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(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_2Esemi__ring_2Esemi__ring__SR0__fupd_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a))),c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))))).
fof(arityeq1_2Ec_2Esemi__ring_2Esemi__ring__SR1__fupd_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a))),c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E0),s(tyop_2Emin_2Efun(A_27a,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_2Esemi__ring_2Esemi__ring__SRM__fupd_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Esemi__ring_2Esemi__ring__SRM__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_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(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_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a))),c_2Esemi__ring_2Esemi__ring__SRM__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_2Esemi__ring_2Esemi__ring__SRP__fupd_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Esemi__ring_2Esemi__ring__SRP__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_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(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_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a))),c_2Esemi__ring_2Esemi__ring__SRP__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(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2Etyop_2Esemi__ring_2Esemi__ring_28A_27a_29_20mono_2Etyop_2Esemi__ring_2Esemi__ring_28A_27a_29,axiom,![A_27a, A_27b]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(A_27b,tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Esemi__ring_2Esemi__ring(A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Esemi__ring_2Esemi__ring(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Esemi__ring_2Esemi__ring(A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Esemi__ring_2Esemi__ring(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Esemi__ring_2Esemi__ring(A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Esemi__ring_2Esemi__ring(A_27a)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Esemi__ring_2Esemi__ring(A_27a)),X1_2E0))))).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Esemi__ring_2Esemi__ring_28A_27a_29_20mono_2Etyop_2Esemi__ring_2Esemi__ring_28A_27a_29_20mono_2Etyop_2Esemi__ring_2Esemi__ring_28A_27a_29,axiom,![A_27a]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),X1_2E0))))).
fof(semi__ringTheory_2Esemi__ring__fupdfupds__comp,axiom,![A_27a, A_27b]: ((![V0g_2E0, V1f_2E0]: (s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0))),s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V0g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Esemi__ring_2Esemi__ring__SR0__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_2Esemi__ring_2Esemi__ring(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V4f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V3g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Esemi__ring_2Esemi__ring(A_27a)),V2h_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Esemi__ring_2Esemi__ring__SR0__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_2Esemi__ring_2Esemi__ring(A_27a)),V2h_2E0))))) & ((![V5g_2E0, V6f_2E0]: (s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V6f_2E0))),s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V5g_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Esemi__ring_2Esemi__ring__SR1__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_2Esemi__ring_2Esemi__ring(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V9f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E1(s(tyop_2Emin_2Efun(A_27a,A_27a),V8g_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Esemi__ring_2Esemi__ring(A_27a)),V7h_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Esemi__ring_2Esemi__ring__SR1__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_2Esemi__ring_2Esemi__ring(A_27a)),V7h_2E0))))) & ((![V10g_2E0, V11f_2E0]: (s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Esemi__ring_2Esemi__ring__SRP__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_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Esemi__ring_2Esemi__ring__SRP__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_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Esemi__ring_2Esemi__ring__SRP__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_2Esemi__ring_2Esemi__ring(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Esemi__ring_2Esemi__ring__SRP__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_2Esemi__ring_2Esemi__ring(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Esemi__ring_2Esemi__ring__SRP__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_2Esemi__ring_2Esemi__ring(A_27a)),V12h_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Esemi__ring_2Esemi__ring__SRP__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_2Esemi__ring_2Esemi__ring(A_27a)),V12h_2E0))))) & (![V15g_2E0, V16f_2E0]: (s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Esemi__ring_2Esemi__ring__SRM__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_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Esemi__ring_2Esemi__ring__SRM__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_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Esemi__ring_2Esemi__ring__SRM__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_2Esemi__ring_2Esemi__ring(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Esemi__ring_2Esemi__ring__SRM__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_2Esemi__ring_2Esemi__ring(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Esemi__ring_2Esemi__ring__SRM__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_2Esemi__ring_2Esemi__ring(A_27a)),V17h_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Esemi__ring_2Esemi__ring(A_27a),tyop_2Esemi__ring_2Esemi__ring(A_27a)),c_2Esemi__ring_2Esemi__ring__SRM__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_2Esemi__ring_2Esemi__ring(A_27a)),V17h_2E0))))))))).
