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_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,![A_27a, A_27b]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))))).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,![A_27a, A_27b]: ![X0_2E0, X1_2E0]: (s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Elist_2ECONS_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))))).
fof(arityeq1_2Ec_2Eupdate_2ELIST__UPDATE_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,![A_27a, A_27b]: ![X0_2E0]: (s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Eupdate_2ELIST__UPDATE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Eupdate_2ELIST__UPDATE_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))))).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,![A_27c, A_27d]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(A_27c,A_27d),c_2Epair_2E_2C_2E2(s(A_27c,X0_2E0),s(A_27d,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(A_27c,A_27d))),c_2Epair_2E_2C_2E0),s(A_27c,X0_2E0))),s(A_27d,X1_2E0))))).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27d_29,axiom,![A_27c, A_27d]: ![X0_2E0, X1_2E0]: (s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27c,A_27d),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)))),c_2Elist_2ECONS_2E0),s(tyop_2Epair_2Eprod(A_27c,A_27d),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),X1_2E0))))).
fof(arityeq1_2Ec_2Eupdate_2ELIST__UPDATE_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,![A_27c, A_27d]: ![X0_2E0]: (s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),c_2Eupdate_2ELIST__UPDATE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d))),c_2Eupdate_2ELIST__UPDATE_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),X0_2E0))))).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27e_20mono_2EA_27f,axiom,![A_27e, A_27f]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(A_27e,A_27f),c_2Epair_2E_2C_2E2(s(A_27e,X0_2E0),s(A_27f,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27e,A_27f),app_2E2(s(tyop_2Emin_2Efun(A_27f,tyop_2Epair_2Eprod(A_27e,A_27f)),app_2E2(s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27f,tyop_2Epair_2Eprod(A_27e,A_27f))),c_2Epair_2E_2C_2E0),s(A_27e,X0_2E0))),s(A_27f,X1_2E0))))).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27e_2CA_27f_29,axiom,![A_27e, A_27f]: ![X0_2E0, X1_2E0]: (s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27e,A_27f),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27e,A_27f),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)))),c_2Elist_2ECONS_2E0),s(tyop_2Epair_2Eprod(A_27e,A_27f),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),X1_2E0))))).
fof(arityeq2_2Ec_2Eupdate_2ELIST__UPDATE_2E2_2Emono_2EA_27e_20mono_2EA_27f,axiom,![A_27e, A_27f]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(A_27e,A_27f),c_2Eupdate_2ELIST__UPDATE_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),X0_2E0),s(tyop_2Emin_2Efun(A_27e,A_27f),X1_2E0))) = s(tyop_2Emin_2Efun(A_27e,A_27f),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27f),tyop_2Emin_2Efun(A_27e,A_27f)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27f),tyop_2Emin_2Efun(A_27e,A_27f))),c_2Eupdate_2ELIST__UPDATE_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),X0_2E0))),s(tyop_2Emin_2Efun(A_27e,A_27f),X1_2E0))))).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27g_20mono_2EA_27h,axiom,![A_27g, A_27h]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(A_27g,A_27h),c_2Epair_2E_2C_2E2(s(A_27g,X0_2E0),s(A_27h,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27g,A_27h),app_2E2(s(tyop_2Emin_2Efun(A_27h,tyop_2Epair_2Eprod(A_27g,A_27h)),app_2E2(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Epair_2Eprod(A_27g,A_27h))),c_2Epair_2E_2C_2E0),s(A_27g,X0_2E0))),s(A_27h,X1_2E0))))).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27g_2CA_27h_29,axiom,![A_27g, A_27h]: ![X0_2E0, X1_2E0]: (s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27g,A_27h),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27g,A_27h),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)))),c_2Elist_2ECONS_2E0),s(tyop_2Epair_2Eprod(A_27g,A_27h),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),X1_2E0))))).
fof(arityeq2_2Ec_2Eupdate_2ELIST__UPDATE_2E2_2Emono_2EA_27g_20mono_2EA_27h,axiom,![A_27g, A_27h]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(A_27g,A_27h),c_2Eupdate_2ELIST__UPDATE_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),X0_2E0),s(tyop_2Emin_2Efun(A_27g,A_27h),X1_2E0))) = s(tyop_2Emin_2Efun(A_27g,A_27h),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,A_27h),tyop_2Emin_2Efun(A_27g,A_27h)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,A_27h),tyop_2Emin_2Efun(A_27g,A_27h))),c_2Eupdate_2ELIST__UPDATE_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),X0_2E0))),s(tyop_2Emin_2Efun(A_27g,A_27h),X1_2E0))))).
fof(arityeq2_2Ec_2Ecombin_2EUPDATE_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,![A_27a, A_27b]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2EUPDATE_2E2(s(A_27a,X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)))),c_2Ecombin_2EUPDATE_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))))).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29,axiom,![A_27a, A_27b]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))))).
fof(arityeq2_2Ec_2Ecombin_2EUPDATE_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,![A_27c, A_27d]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),c_2Ecombin_2EUPDATE_2E2(s(A_27c,X0_2E0),s(A_27d,X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)))),c_2Ecombin_2EUPDATE_2E0),s(A_27c,X0_2E0))),s(A_27d,X1_2E0))))).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27c_2CA_27d_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27d_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27d_29,axiom,![A_27c, A_27d]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),X1_2E0))))).
