TPTP Problem File: SWV906-1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SWV906-1 : TPTP v8.2.0. Released v4.1.0.
% Domain : Software Verification
% Problem : Hoare logic with procedures 454_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-454_1 [Nip10]
% Status : Unsatisfiable
% Rating : 0.10 v8.1.0, 0.11 v7.5.0, 0.16 v7.4.0, 0.18 v7.3.0, 0.17 v7.1.0, 0.08 v7.0.0, 0.20 v6.4.0, 0.13 v6.3.0, 0.09 v6.2.0, 0.20 v6.1.0, 0.00 v6.0.0, 0.10 v5.5.0, 0.45 v5.3.0, 0.44 v5.2.0, 0.38 v5.1.0, 0.47 v5.0.0, 0.36 v4.1.0
% Syntax : Number of clauses : 514 ( 195 unt; 49 nHn; 294 RR)
% Number of literals : 984 ( 354 equ; 498 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 24 ( 23 usr; 2 prp; 0-9 aty)
% Number of functors : 62 ( 62 usr; 14 con; 0-6 aty)
% Number of variables : 1823 ( 580 sgn)
% SPC : CNF_UNS_RFO_SEQ_NHN
% Comments :
%------------------------------------------------------------------------------
cnf(cls_restrict__map__empty_0,axiom,
hAPP(c_Map_Orestrict__map(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),t_a),V_D,t_a,T_b),v_x) = c_Option_Ooption_ONone(T_b) ).
cnf(cls_fun__upd__None__restrict_1,axiom,
( c_Fun_Ofun__upd(c_Map_Orestrict__map(V_m,V_D,T_a,T_b),V_x,c_Option_Ooption_ONone(T_b),T_a,tc_Option_Ooption(T_b)) = c_Map_Orestrict__map(V_m,V_D,T_a,T_b)
| hBOOL(c_in(V_x,V_D,T_a)) ) ).
cnf(cls_restrict__map__to__empty_0,axiom,
hAPP(c_Map_Orestrict__map(V_m,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a,T_b),v_x) = c_Option_Ooption_ONone(T_b) ).
cnf(cls_restrict__in_0,axiom,
( hAPP(c_Map_Orestrict__map(V_m,V_A,T_a,T_b),V_x) = hAPP(V_m,V_x)
| ~ hBOOL(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_restrict__out_0,axiom,
( hAPP(c_Map_Orestrict__map(V_m,V_A,T_a,T_b),V_x) = c_Option_Ooption_ONone(T_b)
| hBOOL(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_restrict__fun__upd_1,axiom,
( c_Map_Orestrict__map(c_Fun_Ofun__upd(V_m,V_x,V_y,T_a,tc_Option_Ooption(T_b)),V_D,T_a,T_b) = c_Map_Orestrict__map(V_m,V_D,T_a,T_b)
| hBOOL(c_in(V_x,V_D,T_a)) ) ).
cnf(cls_restrict__map__insert_0,axiom,
c_Map_Orestrict__map(V_f,c_Set_Oinsert(V_a,V_A,T_a),T_a,T_b) = c_Fun_Ofun__upd(c_Map_Orestrict__map(V_f,V_A,T_a,T_b),V_a,hAPP(V_f,V_a),T_a,tc_Option_Ooption(T_b)) ).
cnf(cls_fun__upd__restrict_0,axiom,
c_Fun_Ofun__upd(c_Map_Orestrict__map(V_m,V_D,T_a,T_b),V_x,V_y,T_a,tc_Option_Ooption(T_b)) = c_Fun_Ofun__upd(c_Map_Orestrict__map(V_m,c_HOL_Ominus__class_Ominus(V_D,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a,T_b),V_x,V_y,T_a,tc_Option_Ooption(T_b)) ).
cnf(cls_fun__upd__restrict__conv_0,axiom,
( c_Fun_Ofun__upd(c_Map_Orestrict__map(V_m,V_D,T_a,T_b),V_x,V_y,T_a,tc_Option_Ooption(T_b)) = c_Fun_Ofun__upd(c_Map_Orestrict__map(V_m,c_HOL_Ominus__class_Ominus(V_D,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a,T_b),V_x,V_y,T_a,tc_Option_Ooption(T_b))
| ~ hBOOL(c_in(V_x,V_D,T_a)) ) ).
cnf(cls_restrict__fun__upd_0,axiom,
( c_Map_Orestrict__map(c_Fun_Ofun__upd(V_m,V_x,V_y,T_a,tc_Option_Ooption(T_b)),V_D,T_a,T_b) = c_Fun_Ofun__upd(c_Map_Orestrict__map(V_m,c_HOL_Ominus__class_Ominus(V_D,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a,T_b),V_x,V_y,T_a,tc_Option_Ooption(T_b))
| ~ hBOOL(c_in(V_x,V_D,T_a)) ) ).
cnf(cls_Un__assoc_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).
cnf(cls_sup__assoc_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) ) ).
cnf(cls_sup__left__commute_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a) ) ).
cnf(cls_inf__sup__aci_I7_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a) ) ).
cnf(cls_inf__sup__aci_I6_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) ) ).
cnf(cls_Un__subset__iff_2,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_B,V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_C,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Un__upper2_0,axiom,
c_lessequals(V_B,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).
cnf(cls_Un__upper1_0,axiom,
c_lessequals(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).
cnf(cls_Un__least_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_B,V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_C,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_le__supI_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),V_x,T_a)
| ~ c_lessequals(V_b,V_x,T_a)
| ~ c_lessequals(V_a,V_x,T_a) ) ).
cnf(cls_sup__ge1_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) ) ).
cnf(cls_sup__ge2_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) ) ).
cnf(cls_sup__least_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),V_x,T_a)
| ~ c_lessequals(V_z,V_x,T_a)
| ~ c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_le__sup__iff_2,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_z,T_a) ) ).
cnf(cls_inf__sup__ord_I4_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_lessequals(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) ) ).
cnf(cls_inf__sup__ord_I3_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_lessequals(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) ) ).
cnf(cls_Diff__partition_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_A,c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_B
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_com_Osimps_I14_J_0,axiom,
c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H) ).
cnf(cls_com_Osimps_I32_J_0,axiom,
c_Com_Ocom_OAss(V_vname,V_fun) != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) ).
cnf(cls_Diff__subset_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) ).
cnf(cls_set__empty__eq_1,axiom,
c_Option_Oset(c_Option_Ooption_ONone(T_a),T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_CollectI_0,axiom,
( hBOOL(c_in(V_a,c_Collect(V_P,T_a),T_a))
| ~ hBOOL(hAPP(V_P,V_a)) ) ).
cnf(cls_CollectD_0,axiom,
( hBOOL(hAPP(V_P,V_a))
| ~ hBOOL(c_in(V_a,c_Collect(V_P,T_a),T_a)) ) ).
cnf(cls_Diff__iff_2,axiom,
( hBOOL(c_in(V_c,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a))
| hBOOL(c_in(V_c,V_B,T_a))
| ~ hBOOL(c_in(V_c,V_A,T_a)) ) ).
cnf(cls_DiffI_0,axiom,
( hBOOL(c_in(V_c,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a))
| hBOOL(c_in(V_c,V_B,T_a))
| ~ hBOOL(c_in(V_c,V_A,T_a)) ) ).
cnf(cls_com_Osimps_I43_J_0,axiom,
c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) != c_Com_Ocom_OLocal(V_loc,V_fun,V_com) ).
cnf(cls_insert__subset_0,axiom,
( hBOOL(c_in(V_x,V_B,T_a))
| ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_SUP__const_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_b)
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,c_COMBK(V_M,T_b,T_a),T_a,T_b) = V_M
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_com_Osimps_I61_J_0,axiom,
c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) != c_Com_Ocom_OWhile(V_fun,V_com) ).
cnf(cls_subset__insert__iff_2,axiom,
( c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| hBOOL(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_subset__insert__iff_1,axiom,
( c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| hBOOL(c_in(V_x,V_A,T_a))
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ) ).
cnf(cls_subset__insert_1,axiom,
( c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| hBOOL(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_subset__insert_0,axiom,
( c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| hBOOL(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_UN__iff_2,axiom,
( hBOOL(c_in(V_b,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_b,tc_fun(T_a,tc_bool)),T_a))
| ~ hBOOL(c_in(V_b,hAPP(V_B,V_x),T_a))
| ~ hBOOL(c_in(V_x,V_A,T_b)) ) ).
cnf(cls_UN__I_0,axiom,
( hBOOL(c_in(V_b,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_bool)),T_b))
| ~ hBOOL(c_in(V_b,hAPP(V_B,V_a),T_b))
| ~ hBOOL(c_in(V_a,V_A,T_a)) ) ).
cnf(cls_Un__Diff__cancel2_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool)) ).
cnf(cls_Un__Diff__cancel_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) ).
