ITP001 Axioms: ITP062^4.ax
%------------------------------------------------------------------------------
% File : ITP062^4 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : bft.ax [Gau19]
% : HL4062^4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 160 ( 55 unt; 91 typ; 0 def)
% Number of atoms : 119 ( 65 equ; 3 cnn)
% Maximal formula atoms : 10 ( 0 avg)
% Number of connectives : 3168 ( 3 ~; 2 |; 12 &;3129 @)
% ( 8 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 39 ( 7 avg;3129 nst)
% Number of types : 6 ( 5 usr)
% Number of type conns : 121 ( 121 >; 0 *; 0 +; 0 <<)
% Number of symbols : 88 ( 86 usr; 35 con; 0-5 aty)
% Number of variables : 224 ( 0 ^ 223 !; 1 ?; 224 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(u,type,
u: $tType ).
thf(d,type,
d: $tType ).
thf(du,type,
du: $tType ).
thf(mono_2Etyop_2Enum_2Enum,type,
mono_2Etyop_2Enum_2Enum: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: $tType ).
thf(tyop_2Elist_2Elist,type,
tyop_2Elist_2Elist: d > d ).
thf(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: d ).
thf(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: d > d > d ).
thf(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: d ).
thf(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: d > d > d ).
thf(s,type,
s: d > u > du ).
thf(app_2E2,type,
app_2E2: du > du > u ).
thf(combin_i_2E0,type,
combin_i_2E0: u ).
thf(combin_k_2E0,type,
combin_k_2E0: u ).
thf(combin_s_2E0,type,
combin_s_2E0: u ).
thf(c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0: u ).
thf(c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1: du > u ).
thf(c_2Epair_2E_2C_2E0,type,
c_2Epair_2E_2C_2E0: u ).
thf(c_2Epair_2E_2C_2E2,type,
c_2Epair_2E_2C_2E2: du > du > u ).
thf(c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: u ).
thf(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: du > du > u ).
thf(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0: u ).
thf(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2: du > du > u ).
thf(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: u ).
thf(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
thf(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0: u ).
thf(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1: du > u ).
thf(c_2Elist_2EALL__DISTINCT_2E0,type,
c_2Elist_2EALL__DISTINCT_2E0: u ).
thf(c_2Elist_2EALL__DISTINCT_2E1,type,
c_2Elist_2EALL__DISTINCT_2E1: du > u ).
thf(c_2Elist_2EAPPEND_2E0,type,
c_2Elist_2EAPPEND_2E0: u ).
thf(c_2Elist_2EAPPEND_2E2,type,
c_2Elist_2EAPPEND_2E2: du > du > u ).
thf(c_2Ebft_2EBFT_2E0,type,
c_2Ebft_2EBFT_2E0: u ).
thf(c_2Ebft_2EBFT_2E5,type,
c_2Ebft_2EBFT_2E5: du > du > du > du > du > u ).
thf(c_2Epred__set_2ECARD_2E0,type,
c_2Epred__set_2ECARD_2E0: u ).
thf(c_2Epred__set_2ECARD_2E1,type,
c_2Epred__set_2ECARD_2E1: du > u ).
thf(c_2Ebool_2ECOND_2E0,type,
c_2Ebool_2ECOND_2E0: u ).
thf(c_2Ebool_2ECOND_2E3,type,
c_2Ebool_2ECOND_2E3: du > du > du > u ).
thf(c_2Elist_2ECONS_2E0,type,
c_2Elist_2ECONS_2E0: u ).
thf(c_2Elist_2ECONS_2E2,type,
c_2Elist_2ECONS_2E2: du > du > u ).
thf(c_2Epred__set_2EDIFF_2E0,type,
c_2Epred__set_2EDIFF_2E0: u ).
thf(c_2Epred__set_2EDIFF_2E2,type,
c_2Epred__set_2EDIFF_2E2: du > du > u ).
thf(c_2EdirGraph_2EEXCLUDE_2E0,type,
c_2EdirGraph_2EEXCLUDE_2E0: u ).
