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_2EDecode_2Edec2enc_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EDecode_2Edec2enc_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X0_2E0))) = s(tyop_2Emin_2Efun(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(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2EDecode_2Edec2enc_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)))),X0_2E0))))).
fof(arityeq1_2Ec_2EDecode_2Edec2enc_2E1_2Emono_2EA_27b,axiom,![A_27b]: ![X0_2E0]: (s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EDecode_2Edec2enc_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,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_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2EDecode_2Edec2enc_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X0_2E0))))).
fof(arityeq2_2Ec_2EDecode_2Eenc2dec_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,![A_27a, A_27b]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),c_2EDecode_2Eenc2dec_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),c_2EDecode_2Eenc2dec_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X1_2E0))))).
fof(arityeq2_2Ec_2EEncode_2Eencode__prod_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,![A_27a, A_27b]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EEncode_2Eencode__prod_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),c_2EEncode_2Eencode__prod_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X1_2E0))))).
fof(arityeq3_2Ec_2EDecode_2Edecode__prod_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,![A_27a, A_27b]: ![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),c_2EDecode_2Edecode__prod_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),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_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),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_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),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_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),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_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))))))),c_2EDecode_2Edecode__prod_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),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_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),X2_2E0))))).
fof(DecodeTheory_2Edecode__prod__def,axiom,![A_27a, A_27b]: ![V0p_2E0, V1d1_2E0, V2d2_2E0]: (s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),c_2EDecode_2Edecode__prod_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0p_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)))),V1d1_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V2d2_2E0))) = s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),c_2EDecode_2Eenc2dec_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0p_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EEncode_2Eencode__prod_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EDecode_2Edec2enc_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V1d1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2EDecode_2Edec2enc_2E1(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))),V2d2_2E0))))))))).
