ITP001 Axioms: ITP074+4.ax
%------------------------------------------------------------------------------
% File : ITP074+4 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : ring.ax [Gau19]
% : HL4074+4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 114 ( 68 unt; 0 def)
% Number of atoms : 259 ( 200 equ)
% Maximal formula atoms : 25 ( 2 avg)
% Number of connectives : 148 ( 3 ~; 3 |; 96 &)
% ( 21 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 6 avg)
% Maximal term depth : 23 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 92 ( 92 usr; 44 con; 0-5 aty)
% Number of variables : 671 ( 642 !; 29 ?)
% 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_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2EDATATYPE_2E0),s(tyop_2Emin_2Ebool,X0_2E0))) ).
fof(arityeq1_2Ec_2Ering_2Eis__ring_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ering_2Eis__ring_2E1(s(tyop_2Ering_2Ering(A_27a),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Ebool),c_2Ering_2Eis__ring_2E0),s(tyop_2Ering_2Ering(A_27a),X0_2E0))) ).
fof(arityeq1_2Ec_2Esemi__ring_2Eis__semi__ring_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Esemi__ring_2Eis__semi__ring_2E1(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Emin_2Ebool),c_2Esemi__ring_2Eis__semi__ring_2E0),s(tyop_2Esemi__ring_2Esemi__ring(A_27a),X0_2E0))) ).
fof(arityeq1_2Ec_2Ering_2Esemi__ring__of_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Esemi__ring_2Esemi__ring(A_27a),c_2Ering_2Esemi__ring__of_2E1(s(tyop_2Ering_2Ering(A_27a),X0_2E0))) = s(tyop_2Esemi__ring_2Esemi__ring(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Ering_2Esemi__ring__of_2E0),s(tyop_2Ering_2Ering(A_27a),X0_2E0))) ).
fof(arityeq1_2Ec_2Ering_2Ering__R0_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(A_27a,c_2Ering_2Ering__R0_2E1(s(tyop_2Ering_2Ering(A_27a),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),A_27a),c_2Ering_2Ering__R0_2E0),s(tyop_2Ering_2Ering(A_27a),X0_2E0))) ).
fof(arityeq2_2Ec_2Ering_2Ering__R0__fupd_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R0__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(tyop_2Ering_2Ering(A_27a),X1_2E0))) = s(tyop_2Ering_2Ering(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a))),c_2Ering_2Ering__R0__fupd_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Ering_2Ering(A_27a),X1_2E0))) ).
fof(arityeq2_2Ec_2Ering_2Ering__R1__fupd_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R1__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(tyop_2Ering_2Ering(A_27a),X1_2E0))) = s(tyop_2Ering_2Ering(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a))),c_2Ering_2Ering__R1__fupd_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Ering_2Ering(A_27a),X1_2E0))) ).
fof(arityeq2_2Ec_2Ering_2Ering__RM__fupd_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RM__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),X0_2E0),s(tyop_2Ering_2Ering(A_27a),X1_2E0))) = s(tyop_2Ering_2Ering(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a))),c_2Ering_2Ering__RM__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),X0_2E0))),s(tyop_2Ering_2Ering(A_27a),X1_2E0))) ).
fof(arityeq2_2Ec_2Ering_2Ering__RN__fupd_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RN__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0),s(tyop_2Ering_2Ering(A_27a),X1_2E0))) = s(tyop_2Ering_2Ering(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a))),c_2Ering_2Ering__RN__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))),s(tyop_2Ering_2Ering(A_27a),X1_2E0))) ).
fof(arityeq2_2Ec_2Ering_2Ering__RP__fupd_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RP__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),X0_2E0),s(tyop_2Ering_2Ering(A_27a),X1_2E0))) = s(tyop_2Ering_2Ering(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a))),c_2Ering_2Ering__RP__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),X0_2E0))),s(tyop_2Ering_2Ering(A_27a),X1_2E0))) ).
fof(arityeq5_2Ec_2Ering_2Erecordtype_2Ering_2E5_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0,X4_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X3_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X4_2E0))) = s(tyop_2Ering_2Ering(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Ering_2Ering(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Ering_2Ering(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Ering_2Ering(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Ering_2Ering(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Ering_2Ering(A_27a)))))),c_2Ering_2Erecordtype_2Ering_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X3_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X4_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))) ).
fof(arityeq1_2Ec_2Ering_2Ering__R0__fupd_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R0__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a))),c_2Ering_2Ering__R0__fupd_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))) ).
fof(arityeq1_2Ec_2Ering_2Ering__R1_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(A_27a,c_2Ering_2Ering__R1_2E1(s(tyop_2Ering_2Ering(A_27a),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),A_27a),c_2Ering_2Ering__R1_2E0),s(tyop_2Ering_2Ering(A_27a),X0_2E0))) ).
fof(arityeq1_2Ec_2Ering_2Ering__R1__fupd_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R1__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a))),c_2Ering_2Ering__R1__fupd_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))) ).
fof(arityeq1_2Ec_2Ering_2Ering__RM_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RM_2E1(s(tyop_2Ering_2Ering(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ering_2Ering__RM_2E0),s(tyop_2Ering_2Ering(A_27a),X0_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),X1_2E0))) ).
fof(arityeq1_2Ec_2Ering_2Ering__RM__fupd_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RM__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a))),c_2Ering_2Ering__RM__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),X0_2E0))) ).
fof(arityeq1_2Ec_2Ering_2Ering__RN_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ering_2Ering__RN_2E1(s(tyop_2Ering_2Ering(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RN_2E0),s(tyop_2Ering_2Ering(A_27a),X0_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27a_29,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0))) ).
fof(arityeq1_2Ec_2Ering_2Ering__RN__fupd_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RN__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a))),c_2Ering_2Ering__RN__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))) ).
fof(arityeq1_2Ec_2Ering_2Ering__RP_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RP_2E1(s(tyop_2Ering_2Ering(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ering_2Ering__RP_2E0),s(tyop_2Ering_2Ering(A_27a),X0_2E0))) ).
fof(arityeq1_2Ec_2Ering_2Ering__RP__fupd_2E1_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RP__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a))),c_2Ering_2Ering__RP__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),X0_2E0))) ).
fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EK_2E1(s(A_27a,X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ecombin_2EK_2E0),s(A_27a,X0_2E0))) ).
fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27a_29,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ecombin_2EK_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))) ).
fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29,axiom,
! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)))),c_2Ecombin_2EK_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),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(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(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_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_29_29_29_29_20mono_2Etyop_2Ering_2Ering_28A_27a_29,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)))))),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))))))),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))))))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)))))),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))))))),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)))))),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))))))),X1_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2Etyop_2Ering_2Ering_28A_27a_29_20mono_2Etyop_2Ering_2Ering_28A_27a_29,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),X1_2E0))) ).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Ering_2Ering_28A_27a_29_20mono_2Etyop_2Ering_2Ering_28A_27a_29_20mono_2Etyop_2Ering_2Ering_28A_27a_29,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),X1_2E0))) ).
fof(arityeq2_2Ec_2Ering_2Ering__CASE_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a,A_27b,X0_2E0,X1_2E0] : s(A_27b,c_2Ering_2Ering__CASE_2E2(s(tyop_2Ering_2Ering(A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b))))),X1_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b))))),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b))))),A_27b)),c_2Ering_2Ering__CASE_2E0),s(tyop_2Ering_2Ering(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b))))),X1_2E0))) ).
