include('Axioms/HL4001+2.ax').
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_2ETL,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Elist_2ETL(A_27a),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))) ) )).
fof(mem_c_2Elist_2EAPPEND,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Elist_2EAPPEND(A_27a),arr(ty_2Elist_2Elist(A_27a),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a)))) ) )).
fof(mem_c_2Elist_2EFRONT,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Elist_2EFRONT(A_27a),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))) ) )).
fof(mem_c_2Elist_2EREV,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Elist_2EREV(A_27a),arr(ty_2Elist_2Elist(A_27a),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(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_3D,axiom,( mem(c_2Earithmetic_2E_3E_3D,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) )).
fof(mem_c_2Enumeral_2EiiSUC,axiom,( mem(c_2Enumeral_2EiiSUC,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Enumeral_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(mem_c_2Enumeral_2Etexp__help,axiom,( mem(c_2Enumeral_2Etexp__help,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) )).
fof(mem_c_2Earithmetic_2E_2D,axiom,( mem(c_2Earithmetic_2E_2D,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) )).
fof(mem_c_2Enumeral__bit_2EiMOD__2EXP,axiom,( mem(c_2Enumeral__bit_2EiMOD__2EXP,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) )).
fof(mem_c_2Enumeral_2EiDUB,axiom,( mem(c_2Enumeral_2EiDUB,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Ebit_2EDIV__2EXP,axiom,( mem(c_2Ebit_2EDIV__2EXP,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) )).
fof(mem_c_2Enumeral__bit_2ESFUNPOW,axiom,( mem(c_2Enumeral__bit_2ESFUNPOW,arr(arr(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)))) )).
fof(mem_c_2Enumeral__bit_2EiDIV2,axiom,( mem(c_2Enumeral__bit_2EiDIV2,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Enumeral__bit_2EiSUC,axiom,( mem(c_2Enumeral__bit_2EiSUC,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Enumeral__bit_2EFDUB,axiom,( mem(c_2Enumeral__bit_2EFDUB,arr(arr(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) )).
fof(mem_c_2Earithmetic_2E_2A,axiom,( mem(c_2Earithmetic_2E_2A,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) )).
fof(mem_c_2Earithmetic_2EMOD,axiom,( mem(c_2Earithmetic_2EMOD,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) )).
fof(mem_c_2Earithmetic_2E_3E,axiom,( mem(c_2Earithmetic_2E_3E,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) )).
fof(mem_c_2Ebit_2ETIMES__2EXP,axiom,( mem(c_2Ebit_2ETIMES__2EXP,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) )).
fof(mem_c_2Ebit_2EMOD__2EXP,axiom,( mem(c_2Ebit_2EMOD__2EXP,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) )).
fof(mem_c_2Earithmetic_2E_2B,axiom,( mem(c_2Earithmetic_2E_2B,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) )).
fof(mem_c_2Enumposrep_2El2n,axiom,( mem(c_2Enumposrep_2El2n,arr(ty_2Enum_2Enum,arr(ty_2Elist_2Elist(ty_2Enum_2Enum),ty_2Enum_2Enum))) )).
fof(ne_ty_2Epair_2Eprod,axiom,( ! [A0] : ( ne(A0) => ( ! [A1] : ( ne(A1) => ne(ty_2Epair_2Eprod(A0,A1)) ) ) ) )).
fof(mem_c_2Ebit_2EDIVMOD__2EXP,axiom,( mem(c_2Ebit_2EDIVMOD__2EXP,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))) )).
fof(mem_c_2Ebool_2ELET,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Ebool_2ELET(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) ) ) )).
fof(mem_c_2Enumposrep_2En2l,axiom,( mem(c_2Enumposrep_2En2l,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Elist_2Elist(ty_2Enum_2Enum)))) )).
fof(mem_c_2Epair_2E_2C,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Epair_2E_2C(A_27a,A_27b),arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27a,A_27b)))) ) ) )).
fof(mem_c_2Epair_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_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(ne_ty_2Estring_2Echar,axiom,( ne(ty_2Estring_2Echar) )).
fof(mem_c_2EASCIInumbers_2Es2n,axiom,( mem(c_2EASCIInumbers_2Es2n,arr(ty_2Enum_2Enum,arr(arr(ty_2Estring_2Echar,ty_2Enum_2Enum),arr(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Enum_2Enum)))) )).
fof(mem_c_2EASCIInumbers_2En2s,axiom,( mem(c_2EASCIInumbers_2En2s,arr(ty_2Enum_2Enum,arr(arr(ty_2Enum_2Enum,ty_2Estring_2Echar),arr(ty_2Enum_2Enum,ty_2Elist_2Elist(ty_2Estring_2Echar))))) )).
fof(mem_c_2Epatricia__casts_2ESKIP1,axiom,( mem(c_2Epatricia__casts_2ESKIP1,arr(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Elist_2Elist(ty_2Estring_2Echar))) )).
fof(mem_c_2Epatricia__casts_2Enum__to__string,axiom,( mem(c_2Epatricia__casts_2Enum__to__string,arr(ty_2Enum_2Enum,ty_2Elist_2Elist(ty_2Estring_2Echar))) )).
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_2Epatricia__casts_2Estring__to__num,axiom,( mem(c_2Epatricia__casts_2Estring__to__num,arr(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Enum_2Enum)) )).
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_2Elogroot_2ELOG,axiom,( mem(c_2Elogroot_2ELOG,arr(ty_2Enum_2Enum,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_2EDIV,axiom,( mem(c_2Earithmetic_2EDIV,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_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_2Elist_2EMAP,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Elist_2EMAP(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27b)))) ) ) )).
fof(mem_c_2Elist_2ELAST,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Elist_2ELAST(A_27a),arr(ty_2Elist_2Elist(A_27a),A_27a)) ) )).
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_2Eprim__rec_2EPRE,axiom,( mem(c_2Eprim__rec_2EPRE,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
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_2Elist_2ENIL,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Elist_2ENIL(A_27a),ty_2Elist_2Elist(A_27a)) ) )).
fof(mem_c_2Elist_2EREVERSE,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Elist_2EREVERSE(A_27a),arr(ty_2Elist_2Elist(A_27a),ty_2Elist_2Elist(A_27a))) ) )).
fof(mem_c_2Elist_2EEVERY,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Elist_2EEVERY(A_27a),arr(arr(A_27a,bool),arr(ty_2Elist_2Elist(A_27a),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_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_2Ecombin_2EFAIL,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => mem(c_2Ecombin_2EFAIL(A_27a,A_27b),arr(A_27a,arr(A_27b,A_27a))) ) ) )).
fof(mem_c_2Ebool_2ECOND,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Ebool_2ECOND(A_27a),arr(bool,arr(A_27a,arr(A_27a,A_27a)))) ) )).
fof(mem_c_2Estring_2EORD,axiom,( mem(c_2Estring_2EORD,arr(ty_2Estring_2Echar,ty_2Enum_2Enum)) )).
fof(mem_c_2Earithmetic_2EZERO,axiom,( mem(c_2Earithmetic_2EZERO,ty_2Enum_2Enum) )).
fof(mem_c_2Earithmetic_2EBIT1,axiom,( mem(c_2Earithmetic_2EBIT1,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Earithmetic_2EBIT2,axiom,( mem(c_2Earithmetic_2EBIT2,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Earithmetic_2ENUMERAL,axiom,( mem(c_2Earithmetic_2ENUMERAL,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) )).
fof(mem_c_2Eprim__rec_2E_3C,axiom,( mem(c_2Eprim__rec_2E_3C,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) )).
fof(mem_c_2Estring_2ECHR,axiom,( mem(c_2Estring_2ECHR,arr(ty_2Enum_2Enum,ty_2Estring_2Echar)) )).
