TPTP Problem File: SWV844-1.p
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%------------------------------------------------------------------------------
% File : SWV844-1 : TPTP v8.2.0. Released v4.1.0.
% Domain : Software Verification
% Problem : Hoare logic with procedures 242_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-242_1 [Nip10]
% Status : Unsatisfiable
% Rating : 0.05 v7.4.0, 0.06 v7.3.0, 0.00 v7.0.0, 0.13 v6.4.0, 0.07 v6.3.0, 0.00 v6.2.0, 0.20 v6.1.0, 0.21 v6.0.0, 0.20 v5.5.0, 0.40 v5.3.0, 0.39 v5.2.0, 0.31 v5.1.0, 0.41 v5.0.0, 0.36 v4.1.0
% Syntax : Number of clauses : 1042 ( 200 unt; 148 nHn; 524 RR)
% Number of literals : 2561 ( 621 equ;1392 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 51 ( 50 usr; 0 prp; 1-6 aty)
% Number of functors : 78 ( 78 usr; 17 con; 0-6 aty)
% Number of variables : 3603 ( 383 sgn)
% SPC : CNF_UNS_RFO_SEQ_NHN
% Comments :
%------------------------------------------------------------------------------
cnf(cls_min__max_Ole__infI1_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_x)) ) ).
cnf(cls_min__max_Ole__infE_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b))) ) ).
cnf(cls_min__max_Ole__infE_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b))) ) ).
cnf(cls_lower__semilattice_Oinf__absorb2_0,axiom,
( hAPP(hAPP(V_inf,V_x),V_y) = V_y
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_y),V_x))
| ~ c_Lattices_Olower__semilattice(V_less__eq,V_less,V_inf,T_a) ) ).
cnf(cls_lower__semilattice_Ole__iff__inf_1,axiom,
( hAPP(hAPP(V_inf,V_x),V_y) != V_x
| ~ c_Lattices_Olower__semilattice(V_less__eq,V_less,V_inf,T_a)
| hBOOL(hAPP(hAPP(V_less__eq,V_x),V_y)) ) ).
cnf(cls_lower__semilattice_Ole__iff__inf_0,axiom,
( hAPP(hAPP(V_inf,V_x),V_y) = V_x
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_x),V_y))
| ~ c_Lattices_Olower__semilattice(V_less__eq,V_less,V_inf,T_a) ) ).
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_less__add__iff2_1,axiom,
( ~ class_Ring__and__Field_Opordered__ring(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_e)),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_e)),V_d)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_b),V_a)),V_e)),V_d))) ) ).
cnf(cls_less__add__iff2_0,axiom,
( ~ class_Ring__and__Field_Opordered__ring(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_b),V_a)),V_e)),V_d)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_e)),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_e)),V_d))) ) ).
cnf(cls_less__add__iff1_1,axiom,
( ~ class_Ring__and__Field_Opordered__ring(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_e)),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_e)),V_d)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)),V_e)),V_c)),V_d)) ) ).
cnf(cls_less__add__iff1_0,axiom,
( ~ class_Ring__and__Field_Opordered__ring(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)),V_e)),V_c)),V_d))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_e)),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_e)),V_d))) ) ).
cnf(cls_setsum__Un__disjoint_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_b)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| c_Finite__Set_Osetsum(V_g,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_b),c_Finite__Set_Osetsum(V_g,V_A,T_a,T_b)),c_Finite__Set_Osetsum(V_g,V_B,T_a,T_b)) ) ).
cnf(cls_min__le__iff__disj_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_z))
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z)) ) ).
cnf(cls_ab__semigroup__idem__mult__max_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omax(T_a),T_a) ) ).
cnf(cls_fun__upd__twist_0,axiom,
( c_Fun_Ofun__upd(c_Fun_Ofun__upd(V_m,V_a,V_b,T_a,T_b),V_c,V_d,T_a,T_b) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(V_m,V_c,V_d,T_a,T_b),V_a,V_b,T_a,T_b)
| V_a = V_c ) ).
cnf(cls_min__max_Ole__sup__iff_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z)) ) ).
cnf(cls_min__max_Ole__sup__iff_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z)) ) ).
cnf(cls_le__max__iff__disj_2,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_z),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_z),V_y)) ) ).
cnf(cls_le__max__iff__disj_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_z),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_z),V_x)) ) ).
cnf(cls_min__max_Ole__supI2_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_b)) ) ).
cnf(cls_min__max_Ole__supI1_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_a)) ) ).
cnf(cls_min__max_Ole__supE_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x)) ) ).
cnf(cls_min__max_Ole__supE_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x)) ) ).
cnf(cls_less__max__iff__disj_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_z),V_y))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_z),V_x))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_z),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))) ) ).
cnf(cls_inf__sup__aci_I2_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z)) ) ).
cnf(cls_inf__sup__aci_I3_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_z)) ) ).
cnf(cls_inf__left__commute_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_z)) ) ).
cnf(cls_inf__assoc_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z)) ) ).
cnf(cls_Int__assoc_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)) ).
cnf(cls_Int__left__commute_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C)) ).
cnf(cls_sup__max_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ class_Lattices_Oupper__semilattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(T_a) = c_Orderings_Oord__class_Omax(T_a) ) ).
cnf(cls_min__less__iff__disj_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_z))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z)) ) ).
cnf(cls_class__ringb_Oadd__mul__solve_0,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_w),V_y)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_z)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_w),V_z)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_y))
| V_y = V_z
| V_w = V_x ) ).
cnf(cls_class__ringb_Onoteq__reduce_0,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_d)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_d)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c))
| V_c = V_d
| V_a = V_b ) ).
cnf(cls_diff__Suc__Suc_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_Suc(V_m)),c_Suc(V_n)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_m),V_n) ).
cnf(cls_neg__less__iff__less_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)) ) ).
cnf(cls_neg__less__iff__less_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a))) ) ).
cnf(cls_less__SucE_0,axiom,
( V_m = V_n
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),c_Suc(V_n))) ) ).
cnf(cls_less__antisym_0,axiom,
( V_m = V_n
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),c_Suc(V_m)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),V_m)) ) ).
cnf(cls_not__less__less__Suc__eq_0,axiom,
( V_n = V_m
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),c_Suc(V_m)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),V_m)) ) ).
cnf(cls_inf__eq__top__eq2_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_A),V_B) != c_Orderings_Otop__class_Otop(T_a)
| V_B = c_Orderings_Otop__class_Otop(T_a) ) ).
cnf(cls_inf__eq__top__eq1_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_A),V_B) != c_Orderings_Otop__class_Otop(T_a)
| V_A = c_Orderings_Otop__class_Otop(T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I13_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) ).
cnf(cls_class__semiring_Osemiring__rules_I14_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) ).
cnf(cls_class__semiring_Osemiring__rules_I15_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) ).
cnf(cls_Diff__Int__distrib_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_B)) ).
cnf(cls_Diff__Int__distrib2_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)) ).
cnf(cls_less__imp__diff__less_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_j),V_n)),V_k))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_j),V_k)) ) ).
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_inf__top__right_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ).
cnf(cls_inf__top__left_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ).
cnf(cls_Int__UNIV__left_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))),V_B) = V_B ).
cnf(cls_Int__UNIV__right_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))) = V_A ).
cnf(cls_Diff__Int2_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C)),V_B) ).
cnf(cls_ivl__disj__int_I15_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_m,T_a)),c_SetInterval_Oord__class_OatLeastAtMost(V_m,V_u,T_a)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_less__le__not__le_2,axiom,
( ~ class_Orderings_Opreorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_psubset__eq_1,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_x),V_x)) ).
cnf(cls_nat__less__le_1,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),V_x)) ).
cnf(cls_less__not__refl_0,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),V_n)) ).
cnf(cls_less__fun__def_2,axiom,
( ~ class_HOL_Oord(T_b)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,T_b)),V_f),V_g))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,T_b)),V_g),V_f))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,T_b)),V_f),V_g)) ) ).
cnf(cls_order__less__le_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_x)) ) ).
cnf(cls_linorder__neq__iff_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_x)) ) ).
cnf(cls_order__less__irrefl_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_x)) ) ).
cnf(cls_sup__inf__absorb_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)) = V_x ) ).
cnf(cls_min__max_Oinf__idem_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ).
cnf(cls_compl__eq__compl__iff_0,axiom,
( ~ class_Lattices_Oboolean__algebra(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_x) != hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_y)
| V_x = V_y ) ).
cnf(cls_neg__equal__iff__equal_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a) != hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)
| V_a = V_b ) ).
cnf(cls_Compl__eq__Compl__iff_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B)
| V_A = V_B ) ).
cnf(cls_atLeastatMost__psubset__iff_6,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a)),c_SetInterval_Oord__class_OatLeastAtMost(V_c,V_d,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_c),V_d))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_d))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_d))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_c),V_a)) ) ).
cnf(cls_atLeastatMost__psubset__iff_5,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a)),c_SetInterval_Oord__class_OatLeastAtMost(V_c,V_d,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_c),V_d))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_c),V_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_d))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_c),V_a)) ) ).
cnf(cls_ab__semigroup__idem__mult_Omult__left__idem_0,axiom,
( hAPP(hAPP(V_times,V_x),hAPP(hAPP(V_times,V_x),V_y)) = hAPP(hAPP(V_times,V_x),V_y)
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(V_times,T_a) ) ).
cnf(cls_ab__semigroup__idem__mult_Omult__idem_0,axiom,
( hAPP(hAPP(V_times,V_x),V_x) = V_x
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(V_times,T_a) ) ).
cnf(cls_linorder__neqE__ordered__idom_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| V_x = V_y ) ).
cnf(cls_not__less__iff__gr__or__eq_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| V_x = V_y
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_le__antisym_0,axiom,
( V_m = V_n
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_n),V_m))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_m),V_n)) ) ).
cnf(cls_nat__neq__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),V_m))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))
| V_m = V_n ) ).
cnf(cls_nat__less__cases_0,axiom,
( hBOOL(hAPP(hAPP(V_P,V_n),V_m))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),V_m))
| V_m = V_n
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n)) ) ).
cnf(cls_linorder__neqE__nat_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_y),V_x))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),V_y))
| V_x = V_y ) ).
cnf(cls_linorder__neqE_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| V_x = V_y ) ).
cnf(cls_linorder__less__linear_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x))
| V_x = V_y
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_linorder__antisym__conv3_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| V_x = V_y
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x)) ) ).
cnf(cls_min__max_Osup__idem_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ).
cnf(cls_add__strict__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_c),V_d))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)) ) ).
cnf(cls_inf__sup__absorb_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)) = V_x ) ).
cnf(cls_less__infI2_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b)),V_x))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_x)) ) ).
cnf(cls_less__infI1_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b)),V_x))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_x)) ) ).
cnf(cls_termination__basic__simps_I5_J_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),V_y)) ) ).
cnf(cls_psubset__eq_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_nat__less__le_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n)) ) ).
cnf(cls_less__fun__def_0,axiom,
( ~ class_HOL_Oord(T_b)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,T_b)),V_f),V_g))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,T_b)),V_f),V_g)) ) ).
cnf(cls_order__le__less_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_order__less__imp__le_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_minus__add__cancel_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)) = V_b ) ).
cnf(cls_add__cancel__end_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_z)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z)) = V_y ) ).
cnf(cls_setsum__Un_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_b)
| c_Finite__Set_Osetsum(V_f,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_b),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_b),c_Finite__Set_Osetsum(V_f,V_A,T_a,T_b)),c_Finite__Set_Osetsum(V_f,V_B,T_a,T_b))),c_Finite__Set_Osetsum(V_f,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b))
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_min__max_Ole__infI2_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_x)) ) ).
cnf(cls_min__le__iff__disj_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_z)) ) ).
cnf(cls_min__le__iff__disj_2,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_z)) ) ).
cnf(cls_min__max_Ole__inf__iff_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))) ) ).
cnf(cls_min__max_Ole__inf__iff_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))) ) ).
cnf(cls_ab__semigroup__idem__mult__min_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omin(T_a),T_a) ) ).
cnf(cls_le__max__iff__disj_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_z),V_y))
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_z),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_z),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))) ) ).
cnf(cls_square__eq__iff_0,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_a) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_b)
| V_a = hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)
| V_a = V_b ) ).
cnf(cls_diff__less__mono2_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_l),V_n)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_l),V_m)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_l))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n)) ) ).
cnf(cls_class__semiring_Oadd__c_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_x) ) ).
cnf(cls_comm__monoid__add_Omult__commute_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a) ) ).
cnf(cls_fold__image__def_0,axiom,
c_Finite__Set_Ofold__image(V_f,V_g,T_a,T_b) = c_Finite__Set_Ofold(c_COMBB(V_f,V_g,T_a,tc_fun(T_a,T_a),T_b),T_b,T_a) ).
cnf(cls_Suc__diff__le_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_Suc(V_m)),V_n) = c_Suc(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_n),V_m)) ) ).
cnf(cls_le__add__iff1_0,axiom,
( ~ class_Ring__and__Field_Opordered__ring(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)),V_e)),V_c)),V_d))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_e)),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_e)),V_d))) ) ).
cnf(cls_le__add__iff1_1,axiom,
( ~ class_Ring__and__Field_Opordered__ring(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_e)),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_e)),V_d)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)),V_e)),V_c)),V_d)) ) ).
cnf(cls_le__add__iff2_0,axiom,
( ~ class_Ring__and__Field_Opordered__ring(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_b),V_a)),V_e)),V_d)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_e)),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_e)),V_d))) ) ).
cnf(cls_le__add__iff2_1,axiom,
( ~ class_Ring__and__Field_Opordered__ring(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_e)),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_e)),V_d)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_b),V_a)),V_e)),V_d))) ) ).
cnf(cls_add__eq__inf__sup_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b)) ) ).
cnf(cls_less__eq__Suc__le_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),V_m))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(V_n)),V_m)) ) ).
cnf(cls_less__eq__Suc__le_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(V_n)),V_m))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),V_m)) ) ).
cnf(cls_Suc__le__eq_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(V_m)),V_n)) ) ).
cnf(cls_Suc__leI_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(V_m)),V_n))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n)) ) ).
cnf(cls_min__max_Oinf__sup__distrib1_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z)) ) ).
cnf(cls_min__max_Oinf__sup__distrib2_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_z),V_x)) ) ).
cnf(cls_psubset__card__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(V_A,T_a)),c_Finite__Set_Ocard(V_B,T_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ c_Finite__Set_Ofinite(V_B,T_a) ) ).
cnf(cls_le__maxI2_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))) ) ).
cnf(cls_le__maxI1_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))) ) ).
cnf(cls_min__max_Ole__supI_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_x)) ) ).
cnf(cls_min__max_Osup__least_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_z),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x)) ) ).
cnf(cls_min__max_Ole__sup__iff_2,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_z)) ) ).
cnf(cls_eq__add__iff1_0,axiom,
( ~ class_Ring__and__Field_Oring(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_e)),V_c) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_e)),V_d)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)),V_e)),V_c) = V_d ) ).
cnf(cls_eq__add__iff2_0,axiom,
( ~ class_Ring__and__Field_Oring(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_e)),V_c) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_e)),V_d)
| V_c = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_b),V_a)),V_e)),V_d) ) ).
cnf(cls_eq__add__iff2_1,axiom,
( ~ class_Ring__and__Field_Oring(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_e)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_b),V_a)),V_e)),V_d)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_e)),V_d) ) ).
cnf(cls_lower__semilattice_Oinf__idem_0,axiom,
( hAPP(hAPP(V_inf,V_x),V_x) = V_x
| ~ c_Lattices_Olower__semilattice(V_less__eq,V_less,V_inf,T_a) ) ).
cnf(cls_lower__semilattice_Oinf__assoc_0,axiom,
( hAPP(hAPP(V_inf,hAPP(hAPP(V_inf,V_x),V_y)),V_z) = hAPP(hAPP(V_inf,V_x),hAPP(hAPP(V_inf,V_y),V_z))
| ~ c_Lattices_Olower__semilattice(V_less__eq,V_less,V_inf,T_a) ) ).
cnf(cls_lower__semilattice_Oinf__commute_0,axiom,
( hAPP(hAPP(V_inf,V_x),V_y) = hAPP(hAPP(V_inf,V_y),V_x)
| ~ c_Lattices_Olower__semilattice(V_less__eq,V_less,V_inf,T_a) ) ).
cnf(cls_lower__semilattice_Oinf__left__idem_0,axiom,
( hAPP(hAPP(V_inf,V_x),hAPP(hAPP(V_inf,V_x),V_y)) = hAPP(hAPP(V_inf,V_x),V_y)
| ~ c_Lattices_Olower__semilattice(V_less__eq,V_less,V_inf,T_a) ) ).
