ITP001 Axioms: ITP038+4.ax
%------------------------------------------------------------------------------
% File : ITP038+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 : state_transformer.ax [Gau19]
% : HL4038+4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 204 ( 175 unt; 0 def)
% Number of atoms : 266 ( 219 equ)
% Maximal formula atoms : 11 ( 1 avg)
% Number of connectives : 67 ( 5 ~; 3 |; 7 &)
% ( 17 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 23 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 112 ( 112 usr; 57 con; 0-3 aty)
% Number of variables : 894 ( 893 !; 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_2Epair_2ECURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Epair_2ECURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Epair_2ECURRY_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) ).
fof(arityeq1_2Ec_2Epair_2ECURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29,axiom,
! [A_27a,A_27b,A_27c,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Epair_2ECURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))),c_2Epair_2ECURRY_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),X0_2E0))) ).
fof(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27d_2CA_27b_29,axiom,
! [A_27a,A_27b,A_27d,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27d,A_27b)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27d,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27d,A_27b))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),X0_2E0))) ).
fof(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27d_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29,axiom,
! [A_27b,A_27c,A_27d,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27d,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27d,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27d,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27d_2CA_27b_29,axiom,
! [A_27a,A_27b,A_27c,A_27d,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27d,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27d,A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27d,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27d,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27d,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27d,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27d,A_27b)),X1_2E0))) ).
fof(arityeq1_2Ec_2Estate__transformer_2EEXT_2E1_2Emono_2EA_27b_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Estate__transformer_2EEXT_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Estate__transformer_2EEXT_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0))) ).
fof(arityeq1_2Ec_2Estate__transformer_2EEXT_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,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Estate__transformer_2EEXT_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))),c_2Estate__transformer_2EEXT_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0))) ).
fof(arityeq2_2Ec_2Estate__transformer_2EMCOMP_2E2_2Emono_2EA_27b_20mono_2EA_27d_20mono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a,A_27b,A_27c,A_27d,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Estate__transformer_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))))),c_2Estate__transformer_2EMCOMP_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),X1_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29_20mono_2EA_27c,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0))) ).
fof(arityeq1_2Ec_2Estate__transformer_2EEXT_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Estate__transformer_2EEXT_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Estate__transformer_2EEXT_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0))) ).
fof(arityeq1_2Ec_2Estate__transformer_2EEXT_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_20mono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a,A_27b,A_27c,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Estate__transformer_2EEXT_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))),c_2Estate__transformer_2EEXT_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29,axiom,
! [A_27state,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29,axiom,
! [A_27state,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0))) ).
fof(arityeq1_2Ec_2Estate__transformer_2EFOR_2E1_2Emono_2EA_27state,axiom,
! [A_27state,X0_2E0] : s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Estate__transformer_2EFOR_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X0_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Estate__transformer_2EFOR_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X0_2E0))) ).
fof(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq2_2Ec_2Earithmetic_2E_2D_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eprim__rec_2E_3C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).
fof(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) ).
fof(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29,axiom,
! [A_27a,A_27state,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),c_2Epair_2E_2C_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),X1_2E0))) ).
fof(arityeq1_2Ec_2Estate__transformer_2EFOREACH_2E1_2Emono_2EA_27a_20mono_2EA_27state,axiom,
! [A_27a,A_27state,X0_2E0] : s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Estate__transformer_2EFOREACH_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Estate__transformer_2EFOREACH_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : 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))) ).
fof(arityeq2_2Ec_2Estate__transformer_2EBIND_2E2_2Emono_2EA_27state_20mono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Eone_2Eone,axiom,
! [A_27state,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Estate__transformer_2EBIND_2E0),s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),X1_2E0))) ).
fof(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29,axiom,
! [A_27state,X0_2E0] : s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Ecombin_2EI_2E1(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Ecombin_2EI_2E0),s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),X0_2E0))) ).
fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29,axiom,
! [A_27state,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),X1_2E0),s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),X2_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),X1_2E0))),s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),X2_2E0))) ).
fof(arityeq1_2Ec_2Estate__transformer_2EJOIN_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Estate__transformer_2EJOIN_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Estate__transformer_2EJOIN_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),X0_2E0))) ).
fof(arityeq1_2Ec_2Estate__transformer_2EJOIN_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a,A_27c,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),c_2Estate__transformer_2EJOIN_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Estate__transformer_2EJOIN_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a)),X0_2E0))) ).
fof(arityeq2_2Ec_2Estate__transformer_2EMMAP_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29_20mono_2EA_27b,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a)),c_2Estate__transformer_2EMMAP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a)))),c_2Estate__transformer_2EMMAP_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),X1_2E0))) ).
fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(A_27b,A_27a),c_2Ecombin_2EK_2E1(s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),c_2Ecombin_2EK_2E0),s(A_27a,X0_2E0))) ).
fof(arityeq1_2Ec_2Estate__transformer_2EMMAP_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Estate__transformer_2EMMAP_2E1(s(tyop_2Emin_2Efun(A_27b,A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Estate__transformer_2EMMAP_2E0),s(tyop_2Emin_2Efun(A_27b,A_27b),X0_2E0))) ).
fof(arityeq1_2Ec_2Estate__transformer_2EMMAP_2E1_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27a,A_27b,A_27c,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Estate__transformer_2EMMAP_2E1(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))),c_2Estate__transformer_2EMMAP_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))) ).
fof(arityeq1_2Ec_2Estate__transformer_2EMMAP_2E1_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27b,axiom,
! [A_27a,A_27b,A_27d,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),c_2Estate__transformer_2EMMAP_2E1(s(tyop_2Emin_2Efun(A_27b,A_27d),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)))),c_2Estate__transformer_2EMMAP_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X0_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2EA_27d_20mono_2EA_27c,axiom,
! [A_27b,A_27c,A_27d,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27b,A_27d),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(A_27b,A_27d))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0))) ).
fof(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27b_20mono_2EA_27state_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27state_29_29,axiom,
! [A_27a,A_27b,A_27state,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),X0_2E0))) ).
fof(arityeq1_2Ec_2Estate__transformer_2EUNIT_2E1_2Emono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Estate__transformer_2EUNIT_2E1(s(tyop_2Elist_2Elist(A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2Estate__transformer_2EUNIT_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27b,axiom,
! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),c_2Elist_2ECONS_2E0),s(A_27b,X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) ).
