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_2Ecombin_2Eo,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [A_27c] : ( ne(A_27c) => mem(c_2Ecombin_2Eo(A_27a,A_27b,A_27c),arr(arr(A_27c,A_27b),arr(arr(A_27a,A_27c),arr(A_27a,A_27b)))) ) ) ) )).
fof(mem_c_2Ecombin_2EI,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Ecombin_2EI(A_27a),arr(A_27a,A_27a)) ) )).
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,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_2EiiSUC,axiom,( mem(c_2Enumeral_2EiiSUC,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Enumeral_2EiZ,axiom,( mem(c_2Enumeral_2EiZ,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Ebool_2ET,axiom,( mem(c_2Ebool_2ET,bool) )).
fof(ax_true_p,axiom,( p(c_2Ebool_2ET) )).
fof(ne_ty_2Epair_2Eprod,axiom,( ! [A0] : ( ne(A0) => ( ! [A1] : ( ne(A1) => ne(ty_2Epair_2Eprod(A0,A1)) ) ) ) )).
fof(mem_c_2Epair_2EUNCURRY,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [A_27c] : ( ne(A_27c) => mem(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),arr(arr(A_27a,arr(A_27b,A_27c)),arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27c))) ) ) ) )).
fof(mem_c_2Epred__set_2ESURJ,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Epred__set_2ESURJ(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),bool)))) ) ) )).
fof(mem_c_2Epred__set_2EINJ,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Epred__set_2EINJ(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),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_2Epair_2EFST,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Epair_2EFST(A_27a,A_27b),arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27a)) ) ) )).
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_2Earithmetic_2EBIT1,axiom,( mem(c_2Earithmetic_2EBIT1,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(ne_ty_2Erealax_2Ereal,axiom,( ne(ty_2Erealax_2Ereal) )).
fof(mem_c_2Erealax_2Einv,axiom,( mem(c_2Erealax_2Einv,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) )).
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_2Ereal_2E_2F,axiom,( mem(c_2Ereal_2E_2F,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))) )).
fof(mem_c_2Erealax_2Ereal__neg,axiom,( mem(c_2Erealax_2Ereal__neg,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) )).
fof(mem_c_2Ebool_2EF,axiom,( mem(c_2Ebool_2EF,bool) )).
fof(ax_false_p,axiom,( ~ p(c_2Ebool_2EF) )).
fof(mem_c_2Ebool_2E_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_2Ereal_2Ereal__sub,axiom,( mem(c_2Ereal_2Ereal__sub,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))) )).
fof(mem_c_2Ereal_2Eabs,axiom,( mem(c_2Ereal_2Eabs,arr(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) )).
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_2Eseq_2E_2D_2D_3E,axiom,( mem(c_2Eseq_2E_2D_2D_3E,arr(arr(ty_2Enum_2Enum,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_2Earithmetic_2EMAX,axiom,( mem(c_2Earithmetic_2EMAX,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) )).
fof(mem_c_2Ereal_2Ereal__lte,axiom,( mem(c_2Ereal_2Ereal__lte,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,bool))) )).
fof(mem_c_2Eseq_2Esuminf,axiom,( mem(c_2Eseq_2Esuminf,arr(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal)) )).
fof(mem_c_2Eseq_2Esummable,axiom,( mem(c_2Eseq_2Esummable,arr(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),bool)) )).
fof(mem_c_2Eseq_2Esums,axiom,( mem(c_2Eseq_2Esums,arr(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool))) )).
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_2Erealax_2Ereal__lt,axiom,( mem(c_2Erealax_2Ereal__lt,arr(ty_2Erealax_2Ereal,arr(ty_2Erealax_2Ereal,bool))) )).
fof(mem_c_2Earithmetic_2E_2B,axiom,( mem(c_2Earithmetic_2E_2B,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) )).
fof(mem_c_2Earithmetic_2E_3C_3D,axiom,( mem(c_2Earithmetic_2E_3C_3D,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) )).
fof(mem_c_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_2Ereal_2Ereal__of__num,axiom,( mem(c_2Ereal_2Ereal__of__num,arr(ty_2Enum_2Enum,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_2Enum_2E0,axiom,( mem(c_2Enum_2E0,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_2Ereal_2Esum,axiom,( mem(c_2Ereal_2Esum,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal),ty_2Erealax_2Ereal))) )).
