TPTP Problem File: SWV830-1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SWV830-1 : TPTP v8.2.0. Released v4.1.0.
% Domain : Software Verification
% Problem : Hoare logic with procedures 183_1
% Version : Especial.
% English : Completeness is taken relative to completeness of the underlying
% logic. Two versions of completeness proof: nested single recursion
% and simultaneous recursion in call rule.
% Refs : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe
% : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% Source : [Nip10]
% Names : Hoare-183_1 [Nip10]
% Status : Unsatisfiable
% Rating : 1.00 v4.1.0
% Syntax : Number of clauses : 720 ( 184 unt; 110 nHn; 374 RR)
% Number of literals : 1666 ( 430 equ; 865 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 35 ( 34 usr; 0 prp; 1-6 aty)
% Number of functors : 72 ( 72 usr; 18 con; 0-6 aty)
% Number of variables : 2570 ( 318 sgn)
% SPC : CNF_UNS_RFO_SEQ_NHN
% Comments :
%------------------------------------------------------------------------------
cnf(cls_linorder_Odual__linorder_0,axiom,
( c_Orderings_Olinorder(c_COMBC(V_less__eq,T_a,T_a,tc_bool),c_COMBC(V_less,T_a,T_a,tc_bool),T_a)
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_Diff__Int__distrib_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_B)) ).
cnf(cls_Diff__Int__distrib2_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)) ).
cnf(cls_setsum__empty_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_Finite__Set_Osetsum(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
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_evaln__Suc_0,axiom,
( c_Natural_Oevaln(V_c,V_s,c_Suc(V_n),V_s_H)
| ~ c_Natural_Oevaln(V_c,V_s,V_n,V_s_H) ) ).
cnf(cls_Diff__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_C),V_D)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_D),V_B))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_C)) ) ).
cnf(cls_inf__top__right_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ).
cnf(cls_inf__top__left_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ).
cnf(cls_Int__UNIV__left_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))),V_B) = V_B ).
cnf(cls_Int__UNIV__right_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))) = V_A ).
cnf(cls_image__vimage__eq_0,axiom,
hAPP(c_Set_Oimage(V_f,T_b,T_a),hAPP(c_Set_Ovimage(V_f,T_b,T_a),V_A)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(c_Set_Oimage(V_f,T_b,T_a),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)))) ).
cnf(cls_distrib__sup__le_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_z)))) ) ).
cnf(cls_Diff__Int2_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C)),V_B) ).
cnf(cls_less__le__not__le_2,axiom,
( ~ class_Orderings_Opreorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_psubset__eq_1,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_x),V_x)) ).
cnf(cls_less__fun__def_2,axiom,
( ~ class_HOL_Oord(T_b)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,T_b)),V_f),V_g))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,T_b)),V_g),V_f))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,T_b)),V_f),V_g)) ) ).
cnf(cls_order__less__le_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_x)) ) ).
cnf(cls_linorder__neq__iff_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_x)) ) ).
cnf(cls_order__less__irrefl_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_x)) ) ).
cnf(cls_top1I_0,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_x)) ).
cnf(cls_card__eq__0__iff_2,axiom,
( c_Finite__Set_Ocard(V_A,T_a) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_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_psubset__insert__iff_3,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_B)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B)) ) ).
cnf(cls_psubset__insert__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_B))) ) ).
cnf(cls_inf__eq__top__eq1_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_A),V_B) != c_Orderings_Otop__class_Otop(T_a)
| V_A = c_Orderings_Otop__class_Otop(T_a) ) ).
cnf(cls_inf__eq__top__eq2_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_A),V_B) != c_Orderings_Otop__class_Otop(T_a)
| V_B = c_Orderings_Otop__class_Otop(T_a) ) ).
cnf(cls_setsum__infinite_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_b)
| c_Finite__Set_Osetsum(V_f,V_A,T_a,T_b) = c_HOL_Ozero__class_Ozero(T_b)
| c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_setsum__def_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_Finite__Set_Osetsum(V_f,V_A,T_b,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| c_Finite__Set_Ofinite(V_A,T_b) ) ).
cnf(cls_Int__left__commute_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C)) ).
cnf(cls_Int__assoc_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)) ).
cnf(cls_inf__assoc_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z)) ) ).
cnf(cls_inf__left__commute_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_z)) ) ).
cnf(cls_inf__sup__aci_I3_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_z)) ) ).
cnf(cls_inf__sup__aci_I2_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z)) ) ).
cnf(cls_endo__inj__surj_0,axiom,
( hAPP(c_Set_Oimage(V_f,T_a,T_a),V_A) = V_A
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(c_Set_Oimage(V_f,T_a,T_a),V_A)),V_A))
| ~ c_Finite__Set_Ofinite(V_A,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_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_atLeastatMost__subset__iff_2,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a)),c_SetInterval_Oord__class_OatLeastAtMost(V_c,V_d,T_a)))
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b)) ) ).
cnf(cls_ab__semigroup__mult_Omult__commute_0,axiom,
( hAPP(hAPP(V_times,V_a),V_b) = hAPP(hAPP(V_times,V_b),V_a)
| ~ c_OrderedGroup_Oab__semigroup__mult(V_times,T_a) ) ).
cnf(cls_ab__semigroup__mult_Omult__left__commute_0,axiom,
( hAPP(hAPP(V_times,V_a),hAPP(hAPP(V_times,V_b),V_c)) = hAPP(hAPP(V_times,V_b),hAPP(hAPP(V_times,V_a),V_c))
| ~ c_OrderedGroup_Oab__semigroup__mult(V_times,T_a) ) ).
cnf(cls_ab__semigroup__mult_Omult__ac_I1_J_0,axiom,
( hAPP(hAPP(V_times,hAPP(hAPP(V_times,V_a),V_b)),V_c) = hAPP(hAPP(V_times,V_a),hAPP(hAPP(V_times,V_b),V_c))
| ~ c_OrderedGroup_Oab__semigroup__mult(V_times,T_a) ) ).
cnf(cls_UNIV__I_0,axiom,
hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)))) ).
cnf(cls_Un__Int__assoc__eq_1,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),V_A)) ) ).
cnf(cls_Un__Int__assoc__eq_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),V_A)) ) ).
cnf(cls_atLeastatMost__subset__iff_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_c),V_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a)),c_SetInterval_Oord__class_OatLeastAtMost(V_c,V_d,T_a))) ) ).
cnf(cls_atLeastatMost__subset__iff_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_d))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a)),c_SetInterval_Oord__class_OatLeastAtMost(V_c,V_d,T_a))) ) ).
cnf(cls_atLeastatMost__subset__iff_3,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a)),c_SetInterval_Oord__class_OatLeastAtMost(V_c,V_d,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_d))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_c),V_a)) ) ).
cnf(cls_image__Int__subset_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(c_Set_Oimage(V_f,T_b,T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_b,tc_bool)),V_A),V_B))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(c_Set_Oimage(V_f,T_b,T_a),V_A)),hAPP(c_Set_Oimage(V_f,T_b,T_a),V_B)))) ).
cnf(cls_class__ringb_Osubr0__iff_1,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_x) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_diff__self_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_diff__0__right_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a ) ).
cnf(cls_right__minus__eq_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_x) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_eq__iff__diff__eq__0_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_x) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_image__Int_0,axiom,
( hAPP(c_Set_Oimage(V_f,T_a,T_b),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_b,tc_bool)),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A)),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_B))
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_finite__Diff2_1,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_B,T_a) ) ).
cnf(cls_finite__Diff2_0,axiom,
( c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),T_a)
| ~ c_Finite__Set_Ofinite(V_B,T_a) ) ).
cnf(cls_lessThan__iff_1,axiom,
( ~ class_HOL_Oord(T_a)
| hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord__class_OlessThan(V_k,T_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_i),V_k)) ) ).
cnf(cls_lessThan__iff_0,axiom,
( ~ class_HOL_Oord(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_i),V_k))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord__class_OlessThan(V_k,T_a))) ) ).
cnf(cls_setsum__0_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_Finite__Set_Osetsum(c_COMBK(c_HOL_Ozero__class_Ozero(T_a),T_a,T_b),V_A,T_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_vimage__UNIV_0,axiom,
hAPP(c_Set_Ovimage(V_f,T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) ).
cnf(cls_setsum__eq__0__iff_0,axiom,
( c_Finite__Set_Osetsum(V_f,V_F,T_a,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Finite__Set_Ofinite(V_F,T_a)
| hAPP(V_f,V_x) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_F)) ) ).
cnf(cls_Zero__neq__Suc_0,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m) ).
cnf(cls_nat_Osimps_I2_J_0,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) ).
cnf(cls_finite__Diff_0,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_below__fold1__iff_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_xa))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xa),V_A))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_A,T_a)))
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_inj__image__subset__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_b,tc_bool)),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A)),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_B)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_inj__image__subset__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_b,tc_bool)),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A)),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_B)))
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_inj__on__image__Int_0,axiom,
( hAPP(c_Set_Oimage(V_f,T_a,T_b),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_b,tc_bool)),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A)),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_B))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_C))
| ~ c_Fun_Oinj__on(V_f,V_C,T_a,T_b) ) ).
cnf(cls_finite__surj_0,axiom,
( c_Finite__Set_Ofinite(V_B,T_b)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_b,tc_bool)),V_B),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A)))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_fold__graph__imp__finite_0,axiom,
( c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Finite__Set_Ofold__graph(V_f,V_z,V_A,V_x,T_a,T_b) ) ).
cnf(cls_finite__vimageI_0,axiom,
( c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(V_h,T_b,T_a),V_F),T_b)
| ~ c_Fun_Oinj__on(V_h,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_a)
| ~ c_Finite__Set_Ofinite(V_F,T_a) ) ).
cnf(cls_order__less__trans_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_z))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_psubset__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_C))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_psubsetD_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_xt1_I10_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_z),V_x))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_z),V_y))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x)) ) ).
cnf(cls_dual__linorder_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_Orderings_Olinorder(c_COMBC(c_lessequals(T_a),T_a,T_a,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(T_a),T_a,T_a,tc_bool),T_a) ) ).
cnf(cls_not__leE_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x)) ) ).
cnf(cls_linorder__antisym__conv2_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_x))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_x)) ) ).
cnf(cls_linorder__antisym__conv1_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_x))
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_x)) ) ).
cnf(cls_linorder__not__less_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x)) ) ).
cnf(cls_linorder__not__less_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_linorder__not__le_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x)) ) ).
cnf(cls_linorder__not__le_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x))
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_less__fun__def_1,axiom,
( ~ class_HOL_Oord(T_b)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,T_b)),V_g),V_f))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,T_b)),V_f),V_g)) ) ).
cnf(cls_less__le__not__le_1,axiom,
( ~ class_Orderings_Opreorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_evaln_OSemi_0,axiom,
( c_Natural_Oevaln(c_Com_Ocom_OSemi(V_c0,V_c1),V_s0,V_n,V_s2)
| ~ c_Natural_Oevaln(V_c1,V_s1,V_n,V_s2)
| ~ c_Natural_Oevaln(V_c0,V_s0,V_n,V_s1) ) ).