fof(arityeq3_2Ec_2Ering_2Ering__RM_2E3_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(A_27a,c_2Ering_2Ering__RM_2E3(s(tyop_2Ering_2Ering(A_27a),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ering_2Ering__RM_2E0),s(tyop_2Ering_2Ering(A_27a),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) ).
fof(arityeq2_2Ec_2Ering_2Ering__RN_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(A_27a,c_2Ering_2Ering__RN_2E2(s(tyop_2Ering_2Ering(A_27a),X0_2E0),s(A_27a,X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RN_2E0),s(tyop_2Ering_2Ering(A_27a),X0_2E0))),s(A_27a,X1_2E0))) ).
fof(arityeq2_2Ec_2Ering_2Ering__size_2E2_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Ering_2Ering__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Ering_2Ering(A_27a),X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Enum_2Enum)),c_2Ering_2Ering__size_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Ering_2Ering(A_27a),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_29_29,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))))),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)))),X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)))),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)))),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))))))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)))),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_29,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)))),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))),X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)))))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27a_29,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))) ).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29,axiom,
! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0))) ).
fof(arityeq3_2Ec_2Eind__type_2ECONSTR_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_29_29_29,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)))))),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))))),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))))))),X2_2E0))) = s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))))))),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))))))),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)))))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))))))),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))))))))),c_2Eind__type_2ECONSTR_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))))),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))))))),X2_2E0))) ).
fof(arityeq3_2Ec_2Ering_2Ering__RP_2E3_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(A_27a,c_2Ering_2Ering__RP_2E3(s(tyop_2Ering_2Ering(A_27a),X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ering_2Ering__RP_2E0),s(tyop_2Ering_2Ering(A_27a),X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) ).
fof(arityeq4_2Ec_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4_2Emono_2EA_27a,axiom,
! [A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0] : s(tyop_2Esemi__ring_2Esemi__ring(A_27a),c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(s(A_27a,X0_2E0),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X3_2E0))) = s(tyop_2Esemi__ring_2Esemi__ring(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Esemi__ring_2Esemi__ring(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Esemi__ring_2Esemi__ring(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Esemi__ring_2Esemi__ring(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Esemi__ring_2Esemi__ring(A_27a))))),c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),X3_2E0))) ).
fof(thm_2Ering_2Ering__TY__DEF,axiom,
! [A_27a,F1_2E0,F0_2E0] :
( ! [V9n_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))))))),F1_2E0),s(tyop_2Enum_2Enum,V9n_2E0))) = s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)))))),c_2Eind__type_2EBOTTOM_2E0)
=> ( ! [V1a0_27_2E0] :
( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)))))),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)))))),V1a0_27_2E0))))
<=> ! [V2_27ring_27_2E0] :
( ! [V3a0_27_2E0] :
( ? [V4a0_2E0,V5a1_2E0,V6a2_2E0,V7a3_2E0,V8a4_2E0] : s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)))))),V3a0_27_2E0) = s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)))))),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))))),c_2Epair_2E_2C_2E2(s(A_27a,V4a0_2E0),s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)))),c_2Epair_2E_2C_2E2(s(A_27a,V5a1_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V6a2_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V7a3_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V8a4_2E0))))))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))))))),F1_2E0)))
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)))))),tyop_2Emin_2Ebool),V2_27ring_27_2E0),s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)))))),V3a0_27_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)))))),tyop_2Emin_2Ebool),V2_27ring_27_2E0),s(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)))))),V1a0_27_2E0)))) ) )
=> ? [V0rep_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)))))),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,A_27a))))))),V0rep_2E0)))) ) ) ).
fof(thm_2Ering_2Ering__case__def,axiom,
! [A_27a,A_27b,V0a0_2E0,V1a1_2E0,V2a2_2E0,V3a3_2E0,V4a4_2E0,V5f_2E0] : s(A_27b,c_2Ering_2Ering__CASE_2E2(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V0a0_2E0),s(A_27a,V1a1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V2a2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3a3_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V4a4_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b))))),V5f_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b))))),V5f_2E0),s(A_27a,V0a0_2E0))),s(A_27a,V1a1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V2a2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3a3_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V4a4_2E0))) ).
fof(thm_2Ering_2Ering__size__def,axiom,
! [A_27a,V0f_2E0,V1a0_2E0,V2a1_2E0,V3a2_2E0,V4a3_2E0,V5a4_2E0] : s(tyop_2Enum_2Enum,c_2Ering_2Ering__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V1a0_2E0),s(A_27a,V2a1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3a2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V4a3_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V5a4_2E0))))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(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_2B_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V1a0_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V2a1_2E0))))))) ).
fof(thm_2Ering_2Ering__R0,axiom,
! [A_27a,V0a_2E0,V1a0_2E0,V2f_2E0,V3f0_2E0,V4f1_2E0] : s(A_27a,c_2Ering_2Ering__R0_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V0a_2E0),s(A_27a,V1a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V4f1_2E0))))) = s(A_27a,V0a_2E0) ).
fof(thm_2Ering_2Ering__R1,axiom,
! [A_27a,V0a_2E0,V1a0_2E0,V2f_2E0,V3f0_2E0,V4f1_2E0] : s(A_27a,c_2Ering_2Ering__R1_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V0a_2E0),s(A_27a,V1a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V4f1_2E0))))) = s(A_27a,V1a0_2E0) ).
fof(thm_2Ering_2Ering__RP,axiom,
! [A_27a,V0a_2E0,V1a0_2E0,V2f_2E0,V3f0_2E0,V4f1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RP_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V0a_2E0),s(A_27a,V1a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V4f1_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V2f_2E0) ).
fof(thm_2Ering_2Ering__RM,axiom,
! [A_27a,V0a_2E0,V1a0_2E0,V2f_2E0,V3f0_2E0,V4f1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RM_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V0a_2E0),s(A_27a,V1a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V4f1_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3f0_2E0) ).
fof(thm_2Ering_2Ering__RN,axiom,
! [A_27a,V0a_2E0,V1a0_2E0,V2f_2E0,V3f0_2E0,V4f1_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ering_2Ering__RN_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V0a_2E0),s(A_27a,V1a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V4f1_2E0))))) = s(tyop_2Emin_2Efun(A_27a,A_27a),V4f1_2E0) ).
fof(thm_2Ering_2Ering__R0__fupd,axiom,
! [A_27a,V0f2_2E0,V1a_2E0,V2a0_2E0,V3f_2E0,V4f0_2E0,V5f1_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R0__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f2_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V1a_2E0),s(A_27a,V2a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V4f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V5f1_2E0))))) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f2_2E0),s(A_27a,V1a_2E0))),s(A_27a,V2a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V4f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V5f1_2E0))) ).
fof(thm_2Ering_2Ering__R1__fupd,axiom,
! [A_27a,V0f2_2E0,V1a_2E0,V2a0_2E0,V3f_2E0,V4f0_2E0,V5f1_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R1__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f2_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V1a_2E0),s(A_27a,V2a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V4f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V5f1_2E0))))) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V1a_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f2_2E0),s(A_27a,V2a0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V4f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V5f1_2E0))) ).
