TPTP Problem File: SWV861-1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SWV861-1 : TPTP v8.2.0. Released v4.1.0.
% Domain : Software Verification
% Problem : Hoare logic with procedures 295_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-295_1 [Nip10]
% Status : Unsatisfiable
% Rating : 0.05 v7.4.0, 0.06 v7.3.0, 0.00 v7.0.0, 0.20 v6.4.0, 0.13 v6.3.0, 0.09 v6.2.0, 0.20 v6.1.0, 0.14 v6.0.0, 0.20 v5.5.0, 0.55 v5.3.0, 0.61 v5.2.0, 0.50 v5.1.0, 0.53 v5.0.0, 0.43 v4.1.0
% Syntax : Number of clauses : 606 ( 165 unt; 86 nHn; 323 RR)
% Number of literals : 1354 ( 310 equ; 695 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 26 ( 25 usr; 0 prp; 1-9 aty)
% Number of functors : 68 ( 68 usr; 18 con; 0-6 aty)
% Number of variables : 2290 ( 376 sgn)
% SPC : CNF_UNS_RFO_SEQ_NHN
% Comments :
%------------------------------------------------------------------------------
cnf(cls_psubset__eq_0,axiom,
( c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_less__fun__def_0,axiom,
( ~ class_HOL_Oord(T_b)
| c_lessequals(V_f,V_g,tc_fun(T_a,T_b))
| ~ c_HOL_Oord__class_Oless(V_f,V_g,tc_fun(T_a,T_b)) ) ).
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_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_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_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_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_Int__lower1_0,axiom,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) ).
cnf(cls_Int__lower2_0,axiom,
c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) ).
cnf(cls_Int__greatest_0,axiom,
( c_lessequals(V_C,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_C,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_C,V_A,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Int__subset__iff_2,axiom,
( c_lessequals(V_C,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_C,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_C,V_A,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_sup__inf__distrib2_0,axiom,
( ~ class_Lattices_Odistrib__lattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),V_x,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_y,V_x,T_a),c_Lattices_Oupper__semilattice__class_Osup(V_z,V_x,T_a),T_a) ) ).
cnf(cls_sup__inf__distrib1_0,axiom,
( ~ class_Lattices_Odistrib__lattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a) ) ).
cnf(cls_Un__Int__distrib_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).
cnf(cls_Un__Int__distrib2_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).
cnf(cls_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_equalityE_0,axiom,
c_lessequals(V_x,V_x,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_subset__inj__on_0,axiom,
( c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Fun_Oinj__on(V_f,V_B,T_a,T_b) ) ).
cnf(cls_predicate1D_0,axiom,
( hBOOL(hAPP(V_Q,V_x))
| ~ hBOOL(hAPP(V_P,V_x))
| ~ c_lessequals(V_P,V_Q,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_psubset__subset__trans_0,axiom,
( c_HOL_Oord__class_Oless(V_A,V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_B,V_C,tc_fun(T_a,tc_bool))
| ~ c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_subset__psubset__trans_0,axiom,
( c_HOL_Oord__class_Oless(V_A,V_C,tc_fun(T_a,tc_bool))
| ~ c_HOL_Oord__class_Oless(V_B,V_C,tc_fun(T_a,tc_bool))
| ~ 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_Int__mono_0,axiom,
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(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_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_fun__upd__apply_1,axiom,
( hAPP(c_Fun_Ofun__upd(V_f,V_x,V_y,T_b,T_a),V_z) = hAPP(V_f,V_z)
| V_z = V_x ) ).
cnf(cls_fun__upd__other_0,axiom,
( hAPP(c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_b),V_z) = hAPP(V_f,V_z)
| V_z = V_x ) ).
cnf(cls_double__diff_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_B),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_C),V_A)) = V_A
| ~ 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_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_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_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_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_psubset__eq_2,axiom,
( c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool))
| V_A = V_B
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_subset__iff__psubset__eq_0,axiom,
( V_A = V_B
| c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
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_fold__graph_OinsertI_0,axiom,
( c_Finite__Set_Ofold__graph(V_f,V_z,c_Set_Oinsert(V_x,V_A,T_a),hAPP(hAPP(V_f,V_x),V_y),T_a,T_b)
| ~ c_Finite__Set_Ofold__graph(V_f,V_z,V_A,V_y,T_a,T_b)
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_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(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
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(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_subset__insert__iff_1,axiom,
( c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_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_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(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_insert__subset_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))
| ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ) ).
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(hAPP(hAPP(c_in(T_a),V_x),V_B)) ) ).
cnf(cls_distrib__inf__le_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a),c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a),T_a) ) ).
cnf(cls_distrib__sup__le_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a),T_a) ) ).
cnf(cls_image__subset__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_x)),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A))
| ~ c_lessequals(c_Set_Oimage(V_f,V_A,T_b,T_a),V_B,tc_fun(T_a,tc_bool)) ) ).
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(hAPP(hAPP(c_in(T_b),V_x),V_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(hAPP(hAPP(c_in(T_a),V_a),V_A)) ) ).
cnf(cls_UN__subset__iff_0,axiom,
( c_lessequals(hAPP(V_A,V_x),V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_I))
| ~ 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_UN__absorb_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(hAPP(V_A,V_k),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_I,V_A,T_a,tc_fun(T_b,tc_bool)),tc_fun(T_b,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_I,V_A,T_a,tc_fun(T_b,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_k),V_I)) ) ).
cnf(cls_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_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_pred__subset__eq_0,axiom,
( c_lessequals(V_R,V_S,tc_fun(T_a,tc_bool))
| ~ c_lessequals(hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_R),hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_S),tc_fun(T_a,tc_bool)) ) ).
cnf(cls_pred__subset__eq_1,axiom,
( c_lessequals(hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_R),hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_S),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_R,V_S,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_UN__extend__simps_I2_J_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_A,T_b,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = V_B ).
cnf(cls_UN__extend__simps_I3_J_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_B,T_b,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A ).
cnf(cls_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_image__Int__subset_0,axiom,
c_lessequals(c_Set_Oimage(V_f,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_b,tc_bool)),T_b,T_a),c_Lattices_Olower__semilattice__class_Oinf(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)),tc_fun(T_a,tc_bool)) ).
cnf(cls_UN__extend__simps_I10_J_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,c_COMBB(V_B,V_f,T_c,tc_fun(T_a,tc_bool),T_b),T_b,tc_fun(T_a,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oimage(V_f,V_A,T_b,T_c),V_B,T_c,tc_fun(T_a,tc_bool)) ).
cnf(cls_UN__simps_I10_J_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oimage(V_f,V_A,T_c,T_b),V_B,T_b,tc_fun(T_a,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,c_COMBB(V_B,V_f,T_b,tc_fun(T_a,tc_bool),T_c),T_c,tc_fun(T_a,tc_bool)) ).
cnf(cls_inj__on__Un__image__eq__iff_0,axiom,
( c_Set_Oimage(V_f,V_A,T_a,T_b) != c_Set_Oimage(V_f,V_B,T_a,T_b)
| ~ c_Fun_Oinj__on(V_f,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a,T_b)
| V_A = V_B ) ).
cnf(cls_card__image_0,axiom,
( c_Finite__Set_Ocard(c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) = c_Finite__Set_Ocard(V_A,T_a)
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
cnf(cls_image__diff__subset_0,axiom,
c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),c_Set_Oimage(V_f,V_A,T_b,T_a)),c_Set_Oimage(V_f,V_B,T_b,T_a)),c_Set_Oimage(V_f,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_b,tc_bool)),V_A),V_B),T_b,T_a),tc_fun(T_a,tc_bool)) ).
cnf(cls_Un__Diff__Int_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = V_A ).
cnf(cls_Diff__Un_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool))) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_C),tc_fun(T_a,tc_bool)) ).
cnf(cls_Diff__Int_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool))) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_C),tc_fun(T_a,tc_bool)) ).
cnf(cls_image__vimage__subset_0,axiom,
c_lessequals(c_Set_Oimage(V_f,c_Set_Ovimage(V_f,V_A,T_b,T_a),T_b,T_a),V_A,tc_fun(T_a,tc_bool)) ).
cnf(cls_inf__sup__absorb_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = V_x ) ).
cnf(cls_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_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_sup__inf__absorb_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = V_x ) ).
cnf(cls_less__fun__def_2,axiom,
( ~ class_HOL_Oord(T_b)
| c_HOL_Oord__class_Oless(V_f,V_g,tc_fun(T_a,T_b))
| c_lessequals(V_g,V_f,tc_fun(T_a,T_b))
| ~ c_lessequals(V_f,V_g,tc_fun(T_a,T_b)) ) ).
cnf(cls_Diff__mono_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_C),V_D),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_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_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_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_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_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_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_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_Un__Int__assoc__eq_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_C,V_A,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Un__Int__assoc__eq_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))
| c_lessequals(V_C,V_A,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_empty__fold__graphE_0,axiom,
( V_x = V_z
| ~ c_Finite__Set_Ofold__graph(V_f,V_z,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x,T_a,T_b) ) ).