fof(arityeq1_2Ec_2Estate__transformer_2EUNIT_2E1_2Emono_2EA_27state_20mono_2Etyop_2Eone_2Eone,axiom,
! [A_27state,X0_2E0] : s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Estate__transformer_2EUNIT_2E1(s(tyop_2Eone_2Eone,X0_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Estate__transformer_2EUNIT_2E0),s(tyop_2Eone_2Eone,X0_2E0))) ).
fof(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29,axiom,
! [A_27a,A_27state,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool)),X0_2E0))) ).
fof(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29_29,axiom,
! [A_27state,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),X0_2E0))) ).
fof(arityeq1_2Ec_2Estate__transformer_2EWIDEN_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27state,axiom,
! [A_27a,A_27b,A_27state,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),c_2Estate__transformer_2EWIDEN_2E1(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),c_2Estate__transformer_2EWIDEN_2E0),s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),X0_2E0))) ).
fof(arityeq1_2Ec_2Estate__transformer_2EmapM_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a,A_27b,A_27c,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b))),c_2Estate__transformer_2EmapM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b)))),c_2Estate__transformer_2EmapM_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0))) ).
fof(arityeq1_2Ec_2Estate__transformer_2Esequence_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Estate__transformer_2Esequence_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2Estate__transformer_2Esequence_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27state,axiom,
! [A_27a,A_27state,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27a,A_27state),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(A_27state,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27state),app_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(A_27state,X1_2E0))) ).
fof(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27b_20mono_2EA_27state,axiom,
! [A_27b,A_27state,X0_2E0] : s(A_27state,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27state),X0_2E0))) = s(A_27state,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),A_27state),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27state),X0_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27state_29,axiom,
! [A_27a,A_27b,A_27state,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27state),X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(tyop_2Epair_2Eprod(A_27b,A_27state),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27state,axiom,
! [A_27b,A_27state,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27b,A_27state),c_2Epair_2E_2C_2E2(s(A_27b,X0_2E0),s(A_27state,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27b,A_27state),app_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27b,A_27state)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27b,A_27state))),c_2Epair_2E_2C_2E0),s(A_27b,X0_2E0))),s(A_27state,X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2E_2C_2E2(s(A_27b,X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Epair_2E_2C_2E0),s(A_27b,X0_2E0))),s(A_27a,X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Eone_2Eone_20mono_2EA_27state,axiom,
! [A_27state,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state),c_2Epair_2E_2C_2E2(s(tyop_2Eone_2Eone,X0_2E0),s(A_27state,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state),app_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Epair_2E_2C_2E0),s(tyop_2Eone_2Eone,X0_2E0))),s(A_27state,X1_2E0))) ).
fof(arityeq2_2Ec_2Estate__transformer_2EBIND_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Estate__transformer_2EBIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0))) ).
fof(arityeq2_2Ec_2Estate__transformer_2EBIND_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))),c_2Estate__transformer_2EBIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X1_2E0))) ).
fof(arityeq2_2Ec_2Estate__transformer_2EBIND_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27d,axiom,
! [A_27a,A_27b,A_27d,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)))),c_2Estate__transformer_2EBIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),X1_2E0))) ).
fof(arityeq2_2Ec_2Estate__transformer_2EBIND_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),c_2Estate__transformer_2EBIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),X1_2E0))) ).
fof(arityeq2_2Ec_2Estate__transformer_2EBIND_2E2_2Emono_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_2Epair_2Eprod(A_27b,A_27a)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Estate__transformer_2EBIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_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,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0))) ).
fof(arityeq2_2Ec_2Estate__transformer_2EBIND_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27a,A_27c,A_27d,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)))),c_2Estate__transformer_2EBIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),X1_2E0))) ).
fof(arityeq2_2Ec_2Estate__transformer_2EBIND_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Eone_2Eone,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)))),c_2Estate__transformer_2EBIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),X1_2E0))) ).
fof(arityeq2_2Ec_2Estate__transformer_2EBIND_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Estate__transformer_2EBIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0))) ).
fof(arityeq2_2Ec_2Estate__transformer_2EBIND_2E2_2Emono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),c_2Estate__transformer_2EBIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),X1_2E0))) ).
fof(arityeq2_2Ec_2Estate__transformer_2EmapM_2E2_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Estate__transformer_2EmapM_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),c_2Estate__transformer_2EmapM_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) ).
fof(arityeq2_2Ec_2Estate__transformer_2EBIND_2E2_2Emono_2EA_27b_20mono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))),c_2Estate__transformer_2EBIND_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X1_2E0))) ).
fof(arityeq1_2Ec_2Estate__transformer_2EUNIT_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Estate__transformer_2EUNIT_2E1(s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Estate__transformer_2EUNIT_2E0),s(A_27a,X0_2E0))) ).
fof(arityeq2_2Ec_2Estate__transformer_2EEXT_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,tyop_2Epair_2Eprod(A_27c,A_27s)),c_2Estate__transformer_2EEXT_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),X0_2E0),s(tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)),tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)),tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s)))),c_2Estate__transformer_2EEXT_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),X0_2E0))),s(tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)),X1_2E0))) ).
fof(arityeq2_2Ec_2Estate__transformer_2EEXT_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,tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Estate__transformer_2EEXT_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Estate__transformer_2EEXT_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2EFOLDR_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27b_29_2CA_27a_29_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2Elist_2EFOLDR_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))))),c_2Elist_2EFOLDR_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),X1_2E0))) ).
fof(arityeq2_2Ec_2Estate__transformer_2EIGNORE__BIND_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Estate__transformer_2EIGNORE__BIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Estate__transformer_2EIGNORE__BIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),X1_2E0))) ).
fof(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27state_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27state_29_29,axiom,
! [A_27a,A_27b,A_27state,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),X0_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27state),X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),X0_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27state),X1_2E0))) ).
fof(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27state_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27state_29_29,axiom,
! [A_27a,A_27b,A_27state,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),X0_2E0))) ).
fof(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27state_29_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27state_29,axiom,
! [A_27a,A_27b,A_27state,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27a,A_27state),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Epair_2Eprod(A_27a,A_27state)),X0_2E0),s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27state),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Epair_2Eprod(A_27a,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Epair_2Eprod(A_27a,A_27state)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Epair_2Eprod(A_27a,A_27state))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Epair_2Eprod(A_27a,A_27state)),X0_2E0))),s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),X1_2E0))) ).
fof(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27state_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27state_29,axiom,
! [A_27a,A_27b,A_27state,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Epair_2Eprod(A_27a,A_27state)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,A_27state))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Epair_2Eprod(A_27a,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,A_27state))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Epair_2Eprod(A_27a,A_27state))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,A_27state))),X0_2E0))) ).
