include('Axioms/HL4001+2.ax').
fof(ne_ty_2Enum_2Enum,axiom,( ne(ty_2Enum_2Enum) )).
fof(ne_ty_2Ebool_2Eitself,axiom,( ! [A0] : ( ne(A0) => ne(ty_2Ebool_2Eitself(A0)) ) )).
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(ne_ty_2Erealax_2Ereal,axiom,( ne(ty_2Erealax_2Ereal) )).
fof(ne_ty_2Efcp_2Ecart,axiom,( ! [A0] : ( ne(A0) => ( ! [A1] : ( ne(A1) => ne(ty_2Efcp_2Ecart(A0,A1)) ) ) ) )).
fof(ne_ty_2Epair_2Eprod,axiom,( ! [A0] : ( ne(A0) => ( ! [A1] : ( ne(A1) => ne(ty_2Epair_2Eprod(A0,A1)) ) ) ) )).
fof(mem_c_2Ebinary__ieee_2EULP,axiom,( ! [A_27t] : ( ne(A_27t) => ! [A_27w] : ( ne(A_27w) => mem(c_2Ebinary__ieee_2EULP(A_27t,A_27w),arr(ty_2Epair_2Eprod(ty_2Efcp_2Ecart(bool,A_27w),ty_2Ebool_2Eitself(A_27t)),ty_2Erealax_2Ereal)) ) ) )).
fof(ne_ty_2Eone_2Eone,axiom,( ne(ty_2Eone_2Eone) )).
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__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_2Ebinary__ieee_2Eexponent__boundary,axiom,( ! [A_27t] : ( ne(A_27t) => ! [A_27w] : ( ne(A_27w) => mem(c_2Ebinary__ieee_2Eexponent__boundary(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),bool))) ) ) )).
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(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_2Ebinary__ieee_2Efloat__is__zero,axiom,( ! [A_27t] : ( ne(A_27t) => ! [A_27w] : ( ne(A_27w) => mem(c_2Ebinary__ieee_2Efloat__is__zero(A_27t,A_27w),arr(ty_2Ebinary__ieee_2Efloat(A_27t,A_27w),bool)) ) ) )).
fof(mem_c_2Emin_2E_40,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Emin_2E_40(A_27a),arr(arr(A_27a,bool),A_27a)) ) )).
fof(mem_c_2Ecombin_2EI,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Ecombin_2EI(A_27a),arr(A_27a,A_27a)) ) )).
fof(mem_c_2Emarker_2EAbbrev,axiom,( mem(c_2Emarker_2EAbbrev,arr(bool,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_2Enumeral_2EiiSUC,axiom,( mem(c_2Enumeral_2EiiSUC,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_2Earithmetic_2EEVEN,axiom,( mem(c_2Earithmetic_2EEVEN,arr(ty_2Enum_2Enum,bool)) )).
fof(mem_c_2Enumeral_2Eonecount,axiom,( mem(c_2Enumeral_2Eonecount,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) )).
fof(mem_c_2Enumeral_2Eexactlog,axiom,( mem(c_2Enumeral_2Eexactlog,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Eprim__rec_2EPRE,axiom,( mem(c_2Eprim__rec_2EPRE,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Earithmetic_2EDIV2,axiom,( mem(c_2Earithmetic_2EDIV2,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Enumeral_2Etexp__help,axiom,( mem(c_2Enumeral_2Etexp__help,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) )).
fof(mem_c_2Ebool_2ELET,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Ebool_2ELET(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) ) ) )).
fof(mem_c_2Enumeral_2EiDUB,axiom,( mem(c_2Enumeral_2EiDUB,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_2Einternal__mult,axiom,( mem(c_2Enumeral_2Einternal__mult,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) )).
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_2Epair_2Epair__CASE,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [A_27c] : ( ne(A_27c) => mem(c_2Epair_2Epair__CASE(A_27a,A_27b,A_27c),arr(ty_2Epair_2Eprod(A_27b,A_27c),arr(arr(A_27b,arr(A_27c,A_27a)),A_27a))) ) ) ) )).
fof(mem_c_2Enum_2ESUC,axiom,( mem(c_2Enum_2ESUC,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_2Ereal_2Eabs,axiom,( mem(c_2Ereal_2Eabs,arr(ty_2Erealax_2Ereal,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_2Earithmetic_2E_2A,axiom,( mem(c_2Earithmetic_2E_2A,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) )).
fof(mem_c_2Earithmetic_2EODD,axiom,( mem(c_2Earithmetic_2EODD,arr(ty_2Enum_2Enum,bool)) )).
fof(mem_c_2Ereal_2Epow,axiom,( mem(c_2Ereal_2Epow,arr(ty_2Erealax_2Ereal,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))) )).
fof(mem_c_2Emarker_2Eunint,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Emarker_2Eunint(A_27a),arr(A_27a,A_27a)) ) )).
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_2Ereal_2E_2F,axiom,( mem(c_2Ereal_2E_2F,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))) )).
fof(mem_c_2Ebool_2ET,axiom,( mem(c_2Ebool_2ET,bool) )).
fof(ax_true_p,axiom,( p(c_2Ebool_2ET) )).
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_2Ereal_2Ereal__lte,axiom,( mem(c_2Ereal_2Ereal__lte,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,bool))) )).
fof(mem_c_2Erealax_2Ereal__neg,axiom,( mem(c_2Erealax_2Ereal__neg,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) )).
fof(mem_c_2Ereal_2Ereal__of__num,axiom,( mem(c_2Ereal_2Ereal__of__num,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) )).
fof(mem_c_2Erealax_2Ereal__lt,axiom,( mem(c_2Erealax_2Ereal__lt,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,bool))) )).
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(mem_c_2Erelation_2EEMPTY__REL,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Erelation_2EEMPTY__REL(A_27a),arr(A_27a,arr(A_27a,bool))) ) )).
fof(mem_c_2Erelation_2ERESTRICT,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Erelation_2ERESTRICT(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,bool)),arr(A_27a,arr(A_27a,A_27b))))) ) ) )).
fof(mem_c_2Erelation_2EWF,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Erelation_2EWF(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)) ) )).
fof(mem_c_2Erelation_2EWFREC,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Erelation_2EWFREC(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(arr(A_27a,A_27b),arr(A_27a,A_27b)),arr(A_27a,A_27b)))) ) ) )).
fof(mem_c_2Ebool_2EF,axiom,( mem(c_2Ebool_2EF,bool) )).
fof(ax_false_p,axiom,( ~ p(c_2Ebool_2EF) )).
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_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_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_2Earithmetic_2EMOD,axiom,( mem(c_2Earithmetic_2EMOD,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) )).
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_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_2Ewords_2Eword__T,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Ewords_2Eword__T(A_27a),ty_2Efcp_2Ecart(bool,A_27a)) ) )).
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_2EBIT1,axiom,( mem(c_2Earithmetic_2EBIT1,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Ewords_2Eword__2comp,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Ewords_2Eword__2comp(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Efcp_2Ecart(bool,A_27a))) ) )).
fof(mem_c_2Ewords_2Ew2n,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Ewords_2Ew2n(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),ty_2Enum_2Enum)) ) )).
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_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_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_2Ewords_2Eword__lo,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Ewords_2Eword__lo(A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),arr(ty_2Efcp_2Ecart(bool,A_27a),bool))) ) )).
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_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_2Earithmetic_2EZERO,axiom,( mem(c_2Earithmetic_2EZERO,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_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_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(ax_thm_2Earithmetic_2EEXP,axiom, ( ( ! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2EEXP,V0m),c_2Enum_2E0) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) ) ) & ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ! [V2n] : ( mem(V2n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2EEXP,V1m),ap(c_2Enum_2ESUC,V2n)) = ap(ap(c_2Earithmetic_2E_2A,V1m),ap(ap(c_2Earithmetic_2EEXP,V1m),V2n)) ) ) ) )).
fof(conj_thm_2Earithmetic_2ETWO,lemma,(( ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)) = ap(c_2Enum_2ESUC,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ))).