thf(c_2EdirGraph_2EEXCLUDE_2E2,type,
c_2EdirGraph_2EEXCLUDE_2E2: du > du > u ).
thf(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: u ).
thf(c_2Epred__set_2EFINITE_2E0,type,
c_2Epred__set_2EFINITE_2E0: u ).
thf(c_2Epred__set_2EFINITE_2E1,type,
c_2Epred__set_2EFINITE_2E1: du > u ).
thf(c_2Elist_2EFOLDR_2E0,type,
c_2Elist_2EFOLDR_2E0: u ).
thf(c_2Elist_2EFOLDR_2E3,type,
c_2Elist_2EFOLDR_2E3: du > du > du > u ).
thf(c_2Ebool_2EIN_2E0,type,
c_2Ebool_2EIN_2E0: u ).
thf(c_2Ebool_2EIN_2E2,type,
c_2Ebool_2EIN_2E2: du > du > u ).
thf(c_2Elist_2ELENGTH_2E0,type,
c_2Elist_2ELENGTH_2E0: u ).
thf(c_2Elist_2ELENGTH_2E1,type,
c_2Elist_2ELENGTH_2E1: du > u ).
thf(c_2Elist_2ELIST__TO__SET_2E0,type,
c_2Elist_2ELIST__TO__SET_2E0: u ).
thf(c_2Elist_2ELIST__TO__SET_2E1,type,
c_2Elist_2ELIST__TO__SET_2E1: du > u ).
thf(c_2Elist_2ENIL_2E0,type,
c_2Elist_2ENIL_2E0: u ).
thf(c_2EdirGraph_2EParents_2E0,type,
c_2EdirGraph_2EParents_2E0: u ).
thf(c_2EdirGraph_2EParents_2E1,type,
c_2EdirGraph_2EParents_2E1: du > u ).
thf(c_2EdirGraph_2EREACH__LIST_2E0,type,
c_2EdirGraph_2EREACH__LIST_2E0: u ).
thf(c_2EdirGraph_2EREACH__LIST_2E2,type,
c_2EdirGraph_2EREACH__LIST_2E2: du > du > u ).
thf(c_2Ebft_2ERel_2E0,type,
c_2Ebft_2ERel_2E0: u ).
thf(c_2Ebft_2ERel_2E1,type,
c_2Ebft_2ERel_2E1: du > u ).
thf(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: u ).
thf(c_2Ebool_2E_5C_2F_2E0,type,
c_2Ebool_2E_5C_2F_2E0: u ).
thf(c_2Ebool_2E_5C_2F_2E2,type,
c_2Ebool_2E_5C_2F_2E2: du > du > u ).
thf(c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: u ).
thf(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: du > u ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
thf(mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
thf(mono_2Ec_2Ebool_2E_2F_5C,type,
mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(mono_2Ec_2Ebool_2EF,type,
mono_2Ec_2Ebool_2EF: $o ).
thf(mono_2Ec_2Ebool_2ET,type,
mono_2Ec_2Ebool_2ET: $o ).
thf(mono_2Ec_2Ebool_2E_5C_2F,type,
mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(mono_2Ec_2Ebool_2E_7E,type,
mono_2Ec_2Ebool_2E_7E: $o > $o ).
thf(i_mono_2Etyop_2Emin_2Ebool,type,
i_mono_2Etyop_2Emin_2Ebool: $o > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > u ).
thf(i_mono_2Etyop_2Enum_2Enum,type,
i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).
thf(i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > u ).
thf(j_mono_2Etyop_2Emin_2Ebool,type,
j_mono_2Etyop_2Emin_2Ebool: du > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
thf(j_mono_2Etyop_2Enum_2Enum,type,
j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).
thf(j_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
j_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
thf(reserved_2Eho_2Eeq__ext,axiom,
! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
( ! [V2x_2E0: u] :
( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
=> ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).
thf(reserved_2Eho_2Ei__thm,axiom,
! [A_27a: d,V0x_2E0: u] :
( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
= ( s @ A_27a @ V0x_2E0 ) ) ).
thf(reserved_2Eho_2Ek__thm,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ combin_k_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) )
= ( s @ A_27a @ V0x_2E0 ) ) ).
