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_2Esum_2EINL_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,![A_27c, A_27d]: ![X0_2E0]: (s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2EINL_2E1(s(A_27c,X0_2E0))) = s(tyop_2Esum_2Esum(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Esum_2Esum(A_27c,A_27d)),c_2Esum_2EINL_2E0),s(A_27c,X0_2E0))))).
fof(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,![A_27c, A_27d]: ![X0_2E0]: (s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2EINR_2E1(s(A_27d,X0_2E0))) = s(tyop_2Esum_2Esum(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Esum_2Esum(A_27c,A_27d)),c_2Esum_2EINR_2E0),s(A_27d,X0_2E0))))).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,![A_27a, A_27b, A_27c]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0))))).
fof(arityeq2_2Ec_2EsimpleSetCat_2Erestr_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,![A_27a, A_27b]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(A_27a,A_27b),c_2EsimpleSetCat_2Erestr_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,A_27b))),c_2EsimpleSetCat_2Erestr_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))))).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27d,axiom,![A_27a, A_27b, A_27d]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27d,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27d),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27d),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27d),X1_2E0))))).
fof(arityeq5_2Ec_2EsimpleSetCat_2ESPOr_2E5_2Emono_2EA_27c_20mono_2EA_27d_20mono_2EA_27a,axiom,![A_27a, A_27c, A_27d]: ![X0_2E0, X1_2E0, X2_2E0, X3_2E0, X4_2E0]: (s(tyop_2Emin_2Ebool,c_2EsimpleSetCat_2ESPOr_2E5(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27d),X2_2E0),s(tyop_2Esum_2Esum(A_27c,A_27d),X3_2E0),s(tyop_2Esum_2Esum(A_27c,A_27d),X4_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27d),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27d),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27d),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27c,A_27d),tyop_2Emin_2Ebool))))),c_2EsimpleSetCat_2ESPOr_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27d),X2_2E0))),s(tyop_2Esum_2Esum(A_27c,A_27d),X3_2E0))),s(tyop_2Esum_2Esum(A_27c,A_27d),X4_2E0))))).
fof(namespace__tagTheory_2ESPOr__lemma0,axiom,![A_27a, A_27b, A_27c, A_27d]: ![V0g_2E0, V1j2_2E0, V2A_2E0, V3f_2E0, V4j1_2E0]: ((s(tyop_2Emin_2Efun(A_27a,A_27b),c_2EsimpleSetCat_2Erestr_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V4j1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V3f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2A_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),c_2EsimpleSetCat_2Erestr_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27d,A_27b),V1j2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27d),V0g_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2A_2E0)))) => ![V5s1_2E0, V6s2_2E0]: (p(s(tyop_2Emin_2Ebool,c_2EsimpleSetCat_2ESPOr_2E5(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2A_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27d),V0g_2E0),s(tyop_2Esum_2Esum(A_27c,A_27d),V5s1_2E0),s(tyop_2Esum_2Esum(A_27c,A_27d),V6s2_2E0)))) => (![V7b1_2E0, V8b2_2E0]: (((s(tyop_2Esum_2Esum(A_27c,A_27d),V5s1_2E0) = s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2EINL_2E1(s(A_27c,V7b1_2E0)))) & (s(tyop_2Esum_2Esum(A_27c,A_27d),V6s2_2E0) = s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2EINL_2E1(s(A_27c,V8b2_2E0))))) => (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V4j1_2E0),s(A_27c,V7b1_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V4j1_2E0),s(A_27c,V8b2_2E0))))) & (![V9b_2E0, V10c_2E0]: (((s(tyop_2Esum_2Esum(A_27c,A_27d),V5s1_2E0) = s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2EINL_2E1(s(A_27c,V9b_2E0)))) & (s(tyop_2Esum_2Esum(A_27c,A_27d),V6s2_2E0) = s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2EINR_2E1(s(A_27d,V10c_2E0))))) => (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V4j1_2E0),s(A_27c,V9b_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27b),V1j2_2E0),s(A_27d,V10c_2E0))))) & (![V11b_2E0, V12c_2E0]: (((s(tyop_2Esum_2Esum(A_27c,A_27d),V5s1_2E0) = s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2EINR_2E1(s(A_27d,V12c_2E0)))) & (s(tyop_2Esum_2Esum(A_27c,A_27d),V6s2_2E0) = s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2EINL_2E1(s(A_27c,V11b_2E0))))) => (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V4j1_2E0),s(A_27c,V11b_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27b),V1j2_2E0),s(A_27d,V12c_2E0))))) & ![V13c1_2E0, V14c2_2E0]: (((s(tyop_2Esum_2Esum(A_27c,A_27d),V5s1_2E0) = s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2EINR_2E1(s(A_27d,V13c1_2E0)))) & (s(tyop_2Esum_2Esum(A_27c,A_27d),V6s2_2E0) = s(tyop_2Esum_2Esum(A_27c,A_27d),c_2Esum_2EINR_2E1(s(A_27d,V14c2_2E0))))) => (s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27b),V1j2_2E0),s(A_27d,V13c1_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27b),V1j2_2E0),s(A_27d,V14c2_2E0))))))))))).