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__CLAUSES,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ( ap(ap(c_2Earithmetic_2E_2B,c_2Enum_2E0),V0m) = V0m ) & ( ( ap(ap(c_2Earithmetic_2E_2B,V0m),c_2Enum_2E0) = V0m ) & ( ( ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enum_2ESUC,V0m)),V1n) = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)) ) & ( ap(ap(c_2Earithmetic_2E_2B,V0m),ap(c_2Enum_2ESUC,V1n)) = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)) ) ) ) ) ) ))).
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_2EADD__COMM,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_2EADD__ASSOC,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ! [V2p] : ( mem(V2p,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2B,V0m),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p)) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)),V2p) ) ) ) ))).
fof(conj_thm_2Earithmetic_2Enum__CASES,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ( ( V0m = c_2Enum_2E0 ) | ? [V1n] : ( mem(V1n,ty_2Enum_2Enum) & ( V0m = ap(c_2Enum_2ESUC,V1n) ) ) ) ))).
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_2ENOT__LESS__EQUAL,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_2Eprim__rec_2E_3C,V1n),V0m)) ) ) ))).
fof(conj_thm_2Earithmetic_2ELESS__EQ__0,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),c_2Enum_2E0)) <=> ( V0n = c_2Enum_2E0 ) ) ))).
fof(conj_thm_2Earithmetic_2EADD1,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ( ap(c_2Enum_2ESUC,V0m) = ap(ap(c_2Earithmetic_2E_2B,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ))).
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__RIGHT__1,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2A,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = 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_2EMULT__COMM,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2A,V0m),V1n) = ap(ap(c_2Earithmetic_2E_2A,V1n),V0m) ) ) ))).
fof(conj_thm_2Earithmetic_2ERIGHT__ADD__DISTRIB,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ! [V2p] : ( mem(V2p,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)),V2p) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V0m),V2p)),ap(ap(c_2Earithmetic_2E_2A,V1n),V2p)) ) ) ) ))).
fof(conj_thm_2Earithmetic_2ELEFT__ADD__DISTRIB,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ! [V2p] : ( mem(V2p,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2A,V2p),ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V2p),V0m)),ap(ap(c_2Earithmetic_2E_2A,V2p),V1n)) ) ) ) ))).
fof(conj_thm_2Earithmetic_2EMULT__ASSOC,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ! [V2p] : ( mem(V2p,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2A,V0m),ap(ap(c_2Earithmetic_2E_2A,V1n),V2p)) = ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),V2p) ) ) ) ))).
fof(conj_thm_2Earithmetic_2EADD__EQ__0,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ( ap(ap(c_2Earithmetic_2E_2B,V0m),V1n) = c_2Enum_2E0 ) <=> ( ( V0m = c_2Enum_2E0 ) & ( V1n = c_2Enum_2E0 ) ) ) ) ))).
fof(conj_thm_2Earithmetic_2EADD__INV__0__EQ,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ( ap(ap(c_2Earithmetic_2E_2B,V0m),V1n) = V0m ) <=> ( V1n = c_2Enum_2E0 ) ) ) ))).
fof(conj_thm_2Earithmetic_2EPRE__SUC__EQ,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) => ( ( V0m = ap(c_2Eprim__rec_2EPRE,V1n) ) <=> ( ap(c_2Enum_2ESUC,V0m) = V1n ) ) ) ) ))).
fof(conj_thm_2Earithmetic_2EEQ__MONO__ADD__EQ,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ! [V2p] : ( mem(V2p,ty_2Enum_2Enum) => ( ( ap(ap(c_2Earithmetic_2E_2B,V0m),V2p) = ap(ap(c_2Earithmetic_2E_2B,V1n),V2p) ) <=> ( 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_2ELESS__EQ__REFL,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V0m)) ))).
fof(conj_thm_2Earithmetic_2ELESS__ADD__1,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m)) => ? [V2p] : ( mem(V2p,ty_2Enum_2Enum) & ( V0m = ap(ap(c_2Earithmetic_2E_2B,V1n),ap(ap(c_2Earithmetic_2E_2B,V2p),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) ) ) ) ) ))).
fof(conj_thm_2Earithmetic_2EEQ__MULT__RCANCEL,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ! [V2p] : ( mem(V2p,ty_2Enum_2Enum) => ( ( ap(ap(c_2Earithmetic_2E_2A,V1n),V0m) = ap(ap(c_2Earithmetic_2E_2A,V2p),V0m) ) <=> ( ( V0m = c_2Enum_2E0 ) | ( V1n = V2p ) ) ) ) ) ))).
fof(conj_thm_2Earithmetic_2ELESS__LESS__CASES,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ( V0m = V1n ) | ( p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) | p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m)) ) ) ) ))).
fof(conj_thm_2Earithmetic_2ELESS__EQUAL__ADD,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) => ? [V2p] : ( mem(V2p,ty_2Enum_2Enum) & ( V1n = ap(ap(c_2Earithmetic_2E_2B,V0m),V2p) ) ) ) ) ))).
fof(conj_thm_2Earithmetic_2EEQ__LESS__EQ,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ( V0m = V1n ) <=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m)) ) ) ) ))).
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_2ENOT__NUM__EQ,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ( ~~ ( V0m = V1n ) ) <=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,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_2EMULT__LESS__EQ__SUC,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,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V2p)),V0m)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V2p)),V1n))) ) ) ) ))).
fof(conj_thm_2Earithmetic_2ELE__MULT__CANCEL__LBARE,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(ap(c_2Earithmetic_2E_2A,V0m),V1n))) <=> ( ( V0m = c_2Enum_2E0 ) | p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) ) ) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(ap(c_2Earithmetic_2E_2A,V1n),V0m))) <=> ( ( V0m = c_2Enum_2E0 ) | p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) ) ) ) ) ))).
fof(conj_thm_2Earithmetic_2ESUB__LEFT__LESS,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ! [V2p] : ( mem(V2p,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(ap(c_2Earithmetic_2E_2D,V1n),V2p))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),V1n)) ) ) ) ))).
fof(conj_thm_2Earithmetic_2ESUB__RIGHT__LESS,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ! [V2p] : ( mem(V2p,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V2p)) <=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p))) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2p)) ) ) ) ) ))).
fof(conj_thm_2Earithmetic_2ELE,lemma,(( ( ! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),c_2Enum_2E0)) <=> ( V0n = c_2Enum_2E0 ) ) ) ) & ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ! [V2n] : ( mem(V2n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),ap(c_2Enum_2ESUC,V2n))) <=> ( ( V1m = ap(c_2Enum_2ESUC,V2n) ) | p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V2n)) ) ) ) ) ))).
fof(conj_thm_2Earithmetic_2ELESS__MOD,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1k] : ( mem(V1k,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,V1k),V0n)) => ( ap(ap(c_2Earithmetic_2EMOD,V1k),V0n) = V1k ) ) ) ))).
fof(conj_thm_2Earithmetic_2EZERO__MOD,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) => ( ap(ap(c_2Earithmetic_2EMOD,c_2Enum_2E0),V0n) = c_2Enum_2E0 ) ) ))).
fof(conj_thm_2Earithmetic_2ESUB__ELIM__THM,lemma,(! [V0P] : ( mem(V0P,arr(ty_2Enum_2Enum,bool)) => ! [V1a] : ( mem(V1a,ty_2Enum_2Enum) => ! [V2b] : ( mem(V2b,ty_2Enum_2Enum) => ( p(ap(V0P,ap(ap(c_2Earithmetic_2E_2D,V1a),V2b))) <=> ! [V3d] : ( mem(V3d,ty_2Enum_2Enum) => ( ( ( V2b = ap(ap(c_2Earithmetic_2E_2B,V1a),V3d) ) => p(ap(V0P,c_2Enum_2E0)) ) & ( ( V1a = ap(ap(c_2Earithmetic_2E_2B,V2b),V3d) ) => p(ap(V0P,V3d)) ) ) ) ) ) ) ))).