cnf(cls_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_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_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_setsum__subtractf_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(T_a),V_f,T_a,tc_fun(T_a,T_a),T_b),V_g,T_b,T_a,T_a),V_A,T_b,T_a) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),c_Finite__Set_Osetsum(V_f,V_A,T_b,T_a)),c_Finite__Set_Osetsum(V_g,V_A,T_b,T_a)) ) ).
cnf(cls_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_Int__Un__distrib2_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_B,V_A,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).
cnf(cls_Int__Un__distrib_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).
cnf(cls_inf__sup__distrib1_0,axiom,
( ~ class_Lattices_Odistrib__lattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a) ) ).
cnf(cls_inf__sup__distrib2_0,axiom,
( ~ class_Lattices_Odistrib__lattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),V_x,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a),c_Lattices_Olower__semilattice__class_Oinf(V_z,V_x,T_a),T_a) ) ).
cnf(cls_Un__absorb_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,V_A,tc_fun(T_a,tc_bool)) = V_A ).
cnf(cls_sup__idem_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,V_x,T_a) = V_x ) ).
cnf(cls_less__fun__def_1,axiom,
( ~ class_HOL_Oord(T_b)
| ~ c_lessequals(V_g,V_f,tc_fun(T_a,T_b))
| ~ c_HOL_Oord__class_Oless(V_f,V_g,tc_fun(T_a,T_b)) ) ).
cnf(cls_Un__left__commute_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).
cnf(cls_Un__assoc_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).
cnf(cls_sup__assoc_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) ) ).
cnf(cls_sup__left__commute_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a) ) ).
cnf(cls_inf__sup__aci_I7_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a) ) ).
cnf(cls_inf__sup__aci_I6_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) ) ).
cnf(cls_Int__absorb2_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) = V_A
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Int__absorb1_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) = V_B
| ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool)) ) ).
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,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_B),V_A),tc_fun(T_a,tc_bool)) = V_B
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Diff__subset_0,axiom,
c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),V_A,tc_fun(T_a,tc_bool)) ).
cnf(cls_Un__Int__crazy_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).
cnf(cls_fold__graph_OemptyI_0,axiom,
c_Finite__Set_Ofold__graph(V_f,V_z,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_z,T_a,T_b) ).
cnf(cls_fold__graph_H_Ointros_I1_J_0,axiom,
c_Nitpick_Ofold__graph_H(V_f,V_z,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_z,T_a,T_b) ).
cnf(cls_vimage__mono_0,axiom,
( c_lessequals(c_Set_Ovimage(V_f,V_A,T_b,T_a),c_Set_Ovimage(V_f,V_B,T_b,T_a),tc_fun(T_b,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Un__empty_1,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| V_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Un__empty_0,axiom,
( c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_sup__eq__bot__eq1_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,T_a) != c_Orderings_Obot__class_Obot(T_a)
| V_A = c_Orderings_Obot__class_Obot(T_a) ) ).
cnf(cls_sup__eq__bot__eq2_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,T_a) != c_Orderings_Obot__class_Obot(T_a)
| V_B = c_Orderings_Obot__class_Obot(T_a) ) ).
cnf(cls_Un__Diff__cancel2_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_B),V_A),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,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_B),V_A),tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) ).
cnf(cls_Int__subset__iff_1,axiom,
( c_lessequals(V_C,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_C,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Int__subset__iff_0,axiom,
( c_lessequals(V_C,V_A,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_C,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Un__Diff_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool))),V_C) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_C),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_B),V_C),tc_fun(T_a,tc_bool)) ).
cnf(cls_Un__commute_0,axiom,
c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(V_B,V_A,tc_fun(T_a,tc_bool)) ).
cnf(cls_sup__commute_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,V_x,T_a) ) ).
cnf(cls_inf__sup__aci_I5_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,V_x,T_a) ) ).
cnf(cls_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_vimage__Un_0,axiom,
c_Set_Ovimage(V_f,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_b,tc_bool)),T_a,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(V_f,V_A,T_a,T_b),c_Set_Ovimage(V_f,V_B,T_a,T_b),tc_fun(T_a,tc_bool)) ).
cnf(cls_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_inj__on__Un_1,axiom,
( c_Fun_Oinj__on(V_f,V_B,T_a,T_b)
| ~ c_Fun_Oinj__on(V_f,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_inj__on__Un_0,axiom,
( c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| ~ c_Fun_Oinj__on(V_f,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_Diff__subset__conv_1,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),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(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),V_C,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_less__supI1_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_HOL_Oord__class_Oless(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_a,T_a) ) ).
cnf(cls_less__supI2_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_HOL_Oord__class_Oless(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_b,T_a) ) ).
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_subset__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_set__rev__mp_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_subsetD_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_set__mp_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_UnCI_1,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A)) ) ).
cnf(cls_UnCI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B)) ) ).
cnf(cls_UnE_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
| hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)))) ) ).
cnf(cls_bex__Un_6,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(V_A,V_B,V_P,T_a)),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool))))
| ~ hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B)) ) ).
cnf(cls_bex__Un_4,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(V_A,V_B,V_P,T_a)),c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool))))
| ~ hBOOL(hAPP(V_P,V_xa))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xa),V_A)) ) ).
cnf(cls_hoare__valids__def_3,axiom,
( c_Hoare__Mirabelle_Ohoare__valids(V_G,V_ts,t_a)
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(V_G,V_ts)),V_ts)) ) ).
cnf(cls_inj__on__fun__updI_0,axiom,
( c_Fun_Oinj__on(c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_b),V_A,T_a,T_b)
| hBOOL(hAPP(hAPP(c_in(T_b),V_y),c_Set_Oimage(V_f,V_A,T_a,T_b)))
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
cnf(cls_insert__def_0,axiom,
c_Set_Oinsert(V_a,V_B,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Collect(hAPP(c_COMBC(c_fequal(T_a),T_a,T_a,tc_bool),V_a),T_a),V_B,tc_fun(T_a,tc_bool)) ).
cnf(cls_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(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_psubset__insert__iff_7,axiom,
( c_HOL_Oord__class_Oless(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(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_psubset__insert__iff_3,axiom,
( c_HOL_Oord__class_Oless(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(hAPP(hAPP(c_in(T_a),V_x),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B)) ) ).
cnf(cls_psubset__insert__iff_2,axiom,
( c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))
| ~ c_HOL_Oord__class_Oless(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ) ).
cnf(cls_inj__on__image__Int_0,axiom,
( c_Set_Oimage(V_f,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),T_a,T_b) = c_Lattices_Olower__semilattice__class_Oinf(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_B,V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_C,tc_fun(T_a,tc_bool))
| ~ c_Fun_Oinj__on(V_f,V_C,T_a,T_b) ) ).
cnf(cls_vimage__insert_0,axiom,
c_Set_Ovimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_a,T_b) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Ovimage(V_f,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b),T_a,T_b),c_Set_Ovimage(V_f,V_B,T_a,T_b),tc_fun(T_a,tc_bool)) ).
cnf(cls_inj__on__image__set__diff_0,axiom,
( c_Set_Oimage(V_f,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_b,tc_bool)),c_Set_Oimage(V_f,V_A,T_a,T_b)),c_Set_Oimage(V_f,V_B,T_a,T_b))
| ~ c_lessequals(V_B,V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_C,tc_fun(T_a,tc_bool))
| ~ c_Fun_Oinj__on(V_f,V_C,T_a,T_b) ) ).
cnf(cls_insert__Diff1_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_x,V_A,T_a)),V_B) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B)) ) ).
cnf(cls_image__ident_0,axiom,
c_Set_Oimage(c_COMBI(T_a),V_Y,T_a,T_a) = V_Y ).
cnf(cls_psubset__insert__iff_1,axiom,
( c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))
| ~ c_HOL_Oord__class_Oless(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ) ).
cnf(cls_psubset__insert__iff_4,axiom,
( c_HOL_Oord__class_Oless(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),V_B,tc_fun(T_a,tc_bool))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B)) ) ).
cnf(cls_com_Osimps_I17_J_0,axiom,
c_Com_Ocom_OWhile(V_fun_H,V_com_H) != c_Com_Ocom_OSKIP ).
cnf(cls_inj__on__diff_0,axiom,
( c_Fun_Oinj__on(V_f,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b)
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
cnf(cls_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_evalc_OWhileFalse_0,axiom,
( c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b,V_c),V_s,V_s)
| hBOOL(hAPP(V_b,V_s)) ) ).
cnf(cls_vimage__Diff_0,axiom,
c_Set_Ovimage(V_f,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_b,tc_bool)),V_A),V_B),T_a,T_b) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),c_Set_Ovimage(V_f,V_A,T_a,T_b)),c_Set_Ovimage(V_f,V_B,T_a,T_b)) ).
cnf(cls_psubset__insert__iff_8,axiom,
( c_HOL_Oord__class_Oless(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),V_B,tc_fun(T_a,tc_bool))
| ~ c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Collect__def_0,axiom,
c_Collect(V_P,T_a) = V_P ).