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_2Enum_2ESUC,axiom,( mem(c_2Enum_2ESUC,arr(ty_2Enum_2Enum,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_2EK,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Ecombin_2EK(A_27a,A_27b),arr(A_27a,arr(A_27b,A_27a))) ) ) )).
fof(mem_c_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_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_2Epred__set_2Ecount,axiom,( mem(c_2Epred__set_2Ecount,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,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_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_2ECROSS,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Epred__set_2ECROSS(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)))) ) ) )).
fof(mem_c_2Epred__set_2EUNIV,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Epred__set_2EUNIV(A_27a),arr(A_27a,bool)) ) )).
fof(mem_c_2Epred__set_2EBIJ,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Epred__set_2EBIJ(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),bool)))) ) ) )).
fof(mem_c_2Emin_2E_3D_3D_3E,axiom,( mem(c_2Emin_2E_3D_3D_3E,arr(bool,arr(bool,bool))) )).
fof(ax_imp_p,axiom,( ! [Q] : ( mem(Q,bool) => ! [R] : ( mem(R,bool) => ( p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R)) <=> ( p(Q) => p(R) ) ) ) ) )).
fof(mem_c_2Ebool_2E_21,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Ebool_2E_21(A_27a),arr(arr(A_27a,bool),bool)) ) )).
fof(ax_all_p,axiom,( ! [A] : ( ne(A) => ! [Q] : ( mem(Q,arr(A,bool)) => ( p(ap(c_2Ebool_2E_21(A),Q)) <=> ! [X] : ( mem(X,A) => p(ap(Q,X)) ) ) ) ) )).
fof(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__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_2ELESS__EQ__MONO,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0n)),ap(c_2Enum_2ESUC,V1m))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m)) ) ) ))).
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_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_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_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_2EGREATER__EQ,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3E_3D,V0n),V1m)) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V0n)) ) ) ))).
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_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(ax_thm_2Ebool_2EBOOL__CASES__AX,axiom, ! [V0t] : ( mem(V0t,bool) => ( ( p(V0t) <=> $true ) | ( p(V0t) <=> $false ) ) )).
fof(ax_thm_2Ebool_2EETA__AX,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0t] : ( mem(V0t,arr(A_27a,A_27b)) => ( f31(A_27b,A_27a,V0t) = V0t ) ) ) ) )).
fof(ax_thm_2Ebool_2ESELECT__AX,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1x] : ( mem(V1x,A_27a) => ( p(ap(V0P,V1x)) => p(ap(V0P,ap(c_2Emin_2E_40(A_27a),V0P))) ) ) ) ) )).
fof(conj_thm_2Ebool_2ETRUTH,lemma,($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_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_2EIMP__F,lemma,(! [V0t] : ( mem(V0t,bool) => ( ( p(V0t) => $false ) => ( ~~ p(V0t) ) ) ))).
fof(conj_thm_2Ebool_2EF__IMP,lemma,(! [V0t] : ( mem(V0t,bool) => ( ( ~~ p(V0t) ) => ( p(V0t) => $false ) ) ))).
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_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_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_2EEXISTS__OR__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__OR__EXISTS__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__OR__EXISTS__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_2ERIGHT__EXISTS__AND__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,bool) => ! [V1Q] : ( mem(V1Q,arr(A_27a,bool)) => ( ( ? [V2x] : ( mem(V2x,A_27a) & ( p(V0P) & p(ap(V1Q,V2x)) ) ) ) <=> ( p(V0P) & ? [V3x] : ( mem(V3x,A_27a) & p(ap(V1Q,V3x)) ) ) ) ) )))).
fof(conj_thm_2Ebool_2ERIGHT__FORALL__OR__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,bool) => ! [V1Q] : ( mem(V1Q,arr(A_27a,bool)) => ( ( ! [V2x] : ( mem(V2x,A_27a) => ( p(V0P) | p(ap(V1Q,V2x)) ) ) ) <=> ( p(V0P) | ! [V3x] : ( mem(V3x,A_27a) => p(ap(V1Q,V3x)) ) ) ) ) )))).
