include('Axioms/HL4001+2.ax').
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_2Ebool_2EBOUNDED,axiom,( mem(c_2Ebool_2EBOUNDED,arr(bool,bool)) )).
fof(ne_ty_2Elist_2Elist,axiom,( ! [A0] : ( ne(A0) => ne(ty_2Elist_2Elist(A0)) ) )).
fof(mem_c_2Elist_2EHD,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Elist_2EHD(A_27a),arr(ty_2Elist_2Elist(A_27a),A_27a)) ) )).
fof(mem_c_2Emarker_2EAbbrev,axiom,( mem(c_2Emarker_2EAbbrev,arr(bool,bool)) )).
fof(mem_c_2Emarker_2ECong,axiom,( mem(c_2Emarker_2ECong,arr(bool,bool)) )).
fof(ne_ty_2Enum_2Enum,axiom,( ne(ty_2Enum_2Enum) )).
fof(mem_c_2Earithmetic_2EEVEN,axiom,( mem(c_2Earithmetic_2EEVEN,arr(ty_2Enum_2Enum,bool)) )).
fof(mem_c_2Earithmetic_2EODD,axiom,( mem(c_2Earithmetic_2EODD,arr(ty_2Enum_2Enum,bool)) )).
fof(mem_c_2Earithmetic_2E_3E_3D,axiom,( mem(c_2Earithmetic_2E_3E_3D,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) )).
fof(mem_c_2Earithmetic_2E_3E,axiom,( mem(c_2Earithmetic_2E_3E,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) )).
fof(mem_c_2Eprim__rec_2EPRE,axiom,( mem(c_2Eprim__rec_2EPRE,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Earithmetic_2EEXP,axiom,( mem(c_2Earithmetic_2EEXP,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) )).
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_2E_2A,axiom,( mem(c_2Earithmetic_2E_2A,arr(ty_2Enum_2Enum,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_2Earithmetic_2E_2B,axiom,( mem(c_2Earithmetic_2E_2B,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) )).
fof(mem_c_2Earithmetic_2EBIT2,axiom,( mem(c_2Earithmetic_2EBIT2,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Earithmetic_2E_3C_3D,axiom,( mem(c_2Earithmetic_2E_3C_3D,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) )).
fof(ne_ty_2Eordinal_2Eordinal,axiom,( ! [A0] : ( ne(A0) => ne(ty_2Eordinal_2Eordinal(A0)) ) )).
fof(ne_ty_2Esum_2Esum,axiom,( ! [A0] : ( ne(A0) => ( ! [A1] : ( ne(A1) => ne(ty_2Esum_2Esum(A0,A1)) ) ) ) )).
fof(ne_ty_2Ewellorder_2Ewellorder,axiom,( ! [A0] : ( ne(A0) => ne(ty_2Ewellorder_2Ewellorder(A0)) ) )).
fof(mem_c_2Eordinal_2Eordinal__ABS,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Eordinal_2Eordinal__ABS(A_27a),arr(ty_2Ewellorder_2Ewellorder(ty_2Esum_2Esum(ty_2Enum_2Enum,A_27a)),ty_2Eordinal_2Eordinal(A_27a))) ) )).
fof(mem_c_2Eordinal_2Eordinal__REP,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Eordinal_2Eordinal__REP(A_27a),arr(ty_2Eordinal_2Eordinal(A_27a),ty_2Ewellorder_2Ewellorder(ty_2Esum_2Esum(ty_2Enum_2Enum,A_27a)))) ) )).
fof(mem_c_2Eordinal_2EordMOD,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Eordinal_2EordMOD(A_27a),arr(ty_2Eordinal_2Eordinal(A_27a),arr(ty_2Eordinal_2Eordinal(A_27a),ty_2Eordinal_2Eordinal(A_27a)))) ) )).
fof(mem_c_2Eordinal_2EordDIV,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Eordinal_2EordDIV(A_27a),arr(ty_2Eordinal_2Eordinal(A_27a),arr(ty_2Eordinal_2Eordinal(A_27a),ty_2Eordinal_2Eordinal(A_27a)))) ) )).
fof(mem_c_2Eordinal_2EordSUC,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Eordinal_2EordSUC(A_27a),arr(ty_2Eordinal_2Eordinal(A_27a),ty_2Eordinal_2Eordinal(A_27a))) ) )).
fof(ne_ty_2Eoption_2Eoption,axiom,( ! [A0] : ( ne(A0) => ne(ty_2Eoption_2Eoption(A0)) ) )).
fof(mem_c_2Eoption_2ENONE,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Eoption_2ENONE(A_27a),ty_2Eoption_2Eoption(A_27a)) ) )).
fof(mem_c_2Eordinal_2Epreds,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Eordinal_2Epreds(A_27a),arr(ty_2Eordinal_2Eordinal(A_27a),arr(ty_2Eordinal_2Eordinal(A_27a),bool))) ) )).
fof(mem_c_2Eordinal_2Eomax,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Eordinal_2Eomax(A_27a),arr(arr(ty_2Eordinal_2Eordinal(A_27a),bool),ty_2Eoption_2Eoption(ty_2Eordinal_2Eordinal(A_27a)))) ) )).
fof(mem_c_2Eordinal_2Esup,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Eordinal_2Esup(A_27a),arr(arr(ty_2Eordinal_2Eordinal(A_27a),bool),ty_2Eordinal_2Eordinal(A_27a))) ) )).
fof(mem_c_2Epred__set_2EUNIV,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2EUNIV(A_27a),arr(A_27a,bool)) ) )).
fof(mem_c_2Ecardinal_2Ecardleq,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Ecardinal_2Ecardleq(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),bool))) ) ) )).
fof(mem_c_2Earithmetic_2EZERO,axiom,( mem(c_2Earithmetic_2EZERO,ty_2Enum_2Enum) )).
fof(mem_c_2Earithmetic_2EBIT1,axiom,( mem(c_2Earithmetic_2EBIT1,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Earithmetic_2ENUMERAL,axiom,( mem(c_2Earithmetic_2ENUMERAL,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Eordinal_2EordEXP,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Eordinal_2EordEXP(A_27a),arr(ty_2Eordinal_2Eordinal(A_27a),arr(ty_2Eordinal_2Eordinal(A_27a),ty_2Eordinal_2Eordinal(A_27a)))) ) )).
fof(mem_c_2Eordinal_2EordMULT,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Eordinal_2EordMULT(A_27a),arr(ty_2Eordinal_2Eordinal(A_27a),arr(ty_2Eordinal_2Eordinal(A_27a),ty_2Eordinal_2Eordinal(A_27a)))) ) )).
fof(mem_c_2Eordinal_2EordADD,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Eordinal_2EordADD(A_27a),arr(ty_2Eordinal_2Eordinal(A_27a),arr(ty_2Eordinal_2Eordinal(A_27a),ty_2Eordinal_2Eordinal(A_27a)))) ) )).
fof(mem_c_2Elist_2ECONS,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Elist_2ECONS(A_27a),arr(A_27a,arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)))) ) )).
fof(mem_c_2Elist_2ENIL,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Elist_2ENIL(A_27a),ty_2Elist_2Elist(A_27a)) ) )).
fof(ne_ty_2Epair_2Eprod,axiom,( ! [A0] : ( ne(A0) => ( ! [A1] : ( ne(A1) => ne(ty_2Epair_2Eprod(A0,A1)) ) ) ) )).
fof(mem_c_2Eordinal_2Eeval__poly,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Eordinal_2Eeval__poly(A_27a),arr(ty_2Eordinal_2Eordinal(A_27a),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Eordinal_2Eordinal(A_27a),ty_2Eordinal_2Eordinal(A_27a))),ty_2Eordinal_2Eordinal(A_27a)))) ) )).
fof(mem_c_2Eordinal_2EfromNat,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Eordinal_2EfromNat(A_27a),arr(ty_2Enum_2Enum,ty_2Eordinal_2Eordinal(A_27a))) ) )).
fof(mem_c_2Elist_2ELIST__TO__SET,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Elist_2ELIST__TO__SET(A_27a),arr(ty_2Elist_2Elist(A_27a),arr(A_27a,bool))) ) )).
fof(mem_c_2Elist_2EEL,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Elist_2EEL(A_27a),arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(A_27a),A_27a))) ) )).
fof(mem_c_2Eordinal_2Eordlt,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Eordinal_2Eordlt(A_27a),arr(ty_2Eordinal_2Eordinal(A_27a),arr(ty_2Eordinal_2Eordinal(A_27a),bool))) ) )).
fof(mem_c_2Elist_2ELENGTH,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Elist_2ELENGTH(A_27a),arr(ty_2Elist_2Elist(A_27a),ty_2Enum_2Enum)) ) )).
fof(mem_c_2Eordinal_2Eis__polyform,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Eordinal_2Eis__polyform(A_27a,A_27b),arr(ty_2Eordinal_2Eordinal(A_27a),arr(ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Eordinal_2Eordinal(A_27a),ty_2Eordinal_2Eordinal(A_27b))),bool))) ) ) )).