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_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_Diff__insert_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_a,V_B,T_a)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) ).
cnf(cls_Diff__insert2_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_a,V_B,T_a)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a))),V_B) ).
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_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_inj__on__id2_0,axiom,
c_Fun_Oinj__on(c_COMBI(T_a),V_A,T_a,T_a) ).
cnf(cls_vimage__singleton__eq_1,axiom,
hBOOL(hAPP(hAPP(c_in(T_aa),V_a),c_Set_Ovimage(V_f,c_Set_Oinsert(hAPP(V_f,V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_aa,T_a))) ).
cnf(cls_insert__inter__insert_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(V_a,V_A,T_a),c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),T_a) ).
cnf(cls_insert__absorb2_0,axiom,
c_Set_Oinsert(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Set_Oinsert(V_x,V_A,T_a) ).
cnf(cls_insert__code_0,axiom,
( hBOOL(hAPP(V_A,V_x))
| V_y = V_x
| ~ hBOOL(hAPP(c_Set_Oinsert(V_y,V_A,T_a),V_x)) ) ).
cnf(cls_UNION__empty__conv_I2_J_0,axiom,
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_b,tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| hAPP(V_B,V_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A)) ) ).
cnf(cls_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_inf__bot__right_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Orderings_Obot__class_Obot(T_a),T_a) = c_Orderings_Obot__class_Obot(T_a) ) ).
cnf(cls_inf__bot__left_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(T_a),V_x,T_a) = c_Orderings_Obot__class_Obot(T_a) ) ).
cnf(cls_Int__empty__left_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_Int__empty__right_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_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_complete__lattice_OSup__binary_0,axiom,
( hAPP(V_Sup,c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)) = hAPP(hAPP(V_sup,V_a),V_b)
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_complete__lattice_OInf__binary_0,axiom,
( hAPP(V_Inf,c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)) = hAPP(hAPP(V_inf,V_a),V_b)
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_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_Diff__empty_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = V_A ).
cnf(cls_Diff__cancel_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_A) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_Suc__inject_0,axiom,
( c_Suc(V_x) != c_Suc(V_y)
| V_x = V_y ) ).
cnf(cls_nat_Oinject_0,axiom,
( c_Suc(V_nat) != c_Suc(V_nat_H)
| V_nat = V_nat_H ) ).
cnf(cls_not__psubset__empty_0,axiom,
~ c_HOL_Oord__class_Oless(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).
cnf(cls_vimage__ident_0,axiom,
c_Set_Ovimage(c_COMBI(T_a),V_Y,T_a,T_a) = V_Y ).
cnf(cls_inf__sup__aci_I2_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ).
cnf(cls_inf__sup__aci_I3_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a) ) ).
cnf(cls_inf__left__commute_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a) ) ).
cnf(cls_inf__assoc_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ).
cnf(cls_Int__assoc_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).
cnf(cls_Int__left__commute_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_B,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).
cnf(cls_UNION__empty__conv_I1_J_0,axiom,
( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_b,tc_fun(T_a,tc_bool))
| hAPP(V_B,V_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A)) ) ).
cnf(cls_empty__Diff_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),V_A) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_com_Osimps_I16_J_0,axiom,
c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H,V_com_H) ).
cnf(cls_bot1E_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x)) ).
cnf(cls_Diff__Int__distrib_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_C,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_C,V_A,tc_fun(T_a,tc_bool))),c_Lattices_Olower__semilattice__class_Oinf(V_C,V_B,tc_fun(T_a,tc_bool))) ).
cnf(cls_Diff__Int__distrib2_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),V_C,tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool))),c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool))) ).
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_psubset__insert__iff_0,axiom,
( c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))
| ~ c_HOL_Oord__class_Oless(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ) ).
cnf(cls_psubset__insert__iff_6,axiom,
( c_HOL_Oord__class_Oless(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))
| ~ c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_disjoint__iff__not__equal_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Diff__Int2_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool))),c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool))) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool))),V_B) ).
cnf(cls_less__le__not__le_2,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| c_lessequals(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_psubset__eq_1,axiom,
~ c_HOL_Oord__class_Oless(V_x,V_x,tc_fun(T_a,tc_bool)) ).
cnf(cls_order__less__le_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
cnf(cls_linorder__neq__iff_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
cnf(cls_order__less__irrefl_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
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_evalc_OSkip_0,axiom,
c_Natural_Oevalc(c_Com_Ocom_OSKIP,V_s,V_s) ).
cnf(cls_linorder__neqE__ordered__idom_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| V_x = V_y ) ).
cnf(cls_not__less__iff__gr__or__eq_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| V_x = V_y
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_le__antisym_0,axiom,
( V_m = V_n
| ~ c_lessequals(V_n,V_m,tc_nat)
| ~ c_lessequals(V_m,V_n,tc_nat) ) ).
cnf(cls_com__det_0,axiom,
( V_u = V_t
| ~ c_Natural_Oevalc(V_c,V_s,V_u)
| ~ c_Natural_Oevalc(V_c,V_s,V_t) ) ).
cnf(cls_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_inj__on__Un_2,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(V_f,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b),c_Set_Oimage(V_f,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_B),V_A),T_a,T_b),tc_fun(T_b,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))
| ~ c_Fun_Oinj__on(V_f,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_inj__on__Un_3,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oimage(V_f,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b),c_Set_Oimage(V_f,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_B),V_A),T_a,T_b),tc_fun(T_b,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))
| ~ c_Fun_Oinj__on(V_f,V_B,T_a,T_b)
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| c_Fun_Oinj__on(V_f,c_Lattices_Oupper__semilattice__class_Osup(V_A,V_B,tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_psubset__insert__iff_5,axiom,
( c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),V_B,tc_fun(T_a,tc_bool))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B)) ) ).
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,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_b,tc_bool)),V_A),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b)),T_b,T_a),T_a)
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A)) ) ).
cnf(cls_hoare__valids__def_4,axiom,
( c_Hoare__Mirabelle_Ohoare__valids(V_G,V_ts,t_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(V_G,V_ts),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(V_G,V_ts),t_a) ) ).
cnf(cls_psubset__insert__iff_9,axiom,
( c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),V_B,tc_fun(T_a,tc_bool))
| ~ c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_vimage__def_0,axiom,
c_Set_Ovimage(V_f,V_B,T_a,T_b) = c_Collect(hAPP(c_COMBC(c_COMBB(c_in(T_b),V_f,T_b,tc_fun(tc_fun(T_b,tc_bool),tc_bool),T_a),T_a,tc_fun(T_b,tc_bool),tc_bool),V_B),T_a) ).
cnf(cls_fold__graph_H_Ointros_I2_J_0,axiom,
( c_Nitpick_Ofold__graph_H(V_f,V_z,V_A,hAPP(hAPP(V_f,V_x),V_y),T_a,T_b)
| ~ c_Nitpick_Ofold__graph_H(V_f,V_z,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),V_y,T_a,T_b)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_subset__insert__iff_0,axiom,
( c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_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(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),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(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_setsum__diff1__nat_1,axiom,
( c_Finite__Set_Osetsum(V_f,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),T_a,tc_nat) = c_Finite__Set_Osetsum(V_f,V_A,T_a,tc_nat)
| hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)) ) ).
cnf(cls_Diff1__fold__graph_0,axiom,
( c_Finite__Set_Ofold__graph(V_f,V_z,V_A,hAPP(hAPP(V_f,V_x),V_y),T_a,T_b)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ c_Finite__Set_Ofold__graph(V_f,V_z,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),V_y,T_a,T_b) ) ).
cnf(cls_card__Suc__eq_5,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))
| c_Finite__Set_Ocard(c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) ) ).