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_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_2Ebool_2E_3F,axiom,( ! [A_27a] : ( ne(A_27a) => mem(c_2Ebool_2E_3F(A_27a),arr(arr(A_27a,bool),bool)) ) )).
fof(ax_ex_p,axiom,( ! [A] : ( ne(A) => ! [Q] : ( mem(Q,arr(A,bool)) => ( p(ap(c_2Ebool_2E_3F(A),Q)) <=> ? [X] : ( mem(X,A) & p(ap(Q,X)) ) ) ) ) )).
fof(mem_c_2Ebool_2E_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(ax_thm_2EASCIInumbers_2Es2n__def,axiom, ! [V0b] : ( mem(V0b,ty_2Enum_2Enum) => ! [V1f] : ( mem(V1f,arr(ty_2Estring_2Echar,ty_2Enum_2Enum)) => ! [V2s] : ( mem(V2s,ty_2Elist_2Elist(ty_2Estring_2Echar)) => ( ap(ap(ap(c_2EASCIInumbers_2Es2n,V0b),V1f),V2s) = ap(ap(c_2Enumposrep_2El2n,V0b),ap(ap(c_2Elist_2EMAP(ty_2Estring_2Echar,ty_2Enum_2Enum),V1f),ap(c_2Elist_2EREVERSE(ty_2Estring_2Echar),V2s))) ) ) ) )).
fof(ax_thm_2EASCIInumbers_2En2s__def,axiom, ! [V0b] : ( mem(V0b,ty_2Enum_2Enum) => ! [V1f] : ( mem(V1f,arr(ty_2Enum_2Enum,ty_2Estring_2Echar)) => ! [V2n] : ( mem(V2n,ty_2Enum_2Enum) => ( ap(ap(ap(c_2EASCIInumbers_2En2s,V0b),V1f),V2n) = ap(c_2Elist_2EREVERSE(ty_2Estring_2Echar),ap(ap(c_2Elist_2EMAP(ty_2Enum_2Enum,ty_2Estring_2Echar),V1f),ap(ap(c_2Enumposrep_2En2l,V0b),V2n))) ) ) ) )).
fof(conj_thm_2EASCIInumbers_2Es2n__n2s,lemma,(! [V0c2n] : ( mem(V0c2n,arr(ty_2Estring_2Echar,ty_2Enum_2Enum)) => ! [V1n2c] : ( mem(V1n2c,arr(ty_2Enum_2Enum,ty_2Estring_2Echar)) => ! [V2b] : ( mem(V2b,ty_2Enum_2Enum) => ! [V3n] : ( mem(V3n,ty_2Enum_2Enum) => ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V2b)) & ! [V4x] : ( mem(V4x,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,V4x),V2b)) => ( ap(V0c2n,ap(V1n2c,V4x)) = V4x ) ) ) ) => ( ap(ap(ap(c_2EASCIInumbers_2Es2n,V2b),V0c2n),ap(ap(ap(c_2EASCIInumbers_2En2s,V2b),V1n2c),V3n)) = V3n ) ) ) ) ) ))).
fof(ax_thm_2Earithmetic_2EGREATER__DEF,axiom, ! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3E,V0m),V1n)) <=> p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m)) ) ) )).
fof(conj_thm_2Earithmetic_2ENORM__0,lemma,(( ap(c_2Earithmetic_2ENUMERAL,c_2Earithmetic_2EZERO) = c_2Enum_2E0 ))).
fof(conj_thm_2Earithmetic_2EADD__CLAUSES,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ( ap(ap(c_2Earithmetic_2E_2B,c_2Enum_2E0),V0m) = V0m ) & ( ( ap(ap(c_2Earithmetic_2E_2B,V0m),c_2Enum_2E0) = V0m ) & ( ( ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enum_2ESUC,V0m)),V1n) = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)) ) & ( ap(ap(c_2Earithmetic_2E_2B,V0m),ap(c_2Enum_2ESUC,V1n)) = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)) ) ) ) ) ) ))).
fof(conj_thm_2Earithmetic_2EADD__SYM,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2B,V0m),V1n) = ap(ap(c_2Earithmetic_2E_2B,V1n),V0m) ) ) ))).
fof(conj_thm_2Earithmetic_2EADD__COMM,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2B,V0m),V1n) = ap(ap(c_2Earithmetic_2E_2B,V1n),V0m) ) ) ))).
fof(conj_thm_2Earithmetic_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_2EPRE__SUB1,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ( ap(c_2Eprim__rec_2EPRE,V0m) = ap(ap(c_2Earithmetic_2E_2D,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) ) ))).
fof(conj_thm_2Earithmetic_2EMULT__LEFT__1,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0m) = V0m ) ))).
fof(conj_thm_2Earithmetic_2EMULT__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_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_2Earithmetic_2EDIVISION,axiom, ! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) => ! [V1k] : ( mem(V1k,ty_2Enum_2Enum) => ( ( V1k = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2EDIV,V1k),V0n)),V0n)),ap(ap(c_2Earithmetic_2EMOD,V1k),V0n)) ) & p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EMOD,V1k),V0n)),V0n)) ) ) ) )).
fof(conj_thm_2Earithmetic_2ELESS__MOD,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1k] : ( mem(V1k,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,V1k),V0n)) => ( ap(ap(c_2Earithmetic_2EMOD,V1k),V0n) = V1k ) ) ) ))).
fof(conj_thm_2Earithmetic_2EMOD__LESS,lemma,(! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) => p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EMOD,V0m),V1n)),V1n)) ) ) ))).
fof(conj_thm_2Earithmetic_2ESUB__ELIM__THM,lemma,(! [V0P] : ( mem(V0P,arr(ty_2Enum_2Enum,bool)) => ! [V1a] : ( mem(V1a,ty_2Enum_2Enum) => ! [V2b] : ( mem(V2b,ty_2Enum_2Enum) => ( p(ap(V0P,ap(ap(c_2Earithmetic_2E_2D,V1a),V2b))) <=> ! [V3d] : ( mem(V3d,ty_2Enum_2Enum) => ( ( ( V2b = ap(ap(c_2Earithmetic_2E_2B,V1a),V3d) ) => p(ap(V0P,c_2Enum_2E0)) ) & ( ( V1a = ap(ap(c_2Earithmetic_2E_2B,V2b),V3d) ) => p(ap(V0P,V3d)) ) ) ) ) ) ) ))).
fof(conj_thm_2Earithmetic_2EEXP__EQ__0,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ( ( ap(ap(c_2Earithmetic_2EEXP,V0n),V1m) = c_2Enum_2E0 ) <=> ( ( V0n = c_2Enum_2E0 ) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1m)) ) ) ) ))).
fof(conj_thm_2Earithmetic_2EZERO__LT__EXP,lemma,(! [V0x] : ( mem(V0x,ty_2Enum_2Enum) => ! [V1y] : ( mem(V1y,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(ap(c_2Earithmetic_2EEXP,V0x),V1y))) <=> ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0x)) | ( V1y = c_2Enum_2E0 ) ) ) ) ))).
fof(conj_thm_2Ebit_2EDIVMOD__2EXP,lemma,(! [V0x] : ( mem(V0x,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ap(ap(c_2Ebit_2EDIVMOD__2EXP,V0x),V1n) = ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Ebit_2EDIV__2EXP,V0x),V1n)),ap(ap(c_2Ebit_2EMOD__2EXP,V0x),V1n)) ) ) ))).
