ITP001 Axioms: ITP051+4.ax
%------------------------------------------------------------------------------
% File : ITP051+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 : 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) ) ).
%------------------------------------------------------------------------------