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(hAPP(hAPP(c_in(T_a),V_i),V_A)) ) ).
cnf(cls_inj__on__insert_0,axiom,
( c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| ~ c_Fun_Oinj__on(V_f,c_Set_Oinsert(V_a,V_A,T_a),T_a,T_b) ) ).
cnf(cls_image__constant_0,axiom,
( c_Set_Oimage(c_COMBK(V_c,T_b,T_a),V_A,T_a,T_b) = c_Set_Oinsert(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_singletonE_0,axiom,
( V_b = V_a
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_b),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a))) ) ).
cnf(cls_Diff__triv_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B) = V_A ) ).
cnf(cls_Int__Collect_1,axiom,
( hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Collect(V_P,T_a),tc_fun(T_a,tc_bool)))) ) ).
cnf(cls_order__less__trans_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_psubset__trans_0,axiom,
( c_HOL_Oord__class_Oless(V_A,V_C,tc_fun(T_a,tc_bool))
| ~ c_HOL_Oord__class_Oless(V_B,V_C,tc_fun(T_a,tc_bool))
| ~ c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_xt1_I10_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
cnf(cls_inj__on__insert_2,axiom,
( c_Fun_Oinj__on(V_f,c_Set_Oinsert(V_a,V_A,T_a),T_a,T_b)
| hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),c_Set_Oimage(V_f,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),T_a,T_b)))
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
cnf(cls_insert__commute_0,axiom,
c_Set_Oinsert(V_x,c_Set_Oinsert(V_y,V_A,T_a),T_a) = c_Set_Oinsert(V_y,c_Set_Oinsert(V_x,V_A,T_a),T_a) ).
cnf(cls_INT__extend__simps_I4_J_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_B,T_b,tc_fun(T_a,tc_bool))) = V_A ).
cnf(cls_COMBB__def_0,axiom,
hAPP(c_COMBB(V_P,V_Q,T_b,T_a,T_c),V_R) = hAPP(V_P,hAPP(V_Q,V_R)) ).
cnf(cls_COMBC__def_0,axiom,
hAPP(hAPP(c_COMBC(V_P,T_b,T_c,T_a),V_Q),V_R) = hAPP(hAPP(V_P,V_R),V_Q) ).
cnf(cls_COMBI__def_0,axiom,
hAPP(c_COMBI(T_a),V_P) = V_P ).
cnf(cls_COMBK__def_0,axiom,
hAPP(c_COMBK(V_P,T_a,T_b),V_Q) = V_P ).
cnf(cls_COMBS__def_0,axiom,
hAPP(c_COMBS(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),hAPP(V_Q,V_R)) ).
cnf(cls_Diff__idemp_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)),V_B) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B) ).
cnf(cls_not__leE_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_linorder__antisym__conv2_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_lessequals(V_x,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
cnf(cls_linorder__antisym__conv1_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| c_lessequals(V_x,V_x,T_a) ) ).
cnf(cls_linorder__not__less_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_linorder__not__less_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_linorder__not__le_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
cnf(cls_linorder__not__le_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_less__le__not__le_1,axiom,
( ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_evalc_OWhileTrue_0,axiom,
( c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b,V_c),V_s0,V_s2)
| ~ c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b,V_c),V_s1,V_s2)
| ~ c_Natural_Oevalc(V_c,V_s0,V_s1)
| ~ hBOOL(hAPP(V_b,V_s0)) ) ).
cnf(cls_doubleton__eq__iff_4,axiom,
c_Set_Oinsert(V_xa,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = c_Set_Oinsert(V_x,c_Set_Oinsert(V_xa,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) ).
cnf(cls_eq__eqI_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_xa),V_y) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_x)
| V_xa = V_y ) ).
cnf(cls_eq__eqI_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_x) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x_H),V_y_H)
| V_x_H = V_y_H ) ).
cnf(cls_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_evalc_OIfTrue_0,axiom,
( c_Natural_Oevalc(c_Com_Ocom_OCond(V_b,V_c0,V_c1),V_s,V_s1)
| ~ c_Natural_Oevalc(V_c0,V_s,V_s1)
| ~ hBOOL(hAPP(V_b,V_s)) ) ).
cnf(cls_evalc__elim__cases_I5_J_1,axiom,
( ~ hBOOL(hAPP(V_b,V_s))
| c_Natural_Oevalc(V_c1,V_s,V_t)
| ~ c_Natural_Oevalc(c_Com_Ocom_OCond(V_b,V_c1,V_c2),V_s,V_t) ) ).
cnf(cls_evalc_OSemi_0,axiom,
( c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0,V_c1),V_s0,V_s2)
| ~ c_Natural_Oevalc(V_c1,V_s1,V_s2)
| ~ c_Natural_Oevalc(V_c0,V_s0,V_s1) ) ).
cnf(cls_inj__on__empty_0,axiom,
c_Fun_Oinj__on(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a,T_b) ).
cnf(cls_le__iff__inf_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_x
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_le__iff__inf_1,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) != V_x
| c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_inf__absorb2_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y
| ~ c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_Int__commute_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_B,V_A,tc_fun(T_a,tc_bool)) ).
cnf(cls_inf__commute_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a) ) ).
cnf(cls_inf__sup__aci_I1_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a) ) ).
cnf(cls_complete__lattice_Odual__complete__lattice_0,axiom,
( c_Complete__Lattice_Ocomplete__lattice(V_Sup,V_Inf,c_COMBC(V_less__eq,T_a,T_a,tc_bool),c_COMBC(V_less,T_a,T_a,tc_bool),V_sup,V_inf,V_top,V_bot,T_a)
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_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_insert__Diff__single_0,axiom,
c_Set_Oinsert(V_a,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),T_a) = c_Set_Oinsert(V_a,V_A,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_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_comm__monoid__add_Ononempty__iff_2,axiom,
( c_Set_Oinsert(V_x,V_xa,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_xa)) ) ).
cnf(cls_not__less__eq__eq_1,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| ~ c_lessequals(c_Suc(V_n),V_m,tc_nat) ) ).
cnf(cls_not__less__eq__eq_0,axiom,
( c_lessequals(c_Suc(V_n),V_m,tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ) ).
cnf(cls_SUP__const_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_b)
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,c_COMBK(V_M,T_b,T_a),T_a,T_b) = V_M
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_insert__code_2,axiom,
( hBOOL(hAPP(c_Set_Oinsert(V_y,V_A,T_a),V_x))
| ~ hBOOL(hAPP(V_A,V_x)) ) ).
cnf(cls_insert__image_0,axiom,
( c_Set_Oinsert(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) = c_Set_Oimage(V_f,V_A,T_a,T_b)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_Int__insert__right_1,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool))
| hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)) ) ).
cnf(cls_Int__insert__left_1,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(V_a,V_B,T_a),V_C,tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool))
| hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_C)) ) ).
cnf(cls_le__infE_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_a,T_a)
| ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a) ) ).
cnf(cls_le__infE_1,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_b,T_a)
| ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a) ) ).
cnf(cls_le__infI1_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a)
| ~ c_lessequals(V_a,V_x,T_a) ) ).
cnf(cls_le__infI2_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a)
| ~ c_lessequals(V_b,V_x,T_a) ) ).
cnf(cls_le__inf__iff_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ).
cnf(cls_le__inf__iff_1,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),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_le__Suc__eq_2,axiom,
c_lessequals(c_Suc(V_n),c_Suc(V_n),tc_nat) ).
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_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_Diff__disjoint_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_B),V_A),tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
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_Int__Collect_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Collect(V_P,T_a),tc_fun(T_a,tc_bool)))) ) ).
cnf(cls_le__SucE_0,axiom,
( V_m = c_Suc(V_n)
| c_lessequals(V_m,V_n,tc_nat)
| ~ c_lessequals(V_m,c_Suc(V_n),tc_nat) ) ).
cnf(cls_inj__on__insert_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),c_Set_Oimage(V_f,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),T_a,T_b)))
| ~ c_Fun_Oinj__on(V_f,c_Set_Oinsert(V_a,V_A,T_a),T_a,T_b) ) ).
cnf(cls_insert__Diff__if_1,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_x,V_A,T_a)),V_B) = c_Set_Oinsert(V_x,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),T_a)
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B)) ) ).
cnf(cls_inf1E_1,axiom,
( hBOOL(hAPP(V_B,V_x))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_x)) ) ).
cnf(cls_inf1E_0,axiom,
( hBOOL(hAPP(V_A,V_x))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_x)) ) ).
cnf(cls_Diff__insert__absorb_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),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)) = V_A
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_vimage__Int_0,axiom,
c_Set_Ovimage(V_f,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_b,tc_bool)),T_a,T_b) = c_Lattices_Olower__semilattice__class_Oinf(c_Set_Ovimage(V_f,V_A,T_a,T_b),c_Set_Ovimage(V_f,V_B,T_a,T_b),tc_fun(T_a,tc_bool)) ).
cnf(cls_evalc__elim__cases_I1_J_0,axiom,
( V_t = V_s
| ~ c_Natural_Oevalc(c_Com_Ocom_OSKIP,V_s,V_t) ) ).
cnf(cls_bexCI_1,axiom,
( hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__XbexCI__1__1(V_A,V_P,T_a)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| ~ hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_Int__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A)) ) ).
cnf(cls_IntI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A)) ) ).
cnf(cls_ball__conj__distrib_9,axiom,
( hBOOL(hAPP(V_Q,V_xb))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xb),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(V_A,V_Q,T_a)),V_A))
| ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(V_A,V_P,T_a))) ) ).
cnf(cls_ball__conj__distrib_8,axiom,
( hBOOL(hAPP(V_P,V_xb))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xb),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(V_A,V_Q,T_a)),V_A))
| ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(V_A,V_P,T_a))) ) ).
