include('Axioms/HL4001+2.ax').
fof(ne_ty_2Efcp_2Ecart,axiom,( ! [A0] : ( ne(A0) => ( ! [A1] : ( ne(A1) => ne(ty_2Efcp_2Ecart(A0,A1)) ) ) ) )).
fof(ne_ty_2Ebinary__ieee_2Efloat,axiom,( ! [A0] : ( ne(A0) => ( ! [A1] : ( ne(A1) => ne(ty_2Ebinary__ieee_2Efloat(A0,A1)) ) ) ) )).
fof(mem_c_2Ebinary__ieee_2Efloat__Significand,axiom,( ! [A_27t] : ( ne(A_27t) => ! [A_27w] : ( ne(A_27w) => mem(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Efcp_2Ecart(bool,A_27t))) ) ) )).
fof(mem_c_2Ebinary__ieee_2Efloat__Exponent,axiom,( ! [A_27t] : ( ne(A_27t) => ! [A_27w] : ( ne(A_27w) => mem(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Efcp_2Ecart(bool,A_27w))) ) ) )).
fof(ne_ty_2Erealax_2Ereal,axiom,( ne(ty_2Erealax_2Ereal) )).
fof(mem_c_2Ereal_2Ereal__sub,axiom,( mem(c_2Ereal_2Ereal__sub,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))) )).
fof(mem_c_2Epred__set_2EUNIV,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2EUNIV(A_27a),arr(A_27a,bool)) ) )).
fof(mem_c_2Epred__set_2EFINITE,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2EFINITE(A_27a),arr(arr(A_27a,bool),bool)) ) )).
fof(ne_ty_2Epair_2Eprod,axiom,( ! [A0] : ( ne(A0) => ( ! [A1] : ( ne(A1) => ne(ty_2Epair_2Eprod(A0,A1)) ) ) ) )).
fof(ne_ty_2Ebool_2Eitself,axiom,( ! [A0] : ( ne(A0) => ne(ty_2Ebool_2Eitself(A0)) ) )).
fof(mem_c_2Ebinary__ieee_2Ethreshold,axiom,( ! [A_27t] : ( ne(A_27t) => ! [A_27w] : ( ne(A_27w) => mem(c_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t,A_27w)),ty_2Erealax_2Ereal)) ) ) )).
fof(mem_c_2Erealax_2Ereal__add,axiom,( mem(c_2Erealax_2Ereal__add,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))) )).
fof(mem_c_2Erealax_2Ereal__mul,axiom,( mem(c_2Erealax_2Ereal__mul,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))) )).
fof(ne_ty_2Enum_2Enum,axiom,( ne(ty_2Enum_2Enum) )).
fof(mem_c_2Ereal_2Epow,axiom,( mem(c_2Ereal_2Epow,arr(ty_2Erealax_2Ereal,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))) )).
fof(mem_c_2Ereal_2Eabs,axiom,( mem(c_2Ereal_2Eabs,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) )).
fof(ne_ty_2Ebinary__ieee_2Erounding,axiom,( ne(ty_2Ebinary__ieee_2Erounding) )).
fof(mem_c_2Ebinary__ieee_2EroundTiesToEven,axiom,( mem(c_2Ebinary__ieee_2EroundTiesToEven,ty_2Ebinary__ieee_2Erounding) )).
fof(mem_c_2Etransc_2Esqrt,axiom,( mem(c_2Etransc_2Esqrt,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) )).
fof(mem_c_2Elift__ieee_2Enormalizes,axiom,( ! [A_27t] : ( ne(A_27t) => ! [A_27w] : ( ne(A_27w) => mem(c_2Elift__ieee_2Enormalizes(A_27t,A_27w),arr(ty_2Ebool_2Eitself(ty_2Epair_2Eprod(A_27t,A_27w)),arr(ty_2Erealax_2Ereal,bool))) ) ) )).
fof(ne_ty_2Eone_2Eone,axiom,( ne(ty_2Eone_2Eone) )).
fof(mem_c_2Ebinary__ieee_2Efloat__Sign,axiom,( ! [A_27t] : ( ne(A_27t) => ! [A_27w] : ( ne(A_27w) => mem(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone))) ) ) )).
fof(mem_c_2Erealax_2Ereal__lt,axiom,( mem(c_2Erealax_2Ereal__lt,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,bool))) )).
fof(mem_c_2Ereal_2Ereal__lte,axiom,( mem(c_2Ereal_2Ereal__lte,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,bool))) )).
fof(mem_c_2Elift__machine__ieee_2Einterval,axiom,( mem(c_2Elift__machine__ieee_2Einterval,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,bool)))) )).
fof(mem_c_2Ebool_2EARB,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Ebool_2EARB(A_27a),A_27a) ) )).
fof(ne_ty_2Efcp_2Ebit1,axiom,( ! [A0] : ( ne(A0) => ne(ty_2Efcp_2Ebit1(A0)) ) )).
fof(ne_ty_2Efcp_2Ebit0,axiom,( ! [A0] : ( ne(A0) => ne(ty_2Efcp_2Ebit0(A0)) ) )).
fof(mem_c_2Ebinary__ieee_2Efloat__Significand__fupd,axiom,( ! [A_27t] : ( ne(A_27t) => ! [A_27u] : ( ne(A_27u) => ! [A_27w] : ( ne(A_27w) => mem(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27t,A_27u,A_27w),arr(arr(ty_2Efcp_2Ecart(bool,A_27t),ty_2Efcp_2Ecart(bool,A_27u)),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efloat(A_27u,A_27w)))) ) ) ) )).
fof(mem_c_2Ebinary__ieee_2Efloat__Exponent__fupd,axiom,( ! [A_27t] : ( ne(A_27t) => ! [A_27w] : ( ne(A_27w) => ! [A_27x] : ( ne(A_27x) => mem(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27t,A_27w,A_27x),arr(arr(ty_2Efcp_2Ecart(bool,A_27w),ty_2Efcp_2Ecart(bool,A_27x)),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efloat(A_27t,A_27x)))) ) ) ) )).
fof(mem_c_2Ecombin_2EK,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Ecombin_2EK(A_27a,A_27b),arr(A_27a,arr(A_27b,A_27a))) ) ) )).
fof(mem_c_2Ebinary__ieee_2Efloat__Sign__fupd,axiom,( ! [A_27t] : ( ne(A_27t) => ! [A_27w] : ( ne(A_27w) => mem(c_2Ebinary__ieee_2Efloat__Sign__fupd(A_27t,A_27w),arr(arr(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)))) ) ) )).
fof(mem_c_2Ebinary__ieee_2Efloat__to__real,axiom,( ! [A_27t] : ( ne(A_27t) => ! [A_27w] : ( ne(A_27w) => mem(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Erealax_2Ereal)) ) ) )).
fof(mem_c_2Emachine__ieee_2Efp64__to__real,axiom,( mem(c_2Emachine__ieee_2Efp64__to__real,arr(ty_2Efcp_2Ecart(bool,ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Eone_2Eone))))))),ty_2Erealax_2Ereal)) )).
fof(ne_ty_2Ebinary__ieee_2Eflags,axiom,( ne(ty_2Ebinary__ieee_2Eflags) )).
fof(mem_c_2Ebinary__ieee_2Efloat__sqrt,axiom,( ! [A_27t] : ( ne(A_27t) => ! [A_27w] : ( ne(A_27w) => mem(c_2Ebinary__ieee_2Efloat__sqrt(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),ty_2Epair_2Eprod(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w))))) ) ) )).
fof(mem_c_2Epair_2ESND,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Epair_2ESND(A_27a,A_27b),arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27b)) ) ) )).
fof(mem_c_2Emachine__ieee_2Efp64__sqrt,axiom,( mem(c_2Emachine__ieee_2Efp64__sqrt,arr(ty_2Ebinary__ieee_2Erounding,arr(ty_2Efcp_2Ecart(bool,ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Eone_2Eone))))))),ty_2Efcp_2Ecart(bool,ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Eone_2Eone)))))))))) )).
fof(mem_c_2Ebinary__ieee_2Efloat__is__finite,axiom,( ! [A_27t] : ( ne(A_27t) => ! [A_27w] : ( ne(A_27w) => mem(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),bool)) ) ) )).
fof(mem_c_2Emachine__ieee_2Efp64__isFinite,axiom,( mem(c_2Emachine__ieee_2Efp64__isFinite,arr(ty_2Efcp_2Ecart(bool,ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Eone_2Eone))))))),bool)) )).
fof(mem_c_2Emachine__ieee_2Efloat__to__fp64,axiom,( mem(c_2Emachine__ieee_2Efloat__to__fp64,arr(ty_2Ebinary__ieee_2Efloat(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Eone_2Eone))))),ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Eone_2Eone)))),ty_2Efcp_2Ecart(bool,ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Eone_2Eone))))))))) )).
fof(mem_c_2Emachine__ieee_2Efp64__to__float,axiom,( mem(c_2Emachine__ieee_2Efp64__to__float,arr(ty_2Efcp_2Ecart(bool,ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Eone_2Eone))))))),ty_2Ebinary__ieee_2Efloat(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Eone_2Eone))))),ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Eone_2Eone)))))) )).
fof(mem_c_2Earithmetic_2EEVEN,axiom,( mem(c_2Earithmetic_2EEVEN,arr(ty_2Enum_2Enum,bool)) )).
fof(mem_c_2Earithmetic_2EODD,axiom,( mem(c_2Earithmetic_2EODD,arr(ty_2Enum_2Enum,bool)) )).