cnf(cls_fun__diff__def_0,axiom,
( ~ class_HOL_Ominus(T_b)
| hAPP(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(t_a,T_b)),v_x) = c_HOL_Ominus__class_Ominus(hAPP(V_A,v_x),hAPP(V_B,v_x),T_b) ) ).
cnf(cls_Un__Diff_0,axiom,
c_HOL_Ominus__class_Ominus(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(V_A,V_C,tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).
cnf(cls_com_Osimps_I34_J_0,axiom,
c_Com_Ocom_OLocal(V_loc,V_fun,V_com) != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ).
cnf(cls_complete__lattice_OInf__lower_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,hAPP(V_Inf,V_A)),V_x))
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_complete__lattice_OSup__upper_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,V_x),hAPP(V_Sup,V_A)))
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_Un__commute_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool)) ).
cnf(cls_sup__commute_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,V_x,T_a) ) ).
cnf(cls_inf__sup__aci_I5_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,V_x,T_a) ) ).
cnf(cls_com_Osimps_I5_J_0,axiom,
( c_Com_Ocom_OWhile(V_fun,V_com) != c_Com_Ocom_OWhile(V_fun_H,V_com_H)
| V_fun = V_fun_H ) ).
cnf(cls_com_Osimps_I5_J_1,axiom,
( c_Com_Ocom_OWhile(V_fun,V_com) != c_Com_Ocom_OWhile(V_fun_H,V_com_H)
| V_com = V_com_H ) ).
cnf(cls_Un__left__absorb_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) ).
cnf(cls_sup__left__idem_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) ) ).
cnf(cls_inf__sup__aci_I8_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) ) ).
cnf(cls_com_Osimps_I15_J_0,axiom,
c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ).
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(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_SUP1__I_0,axiom,
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_bool)),V_b))
| ~ hBOOL(hAPP(hAPP(V_B,V_a),V_b))
| ~ hBOOL(c_in(V_a,V_A,T_a)) ) ).
cnf(cls_com_Osimps_I53_J_0,axiom,
c_Com_Ocom_OWhile(V_fun_H,V_com_H) != c_Com_Ocom_OCond(V_fun,V_com1,V_com2) ).
cnf(cls_finite_0,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(T_a)
| c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_MGT__def_0,axiom,
hAPP(c_Hoare__Mirabelle_OMGT,V_c) = c_Hoare__Mirabelle_Otriple_Otriple(c_fequal(tc_Com_Ostate),V_c,c_Natural_Oevalc(V_c),tc_Com_Ostate) ).
cnf(cls_com_Osimps_I50_J_0,axiom,
c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) ).
cnf(cls_com_Osimps_I27_J_0,axiom,
c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H) != c_Com_Ocom_OAss(V_vname,V_fun) ).
cnf(cls_insert__Diff__if_1,axiom,
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_x,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
| hBOOL(c_in(V_x,V_B,T_a)) ) ).
cnf(cls_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_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_dom__eq__singleton__conv_0,axiom,
( c_Map_Odom(V_f,T_a,T_b) != c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)
| V_f = c_Fun_Ofun__upd(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_x,c_Option_Ooption_OSome(c_Map_Osko__Map__Xdom__eq__singleton__conv__1__1(V_f,V_x,T_a,T_b),T_b),T_a,tc_Option_Ooption(T_b)) ) ).
cnf(cls_fun__upd__None__restrict_0,axiom,
( c_Fun_Ofun__upd(c_Map_Orestrict__map(V_m,V_D,T_a,T_b),V_x,c_Option_Ooption_ONone(T_b),T_a,tc_Option_Ooption(T_b)) = c_Map_Orestrict__map(V_m,c_HOL_Ominus__class_Ominus(V_D,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a,T_b)
| ~ hBOOL(c_in(V_x,V_D,T_a)) ) ).
cnf(cls_Un__left__commute_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).
cnf(cls_evalc_OSemi_0,axiom,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_s2))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s1),V_s2))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0),V_s0),V_s1)) ) ).
cnf(cls_image__diff__subset_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oimage(V_f,V_A,T_b,T_a),c_Set_Oimage(V_f,V_B,T_b,T_a),tc_fun(T_a,tc_bool)),c_Set_Oimage(V_f,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a),tc_fun(T_a,tc_bool)) ).
cnf(cls_evalc__elim__cases_I5_J_1,axiom,
( ~ hBOOL(hAPP(V_b,V_s))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s),V_t))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b,V_c1,V_c2)),V_s),V_t)) ) ).
cnf(cls_evalc_OIfTrue_0,axiom,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b,V_c0,V_c1)),V_s),V_s1))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0),V_s),V_s1))
| ~ hBOOL(hAPP(V_b,V_s)) ) ).
cnf(cls_Max__mono_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(c_Finite__Set_Olinorder__class_OMax(V_M,T_a),c_Finite__Set_Olinorder__class_OMax(V_N,T_a),T_a)
| ~ c_Finite__Set_Ofinite(V_N,T_a)
| V_M = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_M,V_N,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_eq__eqI_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
| V_x_H = V_y_H ) ).
cnf(cls_eq__eqI_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Ominus__class_Ominus(V_xa,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)
| V_xa = V_y ) ).
cnf(cls_evalc_OWhileTrue_0,axiom,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b,V_c)),V_s0),V_s2))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b,V_c)),V_s1),V_s2))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s0),V_s1))
| ~ hBOOL(hAPP(V_b,V_s0)) ) ).
cnf(cls_rangeI_0,axiom,
hBOOL(c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_a),T_a)) ).
cnf(cls_Diff__idemp_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)) ).
cnf(cls_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(c_in(V_x,V_S,T_a)) ) ).
cnf(cls_mem__def_1,axiom,
( hBOOL(c_in(V_x,V_S,T_a))
| ~ hBOOL(hAPP(V_S,V_x)) ) ).
cnf(cls_INT__extend__simps_I4_J_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_B,T_b,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A ).
cnf(cls_com_Osimps_I51_J_0,axiom,
c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ).
cnf(cls_elem__set_0,axiom,
( V_xo = c_Option_Ooption_OSome(V_x,T_a)
| ~ hBOOL(c_in(V_x,c_Option_Oset(V_xo,T_a),T_a)) ) ).
cnf(cls_sup__idem_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,V_x,T_a) = V_x ) ).
cnf(cls_Un__absorb_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,V_A,tc_fun(T_a,tc_bool)) = V_A ).
cnf(cls_sup__fun__eq_0,axiom,
( ~ class_Lattices_Olattice(T_b)
| hAPP(c_Lattices_Oupper__semilattice__class_Osup(V_f,V_g,tc_fun(t_a,T_b)),v_x) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(V_f,v_x),hAPP(V_g,v_x),T_b) ) ).
cnf(cls_image__subset__iff_0,axiom,
( hBOOL(c_in(hAPP(V_f,V_x),V_B,T_a))
| ~ hBOOL(c_in(V_x,V_A,T_b))
| ~ c_lessequals(c_Set_Oimage(V_f,V_A,T_b,T_a),V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_finite__surj_0,axiom,
( c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,tc_bool))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_subset__insert__iff_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ) ).
cnf(cls_subset__insert__iff_3,axiom,
( c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_diff__single__insert_0,axiom,
( c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_fold1__def_0,axiom,
c_Finite__Set_Ofold1(V_f,V_A,T_a) = c_The(c_Finite__Set_Ofold1Set(V_f,V_A,T_a),T_a) ).
cnf(cls_com_Osimps_I56_J_0,axiom,
c_Com_Ocom_OCond(V_fun,V_com1,V_com2) != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) ).
cnf(cls_le__SUPI_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_b)
| c_lessequals(hAPP(V_M,V_i),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_M,T_a,T_b),T_b)
| ~ hBOOL(c_in(V_i,V_A,T_a)) ) ).
cnf(cls_UN__upper_0,axiom,
( c_lessequals(hAPP(V_B,V_a),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_bool)),tc_fun(T_b,tc_bool))
| ~ hBOOL(c_in(V_a,V_A,T_a)) ) ).
cnf(cls_insert__Diff1_0,axiom,
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(c_in(V_x,V_B,T_a)) ) ).
cnf(cls_com_Osimps_I36_J_0,axiom,
c_Com_Ocom_OLocal(V_loc,V_fun,V_com) != c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H) ).
cnf(cls_com_Osimps_I24_J_0,axiom,
c_Com_Ocom_OAss(V_vname,V_fun) != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ).
cnf(cls_com_Osimps_I7_J_2,axiom,
( c_Com_Ocom_OCall(V_vname,V_pname,V_fun) != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H)
| V_fun = V_fun_H ) ).
cnf(cls_com_Osimps_I7_J_1,axiom,
( c_Com_Ocom_OCall(V_vname,V_pname,V_fun) != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H)
| V_pname = V_pname_H ) ).
cnf(cls_com_Osimps_I7_J_0,axiom,
( c_Com_Ocom_OCall(V_vname,V_pname,V_fun) != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H)
| V_vname = V_vname_H ) ).
cnf(cls_complete__lattice_OSup__UNIV_0,axiom,
( hAPP(V_Sup,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))) = V_top
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_complete__lattice_OInf__UNIV_0,axiom,
( hAPP(V_Inf,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))) = V_bot
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_com_Osimps_I17_J_0,axiom,
c_Com_Ocom_OWhile(V_fun_H,V_com_H) != c_Com_Ocom_OSKIP ).
cnf(cls_finite__Diff_0,axiom,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_com_Osimps_I39_J_0,axiom,
c_Com_Ocom_OWhile(V_fun_H,V_com_H) != c_Com_Ocom_OLocal(V_loc,V_fun,V_com) ).
cnf(cls_evalc_OWhileFalse_0,axiom,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b,V_c)),V_s),V_s))
| hBOOL(hAPP(V_b,V_s)) ) ).
cnf(cls_Collect__def_0,axiom,
c_Collect(V_P,T_a) = V_P ).