fof(conj_thm_2Earithmetic_2EEXP__EQ__0,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ( ( ap(ap(c_2Earithmetic_2EEXP,V0n),V1m) = c_2Enum_2E0 ) <=> ( ( V0n = c_2Enum_2E0 ) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1m)) ) ) ) ))).
fof(conj_thm_2Earithmetic_2EEXP__1,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ( ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0n) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) & ( ap(ap(c_2Earithmetic_2EEXP,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = V0n ) ) ))).
fof(conj_thm_2Ebinary__ieee_2Efloat__component__equality,lemma,( ! [A_27t]: ( ne(A_27t) =>  ! [A_27w]: ( ne(A_27w) => ! [V0f1] : ( mem(V0f1,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ! [V1f2] : ( mem(V1f2,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ( V0f1 = V1f2 ) <=> ( ( ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),V0f1) = ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),V1f2) ) & ( ( ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V0f1) = ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V1f2) ) & ( ap(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27w),V0f1) = ap(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27w),V1f2) ) ) ) ) ) ))))).
fof(ax_thm_2Ebinary__ieee_2Efloat__to__real__def,axiom,( ! [A_27t] : ( ne(A_27t) => ! [A_27w] : ( ne(A_27w) => ! [V0x] : ( mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(ap(c_2Emin_2E_3D(ty_2Efcp_2Ecart(bool,A_27w)),ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V0x)),ap(c_2Ewords_2En2w(A_27w),c_2Enum_2E0))),ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Epow,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(c_2Ewords_2Ew2n(ty_2Eone_2Eone),ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),V0x)))),ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,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_2Ewords_2EINT__MAX(A_27w),c_2Ebool_2Ethe__value(A_27w)))))),ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Ewords_2Ew2n(A_27t),ap(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27w),V0x)))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Efcp_2Edimindex(A_27t),c_2Ebool_2Ethe__value(A_27t)))))),ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Epow,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(c_2Ewords_2Ew2n(ty_2Eone_2Eone),ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),V0x)))),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_2Ewords_2Ew2n(A_27w),ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V0x)))),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_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,ap(c_2Ewords_2Ew2n(A_27t),ap(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27w),V0x)))),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(c_2Efcp_2Edimindex(A_27t),c_2Ebool_2Ethe__value(A_27t))))))) ) ) ) ) )).
fof(ax_thm_2Ebinary__ieee_2EULP__primitive__def,axiom,( ! [A_27t] : ( ne(A_27t) => ! [A_27w] : ( ne(A_27w) => ( c_2Ebinary__ieee_2EULP(A_27t,A_27w) = ap(ap(c_2Erelation_2EWFREC(ty_2Epair_2Eprod(ty_2Efcp_2Ecart(bool,A_27w),ty_2Ebool_2Eitself(A_27t)),ty_2Erealax_2Ereal),ap(c_2Emin_2E_40(arr(ty_2Epair_2Eprod(ty_2Efcp_2Ecart(bool,A_27w),ty_2Ebool_2Eitself(A_27t)),arr(ty_2Epair_2Eprod(ty_2Efcp_2Ecart(bool,A_27w),ty_2Ebool_2Eitself(A_27t)),bool))),f3040(A_27t,A_27w))),k(arr(ty_2Epair_2Eprod(ty_2Efcp_2Ecart(bool,A_27w),ty_2Ebool_2Eitself(A_27t)),ty_2Erealax_2Ereal),f3042(A_27w,A_27t))) ) ) ) )).
fof(ax_thm_2Ebinary__ieee_2Eexponent__boundary__def,axiom,( ! [A_27t] : ( ne(A_27t) => ! [A_27w] : ( ne(A_27w) => ! [V0y] : ( mem(V0y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ! [V1x] : ( mem(V1x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( p(ap(ap(c_2Ebinary__ieee_2Eexponent__boundary(A_27t,A_27w),V0y),V1x)) <=> ( ( ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),V1x) = ap(c_2Ebinary__ieee_2Efloat__Sign(A_27t,A_27w),V0y) ) & ( ( ap(c_2Ewords_2Ew2n(A_27w),ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V1x)) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Ewords_2Ew2n(A_27w),ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V0y))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) & ( ( ~~ ( ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27t,A_27w),V1x) = ap(c_2Ewords_2En2w(A_27w),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ) & ( ( ap(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27w),V0y) = ap(c_2Ewords_2Eword__2comp(A_27t),ap(c_2Ewords_2En2w(A_27t),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) ) & ( ap(c_2Ebinary__ieee_2Efloat__Significand(A_27t,A_27w),V1x) = ap(c_2Ewords_2En2w(A_27t),c_2Enum_2E0) ) ) ) ) ) ) ) ) ) ) )).
fof(conj_thm_2Ebinary__ieee_2Ezero__lt__twopow,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),V0n))) ))).
fof(conj_thm_2Ebinary__ieee_2Ezero__le__twopow,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),V0n))) ))).
fof(conj_thm_2Ebinary__ieee_2Ezero__neq__twopow,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ~~ ( ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),V0n) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ))).
fof(conj_thm_2Ebinary__ieee_2Ezero__le__pos__div__twopow,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,V0m)),ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),V1n)))) ) ))).
fof(conj_thm_2Ebinary__ieee_2Ediv__eq0,lemma,(! [V0a] : ( mem(V0a,ty_2Erealax_2Ereal) => ! [V1b] : ( mem(V1b,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1b)) => ( ( ap(ap(c_2Ereal_2E_2F,V0a),V1b) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) <=> ( V0a = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ) ) ))).
fof(conj_thm_2Ebinary__ieee_2Eexp__ge2,lemma,(! [V0b] : ( mem(V0b,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0b))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0b)) ) ))).
fof(conj_thm_2Ebinary__ieee_2Ele2,lemma,(! [V0n] : ( mem(V0n,ty_2Erealax_2Ereal) => ! [V1m] : ( mem(V1m,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),V0n)) & p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),V1m)) ) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Erealax_2Ereal__mul,V0n),V1m))) ) ) ))).
fof(conj_thm_2Ebinary__ieee_2Esign__not__zero,lemma,(! [V0s] : ( mem(V0s,ty_2Efcp_2Ecart(bool,ty_2Eone_2Eone)) => ( ~~ ( ap(ap(c_2Ereal_2Epow,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(c_2Ewords_2Ew2n(ty_2Eone_2Eone),V0s)) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ))).
fof(conj_thm_2Ebinary__ieee_2Efloat__is__zero,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0x] : ( mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)) => ( p(ap(c_2Ebinary__ieee_2Efloat__is__zero(A_27a,A_27b),V0x)) <=> ( ( ap(c_2Ebinary__ieee_2Efloat__Exponent(A_27a,A_27b),V0x) = ap(c_2Ewords_2En2w(A_27b),c_2Enum_2E0) ) & ( ap(c_2Ebinary__ieee_2Efloat__Significand(A_27a,A_27b),V0x) = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0) ) ) ) ))))).
fof(conj_thm_2Ebinary__ieee_2Efloat__is__zero__to__real,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0x] : ( mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27a,A_27b)) => ( p(ap(c_2Ebinary__ieee_2Efloat__is__zero(A_27a,A_27b),V0x)) <=> ( ap(c_2Ebinary__ieee_2Efloat__to__real(A_27a,A_27b),V0x) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ))))).
fof(conj_thm_2Ebit_2EZERO__LT__TWOEXP,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))) ))).
fof(ax_thm_2Ebool_2ELET__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ( c_2Ebool_2ELET(A_27a,A_27b) = f14(A_27b,A_27a) ) ) ) )).
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(ax_thm_2Ebool_2ESELECT__AX,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1x] : ( mem(V1x,A_27a) => ( p(ap(V0P,V1x)) => p(ap(V0P,ap(c_2Emin_2E_40(A_27a),V0P))) ) ) ) ) )).
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_2EEXCLUDED__MIDDLE,lemma,(! [V0t] : ( mem(V0t,bool) => ( p(V0t) | ( ~~ 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_2ECONJ__ASSOC,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_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_2EOR__CLAUSES,lemma,(! [V0t] : ( mem(V0t,bool) => ( ( ( $true | p(V0t) ) <=> $true ) & ( ( ( p(V0t) | $true ) <=> $true ) & ( ( ( $false | p(V0t) ) <=> p(V0t) ) & ( ( ( p(V0t) | $false ) <=> p(V0t) ) & ( ( 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_2EEQ__REFL,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ( V0x = V0x ) )))).