cnf(cls_lower__semilattice_Oinf__left__commute_0,axiom,
( hAPP(hAPP(V_inf,V_x),hAPP(hAPP(V_inf,V_y),V_z)) = hAPP(hAPP(V_inf,V_y),hAPP(hAPP(V_inf,V_x),V_z))
| ~ c_Lattices_Olower__semilattice(V_less__eq,V_less,V_inf,T_a) ) ).
cnf(cls_Compl__subset__Compl__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_A)) ) ).
cnf(cls_Compl__subset__Compl__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_A))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B))) ) ).
cnf(cls_Compl__anti__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_le__imp__neg__le_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b)) ) ).
cnf(cls_neg__le__iff__le_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a))) ) ).
cnf(cls_setsum__Un__Int_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_b)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_b),c_Finite__Set_Osetsum(V_g,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b)),c_Finite__Set_Osetsum(V_g,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_b),c_Finite__Set_Osetsum(V_g,V_A,T_a,T_b)),c_Finite__Set_Osetsum(V_g,V_B,T_a,T_b))
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_min__max_Oinf__le1_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_x)) ) ).
cnf(cls_min__max_Oinf__le2_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_y)) ) ).
cnf(cls_min__max_Ole__infI_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_a)) ) ).
cnf(cls_min__max_Ole__inf__iff_2,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_min__max_Oinf__greatest_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_eq__add__iff1_1,axiom,
( ~ class_Ring__and__Field_Oring(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_e)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_e)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)),V_e)),V_c)) ) ).
cnf(cls_Compl__disjoint2_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A)),V_A) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_Compl__disjoint_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_compl__inf__bot_0,axiom,
( ~ class_Lattices_Oboolean__algebra(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Obot__class_Obot(T_a) ) ).
cnf(cls_inf__compl__bot_0,axiom,
( ~ class_Lattices_Oboolean__algebra(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Obot__class_Obot(T_a) ) ).
cnf(cls_min__diff__distrib__left_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_y),V_z)) ) ).
cnf(cls_max__less__iff__conj_2,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_z))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_z)) ) ).
cnf(cls_greaterThanAtMost__empty__iff_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_SetInterval_Oord__class_OgreaterThanAtMost(V_k,V_l,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_k),V_l)) ) ).
cnf(cls_greaterThanAtMost__empty__iff_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_SetInterval_Oord__class_OgreaterThanAtMost(V_k,V_l,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_k),V_l)) ) ).
cnf(cls_min__less__iff__conj_2,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_z),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_z),V_y))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_z),V_x)) ) ).
cnf(cls_class__ringb_Onoteq__reduce_1,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_c)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_d)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_d)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_c)) ) ).
cnf(cls_class__ringb_Oadd__mul__solve_1,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_z)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_y)) ) ).
cnf(cls_Int__atLeastLessThan_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(V_a,V_b,T_a)),c_SetInterval_Oord__class_OatLeastLessThan(V_c,V_d,T_a)) = c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_d),T_a) ) ).
cnf(cls_ivl__disj__int_I11_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_m,T_a)),c_SetInterval_Oord__class_OatLeastLessThan(V_m,V_u,T_a)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_min__max_Oinf__left__idem_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) ) ).
cnf(cls_diff__add__cancel_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)),V_b) = V_a ) ).
cnf(cls_add__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_c),V_d))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b)) ) ).
cnf(cls_ab__semigroup__idem__mult__sup_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Oupper__semilattice__class_Osup(T_a),T_a) ) ).
cnf(cls_Int__Un__distrib2_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)),V_A) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A)) ).
cnf(cls_Int__Un__distrib_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_C)) ).
cnf(cls_inf__sup__distrib1_0,axiom,
( ~ class_Lattices_Odistrib__lattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_z)) ) ).
cnf(cls_inf__sup__distrib2_0,axiom,
( ~ class_Lattices_Odistrib__lattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_z),V_x)) ) ).
cnf(cls_less__Suc__eq__le_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),c_Suc(V_n)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_m),V_n)) ) ).
cnf(cls_less__Suc__eq__le_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),c_Suc(V_n))) ) ).
cnf(cls_le__less__Suc__eq_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_x),V_x))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),c_Suc(V_x))) ) ).
cnf(cls_class__semiring_Omul__c_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_y) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_x) ) ).
cnf(cls_class__semiring_Osemiring__rules_I7_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_a) ) ).
cnf(cls_diff__less__Suc_0,axiom,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_m),V_n)),c_Suc(V_m))) ).
cnf(cls_add__sup__distrib__left_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add__join(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_b),V_c)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)) ) ).
cnf(cls_add__sup__distrib__right_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add__join(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)) ) ).
cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_b),V_c)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)) ) ).
cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)) ) ).
cnf(cls_inf__Inf__fold__inf_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_B),c_Complete__Lattice_OInf__class_OInf(V_A,T_a)) = hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(T_a),T_a,T_a),V_B),V_A)
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_order__less__trans_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_z))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_psubset__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_C))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_xt1_I10_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_z),V_x))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_z),V_y))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x)) ) ).
cnf(cls_min__max_Ole__iff__sup_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_min__max_Ole__iff__sup_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) != V_y
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_min__max_Osup__absorb1_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x)) ) ).
cnf(cls_class__semiring_Oadd__a_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y)),V_z) ) ).
cnf(cls_add__cancel__21_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z)) ) ).
cnf(cls_comm__monoid__add_Omult__assoc_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)) ) ).
cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)) ) ).
cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom,
( ~ class_OrderedGroup_Oab__semigroup__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)) ) ).
cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),V_d) ) ).
cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),V_b) ) ).
cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_d)) ) ).
cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)) ) ).
cnf(cls_add__cancel__21_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_u)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z) = V_u ) ).
cnf(cls_inf__min_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ class_Lattices_Olower__semilattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(T_a) = c_Orderings_Oord__class_Omin(T_a) ) ).
cnf(cls_lessI_0,axiom,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),c_Suc(V_n))) ).
cnf(cls_less__Suc__eq_2,axiom,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),c_Suc(V_x))) ).
cnf(cls_less__trans__Suc_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(V_i)),V_k))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_j),V_k))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_i),V_j)) ) ).
cnf(cls_add__le__cancel__right_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b)) ) ).
cnf(cls_add__le__cancel__right_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c))) ) ).
cnf(cls_add__le__cancel__left_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b)) ) ).
cnf(cls_add__le__cancel__left_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b))) ) ).
cnf(cls_add__right__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b)) ) ).
cnf(cls_add__left__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b)) ) ).
cnf(cls_minus__mult__right_0,axiom,
( ~ class_Ring__and__Field_Oring(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)) ) ).
cnf(cls_minus__mult__left_0,axiom,
( ~ class_Ring__and__Field_Oring(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),V_b) ) ).
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_lower__semilattice_Oab__semigroup__idem__mult__inf_0,axiom,
( c_OrderedGroup_Oab__semigroup__idem__mult(V_inf,T_a)
| ~ c_Lattices_Olower__semilattice(V_less__eq,V_less,V_inf,T_a) ) ).
cnf(cls_lower__semilattice_Oless__infI2_0,axiom,
( hBOOL(hAPP(hAPP(V_less,hAPP(hAPP(V_inf,V_a),V_b)),V_x))
| ~ hBOOL(hAPP(hAPP(V_less,V_b),V_x))
| ~ c_Lattices_Olower__semilattice(V_less__eq,V_less,V_inf,T_a) ) ).
cnf(cls_lower__semilattice_Oless__infI1_0,axiom,
( hBOOL(hAPP(hAPP(V_less,hAPP(hAPP(V_inf,V_a),V_b)),V_x))
| ~ hBOOL(hAPP(hAPP(V_less,V_a),V_x))
| ~ c_Lattices_Olower__semilattice(V_less__eq,V_less,V_inf,T_a) ) ).
cnf(cls_lower__semilattice_Ole__inf__iff_1,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,V_x),V_z))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_x),hAPP(hAPP(V_inf,V_y),V_z)))
| ~ c_Lattices_Olower__semilattice(V_less__eq,V_less,V_inf,T_a) ) ).
cnf(cls_lower__semilattice_Ole__inf__iff_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,V_x),V_y))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_x),hAPP(hAPP(V_inf,V_y),V_z)))
| ~ c_Lattices_Olower__semilattice(V_less__eq,V_less,V_inf,T_a) ) ).
cnf(cls_lower__semilattice_Ole__infE_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,V_x),V_a))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_x),hAPP(hAPP(V_inf,V_a),V_b)))
| ~ c_Lattices_Olower__semilattice(V_less__eq,V_less,V_inf,T_a) ) ).
cnf(cls_lower__semilattice_Ole__infE_1,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,V_x),V_b))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_x),hAPP(hAPP(V_inf,V_a),V_b)))
| ~ c_Lattices_Olower__semilattice(V_less__eq,V_less,V_inf,T_a) ) ).
cnf(cls_lower__semilattice_Ole__infI1_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,hAPP(hAPP(V_inf,V_a),V_b)),V_x))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_a),V_x))
| ~ c_Lattices_Olower__semilattice(V_less__eq,V_less,V_inf,T_a) ) ).
cnf(cls_lower__semilattice_Ole__infI2_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,hAPP(hAPP(V_inf,V_a),V_b)),V_x))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_b),V_x))
| ~ c_Lattices_Olower__semilattice(V_less__eq,V_less,V_inf,T_a) ) ).
cnf(cls_max__lattice_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_Lattices_Olower__semilattice(c_COMBC(c_lessequals(T_a),T_a,T_a,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(T_a),T_a,T_a,tc_bool),c_Orderings_Oord__class_Omax(T_a),T_a) ) ).
cnf(cls_mult__left__idem_0,axiom,
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_y) ) ).
cnf(cls_inf__sup__ord_I1_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)),V_x)) ) ).
cnf(cls_inf__sup__ord_I2_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)),V_y)) ) ).
cnf(cls_inf__greatest_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_le__inf__iff_2,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_le__infI_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_a)) ) ).
cnf(cls_inf__le2_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)),V_y)) ) ).
cnf(cls_inf__le1_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)),V_x)) ) ).
cnf(cls_Int__lower1_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),V_A)) ).
cnf(cls_Int__lower2_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),V_B)) ).
cnf(cls_Int__greatest_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),V_B))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),V_A)) ) ).
cnf(cls_Int__subset__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),V_B))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),V_A)) ) ).
cnf(cls_minus__mult__commute_0,axiom,
( ~ class_Ring__and__Field_Oring(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),V_b) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)) ) ).
cnf(cls_Suc__leD_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(V_m)),V_n)) ) ).
cnf(cls_le__SucI_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_m),c_Suc(V_n)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_m),V_n)) ) ).
cnf(cls_fun__Compl__def_0,axiom,
( ~ class_HOL_Ouminus(T_b)
| hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(t_a,T_b)),V_A),v_x) = hAPP(c_HOL_Ouminus__class_Ouminus(T_b),hAPP(V_A,v_x)) ) ).
cnf(cls_add__minus__cancel_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),V_b)) = V_b ) ).
cnf(cls_sup__inf__distrib2_0,axiom,
( ~ class_Lattices_Odistrib__lattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_z),V_x)) ) ).
cnf(cls_sup__inf__distrib1_0,axiom,
( ~ class_Lattices_Odistrib__lattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_z)) ) ).
cnf(cls_Un__Int__distrib_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_C)) ).
cnf(cls_Un__Int__distrib2_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)),V_A) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_A)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_C),V_A)) ).
cnf(cls_Suc__n__not__le__n_0,axiom,
~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(V_n)),V_n)) ).
cnf(cls_less__diff__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_m),V_k)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_n),V_k)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_k),V_n))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_k),V_m)) ) ).
cnf(cls_less__diff__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_m),V_k)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_n),V_k)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_k),V_n))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_k),V_m)) ) ).
cnf(cls_inf__sup__aci_I4_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) ) ).
cnf(cls_inf__left__idem_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) ) ).
cnf(cls_Int__left__absorb_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) ).
cnf(cls_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_inf__idem_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_x) = V_x ) ).
cnf(cls_Int__absorb_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_A) = V_A ).
cnf(cls_ivl__disj__int_I16_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(V_l,V_m,T_a)),c_SetInterval_Oord__class_OgreaterThanAtMost(V_m,V_u,T_a)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_add__strict__right__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)) ) ).
cnf(cls_add__less__cancel__right_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)) ) ).
cnf(cls_add__less__cancel__right_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c))) ) ).
cnf(cls_add__strict__left__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)) ) ).
cnf(cls_add__less__cancel__left_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)) ) ).
cnf(cls_add__less__cancel__left_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b))) ) ).
cnf(cls_inf__fun__eq_0,axiom,
( ~ class_Lattices_Olattice(T_b)
| hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,T_b)),V_f),V_g),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_b),hAPP(V_f,v_x)),hAPP(V_g,v_x)) ) ).
cnf(cls_xt1_I7_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_z),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_z),V_y))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x)) ) ).
cnf(cls_xt1_I8_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_z),V_x))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_z),V_y))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x)) ) ).
cnf(cls_le__refl_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_n),V_n)) ).
cnf(cls_le__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_i),V_k))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_j),V_k))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_i),V_j)) ) ).
cnf(cls_eq__imp__le_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_x),V_x)) ).
cnf(cls_psubset__subset__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_subset__psubset__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_C))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_order__le__less__trans_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_order__less__le__trans_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_z))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_le__add__right__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_c),V_d))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c))) ) ).
cnf(cls_atLeastLessThan__empty__iff_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_SetInterval_Oord__class_OatLeastLessThan(V_a,V_b,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)) ) ).
cnf(cls_atLeastLessThan__empty__iff_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_SetInterval_Oord__class_OatLeastLessThan(V_a,V_b,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)) ) ).
cnf(cls_greaterThanAtMost__empty__iff2_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(V_k,V_l,T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_k),V_l)) ) ).
cnf(cls_greaterThanAtMost__empty__iff2_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(V_k,V_l,T_a)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_k),V_l)) ) ).
cnf(cls_ab__semigroup__idem__mult__inf_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Olower__semilattice__class_Oinf(T_a),T_a) ) ).
cnf(cls_Int__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_D)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_D))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_C)) ) ).
cnf(cls_Int__Diff_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_B),V_C)) ).
cnf(cls_mult__idem_0,axiom,
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
cnf(cls_le__less__Suc__eq_0,axiom,
( V_n = V_m
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),c_Suc(V_m)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_m),V_n)) ) ).
cnf(cls_Suc__lessD_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(V_m)),V_n)) ) ).
cnf(cls_less__SucI_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),c_Suc(V_n)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n)) ) ).
cnf(cls_setsum__left__distrib_0,axiom,
( ~ class_Ring__and__Field_Osemiring__0(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Finite__Set_Osetsum(V_f,V_A,T_b,T_a)),V_r) = c_Finite__Set_Osetsum(hAPP(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(T_a),V_f,T_a,tc_fun(T_a,T_a),T_b),T_b,T_a,T_a),V_r),V_A,T_b,T_a) ) ).
cnf(cls_inf1I_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),V_x))
| ~ hBOOL(hAPP(V_B,V_x))
| ~ hBOOL(hAPP(V_A,V_x)) ) ).
cnf(cls_fun__upd__apply_1,axiom,
( hAPP(c_Fun_Ofun__upd(V_f,V_x,V_y,T_b,T_a),V_z) = hAPP(V_f,V_z)
| V_z = V_x ) ).
cnf(cls_fun__upd__other_0,axiom,
( hAPP(c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_b),V_z) = hAPP(V_f,V_z)
| V_z = V_x ) ).
cnf(cls_min__max_Odistrib__sup__le_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)))) ) ).
cnf(cls_sup__eq__neg__inf_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b) = hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b))) ) ).
cnf(cls_less__eqI_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x_H),V_y_H)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x_H),V_y_H))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_less__eqI_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x_H),V_y_H)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x_H),V_y_H)) ) ).
cnf(cls_min__max_Osup__inf__distrib2_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_z),V_x)) ) ).
cnf(cls_min__max_Osup__inf__distrib1_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)) ) ).
cnf(cls_xt1_I11_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_a))
| V_a = V_b
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_a)) ) ).
cnf(cls_xt1_I12_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_a))
| V_a = V_b ) ).
cnf(cls_psubset__eq_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B))
| V_A = V_B
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_nat__less__le_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))
| V_m = V_n
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_m),V_n)) ) ).
cnf(cls_min__max_Ole__iff__inf_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_min__max_Ole__iff__inf_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) != V_x
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_min__max_Oinf__absorb2_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x)) ) ).
cnf(cls_max__diff__distrib__left_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_y),V_z)) ) ).
