TPTP Problem File: SCT059-1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SCT059-1 : TPTP v9.0.0. Released v4.1.0.
% Domain : Social Choice Theory
% Problem : Arrow Order 230_2
% Version : Especial.
% English : Formalization of two proofs of Arrow's impossibility theorem. One
% formalization is based on utility functions, the other one on
% strict partial orders.
% Refs : [Nip09] Nipkow (2009), Social Choice Theory in HOL: Arrow and
% : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe
% : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% Source : [Nip10]
% Names : Arrow_Order-230_22 [Nip10]
% Status : Unsatisfiable
% Rating : 1.00 v8.2.0, 0.95 v7.4.0, 1.00 v7.3.0, 0.92 v7.0.0, 0.93 v6.3.0, 0.91 v6.2.0, 0.90 v6.1.0, 0.93 v6.0.0, 0.90 v5.5.0, 0.95 v5.3.0, 0.94 v5.0.0, 0.93 v4.1.0
% Syntax : Number of clauses : 543 ( 163 unt; 37 nHn; 236 RR)
% Number of literals : 1093 ( 290 equ; 520 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 37 ( 36 usr; 0 prp; 1-9 aty)
% Number of functors : 59 ( 59 usr; 8 con; 0-5 aty)
% Number of variables : 2087 ( 319 sgn)
% SPC : CNF_UNS_RFO_SEQ_NHN
% Comments :
%------------------------------------------------------------------------------
cnf(cls_inf__sup__ord_I1_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y),V_x,T_a) ) ).
cnf(cls_inf__sup__ord_I2_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y),V_y,T_a) ) ).
cnf(cls_inf__greatest_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z),T_a)
| ~ c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_le__inf__iff_2,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z),T_a)
| ~ c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_le__infI_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b),T_a)
| ~ c_lessequals(V_x,V_b,T_a)
| ~ c_lessequals(V_x,V_a,T_a) ) ).
cnf(cls_inf__le2_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y),V_y,T_a) ) ).
cnf(cls_inf__le1_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_y),V_x,T_a) ) ).
cnf(cls_Int__lower1_0,axiom,
c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),V_A,tc_fun(T_a,tc_bool)) ).
cnf(cls_Int__lower2_0,axiom,
c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),V_B,tc_fun(T_a,tc_bool)) ).
cnf(cls_Int__greatest_0,axiom,
( c_lessequals(V_C,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_C,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_C,V_A,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Int__subset__iff_2,axiom,
( c_lessequals(V_C,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_C,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_C,V_A,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_mono__Field_0,axiom,
( c_lessequals(c_Relation_OField(V_r,T_a),c_Relation_OField(V_s,T_a),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_r,V_s,tc_fun(tc_prod(T_a,T_a),tc_bool)) ) ).
cnf(cls_complete__lattice_OSup__empty_0,axiom,
( hAPP(V_Sup,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = V_bot
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_complete__lattice_OInf__empty_0,axiom,
( hAPP(V_Inf,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = V_top
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_le__sup__iff_1,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y),V_z,T_a) ) ).
cnf(cls_le__sup__iff_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y),V_z,T_a) ) ).
cnf(cls_le__supI2_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(V_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b),T_a)
| ~ c_lessequals(V_x,V_b,T_a) ) ).
cnf(cls_le__supI1_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(V_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b),T_a)
| ~ c_lessequals(V_x,V_a,T_a) ) ).
cnf(cls_le__supE_1,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(V_b,V_x,T_a)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b),V_x,T_a) ) ).
cnf(cls_le__supE_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(V_a,V_x,T_a)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b),V_x,T_a) ) ).
cnf(cls_Un__subset__iff_0,axiom,
( c_lessequals(V_A,V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),V_C,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Un__subset__iff_1,axiom,
( c_lessequals(V_B,V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),V_C,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_xt1_I6_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_z,V_x,T_a)
| ~ c_lessequals(V_z,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_order__trans_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_equalityE_0,axiom,
c_lessequals(V_x,V_x,tc_fun(T_a,tc_bool)) ).
cnf(cls_subset__refl_0,axiom,
c_lessequals(V_A,V_A,tc_fun(T_a,tc_bool)) ).
cnf(cls_subset__trans_0,axiom,
( c_lessequals(V_A,V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_B,V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_predicate1D_0,axiom,
( hBOOL(hAPP(V_Q,V_x))
| ~ hBOOL(hAPP(V_P,V_x))
| ~ c_lessequals(V_P,V_Q,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_order__eq__iff_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) ) ).
cnf(cls_order__eq__refl_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_lessequals(V_x,V_x,T_a) ) ).
cnf(cls_antisym__subset_0,axiom,
( c_Relation_Oantisym(V_r,T_a)
| ~ c_Relation_Oantisym(V_s,T_a)
| ~ c_lessequals(V_r,V_s,tc_fun(tc_prod(T_a,T_a),tc_bool)) ) ).
cnf(cls_finite__subset_0,axiom,
( c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Finite__Set_Ofinite(V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_rev__predicate1D_0,axiom,
( hBOOL(hAPP(V_Q,V_x))
| ~ c_lessequals(V_P,V_Q,tc_fun(T_a,tc_bool))
| ~ hBOOL(hAPP(V_P,V_x)) ) ).
cnf(cls_acyclic__subset_0,axiom,
( c_Wellfounded_Oacyclic(V_r,T_a)
| ~ c_lessequals(V_r,V_s,tc_fun(tc_prod(T_a,T_a),tc_bool))
| ~ c_Wellfounded_Oacyclic(V_s,T_a) ) ).
cnf(cls_rev__finite__subset_0,axiom,
( c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_Finite__Set_Ofinite(V_B,T_a) ) ).
cnf(cls_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_Int__mono_0,axiom,
( c_lessequals(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),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_B,V_D,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_C,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_subset__singletonD_0,axiom,
( V_A = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),tc_fun(T_a,tc_bool)) ) ).
cnf(cls_image__mono_0,axiom,
( c_lessequals(c_Set_Oimage(V_f,V_A,T_a,T_b),c_Set_Oimage(V_f,V_B,T_a,T_b),tc_fun(T_b,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_subset__image__iff_2,axiom,
( ~ c_lessequals(V_x,V_A,tc_fun(T_b,tc_bool))
| c_lessequals(c_Set_Oimage(V_f,V_x,T_b,T_a),c_Set_Oimage(V_f,V_A,T_b,T_a),tc_fun(T_a,tc_bool)) ) ).
cnf(cls_insert__mono_0,axiom,
( c_lessequals(c_Set_Oinsert(V_a,V_C,T_a),c_Set_Oinsert(V_a,V_D,T_a),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_C,V_D,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Un__empty_2,axiom,
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_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_linorder__linear_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_sup__le__fold__sup_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_b,V_A,T_a,T_a),T_a)
| ~ hBOOL(c_in(V_a,V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_fold__inf__le__inf_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_b,V_A,T_a,T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b),T_a)
| ~ hBOOL(c_in(V_a,V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_subset__insert_0,axiom,
( c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| hBOOL(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_subset__insert_1,axiom,
( c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| hBOOL(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_subset__insert__iff_1,axiom,
( c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| hBOOL(c_in(V_x,V_A,T_a))
| ~ c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool)) ) ).
cnf(cls_subset__insert__iff_2,axiom,
( c_lessequals(V_A,c_Set_Oinsert(V_x,V_B,T_a),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| hBOOL(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_insert__subset_0,axiom,
( hBOOL(c_in(V_x,V_B,T_a))
| ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_comm__monoid__add_Ononempty__iff_2,axiom,
( c_Set_Oinsert(V_x,V_xa,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| hBOOL(c_in(V_x,V_xa,T_a)) ) ).
cnf(cls_singletonE_0,axiom,
( V_b = V_a
| ~ hBOOL(c_in(V_b,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)) ) ).
cnf(cls_insert__subset_2,axiom,
( c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(c_in(V_x,V_B,T_a)) ) ).
cnf(cls_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__subset__iff_0,axiom,
( hBOOL(c_in(hAPP(V_f,V_x),V_B,T_a))
| ~ hBOOL(c_in(V_x,V_A,T_b))
| ~ c_lessequals(c_Set_Oimage(V_f,V_A,T_b,T_a),V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_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_le__SUPI_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_b)
| c_lessequals(hAPP(V_M,V_i),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_M,T_a,T_b),T_b)
| ~ hBOOL(c_in(V_i,V_A,T_a)) ) ).
cnf(cls_UN__upper_0,axiom,
( c_lessequals(hAPP(V_B,V_a),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_bool)),tc_fun(T_b,tc_bool))
| ~ hBOOL(c_in(V_a,V_A,T_a)) ) ).
cnf(cls_UNION__empty__conv_I2_J_0,axiom,
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_b,tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| hAPP(V_B,V_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ hBOOL(c_in(V_x,V_A,T_b)) ) ).
cnf(cls_UN__subset__iff_0,axiom,
( c_lessequals(hAPP(V_A,V_x),V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(c_in(V_x,V_I,T_b))
| ~ c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_I,V_A,T_b,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_UNION__empty__conv_I1_J_0,axiom,
( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) != c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_b,tc_fun(T_a,tc_bool))
| hAPP(V_B,V_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ hBOOL(c_in(V_x,V_A,T_b)) ) ).
cnf(cls_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_finite__surj_0,axiom,
( c_Finite__Set_Ofinite(V_B,T_b)
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,tc_bool))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_distrib__inf__le_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_lessequals(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)),T_a) ) ).
cnf(cls_distrib__sup__le_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_lessequals(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)),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_UN__extend__simps_I1_J_0,axiom,
c_Set_Oinsert(V_a,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_B,T_b,tc_fun(T_a,tc_bool)),T_a) = c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ).
cnf(cls_image__Int__subset_0,axiom,
c_lessequals(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)),tc_fun(T_a,tc_bool)) ).
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))
| c_lessequals(V_C,V_A,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Un__Int__assoc__eq_1,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C))
| ~ c_lessequals(V_C,V_A,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_UN__extend__simps_I2_J_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_A,T_b,tc_fun(T_a,tc_bool))),V_B) = V_B ).
cnf(cls_UN__extend__simps_I3_J_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_B,T_b,tc_fun(T_a,tc_bool))) = V_A ).
cnf(cls_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_SUP__const_0,axiom,
( ~ class_Complete__Lattice_Ocomplete__lattice(T_b)
| c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,c_COMBK(V_M,T_b,T_a),T_a,T_b) = V_M
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_UN__constant_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),c_COMBK(V_c,tc_fun(T_a,tc_bool),T_b),T_b,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_UN__constant_1,axiom,
( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,c_COMBK(V_c,tc_fun(T_a,tc_bool),T_b),T_b,tc_fun(T_a,tc_bool)) = V_c
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)) ) ).
cnf(cls_UN__empty2_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool),T_b),T_b,tc_fun(T_a,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_complete__lattice_Osup__Sup__fold__sup_0,axiom,
( hAPP(hAPP(V_sup,V_B),hAPP(V_Sup,V_A)) = c_Finite__Set_Ofold(V_sup,V_B,V_A,T_a,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_complete__lattice_Oinf__Inf__fold__inf_0,axiom,
( hAPP(hAPP(V_inf,V_B),hAPP(V_Inf,V_A)) = c_Finite__Set_Ofold(V_inf,V_B,V_A,T_a,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_complete__lattice_OSup__fold__sup_0,axiom,
( hAPP(V_Sup,V_A) = c_Finite__Set_Ofold(V_sup,V_bot,V_A,T_a,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_complete__lattice_OInf__fold__inf_0,axiom,
( hAPP(V_Inf,V_A) = c_Finite__Set_Ofold(V_inf,V_top,V_A,T_a,T_a)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_image__vimage__subset_0,axiom,
c_lessequals(c_Set_Oimage(V_f,c_Set_Ovimage(V_f,V_A,T_b,T_a),T_b,T_a),V_A,tc_fun(T_a,tc_bool)) ).