fof(mem_c_2Earithmetic_2E_3E_3D,axiom,( mem(c_2Earithmetic_2E_3E_3D,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) )).
fof(mem_c_2Earithmetic_2E_3E,axiom,( mem(c_2Earithmetic_2E_3E,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) )).
fof(mem_c_2Eprim__rec_2EPRE,axiom,( mem(c_2Eprim__rec_2EPRE,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Enumeral_2EiiSUC,axiom,( mem(c_2Enumeral_2EiiSUC,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Enumeral_2EiZ,axiom,( mem(c_2Enumeral_2EiZ,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Enumeral_2EiSUB,axiom,( mem(c_2Enumeral_2EiSUB,arr(bool,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)))) )).
fof(mem_c_2Ebool_2ECOND,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Ebool_2ECOND(A_27a),arr(bool,arr(A_27a,arr(A_27a,A_27a)))) ) )).
fof(mem_c_2Ebit_2ETIMES__2EXP,axiom,( mem(c_2Ebit_2ETIMES__2EXP,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) )).
fof(mem_c_2Enumeral__bit_2ESFUNPOW,axiom,( mem(c_2Enumeral__bit_2ESFUNPOW,arr(arr(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)))) )).
fof(mem_c_2Enumeral_2EiDUB,axiom,( mem(c_2Enumeral_2EiDUB,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Enumeral__bit_2EiSUC,axiom,( mem(c_2Enumeral__bit_2EiSUC,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Enumeral__bit_2EFDUB,axiom,( mem(c_2Enumeral__bit_2EFDUB,arr(arr(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) )).
fof(mem_c_2Ebool_2ET,axiom,( mem(c_2Ebool_2ET,bool) )).
fof(ax_true_p,axiom,( p(c_2Ebool_2ET) )).
fof(mem_c_2Epair_2E_2C,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Epair_2E_2C(A_27a,A_27b),arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27a,A_27b)))) ) ) )).
fof(mem_c_2Ebool_2E_3F,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Ebool_2E_3F(A_27a),arr(arr(A_27a,bool),bool)) ) )).
fof(ax_ex_p,axiom,( ! [A] : ( ne(A) => ! [Q] : ( mem(Q,arr(A,bool)) => ( p(ap(c_2Ebool_2E_3F(A),Q)) <=> ? [X] : ( mem(X,A) & p(ap(Q,X)) ) ) ) ) )).
fof(mem_c_2Epred__set_2EGSPEC,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Epred__set_2EGSPEC(A_27a,A_27b),arr(arr(A_27b,ty_2Epair_2Eprod(A_27a,bool)),arr(A_27a,bool))) ) ) )).
fof(mem_c_2Ebool_2EIN,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Ebool_2EIN(A_27a),arr(A_27a,arr(arr(A_27a,bool),bool))) ) )).
fof(mem_c_2Enum_2ESUC,axiom,( mem(c_2Enum_2ESUC,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Ereal_2Ereal__of__num,axiom,( mem(c_2Ereal_2Ereal__of__num,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) )).
fof(mem_c_2Ereal_2E_2F,axiom,( mem(c_2Ereal_2E_2F,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))) )).
fof(mem_c_2Erealax_2Einv,axiom,( mem(c_2Erealax_2Einv,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) )).
fof(mem_c_2Ebool_2EF,axiom,( mem(c_2Ebool_2EF,bool) )).
fof(ax_false_p,axiom,( ~ p(c_2Ebool_2EF) )).
fof(mem_c_2Ebool_2E_5C_2F,axiom,( mem(c_2Ebool_2E_5C_2F,arr(bool,arr(bool,bool))) )).
fof(ax_or_p,axiom,( ! [Q] : ( mem(Q,bool) => ! [R] : ( mem(R,bool) => ( p(ap(ap(c_2Ebool_2E_5C_2F,Q),R)) <=> ( p(Q) | p(R) ) ) ) ) )).
fof(mem_c_2Earithmetic_2EEXP,axiom,( mem(c_2Earithmetic_2EEXP,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) )).
fof(mem_c_2Ewords_2EUINT__MAX,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Ewords_2EUINT__MAX(A_27a),arr(ty_2Ebool_2Eitself(A_27a),ty_2Enum_2Enum)) ) )).
fof(mem_c_2Ewords_2EINT__MAX,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Ewords_2EINT__MAX(A_27a),arr(ty_2Ebool_2Eitself(A_27a),ty_2Enum_2Enum)) ) )).
fof(mem_c_2Ewords_2Eword__msb,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Ewords_2Eword__msb(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),bool)) ) )).
fof(mem_c_2Earithmetic_2E_2D,axiom,( mem(c_2Earithmetic_2E_2D,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) )).
fof(mem_c_2Earithmetic_2EMIN,axiom,( mem(c_2Earithmetic_2EMIN,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) )).
fof(mem_c_2Earithmetic_2E_2B,axiom,( mem(c_2Earithmetic_2E_2B,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) )).
fof(mem_c_2Earithmetic_2E_3C_3D,axiom,( mem(c_2Earithmetic_2E_3C_3D,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) )).
fof(mem_c_2Efcp_2EFCP,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Efcp_2EFCP(A_27a,A_27b),arr(arr(ty_2Enum_2Enum,A_27a),ty_2Efcp_2Ecart(A_27a,A_27b))) ) ) )).
fof(mem_c_2Ewords_2Eword__bits,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Ewords_2Eword__bits(A_27a),arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a))))) ) )).
fof(mem_c_2Ecombin_2Eo,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [A_27c] : ( ne(A_27c) => mem(c_2Ecombin_2Eo(A_27a,A_27b,A_27c),arr(arr(A_27c,A_27b),arr(arr(A_27a,A_27c),arr(A_27a,A_27b)))) ) ) ) )).
fof(mem_c_2Ewords_2Eword__extract,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Ewords_2Eword__extract(A_27a,A_27b),arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27b))))) ) ) )).
fof(mem_c_2Ewords_2EINT__MIN,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Ewords_2EINT__MIN(A_27a),arr(ty_2Ebool_2Eitself(A_27a),ty_2Enum_2Enum)) ) )).
fof(mem_c_2Earithmetic_2E_2A,axiom,( mem(c_2Earithmetic_2E_2A,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) )).
fof(mem_c_2Ewords_2Edimword,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Ewords_2Edimword(A_27a),arr(ty_2Ebool_2Eitself(A_27a),ty_2Enum_2Enum)) ) )).
fof(mem_c_2Enum_2E0,axiom,( mem(c_2Enum_2E0,ty_2Enum_2Enum) )).
fof(mem_c_2Ewords_2En2w,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Ewords_2En2w(A_27a),arr(ty_2Enum_2Enum,ty_2Efcp_2Ecart(bool,A_27a))) ) )).
fof(mem_c_2Ebool_2E_7E,axiom,( mem(c_2Ebool_2E_7E,arr(bool,bool)) )).
fof(ax_neg_p,axiom,( ! [Q] : ( mem(Q,bool) => ( p(ap(c_2Ebool_2E_7E,Q)) <=> ~ p(Q) ) ) )).
fof(mem_c_2Ebool_2E_2F_5C,axiom,( mem(c_2Ebool_2E_2F_5C,arr(bool,arr(bool,bool))) )).
fof(ax_and_p,axiom,( ! [Q] : ( mem(Q,bool) => ! [R] : ( mem(R,bool) => ( p(ap(ap(c_2Ebool_2E_2F_5C,Q),R)) <=> ( p(Q) & p(R) ) ) ) ) )).
fof(mem_c_2Ewords_2Ew2w,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Ewords_2Ew2w(A_27a,A_27b),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27b))) ) ) )).
fof(mem_c_2Efcp_2Efcp__index,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Efcp_2Efcp__index(A_27a,A_27b),arr(ty_2Efcp_2Ecart(A_27a,A_27b),arr(ty_2Enum_2Enum,A_27a))) ) ) )).
fof(mem_c_2Eprim__rec_2E_3C,axiom,( mem(c_2Eprim__rec_2E_3C,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) )).
fof(mem_c_2Emin_2E_3D_3D_3E,axiom,( mem(c_2Emin_2E_3D_3D_3E,arr(bool,arr(bool,bool))) )).
fof(ax_imp_p,axiom,( ! [Q] : ( mem(Q,bool) => ! [R] : ( mem(R,bool) => ( p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R)) <=> ( p(Q) => p(R) ) ) ) ) )).
fof(mem_c_2Ebool_2E_21,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Ebool_2E_21(A_27a),arr(arr(A_27a,bool),bool)) ) )).
fof(ax_all_p,axiom,( ! [A] : ( ne(A) => ! [Q] : ( mem(Q,arr(A,bool)) => ( p(ap(c_2Ebool_2E_21(A),Q)) <=> ! [X] : ( mem(X,A) => p(ap(Q,X)) ) ) ) ) )).
fof(mem_c_2Earithmetic_2EZERO,axiom,( mem(c_2Earithmetic_2EZERO,ty_2Enum_2Enum) )).
fof(mem_c_2Earithmetic_2EBIT1,axiom,( mem(c_2Earithmetic_2EBIT1,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Earithmetic_2EBIT2,axiom,( mem(c_2Earithmetic_2EBIT2,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Earithmetic_2ENUMERAL,axiom,( mem(c_2Earithmetic_2ENUMERAL,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Ebool_2Ethe__value,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Ebool_2Ethe__value(A_27a),ty_2Ebool_2Eitself(A_27a)) ) )).