fof(arityeq3_2Ec_2Ecombin_2EUPDATE_2E3_2Emono_2EA_27e_20mono_2EA_27f,axiom,![A_27e, A_27f]: ![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Emin_2Efun(A_27e,A_27f),c_2Ecombin_2EUPDATE_2E3(s(A_27e,X0_2E0),s(A_27f,X1_2E0),s(tyop_2Emin_2Efun(A_27e,A_27f),X2_2E0))) = s(tyop_2Emin_2Efun(A_27e,A_27f),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27f),tyop_2Emin_2Efun(A_27e,A_27f)),app_2E2(s(tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27f),tyop_2Emin_2Efun(A_27e,A_27f))),app_2E2(s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27f,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27f),tyop_2Emin_2Efun(A_27e,A_27f)))),c_2Ecombin_2EUPDATE_2E0),s(A_27e,X0_2E0))),s(A_27f,X1_2E0))),s(tyop_2Emin_2Efun(A_27e,A_27f),X2_2E0))))).
fof(arityeq3_2Ec_2Ecombin_2EUPDATE_2E3_2Emono_2EA_27g_20mono_2EA_27h,axiom,![A_27g, A_27h]: ![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Emin_2Efun(A_27g,A_27h),c_2Ecombin_2EUPDATE_2E3(s(A_27g,X0_2E0),s(A_27h,X1_2E0),s(tyop_2Emin_2Efun(A_27g,A_27h),X2_2E0))) = s(tyop_2Emin_2Efun(A_27g,A_27h),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,A_27h),tyop_2Emin_2Efun(A_27g,A_27h)),app_2E2(s(tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,A_27h),tyop_2Emin_2Efun(A_27g,A_27h))),app_2E2(s(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27h,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,A_27h),tyop_2Emin_2Efun(A_27g,A_27h)))),c_2Ecombin_2EUPDATE_2E0),s(A_27g,X0_2E0))),s(A_27h,X1_2E0))),s(tyop_2Emin_2Efun(A_27g,A_27h),X2_2E0))))).
fof(namespace__tagTheory_2ELIST__UPDATE1,axiom,![A_27a, A_27b, A_27c, A_27d, A_27e, A_27f, A_27g, A_27h]: (![V0l1_2E0, V1l2_2E0, V2r1_2E0, V3r2_2E0]: (s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2EUPDATE_2E2(s(A_27a,V0l1_2E0),s(A_27b,V2r1_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2EUPDATE_2E2(s(A_27a,V1l2_2E0),s(A_27b,V3r2_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Eupdate_2ELIST__UPDATE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V0l1_2E0),s(A_27b,V2r1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1l2_2E0),s(A_27b,V3r2_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0)))))))) & (![V4l_2E0, V5r_2E0, V6t_2E0]: (s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),c_2Ecombin_2EUPDATE_2E2(s(A_27c,V4l_2E0),s(A_27d,V5r_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),c_2Eupdate_2ELIST__UPDATE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),V6t_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),c_2Eupdate_2ELIST__UPDATE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27c,A_27d),c_2Epair_2E_2C_2E2(s(A_27c,V4l_2E0),s(A_27d,V5r_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27c,A_27d)),V6t_2E0)))))) & (![V7l1_2E0, V8l2_2E0, V9r1_2E0, V10r2_2E0, V11f_2E0]: (s(tyop_2Emin_2Efun(A_27e,A_27f),c_2Ecombin_2EUPDATE_2E3(s(A_27e,V7l1_2E0),s(A_27f,V9r1_2E0),s(tyop_2Emin_2Efun(A_27e,A_27f),c_2Ecombin_2EUPDATE_2E3(s(A_27e,V8l2_2E0),s(A_27f,V10r2_2E0),s(tyop_2Emin_2Efun(A_27e,A_27f),V11f_2E0))))) = s(tyop_2Emin_2Efun(A_27e,A_27f),c_2Eupdate_2ELIST__UPDATE_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27e,A_27f),c_2Epair_2E_2C_2E2(s(A_27e,V7l1_2E0),s(A_27f,V9r1_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27e,A_27f),c_2Epair_2E_2C_2E2(s(A_27e,V8l2_2E0),s(A_27f,V10r2_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27e,A_27f)),c_2Elist_2ENIL_2E0))))),s(tyop_2Emin_2Efun(A_27e,A_27f),V11f_2E0)))) & ![V12l_2E0, V13r_2E0, V14t_2E0, V15f_2E0]: (s(tyop_2Emin_2Efun(A_27g,A_27h),c_2Ecombin_2EUPDATE_2E3(s(A_27g,V12l_2E0),s(A_27h,V13r_2E0),s(tyop_2Emin_2Efun(A_27g,A_27h),c_2Eupdate_2ELIST__UPDATE_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),V14t_2E0),s(tyop_2Emin_2Efun(A_27g,A_27h),V15f_2E0))))) = s(tyop_2Emin_2Efun(A_27g,A_27h),c_2Eupdate_2ELIST__UPDATE_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),c_2Elist_2ECONS_2E2(s(tyop_2Epair_2Eprod(A_27g,A_27h),c_2Epair_2E_2C_2E2(s(A_27g,V12l_2E0),s(A_27h,V13r_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27g,A_27h)),V14t_2E0))),s(tyop_2Emin_2Efun(A_27g,A_27h),V15f_2E0)))))))).
