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_2Einteger_2EABS_2E1,axiom,![X0_2E0]: (s(tyop_2Einteger_2Eint,c_2Einteger_2EABS_2E1(s(tyop_2Einteger_2Eint,X0_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),c_2Einteger_2EABS_2E0),s(tyop_2Einteger_2Eint,X0_2E0))))).
fof(arityeq1_2Ec_2Earithmetic_2EEVEN_2E1,axiom,![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2EEVEN_2E0),s(tyop_2Enum_2Enum,X0_2E0))))).
fof(arityeq1_2Ec_2Einteger_2ENum_2E1,axiom,![X0_2E0]: (s(tyop_2Enum_2Enum,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Enum_2Enum),c_2Einteger_2ENum_2E0),s(tyop_2Einteger_2Eint,X0_2E0))))).
fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Einteger_2Eint,axiom,![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Einteger_2Eint,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Einteger_2Eint,X1_2E0),s(tyop_2Einteger_2Eint,X2_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Einteger_2Eint,X1_2E0))),s(tyop_2Einteger_2Eint,X2_2E0))))).
fof(arityeq1_2Ec_2Eintreal_2EINT__CEILING_2E1,axiom,![X0_2E0]: (s(tyop_2Einteger_2Eint,c_2Eintreal_2EINT__CEILING_2E1(s(tyop_2Erealax_2Ereal,X0_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Einteger_2Eint),c_2Eintreal_2EINT__CEILING_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))))).
fof(arityeq1_2Ec_2Eintreal_2EINT__FLOOR_2E1,axiom,![X0_2E0]: (s(tyop_2Einteger_2Eint,c_2Eintreal_2EINT__FLOOR_2E1(s(tyop_2Erealax_2Ereal,X0_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Einteger_2Eint),c_2Eintreal_2EINT__FLOOR_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))))).
fof(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Einteger_2Eint,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),X0_2E0),s(tyop_2Einteger_2Eint,X1_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),X0_2E0))),s(tyop_2Einteger_2Eint,X1_2E0))))).
fof(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Einteger_2Eint,axiom,![X0_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),c_2Eoption_2ESOME_2E1(s(tyop_2Einteger_2Eint,X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint)),c_2Eoption_2ESOME_2E0),s(tyop_2Einteger_2Eint,X0_2E0))))).
fof(arityeq5_2Ec_2Ebinary__ieee_2Erounding__CASE_2E5_2Emono_2Etyop_2Einteger_2Eint,axiom,![X0_2E0, X1_2E0, X2_2E0, X3_2E0, X4_2E0]: (s(tyop_2Einteger_2Eint,c_2Ebinary__ieee_2Erounding__CASE_2E5(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Einteger_2Eint,X1_2E0),s(tyop_2Einteger_2Eint,X2_2E0),s(tyop_2Einteger_2Eint,X3_2E0),s(tyop_2Einteger_2Eint,X4_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))))),c_2Ebinary__ieee_2Erounding__CASE_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Einteger_2Eint,X1_2E0))),s(tyop_2Einteger_2Eint,X2_2E0))),s(tyop_2Einteger_2Eint,X3_2E0))),s(tyop_2Einteger_2Eint,X4_2E0))))).
fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__Sign_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,![A_27t, A_27w]: ![X0_2E0]: (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ebinary__ieee_2Efloat__Sign_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_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(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,![X0_2E0]: (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone)),c_2Ewords_2En2w_2E0),s(tyop_2Enum_2Enum,X0_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_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(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(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Einteger_2Eint,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Einteger_2Eint,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Einteger_2Eint),X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Einteger_2Eint),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Einteger_2Eint)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Einteger_2Eint),X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))))).
fof(arityeq1_2Ec_2Ereal_2Eabs_2E1,axiom,![X0_2E0]: (s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ereal_2Eabs_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))))).
fof(arityeq1_2Ec_2Eintreal_2Ereal__of__int_2E1,axiom,![X0_2E0]: (s(tyop_2Erealax_2Ereal,c_2Eintreal_2Ereal__of__int_2E1(s(tyop_2Einteger_2Eint,X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Erealax_2Ereal),c_2Eintreal_2Ereal__of__int_2E0),s(tyop_2Einteger_2Eint,X0_2E0))))).
fof(arityeq2_2Ec_2Ereal_2Ereal__sub_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_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_2Ereal__sub_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))))).
fof(arityeq2_2Ec_2Ebinary__ieee_2Efloat__to__int_2E2_2Emono_2EA_27t_20mono_2EA_27w,axiom,![A_27t, A_27w]: ![X0_2E0, X1_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),c_2Ebinary__ieee_2Efloat__to__int_2E2(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint))),c_2Ebinary__ieee_2Efloat__to__int_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))))).
