ITP001 Axioms: ITP051+4.ax


%------------------------------------------------------------------------------
% File     : ITP051+4 : TPTP v9.0.0. 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    : readerMonad.ax [Gau19]
%          : HL4051+4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   64 (  48 unt;   0 def)
%            Number of atoms       :   88 (  56 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   27 (   3   ~;   3   |;   3   &)
%                                         (  13 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :   12 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :   41 (  41 usr;  20 con; 0-3 aty)
%            Number of variables   :  255 ( 254   !;   1   ?)
% SPC      : FOF_SAT_RFO_SEQ

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(reserved_2Eho_2Eboolext,axiom,
    ! [V0_2E0,V1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,V0_2E0))
      <=> p(s(tyop_2Emin_2Ebool,V1_2E0)) )
     => s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0) ) ).

fof(reserved_2Eho_2Etruth,axiom,
    p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ).

fof(reserved_2Eho_2Enotfalse,axiom,
    ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ).

fof(reserved_2Eho_2Ebool__cases__ax,axiom,
    ! [V0t_2E0] :
      ( s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
      | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ).

fof(reserved_2Eho_2Ei__thm,axiom,
    ! [A_27a,V0x_2E0] : 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) ).

fof(reserved_2Eho_2Ek__thm,axiom,
    ! [A_27a,A_27b,V0x_2E0,V1y_2E0] : 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) ).

fof(reserved_2Eho_2Es__thm,axiom,
    ! [A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0,V2x_2E0] : 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))))) ).

fof(reserved_2Elogic_2E_2F_5C,axiom,
    ! [V0_2E0,V1_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
        & p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).

fof(reserved_2Elogic_2E_5C_2F,axiom,
    ! [V0_2E0,V1_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
        | p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).

fof(reserved_2Elogic_2E_7E,axiom,
    ! [V0_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0))))
    <=> ~ p(s(tyop_2Emin_2Ebool,V0_2E0)) ) ).

fof(reserved_2Elogic_2E_3D_3D_3E,axiom,
    ! [V0_2E0,V1_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
       => p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).

fof(reserved_2Elogic_2E_3D,axiom,
    ! [A_27a,V0_2E0,V1_2E0] :
      ( p(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) ) ).

fof(reserved_2Equant_2E_21,axiom,
    ! [A_27a,V0f_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
    <=> ! [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) ) ).

fof(reserved_2Equant_2E_3F,axiom,
    ! [A_27a,V0f_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0))))
    <=> ? [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) ) ).

fof(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
    ! [X0_2E0,X1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
        & p(s(tyop_2Emin_2Ebool,X1_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(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)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).

fof(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
    ! [X0_2E0,X1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
        | p(s(tyop_2Emin_2Ebool,X1_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(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)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).

fof(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
    ! [X0_2E0] :
      ( ~ p(s(tyop_2Emin_2Ebool,X0_2E0))
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) ) ).

fof(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
    ! [X0_2E0,X1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
       => p(s(tyop_2Emin_2Ebool,X1_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(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)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).

fof(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] :
      ( s(A_27a,X0_2E0) = s(A_27a,X1_2E0)
    <=> p(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)))) ) ).

fof(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = 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))) ).

fof(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = 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))) ).

fof(arityeq1_2Ec_2EreaderMonad_2EFMAP_2E1_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),c_2EreaderMonad_2EFMAP_2E1(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))) = 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_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),c_2EreaderMonad_2EFMAP_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27b,A_27c,A_27d,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27b,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27d,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(A_27b,A_27c))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27d,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0))) ).

fof(arityeq1_2Ec_2EreaderMonad_2EJOIN_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27b),c_2EreaderMonad_2EJOIN_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b)),c_2EreaderMonad_2EJOIN_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))) ).

fof(arityeq2_2Ec_2EreaderMonad_2EFMAP_2E2_2Emono_2EA_27c_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),c_2EreaderMonad_2EFMAP_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)))),c_2EreaderMonad_2EFMAP_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0))) ).

fof(arityeq2_2Ec_2EreaderMonad_2EBIND_2E2_2Emono_2EA_27b_20mono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27b),c_2EreaderMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b))),c_2EreaderMonad_2EBIND_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))) ).

fof(arityeq2_2Ec_2EreaderMonad_2EBIND_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27b),c_2EreaderMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b))),c_2EreaderMonad_2EBIND_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0))) ).

fof(arityeq1_2Ec_2EreaderMonad_2EUNIT_2E1_2Emono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a,A_27c,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27c),c_2EreaderMonad_2EUNIT_2E1(s(A_27c,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27c)),c_2EreaderMonad_2EUNIT_2E0),s(A_27c,X0_2E0))) ).

fof(arityeq2_2Ec_2EreaderMonad_2EBIND_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27b),c_2EreaderMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b))),c_2EreaderMonad_2EBIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))) ).