fof(mem_c_2Efcp_2Edimindex,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Efcp_2Edimindex(A_27a),arr(ty_2Ebool_2Eitself(A_27a),ty_2Enum_2Enum)) ) )).
fof(mem_c_2Emin_2E_3D,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Emin_2E_3D(A_27a),arr(A_27a,arr(A_27a,bool))) ) )).
fof(ax_eq_p,axiom,( ! [A] : ( ne(A) => ! [X] : ( mem(X,A) => ! [Y] : ( mem(Y,A) => ( p(ap(ap(c_2Emin_2E_3D(A),X),Y)) <=> X = Y ) ) ) ) )).
fof(conj_thm_2Earithmetic_2ENORM__0,lemma,(( ap(c_2Earithmetic_2ENUMERAL,c_2Earithmetic_2EZERO) = c_2Enum_2E0 ))).
fof(conj_thm_2Earithmetic_2EADD__0,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2B,V0m),c_2Enum_2E0) = V0m ) ))).
fof(conj_thm_2Earithmetic_2EADD__SYM,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2B,V0m),V1n) = ap(ap(c_2Earithmetic_2E_2B,V1n),V0m) ) ) ))).
fof(conj_thm_2Earithmetic_2ELESS__EQ,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0m)),V1n)) ) ) ))).
fof(conj_thm_2Earithmetic_2EZERO__LESS__EQ,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => p(ap(ap(c_2Earithmetic_2E_3C_3D,c_2Enum_2E0),V0n)) ))).
fof(conj_thm_2Earithmetic_2ENOT__LESS,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ( ~~ p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) ) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m)) ) ) ))).
fof(conj_thm_2Earithmetic_2EMULT__LEFT__1,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0m) = V0m ) ))).
fof(conj_thm_2Earithmetic_2EMULT__CLAUSES,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ( ap(ap(c_2Earithmetic_2E_2A,c_2Enum_2E0),V0m) = c_2Enum_2E0 ) & ( ( ap(ap(c_2Earithmetic_2E_2A,V0m),c_2Enum_2E0) = c_2Enum_2E0 ) & ( ( ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0m) = V0m ) & ( ( ap(ap(c_2Earithmetic_2E_2A,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = V0m ) & ( ( ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V0m)),V1n) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),V1n) ) & ( ap(ap(c_2Earithmetic_2E_2A,V0m),ap(c_2Enum_2ESUC,V1n)) = ap(ap(c_2Earithmetic_2E_2B,V0m),ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)) ) ) ) ) ) ) ) ))).
fof(conj_thm_2Earithmetic_2ELESS__EQ__TRANS,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ! [V2p] : ( mem(V2p,ty_2Enum_2Enum) => ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)) ) => p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V2p)) ) ) ) ))).
fof(conj_thm_2Earithmetic_2ETIMES2,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n) = ap(ap(c_2Earithmetic_2E_2B,V0n),V0n) ) ))).
fof(conj_thm_2Earithmetic_2ESUB__EQUAL__0,lemma,(! [V0c] : ( mem(V0c,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2D,V0c),V0c) = c_2Enum_2E0 ) ))).
fof(conj_thm_2Earithmetic_2EADD__MONO__LESS__EQ,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ! [V2p] : ( mem(V2p,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)),ap(ap(c_2Earithmetic_2E_2B,V0m),V2p))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)) ) ) ) ))).
fof(conj_thm_2Earithmetic_2ENOT__LEQ,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ( ~~ p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) ) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V1n)),V0m)) ) ) ))).
fof(conj_thm_2Earithmetic_2ESUC__ONE__ADD,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ap(c_2Enum_2ESUC,V0n) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0n) ) ))).
fof(conj_thm_2Earithmetic_2ESUC__ELIM__NUMERALS,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0f] : ( mem(V0f,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,A_27a))) => ! [V1g] : ( mem(V1g,arr(ty_2Enum_2Enum,A_27a)) => ( ( ! [V2n] : ( mem(V2n,ty_2Enum_2Enum) => ( ap(V1g,ap(c_2Enum_2ESUC,V2n)) = ap(ap(V0f,V2n),ap(c_2Enum_2ESUC,V2n)) ) ) ) <=> ( ( ! [V3n] : ( mem(V3n,ty_2Enum_2Enum) => ( ap(V1g,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n))) = ap(ap(V0f,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n))) ) ) ) & ! [V4n] : ( mem(V4n,ty_2Enum_2Enum) => ( ap(V1g,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V4n))) = ap(ap(V0f,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V4n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V4n))) ) ) ) ) ) )))).
fof(conj_thm_2Earithmetic_2EMIN__LE,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ! [V2p] : ( mem(V2p,ty_2Enum_2Enum) => ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EMIN,V1m),V0n)),V2p)) <=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V2p)) | p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V2p)) ) ) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V2p),ap(ap(c_2Earithmetic_2EMIN,V1m),V0n))) <=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V2p),V1m)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V2p),V0n)) ) ) ) ) ) ))).
fof(conj_thm_2Ebinary__ieee_2Efloat__accfupds,lemma,( ! [A_27t]: ( ne(A_27t) =>  ! [A_27u]: ( ne(A_27u) =>  ! [A_27w]: ( ne(A_27w) =>  ! [A_27x]: ( ne(A_27x) => ( ( ! [V0f0] : ( mem(V0f0,arr(ty_2Efcp_2Ecart(bool,A_27w),ty_2Efcp_2Ecart(bool,A_27x))) => ! [V1f] : ( mem(V1f,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27x),ap(ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27t,A_27w,A_27x),V0f0),V1f)) = ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),V1f) ) ) ) ) & ( ( ! [V2f0] : ( mem(V2f0,arr(ty_2Efcp_2Ecart(bool,A_27t),ty_2Efcp_2Ecart(bool,A_27u))) => ! [V3f] : ( mem(V3f,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ap(c_2Ebinary__ieee_2Efloat__Sign(A_27u,A_27w),ap(ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27t,A_27u,A_27w),V2f0),V3f)) = ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),V3f) ) ) ) ) & ( ( ! [V4f0] : ( mem(V4f0,arr(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone))) => ! [V5f] : ( mem(V5f,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),ap(ap(c_2Ebinary__ieee_2Efloat__Sign__fupd(A_27t,A_27w),V4f0),V5f)) = ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V5f) ) ) ) ) & ( ( ! [V6f0] : ( mem(V6f0,arr(ty_2Efcp_2Ecart(bool,A_27t),ty_2Efcp_2Ecart(bool,A_27u))) => ! [V7f] : ( mem(V7f,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27u,A_27w),ap(ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27t,A_27u,A_27w),V6f0),V7f)) = ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V7f) ) ) ) ) & ( ( ! [V8f0] : ( mem(V8f0,arr(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone))) => ! [V9f] : ( mem(V9f,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ap(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27w),ap(ap(c_2Ebinary__ieee_2Efloat__Sign__fupd(A_27t,A_27w),V8f0),V9f)) = ap(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27w),V9f) ) ) ) ) & ( ( ! [V10f0] : ( mem(V10f0,arr(ty_2Efcp_2Ecart(bool,A_27w),ty_2Efcp_2Ecart(bool,A_27x))) => ! [V11f] : ( mem(V11f,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ap(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27x),ap(ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27t,A_27w,A_27x),V10f0),V11f)) = ap(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27w),V11f) ) ) ) ) & ( ( ! [V12f0] : ( mem(V12f0,arr(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone))) => ! [V13f] : ( mem(V13f,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),ap(ap(c_2Ebinary__ieee_2Efloat__Sign__fupd(A_27t,A_27w),V12f0),V13f)) = ap(V12f0,ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),V13f)) ) ) ) ) & ( ( ! [V14f0] : ( mem(V14f0,arr(ty_2Efcp_2Ecart(bool,A_27w),ty_2Efcp_2Ecart(bool,A_27x))) => ! [V15f] : ( mem(V15f,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27x),ap(ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(A_27t,A_27w,A_27x),V14f0),V15f)) = ap(V14f0,ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V15f)) ) ) ) ) & ! [V16f0] : ( mem(V16f0,arr(ty_2Efcp_2Ecart(bool,A_27t),ty_2Efcp_2Ecart(bool,A_27u))) => ! [V17f] : ( mem(V17f,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ap(c_2Ebinary__ieee_2Efloat__Significand(A_27u,A_27w),ap(ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(A_27t,A_27u,A_27w),V16f0),V17f)) = ap(V16f0,ap(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27w),V17f)) ) ) ) ) ) ) ) ) ) ) ))))))).
fof(ax_thm_2Ebinary__ieee_2Ethreshold__def,axiom,( ! [A_27t] : ( ne(A_27t) => ! [A_27w] : ( ne(A_27w) => ( ap(c_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Ewords_2EUINT__MAX(A_27w),c_2Ebool_2Ethe__value(A_27w))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Ewords_2EINT__MAX(A_27w),c_2Ebool_2Ethe__value(A_27w))))),ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Erealax_2Einv,ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Enum_2ESUC,ap(c_2Efcp_2Edimindex(A_27t),c_2Ebool_2Ethe__value(A_27t))))))) ) ) ) )).
fof(ax_thm_2Ebit_2ETIMES__2EXP__def,axiom, ! [V0x] : ( mem(V0x,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ap(ap(c_2Ebit_2ETIMES__2EXP,V0x),V1n) = ap(ap(c_2Earithmetic_2E_2A,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x)) ) ) )).
fof(ax_thm_2Ebool_2EETA__AX,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0t] : ( mem(V0t,arr(A_27a,A_27b)) => ( f31(A_27b,A_27a,V0t) = V0t ) ) ) ) )).