thf(reserved_2Eho_2Es__thm,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
= ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ).
thf(reserved_2Elogic_2E_2F_5C,axiom,
! [V0: $o,V1: $o] :
( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
<=> ( V0
& V1 ) ) ).
thf(reserved_2Elogic_2E_5C_2F,axiom,
! [V0: $o,V1: $o] :
( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
<=> ( V0
| V1 ) ) ).
thf(reserved_2Elogic_2E_7E,axiom,
! [V0: $o] :
( ( mono_2Ec_2Ebool_2E_7E @ V0 )
<=> ( (~) @ V0 ) ) ).
thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
! [V0: $o,V1: $o] :
( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
<=> ( V0
=> V1 ) ) ).
thf(reserved_2Elogic_2E_3D,axiom,
! [A_27a: d,V0_2E0: u,V1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
<=> ( ( s @ A_27a @ V0_2E0 )
= ( s @ A_27a @ V1_2E0 ) ) ) ).
thf(reserved_2Equant_2E_21,axiom,
! [A_27a: d,V0f_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
<=> ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
thf(reserved_2Equant_2E_3F,axiom,
! [A_27a: d,V0f_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
<=> ? [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [V0_2E0: u] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0_2E0: u] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ V0_2E0 ) ) ) )
= ( s @ tyop_2Enum_2Enum @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ).
thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [V0: $o] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: $o > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: $o > $o > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0 ) ) )
= V0 ) ).
thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27d_29_2CA_27e_29_29,axiom,
! [A_27a: d,A_27c: d,A_27d: d,A_27e: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27c @ X0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) ) @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) ) @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27c @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Elist_2Elist_28A_27b_29_29_20mono_2Etyop_2Epair_2Eprod_28A_27c_2Ctyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27d_29_2CA_27e_29_29_29,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,A_27e: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27b ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27d_29_2CA_27e_29,axiom,
! [A_27a: d,A_27d: d,A_27e: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27d_29_20mono_2EA_27e,axiom,
! [A_27d: d,A_27e: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ X0_2E0 ) @ ( s @ A_27e @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27e @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27e @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ X0_2E0 ) ) ) @ ( s @ A_27e @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( ( s @ A_27a @ X0_2E0 )
= ( s @ A_27a @ X1_2E0 ) )
<=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EALL__DISTINCT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Elist_2EALL__DISTINCT_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2EAPPEND_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq5_2Ec_2Ebft_2EBFT_2E5_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u,X4_2E0: u] :
( ( s @ A_27b @ ( c_2Ebft_2EBFT_2E5 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X3_2E0 ) @ ( s @ A_27b @ X4_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) ) ) @ c_2Ebft_2EBFT_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X3_2E0 ) ) ) @ ( s @ A_27b @ X4_2E0 ) ) ) ) ).
thf(arityeq5_2Ec_2Ebft_2EBFT_2E5_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u,X4_2E0: u] :
( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Ebft_2EBFT_2E5 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X3_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X4_2E0 ) ) )
= ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) ) ) @ c_2Ebft_2EBFT_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X3_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X4_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epred__set_2ECARD_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ c_2Epred__set_2ECARD_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b,axiom,
! [A_27b: d,X0: $o,X1_2E0: u,X2_2E0: u] :
( ( s @ A_27b @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ A_27b @ X1_2E0 ) @ ( s @ A_27b @ X2_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) @ ( s @ A_27b @ X2_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2ECONS_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDIFF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EDIFF_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2EdirGraph_2EEXCLUDE_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2EdirGraph_2EEXCLUDE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ c_2EdirGraph_2EEXCLUDE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EFINITE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ A_27b @ ( c_2Elist_2EFOLDR_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ A_27b ) ) ) @ c_2Elist_2EFOLDR_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27d,axiom,
! [A_27d: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ tyop_2Enum_2Enum ) @ c_2Elist_2ELENGTH_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Elist_2ELIST__TO__SET_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2EdirGraph_2EParents_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2EdirGraph_2EParents_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2EdirGraph_2EParents_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2EdirGraph_2EParents_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2EdirGraph_2EParents_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27b ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2EdirGraph_2EParents_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27b ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2EdirGraph_2EREACH__LIST_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2EdirGraph_2EREACH__LIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2EdirGraph_2EREACH__LIST_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Ebft_2ERel_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d_20mono_2EA_27e,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,A_27e: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( c_2Ebft_2ERel_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) ) ) ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) ) ) ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ c_2Ebft_2ERel_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) ) ) ) @ X0_2E0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: $o > $o,V1: $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: $o > $o > $o,V1: $o] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ c_2Epair_2E_2C_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ V0 @ V1 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: $o > $o,V1: $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: $o > $o > $o,V1: $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(thm_2Ebft_2ERel__def,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,A_27e: d,V0G_2E0: u,V1f_2E0: u,V2seen_2E0: u,V3fringe_2E0: u,V4acc_2E0: u] :
( ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( c_2Ebft_2ERel_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27b ) ) @ V0G_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27c @ V1f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2seen_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ A_27e ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V3fringe_2E0 ) @ ( s @ A_27e @ V4acc_2E0 ) ) ) ) ) ) ) ) ) ) ) )
= ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epred__set_2ECARD_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDIFF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2EdirGraph_2EParents_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27b ) ) @ V0G_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2seen_2E0 ) ) ) ) ) ) ) ) @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ V3fringe_2E0 ) ) ) ) ) ) ).
thf(thm_2Ebft_2EBFT__def,axiom,
! [A_27a: d,A_27b: d,V0t_2E0: u,V1seen_2E0: u,V2h_2E0: u,V3f_2E0: u,V4acc_2E0: u,V5G_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2EdirGraph_2EParents_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V5G_2E0 ) ) ) ) ) )
=> ( ( ( s @ A_27b @ ( c_2Ebft_2EBFT_2E5 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V5G_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ V3f_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1seen_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) @ ( s @ A_27b @ V4acc_2E0 ) ) )
= ( s @ A_27b @ V4acc_2E0 ) )
& ( ( s @ A_27b @ ( c_2Ebft_2EBFT_2E5 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V5G_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ V3f_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1seen_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V2h_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0t_2E0 ) ) ) @ ( s @ A_27b @ V4acc_2E0 ) ) )
= ( s @ A_27b @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2h_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1seen_2E0 ) ) ) ) ) @ ( s @ A_27b @ ( c_2Ebft_2EBFT_2E5 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V5G_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ V3f_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1seen_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0t_2E0 ) @ ( s @ A_27b @ V4acc_2E0 ) ) ) @ ( s @ A_27b @ ( c_2Ebft_2EBFT_2E5 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V5G_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ V3f_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V2h_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1seen_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0t_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V5G_2E0 ) @ ( s @ A_27a @ V2h_2E0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ V3f_2E0 ) @ ( s @ A_27a @ V2h_2E0 ) ) ) @ ( s @ A_27b @ V4acc_2E0 ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ebft_2EBFT__ind,axiom,
! [A_27a: d,A_27b: d,V0P_2E0: u] :
( ! [V1G_2E0: u,V2f_2E0: u,V3seen_2E0: u,V4h_2E0: u,V5t_2E0: u,V6acc_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V1G_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ V2f_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3seen_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) @ ( s @ A_27b @ V6acc_2E0 ) ) ) )
& ( ( ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2EdirGraph_2EParents_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V1G_2E0 ) ) ) ) ) )
& ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V4h_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3seen_2E0 ) ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V1G_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ V2f_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V4h_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3seen_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V5t_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V1G_2E0 ) @ ( s @ A_27a @ V4h_2E0 ) ) ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ V2f_2E0 ) @ ( s @ A_27a @ V4h_2E0 ) ) ) @ ( s @ A_27b @ V6acc_2E0 ) ) ) ) ) ) )
& ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2EdirGraph_2EParents_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V1G_2E0 ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V4h_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3seen_2E0 ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V1G_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ V2f_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3seen_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V5t_2E0 ) ) ) @ ( s @ A_27b @ V6acc_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V1G_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ V2f_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3seen_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V4h_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V5t_2E0 ) ) ) ) ) @ ( s @ A_27b @ V6acc_2E0 ) ) ) ) ) )
=> ! [V7v_2E0: u,V8v1_2E0: u,V9v2_2E0: u,V10v3_2E0: u,V11v4_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V7v_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ V8v1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V9v2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V10v3_2E0 ) ) ) @ ( s @ A_27b @ V11v4_2E0 ) ) ) ) ) ).