fof(thm_2Ering_2Ering__RP__fupd,axiom,
! [A_27a,V0f2_2E0,V1a_2E0,V2a0_2E0,V3f_2E0,V4f0_2E0,V5f1_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RP__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V0f2_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V1a_2E0),s(A_27a,V2a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V4f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V5f1_2E0))))) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V1a_2E0),s(A_27a,V2a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V0f2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V4f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V5f1_2E0))) ).
fof(thm_2Ering_2Ering__RM__fupd,axiom,
! [A_27a,V0f2_2E0,V1a_2E0,V2a0_2E0,V3f_2E0,V4f0_2E0,V5f1_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RM__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V0f2_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V1a_2E0),s(A_27a,V2a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V4f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V5f1_2E0))))) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V1a_2E0),s(A_27a,V2a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V0f2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V4f0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V5f1_2E0))) ).
fof(thm_2Ering_2Ering__RN__fupd,axiom,
! [A_27a,V0f2_2E0,V1a_2E0,V2a0_2E0,V3f_2E0,V4f0_2E0,V5f1_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RN__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V0f2_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V1a_2E0),s(A_27a,V2a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V4f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V5f1_2E0))))) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V1a_2E0),s(A_27a,V2a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V4f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V0f2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V5f1_2E0))))) ).
fof(thm_2Ering_2Eis__ring__def,axiom,
! [A_27a,V0r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ering_2Eis__ring_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0))))
<=> ( ! [V1n_2E0,V2m_2E0] : s(A_27a,c_2Ering_2Ering__RP_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V1n_2E0),s(A_27a,V2m_2E0))) = s(A_27a,c_2Ering_2Ering__RP_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V2m_2E0),s(A_27a,V1n_2E0)))
& ! [V3n_2E0,V4m_2E0,V5p_2E0] : s(A_27a,c_2Ering_2Ering__RP_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V3n_2E0),s(A_27a,c_2Ering_2Ering__RP_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V4m_2E0),s(A_27a,V5p_2E0))))) = s(A_27a,c_2Ering_2Ering__RP_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,c_2Ering_2Ering__RP_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V3n_2E0),s(A_27a,V4m_2E0))),s(A_27a,V5p_2E0)))
& ! [V6n_2E0,V7m_2E0] : s(A_27a,c_2Ering_2Ering__RM_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V6n_2E0),s(A_27a,V7m_2E0))) = s(A_27a,c_2Ering_2Ering__RM_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V7m_2E0),s(A_27a,V6n_2E0)))
& ! [V8n_2E0,V9m_2E0,V10p_2E0] : s(A_27a,c_2Ering_2Ering__RM_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V8n_2E0),s(A_27a,c_2Ering_2Ering__RM_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V9m_2E0),s(A_27a,V10p_2E0))))) = s(A_27a,c_2Ering_2Ering__RM_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,c_2Ering_2Ering__RM_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V8n_2E0),s(A_27a,V9m_2E0))),s(A_27a,V10p_2E0)))
& ! [V11n_2E0] : s(A_27a,c_2Ering_2Ering__RP_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,c_2Ering_2Ering__R0_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0))),s(A_27a,V11n_2E0))) = s(A_27a,V11n_2E0)
& ! [V12n_2E0] : s(A_27a,c_2Ering_2Ering__RM_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,c_2Ering_2Ering__R1_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0))),s(A_27a,V12n_2E0))) = s(A_27a,V12n_2E0)
& ! [V13n_2E0] : s(A_27a,c_2Ering_2Ering__RP_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V13n_2E0),s(A_27a,c_2Ering_2Ering__RN_2E2(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V13n_2E0))))) = s(A_27a,c_2Ering_2Ering__R0_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0)))
& ! [V14n_2E0,V15m_2E0,V16p_2E0] : s(A_27a,c_2Ering_2Ering__RM_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,c_2Ering_2Ering__RP_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V14n_2E0),s(A_27a,V15m_2E0))),s(A_27a,V16p_2E0))) = s(A_27a,c_2Ering_2Ering__RP_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,c_2Ering_2Ering__RM_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V14n_2E0),s(A_27a,V16p_2E0))),s(A_27a,c_2Ering_2Ering__RM_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V15m_2E0),s(A_27a,V16p_2E0))))) ) ) ).
fof(thm_2Ering_2Esemi__ring__of__def,axiom,
! [A_27a,V0r_2E0] : s(tyop_2Esemi__ring_2Esemi__ring(A_27a),c_2Ering_2Esemi__ring__of_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0))) = s(tyop_2Esemi__ring_2Esemi__ring(A_27a),c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4(s(A_27a,c_2Ering_2Ering__R0_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0))),s(A_27a,c_2Ering_2Ering__R1_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RP_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RM_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0))))) ).
fof(thm_2Ering_2Ering__accessors,axiom,
! [A_27a] :
( ! [V0a_2E0,V1a0_2E0,V2f_2E0,V3f0_2E0,V4f1_2E0] : s(A_27a,c_2Ering_2Ering__R0_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V0a_2E0),s(A_27a,V1a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V4f1_2E0))))) = s(A_27a,V0a_2E0)
& ! [V5a_2E0,V6a0_2E0,V7f_2E0,V8f0_2E0,V9f1_2E0] : s(A_27a,c_2Ering_2Ering__R1_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V5a_2E0),s(A_27a,V6a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V7f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V8f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V9f1_2E0))))) = s(A_27a,V6a0_2E0)
& ! [V10a_2E0,V11a0_2E0,V12f_2E0,V13f0_2E0,V14f1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RP_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V10a_2E0),s(A_27a,V11a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V12f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V13f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V14f1_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V12f_2E0)
& ! [V15a_2E0,V16a0_2E0,V17f_2E0,V18f0_2E0,V19f1_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RM_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V15a_2E0),s(A_27a,V16a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V17f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V18f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V19f1_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V18f0_2E0)
& ! [V20a_2E0,V21a0_2E0,V22f_2E0,V23f0_2E0,V24f1_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ering_2Ering__RN_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V20a_2E0),s(A_27a,V21a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V22f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V23f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V24f1_2E0))))) = s(tyop_2Emin_2Efun(A_27a,A_27a),V24f1_2E0) ) ).
fof(thm_2Ering_2Ering__fn__updates,axiom,
! [A_27a] :
( ! [V0f2_2E0,V1a_2E0,V2a0_2E0,V3f_2E0,V4f0_2E0,V5f1_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R0__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f2_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V1a_2E0),s(A_27a,V2a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V4f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V5f1_2E0))))) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f2_2E0),s(A_27a,V1a_2E0))),s(A_27a,V2a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V4f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V5f1_2E0)))
& ! [V6f2_2E0,V7a_2E0,V8a0_2E0,V9f_2E0,V10f0_2E0,V11f1_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R1__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V6f2_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V7a_2E0),s(A_27a,V8a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V9f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V10f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V11f1_2E0))))) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V7a_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V6f2_2E0),s(A_27a,V8a0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V9f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V10f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V11f1_2E0)))
& ! [V12f2_2E0,V13a_2E0,V14a0_2E0,V15f_2E0,V16f0_2E0,V17f1_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RP__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V12f2_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V13a_2E0),s(A_27a,V14a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V15f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V16f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V17f1_2E0))))) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V13a_2E0),s(A_27a,V14a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V12f2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V15f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V16f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V17f1_2E0)))
& ! [V18f2_2E0,V19a_2E0,V20a0_2E0,V21f_2E0,V22f0_2E0,V23f1_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RM__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V18f2_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V19a_2E0),s(A_27a,V20a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V21f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V22f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V23f1_2E0))))) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V19a_2E0),s(A_27a,V20a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V21f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V18f2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V22f0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V23f1_2E0)))
& ! [V24f2_2E0,V25a_2E0,V26a0_2E0,V27f_2E0,V28f0_2E0,V29f1_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RN__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V24f2_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V25a_2E0),s(A_27a,V26a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V27f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V28f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V29f1_2E0))))) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V25a_2E0),s(A_27a,V26a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V27f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V28f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V24f2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V29f1_2E0))))) ) ).