fof(arityeq2_2Ec_2EreaderMonad_2EBIND_2E2_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27s,axiom,
    ! [A_27b,A_27c,A_27s,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27s,A_27c),c_2EreaderMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27s,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,A_27c)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27s,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,A_27c)),tyop_2Emin_2Efun(A_27s,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27s,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,A_27c)),tyop_2Emin_2Efun(A_27s,A_27c))),c_2EreaderMonad_2EBIND_2E0),s(tyop_2Emin_2Efun(A_27s,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,A_27c)),X1_2E0))) ).

fof(arityeq2_2Ec_2EreaderMonad_2EFMAP_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27s,axiom,
    ! [A_27a,A_27b,A_27s,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27s,A_27b),c_2EreaderMonad_2EFMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27s,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(A_27s,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27s,A_27a),tyop_2Emin_2Efun(A_27s,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27s,A_27a),tyop_2Emin_2Efun(A_27s,A_27b))),c_2EreaderMonad_2EFMAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27s,A_27a),X1_2E0))) ).

fof(arityeq2_2Ec_2EreaderMonad_2EFMAP_2E2_2Emono_2EA_27b_20mono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27b),c_2EreaderMonad_2EFMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),c_2EreaderMonad_2EFMAP_2E0),s(tyop_2Emin_2Efun(A_27b,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) ).

fof(arityeq2_2Ec_2EreaderMonad_2EFMAP_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27b),c_2EreaderMonad_2EFMAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b))),c_2EreaderMonad_2EFMAP_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0))) ).

fof(arityeq2_2Ec_2EreaderMonad_2EJOIN_2E2_2Emono_2EA_27a_20mono_2EA_27s,axiom,
    ! [A_27a,A_27s,X0_2E0,X1_2E0] : s(A_27a,c_2EreaderMonad_2EJOIN_2E2(s(tyop_2Emin_2Efun(A_27s,tyop_2Emin_2Efun(A_27s,A_27a)),X0_2E0),s(A_27s,X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27s,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27s,tyop_2Emin_2Efun(A_27s,A_27a)),tyop_2Emin_2Efun(A_27s,A_27a)),c_2EreaderMonad_2EJOIN_2E0),s(tyop_2Emin_2Efun(A_27s,tyop_2Emin_2Efun(A_27s,A_27a)),X0_2E0))),s(A_27s,X1_2E0))) ).

fof(arityeq2_2Ec_2EreaderMonad_2EMCOMPOSE_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2EreaderMonad_2EMCOMPOSE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)))),c_2EreaderMonad_2EMCOMPOSE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0))) ).

fof(arityeq2_2Ec_2EreaderMonad_2EMCOMPOSE_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2EreaderMonad_2EMCOMPOSE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,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_27c,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)))),c_2EreaderMonad_2EMCOMPOSE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0))) ).

fof(arityeq2_2Ec_2EreaderMonad_2EMCOMPOSE_2E2_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,A_27c,A_27d,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2EreaderMonad_2EMCOMPOSE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),X0_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)))),c_2EreaderMonad_2EMCOMPOSE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0))) ).

fof(arityeq2_2Ec_2EreaderMonad_2EMCOMPOSE_2E2_2Emono_2EA_27d_20mono_2EA_27e_20mono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b,A_27c,A_27d,A_27e,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c)),c_2EreaderMonad_2EMCOMPOSE_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27e)),X0_2E0),s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27e)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c)))),c_2EreaderMonad_2EMCOMPOSE_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27e)),X0_2E0))),s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0))) ).

fof(arityeq2_2Ec_2EreaderMonad_2EMCOMPOSE_2E2_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27e_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,A_27d,A_27e,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27e)),c_2EreaderMonad_2EMCOMPOSE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),X0_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27e)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27e)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27e)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27e))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27e)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27e)))),c_2EreaderMonad_2EMCOMPOSE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27e)),X1_2E0))) ).

fof(arityeq2_2Ec_2EreaderMonad_2EMCOMPOSE_2E2_2Emono_2EA_27a_20mono_2EA_27e_20mono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,A_27c,A_27e,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2EreaderMonad_2EMCOMPOSE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27e)),X0_2E0),s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27e)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)))),c_2EreaderMonad_2EMCOMPOSE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27e)),X0_2E0))),s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0))) ).

fof(arityeq2_2Ec_2EreaderMonad_2EUNIT_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(A_27a,c_2EreaderMonad_2EUNIT_2E2(s(A_27a,X0_2E0),s(A_27b,X1_2E0))) = 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)),c_2EreaderMonad_2EUNIT_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27s_20mono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,A_27s,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27s,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27s,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(A_27s,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27s,A_27a),tyop_2Emin_2Efun(A_27s,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27s,A_27a),tyop_2Emin_2Efun(A_27s,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27s,A_27a),X1_2E0))) ).