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_not__leE_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x)) ) ).
cnf(cls_linorder__antisym__conv2_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_x))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_x)) ) ).
cnf(cls_linorder__antisym__conv1_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_x))
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_x)) ) ).
cnf(cls_linorder__not__less_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x)) ) ).
cnf(cls_linorder__not__less_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_linorder__not__le_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x)) ) ).
cnf(cls_linorder__not__le_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x))
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_less__fun__def_1,axiom,
( ~ class_HOL_Oord(T_b)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,T_b)),V_g),V_f))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,T_b)),V_f),V_g)) ) ).
cnf(cls_less__le__not__le_1,axiom,
( ~ class_Orderings_Opreorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_add__inf__distrib__left_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_b),V_c)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)) ) ).
cnf(cls_add__inf__distrib__right_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)) ) ).
cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_b),V_c)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)) ) ).
cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)) ) ).
cnf(cls_min__max_Oinf__assoc_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) ) ).
cnf(cls_min__max_Oinf__left__commute_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z)) ) ).
cnf(cls_diff__le__mono2_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_l),V_n)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_l),V_m)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_m),V_n)) ) ).
cnf(cls_diff__le__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_m),V_l)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_n),V_l)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_m),V_n)) ) ).
cnf(cls_le__diff__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_m),V_k)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_n),V_k)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_k),V_n))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_k),V_m)) ) ).
cnf(cls_le__diff__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_m),V_k)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_n),V_k)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_k),V_n))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_k),V_m)) ) ).
cnf(cls_eq__diff__iff_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_m),V_k) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_n),V_k)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_k),V_n))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_k),V_m))
| V_m = V_n ) ).
cnf(cls_min__max_Oinf__sup__absorb_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = V_x ) ).
cnf(cls_Diff__eq_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B)) ).
cnf(cls_diff__eq_0,axiom,
( ~ class_Lattices_Oboolean__algebra(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_y)) ) ).
cnf(cls_setsum__right__distrib_0,axiom,
( ~ class_Ring__and__Field_Osemiring__0(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_r),c_Finite__Set_Osetsum(V_f,V_A,T_b,T_a)) = c_Finite__Set_Osetsum(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_r),V_f,T_a,T_a,T_b),V_A,T_b,T_a) ) ).
cnf(cls_lower__semilattice_Ole__infI_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,V_x),hAPP(hAPP(V_inf,V_a),V_b)))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_x),V_b))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_x),V_a))
| ~ c_Lattices_Olower__semilattice(V_less__eq,V_less,V_inf,T_a) ) ).
cnf(cls_lower__semilattice_Oinf__le2_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,hAPP(hAPP(V_inf,V_x),V_y)),V_y))
| ~ c_Lattices_Olower__semilattice(V_less__eq,V_less,V_inf,T_a) ) ).
cnf(cls_lower__semilattice_Oinf__le1_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,hAPP(hAPP(V_inf,V_x),V_y)),V_x))
| ~ c_Lattices_Olower__semilattice(V_less__eq,V_less,V_inf,T_a) ) ).
cnf(cls_lower__semilattice_Ole__inf__iff_2,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,V_x),hAPP(hAPP(V_inf,V_y),V_z)))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_x),V_z))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_x),V_y))
| ~ c_Lattices_Olower__semilattice(V_less__eq,V_less,V_inf,T_a) ) ).
cnf(cls_lower__semilattice_Oinf__greatest_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,V_x),hAPP(hAPP(V_inf,V_y),V_z)))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_x),V_z))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_x),V_y))
| ~ c_Lattices_Olower__semilattice(V_less__eq,V_less,V_inf,T_a) ) ).
cnf(cls_Int__absorb2_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_A
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_Int__absorb1_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_B
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_A)) ) ).
cnf(cls_le__iff__inf_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) = V_x
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_le__iff__inf_1,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) != V_x
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_inf__absorb2_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) = V_y
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x)) ) ).
cnf(cls_min__max_Oless__supI1_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_a)) ) ).
cnf(cls_min__max_Oless__supI2_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_b)) ) ).
cnf(cls_less__max__iff__disj_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_z),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_z),V_x)) ) ).
cnf(cls_less__max__iff__disj_2,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_z),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_z),V_y)) ) ).
cnf(cls_max__less__iff__conj_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z)) ) ).
cnf(cls_max__less__iff__conj_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_z))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z)) ) ).
cnf(cls_Int__commute_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_A) ).
cnf(cls_inf__commute_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_x) ) ).
cnf(cls_inf__sup__aci_I1_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_x) ) ).
cnf(cls_min__max_Oinf__commute_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x) ) ).
cnf(cls_combine__common__factor_0,axiom,
( ~ class_Ring__and__Field_Osemiring(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_e)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_e)),V_c)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_e)),V_c) ) ).
cnf(cls_diff__le__self_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_m),V_n)),V_m)) ).
cnf(cls_Un__Int__crazy_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_C),V_A)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_C),V_A)) ).
cnf(cls_min__max_Oless__infI1_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_x)) ) ).
cnf(cls_min__max_Oless__infI2_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_x)) ) ).
cnf(cls_min__less__iff__conj_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_z),V_x))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_z),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y))) ) ).
cnf(cls_min__less__iff__conj_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_z),V_y))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_z),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y))) ) ).
cnf(cls_min__less__iff__disj_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_z)) ) ).
cnf(cls_min__less__iff__disj_2,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_z)) ) ).
cnf(cls_Nat_Odiff__diff__eq_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_m),V_k)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_n),V_k)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_m),V_n)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_k),V_n))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_k),V_m)) ) ).
cnf(cls_diff__commute_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_i),V_j)),V_k) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_i),V_k)),V_j) ).
cnf(cls_Int__atLeastAtMost_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a)),c_SetInterval_Oord__class_OatLeastAtMost(V_c,V_d,T_a)) = c_SetInterval_Oord__class_OatLeastAtMost(hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_d),T_a) ) ).
cnf(cls_diff__less__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_a),V_c)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_b),V_c)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_c),V_a))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_a),V_b)) ) ).
cnf(cls_vimage__Compl_0,axiom,
c_Set_Ovimage(V_f,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_b,tc_bool)),V_A),T_a,T_b) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),c_Set_Ovimage(V_f,V_A,T_a,T_b)) ).
cnf(cls_Suc__lessI_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(V_m)),V_n))
| c_Suc(V_m) = V_n
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n)) ) ).
cnf(cls_not__less__eq__eq_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(V_n)),V_m)) ) ).
cnf(cls_not__less__eq__eq_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(V_n)),V_m))
| hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_m),V_n)) ) ).
cnf(cls_class__ringb_Oadd__cancel_0,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z)
| V_y = V_z ) ).
cnf(cls_add__imp__eq_0,axiom,
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)
| V_b = V_c ) ).
cnf(cls_add__left__cancel_0,axiom,
( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)
| V_b = V_c ) ).
cnf(cls_add__right__cancel_0,axiom,
( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_a) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a)
| V_b = V_c ) ).
cnf(cls_min__add__distrib__left_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z)) ) ).
cnf(cls_dual__semilattice_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_Lattices_Olower__semilattice(c_COMBC(c_lessequals(T_a),T_a,T_a,tc_bool),c_COMBC(c_HOL_Oord__class_Oless(T_a),T_a,T_a,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(T_a),T_a) ) ).
cnf(cls_Int__subset__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),V_B))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B))) ) ).
cnf(cls_Int__subset__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),V_A))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B))) ) ).
cnf(cls_le__infE_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b))) ) ).
cnf(cls_le__infE_1,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b))) ) ).
cnf(cls_le__infI1_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b)),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_x)) ) ).
cnf(cls_le__infI2_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b)),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_x)) ) ).
cnf(cls_le__inf__iff_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z))) ) ).
cnf(cls_le__inf__iff_1,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z))) ) ).
cnf(cls_Suc__diff__diff_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_Suc(V_m)),V_n)),c_Suc(V_k)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_m),V_n)),V_k) ).
cnf(cls_class__ring_Osub__add_0,axiom,
( ~ class_Int_Onumber__ring(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_y)) ) ).
cnf(cls_diff__def_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_y)) ) ).
cnf(cls_diff__minus_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)) ) ).
cnf(cls_ab__diff__minus_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)) ) ).
cnf(cls_ivl__disj__int_I14_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(V_l,V_m,T_a)),c_SetInterval_Oord__class_OgreaterThanAtMost(V_m,V_u,T_a)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_fold__inf__le__inf_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(T_a),T_a,T_a),V_b),V_A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b)))
| ~ hBOOL(c_in(V_a,V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d)) ) ).
cnf(cls_inf__eq__neg__sup_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b) = hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b))) ) ).
cnf(cls_Compl__Int_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B)) ).
cnf(cls_compl__inf_0,axiom,
( ~ class_Lattices_Oboolean__algebra(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_y)) ) ).
cnf(cls_neg__inf__eq__sup_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)) ) ).
cnf(cls_min__max_Osup__commute_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x) ) ).
cnf(cls_atLeastLessThan__empty__iff2_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_SetInterval_Oord__class_OatLeastLessThan(V_a,V_b,T_a)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)) ) ).
cnf(cls_atLeastLessThan__empty__iff2_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(V_a,V_b,T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)) ) ).
cnf(cls_add__cancel__end_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z)) != V_y
| V_x = hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_z) ) ).
cnf(cls_le__Suc__eq_2,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(V_n)),c_Suc(V_n))) ).
cnf(cls_atLeastatMost__psubset__iff_2,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_d))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_c),V_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a)),c_SetInterval_Oord__class_OatLeastAtMost(V_c,V_d,T_a))) ) ).
cnf(cls_min__max_Odistrib__inf__le_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)))) ) ).
cnf(cls_Compl__Un_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B)) ).
cnf(cls_le__eq__less__or__eq_0,axiom,
( V_m = V_n
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_m),V_n)) ) ).
cnf(cls_le__neq__implies__less_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))
| V_m = V_n
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_m),V_n)) ) ).
cnf(cls_order__le__less_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| V_x = V_y
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_order__less__le_2,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_subset__iff__psubset__eq_0,axiom,
( V_A = V_B
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_order__le__neq__trans_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b))
| V_a = V_b
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b)) ) ).
cnf(cls_order__neq__le__trans_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b))
| V_a = V_b ) ).
cnf(cls_linorder__antisym__conv1_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_linorder__antisym__conv2_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| V_x = V_y
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_Int__greaterThanAtMost_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(V_a,V_b,T_a)),c_SetInterval_Oord__class_OgreaterThanAtMost(V_c,V_d,T_a)) = c_SetInterval_Oord__class_OgreaterThanAtMost(hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_d),T_a) ) ).
cnf(cls_Suc__le__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_n),V_m))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(V_n)),c_Suc(V_m))) ) ).
cnf(cls_Suc__le__mono_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(V_n)),c_Suc(V_m)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_n),V_m)) ) ).
cnf(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,axiom,
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c)) ) ).
cnf(cls_class__semiring_Osemiring__rules_I16_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) ).
cnf(cls_class__semiring_Osemiring__rules_I17_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_ly),V_rx)) ) ).
cnf(cls_class__semiring_Osemiring__rules_I18_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry) ) ).
cnf(cls_class__semiring_Osemiring__rules_I19_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) ).
cnf(cls_class__semiring_Omul__a_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_z)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_y)),V_z) ) ).
cnf(cls_class__semiring_Osemiring__rules_I8_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c)) ) ).
cnf(cls_comm__semiring__class_Odistrib_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c)) ) ).
cnf(cls_class__semiring_Omul__d_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_z)) ) ).
cnf(cls_minus__add__distrib_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)) ) ).
cnf(cls_minus__add_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)) ) ).
cnf(cls_xt1_I9_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_a)) ) ).
cnf(cls_not__less__iff__gr__or__eq_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x)) ) ).
cnf(cls_nat__le__linear_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_n),V_m))
| hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_m),V_n)) ) ).
cnf(cls_order__less__asym_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)) ) ).
cnf(cls_order__less__asym_H_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_a))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)) ) ).
cnf(cls_comm__monoid__add_Ofold__image__insert_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_b)
| hAPP(hAPP(c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(T_b),V_g,T_b,T_a),V_z),c_Set_Oinsert(V_a,V_A,T_a)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_b),hAPP(V_g,V_a)),hAPP(hAPP(c_Finite__Set_Ofold__image(c_HOL_Oplus__class_Oplus(T_b),V_g,T_b,T_a),V_z),V_A))
| hBOOL(c_in(V_a,V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_setsum__insert_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_b)
| c_Finite__Set_Osetsum(V_f,c_Set_Oinsert(V_a,V_F,T_a),T_a,T_b) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_b),hAPP(V_f,V_a)),c_Finite__Set_Osetsum(V_f,V_F,T_a,T_b))
| hBOOL(c_in(V_a,V_F,T_a))
| ~ c_Finite__Set_Ofinite(V_F,T_a) ) ).
cnf(cls_fold__image__insert_0,axiom,
( ~ class_OrderedGroup_Oab__semigroup__mult(T_b)
| hAPP(hAPP(c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(T_b),V_g,T_b,T_a),V_z),c_Set_Oinsert(V_a,V_A,T_a)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_b),hAPP(V_g,V_a)),hAPP(hAPP(c_Finite__Set_Ofold__image(c_HOL_Otimes__class_Otimes(T_b),V_g,T_b,T_a),V_z),V_A))
| hBOOL(c_in(V_a,V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_compl__unique_0,axiom,
( ~ class_Lattices_Oboolean__algebra(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) != c_Orderings_Otop__class_Otop(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y) != c_Orderings_Obot__class_Obot(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ).
cnf(cls_card__psubset_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(V_A,T_a)),c_Finite__Set_Ocard(V_B,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ c_Finite__Set_Ofinite(V_B,T_a) ) ).
cnf(cls_setsum__diff__nat_0,axiom,
( c_Finite__Set_Osetsum(V_f,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,tc_nat) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_Finite__Set_Osetsum(V_f,V_A,T_a,tc_nat)),c_Finite__Set_Osetsum(V_f,V_B,T_a,tc_nat))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_A))
| ~ c_Finite__Set_Ofinite(V_B,T_a) ) ).
cnf(cls_card__Diff__subset__Int_0,axiom,
( c_Finite__Set_Ocard(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),T_a) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_Finite__Set_Ocard(V_A,T_a)),c_Finite__Set_Ocard(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),T_a))
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),T_a) ) ).
cnf(cls_ab__semigroup__idem__mult_Ofold1__eq__fold__idem_0,axiom,
( hAPP(c_Finite__Set_Ofold1(V_times,T_a),c_Set_Oinsert(V_a,V_A,T_a)) = hAPP(hAPP(c_Finite__Set_Ofold(V_times,T_a,T_a),V_a),V_A)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(V_times,T_a) ) ).
cnf(cls_fold1__eq__fold__idem_0,axiom,
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(T_a),T_a),c_Set_Oinsert(V_a,V_A,T_a)) = hAPP(hAPP(c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(T_a),T_a,T_a),V_a),V_A)
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_Inf__fold__inf_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| c_Complete__Lattice_OInf__class_OInf(V_A,T_a) = hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(T_a),T_a,T_a),c_Orderings_Otop__class_Otop(T_a)),V_A)
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_disjoint__iff__not__equal_0,axiom,
( ~ hBOOL(c_in(V_x,V_B,T_a))
| ~ hBOOL(c_in(V_x,V_A,T_a))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_greaterThanAtMost__empty_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_SetInterval_Oord__class_OgreaterThanAtMost(V_k,V_l,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_l),V_k)) ) ).
cnf(cls_atLeastLessThan__empty_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_SetInterval_Oord__class_OatLeastLessThan(V_a,V_b,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_a)) ) ).