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_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_2EDISJ__SYM,lemma,(! [V0A] : ( mem(V0A,bool) => ! [V1B] : ( mem(V1B,bool) => ( ( p(V0A) | p(V1B) ) <=> ( p(V1B) | p(V0A) ) ) ) ))).
fof(conj_thm_2Ebool_2EDE__MORGAN__THM,lemma,(! [V0A] : ( mem(V0A,bool) => ! [V1B] : ( mem(V1B,bool) => ( ( ( ~~ ( p(V0A) & p(V1B) ) ) <=> ( ( ~~ p(V0A) ) | ( ~~ p(V1B) ) ) ) & ( ( ~~ ( p(V0A) | p(V1B) ) ) <=> ( ( ~~ p(V0A) ) & ( ~~ p(V1B) ) ) ) ) ) ))).
fof(conj_thm_2Ebool_2EIMP__DISJ__THM,lemma,(! [V0A] : ( mem(V0A,bool) => ! [V1B] : ( mem(V1B,bool) => ( ( p(V0A) => p(V1B) ) <=> ( ( ~~ p(V0A) ) | p(V1B) ) ) ) ))).
fof(conj_thm_2Ebool_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_2ECOND__RATOR,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0b] : ( mem(V0b,bool) => ! [V1f] : ( mem(V1f,arr(A_27a,A_27b)) => ! [V2g] : ( mem(V2g,arr(A_27a,A_27b)) => ! [V3x] : ( mem(V3x,A_27a) => ( ap(ap(ap(ap(c_2Ebool_2ECOND(arr(A_27a,A_27b)),V0b),V1f),V2g),V3x) = ap(ap(ap(c_2Ebool_2ECOND(A_27b),V0b),ap(V1f,V3x)),ap(V2g,V3x)) ) ) ) ) ))))).
fof(conj_thm_2Ebool_2ECOND__RAND,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1b] : ( mem(V1b,bool) => ! [V2x] : ( mem(V2x,A_27a) => ! [V3y] : ( mem(V3y,A_27a) => ( ap(V0f,ap(ap(ap(c_2Ebool_2ECOND(A_27a),V1b),V2x),V3y)) = ap(ap(ap(c_2Ebool_2ECOND(A_27b),V1b),ap(V0f,V2x)),ap(V0f,V3y)) ) ) ) ) ))))).
fof(conj_thm_2Ebool_2ECOND__EXPAND,lemma,(! [V0b] : ( mem(V0b,bool) => ! [V1t1] : ( mem(V1t1,bool) => ! [V2t2] : ( mem(V2t2,bool) => ( p(ap(ap(ap(c_2Ebool_2ECOND(bool),V0b),V1t1),V2t2)) <=> ( ( ( ~~ p(V0b) ) | p(V1t1) ) & ( p(V0b) | p(V2t2) ) ) ) ) ) ))).
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_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_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_2Eo__THM,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) =>  ! [A_27c]: ( ne(A_27c) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1g] : ( mem(V1g,arr(A_27c,A_27a)) => ! [V2x] : ( mem(V2x,A_27c) => ( ap(ap(ap(c_2Ecombin_2Eo(A_27c,A_27b,A_27a),V0f),V1g),V2x) = ap(V0f,ap(V1g,V2x)) ) ) ) )))))).
fof(conj_thm_2Ecombin_2EI__THM,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ( ap(c_2Ecombin_2EI(A_27a),V0x) = V0x ) )))).
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__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__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_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_2EABS__PAIR__THM,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_2EFST,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1y] : ( mem(V1y,A_27b) => ( ap(c_2Epair_2EFST(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y)) = V0x ) ) ))))).