cnf(cls_ball__conj__distrib_7,axiom,
( hBOOL(hAPP(V_Q,V_xa))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xa),V_A))
| ~ hBOOL(hAPP(V_Q,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(V_A,V_Q,T_a)))
| hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(V_A,V_P,T_a)),V_A)) ) ).
cnf(cls_ball__conj__distrib_6,axiom,
( hBOOL(hAPP(V_P,V_xa))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xa),V_A))
| ~ hBOOL(hAPP(V_Q,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(V_A,V_Q,T_a)))
| hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(V_A,V_P,T_a)),V_A)) ) ).
cnf(cls_ord_OatLeastLessThan__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OatLeastLessThan(V_less__eq,V_less,V_l,V_u,T_a)))
| ~ hBOOL(hAPP(hAPP(V_less,V_i),V_u))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_l),V_i)) ) ).
cnf(cls_insert__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Set_Oinsert(V_b,V_A,T_a)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)) ) ).
cnf(cls_insertCI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Set_Oinsert(V_b,V_B,T_a)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_B)) ) ).
cnf(cls_ord_OatLeastAtMost__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OatLeastAtMost(V_less__eq,V_l,V_u,T_a)))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_i),V_u))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_l),V_i)) ) ).
cnf(cls_bexCI_2,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__XbexCI__1__1(V_A,V_P,T_a)),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| ~ hBOOL(hAPP(V_P,V_a)) ) ).
cnf(cls_ex__in__conv_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) ).
cnf(cls_ball__empty_0,axiom,
( hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) ) ).
cnf(cls_empty__iff_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) ).
cnf(cls_emptyE_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) ).
cnf(cls_ord_OgreaterThanLessThan__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OgreaterThanLessThan(V_less,V_l,V_u,T_a)))
| ~ hBOOL(hAPP(hAPP(V_less,V_i),V_u))
| ~ hBOOL(hAPP(hAPP(V_less,V_l),V_i)) ) ).
cnf(cls_insertE_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| V_a = V_b
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Set_Oinsert(V_b,V_A,T_a))) ) ).
cnf(cls_ord_OgreaterThanAtMost__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OgreaterThanAtMost(V_less__eq,V_less,V_l,V_u,T_a)))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_i),V_u))
| ~ hBOOL(hAPP(hAPP(V_less,V_l),V_i)) ) ).
cnf(cls_DiffE_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B))) ) ).
cnf(cls_DiffE_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B))) ) ).
cnf(cls_bexCI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__XbexCI__1__1(V_A,V_P,T_a)),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| ~ hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_bexI_1,axiom,
( hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__XbexI__1__1(V_A,V_P,T_a)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(V_P,V_x)) ) ).
cnf(cls_bexE_1,axiom,
( hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__XbexE__1__1(V_A,V_P,T_a)))
| ~ hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_linorder__neqE_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| V_x = V_y ) ).
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_linorder__less__linear_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| V_x = V_y
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_linorder__antisym__conv3_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| V_x = V_y
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
cnf(cls_less__infI2_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_x,T_a) ) ).
cnf(cls_less__infI1_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_x,T_a) ) ).
cnf(cls_order__le__less_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_order__less__imp__le_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_lessequals(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_doubleton__eq__iff_0,axiom,
( c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) != c_Set_Oinsert(V_c,c_Set_Oinsert(V_d,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)
| V_a = V_d
| V_a = V_c ) ).
cnf(cls_doubleton__eq__iff_1,axiom,
( c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) != c_Set_Oinsert(V_c,c_Set_Oinsert(V_d,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)
| V_b = V_c
| V_a = V_c ) ).
cnf(cls_doubleton__eq__iff_2,axiom,
( c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) != c_Set_Oinsert(V_c,c_Set_Oinsert(V_d,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)
| V_a = V_d
| V_b = V_d ) ).
cnf(cls_doubleton__eq__iff_3,axiom,
( c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) != c_Set_Oinsert(V_c,c_Set_Oinsert(V_d,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)
| V_b = V_c
| V_b = V_d ) ).
cnf(cls_evalc__elim__cases_I5_J_0,axiom,
( c_Natural_Oevalc(V_c2,V_s,V_t)
| hBOOL(hAPP(V_b,V_s))
| ~ c_Natural_Oevalc(c_Com_Ocom_OCond(V_b,V_c1,V_c2),V_s,V_t) ) ).
cnf(cls_evalc_OIfFalse_0,axiom,
( c_Natural_Oevalc(c_Com_Ocom_OCond(V_b,V_c0,V_c1),V_s,V_s1)
| ~ c_Natural_Oevalc(V_c1,V_s,V_s1)
| hBOOL(hAPP(V_b,V_s)) ) ).
cnf(cls_vimage__const_1,axiom,
( c_Set_Ovimage(c_COMBK(V_c,T_b,T_a),V_A,T_a,T_b) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| hBOOL(hAPP(hAPP(c_in(T_b),V_c),V_A)) ) ).
cnf(cls_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_complete__lattice_OSup__insert_0,axiom,
( hAPP(V_Sup,c_Set_Oinsert(V_a,V_A,T_a)) = hAPP(hAPP(V_sup,V_a),hAPP(V_Sup,V_A))
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_complete__lattice_OInf__insert_0,axiom,
( hAPP(V_Inf,c_Set_Oinsert(V_a,V_A,T_a)) = hAPP(hAPP(V_inf,V_a),hAPP(V_Inf,V_A))
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_bex__UN_3,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3(V_A,V_B,V_P,T_b,T_a)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_b,tc_fun(T_a,tc_bool))))
| ~ hBOOL(hAPP(V_P,V_xa))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xa),hAPP(V_B,V_x)))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A)) ) ).
cnf(cls_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_Int__insert__left_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(V_a,V_B,T_a),V_C,tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),T_a)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_C)) ) ).
cnf(cls_Int__insert__right_0,axiom,
( c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) = c_Set_Oinsert(V_a,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)) ) ).
cnf(cls_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_vimage__singleton__eq_0,axiom,
( hAPP(V_f,V_a) = V_b
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Set_Ovimage(V_f,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b),T_a,T_b))) ) ).
cnf(cls_inf__sup__ord_I1_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_x,T_a) ) ).
cnf(cls_inf__sup__ord_I2_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_y,T_a) ) ).
cnf(cls_inf__greatest_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a)
| ~ c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_le__inf__iff_2,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a)
| ~ c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_le__infI_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a)
| ~ c_lessequals(V_x,V_b,T_a)
| ~ c_lessequals(V_x,V_a,T_a) ) ).
cnf(cls_inf__le2_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_y,T_a) ) ).
cnf(cls_inf__le1_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_x,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_com_Osimps_I13_J_0,axiom,
c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ).
cnf(cls_Suc__leD_0,axiom,
( c_lessequals(V_m,V_n,tc_nat)
| ~ c_lessequals(c_Suc(V_m),V_n,tc_nat) ) ).
cnf(cls_le__SucI_0,axiom,
( c_lessequals(V_m,c_Suc(V_n),tc_nat)
| ~ c_lessequals(V_m,V_n,tc_nat) ) ).
cnf(cls_empty__Collect__eq_0,axiom,
( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Collect(V_P,T_a)
| ~ hBOOL(hAPP(V_P,V_x)) ) ).
cnf(cls_insert__code_1,axiom,
hBOOL(hAPP(c_Set_Oinsert(V_x,V_A,T_a),V_x)) ).
cnf(cls_Suc__n__not__le__n_0,axiom,
~ c_lessequals(c_Suc(V_n),V_n,tc_nat) ).
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_inf__sup__aci_I4_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) ) ).
cnf(cls_inf__left__idem_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) ) ).
cnf(cls_Int__left__absorb_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)) ).
cnf(cls_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_complete__lattice_OSup__empty_0,axiom,
( hAPP(V_Sup,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = V_bot
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_complete__lattice_OInf__empty_0,axiom,
( hAPP(V_Inf,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = V_top
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_evalc__WHILE__case_0,axiom,
( hBOOL(hAPP(V_b,V_s))
| V_t = V_s
| ~ c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b,V_c),V_s,V_t) ) ).
cnf(cls_Suc__n__not__n_0,axiom,
c_Suc(V_n) != V_n ).
cnf(cls_n__not__Suc__n_0,axiom,
V_n != c_Suc(V_n) ).
cnf(cls_insert__Diff_0,axiom,
( c_Set_Oinsert(V_a,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),T_a) = V_A
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)) ) ).
cnf(cls_inf__idem_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_x,V_x,T_a) = V_x ) ).
cnf(cls_Int__absorb_0,axiom,
c_Lattices_Olower__semilattice__class_Oinf(V_A,V_A,tc_fun(T_a,tc_bool)) = V_A ).
cnf(cls_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_xt1_I7_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| ~ c_lessequals(V_z,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
cnf(cls_xt1_I8_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(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_le__refl_0,axiom,
c_lessequals(V_n,V_n,tc_nat) ).
cnf(cls_le__trans_0,axiom,
( c_lessequals(V_i,V_k,tc_nat)
| ~ c_lessequals(V_j,V_k,tc_nat)
| ~ c_lessequals(V_i,V_j,tc_nat) ) ).
cnf(cls_eq__imp__le_0,axiom,
c_lessequals(V_x,V_x,tc_nat) ).