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(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_Int__insert__left_1,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,V_B,T_a)),V_C) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)
| hBOOL(c_in(V_a,V_C,T_a)) ) ).
cnf(cls_Int__insert__right_1,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_a,V_B,T_a)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)
| hBOOL(c_in(V_a,V_A,T_a)) ) ).
cnf(cls_psubset__insert__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ hBOOL(c_in(V_x,V_B,T_a))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,V_B,T_a))) ) ).
cnf(cls_psubset__insert__iff_6,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,V_B,T_a)))
| ~ hBOOL(c_in(V_x,V_B,T_a))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_Int__insert__left_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,V_B,T_a)),V_C) = c_Set_Oinsert(V_a,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C),T_a)
| ~ hBOOL(c_in(V_a,V_C,T_a)) ) ).
cnf(cls_Int__insert__right_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_a,V_B,T_a)) = c_Set_Oinsert(V_a,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),T_a)
| ~ hBOOL(c_in(V_a,V_A,T_a)) ) ).
cnf(cls_distrib__inf__le_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_z))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z)))) ) ).
cnf(cls_distrib__sup__le_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z))),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_z)))) ) ).
cnf(cls_atLeastLessThan__subset__iff_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_d))
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(V_a,V_b,T_a)),c_SetInterval_Oord__class_OatLeastLessThan(V_c,V_d,T_a))) ) ).
cnf(cls_atLeastLessThan__subset__iff_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_c),V_a))
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(V_a,V_b,T_a)),c_SetInterval_Oord__class_OatLeastLessThan(V_c,V_d,T_a))) ) ).
cnf(cls_fun__upd__image_1,axiom,
( c_Set_Oimage(c_Fun_Ofun__upd(V_f,V_x,V_y,T_b,T_a),V_A,T_b,T_a) = c_Set_Oimage(V_f,V_A,T_b,T_a)
| hBOOL(c_in(V_x,V_A,T_b)) ) ).
cnf(cls_atLeastatMost__psubset__iff_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_d))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a)),c_SetInterval_Oord__class_OatLeastAtMost(V_c,V_d,T_a))) ) ).
cnf(cls_atLeastatMost__psubset__iff_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_c),V_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a)),c_SetInterval_Oord__class_OatLeastAtMost(V_c,V_d,T_a))) ) ).
cnf(cls_atLeastatMost__psubset__iff_3,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_c),V_d))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a)),c_SetInterval_Oord__class_OatLeastAtMost(V_c,V_d,T_a))) ) ).
cnf(cls_atLeastatMost__psubset__iff_4,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a)),c_SetInterval_Oord__class_OatLeastAtMost(V_c,V_d,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_c),V_d))
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b)) ) ).
cnf(cls_ivl__disj__un_I20_J_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(V_l,V_m,T_a)),c_SetInterval_Oord__class_OgreaterThanAtMost(V_m,V_u,T_a)) = c_SetInterval_Oord__class_OgreaterThanAtMost(V_l,V_u,T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_m),V_u))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_l),V_m)) ) ).
cnf(cls_ivl__disj__un_I17_J_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_m,T_a)),c_SetInterval_Oord__class_OatLeastLessThan(V_m,V_u,T_a)) = c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_u,T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_m),V_u))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_l),V_m)) ) ).
cnf(cls_subset__Compl__self__eq_1,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))) ).
cnf(cls_subset__Compl__self__eq_0,axiom,
( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A))) ) ).
cnf(cls_comm__monoid__add_Ofold__graph__permute__diff_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(T_a),V_a,c_Set_Oinsert(V_b,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_x,T_a,T_a)
| hBOOL(c_in(V_b,V_A,T_a))
| ~ hBOOL(c_in(V_a,V_A,T_a))
| ~ c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(T_a),V_b,V_A,V_x,T_a,T_a) ) ).
cnf(cls_setsum__diff1__nat_0,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) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_Finite__Set_Osetsum(V_f,V_A,T_a,tc_nat)),hAPP(V_f,V_a))
| ~ hBOOL(c_in(V_a,V_A,T_a)) ) ).
cnf(cls_fold__graph__permute__diff_0,axiom,
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(T_a),V_a,c_Set_Oinsert(V_b,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_x,T_a,T_a)
| hBOOL(c_in(V_b,V_A,T_a))
| ~ hBOOL(c_in(V_a,V_A,T_a))
| ~ c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(T_a),V_b,V_A,V_x,T_a,T_a) ) ).
cnf(cls_the__inv__into__f__f_0,axiom,
( hAPP(c_Fun_Othe__inv__into(V_A,V_f,T_a,T_b),hAPP(V_f,V_x)) = V_x
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
cnf(cls_the__inv__into__f__eq_0,axiom,
( ~ c_Fun_Oinj__on(V_f,V_A,T_aa,T_a)
| hAPP(c_Fun_Othe__inv__into(V_A,V_f,T_aa,T_a),hAPP(V_f,V_x)) = V_x
| ~ hBOOL(c_in(V_x,V_A,T_aa)) ) ).
cnf(cls_ivl__diff_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(V_i,V_m,T_a)),c_SetInterval_Oord__class_OatLeastLessThan(V_i,V_n,T_a)) = c_SetInterval_Oord__class_OatLeastLessThan(V_n,V_m,T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_i),V_n)) ) ).
cnf(cls_atLeastatMost__empty_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_a)) ) ).
cnf(cls_compl__top__eq_0,axiom,
( ~ class_Lattices_Oboolean__algebra(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
cnf(cls_compl__bot__eq_0,axiom,
( ~ class_Lattices_Oboolean__algebra(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
cnf(cls_strict__below__fold1__iff_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_xa))
| ~ hBOOL(c_in(V_xa,V_A,T_a))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(T_a),T_a),V_A)))
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_fold1__strict__below__iff_2,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(T_a),T_a),V_A)),V_x))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_xa),V_x))
| ~ hBOOL(c_in(V_xa,V_A,T_a))
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_finite__compl_0,axiom,
( c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a)
| ~ c_Finite__Set_Ofinite(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A),T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_finite__compl_1,axiom,
( c_Finite__Set_Ofinite(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A),T_a)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_Compl__UNIV__eq_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_Compl__empty__eq_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) ).
cnf(cls_fold1__eq__fold_0,axiom,
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(T_a),T_a),c_Set_Oinsert(V_a,V_A,T_a)) = hAPP(hAPP(c_Finite__Set_Ofold(c_HOL_Otimes__class_Otimes(T_a),T_a,T_a),V_a),V_A)
| hBOOL(c_in(V_a,V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_comm__monoid__add_Ofold1__eq__fold_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(T_a),T_a),c_Set_Oinsert(V_a,V_A,T_a)) = hAPP(hAPP(c_Finite__Set_Ofold(c_HOL_Oplus__class_Oplus(T_a),T_a,T_a),V_a),V_A)
| hBOOL(c_in(V_a,V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_image__Int__subset_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Set_Oimage(V_f,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_b,tc_bool)),V_A),V_B),T_b,T_a)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(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)))) ).
cnf(cls_Un__Int__assoc__eq_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C) != hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),V_A)) ) ).
cnf(cls_Un__Int__assoc__eq_1,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),V_A)) ) ).
cnf(cls_sup__compl__top_0,axiom,
( ~ class_Lattices_Oboolean__algebra(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Otop__class_Otop(T_a) ) ).
cnf(cls_compl__sup__top_0,axiom,
( ~ class_Lattices_Oboolean__algebra(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Otop__class_Otop(T_a) ) ).
cnf(cls_Diff__disjoint_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_B),V_A)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_Diff__triv_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B) = V_A ) ).
cnf(cls_comm__monoid__add_Ofold1__Un_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| V_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(T_a),T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(T_a),T_a),V_A)),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(T_a),T_a),V_B)) ) ).
cnf(cls_fold1__Un_0,axiom,
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| V_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(T_a),T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(T_a),T_a),V_A)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(T_a),T_a),V_B)) ) ).
cnf(cls_Compl__partition_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) ).
cnf(cls_Compl__partition2_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A)),V_A) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) ).
cnf(cls_inj__on__the__inv__into_0,axiom,
( c_Fun_Oinj__on(c_Fun_Othe__inv__into(V_A,V_f,T_a,T_b),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b,T_a)
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
cnf(cls_the__inv__into__onto_0,axiom,
( c_Set_Oimage(c_Fun_Othe__inv__into(V_A,V_f,T_a,T_b),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b,T_a) = V_A
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
cnf(cls_Compl__Diff__eq_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A)),V_B) ).
cnf(cls_Un__Diff__Int_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)) = V_A ).
cnf(cls_Diff__Un_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_C)) ).
cnf(cls_Diff__Int_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_C)) ).
cnf(cls_the__inv__f__f_0,axiom,
( hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_f,T_a,T_b),hAPP(V_f,V_x)) = V_x
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_Compl__eq__Diff__UNIV_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))),V_A) ).
cnf(cls_Inf__insert_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(V_a,V_A,T_a),T_a) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),c_Complete__Lattice_OInf__class_OInf(V_A,T_a)) ) ).
cnf(cls_Max__def__raw_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_Finite__Set_Olinorder__class_OMax(T_a) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(T_a),T_a) ) ).
cnf(cls_linorder__class_OMin__def__raw_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_Finite__Set_Olinorder__class_OMin(T_a) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(T_a),T_a) ) ).
cnf(cls_compl__sup_0,axiom,
( ~ class_Lattices_Oboolean__algebra(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_y)) ) ).
cnf(cls_neg__sup__eq__inf_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)) ) ).
cnf(cls_min__max_Osup__inf__absorb_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = V_x ) ).
cnf(cls_mult__less__cancel__left__disj_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_a))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b))) ) ).
cnf(cls_mult__less__cancel__right__disj_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_a))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c))) ) ).
cnf(cls_diff__diff__cancel_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_n),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_n),V_i)) = V_i
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_i),V_n)) ) ).
cnf(cls_le__SucE_0,axiom,
( V_m = c_Suc(V_n)
| hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),V_m),c_Suc(V_n))) ) ).
cnf(cls_not__less__less__Suc__eq_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),V_x))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),c_Suc(V_x))) ) ).
cnf(cls_not__less__eq_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),c_Suc(V_m))) ) ).
cnf(cls_not__less__eq_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),c_Suc(V_m)))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n)) ) ).
cnf(cls_max__add__distrib__left_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z)) ) ).
cnf(cls_Diff__Compl_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) ).
cnf(cls_square__eq__iff_1,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_b) ) ).
cnf(cls_min__max_Osup__assoc_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) ) ).
cnf(cls_minus__mult__minus_0,axiom,
( ~ class_Ring__and__Field_Oring(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b) ) ).
cnf(cls_min__max_Osup__left__commute_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)) ) ).
cnf(cls_diff__minus__eq__add_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b) ) ).
cnf(cls_inf1E_1,axiom,
( hBOOL(hAPP(V_B,V_x))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),V_x)) ) ).
cnf(cls_inf1E_0,axiom,
( hBOOL(hAPP(V_A,V_x))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),V_x)) ) ).
cnf(cls_fun__upd__idem__iff_0,axiom,
( c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_b) != V_f
| hAPP(V_f,V_x) = V_y ) ).
cnf(cls_class__semiring_Osemiring__rules_I1_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_m)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_m) ) ).
cnf(cls_setsum__negf_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_Finite__Set_Osetsum(c_COMBB(c_HOL_Ouminus__class_Ouminus(T_a),V_f,T_a,T_a,T_b),V_A,T_b,T_a) = hAPP(c_HOL_Ouminus__class_Ouminus(T_a),c_Finite__Set_Osetsum(V_f,V_A,T_b,T_a)) ) ).
cnf(cls_disjoint__eq__subset__Compl_1,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B))) ) ).
cnf(cls_disjoint__eq__subset__Compl_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B))) ) ).
cnf(cls_min__max_Osup__left__idem_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) ) ).
cnf(cls_add__diff__cancel_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = V_a ) ).
cnf(cls_double__complement_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A)) = V_A ).
cnf(cls_minus__minus_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ).
cnf(cls_double__compl_0,axiom,
( ~ class_Lattices_Oboolean__algebra(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ).
cnf(cls_equation__minus__iff_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| V_b = hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)) ) ).
cnf(cls_equation__minus__iff_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| V_a = hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)) ) ).
cnf(cls_minus__equation__iff_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)) = V_b ) ).
cnf(cls_less__supI1_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_a)) ) ).
cnf(cls_less__supI2_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_b)) ) ).
cnf(cls_minus__diff__eq_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_b),V_a) ) ).
cnf(cls_add__le__less__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_c),V_d))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b)) ) ).
cnf(cls_add__less__le__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_c),V_d))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)) ) ).
cnf(cls_vimage__Int_0,axiom,
c_Set_Ovimage(V_f,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_b,tc_bool)),V_A),V_B),T_a,T_b) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(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_less__Suc__eq__0__disj_3,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(V_x)),c_Suc(V_n)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),V_n)) ) ).
cnf(cls_Suc__less__eq_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(V_m)),c_Suc(V_n))) ) ).
cnf(cls_Suc__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(V_m)),c_Suc(V_n)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n)) ) ).
cnf(cls_le__minus__iff_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b))) ) ).
cnf(cls_le__minus__iff_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a))) ) ).
cnf(cls_minus__le__iff_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)),V_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ).
cnf(cls_minus__le__iff_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),V_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)),V_a)) ) ).
cnf(cls_less__minus__iff_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b))) ) ).
cnf(cls_less__minus__iff_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a))) ) ).
cnf(cls_minus__less__iff_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)),V_a))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ).
cnf(cls_minus__less__iff_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),V_b))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)),V_a)) ) ).
cnf(cls_Int__iff_2,axiom,
( hBOOL(c_in(V_c,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),T_a))
| ~ hBOOL(c_in(V_c,V_B,T_a))
| ~ hBOOL(c_in(V_c,V_A,T_a)) ) ).
cnf(cls_IntI_0,axiom,
( hBOOL(c_in(V_c,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),T_a))
| ~ hBOOL(c_in(V_c,V_B,T_a))
| ~ hBOOL(c_in(V_c,V_A,T_a)) ) ).
cnf(cls_ComplI_0,axiom,
( hBOOL(c_in(V_c,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A),T_a))
| hBOOL(c_in(V_c,V_A,T_a)) ) ).
cnf(cls_ComplD_0,axiom,
( ~ hBOOL(c_in(V_c,V_A,T_a))
| ~ hBOOL(c_in(V_c,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A),T_a)) ) ).
cnf(cls_psubsetD_0,axiom,
( hBOOL(c_in(V_c,V_B,T_a))
| ~ hBOOL(c_in(V_c,V_A,T_a))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_IntE_1,axiom,
( hBOOL(c_in(V_c,V_B,T_a))
| ~ hBOOL(c_in(V_c,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),T_a)) ) ).
cnf(cls_IntE_0,axiom,
( hBOOL(c_in(V_c,V_A,T_a))
| ~ hBOOL(c_in(V_c,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),T_a)) ) ).
cnf(cls_lower__semilattice_Ofold__inf__le__inf_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,hAPP(hAPP(c_Finite__Set_Ofold(V_inf,T_a,T_a),V_b),V_A)),hAPP(hAPP(V_inf,V_a),V_b)))
| ~ hBOOL(c_in(V_a,V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Lattices_Olower__semilattice(V_less__eq,V_less,V_inf,T_a) ) ).
cnf(cls_fold__graph__insert__swap_0,axiom,
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(T_a),V_z,c_Set_Oinsert(V_b,V_A,T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_z),V_y),T_a,T_a)
| hBOOL(c_in(V_b,V_A,T_a))
| ~ c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(T_a),V_b,V_A,V_y,T_a,T_a) ) ).
cnf(cls_comm__monoid__add_Ofold__graph__insert__swap_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(T_a),V_z,c_Set_Oinsert(V_b,V_A,T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_z),V_y),T_a,T_a)
| hBOOL(c_in(V_b,V_A,T_a))
| ~ c_Finite__Set_Ofold__graph(c_HOL_Oplus__class_Oplus(T_a),V_b,V_A,V_y,T_a,T_a) ) ).
cnf(cls_fold__graph__imp__finite_0,axiom,
( c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Finite__Set_Ofold__graph(V_f,V_z,V_A,V_x,T_a,T_b) ) ).
cnf(cls_finite__Int_1,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_F),V_G),T_a)
| ~ c_Finite__Set_Ofinite(V_G,T_a) ) ).
cnf(cls_finite__Int_0,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_F),V_G),T_a)
| ~ c_Finite__Set_Ofinite(V_F,T_a) ) ).
cnf(cls_inf__bot__left_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = c_Orderings_Obot__class_Obot(T_a) ) ).
cnf(cls_inf__bot__right_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
cnf(cls_fold__image__empty_0,axiom,
hAPP(hAPP(c_Finite__Set_Ofold__image(V_f,V_g,T_a,T_b),V_z),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))) = V_z ).
cnf(cls_fold__empty_0,axiom,
hAPP(hAPP(c_Finite__Set_Ofold(V_f,T_b,T_a),V_z),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))) = V_z ).
cnf(cls_not__psubset__empty_0,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) ).
cnf(cls_empty__fold__graphE_0,axiom,
( V_x = V_z
| ~ c_Finite__Set_Ofold__graph(V_f,V_z,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x,T_a,T_b) ) ).