cnf(cls_Max__mono_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),c_Finite__Set_Olinorder__class_OMax(V_M,T_a)),c_Finite__Set_Olinorder__class_OMax(V_N,T_a)))
| ~ c_Finite__Set_Ofinite(V_N,T_a)
| V_M = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_M),V_N)) ) ).
cnf(cls_linorder_Oneq__iff_1,axiom,
( ~ hBOOL(hAPP(hAPP(V_less,V_x),V_x))
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_linorder_Onot__less__iff__gr__or__eq_2,axiom,
( ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a)
| ~ hBOOL(hAPP(hAPP(V_less,V_x),V_x)) ) ).
cnf(cls_lessThan__subset__iff_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OlessThan(V_x,T_a)),c_SetInterval_Oord__class_OlessThan(V_y,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_lessThan__subset__iff_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OlessThan(V_x,T_a)),c_SetInterval_Oord__class_OlessThan(V_y,T_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),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B))) ) ).
cnf(cls_IntE_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B))) ) ).
cnf(cls_UN__simps_I5_J_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_C,c_COMBB(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B,tc_fun(T_a,tc_bool),tc_fun(T_a,tc_bool),T_b),T_b,tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_C,V_B,T_b,tc_fun(T_a,tc_bool))) ).
cnf(cls_SUP__UN__eq_0,axiom,
hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),c_COMBB(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),V_r,tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool),T_b),T_b,tc_fun(t_a,tc_bool)),v_x) = hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),V_r,T_b,tc_fun(t_a,tc_bool))) ).
cnf(cls_Int__absorb2_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_A
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_Int__absorb1_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_B
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_A)) ) ).
cnf(cls_le__iff__inf_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) = V_x
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_le__iff__inf_1,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) != V_x
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_inf__absorb2_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) = V_y
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x)) ) ).
cnf(cls_Int__commute_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_A) ).
cnf(cls_inf__commute_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_x) ) ).
cnf(cls_inf__sup__aci_I1_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_x) ) ).
cnf(cls_lessThan__eq__iff_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_SetInterval_Oord__class_OlessThan(V_x,T_a) != c_SetInterval_Oord__class_OlessThan(V_y,T_a)
| V_x = V_y ) ).
cnf(cls_distrib__inf__le_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_z))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z)))) ) ).
cnf(cls_Diff__subset_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)),V_A)) ).
cnf(cls_class__ringb_Osubr0__iff_0,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y) != c_HOL_Ozero__class_Ozero(T_a)
| V_x = V_y ) ).
cnf(cls_right__minus__eq_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b) != c_HOL_Ozero__class_Ozero(T_a)
| V_a = V_b ) ).
cnf(cls_eq__iff__diff__eq__0_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b) != c_HOL_Ozero__class_Ozero(T_a)
| V_a = V_b ) ).
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_ab__semigroup__mult_Ofold__graph__insert__swap_0,axiom,
( c_Finite__Set_Ofold__graph(V_times,V_z,hAPP(hAPP(c_Set_Oinsert(T_a),V_b),V_A),hAPP(hAPP(V_times,V_z),V_y),T_a,T_a)
| hBOOL(hAPP(hAPP(c_in(T_a),V_b),V_A))
| ~ c_Finite__Set_Ofold__graph(V_times,V_b,V_A,V_y,T_a,T_a)
| ~ c_OrderedGroup_Oab__semigroup__mult(V_times,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,hAPP(c_Set_Oimage(V_f,T_a,T_a),V_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_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,hAPP(c_Set_Oimage(V_f,T_a,T_a),V_A),T_a,T_b)
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_a) ) ).
cnf(cls_inj__on__image__iff_5,axiom,
( c_Fun_Oinj__on(V_g,hAPP(c_Set_Oimage(V_f,T_a,T_a),V_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_4,axiom,
( c_Fun_Oinj__on(V_g,V_A,T_a,T_b)
| ~ c_Fun_Oinj__on(V_g,hAPP(c_Set_Oimage(V_f,T_a,T_a),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_vimage__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_b,tc_bool)),hAPP(c_Set_Ovimage(V_f,T_b,T_a),V_A)),hAPP(c_Set_Ovimage(V_f,T_b,T_a),V_B)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
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_card__eq__UNIV__imp__eq__UNIV_0,axiom,
( c_Finite__Set_Ocard(V_A,T_a) != c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a)
| V_A = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Inf__set__fold_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| c_Complete__Lattice_OInf__class_OInf(c_List_Oset(V_xs,T_a),T_a) = c_List_Ofoldl(c_Lattices_Olower__semilattice__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a),V_xs,T_a,T_a) ) ).
cnf(cls_Int__subset__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),V_B))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B))) ) ).
cnf(cls_Int__subset__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),V_A))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B))) ) ).
cnf(cls_le__infE_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b))) ) ).
cnf(cls_atLeastatMost__psubset__iff_6,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a)),c_SetInterval_Oord__class_OatLeastAtMost(V_c,V_d,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_c),V_d))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_d))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_d))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_c),V_a)) ) ).
cnf(cls_atLeastatMost__psubset__iff_5,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a)),c_SetInterval_Oord__class_OatLeastAtMost(V_c,V_d,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_c),V_d))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_c),V_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_d))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_c),V_a)) ) ).
cnf(cls_pred__subset__eq_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_R),V_S))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_R)),hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_S))) ) ).
cnf(cls_pred__subset__eq_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_R)),hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_S)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_R),V_S)) ) ).
cnf(cls_linorder__neqE__ordered__idom_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| V_x = V_y ) ).
cnf(cls_not__less__iff__gr__or__eq_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| V_x = V_y
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_equalityI_0,axiom,
( V_A = V_B
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_A))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_set__eq__subset_2,axiom,
( V_A = V_B
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_A))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_order__eq__iff_2,axiom,
( ~ class_Orderings_Oorder(T_a)
| V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_linorder__neqE_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| V_x = V_y ) ).
cnf(cls_order__antisym_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_order__antisym__conv_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x)) ) ).
cnf(cls_linorder__less__linear_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x))
| V_x = V_y
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_linorder__antisym__conv3_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| V_x = V_y
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x)) ) ).
cnf(cls_le__iff__diff__le__0_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)),c_HOL_Ozero__class_Ozero(T_a))) ) ).
cnf(cls_le__iff__diff__le__0_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)),c_HOL_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b)) ) ).
cnf(cls_less__infI2_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b)),V_x))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_x)) ) ).
cnf(cls_less__infI1_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b)),V_x))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_x)) ) ).
cnf(cls_psubset__eq_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_less__fun__def_0,axiom,
( ~ class_HOL_Oord(T_b)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,T_b)),V_f),V_g))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,T_b)),V_f),V_g)) ) ).
cnf(cls_order__le__less_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_order__less__imp__le_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_evaln_OSkip_0,axiom,
c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_s) ).
cnf(cls_inf__Int__eq_0,axiom,
hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),V_R)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),V_S)),v_x) = hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,tc_bool)),V_R),V_S)) ).
cnf(cls_nat_Osimps_I3_J_0,axiom,
c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat) ).
cnf(cls_Suc__neq__Zero_0,axiom,
c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat) ).
cnf(cls_psubset__insert__iff_7,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_B)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_less__iff__diff__less__0_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)),c_HOL_Ozero__class_Ozero(T_a))) ) ).
cnf(cls_less__iff__diff__less__0_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)),c_HOL_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)) ) ).
cnf(cls_linorder_Onot__less__iff__gr__or__eq_1,axiom,
( ~ hBOOL(hAPP(hAPP(V_less,V_x),V_y))
| ~ hBOOL(hAPP(hAPP(V_less,V_y),V_x))
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_linorder_OleD_0,axiom,
( ~ hBOOL(hAPP(hAPP(V_less,V_x),V_y))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_y),V_x))
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_linorder_OleI_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,V_y),V_x))
| hBOOL(hAPP(hAPP(V_less,V_x),V_y))
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_linorder_Olinear_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,V_y),V_x))
| hBOOL(hAPP(hAPP(V_less__eq,V_x),V_y))
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_linorder_Onot__le_0,axiom,
( hBOOL(hAPP(hAPP(V_less,V_y),V_x))
| hBOOL(hAPP(hAPP(V_less__eq,V_x),V_y))
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_linorder_Onot__le_1,axiom,
( ~ hBOOL(hAPP(hAPP(V_less__eq,V_x),V_y))
| ~ hBOOL(hAPP(hAPP(V_less,V_y),V_x))
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_linorder_Onot__leE_0,axiom,
( hBOOL(hAPP(hAPP(V_less,V_x),V_y))
| hBOOL(hAPP(hAPP(V_less__eq,V_y),V_x))
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_linorder_Oantisym__conv1_1,axiom,
( hBOOL(hAPP(hAPP(V_less,V_x),V_x))
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a)
| hBOOL(hAPP(hAPP(V_less__eq,V_x),V_x)) ) ).
cnf(cls_linorder_Oantisym__conv2_1,axiom,
( ~ hBOOL(hAPP(hAPP(V_less__eq,V_x),V_x))
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a)
| ~ hBOOL(hAPP(hAPP(V_less,V_x),V_x)) ) ).
cnf(cls_card__insert__if_0,axiom,
( c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_A),T_a) = c_Finite__Set_Ocard(V_A,T_a)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
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_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__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__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__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_fold1__belowI_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_A,T_a)),V_a))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_card__bij__eq_0,axiom,
( c_Finite__Set_Ocard(V_A,T_a) = c_Finite__Set_Ocard(V_B,T_b)
| ~ c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(c_Set_Oimage(V_g,T_b,T_a),V_B)),V_A))
| ~ c_Fun_Oinj__on(V_g,V_B,T_b,T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_b,tc_bool)),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A)),V_B))
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
cnf(cls_inf__sup__ord_I1_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)),V_x)) ) ).
cnf(cls_inf__sup__ord_I2_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)),V_y)) ) ).
cnf(cls_inf__greatest_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_le__inf__iff_2,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_le__infI_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_a)) ) ).
cnf(cls_inf__le2_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)),V_y)) ) ).
cnf(cls_inf__le1_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)),V_x)) ) ).
cnf(cls_Int__lower1_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),V_A)) ).
cnf(cls_Int__lower2_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),V_B)) ).
cnf(cls_Int__greatest_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),V_B))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),V_A)) ) ).
cnf(cls_Int__subset__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),V_B))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),V_A)) ) ).
cnf(cls_subset__UNIV_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)))) ).
cnf(cls_top__greatest_0,axiom,
( ~ class_Orderings_Otop(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ).
cnf(cls_inf__sup__aci_I4_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) ) ).
cnf(cls_inf__left__idem_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) ) ).
cnf(cls_Int__left__absorb_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) ).
cnf(cls_finite__set_0,axiom,
c_Finite__Set_Ofinite(c_List_Oset(V_xs,T_a),T_a) ).
cnf(cls_finite__UNIV_0,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(T_a)
| c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a) ) ).
cnf(cls_inf__idem_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_x) = V_x ) ).
cnf(cls_Int__absorb_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_A) = V_A ).
cnf(cls_inf__fun__eq_0,axiom,
( ~ class_Lattices_Olattice(T_b)
| hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,T_b)),V_f),V_g),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_b),hAPP(V_f,v_x)),hAPP(V_g,v_x)) ) ).