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_2EDISJ__ASSOC,lemma,(! [V0A] : ( mem(V0A,bool) => ! [V1B] : ( mem(V1B,bool) => ! [V2C] : ( mem(V2C,bool) => ( ( p(V0A) | ( p(V1B) | p(V2C) ) ) <=> ( ( p(V0A) | p(V1B) ) | p(V2C) ) ) ) ) ))).
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_2ELEFT__OR__OVER__AND,lemma,(! [V0A] : ( mem(V0A,bool) => ! [V1B] : ( mem(V1B,bool) => ! [V2C] : ( mem(V2C,bool) => ( ( p(V0A) | ( p(V1B) & p(V2C) ) ) <=> ( ( p(V0A) | p(V1B) ) & ( p(V0A) | p(V2C) ) ) ) ) ) ))).
fof(conj_thm_2Ebool_2ERIGHT__OR__OVER__AND,lemma,(! [V0A] : ( mem(V0A,bool) => ! [V1B] : ( mem(V1B,bool) => ! [V2C] : ( mem(V2C,bool) => ( ( ( p(V1B) & p(V2C) ) | p(V0A) ) <=> ( ( p(V1B) | p(V0A) ) & ( p(V2C) | p(V0A) ) ) ) ) ) ))).
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_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_2EEQ__EXPAND,lemma,(! [V0t1] : ( mem(V0t1,bool) => ! [V1t2] : ( mem(V1t2,bool) => ( ( p(V0t1) <=> p(V1t2) ) <=> ( ( p(V0t1) & p(V1t2) ) | ( ( ~~ p(V0t1) ) & ( ~~ p(V1t2) ) ) ) ) ) ))).
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_2ECOND__CONG,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,bool) => ! [V1Q] : ( mem(V1Q,bool) => ! [V2x] : ( mem(V2x,A_27a) => ! [V3x_27] : ( mem(V3x_27,A_27a) => ! [V4y] : ( mem(V4y,A_27a) => ! [V5y_27] : ( mem(V5y_27,A_27a) => ( ( ( p(V0P) <=> p(V1Q) ) & ( ( p(V1Q) => ( V2x = V3x_27 ) ) & ( ( ~~ p(V1Q) ) => ( V4y = V5y_27 ) ) ) ) => ( ap(ap(ap(c_2Ebool_2ECOND(A_27a),V0P),V2x),V4y) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),V1Q),V3x_27),V5y_27) ) ) ) ) ) ) ) )))).
fof(conj_thm_2Ebool_2Ebool__case__thm,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 ) ) ) ) & ! [V2t1] : ( mem(V2t1,A_27a) => ! [V3t2] : ( mem(V3t2,A_27a) => ( ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2EF),V2t1),V3t2) = V3t2 ) ) ) )))).
fof(conj_thm_2Ecombin_2EI__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ( ap(c_2Ecombin_2EI(A_27a),V0x) = V0x ) )))).
fof(conj_thm_2Efcp_2EDIMINDEX__GE__1,lemma,( ! [A_27a]: ( ne(A_27a) => p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))))).
fof(ax_thm_2Emarker_2EAbbrev__def,axiom, ! [V0x] : ( mem(V0x,bool) => ( p(ap(c_2Emarker_2EAbbrev,V0x)) <=> p(V0x) ) )).
fof(conj_thm_2Enum_2ENOT__SUC,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ~~ ( ap(c_2Enum_2ESUC,V0n) = c_2Enum_2E0 ) ) ))).
fof(conj_thm_2Enum_2EINDUCTION,lemma,(! [V0P] : ( mem(V0P,arr(ty_2Enum_2Enum,bool)) => ( ( p(ap(V0P,c_2Enum_2E0)) & ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( p(ap(V0P,V1n)) => p(ap(V0P,ap(c_2Enum_2ESUC,V1n))) ) ) ) => ! [V2n] : ( mem(V2n,ty_2Enum_2Enum) => p(ap(V0P,V2n)) ) ) ))).
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__eq,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ( ( ( c_2Earithmetic_2EZERO = ap(c_2Earithmetic_2EBIT1,V0n) ) <=> $false ) & ( ( ( ap(c_2Earithmetic_2EBIT1,V0n) = c_2Earithmetic_2EZERO ) <=> $false ) & ( ( ( c_2Earithmetic_2EZERO = ap(c_2Earithmetic_2EBIT2,V0n) ) <=> $false ) & ( ( ( ap(c_2Earithmetic_2EBIT2,V0n) = c_2Earithmetic_2EZERO ) <=> $false ) & ( ( ( ap(c_2Earithmetic_2EBIT1,V0n) = ap(c_2Earithmetic_2EBIT2,V1m) ) <=> $false ) & ( ( ( ap(c_2Earithmetic_2EBIT2,V0n) = ap(c_2Earithmetic_2EBIT1,V1m) ) <=> $false ) & ( ( ( ap(c_2Earithmetic_2EBIT1,V0n) = ap(c_2Earithmetic_2EBIT1,V1m) ) <=> ( V0n = V1m ) ) & ( ( ap(c_2Earithmetic_2EBIT2,V0n) = ap(c_2Earithmetic_2EBIT2,V1m) ) <=> ( 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(conj_thm_2Enumeral_2Enumeral__pre,lemma,(( ( ap(c_2Eprim__rec_2EPRE,c_2Earithmetic_2EZERO) = c_2Earithmetic_2EZERO ) & ( ( ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = c_2Earithmetic_2EZERO ) & ( ( ! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,V0n))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT1,V0n))) ) ) ) & ( ( ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,V1n))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,V1n)) ) ) ) & ! [V2n] : ( mem(V2n,ty_2Enum_2Enum) => ( ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT2,V2n)) = ap(c_2Earithmetic_2EBIT1,V2n) ) ) ) ) ) ))).
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_2Enumeral__mult,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ( ( ap(ap(c_2Earithmetic_2E_2A,c_2Earithmetic_2EZERO),V0n) = c_2Earithmetic_2EZERO ) & ( ( ap(ap(c_2Earithmetic_2E_2A,V0n),c_2Earithmetic_2EZERO) = c_2Earithmetic_2EZERO ) & ( ( ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2EBIT1,V0n)),V1m) = ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enumeral_2EiDUB,ap(ap(c_2Earithmetic_2E_2A,V0n),V1m))),V1m)) ) & ( ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2EBIT2,V0n)),V1m) = ap(c_2Enumeral_2EiDUB,ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V0n),V1m)),V1m))) ) ) ) ) ) ))).
fof(conj_thm_2Enumeral_2Enumeral__evenodd,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( p(ap(c_2Earithmetic_2EEVEN,c_2Earithmetic_2EZERO)) & ( p(ap(c_2Earithmetic_2EEVEN,ap(c_2Earithmetic_2EBIT2,V0n))) & ( ( ~~ p(ap(c_2Earithmetic_2EEVEN,ap(c_2Earithmetic_2EBIT1,V0n))) ) & ( ( ~~ p(ap(c_2Earithmetic_2EODD,c_2Earithmetic_2EZERO)) ) & ( ( ~~ p(ap(c_2Earithmetic_2EODD,ap(c_2Earithmetic_2EBIT2,V0n))) ) & p(ap(c_2Earithmetic_2EODD,ap(c_2Earithmetic_2EBIT1,V0n))) ) ) ) ) ) ))).