fof(arityeq2_2Ec_2Erealax_2Ereal__lt_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,X0_2E0),s(tyop_2Erealax_2Ereal,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)),c_2Erealax_2Ereal__lt_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))))).
fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__value_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,![A_27t, A_27w]: ![X0_2E0]: (s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Ebinary__ieee_2Efloat__value),c_2Ebinary__ieee_2Efloat__value_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))))).
fof(arityeq4_2Ec_2Ebinary__ieee_2Efloat__value__CASE_2E4_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Einteger_2Eint_29,axiom,![X0_2E0, X1_2E0, X2_2E0, X3_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,X0_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint)),X1_2E0),s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),X2_2E0),s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),X3_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat__value,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint))))),c_2Ebinary__ieee_2Efloat__value__CASE_2E0),s(tyop_2Ebinary__ieee_2Efloat__value,X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint)),X1_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),X2_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),X3_2E0))))).
fof(binary__ieeeTheory_2Efloat__to__int__def,axiom,![A_27t, A_27w]: ![F4_2E0, F3_2E0, F1_2E0, F2_2E0, F0_2E0]: (![V4df_2E0, V3f_2E0]: (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)),F4_2E0),s(tyop_2Erealax_2Ereal,V4df_2E0))),s(tyop_2Einteger_2Eint,V3f_2E0)))) <=> (p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,V4df_2E0),s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_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_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),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_2Erealax_2Ereal,V4df_2E0) = s(tyop_2Erealax_2Ereal,c_2Ereal_2E_2F_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_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))),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)))))))))) & p(s(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(s(tyop_2Enum_2Enum,c_2Einteger_2ENum_2E1(s(tyop_2Einteger_2Eint,c_2Einteger_2EABS_2E1(s(tyop_2Einteger_2Eint,V3f_2E0))))))))))) => (![V3f_2E0, V2r_2E0, V4df_2E0]: (s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Einteger_2Eint)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Einteger_2Eint))),F3_2E0),s(tyop_2Einteger_2Eint,V3f_2E0))),s(tyop_2Erealax_2Ereal,V2r_2E0))),s(tyop_2Erealax_2Ereal,V4df_2E0))) = s(tyop_2Einteger_2Eint,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)),F4_2E0),s(tyop_2Erealax_2Ereal,V4df_2E0))),s(tyop_2Einteger_2Eint,V3f_2E0))),s(tyop_2Einteger_2Eint,V3f_2E0),s(tyop_2Einteger_2Eint,c_2Eintreal_2EINT__CEILING_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0)))))) => (![V2r_2E0, V3f_2E0]: (s(tyop_2Einteger_2Eint,app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),F1_2E0),s(tyop_2Erealax_2Ereal,V2r_2E0))),s(tyop_2Einteger_2Eint,V3f_2E0))) = s(tyop_2Einteger_2Eint,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Einteger_2Eint)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Einteger_2Eint))),F3_2E0),s(tyop_2Einteger_2Eint,V3f_2E0))),s(tyop_2Erealax_2Ereal,V2r_2E0))),s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__sub_2E2(s(tyop_2Erealax_2Ereal,V2r_2E0),s(tyop_2Erealax_2Ereal,c_2Eintreal_2Ereal__of__int_2E1(s(tyop_2Einteger_2Eint,V3f_2E0)))))))))) => (![V1x_2E0]: (p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0)))) <=> (s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ebinary__ieee_2Efloat__Sign_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,tyop_2Eone_2Eone),c_2Ewords_2En2w_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))))))) => (![V0mode_2E0, V1x_2E0, V2r_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint)))),F0_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Erealax_2Ereal,V2r_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),c_2Eoption_2ESOME_2E1(s(tyop_2Einteger_2Eint,c_2Ebinary__ieee_2Erounding__CASE_2E5(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Einteger_2Eint,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),F1_2E0),s(tyop_2Erealax_2Ereal,V2r_2E0))),s(tyop_2Einteger_2Eint,c_2Eintreal_2EINT__FLOOR_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0))))),s(tyop_2Einteger_2Eint,c_2Eintreal_2EINT__CEILING_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0))),s(tyop_2Einteger_2Eint,c_2Eintreal_2EINT__FLOOR_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0))),s(tyop_2Einteger_2Eint,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),F2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Einteger_2Eint,c_2Eintreal_2EINT__CEILING_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0))),s(tyop_2Einteger_2Eint,c_2Eintreal_2EINT__FLOOR_2E1(s(tyop_2Erealax_2Ereal,V2r_2E0)))))))))) => ![V0mode_2E0, V1x_2E0]: (s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),c_2Ebinary__ieee_2Efloat__to__int_2E2(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),c_2Ebinary__ieee_2Efloat__value__CASE_2E4(s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint)))),F0_2E0),s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1x_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Einteger_2Eint),c_2Eoption_2ENONE_2E0)))))))))).