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_order__le__less__trans_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_order__less__le__trans_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,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_singleton__conv_0,axiom,
c_Collect(hAPP(c_COMBC(c_fequal(T_a),T_a,T_a,tc_bool),V_a),T_a) = c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ).
cnf(cls_Int__Diff_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool))),V_C) = c_Lattices_Olower__semilattice__class_Oinf(V_A,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_B),V_C),tc_fun(T_a,tc_bool)) ).
cnf(cls_complete__lattice_OSup__singleton_0,axiom,
( hAPP(V_Sup,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) = V_a
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_complete__lattice_OInf__singleton_0,axiom,
( hAPP(V_Inf,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) = V_a
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_singleton__iff_1,axiom,
hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a))) ).
cnf(cls_Int__Collect_2,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Collect(V_P,T_a),tc_fun(T_a,tc_bool))))
| ~ hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_vimage__code_0,axiom,
( hBOOL(hAPP(V_A,hAPP(V_f,V_x)))
| ~ hBOOL(hAPP(c_Set_Ovimage(V_f,V_A,T_a,T_b),V_x)) ) ).
cnf(cls_vimage__code_1,axiom,
( hBOOL(hAPP(c_Set_Ovimage(V_f,V_A,T_a,T_b),V_x))
| ~ hBOOL(hAPP(V_A,hAPP(V_f,V_x))) ) ).
cnf(cls_inf1I_0,axiom,
( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_x))
| ~ hBOOL(hAPP(V_B,V_x))
| ~ hBOOL(hAPP(V_A,V_x)) ) ).
cnf(cls_le__eqI_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x_H),V_y_H)
| 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)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x_H),V_y_H)
| c_lessequals(V_y,V_x,T_a)
| ~ c_lessequals(V_y_H,V_x_H,T_a) ) ).
cnf(cls_less__eqI_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x_H),V_y_H)
| c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_less__eqI_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x_H),V_y_H)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_x_H,V_y_H,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_xt1_I11_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| V_a = V_b
| ~ c_lessequals(V_b,V_a,T_a) ) ).
cnf(cls_xt1_I12_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| V_a = V_b ) ).
cnf(cls_order__le__less_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| V_x = V_y
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_order__less__le_2,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| V_x = V_y
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_order__le__neq__trans_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| V_a = V_b
| ~ c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_order__neq__le__trans_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| V_a = V_b ) ).
cnf(cls_linorder__antisym__conv1_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| V_x = V_y
| ~ c_lessequals(V_x,V_y,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_linorder__antisym__conv2_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| V_x = V_y
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_vimage__empty_0,axiom,
c_Set_Ovimage(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_a,T_b) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_evalc__elim__cases_I5_J_2,axiom,
( c_Natural_Oevalc(V_c2,V_s,V_t)
| c_Natural_Oevalc(V_c1,V_s,V_t)
| ~ c_Natural_Oevalc(c_Com_Ocom_OCond(V_b,V_c1,V_c2),V_s,V_t) ) ).
cnf(cls_Collect__mem__eq_0,axiom,
c_Collect(hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_A),T_a) = V_A ).
cnf(cls_Suc__le__mono_0,axiom,
( c_lessequals(V_n,V_m,tc_nat)
| ~ c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) ) ).
cnf(cls_Suc__le__mono_1,axiom,
( c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat)
| ~ c_lessequals(V_n,V_m,tc_nat) ) ).
cnf(cls_com_Osimps_I12_J_0,axiom,
c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ).
cnf(cls_xt1_I9_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ).
cnf(cls_not__less__iff__gr__or__eq_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
cnf(cls_nat__le__linear_0,axiom,
( c_lessequals(V_n,V_m,tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ) ).
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_order__less__asym_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_order__less__asym_H_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_ord_OgreaterThanAtMost__iff_0,axiom,
( hBOOL(hAPP(hAPP(V_less,V_l),V_i))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OgreaterThanAtMost(V_less__eq,V_less,V_l,V_u,T_a))) ) ).
cnf(cls_ord_OgreaterThanAtMost__iff_1,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,V_i),V_u))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OgreaterThanAtMost(V_less__eq,V_less,V_l,V_u,T_a))) ) ).
cnf(cls_psubsetD_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A))
| ~ c_HOL_Oord__class_Oless(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_insert__iff_1,axiom,
hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Set_Oinsert(V_x,V_A,T_a))) ).
cnf(cls_insertI1_0,axiom,
hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Set_Oinsert(V_a,V_B,T_a))) ).
cnf(cls_insertCI_1,axiom,
hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Set_Oinsert(V_x,V_B,T_a))) ).
cnf(cls_ball__conj__distrib_11,axiom,
( hBOOL(hAPP(V_Q,V_xc))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xc),V_A))
| ~ hBOOL(hAPP(V_Q,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(V_A,V_Q,T_a)))
| ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(V_A,V_P,T_a))) ) ).
cnf(cls_ball__conj__distrib_10,axiom,
( hBOOL(hAPP(V_P,V_xc))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xc),V_A))
| ~ hBOOL(hAPP(V_Q,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(V_A,V_Q,T_a)))
| ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(V_A,V_P,T_a))) ) ).
cnf(cls_ball__conj__distrib_5,axiom,
( hBOOL(hAPP(V_Q,V_x))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(V_A,V_Q,T_a)),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(V_A,V_P,T_a)),V_A)) ) ).
cnf(cls_ball__conj__distrib_4,axiom,
( hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(V_A,V_Q,T_a)),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(V_A,V_P,T_a)),V_A)) ) ).
cnf(cls_ball__conj__distrib_3,axiom,
( hBOOL(hAPP(V_Q,V_xf))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xf),V_A))
| ~ hBOOL(hAPP(V_Q,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(V_A,V_P,V_Q,T_a)))
| ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(V_A,V_P,V_Q,T_a))) ) ).
cnf(cls_ball__conj__distrib_2,axiom,
( hBOOL(hAPP(V_P,V_xg))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xg),V_A))
| ~ hBOOL(hAPP(V_Q,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(V_A,V_P,V_Q,T_a)))
| ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(V_A,V_P,V_Q,T_a))) ) ).
cnf(cls_ballE_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| hBOOL(hAPP(V_P,V_x))
| hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__XballE__1__1(V_A,V_P,T_a)),V_A)) ) ).
cnf(cls_bexCI_3,axiom,
( hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__XbexCI__1__1(V_A,V_P,T_a)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))
| ~ hBOOL(hAPP(V_P,V_a)) ) ).
cnf(cls_ord_OgreaterThanLessThan__iff_0,axiom,
( hBOOL(hAPP(hAPP(V_less,V_l),V_i))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OgreaterThanLessThan(V_less,V_l,V_u,T_a))) ) ).
cnf(cls_ord_OgreaterThanLessThan__iff_1,axiom,
( hBOOL(hAPP(hAPP(V_less,V_i),V_u))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OgreaterThanLessThan(V_less,V_l,V_u,T_a))) ) ).
cnf(cls_IntE_1,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)))) ) ).
cnf(cls_IntE_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)))) ) ).
cnf(cls_inj__on__contraD_0,axiom,
( hAPP(V_f,V_x) != hAPP(V_f,V_y)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_y),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| V_x = V_y
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
cnf(cls_inj__on__iff_0,axiom,
( hAPP(V_f,V_x) != hAPP(V_f,V_y)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_y),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| V_x = V_y ) ).
cnf(cls_inj__on__def_0,axiom,
( hAPP(V_f,V_x) != hAPP(V_f,V_xa)
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xa),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| V_x = V_xa ) ).
cnf(cls_inj__onD_0,axiom,
( hAPP(V_f,V_x) != hAPP(V_f,V_y)
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_y),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_bex__empty_0,axiom,
( ~ hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) ) ).
cnf(cls_pred__equals__eq_0,axiom,
( hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_R) != hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_S)
| V_R = V_S ) ).
cnf(cls_CollectI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Collect(V_P,T_a)))
| ~ hBOOL(hAPP(V_P,V_a)) ) ).
cnf(cls_CollectD_0,axiom,
( hBOOL(hAPP(V_P,V_a))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Collect(V_P,T_a))) ) ).
cnf(cls_ord_OatMost__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OatMost(V_less__eq,V_k,T_a)))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_i),V_k)) ) ).
cnf(cls_ord_OatMost__iff_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,V_i),V_k))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OatMost(V_less__eq,V_k,T_a))) ) ).
cnf(cls_Diff__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)))
| hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A)) ) ).
cnf(cls_DiffI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_c),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)))
| hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A)) ) ).