cnf(cls_complete__lattice_OSup__binary_0,axiom,
( hAPP(V_Sup,c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)) = hAPP(hAPP(V_sup,V_a),V_b)
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_complete__lattice_OInf__binary_0,axiom,
( hAPP(V_Inf,c_Set_Oinsert(V_a,c_Set_Oinsert(V_b,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a)) = hAPP(hAPP(V_inf,V_a),V_b)
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_complete__lattice_OSup__singleton_0,axiom,
( hAPP(V_Sup,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) = V_a
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_complete__lattice_OInf__singleton_0,axiom,
( hAPP(V_Inf,c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)) = V_a
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_rtrancl__Un__subset_0,axiom,
c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_bool)),c_Transitive__Closure_Ortrancl(V_R,T_a)),c_Transitive__Closure_Ortrancl(V_S,T_a)),c_Transitive__Closure_Ortrancl(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_bool)),V_R),V_S),T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) ).
cnf(cls_fun__left__comm_Ofold__fun__comm_0,axiom,
( hAPP(hAPP(V_f,V_x),c_Finite__Set_Ofold(V_f,V_z,V_A,T_a,T_b)) = c_Finite__Set_Ofold(V_f,hAPP(hAPP(V_f,V_x),V_z),V_A,T_a,T_b)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Finite__Set_Ofun__left__comm(V_f,T_a,T_b) ) ).
cnf(cls_trans__O__subset_0,axiom,
( c_lessequals(c_Relation_Orel__comp(V_r,V_r,T_a,T_a,T_a),V_r,tc_fun(tc_prod(T_a,T_a),tc_bool))
| ~ c_Relation_Otrans(V_r,T_a) ) ).
cnf(cls_Un__mono_0,axiom,
( c_lessequals(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),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_B,V_D,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_C,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_total__on__empty_0,axiom,
c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_r,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_fold__empty_0,axiom,
c_Finite__Set_Ofold(V_f,V_z,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a) = V_z ).
cnf(cls_subset__empty_1,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ).
cnf(cls_subset__empty_0,axiom,
( V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)) ) ).
cnf(cls_rtrancl__subset__rtrancl_0,axiom,
( c_lessequals(c_Transitive__Closure_Ortrancl(V_r,T_a),c_Transitive__Closure_Ortrancl(V_s,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool))
| ~ c_lessequals(V_r,c_Transitive__Closure_Ortrancl(V_s,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool)) ) ).
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_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
| c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
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
| ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool)) ) ).
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
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
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
| ~ c_lessequals(V_x,V_y,T_a) ) ).
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
| c_lessequals(V_x,V_y,T_a) ) ).
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
| ~ c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_order__antisym__conv_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| V_x = V_y
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_order__antisym_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| V_x = V_y
| ~ c_lessequals(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_order__eq__iff_2,axiom,
( ~ class_Orderings_Oorder(T_a)
| V_x = V_y
| ~ c_lessequals(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_set__eq__subset_2,axiom,
( V_A = V_B
| ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_equalityI_0,axiom,
( V_A = V_B
| ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_bot1E_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x)) ).
cnf(cls_Un__empty__right_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))) = V_A ).
cnf(cls_Un__empty__left_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),V_B) = V_B ).
cnf(cls_sup__bot__left_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ).
cnf(cls_sup__bot__right_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ).
cnf(cls_finite_OemptyI_0,axiom,
c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ).
cnf(cls_subset__insertI_0,axiom,
c_lessequals(V_B,c_Set_Oinsert(V_a,V_B,T_a),tc_fun(T_a,tc_bool)) ).
cnf(cls_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_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_rtrancl__mono_0,axiom,
( c_lessequals(c_Transitive__Closure_Ortrancl(V_r,T_a),c_Transitive__Closure_Ortrancl(V_s,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool))
| ~ c_lessequals(V_r,V_s,tc_fun(tc_prod(T_a,T_a),tc_bool)) ) ).
cnf(cls_insert__not__empty_0,axiom,
c_Set_Oinsert(V_a,V_A,T_a) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ).
cnf(cls_bot__least_0,axiom,
( ~ class_Orderings_Obot(T_a)
| c_lessequals(c_Orderings_Obot__class_Obot(T_a),V_x,T_a) ) ).
cnf(cls_empty__subsetI_0,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)) ).
cnf(cls_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_subset__insertI2_0,axiom,
( c_lessequals(V_A,c_Set_Oinsert(V_b,V_B,T_a),tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_insert__subset_1,axiom,
( c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_rel__comp__mono_0,axiom,
( c_lessequals(c_Relation_Orel__comp(V_r_H,V_s_H,T_a,T_b,T_c),c_Relation_Orel__comp(V_r,V_s,T_a,T_b,T_c),tc_fun(tc_prod(T_a,T_c),tc_bool))
| ~ c_lessequals(V_s_H,V_s,tc_fun(tc_prod(T_b,T_c),tc_bool))
| ~ c_lessequals(V_r_H,V_r,tc_fun(tc_prod(T_a,T_b),tc_bool)) ) ).
cnf(cls_doubleton__eq__iff_4,axiom,
c_Set_Oinsert(V_xa,c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) = c_Set_Oinsert(V_x,c_Set_Oinsert(V_xa,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a),T_a) ).
cnf(cls_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_Int__absorb2_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B) = V_A
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
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
| ~ c_lessequals(V_B,V_A,tc_fun(T_a,tc_bool)) ) ).
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
| ~ c_lessequals(V_x,V_y,T_a) ) ).
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
| c_lessequals(V_x,V_y,T_a) ) ).
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
| ~ c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_Un__subset__iff_2,axiom,
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_B,V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_C,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Un__upper2_0,axiom,
c_lessequals(V_B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),tc_fun(T_a,tc_bool)) ).
cnf(cls_Un__upper1_0,axiom,
c_lessequals(V_A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),tc_fun(T_a,tc_bool)) ).
cnf(cls_Un__least_0,axiom,
( c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_B,V_C,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_A,V_C,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_le__supI_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b),V_x,T_a)
| ~ c_lessequals(V_b,V_x,T_a)
| ~ c_lessequals(V_a,V_x,T_a) ) ).
cnf(cls_sup__ge1_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(V_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y),T_a) ) ).
cnf(cls_sup__ge2_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(V_y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y),T_a) ) ).
cnf(cls_sup__least_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z),V_x,T_a)
| ~ c_lessequals(V_z,V_x,T_a)
| ~ c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_le__sup__iff_2,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y),V_z,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_z,T_a) ) ).
cnf(cls_inf__sup__ord_I4_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_lessequals(V_y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y),T_a) ) ).
cnf(cls_inf__sup__ord_I3_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_lessequals(V_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y),T_a) ) ).
cnf(cls_rtrancl__subset_0,axiom,
( c_Transitive__Closure_Ortrancl(V_S,T_a) = c_Transitive__Closure_Ortrancl(V_R,T_a)
| ~ c_lessequals(V_S,c_Transitive__Closure_Ortrancl(V_R,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool))
| ~ c_lessequals(V_R,V_S,tc_fun(tc_prod(T_a,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_vimage__mono_0,axiom,
( c_lessequals(c_Set_Ovimage(V_f,V_A,T_b,T_a),c_Set_Ovimage(V_f,V_B,T_b,T_a),tc_fun(T_b,tc_bool))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Un__empty_1,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| V_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Un__empty_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))
| V_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)) ) ).
cnf(cls_sup__eq__bot__eq1_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_A),V_B) != c_Orderings_Obot__class_Obot(T_a)
| V_A = c_Orderings_Obot__class_Obot(T_a) ) ).
cnf(cls_sup__eq__bot__eq2_0,axiom,
( ~ class_Lattices_Obounded__lattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_A),V_B) != c_Orderings_Obot__class_Obot(T_a)
| V_B = c_Orderings_Obot__class_Obot(T_a) ) ).
cnf(cls_Int__subset__iff_1,axiom,
( c_lessequals(V_C,V_B,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_C,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),tc_fun(T_a,tc_bool)) ) ).
cnf(cls_Int__subset__iff_0,axiom,
( c_lessequals(V_C,V_A,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_C,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_B),tc_fun(T_a,tc_bool)) ) ).
cnf(cls_le__infE_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_a,T_a)
| ~ c_lessequals(V_x,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b),T_a) ) ).
cnf(cls_le__infE_1,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_b,T_a)
| ~ c_lessequals(V_x,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b),T_a) ) ).
cnf(cls_le__infI1_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b),V_x,T_a)
| ~ c_lessequals(V_a,V_x,T_a) ) ).
cnf(cls_le__infI2_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),V_b),V_x,T_a)
| ~ c_lessequals(V_b,V_x,T_a) ) ).
cnf(cls_le__inf__iff_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_x,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z),T_a) ) ).
cnf(cls_le__inf__iff_1,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_y),V_z),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_le__funD_0,axiom,
( ~ class_HOL_Oord(T_b)
| c_lessequals(hAPP(V_f,V_x),hAPP(V_g,V_x),T_b)
| ~ c_lessequals(V_f,V_g,tc_fun(T_a,T_b)) ) ).
cnf(cls_subset__iff_0,axiom,
( hBOOL(c_in(V_t,V_B,T_a))
| ~ hBOOL(c_in(V_t,V_A,T_a))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_set__rev__mp_0,axiom,
( hBOOL(c_in(V_x,V_B,T_a))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool))
| ~ hBOOL(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_subsetD_0,axiom,
( hBOOL(c_in(V_c,V_B,T_a))
| ~ hBOOL(c_in(V_c,V_A,T_a))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_set__mp_0,axiom,
( hBOOL(c_in(V_x,V_B,T_a))
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ c_lessequals(V_A,V_B,tc_fun(T_a,tc_bool)) ) ).
cnf(cls_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_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_fold__sup__insert_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_b,c_Set_Oinsert(V_a,V_A,T_a),T_a,T_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_b,V_A,T_a,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_fold__inf__insert_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_b,c_Set_Oinsert(V_a,V_A,T_a),T_a,T_a) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_a),c_Finite__Set_Ofold(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_b,V_A,T_a,T_a))
| ~ c_Finite__Set_Ofinite(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_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_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_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_fun__left__comm__idem_Ofold__insert__idem_0,axiom,
( c_Finite__Set_Ofold(V_f,V_z,c_Set_Oinsert(V_x,V_A,T_a),T_a,T_b) = hAPP(hAPP(V_f,V_x),c_Finite__Set_Ofold(V_f,V_z,V_A,T_a,T_b))
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Finite__Set_Ofun__left__comm__idem(V_f,T_a,T_b) ) ).
cnf(cls_fun__left__comm__idem_Ofold__insert__idem2_0,axiom,
( c_Finite__Set_Ofold(V_f,V_z,c_Set_Oinsert(V_x,V_A,T_a),T_a,T_b) = c_Finite__Set_Ofold(V_f,hAPP(hAPP(V_f,V_x),V_z),V_A,T_a,T_b)
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Finite__Set_Ofun__left__comm__idem(V_f,T_a,T_b) ) ).
cnf(cls_vimage__subsetD_0,axiom,
( c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,tc_bool))
| ~ c_lessequals(c_Set_Ovimage(V_f,V_B,T_a,T_b),V_A,tc_fun(T_a,tc_bool))
| ~ c_Fun_Osurj(V_f,T_a,T_b) ) ).
cnf(cls_vimage__subset__eq_1,axiom,
( c_lessequals(c_Set_Ovimage(V_f,V_B,T_a,T_b),V_A,tc_fun(T_a,tc_bool))
| ~ c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,tc_bool))
| ~ c_Fun_Obij(V_f,T_a,T_b) ) ).