fof(conj_thm_2Ebool_2ETRUTH,lemma,($true)).
fof(conj_thm_2Ebool_2EIMP__ANTISYM__AX,lemma,(! [V0t1] : ( mem(V0t1,bool) => ! [V1t2] : ( mem(V1t2,bool) => ( ( p(V0t1) => p(V1t2) ) => ( ( p(V1t2) => p(V0t1) ) => ( p(V0t1) <=> p(V1t2) ) ) ) ) ))).
fof(conj_thm_2Ebool_2EFALSITY,lemma,(! [V0t] : ( mem(V0t,bool) => ( $false => p(V0t) ) ))).
fof(conj_thm_2Ebool_2EFORALL__SIMP,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0t] : ( mem(V0t,bool) => ( ( ! [V1x] : ( mem(V1x,A_27a) => p(V0t) ) ) <=> p(V0t) ) )))).
fof(conj_thm_2Ebool_2EAND__CLAUSES,lemma,(! [V0t] : ( mem(V0t,bool) => ( ( ( $true & p(V0t) ) <=> p(V0t) ) & ( ( ( p(V0t) & $true ) <=> p(V0t) ) & ( ( ( $false & p(V0t) ) <=> $false ) & ( ( ( p(V0t) & $false ) <=> $false ) & ( ( p(V0t) & p(V0t) ) <=> p(V0t) ) ) ) ) ) ))).
fof(conj_thm_2Ebool_2EIMP__CLAUSES,lemma,(! [V0t] : ( mem(V0t,bool) => ( ( ( $true => p(V0t) ) <=> p(V0t) ) & ( ( ( p(V0t) => $true ) <=> $true ) & ( ( ( $false => p(V0t) ) <=> $true ) & ( ( ( p(V0t) => p(V0t) ) <=> $true ) & ( ( p(V0t) => $false ) <=> ( ~~ p(V0t) ) ) ) ) ) ) ))).
fof(conj_thm_2Ebool_2ENOT__CLAUSES,lemma,(( ( ! [V0t] : ( mem(V0t,bool) => ( ( ~~ ( ~~ p(V0t) ) ) <=> p(V0t) ) ) ) & ( ( (~~ ($true)) <=> $false ) & ( (~~ ($false)) <=> $true ) ) ))).
fof(conj_thm_2Ebool_2EREFL__CLAUSE,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ( ( V0x = V0x ) <=> $true ) )))).
fof(conj_thm_2Ebool_2EEQ__SYM__EQ,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1y] : ( mem(V1y,A_27a) => ( ( V0x = V1y ) <=> ( V1y = V0x ) ) ) )))).
fof(conj_thm_2Ebool_2EEQ__CLAUSES,lemma,(! [V0t] : ( mem(V0t,bool) => ( ( ( $true <=> p(V0t) ) <=> p(V0t) ) & ( ( ( p(V0t) <=> $true ) <=> p(V0t) ) & ( ( ( $false <=> p(V0t) ) <=> ( ~~ p(V0t) ) ) & ( ( p(V0t) <=> $false ) <=> ( ~~ p(V0t) ) ) ) ) ) ))).
fof(conj_thm_2Ebool_2ECOND__CLAUSES,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0t1] : ( mem(V0t1,A_27a) => ! [V1t2] : ( mem(V1t2,A_27a) => ( ( ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2ET),V0t1),V1t2) = V0t1 ) & ( ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2EF),V0t1),V1t2) = V1t2 ) ) ) )))).
fof(conj_thm_2Ebool_2EDE__MORGAN__THM,lemma,(! [V0A] : ( mem(V0A,bool) => ! [V1B] : ( mem(V1B,bool) => ( ( ( ~~ ( p(V0A) & p(V1B) ) ) <=> ( ( ~~ p(V0A) ) | ( ~~ p(V1B) ) ) ) & ( ( ~~ ( p(V0A) | p(V1B) ) ) <=> ( ( ~~ p(V0A) ) & ( ~~ p(V1B) ) ) ) ) ) ))).
fof(conj_thm_2Ebool_2EIMP__DISJ__THM,lemma,(! [V0A] : ( mem(V0A,bool) => ! [V1B] : ( mem(V1B,bool) => ( ( p(V0A) => p(V1B) ) <=> ( ( ~~ p(V0A) ) | p(V1B) ) ) ) ))).
fof(conj_thm_2Ebool_2EDISJ__IMP__THM,lemma,(! [V0P] : ( mem(V0P,bool) => ! [V1Q] : ( mem(V1Q,bool) => ! [V2R] : ( mem(V2R,bool) => ( ( ( p(V0P) | p(V1Q) ) => p(V2R) ) <=> ( ( p(V0P) => p(V2R) ) & ( p(V1Q) => p(V2R) ) ) ) ) ) ))).
fof(conj_thm_2Ebool_2EIMP__F__EQ__F,lemma,(! [V0t] : ( mem(V0t,bool) => ( ( p(V0t) => $false ) <=> ( p(V0t) <=> $false ) ) ))).
fof(conj_thm_2Ebool_2EAND__IMP__INTRO,lemma,(! [V0t1] : ( mem(V0t1,bool) => ! [V1t2] : ( mem(V1t2,bool) => ! [V2t3] : ( mem(V2t3,bool) => ( ( p(V0t1) => ( p(V1t2) => p(V2t3) ) ) <=> ( ( p(V0t1) & p(V1t2) ) => p(V2t3) ) ) ) ) ))).
fof(conj_thm_2Ebool_2EIMP__CONG,lemma,(! [V0x] : ( mem(V0x,bool) => ! [V1x_27] : ( mem(V1x_27,bool) => ! [V2y] : ( mem(V2y,bool) => ! [V3y_27] : ( mem(V3y_27,bool) => ( ( ( p(V0x) <=> p(V1x_27) ) & ( p(V1x_27) => ( p(V2y) <=> p(V3y_27) ) ) ) => ( ( p(V0x) => p(V2y) ) <=> ( p(V1x_27) => p(V3y_27) ) ) ) ) ) ) ))).
fof(conj_thm_2Ebool_2EUNWIND__FORALL__THM2,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0f] : ( mem(V0f,arr(A_27a,bool)) => ! [V1v] : ( mem(V1v,A_27a) => ( ( ! [V2x] : ( mem(V2x,A_27a) => ( ( V2x = V1v ) => p(ap(V0f,V2x)) ) ) ) <=> p(ap(V0f,V1v)) ) ) )))).
fof(conj_thm_2Ecombin_2Eo__THM,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) =>  ! [A_27c]: ( ne(A_27c) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1g] : ( mem(V1g,arr(A_27c,A_27a)) => ! [V2x] : ( mem(V2x,A_27c) => ( ap(ap(ap(c_2Ecombin_2Eo(A_27c,A_27b,A_27a),V0f),V1g),V2x) = ap(V0f,ap(V1g,V2x)) ) ) ) )))))).
fof(conj_thm_2Ecombin_2EK__THM,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1y] : ( mem(V1y,A_27b) => ( ap(ap(c_2Ecombin_2EK(A_27a,A_27b),V0x),V1y) = V0x ) ) ))))).
fof(conj_thm_2Efcp_2ECART__EQ,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0x] : ( mem(V0x,ty_2Efcp_2Ecart(A_27a,A_27b)) => ! [V1y] : ( mem(V1y,ty_2Efcp_2Ecart(A_27a,A_27b)) => ( ( V0x = V1y ) <=> ! [V2i] : ( mem(V2i,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,V2i),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b)))) => ( ap(ap(c_2Efcp_2Efcp__index(A_27a,A_27b),V0x),V2i) = ap(ap(c_2Efcp_2Efcp__index(A_27a,A_27b),V1y),V2i) ) ) ) ) ) ))))).
fof(conj_thm_2Efcp_2EFCP__BETA,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0g] : ( mem(V0g,arr(ty_2Enum_2Enum,A_27a)) => ! [V1i] : ( mem(V1i,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,V1i),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b)))) => ( ap(ap(c_2Efcp_2Efcp__index(A_27a,A_27b),ap(c_2Efcp_2EFCP(A_27a,A_27b),V0g)),V1i) = ap(V0g,V1i) ) ) ) ))))).
fof(conj_thm_2Efcp_2Eindex__bit0,lemma,( ! [A_27a]: ( ne(A_27a) => ( ap(c_2Efcp_2Edimindex(ty_2Efcp_2Ebit0(A_27a)),c_2Ebool_2Ethe__value(ty_2Efcp_2Ebit0(A_27a))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(c_2Epred__set_2EFINITE(A_27a),c_2Epred__set_2EUNIV(A_27a))),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) )))).
fof(conj_thm_2Efcp_2Efinite__bit0,lemma,( ! [A_27a]: ( ne(A_27a) => ( p(ap(c_2Epred__set_2EFINITE(ty_2Efcp_2Ebit0(A_27a)),c_2Epred__set_2EUNIV(ty_2Efcp_2Ebit0(A_27a)))) <=> p(ap(c_2Epred__set_2EFINITE(A_27a),c_2Epred__set_2EUNIV(A_27a))) )))).
fof(conj_thm_2Efcp_2Eindex__bit1,lemma,( ! [A_27a]: ( ne(A_27a) => ( ap(c_2Efcp_2Edimindex(ty_2Efcp_2Ebit1(A_27a)),c_2Ebool_2Ethe__value(ty_2Efcp_2Ebit1(A_27a))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(c_2Epred__set_2EFINITE(A_27a),c_2Epred__set_2EUNIV(A_27a))),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) )))).