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_com_Osimps_I46_J_0,axiom,
c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OWhile(V_fun_H,V_com_H) ).
cnf(cls_Sup__insert_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(V_a,V_A,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_a,c_Complete__Lattice_OSup__class_OSup(V_A,T_a),T_a) ) ).
cnf(cls_sup__top__right_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Orderings_Otop__class_Otop(T_a),T_a) = c_Orderings_Otop__class_Otop(T_a) ) ).
cnf(cls_sup__top__left_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(T_a),V_x,T_a) = c_Orderings_Otop__class_Otop(T_a) ) ).
cnf(cls_Un__UNIV__left_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) ).
cnf(cls_Un__UNIV__right_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) ).
cnf(cls_com_Osimps_I44_J_0,axiom,
c_Com_Ocom_OSemi(V_com1,V_com2) != c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H) ).
cnf(cls_finite__Diff2_0,axiom,
( c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
| ~ c_Finite__Set_Ofinite(V_B,T_a) ) ).
cnf(cls_finite__Diff2_1,axiom,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_B,T_a) ) ).
cnf(cls_com_Osimps_I35_J_0,axiom,
c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OLocal(V_loc,V_fun,V_com) ).
cnf(cls_map__upd__nonempty_0,axiom,
c_Fun_Ofun__upd(V_t,V_k,c_Option_Ooption_OSome(V_x,T_b),T_a,tc_Option_Ooption(T_b)) != c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a) ).
cnf(cls_finite__UN_0,axiom,
( c_Finite__Set_Ofinite(hAPP(V_B,V_x),T_b)
| ~ hBOOL(c_in(V_x,V_A,T_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_com_Osimps_I23_J_0,axiom,
c_Com_Ocom_OLocal(V_loc_H,V_fun_H,V_com_H) != c_Com_Ocom_OAss(V_vname,V_fun) ).
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(c_in(V_x,V_A,T_b)) ) ).
cnf(cls_com_Osimps_I52_J_0,axiom,
c_Com_Ocom_OCond(V_fun,V_com1,V_com2) != c_Com_Ocom_OWhile(V_fun_H,V_com_H) ).
cnf(cls_DiffE_0,axiom,
( hBOOL(c_in(V_c,V_A,T_a))
| ~ hBOOL(c_in(V_c,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)) ) ).
cnf(cls_com_Osimps_I37_J_0,axiom,
c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H) != c_Com_Ocom_OLocal(V_loc,V_fun,V_com) ).
cnf(cls_DiffE_1,axiom,
( ~ hBOOL(c_in(V_c,V_B,T_a))
| ~ hBOOL(c_in(V_c,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)) ) ).
cnf(cls_UN__subset__iff_0,axiom,
( c_lessequals(hAPP(V_A,V_x),V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(c_in(V_x,V_I,T_b))
| ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_I,V_A,T_b,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_com_Osimps_I45_J_0,axiom,
c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ).
cnf(cls_UN__absorb_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(V_A,V_k),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_I,V_A,T_a,tc_fun(T_b,tc_bool)),tc_fun(T_b,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_I,V_A,T_a,tc_fun(T_b,tc_bool))
| ~ hBOOL(c_in(V_k,V_I,T_a)) ) ).
cnf(cls_com_Osimps_I4_J_2,axiom,
( c_Com_Ocom_OCond(V_fun,V_com1,V_com2) != c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H)
| V_com2 = V_com2_H ) ).
cnf(cls_com_Osimps_I4_J_1,axiom,
( c_Com_Ocom_OCond(V_fun,V_com1,V_com2) != c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H)
| V_com1 = V_com1_H ) ).
cnf(cls_com_Osimps_I4_J_0,axiom,
( c_Com_Ocom_OCond(V_fun,V_com1,V_com2) != c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H)
| V_fun = V_fun_H ) ).
cnf(cls_finite__Un_2,axiom,
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(V_F,V_G,tc_fun(T_a,tc_bool)),T_a)
| ~ c_Finite__Set_Ofinite(V_G,T_a)
| ~ c_Finite__Set_Ofinite(V_F,T_a) ) ).
cnf(cls_finite__UnI_0,axiom,
( c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(V_F,V_G,tc_fun(T_a,tc_bool)),T_a)
| ~ c_Finite__Set_Ofinite(V_G,T_a)
| ~ c_Finite__Set_Ofinite(V_F,T_a) ) ).
cnf(cls_atLeastatMost__subset__iff_3,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a),c_SetInterval_Oord__class_OatLeastAtMost(V_c,V_d,T_a),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_b,V_d,T_a)
| ~ c_lessequals(V_c,V_a,T_a) ) ).
cnf(cls_atLeastatMost__subset__iff_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_b,V_d,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a),c_SetInterval_Oord__class_OatLeastAtMost(V_c,V_d,T_a),tc_fun(T_a,tc_bool)) ) ).
cnf(cls_atLeastatMost__subset__iff_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_c,V_a,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a),c_SetInterval_Oord__class_OatLeastAtMost(V_c,V_d,T_a),tc_fun(T_a,tc_bool)) ) ).
cnf(cls_UNIV__I_0,axiom,
hBOOL(c_in(V_x,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a)) ).
cnf(cls_com_Osimps_I57_J_0,axiom,
c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) != c_Com_Ocom_OCond(V_fun,V_com1,V_com2) ).
cnf(cls_com_Osimps_I28_J_0,axiom,
c_Com_Ocom_OAss(V_vname,V_fun) != c_Com_Ocom_OWhile(V_fun_H,V_com_H) ).
cnf(cls_atLeastatMost__subset__iff_2,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a),c_SetInterval_Oord__class_OatLeastAtMost(V_c,V_d,T_a),tc_fun(T_a,tc_bool))
| c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_com_Osimps_I22_J_0,axiom,
c_Com_Ocom_OAss(V_vname,V_fun) != c_Com_Ocom_OLocal(V_loc_H,V_fun_H,V_com_H) ).
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_sup1E_0,axiom,
( hBOOL(hAPP(V_B,V_x))
| hBOOL(hAPP(V_A,V_x))
| ~ hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_x)) ) ).
cnf(cls_sup1CI_0,axiom,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_x))
| ~ hBOOL(hAPP(V_B,V_x)) ) ).
cnf(cls_sup1CI_1,axiom,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_x))
| ~ hBOOL(hAPP(V_A,V_x)) ) ).
cnf(cls_UnE_0,axiom,
( hBOOL(c_in(V_c,V_B,T_a))
| hBOOL(c_in(V_c,V_A,T_a))
| ~ hBOOL(c_in(V_c,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)) ) ).
cnf(cls_com_Osimps_I38_J_0,axiom,
c_Com_Ocom_OLocal(V_loc,V_fun,V_com) != c_Com_Ocom_OWhile(V_fun_H,V_com_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(c_in(V_x,V_A,T_b)) ) ).
cnf(cls_domIff_0,axiom,
( hAPP(V_m,V_a) != c_Option_Ooption_ONone(T_b)
| ~ hBOOL(c_in(V_a,c_Map_Odom(V_m,T_a,T_b),T_a)) ) ).
cnf(cls_domIff_1,axiom,
( hBOOL(c_in(V_a,c_Map_Odom(V_m,T_a,T_b),T_a))
| hAPP(V_m,V_a) = c_Option_Ooption_ONone(T_b) ) ).
cnf(cls_finite__Un_0,axiom,
( c_Finite__Set_Ofinite(V_F,T_a)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(V_F,V_G,tc_fun(T_a,tc_bool)),T_a) ) ).
cnf(cls_finite__Un_1,axiom,
( c_Finite__Set_Ofinite(V_G,T_a)
| ~ c_Finite__Set_Ofinite(c_Lattices_Oupper__semilattice__class_Osup(V_F,V_G,tc_fun(T_a,tc_bool)),T_a) ) ).
cnf(cls_UN__extend__simps_I2_J_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_A,T_b,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = V_B ).
cnf(cls_UN__extend__simps_I3_J_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_B,T_b,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A ).
cnf(cls_com_Osimps_I26_J_0,axiom,
c_Com_Ocom_OAss(V_vname,V_fun) != c_Com_Ocom_OCond(V_fun_H,V_com1_H,V_com2_H) ).
cnf(cls_com_Osimps_I16_J_0,axiom,
c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H,V_com_H) ).
cnf(cls_com_Osimps_I10_J_0,axiom,
c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(V_loc_H,V_fun_H,V_com_H) ).