fof(conj_thm_2Ebit_2EDIV__MULT__1,lemma,(! [V0r] : ( mem(V0r,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,V0r),V1n)) => ( ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2B,V1n),V0r)),V1n) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) ) ) ))).
fof(ax_thm_2Ebool_2ELET__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ( c_2Ebool_2ELET(A_27a,A_27b) = f14(A_27b,A_27a) ) ) ) )).
fof(ax_thm_2Ebool_2EETA__AX,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ! [V0t] : ( mem(V0t,arr(A_27a,A_27b)) => ( f31(A_27b,A_27a,V0t) = V0t ) ) ) ) )).
fof(conj_thm_2Ebool_2ETRUTH,lemma,($true)).
fof(conj_thm_2Ebool_2EIMP__ANTISYM__AX,lemma,(! [V0t1] : ( mem(V0t1,bool) => ! [V1t2] : ( mem(V1t2,bool) => ( ( p(V0t1) => p(V1t2) ) => ( ( p(V1t2) => p(V0t1) ) => ( p(V0t1) <=> p(V1t2) ) ) ) ) ))).
fof(conj_thm_2Ebool_2EFALSITY,lemma,(! [V0t] : ( mem(V0t,bool) => ( $false => p(V0t) ) ))).
fof(conj_thm_2Ebool_2EEXCLUDED__MIDDLE,lemma,(! [V0t] : ( mem(V0t,bool) => ( p(V0t) | ( ~~ p(V0t) ) ) ))).
fof(conj_thm_2Ebool_2EFORALL__SIMP,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0t] : ( mem(V0t,bool) => ( ( ! [V1x] : ( mem(V1x,A_27a) => p(V0t) ) ) <=> p(V0t) ) )))).
fof(conj_thm_2Ebool_2ECONJ__ASSOC,lemma,(! [V0t1] : ( mem(V0t1,bool) => ! [V1t2] : ( mem(V1t2,bool) => ! [V2t3] : ( mem(V2t3,bool) => ( ( p(V0t1) & ( p(V1t2) & p(V2t3) ) ) <=> ( ( p(V0t1) & p(V1t2) ) & p(V2t3) ) ) ) ) ))).
fof(conj_thm_2Ebool_2EAND__CLAUSES,lemma,(! [V0t] : ( mem(V0t,bool) => ( ( ( $true & p(V0t) ) <=> p(V0t) ) & ( ( ( p(V0t) & $true ) <=> p(V0t) ) & ( ( ( $false & p(V0t) ) <=> $false ) & ( ( ( p(V0t) & $false ) <=> $false ) & ( ( p(V0t) & p(V0t) ) <=> p(V0t) ) ) ) ) ) ))).
fof(conj_thm_2Ebool_2EOR__CLAUSES,lemma,(! [V0t] : ( mem(V0t,bool) => ( ( ( $true | p(V0t) ) <=> $true ) & ( ( ( p(V0t) | $true ) <=> $true ) & ( ( ( $false | p(V0t) ) <=> p(V0t) ) & ( ( ( p(V0t) | $false ) <=> p(V0t) ) & ( ( p(V0t) | p(V0t) ) <=> p(V0t) ) ) ) ) ) ))).
fof(conj_thm_2Ebool_2EIMP__CLAUSES,lemma,(! [V0t] : ( mem(V0t,bool) => ( ( ( $true => p(V0t) ) <=> p(V0t) ) & ( ( ( p(V0t) => $true ) <=> $true ) & ( ( ( $false => p(V0t) ) <=> $true ) & ( ( ( p(V0t) => p(V0t) ) <=> $true ) & ( ( p(V0t) => $false ) <=> ( ~~ p(V0t) ) ) ) ) ) ) ))).
fof(conj_thm_2Ebool_2ENOT__CLAUSES,lemma,(( ( ! [V0t] : ( mem(V0t,bool) => ( ( ~~ ( ~~ p(V0t) ) ) <=> p(V0t) ) ) ) & ( ( (~~ ($true)) <=> $false ) & ( (~~ ($false)) <=> $true ) ) ))).
fof(conj_thm_2Ebool_2EEQ__REFL,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ( V0x = V0x ) )))).
fof(conj_thm_2Ebool_2EREFL__CLAUSE,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ( ( V0x = V0x ) <=> $true ) )))).
fof(conj_thm_2Ebool_2EEQ__SYM__EQ,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0x] : ( mem(V0x,A_27a) => ! [V1y] : ( mem(V1y,A_27a) => ( ( V0x = V1y ) <=> ( V1y = V0x ) ) ) )))).
fof(conj_thm_2Ebool_2EEQ__CLAUSES,lemma,(! [V0t] : ( mem(V0t,bool) => ( ( ( $true <=> p(V0t) ) <=> p(V0t) ) & ( ( ( p(V0t) <=> $true ) <=> p(V0t) ) & ( ( ( $false <=> p(V0t) ) <=> ( ~~ p(V0t) ) ) & ( ( p(V0t) <=> $false ) <=> ( ~~ p(V0t) ) ) ) ) ) ))).
fof(conj_thm_2Ebool_2ECOND__CLAUSES,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0t1] : ( mem(V0t1,A_27a) => ! [V1t2] : ( mem(V1t2,A_27a) => ( ( ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2ET),V0t1),V1t2) = V0t1 ) & ( ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2EF),V0t1),V1t2) = V1t2 ) ) ) )))).
fof(conj_thm_2Ebool_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_2EDISJ__ASSOC,lemma,(! [V0A] : ( mem(V0A,bool) => ! [V1B] : ( mem(V1B,bool) => ! [V2C] : ( mem(V2C,bool) => ( ( p(V0A) | ( p(V1B) | p(V2C) ) ) <=> ( ( p(V0A) | p(V1B) ) | p(V2C) ) ) ) ) ))).
fof(conj_thm_2Ebool_2EDE__MORGAN__THM,lemma,(! [V0A] : ( mem(V0A,bool) => ! [V1B] : ( mem(V1B,bool) => ( ( ( ~~ ( p(V0A) & p(V1B) ) ) <=> ( ( ~~ p(V0A) ) | ( ~~ p(V1B) ) ) ) & ( ( ~~ ( p(V0A) | p(V1B) ) ) <=> ( ( ~~ p(V0A) ) & ( ~~ p(V1B) ) ) ) ) ) ))).
fof(conj_thm_2Ebool_2ELEFT__OR__OVER__AND,lemma,(! [V0A] : ( mem(V0A,bool) => ! [V1B] : ( mem(V1B,bool) => ! [V2C] : ( mem(V2C,bool) => ( ( p(V0A) | ( p(V1B) & p(V2C) ) ) <=> ( ( p(V0A) | p(V1B) ) & ( p(V0A) | p(V2C) ) ) ) ) ) ))).
fof(conj_thm_2Ebool_2ERIGHT__OR__OVER__AND,lemma,(! [V0A] : ( mem(V0A,bool) => ! [V1B] : ( mem(V1B,bool) => ! [V2C] : ( mem(V2C,bool) => ( ( ( p(V1B) & p(V2C) ) | p(V0A) ) <=> ( ( p(V1B) | p(V0A) ) & ( p(V2C) | p(V0A) ) ) ) ) ) ))).
fof(conj_thm_2Ebool_2EIMP__DISJ__THM,lemma,(! [V0A] : ( mem(V0A,bool) => ! [V1B] : ( mem(V1B,bool) => ( ( p(V0A) => p(V1B) ) <=> ( ( ~~ p(V0A) ) | p(V1B) ) ) ) ))).