fof(conj_thm_2Efcp_2Efinite__bit1,lemma,( ! [A_27a]: ( ne(A_27a) => ( p(ap(c_2Epred__set_2EFINITE(ty_2Efcp_2Ebit1(A_27a)),c_2Epred__set_2EUNIV(ty_2Efcp_2Ebit1(A_27a)))) <=> p(ap(c_2Epred__set_2EFINITE(A_27a),c_2Epred__set_2EUNIV(A_27a))) )))).
fof(conj_thm_2Efcp_2Eindex__one,lemma,(( ap(c_2Efcp_2Edimindex(ty_2Eone_2Eone),c_2Ebool_2Ethe__value(ty_2Eone_2Eone)) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ))).
fof(conj_thm_2Efcp_2Efinite__one,lemma,(p(ap(c_2Epred__set_2EFINITE(ty_2Eone_2Eone),c_2Epred__set_2EUNIV(ty_2Eone_2Eone))))).
fof(ax_thm_2Elift__ieee_2Enormalizes__def,axiom,( ! [A_27t] : ( ne(A_27t) => ! [A_27w] : ( ne(A_27w) => ! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Elift__ieee_2Enormalizes(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))),V0x)) <=> ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Ewords_2EINT__MAX(A_27w),c_2Ebool_2Ethe__value(A_27w)))) & ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Einv,ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Ewords_2EINT__MAX(A_27w),c_2Ebool_2Ethe__value(A_27w))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))),ap(c_2Ereal_2Eabs,V0x))) & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,V0x)),ap(c_2Ebinary__ieee_2Ethreshold(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))))) ) ) ) ) ) ) )).
fof(conj_thm_2Elift__ieee_2Efloat__sqrt__relative,lemma,( ! [A_27t]: ( ne(A_27t) =>  ! [A_27w]: ( ne(A_27w) => ! [V0a] : ( mem(V0a,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),V0a)) & ( ( ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),V0a) = ap(c_2Ewords_2En2w(ty_2Eone_2Eone),c_2Enum_2E0) ) & p(ap(ap(c_2Elift__ieee_2Enormalizes(A_27t,A_27w),c_2Ebool_2Ethe__value(ty_2Epair_2Eprod(A_27t,A_27w))),ap(c_2Etransc_2Esqrt,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a)))) ) ) => ( p(ap(c_2Ebinary__ieee_2Efloat__is__finite(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(c_2Ebinary__ieee_2Efloat__sqrt(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a)))) & ? [V1e] : ( mem(V1e,ty_2Erealax_2Ereal) & ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,V1e)),ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Efcp_2Edimindex(A_27t),c_2Ebool_2Ethe__value(A_27t))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))) & ( ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),ap(c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)),ap(ap(c_2Ebinary__ieee_2Efloat__sqrt(A_27t,A_27w),c_2Ebinary__ieee_2EroundTiesToEven),V0a))) = ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Etransc_2Esqrt,ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0a))),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1e)) ) ) ) ) ) ))))).
fof(ax_thm_2Elift__machine__ieee_2Einterval__def,axiom, ! [V0a] : ( mem(V0a,ty_2Erealax_2Ereal) => ! [V1b] : ( mem(V1b,ty_2Erealax_2Ereal) => ( ap(ap(c_2Elift__machine__ieee_2Einterval,V0a),V1b) = ap(c_2Epred__set_2EGSPEC(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),f3259(V1b,V0a)) ) ) )).
fof(ax_thm_2Emachine__ieee_2Efp64__to__float__def,axiom, ! [V0w] : ( mem(V0w,ty_2Efcp_2Ecart(bool,ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Eone_2Eone)))))))) => ( ap(c_2Emachine__ieee_2Efp64__to__float,V0w) = ap(ap(c_2Ebinary__ieee_2Efloat__Sign__fupd(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Eone_2Eone))))),ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Eone_2Eone)))),ap(c_2Ecombin_2EK(ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone),ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)),ap(ap(ap(c_2Ewords_2Eword__extract(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Eone_2Eone)))))),ty_2Eone_2Eone),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))),V0w))),ap(ap(c_2Ebinary__ieee_2Efloat__Exponent__fupd(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Eone_2Eone))))),ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Eone_2Eone))),ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Eone_2Eone)))),ap(c_2Ecombin_2EK(ty_2Efcp_2Ecart(bool,ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Eone_2Eone)))),ty_2Efcp_2Ecart(bool,ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Eone_2Eone))))),ap(ap(ap(c_2Ewords_2Eword__extract(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Eone_2Eone)))))),ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Eone_2Eone)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))),V0w))),ap(ap(c_2Ebinary__ieee_2Efloat__Significand__fupd(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Eone_2Eone))))),ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Eone_2Eone))))),ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Eone_2Eone)))),ap(c_2Ecombin_2EK(ty_2Efcp_2Ecart(bool,ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Eone_2Eone)))))),ty_2Efcp_2Ecart(bool,ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Eone_2Eone))))))),ap(ap(ap(c_2Ewords_2Eword__extract(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Eone_2Eone)))))),ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Eone_2Eone)))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))),c_2Enum_2E0),V0w))),c_2Ebool_2EARB(ty_2Ebinary__ieee_2Efloat(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Eone_2Eone))))),ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Eone_2Eone)))))))) ) )).
fof(ax_thm_2Emachine__ieee_2Efp64__to__real__def,axiom, ( c_2Emachine__ieee_2Efp64__to__real = ap(ap(c_2Ecombin_2Eo(ty_2Efcp_2Ecart(bool,ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Eone_2Eone))))))),ty_2Erealax_2Ereal,ty_2Ebinary__ieee_2Efloat(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Eone_2Eone))))),ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Eone_2Eone))))),c_2Ebinary__ieee_2Efloat__to__real(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Eone_2Eone))))),ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Eone_2Eone))))),c_2Emachine__ieee_2Efp64__to__float) )).
fof(ax_thm_2Emachine__ieee_2Efp64__sqrt__def,axiom, ! [V0mode] : ( mem(V0mode,ty_2Ebinary__ieee_2Erounding) => ( ap(c_2Emachine__ieee_2Efp64__sqrt,V0mode) = ap(ap(c_2Ecombin_2Eo(ty_2Efcp_2Ecart(bool,ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Eone_2Eone))))))),ty_2Efcp_2Ecart(bool,ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Eone_2Eone))))))),ty_2Ebinary__ieee_2Efloat(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Eone_2Eone))))),ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Eone_2Eone))))),c_2Emachine__ieee_2Efloat__to__fp64),ap(ap(c_2Ecombin_2Eo(ty_2Efcp_2Ecart(bool,ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Eone_2Eone))))))),ty_2Ebinary__ieee_2Efloat(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Eone_2Eone))))),ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Eone_2Eone)))),ty_2Epair_2Eprod(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Eone_2Eone))))),ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Eone_2Eone)))))),c_2Epair_2ESND(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Eone_2Eone))))),ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Eone_2Eone)))))),ap(ap(c_2Ecombin_2Eo(ty_2Efcp_2Ecart(bool,ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Eone_2Eone))))))),ty_2Epair_2Eprod(ty_2Ebinary__ieee_2Eflags,ty_2Ebinary__ieee_2Efloat(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Eone_2Eone))))),ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Eone_2Eone))))),ty_2Ebinary__ieee_2Efloat(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Eone_2Eone))))),ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Eone_2Eone))))),ap(c_2Ebinary__ieee_2Efloat__sqrt(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Eone_2Eone))))),ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Eone_2Eone)))),V0mode)),c_2Emachine__ieee_2Efp64__to__float))) ) )).
fof(ax_thm_2Emachine__ieee_2Efp64__isFinite__def,axiom, ( c_2Emachine__ieee_2Efp64__isFinite = ap(ap(c_2Ecombin_2Eo(ty_2Efcp_2Ecart(bool,ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Eone_2Eone))))))),bool,ty_2Ebinary__ieee_2Efloat(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Eone_2Eone))))),ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Eone_2Eone))))),c_2Ebinary__ieee_2Efloat__is__finite(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Eone_2Eone))))),ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Eone_2Eone))))),c_2Emachine__ieee_2Efp64__to__float) )).
fof(conj_thm_2Emachine__ieee_2Efp64__to__float__float__to__fp64,lemma,(! [V0x] : ( mem(V0x,ty_2Ebinary__ieee_2Efloat(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit1(ty_2Eone_2Eone))))),ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit1(ty_2Efcp_2Ebit0(ty_2Eone_2Eone))))) => ( ap(c_2Emachine__ieee_2Efp64__to__float,ap(c_2Emachine__ieee_2Efloat__to__fp64,V0x)) = V0x ) ))).
fof(conj_thm_2Enumeral_2Enumeral__suc,lemma,(( ( ap(c_2Enum_2ESUC,c_2Earithmetic_2EZERO) = ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO) ) & ( ( ! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ap(c_2Enum_2ESUC,ap(c_2Earithmetic_2EBIT1,V0n)) = ap(c_2Earithmetic_2EBIT2,V0n) ) ) ) & ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ap(c_2Enum_2ESUC,ap(c_2Earithmetic_2EBIT2,V1n)) = ap(c_2Earithmetic_2EBIT1,ap(c_2Enum_2ESUC,V1n)) ) ) ) ))).