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_Diff__mono_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_C,V_D,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_D,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_C,tc_fun(T_a,tc_bool)) ) ).
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_top1I_0,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_x)) ).
cnf(cls_top__fun__eq_0,axiom,
( ~ class_Orderings_Otop(T_b)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,T_b)),v_x) = c_Orderings_Otop__class_Otop(T_b) ) ).
cnf(cls_set__empty__eq_0,axiom,
( c_Option_Oset(V_xo,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| V_xo = c_Option_Ooption_ONone(T_a) ) ).
cnf(cls_Diff__subset__conv_1,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Diff__subset__conv_0,axiom,
( c_lessequals(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_evalc__elim__cases_I1_J_0,axiom,
( V_t = V_s
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_t)) ) ).
cnf(cls_le__funD_0,axiom,
( ~ class_HOL_Oord(T_b)
| c_lessequals(hAPP(V_f,V_x),hAPP(V_g,V_x),T_b)
| ~ c_lessequals(V_f,V_g,tc_fun(T_a,T_b)) ) ).
cnf(cls_sup__bot__left_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(T_a),V_x,T_a) = V_x ) ).
cnf(cls_sup__bot__right_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Orderings_Obot__class_Obot(T_a),T_a) = V_x ) ).
cnf(cls_bot__least_0,axiom,
( ~ class_Orderings_Obot(T_a)
| c_lessequals(c_Orderings_Obot__class_Obot(T_a),V_x,T_a) ) ).
cnf(cls_sup__eq__bot__eq1_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,T_a) != c_Orderings_Obot__class_Obot(T_a)
| V_A = c_Orderings_Obot__class_Obot(T_a) ) ).
cnf(cls_sup__eq__bot__eq2_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,T_a) != c_Orderings_Obot__class_Obot(T_a)
| V_B = c_Orderings_Obot__class_Obot(T_a) ) ).
cnf(cls_Un__empty_2,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_complete__lattice_OInf__empty_0,axiom,
( hAPP(V_Inf,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = V_top
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_complete__lattice_OSup__empty_0,axiom,
( hAPP(V_Sup,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = V_bot
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_empty__Collect__eq_0,axiom,
( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Collect(V_P,T_a)
| ~ hBOOL(hAPP(V_P,V_x)) ) ).
cnf(cls_ex__in__conv_0,axiom,
~ hBOOL(c_in(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) ).
cnf(cls_ball__empty_0,axiom,
( hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(c_in(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) ) ).
cnf(cls_empty__iff_0,axiom,
~ hBOOL(c_in(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) ).
cnf(cls_emptyE_0,axiom,
~ hBOOL(c_in(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) ).
cnf(cls_subset__empty_1,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).
cnf(cls_subset__empty_0,axiom,
( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Collect__empty__eq_0,axiom,
( c_Collect(V_P,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(V_P,V_x)) ) ).
cnf(cls_empty__fold1SetE_0,axiom,
~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_x)) ).
cnf(cls_UNIV__not__empty_0,axiom,
c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_empty__Diff_0,axiom,
c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_Un__empty__right_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A ).
cnf(cls_Un__empty__left_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = V_B ).
cnf(cls_Diff__cancel_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,V_A,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_Diff__empty_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A ).
cnf(cls_finite_OemptyI_0,axiom,
c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ).
cnf(cls_empty__subsetI_0,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) ).
cnf(cls_bex__empty_0,axiom,
( ~ hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(c_in(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) ) ).
cnf(cls_Un__empty_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| V_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Un__empty_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_finite__range__imageI_0,axiom,
( c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(V_f,V_g,T_a,T_c,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_c),T_c)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(V_g,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_a),T_a) ) ).
cnf(cls_insert__Diff_0,axiom,
( c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = V_A
| ~ hBOOL(c_in(V_a,V_A,T_a)) ) ).
cnf(cls_Sup__binary_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a) ) ).
cnf(cls_subset__insert__iff_4,axiom,
( c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Diff__insert__absorb_0,axiom,
( c_HOL_Ominus__class_Ominus(c_Set_Oinsert(V_x,V_A,T_a),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)) = V_A
| hBOOL(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_insert__mono_0,axiom,
( c_lessequals(c_Set_Oinsert(V_a,V_C,T_a),c_Set_Oinsert(V_a,V_D,T_a),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_C,V_D,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_insert__iff_2,axiom,
( hBOOL(c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a))
| ~ hBOOL(c_in(V_a,V_A,T_a)) ) ).
cnf(cls_insertCI_0,axiom,
( hBOOL(c_in(V_a,c_Set_Oinsert(V_b,V_B,T_a),T_a))
| ~ hBOOL(c_in(V_a,V_B,T_a)) ) ).
cnf(cls_complete__lattice_OInf__insert_0,axiom,
( hAPP(V_Inf,c_Set_Oinsert(V_a,V_A,T_a)) = hAPP(hAPP(V_inf,V_a),hAPP(V_Inf,V_A))
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_complete__lattice_OSup__insert_0,axiom,
( hAPP(V_Sup,c_Set_Oinsert(V_a,V_A,T_a)) = hAPP(hAPP(V_sup,V_a),hAPP(V_Sup,V_A))
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_insertE_0,axiom,
( hBOOL(c_in(V_a,V_A,T_a))
| V_a = V_b
| ~ hBOOL(c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a)) ) ).
cnf(cls_finite__insert_1,axiom,
( c_Finite__Set_Ofinite(c_Set_Oinsert(V_a,V_A,T_a),T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_finite__insert_0,axiom,
( c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(V_a,V_A,T_a),T_a) ) ).
cnf(cls_subset__insertI_0,axiom,
c_lessequals(V_B,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) ).
cnf(cls_Un__insert__right_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ).
cnf(cls_Un__insert__left_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,V_B,T_a),V_C,tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),T_a) ).
cnf(cls_subset__insertI2_0,axiom,
( c_lessequals(V_A,c_Set_Oinsert(V_b,V_B,T_a),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_insert__subset_1,axiom,
( c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_insert__iff_1,axiom,
hBOOL(c_in(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a)) ).
cnf(cls_insertI1_0,axiom,
hBOOL(c_in(V_a,c_Set_Oinsert(V_a,V_B,T_a),T_a)) ).
cnf(cls_insertCI_1,axiom,
hBOOL(c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a)) ).
cnf(cls_insert__ident_0,axiom,
( c_Set_Oinsert(V_x,V_A,T_a) != c_Set_Oinsert(V_x,V_B,T_a)
| hBOOL(c_in(V_x,V_B,T_a))
| hBOOL(c_in(V_x,V_A,T_a))
| V_A = V_B ) ).
cnf(cls_insert__absorb_0,axiom,
( c_Set_Oinsert(V_a,V_A,T_a) = V_A
| ~ hBOOL(c_in(V_a,V_A,T_a)) ) ).
cnf(cls_fun__upd__image_0,axiom,
( c_Set_Oimage(c_Fun_Ofun__upd(V_f,V_x,V_y,T_b,T_a),V_A,T_b,T_a) = c_Set_Oinsert(V_y,c_Set_Oimage(V_f,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b),tc_fun(T_b,tc_bool)),T_b,T_a),T_a)
| ~ hBOOL(c_in(V_x,V_A,T_b)) ) ).
cnf(cls_image__Un_0,axiom,
c_Set_Oimage(V_f,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(V_f,V_A,T_b,T_a),c_Set_Oimage(V_f,V_B,T_b,T_a),tc_fun(T_a,tc_bool)) ).
cnf(cls_subset__image__iff_2,axiom,
( ~ c_lessequals(V_x,V_A,tc_fun(T_b,tc_bool))
| c_lessequals(c_Set_Oimage(V_f,V_x,T_b,T_a),c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool)) ) ).
cnf(cls_image__mono_0,axiom,
( c_lessequals(c_Set_Oimage(V_f,V_A,T_a,T_b),c_Set_Oimage(V_f,V_B,T_a,T_b),tc_fun(T_b,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_finite__imageI_0,axiom,
( c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b)
| ~ c_Finite__Set_Ofinite(V_F,T_a) ) ).
cnf(cls_rev__image__eqI_0,axiom,
( ~ hBOOL(c_in(V_x,V_A,T_aa))
| hBOOL(c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_aa,T_a),T_a)) ) ).
cnf(cls_image__iff_2,axiom,
( ~ hBOOL(c_in(V_x,V_A,T_b))
| hBOOL(c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_b,T_a),T_a)) ) ).