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_2Epair_2EUNCURRY__DEF,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) =>  ! [A_27c]: ( ne(A_27c) => ! [V0f] : ( mem(V0f,arr(A_27a,arr(A_27b,A_27c))) => ! [V1x] : ( mem(V1x,A_27a) => ! [V2y] : ( mem(V2y,A_27b) => ( ap(ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V2y)) = ap(ap(V0f,V1x),V2y) ) ) ) )))))).
fof(conj_thm_2Epred__set_2EIN__UNIV,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),c_2Epred__set_2EUNIV(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__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(ax_thm_2Epred__set_2EINJ__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ! [V2t] : ( mem(V2t,arr(A_27b,bool)) => ( p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V1s),V2t)) <=> ( ( ! [V3x] : ( mem(V3x,A_27a) => ( p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V1s)) => p(ap(ap(c_2Ebool_2EIN(A_27b),ap(V0f,V3x)),V2t)) ) ) ) & ! [V4x] : ( mem(V4x,A_27a) => ! [V5y] : ( mem(V5y,A_27a) => ( ( p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),V1s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V5y),V1s)) ) => ( ( ap(V0f,V4x) = ap(V0f,V5y) ) => ( V4x = V5y ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(ax_thm_2Epred__set_2EBIJ__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1s] : ( mem(V1s,arr(A_27a,bool)) => ! [V2t] : ( mem(V2t,arr(A_27b,bool)) => ( p(ap(ap(ap(c_2Epred__set_2EBIJ(A_27a,A_27b),V0f),V1s),V2t)) <=> ( p(ap(ap(ap(c_2Epred__set_2EINJ(A_27a,A_27b),V0f),V1s),V2t)) & p(ap(ap(ap(c_2Epred__set_2ESURJ(A_27a,A_27b),V0f),V1s),V2t)) ) ) ) ) ) ) ) )).
fof(conj_thm_2Epred__set_2EIN__COUNT,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V0m),ap(c_2Epred__set_2Ecount,V1n))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) ) ) ))).
fof(conj_thm_2Epred__set_2EIN__CROSS,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1Q] : ( mem(V1Q,arr(A_27b,bool)) => ! [V2x] : ( mem(V2x,ty_2Epair_2Eprod(A_27a,A_27b)) => ( p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),V2x),ap(ap(c_2Epred__set_2ECROSS(A_27a,A_27b),V0P),V1Q))) <=> ( p(ap(ap(c_2Ebool_2EIN(A_27a),ap(c_2Epair_2EFST(A_27a,A_27b),V2x)),V0P)) & p(ap(ap(c_2Ebool_2EIN(A_27b),ap(c_2Epair_2ESND(A_27a,A_27b),V2x)),V1Q)) ) ) ) ) ))))).
fof(conj_thm_2Eprim__rec_2ELESS__REFL,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ~~ p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V0n)) ) ))).
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_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__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__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(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(ax_thm_2Ereal_2Ereal__div,axiom, ! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(ap(c_2Ereal_2E_2F,V0x),V1y) = ap(ap(c_2Erealax_2Ereal__mul,V0x),ap(c_2Erealax_2Einv,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__RINV,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ( ~~ ( V0x = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) => ( ap(ap(c_2Erealax_2Ereal__mul,V0x),ap(c_2Erealax_2Einv,V0x)) = ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ) ))).
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__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__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__RADD,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_2Erealax_2Ereal__add,V0x),V2z)),ap(ap(c_2Erealax_2Ereal__add,V1y),V2z))) <=> p(ap(ap(c_2Ereal_2Ereal__lte,V0x),V1y)) ) ) ) ))).
fof(conj_thm_2Ereal_2EREAL__INJ,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ( ap(c_2Ereal_2Ereal__of__num,V0m) = ap(c_2Ereal_2Ereal__of__num,V1n) ) <=> ( V0m = V1n ) ) ) ))).