cnf(cls_xt1_I6_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_z),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_z),V_y))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x)) ) ).
cnf(cls_xt1_I7_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_z),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_z),V_y))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x)) ) ).
cnf(cls_xt1_I8_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_z),V_x))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_z),V_y))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x)) ) ).
cnf(cls_order__trans_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_set__mp_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_subsetD_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_equalityE_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_x),V_x)) ).
cnf(cls_set__rev__mp_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_subset__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_subset__refl_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_A)) ).
cnf(cls_subset__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_subset__inj__on_0,axiom,
( c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ c_Fun_Oinj__on(V_f,V_B,T_a,T_b) ) ).
cnf(cls_predicate1D_0,axiom,
( hBOOL(hAPP(V_Q,V_x))
| ~ hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_P),V_Q)) ) ).
cnf(cls_order__eq__iff_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_x)) ) ).
cnf(cls_order__eq__refl_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_x)) ) ).
cnf(cls_finite__subset_0,axiom,
( c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_psubset__subset__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_subset__psubset__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_C))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_rev__predicate1D_0,axiom,
( hBOOL(hAPP(V_Q,V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_P),V_Q))
| ~ hBOOL(hAPP(V_P,V_x)) ) ).
cnf(cls_rev__finite__subset_0,axiom,
( c_Finite__Set_Ofinite(V_A,T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ c_Finite__Set_Ofinite(V_B,T_a) ) ).
cnf(cls_order__le__less__trans_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_order__less__le__trans_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_z))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_atLeastatMost__psubset__iff_3,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_c),V_d))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a)),c_SetInterval_Oord__class_OatLeastAtMost(V_c,V_d,T_a))) ) ).
cnf(cls_card__eq__0__iff_0,axiom,
( c_Finite__Set_Ocard(V_A,T_a) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Int__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_D)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_D))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_C)) ) ).
cnf(cls_Int__Diff_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_B),V_C)) ).
cnf(cls_eq__card__imp__inj__on_0,axiom,
( c_Finite__Set_Ocard(hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A),T_b) != c_Finite__Set_Ocard(V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
cnf(cls_inj__on__iff__eq__card_0,axiom,
( c_Finite__Set_Ocard(hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A),T_b) = c_Finite__Set_Ocard(V_A,T_a)
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_linorder_Onot__less__iff__gr__or__eq_0,axiom,
( V_x = V_y
| hBOOL(hAPP(hAPP(V_less,V_y),V_x))
| hBOOL(hAPP(hAPP(V_less,V_x),V_y))
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_linorder_OneqE_0,axiom,
( hBOOL(hAPP(hAPP(V_less,V_y),V_x))
| hBOOL(hAPP(hAPP(V_less,V_x),V_y))
| V_x = V_y
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_linorder_Oless__linear_0,axiom,
( hBOOL(hAPP(hAPP(V_less,V_y),V_x))
| V_x = V_y
| hBOOL(hAPP(hAPP(V_less,V_x),V_y))
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_linorder_Oantisym__conv3_0,axiom,
( V_x = V_y
| hBOOL(hAPP(hAPP(V_less,V_x),V_y))
| hBOOL(hAPP(hAPP(V_less,V_y),V_x))
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_IntI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A)) ) ).
cnf(cls_le__infE_1,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b))) ) ).
cnf(cls_le__infI1_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b)),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_x)) ) ).
cnf(cls_le__infI2_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b)),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_x)) ) ).
cnf(cls_le__inf__iff_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z))) ) ).
cnf(cls_le__inf__iff_1,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z))) ) ).
cnf(cls_Int__UN__distrib_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_I,V_A,T_b,tc_fun(T_a,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_I,c_COMBB(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_A,tc_fun(T_a,tc_bool),tc_fun(T_a,tc_bool),T_b),T_b,tc_fun(T_a,tc_bool)) ).
cnf(cls_UN__extend__simps_I5_J_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_C,V_B,T_b,tc_fun(T_a,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_C,c_COMBB(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B,tc_fun(T_a,tc_bool),tc_fun(T_a,tc_bool),T_b),T_b,tc_fun(T_a,tc_bool)) ).
cnf(cls_setsum__diff_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_b)
| c_Finite__Set_Osetsum(V_f,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_b),c_Finite__Set_Osetsum(V_f,V_A,T_a,T_b)),c_Finite__Set_Osetsum(V_f,V_B,T_a,T_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_A))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_atLeastatMost__psubset__iff_2,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_d))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_c),V_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a)),c_SetInterval_Oord__class_OatLeastAtMost(V_c,V_d,T_a))) ) ).
cnf(cls_ab__semigroup__mult_Ofold1__Un_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| V_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_OrderedGroup_Oab__semigroup__mult(V_times,T_a)
| c_Finite__Set_Ofold1(V_times,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),T_a) = hAPP(hAPP(V_times,c_Finite__Set_Ofold1(V_times,V_A,T_a)),c_Finite__Set_Ofold1(V_times,V_B,T_a)) ) ).
cnf(cls_finite_0,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(T_a)
| c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_card__empty_0,axiom,
c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) = c_HOL_Ozero__class_Ozero(tc_nat) ).
cnf(cls_linorder_Oantisym__conv2_0,axiom,
( V_x = V_y
| hBOOL(hAPP(hAPP(V_less,V_x),V_y))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_x),V_y))
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_linorder_Oantisym__conv1_0,axiom,
( V_x = V_y
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_x),V_y))
| hBOOL(hAPP(hAPP(V_less,V_x),V_y))
| ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a) ) ).
cnf(cls_inf1E_1,axiom,
( hBOOL(hAPP(V_B,V_x))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),V_x)) ) ).
cnf(cls_inf1E_0,axiom,
( hBOOL(hAPP(V_A,V_x))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),V_x)) ) ).
cnf(cls_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_finite__surj__inj_0,axiom,
( c_Fun_Oinj__on(V_f,V_A,T_a,T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),hAPP(c_Set_Oimage(V_f,T_a,T_a),V_A)))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_evaln__elim__cases_I1_J_0,axiom,
( V_t = V_s
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) ) ).
cnf(cls_Sup__UNIV_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| c_Complete__Lattice_OSup__class_OSup(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a) = c_Orderings_Otop__class_Otop(T_a) ) ).
cnf(cls_atLeastatMost__psubset__iff_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_c),V_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a)),c_SetInterval_Oord__class_OatLeastAtMost(V_c,V_d,T_a))) ) ).
cnf(cls_atLeastatMost__psubset__iff_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_d))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a)),c_SetInterval_Oord__class_OatLeastAtMost(V_c,V_d,T_a))) ) ).
cnf(cls_vimage__Int_0,axiom,
hAPP(c_Set_Ovimage(V_f,T_a,T_b),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_b,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(c_Set_Ovimage(V_f,T_a,T_b),V_A)),hAPP(c_Set_Ovimage(V_f,T_a,T_b),V_B)) ).
cnf(cls_finite__Int_1,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_F),V_G),T_a)
| ~ c_Finite__Set_Ofinite(V_G,T_a) ) ).
cnf(cls_finite__Int_0,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_F),V_G),T_a)
| ~ c_Finite__Set_Ofinite(V_F,T_a) ) ).
cnf(cls_evaln__evalc_0,axiom,
( c_Natural_Oevalc(V_c,V_s,V_t)
| ~ c_Natural_Oevaln(V_c,V_s,V_n,V_t) ) ).
cnf(cls_eval__eq_1,axiom,
( c_Natural_Oevalc(V_c,V_s,V_t)
| ~ c_Natural_Oevaln(V_c,V_s,V_x,V_t) ) ).
cnf(cls_le__funD_0,axiom,
( ~ class_HOL_Oord(T_b)
| hBOOL(hAPP(hAPP(c_lessequals(T_b),hAPP(V_f,V_x)),hAPP(V_g,V_x)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,T_b)),V_f),V_g)) ) ).
cnf(cls_inf__bot__left_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = c_Orderings_Obot__class_Obot(T_a) ) ).
cnf(cls_inf__bot__right_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
cnf(cls_bot__least_0,axiom,
( ~ class_Orderings_Obot(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ).
cnf(cls_subset__empty_1,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) ).
cnf(cls_subset__empty_0,axiom,
( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) ) ).
cnf(cls_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_not__psubset__empty_0,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) ).
cnf(cls_finite_OemptyI_0,axiom,
c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ).
cnf(cls_empty__fold__graphE_0,axiom,
( V_x = V_z
| ~ c_Finite__Set_Ofold__graph(V_f,V_z,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x,T_a,T_b) ) ).
cnf(cls_Int__empty__right_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_Int__empty__left_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),V_B) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_empty__subsetI_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),V_A)) ).
cnf(cls_fold__graph_OemptyI_0,axiom,
c_Finite__Set_Ofold__graph(V_f,V_z,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_z,T_a,T_b) ).
cnf(cls_fold__graph_H_Ointros_I1_J_0,axiom,
c_Nitpick_Ofold__graph_H(V_f,V_z,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_z,T_a,T_b) ).
cnf(cls_finite__range__imageI_0,axiom,
( c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(c_COMBB(V_f,V_g,T_a,T_c,T_b),T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool))),T_c)
| ~ c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(V_g,T_b,T_a),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool))),T_a) ) ).
cnf(cls_insert__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_C)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_D)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),V_D)) ) ).
cnf(cls_finite__insert_1,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_A),T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_finite__insert_0,axiom,
( c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_A),T_a) ) ).
cnf(cls_subset__insertI_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B))) ).
cnf(cls_insert__inter__insert_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_A)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)) ).
cnf(cls_subset__insertI2_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_b),V_B)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_insert__subset_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_A)),V_B)) ) ).
cnf(cls_le__supE_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b)),V_x)) ) ).
cnf(cls_le__supE_1,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b)),V_x)) ) ).
cnf(cls_le__supI1_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_a)) ) ).
cnf(cls_le__supI2_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_b)) ) ).
cnf(cls_le__sup__iff_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)),V_z)) ) ).
cnf(cls_le__sup__iff_1,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)),V_z)) ) ).
cnf(cls_sup__inf__distrib1_0,axiom,
( ~ class_Lattices_Odistrib__lattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_z)) ) ).
cnf(cls_sup__inf__distrib2_0,axiom,
( ~ class_Lattices_Odistrib__lattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_z),V_x)) ) ).
cnf(cls_le__iff__sup_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) = V_y
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_le__iff__sup_1,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) != V_y
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_sup__absorb1_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) = V_x
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x)) ) ).
cnf(cls_inf__sup__absorb_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)) = V_x ) ).
cnf(cls_sup__inf__absorb_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)) = V_x ) ).
cnf(cls_sup__top__left_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = c_Orderings_Otop__class_Otop(T_a) ) ).
cnf(cls_sup__top__right_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
cnf(cls_inf__sup__distrib1_0,axiom,
( ~ class_Lattices_Odistrib__lattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_z)) ) ).
cnf(cls_inf__sup__distrib2_0,axiom,
( ~ class_Lattices_Odistrib__lattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_z),V_x)) ) ).
cnf(cls_le__supI_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b)),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_x)) ) ).
cnf(cls_sup__ge1_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y))) ) ).
