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__value_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,![A_27a, A_27b]: ![X0_2E0]: (s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Ebinary__ieee_2Efloat__value),c_2Ebinary__ieee_2Efloat__value_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))))).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Ebinary__ieee_2Eflags_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27a_2CA_27b_29,axiom,![A_27a, A_27b]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)))),c_2Epair_2E_2C_2E0),s(tyop_2Ebinary__ieee_2Eflags,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0))))).
fof(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27a_2CA_27b_29,axiom,![A_27a, A_27b]: ![X0_2E0, X1_2E0]: (s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)))),c_2Elist_2ECONS_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),X1_2E0))))).
fof(arityeq3_2Ec_2Ebinary__ieee_2EFP__Mul_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,![A_27a, A_27b]: ![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X2_2E0))) = s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b)))),c_2Ebinary__ieee_2EFP__Mul_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X2_2E0))))).
fof(arityeq1_2Ec_2Ebinary__ieee_2Echeck__for__signalling_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,![A_27a, A_27b]: ![X0_2E0]: (s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),X0_2E0))) = s(tyop_2Ebinary__ieee_2Eflags,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),tyop_2Ebinary__ieee_2Eflags),c_2Ebinary__ieee_2Echeck__for__signalling_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),X0_2E0))))).
fof(arityeq1_2Ec_2Ebinary__ieee_2Efloat__some__qnan_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,![A_27a, A_27b]: ![X0_2E0]: (s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),X0_2E0))) = s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Efloat__some__qnan_2E0),s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),X0_2E0))))).
fof(arityeq3_2Ec_2Ebinary__ieee_2Efloat__mul_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,![A_27a, A_27b]: ![X0_2E0, X1_2E0, X2_2E0]: (s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Efloat__mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,X0_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Erounding,tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b))))),c_2Ebinary__ieee_2Efloat__mul_2E0),s(tyop_2Ebinary__ieee_2Erounding,X0_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X1_2E0))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),X2_2E0))))).
fof(binary__ieeeTheory_2Efloat__mul__nan,axiom,![A_27a, A_27b]: ![V0mode_2E0, V1x_2E0, V2y_2E0]: (((s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2ENaN_2E0)) | (s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2Efloat__value_2E1(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0))) = s(tyop_2Ebinary__ieee_2Efloat__value,c_2Ebinary__ieee_2ENaN_2E0))) => (s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Ebinary__ieee_2Efloat__mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Echeck__for__signalling_2E1(s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Elist_2ECONS_2E2(s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0),s(tyop_2Elist_2Elist(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b)),c_2Elist_2ENIL_2E0))))))),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),c_2Ebinary__ieee_2Efloat__some__qnan_2E1(s(tyop_2Ebinary__ieee_2Efp__op(A_27a,A_27b),c_2Ebinary__ieee_2EFP__Mul_2E3(s(tyop_2Ebinary__ieee_2Erounding,V0mode_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V1x_2E0),s(tyop_2Ebinary__ieee_2Efloat(A_27a,A_27b),V2y_2E0)))))))))).