fof(arityeq1_2Ec_2EreaderMonad_2EFMAP_2E1_2Emono_2EA_27b_20mono_2EA_27d_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,A_27d,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27d)),c_2EreaderMonad_2EFMAP_2E1(s(tyop_2Emin_2Efun(A_27b,A_27d),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27d))),c_2EreaderMonad_2EFMAP_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X0_2E0))) ).

fof(arityeq1_2Ec_2EreaderMonad_2EFMAP_2E1_2Emono_2EA_27d_20mono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a,A_27c,A_27d,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27d),tyop_2Emin_2Efun(A_27a,A_27c)),c_2EreaderMonad_2EFMAP_2E1(s(tyop_2Emin_2Efun(A_27d,A_27c),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27d),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27d),tyop_2Emin_2Efun(A_27a,A_27c))),c_2EreaderMonad_2EFMAP_2E0),s(tyop_2Emin_2Efun(A_27d,A_27c),X0_2E0))) ).

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27c_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27d_29,axiom,
    ! [A_27a,A_27b,A_27c,A_27d,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27d),tyop_2Emin_2Efun(A_27a,A_27c)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27d)),X1_2E0))) = 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(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27d)),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(tyop_2Emin_2Efun(A_27a,A_27d),tyop_2Emin_2Efun(A_27a,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27d),tyop_2Emin_2Efun(A_27a,A_27c)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27d)),X1_2E0))) ).

fof(arityeq3_2Ec_2EreaderMonad_2EBIND_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27s,axiom,
    ! [A_27a,A_27b,A_27s,X0_2E0,X1_2E0,X2_2E0] : s(A_27b,c_2EreaderMonad_2EBIND_2E3(s(tyop_2Emin_2Efun(A_27s,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,A_27b)),X1_2E0),s(A_27s,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27s,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,A_27b)),tyop_2Emin_2Efun(A_27s,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27s,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,A_27b)),tyop_2Emin_2Efun(A_27s,A_27b))),c_2EreaderMonad_2EBIND_2E0),s(tyop_2Emin_2Efun(A_27s,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,A_27b)),X1_2E0))),s(A_27s,X2_2E0))) ).

fof(arityeq3_2Ec_2EreaderMonad_2EMCOMPOSE_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27s,axiom,
    ! [A_27a,A_27b,A_27c,A_27s,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Efun(A_27s,A_27c),c_2EreaderMonad_2EMCOMPOSE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,A_27c)),X1_2E0),s(A_27a,X2_2E0))) = s(tyop_2Emin_2Efun(A_27s,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,A_27c)))),c_2EreaderMonad_2EMCOMPOSE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,A_27c)),X1_2E0))),s(A_27a,X2_2E0))) ).

fof(thm_2EreaderMonad_2EBIND__def,axiom,
    ! [A_27a,A_27b,A_27s,V0M_2E0,V1f_2E0,V2s_2E0] : s(A_27b,c_2EreaderMonad_2EBIND_2E3(s(tyop_2Emin_2Efun(A_27s,A_27a),V0M_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,A_27b)),V1f_2E0),s(A_27s,V2s_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27s,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,A_27b)),V1f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27s,A_27a),V0M_2E0),s(A_27s,V2s_2E0))))),s(A_27s,V2s_2E0))) ).

fof(thm_2EreaderMonad_2EUNIT__def,axiom,
    ! [A_27a,A_27b,V0x_2E0,V1s_2E0] : s(A_27a,c_2EreaderMonad_2EUNIT_2E2(s(A_27a,V0x_2E0),s(A_27b,V1s_2E0))) = s(A_27a,V0x_2E0) ).

fof(thm_2EreaderMonad_2EMCOMPOSE__def,axiom,
    ! [A_27a,A_27b,A_27c,A_27s,V0f1_2E0,V1f2_2E0,V2a_2E0] : s(tyop_2Emin_2Efun(A_27s,A_27c),c_2EreaderMonad_2EMCOMPOSE_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,A_27b)),V0f1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,A_27c)),V1f2_2E0),s(A_27a,V2a_2E0))) = s(tyop_2Emin_2Efun(A_27s,A_27c),c_2EreaderMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27s,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,A_27b)),V0f1_2E0),s(A_27a,V2a_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,A_27c)),V1f2_2E0))) ).

fof(thm_2EreaderMonad_2EFMAP__def,axiom,
    ! [A_27a,A_27b,A_27s,V0f_2E0,V1M1_2E0] : s(tyop_2Emin_2Efun(A_27s,A_27b),c_2EreaderMonad_2EFMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27s,A_27a),V1M1_2E0))) = s(tyop_2Emin_2Efun(A_27s,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27s,A_27a),V1M1_2E0))) ).