cnf(cls_vimage__subset__eq_0,axiom,
( c_lessequals(V_B,c_Set_Oimage(V_f,V_A,T_a,T_b),tc_fun(T_b,tc_bool))
| ~ c_lessequals(c_Set_Ovimage(V_f,V_B,T_a,T_b),V_A,tc_fun(T_a,tc_bool))
| ~ c_Fun_Obij(V_f,T_a,T_b) ) ).
cnf(cls_refl__on__comp__subset_0,axiom,
( c_lessequals(V_r,c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(T_a,T_a),V_r),V_r,T_a,T_a,T_a),tc_fun(tc_prod(T_a,T_a),tc_bool))
| ~ c_Relation_Orefl__on(V_A,V_r,T_a) ) ).
cnf(cls_trancl__Int__subset_0,axiom,
( c_lessequals(c_Transitive__Closure_Otrancl(V_r,T_a),V_s,tc_fun(tc_prod(T_a,T_a),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_bool)),c_Transitive__Closure_Otrancl(V_r,T_a)),V_s),V_r,T_a,T_a,T_a),V_s,tc_fun(tc_prod(T_a,T_a),tc_bool))
| ~ c_lessequals(V_r,V_s,tc_fun(tc_prod(T_a,T_a),tc_bool)) ) ).
cnf(cls_sym__Id__on_0,axiom,
c_Relation_Osym(c_Relation_OId__on(V_A,T_a),T_a) ).
cnf(cls_trancl__reflcl_0,axiom,
c_Transitive__Closure_Otrancl(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_bool)),V_r),c_Relation_OId(T_a)),T_a) = c_Transitive__Closure_Ortrancl(V_r,T_a) ).
cnf(cls_refl__on__Id__on_0,axiom,
c_Relation_Orefl__on(V_A,c_Relation_OId__on(V_A,T_a),T_a) ).
cnf(cls_r__comp__rtrancl__eq_0,axiom,
c_Relation_Orel__comp(V_r,c_Transitive__Closure_Ortrancl(V_r,T_a),T_a,T_a,T_a) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(V_r,T_a),V_r,T_a,T_a,T_a) ).
cnf(cls_antisym__reflcl_0,axiom,
( c_Relation_Oantisym(V_r,T_a)
| ~ c_Relation_Oantisym(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_bool)),V_r),c_Relation_OId(T_a)),T_a) ) ).
cnf(cls_antisym__reflcl_1,axiom,
( c_Relation_Oantisym(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_bool)),V_r),c_Relation_OId(T_a)),T_a)
| ~ c_Relation_Oantisym(V_r,T_a) ) ).
cnf(cls_fun__left__comm_Ofun__left__comm_0,axiom,
( hAPP(hAPP(V_f,V_x),hAPP(hAPP(V_f,V_y),V_z)) = hAPP(hAPP(V_f,V_y),hAPP(hAPP(V_f,V_x),V_z))
| ~ c_Finite__Set_Ofun__left__comm(V_f,T_a,T_b) ) ).
cnf(cls_rtrancl__reflcl_0,axiom,
c_Transitive__Closure_Ortrancl(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_bool)),V_R),c_Relation_OId(T_a)),T_a) = c_Transitive__Closure_Ortrancl(V_R,T_a) ).
cnf(cls_sym__inv__image_0,axiom,
( c_Relation_Osym(c_Relation_Oinv__image(V_r,V_f,T_a,T_b),T_b)
| ~ c_Relation_Osym(V_r,T_a) ) ).
cnf(cls_rtrancl__trancl__absorb_0,axiom,
c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(V_R,T_a),T_a) = c_Transitive__Closure_Ortrancl(V_R,T_a) ).
cnf(cls_reflcl__trancl_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_bool)),c_Transitive__Closure_Otrancl(V_r,T_a)),c_Relation_OId(T_a)) = c_Transitive__Closure_Ortrancl(V_r,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_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_isomorphic__tuple_Oiso__tuple__access__update__snd__fst_0,axiom,
( c_Fun_Ocomp(c_Fun_Ocomp(V_f,c_Record_Oiso__tuple__snd(V_isom,T_a,T_b,T_c),T_c,T_d,T_a),hAPP(c_Fun_Ocomp(c_Record_Oiso__tuple__fst__update(V_isom,T_a,T_b,T_c),V_h,tc_fun(T_b,T_b),tc_fun(T_a,T_a),T_e),V_g),T_a,T_d,T_a) = c_Fun_Ocomp(c_Fun_Oid(T_d),c_Fun_Ocomp(V_f,c_Record_Oiso__tuple__snd(V_isom,T_a,T_b,T_c),T_c,T_d,T_a),T_d,T_d,T_a)
| ~ c_Record_Oisomorphic__tuple(V_isom,T_a,T_b,T_c) ) ).
cnf(cls_isomorphic__tuple_Oiso__tuple__access__update__fst__snd_0,axiom,
( c_Fun_Ocomp(c_Fun_Ocomp(V_f,c_Record_Oiso__tuple__fst(V_isom,T_a,T_b,T_c),T_b,T_d,T_a),hAPP(c_Fun_Ocomp(c_Record_Oiso__tuple__snd__update(V_isom,T_a,T_b,T_c),V_h,tc_fun(T_c,T_c),tc_fun(T_a,T_a),T_e),V_g),T_a,T_d,T_a) = c_Fun_Ocomp(c_Fun_Oid(T_d),c_Fun_Ocomp(V_f,c_Record_Oiso__tuple__fst(V_isom,T_a,T_b,T_c),T_b,T_d,T_a),T_d,T_d,T_a)
| ~ c_Record_Oisomorphic__tuple(V_isom,T_a,T_b,T_c) ) ).
cnf(cls_isomorphic__tuple_Oiso__tuple__access__update__fst__fst_0,axiom,
( c_Fun_Ocomp(V_f,hAPP(V_h,V_g),T_b,T_d,T_b) != c_Fun_Ocomp(V_j,V_f,T_d,T_d,T_b)
| ~ c_Record_Oisomorphic__tuple(V_isom,T_a,T_b,T_c)
| c_Fun_Ocomp(c_Fun_Ocomp(V_f,c_Record_Oiso__tuple__fst(V_isom,T_a,T_b,T_c),T_b,T_d,T_a),hAPP(c_Fun_Ocomp(c_Record_Oiso__tuple__fst__update(V_isom,T_a,T_b,T_c),V_h,tc_fun(T_b,T_b),tc_fun(T_a,T_a),T_e),V_g),T_a,T_d,T_a) = c_Fun_Ocomp(V_j,c_Fun_Ocomp(V_f,c_Record_Oiso__tuple__fst(V_isom,T_a,T_b,T_c),T_b,T_d,T_a),T_d,T_d,T_a) ) ).
cnf(cls_isomorphic__tuple_Oiso__tuple__access__update__snd__snd_0,axiom,
( c_Fun_Ocomp(V_f,hAPP(V_h,V_g),T_c,T_d,T_c) != c_Fun_Ocomp(V_j,V_f,T_d,T_d,T_c)
| ~ c_Record_Oisomorphic__tuple(V_isom,T_a,T_b,T_c)
| c_Fun_Ocomp(c_Fun_Ocomp(V_f,c_Record_Oiso__tuple__snd(V_isom,T_a,T_b,T_c),T_c,T_d,T_a),hAPP(c_Fun_Ocomp(c_Record_Oiso__tuple__snd__update(V_isom,T_a,T_b,T_c),V_h,tc_fun(T_c,T_c),tc_fun(T_a,T_a),T_e),V_g),T_a,T_d,T_a) = c_Fun_Ocomp(V_j,c_Fun_Ocomp(V_f,c_Record_Oiso__tuple__snd(V_isom,T_a,T_b,T_c),T_c,T_d,T_a),T_d,T_d,T_a) ) ).
cnf(cls_rtrancl__Int__subset_0,axiom,
( c_lessequals(c_Transitive__Closure_Ortrancl(V_r,T_a),V_s,tc_fun(tc_prod(T_a,T_a),tc_bool))
| ~ c_lessequals(c_Relation_Orel__comp(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_bool)),c_Transitive__Closure_Ortrancl(V_r,T_a)),V_s),V_r,T_a,T_a,T_a),V_s,tc_fun(tc_prod(T_a,T_a),tc_bool))
| ~ c_lessequals(c_Relation_OId(T_a),V_s,tc_fun(tc_prod(T_a,T_a),tc_bool)) ) ).
cnf(cls_sym__trans__comp__subset_0,axiom,
( c_lessequals(c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(T_a,T_a),V_r),V_r,T_a,T_a,T_a),V_r,tc_fun(tc_prod(T_a,T_a),tc_bool))
| ~ c_Relation_Otrans(V_r,T_a)
| ~ c_Relation_Osym(V_r,T_a) ) ).
cnf(cls_funcset__image_0,axiom,
( c_lessequals(c_Set_Oimage(V_f,V_A,T_a,T_b),V_B,tc_fun(T_b,tc_bool))
| ~ hBOOL(c_in(V_f,c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b),tc_fun(T_a,T_b))) ) ).
cnf(cls_fun__left__comm_Ofold__insert2_0,axiom,
( c_Finite__Set_Ofold(V_f,V_z,c_Set_Oinsert(V_x,V_A,T_a),T_a,T_b) = c_Finite__Set_Ofold(V_f,hAPP(hAPP(V_f,V_x),V_z),V_A,T_a,T_b)
| hBOOL(c_in(V_x,V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Finite__Set_Ofun__left__comm(V_f,T_a,T_b) ) ).
cnf(cls_fun__left__comm_Ofold__insert_0,axiom,
( c_Finite__Set_Ofold(V_f,V_z,c_Set_Oinsert(V_x,V_A,T_a),T_a,T_b) = hAPP(hAPP(V_f,V_x),c_Finite__Set_Ofold(V_f,V_z,V_A,T_a,T_b))
| hBOOL(c_in(V_x,V_A,T_a))
| ~ c_Finite__Set_Ofinite(V_A,T_a)
| ~ c_Finite__Set_Ofun__left__comm(V_f,T_a,T_b) ) ).
cnf(cls_funcsetI_0,axiom,
( hBOOL(c_in(V_f,c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b),tc_fun(T_a,T_b)))
| hBOOL(c_in(c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(V_A,V_B,V_f,T_a,T_b),V_A,T_a)) ) ).
cnf(cls_funcsetI_1,axiom,
( hBOOL(c_in(V_f,c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b),tc_fun(T_a,T_b)))
| ~ hBOOL(c_in(hAPP(V_f,c_FuncSet_Osko__FuncSet__XfuncsetI__1__1(V_A,V_B,V_f,T_a,T_b)),V_B,T_b)) ) ).
cnf(cls_image__constant_0,axiom,
( c_Set_Oimage(c_COMBK(V_c,T_b,T_a),V_A,T_a,T_b) = c_Set_Oinsert(V_c,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b)
| ~ hBOOL(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_finite__trancl_1,axiom,
( c_Finite__Set_Ofinite(c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_Finite__Set_Ofinite(V_r,tc_prod(T_a,T_a)) ) ).
cnf(cls_finite__trancl_0,axiom,
( c_Finite__Set_Ofinite(V_r,tc_prod(T_a,T_a))
| ~ c_Finite__Set_Ofinite(c_Transitive__Closure_Otrancl(V_r,T_a),tc_prod(T_a,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_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_linear__order__on__def_2,axiom,
( c_Order__Relation_Olinear__order__on(V_A,V_r,T_a)
| ~ c_Relation_Ototal__on(V_A,V_r,T_a)
| ~ c_Order__Relation_Opartial__order__on(V_A,V_r,T_a) ) ).
cnf(cls_swap__nilpotent_0,axiom,
c_Fun_Oswap(V_a,V_b,c_Fun_Oswap(V_a,V_b,V_f,T_a,T_b),T_a,T_b) = V_f ).
cnf(cls_swap__commute_0,axiom,
c_Fun_Oswap(V_a,V_b,V_f,T_a,T_b) = c_Fun_Oswap(V_b,V_a,V_f,T_a,T_b) ).
cnf(cls_Un__absorb_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_A) = V_A ).
cnf(cls_sup__idem_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_x) = V_x ) ).
cnf(cls_trans__trancl_0,axiom,
c_Relation_Otrans(c_Transitive__Closure_Otrancl(V_r,T_a),T_a) ).
cnf(cls_Nitpick_Ortrancl__def_0,axiom,
c_Transitive__Closure_Ortrancl(V_r,T_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_bool)),c_Transitive__Closure_Otrancl(V_r,T_a)),c_Relation_OId(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_COMBK__def_0,axiom,
hAPP(c_COMBK(V_P,T_a,T_b),V_Q) = V_P ).
cnf(cls_Un__left__commute_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_C)) ).
cnf(cls_Un__assoc_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)) ).
cnf(cls_sup__assoc_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z)) ) ).
cnf(cls_sup__left__commute_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_z)) ) ).
cnf(cls_inf__sup__aci_I7_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_z)) ) ).
cnf(cls_inf__sup__aci_I6_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z)) ) ).
cnf(cls_rtrancl__reflcl__absorb_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_bool)),c_Transitive__Closure_Ortrancl(V_R,T_a)),c_Relation_OId(T_a)) = c_Transitive__Closure_Ortrancl(V_R,T_a) ).
