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_2Einftree_2Eis__tree_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,![A_27a, A_27b, A_27c]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Einftree_2Eis__tree_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Esum_2Esum(A_27a,A_27b)),tyop_2Emin_2Ebool),c_2Einftree_2Eis__tree_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0))))).
fof(arityeq1_2Ec_2Einftree_2Eto__inftree_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,![A_27a, A_27b, A_27c]: ![X0_2E0]: (s(tyop_2Einftree_2Einftree(A_27a,A_27b,A_27c),c_2Einftree_2Eto__inftree_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0))) = s(tyop_2Einftree_2Einftree(A_27a,A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Esum_2Esum(A_27a,A_27b)),tyop_2Einftree_2Einftree(A_27a,A_27b,A_27c)),c_2Einftree_2Eto__inftree_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0))))).
fof(namespace__tagTheory_2Eforall__inftree,axiom,![A_27a, A_27b, A_27c]: ![V0P_2E0]: (![V1t_2E0]: p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einftree_2Einftree(A_27a,A_27b,A_27c),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Einftree_2Einftree(A_27a,A_27b,A_27c),V1t_2E0)))) <=> ![V2f_2E0]: (p(s(tyop_2Emin_2Ebool,c_2Einftree_2Eis__tree_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Esum_2Esum(A_27a,A_27b)),V2f_2E0)))) => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einftree_2Einftree(A_27a,A_27b,A_27c),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Einftree_2Einftree(A_27a,A_27b,A_27c),c_2Einftree_2Eto__inftree_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Esum_2Esum(A_27a,A_27b)),V2f_2E0))))))))).
