),V_x) ) ).

cnf(cls_fun__upd__idem__iff_0,axiom,
    ( c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_b) != V_f
    | hAPP(V_f,V_x) = V_y ) ).

cnf(cls_CHAINED_0,axiom,
    c_WellTypeRT_OWTrt(v_P,v_ha____,v_E____,c_Expr_Oexp_OBlock(v_V____,v_T____,v_ea____,tc_List_Olist(tc_String_Ochar)),v_Te____) ).

cnf(cls_CHAINED_0_01,axiom,
    c_TypeSafe__Mirabelle_Osconf(v_P,v_E____,c_Pair(v_ha____,v_la____,tc_fun(tc_nat,tc_Option_Ooption(tc_prod(tc_List_Olist(tc_String_Ochar),tc_fun(tc_prod(tc_List_Olist(tc_String_Ochar),tc_List_Olist(tc_String_Ochar)),tc_Option_Ooption(tc_Value_Oval))))),tc_fun(tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Value_Oval)))) ).

cnf(cls_conjecture_0,negated_conjecture,
    ~ c_Conform_Olconf(v_P,v_h_Ha____,v_l_Ha____,c_Fun_Ofun__upd(v_E____,v_V____,hAPP(c_Option_Ooption_OSome(tc_Type_Oty),v_T____),tc_List_Olist(tc_String_Ochar),tc_Option_Ooption(tc_Type_Oty)),tc_prod(tc_List_Olist(tc_List_Olist(tc_String_Ochar)),tc_Expr_Oexp(tc_List_Olist(tc_String_Ochar)))) ).

cnf(clsarity_fun__Lattices_Oboolean__algebra,axiom,
    ( class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))
    | ~ class_Lattices_Oboolean__algebra(T_1) ) ).

cnf(clsarity_fun__Orderings_Otop,axiom,
    ( class_Orderings_Otop(tc_fun(T_2,T_1))
    | ~ class_Orderings_Otop(T_1) ) ).

cnf(clsarity_fun__Orderings_Obot,axiom,
    ( class_Orderings_Obot(tc_fun(T_2,T_1))
    | ~ class_Orderings_Obot(T_1) ) ).

cnf(clsarity_fun__HOL_Ouminus,axiom,
    ( class_HOL_Ouminus(tc_fun(T_2,T_1))
    | ~ class_HOL_Ouminus(T_1) ) ).

cnf(clsarity_fun__HOL_Ominus,axiom,
    ( class_HOL_Ominus(tc_fun(T_2,T_1))
    | ~ class_HOL_Ominus(T_1) ) ).

cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__mult,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ).

cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat) ).

cnf(clsarity_nat__Orderings_Obot,axiom,
    class_Orderings_Obot(tc_nat) ).

cnf(clsarity_nat__HOL_Ominus,axiom,
    class_HOL_Ominus(tc_nat) ).

cnf(clsarity_bool__Lattices_Oboolean__algebra,axiom,
    class_Lattices_Oboolean__algebra(tc_bool) ).

cnf(clsarity_bool__Orderings_Otop,axiom,
    class_Orderings_Otop(tc_bool) ).

cnf(clsarity_bool__Orderings_Obot,axiom,
    class_Orderings_Obot(tc_bool) ).

cnf(clsarity_bool__HOL_Ouminus,axiom,
    class_HOL_Ouminus(tc_bool) ).

cnf(clsarity_bool__HOL_Ominus,axiom,
    class_HOL_Ominus(tc_bool) ).

cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
    hBOOL(c_fequal(V_x,V_x,T_a)) ).

cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom,
    ( V_X = V_Y
    | ~ hBOOL(c_fequal(V_X,V_Y,T_a)) ) ).

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