cnf(cls_Int__empty__right_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_Int__empty__left_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),V_B) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_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_setsum__addf_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(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_Oplus__class_Oplus(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_fold__inf__insert_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(T_a),T_a,T_a),V_b),c_Set_Oinsert(V_a,V_A,T_a)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(T_a),T_a,T_a),V_b),V_A))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_lower__semilattice_Ofold__inf__insert_0,axiom,
( hAPP(hAPP(c_Finite__Set_Ofold(V_inf,T_a,T_a),V_b),c_Set_Oinsert(V_a,V_A,T_a)) = hAPP(hAPP(V_inf,V_a),hAPP(hAPP(c_Finite__Set_Ofold(V_inf,T_a,T_a),V_b),V_A))
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Lattices_Olower__semilattice(V_less__eq,V_less,V_inf,T_a) ) ).
cnf(cls_insert__inter__insert_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,V_A,T_a)),c_Set_Oinsert(V_a,V_B,T_a)) = c_Set_Oinsert(V_a,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),T_a) ).
cnf(cls_setsum__diff1_H_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_b)
| c_Finite__Set_Osetsum(V_f,V_A,T_a,T_b) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_b),hAPP(V_f,V_a)),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,T_b))
| ~ hBOOL(c_in(V_a,V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,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_psubset__insert__iff_7,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,V_B,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| hBOOL(c_in(V_x,V_A,T_a))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_psubset__insert__iff_3,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,V_B,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| hBOOL(c_in(V_x,V_A,T_a))
| hBOOL(c_in(V_x,V_B,T_a)) ) ).
cnf(cls_psubset__insert__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| hBOOL(c_in(V_x,V_A,T_a))
| hBOOL(c_in(V_x,V_B,T_a))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,V_B,T_a))) ) ).
cnf(cls_fold__sup__insert_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(T_a),T_a,T_a),V_b),c_Set_Oinsert(V_a,V_A,T_a)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(T_a),T_a,T_a),V_b),V_A))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_ivl__disj__un_I21_J_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_m,T_a)),c_SetInterval_Oord__class_OatLeastAtMost(V_m,V_u,T_a)) = c_SetInterval_Oord__class_OatLeastAtMost(V_l,V_u,T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_m),V_u))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_l),V_m)) ) ).
cnf(cls_ivl__disj__un_I22_J_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(V_l,V_m,T_a)),c_SetInterval_Oord__class_OgreaterThanAtMost(V_m,V_u,T_a)) = c_SetInterval_Oord__class_OatLeastAtMost(V_l,V_u,T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_m),V_u))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_l),V_m)) ) ).
cnf(cls_inj__on__fun__updI_0,axiom,
( c_Fun_Oinj__on(c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_b),V_A,T_a,T_b)
| hBOOL(c_in(V_y,c_Set_Oimage(V_f,V_A,T_a,T_b),T_b))
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
cnf(cls_f__the__inv__into__f_0,axiom,
( hAPP(V_f,hAPP(c_Fun_Othe__inv__into(V_A,V_f,T_a,T_b),V_y)) = V_y
| ~ hBOOL(c_in(V_y,c_Set_Oimage(V_f,V_A,T_a,T_b),T_b))
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
cnf(cls_card__insert__le_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Finite__Set_Ocard(V_A,T_a)),c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a)))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_card__seteq_0,axiom,
( V_A = V_B
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Finite__Set_Ocard(V_B,T_a)),c_Finite__Set_Ocard(V_A,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ c_Finite__Set_Ofinite(V_B,T_a) ) ).
cnf(cls_card__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Finite__Set_Ocard(V_A,T_a)),c_Finite__Set_Ocard(V_B,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ c_Finite__Set_Ofinite(V_B,T_a) ) ).
cnf(cls_lower__semilattice_Ofold1__belowI_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,hAPP(c_Finite__Set_Ofold1(V_inf,T_a),V_A)),V_a))
| ~ hBOOL(c_in(V_a,V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Lattices_Olower__semilattice(V_less__eq,V_less,V_inf,T_a) ) ).
cnf(cls_card__image__le_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),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_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_inj__on__image__Int_0,axiom,
( c_Set_Oimage(V_f,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(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))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_C))
| ~ c_Fun_Oinj__on(V_f,V_C,T_a,T_b) ) ).
cnf(cls_image__Int_0,axiom,
( c_Set_Oimage(V_f,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(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_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_Inf__binary_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a),T_a) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b) ) ).
cnf(cls_image__vimage__eq_0,axiom,
c_Set_Oimage(V_f,c_Set_Ovimage(V_f,V_A,T_b,T_a),T_b,T_a) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_Set_Oimage(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_a)) ).
cnf(cls_Min__eqI_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(c_Finite__Set_Olinorder__class_OMin(T_a),V_A) = V_x
| ~ hBOOL(c_in(V_x,V_A,T_a))
| hBOOL(c_in(c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(V_A,V_x,T_a),V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_Max__eqI_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(c_Finite__Set_Olinorder__class_OMax(T_a),V_A) = V_x
| ~ hBOOL(c_in(V_x,V_A,T_a))
| hBOOL(c_in(c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(V_A,V_x,T_a),V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_ab__semigroup__mult_Ofold__graph__insert__swap_0,axiom,
( c_Finite__Set_Ofold__graph(V_times,V_z,c_Set_Oinsert(V_b,V_A,T_a),hAPP(hAPP(V_times,V_z),V_y),T_a,T_a)
| hBOOL(c_in(V_b,V_A,T_a))
| ~ c_Finite__Set_Ofold__graph(V_times,V_b,V_A,V_y,T_a,T_a)
| ~ c_OrderedGroup_Oab__semigroup__mult(V_times,T_a) ) ).
cnf(cls_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_sup__le__fold__sup_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b)),hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(T_a),T_a,T_a),V_b),V_A)))
| ~ hBOOL(c_in(V_a,V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_inj__on__Un_0,axiom,
( c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| ~ c_Fun_Oinj__on(V_f,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b) ) ).
cnf(cls_inj__on__Un_1,axiom,
( c_Fun_Oinj__on(V_f,V_B,T_a,T_b)
| ~ c_Fun_Oinj__on(V_f,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b) ) ).
cnf(cls_vimage__Un_0,axiom,
c_Set_Ovimage(V_f,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_b,tc_bool)),V_A),V_B),T_a,T_b) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(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_inf__sup__aci_I8_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) ) ).
cnf(cls_sup__left__idem_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) ) ).
cnf(cls_Un__left__absorb_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B) ).
cnf(cls_inf__sup__aci_I5_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_x) ) ).
cnf(cls_sup__commute_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_x) ) ).
cnf(cls_Un__commute_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_A) ).
cnf(cls_Un__Diff_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_C)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_B),V_C)) ).
cnf(cls_fun__diff__def_0,axiom,
( ~ class_HOL_Ominus(T_b)
| hAPP(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(t_a,T_b)),V_A),V_B),v_x) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_b),hAPP(V_A,v_x)),hAPP(V_B,v_x)) ) ).
cnf(cls_Un__Diff__cancel_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_B),V_A)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B) ).
cnf(cls_Un__Diff__cancel2_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_B),V_A)),V_A) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_A) ).
cnf(cls_card__eq__UNIV__imp__eq__UNIV_0,axiom,
( c_Finite__Set_Ocard(V_A,T_a) != c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a)
| ~ c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a)
| V_A = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_vimage__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_b,tc_bool)),c_Set_Ovimage(V_f,V_A,T_b,T_a)),c_Set_Ovimage(V_f,V_B,T_b,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_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_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_Diff__subset_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)),V_A)) ).
cnf(cls_Diff__partition_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_B),V_A)) = V_B
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_inf__sup__ord_I3_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y))) ) ).
cnf(cls_inf__sup__ord_I4_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y))) ) ).
cnf(cls_le__sup__iff_2,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_z)) ) ).
cnf(cls_sup__least_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z)),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_z),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x)) ) ).
cnf(cls_sup__ge2_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y))) ) ).
cnf(cls_sup__ge1_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y))) ) ).
cnf(cls_le__supI_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b)),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_x)) ) ).
cnf(cls_Un__least_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_C)) ) ).
cnf(cls_Un__upper1_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B))) ).
cnf(cls_card__Diff2__less_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(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_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a))),c_Set_Oinsert(V_y,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),T_a)),c_Finite__Set_Ocard(V_A,T_a)))
| ~ hBOOL(c_in(V_y,V_A,T_a))
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_card__Diff1__less_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Finite__Set_Ocard(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)),T_a)),c_Finite__Set_Ocard(V_A,T_a)))
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_card__Suc__Diff1_0,axiom,
( c_Suc(c_Finite__Set_Ocard(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),T_a)) = c_Finite__Set_Ocard(V_A,T_a)
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_setsum__diff1_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_b)
| c_Finite__Set_Osetsum(V_f,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),T_a,T_b) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_b),c_Finite__Set_Osetsum(V_f,V_A,T_a,T_b)),hAPP(V_f,V_a))
| ~ hBOOL(c_in(V_a,V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_setsum__diff1__ring_0,axiom,
( ~ class_Ring__and__Field_Oring(T_b)
| c_Finite__Set_Osetsum(V_f,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),T_a,T_b) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_b),c_Finite__Set_Osetsum(V_f,V_A,T_a,T_b)),hAPP(V_f,V_a))
| ~ hBOOL(c_in(V_a,V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_ab__semigroup__mult_Ofold1__Un_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| V_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_OrderedGroup_Oab__semigroup__mult(V_times,T_a)
| hAPP(c_Finite__Set_Ofold1(V_times,T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(V_times,hAPP(c_Finite__Set_Ofold1(V_times,T_a),V_A)),hAPP(c_Finite__Set_Ofold1(V_times,T_a),V_B)) ) ).
cnf(cls_ab__semigroup__mult_Ofold1__eq__fold_0,axiom,
( hAPP(c_Finite__Set_Ofold1(V_times,T_a),c_Set_Oinsert(V_a,V_A,T_a)) = hAPP(hAPP(c_Finite__Set_Ofold(V_times,T_a,T_a),V_a),V_A)
| hBOOL(c_in(V_a,V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_OrderedGroup_Oab__semigroup__mult(V_times,T_a) ) ).
cnf(cls_ab__semigroup__mult_Ofold__graph__permute__diff_0,axiom,
( c_Finite__Set_Ofold__graph(V_times,V_a,c_Set_Oinsert(V_b,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_x,T_a,T_a)
| hBOOL(c_in(V_b,V_A,T_a))
| ~ hBOOL(c_in(V_a,V_A,T_a))
| ~ c_Finite__Set_Ofold__graph(V_times,V_b,V_A,V_x,T_a,T_a)
| ~ c_OrderedGroup_Oab__semigroup__mult(V_times,T_a) ) ).
cnf(cls_inj__on__Un_2,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_b,tc_bool)),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)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))
| ~ c_Fun_Oinj__on(V_f,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b) ) ).
cnf(cls_inj__on__Un_3,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_b,tc_bool)),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)) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))
| ~ c_Fun_Oinj__on(V_f,V_B,T_a,T_b)
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| c_Fun_Oinj__on(V_f,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b) ) ).
cnf(cls_card__inj__on__le_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Finite__Set_Ocard(V_A,T_a)),c_Finite__Set_Ocard(V_B,T_b)))
| ~ c_Finite__Set_Ofinite(V_B,T_b)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_b,tc_bool)),c_Set_Oimage(V_f,V_A,T_a,T_b)),V_B))
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
cnf(cls_card__insert_0,axiom,
( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(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)),T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_card__Diff1__le_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Finite__Set_Ocard(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)),T_a)),c_Finite__Set_Ocard(V_A,T_a)))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_fold1__antimono_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(T_a),T_a),V_B)),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(T_a),T_a),V_A)))
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_fold1__insert_0,axiom,
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(T_a),T_a),c_Set_Oinsert(V_x,V_A,T_a)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(T_a),T_a),V_A))
| hBOOL(c_in(V_x,V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_comm__monoid__add_Ofold1__insert_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(T_a),T_a),c_Set_Oinsert(V_x,V_A,T_a)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(c_Finite__Set_Ofold1(c_HOL_Oplus__class_Oplus(T_a),T_a),V_A))
| hBOOL(c_in(V_x,V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
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(c_in(V_x,V_A,T_b)) ) ).
cnf(cls_psubset__insert__iff_5,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,V_B,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a))),V_B))
| hBOOL(c_in(V_x,V_B,T_a)) ) ).
cnf(cls_ivl__disj__un_I5_J_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_l,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),c_SetInterval_Oord__class_OgreaterThanAtMost(V_l,V_u,T_a)) = c_SetInterval_Oord__class_OatLeastAtMost(V_l,V_u,T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_l),V_u)) ) ).
cnf(cls_ivl__disj__un_I6_J_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(V_l,V_u,T_a)),c_Set_Oinsert(V_u,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) = c_SetInterval_Oord__class_OatLeastAtMost(V_l,V_u,T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_l),V_u)) ) ).
cnf(cls_fold1__below__iff_2,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(T_a),T_a),V_A)),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_xa),V_x))
| ~ hBOOL(c_in(V_xa,V_A,T_a))
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_below__fold1__iff_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_xa))
| ~ hBOOL(c_in(V_xa,V_A,T_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(T_a),T_a),V_A)))
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_setsum__diff1_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_b)
| c_Finite__Set_Osetsum(V_f,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),T_a,T_b) = c_Finite__Set_Osetsum(V_f,V_A,T_a,T_b)
| hBOOL(c_in(V_a,V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_escape_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),v_sko__Hoare__Mirabelle__Xescape__2(V_G,V_P,V_Q,V_c)),tc_fun(tc_Com_Ostate,tc_bool),t_a)),V_c),c_COMBK(hAPP(V_Q,v_sko__Hoare__Mirabelle__Xescape__1(V_G,V_P,V_Q,V_c)),tc_fun(tc_Com_Ostate,tc_bool),t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ) ).
cnf(cls_Min__Un_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(c_Finite__Set_Olinorder__class_OMin(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(c_Finite__Set_Olinorder__class_OMin(T_a),V_A)),hAPP(c_Finite__Set_Olinorder__class_OMin(T_a),V_B))
| V_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_Max__Un_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(c_Finite__Set_Olinorder__class_OMax(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(c_Finite__Set_Olinorder__class_OMax(T_a),V_A)),hAPP(c_Finite__Set_Olinorder__class_OMax(T_a),V_B))
| V_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_Max__insert_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(c_Finite__Set_Olinorder__class_OMax(T_a),c_Set_Oinsert(V_x,V_A,T_a)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(c_Finite__Set_Olinorder__class_OMax(T_a),V_A))
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_Min__insert_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(c_Finite__Set_Olinorder__class_OMin(T_a),c_Set_Oinsert(V_x,V_A,T_a)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(c_Finite__Set_Olinorder__class_OMin(T_a),V_A))
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_ab__semigroup__mult_Ofold__image__insert_0,axiom,
( hAPP(hAPP(c_Finite__Set_Ofold__image(V_times,V_g,T_a,T_b),V_z),c_Set_Oinsert(V_a,V_A,T_b)) = hAPP(hAPP(V_times,hAPP(V_g,V_a)),hAPP(hAPP(c_Finite__Set_Ofold__image(V_times,V_g,T_a,T_b),V_z),V_A))
| hBOOL(c_in(V_a,V_A,T_b))
| ~ c_Finite__Set_Ofinite(V_A,T_b)
| ~ c_OrderedGroup_Oab__semigroup__mult(V_times,T_a) ) ).
cnf(cls_Max__eqI_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(c_Finite__Set_Olinorder__class_OMax(T_a),V_A) = V_x
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1(V_A,V_x,T_a)),V_x))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_Min__eqI_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(c_Finite__Set_Olinorder__class_OMin(T_a),V_A) = V_x
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1(V_A,V_x,T_a)))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_inj__image__Compl__subset_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_b,tc_bool)),c_Set_Oimage(V_f,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A),T_a,T_b)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_b,tc_bool)),c_Set_Oimage(V_f,V_A,T_a,T_b))))
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_ab__semigroup__idem__mult_Ofold1__Un2_0,axiom,
( hAPP(c_Finite__Set_Ofold1(V_times,T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(V_times,hAPP(c_Finite__Set_Ofold1(V_times,T_a),V_A)),hAPP(c_Finite__Set_Ofold1(V_times,T_a),V_B))
| V_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(V_times,T_a) ) ).
cnf(cls_fold1__Un2_0,axiom,
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(T_a),T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(T_a),T_a),V_A)),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(T_a),T_a),V_B))
| V_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_card__Diff__subset_0,axiom,
( c_Finite__Set_Ocard(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),T_a) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_Finite__Set_Ocard(V_A,T_a)),c_Finite__Set_Ocard(V_B,T_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_A))
| ~ c_Finite__Set_Ofinite(V_B,T_a) ) ).