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__NZ__IMP__LT,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ( ~~ ( V0n = c_2Enum_2E0 ) ) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Ereal_2Ereal__of__num,V0n))) ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__HALF1,lemma,(! [V0d] : ( mem(V0d,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(c_2Ereal_2E_2F,V0d),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))) <=> p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V0d)) ) ))).
fof(conj_thm_2Ereal_2EREAL__HALF__DOUBLE,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2E_2F,V0x),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))),ap(ap(c_2Ereal_2E_2F,V0x),ap(c_2Ereal_2Ereal__of__num,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) = V0x ) ))).
fof(conj_thm_2Ereal_2EREAL__LT__DIV,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_2Ereal_2E_2F,V0x),V1y))) ) ) ))).
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__SUB,lemma,(! [V0x] : ( mem(V0x,ty_2Erealax_2Ereal) => ! [V1y] : ( mem(V1y,ty_2Erealax_2Ereal) => ( ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,V0x),V1y)) = ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,V1y),V0x)) ) ) ))).
fof(conj_thm_2Ereal_2Esum,lemma,(( ( ! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1f] : ( mem(V1f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ( ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0n),c_2Enum_2E0)),V1f) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ) ) & ! [V2n] : ( mem(V2n,ty_2Enum_2Enum) => ! [V3m] : ( mem(V3m,ty_2Enum_2Enum) => ! [V4f] : ( mem(V4f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ( ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2n),ap(c_2Enum_2ESUC,V3m))),V4f) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2n),V3m)),V4f)),ap(V4f,ap(ap(c_2Earithmetic_2E_2B,V2n),V3m))) ) ) ) ) ))).
fof(conj_thm_2Ereal_2ESUM__LE,lemma,(! [V0f] : ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ! [V1g] : ( mem(V1g,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ! [V2m] : ( mem(V2m,ty_2Enum_2Enum) => ! [V3n] : ( mem(V3n,ty_2Enum_2Enum) => ( ( ! [V4r] : ( mem(V4r,ty_2Enum_2Enum) => ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V2m),V4r)) & p(ap(ap(c_2Eprim__rec_2E_3C,V4r),ap(ap(c_2Earithmetic_2E_2B,V3n),V2m))) ) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(V0f,V4r)),ap(V1g,V4r))) ) ) ) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2m),V3n)),V0f)),ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2m),V3n)),V1g))) ) ) ) ) ))).
fof(conj_thm_2Ereal_2ESUM__ZERO,lemma,(! [V0f] : ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ! [V1N] : ( mem(V1N,ty_2Enum_2Enum) => ( ( ! [V2n] : ( mem(V2n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3E_3D,V2n),V1N)) => ( ap(V0f,V2n) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ) ) => ! [V3m] : ( mem(V3m,ty_2Enum_2Enum) => ! [V4n] : ( mem(V4n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3E_3D,V3m),V1N)) => ( ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V3m),V4n)),V0f) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ) ) ) ) ))).
fof(conj_thm_2Ereal_2ESUM__ADD,lemma,(! [V0f] : ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ! [V1g] : ( mem(V1g,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ! [V2m] : ( mem(V2m,ty_2Enum_2Enum) => ! [V3n] : ( mem(V3n,ty_2Enum_2Enum) => ( ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2m),V3n)),f2730(V0f,V1g)) = ap(ap(c_2Erealax_2Ereal__add,ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2m),V3n)),V0f)),ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2m),V3n)),V1g)) ) ) ) ) ))).
fof(conj_thm_2Ereal_2ESUM__0,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0m),V1n)),k(ty_2Enum_2Enum,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0))) = ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0) ) ) ))).
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__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_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_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_2Eseq_2ESEQ,lemma,(! [V0x] : ( mem(V0x,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ! [V1x0] : ( mem(V1x0,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Eseq_2E_2D_2D_3E,V0x),V1x0)) <=> ! [V2e] : ( mem(V2e,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V2e)) => ? [V3N] : ( mem(V3N,ty_2Enum_2Enum) & ! [V4n] : ( mem(V4n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3E_3D,V4n),V3N)) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Eabs,ap(ap(c_2Ereal_2Ereal__sub,ap(V0x,V4n)),V1x0))),V2e)) ) ) ) ) ) ) ) ))).