fof(mem_c_2Epair_2ESND,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Epair_2ESND(A_27a,A_27b),arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27b)) ) ) )).
fof(mem_c_2Ebool_2ET,axiom,( mem(c_2Ebool_2ET,bool) )).
fof(ax_true_p,axiom,( p(c_2Ebool_2ET) )).
fof(mem_c_2Epair_2E_2C,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Epair_2E_2C(A_27a,A_27b),arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27a,A_27b)))) ) ) )).
fof(mem_c_2Epred__set_2EGSPEC,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Epred__set_2EGSPEC(A_27a,A_27b),arr(arr(A_27b,ty_2Epair_2Eprod(A_27a,bool)),arr(A_27a,bool))) ) ) )).
fof(mem_c_2Epred__set_2EEMPTY,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2EEMPTY(A_27a),arr(A_27a,bool)) ) )).
fof(mem_c_2Epred__set_2ESUBSET,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2ESUBSET(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))) ) )).
fof(mem_c_2Epred__set_2EINSERT,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2EINSERT(A_27a),arr(A_27a,arr(arr(A_27a,bool),arr(A_27a,bool)))) ) )).
fof(mem_c_2Ebool_2E_3F,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Ebool_2E_3F(A_27a),arr(arr(A_27a,bool),bool)) ) )).
fof(ax_ex_p,axiom,( ! [A] : ( ne(A) => ! [Q] : ( mem(Q,arr(A,bool)) => ( p(ap(c_2Ebool_2E_3F(A),Q)) <=> ? [X] : ( mem(X,A) & p(ap(Q,X)) ) ) ) ) )).
fof(mem_c_2Epred__set_2EIMAGE,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Epred__set_2EIMAGE(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,bool),arr(A_27b,bool)))) ) ) )).
fof(mem_c_2Ebool_2EIN,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Ebool_2EIN(A_27a),arr(A_27a,arr(arr(A_27a,bool),bool))) ) )).
fof(mem_c_2Enum_2ESUC,axiom,( mem(c_2Enum_2ESUC,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Enum_2E0,axiom,( mem(c_2Enum_2E0,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_2Ecombin_2EI,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Ecombin_2EI(A_27a),arr(A_27a,A_27a)) ) )).
fof(mem_c_2Equotient_2E_2D_2D_3E,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [A_27c] : ( ne(A_27c) => ! [A_27d] : ( ne(A_27d) => mem(c_2Equotient_2E_2D_2D_3E(A_27a,A_27b,A_27c,A_27d),arr(arr(A_27a,A_27c),arr(arr(A_27b,A_27d),arr(arr(A_27c,A_27b),arr(A_27a,A_27d))))) ) ) ) ) )).
fof(mem_c_2Equotient_2E_3D_3D_3D_3E,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27b,arr(A_27b,bool)),arr(arr(A_27a,A_27b),arr(arr(A_27a,A_27b),bool))))) ) ) )).
fof(mem_c_2Equotient_2EQUOTIENT,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Equotient_2EQUOTIENT(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27a,A_27b),arr(arr(A_27b,A_27a),bool)))) ) ) )).
fof(mem_c_2Equotient_2Erespects,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Equotient_2Erespects(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,A_27b)),arr(A_27a,A_27b))) ) ) )).
fof(mem_c_2Ebool_2ERES__FORALL,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Ebool_2ERES__FORALL(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))) ) )).
fof(mem_c_2Equotient_2EEQUIV,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Equotient_2EEQUIV(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)) ) )).
fof(mem_c_2Ebool_2EF,axiom,( mem(c_2Ebool_2EF,bool) )).
fof(ax_false_p,axiom,( ~ p(c_2Ebool_2EF) )).
fof(mem_c_2Ebool_2E_5C_2F,axiom,( mem(c_2Ebool_2E_5C_2F,arr(bool,arr(bool,bool))) )).
fof(ax_or_p,axiom,( ! [Q] : ( mem(Q,bool) => ! [R] : ( mem(R,bool) => ( p(ap(ap(c_2Ebool_2E_5C_2F,Q),R)) <=> ( p(Q) | p(R) ) ) ) ) )).
fof(mem_c_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_2Ewellorder_2Eorderlt,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Ewellorder_2Eorderlt(A_27a,A_27b),arr(ty_2Ewellorder_2Ewellorder(A_27a),arr(ty_2Ewellorder_2Ewellorder(A_27b),bool))) ) ) )).
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(mem_c_2Ewellorder_2Eorderiso,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Ewellorder_2Eorderiso(A_27a,A_27b),arr(ty_2Ewellorder_2Ewellorder(A_27a),arr(ty_2Ewellorder_2Ewellorder(A_27b),bool))) ) ) )).
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_2Emin_2E_3D_3D_3E,axiom,( mem(c_2Emin_2E_3D_3D_3E,arr(bool,arr(bool,bool))) )).
fof(ax_imp_p,axiom,( ! [Q] : ( mem(Q,bool) => ! [R] : ( mem(R,bool) => ( p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R)) <=> ( p(Q) => p(R) ) ) ) ) )).
fof(mem_c_2Ebool_2E_21,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Ebool_2E_21(A_27a),arr(arr(A_27a,bool),bool)) ) )).
fof(ax_all_p,axiom,( ! [A] : ( ne(A) => ! [Q] : ( mem(Q,arr(A,bool)) => ( p(ap(c_2Ebool_2E_21(A),Q)) <=> ! [X] : ( mem(X,A) => p(ap(Q,X)) ) ) ) ) )).
fof(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__MONO__EQ,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enum_2ESUC,V0m)),ap(c_2Enum_2ESUC,V1n))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),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_2EMULT__CLAUSES,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ( ap(ap(c_2Earithmetic_2E_2A,c_2Enum_2E0),V0m) = c_2Enum_2E0 ) & ( ( ap(ap(c_2Earithmetic_2E_2A,V0m),c_2Enum_2E0) = c_2Enum_2E0 ) & ( ( ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0m) = V0m ) & ( ( ap(ap(c_2Earithmetic_2E_2A,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = V0m ) & ( ( ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V0m)),V1n) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),V1n) ) & ( ap(ap(c_2Earithmetic_2E_2A,V0m),ap(c_2Enum_2ESUC,V1n)) = ap(ap(c_2Earithmetic_2E_2B,V0m),ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)) ) ) ) ) ) ) ) ))).
fof(conj_thm_2Earithmetic_2ELESS__EQ__TRANS,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ! [V2p] : ( mem(V2p,ty_2Enum_2Enum) => ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)) ) => p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V2p)) ) ) ) ))).
fof(conj_thm_2Earithmetic_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__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(ax_thm_2Ebool_2EEXISTS__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ( c_2Ebool_2E_3F(A_27a) = f2(A_27a) ) ) )).
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_2EEXISTS__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_2EFUN__EQ__THM,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1g] : ( mem(V1g,arr(A_27a,A_27b)) => ( ( V0f = V1g ) <=> ! [V2x] : ( mem(V2x,A_27a) => ( ap(V0f,V2x) = ap(V1g,V2x) ) ) ) ) ))))).
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_2ENOT__FORALL__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ( ( ~~ ! [V1x] : ( mem(V1x,A_27a) => p(ap(V0P,V1x)) ) ) <=> ? [V2x] : ( mem(V2x,A_27a) & ( ~~ p(ap(V0P,V2x)) ) ) ) )))).
fof(conj_thm_2Ebool_2ENOT__EXISTS__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ( ( ~~ ? [V1x] : ( mem(V1x,A_27a) & p(ap(V0P,V1x)) ) ) <=> ! [V2x] : ( mem(V2x,A_27a) => ( ~~ p(ap(V0P,V2x)) ) ) ) )))).
fof(conj_thm_2Ebool_2EFORALL__AND__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1Q] : ( mem(V1Q,arr(A_27a,bool)) => ( ( ! [V2x] : ( mem(V2x,A_27a) => ( p(ap(V0P,V2x)) & p(ap(V1Q,V2x)) ) ) ) <=> ( ( ! [V3x] : ( mem(V3x,A_27a) => p(ap(V0P,V3x)) ) ) & ! [V4x] : ( mem(V4x,A_27a) => p(ap(V1Q,V4x)) ) ) ) ) )))).
fof(conj_thm_2Ebool_2ELEFT__AND__FORALL__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1Q] : ( mem(V1Q,bool) => ( ( ( ! [V2x] : ( mem(V2x,A_27a) => p(ap(V0P,V2x)) ) ) & p(V1Q) ) <=> ! [V3x] : ( mem(V3x,A_27a) => ( p(ap(V0P,V3x)) & p(V1Q) ) ) ) ) )))).
fof(conj_thm_2Ebool_2ERIGHT__AND__FORALL__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,bool) => ! [V1Q] : ( mem(V1Q,arr(A_27a,bool)) => ( ( p(V0P) & ! [V2x] : ( mem(V2x,A_27a) => p(ap(V1Q,V2x)) ) ) <=> ! [V3x] : ( mem(V3x,A_27a) => ( p(V0P) & p(ap(V1Q,V3x)) ) ) ) ) )))).