cnf(cls_ab__semigroup__idem__mult_Ofold1__insert__idem_0,axiom,
( hAPP(c_Finite__Set_Ofold1(V_times,T_a),c_Set_Oinsert(V_x,V_A,T_a)) = hAPP(hAPP(V_times,V_x),hAPP(c_Finite__Set_Ofold1(V_times,T_a),V_A))
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__idem__mult(V_times,T_a) ) ).
cnf(cls_fold1__insert__idem_0,axiom,
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a)
| hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(T_a),T_a),c_Set_Oinsert(V_x,V_A,T_a)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),hAPP(c_Finite__Set_Ofold1(c_HOL_Otimes__class_Otimes(T_a),T_a),V_A))
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_range__ex1__eq_2,axiom,
( ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_aa,tc_bool)),T_aa,T_a)
| hBOOL(c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_aa,tc_bool)),T_aa,T_a),T_a))
| hAPP(V_f,V_x) = hAPP(V_f,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2(hAPP(V_f,V_x),V_f,V_x,T_a,T_aa)) ) ).
cnf(cls_inj__transfer_0,axiom,
( hBOOL(hAPP(V_P,V_x))
| hBOOL(c_in(c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(V_P,V_f,T_a,T_b),c_Set_Oimage(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b),T_b))
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_range__ex1__eq_3,axiom,
( c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2(hAPP(V_f,V_x),V_f,V_x,T_a,T_aa) != V_x
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_aa,tc_bool)),T_aa,T_a)
| hBOOL(c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_aa,tc_bool)),T_aa,T_a),T_a)) ) ).
cnf(cls_range__ex1__eq_0,axiom,
( V_b = hAPP(V_f,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(V_b,V_f,T_b,T_a))
| ~ hBOOL(c_in(V_b,c_Set_Oimage(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b),T_b))
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_range__ex1__eq_1,axiom,
( ~ hBOOL(c_in(hAPP(V_f,V_y),c_Set_Oimage(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_aa,tc_bool)),T_aa,T_a),T_a))
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_aa,tc_bool)),T_aa,T_a)
| V_y = c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(hAPP(V_f,V_y),V_f,T_a,T_aa) ) ).
cnf(cls_psubset__insert__iff_9,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,V_B,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a))),V_B))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_lower__semilattice_Obelow__fold1__iff_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,V_x),V_xa))
| ~ hBOOL(c_in(V_xa,V_A,T_a))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_x),hAPP(c_Finite__Set_Ofold1(V_inf,T_a),V_A)))
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Lattices_Olower__semilattice(V_less__eq,V_less,V_inf,T_a) ) ).
cnf(cls_the__inv__into__into_0,axiom,
( hBOOL(c_in(hAPP(c_Fun_Othe__inv__into(V_A,V_f,T_a,T_b),V_x),V_B,T_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ hBOOL(c_in(V_x,c_Set_Oimage(V_f,V_A,T_a,T_b),T_b))
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
cnf(cls_setsum__diff_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_b)
| c_Finite__Set_Osetsum(V_f,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_b),c_Finite__Set_Osetsum(V_f,V_A,T_a,T_b)),c_Finite__Set_Osetsum(V_f,V_B,T_a,T_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_A))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_fold1__belowI_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(T_a),T_a),V_A)),V_a))
| ~ hBOOL(c_in(V_a,V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,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(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_psubset__insert__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a))),V_B))
| ~ hBOOL(c_in(V_x,V_A,T_a))
| hBOOL(c_in(V_x,V_B,T_a))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,V_B,T_a))) ) ).
cnf(cls_psubset__insert__iff_4,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,V_B,T_a)))
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a))),V_B))
| hBOOL(c_in(V_x,V_B,T_a)) ) ).
cnf(cls_psubset__insert__iff_8,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,V_B,T_a)))
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a))),V_B))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_setsum__diff1__nat_1,axiom,
( c_Finite__Set_Osetsum(V_f,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),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(c_in(V_a,V_A,T_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(c_in(V_x,V_A,T_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(c_in(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a))
| 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_card__insert__if_1,axiom,
( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a))
| hBOOL(c_in(V_x,V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_vimage__subsetI_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Set_Ovimage(V_f,V_B,T_a,T_b)),V_A))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_b,tc_bool)),V_B),c_Set_Oimage(V_f,V_A,T_a,T_b)))
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_Diff__subset__conv_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C))) ) ).
cnf(cls_Diff__subset__conv_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C)) ) ).
cnf(cls_le__funD_0,axiom,
( ~ class_HOL_Oord(T_b)
| hBOOL(hAPP(hAPP(c_lessequals(T_b),hAPP(V_f,V_x)),hAPP(V_g,V_x)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,T_b)),V_f),V_g)) ) ).
cnf(cls_subset__iff_0,axiom,
( hBOOL(c_in(V_t,V_B,T_a))
| ~ hBOOL(c_in(V_t,V_A,T_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_set__rev__mp_0,axiom,
( hBOOL(c_in(V_x,V_B,T_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ hBOOL(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_subsetD_0,axiom,
( hBOOL(c_in(V_c,V_B,T_a))
| ~ hBOOL(c_in(V_c,V_A,T_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_set__mp_0,axiom,
( hBOOL(c_in(V_x,V_B,T_a))
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_UnCI_1,axiom,
( hBOOL(c_in(V_c,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),T_a))
| ~ hBOOL(c_in(V_c,V_A,T_a)) ) ).
cnf(cls_UnCI_0,axiom,
( hBOOL(c_in(V_c,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),T_a))
| ~ hBOOL(c_in(V_c,V_B,T_a)) ) ).
cnf(cls_UnE_0,axiom,
( hBOOL(c_in(V_c,V_B,T_a))
| hBOOL(c_in(V_c,V_A,T_a))
| ~ hBOOL(c_in(V_c,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),T_a)) ) ).
cnf(cls_UNIV__I_0,axiom,
hBOOL(c_in(V_x,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a)) ).
cnf(cls_DiffE_1,axiom,
( ~ hBOOL(c_in(V_c,V_B,T_a))
| ~ hBOOL(c_in(V_c,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),T_a)) ) ).
cnf(cls_DiffE_0,axiom,
( hBOOL(c_in(V_c,V_A,T_a))
| ~ hBOOL(c_in(V_c,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),T_a)) ) ).
cnf(cls_inj__on__contraD_0,axiom,
( hAPP(V_f,V_x) != hAPP(V_f,V_y)
| ~ hBOOL(c_in(V_y,V_A,T_a))
| ~ hBOOL(c_in(V_x,V_A,T_a))
| V_x = V_y
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
cnf(cls_inj__on__iff_0,axiom,
( hAPP(V_f,V_x) != hAPP(V_f,V_y)
| ~ hBOOL(c_in(V_y,V_A,T_a))
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| V_x = V_y ) ).
cnf(cls_inj__on__def_0,axiom,
( hAPP(V_f,V_x) != hAPP(V_f,V_xa)
| ~ hBOOL(c_in(V_xa,V_A,T_a))
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| V_x = V_xa ) ).
cnf(cls_inj__onD_0,axiom,
( hAPP(V_f,V_x) != hAPP(V_f,V_y)
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| V_x = V_y
| ~ hBOOL(c_in(V_y,V_A,T_a))
| ~ hBOOL(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_Diff__iff_2,axiom,
( hBOOL(c_in(V_c,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),T_a))
| hBOOL(c_in(V_c,V_B,T_a))
| ~ hBOOL(c_in(V_c,V_A,T_a)) ) ).
cnf(cls_DiffI_0,axiom,
( hBOOL(c_in(V_c,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),T_a))
| hBOOL(c_in(V_c,V_B,T_a))
| ~ hBOOL(c_in(V_c,V_A,T_a)) ) ).
cnf(cls_vimage__eq_1,axiom,
( hBOOL(c_in(V_a,c_Set_Ovimage(V_f,V_B,T_a,T_b),T_a))
| ~ hBOOL(c_in(hAPP(V_f,V_a),V_B,T_b)) ) ).
cnf(cls_vimageI2_0,axiom,
( hBOOL(c_in(V_a,c_Set_Ovimage(V_f,V_A,T_b,T_a),T_b))
| ~ hBOOL(c_in(hAPP(V_f,V_a),V_A,T_a)) ) ).
cnf(cls_vimageI_0,axiom,
( hBOOL(c_in(V_a,c_Set_Ovimage(V_f,V_B,T_b,T_a),T_b))
| ~ hBOOL(c_in(hAPP(V_f,V_a),V_B,T_a)) ) ).
cnf(cls_vimageE_0,axiom,
( hBOOL(c_in(hAPP(V_f,V_a),V_B,T_b))
| ~ hBOOL(c_in(V_a,c_Set_Ovimage(V_f,V_B,T_a,T_b),T_a)) ) ).
cnf(cls_vimageD_0,axiom,
( hBOOL(c_in(hAPP(V_f,V_a),V_A,T_b))
| ~ hBOOL(c_in(V_a,c_Set_Ovimage(V_f,V_A,T_a,T_b),T_a)) ) ).
cnf(cls_Max__ge_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(c_Finite__Set_Olinorder__class_OMax(T_a),V_A)))
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_Min__le_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(c_Finite__Set_Olinorder__class_OMin(T_a),V_A)),V_x))
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
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(c_in(V_c,V_A,T_b)) ) ).
cnf(cls_rev__finite__subset_0,axiom,
( c_Finite__Set_Ofinite(V_A,T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ c_Finite__Set_Ofinite(V_B,T_a) ) ).
cnf(cls_finite__subset_0,axiom,
( c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_finite__UNIV_0,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(T_a)
| c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a) ) ).
cnf(cls_finite__Un_1,axiom,
( c_Finite__Set_Ofinite(V_G,T_a)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_F),V_G),T_a) ) ).
cnf(cls_finite__Un_0,axiom,
( c_Finite__Set_Ofinite(V_F,T_a)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_F),V_G),T_a) ) ).
cnf(cls_finite__UnI_0,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_F),V_G),T_a)
| ~ c_Finite__Set_Ofinite(V_G,T_a)
| ~ c_Finite__Set_Ofinite(V_F,T_a) ) ).
cnf(cls_finite__Un_2,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_F),V_G),T_a)
| ~ c_Finite__Set_Ofinite(V_G,T_a)
| ~ c_Finite__Set_Ofinite(V_F,T_a) ) ).
cnf(cls_finite__Diff2_1,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_B,T_a) ) ).
cnf(cls_finite__Diff2_0,axiom,
( c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),T_a)
| ~ c_Finite__Set_Ofinite(V_B,T_a) ) ).
cnf(cls_finite__Diff_0,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_sup__bot__left_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ).
cnf(cls_sup__bot__right_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ).
cnf(cls_bot__least_0,axiom,
( ~ class_Orderings_Obot(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ).
cnf(cls_sup__eq__bot__eq1_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_A),V_B) != c_Orderings_Obot__class_Obot(T_a)
| V_A = c_Orderings_Obot__class_Obot(T_a) ) ).
cnf(cls_sup__eq__bot__eq2_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_A),V_B) != c_Orderings_Obot__class_Obot(T_a)
| V_B = c_Orderings_Obot__class_Obot(T_a) ) ).
cnf(cls_inj__image__mem__iff_1,axiom,
( hBOOL(c_in(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b))
| ~ hBOOL(c_in(V_a,V_A,T_a))
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_inj__image__mem__iff_0,axiom,
( hBOOL(c_in(V_a,V_A,T_a))
| ~ hBOOL(c_in(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b))
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_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_Un__empty_2,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_subset__empty_1,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) ).
cnf(cls_subset__empty_0,axiom,
( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))) ) ).
cnf(cls_UNIV__not__empty_0,axiom,
c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_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_Un__empty__right_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = V_A ).
cnf(cls_Un__empty__left_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),V_B) = V_B ).
cnf(cls_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_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_empty__subsetI_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),V_A)) ).
cnf(cls_inj__on__empty_0,axiom,
c_Fun_Oinj__on(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a,T_b) ).
cnf(cls_Un__empty_1,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| V_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Un__empty_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_vimage__insert_0,axiom,
c_Set_Ovimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_a,T_b) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),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)) ).
cnf(cls_subset__insert__iff_4,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,V_B,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a))),V_B)) ) ).
cnf(cls_inj__on__iff__eq__card_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)
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_eq__card__imp__inj__on_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_Finite__Set_Ofinite(V_A,T_a)
| c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
cnf(cls_endo__inj__surj_0,axiom,
( c_Set_Oimage(V_f,V_A,T_a,T_a) = V_A
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Set_Oimage(V_f,V_A,T_a,T_a)),V_A))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_finite__surj__inj_0,axiom,
( c_Fun_Oinj__on(V_f,V_A,T_a,T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),c_Set_Oimage(V_f,V_A,T_a,T_a)))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_insert__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,V_C,T_a)),c_Set_Oinsert(V_a,V_D,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_C),V_D)) ) ).
cnf(cls_subset__insertI_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),c_Set_Oinsert(V_a,V_B,T_a))) ).
cnf(cls_Un__insert__right_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_a,V_B,T_a)) = c_Set_Oinsert(V_a,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),T_a) ).
cnf(cls_Un__insert__left_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,V_B,T_a)),V_C) = c_Set_Oinsert(V_a,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C),T_a) ).
cnf(cls_subset__insertI2_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_b,V_B,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_insert__subset_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_x,V_A,T_a)),V_B)) ) ).
cnf(cls_inj__on__insert_0,axiom,
( c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| ~ c_Fun_Oinj__on(V_f,c_Set_Oinsert(V_a,V_A,T_a),T_a,T_b) ) ).
cnf(cls_image__Un_0,axiom,
c_Set_Oimage(V_f,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_b,tc_bool)),V_A),V_B),T_b,T_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(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)) ).
cnf(cls_subset__image__iff_2,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_b,tc_bool)),V_x),V_A))
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Set_Oimage(V_f,V_x,T_b,T_a)),c_Set_Oimage(V_f,V_A,T_b,T_a))) ) ).
cnf(cls_image__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(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)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_diff__single__insert_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,V_B,T_a)))
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a))),V_B)) ) ).
cnf(cls_subset__insert__iff_3,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,V_B,T_a)))
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a))),V_B)) ) ).
cnf(cls_subset__insert__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a))),V_B))
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,V_B,T_a))) ) ).
cnf(cls_insert__subset_2,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_x,V_A,T_a)),V_B))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ hBOOL(c_in(V_x,V_B,T_a)) ) ).
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(c_in(V_x,V_B,T_a)) ) ).
cnf(cls_insert__subset_0,axiom,
( hBOOL(c_in(V_x,V_B,T_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_x,V_A,T_a)),V_B)) ) ).
cnf(cls_subset__insert__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,V_B,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| hBOOL(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_subset__insert__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| hBOOL(c_in(V_x,V_A,T_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,V_B,T_a))) ) ).
cnf(cls_subset__insert_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,V_B,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| hBOOL(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_subset__insert_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,V_B,T_a)))
| hBOOL(c_in(V_x,V_A,T_a)) ) ).