fof(conj_thm_2Ebool_2EIMP__F__EQ__F,lemma,(! [V0t] : ( mem(V0t,bool) => ( ( p(V0t) => $false ) <=> ( p(V0t) <=> $false ) ) ))).
fof(conj_thm_2Ebool_2EAND__IMP__INTRO,lemma,(! [V0t1] : ( mem(V0t1,bool) => ! [V1t2] : ( mem(V1t2,bool) => ! [V2t3] : ( mem(V2t3,bool) => ( ( p(V0t1) => ( p(V1t2) => p(V2t3) ) ) <=> ( ( p(V0t1) & p(V1t2) ) => p(V2t3) ) ) ) ) ))).
fof(conj_thm_2Ebool_2EEQ__EXPAND,lemma,(! [V0t1] : ( mem(V0t1,bool) => ! [V1t2] : ( mem(V1t2,bool) => ( ( p(V0t1) <=> p(V1t2) ) <=> ( ( p(V0t1) & p(V1t2) ) | ( ( ~~ p(V0t1) ) & ( ~~ p(V1t2) ) ) ) ) ) ))).
fof(conj_thm_2Ebool_2EIMP__CONG,lemma,(! [V0x] : ( mem(V0x,bool) => ! [V1x_27] : ( mem(V1x_27,bool) => ! [V2y] : ( mem(V2y,bool) => ! [V3y_27] : ( mem(V3y_27,bool) => ( ( ( p(V0x) <=> p(V1x_27) ) & ( p(V1x_27) => ( p(V2y) <=> p(V3y_27) ) ) ) => ( ( p(V0x) => p(V2y) ) <=> ( p(V1x_27) => p(V3y_27) ) ) ) ) ) ) ))).
fof(conj_thm_2Ebool_2ECOND__CONG,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,bool) => ! [V1Q] : ( mem(V1Q,bool) => ! [V2x] : ( mem(V2x,A_27a) => ! [V3x_27] : ( mem(V3x_27,A_27a) => ! [V4y] : ( mem(V4y,A_27a) => ! [V5y_27] : ( mem(V5y_27,A_27a) => ( ( ( p(V0P) <=> p(V1Q) ) & ( ( p(V1Q) => ( V2x = V3x_27 ) ) & ( ( ~~ p(V1Q) ) => ( V4y = V5y_27 ) ) ) ) => ( ap(ap(ap(c_2Ebool_2ECOND(A_27a),V0P),V2x),V4y) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),V1Q),V3x_27),V5y_27) ) ) ) ) ) ) ) )))).
fof(conj_thm_2Ebool_2Ebool__case__thm,lemma,( ! [A_27a]: ( ne(A_27a) => ( ( ! [V0t1] : ( mem(V0t1,A_27a) => ! [V1t2] : ( mem(V1t2,A_27a) => ( ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2ET),V0t1),V1t2) = V0t1 ) ) ) ) & ! [V2t1] : ( mem(V2t1,A_27a) => ! [V3t2] : ( mem(V3t2,A_27a) => ( ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2EF),V2t1),V3t2) = V3t2 ) ) ) )))).
fof(conj_thm_2Ebool_2EBOUNDED__THM,lemma,(! [V0v] : ( mem(V0v,bool) => ( p(ap(c_2Ebool_2EBOUNDED,V0v)) <=> $true ) ))).
fof(ax_thm_2Elist_2ETL__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ( ( ap(c_2Elist_2ETL(A_27a),c_2Elist_2ENIL(A_27a)) = c_2Elist_2ENIL(A_27a) ) & ! [V0h] : ( mem(V0h,A_27a) => ! [V1t] : ( mem(V1t,ty_2Elist_2Elist(A_27a)) => ( ap(c_2Elist_2ETL(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V1t)) = V1t ) ) ) ) ) )).
fof(ax_thm_2Elist_2EAPPEND,axiom,( ! [A_27a] : ( ne(A_27a) => ( ( ! [V0l] : ( mem(V0l,ty_2Elist_2Elist(A_27a)) => ( ap(ap(c_2Elist_2EAPPEND(A_27a),c_2Elist_2ENIL(A_27a)),V0l) = V0l ) ) ) & ! [V1l1] : ( mem(V1l1,ty_2Elist_2Elist(A_27a)) => ! [V2l2] : ( mem(V2l2,ty_2Elist_2Elist(A_27a)) => ! [V3h] : ( mem(V3h,A_27a) => ( ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V3h),V1l1)),V2l2) = ap(ap(c_2Elist_2ECONS(A_27a),V3h),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l1),V2l2)) ) ) ) ) ) ) )).
fof(ax_thm_2Elist_2EMAP,axiom,( ! [A_27a] : ( ne(A_27a) => ! [A_27b] : ( ne(A_27b) => ( ( ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ( ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),c_2Elist_2ENIL(A_27a)) = c_2Elist_2ENIL(A_27b) ) ) ) & ! [V1f] : ( mem(V1f,arr(A_27a,A_27b)) => ! [V2h] : ( mem(V2h,A_27a) => ! [V3t] : ( mem(V3t,ty_2Elist_2Elist(A_27a)) => ( ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V1f),ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3t)) = ap(ap(c_2Elist_2ECONS(A_27b),ap(V1f,V2h)),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V1f),V3t)) ) ) ) ) ) ) ) )).
fof(ax_thm_2Elist_2EEVERY__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ( ( ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ( p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),c_2Elist_2ENIL(A_27a))) <=> $true ) ) ) & ! [V1P] : ( mem(V1P,arr(A_27a,bool)) => ! [V2h] : ( mem(V2h,A_27a) => ! [V3t] : ( mem(V3t,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Elist_2EEVERY(A_27a),V1P),ap(ap(c_2Elist_2ECONS(A_27a),V2h),V3t))) <=> ( p(ap(V1P,V2h)) & p(ap(ap(c_2Elist_2EEVERY(A_27a),V1P),V3t)) ) ) ) ) ) ) ) )).
fof(conj_thm_2Elist_2Elist__induction,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(ty_2Elist_2Elist(A_27a),bool)) => ( ( p(ap(V0P,c_2Elist_2ENIL(A_27a))) & ! [V1t] : ( mem(V1t,ty_2Elist_2Elist(A_27a)) => ( p(ap(V0P,V1t)) => ! [V2h] : ( mem(V2h,A_27a) => p(ap(V0P,ap(ap(c_2Elist_2ECONS(A_27a),V2h),V1t))) ) ) ) ) => ! [V3l] : ( mem(V3l,ty_2Elist_2Elist(A_27a)) => p(ap(V0P,V3l)) ) ) )))).
fof(conj_thm_2Elist_2ECONS__11,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0a0] : ( mem(V0a0,A_27a) => ! [V1a1] : ( mem(V1a1,ty_2Elist_2Elist(A_27a)) => ! [V2a0_27] : ( mem(V2a0_27,A_27a) => ! [V3a1_27] : ( mem(V3a1_27,ty_2Elist_2Elist(A_27a)) => ( ( ap(ap(c_2Elist_2ECONS(A_27a),V0a0),V1a1) = ap(ap(c_2Elist_2ECONS(A_27a),V2a0_27),V3a1_27) ) <=> ( ( V0a0 = V2a0_27 ) & ( V1a1 = V3a1_27 ) ) ) ) ) ) )))).