fof(conj_thm_2Ebool_2ELEFT__EXISTS__AND__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1Q] : ( mem(V1Q,bool) => ( ( ? [V2x] : ( mem(V2x,A_27a) & ( p(ap(V0P,V2x)) & p(V1Q) ) ) ) <=> ( ( ? [V3x] : ( mem(V3x,A_27a) & p(ap(V0P,V3x)) ) ) & p(V1Q) ) ) ) )))).
fof(conj_thm_2Ebool_2ELEFT__FORALL__OR__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0Q] : ( mem(V0Q,bool) => ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ( ( ! [V2x] : ( mem(V2x,A_27a) => ( p(ap(V1P,V2x)) | p(V0Q) ) ) ) <=> ( ( ! [V3x] : ( mem(V3x,A_27a) => p(ap(V1P,V3x)) ) ) | p(V0Q) ) ) ) )))).
fof(conj_thm_2Ebool_2ELEFT__FORALL__IMP__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1Q] : ( mem(V1Q,bool) => ( ( ! [V2x] : ( mem(V2x,A_27a) => ( p(ap(V0P,V2x)) => p(V1Q) ) ) ) <=> ( ( ? [V3x] : ( mem(V3x,A_27a) & p(ap(V0P,V3x)) ) ) => p(V1Q) ) ) ) )))).
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_2EDISJ__IMP__THM,lemma,(! [V0P] : ( mem(V0P,bool) => ! [V1Q] : ( mem(V1Q,bool) => ! [V2R] : ( mem(V2R,bool) => ( ( ( p(V0P) | p(V1Q) ) => p(V2R) ) <=> ( ( p(V0P) => p(V2R) ) & ( p(V1Q) => p(V2R) ) ) ) ) ) ))).
fof(conj_thm_2Ebool_2EIMP__CONJ__THM,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) ) ) ) ) ) ))).
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__IMP__THM,lemma,(! [V0t1] : ( mem(V0t1,bool) => ! [V1t2] : ( mem(V1t2,bool) => ( ( p(V0t1) <=> p(V1t2) ) <=> ( ( p(V0t1) => p(V1t2) ) & ( p(V1t2) => p(V0t1) ) ) ) ) ))).
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_2EEXISTS__REFL,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0a] : ( mem(V0a,A_27a) => ? [V1x] : ( mem(V1x,A_27a) & ( V1x = V0a ) ) )))).
fof(conj_thm_2Ebool_2EUNWIND__THM2,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1a] : ( mem(V1a,A_27a) => ( ( ? [V2x] : ( mem(V2x,A_27a) & ( ( V2x = V1a ) & p(ap(V0P,V2x)) ) ) ) <=> p(ap(V0P,V1a)) ) ) )))).
fof(conj_thm_2Ebool_2EBOUNDED__THM,lemma,(! [V0v] : ( mem(V0v,bool) => ( p(ap(c_2Ebool_2EBOUNDED,V0v)) <=> $true ) ))).
fof(conj_thm_2Ecardinal_2Ecardleq__TRANS,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) =>  ! [A_27c]: ( ne(A_27c) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27b,bool)) => ! [V2u] : ( mem(V2u,arr(A_27c,bool)) => ( ( p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) & p(ap(ap(c_2Ecardinal_2Ecardleq(A_27b,A_27c),V1t),V2u)) ) => p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27c),V0s),V2u)) ) ) ) )))))).
fof(conj_thm_2Ecardinal_2ESUBSET__CARDLEQ,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,arr(A_27a,bool)) => ! [V1y] : ( mem(V1y,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0x),V1y)) => p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27a),V0x),V1y)) ) ) )))).
fof(conj_thm_2Ecardinal_2EIMAGE__cardleq__rwt,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) =>  ! [A_27c]: ( ne(A_27c) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27c)) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ! [V2t] : ( mem(V2t,arr(A_27b,bool)) => ( p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V1s),V2t)) => p(ap(ap(c_2Ecardinal_2Ecardleq(A_27c,A_27b),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27c),V0f),V1s)),V2t)) ) ) ) )))))).
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(ax_thm_2Elist_2EHD,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0h] : ( mem(V0h,A_27a) => ! [V1t] : ( mem(V1t,ty_2Elist_2Elist(A_27a)) => ( ap(c_2Elist_2EHD(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V1t)) = V0h ) ) ) ) )).
fof(ax_thm_2Elist_2ELENGTH,axiom,( ! [A_27a] : ( ne(A_27a) => ( ( ap(c_2Elist_2ELENGTH(A_27a),c_2Elist_2ENIL(A_27a)) = c_2Enum_2E0 ) & ! [V0h] : ( mem(V0h,A_27a) => ! [V1t] : ( mem(V1t,ty_2Elist_2Elist(A_27a)) => ( ap(c_2Elist_2ELENGTH(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V1t)) = ap(c_2Enum_2ESUC,ap(c_2Elist_2ELENGTH(A_27a),V1t)) ) ) ) ) ) )).
fof(conj_thm_2Elist_2ELIST__TO__SET,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0h] : ( mem(V0h,A_27b) => ! [V1t] : ( mem(V1t,ty_2Elist_2Elist(A_27b)) => ( ( ap(c_2Elist_2ELIST__TO__SET(A_27a),c_2Elist_2ENIL(A_27a)) = c_2Epred__set_2EEMPTY(A_27a) ) & ( ap(c_2Elist_2ELIST__TO__SET(A_27b),ap(ap(c_2Elist_2ECONS(A_27b),V0h),V1t)) = ap(ap(c_2Epred__set_2EINSERT(A_27b),V0h),ap(c_2Elist_2ELIST__TO__SET(A_27b),V1t)) ) ) ) ))))).
fof(conj_thm_2Elist_2Elist__CASES,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l] : ( mem(V0l,ty_2Elist_2Elist(A_27a)) => ( ( V0l = c_2Elist_2ENIL(A_27a) ) | ? [V1h] : ( mem(V1h,A_27a) & ? [V2t] : ( mem(V2t,ty_2Elist_2Elist(A_27a)) & ( V0l = ap(ap(c_2Elist_2ECONS(A_27a),V1h),V2t) ) ) ) ) )))).
fof(conj_thm_2Elist_2EMEM,lemma,( ! [A_27a]: ( ne(A_27a) => ( ( ! [V0x] : ( mem(V0x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Elist_2ELIST__TO__SET(A_27a),c_2Elist_2ENIL(A_27a)))) <=> $false ) ) ) & ! [V1x] : ( mem(V1x,A_27a) => ! [V2h] : ( mem(V2h,A_27a) => ! [V3t] : ( mem(V3t,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Elist_2ELIST__TO__SET(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3t)))) <=> ( ( V1x = V2h ) | p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(c_2Elist_2ELIST__TO__SET(A_27a),V3t))) ) ) ) ) ) )))).
fof(conj_thm_2Elist_2EEL__restricted,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1l] : ( mem(V1l,A_27b) => ! [V2ls] : ( mem(V2ls,ty_2Elist_2Elist(A_27b)) => ( ( ap(c_2Elist_2EEL(A_27a),c_2Enum_2E0) = c_2Elist_2EHD(A_27a) ) & ( ap(ap(c_2Elist_2EEL(A_27b),ap(c_2Enum_2ESUC,V0n)),ap(ap(c_2Elist_2ECONS(A_27b),V1l),V2ls)) = ap(ap(c_2Elist_2EEL(A_27b),V0n),V2ls) ) ) ) ) ))))).
fof(ax_thm_2Emarker_2EAbbrev__def,axiom, ! [V0x] : ( mem(V0x,bool) => ( p(ap(c_2Emarker_2EAbbrev,V0x)) <=> p(V0x) ) )).
fof(ax_thm_2Emarker_2ECong__def,axiom, ! [V0x] : ( mem(V0x,bool) => ( p(ap(c_2Emarker_2ECong,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_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__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_2Eordinal_2Eordinal__QUOTIENT,lemma,( ! [A_27a]: ( ne(A_27a) => p(ap(ap(ap(c_2Equotient_2EQUOTIENT(ty_2Ewellorder_2Ewellorder(ty_2Esum_2Esum(ty_2Enum_2Enum,A_27a)),ty_2Eordinal_2Eordinal(A_27a)),c_2Ewellorder_2Eorderiso(ty_2Esum_2Esum(ty_2Enum_2Enum,A_27a),ty_2Esum_2Esum(ty_2Enum_2Enum,A_27a))),c_2Eordinal_2Eordinal__ABS(A_27a)),c_2Eordinal_2Eordinal__REP(A_27a)))))).