cnf(cls_image__eqI_0,axiom,
( hBOOL(c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_b,T_a),T_a))
| ~ hBOOL(c_in(V_x,V_A,T_b)) ) ).
cnf(cls_imageI_0,axiom,
( hBOOL(c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b))
| ~ hBOOL(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_dom__fun__upd_0,axiom,
c_Map_Odom(c_Fun_Ofun__upd(V_f,V_x,c_Option_Ooption_ONone(T_b),T_a,tc_Option_Ooption(T_b)),T_a,T_b) = c_HOL_Ominus__class_Ominus(c_Map_Odom(V_f,T_a,T_b),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)) ).
cnf(cls_dom__eq__empty__conv_0,axiom,
( c_Map_Odom(V_f,T_a,T_b) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| V_f = c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a) ) ).
cnf(cls_dom__empty_0,axiom,
c_Map_Odom(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),T_a,T_b) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_dom__minus_0,axiom,
( hAPP(V_f,V_x) != c_Option_Ooption_ONone(T_a)
| c_HOL_Ominus__class_Ominus(c_Map_Odom(V_f,T_b,T_a),c_Set_Oinsert(V_x,V_A,T_b),tc_fun(T_b,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Map_Odom(V_f,T_b,T_a),V_A,tc_fun(T_b,tc_bool)) ) ).
cnf(cls_dom__fun__upd_1,axiom,
( c_Map_Odom(c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,tc_Option_Ooption(T_b)),T_a,T_b) = c_Set_Oinsert(V_x,c_Map_Odom(V_f,T_a,T_b),T_a)
| V_y = c_Option_Ooption_ONone(T_b) ) ).
cnf(cls_map__upd__eqD1_0,axiom,
( c_Fun_Ofun__upd(V_m,V_a,c_Option_Ooption_OSome(V_x,T_b),T_a,tc_Option_Ooption(T_b)) != c_Fun_Ofun__upd(V_n,V_a,c_Option_Ooption_OSome(V_y,T_b),T_a,tc_Option_Ooption(T_b))
| V_x = V_y ) ).
cnf(cls_the_Osimps_0,axiom,
hAPP(c_Option_Othe(T_a),c_Option_Ooption_OSome(V_x,T_a)) = V_x ).
cnf(cls_map__upd__triv_0,axiom,
( hAPP(V_t,V_k) != c_Option_Ooption_OSome(V_x,T_a)
| c_Fun_Ofun__upd(V_t,V_k,c_Option_Ooption_OSome(V_x,T_a),T_b,tc_Option_Ooption(T_a)) = V_t ) ).
cnf(cls_map__upd__Some__unfold_3,axiom,
hAPP(c_Fun_Ofun__upd(V_m,V_xa,c_Option_Ooption_OSome(V_x,T_a),T_aa,tc_Option_Ooption(T_a)),V_xa) = c_Option_Ooption_OSome(V_x,T_a) ).
cnf(cls_not__None__eq_1,axiom,
c_Option_Ooption_OSome(V_xa,T_a) != c_Option_Ooption_ONone(T_a) ).
cnf(cls_option_Osimps_I3_J_0,axiom,
c_Option_Ooption_OSome(V_a_H,T_a) != c_Option_Ooption_ONone(T_a) ).
cnf(cls_map__upd__Some__unfold_4,axiom,
( hAPP(V_m,V_x) != c_Option_Ooption_OSome(V_y,T_a)
| V_x = V_a
| hAPP(c_Fun_Ofun__upd(V_m,V_a,c_Option_Ooption_OSome(V_b,T_a),T_b,tc_Option_Ooption(T_a)),V_x) = c_Option_Ooption_OSome(V_y,T_a) ) ).
cnf(cls_map__upd__Some__unfold_2,axiom,
( hAPP(c_Fun_Ofun__upd(V_m,V_a,c_Option_Ooption_OSome(V_b,T_a),T_b,tc_Option_Ooption(T_a)),V_x) != c_Option_Ooption_OSome(V_y,T_a)
| hAPP(V_m,V_x) = c_Option_Ooption_OSome(V_y,T_a)
| V_b = V_y ) ).
cnf(cls_map__upd__Some__unfold_0,axiom,
( hAPP(c_Fun_Ofun__upd(V_m,V_a,c_Option_Ooption_OSome(V_b,T_a),T_b,tc_Option_Ooption(T_a)),V_x) != c_Option_Ooption_OSome(V_y,T_a)
| hAPP(V_m,V_x) = c_Option_Ooption_OSome(V_y,T_a)
| V_x = V_a ) ).
cnf(cls_map__upd__Some__unfold_1,axiom,
( V_b = V_y
| hAPP(c_Fun_Ofun__upd(V_m,V_x,c_Option_Ooption_OSome(V_b,T_aa),T_a,tc_Option_Ooption(T_aa)),V_x) != c_Option_Ooption_OSome(V_y,T_aa) ) ).
cnf(cls_not__Some__eq_1,axiom,
c_Option_Ooption_ONone(T_a) != c_Option_Ooption_OSome(V_y,T_a) ).
cnf(cls_option_Osimps_I2_J_0,axiom,
c_Option_Ooption_ONone(T_a) != c_Option_Ooption_OSome(V_a_H,T_a) ).
cnf(cls_com_Osimps_I19_J_0,axiom,
hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP ).
cnf(cls_com_Osimps_I58_J_0,axiom,
c_Com_Ocom_OWhile(V_fun,V_com) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
cnf(cls_com_Osimps_I55_J_0,axiom,
hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OCond(V_fun,V_com1,V_com2) ).
cnf(cls_com_Osimps_I54_J_0,axiom,
c_Com_Ocom_OCond(V_fun,V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
cnf(cls_com_Osimps_I31_J_0,axiom,
hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OAss(V_vname,V_fun) ).
cnf(cls_com_Osimps_I30_J_0,axiom,
c_Com_Ocom_OAss(V_vname,V_fun) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
cnf(cls_com_Osimps_I41_J_0,axiom,
hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OLocal(V_loc,V_fun,V_com) ).
cnf(cls_com_Osimps_I59_J_0,axiom,
hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OWhile(V_fun,V_com) ).
cnf(cls_com_Osimps_I63_J_0,axiom,
c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) != hAPP(c_Com_Ocom_OBODY,V_pname) ).
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_I48_J_0,axiom,
c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
cnf(cls_com_Osimps_I40_J_0,axiom,
c_Com_Ocom_OLocal(V_loc,V_fun,V_com) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
cnf(cls_com_Osimps_I62_J_0,axiom,
hAPP(c_Com_Ocom_OBODY,V_pname) != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) ).
cnf(cls_com_Osimps_I18_J_0,axiom,
c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
cnf(cls_weaken_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_lessequals(V_ts,V_ts_H,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts_H,T_a) ) ).
cnf(cls_thin_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_lessequals(V_G_H,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_H,V_ts,T_a) ) ).
cnf(cls_hoare__sound_0,axiom,
( c_Hoare__Mirabelle_Ohoare__valids(V_G,V_ts,T_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a) ) ).
cnf(cls_asm_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_lessequals(V_ts,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)) ) ).
cnf(cls_dom__const_0,axiom,
c_Map_Odom(c_COMBK(c_Option_Ooption_OSome(V_y,T_b),tc_Option_Ooption(T_b),T_a),T_a,T_b) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) ).
cnf(cls_com_Osimps_I60_J_0,axiom,
c_Com_Ocom_OWhile(V_fun,V_com) != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) ).
cnf(cls_evalc_OSkip_0,axiom,
hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)) ).
cnf(cls_com_Osimps_I25_J_0,axiom,
c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OAss(V_vname,V_fun) ).
cnf(cls_equalityI_0,axiom,
( V_A = V_B
| ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_com__det_0,axiom,
( V_u = V_t
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_u))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) ) ).
cnf(cls_set__eq__subset_2,axiom,
( V_A = V_B
| ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_order__eq__iff_2,axiom,
( ~ class_Orderings_Oorder(T_a)
| V_x = V_y
| ~ c_lessequals(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_order__antisym_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| V_x = V_y
| ~ c_lessequals(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_order__antisym__conv_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| V_x = V_y
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_com_Osimps_I11_J_0,axiom,
c_Com_Ocom_OLocal(V_loc_H,V_fun_H,V_com_H) != c_Com_Ocom_OSKIP ).
cnf(cls_sup__absorb1_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_x
| ~ c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_le__iff__sup_1,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) != V_y
| c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_le__iff__sup_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_y
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_Un__absorb1_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) = V_B
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Un__absorb2_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) = V_A
| ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_subset__Un__eq_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) != V_B
| c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_bot__empty__eq_0,axiom,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) ).