fof(conj_thm_2Elist_2ENOT__NIL__CONS,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0a1] : ( mem(V0a1,ty_2Elist_2Elist(A_27a)) => ! [V1a0] : ( mem(V1a0,A_27a) => ( ~~ ( c_2Elist_2ENIL(A_27a) = ap(ap(c_2Elist_2ECONS(A_27a),V1a0),V0a1) ) ) ) )))).
fof(conj_thm_2Elist_2EAPPEND__NIL,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l] : ( mem(V0l,ty_2Elist_2Elist(A_27a)) => ( ap(ap(c_2Elist_2EAPPEND(A_27a),V0l),c_2Elist_2ENIL(A_27a)) = V0l ) )))).
fof(conj_thm_2Elist_2EAPPEND__ASSOC,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l1] : ( mem(V0l1,ty_2Elist_2Elist(A_27a)) => ! [V1l2] : ( mem(V1l2,ty_2Elist_2Elist(A_27a)) => ! [V2l3] : ( mem(V2l3,ty_2Elist_2Elist(A_27a)) => ( ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),ap(ap(c_2Elist_2EAPPEND(A_27a),V1l2),V2l3)) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2)),V2l3) ) ) ) )))).
fof(conj_thm_2Elist_2EAPPEND__11,lemma,( ! [A_27a]: ( ne(A_27a) => ( ( ! [V0l1] : ( mem(V0l1,ty_2Elist_2Elist(A_27a)) => ! [V1l2] : ( mem(V1l2,ty_2Elist_2Elist(A_27a)) => ! [V2l3] : ( mem(V2l3,ty_2Elist_2Elist(A_27a)) => ( ( ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2) = ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V2l3) ) <=> ( V1l2 = V2l3 ) ) ) ) ) ) & ! [V3l1] : ( mem(V3l1,ty_2Elist_2Elist(A_27a)) => ! [V4l2] : ( mem(V4l2,ty_2Elist_2Elist(A_27a)) => ! [V5l3] : ( mem(V5l3,ty_2Elist_2Elist(A_27a)) => ( ( ap(ap(c_2Elist_2EAPPEND(A_27a),V4l2),V3l1) = ap(ap(c_2Elist_2EAPPEND(A_27a),V5l3),V3l1) ) <=> ( V4l2 = V5l3 ) ) ) ) ) )))).
fof(ax_thm_2Elist_2EREVERSE__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ( ( ap(c_2Elist_2EREVERSE(A_27a),c_2Elist_2ENIL(A_27a)) = c_2Elist_2ENIL(A_27a) ) & ! [V0h] : ( mem(V0h,A_27a) => ! [V1t] : ( mem(V1t,ty_2Elist_2Elist(A_27a)) => ( ap(c_2Elist_2EREVERSE(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V1t)) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(c_2Elist_2EREVERSE(A_27a),V1t)),ap(ap(c_2Elist_2ECONS(A_27a),V0h),c_2Elist_2ENIL(A_27a))) ) ) ) ) ) )).
fof(conj_thm_2Elist_2EREVERSE__APPEND,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l1] : ( mem(V0l1,ty_2Elist_2Elist(A_27a)) => ! [V1l2] : ( mem(V1l2,ty_2Elist_2Elist(A_27a)) => ( ap(c_2Elist_2EREVERSE(A_27a),ap(ap(c_2Elist_2EAPPEND(A_27a),V0l1),V1l2)) = ap(ap(c_2Elist_2EAPPEND(A_27a),ap(c_2Elist_2EREVERSE(A_27a),V1l2)),ap(c_2Elist_2EREVERSE(A_27a),V0l1)) ) ) )))).
fof(conj_thm_2Elist_2EREVERSE__EQ__NIL,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l] : ( mem(V0l,ty_2Elist_2Elist(A_27a)) => ( ( ap(c_2Elist_2EREVERSE(A_27a),V0l) = c_2Elist_2ENIL(A_27a) ) <=> ( V0l = c_2Elist_2ENIL(A_27a) ) ) )))).
fof(ax_thm_2Elist_2ELAST__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0h] : ( mem(V0h,A_27a) => ! [V1t] : ( mem(V1t,ty_2Elist_2Elist(A_27a)) => ( ap(c_2Elist_2ELAST(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V1t)) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(ap(c_2Emin_2E_3D(ty_2Elist_2Elist(A_27a)),V1t),c_2Elist_2ENIL(A_27a))),V0h),ap(c_2Elist_2ELAST(A_27a),V1t)) ) ) ) ) )).
fof(ax_thm_2Elist_2EFRONT__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ! [V0h] : ( mem(V0h,A_27a) => ! [V1t] : ( mem(V1t,ty_2Elist_2Elist(A_27a)) => ( ap(c_2Elist_2EFRONT(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V0h),V1t)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Elist_2Elist(A_27a)),V1t),c_2Elist_2ENIL(A_27a))),c_2Elist_2ENIL(A_27a)),ap(ap(c_2Elist_2ECONS(A_27a),V0h),ap(c_2Elist_2EFRONT(A_27a),V1t))) ) ) ) ) )).
fof(ax_thm_2Elist_2EREV__DEF,axiom,( ! [A_27a] : ( ne(A_27a) => ( ( ! [V0acc] : ( mem(V0acc,ty_2Elist_2Elist(A_27a)) => ( ap(ap(c_2Elist_2EREV(A_27a),c_2Elist_2ENIL(A_27a)),V0acc) = V0acc ) ) ) & ! [V1h] : ( mem(V1h,A_27a) => ! [V2t] : ( mem(V2t,ty_2Elist_2Elist(A_27a)) => ! [V3acc] : ( mem(V3acc,ty_2Elist_2Elist(A_27a)) => ( ap(ap(c_2Elist_2EREV(A_27a),ap(ap(c_2Elist_2ECONS(A_27a),V1h),V2t)),V3acc) = ap(ap(c_2Elist_2EREV(A_27a),V2t),ap(ap(c_2Elist_2ECONS(A_27a),V1h),V3acc)) ) ) ) ) ) ) )).
fof(conj_thm_2Elist_2EREVERSE__REV,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0L] : ( mem(V0L,ty_2Elist_2Elist(A_27a)) => ( ap(c_2Elist_2EREVERSE(A_27a),V0L) = ap(ap(c_2Elist_2EREV(A_27a),V0L),c_2Elist_2ENIL(A_27a)) ) )))).
fof(conj_thm_2Elogroot_2ELOG__ADD,lemma,(! [V0a] : ( mem(V0a,ty_2Enum_2Enum) => ! [V1b] : ( mem(V1b,ty_2Enum_2Enum) => ! [V2c] : ( mem(V2c,ty_2Enum_2Enum) => ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0a)) & p(ap(ap(c_2Eprim__rec_2E_3C,V1b),ap(ap(c_2Earithmetic_2EEXP,V0a),V2c))) ) => ( ap(ap(c_2Elogroot_2ELOG,V0a),ap(ap(c_2Earithmetic_2E_2B,V1b),ap(ap(c_2Earithmetic_2EEXP,V0a),V2c))) = V2c ) ) ) ) ))).