fof(ax_thm_2Eordinal_2Eordlt__def,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0T1] : ( mem(V0T1,ty_2Eordinal_2Eordinal(A_27a)) => ! [V1T2] : ( mem(V1T2,ty_2Eordinal_2Eordinal(A_27a)) => ( p(ap(ap(c_2Eordinal_2Eordlt(A_27a),V0T1),V1T2)) <=> p(ap(ap(c_2Ewellorder_2Eorderlt(ty_2Esum_2Esum(ty_2Enum_2Enum,A_27a),ty_2Esum_2Esum(ty_2Enum_2Enum,A_27a)),ap(c_2Eordinal_2Eordinal__REP(A_27a),V0T1)),ap(c_2Eordinal_2Eordinal__REP(A_27a),V1T2))) ) ) ) ) )).
fof(conj_thm_2Eordinal_2Eordlt__REFL,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0w] : ( mem(V0w,ty_2Eordinal_2Eordinal(A_27a)) => ( ~~ p(ap(ap(c_2Eordinal_2Eordlt(A_27a),V0w),V0w)) ) )))).
fof(conj_thm_2Eordinal_2EIN__preds,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,ty_2Eordinal_2Eordinal(A_27a)) => ! [V1w] : ( mem(V1w,ty_2Eordinal_2Eordinal(A_27a)) => ( p(ap(ap(c_2Ebool_2EIN(ty_2Eordinal_2Eordinal(A_27a)),V0x),ap(c_2Eordinal_2Epreds(A_27a),V1w))) <=> p(ap(ap(c_2Eordinal_2Eordlt(A_27a),V0x),V1w)) ) ) )))).
fof(conj_thm_2Eordinal_2Epreds__inj__univ,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0ord] : ( mem(V0ord,ty_2Eordinal_2Eordinal(A_27a)) => p(ap(ap(c_2Ecardinal_2Ecardleq(ty_2Eordinal_2Eordinal(A_27a),ty_2Esum_2Esum(ty_2Enum_2Enum,A_27a)),ap(c_2Eordinal_2Epreds(A_27a),V0ord)),c_2Epred__set_2EUNIV(ty_2Esum_2Esum(ty_2Enum_2Enum,A_27a)))) )))).
fof(conj_thm_2Eordinal_2Eordle__lteq,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0b] : ( mem(V0b,ty_2Eordinal_2Eordinal(A_27a)) => ! [V1a] : ( mem(V1a,ty_2Eordinal_2Eordinal(A_27a)) => ( ( ~~ p(ap(ap(c_2Eordinal_2Eordlt(A_27a),V0b),V1a)) ) <=> ( p(ap(ap(c_2Eordinal_2Eordlt(A_27a),V1a),V0b)) | ( V1a = V0b ) ) ) ) )))).
fof(conj_thm_2Eordinal_2Eordle__TRANS,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,ty_2Eordinal_2Eordinal(A_27a)) => ! [V1y] : ( mem(V1y,ty_2Eordinal_2Eordinal(A_27a)) => ! [V2z] : ( mem(V2z,ty_2Eordinal_2Eordinal(A_27a)) => ( ( ( ~~ p(ap(ap(c_2Eordinal_2Eordlt(A_27a),V1y),V0x)) ) & ( ~~ p(ap(ap(c_2Eordinal_2Eordlt(A_27a),V2z),V1y)) ) ) => ( ~~ p(ap(ap(c_2Eordinal_2Eordlt(A_27a),V2z),V0x)) ) ) ) ) )))).
fof(conj_thm_2Eordinal_2Eordlt__SUC,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0a] : ( mem(V0a,ty_2Eordinal_2Eordinal(A_27a)) => p(ap(ap(c_2Eordinal_2Eordlt(A_27a),V0a),ap(c_2Eordinal_2EordSUC(A_27a),V0a))) )))).
fof(conj_thm_2Eordinal_2Eordlt__SUC__DISCRETE,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0a] : ( mem(V0a,ty_2Eordinal_2Eordinal(A_27a)) => ! [V1b] : ( mem(V1b,ty_2Eordinal_2Eordinal(A_27a)) => ( p(ap(ap(c_2Eordinal_2Eordlt(A_27a),V0a),ap(c_2Eordinal_2EordSUC(A_27a),V1b))) <=> ( p(ap(ap(c_2Eordinal_2Eordlt(A_27a),V0a),V1b)) | ( V0a = V1b ) ) ) ) )))).
fof(conj_thm_2Eordinal_2Eord__induction,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(ty_2Eordinal_2Eordinal(A_27a),bool)) => ( ( ! [V1min] : ( mem(V1min,ty_2Eordinal_2Eordinal(A_27a)) => ( ( ! [V2b] : ( mem(V2b,ty_2Eordinal_2Eordinal(A_27a)) => ( p(ap(ap(c_2Eordinal_2Eordlt(A_27a),V2b),V1min)) => p(ap(V0P,V2b)) ) ) ) => p(ap(V0P,V1min)) ) ) ) => ! [V3a] : ( mem(V3a,ty_2Eordinal_2Eordinal(A_27a)) => p(ap(V0P,V3a)) ) ) )))).
fof(conj_thm_2Eordinal_2Esup__thm,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(ty_2Eordinal_2Eordinal(A_27a),bool)) => ( p(ap(ap(c_2Ecardinal_2Ecardleq(ty_2Eordinal_2Eordinal(A_27a),ty_2Esum_2Esum(ty_2Enum_2Enum,A_27a)),V0s),c_2Epred__set_2EUNIV(ty_2Esum_2Esum(ty_2Enum_2Enum,A_27a)))) => ! [V1a] : ( mem(V1a,ty_2Eordinal_2Eordinal(A_27a)) => ( p(ap(ap(c_2Eordinal_2Eordlt(A_27a),V1a),ap(c_2Eordinal_2Esup(A_27a),V0s))) <=> ? [V2b] : ( mem(V2b,ty_2Eordinal_2Eordinal(A_27a)) & ( p(ap(ap(c_2Ebool_2EIN(ty_2Eordinal_2Eordinal(A_27a)),V2b),V0s)) & p(ap(ap(c_2Eordinal_2Eordlt(A_27a),V1a),V2b)) ) ) ) ) ) )))).
fof(conj_thm_2Eordinal_2Esuple__thm,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0b] : ( mem(V0b,ty_2Eordinal_2Eordinal(A_27a)) => ! [V1s] : ( mem(V1s,arr(ty_2Eordinal_2Eordinal(A_27a),bool)) => ( ( p(ap(ap(c_2Ecardinal_2Ecardleq(ty_2Eordinal_2Eordinal(A_27a),ty_2Esum_2Esum(ty_2Enum_2Enum,A_27a)),V1s),c_2Epred__set_2EUNIV(ty_2Esum_2Esum(ty_2Enum_2Enum,A_27a)))) & p(ap(ap(c_2Ebool_2EIN(ty_2Eordinal_2Eordinal(A_27a)),V0b),V1s)) ) => ( ~~ p(ap(ap(c_2Eordinal_2Eordlt(A_27a),ap(c_2Eordinal_2Esup(A_27a),V1s)),V0b)) ) ) ) )))).
fof(conj_thm_2Eordinal_2Eordleq0,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,ty_2Eordinal_2Eordinal(A_27a)) => ( ( ~~ p(ap(ap(c_2Eordinal_2Eordlt(A_27a),ap(c_2Eordinal_2EfromNat(A_27a),c_2Enum_2E0)),V0x)) ) <=> ( V0x = ap(c_2Eordinal_2EfromNat(A_27a),c_2Enum_2E0) ) ) )))).
fof(conj_thm_2Eordinal_2EfromNat__11,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,ty_2Enum_2Enum) => ! [V1y] : ( mem(V1y,ty_2Enum_2Enum) => ( ( ap(c_2Eordinal_2EfromNat(A_27a),V0x) = ap(c_2Eordinal_2EfromNat(A_27a),V1y) ) <=> ( V0x = V1y ) ) ) )))).
fof(conj_thm_2Eordinal_2EfromNat__ordlt,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eordinal_2Eordlt(A_27a),ap(c_2Eordinal_2EfromNat(A_27a),V0n)),ap(c_2Eordinal_2EfromNat(A_27a),V1m))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m)) ) ) )))).
fof(conj_thm_2Eordinal_2EordADD__0L,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0a] : ( mem(V0a,ty_2Eordinal_2Eordinal(A_27a)) => ( ap(ap(c_2Eordinal_2EordADD(A_27a),ap(c_2Eordinal_2EfromNat(A_27a),c_2Enum_2E0)),V0a) = V0a ) )))).
fof(conj_thm_2Eordinal_2EordADD__RIGHT__CANCEL,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0b] : ( mem(V0b,ty_2Eordinal_2Eordinal(A_27a)) => ! [V1a] : ( mem(V1a,ty_2Eordinal_2Eordinal(A_27a)) => ! [V2c] : ( mem(V2c,ty_2Eordinal_2Eordinal(A_27a)) => ( ( ap(ap(c_2Eordinal_2EordADD(A_27a),V1a),V0b) = ap(ap(c_2Eordinal_2EordADD(A_27a),V1a),V2c) ) <=> ( V0b = V2c ) ) ) ) )))).