cnf(cls_sup__ge2_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y))) ) ).
cnf(cls_sup__least_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z)),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_z),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x)) ) ).
cnf(cls_le__sup__iff_2,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_z)) ) ).
cnf(cls_inf__sup__ord_I4_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y))) ) ).
cnf(cls_inf__sup__ord_I3_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y))) ) ).
cnf(cls_less__supI1_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_a)) ) ).
cnf(cls_less__supI2_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_b)) ) ).
cnf(cls_subset__image__iff_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_b,tc_bool)),V_x),V_A))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(c_Set_Oimage(V_f,T_b,T_a),V_x)),hAPP(c_Set_Oimage(V_f,T_b,T_a),V_A))) ) ).
cnf(cls_image__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_b,tc_bool)),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A)),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_B)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_finite__imageI_0,axiom,
( c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(V_h,T_a,T_b),V_F),T_b)
| ~ c_Finite__Set_Ofinite(V_F,T_a) ) ).
cnf(cls_Un__subset__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C)) ) ).
cnf(cls_Un__subset__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C)) ) ).
cnf(cls_Un__Int__distrib2_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)),V_A) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_A)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_C),V_A)) ).
cnf(cls_Un__Int__distrib_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_C)) ).
cnf(cls_Un__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_C),V_D)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_D))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_C)) ) ).
cnf(cls_subset__Un__eq_1,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B) != V_B
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_Un__absorb2_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B) = V_A
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_A)) ) ).
cnf(cls_Un__absorb1_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B) = V_B
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_finite__Un_1,axiom,
( c_Finite__Set_Ofinite(V_G,T_a)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_F),V_G),T_a) ) ).
cnf(cls_finite__Un_0,axiom,
( c_Finite__Set_Ofinite(V_F,T_a)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_F),V_G),T_a) ) ).
cnf(cls_finite__UnI_0,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_F),V_G),T_a)
| ~ c_Finite__Set_Ofinite(V_G,T_a)
| ~ c_Finite__Set_Ofinite(V_F,T_a) ) ).
cnf(cls_finite__Un_2,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_F),V_G),T_a)
| ~ c_Finite__Set_Ofinite(V_G,T_a)
| ~ c_Finite__Set_Ofinite(V_F,T_a) ) ).
cnf(cls_Un__UNIV__right_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) ).
cnf(cls_Un__UNIV__left_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))),V_B) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) ).
cnf(cls_Int__Un__distrib2_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)),V_A) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A)) ).
cnf(cls_Int__Un__distrib_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C)) ).
cnf(cls_Un__subset__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_C)) ) ).
cnf(cls_Un__upper2_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B))) ).
cnf(cls_Un__upper1_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B))) ).
cnf(cls_Un__least_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_C)) ) ).
cnf(cls_Un__Int__crazy_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_C),V_A)) ).
cnf(cls_Int__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A)) ) ).
cnf(cls_inf1I_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),V_x))
| ~ hBOOL(hAPP(V_B,V_x))
| ~ hBOOL(hAPP(V_A,V_x)) ) ).
cnf(cls_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_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_double__diff_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_B),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_C),V_A)) = V_A
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_le__eqI_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x_H),V_y_H)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y_H),V_x_H))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x)) ) ).
cnf(cls_le__eqI_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x_H),V_y_H)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y_H),V_x_H)) ) ).
cnf(cls_less__eqI_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x_H),V_y_H)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x_H),V_y_H))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_less__eqI_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x_H),V_y_H)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x_H),V_y_H)) ) ).
cnf(cls_ivl__disj__int_I4_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OlessThan(V_l,T_a)),c_SetInterval_Oord__class_OatLeastAtMost(V_l,V_u,T_a)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_xt1_I11_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_a))
| V_a = V_b
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_a)) ) ).
cnf(cls_xt1_I12_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_a))
| V_a = V_b ) ).
cnf(cls_psubset__eq_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B))
| V_A = V_B
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_order__le__less_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| V_x = V_y
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_order__less__le_2,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_subset__iff__psubset__eq_0,axiom,
( V_A = V_B
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_order__le__neq__trans_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b))
| V_a = V_b
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b)) ) ).
cnf(cls_order__neq__le__trans_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b))
| V_a = V_b ) ).
cnf(cls_linorder__antisym__conv1_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_linorder__antisym__conv2_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| V_x = V_y
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_Max__ge_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),c_Finite__Set_Olinorder__class_OMax(V_A,T_a)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_atLeastatMost__psubset__iff_4,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a)),c_SetInterval_Oord__class_OatLeastAtMost(V_c,V_d,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_c),V_d))
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b)) ) ).
cnf(cls_xt1_I9_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_a)) ) ).
cnf(cls_not__less__iff__gr__or__eq_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x)) ) ).
cnf(cls_linorder__linear_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x))
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_order__less__asym_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_order__less__asym_H_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_a))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)) ) ).
cnf(cls_card__insert__if_1,axiom,
( c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_A),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_card__Suc__eq_4,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_xa))
| c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_xa),T_a) = c_Suc(c_Finite__Set_Ocard(V_xa,T_a))
| c_Finite__Set_Ocard(V_xa,T_a) = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
cnf(cls_the__inv__into__into_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),hAPP(c_Fun_Othe__inv__into(V_A,V_f,T_a,T_b),V_x)),V_B))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A)))
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
cnf(cls_psubset__insert__iff_9,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_B)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))),V_B))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_Sup__set__fold_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| c_Complete__Lattice_OSup__class_OSup(c_List_Oset(V_xs,T_a),T_a) = c_List_Ofoldl(c_Lattices_Oupper__semilattice__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a),V_xs,T_a,T_a) ) ).
cnf(cls_vimage__subsetI_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(c_Set_Ovimage(V_f,T_a,T_b),V_B)),V_A))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_b,tc_bool)),V_B),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A)))
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_disjoint__iff__not__equal_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_fold__graph_OinsertI_0,axiom,
( c_Finite__Set_Ofold__graph(V_f,V_z,hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_A),hAPP(hAPP(V_f,V_x),V_y),T_a,T_b)
| ~ c_Finite__Set_Ofold__graph(V_f,V_z,V_A,V_y,T_a,T_b)
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_Int__insert__left_1,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B)),V_C) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)
| hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_C)) ) ).
cnf(cls_Int__insert__right_1,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)
| hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)) ) ).
cnf(cls_subset__insert_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_B)))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_subset__insert_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_B)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_subset__insert__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_B))) ) ).
cnf(cls_subset__insert__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_B)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_insert__subset_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_A)),V_B)) ) ).
cnf(cls_psubset__insert__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_B))) ) ).
cnf(cls_psubset__insert__iff_6,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_B)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_Int__insert__left_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B)),V_C) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_C)) ) ).
cnf(cls_Int__insert__right_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)) ) ).
cnf(cls_insert__subset_2,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_A)),V_B))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B)) ) ).
cnf(cls_rangeI_0,axiom,
hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_x)),hAPP(c_Set_Oimage(V_f,T_b,T_a),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool))))) ).
cnf(cls_image__subset__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_x)),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(c_Set_Oimage(V_f,T_b,T_a),V_A)),V_B)) ) ).
cnf(cls_fun__upd__image_1,axiom,
( hAPP(c_Set_Oimage(c_Fun_Ofun__upd(V_f,V_x,V_y,T_b,T_a),T_b,T_a),V_A) = hAPP(c_Set_Oimage(V_f,T_b,T_a),V_A)
| hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A)) ) ).
cnf(cls_le__SUPI_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_b)
| hBOOL(hAPP(hAPP(c_lessequals(T_b),hAPP(V_M,V_i)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_M,T_a,T_b)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_i),V_A)) ) ).
cnf(cls_UN__upper_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_b,tc_bool)),hAPP(V_B,V_a)),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_a),V_a),V_A)) ) ).
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_UN__subset__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(V_A,V_x)),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_I))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_I,V_A,T_b,tc_fun(T_a,tc_bool))),V_B)) ) ).
cnf(cls_range__composition_0,axiom,
hAPP(c_Set_Oimage(c_COMBB(V_f,V_g,T_c,T_a,T_b),T_b,T_a),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool))) = hAPP(c_Set_Oimage(V_f,T_c,T_a),hAPP(c_Set_Oimage(V_g,T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)))) ).
cnf(cls_subset__singletonD_0,axiom,
( V_A = hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))) ) ).
cnf(cls_ab__semigroup__mult_Ofold__graph__permute__diff_0,axiom,
( c_Finite__Set_Ofold__graph(V_times,V_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_b),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))),V_x,T_a,T_a)
| hBOOL(hAPP(hAPP(c_in(T_a),V_b),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| ~ c_Finite__Set_Ofold__graph(V_times,V_b,V_A,V_x,T_a,T_a)
| ~ c_OrderedGroup_Oab__semigroup__mult(V_times,T_a) ) ).
cnf(cls_psubset__insert__iff_5,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_B)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))),V_B))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B)) ) ).
cnf(cls_setsum__diff1_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_b)
| c_Finite__Set_Osetsum(V_f,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),T_a,T_b) = c_Finite__Set_Osetsum(V_f,V_A,T_a,T_b)
| hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_card__Diff__singleton__if_1,axiom,
( c_Finite__Set_Ocard(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),T_a) = c_Finite__Set_Ocard(V_A,T_a)
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
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(hAPP(hAPP(c_in(T_a),V_x),V_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(hAPP(hAPP(c_in(T_aa),V_x),V_A)) ) ).
cnf(cls_Sup__upper_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),c_Complete__Lattice_OSup__class_OSup(V_A,T_a)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_atLeastatMost__empty_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_a)) ) ).
cnf(cls_atLeastatMost__empty__iff2_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b)) ) ).
cnf(cls_atLeastatMost__empty__iff2_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b)) ) ).
cnf(cls_atLeastatMost__empty__iff_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b)) ) ).
cnf(cls_atLeastatMost__empty__iff_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b)) ) ).
cnf(cls_UNION__empty__conv_I2_J_2,axiom,
( hAPP(V_B,c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__2__1(V_A,V_B,T_b,T_a)) != 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)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_UNION__empty__conv_I1_J_2,axiom,
( hAPP(V_B,c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__1__1(V_A,V_B,T_b,T_a)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| 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)) ) ).
cnf(cls_card__insert_0,axiom,
( c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_A),T_a) = c_Suc(c_Finite__Set_Ocard(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_ab__semigroup__mult_Ofold1__insert_0,axiom,
( c_Finite__Set_Ofold1(V_times,hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_A),T_a) = hAPP(hAPP(V_times,V_x),c_Finite__Set_Ofold1(V_times,V_A,T_a))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(V_times,T_a) ) ).
cnf(cls_Diff__disjoint_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_B),V_A)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_Diff__triv_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B) = V_A ) ).
cnf(cls_Diff__UNIV_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_UN__extend__simps_I10_J_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,c_COMBB(V_B,V_f,T_c,tc_fun(T_a,tc_bool),T_b),T_b,tc_fun(T_a,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(V_f,T_b,T_c),V_A),V_B,T_c,tc_fun(T_a,tc_bool)) ).