fof(ax_thm_2Enumeral_2Eonecount__def,axiom, ( ( ! [V0x] : ( mem(V0x,ty_2Enum_2Enum) => ( ap(ap(c_2Enumeral_2Eonecount,c_2Earithmetic_2EZERO),V0x) = V0x ) ) ) & ( ( ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ! [V2x] : ( mem(V2x,ty_2Enum_2Enum) => ( ap(ap(c_2Enumeral_2Eonecount,ap(c_2Earithmetic_2EBIT1,V1n)),V2x) = ap(ap(c_2Enumeral_2Eonecount,V1n),ap(c_2Enum_2ESUC,V2x)) ) ) ) ) & ! [V3n] : ( mem(V3n,ty_2Enum_2Enum) => ! [V4x] : ( mem(V4x,ty_2Enum_2Enum) => ( ap(ap(c_2Enumeral_2Eonecount,ap(c_2Earithmetic_2EBIT2,V3n)),V4x) = c_2Earithmetic_2EZERO ) ) ) ) )).
fof(ax_thm_2Enumeral_2Eexactlog__def,axiom, ( ( ap(c_2Enumeral_2Eexactlog,c_2Earithmetic_2EZERO) = c_2Earithmetic_2EZERO ) & ( ( ! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ap(c_2Enumeral_2Eexactlog,ap(c_2Earithmetic_2EBIT1,V0n)) = c_2Earithmetic_2EZERO ) ) ) & ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ap(c_2Enumeral_2Eexactlog,ap(c_2Earithmetic_2EBIT2,V1n)) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Enum_2Enum),f202),ap(ap(c_2Enumeral_2Eonecount,V1n),c_2Earithmetic_2EZERO)) ) ) ) )).
fof(conj_thm_2Enumeral_2Eenumeral__mult,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1x] : ( mem(V1x,ty_2Enum_2Enum) => ! [V2y] : ( mem(V2y,ty_2Enum_2Enum) => ( ( ap(ap(c_2Earithmetic_2E_2A,c_2Earithmetic_2EZERO),V0n) = c_2Earithmetic_2EZERO ) & ( ( ap(ap(c_2Earithmetic_2E_2A,V0n),c_2Earithmetic_2EZERO) = c_2Earithmetic_2EZERO ) & ( ( ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2EBIT1,V1x)),ap(c_2Earithmetic_2EBIT1,V2y)) = ap(ap(c_2Enumeral_2Einternal__mult,ap(c_2Earithmetic_2EBIT1,V1x)),ap(c_2Earithmetic_2EBIT1,V2y)) ) & ( ( ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2EBIT1,V1x)),ap(c_2Earithmetic_2EBIT2,V2y)) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Enum_2Enum),f203(V1x,V2y)),ap(c_2Enumeral_2Eexactlog,ap(c_2Earithmetic_2EBIT2,V2y))) ) & ( ( ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2EBIT2,V1x)),ap(c_2Earithmetic_2EBIT1,V2y)) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Enum_2Enum),f204(V1x,V2y)),ap(c_2Enumeral_2Eexactlog,ap(c_2Earithmetic_2EBIT2,V1x))) ) & ( ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2EBIT2,V1x)),ap(c_2Earithmetic_2EBIT2,V2y)) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Enum_2Enum),f206(V1x,V2y)),ap(c_2Enumeral_2Eexactlog,ap(c_2Earithmetic_2EBIT2,V1x))) ) ) ) ) ) ) ) ) ))).
fof(conj_thm_2Enumeral_2Einternal__mult__characterisation,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ( ( ap(ap(c_2Enumeral_2Einternal__mult,c_2Earithmetic_2EZERO),V0n) = c_2Earithmetic_2EZERO ) & ( ( ap(ap(c_2Enumeral_2Einternal__mult,V0n),c_2Earithmetic_2EZERO) = c_2Earithmetic_2EZERO ) & ( ( ap(ap(c_2Enumeral_2Einternal__mult,ap(c_2Earithmetic_2EBIT1,V0n)),V1m) = ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enumeral_2EiDUB,ap(ap(c_2Enumeral_2Einternal__mult,V0n),V1m))),V1m)) ) & ( ap(ap(c_2Enumeral_2Einternal__mult,ap(c_2Earithmetic_2EBIT2,V0n)),V1m) = ap(c_2Enumeral_2EiDUB,ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Enumeral_2Einternal__mult,V0n),V1m)),V1m))) ) ) ) ) ) ))).
fof(conj_thm_2Epair_2Epair__case__thm,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) =>  ! [A_27c]: ( ne(A_27c) => ! [V0x] : ( mem(V0x,A_27b) => ! [V1y] : ( mem(V1y,A_27c) => ! [V2f] : ( mem(V2f,arr(A_27b,arr(A_27c,A_27a))) => ( ap(ap(c_2Epair_2Epair__CASE(A_27a,A_27b,A_27c),ap(ap(c_2Epair_2E_2C(A_27b,A_27c),V0x),V1y)),V2f) = ap(ap(V2f,V0x),V1y) ) ) ) )))))).
fof(conj_thm_2Ereal_2EREAL__ADD__SYM,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__add,V0x),V1y) = ap(ap(c_2Erealax_2Ereal__add,V1y),V0x) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__ADD__ASSOC,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__add,V0x),ap(ap(c_2Erealax_2Ereal__add,V1y),V2z)) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)),V2z) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__ADD__LID,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x) = V0x ) ))).
fof(conj_thm_2Ereal_2EREAL__ADD__LINV,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__add,ap(c_2Erealax_2Ereal__neg,V0x)),V0x) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ))).
fof(conj_thm_2Ereal_2EREAL__LDISTRIB,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,V0x),ap(ap(c_2Erealax_2Ereal__add,V1y),V2z)) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)),ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__TRANS,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) & p(ap(ap(c_2Erealax_2Ereal__lt,V1y),V2z)) ) => p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V2z)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__MUL__SYM,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y) = ap(ap(c_2Erealax_2Ereal__mul,V1y),V0x) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__MUL__COMM,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y) = ap(ap(c_2Erealax_2Ereal__mul,V1y),V0x) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__MUL__ASSOC,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,V0x),ap(ap(c_2Erealax_2Ereal__mul,V1y),V2z)) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)),V2z) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__MUL__LID,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0x) = V0x ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__MUL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) & p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y)) ) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y))) ) ) ))).
fof(ax_thm_2Ereal_2Ereal__sub,axiom, ! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y) = ap(ap(c_2Erealax_2Ereal__add,V0x),ap(c_2Erealax_2Ereal__neg,V1y)) ) ) )).
fof(conj_thm_2Ereal_2EREAL__ADD__RID,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__add,V0x),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)) = V0x ) ))).
fof(conj_thm_2Ereal_2EREAL__ADD__RINV,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__add,V0x),ap(c_2Erealax_2Ereal__neg,V0x)) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ))).
fof(conj_thm_2Ereal_2EREAL__MUL__RID,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,V0x),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = V0x ) ))).
fof(conj_thm_2Ereal_2EREAL__RDISTRIB,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)),V2z) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z)),ap(ap(c_2Erealax_2Ereal__mul,V1y),V2z)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__EQ__LADD,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( ap(ap(c_2Erealax_2Ereal__add,V0x),V1y) = ap(ap(c_2Erealax_2Ereal__add,V0x),V2z) ) <=> ( V1y = V2z ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__NEG__ADD,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)) = ap(ap(c_2Erealax_2Ereal__add,ap(c_2Erealax_2Ereal__neg,V0x)),ap(c_2Erealax_2Ereal__neg,V1y)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__MUL__LZERO,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ))).
fof(conj_thm_2Ereal_2EREAL__MUL__RZERO,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,V0x),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ))).
fof(conj_thm_2Ereal_2EREAL__ENTIRE,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) <=> ( ( V0x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) | ( V1y = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__LADD,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)),ap(ap(c_2Erealax_2Ereal__add,V0x),V2z))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,V1y),V2z)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__NOT__LE,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( ~~ p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) ) <=> p(ap(ap(c_2Erealax_2Ereal__lt,V1y),V0x)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__TOTAL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) | p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V0x)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__REFL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V0x)) ))).