fof(conj_thm_2Eordinal_2Eordle__CANCEL__ADDR,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,ty_2Eordinal_2Eordinal(A_27a)) => ! [V1a] : ( mem(V1a,ty_2Eordinal_2Eordinal(A_27a)) => ( ~~ p(ap(ap(c_2Eordinal_2Eordlt(A_27a),ap(ap(c_2Eordinal_2EordADD(A_27a),V0x),V1a)),V0x)) ) ) )))).
fof(ax_thm_2Eordinal_2EordMULT__def,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0b] : ( mem(V0b,ty_2Eordinal_2Eordinal(A_27a)) => ( ( ap(ap(c_2Eordinal_2EordMULT(A_27a),V0b),ap(c_2Eordinal_2EfromNat(A_27a),c_2Enum_2E0)) = ap(c_2Eordinal_2EfromNat(A_27a),c_2Enum_2E0) ) & ( ( ! [V1a] : ( mem(V1a,ty_2Eordinal_2Eordinal(A_27a)) => ( ap(ap(c_2Eordinal_2EordMULT(A_27a),V0b),ap(c_2Eordinal_2EordSUC(A_27a),V1a)) = ap(ap(c_2Eordinal_2EordADD(A_27a),ap(ap(c_2Eordinal_2EordMULT(A_27a),V0b),V1a)),V0b) ) ) ) & ! [V2a] : ( mem(V2a,ty_2Eordinal_2Eordinal(A_27a)) => ( ( p(ap(ap(c_2Eordinal_2Eordlt(A_27a),ap(c_2Eordinal_2EfromNat(A_27a),c_2Enum_2E0)),V2a)) & ( ap(c_2Eordinal_2Eomax(A_27a),ap(c_2Eordinal_2Epreds(A_27a),V2a)) = c_2Eoption_2ENONE(ty_2Eordinal_2Eordinal(A_27a)) ) ) => ( ap(ap(c_2Eordinal_2EordMULT(A_27a),V0b),V2a) = ap(c_2Eordinal_2Esup(A_27a),ap(ap(c_2Epred__set_2EIMAGE(ty_2Eordinal_2Eordinal(A_27a),ty_2Eordinal_2Eordinal(A_27a)),ap(c_2Eordinal_2EordMULT(A_27a),V0b)),ap(c_2Eordinal_2Epreds(A_27a),V2a))) ) ) ) ) ) ) ) )).
fof(conj_thm_2Eordinal_2EordMULT__1R,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0a] : ( mem(V0a,ty_2Eordinal_2Eordinal(A_27a)) => ( ap(ap(c_2Eordinal_2EordMULT(A_27a),V0a),ap(c_2Eordinal_2EfromNat(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = V0a ) )))).
fof(conj_thm_2Eordinal_2EordMULT__le__MONO__R,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0a] : ( mem(V0a,ty_2Eordinal_2Eordinal(A_27a)) => ! [V1b] : ( mem(V1b,ty_2Eordinal_2Eordinal(A_27a)) => ! [V2c] : ( mem(V2c,ty_2Eordinal_2Eordinal(A_27a)) => ( ( ~~ p(ap(ap(c_2Eordinal_2Eordlt(A_27a),V1b),V0a)) ) => ( ~~ p(ap(ap(c_2Eordinal_2Eordlt(A_27a),ap(ap(c_2Eordinal_2EordMULT(A_27a),V2c),V1b)),ap(ap(c_2Eordinal_2EordMULT(A_27a),V2c),V0a))) ) ) ) ) )))).
fof(conj_thm_2Eordinal_2EordMULT__lt__MONO__R__EQN,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0c] : ( mem(V0c,ty_2Eordinal_2Eordinal(A_27a)) => ! [V1a] : ( mem(V1a,ty_2Eordinal_2Eordinal(A_27a)) => ! [V2b] : ( mem(V2b,ty_2Eordinal_2Eordinal(A_27a)) => ( p(ap(ap(c_2Eordinal_2Eordlt(A_27a),ap(ap(c_2Eordinal_2EordMULT(A_27a),V0c),V1a)),ap(ap(c_2Eordinal_2EordMULT(A_27a),V0c),V2b))) <=> ( p(ap(ap(c_2Eordinal_2Eordlt(A_27a),V1a),V2b)) & p(ap(ap(c_2Eordinal_2Eordlt(A_27a),ap(c_2Eordinal_2EfromNat(A_27a),c_2Enum_2E0)),V0c)) ) ) ) ) )))).
fof(conj_thm_2Eordinal_2EordADD__le__MONO__L,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0y] : ( mem(V0y,ty_2Eordinal_2Eordinal(A_27a)) => ! [V1x] : ( mem(V1x,ty_2Eordinal_2Eordinal(A_27a)) => ! [V2z] : ( mem(V2z,ty_2Eordinal_2Eordinal(A_27a)) => ( ( ~~ p(ap(ap(c_2Eordinal_2Eordlt(A_27a),V0y),V1x)) ) => ( ~~ p(ap(ap(c_2Eordinal_2Eordlt(A_27a),ap(ap(c_2Eordinal_2EordADD(A_27a),V0y),V2z)),ap(ap(c_2Eordinal_2EordADD(A_27a),V1x),V2z))) ) ) ) ) )))).
fof(ax_thm_2Eordinal_2EordDIVISION,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0a] : ( mem(V0a,ty_2Eordinal_2Eordinal(A_27a)) => ! [V1b] : ( mem(V1b,ty_2Eordinal_2Eordinal(A_27a)) => ( p(ap(ap(c_2Eordinal_2Eordlt(A_27a),ap(c_2Eordinal_2EfromNat(A_27a),c_2Enum_2E0)),V1b)) => ( ( V0a = ap(ap(c_2Eordinal_2EordADD(A_27a),ap(ap(c_2Eordinal_2EordMULT(A_27a),V1b),ap(ap(c_2Eordinal_2EordDIV(A_27a),V0a),V1b))),ap(ap(c_2Eordinal_2EordMOD(A_27a),V0a),V1b)) ) & p(ap(ap(c_2Eordinal_2Eordlt(A_27a),ap(ap(c_2Eordinal_2EordMOD(A_27a),V0a),V1b)),V1b)) ) ) ) ) ) )).
fof(ax_thm_2Eordinal_2EordEXP__def,axiom,( ! [A_27a] : ( ne(A_27a) => ( ( ! [V0a] : ( mem(V0a,ty_2Eordinal_2Eordinal(A_27a)) => ( ap(ap(c_2Eordinal_2EordEXP(A_27a),V0a),ap(c_2Eordinal_2EfromNat(A_27a),c_2Enum_2E0)) = ap(c_2Eordinal_2EfromNat(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ) ) & ( ( ! [V1a] : ( mem(V1a,ty_2Eordinal_2Eordinal(A_27a)) => ! [V2a_27] : ( mem(V2a_27,ty_2Eordinal_2Eordinal(A_27a)) => ( ap(ap(c_2Eordinal_2EordEXP(A_27a),V1a),ap(c_2Eordinal_2EordSUC(A_27a),V2a_27)) = ap(ap(c_2Eordinal_2EordMULT(A_27a),ap(ap(c_2Eordinal_2EordEXP(A_27a),V1a),V2a_27)),V1a) ) ) ) ) & ! [V3a] : ( mem(V3a,ty_2Eordinal_2Eordinal(A_27a)) => ! [V4a_27] : ( mem(V4a_27,ty_2Eordinal_2Eordinal(A_27a)) => ( ( p(ap(ap(c_2Eordinal_2Eordlt(A_27a),ap(c_2Eordinal_2EfromNat(A_27a),c_2Enum_2E0)),V4a_27)) & ( ap(c_2Eordinal_2Eomax(A_27a),ap(c_2Eordinal_2Epreds(A_27a),V4a_27)) = c_2Eoption_2ENONE(ty_2Eordinal_2Eordinal(A_27a)) ) ) => ( ap(ap(c_2Eordinal_2EordEXP(A_27a),V3a),V4a_27) = ap(c_2Eordinal_2Esup(A_27a),ap(ap(c_2Epred__set_2EIMAGE(ty_2Eordinal_2Eordinal(A_27a),ty_2Eordinal_2Eordinal(A_27a)),ap(c_2Eordinal_2EordEXP(A_27a),V3a)),ap(c_2Eordinal_2Epreds(A_27a),V4a_27))) ) ) ) ) ) ) ) )).
fof(conj_thm_2Eordinal_2EIFF__ZERO__lt,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,ty_2Eordinal_2Eordinal(A_27a)) => ( ( ( ~~ ( V0x = ap(c_2Eordinal_2EfromNat(A_27a),c_2Enum_2E0) ) ) <=> p(ap(ap(c_2Eordinal_2Eordlt(A_27a),ap(c_2Eordinal_2EfromNat(A_27a),c_2Enum_2E0)),V0x)) ) & ( ( ~~ p(ap(ap(c_2Eordinal_2Eordlt(A_27a),V0x),ap(c_2Eordinal_2EfromNat(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) ) <=> p(ap(ap(c_2Eordinal_2Eordlt(A_27a),ap(c_2Eordinal_2EfromNat(A_27a),c_2Enum_2E0)),V0x)) ) ) )))).