cnf(cls_image__UN_0,axiom,
hAPP(c_Set_Oimage(V_f,T_b,T_a),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_c,tc_fun(T_b,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,c_COMBB(c_Set_Oimage(V_f,T_b,T_a),V_B,tc_fun(T_b,tc_bool),tc_fun(T_a,tc_bool),T_c),T_c,tc_fun(T_a,tc_bool)) ).
cnf(cls_UN__simps_I10_J_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(V_f,T_c,T_b),V_A),V_B,T_b,tc_fun(T_a,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,c_COMBB(V_B,V_f,T_b,tc_fun(T_a,tc_bool),T_c),T_c,tc_fun(T_a,tc_bool)) ).
cnf(cls_finite__Diff__insert_0,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),T_a)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B)),T_a) ) ).
cnf(cls_finite__Diff__insert_1,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B)),T_a)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_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),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A),T_b,T_a)
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
cnf(cls_inj__image__eq__iff_0,axiom,
( hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A) != hAPP(c_Set_Oimage(V_f,T_a,T_b),V_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,
( hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(V_A,V_f,T_a,T_b),T_b,T_a),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A)) = V_A
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
cnf(cls_card__image_0,axiom,
( c_Finite__Set_Ocard(hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A),T_b) = c_Finite__Set_Ocard(V_A,T_a)
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
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(hAPP(c_Set_Oimage(V_f,T_b,T_a),V_A),T_a) ) ).
cnf(cls_image__diff__subset_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),hAPP(c_Set_Oimage(V_f,T_b,T_a),V_A)),hAPP(c_Set_Oimage(V_f,T_b,T_a),V_B))),hAPP(c_Set_Oimage(V_f,T_b,T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_b,tc_bool)),V_A),V_B)))) ).
cnf(cls_vimage__eq__UN_0,axiom,
hAPP(c_Set_Ovimage(V_f,T_a,T_b),V_B) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_B,c_COMBB(c_Set_Ovimage(V_f,T_a,T_b),hAPP(c_COMBC(c_Set_Oinsert(T_b),T_b,tc_fun(T_b,tc_bool),tc_fun(T_b,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))),tc_fun(T_b,tc_bool),tc_fun(T_a,tc_bool),T_b),T_b,tc_fun(T_a,tc_bool)) ).
cnf(cls_Diff__subset__conv_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C)) ) ).
cnf(cls_Diff__subset__conv_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C))) ) ).
cnf(cls_Diff__partition_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_B),V_A)) = V_B
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_Un__Diff__Int_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)) = V_A ).
cnf(cls_Diff__Un_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_C)) ).
cnf(cls_Diff__Int_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_C)) ).
cnf(cls_Inf__lower_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),c_Complete__Lattice_OInf__class_OInf(V_A,T_a)),V_x))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_Inf__UNIV_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a) = c_Orderings_Obot__class_Obot(T_a) ) ).
cnf(cls_Inf__empty_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) = c_Orderings_Otop__class_Otop(T_a) ) ).
cnf(cls_Inf__insert_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_A),T_a) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),c_Complete__Lattice_OInf__class_OInf(V_A,T_a)) ) ).
cnf(cls_image__vimage__subset_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(c_Set_Oimage(V_f,T_b,T_a),hAPP(c_Set_Ovimage(V_f,T_b,T_a),V_A))),V_A)) ).
cnf(cls_vimage__UN_0,axiom,
hAPP(c_Set_Ovimage(V_f,T_a,T_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_c,tc_fun(T_b,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,c_COMBB(c_Set_Ovimage(V_f,T_a,T_b),V_B,tc_fun(T_b,tc_bool),tc_fun(T_a,tc_bool),T_c),T_c,tc_fun(T_a,tc_bool)) ).
cnf(cls_triple__valid__def2_0,axiom,
( hBOOL(hAPP(hAPP(V_Q,V_Z),V_s_H))
| ~ c_Natural_Oevaln(V_c,V_s,V_n,V_s_H)
| ~ hBOOL(hAPP(hAPP(V_P,V_Z),V_s))
| ~ c_Hoare__Mirabelle_Otriple__valid(V_n,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q),t_a) ) ).
cnf(cls_UN__extend__simps_I1_J_0,axiom,
hAPP(hAPP(c_Set_Oinsert(T_a),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))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) ).
cnf(cls_Diff__insert2_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))),V_B) ).
cnf(cls_Diff__insert_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) ).
cnf(cls_singletonE_0,axiom,
( V_b = V_a
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_b),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))) ) ).
cnf(cls_inj__on__Un_3,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_b,tc_bool)),hAPP(c_Set_Oimage(V_f,T_a,T_b),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B))),hAPP(c_Set_Oimage(V_f,T_a,T_b),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_B),V_A))) != 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,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b) ) ).
cnf(cls_inj__on__Un_2,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_b,tc_bool)),hAPP(c_Set_Oimage(V_f,T_a,T_b),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B))),hAPP(c_Set_Oimage(V_f,T_a,T_b),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_B),V_A))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))
| ~ c_Fun_Oinj__on(V_f,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b) ) ).
cnf(cls_fun__upd__image_0,axiom,
( hAPP(c_Set_Oimage(c_Fun_Ofun__upd(V_f,V_x,V_y,T_b,T_a),T_b,T_a),V_A) = hAPP(hAPP(c_Set_Oinsert(T_a),V_y),hAPP(c_Set_Oimage(V_f,T_b,T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_b,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_b),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))))))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A)) ) ).
cnf(cls_evaln_OBody_0,axiom,
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_pn),V_s0,c_Suc(V_n),V_s1)
| ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn)),V_s0,V_n,V_s1) ) ).
cnf(cls_Diff1__fold__graph_0,axiom,
( c_Finite__Set_Ofold__graph(V_f,V_z,V_A,hAPP(hAPP(V_f,V_x),V_y),T_a,T_b)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ c_Finite__Set_Ofold__graph(V_f,V_z,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),V_y,T_a,T_b) ) ).
cnf(cls_setsum__diff1__nat_1,axiom,
( c_Finite__Set_Osetsum(V_f,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),T_a,tc_nat) = c_Finite__Set_Osetsum(V_f,V_A,T_a,tc_nat)
| hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)) ) ).
cnf(cls_psubset__insert__iff_8,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_B)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))),V_B))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_psubset__insert__iff_4,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_B)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))),V_B))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B)) ) ).
cnf(cls_psubset__insert__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_B))) ) ).
cnf(cls_diff__single__insert_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_B)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))),V_B)) ) ).
cnf(cls_subset__insert__iff_3,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_B)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))),V_B)) ) ).
cnf(cls_subset__insert__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_B))) ) ).
cnf(cls_fold__graph_H_Ointros_I2_J_0,axiom,
( c_Nitpick_Ofold__graph_H(V_f,V_z,V_A,hAPP(hAPP(V_f,V_x),V_y),T_a,T_b)
| ~ c_Nitpick_Ofold__graph_H(V_f,V_z,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),V_y,T_a,T_b)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_card__Suc__eq_5,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))
| c_Finite__Set_Ocard(hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),T_a) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) ) ).
cnf(cls_Body__triple__valid__0_0,axiom,
c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P),hAPP(c_Com_Ocom_OBODY,V_pn)),V_Q),T_a) ).
cnf(cls_Max__in_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_in(T_a),c_Finite__Set_Olinorder__class_OMax(V_A,T_a)),V_A))
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_inj__vimage__image__eq_0,axiom,
( hAPP(c_Set_Ovimage(V_f,T_a,T_b),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A)) = V_A
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_vimage__const_0,axiom,
( hAPP(c_Set_Ovimage(c_COMBK(V_c,T_b,T_a),T_a,T_b),V_A) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_c),V_A)) ) ).
cnf(cls_Inf__binary_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(T_a),V_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_b),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),T_a) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b) ) ).
cnf(cls_inj__on__image__set__diff_0,axiom,
( hAPP(c_Set_Oimage(V_f,T_a,T_b),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_b,tc_bool)),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A)),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_B))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_C))
| ~ c_Fun_Oinj__on(V_f,V_C,T_a,T_b) ) ).
cnf(cls_image__set__diff_0,axiom,
( hAPP(c_Set_Oimage(V_f,T_a,T_b),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_b,tc_bool)),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A)),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_B))
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_linorder_OMax__singleton_0,axiom,
( ~ c_Orderings_Olinorder(V_less__eq,V_less,T_a)
| c_Finite__Set_Ofold1(V_f,hAPP(hAPP(c_Set_Oinsert(T_b),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))),T_b) = V_a ) ).
cnf(cls_single__Diff__lessThan_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_k),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),c_SetInterval_Oord__class_OlessThan(V_k,T_a)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_k),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) ) ).
cnf(cls_subset__insert__iff_4,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_B)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))),V_B)) ) ).
cnf(cls_UN__extend__simps_I3_J_1,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_C,V_B,T_b,tc_fun(T_a,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_C,c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B,tc_fun(T_a,tc_bool),tc_fun(T_a,tc_bool),T_b),T_b,tc_fun(T_a,tc_bool))
| V_C = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)) ) ).
cnf(cls_UN__simps_I3_J_1,axiom,
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_C,c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B,tc_fun(T_a,tc_bool),tc_fun(T_a,tc_bool),T_b),T_b,tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_C,V_B,T_b,tc_fun(T_a,tc_bool)))
| V_C = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)) ) ).
cnf(cls_UN__simps_I3_J_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B,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_UN__singleton_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,hAPP(c_COMBC(c_Set_Oinsert(T_a),T_a,tc_fun(T_a,tc_bool),tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),T_a,tc_fun(T_a,tc_bool)) = V_A ).
cnf(cls_UN__simps_I1_J_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),c_COMBB(hAPP(c_Set_Oinsert(T_a),V_a),V_B,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_UN__simps_I1_J_1,axiom,
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_C,c_COMBB(hAPP(c_Set_Oinsert(T_a),V_a),V_B,tc_fun(T_a,tc_bool),tc_fun(T_a,tc_bool),T_b),T_b,tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_C,V_B,T_b,tc_fun(T_a,tc_bool)))
| V_C = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)) ) ).
cnf(cls_UN__extend__simps_I1_J_1,axiom,
( hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_C,V_B,T_b,tc_fun(T_a,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_C,c_COMBB(hAPP(c_Set_Oinsert(T_a),V_a),V_B,tc_fun(T_a,tc_bool),tc_fun(T_a,tc_bool),T_b),T_b,tc_fun(T_a,tc_bool))
| V_C = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)) ) ).
cnf(cls_sup__Un__eq_0,axiom,
hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),V_R)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),V_S)),v_x) = hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),V_R),V_S)) ).
cnf(cls_inj__on__image__iff_1,axiom,
( c_Fun_Oinj__on(V_g,hAPP(c_Set_Oimage(V_f,T_a,T_a),V_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(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(V_A,V_f,V_g,T_a,T_b)),V_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,hAPP(c_Set_Oimage(V_f,T_a,T_a),V_A),T_a,T_b)
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_a)
| hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1(V_A,V_f,V_g,T_a,T_b)),V_A)) ) ).
cnf(cls_inj__on__image__iff_3,axiom,
( c_Fun_Oinj__on(V_g,hAPP(c_Set_Oimage(V_f,T_a,T_a),V_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(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(V_A,V_f,V_g,T_a,T_b)),V_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,hAPP(c_Set_Oimage(V_f,T_a,T_a),V_A),T_a,T_b)
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_a)
| hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2(V_A,V_f,V_g,T_a,T_b)),V_A)) ) ).
