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_2Efcp_2EFCP_2E1_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Eone_2Eone,axiom,![X0_2E0]: (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Efcp_2EFCP_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Efcp_2EFCP_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq2_2Ec_2Elist_2EGENLIST_2E2_2Emono_2Etyop_2Emin_2Ebool,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Elist_2EGENLIST_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))))).
fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Enum_2Enum,axiom,![X0_2E0]: (s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Ecombin_2EK_2E0),s(tyop_2Emin_2Ebool,X0_2E0))))).
fof(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X1_2E0))))).
fof(arityeq1_2Ec_2Efcp_2Edimindex_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27a),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Enum_2Enum),c_2Efcp_2Edimindex_2E0),s(tyop_2Ebool_2Eitself(A_27a),X0_2E0))))).
fof(arityeq2_2Ec_2Earithmetic_2E_2D_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Earithmetic_2E_2D_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))))).
fof(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,![X0_2E0]: (s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0))))).
fof(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,![X0_2E0]: (s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0))))).
fof(arityeq2_2Ec_2Efcp_2Efcp__index_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Ebool,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Efcp_2Efcp__index_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))))).
fof(arityeq2_2Ec_2Ewords_2Eword__reduce_2E2_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0]: (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2Eword__reduce_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone))),c_2Ewords_2Eword__reduce_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0))))).
fof(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Emin_2Ebool,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Elist_2EFOLDL_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X2_2E0))))).
fof(arityeq1_2Ec_2Elist_2EHD_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Elist_2EHD_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq1_2Ec_2Elist_2ETL_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,![X0_2E0]: (s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Elist_2ETL_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0))))).
fof(wordsTheory_2Eword__reduce__def,axiom,![A_27a]: ![F0_2E0, F1_2E0]: (![V0f_2E0, V2l_2E0]: (s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V0f_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V2l_2E0))) = s(tyop_2Emin_2Ebool,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Emin_2Ebool,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V2l_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V2l_2E0)))))) => (![V1w_2E0, V3i_2E0]: (s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1w_2E0))),s(tyop_2Enum_2Enum,V3i_2E0))) = s(tyop_2Emin_2Ebool,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1w_2E0),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,V3i_2E0)))))) => ![V0f_2E0, V1w_2E0]: (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2Eword__reduce_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V0f_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1w_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Efcp_2EFCP_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E1(s(tyop_2Emin_2Ebool,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V0f_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1w_2E0))),s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))))))))))))))).