fof(thm_2EreaderMonad_2EJOIN__def,axiom,
    ! [A_27a,A_27s,V0MM_2E0,V1s_2E0] : s(A_27a,c_2EreaderMonad_2EJOIN_2E2(s(tyop_2Emin_2Efun(A_27s,tyop_2Emin_2Efun(A_27s,A_27a)),V0MM_2E0),s(A_27s,V1s_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27s,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27s,tyop_2Emin_2Efun(A_27s,A_27a)),V0MM_2E0),s(A_27s,V1s_2E0))),s(A_27s,V1s_2E0))) ).

fof(thm_2EreaderMonad_2EBIND__UNITR,axiom,
    ! [A_27a,A_27b,V0m_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27b),c_2EreaderMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0m_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),c_2EreaderMonad_2EUNIT_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0m_2E0) ).

fof(thm_2EreaderMonad_2EBIND__UNITL,axiom,
    ! [A_27a,A_27b,A_27c,V0x_2E0,V1f_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27b),c_2EreaderMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),c_2EreaderMonad_2EUNIT_2E1(s(A_27c,V0x_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b)),V1f_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b)),V1f_2E0),s(A_27c,V0x_2E0))) ).

fof(thm_2EreaderMonad_2EMCOMPOSE__LEFT__ID,axiom,
    ! [A_27a,A_27b,A_27c,V0g_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2EreaderMonad_2EMCOMPOSE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),c_2EreaderMonad_2EUNIT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0g_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0g_2E0) ).

fof(thm_2EreaderMonad_2EMCOMPOSE__RIGHT__ID,axiom,
    ! [A_27a,A_27b,A_27c,V0f_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2EreaderMonad_2EMCOMPOSE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27c)),c_2EreaderMonad_2EUNIT_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0) ).

fof(thm_2EreaderMonad_2EMCOMPOSE__ASSOC,axiom,
    ! [A_27a,A_27b,A_27c,A_27d,A_27e,V0h_2E0,V1g_2E0,V2f_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2EreaderMonad_2EMCOMPOSE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),V2f_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27c)),c_2EreaderMonad_2EMCOMPOSE_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27e)),V1g_2E0),s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,A_27c)),V0h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2EreaderMonad_2EMCOMPOSE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27e)),c_2EreaderMonad_2EMCOMPOSE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27d)),V2f_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,A_27e)),V1g_2E0))),s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,A_27c)),V0h_2E0))) ).

fof(thm_2EreaderMonad_2EFMAP__ID,axiom,
    ! [A_27a,A_27b,F0_2E0] :
      ( ! [V1x_2E0] : s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),F0_2E0),s(A_27b,V1x_2E0))) = s(A_27b,V1x_2E0)
     => ! [V0M_2E0] :
          ( s(tyop_2Emin_2Efun(A_27a,A_27b),c_2EreaderMonad_2EFMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0M_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0M_2E0)
          & s(tyop_2Emin_2Efun(A_27a,A_27b),c_2EreaderMonad_2EFMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),c_2Ecombin_2EI_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0M_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0M_2E0) ) ) ).

fof(thm_2EreaderMonad_2EFMAP__o,axiom,
    ! [A_27a,A_27b,A_27c,A_27d,V0g_2E0,V1f_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),c_2EreaderMonad_2EFMAP_2E1(s(tyop_2Emin_2Efun(A_27b,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27d,A_27c),V1f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V0g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27d),tyop_2Emin_2Efun(A_27a,A_27c)),c_2EreaderMonad_2EFMAP_2E1(s(tyop_2Emin_2Efun(A_27d,A_27c),V1f_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27d)),c_2EreaderMonad_2EFMAP_2E1(s(tyop_2Emin_2Efun(A_27b,A_27d),V0g_2E0))))) ).

fof(thm_2EreaderMonad_2EFMAP__BIND,axiom,
    ! [A_27a,A_27b,A_27c,V0f_2E0,V1M_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27b),c_2EreaderMonad_2EFMAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1M_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2EreaderMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1M_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),c_2EreaderMonad_2EUNIT_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),V0f_2E0))))) ).

fof(thm_2EreaderMonad_2EBIND__JOIN,axiom,
    ! [A_27a,A_27b,A_27c,V0f_2E0,V1M_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27b),c_2EreaderMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1M_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2EreaderMonad_2EJOIN_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),c_2EreaderMonad_2EFMAP_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1M_2E0))))) ).

fof(thm_2EreaderMonad_2EJOIN__BIND,axiom,
    ! [A_27a,A_27b,V0M_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27b),c_2EreaderMonad_2EJOIN_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V0M_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2EreaderMonad_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V0M_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2EI_2E0))) ).

fof(reserved_2Eho_2Eeq__ext,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1g_2E0] :
      ( ! [V2x_2E0] : 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) ) ).

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