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(hAPP(hAPP(c_in(T_b),V_y),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A)))
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
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(hAPP(hAPP(c_in(T_b),V_y),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A)))
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
cnf(cls_inj__image__mem__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_inj__image__mem__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A)))
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_UN__insert__distrib_0,axiom,
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,c_COMBB(hAPP(c_Set_Oinsert(T_b),V_a),V_B,tc_fun(T_b,tc_bool),tc_fun(T_b,tc_bool),T_a),T_a,tc_fun(T_b,tc_bool)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a),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_a),V_u),V_A)) ) ).
cnf(cls_UNION__empty__conv_I1_J_1,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))
| hBOOL(hAPP(hAPP(c_in(T_b),c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__1__1(V_A,V_B,T_b,T_a)),V_A)) ) ).
cnf(cls_UNION__empty__conv_I2_J_1,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))
| hBOOL(hAPP(hAPP(c_in(T_b),c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__2__1(V_A,V_B,T_b,T_a)),V_A)) ) ).
cnf(cls_setsum__subtractf_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(T_a),V_f,T_a,tc_fun(T_a,T_a),T_b),V_g,T_b,T_a,T_a),V_A,T_b,T_a) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),c_Finite__Set_Osetsum(V_f,V_A,T_b,T_a)),c_Finite__Set_Osetsum(V_g,V_A,T_b,T_a)) ) ).
cnf(cls_ab__semigroup__mult_Ononempty__iff_2,axiom,
( hAPP(hAPP(c_Set_Oinsert(T_b),V_x),V_xa) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))
| hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_xa))
| ~ c_OrderedGroup_Oab__semigroup__mult(V_times,T_a) ) ).
cnf(cls_card__Suc__Diff1_0,axiom,
( c_Suc(c_Finite__Set_Ocard(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),T_a)) = c_Finite__Set_Ocard(V_A,T_a)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_SUPR__set__fold_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_List_Oset(V_xs,T_b),V_f,T_b,T_a) = c_List_Ofoldl(c_COMBC(c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_f,T_a,tc_fun(T_a,T_a),T_b),T_b,T_a,T_a),c_Orderings_Obot__class_Obot(T_a),V_xs,T_a,T_b) ) ).
cnf(cls_setsum__diff1__ring_0,axiom,
( ~ class_Ring__and__Field_Oring(T_b)
| c_Finite__Set_Osetsum(V_f,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),T_a,T_b) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_b),c_Finite__Set_Osetsum(V_f,V_A,T_a,T_b)),hAPP(V_f,V_a))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_setsum__diff1_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_b)
| c_Finite__Set_Osetsum(V_f,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),T_a,T_b) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_b),c_Finite__Set_Osetsum(V_f,V_A,T_a,T_b)),hAPP(V_f,V_a))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_Sup__singleton_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),T_a) = V_a ) ).
cnf(cls_singleton__iff_1,axiom,
hBOOL(hAPP(hAPP(c_in(T_a),V_x),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))) ).
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_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_image__constant_0,axiom,
( hAPP(c_Set_Oimage(c_COMBK(V_c,T_b,T_a),T_a,T_b),V_A) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_COMBS__def__raw_0,axiom,
hAPP(c_COMBS(v_P,v_Q,t_a,t_b,t_c),v_R) = hAPP(hAPP(v_P,v_R),hAPP(v_Q,v_R)) ).
cnf(cls_com_Osimps_I18_J_0,axiom,
c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
cnf(cls_com_Osimps_I48_J_0,axiom,
c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
cnf(cls_com_Osimps_I49_J_0,axiom,
hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ).
cnf(cls_com_Osimps_I19_J_0,axiom,
hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP ).
cnf(cls_inj__on__Un_0,axiom,
( c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| ~ c_Fun_Oinj__on(V_f,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b) ) ).
cnf(cls_inj__on__Un_1,axiom,
( c_Fun_Oinj__on(V_f,V_B,T_a,T_b)
| ~ c_Fun_Oinj__on(V_f,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b) ) ).
cnf(cls_vimage__Un_0,axiom,
hAPP(c_Set_Ovimage(V_f,T_a,T_b),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_b,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(c_Set_Ovimage(V_f,T_a,T_b),V_A)),hAPP(c_Set_Ovimage(V_f,T_a,T_b),V_B)) ).
cnf(cls_Un__Diff_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_C)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_B),V_C)) ).
cnf(cls_Un__Diff__cancel_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_B),V_A)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B) ).
cnf(cls_Un__Diff__cancel2_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_B),V_A)),V_A) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_A) ).
cnf(cls_UnE_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
| hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B))) ) ).
cnf(cls_UnCI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B)) ) ).
cnf(cls_UnCI_1,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A)) ) ).
cnf(cls_UN__Un_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_b,tc_bool)),V_A),V_B),V_M,T_b,tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),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))) ).
cnf(cls_imageI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_image__eqI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_x)),hAPP(c_Set_Oimage(V_f,T_b,T_a),V_A)))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_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)),hAPP(c_Set_Oimage(V_f,T_b,T_a),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)),hAPP(c_Set_Oimage(V_f,T_aa,T_a),V_A))) ) ).
cnf(cls_insert__absorb_0,axiom,
( hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_A) = V_A
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)) ) ).
cnf(cls_insert__ident_0,axiom,
( hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_A) != hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_B)
| 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_insertCI_1,axiom,
hBOOL(hAPP(hAPP(c_in(T_a),V_x),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_B))) ).
cnf(cls_insertI1_0,axiom,
hBOOL(hAPP(hAPP(c_in(T_a),V_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B))) ).
cnf(cls_insert__iff_1,axiom,
hBOOL(hAPP(hAPP(c_in(T_a),V_x),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_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,hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_A),T_a,T_b) ) ).
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),hAPP(hAPP(c_Set_Oinsert(T_a),V_b),V_A))) ) ).
cnf(cls_insertCI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_b),V_B)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_B)) ) ).
cnf(cls_insert__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_b),V_A)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)) ) ).
cnf(cls_inj__on__insert_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),hAPP(c_Set_Oimage(V_f,T_a,T_b),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))))))
| ~ c_Fun_Oinj__on(V_f,hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_A),T_a,T_b) ) ).
cnf(cls_inj__on__insert_2,axiom,
( c_Fun_Oinj__on(V_f,hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_A),T_a,T_b)
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),hAPP(c_Set_Oimage(V_f,T_a,T_b),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))))))
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
cnf(cls_Diff__insert__absorb_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_A)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) = V_A
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_vimage__singleton__eq_1,axiom,
hBOOL(hAPP(hAPP(c_in(T_aa),V_a),hAPP(c_Set_Ovimage(V_f,T_aa,T_a),hAPP(hAPP(c_Set_Oinsert(T_a),hAPP(V_f,V_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))))) ).
cnf(cls_vimage__singleton__eq_0,axiom,
( hAPP(V_f,V_a) = V_b
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),hAPP(c_Set_Ovimage(V_f,T_a,T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)))))) ) ).
cnf(cls_insert__Diff_0,axiom,
( hAPP(hAPP(c_Set_Oinsert(T_a),V_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))) = V_A
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),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_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_Diff__empty_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = V_A ).
cnf(cls_Diff__cancel_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_A) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_empty__Diff_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(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_emptyE_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) ).
cnf(cls_empty__iff_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) ).
cnf(cls_ball__empty_0,axiom,
( hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) ) ).
cnf(cls_ex__in__conv_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) ).
cnf(cls_vimage__empty_0,axiom,
hAPP(c_Set_Ovimage(V_f,T_a,T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_evalc__elim__cases_I1_J_0,axiom,
( V_t = V_s
| ~ c_Natural_Oevalc(c_Com_Ocom_OSKIP,V_s,V_t) ) ).
cnf(cls_insert__Diff__if_1,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_A)),V_B) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B)) ) ).
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_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_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),hAPP(c_Set_Ovimage(V_f,T_a,T_b),V_A))) ) ).
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),hAPP(c_Set_Ovimage(V_f,T_a,T_b),V_B))) ) ).
cnf(cls_vimageI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_b),V_a),hAPP(c_Set_Ovimage(V_f,T_b,T_a),V_B)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_a)),V_B)) ) ).
cnf(cls_vimageI2_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_b),V_a),hAPP(c_Set_Ovimage(V_f,T_b,T_a),V_A)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_a)),V_A)) ) ).
cnf(cls_vimage__eq_1,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_a),hAPP(c_Set_Ovimage(V_f,T_a,T_b),V_B)))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),V_B)) ) ).
cnf(cls_fun__diff__def_0,axiom,
( ~ class_HOL_Ominus(T_b)
| hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(t_a,T_b)),V_A),V_B),v_x) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_b),hAPP(V_A,v_x)),hAPP(V_B,v_x)) ) ).
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_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_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_DiffI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)))
| hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A)) ) ).
cnf(cls_Diff__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)))
| hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A)) ) ).
cnf(cls_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_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__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__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_evalc_OSemi_0,axiom,
( c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0,V_c1),V_s0,V_s2)
| ~ c_Natural_Oevalc(V_c1,V_s1,V_s2)
| ~ c_Natural_Oevalc(V_c0,V_s0,V_s1) ) ).
cnf(cls_eq__eqI_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_x) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x_H),V_y_H)
| V_x_H = V_y_H ) ).
cnf(cls_eq__eqI_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_xa),V_y) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_x)
| V_xa = V_y ) ).
cnf(cls_Diff__idemp_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)),V_B) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B) ).
cnf(cls_COMBS__def_0,axiom,
hAPP(c_COMBS(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),hAPP(V_Q,V_R)) ).
cnf(cls_COMBK__def_0,axiom,
hAPP(c_COMBK(V_P,T_a,T_b),V_Q) = V_P ).
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_mem__def_1,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_S))
| ~ hBOOL(hAPP(V_S,V_x)) ) ).
cnf(cls_INT__extend__simps_I4_J_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),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))) = V_A ).
cnf(cls_insert__Diff1_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_A)),V_B) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B)) ) ).
cnf(cls_inj__on__diff_0,axiom,
( c_Fun_Oinj__on(V_f,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b)
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
cnf(cls_vimage__Diff_0,axiom,
hAPP(c_Set_Ovimage(V_f,T_a,T_b),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_b,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),hAPP(c_Set_Ovimage(V_f,T_a,T_b),V_A)),hAPP(c_Set_Ovimage(V_f,T_a,T_b),V_B)) ).
cnf(cls_com_Osimps_I3_J_1,axiom,
( c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OSemi(V_com1_H,V_com2_H)
| V_com2 = V_com2_H ) ).
cnf(cls_com_Osimps_I3_J_0,axiom,
( c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OSemi(V_com1_H,V_com2_H)
| V_com1 = V_com1_H ) ).
cnf(cls_triple__valid__Suc_0,axiom,
( c_Hoare__Mirabelle_Otriple__valid(V_n,V_t,T_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(c_Suc(V_n),V_t,T_a) ) ).