fof(conj_thm_2Eordinal_2EordADD__EQ__0,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0y] : ( mem(V0y,ty_2Eordinal_2Eordinal(A_27a)) => ! [V1x] : ( mem(V1x,ty_2Eordinal_2Eordinal(A_27a)) => ( ( ap(ap(c_2Eordinal_2EordADD(A_27a),V1x),V0y) = ap(c_2Eordinal_2EfromNat(A_27a),c_2Enum_2E0) ) <=> ( ( V1x = ap(c_2Eordinal_2EfromNat(A_27a),c_2Enum_2E0) ) & ( V0y = ap(c_2Eordinal_2EfromNat(A_27a),c_2Enum_2E0) ) ) ) ) )))).
fof(conj_thm_2Eordinal_2EordMULT__EQ__0,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,ty_2Eordinal_2Eordinal(A_27a)) => ! [V1y] : ( mem(V1y,ty_2Eordinal_2Eordinal(A_27a)) => ( ( ap(ap(c_2Eordinal_2EordMULT(A_27a),V0x),V1y) = ap(c_2Eordinal_2EfromNat(A_27a),c_2Enum_2E0) ) <=> ( ( V0x = ap(c_2Eordinal_2EfromNat(A_27a),c_2Enum_2E0) ) | ( V1y = ap(c_2Eordinal_2EfromNat(A_27a),c_2Enum_2E0) ) ) ) ) )))).
fof(conj_thm_2Eordinal_2EZERO__lt__ordEXP,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0a] : ( mem(V0a,ty_2Eordinal_2Eordinal(A_27a)) => ! [V1x] : ( mem(V1x,ty_2Eordinal_2Eordinal(A_27a)) => ( p(ap(ap(c_2Eordinal_2Eordlt(A_27a),ap(c_2Eordinal_2EfromNat(A_27a),c_2Enum_2E0)),ap(ap(c_2Eordinal_2EordEXP(A_27a),V0a),V1x))) <=> ( p(ap(ap(c_2Eordinal_2Eordlt(A_27a),ap(c_2Eordinal_2EfromNat(A_27a),c_2Enum_2E0)),V0a)) | ( ap(c_2Eordinal_2Eomax(A_27a),ap(c_2Eordinal_2Epreds(A_27a),V1x)) = c_2Eoption_2ENONE(ty_2Eordinal_2Eordinal(A_27a)) ) ) ) ) )))).
fof(conj_thm_2Eordinal_2EordEXP__le__MONO__R,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,ty_2Eordinal_2Eordinal(A_27a)) => ! [V1y] : ( mem(V1y,ty_2Eordinal_2Eordinal(A_27a)) => ! [V2a] : ( mem(V2a,ty_2Eordinal_2Eordinal(A_27a)) => ( ( p(ap(ap(c_2Eordinal_2Eordlt(A_27a),ap(c_2Eordinal_2EfromNat(A_27a),c_2Enum_2E0)),V2a)) & ( ~~ p(ap(ap(c_2Eordinal_2Eordlt(A_27a),V1y),V0x)) ) ) => ( ~~ p(ap(ap(c_2Eordinal_2Eordlt(A_27a),ap(ap(c_2Eordinal_2EordEXP(A_27a),V2a),V1y)),ap(ap(c_2Eordinal_2EordEXP(A_27a),V2a),V0x))) ) ) ) ) )))).
fof(conj_thm_2Eordinal_2EordEXP__continuous,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0a] : ( mem(V0a,ty_2Eordinal_2Eordinal(A_27a)) => ! [V1s] : ( mem(V1s,arr(ty_2Eordinal_2Eordinal(A_27a),bool)) => ( ( p(ap(ap(c_2Eordinal_2Eordlt(A_27a),ap(c_2Eordinal_2EfromNat(A_27a),c_2Enum_2E0)),V0a)) & ( p(ap(ap(c_2Ecardinal_2Ecardleq(ty_2Eordinal_2Eordinal(A_27a),ty_2Esum_2Esum(ty_2Enum_2Enum,A_27a)),V1s),c_2Epred__set_2EUNIV(ty_2Esum_2Esum(ty_2Enum_2Enum,A_27a)))) & ( ~~ ( V1s = c_2Epred__set_2EEMPTY(ty_2Eordinal_2Eordinal(A_27a)) ) ) ) ) => ( ap(ap(c_2Eordinal_2EordEXP(A_27a),V0a),ap(c_2Eordinal_2Esup(A_27a),V1s)) = ap(c_2Eordinal_2Esup(A_27a),ap(ap(c_2Epred__set_2EIMAGE(ty_2Eordinal_2Eordinal(A_27a),ty_2Eordinal_2Eordinal(A_27a)),ap(c_2Eordinal_2EordEXP(A_27a),V0a)),V1s)) ) ) ) )))).
fof(conj_thm_2Eordinal_2Ex__le__ordEXP__x,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0a] : ( mem(V0a,ty_2Eordinal_2Eordinal(A_27a)) => ! [V1x] : ( mem(V1x,ty_2Eordinal_2Eordinal(A_27a)) => ( p(ap(ap(c_2Eordinal_2Eordlt(A_27a),ap(c_2Eordinal_2EfromNat(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0a)) => ( ~~ p(ap(ap(c_2Eordinal_2Eordlt(A_27a),ap(ap(c_2Eordinal_2EordEXP(A_27a),V0a),V1x)),V1x)) ) ) ) )))).
fof(conj_thm_2Eordinal_2Eeval__poly__def,lemma,( ! [A_27a]: ( ne(A_27a) => ( ( ! [V0a] : ( mem(V0a,ty_2Eordinal_2Eordinal(A_27a)) => ( ap(ap(c_2Eordinal_2Eeval__poly(A_27a),V0a),c_2Elist_2ENIL(ty_2Epair_2Eprod(ty_2Eordinal_2Eordinal(A_27a),ty_2Eordinal_2Eordinal(A_27a)))) = ap(c_2Eordinal_2EfromNat(A_27a),c_2Enum_2E0) ) ) ) & ! [V1t] : ( mem(V1t,ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Eordinal_2Eordinal(A_27a),ty_2Eordinal_2Eordinal(A_27a)))) => ! [V2e] : ( mem(V2e,ty_2Eordinal_2Eordinal(A_27a)) => ! [V3c] : ( mem(V3c,ty_2Eordinal_2Eordinal(A_27a)) => ! [V4a] : ( mem(V4a,ty_2Eordinal_2Eordinal(A_27a)) => ( ap(ap(c_2Eordinal_2Eeval__poly(A_27a),V4a),ap(ap(c_2Elist_2ECONS(ty_2Epair_2Eprod(ty_2Eordinal_2Eordinal(A_27a),ty_2Eordinal_2Eordinal(A_27a))),ap(ap(c_2Epair_2E_2C(ty_2Eordinal_2Eordinal(A_27a),ty_2Eordinal_2Eordinal(A_27a)),V3c),V2e)),V1t)) = ap(ap(c_2Eordinal_2EordADD(A_27a),ap(ap(c_2Eordinal_2EordMULT(A_27a),ap(ap(c_2Eordinal_2EordEXP(A_27a),V4a),V2e)),V3c)),ap(ap(c_2Eordinal_2Eeval__poly(A_27a),V4a),V1t)) ) ) ) ) ) )))).
fof(conj_thm_2Eordinal_2Eis__polyform__ELthm,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0a] : ( mem(V0a,ty_2Eordinal_2Eordinal(A_27a)) => ! [V1ces] : ( mem(V1ces,ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Eordinal_2Eordinal(A_27a),ty_2Eordinal_2Eordinal(A_27b)))) => ( p(ap(ap(c_2Eordinal_2Eis__polyform(A_27a,A_27b),V0a),V1ces)) <=> ( ( ! [V2i] : ( mem(V2i,ty_2Enum_2Enum) => ! [V3j] : ( mem(V3j,ty_2Enum_2Enum) => ( ( p(ap(ap(c_2Eprim__rec_2E_3C,V2i),V3j)) & p(ap(ap(c_2Eprim__rec_2E_3C,V3j),ap(c_2Elist_2ELENGTH(ty_2Epair_2Eprod(ty_2Eordinal_2Eordinal(A_27a),ty_2Eordinal_2Eordinal(A_27b))),V1ces))) ) => p(ap(ap(c_2Eordinal_2Eordlt(A_27b),ap(c_2Epair_2ESND(ty_2Eordinal_2Eordinal(A_27a),ty_2Eordinal_2Eordinal(A_27b)),ap(ap(c_2Elist_2EEL(ty_2Epair_2Eprod(ty_2Eordinal_2Eordinal(A_27a),ty_2Eordinal_2Eordinal(A_27b))),V3j),V1ces))),ap(c_2Epair_2ESND(ty_2Eordinal_2Eordinal(A_27a),ty_2Eordinal_2Eordinal(A_27b)),ap(ap(c_2Elist_2EEL(ty_2Epair_2Eprod(ty_2Eordinal_2Eordinal(A_27a),ty_2Eordinal_2Eordinal(A_27b))),V2i),V1ces)))) ) ) ) ) & ! [V4c] : ( mem(V4c,ty_2Eordinal_2Eordinal(A_27a)) => ! [V5e] : ( mem(V5e,ty_2Eordinal_2Eordinal(A_27b)) => ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(ty_2Eordinal_2Eordinal(A_27a),ty_2Eordinal_2Eordinal(A_27b))),ap(ap(c_2Epair_2E_2C(ty_2Eordinal_2Eordinal(A_27a),ty_2Eordinal_2Eordinal(A_27b)),V4c),V5e)),ap(c_2Elist_2ELIST__TO__SET(ty_2Epair_2Eprod(ty_2Eordinal_2Eordinal(A_27a),ty_2Eordinal_2Eordinal(A_27b))),V1ces))) => ( p(ap(ap(c_2Eordinal_2Eordlt(A_27a),ap(c_2Eordinal_2EfromNat(A_27a),c_2Enum_2E0)),V4c)) & p(ap(ap(c_2Eordinal_2Eordlt(A_27a),V4c),V0a)) ) ) ) ) ) ) ) ))))).