cnf(cls_Min__antimono_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(V_N,T_a),c_Finite__Set_Olinorder__class_OMin(V_M,T_a),T_a)
| ~ c_Finite__Set_Ofinite(V_N,T_a)
| V_M = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_M,V_N,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_evalc__elim__cases_I5_J_0,axiom,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2),V_s),V_t))
| hBOOL(hAPP(V_b,V_s))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b,V_c1,V_c2)),V_s),V_t)) ) ).
cnf(cls_evalc_OIfFalse_0,axiom,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b,V_c0,V_c1)),V_s),V_s1))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s),V_s1))
| hBOOL(hAPP(V_b,V_s)) ) ).
cnf(cls_com_Osimps_I8_J_0,axiom,
c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(V_vname_H,V_fun_H) ).
cnf(cls_UN__insert_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(V_a,V_A,T_b),V_B,T_b,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(V_B,V_a),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_b,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).
cnf(cls_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_triple_Oinject_0,axiom,
( c_Hoare__Mirabelle_Otriple_Otriple(V_fun1,V_com,V_fun2,T_a) != c_Hoare__Mirabelle_Otriple_Otriple(V_fun1_H,V_com_H,V_fun2_H,T_a)
| V_fun1 = V_fun1_H ) ).
cnf(cls_triple_Oinject_1,axiom,
( c_Hoare__Mirabelle_Otriple_Otriple(V_fun1,V_com,V_fun2,T_a) != c_Hoare__Mirabelle_Otriple_Otriple(V_fun1_H,V_com_H,V_fun2_H,T_a)
| V_com = V_com_H ) ).
cnf(cls_triple_Oinject_2,axiom,
( c_Hoare__Mirabelle_Otriple_Otriple(V_fun1,V_com,V_fun2,T_a) != c_Hoare__Mirabelle_Otriple_Otriple(V_fun1_H,V_com_H,V_fun2_H,T_a)
| V_fun2 = V_fun2_H ) ).
cnf(cls_com_Osimps_I29_J_0,axiom,
c_Com_Ocom_OWhile(V_fun_H,V_com_H) != c_Com_Ocom_OAss(V_vname,V_fun) ).
cnf(cls_Inf__lower_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(V_A,T_a),V_x,T_a)
| ~ hBOOL(c_in(V_x,V_A,T_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)
| c_lessequals(V_a,V_b,T_a) ) ).
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)
| ~ c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_Diff__UNIV_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_Un__mono_0,axiom,
( c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_C,V_D,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_B,V_D,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_C,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_subset__UNIV_0,axiom,
c_lessequals(V_A,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).
cnf(cls_top__greatest_0,axiom,
( ~ class_Orderings_Otop(T_a)
| c_lessequals(V_x,c_Orderings_Otop__class_Otop(T_a),T_a) ) ).
cnf(cls_fun__upd__image_1,axiom,
( c_Set_Oimage(c_Fun_Ofun__upd(V_f,V_x,V_y,T_b,T_a),V_A,T_b,T_a) = c_Set_Oimage(V_f,V_A,T_b,T_a)
| hBOOL(c_in(V_x,V_A,T_b)) ) ).
cnf(cls_com_Osimps_I1_J_1,axiom,
( c_Com_Ocom_OAss(V_vname,V_fun) != c_Com_Ocom_OAss(V_vname_H,V_fun_H)
| V_fun = V_fun_H ) ).
cnf(cls_com_Osimps_I1_J_0,axiom,
( c_Com_Ocom_OAss(V_vname,V_fun) != c_Com_Ocom_OAss(V_vname_H,V_fun_H)
| V_vname = V_vname_H ) ).
cnf(cls_com_Osimps_I33_J_0,axiom,
c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) != c_Com_Ocom_OAss(V_vname,V_fun) ).
cnf(cls_com_Osimps_I13_J_0,axiom,
c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ).
cnf(cls_insert__subset_2,axiom,
( c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(c_in(V_x,V_B,T_a)) ) ).
cnf(cls_com_Osimps_I2_J_2,axiom,
( c_Com_Ocom_OLocal(V_loc,V_fun,V_com) != c_Com_Ocom_OLocal(V_loc_H,V_fun_H,V_com_H)
| V_com = V_com_H ) ).
cnf(cls_com_Osimps_I2_J_1,axiom,
( c_Com_Ocom_OLocal(V_loc,V_fun,V_com) != c_Com_Ocom_OLocal(V_loc_H,V_fun_H,V_com_H)
| V_fun = V_fun_H ) ).
cnf(cls_com_Osimps_I2_J_0,axiom,
( c_Com_Ocom_OLocal(V_loc,V_fun,V_com) != c_Com_Ocom_OLocal(V_loc_H,V_fun_H,V_com_H)
| V_loc = V_loc_H ) ).
cnf(cls_elem__set_1,axiom,
hBOOL(c_in(V_x,c_Option_Oset(c_Option_Ooption_OSome(V_x,T_a),T_a),T_a)) ).
cnf(cls_finite__Diff__insert_0,axiom,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)),T_a) ) ).
cnf(cls_finite__Diff__insert_1,axiom,
( c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)),T_a)
| ~ c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ) ).
cnf(cls_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_com_Osimps_I20_J_0,axiom,
c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) ).
cnf(cls_com_Osimps_I47_J_0,axiom,
c_Com_Ocom_OWhile(V_fun_H,V_com_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ).
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_UnCI_0,axiom,
( hBOOL(c_in(V_c,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a))
| ~ hBOOL(c_in(V_c,V_B,T_a)) ) ).
cnf(cls_UnCI_1,axiom,
( hBOOL(c_in(V_c,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a))
| ~ hBOOL(c_in(V_c,V_A,T_a)) ) ).
cnf(cls_evalc__WHILE__case_0,axiom,
( hBOOL(hAPP(V_b,V_s))
| V_t = V_s
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b,V_c)),V_s),V_t)) ) ).
cnf(cls_le__sup__iff_1,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a) ) ).
cnf(cls_le__sup__iff_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a) ) ).
cnf(cls_le__supI2_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),T_a)
| ~ c_lessequals(V_x,V_b,T_a) ) ).
cnf(cls_le__supI1_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),T_a)
| ~ c_lessequals(V_x,V_a,T_a) ) ).
cnf(cls_le__supE_1,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(V_b,V_x,T_a)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),V_x,T_a) ) ).
cnf(cls_le__supE_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(V_a,V_x,T_a)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),V_x,T_a) ) ).
cnf(cls_Un__subset__iff_0,axiom,
( c_lessequals(V_A,V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Un__subset__iff_1,axiom,
( c_lessequals(V_B,V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Max__in_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(V_A,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_xt1_I6_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_z,V_x,T_a)
| ~ c_lessequals(V_z,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_order__trans_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_set__mp_0,axiom,
( hBOOL(c_in(V_x,V_B,T_a))
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_subsetD_0,axiom,
( hBOOL(c_in(V_c,V_B,T_a))
| ~ hBOOL(c_in(V_c,V_A,T_a))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_equalityE_0,axiom,
c_lessequals(V_x,V_x,tc_fun(T_a,tc_bool)) ).
cnf(cls_set__rev__mp_0,axiom,
( hBOOL(c_in(V_x,V_B,T_a))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_subset__iff_0,axiom,
( hBOOL(c_in(V_t,V_B,T_a))
| ~ hBOOL(c_in(V_t,V_A,T_a))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_subset__refl_0,axiom,
c_lessequals(V_A,V_A,tc_fun(T_a,tc_bool)) ).
cnf(cls_subset__trans_0,axiom,
( c_lessequals(V_A,V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_B,V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_predicate1D_0,axiom,
( hBOOL(hAPP(V_Q,V_x))
| ~ hBOOL(hAPP(V_P,V_x))
| ~ c_lessequals(V_P,V_Q,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_order__eq__iff_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) ) ).
cnf(cls_order__eq__refl_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_lessequals(V_x,V_x,T_a) ) ).
cnf(cls_finite__subset_0,axiom,
( c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_rev__predicate1D_0,axiom,
( hBOOL(hAPP(V_Q,V_x))
| ~ c_lessequals(V_P,V_Q,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(V_P,V_x)) ) ).
cnf(cls_rev__finite__subset_0,axiom,
( c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a) ) ).
cnf(cls_com_Osimps_I21_J_0,axiom,
c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) != c_Com_Ocom_OSKIP ).
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))
| c_lessequals(V_a,V_b,T_a) ) ).