fof(conj_thm_2Ereal_2EREAL__LTE__TRANS,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V1y)) & p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V2z)) ) => p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V2z)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LET__TRANS,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) & p(ap(ap(c_2Erealax_2Ereal__lt,V1y),V2z)) ) => p(ap(ap(c_2Erealax_2Ereal__lt,V0x),V2z)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__TRANS,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) & p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V2z)) ) => p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V2z)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__ANTISYM,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) & p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V0x)) ) <=> ( V0x = V1y ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__MUL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) & p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y)) ) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y))) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__SUB__REFL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Ereal_2Ereal__sub,V0x),V0x) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ))).
fof(conj_thm_2Ereal_2EREAL__EQ__LMUL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y) = ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z) ) <=> ( ( V0x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) | ( V1y = V2z ) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__SUB__RDISTRIB,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y)),V2z) = ap(ap(c_2Ereal_2Ereal__sub,ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z)),ap(ap(c_2Erealax_2Ereal__mul,V1y),V2z)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__LMUL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)),ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,V1y),V2z)) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__POS,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Ereal_2Ereal__of__num,V0n))) ))).
fof(conj_thm_2Ereal_2EREAL__ADD,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ap(ap(c_2Erealax_2Ereal__add,ap(c_2Ereal_2Ereal__of__num,V0m)),ap(c_2Ereal_2Ereal__of__num,V1n)) = ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__DIV__REFL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ( ~~ ( V0x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) => ( ap(ap(c_2Ereal_2E_2F,V0x),V0x) = ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__DIV__LZERO,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Ereal_2E_2F,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__RDIV__0,lemma,(! [V0y] : ( mem(V0y,ty_2Erealax_2Ereal) => ! [V1z] : ( mem(V1z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1z)) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Ereal_2E_2F,V0y),V1z))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0y)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__DIV__RMUL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( ~~ ( V1y = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) => ( ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2E_2F,V0x),V1y)),V1y) = V0x ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__SUB__LADD,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,V0x),ap(ap(c_2Ereal_2Ereal__sub,V1y),V2z))) <=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__add,V0x),V2z)),V1y)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__EQ__SUB__RADD,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ( ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y) = V2z ) <=> ( V0x = ap(ap(c_2Erealax_2Ereal__add,V2z),V1y) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__LMUL,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)),ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z))) <=> p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V2z)) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__DIV,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) & p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V1y)) ) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Ereal_2E_2F,V0x),V1y))) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__POS__NZ,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)) => ( ~~ ( V0x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ) ))).
fof(ax_thm_2Ereal_2Eabs,axiom, ! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(c_2Ereal_2Eabs,V0x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0x)),V0x),ap(c_2Erealax_2Ereal__neg,V0x)) ) )).
fof(conj_thm_2Ereal_2EABS__NEG,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(c_2Ereal_2Eabs,ap(c_2Erealax_2Ereal__neg,V0x)) = ap(c_2Ereal_2Eabs,V0x) ) ))).
fof(ax_thm_2Ereal_2Epow,axiom, ( ( ! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Ereal_2Epow,V0x),c_2Enum_2E0) = ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ) ) & ! [V1x] : ( mem(V1x,ty_2Erealax_2Ereal) => ! [V2n] : ( mem(V2n,ty_2Enum_2Enum) => ( ap(ap(c_2Ereal_2Epow,V1x),ap(c_2Enum_2ESUC,V2n)) = ap(ap(c_2Erealax_2Ereal__mul,V1x),ap(ap(c_2Ereal_2Epow,V1x),V2n)) ) ) ) )).
fof(conj_thm_2Ereal_2EPOW__ADD,lemma,(! [V0c] : ( mem(V0c,ty_2Erealax_2Ereal) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ! [V2n] : ( mem(V2n,ty_2Enum_2Enum) => ( ap(ap(c_2Ereal_2Epow,V0c),ap(ap(c_2Earithmetic_2E_2B,V1m),V2n)) = ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Ereal_2Epow,V0c),V1m)),ap(ap(c_2Ereal_2Epow,V0c),V2n)) ) ) ) ))).
fof(conj_thm_2Ereal_2EPOW__2__LE1,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => p(ap(ap(c_2Ereal_2Ereal__lte,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)))),V0n))) ))).
fof(conj_thm_2Ereal_2EREAL__MUL__RNEG,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,V0x),ap(c_2Erealax_2Ereal__neg,V1y)) = ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__MUL__LNEG,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Erealax_2Ereal__neg,V0x)),V1y) = ap(c_2Erealax_2Ereal__neg,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)) ) ) ))).
fof(conj_thm_2Ereal_2Ereal__lt,lemma,(! [V0y] : ( mem(V0y,ty_2Erealax_2Ereal) => ! [V1x] : ( mem(V1x,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,V1x),V0y)) <=> ( ~~ p(ap(ap(c_2Ereal_2Ereal__lte,V0y),V1x)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__LADD__IMP,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V2z)) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)),ap(ap(c_2Erealax_2Ereal__add,V0x),V2z))) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__LNEG,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,V0x)),V1y)) <=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Erealax_2Ereal__add,V0x),V1y))) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__NEG2,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,V0x)),ap(c_2Erealax_2Ereal__neg,V1y))) <=> p(ap(ap(c_2Ereal_2Ereal__lte,V1y),V0x)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__NEG__NEG,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(c_2Erealax_2Ereal__neg,ap(c_2Erealax_2Ereal__neg,V0x)) = V0x ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__RNEG,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,V0x),ap(c_2Erealax_2Ereal__neg,V1y))) <=> p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__LDIV__EQ,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V2z)) => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2E_2F,V0x),V2z)),V1y)) <=> p(ap(ap(c_2Ereal_2Ereal__lte,V0x),ap(ap(c_2Erealax_2Ereal__mul,V1y),V2z))) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__RDIV__EQ,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V2z)) => ( p(ap(ap(c_2Erealax_2Ereal__lt,V0x),ap(ap(c_2Ereal_2E_2F,V1y),V2z))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z)),V1y)) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__LDIV__EQ,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V2z)) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Ereal_2E_2F,V0x),V2z)),V1y)) <=> p(ap(ap(c_2Erealax_2Ereal__lt,V0x),ap(ap(c_2Erealax_2Ereal__mul,V1y),V2z))) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__EQ__RDIV__EQ,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V2z)) => ( ( V0x = ap(ap(c_2Ereal_2E_2F,V1y),V2z) ) <=> ( ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z) = V1y ) ) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__OF__NUM__POW,lemma,(! [V0x] : ( mem(V0x,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,V0x)),V1n) = ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2EEXP,V0x),V1n)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__ADD__LDISTRIB,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,V0x),ap(ap(c_2Erealax_2Ereal__add,V1y),V2z)) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)),ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__ADD__RDISTRIB,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,ap(ap(c_2Erealax_2Ereal__add,V0x),V1y)),V2z) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z)),ap(ap(c_2Erealax_2Ereal__mul,V1y),V2z)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__OF__NUM__LE,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,V0m)),ap(c_2Ereal_2Ereal__of__num,V1n))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__OF__NUM__MUL,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,V0m)),ap(c_2Ereal_2Ereal__of__num,V1n)) = ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__ABS__0,lemma,(( ap(c_2Ereal_2Eabs,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ))).
fof(conj_thm_2Ereal_2EREAL__DIV__ADD,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2E_2F,V1y),V0x)),ap(ap(c_2Ereal_2E_2F,V2z),V0x)) = ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Erealax_2Ereal__add,V1y),V2z)),V0x) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__LE__SUB__CANCEL2,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2Ereal__sub,V0x),V2z)),ap(ap(c_2Ereal_2Ereal__sub,V1y),V2z))) <=> p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) ) ) ) ))).
fof(conj_thm_2Ereal_2Emult__ratr,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,V0x),ap(ap(c_2Ereal_2E_2F,V1y),V2z)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),V2z),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))),ap(ap(c_2Erealax_2Ereal__mul,V0x),ap(c_2Emarker_2Eunint(ty_2Erealax_2Ereal),ap(ap(c_2Ereal_2E_2F,V1y),V2z)))),ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)),V2z)) ) ) ) ))).
