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_2Ecombin_2EI_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Ecombin_2EI_2E1(s(tyop_2Emin_2Ebool,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EI_2E0),s(tyop_2Emin_2Ebool,X0_2E0))))).
fof(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Epatricia_2Eptree_28A_27a_29,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)),X0_2E0))))).
fof(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28A_27a_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28A_27a_29_2Ctyop_2Emin_2Ebool_29_29,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool))),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Epatricia_2Eptree_28A_27a_29_20mono_2Etyop_2Emin_2Ebool,axiom,![A_27a]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool))),c_2Erelation_2EWFREC_2E0),s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)),X1_2E0))))).
fof(arityeq4_2Ec_2Epatricia_2Eptree__CASE_2E4_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,![A_27a]: ![X0_2E0, X1_2E0, X2_2E0, X3_2E0]: (s(tyop_2Emin_2Ebool,c_2Epatricia_2Eptree__CASE_2E4(s(tyop_2Epatricia_2Eptree(A_27a),X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)))),X3_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool)))),c_2Epatricia_2Eptree__CASE_2E0),s(tyop_2Epatricia_2Eptree(A_27a),X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X2_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)))),X3_2E0))))).
fof(patriciaTheory_2EIS__EMPTY__primitive__def,axiom,![A_27a]: ![F0_2E0, F3_2E0, F2_2E0, F1_2E0]: (![V0R_2E0]: (s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)),V0R_2E0)))) => (![V5v8_2E0, V6v9_2E0, V7v10_2E0, V8v11_2E0]: (s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)))),F3_2E0),s(tyop_2Enum_2Enum,V5v8_2E0))),s(tyop_2Enum_2Enum,V6v9_2E0))),s(tyop_2Epatricia_2Eptree(A_27a),V7v10_2E0))),s(tyop_2Epatricia_2Eptree(A_27a),V8v11_2E0))) = s(tyop_2Emin_2Ebool,c_2Ecombin_2EI_2E1(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))) => (![V3v6_2E0, V4v7_2E0]: (s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0),s(tyop_2Enum_2Enum,V3v6_2E0))),s(A_27a,V4v7_2E0))) = s(tyop_2Emin_2Ebool,c_2Ecombin_2EI_2E1(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)))) => (![V1IS__EMPTY_2E0, V2a_2E0]: (s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool),V1IS__EMPTY_2E0))),s(tyop_2Epatricia_2Eptree(A_27a),V2a_2E0))) = s(tyop_2Emin_2Ebool,c_2Epatricia_2Eptree__CASE_2E4(s(tyop_2Epatricia_2Eptree(A_27a),V2a_2E0),s(tyop_2Emin_2Ebool,c_2Ecombin_2EI_2E1(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)))),F3_2E0)))) => (s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool),c_2Epatricia_2EIS__EMPTY_2E0) = s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)),F1_2E0))))))))).