fof(conj_thm_2Enumeral_2Enumeral__distrib,lemma,(( ( ! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2B,c_2Enum_2E0),V0n) = V0n ) ) ) & ( ( ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2B,V1n),c_2Enum_2E0) = V1n ) ) ) & ( ( ! [V2n] : ( mem(V2n,ty_2Enum_2Enum) => ! [V3m] : ( mem(V3m,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,V2n)),ap(c_2Earithmetic_2ENUMERAL,V3m)) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,V2n),V3m))) ) ) ) ) & ( ( ! [V4n] : ( mem(V4n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2A,c_2Enum_2E0),V4n) = c_2Enum_2E0 ) ) ) & ( ( ! [V5n] : ( mem(V5n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2A,V5n),c_2Enum_2E0) = c_2Enum_2E0 ) ) ) & ( ( ! [V6n] : ( mem(V6n,ty_2Enum_2Enum) => ! [V7m] : ( mem(V7m,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,V6n)),ap(c_2Earithmetic_2ENUMERAL,V7m)) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Earithmetic_2E_2A,V6n),V7m)) ) ) ) ) & ( ( ! [V8n] : ( mem(V8n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2D,c_2Enum_2E0),V8n) = c_2Enum_2E0 ) ) ) & ( ( ! [V9n] : ( mem(V9n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2D,V9n),c_2Enum_2E0) = V9n ) ) ) & ( ( ! [V10n] : ( mem(V10n,ty_2Enum_2Enum) => ! [V11m] : ( mem(V11m,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,V10n)),ap(c_2Earithmetic_2ENUMERAL,V11m)) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Earithmetic_2E_2D,V10n),V11m)) ) ) ) ) & ( ( ! [V12n] : ( mem(V12n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2EEXP,c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V12n))) = c_2Enum_2E0 ) ) ) & ( ( ! [V13n] : ( mem(V13n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2EEXP,c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V13n))) = c_2Enum_2E0 ) ) ) & ( ( ! [V14n] : ( mem(V14n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2EEXP,V14n),c_2Enum_2E0) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) ) ) & ( ( ! [V15n] : ( mem(V15n,ty_2Enum_2Enum) => ! [V16m] : ( mem(V16m,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,V15n)),ap(c_2Earithmetic_2ENUMERAL,V16m)) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Earithmetic_2EEXP,V15n),V16m)) ) ) ) ) & ( ( ap(c_2Enum_2ESUC,c_2Enum_2E0) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) & ( ( ! [V17n] : ( mem(V17n,ty_2Enum_2Enum) => ( ap(c_2Enum_2ESUC,ap(c_2Earithmetic_2ENUMERAL,V17n)) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Enum_2ESUC,V17n)) ) ) ) & ( ( ap(c_2Eprim__rec_2EPRE,c_2Enum_2E0) = c_2Enum_2E0 ) & ( ( ! [V18n] : ( mem(V18n,ty_2Enum_2Enum) => ( ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2ENUMERAL,V18n)) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Eprim__rec_2EPRE,V18n)) ) ) ) & ( ( ! [V19n] : ( mem(V19n,ty_2Enum_2Enum) => ( ( ap(c_2Earithmetic_2ENUMERAL,V19n) = c_2Enum_2E0 ) <=> ( V19n = c_2Earithmetic_2EZERO ) ) ) ) & ( ( ! [V20n] : ( mem(V20n,ty_2Enum_2Enum) => ( ( c_2Enum_2E0 = ap(c_2Earithmetic_2ENUMERAL,V20n) ) <=> ( V20n = c_2Earithmetic_2EZERO ) ) ) ) & ( ( ! [V21n] : ( mem(V21n,ty_2Enum_2Enum) => ! [V22m] : ( mem(V22m,ty_2Enum_2Enum) => ( ( ap(c_2Earithmetic_2ENUMERAL,V21n) = ap(c_2Earithmetic_2ENUMERAL,V22m) ) <=> ( V21n = V22m ) ) ) ) ) & ( ( ! [V23n] : ( mem(V23n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,V23n),c_2Enum_2E0)) <=> $false ) ) ) & ( ( ! [V24n] : ( mem(V24n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,V24n))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Earithmetic_2EZERO),V24n)) ) ) ) & ( ( ! [V25n] : ( mem(V25n,ty_2Enum_2Enum) => ! [V26m] : ( mem(V26m,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,V25n)),ap(c_2Earithmetic_2ENUMERAL,V26m))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,V25n),V26m)) ) ) ) ) & ( ( ! [V27n] : ( mem(V27n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3E,c_2Enum_2E0),V27n)) <=> $false ) ) ) & ( ( ! [V28n] : ( mem(V28n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Earithmetic_2ENUMERAL,V28n)),c_2Enum_2E0)) <=> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Earithmetic_2EZERO),V28n)) ) ) ) & ( ( ! [V29n] : ( mem(V29n,ty_2Enum_2Enum) => ! [V30m] : ( mem(V30m,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Earithmetic_2ENUMERAL,V29n)),ap(c_2Earithmetic_2ENUMERAL,V30m))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,V30m),V29n)) ) ) ) ) & ( ( ! [V31n] : ( mem(V31n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,c_2Enum_2E0),V31n)) <=> $true ) ) ) & ( ( ! [V32n] : ( mem(V32n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,V32n)),c_2Enum_2E0)) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V32n),c_2Earithmetic_2EZERO)) ) ) ) & ( ( ! [V33n] : ( mem(V33n,ty_2Enum_2Enum) => ! [V34m] : ( mem(V34m,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,V33n)),ap(c_2Earithmetic_2ENUMERAL,V34m))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V33n),V34m)) ) ) ) ) & ( ( ! [V35n] : ( mem(V35n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3E_3D,V35n),c_2Enum_2E0)) <=> $true ) ) ) & ( ( ! [V36n] : ( mem(V36n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3E_3D,c_2Enum_2E0),V36n)) <=> ( V36n = c_2Enum_2E0 ) ) ) ) & ( ( ! [V37n] : ( mem(V37n,ty_2Enum_2Enum) => ! [V38m] : ( mem(V38m,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Earithmetic_2ENUMERAL,V37n)),ap(c_2Earithmetic_2ENUMERAL,V38m))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V38m),V37n)) ) ) ) ) & ( ( ! [V39n] : ( mem(V39n,ty_2Enum_2Enum) => ( p(ap(c_2Earithmetic_2EODD,ap(c_2Earithmetic_2ENUMERAL,V39n))) <=> p(ap(c_2Earithmetic_2EODD,V39n)) ) ) ) & ( ( ! [V40n] : ( mem(V40n,ty_2Enum_2Enum) => ( p(ap(c_2Earithmetic_2EEVEN,ap(c_2Earithmetic_2ENUMERAL,V40n))) <=> p(ap(c_2Earithmetic_2EEVEN,V40n)) ) ) ) & ( ( ~~ p(ap(c_2Earithmetic_2EODD,c_2Enum_2E0)) ) & p(ap(c_2Earithmetic_2EEVEN,c_2Enum_2E0)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
fof(conj_thm_2Enumeral_2Enumeral__add,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ( ( ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,c_2Earithmetic_2EZERO),V0n)) = V0n ) & ( ( ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,V0n),c_2Earithmetic_2EZERO)) = V0n ) & ( ( ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ( ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) = ap(c_2Earithmetic_2EBIT1,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ( ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) = ap(c_2Earithmetic_2EBIT1,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ( ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ( ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,c_2Earithmetic_2EZERO),V0n)) = ap(c_2Enum_2ESUC,V0n) ) & ( ( ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),c_2Earithmetic_2EZERO)) = ap(c_2Enum_2ESUC,V0n) ) & ( ( ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) = ap(c_2Earithmetic_2EBIT1,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ( ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ( ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ( ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) = ap(c_2Earithmetic_2EBIT1,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ( ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,c_2Earithmetic_2EZERO),V0n)) = ap(c_2Enumeral_2EiiSUC,V0n) ) & ( ( ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,V0n),c_2Earithmetic_2EZERO)) = ap(c_2Enumeral_2EiiSUC,V0n) ) & ( ( ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ( ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) = ap(c_2Earithmetic_2EBIT1,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ( ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) = ap(c_2Earithmetic_2EBIT1,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
fof(conj_thm_2Enumeral_2Enumeral__lt,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Earithmetic_2EZERO),ap(c_2Earithmetic_2EBIT1,V0n))) <=> $true ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Earithmetic_2EZERO),ap(c_2Earithmetic_2EBIT2,V0n))) <=> $true ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,V0n),c_2Earithmetic_2EZERO)) <=> $false ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m)) ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m)) ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) <=> ( ~~ p(ap(ap(c_2Eprim__rec_2E_3C,V1m),V0n)) ) ) & ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m)) ) ) ) ) ) ) ) ) ))).
fof(conj_thm_2Enumeral_2Enumeral__lte,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,c_2Earithmetic_2EZERO),V0n)) <=> $true ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT1,V0n)),c_2Earithmetic_2EZERO)) <=> $false ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT2,V0n)),c_2Earithmetic_2EZERO)) <=> $false ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m)) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m)) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) <=> ( ~~ p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V0n)) ) ) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m)) ) ) ) ) ) ) ) ) ))).
fof(ax_thm_2Enumeral_2EiDUB,axiom, ! [V0x] : ( mem(V0x,ty_2Enum_2Enum) => ( ap(c_2Enumeral_2EiDUB,V0x) = ap(ap(c_2Earithmetic_2E_2B,V0x),V0x) ) )).