cnf(cls_ball__conj__distrib_1,axiom,
( hBOOL(hAPP(V_Q,V_xd))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xd),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(V_A,V_P,V_Q,T_a)),V_A)) ) ).
cnf(cls_ball__conj__distrib_0,axiom,
( hBOOL(hAPP(V_P,V_xe))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xe),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1(V_A,V_P,V_Q,T_a)),V_A)) ) ).
cnf(cls_ballE_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__XballE__1__1(V_A,V_P,T_a))) ) ).
cnf(cls_insert__ident_0,axiom,
( c_Set_Oinsert(V_x,V_A,T_a) != c_Set_Oinsert(V_x,V_B,T_a)
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))
| hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| V_A = V_B ) ).
cnf(cls_bexI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__XbexI__1__1(V_A,V_P,T_a)),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ hBOOL(hAPP(V_P,V_x)) ) ).
cnf(cls_UN__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_b,tc_fun(T_a,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_b),hAPP(V_B,V_x)))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A)) ) ).
cnf(cls_UN__I_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_b),V_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_bool))))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_b),hAPP(V_B,V_a)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)) ) ).
cnf(cls_ord_OgreaterThan__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OgreaterThan(V_less,V_k,T_a)))
| ~ hBOOL(hAPP(hAPP(V_less,V_k),V_i)) ) ).
cnf(cls_ord_OgreaterThan__iff_0,axiom,
( hBOOL(hAPP(hAPP(V_less,V_k),V_i))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OgreaterThan(V_less,V_k,T_a))) ) ).
cnf(cls_bex__UN_4,axiom,
( hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3(V_A,V_B,V_P,T_b,T_a)))
| ~ hBOOL(hAPP(V_P,V_xa))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xa),hAPP(V_B,V_x)))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A)) ) ).
cnf(cls_vimage__eq_1,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Set_Ovimage(V_f,V_B,T_a,T_b)))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),V_B)) ) ).
cnf(cls_vimageI2_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_b),V_a),c_Set_Ovimage(V_f,V_A,T_b,T_a)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_a)),V_A)) ) ).
cnf(cls_vimageI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_b),V_a),c_Set_Ovimage(V_f,V_B,T_b,T_a)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_a)),V_B)) ) ).
cnf(cls_vimageE_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),V_B))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Set_Ovimage(V_f,V_B,T_a,T_b))) ) ).
cnf(cls_vimageD_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),V_A))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Set_Ovimage(V_f,V_A,T_a,T_b))) ) ).
cnf(cls_complete__lattice_OInf__lower_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,hAPP(V_Inf,V_A)),V_x))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_complete__lattice_OSup__upper_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,V_x),hAPP(V_Sup,V_A)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_ord_OatLeastAtMost__iff_1,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,V_i),V_u))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OatLeastAtMost(V_less__eq,V_l,V_u,T_a))) ) ).
cnf(cls_ord_OatLeastAtMost__iff_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,V_l),V_i))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OatLeastAtMost(V_less__eq,V_l,V_u,T_a))) ) ).
cnf(cls_bex__Un_7,axiom,
( hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(V_A,V_B,V_P,T_a)))
| ~ hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B)) ) ).
cnf(cls_bex__Un_5,axiom,
( hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(V_A,V_B,V_P,T_a)))
| ~ hBOOL(hAPP(V_P,V_xa))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_xa),V_A)) ) ).
cnf(cls_bexE_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__XbexE__1__1(V_A,V_P,T_a)),V_A))
| ~ hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_insert__absorb_0,axiom,
( c_Set_Oinsert(V_a,V_A,T_a) = V_A
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)) ) ).
cnf(cls_ord_OlessThan__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OlessThan(V_less,V_k,T_a)))
| ~ hBOOL(hAPP(hAPP(V_less,V_i),V_k)) ) ).
cnf(cls_ord_OlessThan__iff_0,axiom,
( hBOOL(hAPP(hAPP(V_less,V_i),V_k))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OlessThan(V_less,V_k,T_a))) ) ).
cnf(cls_SUP2__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_fun(T_c,tc_bool))),V_b),V_c))
| ~ hBOOL(hAPP(hAPP(hAPP(V_B,V_x),V_b),V_c))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_SUP1__iff_2,axiom,
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_bool)),V_b))
| ~ hBOOL(hAPP(hAPP(V_B,V_x),V_b))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_SUP2__I_0,axiom,
( hBOOL(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_fun(T_c,tc_bool))),V_b),V_c))
| ~ hBOOL(hAPP(hAPP(hAPP(V_B,V_a),V_b),V_c))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)) ) ).
cnf(cls_SUP1__I_0,axiom,
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_bool)),V_b))
| ~ hBOOL(hAPP(hAPP(V_B,V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)) ) ).
cnf(cls_ord_OatLeastLessThan__iff_1,axiom,
( hBOOL(hAPP(hAPP(V_less,V_i),V_u))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OatLeastLessThan(V_less__eq,V_less,V_l,V_u,T_a))) ) ).
cnf(cls_ord_OatLeastLessThan__iff_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,V_l),V_i))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_i),c_SetInterval_Oord_OatLeastLessThan(V_less__eq,V_less,V_l,V_u,T_a))) ) ).
cnf(cls_rev__bexI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(V_A,V_P,T_a)),V_A))
| ~ hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_rev__bexI_1,axiom,
( hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(V_A,V_P,T_a)))
| ~ hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_rev__image__eqI_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_aa),V_x),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_x)),c_Set_Oimage(V_f,V_A,T_aa,T_a))) ) ).
cnf(cls_image__iff_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A))
| hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_x)),c_Set_Oimage(V_f,V_A,T_b,T_a))) ) ).
cnf(cls_image__eqI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_x)),c_Set_Oimage(V_f,V_A,T_b,T_a)))
| ~ hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A)) ) ).
cnf(cls_imageI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),c_Set_Oimage(V_f,V_A,T_a,T_b)))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)) ) ).
cnf(cls_evaln__elim__cases_I5_J_2,axiom,
( c_Natural_Oevaln(V_c2,V_s,V_n,V_t)
| c_Natural_Oevaln(V_c1,V_s,V_n,V_t)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(V_b,V_c1,V_c2),V_s,V_n,V_t) ) ).
cnf(cls_evaln__WHILE__case_0,axiom,
( hBOOL(hAPP(V_b,V_s))
| V_t = V_s
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b,V_c),V_s,V_n,V_t) ) ).
cnf(cls_evaln__nonstrict_0,axiom,
( c_Natural_Oevaln(V_c,V_s,V_m,V_t)
| ~ c_lessequals(V_n,V_m,tc_nat)
| ~ c_Natural_Oevaln(V_c,V_s,V_n,V_t) ) ).
cnf(cls_evaln_OSkip_0,axiom,
c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_s) ).
cnf(cls_evaln_OIfFalse_0,axiom,
( c_Natural_Oevaln(c_Com_Ocom_OCond(V_b,V_c0,V_c1),V_s,V_n,V_s1)
| ~ c_Natural_Oevaln(V_c1,V_s,V_n,V_s1)
| hBOOL(hAPP(V_b,V_s)) ) ).
cnf(cls_evaln__elim__cases_I5_J_0,axiom,
( c_Natural_Oevaln(V_c2,V_s,V_n,V_t)
| hBOOL(hAPP(V_b,V_s))
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(V_b,V_c1,V_c2),V_s,V_n,V_t) ) ).
cnf(cls_evaln__Suc_0,axiom,
( c_Natural_Oevaln(V_c,V_s,c_Suc(V_n),V_s_H)
| ~ c_Natural_Oevaln(V_c,V_s,V_n,V_s_H) ) ).
cnf(cls_evaln__max2_1,axiom,
( c_Natural_Oevaln(V_c2,V_s2,c_Natural_Osko__Natural__Xevaln__max2__1__1(V_c1,V_c2,V_s1,V_s2,V_t1,V_t2),V_t2)
| ~ c_Natural_Oevaln(V_c2,V_s2,V_n2,V_t2)
| ~ c_Natural_Oevaln(V_c1,V_s1,V_n1,V_t1) ) ).
cnf(cls_evaln__max2_0,axiom,
( c_Natural_Oevaln(V_c1,V_s1,c_Natural_Osko__Natural__Xevaln__max2__1__1(V_c1,V_c2,V_s1,V_s2,V_t1,V_t2),V_t1)
| ~ c_Natural_Oevaln(V_c2,V_s2,V_n2,V_t2)
| ~ c_Natural_Oevaln(V_c1,V_s1,V_n1,V_t1) ) ).
cnf(cls_evaln_OWhileFalse_0,axiom,
( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b,V_c),V_s,V_n,V_s)
| hBOOL(hAPP(V_b,V_s)) ) ).
cnf(cls_evaln_OIfTrue_0,axiom,
( c_Natural_Oevaln(c_Com_Ocom_OCond(V_b,V_c0,V_c1),V_s,V_n,V_s1)
| ~ c_Natural_Oevaln(V_c0,V_s,V_n,V_s1)
| ~ hBOOL(hAPP(V_b,V_s)) ) ).