fof(arityeq2_2Ec_2Estate__transformer_2EMCOMP_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,tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Estate__transformer_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))))),c_2Estate__transformer_2EMCOMP_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),X1_2E0))) ).
fof(arityeq2_2Ec_2Estate__transformer_2EMCOMP_2E2_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] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),c_2Estate__transformer_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))))),c_2Estate__transformer_2EMCOMP_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s))),X1_2E0))) ).
fof(arityeq2_2Ec_2Estate__transformer_2EMCOMP_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,tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Estate__transformer_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))))),c_2Estate__transformer_2EMCOMP_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),X1_2E0))) ).
fof(arityeq2_2Ec_2Estate__transformer_2EMCOMP_2E2_2Emono_2EA_27a_20mono_2EA_27e_20mono_2EA_27d_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,tyop_2Epair_2Eprod(A_27d,A_27b))),c_2Estate__transformer_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27e,A_27b))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27e,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27e,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))))),c_2Estate__transformer_2EMCOMP_2E0),s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27e,A_27b))),X1_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27d_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27b_29_29_20mono_2EA_27c,axiom,
! [A_27b,A_27c,A_27d,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0),s(tyop_2Emin_2Efun(A_27d,A_27c),X1_2E0))) = s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27c),X1_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Epair_2Eprod_28A_27d_2CA_27b_29_29_20mono_2EA_27d,axiom,
! [A_27a,A_27b,A_27d,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27d),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27d),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27d),X1_2E0))) ).
fof(arityeq2_2Ec_2Estate__transformer_2EMCOMP_2E2_2Emono_2EA_27e_20mono_2EA_27d_20mono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b,A_27c,A_27d,A_27e,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Estate__transformer_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0),s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))))),c_2Estate__transformer_2EMCOMP_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0))),s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),X1_2E0))) ).
fof(arityeq2_2Ec_2Estate__transformer_2EMCOMP_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,tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Estate__transformer_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27e,A_27b))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27e,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27e,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))))),c_2Estate__transformer_2EMCOMP_2E0),s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27e,A_27b))),X1_2E0))) ).
fof(arityeq2_2Ec_2Estate__transformer_2EMCOMP_2E2_2Emono_2EA_27d_20mono_2EA_27f_20mono_2EA_27f_20mono_2EA_27e,axiom,
! [A_27d,A_27e,A_27f,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27f,A_27e))),c_2Estate__transformer_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27f,A_27e))),X0_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27f,A_27e))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27f,A_27e))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27f,A_27e))),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27f,A_27e)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27f,A_27e))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27f,A_27e))),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27f,A_27e))))),c_2Estate__transformer_2EMCOMP_2E0),s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27f,A_27e))),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27f,A_27e))),X1_2E0))) ).
fof(arityeq2_2Ec_2Estate__transformer_2EMMAP_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Estate__transformer_2EMMAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Estate__transformer_2EMMAP_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),X1_2E0))) ).
fof(arityeq2_2Ec_2Estate__transformer_2EMWHILE_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),c_2Estate__transformer_2EMWHILE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)))),c_2Estate__transformer_2EMWHILE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),X1_2E0))) ).
fof(arityeq2_2Ec_2Estate__transformer_2EREAD_2E2_2Emono_2EA_27a_20mono_2EA_27state,axiom,
! [A_27a,A_27state,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27a,A_27state),c_2Estate__transformer_2EREAD_2E2(s(tyop_2Emin_2Efun(A_27state,A_27a),X0_2E0),s(A_27state,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27state),app_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state))),c_2Estate__transformer_2EREAD_2E0),s(tyop_2Emin_2Efun(A_27state,A_27a),X0_2E0))),s(A_27state,X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2EUNCURRY_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2EUNCURRY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),X0_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),X0_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0))) ).
fof(arityeq2_2Ec_2Estate__transformer_2EUNIT_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Estate__transformer_2EUNIT_2E2(s(A_27b,X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Estate__transformer_2EUNIT_2E0),s(A_27b,X0_2E0))),s(A_27a,X1_2E0))) ).
fof(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [A_27a,A_27state,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool))),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29,axiom,
! [A_27a,A_27state,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Erelation_2EWFREC_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0))) ).
fof(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [A_27state,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool))),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))) ).
fof(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29_29_20mono_2Etyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29,axiom,
! [A_27state,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Erelation_2EWFREC_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0))) ).
fof(arityeq2_2Ec_2Estate__transformer_2EWRITE_2E2_2Emono_2EA_27state,axiom,
! [A_27state,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state),c_2Estate__transformer_2EWRITE_2E2(s(tyop_2Emin_2Efun(A_27state,A_27state),X0_2E0),s(A_27state,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state),app_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,A_27state),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Estate__transformer_2EWRITE_2E0),s(tyop_2Emin_2Efun(A_27state,A_27state),X0_2E0))),s(A_27state,X1_2E0))) ).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27c,axiom,
! [A_27c,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) = s(tyop_2Elist_2Elist(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c))),c_2Elist_2ECONS_2E0),s(A_27c,X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_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_27c,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29,axiom,
! [A_27a,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27c,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Emin_2Efun(A_27c,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Emin_2Efun(A_27c,A_27a))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c)),X1_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27b_29_29_20mono_2EA_27c,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27a,A_27c,A_27d,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27d,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27d),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(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_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27d,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27d),X1_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0))) ).
fof(arityeq1_2Ec_2Estate__transformer_2EMMAP_2E1_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27c,axiom,
! [A_27a,A_27c,A_27d,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),c_2Estate__transformer_2EMMAP_2E1(s(tyop_2Emin_2Efun(A_27c,A_27d),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)))),c_2Estate__transformer_2EMMAP_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),X0_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27d_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29,axiom,
! [A_27a,A_27b,A_27c,A_27d,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X1_2E0))) ).
fof(arityeq1_2Ec_2Estate__transformer_2EEXT_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,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),c_2Estate__transformer_2EEXT_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)))),c_2Estate__transformer_2EEXT_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),X0_2E0))) ).
fof(arityeq1_2Ec_2Estate__transformer_2EEXT_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,tyop_2Epair_2Eprod(A_27d,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Estate__transformer_2EEXT_2E1(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))),c_2Estate__transformer_2EEXT_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27d_2CA_27a_29_29,axiom,
! [A_27a,A_27b,A_27c,A_27d,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),X1_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_2CA_27a_29_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a))),X1_2E0))) ).
fof(arityeq1_2Ec_2Estate__transformer_2EMMAP_2E1_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a))),c_2Estate__transformer_2EMMAP_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)))),c_2Estate__transformer_2EMMAP_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_2CA_27a_29_29_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_2CA_27a_29_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a))),X1_2E0))) ).