fof(conj_thm_2Enumeral_2Enumeral__distrib,lemma,(( ( ! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2B,c_2Enum_2E0),V0n) = V0n ) ) ) & ( ( ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2B,V1n),c_2Enum_2E0) = V1n ) ) ) & ( ( ! [V2n] : ( mem(V2n,ty_2Enum_2Enum) => ! [V3m] : ( mem(V3m,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,V2n)),ap(c_2Earithmetic_2ENUMERAL,V3m)) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,V2n),V3m))) ) ) ) ) & ( ( ! [V4n] : ( mem(V4n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2A,c_2Enum_2E0),V4n) = c_2Enum_2E0 ) ) ) & ( ( ! [V5n] : ( mem(V5n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2A,V5n),c_2Enum_2E0) = c_2Enum_2E0 ) ) ) & ( ( ! [V6n] : ( mem(V6n,ty_2Enum_2Enum) => ! [V7m] : ( mem(V7m,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,V6n)),ap(c_2Earithmetic_2ENUMERAL,V7m)) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Earithmetic_2E_2A,V6n),V7m)) ) ) ) ) & ( ( ! [V8n] : ( mem(V8n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2D,c_2Enum_2E0),V8n) = c_2Enum_2E0 ) ) ) & ( ( ! [V9n] : ( mem(V9n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2D,V9n),c_2Enum_2E0) = V9n ) ) ) & ( ( ! [V10n] : ( mem(V10n,ty_2Enum_2Enum) => ! [V11m] : ( mem(V11m,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,V10n)),ap(c_2Earithmetic_2ENUMERAL,V11m)) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Earithmetic_2E_2D,V10n),V11m)) ) ) ) ) & ( ( ! [V12n] : ( mem(V12n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2EEXP,c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V12n))) = c_2Enum_2E0 ) ) ) & ( ( ! [V13n] : ( mem(V13n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2EEXP,c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V13n))) = c_2Enum_2E0 ) ) ) & ( ( ! [V14n] : ( mem(V14n,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2EEXP,V14n),c_2Enum_2E0) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) ) ) & ( ( ! [V15n] : ( mem(V15n,ty_2Enum_2Enum) => ! [V16m] : ( mem(V16m,ty_2Enum_2Enum) => ( ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,V15n)),ap(c_2Earithmetic_2ENUMERAL,V16m)) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Earithmetic_2EEXP,V15n),V16m)) ) ) ) ) & ( ( ap(c_2Enum_2ESUC,c_2Enum_2E0) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) & ( ( ! [V17n] : ( mem(V17n,ty_2Enum_2Enum) => ( ap(c_2Enum_2ESUC,ap(c_2Earithmetic_2ENUMERAL,V17n)) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Enum_2ESUC,V17n)) ) ) ) & ( ( ap(c_2Eprim__rec_2EPRE,c_2Enum_2E0) = c_2Enum_2E0 ) & ( ( ! [V18n] : ( mem(V18n,ty_2Enum_2Enum) => ( ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2ENUMERAL,V18n)) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Eprim__rec_2EPRE,V18n)) ) ) ) & ( ( ! [V19n] : ( mem(V19n,ty_2Enum_2Enum) => ( ( ap(c_2Earithmetic_2ENUMERAL,V19n) = c_2Enum_2E0 ) <=> ( V19n = c_2Earithmetic_2EZERO ) ) ) ) & ( ( ! [V20n] : ( mem(V20n,ty_2Enum_2Enum) => ( ( c_2Enum_2E0 = ap(c_2Earithmetic_2ENUMERAL,V20n) ) <=> ( V20n = c_2Earithmetic_2EZERO ) ) ) ) & ( ( ! [V21n] : ( mem(V21n,ty_2Enum_2Enum) => ! [V22m] : ( mem(V22m,ty_2Enum_2Enum) => ( ( ap(c_2Earithmetic_2ENUMERAL,V21n) = ap(c_2Earithmetic_2ENUMERAL,V22m) ) <=> ( V21n = V22m ) ) ) ) ) & ( ( ! [V23n] : ( mem(V23n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,V23n),c_2Enum_2E0)) <=> $false ) ) ) & ( ( ! [V24n] : ( mem(V24n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,V24n))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Earithmetic_2EZERO),V24n)) ) ) ) & ( ( ! [V25n] : ( mem(V25n,ty_2Enum_2Enum) => ! [V26m] : ( mem(V26m,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,V25n)),ap(c_2Earithmetic_2ENUMERAL,V26m))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,V25n),V26m)) ) ) ) ) & ( ( ! [V27n] : ( mem(V27n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3E,c_2Enum_2E0),V27n)) <=> $false ) ) ) & ( ( ! [V28n] : ( mem(V28n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Earithmetic_2ENUMERAL,V28n)),c_2Enum_2E0)) <=> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Earithmetic_2EZERO),V28n)) ) ) ) & ( ( ! [V29n] : ( mem(V29n,ty_2Enum_2Enum) => ! [V30m] : ( mem(V30m,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Earithmetic_2ENUMERAL,V29n)),ap(c_2Earithmetic_2ENUMERAL,V30m))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,V30m),V29n)) ) ) ) ) & ( ( ! [V31n] : ( mem(V31n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,c_2Enum_2E0),V31n)) <=> $true ) ) ) & ( ( ! [V32n] : ( mem(V32n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,V32n)),c_2Enum_2E0)) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V32n),c_2Earithmetic_2EZERO)) ) ) ) & ( ( ! [V33n] : ( mem(V33n,ty_2Enum_2Enum) => ! [V34m] : ( mem(V34m,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,V33n)),ap(c_2Earithmetic_2ENUMERAL,V34m))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V33n),V34m)) ) ) ) ) & ( ( ! [V35n] : ( mem(V35n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3E_3D,V35n),c_2Enum_2E0)) <=> $true ) ) ) & ( ( ! [V36n] : ( mem(V36n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3E_3D,c_2Enum_2E0),V36n)) <=> ( V36n = c_2Enum_2E0 ) ) ) ) & ( ( ! [V37n] : ( mem(V37n,ty_2Enum_2Enum) => ! [V38m] : ( mem(V38m,ty_2Enum_2Enum) => ( p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Earithmetic_2ENUMERAL,V37n)),ap(c_2Earithmetic_2ENUMERAL,V38m))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V38m),V37n)) ) ) ) ) & ( ( ! [V39n] : ( mem(V39n,ty_2Enum_2Enum) => ( p(ap(c_2Earithmetic_2EODD,ap(c_2Earithmetic_2ENUMERAL,V39n))) <=> p(ap(c_2Earithmetic_2EODD,V39n)) ) ) ) & ( ( ! [V40n] : ( mem(V40n,ty_2Enum_2Enum) => ( p(ap(c_2Earithmetic_2EEVEN,ap(c_2Earithmetic_2ENUMERAL,V40n))) <=> p(ap(c_2Earithmetic_2EEVEN,V40n)) ) ) ) & ( ( ~~ p(ap(c_2Earithmetic_2EODD,c_2Enum_2E0)) ) & p(ap(c_2Earithmetic_2EEVEN,c_2Enum_2E0)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
fof(conj_thm_2Enumeral_2Enumeral__add,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ( ( ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,c_2Earithmetic_2EZERO),V0n)) = V0n ) & ( ( ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,V0n),c_2Earithmetic_2EZERO)) = V0n ) & ( ( ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ( ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) = ap(c_2Earithmetic_2EBIT1,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ( ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) = ap(c_2Earithmetic_2EBIT1,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ( ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ( ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,c_2Earithmetic_2EZERO),V0n)) = ap(c_2Enum_2ESUC,V0n) ) & ( ( ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),c_2Earithmetic_2EZERO)) = ap(c_2Enum_2ESUC,V0n) ) & ( ( ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) = ap(c_2Earithmetic_2EBIT1,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ( ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ( ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ( ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) = ap(c_2Earithmetic_2EBIT1,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ( ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,c_2Earithmetic_2EZERO),V0n)) = ap(c_2Enumeral_2EiiSUC,V0n) ) & ( ( ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,V0n),c_2Earithmetic_2EZERO)) = ap(c_2Enumeral_2EiiSUC,V0n) ) & ( ( ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ( ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) = ap(c_2Earithmetic_2EBIT1,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ( ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) = ap(c_2Earithmetic_2EBIT1,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) & ( ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
fof(conj_thm_2Enumeral_2Enumeral__eq,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ( ( ( c_2Earithmetic_2EZERO = ap(c_2Earithmetic_2EBIT1,V0n) ) <=> $false ) & ( ( ( ap(c_2Earithmetic_2EBIT1,V0n) = c_2Earithmetic_2EZERO ) <=> $false ) & ( ( ( c_2Earithmetic_2EZERO = ap(c_2Earithmetic_2EBIT2,V0n) ) <=> $false ) & ( ( ( ap(c_2Earithmetic_2EBIT2,V0n) = c_2Earithmetic_2EZERO ) <=> $false ) & ( ( ( ap(c_2Earithmetic_2EBIT1,V0n) = ap(c_2Earithmetic_2EBIT2,V1m) ) <=> $false ) & ( ( ( ap(c_2Earithmetic_2EBIT2,V0n) = ap(c_2Earithmetic_2EBIT1,V1m) ) <=> $false ) & ( ( ( ap(c_2Earithmetic_2EBIT1,V0n) = ap(c_2Earithmetic_2EBIT1,V1m) ) <=> ( V0n = V1m ) ) & ( ( ap(c_2Earithmetic_2EBIT2,V0n) = ap(c_2Earithmetic_2EBIT2,V1m) ) <=> ( V0n = V1m ) ) ) ) ) ) ) ) ) ) ))).