fof(thm_2Ering_2Ering__accfupds,axiom,
! [A_27a] :
( ! [V0r_2E0,V1f_2E0] : s(A_27a,c_2Ering_2Ering__R0_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R1__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Ering_2Ering(A_27a),V0r_2E0))))) = s(A_27a,c_2Ering_2Ering__R0_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0)))
& ! [V2r_2E0,V3f_2E0] : s(A_27a,c_2Ering_2Ering__R0_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RP__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V3f_2E0),s(tyop_2Ering_2Ering(A_27a),V2r_2E0))))) = s(A_27a,c_2Ering_2Ering__R0_2E1(s(tyop_2Ering_2Ering(A_27a),V2r_2E0)))
& ! [V4r_2E0,V5f_2E0] : s(A_27a,c_2Ering_2Ering__R0_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RM__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V5f_2E0),s(tyop_2Ering_2Ering(A_27a),V4r_2E0))))) = s(A_27a,c_2Ering_2Ering__R0_2E1(s(tyop_2Ering_2Ering(A_27a),V4r_2E0)))
& ! [V6r_2E0,V7f_2E0] : s(A_27a,c_2Ering_2Ering__R0_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RN__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V7f_2E0),s(tyop_2Ering_2Ering(A_27a),V6r_2E0))))) = s(A_27a,c_2Ering_2Ering__R0_2E1(s(tyop_2Ering_2Ering(A_27a),V6r_2E0)))
& ! [V8r_2E0,V9f_2E0] : s(A_27a,c_2Ering_2Ering__R1_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R0__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V9f_2E0),s(tyop_2Ering_2Ering(A_27a),V8r_2E0))))) = s(A_27a,c_2Ering_2Ering__R1_2E1(s(tyop_2Ering_2Ering(A_27a),V8r_2E0)))
& ! [V10r_2E0,V11f_2E0] : s(A_27a,c_2Ering_2Ering__R1_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RP__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V11f_2E0),s(tyop_2Ering_2Ering(A_27a),V10r_2E0))))) = s(A_27a,c_2Ering_2Ering__R1_2E1(s(tyop_2Ering_2Ering(A_27a),V10r_2E0)))
& ! [V12r_2E0,V13f_2E0] : s(A_27a,c_2Ering_2Ering__R1_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RM__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V13f_2E0),s(tyop_2Ering_2Ering(A_27a),V12r_2E0))))) = s(A_27a,c_2Ering_2Ering__R1_2E1(s(tyop_2Ering_2Ering(A_27a),V12r_2E0)))
& ! [V14r_2E0,V15f_2E0] : s(A_27a,c_2Ering_2Ering__R1_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RN__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V15f_2E0),s(tyop_2Ering_2Ering(A_27a),V14r_2E0))))) = s(A_27a,c_2Ering_2Ering__R1_2E1(s(tyop_2Ering_2Ering(A_27a),V14r_2E0)))
& ! [V16r_2E0,V17f_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RP_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R0__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V17f_2E0),s(tyop_2Ering_2Ering(A_27a),V16r_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RP_2E1(s(tyop_2Ering_2Ering(A_27a),V16r_2E0)))
& ! [V18r_2E0,V19f_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RP_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R1__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V19f_2E0),s(tyop_2Ering_2Ering(A_27a),V18r_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RP_2E1(s(tyop_2Ering_2Ering(A_27a),V18r_2E0)))
& ! [V20r_2E0,V21f_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RP_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RM__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V21f_2E0),s(tyop_2Ering_2Ering(A_27a),V20r_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RP_2E1(s(tyop_2Ering_2Ering(A_27a),V20r_2E0)))
& ! [V22r_2E0,V23f_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RP_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RN__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V23f_2E0),s(tyop_2Ering_2Ering(A_27a),V22r_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RP_2E1(s(tyop_2Ering_2Ering(A_27a),V22r_2E0)))
& ! [V24r_2E0,V25f_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RM_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R0__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V25f_2E0),s(tyop_2Ering_2Ering(A_27a),V24r_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RM_2E1(s(tyop_2Ering_2Ering(A_27a),V24r_2E0)))
& ! [V26r_2E0,V27f_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RM_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R1__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V27f_2E0),s(tyop_2Ering_2Ering(A_27a),V26r_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RM_2E1(s(tyop_2Ering_2Ering(A_27a),V26r_2E0)))
& ! [V28r_2E0,V29f_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RM_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RP__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V29f_2E0),s(tyop_2Ering_2Ering(A_27a),V28r_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RM_2E1(s(tyop_2Ering_2Ering(A_27a),V28r_2E0)))
& ! [V30r_2E0,V31f_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RM_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RN__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V31f_2E0),s(tyop_2Ering_2Ering(A_27a),V30r_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RM_2E1(s(tyop_2Ering_2Ering(A_27a),V30r_2E0)))
& ! [V32r_2E0,V33f_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ering_2Ering__RN_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R0__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V33f_2E0),s(tyop_2Ering_2Ering(A_27a),V32r_2E0))))) = s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ering_2Ering__RN_2E1(s(tyop_2Ering_2Ering(A_27a),V32r_2E0)))
& ! [V34r_2E0,V35f_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ering_2Ering__RN_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R1__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V35f_2E0),s(tyop_2Ering_2Ering(A_27a),V34r_2E0))))) = s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ering_2Ering__RN_2E1(s(tyop_2Ering_2Ering(A_27a),V34r_2E0)))
& ! [V36r_2E0,V37f_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ering_2Ering__RN_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RP__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V37f_2E0),s(tyop_2Ering_2Ering(A_27a),V36r_2E0))))) = s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ering_2Ering__RN_2E1(s(tyop_2Ering_2Ering(A_27a),V36r_2E0)))
& ! [V38r_2E0,V39f_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ering_2Ering__RN_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RM__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V39f_2E0),s(tyop_2Ering_2Ering(A_27a),V38r_2E0))))) = s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ering_2Ering__RN_2E1(s(tyop_2Ering_2Ering(A_27a),V38r_2E0)))
& ! [V40r_2E0,V41f_2E0] : s(A_27a,c_2Ering_2Ering__R0_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R0__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V41f_2E0),s(tyop_2Ering_2Ering(A_27a),V40r_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V41f_2E0),s(A_27a,c_2Ering_2Ering__R0_2E1(s(tyop_2Ering_2Ering(A_27a),V40r_2E0)))))
& ! [V42r_2E0,V43f_2E0] : s(A_27a,c_2Ering_2Ering__R1_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R1__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V43f_2E0),s(tyop_2Ering_2Ering(A_27a),V42r_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V43f_2E0),s(A_27a,c_2Ering_2Ering__R1_2E1(s(tyop_2Ering_2Ering(A_27a),V42r_2E0)))))
& ! [V44r_2E0,V45f_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RP_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RP__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V45f_2E0),s(tyop_2Ering_2Ering(A_27a),V44r_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V45f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RP_2E1(s(tyop_2Ering_2Ering(A_27a),V44r_2E0)))))
& ! [V46r_2E0,V47f_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RM_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RM__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V47f_2E0),s(tyop_2Ering_2Ering(A_27a),V46r_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V47f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RM_2E1(s(tyop_2Ering_2Ering(A_27a),V46r_2E0)))))
& ! [V48r_2E0,V49f_2E0] : s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ering_2Ering__RN_2E1(s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RN__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V49f_2E0),s(tyop_2Ering_2Ering(A_27a),V48r_2E0))))) = s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V49f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ering_2Ering__RN_2E1(s(tyop_2Ering_2Ering(A_27a),V48r_2E0))))) ) ).