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(c_in(V_x,V_B,T_a)) ) ).
cnf(cls_card__Diff__singleton__if_1,axiom,
( c_Finite__Set_Ocard(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),T_a) = c_Finite__Set_Ocard(V_A,T_a)
| hBOOL(c_in(V_x,V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_ab__semigroup__mult_Ofold1__insert_0,axiom,
( hAPP(c_Finite__Set_Ofold1(V_times,T_a),c_Set_Oinsert(V_x,V_A,T_a)) = hAPP(hAPP(V_times,V_x),hAPP(c_Finite__Set_Ofold1(V_times,T_a),V_A))
| hBOOL(c_in(V_x,V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_OrderedGroup_Oab__semigroup__mult(V_times,T_a) ) ).
cnf(cls_image__subset__iff_0,axiom,
( hBOOL(c_in(hAPP(V_f,V_x),V_B,T_a))
| ~ hBOOL(c_in(V_x,V_A,T_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Set_Oimage(V_f,V_A,T_b,T_a)),V_B)) ) ).
cnf(cls_rangeI_0,axiom,
hBOOL(c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_a),T_a)) ).
cnf(cls_inj__on__insert_2,axiom,
( c_Fun_Oinj__on(V_f,c_Set_Oinsert(V_a,V_A,T_a),T_a,T_b)
| hBOOL(c_in(hAPP(V_f,V_a),c_Set_Oimage(V_f,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),T_b))
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
cnf(cls_inj__on__insert_1,axiom,
( ~ hBOOL(c_in(hAPP(V_f,V_a),c_Set_Oimage(V_f,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),T_b))
| ~ c_Fun_Oinj__on(V_f,c_Set_Oinsert(V_a,V_A,T_a),T_a,T_b) ) ).
cnf(cls_range__composition_0,axiom,
c_Set_Oimage(c_COMBB(V_f,V_g,T_c,T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_a) = c_Set_Oimage(V_f,c_Set_Oimage(V_g,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_c),T_c,T_a) ).
cnf(cls_finite__Diff__insert_1,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_a,V_B,T_a)),T_a)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),T_a) ) ).
cnf(cls_finite__Diff__insert_0,axiom,
( c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),T_a)
| ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Set_Oinsert(V_a,V_B,T_a)),T_a) ) ).
cnf(cls_subset__singletonD_0,axiom,
( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(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))) ) ).
cnf(cls_Nitpick_OEx1__def_2,axiom,
hBOOL(hAPP(c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a))) ).
cnf(cls_Min__singleton_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(c_Finite__Set_Olinorder__class_OMin(T_a),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) = V_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_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_Un__upper2_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B))) ).
cnf(cls_Un__subset__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_C)) ) ).
cnf(cls_inf__sup__aci_I6_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z)) ) ).
cnf(cls_inf__sup__aci_I7_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_z)) ) ).
cnf(cls_sup__left__commute_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_z)) ) ).
cnf(cls_sup__assoc_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z)) ) ).
cnf(cls_Un__assoc_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)) ).
cnf(cls_Un__left__commute_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_C)) ).
cnf(cls_image__diff__subset_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),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))) ).
cnf(cls_Max__mono_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(c_Finite__Set_Olinorder__class_OMax(T_a),V_M)),hAPP(c_Finite__Set_Olinorder__class_OMax(T_a),V_N)))
| ~ c_Finite__Set_Ofinite(V_N,T_a)
| V_M = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_M),V_N)) ) ).
cnf(cls_eq__eqI_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_x) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x_H),V_y_H)
| V_x_H = V_y_H ) ).
cnf(cls_eq__eqI_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_xa),V_y) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_x)
| V_xa = V_y ) ).
cnf(cls_Diff__idemp_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)),V_B) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B) ).
cnf(cls_COMBK__def_0,axiom,
hAPP(c_COMBK(V_P,T_a,T_b),V_Q) = V_P ).
cnf(cls_sup__idem_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_x) = V_x ) ).
cnf(cls_Un__absorb_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_A) = V_A ).
cnf(cls_finite__vimageI_0,axiom,
( c_Finite__Set_Ofinite(c_Set_Ovimage(V_h,V_F,T_b,T_a),T_b)
| ~ c_Fun_Oinj__on(V_h,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_a)
| ~ c_Finite__Set_Ofinite(V_F,T_a) ) ).
cnf(cls_sup__fun__eq_0,axiom,
( ~ class_Lattices_Olattice(T_b)
| hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,T_b)),V_f),V_g),v_x) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_b),hAPP(V_f,v_x)),hAPP(V_g,v_x)) ) ).
cnf(cls_inj__image__subset__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_b,tc_bool)),c_Set_Oimage(V_f,V_A,T_a,T_b)),c_Set_Oimage(V_f,V_B,T_a,T_b)))
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_inj__image__subset__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(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)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_inj__on__diff_0,axiom,
( c_Fun_Oinj__on(V_f,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b)
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
cnf(cls_vimage__Diff_0,axiom,
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_image__vimage__subset_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Set_Oimage(V_f,c_Set_Ovimage(V_f,V_A,T_b,T_a),T_b,T_a)),V_A)) ).
cnf(cls_inj__vimage__image__eq_0,axiom,
( c_Set_Ovimage(V_f,c_Set_Oimage(V_f,V_A,T_a,T_b),T_a,T_b) = V_A
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b) ) ).
cnf(cls_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_vimage__UNIV_0,axiom,
c_Set_Ovimage(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_a,T_b) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) ).
cnf(cls_sup__top__right_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
cnf(cls_sup__top__left_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = c_Orderings_Otop__class_Otop(T_a) ) ).
cnf(cls_Un__UNIV__left_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))),V_B) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) ).
cnf(cls_Un__UNIV__right_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) ).
cnf(cls_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,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b)
| V_A = V_B ) ).
cnf(cls_atLeastatMost__subset__iff_3,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a)),c_SetInterval_Oord__class_OatLeastAtMost(V_c,V_d,T_a)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_d))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_c),V_a)) ) ).
cnf(cls_atLeastatMost__subset__iff_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_d))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a)),c_SetInterval_Oord__class_OatLeastAtMost(V_c,V_d,T_a))) ) ).
cnf(cls_atLeastatMost__subset__iff_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_c),V_a))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a)),c_SetInterval_Oord__class_OatLeastAtMost(V_c,V_d,T_a))) ) ).
cnf(cls_ab__semigroup__mult_Omult__ac_I1_J_0,axiom,
( hAPP(hAPP(V_times,hAPP(hAPP(V_times,V_a),V_b)),V_c) = hAPP(hAPP(V_times,V_a),hAPP(hAPP(V_times,V_b),V_c))
| ~ c_OrderedGroup_Oab__semigroup__mult(V_times,T_a) ) ).
cnf(cls_ab__semigroup__mult_Omult__left__commute_0,axiom,
( hAPP(hAPP(V_times,V_a),hAPP(hAPP(V_times,V_b),V_c)) = hAPP(hAPP(V_times,V_b),hAPP(hAPP(V_times,V_a),V_c))
| ~ c_OrderedGroup_Oab__semigroup__mult(V_times,T_a) ) ).
cnf(cls_ab__semigroup__mult_Omult__commute_0,axiom,
( hAPP(hAPP(V_times,V_a),V_b) = hAPP(hAPP(V_times,V_b),V_a)
| ~ c_OrderedGroup_Oab__semigroup__mult(V_times,T_a) ) ).
cnf(cls_atLeastatMost__subset__iff_2,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a)),c_SetInterval_Oord__class_OatLeastAtMost(V_c,V_d,T_a)))
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b)) ) ).
cnf(cls_injD_0,axiom,
( hAPP(V_f,V_x) != hAPP(V_f,V_y)
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b)
| V_x = V_y ) ).
cnf(cls_sup1E_0,axiom,
( hBOOL(hAPP(V_B,V_x))
| hBOOL(hAPP(V_A,V_x))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),V_x)) ) ).
cnf(cls_sup1CI_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),V_x))
| ~ hBOOL(hAPP(V_B,V_x)) ) ).
cnf(cls_sup1CI_1,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),V_x))
| ~ hBOOL(hAPP(V_A,V_x)) ) ).
cnf(cls_inj__image__eq__iff_0,axiom,
( c_Set_Oimage(V_f,V_A,T_a,T_b) != c_Set_Oimage(V_f,V_B,T_a,T_b)
| ~ c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b)
| V_A = V_B ) ).
cnf(cls_Diff__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_C),V_D)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_D),V_B))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_C)) ) ).
cnf(cls_Inf__UNIV_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a) = c_Orderings_Obot__class_Obot(T_a) ) ).
cnf(cls_top1I_0,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_x)) ).
cnf(cls_top__fun__eq_0,axiom,
( ~ class_Orderings_Otop(T_b)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,T_b)),v_x) = c_Orderings_Otop__class_Otop(T_b) ) ).
cnf(cls_equalityI_0,axiom,
( V_A = V_B
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_A))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_set__eq__subset_2,axiom,
( V_A = V_B
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_A))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_order__eq__iff_2,axiom,
( ~ class_Orderings_Oorder(T_a)
| V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_order__antisym_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_order__antisym__conv_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x)) ) ).
cnf(cls_sup__absorb1_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) = V_x
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x)) ) ).
cnf(cls_le__iff__sup_1,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) != V_y
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_le__iff__sup_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) = V_y
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_Un__absorb1_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B) = V_B
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_Un__absorb2_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B) = V_A
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_A)) ) ).
cnf(cls_subset__Un__eq_1,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B) != V_B
| hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_Min__antimono_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(c_Finite__Set_Olinorder__class_OMin(T_a),V_N)),hAPP(c_Finite__Set_Olinorder__class_OMin(T_a),V_M)))
| ~ c_Finite__Set_Ofinite(V_N,T_a)
| V_M = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_M),V_N)) ) ).
cnf(cls_Inf__lower_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),c_Complete__Lattice_OInf__class_OInf(V_A,T_a)),V_x))
| ~ hBOOL(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_card__bij__eq_0,axiom,
( c_Finite__Set_Ocard(V_A,T_a) = c_Finite__Set_Ocard(V_B,T_b)
| ~ c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),c_Set_Oimage(V_g,V_B,T_b,T_a)),V_A))
| ~ c_Fun_Oinj__on(V_g,V_B,T_b,T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_b,tc_bool)),c_Set_Oimage(V_f,V_A,T_a,T_b)),V_B))
| ~ c_Fun_Oinj__on(V_f,V_A,T_a,T_b) ) ).
cnf(cls_atLeastatMost__empty__iff2_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b)) ) ).
cnf(cls_atLeastatMost__empty__iff2_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a)
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b)) ) ).
cnf(cls_Diff__UNIV_0,axiom,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_Un__mono_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_C),V_D)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_D))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_C)) ) ).
cnf(cls_subset__UNIV_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)))) ).
cnf(cls_top__greatest_0,axiom,
( ~ class_Orderings_Otop(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ).
cnf(cls_com_Osimps_I13_J_0,axiom,
c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ).
cnf(cls_Inf__empty_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) = c_Orderings_Otop__class_Otop(T_a) ) ).
cnf(cls_le__sup__iff_1,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)),V_z)) ) ).
cnf(cls_le__sup__iff_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)),V_z)) ) ).
cnf(cls_le__supI2_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_b)) ) ).
cnf(cls_le__supI1_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_a)) ) ).
cnf(cls_le__supE_1,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_b),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b)),V_x)) ) ).
cnf(cls_le__supE_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b)),V_x)) ) ).
cnf(cls_Un__subset__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C)) ) ).
cnf(cls_Un__subset__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C)) ) ).
cnf(cls_xt1_I6_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_z),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_z),V_y))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x)) ) ).
cnf(cls_order__trans_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_z))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_equalityE_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_x),V_x)) ).
cnf(cls_subset__refl_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_A)) ).
cnf(cls_subset__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_subset__inj__on_0,axiom,
( c_Fun_Oinj__on(V_f,V_A,T_a,T_b)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B))
| ~ c_Fun_Oinj__on(V_f,V_B,T_a,T_b) ) ).
cnf(cls_predicate1D_0,axiom,
( hBOOL(hAPP(V_Q,V_x))
| ~ hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_P),V_Q)) ) ).
cnf(cls_order__eq__iff_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_x)) ) ).
cnf(cls_order__eq__refl_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_x)) ) ).
cnf(cls_rev__predicate1D_0,axiom,
( hBOOL(hAPP(V_Q,V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_P),V_Q))
| ~ hBOOL(hAPP(V_P,V_x)) ) ).
cnf(cls_atLeastatMost__empty__iff_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b)) ) ).
cnf(cls_atLeastatMost__empty__iff_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_b,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_a),V_b)) ) ).
cnf(cls_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))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_C))
| ~ c_Fun_Oinj__on(V_f,V_C,T_a,T_b) ) ).
cnf(cls_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_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_vimage__const_0,axiom,
( c_Set_Ovimage(c_COMBK(V_c,T_b,T_a),V_A,T_a,T_b) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))
| ~ hBOOL(c_in(V_c,V_A,T_b)) ) ).
cnf(cls_double__diff_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_B),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(T_a,tc_bool)),V_C),V_A)) = V_A
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_a,tc_bool)),V_A),V_B)) ) ).
cnf(cls_le__eqI_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x_H),V_y_H)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y_H),V_x_H))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x)) ) ).
cnf(cls_le__eqI_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x_H),V_y_H)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y_H),V_x_H)) ) ).
cnf(cls_com_Osimps_I12_J_0,axiom,
c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ).
cnf(cls_linorder__linear_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_y),V_x))
| hBOOL(hAPP(hAPP(c_lessequals(T_a),V_x),V_y)) ) ).
cnf(cls_Nitpick_OEx1__def_3,axiom,
( V_y = c_Nitpick_Osko__Nitpick__XEx1__def__1__3(c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)
| ~ hBOOL(hAPP(c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),V_y)) ) ).
cnf(cls_fold1__singleton_0,axiom,
hAPP(c_Finite__Set_Ofold1(V_f,T_a),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) = V_a ).
cnf(cls_Max__singleton_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hAPP(c_Finite__Set_Olinorder__class_OMax(T_a),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) = V_a ) ).
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_atLeastAtMost__singleton_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_SetInterval_Oord__class_OatLeastAtMost(V_a,V_a,T_a) = c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ) ).
cnf(cls_insert__is__Un_0,axiom,
c_Set_Oinsert(V_a,V_A,T_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),V_A) ).
cnf(cls_Inf__singleton_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_a)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = V_a ) ).
cnf(cls_finite__imageD_0,axiom,
( c_Finite__Set_Ofinite(V_A,T_b)
| ~ c_Fun_Oinj__on(V_f,V_A,T_b,T_a)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(V_f,V_A,T_b,T_a),T_a) ) ).
cnf(cls_finite__surj_0,axiom,
( c_Finite__Set_Ofinite(V_B,T_b)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_fun(T_b,tc_bool)),V_B),c_Set_Oimage(V_f,V_A,T_a,T_b)))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_image__constant__conv_0,axiom,
c_Set_Oimage(c_COMBK(V_c,T_a,T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_conseq_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(V_xa,V_Z_H),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(V_G,V_P,V_Q,V_c,V_x,V_xa)))
| ~ hBOOL(hAPP(hAPP(V_x,V_Z_H),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(V_G,V_P,V_Q,V_c)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_x),V_c),V_xa),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ) ).
cnf(cls_conseq12_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(V_Q_H,V_Z_H),v_sko__Hoare__Mirabelle__Xconseq12__3(V_P,V_P_H,V_Q,V_Q_H)))
| ~ hBOOL(hAPP(hAPP(V_P_H,V_Z_H),v_sko__Hoare__Mirabelle__Xconseq12__2(V_P,V_P_H,V_Q,V_Q_H)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P_H),V_c),V_Q_H),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ) ).
cnf(cls_hoare__derivs_Ointros_I6_J_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(V_xa,V_Z_H),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(V_G,V_P,V_Q,V_c,V_x,V_xa)))
| ~ hBOOL(hAPP(hAPP(V_x,V_Z_H),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(V_G,V_P,V_Q,V_c)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_x),V_c),V_xa),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ) ).
cnf(cls_hoare__derivs_Ointros_I6_J_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(V_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(V_G,V_P,V_Q,V_c))) ) ).
cnf(cls_hoare__derivs_Ointros_I6_J_2,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(V_Q,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(V_G,V_P,V_Q,V_c,V_x,V_xa)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_x),V_c),V_xa),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ) ).
cnf(cls_conseq_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(V_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(V_G,V_P,V_Q,V_c))) ) ).
cnf(cls_conseq2_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(V_Q_H,v_sko__Hoare__Mirabelle__Xconseq2__1(V_Q,V_Q_H)),v_sko__Hoare__Mirabelle__Xconseq2__2(V_Q,V_Q_H)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q_H),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ) ).
cnf(cls_conseq12_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(V_P,v_sko__Hoare__Mirabelle__Xconseq12__1(V_P,V_P_H,V_Q,V_Q_H)),v_sko__Hoare__Mirabelle__Xconseq12__2(V_P,V_P_H,V_Q,V_Q_H)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P_H),V_c),V_Q_H),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ) ).
cnf(cls_conseq1_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(V_P,v_sko__Hoare__Mirabelle__Xconseq1__1(V_P,V_P_H)),v_sko__Hoare__Mirabelle__Xconseq1__2(V_P,V_P_H)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P_H),V_c),V_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ) ).
cnf(cls_conseq_2,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(V_Q,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(V_G,V_P,V_Q,V_c,V_x,V_xa)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_x),V_c),V_xa),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ) ).
cnf(cls_conseq1_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(V_P_H,v_sko__Hoare__Mirabelle__Xconseq1__1(V_P,V_P_H)),v_sko__Hoare__Mirabelle__Xconseq1__2(V_P,V_P_H)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P_H),V_c),V_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ) ).
cnf(cls_conseq12_2,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(V_Q,v_sko__Hoare__Mirabelle__Xconseq12__1(V_P,V_P_H,V_Q,V_Q_H)),v_sko__Hoare__Mirabelle__Xconseq12__3(V_P,V_P_H,V_Q,V_Q_H)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P_H),V_c),V_Q_H),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ) ).
cnf(cls_conseq2_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(V_Q,v_sko__Hoare__Mirabelle__Xconseq2__1(V_Q,V_Q_H)),v_sko__Hoare__Mirabelle__Xconseq2__2(V_Q,V_Q_H)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q_H),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ) ).
cnf(cls_escape_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(V_P,v_sko__Hoare__Mirabelle__Xescape__1(V_G,V_P,V_Q,V_c)),v_sko__Hoare__Mirabelle__Xescape__2(V_G,V_P,V_Q,V_c))) ) ).
cnf(cls_COMBK__def__raw_0,axiom,
hAPP(c_COMBK(v_P,t_a,t_b),v_Q) = v_P ).
cnf(cls_Min__in_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(c_in(hAPP(c_Finite__Set_Olinorder__class_OMin(T_a),V_A),V_A,T_a))
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_Max__in_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| hBOOL(c_in(hAPP(c_Finite__Set_Olinorder__class_OMax(T_a),V_A),V_A,T_a))
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_card__insert__if_0,axiom,
( c_Finite__Set_Ocard(c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Finite__Set_Ocard(V_A,T_a)
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
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(c_in(V_a,V_A,T_a)) ) ).
cnf(cls_vimage__singleton__eq_0,axiom,
( hAPP(V_f,V_a) = V_b
| ~ hBOOL(c_in(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),T_a)) ) ).
cnf(cls_vimage__singleton__eq_1,axiom,
hBOOL(c_in(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),T_aa)) ).
cnf(cls_ab__semigroup__mult_Ononempty__iff_2,axiom,
( c_Set_Oinsert(V_x,V_xa,T_b) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))
| hBOOL(c_in(V_x,V_xa,T_b))
| ~ c_OrderedGroup_Oab__semigroup__mult(V_times,T_a) ) ).