fof(conj_thm_2Enumeral_2Enumeral__lt,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Earithmetic_2EZERO),ap(c_2Earithmetic_2EBIT1,V0n))) <=> $true ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Earithmetic_2EZERO),ap(c_2Earithmetic_2EBIT2,V0n))) <=> $true ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,V0n),c_2Earithmetic_2EZERO)) <=> $false ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m)) ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m)) ) & ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) <=> ( ~~ p(ap(ap(c_2Eprim__rec_2E_3C,V1m),V0n)) ) ) & ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) <=> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m)) ) ) ) ) ) ) ) ) ))).
fof(conj_thm_2Enumeral_2Enumeral__lte,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1m] : ( mem(V1m,ty_2Enum_2Enum) => ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,c_2Earithmetic_2EZERO),V0n)) <=> $true ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT1,V0n)),c_2Earithmetic_2EZERO)) <=> $false ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT2,V0n)),c_2Earithmetic_2EZERO)) <=> $false ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m)) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m)) ) & ( ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) <=> ( ~~ p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V0n)) ) ) & ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m)) ) ) ) ) ) ) ) ) ))).
fof(conj_thm_2Enumeral_2Enumeral__pre,lemma,(( ( ap(c_2Eprim__rec_2EPRE,c_2Earithmetic_2EZERO) = c_2Earithmetic_2EZERO ) & ( ( ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = c_2Earithmetic_2EZERO ) & ( ( ! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,V0n))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT1,V0n))) ) ) ) & ( ( ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,V1n))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,V1n)) ) ) ) & ! [V2n] : ( mem(V2n,ty_2Enum_2Enum) => ( ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT2,V2n)) = ap(c_2Earithmetic_2EBIT1,V2n) ) ) ) ) ) ))).
fof(conj_thm_2Enumeral_2Enumeral__texp__help,lemma,(! [V0acc] : ( mem(V0acc,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ( ap(ap(c_2Enumeral_2Etexp__help,c_2Earithmetic_2EZERO),V0acc) = ap(c_2Earithmetic_2EBIT2,V0acc) ) & ( ( ap(ap(c_2Enumeral_2Etexp__help,ap(c_2Earithmetic_2EBIT1,V1n)),V0acc) = ap(ap(c_2Enumeral_2Etexp__help,ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT1,V1n))),ap(c_2Earithmetic_2EBIT1,V0acc)) ) & ( ap(ap(c_2Enumeral_2Etexp__help,ap(c_2Earithmetic_2EBIT2,V1n)),V0acc) = ap(ap(c_2Enumeral_2Etexp__help,ap(c_2Earithmetic_2EBIT1,V1n)),ap(c_2Earithmetic_2EBIT1,V0acc)) ) ) ) ) ))).
fof(conj_thm_2Enumeral_2ETWO__EXP__THM,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ( ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),c_2Enum_2E0) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) & ( ( ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Enumeral_2Etexp__help,ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT1,V0n))),c_2Earithmetic_2EZERO)) ) & ( ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V0n))) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Enumeral_2Etexp__help,ap(c_2Earithmetic_2EBIT1,V0n)),c_2Earithmetic_2EZERO)) ) ) ) ))).
fof(conj_thm_2Enumeral__bit_2Enumeral__imod__2exp,lemma,( ! [A_27a]: ( ne(A_27a) => ( ( ! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ap(ap(c_2Enumeral__bit_2EiMOD__2EXP,c_2Enum_2E0),V0n) = c_2Earithmetic_2EZERO ) ) ) & ( ( ! [V1x] : ( mem(V1x,ty_2Enum_2Enum) => ! [V2n] : ( mem(V2n,A_27a) => ( ap(ap(c_2Enumeral__bit_2EiMOD__2EXP,V1x),c_2Earithmetic_2EZERO) = c_2Earithmetic_2EZERO ) ) ) ) & ( ( ! [V3x] : ( mem(V3x,ty_2Enum_2Enum) => ! [V4n] : ( mem(V4n,ty_2Enum_2Enum) => ( ap(ap(c_2Enumeral__bit_2EiMOD__2EXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3x))),ap(c_2Earithmetic_2EBIT1,V4n)) = ap(c_2Earithmetic_2EBIT1,ap(ap(c_2Enumeral__bit_2EiMOD__2EXP,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V4n)) ) ) ) ) & ( ( ! [V5x] : ( mem(V5x,ty_2Enum_2Enum) => ! [V6n] : ( mem(V6n,ty_2Enum_2Enum) => ( ap(ap(c_2Enumeral__bit_2EiMOD__2EXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V5x))),ap(c_2Earithmetic_2EBIT1,V6n)) = ap(c_2Earithmetic_2EBIT1,ap(ap(c_2Enumeral__bit_2EiMOD__2EXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V5x))),V6n)) ) ) ) ) & ( ( ! [V7x] : ( mem(V7x,ty_2Enum_2Enum) => ! [V8n] : ( mem(V8n,ty_2Enum_2Enum) => ( ap(ap(c_2Enumeral__bit_2EiMOD__2EXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V7x))),ap(c_2Earithmetic_2EBIT2,V8n)) = ap(c_2Enumeral_2EiDUB,ap(ap(c_2Enumeral__bit_2EiMOD__2EXP,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V7x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Enum_2ESUC,V8n))) ) ) ) ) & ! [V9x] : ( mem(V9x,ty_2Enum_2Enum) => ! [V10n] : ( mem(V10n,ty_2Enum_2Enum) => ( ap(ap(c_2Enumeral__bit_2EiMOD__2EXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V9x))),ap(c_2Earithmetic_2EBIT2,V10n)) = ap(c_2Enumeral_2EiDUB,ap(ap(c_2Enumeral__bit_2EiMOD__2EXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V9x))),ap(c_2Enum_2ESUC,V10n))) ) ) ) ) ) ) ) )))).