fof(thm_2Ering_2Ering__fupdfupds,axiom,
! [A_27a] :
( ! [V0r_2E0,V1g_2E0,V2f_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R0__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R0__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1g_2E0),s(tyop_2Ering_2Ering(A_27a),V0r_2E0))))) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R0__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1g_2E0))),s(tyop_2Ering_2Ering(A_27a),V0r_2E0)))
& ! [V3r_2E0,V4g_2E0,V5f_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R1__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V5f_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R1__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V4g_2E0),s(tyop_2Ering_2Ering(A_27a),V3r_2E0))))) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R1__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V5f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V4g_2E0))),s(tyop_2Ering_2Ering(A_27a),V3r_2E0)))
& ! [V6r_2E0,V7g_2E0,V8f_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RP__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V8f_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RP__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V7g_2E0),s(tyop_2Ering_2Ering(A_27a),V6r_2E0))))) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RP__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V8f_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V7g_2E0))),s(tyop_2Ering_2Ering(A_27a),V6r_2E0)))
& ! [V9r_2E0,V10g_2E0,V11f_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RM__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V11f_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RM__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V10g_2E0),s(tyop_2Ering_2Ering(A_27a),V9r_2E0))))) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RM__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V11f_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V10g_2E0))),s(tyop_2Ering_2Ering(A_27a),V9r_2E0)))
& ! [V12r_2E0,V13g_2E0,V14f_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RN__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V14f_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RN__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V13g_2E0),s(tyop_2Ering_2Ering(A_27a),V12r_2E0))))) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RN__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V14f_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V13g_2E0))),s(tyop_2Ering_2Ering(A_27a),V12r_2E0))) ) ).
fof(thm_2Ering_2Ering__fupdfupds__comp,axiom,
! [A_27a,A_27b] :
( ! [V0g_2E0,V1f_2E0] : s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R0__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0))),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R0__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V0g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R0__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V0g_2E0)))))
& ! [V2h_2E0,V3g_2E0,V4f_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R0__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V4f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R0__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V3g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),V2h_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R0__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V4f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V3g_2E0))))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),V2h_2E0)))
& ! [V5g_2E0,V6f_2E0] : s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R1__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V6f_2E0))),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R1__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V5g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R1__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V6f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V5g_2E0)))))
& ! [V7h_2E0,V8g_2E0,V9f_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R1__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V9f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R1__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V8g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),V7h_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R1__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V9f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V8g_2E0))))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),V7h_2E0)))
& ! [V10g_2E0,V11f_2E0] : s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RP__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V11f_2E0))),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RP__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V10g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RP__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V11f_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V10g_2E0)))))
& ! [V12h_2E0,V13g_2E0,V14f_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RP__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V14f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RP__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V13g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),V12h_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RP__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V14f_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V13g_2E0))))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),V12h_2E0)))
& ! [V15g_2E0,V16f_2E0] : s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RM__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V16f_2E0))),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RM__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V15g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RM__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V16f_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V15g_2E0)))))
& ! [V17h_2E0,V18g_2E0,V19f_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RM__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V19f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RM__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V18g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),V17h_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RM__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V19f_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V18g_2E0))))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),V17h_2E0)))
& ! [V20g_2E0,V21f_2E0] : s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RN__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V21f_2E0))),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RN__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V20g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RN__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V21f_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V20g_2E0)))))
& ! [V22h_2E0,V23g_2E0,V24f_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RN__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V24f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RN__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V23g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),V22h_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RN__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V24f_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V23g_2E0))))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),V22h_2E0))) ) ).
fof(thm_2Ering_2Ering__fupdcanon,axiom,
! [A_27a] :
( ! [V0r_2E0,V1g_2E0,V2f_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R1__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R0__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1g_2E0),s(tyop_2Ering_2Ering(A_27a),V0r_2E0))))) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R0__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1g_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R1__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(tyop_2Ering_2Ering(A_27a),V0r_2E0)))))
& ! [V3r_2E0,V4g_2E0,V5f_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RP__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V5f_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R0__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V4g_2E0),s(tyop_2Ering_2Ering(A_27a),V3r_2E0))))) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R0__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V4g_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RP__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V5f_2E0),s(tyop_2Ering_2Ering(A_27a),V3r_2E0)))))
& ! [V6r_2E0,V7g_2E0,V8f_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RP__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V8f_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R1__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V7g_2E0),s(tyop_2Ering_2Ering(A_27a),V6r_2E0))))) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R1__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V7g_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RP__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V8f_2E0),s(tyop_2Ering_2Ering(A_27a),V6r_2E0)))))
& ! [V9r_2E0,V10g_2E0,V11f_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RM__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V11f_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R0__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V10g_2E0),s(tyop_2Ering_2Ering(A_27a),V9r_2E0))))) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R0__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V10g_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RM__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V11f_2E0),s(tyop_2Ering_2Ering(A_27a),V9r_2E0)))))
& ! [V12r_2E0,V13g_2E0,V14f_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RM__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V14f_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R1__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V13g_2E0),s(tyop_2Ering_2Ering(A_27a),V12r_2E0))))) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R1__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V13g_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RM__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V14f_2E0),s(tyop_2Ering_2Ering(A_27a),V12r_2E0)))))
& ! [V15r_2E0,V16g_2E0,V17f_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RM__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V17f_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RP__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V16g_2E0),s(tyop_2Ering_2Ering(A_27a),V15r_2E0))))) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RP__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V16g_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RM__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V17f_2E0),s(tyop_2Ering_2Ering(A_27a),V15r_2E0)))))
& ! [V18r_2E0,V19g_2E0,V20f_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RN__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V20f_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R0__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V19g_2E0),s(tyop_2Ering_2Ering(A_27a),V18r_2E0))))) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R0__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V19g_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RN__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V20f_2E0),s(tyop_2Ering_2Ering(A_27a),V18r_2E0)))))
& ! [V21r_2E0,V22g_2E0,V23f_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RN__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V23f_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R1__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V22g_2E0),s(tyop_2Ering_2Ering(A_27a),V21r_2E0))))) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R1__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V22g_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RN__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V23f_2E0),s(tyop_2Ering_2Ering(A_27a),V21r_2E0)))))
& ! [V24r_2E0,V25g_2E0,V26f_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RN__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V26f_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RP__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V25g_2E0),s(tyop_2Ering_2Ering(A_27a),V24r_2E0))))) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RP__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V25g_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RN__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V26f_2E0),s(tyop_2Ering_2Ering(A_27a),V24r_2E0)))))
& ! [V27r_2E0,V28g_2E0,V29f_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RN__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V29f_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RM__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V28g_2E0),s(tyop_2Ering_2Ering(A_27a),V27r_2E0))))) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RM__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V28g_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RN__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V29f_2E0),s(tyop_2Ering_2Ering(A_27a),V27r_2E0))))) ) ).