fof(conj_thm_2Ereal_2Emult__ints,lemma,(! [V0a] : ( mem(V0a,ty_2Enum_2Enum) => ! [V1b] : ( mem(V1b,ty_2Enum_2Enum) => ( ( ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,V0a)),ap(c_2Ereal_2Ereal__of__num,V1b)) = ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2A,V0a),V1b)) ) & ( ( ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,V0a))),ap(c_2Ereal_2Ereal__of__num,V1b)) = ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2A,V0a),V1b))) ) & ( ( ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,V0a)),ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,V1b))) = ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2A,V0a),V1b))) ) & ( ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,V0a))),ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,V1b))) = ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2E_2A,V0a),V1b)) ) ) ) ) ) ))).
fof(conj_thm_2Ereal_2Epow__rat,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ! [V2a] : ( mem(V2a,ty_2Enum_2Enum) => ! [V3y] : ( mem(V3y,ty_2Erealax_2Ereal) => ( ( ap(ap(c_2Ereal_2Epow,V0x),c_2Enum_2E0) = 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,c_2Enum_2E0)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1n))) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) & ( ( ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V1n))) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) & ( ( ap(ap(c_2Ereal_2Epow,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,V2a))),ap(c_2Earithmetic_2ENUMERAL,V1n)) = ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,V2a)),ap(c_2Earithmetic_2ENUMERAL,V1n))) ) & ( ( ap(ap(c_2Ereal_2Epow,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,V2a)))),ap(c_2Earithmetic_2ENUMERAL,V1n)) = ap(ap(ap(ap(c_2Ebool_2ECOND(arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)),ap(c_2Earithmetic_2EODD,ap(c_2Earithmetic_2ENUMERAL,V1n))),c_2Erealax_2Ereal__neg),i(ty_2Erealax_2Ereal)),ap(c_2Ereal_2Ereal__of__num,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,V2a)),ap(c_2Earithmetic_2ENUMERAL,V1n)))) ) & ( ap(ap(c_2Ereal_2Epow,ap(ap(c_2Ereal_2E_2F,V0x),V3y)),V1n) = ap(ap(c_2Ereal_2E_2F,ap(ap(c_2Ereal_2Epow,V0x),V1n)),ap(ap(c_2Ereal_2Epow,V3y),V1n)) ) ) ) ) ) ) ) ) ) ))).
fof(conj_thm_2Ereal_2Eeq__rat,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2u] : ( mem(V2u,ty_2Erealax_2Ereal) => ! [V3v] : ( mem(V3v,ty_2Erealax_2Ereal) => ( ( ap(ap(c_2Ereal_2E_2F,V0x),V1y) = ap(ap(c_2Ereal_2E_2F,V2u),V3v) ) <=> p(ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),V1y),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))),ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),ap(c_2Emarker_2Eunint(ty_2Erealax_2Ereal),ap(ap(c_2Ereal_2E_2F,V0x),V1y))),ap(ap(c_2Ereal_2E_2F,V2u),V3v))),ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),V3v),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))),ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),ap(ap(c_2Ereal_2E_2F,V0x),V1y)),ap(c_2Emarker_2Eunint(ty_2Erealax_2Ereal),ap(ap(c_2Ereal_2E_2F,V2u),V3v)))),ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),V1y),V3v)),ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),V0x),V2u)),ap(ap(c_2Emin_2E_3D(ty_2Erealax_2Ereal),ap(ap(c_2Erealax_2Ereal__mul,V0x),V3v)),ap(ap(c_2Erealax_2Ereal__mul,V1y),V2u)))))) ) ) ) ) ))).
fof(conj_thm_2Ereal_2Eeq__ints,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ( ( ( ap(c_2Ereal_2Ereal__of__num,V0n) = ap(c_2Ereal_2Ereal__of__num,V1m) ) <=> ( V0n = V1m ) ) & ( ( ( ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,V0n)) = ap(c_2Ereal_2Ereal__of__num,V1m) ) <=> ( ( V0n = c_2Enum_2E0 ) & ( V1m = c_2Enum_2E0 ) ) ) & ( ( ( ap(c_2Ereal_2Ereal__of__num,V0n) = ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,V1m)) ) <=> ( ( V0n = c_2Enum_2E0 ) & ( V1m = c_2Enum_2E0 ) ) ) & ( ( ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,V0n)) = ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,V1m)) ) <=> ( V0n = V1m ) ) ) ) ) ) ))).
fof(conj_thm_2Ereal_2Ele__int,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,V0n)),ap(c_2Ereal_2Ereal__of__num,V1m))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m)) ) & ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,V0n))),ap(c_2Ereal_2Ereal__of__num,V1m))) <=> $true ) & ( ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,V0n)),ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,V1m)))) <=> ( ( V0n = c_2Enum_2E0 ) & ( V1m = c_2Enum_2E0 ) ) ) & ( p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,V0n))),ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,V1m)))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V0n)) ) ) ) ) ) ))).
fof(conj_thm_2Ereal_2Elt__int,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,V0n)),ap(c_2Ereal_2Ereal__of__num,V1m))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m)) ) & ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,V0n))),ap(c_2Ereal_2Ereal__of__num,V1m))) <=> ( ( ~~ ( V0n = c_2Enum_2E0 ) ) | ( ~~ ( V1m = c_2Enum_2E0 ) ) ) ) & ( ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,V0n)),ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,V1m)))) <=> $false ) & ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,V0n))),ap(c_2Erealax_2Ereal__neg,ap(c_2Ereal_2Ereal__of__num,V1m)))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,V1m),V0n)) ) ) ) ) ) ))).
fof(conj_thm_2Erealax_2EREAL__LDISTRIB,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ! [V2z] : ( mem(V2z,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__mul,V0x),ap(ap(c_2Erealax_2Ereal__add,V1y),V2z)) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Erealax_2Ereal__mul,V0x),V1y)),ap(ap(c_2Erealax_2Ereal__mul,V0x),V2z)) ) ) ) ))).
fof(conj_thm_2Erelation_2EWF__EMPTY__REL,lemma,( ! [A_27a]: ( ne(A_27a) => p(ap(c_2Erelation_2EWF(A_27a),c_2Erelation_2EEMPTY__REL(A_27a)))))).
fof(conj_thm_2Erelation_2EWFREC__COROLLARY,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0M] : ( mem(V0M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) => ! [V1R] : ( mem(V1R,arr(A_27a,arr(A_27a,bool))) => ! [V2f] : ( mem(V2f,arr(A_27a,A_27b)) => ( ( V2f = ap(ap(c_2Erelation_2EWFREC(A_27a,A_27b),V1R),V0M) ) => ( p(ap(c_2Erelation_2EWF(A_27a),V1R)) => ! [V3x] : ( mem(V3x,A_27a) => ( ap(V2f,V3x) = ap(ap(V0M,ap(ap(ap(c_2Erelation_2ERESTRICT(A_27a,A_27b),V2f),V1R),V3x)),V3x) ) ) ) ) ) ) ))))).
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__conj,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(V1q) | ( ~~ p(V0p) ) ) & ( p(V2r) | ( ~~ p(V0p) ) ) ) ) ) ) ) ))).
fof(conj_thm_2Esat_2Edc__disj,lemma,(! [V0p] : ( mem(V0p,bool) => ! [V1q] : ( mem(V1q,bool) => ! [V2r] : ( mem(V2r,bool) => ( ( p(V0p) <=> ( p(V1q) | p(V2r) ) ) <=> ( ( p(V0p) | ( ~~ p(V1q) ) ) & ( ( p(V0p) | ( ~~ p(V2r) ) ) & ( p(V1q) | ( p(V2r) | ( ~~ p(V0p) ) ) ) ) ) ) ) ) ))).
fof(conj_thm_2Esat_2Edc__imp,lemma,(! [V0p] : ( mem(V0p,bool) => ! [V1q] : ( mem(V1q,bool) => ! [V2r] : ( mem(V2r,bool) => ( ( p(V0p) <=> ( p(V1q) => p(V2r) ) ) <=> ( ( p(V0p) | p(V1q) ) & ( ( p(V0p) | ( ~~ p(V2r) ) ) & ( ( ~~ p(V1q) ) | ( p(V2r) | ( ~~ 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(conj_thm_2Esat_2Epth__ni1,lemma,(! [V0p] : ( mem(V0p,bool) => ! [V1q] : ( mem(V1q,bool) => ( ( ~~ ( p(V0p) => p(V1q) ) ) => p(V0p) ) ) ))).
