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_2Earithmetic_2E_2B_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_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_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))))).
fof(arityeq2_2Ec_2Ereal_2E_2F_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),c_2Ereal_2E_2F_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,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_2EBIT2_2E1,axiom,![X0_2E0]: (s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_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_2EBIT2_2E0),s(tyop_2Enum_2Enum,X0_2E0))))).
fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))))).
fof(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Erealax_2Ereal,axiom,![X0_2E0]: (s(tyop_2Erealax_2Ereal,c_2Ecombin_2EI_2E1(s(tyop_2Erealax_2Ereal,X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecombin_2EI_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))))).
fof(arityeq1_2Ec_2Ewords_2EINT__MAX_2E1_2Emono_2EA_27w,axiom,![A_27w]: ![X0_2E0]: (s(tyop_2Enum_2Enum,c_2Ewords_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27w),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27w),tyop_2Enum_2Enum),c_2Ewords_2EINT__MAX_2E0),s(tyop_2Ebool_2Eitself(A_27w),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(arityeq1_2Ec_2Efcp_2Edimindex_2E1_2Emono_2EA_27t,axiom,![A_27t]: ![X0_2E0]: (s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27t),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27t),tyop_2Enum_2Enum),c_2Efcp_2Edimindex_2E0),s(tyop_2Ebool_2Eitself(A_27t),X0_2E0))))).
fof(arityeq2_2Ec_2Ereal_2Epow_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),c_2Ereal_2Epow_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))))).
fof(arityeq1_2Ec_2Ereal_2Ereal__of__num_2E1,axiom,![X0_2E0]: (s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),c_2Ereal_2Ereal__of__num_2E0),s(tyop_2Enum_2Enum,X0_2E0))))).
fof(arityeq1_2Ec_2Ewords_2Ew2n_2E1_2Emono_2EA_27w,axiom,![A_27w]: ![X0_2E0]: (s(tyop_2Enum_2Enum,c_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Enum_2Enum),c_2Ewords_2Ew2n_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),X0_2E0))))).
fof(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27w_29_2Ctyop_2Ebool_2Eitself_28A_27t_29_29,axiom,![A_27t, A_27w]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2EWF_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),X0_2E0))))).
fof(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27w,axiom,![A_27w]: ![X0_2E0]: (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w)),c_2Ewords_2En2w_2E0),s(tyop_2Enum_2Enum,X0_2E0))))).
fof(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27w_29_2Ctyop_2Ebool_2Eitself_28A_27t_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27w_29_2Ctyop_2Ebool_2Eitself_28A_27t_29_29_2Ctyop_2Emin_2Ebool_29_29,axiom,![A_27t, A_27w]: ![X0_2E0]: (s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool))),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27w_29_2Ctyop_2Ebool_2Eitself_28A_27t_29_29_20mono_2Etyop_2Erealax_2Ereal,axiom,![A_27t, A_27w]: ![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal))),c_2Erelation_2EWFREC_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal)),X1_2E0))))).
fof(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27w_29_20mono_2Etyop_2Ebool_2Eitself_28A_27t_29,axiom,![A_27t, A_27w]: ![X0_2E0, X1_2E0]: (s(tyop_2Erealax_2Ereal,c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27t),tyop_2Erealax_2Ereal)),X1_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27t),tyop_2Erealax_2Ereal)),tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27t),tyop_2Erealax_2Ereal)),tyop_2Erealax_2Ereal)),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27t),tyop_2Erealax_2Ereal)),X1_2E0))))).
fof(binary__ieeeTheory_2EULP__primitive__def,axiom,![A_27t, A_27w]: ![F3_2E0, F2_2E0, F1_2E0, F0_2E0]: (![V3v_2E0]: (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Ebool),F3_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V3v_2E0)))) <=> (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V3v_2E0) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0))))) => (![V3v_2E0, V4v1_2E0]: (s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27t),tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27t),tyop_2Erealax_2Ereal)),F2_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V3v_2E0))),s(tyop_2Ebool_2Eitself(A_27t),V4v1_2E0))) = s(tyop_2Erealax_2Ereal,c_2Ecombin_2EI_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Ebool),F3_2E0),s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V3v_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,c_2Ewords_2Ew2n_2E1(s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),V3v_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Epow_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Ewords_2EINT__MAX_2E1(s(tyop_2Ebool_2Eitself(A_27w),c_2Ebool_2Ethe__value_2E0))),s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27t),c_2Ebool_2Ethe__value_2E0)))))))))))) => (![V1ULP_2E0, V2a_2E0]: (s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal)),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal),V1ULP_2E0))),s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),V2a_2E0))) = s(tyop_2Erealax_2Ereal,c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),V2a_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27t),tyop_2Erealax_2Ereal)),F2_2E0)))) => (![V0R_2E0]: (s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),V0R_2E0))) = s(tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),V0R_2E0)))) => (s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2EULP_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal),c_2Erelation_2EWFREC_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),F0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27w),tyop_2Ebool_2Eitself(A_27t)),tyop_2Erealax_2Ereal)),F1_2E0))))))))).
