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_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(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__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(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(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(ringTheory_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))))))))))))))))))))))))))))))).