fof(arityeq1_2Ec_2Estate__transformer_2EMMAP_2E1_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_2CA_27a_29_29,axiom,
! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a))),c_2Estate__transformer_2EMMAP_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)))),c_2Estate__transformer_2EMMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0))) ).
fof(arityeq1_2Ec_2Estate__transformer_2EMMAP_2E1_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29_20mono_2EA_27b,axiom,
! [A_27a,A_27b,A_27c,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a))),c_2Estate__transformer_2EMMAP_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a)))),c_2Estate__transformer_2EMMAP_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29_2CA_27a_29_29,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a))),X1_2E0))) ).
fof(arityeq1_2Ec_2Estate__transformer_2EMMAP_2E1_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29,axiom,
! [A_27a,A_27b,A_27c,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a))),c_2Estate__transformer_2EMMAP_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a)))),c_2Estate__transformer_2EMMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29_2CA_27a_29_29,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a))),X1_2E0))) ).
fof(arityeq1_2Ec_2Estate__transformer_2EEXT_2E1_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27a,A_27b,A_27c,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Estate__transformer_2EEXT_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))),c_2Estate__transformer_2EEXT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27b_29_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),X1_2E0))) ).
fof(arityeq1_2Ec_2Estate__transformer_2EEXT_2E1_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27s,axiom,
! [A_27b,A_27c,A_27s,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)),tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),c_2Estate__transformer_2EEXT_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)),tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)),tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s)))),c_2Estate__transformer_2EEXT_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),X0_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27s_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27s_29_29_20mono_2Etyop_2Emin_2Efun_28A_27s_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27s_29_29,axiom,
! [A_27a,A_27b,A_27c,A_27s,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)),tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)),tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)),tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s))),X1_2E0))) ).
fof(arityeq1_2Ec_2Elist_2EMAP_2E1_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27b_29_29,axiom,
! [A_27a,A_27b,A_27c,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))),c_2Elist_2EMAP_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27c_29_2CA_27b_29_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Efun_28A_27b_2Ctyop_2Epair_2Eprod_28A_27c_2CA_27b_29_29_29,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))),X1_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27b,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,A_27a))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27b,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ).
fof(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27b_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27a_29,axiom,
! [A_27a,A_27b,A_27c,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27c,A_27a)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27c,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27c,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27c,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),X1_2E0))) ).
fof(arityeq2_2Ec_2Estate__transformer_2EMMAP_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_27c,tyop_2Epair_2Eprod(A_27b,A_27c)),c_2Estate__transformer_2EMMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27c)))),c_2Estate__transformer_2EMMAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c)),X1_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29,axiom,
! [A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27c,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27c)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Efun(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Efun(A_27c,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27c)),X1_2E0))) ).
fof(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27b_20mono_2EA_27s_20mono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27s_29,axiom,
! [A_27b,A_27c,A_27s,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27s),tyop_2Epair_2Eprod(A_27c,A_27s)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27s),tyop_2Epair_2Eprod(A_27c,A_27s)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27s),tyop_2Epair_2Eprod(A_27c,A_27s))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),X0_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27s_20mono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27s_29_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27s_29,axiom,
! [A_27b,A_27c,A_27s,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27s),tyop_2Epair_2Eprod(A_27c,A_27s)),X0_2E0),s(tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)),tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27s),tyop_2Epair_2Eprod(A_27c,A_27s)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)),tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27s),tyop_2Epair_2Eprod(A_27c,A_27s)),X0_2E0))),s(tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29,axiom,
! [A_27a,A_27state,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_20mono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29,axiom,
! [A_27state,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_20mono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29_29_29,axiom,
! [A_27state,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X1_2E0))) ).
fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27a_29_29,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),X2_2E0))) ).
fof(arityeq2_2Ec_2Estate__transformer_2EIGNORE__BIND_2E2_2Emono_2EA_27a_20mono_2Etyop_2Eone_2Eone_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),c_2Estate__transformer_2EIGNORE__BIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)))),c_2Estate__transformer_2EIGNORE__BIND_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),X1_2E0))) ).
fof(arityeq1_2Ec_2Estate__transformer_2EUNIT_2E1_2Emono_2EA_27a_20mono_2Etyop_2Eone_2Eone,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),c_2Estate__transformer_2EUNIT_2E1(s(tyop_2Eone_2Eone,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),c_2Estate__transformer_2EUNIT_2E0),s(tyop_2Eone_2Eone,X0_2E0))) ).
fof(arityeq3_2Ec_2Estate__transformer_2ENARROW_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27state,axiom,
! [A_27a,A_27b,A_27state,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Epair_2Eprod(A_27a,A_27state),c_2Estate__transformer_2ENARROW_2E3(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),X1_2E0),s(A_27state,X2_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27state),app_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)))),c_2Estate__transformer_2ENARROW_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),X1_2E0))),s(A_27state,X2_2E0))) ).
fof(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27state_2Ctyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2CA_27state_29_29,axiom,
! [A_27a,A_27state,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X2_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Elist_2Elist__CASE_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),X2_2E0))) ).
fof(thm_2Estate__transformer_2EUNIT__DEF,axiom,
! [A_27a,A_27b,V0x_2E0,V1x_27_2E0] : s(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Estate__transformer_2EUNIT_2E2(s(A_27b,V0x_2E0),s(A_27a,V1x_27_2E0))) = s(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2E_2C_2E2(s(A_27b,V0x_2E0),s(A_27a,V1x_27_2E0))) ).
fof(thm_2Estate__transformer_2EBIND__DEF,axiom,
! [A_27a,A_27b,A_27c,V0g_2E0,V1f_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),V0g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),V1f_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27c,A_27a)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),V1f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),V0g_2E0))) ).
fof(thm_2Estate__transformer_2EIGNORE__BIND__DEF,axiom,
! [A_27a,A_27b,A_27c,F0_2E0] :
( ! [V1g_2E0,V2x_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),V1g_2E0))),s(A_27c,V2x_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),V1g_2E0)
=> ! [V0f_2E0,V1g_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Estate__transformer_2EIGNORE__BIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),V1g_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),V0f_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),V1g_2E0))))) ) ).
fof(thm_2Estate__transformer_2EMMAP__DEF,axiom,
! [A_27a,A_27b,A_27c,V0f_2E0,V1m_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Estate__transformer_2EMMAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),V1m_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),V1m_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Estate__transformer_2EUNIT_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),V0f_2E0))))) ).