fof(conj_thm_2Esat_2Epth__ni2,lemma,(! [V0p] : ( mem(V0p,bool) => ! [V1q] : ( mem(V1q,bool) => ( ( ~~ ( p(V0p) => p(V1q) ) ) => ( ~~ p(V1q) ) ) ) ))).
fof(conj_thm_2Esat_2Epth__no1,lemma,(! [V0p] : ( mem(V0p,bool) => ! [V1q] : ( mem(V1q,bool) => ( ( ~~ ( p(V0p) | p(V1q) ) ) => ( ~~ p(V0p) ) ) ) ))).
fof(conj_thm_2Esat_2Epth__no2,lemma,(! [V0p] : ( mem(V0p,bool) => ! [V1q] : ( mem(V1q,bool) => ( ( ~~ ( p(V0p) | p(V1q) ) ) => ( ~~ p(V1q) ) ) ) ))).
fof(conj_thm_2Esat_2Epth__nn,lemma,(! [V0p] : ( mem(V0p,bool) => ( ( ~~ ( ~~ p(V0p) ) ) => p(V0p) ) ))).
fof(ax_thm_2Ewords_2Edimword__def,axiom,( ! [A_27a] : ( ne(A_27a) => ( ap(c_2Ewords_2Edimword(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(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))) ) ) )).
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_2Eword__T__def,axiom,( ! [A_27a] : ( ne(A_27a) => ( c_2Ewords_2Eword__T(A_27a) = ap(c_2Ewords_2En2w(A_27a),ap(c_2Ewords_2EUINT__MAX(A_27a),c_2Ebool_2Ethe__value(A_27a))) ) ) )).
fof(conj_thm_2Ewords_2EZERO__LT__dimword,lemma,( ! [A_27a]: ( ne(A_27a) => p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a))))))).
fof(conj_thm_2Ewords_2EDIMINDEX__GT__0,lemma,( ! [A_27a]: ( ne(A_27a) => p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))))).
fof(conj_thm_2Ewords_2EONE__LT__dimword,lemma,( ! [A_27a]: ( ne(A_27a) => p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a))))))).
fof(conj_thm_2Ewords_2Ew2n__n2w,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ap(c_2Ewords_2Ew2n(A_27a),ap(c_2Ewords_2En2w(A_27a),V0n)) = ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a))) ) )))).
fof(conj_thm_2Ewords_2En2w__11,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ( ap(c_2Ewords_2En2w(A_27a),V0m) = ap(c_2Ewords_2En2w(A_27a),V1n) ) <=> ( ap(ap(c_2Earithmetic_2EMOD,V0m),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a))) = ap(ap(c_2Earithmetic_2EMOD,V1n),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a))) ) ) ) )))).
fof(conj_thm_2Ewords_2Eranged__word__nchotomy,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0w] : ( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a)) => ? [V1n] : ( mem(V1n,ty_2Enum_2Enum) & ( ( V0w = ap(c_2Ewords_2En2w(A_27a),V1n) ) & p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ) )))).
fof(conj_thm_2Ewords_2Ew2n__11,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0v] : ( mem(V0v,ty_2Efcp_2Ecart(bool,A_27a)) => ! [V1w] : ( mem(V1w,ty_2Efcp_2Ecart(bool,A_27a)) => ( ( ap(c_2Ewords_2Ew2n(A_27a),V0v) = ap(c_2Ewords_2Ew2n(A_27a),V1w) ) <=> ( V0v = V1w ) ) ) )))).
fof(conj_thm_2Ewords_2Ew2n__lt,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0w] : ( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a)) => p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Ewords_2Ew2n(A_27a),V0w)),ap(c_2Ewords_2Edimword(A_27a),c_2Ebool_2Ethe__value(A_27a)))) )))).
fof(conj_thm_2Ewords_2Eword__0__n2w,lemma,( ! [A_27a]: ( ne(A_27a) => ( ap(c_2Ewords_2Ew2n(A_27a),ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)) = c_2Enum_2E0 )))).
fof(conj_thm_2Ewords_2Eword__1__n2w,lemma,( ! [A_27a]: ( ne(A_27a) => ( ap(c_2Ewords_2Ew2n(A_27a),ap(c_2Ewords_2En2w(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_2Ewords_2Ew2n__eq__0,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0w] : ( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a)) => ( ( ap(c_2Ewords_2Ew2n(A_27a),V0w) = c_2Enum_2E0 ) <=> ( V0w = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0) ) ) )))).
fof(conj_thm_2Ewords_2ENUMERAL__LESS__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_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1n)))) <=> ( ( V0m = ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) | p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ) ) ) ) ) & ! [V2m] : ( mem(V2m,ty_2Enum_2Enum) => ! [V3n] : ( mem(V3n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,V2m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V3n)))) <=> ( ( V2m = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n)) ) | p(ap(ap(c_2Eprim__rec_2E_3C,V2m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n)))) ) ) ) ) ))).
fof(conj_thm_2Ewords_2EWORD__NEG__1,lemma,( ! [A_27a]: ( ne(A_27a) => ( ap(c_2Ewords_2Eword__2comp(A_27a),ap(c_2Ewords_2En2w(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = c_2Ewords_2Eword__T(A_27a) )))).
fof(conj_thm_2Ewords_2Ew2n__minus1,lemma,( ! [A_27a]: ( ne(A_27a) => ( ap(c_2Ewords_2Ew2n(A_27a),ap(c_2Ewords_2Eword__2comp(A_27a),ap(c_2Ewords_2En2w(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) = 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(conj_thm_2Ewords_2EWORD__LO,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0a] : ( mem(V0a,ty_2Efcp_2Ecart(bool,A_27a)) => ! [V1b] : ( mem(V1b,ty_2Efcp_2Ecart(bool,A_27a)) => ( p(ap(ap(c_2Ewords_2Eword__lo(A_27a),V0a),V1b)) <=> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Ewords_2Ew2n(A_27a),V0a)),ap(c_2Ewords_2Ew2n(A_27a),V1b))) ) ) )))).
fof(conj_thm_2Ewords_2EWORD__LO__word__0,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ( ( ! [V0n] : ( mem(V0n,ty_2Efcp_2Ecart(bool,A_27a)) => ( p(ap(ap(c_2Ewords_2Eword__lo(A_27a),ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0)),V0n)) <=> ( ~~ ( V0n = ap(c_2Ewords_2En2w(A_27a),c_2Enum_2E0) ) ) ) ) ) & ! [V1n] : ( mem(V1n,ty_2Efcp_2Ecart(bool,A_27b)) => ( ~~ p(ap(ap(c_2Ewords_2Eword__lo(A_27b),V1n),ap(c_2Ewords_2En2w(A_27b),c_2Enum_2E0))) ) ) ))))).
fof(conj_thm_2Ewords_2Edimword__1,lemma,(( ap(c_2Ewords_2Edimword(ty_2Eone_2Eone),c_2Ebool_2Ethe__value(ty_2Eone_2Eone)) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)) ))).
fof(conj_thm_2Ebinary__ieee_2Efloat__to__real__eq,conjecture,( ! [A_27t]: ( ne(A_27t) =>  ! [A_27w]: ( ne(A_27w) => ! [V0x] : ( mem(V0x,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ! [V1y] : ( mem(V1y,ty_2Ebinary__ieee_2Efloat(A_27t,A_27w)) => ( ( ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V0x) = ap(c_2Ebinary__ieee_2Efloat__to__real(A_27t,A_27w),V1y) ) <=> ( ( V0x = V1y ) | ( p(ap(c_2Ebinary__ieee_2Efloat__is__zero(A_27t,A_27w),V0x)) & p(ap(c_2Ebinary__ieee_2Efloat__is__zero(A_27t,A_27w),V1y)) ) ) ) ) ))))).
