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_2Eoption_2Eoption_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,![A_27a]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),c_2Epair_2E_2C_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X1_2E0))))).
fof(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2ESOME_2E0),s(A_27a,X0_2E0))))).
fof(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Eoption_2Eoption_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),c_2Eoption_2ESOME_2E0),s(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0))))).
fof(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eoption_2Eoption_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_20mono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,![A_27a]: ![X0_2E0, X1_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),X1_2E0))))).
fof(arityeq2_2Ec_2EDecode_2Ewf__decoder_2E2_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Ebool,c_2EDecode_2Ewf__decoder_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Ebool)),c_2EDecode_2Ewf__decoder_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X1_2E0))))).
fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eoption_2Eoption_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,axiom,![A_27a]: ![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X1_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X1_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X2_2E0))))).
fof(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eoption_2Eoption_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,axiom,![A_27a]: ![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X2_2E0))))).
fof(arityeq3_2Ec_2EDecode_2Edecode__option_2E3_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2EDecode_2Edecode__option_2E3(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X1_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),c_2EDecode_2Edecode__option_2E0),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X1_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X2_2E0))))).
fof(arityeq1_2Ec_2EEncode_2Elift__option_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),c_2EEncode_2Elift__option_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool)),c_2EEncode_2Elift__option_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eoption_2Eoption_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29,axiom,![A_27a]: ![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),c_2Elist_2Elist__CASE_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),X2_2E0))))).
fof(DecodeTheory_2Edecode__option,axiom,![A_27a]: ![F2_2E0, F1_2E0, F0_2E0]: (![V6x_2E0, V7t_27_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F2_2E0),s(A_27a,V6x_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V7t_27_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V6x_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V7t_27_2E0)))))) => (![V5v_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F1_2E0),s(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),V5v_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),V5v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),F2_2E0)))) => (![V1d_2E0, V3v1_2E0, V4t_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V1d_2E0))),s(tyop_2Emin_2Ebool,V3v1_2E0))),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V4t_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,V3v1_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V1d_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V4t_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),F1_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E2(s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V4t_2E0)))))))) => ![V0l_2E0, V1d_2E0, V2p_2E0]: (p(s(tyop_2Emin_2Ebool,c_2EDecode_2Ewf__decoder_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2p_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V1d_2E0)))) => (s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2EDecode_2Edecode__option_2E3(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),c_2EEncode_2Elift__option_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2p_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V1d_2E0),s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V0l_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Elist_2Elist__CASE_2E3(s(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V0l_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V1d_2E0))))))))))).