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_DiffE_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B))) ) ).
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),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B))) ) ).
cnf(cls_UN__absorb_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_b,tc_bool)),hAPP(V_A,V_k)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_I,V_A,T_a,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_Suc__inject_0,axiom,
( c_Suc(V_x) != c_Suc(V_y)
| V_x = V_y ) ).
cnf(cls_nat_Oinject_0,axiom,
( c_Suc(V_nat) != c_Suc(V_nat_H)
| V_nat = V_nat_H ) ).
cnf(cls_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_evalc_OSkip_0,axiom,
c_Natural_Oevalc(c_Com_Ocom_OSKIP,V_s,V_s) ).
cnf(cls_com__det_0,axiom,
( V_u = V_t
| ~ c_Natural_Oevalc(V_c,V_s,V_u)
| ~ c_Natural_Oevalc(V_c,V_s,V_t) ) ).
cnf(cls_bot__empty__eq_0,axiom,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = hAPP(hAPP(c_in(t_a),v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))) ).
cnf(cls_vimage__const_1,axiom,
( hAPP(c_Set_Ovimage(c_COMBK(V_c,T_b,T_a),T_a,T_b),V_A) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| hBOOL(hAPP(hAPP(c_in(T_b),V_c),V_A)) ) ).
cnf(cls_com_Osimps_I13_J_0,axiom,
c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ).
cnf(cls_Suc__n__not__n_0,axiom,
c_Suc(V_n) != V_n ).
cnf(cls_n__not__Suc__n_0,axiom,
V_n != c_Suc(V_n) ).
cnf(cls_vimage__code_0,axiom,
( hBOOL(hAPP(V_A,hAPP(V_f,V_x)))
| ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(V_f,T_a,T_b),V_A),V_x)) ) ).
cnf(cls_vimage__code_1,axiom,
( hBOOL(hAPP(hAPP(c_Set_Ovimage(V_f,T_a,T_b),V_A),V_x))
| ~ hBOOL(hAPP(V_A,hAPP(V_f,V_x))) ) ).
cnf(cls_com_Osimps_I12_J_0,axiom,
c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ).
cnf(cls_fold1__singleton_0,axiom,
c_Finite__Set_Ofold1(V_f,hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),T_a) = V_a ).
cnf(cls_Max__singleton_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_Finite__Set_Olinorder__class_OMax(hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),T_a) = V_a ) ).
cnf(cls_insert__Diff__single_0,axiom,
hAPP(hAPP(c_Set_Oinsert(T_a),V_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_A) ).
cnf(cls_atLeastAtMost__singleton_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_a,T_a) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) ) ).
cnf(cls_comm__monoid__add_Ononempty__iff_2,axiom,
( hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_xa) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_xa)) ) ).
cnf(cls_Inf__singleton_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| c_Complete__Lattice_OInf__class_OInf(hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),T_a) = V_a ) ).
cnf(cls_image__constant__conv_0,axiom,
hAPP(c_Set_Oimage(c_COMBK(V_c,T_a,T_b),T_b,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_Sup__insert_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_A),T_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),c_Complete__Lattice_OSup__class_OSup(V_A,T_a)) ) ).
cnf(cls_UN__extend__simps_I3_J_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),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))) = V_A ).
cnf(cls_UN__extend__simps_I2_J_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),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) = V_B ).
cnf(cls_insert__image_0,axiom,
( hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f,V_x)),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A)) = hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_sup__fun__eq_0,axiom,
( ~ class_Lattices_Olattice(T_b)
| hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,T_b)),V_f),V_g),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_b),hAPP(V_f,v_x)),hAPP(V_g,v_x)) ) ).
cnf(cls_UN__insert_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Set_Oinsert(T_b),V_a),V_A),V_B,T_b,tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(V_B,V_a)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_b,tc_fun(T_a,tc_bool))) ).
cnf(cls_inj__on__Un__image__eq__iff_0,axiom,
( hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A) != hAPP(c_Set_Oimage(V_f,T_a,T_b),V_B)
| ~ c_Fun_Oinj__on(V_f,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b)
| V_A = V_B ) ).
cnf(cls_conseq_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(V_xa,V_Z_H),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(V_G,V_P,V_Q,V_c,V_x,V_xa)))
| ~ hBOOL(hAPP(hAPP(V_x,V_Z_H),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(V_G,V_P,V_Q,V_c)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_x),V_c),V_xa)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ) ).
cnf(cls_conseq12_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(V_Q_H,V_Z_H),v_sko__Hoare__Mirabelle__Xconseq12__3(V_P,V_P_H,V_Q,V_Q_H)))
| ~ hBOOL(hAPP(hAPP(V_P_H,V_Z_H),v_sko__Hoare__Mirabelle__Xconseq12__2(V_P,V_P_H,V_Q,V_Q_H)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P_H),V_c),V_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ) ).
cnf(cls_hoare__derivs_Ointros_I6_J_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(V_xa,V_Z_H),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(V_G,V_P,V_Q,V_c,V_x,V_xa)))
| ~ hBOOL(hAPP(hAPP(V_x,V_Z_H),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(V_G,V_P,V_Q,V_c)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_x),V_c),V_xa)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ) ).
cnf(cls_hoare__derivs_Ointros_I6_J_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(V_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(V_G,V_P,V_Q,V_c))) ) ).
cnf(cls_hoare__derivs_Ointros_I6_J_2,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_Q,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(V_G,V_P,V_Q,V_c,V_x,V_xa)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_x),V_c),V_xa)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ) ).
cnf(cls_conseq_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(V_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(V_G,V_P,V_Q,V_c))) ) ).
cnf(cls_conseq2_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(V_Q_H,v_sko__Hoare__Mirabelle__Xconseq2__1(V_Q,V_Q_H)),v_sko__Hoare__Mirabelle__Xconseq2__2(V_Q,V_Q_H)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ) ).
cnf(cls_conseq12_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(V_P,v_sko__Hoare__Mirabelle__Xconseq12__1(V_P,V_P_H,V_Q,V_Q_H)),v_sko__Hoare__Mirabelle__Xconseq12__2(V_P,V_P_H,V_Q,V_Q_H)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P_H),V_c),V_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ) ).
cnf(cls_conseq1_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(V_P,v_sko__Hoare__Mirabelle__Xconseq1__1(V_P,V_P_H)),v_sko__Hoare__Mirabelle__Xconseq1__2(V_P,V_P_H)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P_H),V_c),V_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ) ).
cnf(cls_conseq_2,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_Q,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(V_G,V_P,V_Q,V_c,V_x,V_xa)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_x),V_c),V_xa)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ) ).
cnf(cls_conseq1_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_P_H,v_sko__Hoare__Mirabelle__Xconseq1__1(V_P,V_P_H)),v_sko__Hoare__Mirabelle__Xconseq1__2(V_P,V_P_H)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P_H),V_c),V_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ) ).
cnf(cls_conseq12_2,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_Q,v_sko__Hoare__Mirabelle__Xconseq12__1(V_P,V_P_H,V_Q,V_Q_H)),v_sko__Hoare__Mirabelle__Xconseq12__3(V_P,V_P_H,V_Q,V_Q_H)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P_H),V_c),V_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ) ).
cnf(cls_conseq2_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(V_Q,v_sko__Hoare__Mirabelle__Xconseq2__1(V_Q,V_Q_H)),v_sko__Hoare__Mirabelle__Xconseq2__2(V_Q,V_Q_H)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ) ).
cnf(cls_COMBK__def__raw_0,axiom,
hAPP(c_COMBK(v_P,t_a,t_b),v_Q) = v_P ).
cnf(cls_Body__triple__valid__Suc_0,axiom,
( c_Hoare__Mirabelle_Otriple__valid(c_Suc(V_n),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P),hAPP(c_Com_Ocom_OBODY,V_pn)),V_Q),T_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(V_n,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_Q),T_a) ) ).
cnf(cls_Body__triple__valid__Suc_1,axiom,
( c_Hoare__Mirabelle_Otriple__valid(V_n,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_Q),T_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(c_Suc(V_n),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P),hAPP(c_Com_Ocom_OBODY,V_pn)),V_Q),T_a) ) ).
cnf(cls_Sup__binary_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| c_Complete__Lattice_OSup__class_OSup(hAPP(hAPP(c_Set_Oinsert(T_a),V_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_b),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),T_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b) ) ).
cnf(cls_image__constant__conv_1,axiom,
( hAPP(c_Set_Oimage(c_COMBK(V_c,T_a,T_b),T_b,T_a),V_A) = hAPP(hAPP(c_Set_Oinsert(T_a),V_c),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_vimage__insert_0,axiom,
hAPP(c_Set_Ovimage(V_f,T_a,T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a),V_B)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(c_Set_Ovimage(V_f,T_a,T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))))),hAPP(c_Set_Ovimage(V_f,T_a,T_b),V_B)) ).
cnf(cls_COMBB__def__raw_0,axiom,
hAPP(c_COMBB(v_P,v_Q,t_a,t_b,t_c),v_R) = hAPP(v_P,hAPP(v_Q,v_R)) ).
cnf(cls_COMBC__def__raw_0,axiom,
hAPP(hAPP(c_COMBC(v_P,t_a,t_b,t_c),v_Q),v_R) = hAPP(hAPP(v_P,v_R),v_Q) ).
cnf(cls_Body1_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(V_P,V_pn)),hAPP(c_Com_Ocom_OBODY,V_pn)),hAPP(V_Q,V_pn))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))),T_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),V_pn),V_Procs))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),V_G),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a))),V_Q,tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a)),V_Procs)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a))),V_Q,tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a)),V_Procs),T_a) ) ).
cnf(cls_evalc_OBody_0,axiom,
( c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pn),V_s0,V_s1)
| ~ c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn)),V_s0,V_s1) ) ).
cnf(cls_evalc__elim__cases_I6_J_0,axiom,
( c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P)),V_s,V_s1)
| ~ c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_P),V_s,V_s1) ) ).
cnf(cls_hoare__derivs_OBody_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a))),V_Q,tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a)),V_Procs),T_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),V_G),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a))),V_Q,tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a)),V_Procs)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a))),V_Q,tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a)),V_Procs),T_a) ) ).
cnf(cls_hoare__derivs_OSkip_0,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P),c_Com_Ocom_OSKIP),V_P)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))),T_a) ).
cnf(cls_Comp_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P),c_Com_Ocom_OSemi(V_c,V_d)),V_R)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))),T_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_Q),V_d),V_R)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))),T_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P),V_c),V_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))),T_a) ) ).
cnf(cls_image__Un_0,axiom,
hAPP(c_Set_Oimage(V_f,T_b,T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_b,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(c_Set_Oimage(V_f,T_b,T_a),V_A)),hAPP(c_Set_Oimage(V_f,T_b,T_a),V_B)) ).
cnf(cls_Un__empty_2,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_hoare__derivs_Oinsert_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t),V_ts),T_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))),T_a) ) ).
cnf(cls_image__is__empty_0,axiom,
( hAPP(c_Set_Oimage(V_f,T_b,T_a),V_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_image__image_0,axiom,
hAPP(c_Set_Oimage(V_f,T_b,T_a),hAPP(c_Set_Oimage(V_g,T_c,T_b),V_A)) = hAPP(c_Set_Oimage(c_COMBB(V_f,V_g,T_b,T_a,T_c),T_c,T_a),V_A) ).
