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_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),X1_2E0))))).
fof(arityeq2_2Ec_2Etransc_2Efine_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Ebool,c_2Etransc_2Efine_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),tyop_2Emin_2Ebool)),c_2Etransc_2Efine_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),X1_2E0))))).
fof(arityeq2_2Ec_2Erealax_2Ereal__add_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),c_2Erealax_2Ereal__add_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))))).
fof(arityeq2_2Ec_2Etransc_2Ersum_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Erealax_2Ereal,c_2Etransc_2Ersum_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X1_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Erealax_2Ereal)),c_2Etransc_2Ersum_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X1_2E0))))).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))),c_2Epair_2E_2C_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))))).
fof(arityeq2_2Ec_2Etransc_2Etdiv_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Ebool,c_2Etransc_2Etdiv_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),tyop_2Emin_2Ebool)),c_2Etransc_2Etdiv_2E0),s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),X1_2E0))))).
fof(integralTheory_2EDIVISION__APPEND__STRONG,axiom,![V0g_2E0, V1a_2E0, V2b_2E0, V3c_2E0, V4D1_2E0, V5p1_2E0, V6D2_2E0, V7p2_2E0]: ((p(s(tyop_2Emin_2Ebool,c_2Etransc_2Etdiv_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V2b_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4D1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V5p1_2E0)))))) & (p(s(tyop_2Emin_2Ebool,c_2Etransc_2Efine_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0g_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4D1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V5p1_2E0)))))) & (p(s(tyop_2Emin_2Ebool,c_2Etransc_2Etdiv_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V2b_2E0),s(tyop_2Erealax_2Ereal,V3c_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V6D2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V7p2_2E0)))))) & p(s(tyop_2Emin_2Ebool,c_2Etransc_2Efine_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0g_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V6D2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V7p2_2E0))))))))) => ?[V8D_2E0, V9p_2E0]: (p(s(tyop_2Emin_2Ebool,c_2Etransc_2Etdiv_2E2(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V1a_2E0),s(tyop_2Erealax_2Ereal,V3c_2E0))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V8D_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V9p_2E0)))))) & (p(s(tyop_2Emin_2Ebool,c_2Etransc_2Efine_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V0g_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V8D_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V9p_2E0)))))) & ![V10f_2E0]: (s(tyop_2Erealax_2Ereal,c_2Etransc_2Ersum_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V8D_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V9p_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V10f_2E0))) = s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Etransc_2Ersum_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4D1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V5p1_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V10f_2E0))),s(tyop_2Erealax_2Ereal,c_2Etransc_2Ersum_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V6D2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V7p2_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),V10f_2E0)))))))))).