fof(conj_thm_2Enumeral_2EiSUB__THM,lemma,(! [V0x] : ( mem(V0x,ty_2Enum_2Enum) => ! [V1b] : ( mem(V1b,bool) => ! [V2n] : ( mem(V2n,ty_2Enum_2Enum) => ! [V3m] : ( mem(V3m,ty_2Enum_2Enum) => ( ( ap(ap(ap(c_2Enumeral_2EiSUB,V1b),c_2Earithmetic_2EZERO),V0x) = c_2Earithmetic_2EZERO ) & ( ( ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),V2n),c_2Earithmetic_2EZERO) = V2n ) & ( ( ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),ap(c_2Earithmetic_2EBIT1,V2n)),c_2Earithmetic_2EZERO) = ap(c_2Enumeral_2EiDUB,V2n) ) & ( ( ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),ap(c_2Earithmetic_2EBIT1,V2n)),ap(c_2Earithmetic_2EBIT1,V3m)) = ap(c_2Enumeral_2EiDUB,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),V2n),V3m)) ) & ( ( ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),ap(c_2Earithmetic_2EBIT1,V2n)),ap(c_2Earithmetic_2EBIT1,V3m)) = ap(c_2Earithmetic_2EBIT1,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),V2n),V3m)) ) & ( ( ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),ap(c_2Earithmetic_2EBIT1,V2n)),ap(c_2Earithmetic_2EBIT2,V3m)) = ap(c_2Earithmetic_2EBIT1,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),V2n),V3m)) ) & ( ( ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),ap(c_2Earithmetic_2EBIT1,V2n)),ap(c_2Earithmetic_2EBIT2,V3m)) = ap(c_2Enumeral_2EiDUB,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),V2n),V3m)) ) & ( ( ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),ap(c_2Earithmetic_2EBIT2,V2n)),c_2Earithmetic_2EZERO) = ap(c_2Earithmetic_2EBIT1,V2n) ) & ( ( ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),ap(c_2Earithmetic_2EBIT2,V2n)),ap(c_2Earithmetic_2EBIT1,V3m)) = ap(c_2Earithmetic_2EBIT1,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),V2n),V3m)) ) & ( ( ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),ap(c_2Earithmetic_2EBIT2,V2n)),ap(c_2Earithmetic_2EBIT1,V3m)) = ap(c_2Enumeral_2EiDUB,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),V2n),V3m)) ) & ( ( ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),ap(c_2Earithmetic_2EBIT2,V2n)),ap(c_2Earithmetic_2EBIT2,V3m)) = ap(c_2Enumeral_2EiDUB,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),V2n),V3m)) ) & ( ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),ap(c_2Earithmetic_2EBIT2,V2n)),ap(c_2Earithmetic_2EBIT2,V3m)) = ap(c_2Earithmetic_2EBIT1,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),V2n),V3m)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
fof(conj_thm_2Enumeral_2Enumeral__sub,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ( ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Earithmetic_2E_2D,V0n),V1m)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V1m),V0n)),ap(c_2Earithmetic_2ENUMERAL,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),V0n),V1m))),c_2Enum_2E0) ) ) ))).
fof(conj_thm_2Enumeral_2EiDUB__removal,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ( ap(c_2Enumeral_2EiDUB,ap(c_2Earithmetic_2EBIT1,V0n)) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enumeral_2EiDUB,V0n)) ) & ( ( ap(c_2Enumeral_2EiDUB,ap(c_2Earithmetic_2EBIT2,V0n)) = ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,V0n)) ) & ( ap(c_2Enumeral_2EiDUB,c_2Earithmetic_2EZERO) = c_2Earithmetic_2EZERO ) ) ) ))).
fof(conj_thm_2Enumeral__bit_2EiDUB__NUMERAL,lemma,(! [V0i] : ( mem(V0i,ty_2Enum_2Enum) => ( ap(c_2Enumeral_2EiDUB,ap(c_2Earithmetic_2ENUMERAL,V0i)) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Enumeral_2EiDUB,V0i)) ) ))).
fof(conj_thm_2Enumeral__bit_2ENUMERAL__TIMES__2EXP,lemma,(( ( ! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ap(ap(c_2Ebit_2ETIMES__2EXP,V0n),c_2Enum_2E0) = c_2Enum_2E0 ) ) ) & ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ! [V2x] : ( mem(V2x,ty_2Enum_2Enum) => ( ap(ap(c_2Ebit_2ETIMES__2EXP,V1n),ap(c_2Earithmetic_2ENUMERAL,V2x)) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,c_2Enumeral_2EiDUB),V1n),V2x)) ) ) ) ))).
fof(conj_thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__iDUB,lemma,(( ( ! [V0x] : ( mem(V0x,ty_2Enum_2Enum) => ( ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,c_2Enumeral_2EiDUB),c_2Enum_2E0),V0x) = V0x ) ) ) & ( ( ! [V1y] : ( mem(V1y,ty_2Enum_2Enum) => ( ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,c_2Enumeral_2EiDUB),V1y),c_2Enum_2E0) = c_2Enum_2E0 ) ) ) & ( ( ! [V2n] : ( mem(V2n,ty_2Enum_2Enum) => ! [V3x] : ( mem(V3x,ty_2Enum_2Enum) => ( ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,c_2Enumeral_2EiDUB),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V2n))),V3x) = ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,ap(c_2Enumeral__bit_2EFDUB,c_2Enumeral_2EiDUB)),ap(c_2Earithmetic_2ENUMERAL,V2n)),ap(c_2Enumeral_2EiDUB,V3x)) ) ) ) ) & ! [V4n] : ( mem(V4n,ty_2Enum_2Enum) => ! [V5x] : ( mem(V5x,ty_2Enum_2Enum) => ( ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,c_2Enumeral_2EiDUB),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V4n))),V5x) = ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,ap(c_2Enumeral__bit_2EFDUB,c_2Enumeral_2EiDUB)),ap(c_2Earithmetic_2ENUMERAL,V4n)),ap(c_2Enumeral_2EiDUB,ap(c_2Enumeral_2EiDUB,V5x))) ) ) ) ) ) ))).
fof(conj_thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__FDUB,lemma,(! [V0f] : ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) => ( ( ! [V1x] : ( mem(V1x,ty_2Enum_2Enum) => ( ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,ap(c_2Enumeral__bit_2EFDUB,V0f)),c_2Enum_2E0),V1x) = V1x ) ) ) & ( ( ! [V2y] : ( mem(V2y,ty_2Enum_2Enum) => ( ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,ap(c_2Enumeral__bit_2EFDUB,V0f)),V2y),c_2Enum_2E0) = c_2Enum_2E0 ) ) ) & ( ( ! [V3n] : ( mem(V3n,ty_2Enum_2Enum) => ! [V4x] : ( mem(V4x,ty_2Enum_2Enum) => ( ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,ap(c_2Enumeral__bit_2EFDUB,V0f)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n))),V4x) = ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,ap(c_2Enumeral__bit_2EFDUB,ap(c_2Enumeral__bit_2EFDUB,V0f))),ap(c_2Earithmetic_2ENUMERAL,V3n)),ap(ap(c_2Enumeral__bit_2EFDUB,V0f),V4x)) ) ) ) ) & ! [V5n] : ( mem(V5n,ty_2Enum_2Enum) => ! [V6x] : ( mem(V6x,ty_2Enum_2Enum) => ( ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,ap(c_2Enumeral__bit_2EFDUB,V0f)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V5n))),V6x) = ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,ap(c_2Enumeral__bit_2EFDUB,ap(c_2Enumeral__bit_2EFDUB,V0f))),ap(c_2Earithmetic_2ENUMERAL,V5n)),ap(ap(c_2Enumeral__bit_2EFDUB,V0f),ap(ap(c_2Enumeral__bit_2EFDUB,V0f),V6x))) ) ) ) ) ) ) ))).
fof(conj_thm_2Enumeral__bit_2EFDUB__iDUB,lemma,(! [V0x] : ( mem(V0x,ty_2Enum_2Enum) => ( ap(ap(c_2Enumeral__bit_2EFDUB,c_2Enumeral_2EiDUB),V0x) = ap(c_2Enumeral_2EiDUB,ap(c_2Enumeral_2EiDUB,V0x)) ) ))).
fof(conj_thm_2Enumeral__bit_2EFDUB__FDUB,lemma,(! [V0f] : ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) => ( ( ap(ap(c_2Enumeral__bit_2EFDUB,ap(c_2Enumeral__bit_2EFDUB,V0f)),c_2Earithmetic_2EZERO) = c_2Earithmetic_2EZERO ) & ( ( ! [V1x] : ( mem(V1x,ty_2Enum_2Enum) => ( ap(ap(c_2Enumeral__bit_2EFDUB,ap(c_2Enumeral__bit_2EFDUB,V0f)),ap(c_2Enumeral__bit_2EiSUC,V1x)) = ap(ap(c_2Enumeral__bit_2EFDUB,V0f),ap(ap(c_2Enumeral__bit_2EFDUB,V0f),ap(c_2Enumeral__bit_2EiSUC,V1x))) ) ) ) & ( ( ! [V2x] : ( mem(V2x,ty_2Enum_2Enum) => ( ap(ap(c_2Enumeral__bit_2EFDUB,ap(c_2Enumeral__bit_2EFDUB,V0f)),ap(c_2Earithmetic_2EBIT1,V2x)) = ap(ap(c_2Enumeral__bit_2EFDUB,V0f),ap(ap(c_2Enumeral__bit_2EFDUB,V0f),ap(c_2Earithmetic_2EBIT1,V2x))) ) ) ) & ! [V3x] : ( mem(V3x,ty_2Enum_2Enum) => ( ap(ap(c_2Enumeral__bit_2EFDUB,ap(c_2Enumeral__bit_2EFDUB,V0f)),ap(c_2Earithmetic_2EBIT2,V3x)) = ap(ap(c_2Enumeral__bit_2EFDUB,V0f),ap(ap(c_2Enumeral__bit_2EFDUB,V0f),ap(c_2Earithmetic_2EBIT2,V3x))) ) ) ) ) ) ))).
