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_2Ebinary__ieee_2Efloat__is__finite_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,![A_27t, A_27w]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Ebool),c_2Ebinary__ieee_2Efloat__is__finite_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))))).
fof(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Ebinary__ieee_2Eflags_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29,axiom,![A_27t, A_27w]: ![X0_2E0]: (s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X0_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Epair_2ESND_2E0),s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),X0_2E0))))).
fof(arityeq4_2Ec_2Ebinary__ieee_2Efloat__mul__add_2E4_2Emono_2EA_27t_20mono_2EA_27w,axiom,![A_27t, A_27w]: ![X0_2E0, X1_2E0, X2_2E0, X3_2E0]: (s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__mul__add_2E4(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X3_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w))))),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_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)))))),c_2Ebinary__ieee_2Efloat__mul__add_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X2_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X3_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_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,![A_27t, A_27w]: ![X0_2E0]: (s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Efloat__to__real_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),X0_2E0))))).
fof(arityeq2_2Ec_2Erealax_2Ereal__add_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_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_2Erealax_2Ereal__add_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,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(arityeq2_2Ec_2Erealax_2Ereal__mul_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_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_2Erealax_2Ereal__mul_2E0),s(tyop_2Erealax_2Ereal,X0_2E0))),s(tyop_2Erealax_2Ereal,X1_2E0))))).
fof(arityeq1_2Ec_2Ebinary__ieee_2Ethreshold_2E1_2Emono_2EA_27t_20mono_2EA_27w,axiom,![A_27t, A_27w]: ![X0_2E0]: (s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Ethreshold_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),X0_2E0))) = s(tyop_2Erealax_2Ereal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),tyop_2Erealax_2Ereal),c_2Ebinary__ieee_2Ethreshold_2E0),s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),X0_2E0))))).
fof(lift__ieeeTheory_2Efloat__mul__add__finite,axiom,![A_27t, A_27w]: ![V0a_2E0, V1b_2E0, V2c_2E0]: ((p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0)))) & (p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0)))) & (p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2c_2E0)))) & p(s(tyop_2Emin_2Ebool,c_2Erealax_2Ereal__lt_2E2(s(tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E1(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__add_2E2(s(tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E2(s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0))))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Efloat__to__real_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2c_2E0))))))),s(tyop_2Erealax_2Ereal,c_2Ebinary__ieee_2Ethreshold_2E1(s(tyop_2Ebool_2Eitself(tyop_2Epair_2Eprod(A_27t,A_27w)),c_2Ebool_2Ethe__value_2E0))))))))) => p(s(tyop_2Emin_2Ebool,c_2Ebinary__ieee_2Efloat__is__finite_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w)),c_2Ebinary__ieee_2Efloat__mul__add_2E4(s(tyop_2Ebinary__ieee_2Erounding,c_2Ebinary__ieee_2EroundTiesToEven_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V0a_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V1b_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27t,A_27w),V2c_2E0)))))))))).