fof(conj_thm_2Epair_2EPAIR__EQ,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1y] : ( mem(V1y,A_27b) => ! [V2a] : ( mem(V2a,A_27a) => ! [V3b] : ( mem(V3b,A_27b) => ( ( ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y) = ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2a),V3b) ) <=> ( ( V0x = V2a ) & ( V1y = V3b ) ) ) ) ) ) ))))).
fof(conj_thm_2Epair_2ECLOSED__PAIR__EQ,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1y] : ( mem(V1y,A_27b) => ! [V2a] : ( mem(V2a,A_27a) => ! [V3b] : ( mem(V3b,A_27b) => ( ( ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y) = ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2a),V3b) ) <=> ( ( V0x = V2a ) & ( V1y = V3b ) ) ) ) ) ) ))))).
fof(conj_thm_2Epair_2Epair__CASES,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0x] : ( mem(V0x,ty_2Epair_2Eprod(A_27a,A_27b)) => ? [V1q] : ( mem(V1q,A_27a) & ? [V2r] : ( mem(V2r,A_27b) & ( V0x = ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1q),V2r) ) ) ) ))))).
fof(conj_thm_2Epair_2ESND,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1y] : ( mem(V1y,A_27b) => ( ap(c_2Epair_2ESND(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y)) = V1y ) ) ))))).
fof(conj_thm_2Epred__set_2EEXTENSION,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( ( V0s = V1t ) <=> ! [V2x] : ( mem(V2x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) <=> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)) ) ) ) ) )))).
fof(ax_thm_2Epred__set_2EGSPECIFICATION,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27b,ty_2Epair_2Eprod(A_27a,bool))) => ! [V1v] : ( mem(V1v,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V1v),ap(c_2Epred__set_2EGSPEC(A_27a,A_27b),V0f))) <=> ? [V2x] : ( mem(V2x,A_27b) & ( ap(ap(c_2Epair_2E_2C(A_27a,bool),V1v),c_2Ebool_2ET) = ap(V0f,V2x) ) ) ) ) ) ) ) )).
fof(conj_thm_2Epred__set_2ENOT__IN__EMPTY,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ( ~~ p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a))) ) )))).
fof(ax_thm_2Epred__set_2ESUBSET__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0s] : ( mem(V0s,arr(A_27a,bool)) => ! [V1t] : ( mem(V1t,arr(A_27a,bool)) => ( p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) <=> ! [V2x] : ( mem(V2x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) => p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)) ) ) ) ) ) ) )).
fof(conj_thm_2Epred__set_2EIN__INSERT,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1y] : ( mem(V1y,A_27a) => ! [V2s] : ( mem(V2s,arr(A_27a,bool)) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1y),V2s))) <=> ( ( V0x = V1y ) | p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V2s)) ) ) ) ) )))).
fof(conj_thm_2Epred__set_2EIN__IMAGE,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0y] : ( mem(V0y,A_27b) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ! [V2f] : ( mem(V2f,arr(A_27a,A_27b)) => ( p(ap(ap(c_2Ebool_2EIN(A_27b),V0y),ap(ap(c_2Epred__set_2EIMAGE(A_27a,A_27b),V2f),V1s))) <=> ? [V3x] : ( mem(V3x,A_27a) & ( ( V0y = ap(V2f,V3x) ) & p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s)) ) ) ) ) ) ))))).
fof(conj_thm_2Eprim__rec_2EINV__SUC__EQ,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ( ap(c_2Enum_2ESUC,V0m) = ap(c_2Enum_2ESUC,V1n) ) <=> ( V0m = V1n ) ) ) ))).
fof(conj_thm_2Eprim__rec_2ENOT__LESS__0,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ~~ p(ap(ap(c_2Eprim__rec_2E_3C,V0n),c_2Enum_2E0)) ) ))).
fof(conj_thm_2Eprim__rec_2ELESS__0,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Enum_2ESUC,V0n))) ))).
fof(ax_thm_2Equotient_2EEQUIV__def,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0E] : ( mem(V0E,arr(A_27a,arr(A_27a,bool))) => ( p(ap(c_2Equotient_2EEQUIV(A_27a),V0E)) <=> ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27a) => ( p(ap(ap(V0E,V1x),V2y)) <=> ( ap(V0E,V1x) = ap(V0E,V2y) ) ) ) ) ) ) ) )).
fof(conj_thm_2Equotient_2EIDENTITY__QUOTIENT,lemma,( ! [A_27a]: ( ne(A_27a) => p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27a),c_2Emin_2E_3D(A_27a)),c_2Ecombin_2EI(A_27a)),c_2Ecombin_2EI(A_27a)))))).
fof(ax_thm_2Equotient_2EFUN__REL,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0R1] : ( mem(V0R1,arr(A_27a,arr(A_27a,bool))) => ! [V1R2] : ( mem(V1R2,arr(A_27b,arr(A_27b,bool))) => ! [V2f] : ( mem(V2f,arr(A_27a,A_27b)) => ! [V3g] : ( mem(V3g,arr(A_27a,A_27b)) => ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0R1),V1R2),V2f),V3g)) <=> ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ( p(ap(ap(V0R1,V4x),V5y)) => p(ap(ap(V1R2,ap(V2f,V4x)),ap(V3g,V5y))) ) ) ) ) ) ) ) ) ) ) )).
fof(conj_thm_2Equotient_2EFUN__QUOTIENT,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) =>  ! [A_27c]: ( ne(A_27c) =>  ! [A_27d]: ( ne(A_27d) => ! [V0R1] : ( mem(V0R1,arr(A_27a,arr(A_27a,bool))) => ! [V1abs1] : ( mem(V1abs1,arr(A_27a,A_27c)) => ! [V2rep1] : ( mem(V2rep1,arr(A_27c,A_27a)) => ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1)) => ! [V3R2] : ( mem(V3R2,arr(A_27b,arr(A_27b,bool))) => ! [V4abs2] : ( mem(V4abs2,arr(A_27b,A_27d)) => ! [V5rep2] : ( mem(V5rep2,arr(A_27d,A_27b)) => ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2)) => p(ap(ap(ap(c_2Equotient_2EQUOTIENT(arr(A_27a,A_27b),arr(A_27c,A_27d)),ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0R1),V3R2)),ap(ap(c_2Equotient_2E_2D_2D_3E(A_27c,A_27b,A_27a,A_27d),V2rep1),V4abs2)),ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,A_27d,A_27c,A_27b),V1abs1),V5rep2))) ) ) ) ) ) ) ) ))))))).
fof(conj_thm_2Equotient_2ELAMBDA__PRS,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) =>  ! [A_27c]: ( ne(A_27c) =>  ! [A_27d]: ( ne(A_27d) => ! [V0R1] : ( mem(V0R1,arr(A_27a,arr(A_27a,bool))) => ! [V1abs1] : ( mem(V1abs1,arr(A_27a,A_27c)) => ! [V2rep1] : ( mem(V2rep1,arr(A_27c,A_27a)) => ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1)) => ! [V3R2] : ( mem(V3R2,arr(A_27b,arr(A_27b,bool))) => ! [V4abs2] : ( mem(V4abs2,arr(A_27b,A_27d)) => ! [V5rep2] : ( mem(V5rep2,arr(A_27d,A_27b)) => ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2)) => ! [V6f] : ( mem(V6f,arr(A_27c,A_27d)) => ( f1256(A_27d,A_27c,V6f) = ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27c,A_27b,A_27a,A_27d),V2rep1),V4abs2),f1257(A_27a,A_27c,A_27d,A_27b,V6f,V1abs1,V5rep2)) ) ) ) ) ) ) ) ) ) ))))))).