fof(thm_2Ering_2Ering__fupdcanon__comp,axiom,
! [A_27a,A_27b] :
( ! [V0g_2E0,V1f_2E0] : s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R1__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0))),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R0__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V0g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R0__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V0g_2E0))),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R1__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0)))))
& ! [V2h_2E0,V3g_2E0,V4f_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R1__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V4f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R0__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V3g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),V2h_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R0__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V3g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R1__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V4f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),V2h_2E0)))))
& ! [V5g_2E0,V6f_2E0] : s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RP__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V6f_2E0))),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R0__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V5g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R0__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V5g_2E0))),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RP__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V6f_2E0)))))
& ! [V7h_2E0,V8g_2E0,V9f_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RP__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V9f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R0__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V8g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),V7h_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R0__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V8g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RP__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V9f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),V7h_2E0)))))
& ! [V10g_2E0,V11f_2E0] : s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RP__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V11f_2E0))),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R1__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V10g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R1__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V10g_2E0))),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RP__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V11f_2E0)))))
& ! [V12h_2E0,V13g_2E0,V14f_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RP__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V14f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R1__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V13g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),V12h_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R1__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V13g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RP__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V14f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),V12h_2E0)))))
& ! [V15g_2E0,V16f_2E0] : s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RM__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V16f_2E0))),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R0__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V15g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R0__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V15g_2E0))),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RM__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V16f_2E0)))))
& ! [V17h_2E0,V18g_2E0,V19f_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RM__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V19f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R0__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V18g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),V17h_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R0__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V18g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RM__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V19f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),V17h_2E0)))))
& ! [V20g_2E0,V21f_2E0] : s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RM__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V21f_2E0))),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R1__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V20g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R1__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V20g_2E0))),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RM__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V21f_2E0)))))
& ! [V22h_2E0,V23g_2E0,V24f_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RM__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V24f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R1__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V23g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),V22h_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R1__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V23g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RM__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V24f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),V22h_2E0)))))
& ! [V25g_2E0,V26f_2E0] : s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RM__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V26f_2E0))),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RP__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V25g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RP__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V25g_2E0))),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RM__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V26f_2E0)))))
& ! [V27h_2E0,V28g_2E0,V29f_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RM__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V29f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RP__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V28g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),V27h_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RP__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V28g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RM__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V29f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),V27h_2E0)))))
& ! [V30g_2E0,V31f_2E0] : s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RN__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V31f_2E0))),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R0__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V30g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R0__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V30g_2E0))),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RN__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V31f_2E0)))))
& ! [V32h_2E0,V33g_2E0,V34f_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RN__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V34f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R0__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V33g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),V32h_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R0__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V33g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RN__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V34f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),V32h_2E0)))))
& ! [V35g_2E0,V36f_2E0] : s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RN__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V36f_2E0))),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R1__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V35g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R1__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V35g_2E0))),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RN__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V36f_2E0)))))
& ! [V37h_2E0,V38g_2E0,V39f_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RN__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V39f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R1__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V38g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),V37h_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__R1__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V38g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RN__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V39f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),V37h_2E0)))))
& ! [V40g_2E0,V41f_2E0] : s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RN__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V41f_2E0))),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RP__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V40g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RP__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V40g_2E0))),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RN__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V41f_2E0)))))
& ! [V42h_2E0,V43g_2E0,V44f_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RN__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V44f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RP__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V43g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),V42h_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RP__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V43g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RN__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V44f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),V42h_2E0)))))
& ! [V45g_2E0,V46f_2E0] : s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RN__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V46f_2E0))),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RM__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V45g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RM__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V45g_2E0))),s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RN__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V46f_2E0)))))
& ! [V47h_2E0,V48g_2E0,V49f_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RN__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V49f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RM__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V48g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),V47h_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RM__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),V48g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Ering_2Ering(A_27a)),c_2Ering_2Ering__RN__fupd_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),V49f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Ering_2Ering(A_27a)),V47h_2E0))))) ) ).
fof(thm_2Ering_2Ering__component__equality,axiom,
! [A_27a,V0r1_2E0,V1r2_2E0] :
( s(tyop_2Ering_2Ering(A_27a),V0r1_2E0) = s(tyop_2Ering_2Ering(A_27a),V1r2_2E0)
<=> ( s(A_27a,c_2Ering_2Ering__R0_2E1(s(tyop_2Ering_2Ering(A_27a),V0r1_2E0))) = s(A_27a,c_2Ering_2Ering__R0_2E1(s(tyop_2Ering_2Ering(A_27a),V1r2_2E0)))
& s(A_27a,c_2Ering_2Ering__R1_2E1(s(tyop_2Ering_2Ering(A_27a),V0r1_2E0))) = s(A_27a,c_2Ering_2Ering__R1_2E1(s(tyop_2Ering_2Ering(A_27a),V1r2_2E0)))
& s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RP_2E1(s(tyop_2Ering_2Ering(A_27a),V0r1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RP_2E1(s(tyop_2Ering_2Ering(A_27a),V1r2_2E0)))
& s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RM_2E1(s(tyop_2Ering_2Ering(A_27a),V0r1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ering_2Ering__RM_2E1(s(tyop_2Ering_2Ering(A_27a),V1r2_2E0)))
& s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ering_2Ering__RN_2E1(s(tyop_2Ering_2Ering(A_27a),V0r1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ering_2Ering__RN_2E1(s(tyop_2Ering_2Ering(A_27a),V1r2_2E0))) ) ) ).
fof(thm_2Ering_2Ering__updates__eq__literal,axiom,
! [A_27a,V0r_2E0,V1a0_2E0,V2a_2E0,V3f1_2E0,V4f0_2E0,V5f_2E0] : s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R0__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EK_2E1(s(A_27a,V1a0_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R1__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EK_2E1(s(A_27a,V2a_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RP__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3f1_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RM__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V4f0_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RN__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V5f_2E0))),s(tyop_2Ering_2Ering(A_27a),V0r_2E0))))))))))) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R0__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EK_2E1(s(A_27a,V1a0_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R1__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EK_2E1(s(A_27a,V2a_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RP__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3f1_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RM__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V4f0_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RN__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V5f_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ebool_2EARB_2E0))))))))))) ).