cnf(cls_evaln__elim__cases_I5_J_1,axiom,
( ~ hBOOL(hAPP(V_b,V_s))
| c_Natural_Oevaln(V_c1,V_s,V_n,V_t)
| ~ c_Natural_Oevaln(c_Com_Ocom_OCond(V_b,V_c1,V_c2),V_s,V_n,V_t) ) ).
cnf(cls_evaln_OWhileTrue_0,axiom,
( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b,V_c),V_s0,V_n,V_s2)
| ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b,V_c),V_s1,V_n,V_s2)
| ~ c_Natural_Oevaln(V_c,V_s0,V_n,V_s1)
| ~ hBOOL(hAPP(V_b,V_s0)) ) ).
cnf(cls_evaln_OSemi_0,axiom,
( c_Natural_Oevaln(c_Com_Ocom_OSemi(V_c0,V_c1),V_s0,V_n,V_s2)
| ~ c_Natural_Oevaln(V_c1,V_s1,V_n,V_s2)
| ~ c_Natural_Oevaln(V_c0,V_s0,V_n,V_s1) ) ).
cnf(cls_evaln__elim__cases_I1_J_0,axiom,
( V_t = V_s
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t) ) ).
cnf(cls_evaln__evalc_0,axiom,
( c_Natural_Oevalc(V_c,V_s,V_t)
| ~ c_Natural_Oevaln(V_c,V_s,V_n,V_t) ) ).
cnf(cls_eval__eq_1,axiom,
( c_Natural_Oevalc(V_c,V_s,V_t)
| ~ c_Natural_Oevaln(V_c,V_s,V_x,V_t) ) ).
cnf(cls_COMBI__def__raw_0,axiom,
hAPP(c_COMBI(t_a),v_P) = v_P ).
cnf(cls_triple__valid__Suc_0,axiom,
( c_Hoare__Mirabelle_Otriple__valid(V_n,V_t,T_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(c_Suc(V_n),V_t,T_a) ) ).
cnf(cls_hoare__valids__def_0,axiom,
( c_Hoare__Mirabelle_Otriple__valid(V_n,V_na,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_na),V_ts))
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(V_G,V_n)),V_G))
| ~ c_Hoare__Mirabelle_Ohoare__valids(V_G,V_ts,t_a) ) ).
cnf(cls_triples__valid__Suc_1,axiom,
( c_Hoare__Mirabelle_Otriple__valid(V_n,V_xa,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xa),V_ts))
| ~ c_Hoare__Mirabelle_Otriple__valid(c_Suc(V_n),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(V_n,V_ts),t_a) ) ).
cnf(cls_hoare__valids__def_2,axiom,
( c_Hoare__Mirabelle_Ohoare__valids(V_G,V_ts,t_a)
| c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(V_G,V_ts),V_x,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_x),V_G)) ) ).
cnf(cls_hoare__valids__def_1,axiom,
( c_Hoare__Mirabelle_Otriple__valid(V_n,V_nb,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nb),V_ts))
| ~ c_Hoare__Mirabelle_Otriple__valid(V_n,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(V_G,V_n),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__valids(V_G,V_ts,t_a) ) ).
cnf(cls_peek__and__def__raw_0,axiom,
c_Hoare__Mirabelle_Opeek__and(v_P,v_p,v_Z,v_s,t_a) = c_and(hAPP(hAPP(v_P,v_Z),v_s),hAPP(v_p,v_s)) ).
cnf(cls_peek__and__def_0,axiom,
c_Hoare__Mirabelle_Opeek__and(V_P,V_p,v_Z,v_s,t_a) = c_and(hAPP(hAPP(V_P,v_Z),v_s),hAPP(V_p,v_s)) ).
cnf(cls_triple__valid__def2_0,axiom,
( hBOOL(hAPP(hAPP(V_Q,V_Z),V_s_H))
| ~ c_Natural_Oevaln(V_c,V_s,V_n,V_s_H)
| ~ hBOOL(hAPP(hAPP(V_P,V_Z),V_s))
| ~ c_Hoare__Mirabelle_Otriple__valid(V_n,c_Hoare__Mirabelle_Otriple_Otriple(V_P,V_c,V_Q,t_a),t_a) ) ).
cnf(cls_COMBK__def__raw_0,axiom,
hAPP(c_COMBK(v_P,t_a,t_b),v_Q) = v_P ).
cnf(cls_triples__valid__Suc_0,axiom,
( c_Hoare__Mirabelle_Otriple__valid(V_n,V_x,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_x),V_ts))
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(V_n,V_ts)),V_ts)) ) ).
cnf(cls_COMBB__def__raw_0,axiom,
hAPP(c_COMBB(v_P,v_Q,t_a,t_b,t_c),v_R) = hAPP(v_P,hAPP(v_Q,v_R)) ).
cnf(cls_COMBS__def__raw_0,axiom,
hAPP(c_COMBS(v_P,v_Q,t_a,t_b,t_c),v_R) = hAPP(hAPP(v_P,v_R),hAPP(v_Q,v_R)) ).
cnf(cls_COMBC__def__raw_0,axiom,
hAPP(hAPP(c_COMBC(v_P,t_a,t_b,t_c),v_Q),v_R) = hAPP(hAPP(v_P,v_R),v_Q) ).
cnf(cls_mem__def_1,axiom,
( hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_S))
| ~ hBOOL(hAPP(V_S,V_x)) ) ).
cnf(cls_mem__def_0,axiom,
( hBOOL(hAPP(V_S,V_x))
| ~ hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_S)) ) ).
cnf(cls_conjecture_0,negated_conjecture,
hBOOL(hAPP(hAPP(v_P,v_Z),v_s)) ).
cnf(cls_conjecture_1,negated_conjecture,
c_Natural_Oevaln(v_c,v_s,v_n,v_s1) ).
cnf(cls_conjecture_2,negated_conjecture,
c_Natural_Oevaln(v_d,v_s1,v_n,v_s_H) ).
cnf(cls_conjecture_3,negated_conjecture,
~ hBOOL(hAPP(hAPP(v_R,v_Z),v_s_H)) ).
cnf(cls_conjecture_4,negated_conjecture,
( c_Hoare__Mirabelle_Otriple__valid(v_n,V_x,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_x),v_Ga)) ) ).
cnf(cls_conjecture_5,negated_conjecture,
( hBOOL(hAPP(hAPP(v_Q,V_Z),V_s_H))
| ~ c_Natural_Oevaln(v_c,V_s,v_n,V_s_H)
| ~ hBOOL(hAPP(hAPP(v_P,V_Z),V_s)) ) ).
cnf(cls_conjecture_6,negated_conjecture,
( hBOOL(hAPP(hAPP(v_R,V_Z),V_s_H))
| ~ c_Natural_Oevaln(v_d,V_s,v_n,V_s_H)
| ~ hBOOL(hAPP(hAPP(v_Q,V_Z),V_s)) ) ).
cnf(clsarity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_1) ) ).
cnf(clsarity_fun__Lattices_Oupper__semilattice,axiom,
( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ) ).
cnf(clsarity_fun__Lattices_Olower__semilattice,axiom,
( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ) ).
cnf(clsarity_fun__Lattices_Odistrib__lattice,axiom,
( class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Odistrib__lattice(T_1) ) ).
cnf(clsarity_fun__Lattices_Obounded__lattice,axiom,
( class_Lattices_Obounded__lattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Obounded__lattice(T_1) ) ).
cnf(clsarity_fun__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_Obot,axiom,
( class_Orderings_Obot(tc_fun(T_2,T_1))
| ~ class_Orderings_Obot(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__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_nat) ).
cnf(clsarity_nat__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_nat) ).
cnf(clsarity_nat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_nat) ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat) ).
cnf(clsarity_nat__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_nat) ).
cnf(clsarity_nat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_nat) ).
cnf(clsarity_nat__Orderings_Obot,axiom,
class_Orderings_Obot(tc_nat) ).
cnf(clsarity_nat__HOL_Oord,axiom,
class_HOL_Oord(tc_nat) ).
cnf(clsarity_bool__Complete__Lattice_Ocomplete__lattice,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool) ).
cnf(clsarity_bool__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_bool) ).
cnf(clsarity_bool__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_bool) ).
cnf(clsarity_bool__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_bool) ).
cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_bool) ).
cnf(clsarity_bool__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_Obot,axiom,
class_Orderings_Obot(tc_bool) ).
cnf(clsarity_bool__HOL_Oord,axiom,
class_HOL_Oord(tc_bool) ).
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
hBOOL(hAPP(hAPP(c_fequal(T_a),V_x),V_x)) ).
cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom,
( V_X = V_Y
| ~ hBOOL(hAPP(hAPP(c_fequal(T_a),V_X),V_Y)) ) ).
%------------------------------------------------------------------------------