fof(thm_2Estate__transformer_2EJOIN__DEF,axiom,
! [A_27a,A_27b,V0z_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Estate__transformer_2EJOIN_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),V0z_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),V0z_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Ecombin_2EI_2E0))) ).
fof(thm_2Estate__transformer_2EEXT__DEF,axiom,
! [A_27b,A_27c,A_27s,V0f_2E0,V1m_2E0] : s(tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s)),c_2Estate__transformer_2EEXT_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),V0f_2E0),s(tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)),V1m_2E0))) = s(tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27s),tyop_2Epair_2Eprod(A_27c,A_27s)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),V0f_2E0))),s(tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)),V1m_2E0))) ).
fof(thm_2Estate__transformer_2EMCOMP__DEF,axiom,
! [A_27a,A_27b,A_27c,A_27s,V0g_2E0,V1f_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),c_2Estate__transformer_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),V0g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s))),V1f_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s)),tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),c_2Estate__transformer_2EEXT_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27c,A_27s))),V0g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27s,tyop_2Epair_2Eprod(A_27b,A_27s))),V1f_2E0))) ).
fof(thm_2Estate__transformer_2EFOR__primitive__def,axiom,
! [A_27state,F0_2E0,F4_2E0,F5_2E0,F3_2E0,F2_2E0,F1_2E0] :
( ! [V0R_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),V0R_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),V0R_2E0))))
& ! [V1a_2E0,V2j_2E0,V3i_2E0] :
( s(tyop_2Enum_2Enum,V3i_2E0) != s(tyop_2Enum_2Enum,V2j_2E0)
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,V2j_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2j_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V1a_2E0))))))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V3i_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2j_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V1a_2E0)))))))) ) ) )
=> ( ! [V6i_2E0,V8j_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F4_2E0),s(tyop_2Enum_2Enum,V6i_2E0))),s(tyop_2Enum_2Enum,V8j_2E0))))
<=> s(tyop_2Enum_2Enum,V6i_2E0) = s(tyop_2Enum_2Enum,V8j_2E0) )
=> ( ! [V4FOR_2E0,V6i_2E0,V8j_2E0,V9a_2E0,V10u_2E0] : s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))))),F5_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V4FOR_2E0))),s(tyop_2Enum_2Enum,V6i_2E0))),s(tyop_2Enum_2Enum,V8j_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V9a_2E0))),s(tyop_2Eone_2Eone,V10u_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V4FOR_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V6i_2E0),s(tyop_2Enum_2Enum,V8j_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V6i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V6i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V8j_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V9a_2E0)))))))
=> ( ! [V6i_2E0,V4FOR_2E0,V8j_2E0,V9a_2E0] : s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),F3_2E0),s(tyop_2Enum_2Enum,V6i_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V4FOR_2E0))),s(tyop_2Enum_2Enum,V8j_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V9a_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Ecombin_2EI_2E1(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F4_2E0),s(tyop_2Enum_2Enum,V6i_2E0))),s(tyop_2Enum_2Enum,V8j_2E0))),s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V9a_2E0),s(tyop_2Enum_2Enum,V6i_2E0))),s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V9a_2E0),s(tyop_2Enum_2Enum,V6i_2E0))),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))))),F5_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V4FOR_2E0))),s(tyop_2Enum_2Enum,V6i_2E0))),s(tyop_2Enum_2Enum,V8j_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V9a_2E0)))))))))
=> ( ! [V4FOR_2E0,V6i_2E0,V7v1_2E0] : s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),F2_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V4FOR_2E0))),s(tyop_2Enum_2Enum,V6i_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V7v1_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V7v1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),F3_2E0),s(tyop_2Enum_2Enum,V6i_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V4FOR_2E0)))))
=> ( ! [V4FOR_2E0,V5a_27_2E0] : s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V4FOR_2E0))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),V5a_27_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),V5a_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),F2_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V4FOR_2E0)))))
=> s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Estate__transformer_2EFOR_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),F1_2E0))) ) ) ) ) ) ) ).
fof(thm_2Estate__transformer_2EFOREACH__primitive__def,axiom,
! [A_27a,A_27state,F0_2E0,F4_2E0,F3_2E0,F2_2E0,F1_2E0] :
( ! [V0R_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool)),V0R_2E0))))
<=> ( p(s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool)),V0R_2E0))))
& ! [V1h_2E0,V2a_2E0,V3t_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V3t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V2a_2E0))))),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V2a_2E0)))))) ) )
=> ( ! [V4FOREACH_2E0,V9t_2E0,V7a_2E0,V10u_2E0] : s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),F4_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V4FOREACH_2E0))),s(tyop_2Elist_2Elist(A_27a),V9t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V7a_2E0))),s(tyop_2Eone_2Eone,V10u_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V4FOREACH_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V9t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V7a_2E0)))))
=> ( ! [V7a_2E0,V4FOREACH_2E0,V8h_2E0,V9t_2E0] : s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),F3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V7a_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V4FOREACH_2E0))),s(A_27a,V8h_2E0))),s(tyop_2Elist_2Elist(A_27a),V9t_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Ecombin_2EI_2E1(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V7a_2E0),s(A_27a,V8h_2E0))),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),F4_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V4FOREACH_2E0))),s(tyop_2Elist_2Elist(A_27a),V9t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V7a_2E0)))))))
=> ( ! [V4FOREACH_2E0,V6v_2E0,V7a_2E0] : s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),F2_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V4FOREACH_2E0))),s(tyop_2Elist_2Elist(A_27a),V6v_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V7a_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(A_27a),V6v_2E0),s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Ecombin_2EI_2E1(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Estate__transformer_2EUNIT_2E1(s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),F3_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V7a_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V4FOREACH_2E0)))))
=> ( ! [V4FOREACH_2E0,V5a_27_2E0] : s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V4FOREACH_2E0))),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V5a_27_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),V5a_27_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),F2_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V4FOREACH_2E0)))))
=> s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Estate__transformer_2EFOREACH_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),F1_2E0))) ) ) ) ) ) ).
fof(thm_2Estate__transformer_2EREAD__def,axiom,
! [A_27a,A_27state,V0f_2E0,V1x_2E0] : s(tyop_2Epair_2Eprod(A_27a,A_27state),c_2Estate__transformer_2EREAD_2E2(s(tyop_2Emin_2Efun(A_27state,A_27a),V0f_2E0),s(A_27state,V1x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27state),c_2Epair_2E_2C_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27state,A_27a),V0f_2E0),s(A_27state,V1x_2E0))),s(A_27state,V1x_2E0))) ).