thf(thm_2Ebft_2EBFT__CONS,axiom,
! [A_27a: d,V0G_2E0: u,V1f_2E0: u,V2seen_2E0: u,V3fringe_2E0: u,V4acc_2E0: u,V5a_2E0: u,V6b_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2EdirGraph_2EParents_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V0G_2E0 ) ) ) ) ) )
& ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V1f_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2ECONS_2E0 ) )
& ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4acc_2E0 )
= ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V5a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V6b_2E0 ) ) ) ) )
=> ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Ebft_2EBFT_2E5 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V0G_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V1f_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2seen_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3fringe_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4acc_2E0 ) ) )
= ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Ebft_2EBFT_2E5 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V0G_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V1f_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2seen_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3fringe_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V5a_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V6b_2E0 ) ) ) ) ) ).
thf(thm_2Ebft_2EBFT__FOLD,axiom,
! [A_27a: d,A_27b: d,V0G_2E0: u,V1f_2E0: u,V2seen_2E0: u,V3fringe_2E0: u,V4acc_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2EdirGraph_2EParents_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V0G_2E0 ) ) ) ) ) )
=> ( ( s @ A_27b @ ( c_2Ebft_2EBFT_2E5 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V0G_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ V1f_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2seen_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3fringe_2E0 ) @ ( s @ A_27b @ V4acc_2E0 ) ) )
= ( s @ A_27b @ ( c_2Elist_2EFOLDR_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ V1f_2E0 ) @ ( s @ A_27b @ V4acc_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Ebft_2EBFT_2E5 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V0G_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2ECONS_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2seen_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3fringe_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ebft_2EBFT__ALL__DISTINCT,axiom,
! [A_27a: d,V0G_2E0: u,V1seen_2E0: u,V2fringe_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2EdirGraph_2EParents_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V0G_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EALL__DISTINCT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Ebft_2EBFT_2E5 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V0G_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2ECONS_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1seen_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2fringe_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ebft_2EBFT__REACH__1,axiom,
! [A_27a: d,V0G_2E0: u,V1f_2E0: u,V2seen_2E0: u,V3fringe_2E0: u,V4acc_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2EdirGraph_2EParents_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V0G_2E0 ) ) ) ) ) )
& ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V1f_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2ECONS_2E0 ) ) )
=> ! [V5x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Ebft_2EBFT_2E5 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V0G_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V1f_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2seen_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3fringe_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4acc_2E0 ) ) ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2EdirGraph_2EREACH__LIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V0G_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3fringe_2E0 ) ) ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4acc_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ebft_2EBFT__REACH__2,axiom,
! [A_27a: d,V0G_2E0: u,V1f_2E0: u,V2seen_2E0: u,V3fringe_2E0: u,V4acc_2E0: u,V5x_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2EdirGraph_2EParents_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V0G_2E0 ) ) ) ) ) )
& ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V1f_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2ECONS_2E0 ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2EdirGraph_2EREACH__LIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2EdirGraph_2EEXCLUDE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V0G_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2seen_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3fringe_2E0 ) ) ) ) ) )
& ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2seen_2E0 ) ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Ebft_2EBFT_2E5 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V0G_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ V1f_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2seen_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3fringe_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4acc_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ebft_2EBFT__REACH__THM,axiom,
! [A_27a: d,V0G_2E0: u,V1fringe_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2EdirGraph_2EParents_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V0G_2E0 ) ) ) ) ) )
=> ! [V2x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2EdirGraph_2EREACH__LIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V0G_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1fringe_2E0 ) ) ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Ebft_2EBFT_2E5 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ A_27a ) ) @ V0G_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2ECONS_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1fringe_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------