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_sym__rtrancl_0,axiom,
( c_Relation_Osym(c_Transitive__Closure_Ortrancl(V_r,T_a),T_a)
| ~ c_Relation_Osym(V_r,T_a) ) ).
cnf(cls_partial__order__on__def_2,axiom,
( c_Order__Relation_Opartial__order__on(V_A,V_r,T_a)
| ~ c_Relation_Oantisym(V_r,T_a)
| ~ c_Order__Relation_Opreorder__on(V_A,V_r,T_a) ) ).
cnf(cls_dictator__def_2,axiom,
( hAPP(V_F,v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(V_F,V_i)) != hAPP(v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(V_F,V_i),V_i)
| c_Arrow__Order__Mirabelle_Odictator(V_F,V_i) ) ).
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_swap__triple_0,axiom,
( c_Fun_Oswap(V_a,V_b,c_Fun_Oswap(V_b,V_c,c_Fun_Oswap(V_a,V_b,V_f,T_a,T_b),T_a,T_b),T_a,T_b) = c_Fun_Oswap(V_a,V_c,V_f,T_a,T_b)
| V_b = V_c
| V_a = V_c ) ).
cnf(cls_bij__id_0,axiom,
c_Fun_Obij(c_Fun_Oid(T_a),T_a,T_a) ).
cnf(cls_partial__order__on__def_0,axiom,
( c_Order__Relation_Opreorder__on(V_A,V_r,T_a)
| ~ c_Order__Relation_Opartial__order__on(V_A,V_r,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_antisym__Id__on_0,axiom,
c_Relation_Oantisym(c_Relation_OId__on(V_A,T_a),T_a) ).
cnf(cls_R__O__Id_0,axiom,
c_Relation_Orel__comp(V_R,c_Relation_OId(T_b),T_a,T_b,T_b) = V_R ).
cnf(cls_Id__O__R_0,axiom,
c_Relation_Orel__comp(c_Relation_OId(T_a),V_R,T_a,T_a,T_b) = V_R ).
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_finite__Field_0,axiom,
( c_Finite__Set_Ofinite(c_Relation_OField(V_r,T_a),T_a)
| ~ c_Finite__Set_Ofinite(V_r,tc_prod(T_a,T_a)) ) ).
cnf(cls_apsnd__apfst__commute_0,axiom,
c_Product__Type_Oapsnd(V_f,c_Product__Type_Oapfst(V_g,V_p,T_d,T_a,T_c),T_c,T_b,T_a) = c_Product__Type_Oapfst(V_g,c_Product__Type_Oapsnd(V_f,V_p,T_c,T_b,T_d),T_d,T_a,T_b) ).
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_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_UN__o_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,c_Fun_Ocomp(V_g,V_f,T_c,tc_fun(T_a,tc_bool),T_b),T_b,tc_fun(T_a,tc_bool)) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oimage(V_f,V_A,T_b,T_c),V_g,T_c,tc_fun(T_a,tc_bool)) ).
cnf(cls_rel__comp__distrib2_0,axiom,
c_Relation_Orel__comp(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_prod(T_a,T_c),tc_bool)),V_S),V_T),V_R,T_a,T_c,T_b) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_bool)),c_Relation_Orel__comp(V_S,V_R,T_a,T_c,T_b)),c_Relation_Orel__comp(V_T,V_R,T_a,T_c,T_b)) ).
cnf(cls_rel__comp__distrib_0,axiom,
c_Relation_Orel__comp(V_R,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_bool)),V_S),V_T),T_a,T_c,T_b) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_bool)),c_Relation_Orel__comp(V_R,V_S,T_a,T_c,T_b)),c_Relation_Orel__comp(V_R,V_T,T_a,T_c,T_b)) ).
cnf(cls_trans__Id__on_0,axiom,
c_Relation_Otrans(c_Relation_OId__on(V_A,T_a),T_a) ).
cnf(cls_Field__Un_0,axiom,
c_Relation_OField(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_bool)),V_r),V_s),T_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Relation_OField(V_r,T_a)),c_Relation_OField(V_s,T_a)) ).
cnf(cls_vimage__id_0,axiom,
c_Set_Ovimage(c_Fun_Oid(T_a),V_A,T_a,T_a) = V_A ).
cnf(cls_sym__Id_0,axiom,
c_Relation_Osym(c_Relation_OId(T_a),T_a) ).
cnf(cls_bij__betw__imp__funcset_0,axiom,
( hBOOL(c_in(V_f,c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b),tc_fun(T_a,T_b)))
| ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b) ) ).
cnf(cls_finite__vimage__iff_1,axiom,
( c_Finite__Set_Ofinite(c_Set_Ovimage(V_h,V_F,T_a,T_b),T_a)
| ~ c_Finite__Set_Ofinite(V_F,T_b)
| ~ c_Fun_Obij(V_h,T_a,T_b) ) ).
cnf(cls_finite__vimage__iff_0,axiom,
( c_Finite__Set_Ofinite(V_F,T_b)
| ~ c_Finite__Set_Ofinite(c_Set_Ovimage(V_h,V_F,T_a,T_b),T_a)
| ~ c_Fun_Obij(V_h,T_a,T_b) ) ).
cnf(cls_surj__swap__iff_1,axiom,
( c_Fun_Osurj(c_Fun_Oswap(V_a,V_b,V_f,T_a,T_b),T_a,T_b)
| ~ c_Fun_Osurj(V_f,T_a,T_b) ) ).
cnf(cls_surj__swap__iff_0,axiom,
( c_Fun_Osurj(V_f,T_a,T_b)
| ~ c_Fun_Osurj(c_Fun_Oswap(V_a,V_b,V_f,T_a,T_b),T_a,T_b) ) ).
cnf(cls_Un__commute_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_A) ).
cnf(cls_sup__commute_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_x) ) ).
cnf(cls_inf__sup__aci_I5_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_x) ) ).
cnf(cls_image__id_0,axiom,
c_Set_Oimage(c_Fun_Oid(T_a),V_Y,T_a,T_a) = 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_sup__left__idem_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) ) ).
cnf(cls_inf__sup__aci_I8_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y) ) ).
cnf(cls_surj__id_0,axiom,
c_Fun_Osurj(c_Fun_Oid(T_a),T_a,T_a) ).
cnf(cls_sym__Un__converse_0,axiom,
c_Relation_Osym(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_bool)),V_r),hAPP(c_Relation_Oconverse(T_a,T_a),V_r)),T_a) ).
cnf(cls_finite_0,axiom,
( ~ class_Finite__Set_Ofinite_Ofinite(T_a)
| c_Finite__Set_Ofinite(V_A,T_a) ) ).
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_rtrancl__Un__rtrancl_0,axiom,
c_Transitive__Closure_Ortrancl(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_bool)),c_Transitive__Closure_Ortrancl(V_R,T_a)),c_Transitive__Closure_Ortrancl(V_S,T_a)),T_a) = c_Transitive__Closure_Ortrancl(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_bool)),V_R),V_S),T_a) ).
cnf(cls_iso__tuple__update__accessor__cong__assist__id_0,axiom,
( hAPP(V_upd,c_Fun_Oid(T_a)) = c_Fun_Oid(T_b)
| ~ c_Record_Oiso__tuple__update__accessor__cong__assist(V_upd,V_acc,T_a,T_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_sym__Int_0,axiom,
( c_Relation_Osym(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_bool)),V_r),V_s),T_a)
| ~ c_Relation_Osym(V_s,T_a)
| ~ c_Relation_Osym(V_r,T_a) ) ).
cnf(cls_trancl__id_0,axiom,
( c_Transitive__Closure_Otrancl(V_r,T_a) = V_r
| ~ c_Relation_Otrans(V_r,T_a) ) ).
cnf(cls_sym__trancl_0,axiom,
( c_Relation_Osym(c_Transitive__Closure_Otrancl(V_r,T_a),T_a)
| ~ c_Relation_Osym(V_r,T_a) ) ).
cnf(cls_id__apply_0,axiom,
hAPP(c_Fun_Oid(T_a),V_x) = V_x ).
cnf(cls_trancl__unfold_0,axiom,
c_Transitive__Closure_Otrancl(V_r,T_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_bool)),V_r),c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(V_r,T_a),V_r,T_a,T_a,T_a)) ).
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_fun__left__comm__idem__inf_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Olower__semilattice__class_Oinf(T_a),T_a,T_a) ) ).
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_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_ord_OatLeastLessThan__iff_2,axiom,
( hBOOL(c_in(V_i,c_SetInterval_Oord_OatLeastLessThan(V_less__eq,V_less,V_l,V_u,T_a),T_a))
| ~ hBOOL(hAPP(hAPP(V_less,V_i),V_u))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_l),V_i)) ) ).
cnf(cls_insert__iff_2,axiom,
( hBOOL(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_ord_OatLeastAtMost__iff_2,axiom,
( hBOOL(c_in(V_i,c_SetInterval_Oord_OatLeastAtMost(V_less__eq,V_l,V_u,T_a),T_a))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_i),V_u))
| ~ hBOOL(hAPP(hAPP(V_less__eq,V_l),V_i)) ) ).