fof(thm_2Estate__transformer_2EWRITE__def,axiom,
! [A_27state,V0f_2E0,V1x_2E0] : s(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state),c_2Estate__transformer_2EWRITE_2E2(s(tyop_2Emin_2Efun(A_27state,A_27state),V0f_2E0),s(A_27state,V1x_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state),c_2Epair_2E_2C_2E2(s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0),s(A_27state,app_2E2(s(tyop_2Emin_2Efun(A_27state,A_27state),V0f_2E0),s(A_27state,V1x_2E0))))) ).
fof(thm_2Estate__transformer_2ENARROW__def,axiom,
! [A_27a,A_27b,A_27state,F0_2E0] :
( ! [V3r_2E0,V4s1_2E0] : s(tyop_2Epair_2Eprod(A_27a,A_27state),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,A_27state)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,A_27state))),F0_2E0),s(A_27a,V3r_2E0))),s(tyop_2Epair_2Eprod(A_27b,A_27state),V4s1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27state),c_2Epair_2E_2C_2E2(s(A_27a,V3r_2E0),s(A_27state,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27state),V4s1_2E0)))))
=> ! [V0v_2E0,V1f_2E0,V2x_2E0] : s(tyop_2Epair_2Eprod(A_27a,A_27state),c_2Estate__transformer_2ENARROW_2E3(s(A_27b,V0v_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),V1f_2E0),s(A_27state,V2x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27state),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),tyop_2Epair_2Eprod(A_27a,A_27state)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,A_27state))),F0_2E0))),s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),V1f_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27state),c_2Epair_2E_2C_2E2(s(A_27b,V0v_2E0),s(A_27state,V2x_2E0))))))) ) ).
fof(thm_2Estate__transformer_2EWIDEN__def,axiom,
! [A_27a,A_27b,A_27state,F1_2E0,F0_2E0] :
( ! [V1s1_2E0,V3r_2E0,V4s3_2E0] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),app_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),F1_2E0),s(A_27b,V1s1_2E0))),s(A_27a,V3r_2E0))),s(A_27state,V4s3_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),c_2Epair_2E_2C_2E2(s(A_27a,V3r_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27state),c_2Epair_2E_2C_2E2(s(A_27b,V1s1_2E0),s(A_27state,V4s3_2E0)))))
=> ( ! [V0f_2E0,V1s1_2E0,V2s2_2E0] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),app_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),F0_2E0),s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),V0f_2E0))),s(A_27b,V1s1_2E0))),s(A_27state,V2s2_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),F1_2E0),s(A_27b,V1s1_2E0))))),s(tyop_2Epair_2Eprod(A_27a,A_27state),app_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),V0f_2E0),s(A_27state,V2s2_2E0)))))
=> ! [V0f_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),c_2Estate__transformer_2EWIDEN_2E1(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),V0f_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),F0_2E0),s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),V0f_2E0))))) ) ) ).
fof(thm_2Estate__transformer_2Esequence__def,axiom,
! [A_27a,A_27b,F2_2E0,F1_2E0,F0_2E0] :
( ! [V2x_2E0,V3xs_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),F2_2E0),s(A_27b,V2x_2E0))),s(tyop_2Elist_2Elist(A_27b),V3xs_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Estate__transformer_2EUNIT_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V2x_2E0),s(tyop_2Elist_2Elist(A_27b),V3xs_2E0)))))
=> ( ! [V1ms_2E0,V2x_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),V1ms_2E0))),s(A_27b,V2x_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),V1ms_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),F2_2E0),s(A_27b,V2x_2E0)))))
=> ( ! [V0m_2E0,V1ms_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),V0m_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),V1ms_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),V0m_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),V1ms_2E0)))))
=> s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2Estate__transformer_2Esequence_2E0) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),c_2Elist_2EFOLDR_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Estate__transformer_2EUNIT_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))))) ) ) ) ).
fof(thm_2Estate__transformer_2EmapM__def,axiom,
! [A_27a,A_27b,A_27c,V0f_2E0] : s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b))),c_2Estate__transformer_2EmapM_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),V0f_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27b))),c_2Estate__transformer_2Esequence_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)))),c_2Elist_2EMAP_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),V0f_2E0))))) ).
fof(thm_2Estate__transformer_2EMWHILE__DEF,axiom,
! [A_27a,A_27b,F0_2E0] :
( ! [V1b_2E0,V0g_2E0,V2gv_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),V1b_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),V0g_2E0))),s(tyop_2Emin_2Ebool,V2gv_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V2gv_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),c_2Estate__transformer_2EIGNORE__BIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),V1b_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),c_2Estate__transformer_2EMWHILE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),V0g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),V1b_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),c_2Estate__transformer_2EUNIT_2E1(s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0)))))
=> ! [V0g_2E0,V1b_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),c_2Estate__transformer_2EMWHILE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),V0g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),V1b_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),V0g_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27a))))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),V1b_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),V0g_2E0))))) ) ).
fof(thm_2Estate__transformer_2EFOR__ind,axiom,
! [A_27state,V0P_2E0] :
( ! [V1i_2E0,V2j_2E0,V3a_2E0] :
( ( s(tyop_2Enum_2Enum,V1i_2E0) != s(tyop_2Enum_2Enum,V2j_2E0)
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,V2j_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2j_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V3a_2E0)))))))) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V2j_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V3a_2E0)))))))) )
=> ! [V4v_2E0,V5v1_2E0,V6v2_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V4v_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V5v1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V6v2_2E0)))))))) ) ).
fof(thm_2Estate__transformer_2EFOR__def,axiom,
! [A_27state,F0_2E0,F1_2E0] :
( ! [V1i_2E0,V0j_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Enum_2Enum,V1i_2E0))),s(tyop_2Enum_2Enum,V0j_2E0))))
<=> s(tyop_2Enum_2Enum,V1i_2E0) = s(tyop_2Enum_2Enum,V0j_2E0) )
=> ( ! [V1i_2E0,V0j_2E0,V2a_2E0,V3u_2E0] : s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),F1_2E0),s(tyop_2Enum_2Enum,V1i_2E0))),s(tyop_2Enum_2Enum,V0j_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V2a_2E0))),s(tyop_2Eone_2Eone,V3u_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Estate__transformer_2EFOR_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,V0j_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V0j_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V2a_2E0)))))))
=> ! [V0j_2E0,V1i_2E0,V2a_2E0] : s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Estate__transformer_2EFOR_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V1i_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,V0j_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V2a_2E0))))))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Enum_2Enum,V1i_2E0))),s(tyop_2Enum_2Enum,V0j_2E0))),s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V2a_2E0),s(tyop_2Enum_2Enum,V1i_2E0))),s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V2a_2E0),s(tyop_2Enum_2Enum,V1i_2E0))),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))))),F1_2E0),s(tyop_2Enum_2Enum,V1i_2E0))),s(tyop_2Enum_2Enum,V0j_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V2a_2E0))))))) ) ) ).