fof(thm_2Ering_2Ering__literal__nchotomy,axiom,
! [A_27a,V0r_2E0] :
? [V1a0_2E0,V2a_2E0,V3f1_2E0,V4f0_2E0,V5f_2E0] : s(tyop_2Ering_2Ering(A_27a),V0r_2E0) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R0__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EK_2E1(s(A_27a,V1a0_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R1__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EK_2E1(s(A_27a,V2a_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RP__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3f1_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RM__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V4f0_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RN__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V5f_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ebool_2EARB_2E0))))))))))) ).
fof(thm_2Ering_2EFORALL__ring,axiom,
! [A_27a,V0P_2E0] :
( ! [V1r_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ering_2Ering(A_27a),V1r_2E0))))
<=> ! [V2a0_2E0,V3a_2E0,V4f1_2E0,V5f0_2E0,V6f_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R0__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EK_2E1(s(A_27a,V2a0_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R1__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EK_2E1(s(A_27a,V3a_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RP__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V4f1_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RM__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V5f0_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RN__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V6f_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ebool_2EARB_2E0)))))))))))))) ) ).
fof(thm_2Ering_2EEXISTS__ring,axiom,
! [A_27a,V0P_2E0] :
( ? [V1r_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ering_2Ering(A_27a),V1r_2E0))))
<=> ? [V2a0_2E0,V3a_2E0,V4f1_2E0,V5f0_2E0,V6f_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R0__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EK_2E1(s(A_27a,V2a0_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R1__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EK_2E1(s(A_27a,V3a_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RP__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V4f1_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RM__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V5f0_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RN__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V6f_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ebool_2EARB_2E0)))))))))))))) ) ).
fof(thm_2Ering_2Ering__literal__11,axiom,
! [A_27a,V0a01_2E0,V1a1_2E0,V2f11_2E0,V3f01_2E0,V4f1_2E0,V5a02_2E0,V6a2_2E0,V7f12_2E0,V8f02_2E0,V9f2_2E0] :
( s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R0__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EK_2E1(s(A_27a,V0a01_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R1__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EK_2E1(s(A_27a,V1a1_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RP__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V2f11_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RM__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3f01_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RN__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V4f1_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ebool_2EARB_2E0))))))))))) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R0__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EK_2E1(s(A_27a,V5a02_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__R1__fupd_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EK_2E1(s(A_27a,V6a2_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RP__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V7f12_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RM__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V8f02_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Ering__RN__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V9f2_2E0))),s(tyop_2Ering_2Ering(A_27a),c_2Ebool_2EARB_2E0)))))))))))
<=> ( s(A_27a,V0a01_2E0) = s(A_27a,V5a02_2E0)
& s(A_27a,V1a1_2E0) = s(A_27a,V6a2_2E0)
& s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V2f11_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V7f12_2E0)
& s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3f01_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V8f02_2E0)
& s(tyop_2Emin_2Efun(A_27a,A_27a),V4f1_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27a),V9f2_2E0) ) ) ).
fof(thm_2Ering_2Edatatype__ring,axiom,
! [A_27a,V0ring_2E0,V1record_2E0,V2RP_2E0,V3RN_2E0,V4RM_2E0,V5R1_2E0,V6R0_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool)))))),V1record_2E0),s(tyop_2Ering_2Ering(A_27a),V0ring_2E0))),s(A_27a,V6R0_2E0))),s(A_27a,V5R1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V2RP_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V4RM_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V3RN_2E0)))))) ).
fof(thm_2Ering_2Ering__11,axiom,
! [A_27a,V0a0_2E0,V1a1_2E0,V2a2_2E0,V3a3_2E0,V4a4_2E0,V5a0_27_2E0,V6a1_27_2E0,V7a2_27_2E0,V8a3_27_2E0,V9a4_27_2E0] :
( s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V0a0_2E0),s(A_27a,V1a1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V2a2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3a3_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V4a4_2E0))) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V5a0_27_2E0),s(A_27a,V6a1_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V7a2_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V8a3_27_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V9a4_27_2E0)))
<=> ( s(A_27a,V0a0_2E0) = s(A_27a,V5a0_27_2E0)
& s(A_27a,V1a1_2E0) = s(A_27a,V6a1_27_2E0)
& s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V2a2_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V7a2_27_2E0)
& s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3a3_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V8a3_27_2E0)
& s(tyop_2Emin_2Efun(A_27a,A_27a),V4a4_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27a),V9a4_27_2E0) ) ) ).
fof(thm_2Ering_2Ering__nchotomy,axiom,
! [A_27a,V0rr_2E0] :
? [V1a_2E0,V2a0_2E0,V3f_2E0,V4f0_2E0,V5f1_2E0] : s(tyop_2Ering_2Ering(A_27a),V0rr_2E0) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V1a_2E0),s(A_27a,V2a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V4f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V5f1_2E0))) ).
fof(thm_2Ering_2Ering__Axiom,axiom,
! [A_27a,A_27b,V0f_2E0] :
? [V1fn_2E0] :
! [V2a0_2E0,V3a1_2E0,V4a2_2E0,V5a3_2E0,V6a4_2E0] : s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),A_27b),V1fn_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V2a0_2E0),s(A_27a,V3a1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V4a2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V5a3_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V6a4_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b))))),V0f_2E0),s(A_27a,V2a0_2E0))),s(A_27a,V3a1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V4a2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V5a3_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V6a4_2E0))) ).
fof(thm_2Ering_2Ering__induction,axiom,
! [A_27a,V0P_2E0] :
( ! [V1a_2E0,V2a0_2E0,V3f_2E0,V4f0_2E0,V5f1_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V1a_2E0),s(A_27a,V2a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V4f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V5f1_2E0))))))
=> ! [V6r_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ering_2Ering(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ering_2Ering(A_27a),V6r_2E0)))) ) ).
fof(thm_2Ering_2Ering__case__cong,axiom,
! [A_27a,A_27b,V0f_27_2E0,V1M_2E0,V2M_27_2E0,V3f_2E0] :
( ( s(tyop_2Ering_2Ering(A_27a),V1M_2E0) = s(tyop_2Ering_2Ering(A_27a),V2M_27_2E0)
& ! [V4a0_2E0,V5a1_2E0,V6a2_2E0,V7a3_2E0,V8a4_2E0] :
( s(tyop_2Ering_2Ering(A_27a),V2M_27_2E0) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V4a0_2E0),s(A_27a,V5a1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V6a2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V7a3_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V8a4_2E0)))
=> s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b))))),V3f_2E0),s(A_27a,V4a0_2E0))),s(A_27a,V5a1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V6a2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V7a3_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V8a4_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b))))),V0f_27_2E0),s(A_27a,V4a0_2E0))),s(A_27a,V5a1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V6a2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V7a3_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V8a4_2E0))) ) )
=> s(A_27b,c_2Ering_2Ering__CASE_2E2(s(tyop_2Ering_2Ering(A_27a),V1M_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b))))),V3f_2E0))) = s(A_27b,c_2Ering_2Ering__CASE_2E2(s(tyop_2Ering_2Ering(A_27a),V2M_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b))))),V0f_27_2E0))) ) ).