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_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_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_bexE_1,axiom,
( hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__XbexE__1__1(V_A,V_P,T_a)))
| ~ hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(c_in(V_x,V_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_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_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_UN__iff_2,axiom,
( hBOOL(c_in(V_b,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_b,tc_fun(T_a,tc_bool)),T_a))
| ~ hBOOL(c_in(V_b,hAPP(V_B,V_x),T_a))
| ~ hBOOL(c_in(V_x,V_A,T_b)) ) ).
cnf(cls_UN__I_0,axiom,
( hBOOL(c_in(V_b,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_bool)),T_b))
| ~ hBOOL(c_in(V_b,hAPP(V_B,V_a),T_b))
| ~ hBOOL(c_in(V_a,V_A,T_a)) ) ).
cnf(cls_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_trans__rtrancl_0,axiom,
c_Relation_Otrans(c_Transitive__Closure_Ortrancl(V_r,T_a),T_a) ).
cnf(cls_fun__left__comm__idem__sup_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Oupper__semilattice__class_Osup(T_a),T_a,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_insert__absorb2_0,axiom,
c_Set_Oinsert(V_x,c_Set_Oinsert(V_x,V_A,T_a),T_a) = c_Set_Oinsert(V_x,V_A,T_a) ).
cnf(cls_swap__self_0,axiom,
c_Fun_Oswap(V_a,V_a,V_f,T_a,T_b) = V_f ).
cnf(cls_O__assoc_0,axiom,
c_Relation_Orel__comp(c_Relation_Orel__comp(V_R,V_S,T_a,T_d,T_c),V_T,T_a,T_c,T_b) = c_Relation_Orel__comp(V_R,c_Relation_Orel__comp(V_S,V_T,T_d,T_c,T_b),T_a,T_d,T_b) ).
cnf(cls_finite__UN_0,axiom,
( c_Finite__Set_Ofinite(hAPP(V_B,V_x),T_b)
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_bool)),T_b)
| ~ c_Finite__Set_Ofinite(V_A,T_a) ) ).
cnf(cls_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_sym__Un_0,axiom,
( c_Relation_Osym(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_bool)),V_r),V_s),T_a)
| ~ c_Relation_Osym(V_s,T_a)
| ~ c_Relation_Osym(V_r,T_a) ) ).
cnf(cls_finite__vimageD_0,axiom,
( c_Finite__Set_Ofinite(V_F,T_b)
| ~ c_Fun_Osurj(V_h,T_a,T_b)
| ~ c_Finite__Set_Ofinite(c_Set_Ovimage(V_h,V_F,T_a,T_b),T_a) ) ).
cnf(cls_K__record__comp_0,axiom,
hAPP(c_Fun_Ocomp(c_COMBK(V_c,T_b,T_c),V_f,T_c,T_b,t_a),v_x) = V_c ).
cnf(cls_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_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_trans__inv__image_0,axiom,
( c_Relation_Otrans(c_Relation_Oinv__image(V_r,V_f,T_a,T_b),T_b)
| ~ c_Relation_Otrans(V_r,T_a) ) ).
cnf(cls_isomorphic__tuple_Oiso__tuple__update__swap__fst__snd_0,axiom,
( c_Fun_Ocomp(hAPP(c_Fun_Ocomp(c_Record_Oiso__tuple__snd__update(V_isom,T_a,T_b,T_c),V_h,tc_fun(T_c,T_c),tc_fun(T_a,T_a),T_d),V_f),hAPP(c_Fun_Ocomp(c_Record_Oiso__tuple__fst__update(V_isom,T_a,T_b,T_c),V_j,tc_fun(T_b,T_b),tc_fun(T_a,T_a),T_e),V_g),T_a,T_a,T_a) = c_Fun_Ocomp(hAPP(c_Fun_Ocomp(c_Record_Oiso__tuple__fst__update(V_isom,T_a,T_b,T_c),V_j,tc_fun(T_b,T_b),tc_fun(T_a,T_a),T_e),V_g),hAPP(c_Fun_Ocomp(c_Record_Oiso__tuple__snd__update(V_isom,T_a,T_b,T_c),V_h,tc_fun(T_c,T_c),tc_fun(T_a,T_a),T_d),V_f),T_a,T_a,T_a)
| ~ c_Record_Oisomorphic__tuple(V_isom,T_a,T_b,T_c) ) ).
cnf(cls_iso__tuple__update__accessor__cong__assist__def_0,axiom,
( hAPP(hAPP(V_upd,c_COMBK(hAPP(V_f,hAPP(V_acc,V_va)),T_a,T_a)),V_va) = hAPP(hAPP(V_upd,V_f),V_va)
| ~ c_Record_Oiso__tuple__update__accessor__cong__assist(V_upd,V_acc,T_a,T_b) ) ).
cnf(cls_UN__absorb_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_b,tc_bool)),hAPP(V_A,V_k)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_I,V_A,T_a,tc_fun(T_b,tc_bool))) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_I,V_A,T_a,tc_fun(T_b,tc_bool))
| ~ hBOOL(c_in(V_k,V_I,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__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_antisym__Id_0,axiom,
c_Relation_Oantisym(c_Relation_OId(T_a),T_a) ).
cnf(cls_surj__image__vimage__eq_0,axiom,
( c_Set_Oimage(V_f,c_Set_Ovimage(V_f,V_A,T_a,T_b),T_a,T_b) = V_A
| ~ c_Fun_Osurj(V_f,T_a,T_b) ) ).
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_trans__reflclI_0,axiom,
( c_Relation_Otrans(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_bool)),V_r),c_Relation_OId(T_a)),T_a)
| ~ c_Relation_Otrans(V_r,T_a) ) ).
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_rtrancl__unfold_0,axiom,
c_Transitive__Closure_Ortrancl(V_r,T_a) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_bool)),c_Relation_OId(T_a)),c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(V_r,T_a),V_r,T_a,T_a,T_a)) ).
cnf(cls_partial__order__on__def_1,axiom,
( c_Relation_Oantisym(V_r,T_a)
| ~ c_Order__Relation_Opartial__order__on(V_A,V_r,T_a) ) ).
cnf(cls_refl__on__Un_0,axiom,
( c_Relation_Orefl__on(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(tc_prod(T_a,T_a),tc_bool)),V_r),V_s),T_a)
| ~ c_Relation_Orefl__on(V_B,V_s,T_a)
| ~ c_Relation_Orefl__on(V_A,V_r,T_a) ) ).
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_id__def_0,axiom,
hAPP(c_Fun_Oid(t_a),v_x) = v_x ).
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__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_trans__Id_0,axiom,
c_Relation_Otrans(c_Relation_OId(T_a),T_a) ).
cnf(cls_rtrancl__idemp__self__comp_0,axiom,
c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(V_R,T_a),c_Transitive__Closure_Ortrancl(V_R,T_a),T_a,T_a,T_a) = c_Transitive__Closure_Ortrancl(V_R,T_a) ).
cnf(cls_bij__def_1,axiom,
( c_Fun_Osurj(V_f,T_a,T_b)
| ~ c_Fun_Obij(V_f,T_a,T_b) ) ).
cnf(cls_fun__upd__upd_0,axiom,
c_Fun_Ofun__upd(c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_b),V_x,V_z,T_a,T_b) = c_Fun_Ofun__upd(V_f,V_x,V_z,T_a,T_b) ).
cnf(cls_trans__Int_0,axiom,
( c_Relation_Otrans(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_bool)),V_r),V_s),T_a)
| ~ c_Relation_Otrans(V_s,T_a)
| ~ c_Relation_Otrans(V_r,T_a) ) ).
cnf(cls_acyclic__impl__antisym__rtrancl_0,axiom,
( c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(V_r,T_a),T_a)
| ~ c_Wellfounded_Oacyclic(V_r,T_a) ) ).
cnf(cls_linear__order__on__def_0,axiom,
( c_Order__Relation_Opartial__order__on(V_A,V_r,T_a)
| ~ c_Order__Relation_Olinear__order__on(V_A,V_r,T_a) ) ).
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_extensionalityI_1,axiom,
( hAPP(V_f,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(V_A,V_f,V_g,T_a,T_b)) != hAPP(V_g,c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(V_A,V_f,V_g,T_a,T_b))
| ~ hBOOL(c_in(V_g,c_FuncSet_Oextensional(V_A,T_a,T_b),tc_fun(T_a,T_b)))
| ~ hBOOL(c_in(V_f,c_FuncSet_Oextensional(V_A,T_a,T_b),tc_fun(T_a,T_b)))
| V_f = V_g ) ).
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_refl__on__Int_0,axiom,
( c_Relation_Orefl__on(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(tc_prod(T_a,T_a),tc_bool)),V_r),V_s),T_a)
| ~ c_Relation_Orefl__on(V_B,V_s,T_a)
| ~ c_Relation_Orefl__on(V_A,V_r,T_a) ) ).
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_preorder__on__def_1,axiom,
( c_Relation_Otrans(V_r,T_a)
| ~ c_Order__Relation_Opreorder__on(V_A,V_r,T_a) ) ).
cnf(cls_UN__insert_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(V_a,V_A,T_b),V_B,T_b,tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(V_B,V_a)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_b,tc_fun(T_a,tc_bool))) ).
cnf(cls_bij__swap__iff_0,axiom,
( c_Fun_Obij(V_f,T_a,T_b)
| ~ c_Fun_Obij(c_Fun_Oswap(V_a,V_b,V_f,T_a,T_b),T_a,T_b) ) ).
cnf(cls_bij__swap__iff_1,axiom,
( c_Fun_Obij(c_Fun_Oswap(V_a,V_b,V_f,T_a,T_b),T_a,T_b)
| ~ c_Fun_Obij(V_f,T_a,T_b) ) ).
cnf(cls_swap__def_0,axiom,
c_Fun_Oswap(V_a,V_b,V_f,T_a,T_b) = c_Fun_Ofun__upd(c_Fun_Ofun__upd(V_f,V_a,hAPP(V_f,V_b),T_a,T_b),V_b,hAPP(V_f,V_a),T_a,T_b) ).
cnf(cls_fun__upd__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_bex__Un_4,axiom,
( hBOOL(c_in(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(V_A,V_B,V_P,T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),T_a))
| ~ hBOOL(hAPP(V_P,V_xa))
| ~ hBOOL(c_in(V_xa,V_A,T_a)) ) ).
cnf(cls_bex__Un_6,axiom,
( hBOOL(c_in(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(V_A,V_B,V_P,T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),T_a))
| ~ hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(c_in(V_x,V_B,T_a)) ) ).
cnf(cls_linear__order__on__def_1,axiom,
( c_Relation_Ototal__on(V_A,V_r,T_a)
| ~ c_Order__Relation_Olinear__order__on(V_A,V_r,T_a) ) ).
cnf(cls_iso__tuple__update__accessor__cong__assist__def_1,axiom,
( hAPP(hAPP(V_upd,c_Fun_Oid(T_a)),V_v) = V_v
| ~ c_Record_Oiso__tuple__update__accessor__cong__assist(V_upd,V_acc,T_a,T_b) ) ).
cnf(cls_complete__lattice_OSup__insert_0,axiom,
( hAPP(V_Sup,c_Set_Oinsert(V_a,V_A,T_a)) = hAPP(hAPP(V_sup,V_a),hAPP(V_Sup,V_A))
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_complete__lattice_OInf__insert_0,axiom,
( hAPP(V_Inf,c_Set_Oinsert(V_a,V_A,T_a)) = hAPP(hAPP(V_inf,V_a),hAPP(V_Inf,V_A))
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_update__accessor__congruence__foldE_0,axiom,
( hAPP(V_f,hAPP(V_acc,V_x)) != hAPP(V_f_H,hAPP(V_acc,V_x))
| ~ c_Record_Oiso__tuple__update__accessor__cong__assist(V_upd,V_acc,T_a,T_aa)
| hAPP(hAPP(V_upd,V_f),V_x) = hAPP(hAPP(V_upd,V_f_H),V_x) ) ).
cnf(cls_update__accessor__noopE_0,axiom,
( hAPP(V_f,hAPP(V_acc,V_x)) != hAPP(V_acc,V_x)
| ~ c_Record_Oiso__tuple__update__accessor__cong__assist(V_upd,V_acc,T_a,T_b)
| hAPP(hAPP(V_upd,V_f),V_x) = V_x ) ).
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_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_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_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_insert__code_1,axiom,
hBOOL(hAPP(c_Set_Oinsert(V_x,V_A,T_a),V_x)) ).