cnf(cls_insert__code_1,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_A),V_x)) ).
cnf(cls_image__insert_0,axiom,
hAPP(c_Set_Oimage(V_f,T_b,T_a),hAPP(hAPP(c_Set_Oinsert(T_b),V_a),V_B)) = hAPP(hAPP(c_Set_Oinsert(T_a),hAPP(V_f,V_a)),hAPP(c_Set_Oimage(V_f,T_b,T_a),V_B)) ).
cnf(cls_cut_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_G_H,T_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_H,V_ts,T_a) ) ).
cnf(cls_empty__not__insert_0,axiom,
c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_A) ).
cnf(cls_triple_Oinject_2,axiom,
( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1),V_com),V_fun2) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_H),V_com_H),V_fun2_H)
| V_fun2 = V_fun2_H ) ).
cnf(cls_triple_Oinject_1,axiom,
( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1),V_com),V_fun2) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_H),V_com_H),V_fun2_H)
| V_com = V_com_H ) ).
cnf(cls_triple_Oinject_0,axiom,
( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1),V_com),V_fun2) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_H),V_com_H),V_fun2_H)
| V_fun1 = V_fun1_H ) ).
cnf(cls_doubleton__eq__iff_3,axiom,
( hAPP(hAPP(c_Set_Oinsert(T_a),V_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_b),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(T_a),V_c),hAPP(hAPP(c_Set_Oinsert(T_a),V_d),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))
| V_b = V_c
| V_b = V_d ) ).
cnf(cls_doubleton__eq__iff_2,axiom,
( hAPP(hAPP(c_Set_Oinsert(T_a),V_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_b),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(T_a),V_c),hAPP(hAPP(c_Set_Oinsert(T_a),V_d),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))
| V_a = V_d
| V_b = V_d ) ).
cnf(cls_doubleton__eq__iff_1,axiom,
( hAPP(hAPP(c_Set_Oinsert(T_a),V_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_b),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(T_a),V_c),hAPP(hAPP(c_Set_Oinsert(T_a),V_d),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))
| V_b = V_c
| V_a = V_c ) ).
cnf(cls_doubleton__eq__iff_0,axiom,
( hAPP(hAPP(c_Set_Oinsert(T_a),V_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_b),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) != hAPP(hAPP(c_Set_Oinsert(T_a),V_c),hAPP(hAPP(c_Set_Oinsert(T_a),V_d),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))
| V_a = V_d
| V_a = V_c ) ).
cnf(cls_bot1E_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x)) ).
cnf(cls_empty_0,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),T_a) ).
cnf(cls_Un__empty__right_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = V_A ).
cnf(cls_Un__empty__left_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),V_B) = V_B ).
cnf(cls_sup__bot__left_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ).
cnf(cls_sup__bot__right_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ).
cnf(cls_sup1CI_1,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),V_x))
| ~ hBOOL(hAPP(V_A,V_x)) ) ).
cnf(cls_sup1CI_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),V_x))
| ~ hBOOL(hAPP(V_B,V_x)) ) ).
cnf(cls_sup1E_0,axiom,
( hBOOL(hAPP(V_B,V_x))
| hBOOL(hAPP(V_A,V_x))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),V_x)) ) ).
cnf(cls_insert__code_0,axiom,
( hBOOL(hAPP(V_A,V_x))
| V_y = V_x
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_a),V_y),V_A),V_x)) ) ).
cnf(cls_insert__absorb2_0,axiom,
hAPP(hAPP(c_Set_Oinsert(T_a),V_x),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_A)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_A) ).
cnf(cls_insert__not__empty_0,axiom,
hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_A) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_Un__insert__right_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)) ).
cnf(cls_Un__insert__left_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_B)),V_C) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)) ).
cnf(cls_empty__is__image_0,axiom,
( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != hAPP(c_Set_Oimage(V_f,T_b,T_a),V_A)
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)) ) ).
cnf(cls_Un__absorb_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_A) = V_A ).
cnf(cls_sup__idem_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_x) = V_x ) ).
cnf(cls_insert__commute_0,axiom,
hAPP(hAPP(c_Set_Oinsert(T_a),V_x),hAPP(hAPP(c_Set_Oinsert(T_a),V_y),V_A)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_y),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),V_A)) ).
cnf(cls_COMBB__def_0,axiom,
hAPP(c_COMBB(V_P,V_Q,T_b,T_a,T_c),V_R) = hAPP(V_P,hAPP(V_Q,V_R)) ).
cnf(cls_COMBC__def_0,axiom,
hAPP(hAPP(c_COMBC(V_P,T_b,T_c,T_a),V_Q),V_R) = hAPP(hAPP(V_P,V_R),V_Q) ).
cnf(cls_doubleton__eq__iff_4,axiom,
hAPP(hAPP(c_Set_Oinsert(T_a),V_xa),hAPP(hAPP(c_Set_Oinsert(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x),hAPP(hAPP(c_Set_Oinsert(T_a),V_xa),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) ).
cnf(cls_image__empty_0,axiom,
hAPP(c_Set_Oimage(V_f,T_b,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_Un__left__commute_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_C)) ).
cnf(cls_Un__assoc_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)) ).
cnf(cls_sup__assoc_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z)) ) ).
cnf(cls_sup__left__commute_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_z)) ) ).
cnf(cls_inf__sup__aci_I7_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_z)) ) ).
cnf(cls_inf__sup__aci_I6_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z)) ) ).
cnf(cls_singleton__inject_0,axiom,
( hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) != hAPP(hAPP(c_Set_Oinsert(T_a),V_b),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))
| V_a = V_b ) ).
cnf(cls_insert__code_2,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_a),V_y),V_A),V_x))
| ~ hBOOL(hAPP(V_A,V_x)) ) ).
cnf(cls_Un__empty_1,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| V_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Un__empty_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_sup__eq__bot__eq1_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_A),V_B) != c_Orderings_Obot__class_Obot(T_a)
| V_A = c_Orderings_Obot__class_Obot(T_a) ) ).
cnf(cls_sup__eq__bot__eq2_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_A),V_B) != c_Orderings_Obot__class_Obot(T_a)
| V_B = c_Orderings_Obot__class_Obot(T_a) ) ).
cnf(cls_Un__commute_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_A) ).
cnf(cls_sup__commute_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_x) ) ).
cnf(cls_inf__sup__aci_I5_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_x) ) ).
cnf(cls_com_Osimps_I6_J_0,axiom,
( hAPP(c_Com_Ocom_OBODY,V_pname) != hAPP(c_Com_Ocom_OBODY,V_pname_H)
| V_pname = V_pname_H ) ).
cnf(cls_insert__is__Un_0,axiom,
hAPP(hAPP(c_Set_Oinsert(T_a),V_a),V_A) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),V_A) ).
cnf(cls_Un__left__absorb_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B) ).
cnf(cls_sup__left__idem_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) ) ).
cnf(cls_inf__sup__aci_I8_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) ) ).
cnf(cls_empty__is__image_1,axiom,
c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) = hAPP(c_Set_Oimage(V_f,T_b,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))) ).
cnf(cls_conjecture_0,negated_conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ).
cnf(cls_conjecture_1,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),hAPP(c_Set_Oimage(hAPP(c_COMBC(c_COMBB(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),c_Com_Ocom_OBODY,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Q),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs)),hAPP(c_Set_Oimage(hAPP(c_COMBC(c_COMBB(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),v_Q),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs),t_a) ).
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__Orderings_Opreorder,axiom,
( class_Orderings_Opreorder(tc_fun(T_2,T_1))
| ~ class_Orderings_Opreorder(T_1) ) ).
cnf(clsarity_fun__Lattices_Olattice,axiom,
( class_Lattices_Olattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ) ).
cnf(clsarity_fun__Orderings_Oorder,axiom,
( class_Orderings_Oorder(tc_fun(T_2,T_1))
| ~ class_Orderings_Oorder(T_1) ) ).
cnf(clsarity_fun__Orderings_Otop,axiom,
( class_Orderings_Otop(tc_fun(T_2,T_1))
| ~ class_Orderings_Otop(T_1) ) ).
cnf(clsarity_fun__Orderings_Obot,axiom,
( class_Orderings_Obot(tc_fun(T_2,T_1))
| ~ class_Orderings_Obot(T_1) ) ).
cnf(clsarity_fun__HOL_Ominus,axiom,
( class_HOL_Ominus(tc_fun(T_2,T_1))
| ~ class_HOL_Ominus(T_1) ) ).
cnf(clsarity_fun__HOL_Oord,axiom,
( class_HOL_Oord(tc_fun(T_2,T_1))
| ~ class_HOL_Oord(T_1) ) ).
cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat) ).
cnf(clsarity_nat__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_nat) ).
cnf(clsarity_nat__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_nat) ).
cnf(clsarity_nat__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_nat) ).
cnf(clsarity_nat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_nat) ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat) ).
cnf(clsarity_nat__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_nat) ).
cnf(clsarity_nat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_nat) ).
cnf(clsarity_nat__Orderings_Obot,axiom,
class_Orderings_Obot(tc_nat) ).
cnf(clsarity_nat__HOL_Ominus,axiom,
class_HOL_Ominus(tc_nat) ).
cnf(clsarity_nat__HOL_Oord,axiom,
class_HOL_Oord(tc_nat) ).
cnf(clsarity_bool__Complete__Lattice_Ocomplete__lattice,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool) ).
cnf(clsarity_bool__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_bool) ).
cnf(clsarity_bool__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_bool) ).
cnf(clsarity_bool__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_bool) ).
cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_bool) ).
cnf(clsarity_bool__Finite__Set_Ofinite_Ofinite,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool) ).
cnf(clsarity_bool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_bool) ).
cnf(clsarity_bool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_bool) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool) ).
cnf(clsarity_bool__Orderings_Otop,axiom,
class_Orderings_Otop(tc_bool) ).
cnf(clsarity_bool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_bool) ).
cnf(clsarity_bool__HOL_Ominus,axiom,
class_HOL_Ominus(tc_bool) ).
cnf(clsarity_bool__HOL_Oord,axiom,
class_HOL_Oord(tc_bool) ).
cnf(clsarity_Option__Ooption__Finite__Set_Ofinite_Ofinite,axiom,
( class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(T_1))
| ~ class_Finite__Set_Ofinite_Ofinite(T_1) ) ).
cnf(cls_ATP__Linkup_OCOMBC__def_0,axiom,
hAPP(hAPP(c_COMBC(V_P,T_b,T_c,T_a),V_Q),V_R) = hAPP(hAPP(V_P,V_R),V_Q) ).
cnf(cls_ATP__Linkup_OCOMBB__def_0,axiom,
hAPP(c_COMBB(V_P,V_Q,T_b,T_a,T_c),V_R) = hAPP(V_P,hAPP(V_Q,V_R)) ).
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
c_fequal(V_x,V_x,T_a) ).
cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom,
( V_X = V_Y
| ~ c_fequal(V_X,V_Y,T_a) ) ).
%------------------------------------------------------------------------------