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(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_finite__range__imageI_0,axiom,
( c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(V_f,V_g,T_a,T_c,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_c),T_c)
| ~ c_Finite__Set_Ofinite(c_Set_Oimage(V_g,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_a),T_a) ) ).
cnf(cls_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_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_image__constant_0,axiom,
( c_Set_Oimage(c_COMBK(V_c,T_b,T_a),V_A,T_a,T_b) = c_Set_Oinsert(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b)
| ~ hBOOL(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_hoare__derivs_OSkip_0,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P),c_Com_Ocom_OSKIP),V_P),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a)),T_a) ).
cnf(cls_Comp_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P),c_Com_Ocom_OSemi(V_c,V_d)),V_R),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a)),T_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_Q),V_d),V_R),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a)),T_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P),V_c),V_Q),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a)),T_a) ) ).
cnf(cls_hoare__derivs_Oinsert_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(V_t,V_ts,tc_Hoare__Mirabelle_Otriple(T_a)),T_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(V_t,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a)),T_a) ) ).
cnf(cls_derivs__insertD_1,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(V_t,V_ts,tc_Hoare__Mirabelle_Otriple(T_a)),T_a) ) ).
cnf(cls_singleton__iff_1,axiom,
hBOOL(c_in(V_x,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)) ).
cnf(cls_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_insert__iff_2,axiom,
( hBOOL(c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a))
| ~ hBOOL(c_in(V_a,V_A,T_a)) ) ).
cnf(cls_insertCI_0,axiom,
( hBOOL(c_in(V_a,c_Set_Oinsert(V_b,V_B,T_a),T_a))
| ~ hBOOL(c_in(V_a,V_B,T_a)) ) ).
cnf(cls_image__image_0,axiom,
c_Set_Oimage(V_f,c_Set_Oimage(V_g,V_A,T_c,T_b),T_b,T_a) = c_Set_Oimage(c_COMBB(V_f,V_g,T_b,T_a,T_c),V_A,T_c,T_a) ).
cnf(cls_insert__code_1,axiom,
hBOOL(hAPP(c_Set_Oinsert(V_x,V_A,T_a),V_x)) ).
cnf(cls_image__insert_0,axiom,
c_Set_Oimage(V_f,c_Set_Oinsert(V_a,V_B,T_b),T_b,T_a) = c_Set_Oinsert(hAPP(V_f,V_a),c_Set_Oimage(V_f,V_B,T_b,T_a),T_a) ).
cnf(cls_cut_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_G_H,T_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_H,V_ts,T_a) ) ).
cnf(cls_ex__in__conv_0,axiom,
~ hBOOL(c_in(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) ).
cnf(cls_ball__empty_0,axiom,
( hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(c_in(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) ) ).
cnf(cls_empty__iff_0,axiom,
~ hBOOL(c_in(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) ).
cnf(cls_emptyE_0,axiom,
~ hBOOL(c_in(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) ).
cnf(cls_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_triple_Oinject_2,axiom,
( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1),V_com),V_fun2) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_H),V_com_H),V_fun2_H)
| V_fun2 = V_fun2_H ) ).
cnf(cls_triple_Oinject_1,axiom,
( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1),V_com),V_fun2) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_H),V_com_H),V_fun2_H)
| V_com = V_com_H ) ).
cnf(cls_triple_Oinject_0,axiom,
( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1),V_com),V_fun2) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_H),V_com_H),V_fun2_H)
| V_fun1 = V_fun1_H ) ).
cnf(cls_bot__empty__eq_0,axiom,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_in(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a) ).
cnf(cls_doubleton__eq__iff_3,axiom,
( c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) != c_Set_Oinsert(V_c,c_Set_Oinsert(V_d,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)
| V_b = V_c
| V_b = V_d ) ).
cnf(cls_doubleton__eq__iff_2,axiom,
( c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) != c_Set_Oinsert(V_c,c_Set_Oinsert(V_d,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)
| V_a = V_d
| V_b = V_d ) ).
cnf(cls_doubleton__eq__iff_1,axiom,
( c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) != c_Set_Oinsert(V_c,c_Set_Oinsert(V_d,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)
| V_b = V_c
| V_a = V_c ) ).
cnf(cls_doubleton__eq__iff_0,axiom,
( c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) != c_Set_Oinsert(V_c,c_Set_Oinsert(V_d,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)
| V_a = V_d
| V_a = V_c ) ).
cnf(cls_finite__imageI_0,axiom,
( c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b)
| ~ c_Finite__Set_Ofinite(V_F,T_a) ) ).
cnf(cls_insertE_0,axiom,
( hBOOL(c_in(V_a,V_A,T_a))
| V_a = V_b
| ~ hBOOL(c_in(V_a,c_Set_Oinsert(V_b,V_A,T_a),T_a)) ) ).
cnf(cls_bot1E_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x)) ).
cnf(cls_empty_0,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),T_a) ).
cnf(cls_finite_OemptyI_0,axiom,
c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ).
cnf(cls_finite__insert_1,axiom,
( c_Finite__Set_Ofinite(c_Set_Oinsert(V_a,V_A,T_a),T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_finite__insert_0,axiom,
( c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(V_a,V_A,T_a),T_a) ) ).
cnf(cls_insert__code_0,axiom,
( hBOOL(hAPP(V_A,V_x))
| V_y = V_x
| ~ hBOOL(hAPP(c_Set_Oinsert(V_y,V_A,T_a),V_x)) ) ).
cnf(cls_insert__absorb2_0,axiom,
c_Set_Oinsert(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Set_Oinsert(V_x,V_A,T_a) ).
cnf(cls_insert__not__empty_0,axiom,
c_Set_Oinsert(V_a,V_A,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_empty__is__image_0,axiom,
( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Set_Oimage(V_f,V_A,T_b,T_a)
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)) ) ).
cnf(cls_bot__fun__eq_0,axiom,
( ~ class_Orderings_Obot(T_b)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,T_b)),v_x) = c_Orderings_Obot__class_Obot(T_b) ) ).
cnf(cls_singletonE_0,axiom,
( V_b = V_a
| ~ hBOOL(c_in(V_b,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)) ) ).
cnf(cls_insert__iff_1,axiom,
hBOOL(c_in(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a)) ).
cnf(cls_insertI1_0,axiom,
hBOOL(c_in(V_a,c_Set_Oinsert(V_a,V_B,T_a),T_a)) ).
cnf(cls_insertCI_1,axiom,
hBOOL(c_in(V_x,c_Set_Oinsert(V_x,V_B,T_a),T_a)) ).
cnf(cls_insert__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_mem__def_1,axiom,
( hBOOL(c_in(V_x,V_S,T_a))
| ~ hBOOL(hAPP(V_S,V_x)) ) ).
cnf(cls_mem__def_0,axiom,
( hBOOL(hAPP(V_S,V_x))
| ~ hBOOL(c_in(V_x,V_S,T_a)) ) ).
cnf(cls_COMBB__def_0,axiom,
hAPP(c_COMBB(V_P,V_Q,T_b,T_a,T_c),V_R) = hAPP(V_P,hAPP(V_Q,V_R)) ).
cnf(cls_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_doubleton__eq__iff_4,axiom,
c_Set_Oinsert(V_xa,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = c_Set_Oinsert(V_x,c_Set_Oinsert(V_xa,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) ).
cnf(cls_image__empty_0,axiom,
c_Set_Oimage(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_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_bex__empty_0,axiom,
( ~ hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(c_in(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) ) ).
cnf(cls_comm__monoid__add_Ononempty__iff_2,axiom,
( c_Set_Oinsert(V_x,V_xa,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| hBOOL(c_in(V_x,V_xa,T_a)) ) ).
cnf(cls_derivs__insertD_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(V_t,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a)),T_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Set_Oinsert(V_t,V_ts,tc_Hoare__Mirabelle_Otriple(T_a)),T_a) ) ).
cnf(cls_insert__code_2,axiom,
( hBOOL(hAPP(c_Set_Oinsert(V_y,V_A,T_a),V_x))
| ~ hBOOL(hAPP(V_A,V_x)) ) ).
cnf(cls_insert__image_0,axiom,
( c_Set_Oinsert(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b) = c_Set_Oimage(V_f,V_A,T_a,T_b)
| ~ hBOOL(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_insert__ident_0,axiom,
( c_Set_Oinsert(V_x,V_A,T_a) != c_Set_Oinsert(V_x,V_B,T_a)
| hBOOL(c_in(V_x,V_B,T_a))
| hBOOL(c_in(V_x,V_A,T_a))
| V_A = V_B ) ).
cnf(cls_insert__absorb_0,axiom,
( c_Set_Oinsert(V_a,V_A,T_a) = V_A
| ~ hBOOL(c_in(V_a,V_A,T_a)) ) ).
cnf(cls_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_finite_0,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(T_a)
| c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_rev__image__eqI_0,axiom,
( ~ hBOOL(c_in(V_x,V_A,T_aa))
| hBOOL(c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_aa,T_a),T_a)) ) ).
cnf(cls_image__iff_2,axiom,
( ~ hBOOL(c_in(V_x,V_A,T_b))
| hBOOL(c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_b,T_a),T_a)) ) ).
cnf(cls_image__eqI_0,axiom,
( hBOOL(c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_b,T_a),T_a))
| ~ hBOOL(c_in(V_x,V_A,T_b)) ) ).
cnf(cls_imageI_0,axiom,
( hBOOL(c_in(hAPP(V_f,V_x),c_Set_Oimage(V_f,V_A,T_a,T_b),T_b))
| ~ hBOOL(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_conjecture_0,negated_conjecture,
c_Finite__Set_Ofinite(v_F,t_a) ).
cnf(cls_conjecture_1,negated_conjecture,
~ hBOOL(c_in(v_x,v_F,t_a)) ).
cnf(cls_conjecture_2,negated_conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q_H,v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b) ).
cnf(cls_conjecture_3,negated_conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),v_P_H,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_c0,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),v_Q_H,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),v_F,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b) ).
cnf(cls_conjecture_4,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b) ).
cnf(cls_conjecture_5,negated_conjecture,
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,V_p)),hAPP(v_c0,V_p)),hAPP(v_Q,V_p)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,V_p)),hAPP(v_c0,V_p)),hAPP(v_Q_H,V_p)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b) ) ).
cnf(cls_conjecture_6,negated_conjecture,
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),v_P,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_c0,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),v_Q,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),v_F,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),v_P_H,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_c0,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),v_Q_H,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),v_F,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b) ) ).
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__Lattices_Oboolean__algebra,axiom,
( class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))
| ~ class_Lattices_Oboolean__algebra(T_1) ) ).
cnf(clsarity_fun__Finite__Set_Ofinite_Ofinite,axiom,
( class_Finite__Set_Ofinite_Ofinite(tc_fun(T_2,T_1))
| ~ class_Finite__Set_Ofinite_Ofinite(T_1)
| ~ class_Finite__Set_Ofinite_Ofinite(T_2) ) ).
cnf(clsarity_fun__Orderings_Opreorder,axiom,
( class_Orderings_Opreorder(tc_fun(T_2,T_1))
| ~ class_Orderings_Opreorder(T_1) ) ).
cnf(clsarity_fun__Lattices_Olattice,axiom,
( class_Lattices_Olattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ) ).
cnf(clsarity_fun__Orderings_Oorder,axiom,
( class_Orderings_Oorder(tc_fun(T_2,T_1))
| ~ class_Orderings_Oorder(T_1) ) ).
cnf(clsarity_fun__Orderings_Otop,axiom,
( class_Orderings_Otop(tc_fun(T_2,T_1))
| ~ class_Orderings_Otop(T_1) ) ).
cnf(clsarity_fun__Orderings_Obot,axiom,
( class_Orderings_Obot(tc_fun(T_2,T_1))
| ~ class_Orderings_Obot(T_1) ) ).
cnf(clsarity_fun__HOL_Ouminus,axiom,
( class_HOL_Ouminus(tc_fun(T_2,T_1))
| ~ class_HOL_Ouminus(T_1) ) ).
cnf(clsarity_fun__HOL_Ominus,axiom,
( class_HOL_Ominus(tc_fun(T_2,T_1))
| ~ class_HOL_Ominus(T_1) ) ).
cnf(clsarity_fun__HOL_Oord,axiom,
( class_HOL_Oord(tc_fun(T_2,T_1))
| ~ class_HOL_Oord(T_1) ) ).
cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Oab__semigroup__mult,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat) ).
cnf(clsarity_nat__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_nat) ).
cnf(clsarity_nat__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring__0,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat) ).
cnf(clsarity_nat__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring,axiom,
class_Ring__and__Field_Osemiring(tc_nat) ).
cnf(clsarity_nat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_nat) ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat) ).
cnf(clsarity_nat__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_nat) ).
cnf(clsarity_nat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_nat) ).
cnf(clsarity_nat__Orderings_Obot,axiom,
class_Orderings_Obot(tc_nat) ).
cnf(clsarity_nat__HOL_Ominus,axiom,
class_HOL_Ominus(tc_nat) ).
cnf(clsarity_nat__HOL_Oord,axiom,
class_HOL_Oord(tc_nat) ).
cnf(clsarity_bool__Complete__Lattice_Ocomplete__lattice,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool) ).
cnf(clsarity_bool__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_bool) ).
cnf(clsarity_bool__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_bool) ).
cnf(clsarity_bool__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_bool) ).
cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_bool) ).
cnf(clsarity_bool__Lattices_Oboolean__algebra,axiom,
class_Lattices_Oboolean__algebra(tc_bool) ).
cnf(clsarity_bool__Finite__Set_Ofinite_Ofinite,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool) ).
cnf(clsarity_bool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_bool) ).
cnf(clsarity_bool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_bool) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool) ).
cnf(clsarity_bool__Orderings_Otop,axiom,
class_Orderings_Otop(tc_bool) ).
cnf(clsarity_bool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_bool) ).
cnf(clsarity_bool__HOL_Ouminus,axiom,
class_HOL_Ouminus(tc_bool) ).
cnf(clsarity_bool__HOL_Ominus,axiom,
class_HOL_Ominus(tc_bool) ).
cnf(clsarity_bool__HOL_Oord,axiom,
class_HOL_Oord(tc_bool) ).
cnf(cls_ATP__Linkup_OCOMBS__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_ATP__Linkup_OCOMBC__def_0,axiom,
hAPP(hAPP(c_COMBC(V_P,T_b,T_c,T_a),V_Q),V_R) = hAPP(hAPP(V_P,V_R),V_Q) ).
cnf(cls_ATP__Linkup_OCOMBB__def_0,axiom,
hAPP(c_COMBB(V_P,V_Q,T_b,T_a,T_c),V_R) = hAPP(V_P,hAPP(V_Q,V_R)) ).
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
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)) ) ).
%------------------------------------------------------------------------------