fof(conj_thm_2Equotient_2EREP__ABS__RSP,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0REL] : ( mem(V0REL,arr(A_27a,arr(A_27a,bool))) => ! [V1abs] : ( mem(V1abs,arr(A_27a,A_27b)) => ! [V2rep] : ( mem(V2rep,arr(A_27b,A_27a)) => ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0REL),V1abs),V2rep)) => ! [V3x1] : ( mem(V3x1,A_27a) => ! [V4x2] : ( mem(V4x2,A_27a) => ( p(ap(ap(V0REL,V3x1),V4x2)) => p(ap(ap(V0REL,V3x1),ap(V2rep,ap(V1abs,V4x2)))) ) ) ) ) ) ) ))))).
fof(conj_thm_2Equotient_2EFORALL__PRS,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1abs] : ( mem(V1abs,arr(A_27a,A_27b)) => ! [V2rep] : ( mem(V2rep,arr(A_27b,A_27a)) => ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep)) => ! [V3f] : ( mem(V3f,arr(A_27b,bool)) => ( p(ap(c_2Ebool_2E_21(A_27b),V3f)) <=> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),ap(c_2Equotient_2Erespects(A_27a,bool),V0R)),ap(ap(ap(c_2Equotient_2E_2D_2D_3E(A_27a,bool,A_27b,bool),V1abs),c_2Ecombin_2EI(bool)),V3f))) ) ) ) ) ) ))))).
fof(conj_thm_2Equotient_2ERES__FORALL__RSP,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0R] : ( mem(V0R,arr(A_27a,arr(A_27a,bool))) => ! [V1abs] : ( mem(V1abs,arr(A_27a,A_27b)) => ! [V2rep] : ( mem(V2rep,arr(A_27b,A_27a)) => ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27b),V0R),V1abs),V2rep)) => ! [V3f] : ( mem(V3f,arr(A_27a,bool)) => ! [V4g] : ( mem(V4g,arr(A_27a,bool)) => ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,bool),V0R),c_2Emin_2E_3D(bool)),V3f),V4g)) => ( p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),ap(c_2Equotient_2Erespects(A_27a,bool),V0R)),V3f)) <=> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),ap(c_2Equotient_2Erespects(A_27a,bool),V0R)),V4g)) ) ) ) ) ) ) ) ))))).
fof(conj_thm_2Equotient_2EAPPLY__RSP,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) =>  ! [A_27c]: ( ne(A_27c) =>  ! [A_27d]: ( ne(A_27d) => ! [V0R1] : ( mem(V0R1,arr(A_27a,arr(A_27a,bool))) => ! [V1abs1] : ( mem(V1abs1,arr(A_27a,A_27c)) => ! [V2rep1] : ( mem(V2rep1,arr(A_27c,A_27a)) => ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27a,A_27c),V0R1),V1abs1),V2rep1)) => ! [V3R2] : ( mem(V3R2,arr(A_27b,arr(A_27b,bool))) => ! [V4abs2] : ( mem(V4abs2,arr(A_27b,A_27d)) => ! [V5rep2] : ( mem(V5rep2,arr(A_27d,A_27b)) => ( p(ap(ap(ap(c_2Equotient_2EQUOTIENT(A_27b,A_27d),V3R2),V4abs2),V5rep2)) => ! [V6f] : ( mem(V6f,arr(A_27a,A_27b)) => ! [V7g] : ( mem(V7g,arr(A_27a,A_27b)) => ! [V8x] : ( mem(V8x,A_27a) => ! [V9y] : ( mem(V9y,A_27a) => ( ( p(ap(ap(ap(ap(c_2Equotient_2E_3D_3D_3D_3E(A_27a,A_27b),V0R1),V3R2),V6f),V7g)) & p(ap(ap(V0R1,V8x),V9y)) ) => p(ap(ap(V3R2,ap(V6f,V8x)),ap(V7g,V9y))) ) ) ) ) ) ) ) ) ) ) ) ) ))))))).
fof(conj_thm_2Equotient_2EEQUIV__RES__FORALL,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0E] : ( mem(V0E,arr(A_27a,arr(A_27a,bool))) => ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ( p(ap(c_2Equotient_2EEQUIV(A_27a),V0E)) => ( p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),ap(c_2Equotient_2Erespects(A_27a,bool),V0E)),V1P)) <=> p(ap(c_2Ebool_2E_21(A_27a),V1P)) ) ) ) )))).
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(conj_thm_2Ewellorder_2Eorderiso__REFL,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0w] : ( mem(V0w,ty_2Ewellorder_2Ewellorder(A_27a)) => p(ap(ap(c_2Ewellorder_2Eorderiso(A_27a,A_27a),V0w),V0w)) )))).
fof(conj_thm_2Ewellorder_2Eorderiso__SYM,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0w1] : ( mem(V0w1,ty_2Ewellorder_2Ewellorder(A_27a)) => ! [V1w2] : ( mem(V1w2,ty_2Ewellorder_2Ewellorder(A_27b)) => ( p(ap(ap(c_2Ewellorder_2Eorderiso(A_27a,A_27b),V0w1),V1w2)) => p(ap(ap(c_2Ewellorder_2Eorderiso(A_27b,A_27a),V1w2),V0w1)) ) ) ))))).
fof(conj_thm_2Ewellorder_2Eorderiso__TRANS,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) =>  ! [A_27c]: ( ne(A_27c) => ! [V0w1] : ( mem(V0w1,ty_2Ewellorder_2Ewellorder(A_27a)) => ! [V1w2] : ( mem(V1w2,ty_2Ewellorder_2Ewellorder(A_27b)) => ! [V2w3] : ( mem(V2w3,ty_2Ewellorder_2Ewellorder(A_27c)) => ( ( p(ap(ap(c_2Ewellorder_2Eorderiso(A_27a,A_27b),V0w1),V1w2)) & p(ap(ap(c_2Ewellorder_2Eorderiso(A_27b,A_27c),V1w2),V2w3)) ) => p(ap(ap(c_2Ewellorder_2Eorderiso(A_27a,A_27c),V0w1),V2w3)) ) ) ) )))))).
fof(conj_thm_2Ewellorder_2Eorderlt__TRANS,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) =>  ! [A_27c]: ( ne(A_27c) => ! [V0w1] : ( mem(V0w1,ty_2Ewellorder_2Ewellorder(A_27a)) => ! [V1w2] : ( mem(V1w2,ty_2Ewellorder_2Ewellorder(A_27b)) => ! [V2w3] : ( mem(V2w3,ty_2Ewellorder_2Ewellorder(A_27c)) => ( ( p(ap(ap(c_2Ewellorder_2Eorderlt(A_27a,A_27b),V0w1),V1w2)) & p(ap(ap(c_2Ewellorder_2Eorderlt(A_27b,A_27c),V1w2),V2w3)) ) => p(ap(ap(c_2Ewellorder_2Eorderlt(A_27a,A_27c),V0w1),V2w3)) ) ) ) )))))).
fof(conj_thm_2Ewellorder_2Eorderlt__orderiso,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) =>  ! [A_27c]: ( ne(A_27c) =>  ! [A_27d]: ( ne(A_27d) => ! [V0x0] : ( mem(V0x0,ty_2Ewellorder_2Ewellorder(A_27a)) => ! [V1y0] : ( mem(V1y0,ty_2Ewellorder_2Ewellorder(A_27b)) => ! [V2a0] : ( mem(V2a0,ty_2Ewellorder_2Ewellorder(A_27c)) => ! [V3b0] : ( mem(V3b0,ty_2Ewellorder_2Ewellorder(A_27d)) => ( ( p(ap(ap(c_2Ewellorder_2Eorderiso(A_27a,A_27b),V0x0),V1y0)) & p(ap(ap(c_2Ewellorder_2Eorderiso(A_27c,A_27d),V2a0),V3b0)) ) => ( p(ap(ap(c_2Ewellorder_2Eorderlt(A_27a,A_27c),V0x0),V2a0)) <=> p(ap(ap(c_2Ewellorder_2Eorderlt(A_27b,A_27d),V1y0),V3b0)) ) ) ) ) ) ))))))).
fof(conj_thm_2Eordinal_2Epolyform__exists,conjecture,( ! [A_27a]: ( ne(A_27a) => ! [V0a] : ( mem(V0a,ty_2Eordinal_2Eordinal(A_27a)) => ! [V1b] : ( mem(V1b,ty_2Eordinal_2Eordinal(A_27a)) => ( p(ap(ap(c_2Eordinal_2Eordlt(A_27a),ap(c_2Eordinal_2EfromNat(A_27a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0a)) => ? [V2ces] : ( mem(V2ces,ty_2Elist_2Elist(ty_2Epair_2Eprod(ty_2Eordinal_2Eordinal(A_27a),ty_2Eordinal_2Eordinal(A_27a)))) & ( p(ap(ap(c_2Eordinal_2Eis__polyform(A_27a,A_27a),V0a),V2ces)) & ( V1b = ap(ap(c_2Eordinal_2Eeval__poly(A_27a),V0a),V2ces) ) ) ) ) ) )))).