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_fun__left__comm__idem_Ofun__left__idem_0,axiom,
( hAPP(hAPP(V_f,V_x),hAPP(hAPP(V_f,V_x),V_z)) = hAPP(hAPP(V_f,V_x),V_z)
| ~ c_Finite__Set_Ofun__left__comm__idem(V_f,T_a,T_b) ) ).
cnf(cls_bij__betw__def_1,axiom,
( c_Set_Oimage(V_f,V_A,T_a,T_b) = V_B
| ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b) ) ).
cnf(cls_inf__idem_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_a),V_x),V_x) = V_x ) ).
cnf(cls_Int__absorb_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),V_A) = V_A ).
cnf(cls_inf__fun__eq_0,axiom,
( ~ class_Lattices_Olattice(T_b)
| hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(t_a,T_b)),V_f),V_g),v_x) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(T_b),hAPP(V_f,v_x)),hAPP(V_g,v_x)) ) ).
cnf(cls_preorder__on__def_0,axiom,
( c_Relation_Orefl__on(V_A,V_r,T_a)
| ~ c_Order__Relation_Opreorder__on(V_A,V_r,T_a) ) ).
cnf(cls_trancl__unfold__right_0,axiom,
c_Transitive__Closure_Otrancl(V_r,T_a) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(V_r,T_a),V_r,T_a,T_a,T_a) ).
cnf(cls_trancl__unfold__left_0,axiom,
c_Transitive__Closure_Otrancl(V_r,T_a) = c_Relation_Orel__comp(V_r,c_Transitive__Closure_Ortrancl(V_r,T_a),T_a,T_a,T_a) ).
cnf(cls_UN__Un_0,axiom,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_b,tc_bool)),V_A),V_B),V_M,T_b,tc_fun(T_a,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_M,T_b,tc_fun(T_a,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_B,V_M,T_b,tc_fun(T_a,tc_bool))) ).
cnf(cls_vimage__code_0,axiom,
( hBOOL(hAPP(V_A,hAPP(V_f,V_x)))
| ~ hBOOL(hAPP(c_Set_Ovimage(V_f,V_A,T_a,T_b),V_x)) ) ).
cnf(cls_vimage__code_1,axiom,
( hBOOL(hAPP(c_Set_Ovimage(V_f,V_A,T_a,T_b),V_x))
| ~ hBOOL(hAPP(V_A,hAPP(V_f,V_x))) ) ).
cnf(cls_inf1I_0,axiom,
( hBOOL(hAPP(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_sym__Int__converse_0,axiom,
c_Relation_Osym(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_bool)),V_r),hAPP(c_Relation_Oconverse(T_a,T_a),V_r)),T_a) ).
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_trancl__rtrancl__absorb_0,axiom,
c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(V_R,T_a),T_a) = c_Transitive__Closure_Ortrancl(V_R,T_a) ).
cnf(cls_preorder__on__def_2,axiom,
( c_Order__Relation_Opreorder__on(V_A,V_r,T_a)
| ~ c_Relation_Otrans(V_r,T_a)
| ~ c_Relation_Orefl__on(V_A,V_r,T_a) ) ).
cnf(cls_rtrancl__idemp_0,axiom,
c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(V_r,T_a),T_a) = c_Transitive__Closure_Ortrancl(V_r,T_a) ).
cnf(cls_isomorphic__tuple_Oiso__tuple__update__swap__snd__fst_0,axiom,
( c_Fun_Ocomp(hAPP(c_Fun_Ocomp(c_Record_Oiso__tuple__fst__update(V_isom,T_a,T_b,T_c),V_h,tc_fun(T_b,T_b),tc_fun(T_a,T_a),T_d),V_f),hAPP(c_Fun_Ocomp(c_Record_Oiso__tuple__snd__update(V_isom,T_a,T_b,T_c),V_j,tc_fun(T_c,T_c),tc_fun(T_a,T_a),T_e),V_g),T_a,T_a,T_a) = c_Fun_Ocomp(hAPP(c_Fun_Ocomp(c_Record_Oiso__tuple__snd__update(V_isom,T_a,T_b,T_c),V_j,tc_fun(T_c,T_c),tc_fun(T_a,T_a),T_e),V_g),hAPP(c_Fun_Ocomp(c_Record_Oiso__tuple__fst__update(V_isom,T_a,T_b,T_c),V_h,tc_fun(T_b,T_b),tc_fun(T_a,T_a),T_d),V_f),T_a,T_a,T_a)
| ~ c_Record_Oisomorphic__tuple(V_isom,T_a,T_b,T_c) ) ).
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_complete__lattice_OInf__lower_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,hAPP(V_Inf,V_A)),V_x))
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_complete__lattice_OSup__upper_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,V_x),hAPP(V_Sup,V_A)))
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ c_Complete__Lattice_Ocomplete__lattice(V_Inf,V_Sup,V_less__eq,V_less,V_inf,V_sup,V_bot,V_top,T_a) ) ).
cnf(cls_ord_OatLeastAtMost__iff_1,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,V_i),V_u))
| ~ hBOOL(c_in(V_i,c_SetInterval_Oord_OatLeastAtMost(V_less__eq,V_l,V_u,T_a),T_a)) ) ).
cnf(cls_ord_OatLeastAtMost__iff_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,V_l),V_i))
| ~ hBOOL(c_in(V_i,c_SetInterval_Oord_OatLeastAtMost(V_less__eq,V_l,V_u,T_a),T_a)) ) ).
cnf(cls_bex__Un_7,axiom,
( hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(V_A,V_B,V_P,T_a)))
| ~ hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(c_in(V_x,V_B,T_a)) ) ).
cnf(cls_bex__Un_5,axiom,
( hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(V_A,V_B,V_P,T_a)))
| ~ hBOOL(hAPP(V_P,V_xa))
| ~ hBOOL(c_in(V_xa,V_A,T_a)) ) ).
cnf(cls_bexE_0,axiom,
( hBOOL(c_in(c_ATP__Linkup_Osko__Set__XbexE__1__1(V_A,V_P,T_a),V_A,T_a))
| ~ hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_insert__absorb_0,axiom,
( c_Set_Oinsert(V_a,V_A,T_a) = V_A
| ~ hBOOL(c_in(V_a,V_A,T_a)) ) ).
cnf(cls_ord_OlessThan__iff_1,axiom,
( hBOOL(c_in(V_i,c_SetInterval_Oord_OlessThan(V_less,V_k,T_a),T_a))
| ~ hBOOL(hAPP(hAPP(V_less,V_i),V_k)) ) ).
cnf(cls_ord_OlessThan__iff_0,axiom,
( hBOOL(hAPP(hAPP(V_less,V_i),V_k))
| ~ hBOOL(c_in(V_i,c_SetInterval_Oord_OlessThan(V_less,V_k,T_a),T_a)) ) ).
cnf(cls_SUP2__iff_2,axiom,
( hBOOL(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_fun(T_c,tc_bool))),V_b),V_c))
| ~ hBOOL(hAPP(hAPP(hAPP(V_B,V_x),V_b),V_c))
| ~ hBOOL(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_SUP1__iff_2,axiom,
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_bool)),V_b))
| ~ hBOOL(hAPP(hAPP(V_B,V_x),V_b))
| ~ hBOOL(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_SUP2__I_0,axiom,
( hBOOL(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_fun(T_c,tc_bool))),V_b),V_c))
| ~ hBOOL(hAPP(hAPP(hAPP(V_B,V_a),V_b),V_c))
| ~ hBOOL(c_in(V_a,V_A,T_a)) ) ).
cnf(cls_SUP1__I_0,axiom,
( hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_bool)),V_b))
| ~ hBOOL(hAPP(hAPP(V_B,V_a),V_b))
| ~ hBOOL(c_in(V_a,V_A,T_a)) ) ).
cnf(cls_ord_OatLeastLessThan__iff_1,axiom,
( hBOOL(hAPP(hAPP(V_less,V_i),V_u))
| ~ hBOOL(c_in(V_i,c_SetInterval_Oord_OatLeastLessThan(V_less__eq,V_less,V_l,V_u,T_a),T_a)) ) ).
cnf(cls_ord_OatLeastLessThan__iff_0,axiom,
( hBOOL(hAPP(hAPP(V_less__eq,V_l),V_i))
| ~ hBOOL(c_in(V_i,c_SetInterval_Oord_OatLeastLessThan(V_less__eq,V_less,V_l,V_u,T_a),T_a)) ) ).
cnf(cls_rev__bexI_0,axiom,
( hBOOL(c_in(c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(V_A,V_P,T_a),V_A,T_a))
| ~ hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(c_in(V_x,V_A,T_a)) ) ).
cnf(cls_rev__bexI_1,axiom,
( hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(V_A,V_P,T_a)))
| ~ hBOOL(hAPP(V_P,V_x))
| ~ hBOOL(c_in(V_x,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_Pi__I_0,axiom,
( hBOOL(c_in(V_f,c_FuncSet_OPi(V_A,V_B,T_a,T_b),tc_fun(T_a,T_b)))
| hBOOL(c_in(c_FuncSet_Osko__FuncSet__XPi__I__1__1(V_A,V_B,V_f,T_a,T_b),V_A,T_a)) ) ).
cnf(cls_Pi__I_H_0,axiom,
( hBOOL(c_in(V_f,c_FuncSet_OPi(V_A,V_B,T_a,T_b),tc_fun(T_a,T_b)))
| hBOOL(c_in(c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(V_A,V_B,V_f,T_a,T_b),V_A,T_a)) ) ).
cnf(cls_extensional__arb_0,axiom,
( hAPP(V_f,V_x) = c_HOL_Oundefined(T_b)
| hBOOL(c_in(V_x,V_A,T_a))
| ~ hBOOL(c_in(V_f,c_FuncSet_Oextensional(V_A,T_a,T_b),tc_fun(T_a,T_b))) ) ).
cnf(cls_Pi__I_1,axiom,
( hBOOL(c_in(V_f,c_FuncSet_OPi(V_A,V_B,T_a,T_b),tc_fun(T_a,T_b)))
| ~ hBOOL(c_in(hAPP(V_f,c_FuncSet_Osko__FuncSet__XPi__I__1__1(V_A,V_B,V_f,T_a,T_b)),hAPP(V_B,c_FuncSet_Osko__FuncSet__XPi__I__1__1(V_A,V_B,V_f,T_a,T_b)),T_b)) ) ).
cnf(cls_extensionalityI_0,axiom,
( V_f = V_g
| hBOOL(c_in(c_FuncSet_Osko__FuncSet__XextensionalityI__1__1(V_A,V_f,V_g,T_a,T_b),V_A,T_a))
| ~ hBOOL(c_in(V_g,c_FuncSet_Oextensional(V_A,T_a,T_b),tc_fun(T_a,T_b)))
| ~ hBOOL(c_in(V_f,c_FuncSet_Oextensional(V_A,T_a,T_b),tc_fun(T_a,T_b))) ) ).
cnf(cls_funcset__mem_0,axiom,
( hBOOL(c_in(hAPP(V_f,V_x),V_B,T_b))
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ hBOOL(c_in(V_f,c_FuncSet_OPi(V_A,c_COMBK(V_B,tc_fun(T_b,tc_bool),T_a),T_a,T_b),tc_fun(T_a,T_b))) ) ).
cnf(cls_Pi__I_H_1,axiom,
( hBOOL(c_in(V_f,c_FuncSet_OPi(V_A,V_B,T_a,T_b),tc_fun(T_a,T_b)))
| ~ hBOOL(c_in(hAPP(V_f,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(V_A,V_B,V_f,T_a,T_b)),hAPP(V_B,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(V_A,V_B,V_f,T_a,T_b)),T_b)) ) ).
cnf(cls_fun__left__comm__idem_Ofun__comp__idem_0,axiom,
( c_Fun_Ocomp(hAPP(V_f,V_x),hAPP(V_f,V_x),T_b,T_b,T_b) = hAPP(V_f,V_x)
| ~ c_Finite__Set_Ofun__left__comm__idem(V_f,T_a,T_b) ) ).