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))
| ~ c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_Min__in_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(V_A,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_UN__Un_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_b,tc_bool)),V_M,T_b,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_M,T_b,tc_fun(T_a,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_B,V_M,T_b,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).
cnf(cls_the__sym__eq__trivial_0,axiom,
c_The(hAPP(c_fequal(T_a),V_x),T_a) = V_x ).
cnf(cls_Min__le_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(c_Finite__Set_Olinorder__class_OMin(V_A,T_a),V_x,T_a)
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
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,
( c_HOL_Ominus__class_Ominus(V_B,c_HOL_Ominus__class_Ominus(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A
| ~ c_lessequals(V_B,V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_le__eqI_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
| c_lessequals(V_y_H,V_x_H,T_a)
| ~ c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_le__eqI_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
| c_lessequals(V_y,V_x,T_a)
| ~ c_lessequals(V_y_H,V_x_H,T_a) ) ).
cnf(cls_com_Osimps_I9_J_0,axiom,
c_Com_Ocom_OAss(V_vname_H,V_fun_H) != c_Com_Ocom_OSKIP ).
cnf(cls_Max__ge_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_x,c_Finite__Set_Olinorder__class_OMax(V_A,T_a),T_a)
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_com_Osimps_I42_J_0,axiom,
c_Com_Ocom_OLocal(V_loc,V_fun,V_com) != c_Com_Ocom_OCall(V_vname_H,V_pname_H,V_fun_H) ).
cnf(cls_evalc__elim__cases_I5_J_2,axiom,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2),V_s),V_t))
| hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s),V_t))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_b,V_c1,V_c2)),V_s),V_t)) ) ).
cnf(cls_Sup__upper_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| c_lessequals(V_x,c_Complete__Lattice_OSup__class_OSup(V_A,T_a),T_a)
| ~ hBOOL(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_com_Osimps_I12_J_0,axiom,
c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ).
cnf(cls_linorder__linear_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_escape_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(V_P,V_c,V_Q,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(V_P,v_sko__Hoare__Mirabelle__Xescape__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xescape__2(V_G,V_P,V_Q,V_c))) ) ).
cnf(cls_evalc_OBody_0,axiom,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),V_s1))
| ~ hBOOL(hAPP(hAPP(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,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),V_s1))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_s1)) ) ).
cnf(cls_WTs__elim__cases_I5_J_0,axiom,
( c_Com_OWT(V_c1)
| ~ c_Com_OWT(c_Com_Ocom_OCond(V_b,V_c1,V_c2)) ) ).
cnf(cls_WTs__elim__cases_I5_J_1,axiom,
( c_Com_OWT(V_c2)
| ~ c_Com_OWT(c_Com_Ocom_OCond(V_b,V_c1,V_c2)) ) ).
cnf(cls_WT_OSemi_0,axiom,
( c_Com_OWT(c_Com_Ocom_OSemi(V_c0,V_c1))
| ~ c_Com_OWT(V_c1)
| ~ c_Com_OWT(V_c0) ) ).
cnf(cls_WTs__elim__cases_I4_J_0,axiom,
( c_Com_OWT(V_c1)
| ~ c_Com_OWT(c_Com_Ocom_OSemi(V_c1,V_c2)) ) ).
cnf(cls_WTs__elim__cases_I4_J_1,axiom,
( c_Com_OWT(V_c2)
| ~ c_Com_OWT(c_Com_Ocom_OSemi(V_c1,V_c2)) ) ).
cnf(cls_WT_OIf_0,axiom,
( c_Com_OWT(c_Com_Ocom_OCond(V_b,V_c0,V_c1))
| ~ c_Com_OWT(V_c1)
| ~ c_Com_OWT(V_c0) ) ).
cnf(cls_WT_OSkip_0,axiom,
c_Com_OWT(c_Com_Ocom_OSKIP) ).
cnf(cls_WT_OAssign_0,axiom,
c_Com_OWT(c_Com_Ocom_OAss(V_X,V_a)) ).
cnf(cls_While_0,axiom,
( c_Com_OWT(c_Com_Ocom_OWhile(V_b,V_c))
| ~ c_Com_OWT(V_c) ) ).
cnf(cls_WTs__elim__cases_I6_J_0,axiom,
( c_Com_OWT(V_c)
| ~ c_Com_OWT(c_Com_Ocom_OWhile(V_b,V_c)) ) ).
cnf(cls_WT_OLocal_0,axiom,
( c_Com_OWT(c_Com_Ocom_OLocal(V_Y,V_a,V_c))
| ~ c_Com_OWT(V_c) ) ).
cnf(cls_WTs__elim__cases_I3_J_0,axiom,
( c_Com_OWT(V_c)
| ~ c_Com_OWT(c_Com_Ocom_OLocal(V_Y,V_a,V_c)) ) ).
cnf(cls_MGT__def__raw_0,axiom,
hAPP(c_Hoare__Mirabelle_OMGT,v_c) = c_Hoare__Mirabelle_Otriple_Otriple(c_fequal(tc_Com_Ostate),v_c,c_Natural_Oevalc(v_c),tc_Com_Ostate) ).
cnf(cls_dom__eq__singleton__conv_1,axiom,
c_Map_Odom(c_Fun_Ofun__upd(c_COMBK(c_Option_Ooption_ONone(T_b),tc_Option_Ooption(T_b),T_a),V_x,c_Option_Ooption_OSome(V_xa,T_b),T_a,tc_Option_Ooption(T_b)),T_a,T_b) = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ).
cnf(cls_single__stateE_0,axiom,
( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(V_t) != V_t
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ) ).
cnf(cls_image__constant_0,axiom,
( c_Set_Oimage(c_COMBK(V_c,T_b,T_a),V_A,T_a,T_b) = c_Set_Oinsert(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b)
| ~ hBOOL(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_hoare__derivs_OSkip_0,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OSKIP,V_P,T_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a)),T_a) ).
cnf(cls_Comp_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(V_P,c_Com_Ocom_OSemi(V_c,V_d),V_R,T_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a)),T_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(V_Q,V_d,V_R,T_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a)),T_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(V_P,V_c,V_Q,T_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a)),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_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_range__composition_0,axiom,
c_Set_Oimage(c_COMBB(V_f,V_g,T_c,T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_a) = c_Set_Oimage(V_f,c_Set_Oimage(V_g,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_c),T_c,T_a) ).
cnf(cls_singleton__conv2_0,axiom,
c_Collect(hAPP(c_fequal(T_a),V_a),T_a) = c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ).
cnf(cls_subset__singletonD_0,axiom,
( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)) ) ).
cnf(cls_singleton__iff_1,axiom,
hBOOL(c_in(V_x,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)) ).
cnf(cls_complete__lattice_OInf__singleton_0,axiom,
( hAPP(V_Inf,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) = V_a
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_complete__lattice_OSup__singleton_0,axiom,
( hAPP(V_Sup,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) = V_a
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_Sup__singleton_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = V_a ) ).
cnf(cls_Nitpick_OEx1__def_2,axiom,
hBOOL(hAPP(c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a))) ).
cnf(cls_UN__extend__simps_I1_J_0,axiom,
c_Set_Oinsert(V_a,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_B,T_b,tc_fun(T_a,tc_bool)),T_a) = c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ).
cnf(cls_fold1Set__sing_1,axiom,
hBOOL(hAPP(c_Finite__Set_Ofold1Set(V_f,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a),V_x)) ).
cnf(cls_Min__singleton_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = V_a ) ).
cnf(cls_Nitpick_OThe__psimp_0,axiom,
c_The(c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = V_x ).
cnf(cls_complete__lattice_OInf__binary_0,axiom,
( hAPP(V_Inf,c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)) = hAPP(hAPP(V_inf,V_a),V_b)
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_complete__lattice_OSup__binary_0,axiom,
( hAPP(V_Sup,c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)) = hAPP(hAPP(V_sup,V_a),V_b)
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_Diff__insert2_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) ).
cnf(cls_Diff__insert_0,axiom,
c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)) ).
cnf(cls_fold1Set__sing_0,axiom,
( V_a = V_b
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(V_f,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a),V_b)) ) ).
cnf(cls_contents__eq_0,axiom,
c_Set_Ocontents(c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = V_x ).
cnf(cls_Nitpick_OEx1__def_3,axiom,
( V_y = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)
| ~ hBOOL(hAPP(c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_y)) ) ).
cnf(cls_singletonE_0,axiom,
( V_b = V_a
| ~ hBOOL(c_in(V_b,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)) ) ).
cnf(cls_fold1__singleton_0,axiom,
c_Finite__Set_Ofold1(V_f,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = V_a ).
cnf(cls_Max__singleton_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = V_a ) ).
cnf(cls_insert__Diff__single_0,axiom,
c_Set_Oinsert(V_a,c_HOL_Ominus__class_Ominus(V_A,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)),T_a) = c_Set_Oinsert(V_a,V_A,T_a) ).
cnf(cls_atLeastAtMost__singleton_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_a,T_a) = c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ) ).
cnf(cls_comm__monoid__add_Ononempty__iff_2,axiom,
( c_Set_Oinsert(V_x,V_xa,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| hBOOL(c_in(V_x,V_xa,T_a)) ) ).
cnf(cls_insert__is__Un_0,axiom,
c_Set_Oinsert(V_a,V_A,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_A,tc_fun(T_a,tc_bool)) ).
cnf(cls_Inf__singleton_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = V_a ) ).