fof(ax_thm_2Eseq_2Esums,axiom, ! [V0f] : ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ! [V1s] : ( mem(V1s,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Eseq_2Esums,V0f),V1s)) <=> p(ap(ap(c_2Eseq_2E_2D_2D_3E,f2880(V0f)),V1s)) ) ) )).
fof(conj_thm_2Eseq_2ESUMMABLE__SUM,lemma,(! [V0f] : ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ( p(ap(c_2Eseq_2Esummable,V0f)) => p(ap(ap(c_2Eseq_2Esums,V0f),ap(c_2Eseq_2Esuminf,V0f))) ) ))).
fof(conj_thm_2Eseq_2ESER__POS__LE,lemma,(! [V0f] : ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ( p(ap(c_2Eseq_2Esummable,V0f)) & ! [V2m] : ( mem(V2m,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2m)) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(V0f,V2m))) ) ) ) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Enum_2E0),V1n)),V0f)),ap(c_2Eseq_2Esuminf,V0f))) ) ) ))).
fof(conj_thm_2Eseq_2EINCREASING__SEQ,lemma,(! [V0f] : ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ! [V1l] : ( mem(V1l,ty_2Erealax_2Ereal) => ( ( ( ! [V2n] : ( mem(V2n,ty_2Enum_2Enum) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(V0f,V2n)),ap(V0f,ap(c_2Enum_2ESUC,V2n)))) ) ) & ( ( ! [V3n] : ( mem(V3n,ty_2Enum_2Enum) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(V0f,V3n)),V1l)) ) ) & ! [V4e] : ( mem(V4e,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Erealax_2Ereal__lt,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),V4e)) => ? [V5n] : ( mem(V5n,ty_2Enum_2Enum) & p(ap(ap(c_2Erealax_2Ereal__lt,V1l),ap(ap(c_2Erealax_2Ereal__add,ap(V0f,V5n)),V4e))) ) ) ) ) ) => p(ap(ap(c_2Eseq_2E_2D_2D_3E,V0f),V1l)) ) ) ))).
fof(conj_thm_2Eseq_2EX__LE__MAX,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ! [V2k] : ( mem(V2k,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V2k),ap(ap(c_2Earithmetic_2EMAX,V0m),V1n))) <=> ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V2k),V0m)) | p(ap(ap(c_2Earithmetic_2E_3C_3D,V2k),V1n)) ) ) ) ) ))).
fof(conj_thm_2Eseq_2ESER__POS,lemma,(! [V0f] : ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ( ( p(ap(c_2Eseq_2Esummable,V0f)) & ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(V0f,V1n))) ) ) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(c_2Eseq_2Esuminf,V0f))) ) ))).
fof(conj_thm_2Eseq_2ESUMS__EQ,lemma,(! [V0f] : ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ! [V1x] : ( mem(V1x,ty_2Erealax_2Ereal) => ( p(ap(ap(c_2Eseq_2Esums,V0f),V1x)) <=> ( p(ap(c_2Eseq_2Esummable,V0f)) & ( ap(c_2Eseq_2Esuminf,V0f) = V1x ) ) ) ) ))).
fof(conj_thm_2Eseq_2ESUM__PICK,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1k] : ( mem(V1k,ty_2Enum_2Enum) => ! [V2x] : ( mem(V2x,ty_2Erealax_2Ereal) => ( ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Enum_2E0),V0n)),f2890(V2x,V1k)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Erealax_2Ereal),ap(ap(c_2Eprim__rec_2E_3C,V1k),V0n)),V2x),ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)) ) ) ) ))).
fof(conj_thm_2Eseq_2ESUM__LT,lemma,(! [V0f] : ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ! [V1g] : ( mem(V1g,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ! [V2m] : ( mem(V2m,ty_2Enum_2Enum) => ! [V3n] : ( mem(V3n,ty_2Enum_2Enum) => ( ( ( ! [V4r] : ( mem(V4r,ty_2Enum_2Enum) => ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,V2m),V4r)) & p(ap(ap(c_2Eprim__rec_2E_3C,V4r),ap(ap(c_2Earithmetic_2E_2B,V3n),V2m))) ) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(V0f,V4r)),ap(V1g,V4r))) ) ) ) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V3n)) ) => p(ap(ap(c_2Erealax_2Ereal__lt,ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2m),V3n)),V0f)),ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2m),V3n)),V1g))) ) ) ) ) ))).