cnf(cls_apfst__compose_0,axiom,
c_Product__Type_Oapfst(V_f,c_Product__Type_Oapfst(V_g,V_x,T_d,T_c,T_b),T_c,T_a,T_b) = c_Product__Type_Oapfst(c_Fun_Ocomp(V_f,V_g,T_c,T_a,T_d),V_x,T_d,T_a,T_b) ).
cnf(cls_update__accessor__noop__compE_0,axiom,
( hAPP(V_f,hAPP(V_acc,V_x)) != hAPP(V_acc,V_x)
| ~ c_Record_Oiso__tuple__update__accessor__cong__assist(V_upd,V_acc,T_a,T_b)
| hAPP(hAPP(V_upd,c_Fun_Ocomp(V_g,V_f,T_a,T_a,T_a)),V_x) = hAPP(hAPP(V_upd,V_g),V_x) ) ).
cnf(cls_image__compose_0,axiom,
c_Set_Oimage(c_Fun_Ocomp(V_f,V_g,T_c,T_a,T_b),V_r,T_b,T_a) = c_Set_Oimage(V_f,c_Set_Oimage(V_g,V_r,T_b,T_c),T_c,T_a) ).
cnf(cls_o__def_0,axiom,
hAPP(c_Fun_Ocomp(V_f,V_g,T_c,T_b,t_a),v_x) = hAPP(V_f,hAPP(V_g,v_x)) ).
cnf(cls_bij__betw__trans_0,axiom,
( c_Fun_Obij__betw(c_Fun_Ocomp(V_g,V_f,T_b,T_c,T_a),V_A,V_C,T_a,T_c)
| ~ c_Fun_Obij__betw(V_g,V_B,V_C,T_b,T_c)
| ~ c_Fun_Obij__betw(V_f,V_A,V_B,T_a,T_b) ) ).
cnf(cls_option__map__comp_0,axiom,
c_Option_Omap(V_f,c_Option_Omap(V_g,V_opt,T_c,T_b),T_b,T_a) = c_Option_Omap(c_Fun_Ocomp(V_f,V_g,T_b,T_a,T_c),V_opt,T_c,T_a) ).
cnf(cls_fun__left__comm_Ofun__comp__comm_0,axiom,
( c_Fun_Ocomp(hAPP(V_f,V_x),hAPP(V_f,V_y),T_b,T_b,T_b) = c_Fun_Ocomp(hAPP(V_f,V_y),hAPP(V_f,V_x),T_b,T_b,T_b)
| ~ c_Finite__Set_Ofun__left__comm(V_f,T_a,T_b) ) ).
cnf(cls_comp__surj_0,axiom,
( c_Fun_Osurj(c_Fun_Ocomp(V_g,V_f,T_b,T_c,T_a),T_a,T_c)
| ~ c_Fun_Osurj(V_g,T_b,T_c)
| ~ c_Fun_Osurj(V_f,T_a,T_b) ) ).
cnf(cls_bij__comp_0,axiom,
( c_Fun_Obij(c_Fun_Ocomp(V_g,V_f,T_b,T_c,T_a),T_a,T_c)
| ~ c_Fun_Obij(V_g,T_b,T_c)
| ~ c_Fun_Obij(V_f,T_a,T_b) ) ).
cnf(cls_o__id_0,axiom,
c_Fun_Ocomp(V_f,c_Fun_Oid(T_a),T_a,T_b,T_a) = V_f ).
cnf(cls_id__o_0,axiom,
c_Fun_Ocomp(c_Fun_Oid(T_b),V_g,T_b,T_b,T_a) = V_g ).
cnf(cls_fun__upd__comp_0,axiom,
c_Fun_Ocomp(V_f,c_Fun_Ofun__upd(V_g,V_x,V_y,T_a,T_c),T_c,T_b,T_a) = c_Fun_Ofun__upd(c_Fun_Ocomp(V_f,V_g,T_c,T_b,T_a),V_x,hAPP(V_f,V_y),T_a,T_b) ).
cnf(cls_map__map_0,axiom,
c_List_Omap(V_f,c_List_Omap(V_g,V_xs,T_c,T_b),T_b,T_a) = c_List_Omap(c_Fun_Ocomp(V_f,V_g,T_b,T_a,T_c),V_xs,T_c,T_a) ).
cnf(cls_o__eq__id__dest_0,axiom,
( c_Fun_Ocomp(V_a,V_b,T_c,T_b,T_a) != c_Fun_Ocomp(c_Fun_Oid(T_b),V_c,T_b,T_b,T_a)
| hAPP(V_a,hAPP(V_b,V_v)) = hAPP(V_c,V_v) ) ).
cnf(cls_apsnd__compose_0,axiom,
c_Product__Type_Oapsnd(V_f,c_Product__Type_Oapsnd(V_g,V_x,T_d,T_c,T_a),T_c,T_b,T_a) = c_Product__Type_Oapsnd(c_Fun_Ocomp(V_f,V_g,T_c,T_b,T_d),V_x,T_d,T_b,T_a) ).
cnf(cls_vimage__compose_0,axiom,
c_Set_Ovimage(c_Fun_Ocomp(V_g,V_f,T_c,T_b,T_a),V_x,T_a,T_b) = c_Set_Ovimage(V_f,c_Set_Ovimage(V_g,V_x,T_c,T_b),T_a,T_c) ).
cnf(cls_comp__swap_0,axiom,
c_Fun_Ocomp(V_f,c_Fun_Oswap(V_a,V_b,V_g,T_a,T_c),T_c,T_b,T_a) = c_Fun_Oswap(V_a,V_b,c_Fun_Ocomp(V_f,V_g,T_c,T_b,T_a),T_a,T_b) ).
cnf(cls_partial__order__on__converse_0,axiom,
( c_Order__Relation_Opartial__order__on(V_A,V_r,T_a)
| ~ c_Order__Relation_Opartial__order__on(V_A,hAPP(c_Relation_Oconverse(T_a,T_a),V_r),T_a) ) ).
cnf(cls_partial__order__on__converse_1,axiom,
( c_Order__Relation_Opartial__order__on(V_A,hAPP(c_Relation_Oconverse(T_a,T_a),V_r),T_a)
| ~ c_Order__Relation_Opartial__order__on(V_A,V_r,T_a) ) ).
cnf(cls_total__on__converse_1,axiom,
( c_Relation_Ototal__on(V_A,hAPP(c_Relation_Oconverse(T_a,T_a),V_r),T_a)
| ~ c_Relation_Ototal__on(V_A,V_r,T_a) ) ).
cnf(cls_total__on__converse_0,axiom,
( c_Relation_Ototal__on(V_A,V_r,T_a)
| ~ c_Relation_Ototal__on(V_A,hAPP(c_Relation_Oconverse(T_a,T_a),V_r),T_a) ) ).
cnf(cls_linear__order__on__converse_0,axiom,
( c_Order__Relation_Olinear__order__on(V_A,V_r,T_a)
| ~ c_Order__Relation_Olinear__order__on(V_A,hAPP(c_Relation_Oconverse(T_a,T_a),V_r),T_a) ) ).
cnf(cls_linear__order__on__converse_1,axiom,
( c_Order__Relation_Olinear__order__on(V_A,hAPP(c_Relation_Oconverse(T_a,T_a),V_r),T_a)
| ~ c_Order__Relation_Olinear__order__on(V_A,V_r,T_a) ) ).
cnf(cls_converse__Un_0,axiom,
hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_bool)),V_r),V_s)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_bool)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r)),hAPP(c_Relation_Oconverse(T_b,T_a),V_s)) ).
cnf(cls_preorder__on__converse_1,axiom,
( c_Order__Relation_Opreorder__on(V_A,hAPP(c_Relation_Oconverse(T_a,T_a),V_r),T_a)
| ~ c_Order__Relation_Opreorder__on(V_A,V_r,T_a) ) ).
cnf(cls_preorder__on__converse_0,axiom,
( c_Order__Relation_Opreorder__on(V_A,V_r,T_a)
| ~ c_Order__Relation_Opreorder__on(V_A,hAPP(c_Relation_Oconverse(T_a,T_a),V_r),T_a) ) ).
cnf(cls_rtrancl__converse_0,axiom,
c_Transitive__Closure_Ortrancl(hAPP(c_Relation_Oconverse(T_a,T_a),V_r),T_a) = hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a)) ).
cnf(cls_acyclic__converse_1,axiom,
( c_Wellfounded_Oacyclic(hAPP(c_Relation_Oconverse(T_a,T_a),V_r),T_a)
| ~ c_Wellfounded_Oacyclic(V_r,T_a) ) ).
cnf(cls_acyclic__converse_0,axiom,
( c_Wellfounded_Oacyclic(V_r,T_a)
| ~ c_Wellfounded_Oacyclic(hAPP(c_Relation_Oconverse(T_a,T_a),V_r),T_a) ) ).
cnf(cls_antisym__converse_1,axiom,
( c_Relation_Oantisym(hAPP(c_Relation_Oconverse(T_a,T_a),V_r),T_a)
| ~ c_Relation_Oantisym(V_r,T_a) ) ).
cnf(cls_antisym__converse_0,axiom,
( c_Relation_Oantisym(V_r,T_a)
| ~ c_Relation_Oantisym(hAPP(c_Relation_Oconverse(T_a,T_a),V_r),T_a) ) ).
cnf(cls_converse__Id__on_0,axiom,
hAPP(c_Relation_Oconverse(T_a,T_a),c_Relation_OId__on(V_A,T_a)) = c_Relation_OId__on(V_A,T_a) ).
cnf(cls_trancl__converse_0,axiom,
c_Transitive__Closure_Otrancl(hAPP(c_Relation_Oconverse(T_a,T_a),V_r),T_a) = hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(V_r,T_a)) ).
cnf(cls_converse__inv__image_0,axiom,
hAPP(c_Relation_Oconverse(T_a,T_a),c_Relation_Oinv__image(V_R,V_f,T_b,T_a)) = c_Relation_Oinv__image(hAPP(c_Relation_Oconverse(T_b,T_b),V_R),V_f,T_b,T_a) ).
cnf(cls_converse__Id_0,axiom,
hAPP(c_Relation_Oconverse(T_a,T_a),c_Relation_OId(T_a)) = c_Relation_OId(T_a) ).
cnf(cls_trans__converse_1,axiom,
( c_Relation_Otrans(hAPP(c_Relation_Oconverse(T_a,T_a),V_r),T_a)
| ~ c_Relation_Otrans(V_r,T_a) ) ).
cnf(cls_trans__converse_0,axiom,
( c_Relation_Otrans(V_r,T_a)
| ~ c_Relation_Otrans(hAPP(c_Relation_Oconverse(T_a,T_a),V_r),T_a) ) ).
cnf(cls_converse__rel__comp_0,axiom,
hAPP(c_Relation_Oconverse(T_b,T_a),c_Relation_Orel__comp(V_r,V_s,T_b,T_c,T_a)) = c_Relation_Orel__comp(hAPP(c_Relation_Oconverse(T_c,T_a),V_s),hAPP(c_Relation_Oconverse(T_b,T_c),V_r),T_a,T_c,T_b) ).
cnf(cls_sym__conv__converse__eq_1,axiom,
( hAPP(c_Relation_Oconverse(T_a,T_a),V_r) != V_r
| c_Relation_Osym(V_r,T_a) ) ).
cnf(cls_sym__conv__converse__eq_0,axiom,
( hAPP(c_Relation_Oconverse(T_a,T_a),V_r) = V_r
| ~ c_Relation_Osym(V_r,T_a) ) ).
cnf(cls_refl__on__converse_1,axiom,
( c_Relation_Orefl__on(V_A,hAPP(c_Relation_Oconverse(T_a,T_a),V_r),T_a)
| ~ c_Relation_Orefl__on(V_A,V_r,T_a) ) ).