fof(thm_2Estate__transformer_2EFOREACH__ind,axiom,
! [A_27a,A_27state,V0P_2E0] :
( ( ! [V1a_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V1a_2E0))))))
& ! [V2h_2E0,V3t_2E0,V4a_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V3t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V4a_2E0))))))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V4a_2E0)))))) ) )
=> ! [V5v_2E0,V6v1_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V5v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V6v1_2E0)))))) ) ).
fof(thm_2Estate__transformer_2EFOREACH__def,axiom,
! [A_27a,A_27state,F0_2E0] :
( ! [V1t_2E0,V3a_2E0,V4u_2E0] : s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V3a_2E0))),s(tyop_2Eone_2Eone,V4u_2E0))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Estate__transformer_2EFOREACH_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V3a_2E0)))))
=> ( ! [V0a_2E0] : s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Estate__transformer_2EFOREACH_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V0a_2E0))))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Estate__transformer_2EUNIT_2E1(s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0)))
& ! [V1t_2E0,V2h_2E0,V3a_2E0] : s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Estate__transformer_2EFOREACH_2E1(s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V3a_2E0))))) = s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V3a_2E0),s(A_27a,V2h_2E0))),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))))),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(tyop_2Eone_2Eone,A_27state))),V3a_2E0))))) ) ) ).
fof(thm_2Estate__transformer_2EUNIT__CURRY,axiom,
! [A_27a,A_27b] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Estate__transformer_2EUNIT_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Epair_2ECURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ecombin_2EI_2E0))) ).
fof(thm_2Estate__transformer_2EMCOMP__ALT,axiom,
! [A_27a,A_27b,A_27c,A_27d,V0g_2E0,V1f_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Estate__transformer_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),V0g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),V1f_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Epair_2ECURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27d,A_27b),tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),V0g_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27d,A_27b)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),V1f_2E0))))))) ).
fof(thm_2Estate__transformer_2EMCOMP__ID,axiom,
! [A_27a,A_27b,A_27c,A_27d,A_27e,A_27f,V0g_2E0,V1f_2E0] :
( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Estate__transformer_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),V0g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Estate__transformer_2EUNIT_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),V0g_2E0)
& s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27f,A_27e))),c_2Estate__transformer_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27f,A_27e))),c_2Estate__transformer_2EUNIT_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27f,A_27e))),V1f_2E0))) = s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27f,A_27e))),V1f_2E0) ) ).
fof(thm_2Estate__transformer_2EMCOMP__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,tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Estate__transformer_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),c_2Estate__transformer_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),V1g_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27e,A_27b))),V0h_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Estate__transformer_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Estate__transformer_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),V2f_2E0),s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),V1g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27e,A_27b))),V0h_2E0))) ).
fof(thm_2Estate__transformer_2EEXT__UNIT,axiom,
! [A_27a,A_27b] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Estate__transformer_2EEXT_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Estate__transformer_2EUNIT_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Ecombin_2EI_2E0) ).
fof(thm_2Estate__transformer_2EEXT__MCOMP,axiom,
! [A_27a,A_27b,A_27c,A_27d,V0g_2E0,V1f_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Estate__transformer_2EEXT_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Estate__transformer_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),V0g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),V1f_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Estate__transformer_2EEXT_2E1(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),V0g_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),c_2Estate__transformer_2EEXT_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),V1f_2E0))))) ).
fof(thm_2Estate__transformer_2EEXT__o__UNIT,axiom,
! [A_27a,A_27b,A_27c,V0f_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Estate__transformer_2EEXT_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Estate__transformer_2EUNIT_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),V0f_2E0) ).
fof(thm_2Estate__transformer_2EUNIT__o__MCOMP,axiom,
! [A_27a,A_27b,A_27c,A_27d,V0g_2E0,V1f_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Estate__transformer_2EMCOMP_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Estate__transformer_2EUNIT_2E0),s(tyop_2Emin_2Efun(A_27d,A_27c),V0g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27d,A_27b))),c_2Estate__transformer_2EUNIT_2E0),s(tyop_2Emin_2Efun(A_27a,A_27d),V1f_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Estate__transformer_2EUNIT_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27d,A_27c),V0g_2E0),s(tyop_2Emin_2Efun(A_27a,A_27d),V1f_2E0))))) ).
fof(thm_2Estate__transformer_2EBIND__EXT,axiom,
! [A_27a,A_27b,A_27c,V0m_2E0,V1f_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),V0m_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),V1f_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Estate__transformer_2EEXT_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),V0m_2E0))) ).
fof(thm_2Estate__transformer_2EMMAP__EXT,axiom,
! [A_27a,A_27b,A_27c,V0f_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Estate__transformer_2EMMAP_2E1(s(tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Estate__transformer_2EEXT_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Estate__transformer_2EUNIT_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0))))) ).
fof(thm_2Estate__transformer_2EJOIN__EXT,axiom,
! [A_27a,A_27b] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Estate__transformer_2EJOIN_2E0) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Estate__transformer_2EEXT_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Ecombin_2EI_2E0))) ).
fof(thm_2Estate__transformer_2EEXT__JM,axiom,
! [A_27a,A_27b,A_27c,V0f_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Estate__transformer_2EEXT_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),V0f_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Estate__transformer_2EJOIN_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a))),c_2Estate__transformer_2EMMAP_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),V0f_2E0))))) ).
fof(thm_2Estate__transformer_2EBIND__LEFT__UNIT,axiom,
! [A_27a,A_27b,A_27c,V0k_2E0,V1x_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Estate__transformer_2EUNIT_2E1(s(A_27a,V1x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),V0k_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,A_27b))),V0k_2E0),s(A_27a,V1x_2E0))) ).
fof(thm_2Estate__transformer_2EUNIT__UNCURRY,axiom,
! [A_27a,A_27b,V0s_2E0] : s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2EUNCURRY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Estate__transformer_2EUNIT_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),V0s_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),V0s_2E0) ).
fof(thm_2Estate__transformer_2EBIND__RIGHT__UNIT,axiom,
! [A_27a,A_27b,V0k_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),V0k_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Estate__transformer_2EUNIT_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),V0k_2E0) ).