cnf(cls_image__constant__conv_0,axiom,
c_Set_Oimage(c_COMBK(V_c,T_a,T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_insert__image_0,axiom,
( c_Set_Oinsert(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) = c_Set_Oimage(V_f,V_A,T_a,T_b)
| ~ hBOOL(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_MGT__Body_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),V_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Finite__Set_Ofinite(V_Procs,tc_Com_Opname)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Lattices_Oupper__semilattice__class_Osup(V_G,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),V_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,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_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),V_Procs,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ) ).
cnf(cls_domI_0,axiom,
( hAPP(V_m,V_a) != c_Option_Ooption_OSome(V_b,T_a)
| hBOOL(c_in(V_a,c_Map_Odom(V_m,T_b,T_a),T_b)) ) ).
cnf(cls_WT_OCall_0,axiom,
( c_Com_OWT(c_Com_Ocom_OCall(V_X,V_pn,V_a))
| ~ c_Com_OWT(hAPP(c_Com_Ocom_OBODY,V_pn)) ) ).
cnf(cls_WTs__elim__cases_I8_J_0,axiom,
( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,V_P))
| ~ c_Com_OWT(c_Com_Ocom_OCall(V_X,V_P,V_a)) ) ).
cnf(cls_MGF__complete_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(V_P,V_c,V_Q,tc_Com_Ostate),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(V_P,V_c,V_Q,tc_Com_Ostate),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ) ).
cnf(cls_BodyN_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(V_P,hAPP(c_Com_Ocom_OBODY,V_pn),V_Q,T_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a)),T_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(V_P,hAPP(c_Com_Ocom_OBODY,V_pn),V_Q,T_a),V_G,tc_Hoare__Mirabelle_Otriple(T_a)),c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(V_P,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn)),V_Q,T_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a)),T_a) ) ).
cnf(cls_weak__Body_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(V_P,hAPP(c_Com_Ocom_OBODY,V_pn),V_Q,T_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a)),T_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(V_P,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn)),V_Q,T_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a)),T_a) ) ).
cnf(cls_finite__dom__body_0,axiom,
c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname) ).
cnf(cls_image__constant__conv_1,axiom,
( c_Set_Oimage(c_COMBK(V_c,T_a,T_b),V_A,T_b,T_a) = c_Set_Oinsert(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)) ) ).
cnf(cls_Option_Oset_Osimps_I2_J_0,axiom,
c_Option_Oset(c_Option_Ooption_OSome(V_x,T_a),T_a) = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ).
cnf(cls_WT_OBody_0,axiom,
( c_Com_OWT(hAPP(c_Com_Ocom_OBODY,V_pn))
| hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ).
cnf(cls_MGF__lemma2__simult_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),V_F,tc_Com_Ostate)
| ~ c_lessequals(V_F,c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,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_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ) ).
cnf(cls_MGF__lemma1_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(V_c)
| hBOOL(c_in(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(V_G),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname))
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ) ).
cnf(cls_WTs__elim__cases_I7_J_0,axiom,
( hAPP(c_Com_Obody,V_P) = c_Option_Ooption_OSome(c_Com_Osko__Com__XWTs__elim__cases__7__1(V_P),tc_Com_Ocom)
| ~ c_Com_OWT(hAPP(c_Com_Ocom_OBODY,V_P)) ) ).
cnf(cls_MGT__BodyN_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,V_pn)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,V_pn)),V_G,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ) ).
cnf(cls_MGF__lemma1_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(V_c)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_sko__Hoare__Mirabelle__XMGF__lemma1__1(V_G))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ) ).
cnf(cls_hoare__derivs_Oinsert_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(V_t,V_ts,tc_Hoare__Mirabelle_Otriple(T_a)),T_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(V_t,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a)),T_a) ) ).
cnf(cls_derivs__insertD_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(V_t,V_ts,tc_Hoare__Mirabelle_Otriple(T_a)),T_a) ) ).
cnf(cls_image__is__empty_0,axiom,
( c_Set_Oimage(V_f,V_A,T_b,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)) ) ).
cnf(cls_WT__bodiesD_0,axiom,
( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom)
| ~ c_Com_OWT__bodies
| c_Com_OWT(V_b) ) ).
cnf(cls_image__image_0,axiom,
c_Set_Oimage(V_f,c_Set_Oimage(V_g,V_A,T_c,T_b),T_b,T_a) = c_Set_Oimage(c_COMBB(V_f,V_g,T_b,T_a,T_c),V_A,T_c,T_a) ).
cnf(cls_insert__code_1,axiom,
hBOOL(hAPP(c_Set_Oinsert(V_x,V_A,T_a),V_x)) ).
cnf(cls_image__insert_0,axiom,
c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a) ).
cnf(cls_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)) != c_Set_Oinsert(V_a,V_A,T_a) ).
cnf(cls_MGF_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(V_c)
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ) ).
cnf(cls_doubleton__eq__iff_3,axiom,
( c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) != c_Set_Oinsert(V_c,c_Set_Oinsert(V_d,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)
| V_b = V_c
| V_b = V_d ) ).
cnf(cls_doubleton__eq__iff_2,axiom,
( c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) != c_Set_Oinsert(V_c,c_Set_Oinsert(V_d,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)
| V_a = V_d
| V_b = V_d ) ).
cnf(cls_doubleton__eq__iff_1,axiom,
( c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) != c_Set_Oinsert(V_c,c_Set_Oinsert(V_d,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)
| V_b = V_c
| V_a = V_c ) ).
cnf(cls_doubleton__eq__iff_0,axiom,
( c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) != c_Set_Oinsert(V_c,c_Set_Oinsert(V_d,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)
| V_a = V_d
| V_a = V_c ) ).
cnf(cls_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_option_Oinject_0,axiom,
( c_Option_Ooption_OSome(V_a,T_a) != c_Option_Ooption_OSome(V_a_H,T_a)
| V_a = V_a_H ) ).
cnf(cls_state__not__singleton__def_1,axiom,
( c_Hoare__Mirabelle_Ostate__not__singleton
| V_x = V_xa ) ).
cnf(cls_insert__code_0,axiom,
( hBOOL(hAPP(V_A,V_x))
| V_y = V_x
| ~ hBOOL(hAPP(c_Set_Oinsert(V_y,V_A,T_a),V_x)) ) ).
cnf(cls_insert__absorb2_0,axiom,
c_Set_Oinsert(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Set_Oinsert(V_x,V_A,T_a) ).
cnf(cls_insert__not__empty_0,axiom,
c_Set_Oinsert(V_a,V_A,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_empty__is__image_0,axiom,
( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Set_Oimage(V_f,V_A,T_b,T_a)
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)) ) ).
cnf(cls_insert__commute_0,axiom,
c_Set_Oinsert(V_x,c_Set_Oinsert(V_y,V_A,T_a),T_a) = c_Set_Oinsert(V_y,c_Set_Oinsert(V_x,V_A,T_a),T_a) ).
cnf(cls_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_doubleton__eq__iff_4,axiom,
c_Set_Oinsert(V_xa,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = c_Set_Oinsert(V_x,c_Set_Oinsert(V_xa,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) ).
cnf(cls_image__empty_0,axiom,
c_Set_Oimage(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_insert__dom_0,axiom,
( hAPP(V_f,V_x) != c_Option_Ooption_OSome(V_y,T_a)
| c_Set_Oinsert(V_x,c_Map_Odom(V_f,T_b,T_a),T_b) = c_Map_Odom(V_f,T_b,T_a) ) ).
cnf(cls_singleton__inject_0,axiom,
( c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) != c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)
| V_a = V_b ) ).
cnf(cls_derivs__insertD_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(V_t,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a)),T_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(V_t,V_ts,tc_Hoare__Mirabelle_Otriple(T_a)),T_a) ) ).
cnf(cls_insert__code_2,axiom,
( hBOOL(hAPP(c_Set_Oinsert(V_y,V_A,T_a),V_x))
| ~ hBOOL(hAPP(V_A,V_x)) ) ).
cnf(cls_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_empty__is__image_1,axiom,
c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) = c_Set_Oimage(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a) ).
cnf(cls_conjecture_0,negated_conjecture,
c_Hoare__Mirabelle_Ostate__not__singleton ).
cnf(cls_conjecture_1,negated_conjecture,
c_Com_OWT__bodies ).
cnf(cls_conjecture_2,negated_conjecture,
c_Com_OWT(v_c) ).
cnf(cls_conjecture_3,negated_conjecture,
hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_OSome(v_y,tc_Com_Ocom) ).
cnf(cls_conjecture_4,negated_conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ).
cnf(cls_conjecture_5,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ).
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_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__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(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_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,
c_COMBC(V_P,V_Q,V_R,T_b,T_c,T_a) = 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,
hBOOL(hAPP(hAPP(c_fequal(T_a),V_x),V_x)) ).
cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom,
( V_X = V_Y
| ~ hBOOL(hAPP(hAPP(c_fequal(T_a),V_X),V_Y)) ) ).
%------------------------------------------------------------------------------