cnf(cls_refl__on__converse_0,axiom,
( c_Relation_Orefl__on(V_A,V_r,T_a)
| ~ c_Relation_Orefl__on(V_A,hAPP(c_Relation_Oconverse(T_a,T_a),V_r),T_a) ) ).
cnf(cls_Field__converse_0,axiom,
c_Relation_OField(hAPP(c_Relation_Oconverse(T_a,T_a),V_r),T_a) = c_Relation_OField(V_r,T_a) ).
cnf(cls_converse__Int_0,axiom,
hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_prod(T_b,T_a),tc_bool)),V_r),V_s)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_bool)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r)),hAPP(c_Relation_Oconverse(T_b,T_a),V_s)) ).
cnf(cls_finite__converse_1,axiom,
( c_Finite__Set_Ofinite(hAPP(c_Relation_Oconverse(T_b,T_a),V_r),tc_prod(T_a,T_b))
| ~ c_Finite__Set_Ofinite(V_r,tc_prod(T_b,T_a)) ) ).
cnf(cls_finite__converse_0,axiom,
( c_Finite__Set_Ofinite(V_r,tc_prod(T_b,T_a))
| ~ c_Finite__Set_Ofinite(hAPP(c_Relation_Oconverse(T_b,T_a),V_r),tc_prod(T_a,T_b)) ) ).
cnf(cls_sym__converse_1,axiom,
( c_Relation_Osym(hAPP(c_Relation_Oconverse(T_a,T_a),V_r),T_a)
| ~ c_Relation_Osym(V_r,T_a) ) ).
cnf(cls_sym__converse_0,axiom,
( c_Relation_Osym(V_r,T_a)
| ~ c_Relation_Osym(hAPP(c_Relation_Oconverse(T_a,T_a),V_r),T_a) ) ).
cnf(cls_isomorphic__tuple_Oiso__tuple__update__swap__snd__snd_0,axiom,
( c_Fun_Ocomp(hAPP(V_h,V_f),hAPP(V_j,V_g),T_c,T_c,T_c) != c_Fun_Ocomp(hAPP(V_j,V_g),hAPP(V_h,V_f),T_c,T_c,T_c)
| ~ c_Record_Oisomorphic__tuple(V_isom,T_a,T_b,T_c)
| c_Fun_Ocomp(hAPP(c_Fun_Ocomp(c_Record_Oiso__tuple__snd__update(V_isom,T_a,T_b,T_c),V_h,tc_fun(T_c,T_c),tc_fun(T_a,T_a),T_d),V_f),hAPP(c_Fun_Ocomp(c_Record_Oiso__tuple__snd__update(V_isom,T_a,T_b,T_c),V_j,tc_fun(T_c,T_c),tc_fun(T_a,T_a),T_e),V_g),T_a,T_a,T_a) = c_Fun_Ocomp(hAPP(c_Fun_Ocomp(c_Record_Oiso__tuple__snd__update(V_isom,T_a,T_b,T_c),V_j,tc_fun(T_c,T_c),tc_fun(T_a,T_a),T_e),V_g),hAPP(c_Fun_Ocomp(c_Record_Oiso__tuple__snd__update(V_isom,T_a,T_b,T_c),V_h,tc_fun(T_c,T_c),tc_fun(T_a,T_a),T_d),V_f),T_a,T_a,T_a) ) ).
cnf(cls_isomorphic__tuple_Oiso__tuple__update__swap__fst__fst_0,axiom,
( c_Fun_Ocomp(hAPP(V_h,V_f),hAPP(V_j,V_g),T_b,T_b,T_b) != c_Fun_Ocomp(hAPP(V_j,V_g),hAPP(V_h,V_f),T_b,T_b,T_b)
| ~ c_Record_Oisomorphic__tuple(V_isom,T_a,T_b,T_c)
| c_Fun_Ocomp(hAPP(c_Fun_Ocomp(c_Record_Oiso__tuple__fst__update(V_isom,T_a,T_b,T_c),V_h,tc_fun(T_b,T_b),tc_fun(T_a,T_a),T_d),V_f),hAPP(c_Fun_Ocomp(c_Record_Oiso__tuple__fst__update(V_isom,T_a,T_b,T_c),V_j,tc_fun(T_b,T_b),tc_fun(T_a,T_a),T_e),V_g),T_a,T_a,T_a) = c_Fun_Ocomp(hAPP(c_Fun_Ocomp(c_Record_Oiso__tuple__fst__update(V_isom,T_a,T_b,T_c),V_j,tc_fun(T_b,T_b),tc_fun(T_a,T_a),T_e),V_g),hAPP(c_Fun_Ocomp(c_Record_Oiso__tuple__fst__update(V_isom,T_a,T_b,T_c),V_h,tc_fun(T_b,T_b),tc_fun(T_a,T_a),T_d),V_f),T_a,T_a,T_a) ) ).
cnf(cls_IIA__def_4,axiom,
( c_Arrow__Order__Mirabelle_OIIA(V_F)
| hBOOL(c_in(v_sko__Arrow__Order__Mirabelle__XIIA__def__2(V_F),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ) ).
cnf(cls_unanimity__def_1,axiom,
( c_Arrow__Order__Mirabelle_Ounanimity(V_F)
| hBOOL(c_in(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2(V_F),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ) ).
cnf(cls_dictator__def_1,axiom,
( c_Arrow__Order__Mirabelle_Odictator(V_F,V_i)
| hBOOL(c_in(v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(V_F,V_i),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ) ).
cnf(cls_IIA__def_5,axiom,
( c_Arrow__Order__Mirabelle_OIIA(V_F)
| hBOOL(c_in(v_sko__Arrow__Order__Mirabelle__XIIA__def__3(V_F),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ) ).
cnf(cls_Pi__mem_0,axiom,
( hBOOL(c_in(hAPP(V_f,V_x),hAPP(V_B,V_x),T_b))
| ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ hBOOL(c_in(V_f,c_FuncSet_OPi(V_A,V_B,T_a,T_b),tc_fun(T_a,T_b))) ) ).
cnf(cls_PiE_0,axiom,
( ~ hBOOL(c_in(V_x,V_A,T_a))
| hBOOL(c_in(hAPP(V_f,V_x),hAPP(V_B,V_x),T_b))
| ~ hBOOL(c_in(V_f,c_FuncSet_OPi(V_A,V_B,T_a,T_b),tc_fun(T_a,T_b))) ) ).
cnf(cls_A_I5_J_0,axiom,
hBOOL(c_in(v_P_H____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ).
cnf(cls_dictator__def_0,axiom,
( hAPP(V_F,V_x) = hAPP(V_x,V_i)
| ~ hBOOL(c_in(V_x,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))))
| ~ c_Arrow__Order__Mirabelle_Odictator(V_F,V_i) ) ).
cnf(cls_A_I4_J_0,axiom,
hBOOL(c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ).
cnf(cls_comp__cong_0,axiom,
( hAPP(V_f,hAPP(V_g,V_x)) != hAPP(V_f_H,hAPP(V_g_H,V_x_H))
| hAPP(c_Fun_Ocomp(V_f,V_g,T_b,T_a,T_c),V_x) = hAPP(c_Fun_Ocomp(V_f_H,V_g_H,T_d,T_a,T_e),V_x_H) ) ).
cnf(cls_o__eq__dest_0,axiom,
( c_Fun_Ocomp(V_a,V_b,T_c,T_b,T_a) != c_Fun_Ocomp(V_c,V_d,T_d,T_b,T_a)
| hAPP(V_a,hAPP(V_b,V_v)) = hAPP(V_c,hAPP(V_d,V_v)) ) ).
cnf(cls_o__assoc_0,axiom,
c_Fun_Ocomp(V_f,c_Fun_Ocomp(V_g,V_h,T_d,T_c,T_a),T_c,T_b,T_a) = c_Fun_Ocomp(c_Fun_Ocomp(V_f,V_g,T_c,T_b,T_d),V_h,T_d,T_b,T_a) ).
cnf(cls_converse__converse_0,axiom,
hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(c_Relation_Oconverse(T_a,T_b),V_r)) = V_r ).
cnf(cls_o__eq__dest__lhs_0,axiom,
hAPP(V_a,hAPP(V_b,V_v)) = hAPP(c_Fun_Ocomp(V_a,V_b,T_c,T_b,T_a),V_v) ).
cnf(cls_o__apply_0,axiom,
hAPP(c_Fun_Ocomp(V_f,V_g,T_b,T_a,T_c),V_x) = hAPP(V_f,hAPP(V_g,V_x)) ).
cnf(cls_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_CHAINED_0,axiom,
hBOOL(c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ).
cnf(cls_conjecture_0,negated_conjecture,
~ hBOOL(c_in(c_Fun_Ocomp(c_Relation_Oconverse(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))) ).
cnf(clsarity_prod__Finite__Set_Ofinite_Ofinite,axiom,
( class_Finite__Set_Ofinite_Ofinite(tc_prod(T_2,T_1))
| ~ class_Finite__Set_Ofinite_Ofinite(T_1)
| ~ class_Finite__Set_Ofinite_Ofinite(T_2) ) ).
cnf(clsarity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_1) ) ).
cnf(clsarity_fun__Lattices_Oupper__semilattice,axiom,
( class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ) ).
cnf(clsarity_fun__Lattices_Olower__semilattice,axiom,
( class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ) ).
cnf(clsarity_fun__Lattices_Odistrib__lattice,axiom,
( class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Odistrib__lattice(T_1) ) ).
cnf(clsarity_fun__Lattices_Obounded__lattice,axiom,
( class_Lattices_Obounded__lattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Obounded__lattice(T_1) ) ).
cnf(clsarity_fun__Finite__Set_Ofinite_Ofinite,axiom,
( class_Finite__Set_Ofinite_Ofinite(tc_fun(T_2,T_1))
| ~ class_Finite__Set_Ofinite_Ofinite(T_1)
| ~ class_Finite__Set_Ofinite_Ofinite(T_2) ) ).
cnf(clsarity_fun__Orderings_Opreorder,axiom,
( class_Orderings_Opreorder(tc_fun(T_2,T_1))
| ~ class_Orderings_Opreorder(T_1) ) ).
cnf(clsarity_fun__Lattices_Olattice,axiom,
( class_Lattices_Olattice(tc_fun(T_2,T_1))
| ~ class_Lattices_Olattice(T_1) ) ).
cnf(clsarity_fun__Orderings_Oorder,axiom,
( class_Orderings_Oorder(tc_fun(T_2,T_1))
| ~ class_Orderings_Oorder(T_1) ) ).
cnf(clsarity_fun__Orderings_Obot,axiom,
( class_Orderings_Obot(tc_fun(T_2,T_1))
| ~ class_Orderings_Obot(T_1) ) ).
cnf(clsarity_fun__HOL_Oord,axiom,
( class_HOL_Oord(tc_fun(T_2,T_1))
| ~ class_HOL_Oord(T_1) ) ).
cnf(clsarity_bool__Complete__Lattice_Ocomplete__lattice,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool) ).
cnf(clsarity_bool__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_bool) ).
cnf(clsarity_bool__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_bool) ).
cnf(clsarity_bool__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_bool) ).
cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_bool) ).
cnf(clsarity_bool__Finite__Set_Ofinite_Ofinite,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool) ).
cnf(clsarity_bool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_bool) ).
cnf(clsarity_bool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_bool) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool) ).
cnf(clsarity_bool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_bool) ).
cnf(clsarity_bool__HOL_Oord,axiom,
class_HOL_Oord(tc_bool) ).
cnf(clsarity_Option__Ooption__Finite__Set_Ofinite_Ofinite,axiom,
( class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(T_1))
| ~ class_Finite__Set_Ofinite_Ofinite(T_1) ) ).
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
c_fequal(V_x,V_x,T_a) ).
cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom,
( V_X = V_Y
| ~ c_fequal(V_X,V_Y,T_a) ) ).
%------------------------------------------------------------------------------