fof(thm_2Ering_2Ering__case__eq,axiom,
! [A_27a,A_27b,V0x_2E0,V1v_2E0,V2f_2E0] :
( s(A_27b,c_2Ering_2Ering__CASE_2E2(s(tyop_2Ering_2Ering(A_27a),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b))))),V2f_2E0))) = s(A_27b,V1v_2E0)
<=> ? [V3a_2E0,V4a0_2E0,V5f_27_2E0,V6f0_2E0,V7f1_2E0] :
( s(tyop_2Ering_2Ering(A_27a),V0x_2E0) = s(tyop_2Ering_2Ering(A_27a),c_2Ering_2Erecordtype_2Ering_2E5(s(A_27a,V3a_2E0),s(A_27a,V4a0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V5f_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V6f0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V7f1_2E0)))
& s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),A_27b))))),V2f_2E0),s(A_27a,V3a_2E0))),s(A_27a,V4a0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V5f_27_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),V6f0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),V7f1_2E0))) = s(A_27b,V1v_2E0) ) ) ).
fof(thm_2Ering_2Eplus__sym,axiom,
! [A_27a,V0r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ering_2Eis__ring_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0))))
=> ! [V1n_2E0,V2m_2E0] : s(A_27a,c_2Ering_2Ering__RP_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V1n_2E0),s(A_27a,V2m_2E0))) = s(A_27a,c_2Ering_2Ering__RP_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V2m_2E0),s(A_27a,V1n_2E0))) ) ).
fof(thm_2Ering_2Eplus__assoc,axiom,
! [A_27a,V0r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ering_2Eis__ring_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0))))
=> ! [V1n_2E0,V2m_2E0,V3p_2E0] : s(A_27a,c_2Ering_2Ering__RP_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V1n_2E0),s(A_27a,c_2Ering_2Ering__RP_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V2m_2E0),s(A_27a,V3p_2E0))))) = s(A_27a,c_2Ering_2Ering__RP_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,c_2Ering_2Ering__RP_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V1n_2E0),s(A_27a,V2m_2E0))),s(A_27a,V3p_2E0))) ) ).
fof(thm_2Ering_2Emult__sym,axiom,
! [A_27a,V0r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ering_2Eis__ring_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0))))
=> ! [V1n_2E0,V2m_2E0] : s(A_27a,c_2Ering_2Ering__RM_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V1n_2E0),s(A_27a,V2m_2E0))) = s(A_27a,c_2Ering_2Ering__RM_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V2m_2E0),s(A_27a,V1n_2E0))) ) ).
fof(thm_2Ering_2Emult__assoc,axiom,
! [A_27a,V0r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ering_2Eis__ring_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0))))
=> ! [V1n_2E0,V2m_2E0,V3p_2E0] : s(A_27a,c_2Ering_2Ering__RM_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V1n_2E0),s(A_27a,c_2Ering_2Ering__RM_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V2m_2E0),s(A_27a,V3p_2E0))))) = s(A_27a,c_2Ering_2Ering__RM_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,c_2Ering_2Ering__RM_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V1n_2E0),s(A_27a,V2m_2E0))),s(A_27a,V3p_2E0))) ) ).
fof(thm_2Ering_2Eplus__zero__left,axiom,
! [A_27a,V0r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ering_2Eis__ring_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0))))
=> ! [V1n_2E0] : s(A_27a,c_2Ering_2Ering__RP_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,c_2Ering_2Ering__R0_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0))),s(A_27a,V1n_2E0))) = s(A_27a,V1n_2E0) ) ).
fof(thm_2Ering_2Emult__one__left,axiom,
! [A_27a,V0r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ering_2Eis__ring_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0))))
=> ! [V1n_2E0] : s(A_27a,c_2Ering_2Ering__RM_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,c_2Ering_2Ering__R1_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0))),s(A_27a,V1n_2E0))) = s(A_27a,V1n_2E0) ) ).
fof(thm_2Ering_2Eopp__def,axiom,
! [A_27a,V0r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ering_2Eis__ring_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0))))
=> ! [V1n_2E0] : s(A_27a,c_2Ering_2Ering__RP_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V1n_2E0),s(A_27a,c_2Ering_2Ering__RN_2E2(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V1n_2E0))))) = s(A_27a,c_2Ering_2Ering__R0_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0))) ) ).
fof(thm_2Ering_2Edistr__left,axiom,
! [A_27a,V0r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ering_2Eis__ring_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0))))
=> ! [V1n_2E0,V2m_2E0,V3p_2E0] : s(A_27a,c_2Ering_2Ering__RM_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,c_2Ering_2Ering__RP_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V1n_2E0),s(A_27a,V2m_2E0))),s(A_27a,V3p_2E0))) = s(A_27a,c_2Ering_2Ering__RP_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,c_2Ering_2Ering__RM_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V1n_2E0),s(A_27a,V3p_2E0))),s(A_27a,c_2Ering_2Ering__RM_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V2m_2E0),s(A_27a,V3p_2E0))))) ) ).
fof(thm_2Ering_2Eplus__zero__right,axiom,
! [A_27a,V0r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ering_2Eis__ring_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0))))
=> ! [V1n_2E0] : s(A_27a,c_2Ering_2Ering__RP_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V1n_2E0),s(A_27a,c_2Ering_2Ering__R0_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0))))) = s(A_27a,V1n_2E0) ) ).
fof(thm_2Ering_2Emult__zero__left,axiom,
! [A_27a,V0r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ering_2Eis__ring_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0))))
=> ! [V1n_2E0] : s(A_27a,c_2Ering_2Ering__RM_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,c_2Ering_2Ering__R0_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0))),s(A_27a,V1n_2E0))) = s(A_27a,c_2Ering_2Ering__R0_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0))) ) ).
fof(thm_2Ering_2Emult__zero__right,axiom,
! [A_27a,V0r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ering_2Eis__ring_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0))))
=> ! [V1n_2E0] : s(A_27a,c_2Ering_2Ering__RM_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V1n_2E0),s(A_27a,c_2Ering_2Ering__R0_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0))))) = s(A_27a,c_2Ering_2Ering__R0_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0))) ) ).
fof(thm_2Ering_2Ering__is__semi__ring,axiom,
! [A_27a,V0r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ering_2Eis__ring_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0))))
=> p(s(tyop_2Emin_2Ebool,c_2Esemi__ring_2Eis__semi__ring_2E1(s(tyop_2Esemi__ring_2Esemi__ring(A_27a),c_2Ering_2Esemi__ring__of_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0)))))) ) ).
fof(thm_2Ering_2Emult__one__right,axiom,
! [A_27a,V0r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ering_2Eis__ring_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0))))
=> ! [V1n_2E0] : s(A_27a,c_2Ering_2Ering__RM_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V1n_2E0),s(A_27a,c_2Ering_2Ering__R1_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0))))) = s(A_27a,V1n_2E0) ) ).
fof(thm_2Ering_2Eneg__mult,axiom,
! [A_27a,V0r_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ering_2Eis__ring_2E1(s(tyop_2Ering_2Ering(A_27a),V0r_2E0))))
=> ! [V1a_2E0,V2b_2E0] : s(A_27a,c_2Ering_2Ering__RM_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,c_2Ering_2Ering__RN_2E2(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V1a_2E0))),s(A_27a,V2b_2E0))) = s(A_27a,c_2Ering_2Ering__RN_2E2(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,c_2Ering_2Ering__RM_2E3(s(tyop_2Ering_2Ering(A_27a),V0r_2E0),s(A_27a,V1a_2E0),s(A_27a,V2b_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) ) ).
%------------------------------------------------------------------------------