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_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Ebinary__ieee_2Eflags,X1_2E0))) = s(tyop_2Ebinary__ieee_2Eflags,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags)),c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Ebinary__ieee_2Eflags,X1_2E0))))).
fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X1_2E0))))).
fof(arityeq2_2Ec_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Ebinary__ieee_2Eflags,X1_2E0))) = s(tyop_2Ebinary__ieee_2Eflags,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags)),c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Ebinary__ieee_2Eflags,X1_2E0))))).
fof(arityeq2_2Ec_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Ebinary__ieee_2Eflags,X1_2E0))) = s(tyop_2Ebinary__ieee_2Eflags,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags)),c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Ebinary__ieee_2Eflags,X1_2E0))))).
fof(arityeq2_2Ec_2Ebinary__ieee_2Eflags__Precision__fupd_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Ebinary__ieee_2Eflags,X1_2E0))) = s(tyop_2Ebinary__ieee_2Eflags,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags)),c_2Ebinary__ieee_2Eflags__Precision__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Ebinary__ieee_2Eflags,X1_2E0))))).
fof(arityeq2_2Ec_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Ebinary__ieee_2Eflags,X1_2E0))) = s(tyop_2Ebinary__ieee_2Eflags,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags)),c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Ebinary__ieee_2Eflags,X1_2E0))))).
fof(arityeq2_2Ec_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2,axiom,![X0_2E0, X1_2E0]: (s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Ebinary__ieee_2Eflags,X1_2E0))) = s(tyop_2Ebinary__ieee_2Eflags,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ebinary__ieee_2Eflags,tyop_2Ebinary__ieee_2Eflags)),c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Ebinary__ieee_2Eflags,X1_2E0))))).
fof(binary__ieeeTheory_2Eflags__fupdfupds,axiom,(![V0g_2E0, V1f0_2E0, V2f_2E0]: (s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V1f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0g_2E0),s(tyop_2Ebinary__ieee_2Eflags,V2f_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__DivideByZero__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V1f0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0g_2E0))),s(tyop_2Ebinary__ieee_2Eflags,V2f_2E0)))) & (![V3g_2E0, V4f0_2E0, V5f_2E0]: (s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V4f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V3g_2E0),s(tyop_2Ebinary__ieee_2Eflags,V5f_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__InvalidOp__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V4f0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V3g_2E0))),s(tyop_2Ebinary__ieee_2Eflags,V5f_2E0)))) & (![V6g_2E0, V7f0_2E0, V8f_2E0]: (s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V7f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V6g_2E0),s(tyop_2Ebinary__ieee_2Eflags,V8f_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Overflow__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V7f0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V6g_2E0))),s(tyop_2Ebinary__ieee_2Eflags,V8f_2E0)))) & (![V9g_2E0, V10f0_2E0, V11f_2E0]: (s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V10f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V9g_2E0),s(tyop_2Ebinary__ieee_2Eflags,V11f_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Precision__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V10f0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V9g_2E0))),s(tyop_2Ebinary__ieee_2Eflags,V11f_2E0)))) & (![V12g_2E0, V13f0_2E0, V14f_2E0]: (s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V13f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V12g_2E0),s(tyop_2Ebinary__ieee_2Eflags,V14f_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__BeforeRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V13f0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V12g_2E0))),s(tyop_2Ebinary__ieee_2Eflags,V14f_2E0)))) & ![V15g_2E0, V16f0_2E0, V17f_2E0]: (s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V16f0_2E0),s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V15g_2E0),s(tyop_2Ebinary__ieee_2Eflags,V17f_2E0))))) = s(tyop_2Ebinary__ieee_2Eflags,c_2Ebinary__ieee_2Eflags__Underflow__AfterRounding__fupd_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V16f0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V15g_2E0))),s(tyop_2Ebinary__ieee_2Eflags,V17f_2E0)))))))))).