fof(conj_thm_2Eseq_2ESUM__CONST__R,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1r] : ( mem(V1r,ty_2Erealax_2Ereal) => ( ap(ap(c_2Ereal_2Esum,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Enum_2E0),V0n)),ap(c_2Ecombin_2EK(ty_2Erealax_2Ereal,ty_2Enum_2Enum),V1r)) = ap(ap(c_2Erealax_2Ereal__mul,ap(c_2Ereal_2Ereal__of__num,V0n)),V1r) ) ) ))).
fof(conj_thm_2Eseq_2ELT__SUC,lemma,(! [V0a] : ( mem(V0a,ty_2Enum_2Enum) => ! [V1b] : ( mem(V1b,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,V0a),ap(c_2Enum_2ESUC,V1b))) <=> ( p(ap(ap(c_2Eprim__rec_2E_3C,V0a),V1b)) | ( V0a = V1b ) ) ) ) ))).
fof(conj_thm_2Eseq_2EK__PARTIAL,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0x] : ( mem(V0x,A_27a) => ( ap(c_2Ecombin_2EK(A_27a,A_27b),V0x) = k(A_27b,V0x) ) ))))).
fof(conj_thm_2Eseq_2ENUM__2D__BIJ__BIG__SQUARE,lemma,(! [V0f] : ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))) => ! [V1N] : ( mem(V1N,ty_2Enum_2Enum) => ( p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V0f),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))) => ? [V2k] : ( mem(V2k,ty_2Enum_2Enum) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V0f),ap(c_2Epred__set_2Ecount,V1N))),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Epred__set_2Ecount,V2k)),ap(c_2Epred__set_2Ecount,V2k)))) ) ) ) ))).
fof(conj_thm_2Eseq_2ENUM__2D__BIJ__SMALL__SQUARE,lemma,(! [V0f] : ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))) => ! [V1k] : ( mem(V1k,ty_2Enum_2Enum) => ( p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V0f),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))) => ? [V2N] : ( mem(V2N,ty_2Enum_2Enum) & p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Epred__set_2Ecount,V1k)),ap(c_2Epred__set_2Ecount,V1k))),ap(ap(c_2Epred__set_2EIMAGE(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V0f),ap(c_2Epred__set_2Ecount,V2N)))) ) ) ) ))).
fof(conj_thm_2Eseq_2ESUMINF__2D,conjecture,(! [V0f] : ( mem(V0f,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal))) => ! [V1g] : ( mem(V1g,arr(ty_2Enum_2Enum,ty_2Erealax_2Ereal)) => ! [V2h] : ( mem(V2h,arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))) => ( ( ( ! [V3m] : ( mem(V3m,ty_2Enum_2Enum) => ! [V4n] : ( mem(V4n,ty_2Enum_2Enum) => p(ap(ap(c_2Ereal_2Ereal__lte,ap(c_2Ereal_2Ereal__of__num,c_2Enum_2E0)),ap(ap(V0f,V3m),V4n))) ) ) ) & ( ( ! [V5n] : ( mem(V5n,ty_2Enum_2Enum) => p(ap(ap(c_2Eseq_2Esums,ap(V0f,V5n)),ap(V1g,V5n))) ) ) & ( p(ap(c_2Eseq_2Esummable,V1g)) & p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V2h),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))) ) ) ) => p(ap(ap(c_2Eseq_2Esums,ap(ap(c_2Ecombin_2Eo(ty_2Enum_2Enum,ty_2Erealax_2Ereal,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(c_2Epair_2EUNCURRY(ty_2Enum_2Enum,ty_2Enum_2Enum,ty_2Erealax_2Ereal),V0f)),V2h)),ap(c_2Eseq_2Esuminf,V1g))) ) ) ) ))).