fof(thm_2Estate__transformer_2EBIND__ASSOC,axiom,
! [A_27a,A_27b,A_27c,A_27d,F0_2E0] :
( ! [V1m_2E0,V2n_2E0,V3a_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),V1m_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),V2n_2E0))),s(A_27b,V3a_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),V1m_2E0),s(A_27b,V3a_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),V2n_2E0)))
=> ! [V0k_2E0,V1m_2E0,V2n_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),V0k_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),V1m_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),V2n_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),V0k_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),V1m_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),V2n_2E0))) ) ).
fof(thm_2Estate__transformer_2EMMAP__ID,axiom,
! [A_27a,A_27b] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Estate__transformer_2EMMAP_2E1(s(tyop_2Emin_2Efun(A_27b,A_27b),c_2Ecombin_2EI_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Ecombin_2EI_2E0) ).
fof(thm_2Estate__transformer_2EMMAP__COMP,axiom,
! [A_27a,A_27b,A_27c,A_27d,V0f_2E0,V1g_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),c_2Estate__transformer_2EMMAP_2E1(s(tyop_2Emin_2Efun(A_27b,A_27d),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27d,A_27a))),c_2Estate__transformer_2EMMAP_2E1(s(tyop_2Emin_2Efun(A_27c,A_27d),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Estate__transformer_2EMMAP_2E1(s(tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0))))) ).
fof(thm_2Estate__transformer_2EMMAP__UNIT,axiom,
! [A_27a,A_27b,A_27c,V0f_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Estate__transformer_2EMMAP_2E1(s(tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Estate__transformer_2EUNIT_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Estate__transformer_2EUNIT_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0))) ).
fof(thm_2Estate__transformer_2EEXT__o__JOIN,axiom,
! [A_27a,A_27b,A_27c,V0f_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Estate__transformer_2EEXT_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Estate__transformer_2EJOIN_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Estate__transformer_2EEXT_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Estate__transformer_2EEXT_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),V0f_2E0))))) ).
fof(thm_2Estate__transformer_2EMMAP__JOIN,axiom,
! [A_27a,A_27b,A_27c,V0f_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Estate__transformer_2EMMAP_2E1(s(tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Estate__transformer_2EJOIN_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Estate__transformer_2EJOIN_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a))),c_2Estate__transformer_2EMMAP_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),c_2Estate__transformer_2EMMAP_2E1(s(tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0))))))) ).
fof(thm_2Estate__transformer_2EJOIN__UNIT,axiom,
! [A_27a,A_27b] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Estate__transformer_2EJOIN_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a))),c_2Estate__transformer_2EUNIT_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Ecombin_2EI_2E0) ).
fof(thm_2Estate__transformer_2EJOIN__MMAP__UNIT,axiom,
! [A_27a,A_27b] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Estate__transformer_2EJOIN_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a))),c_2Estate__transformer_2EMMAP_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Estate__transformer_2EUNIT_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Ecombin_2EI_2E0) ).
fof(thm_2Estate__transformer_2EJOIN__MAP__JOIN,axiom,
! [A_27a,A_27b] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Estate__transformer_2EJOIN_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a))),c_2Estate__transformer_2EMMAP_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Estate__transformer_2EJOIN_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Estate__transformer_2EJOIN_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a)),A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),A_27a))),c_2Estate__transformer_2EJOIN_2E0))) ).
fof(thm_2Estate__transformer_2EJOIN__MAP,axiom,
! [A_27a,A_27b,A_27c,V0k_2E0,V1m_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),V0k_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),V1m_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),c_2Estate__transformer_2EJOIN_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a)),A_27a)),c_2Estate__transformer_2EMMAP_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27a))),V1m_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),V0k_2E0))))) ).
fof(thm_2Estate__transformer_2EFST__o__UNIT,axiom,
! [A_27a,A_27b,V0x_2E0] : s(tyop_2Emin_2Efun(A_27b,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Estate__transformer_2EUNIT_2E1(s(A_27a,V0x_2E0))))) = s(tyop_2Emin_2Efun(A_27b,A_27a),c_2Ecombin_2EK_2E1(s(A_27a,V0x_2E0))) ).
fof(thm_2Estate__transformer_2ESND__o__UNIT,axiom,
! [A_27a,A_27b,V0x_2E0] : s(tyop_2Emin_2Efun(A_27b,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Estate__transformer_2EUNIT_2E1(s(A_27a,V0x_2E0))))) = s(tyop_2Emin_2Efun(A_27b,A_27b),c_2Ecombin_2EI_2E0) ).
fof(thm_2Estate__transformer_2EFST__o__MMAP,axiom,
! [A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0] : s(tyop_2Emin_2Efun(A_27c,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27b),c_2Epair_2EFST_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27b,A_27c)),c_2Estate__transformer_2EMMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c)),V1g_2E0))))) = s(tyop_2Emin_2Efun(A_27c,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c)),V1g_2E0))))) ).
fof(thm_2Estate__transformer_2Esequence__nil,axiom,
! [A_27a,A_27b] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Estate__transformer_2Esequence_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Elist_2ENIL_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Estate__transformer_2EUNIT_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) ).
fof(thm_2Estate__transformer_2EmapM__nil,axiom,
! [A_27a,A_27b,A_27c,V0f_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Estate__transformer_2EmapM_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),V0f_2E0),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ENIL_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Estate__transformer_2EUNIT_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) ).
fof(thm_2Estate__transformer_2EmapM__cons,axiom,
! [A_27a,A_27b,A_27c,F1_2E0,F0_2E0] :
( ! [V3y_2E0,V4ys_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),F1_2E0),s(A_27b,V3y_2E0))),s(tyop_2Elist_2Elist(A_27b),V4ys_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Estate__transformer_2EUNIT_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V3y_2E0),s(tyop_2Elist_2Elist(A_27b),V4ys_2E0)))))
=> ( ! [V2f_2E0,V0xs_2E0,V3y_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))))),F0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),V2f_2E0))),s(tyop_2Elist_2Elist(A_27c),V0xs_2E0))),s(A_27b,V3y_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Estate__transformer_2EmapM_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),V2f_2E0),s(tyop_2Elist_2Elist(A_27c),V0xs_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),F1_2E0),s(A_27b,V3y_2E0)))))
=> ! [V0xs_2E0,V1x_2E0,V2f_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Estate__transformer_2EmapM_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),V2f_2E0),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V1x_2E0),s(tyop_2Elist_2Elist(A_27c),V0xs_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Estate__transformer_2EBIND_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),V2f_2E0),s(A_27c,V1x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27a))))),F0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a))),V2f_2E0))),s(tyop_2Elist_2Elist(A_27c),V0xs_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) ) ).
%------------------------------------------------------------------------------