fof(conj_thm_2Epair_2EPAIR__EQ,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1y] : ( mem(V1y,A_27b) => ! [V2a] : ( mem(V2a,A_27a) => ! [V3b] : ( mem(V3b,A_27b) => ( ( ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y) = ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2a),V3b) ) <=> ( ( V0x = V2a ) & ( V1y = V3b ) ) ) ) ) ) ))))).
fof(ax_thm_2Epred__set_2EGSPECIFICATION,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27b,ty_2Epair_2Eprod(A_27a,bool))) => ! [V1v] : ( mem(V1v,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1v),ap(c_2Epred__set_2EGSPEC(A_27a,A_27b),V0f))) <=> ? [V2x] : ( mem(V2x,A_27b) & ( ap(ap(c_2Epair_2E_2C(A_27a,bool),V1v),c_2Ebool_2ET) = ap(V0f,V2x) ) ) ) ) ) ) ) )).
fof(conj_thm_2Eprim__rec_2ENOT__LESS__0,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ~~ p(ap(ap(c_2Eprim__rec_2E_3C,V0n),c_2Enum_2E0)) ) ))).
fof(conj_thm_2Eprim__rec_2ELESS__THM,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(c_2Enum_2ESUC,V1n))) <=> ( ( V0m = V1n ) | p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__INV__1OVER,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(c_2Erealax_2Einv,V0x) = ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0x) ) ))).
fof(conj_thm_2Esat_2ENOT__NOT,lemma,(! [V0t] : ( mem(V0t,bool) => ( ( ~~ ( ~~ p(V0t) ) ) <=> p(V0t) ) ))).
fof(conj_thm_2Esat_2EAND__INV__IMP,lemma,(! [V0A] : ( mem(V0A,bool) => ( p(V0A) => ( ( ~~ p(V0A) ) => $false ) ) ))).
fof(conj_thm_2Esat_2EOR__DUAL2,lemma,(! [V0A] : ( mem(V0A,bool) => ! [V1B] : ( mem(V1B,bool) => ( ( ( ~~ ( p(V0A) | p(V1B) ) ) => $false ) <=> ( ( p(V0A) => $false ) => ( ( ~~ p(V1B) ) => $false ) ) ) ) ))).
fof(conj_thm_2Esat_2EOR__DUAL3,lemma,(! [V0A] : ( mem(V0A,bool) => ! [V1B] : ( mem(V1B,bool) => ( ( ( ~~ ( ( ~~ p(V0A) ) | p(V1B) ) ) => $false ) <=> ( p(V0A) => ( ( ~~ p(V1B) ) => $false ) ) ) ) ))).
fof(conj_thm_2Esat_2EAND__INV2,lemma,(! [V0A] : ( mem(V0A,bool) => ( ( ( ~~ p(V0A) ) => $false ) => ( ( p(V0A) => $false ) => $false ) ) ))).
fof(conj_thm_2Esat_2Edc__eq,lemma,(! [V0p] : ( mem(V0p,bool) => ! [V1q] : ( mem(V1q,bool) => ! [V2r] : ( mem(V2r,bool) => ( ( p(V0p) <=> ( p(V1q) <=> p(V2r) ) ) <=> ( ( p(V0p) | ( p(V1q) | p(V2r) ) ) & ( ( p(V0p) | ( ( ~~ p(V2r) ) | ( ~~ p(V1q) ) ) ) & ( ( p(V1q) | ( ( ~~ p(V2r) ) | ( ~~ p(V0p) ) ) ) & ( p(V2r) | ( ( ~~ p(V1q) ) | ( ~~ p(V0p) ) ) ) ) ) ) ) ) ) ))).
fof(conj_thm_2Esat_2Edc__neg,lemma,(! [V0p] : ( mem(V0p,bool) => ! [V1q] : ( mem(V1q,bool) => ( ( p(V0p) <=> ( ~~ p(V1q) ) ) <=> ( ( p(V0p) | p(V1q) ) & ( ( ~~ p(V1q) ) | ( ~~ p(V0p) ) ) ) ) ) ))).
fof(ax_thm_2Ewords_2EINT__MIN__def,axiom,( ! [A_27a] : ( ne(A_27a) => ( ap(c_2Ewords_2EINT__MIN(A_27a),c_2Ebool_2Ethe__value(A_27a)) = ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) ) ) )).
fof(ax_thm_2Ewords_2EUINT__MAX__def,axiom,( ! [A_27a] : ( ne(A_27a) => ( ap(c_2Ewords_2EUINT__MAX(A_27a),c_2Ebool_2Ethe__value(A_27a)) = ap(ap(c_2Earithmetic_2E_2D,ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ) )).
fof(ax_thm_2Ewords_2EINT__MAX__def,axiom,( ! [A_27a] : ( ne(A_27a) => ( ap(c_2Ewords_2EINT__MAX(A_27a),c_2Ebool_2Ethe__value(A_27a)) = ap(ap(c_2Earithmetic_2E_2D,ap(c_2Ewords_2EINT__MIN(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ) )).
fof(ax_thm_2Ewords_2Eword__msb__def,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0w] : ( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a)) => ( p(ap(c_2Ewords_2Eword__msb(A_27a),V0w)) <=> p(ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0w),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ) ) ) )).
fof(ax_thm_2Ewords_2Eword__bits__def,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0h] : ( mem(V0h,ty_2Enum_2Enum) => ! [V1l] : ( mem(V1l,ty_2Enum_2Enum) => ( ap(ap(c_2Ewords_2Eword__bits(A_27a),V0h),V1l) = f2179(A_27a,V1l,V0h) ) ) ) ) )).
fof(ax_thm_2Ewords_2Eword__extract__def,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0h] : ( mem(V0h,ty_2Enum_2Enum) => ! [V1l] : ( mem(V1l,ty_2Enum_2Enum) => ( ap(ap(c_2Ewords_2Eword__extract(A_27a,A_27b),V0h),V1l) = ap(ap(c_2Ecombin_2Eo(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27b),ty_2Efcp_2Ecart(bool,A_27a)),c_2Ewords_2Ew2w(A_27a,A_27b)),ap(ap(c_2Ewords_2Eword__bits(A_27a),V0h),V1l)) ) ) ) ) ) )).
fof(conj_thm_2Ewords_2Edimword__IS__TWICE__INT__MIN,lemma,( ! [A_27a]: ( ne(A_27a) => ( ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a)) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Ewords_2EINT__MIN(A_27a),c_2Ebool_2Ethe__value(A_27a))) )))).
fof(conj_thm_2Ewords_2Eword__0,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0i] : ( mem(V0i,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,V0i),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))) => ( ~~ p(ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)),V0i)) ) ) )))).
fof(conj_thm_2Ewords_2Ew2w,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0w] : ( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a)) => ! [V1i] : ( mem(V1i,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,V1i),ap(c_2Efcp_2Edimindex(A_27b),c_2Ebool_2Ethe__value(A_27b)))) => ( p(ap(ap(c_2Efcp_2Efcp__index(bool,A_27b),ap(c_2Ewords_2Ew2w(A_27a,A_27b),V0w)),V1i)) <=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V1i),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))) & p(ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0w),V1i)) ) ) ) ) ))))).
fof(conj_thm_2Ewords_2Edimindex__1,lemma,(( ap(c_2Efcp_2Edimindex(ty_2Eone_2Eone),c_2Ebool_2Ethe__value(ty_2Eone_2Eone)) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ))).
fof(conj_thm_2Ewords_2Edimindex__64,lemma,(( ap(c_2Efcp_2Edimindex(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Eone_2Eone))))))),c_2Ebool_2Ethe__value(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Eone_2Eone)))))))) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))) ))).
fof(conj_thm_2Elift__machine__ieee_2Efp64__float__sqrt__relative,conjecture,(! [V0a] : ( mem(V0a,ty_2Efcp_2Ecart(bool,ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Eone_2Eone)))))))) => ( ( p(ap(c_2Emachine__ieee_2Efp64__isFinite,V0a)) & ( ( ~~ p(ap(c_2Ewords_2Eword__msb(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Efcp_2Ebit0(ty_2Eone_2Eone))))))),V0a)) ) & p(ap(ap(c_2Ebool_2EIN(ty_2Erealax_2Ereal),ap(c_2Ereal_2Eabs,ap(c_2Etransc_2Esqrt,ap(c_2Emachine__ieee_2Efp64__to__real,V0a)))),ap(ap(c_2Elift__machine__ieee_2Einterval,ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))))))))),ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))))))))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))))))),ap(ap(c_2Ereal_2Ereal__sub,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))))))))) ) ) => ( p(ap(c_2Emachine__ieee_2Efp64__isFinite,ap(ap(c_2Emachine__ieee_2Efp64__sqrt,c_2Ebinary__ieee_2EroundTiesToEven),V0a))) & ? [V1e] : ( mem(V1e,ty_2Erealax_2Ereal) & ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Eabs,V1e)),ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))))))) & ( ap(c_2Emachine__ieee_2Efp64__to__real,ap(ap(c_2Emachine__ieee_2Efp64__sqrt,c_2Ebinary__ieee_2EroundTiesToEven),V0a)) = ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Etransc_2Esqrt,ap(c_2Emachine__ieee_2Efp64__to__real,V0a))),ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V1e)) ) ) ) ) ) ))).