fof(conj_thm_2Enumeral__bit_2EMOD__2EXP,lemma,(( ( ! [V0x] : ( mem(V0x,ty_2Enum_2Enum) => ( ap(ap(c_2Ebit_2EMOD__2EXP,V0x),c_2Enum_2E0) = c_2Enum_2E0 ) ) ) & ! [V1x] : ( mem(V1x,ty_2Enum_2Enum) => ! [V2n] : ( mem(V2n,ty_2Enum_2Enum) => ( ap(ap(c_2Ebit_2EMOD__2EXP,V1x),ap(c_2Earithmetic_2ENUMERAL,V2n)) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Enumeral__bit_2EiMOD__2EXP,V1x),V2n)) ) ) ) ))).
fof(conj_thm_2Enumeral__bit_2ENUMERAL__TIMES__2EXP,lemma,(( ( ! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ap(ap(c_2Ebit_2ETIMES__2EXP,V0n),c_2Enum_2E0) = c_2Enum_2E0 ) ) ) & ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ! [V2x] : ( mem(V2x,ty_2Enum_2Enum) => ( ap(ap(c_2Ebit_2ETIMES__2EXP,V1n),ap(c_2Earithmetic_2ENUMERAL,V2x)) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,c_2Enumeral_2EiDUB),V1n),V2x)) ) ) ) ))).
fof(conj_thm_2Enumeral__bit_2ENUMERAL__iDIV2,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ( ap(c_2Enumeral__bit_2EiDIV2,c_2Earithmetic_2EZERO) = c_2Earithmetic_2EZERO ) & ( ( ap(c_2Enumeral__bit_2EiDIV2,ap(c_2Enumeral__bit_2EiSUC,c_2Earithmetic_2EZERO)) = c_2Earithmetic_2EZERO ) & ( ( ap(c_2Enumeral__bit_2EiDIV2,ap(c_2Earithmetic_2EBIT1,V0n)) = V0n ) & ( ( ap(c_2Enumeral__bit_2EiDIV2,ap(c_2Enumeral__bit_2EiSUC,ap(c_2Earithmetic_2EBIT1,V0n))) = ap(c_2Enumeral__bit_2EiSUC,V0n) ) & ( ( ap(c_2Enumeral__bit_2EiDIV2,ap(c_2Earithmetic_2EBIT2,V0n)) = ap(c_2Enumeral__bit_2EiSUC,V0n) ) & ( ( ap(c_2Enumeral__bit_2EiDIV2,ap(c_2Enumeral__bit_2EiSUC,ap(c_2Earithmetic_2EBIT2,V0n))) = ap(c_2Enumeral__bit_2EiSUC,V0n) ) & ( ap(c_2Earithmetic_2ENUMERAL,ap(c_2Enumeral__bit_2EiSUC,V0n)) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Enum_2ESUC,V0n)) ) ) ) ) ) ) ) ))).
fof(conj_thm_2Enumeral__bit_2ENUMERAL__DIV__2EXP,lemma,(( ( ! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ap(ap(c_2Ebit_2EDIV__2EXP,V0n),c_2Enum_2E0) = c_2Enum_2E0 ) ) ) & ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ! [V2x] : ( mem(V2x,ty_2Enum_2Enum) => ( ap(ap(c_2Ebit_2EDIV__2EXP,V1n),ap(c_2Earithmetic_2ENUMERAL,V2x)) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,c_2Enumeral__bit_2EiDIV2),V1n),V2x)) ) ) ) ))).
fof(conj_thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__iDIV2,lemma,(( ( ! [V0x] : ( mem(V0x,ty_2Enum_2Enum) => ( ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,c_2Enumeral__bit_2EiDIV2),c_2Enum_2E0),V0x) = V0x ) ) ) & ( ( ! [V1y] : ( mem(V1y,ty_2Enum_2Enum) => ( ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,c_2Enumeral__bit_2EiDIV2),V1y),c_2Enum_2E0) = c_2Enum_2E0 ) ) ) & ( ( ! [V2n] : ( mem(V2n,ty_2Enum_2Enum) => ! [V3x] : ( mem(V3x,ty_2Enum_2Enum) => ( ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,c_2Enumeral__bit_2EiDIV2),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V2n))),V3x) = ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,ap(c_2Enumeral__bit_2EFDUB,c_2Enumeral__bit_2EiDIV2)),ap(c_2Earithmetic_2ENUMERAL,V2n)),ap(c_2Enumeral__bit_2EiDIV2,V3x)) ) ) ) ) & ! [V4n] : ( mem(V4n,ty_2Enum_2Enum) => ! [V5x] : ( mem(V5x,ty_2Enum_2Enum) => ( ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,c_2Enumeral__bit_2EiDIV2),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V4n))),V5x) = ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,ap(c_2Enumeral__bit_2EFDUB,c_2Enumeral__bit_2EiDIV2)),ap(c_2Earithmetic_2ENUMERAL,V4n)),ap(c_2Enumeral__bit_2EiDIV2,ap(c_2Enumeral__bit_2EiDIV2,V5x))) ) ) ) ) ) ))).
fof(conj_thm_2Enumeral__bit_2ENUMERAL__SFUNPOW__FDUB,lemma,(! [V0f] : ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) => ( ( ! [V1x] : ( mem(V1x,ty_2Enum_2Enum) => ( ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,ap(c_2Enumeral__bit_2EFDUB,V0f)),c_2Enum_2E0),V1x) = V1x ) ) ) & ( ( ! [V2y] : ( mem(V2y,ty_2Enum_2Enum) => ( ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,ap(c_2Enumeral__bit_2EFDUB,V0f)),V2y),c_2Enum_2E0) = c_2Enum_2E0 ) ) ) & ( ( ! [V3n] : ( mem(V3n,ty_2Enum_2Enum) => ! [V4x] : ( mem(V4x,ty_2Enum_2Enum) => ( ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,ap(c_2Enumeral__bit_2EFDUB,V0f)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n))),V4x) = ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,ap(c_2Enumeral__bit_2EFDUB,ap(c_2Enumeral__bit_2EFDUB,V0f))),ap(c_2Earithmetic_2ENUMERAL,V3n)),ap(ap(c_2Enumeral__bit_2EFDUB,V0f),V4x)) ) ) ) ) & ! [V5n] : ( mem(V5n,ty_2Enum_2Enum) => ! [V6x] : ( mem(V6x,ty_2Enum_2Enum) => ( ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,ap(c_2Enumeral__bit_2EFDUB,V0f)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V5n))),V6x) = ap(ap(ap(c_2Enumeral__bit_2ESFUNPOW,ap(c_2Enumeral__bit_2EFDUB,ap(c_2Enumeral__bit_2EFDUB,V0f))),ap(c_2Earithmetic_2ENUMERAL,V5n)),ap(ap(c_2Enumeral__bit_2EFDUB,V0f),ap(ap(c_2Enumeral__bit_2EFDUB,V0f),V6x))) ) ) ) ) ) ) ))).
fof(conj_thm_2Enumeral__bit_2EFDUB__iDIV2,lemma,(! [V0x] : ( mem(V0x,ty_2Enum_2Enum) => ( ap(ap(c_2Enumeral__bit_2EFDUB,c_2Enumeral__bit_2EiDIV2),V0x) = ap(c_2Enumeral__bit_2EiDIV2,ap(c_2Enumeral__bit_2EiDIV2,V0x)) ) ))).
fof(conj_thm_2Enumeral__bit_2EFDUB__FDUB,lemma,(! [V0f] : ( mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) => ( ( ap(ap(c_2Enumeral__bit_2EFDUB,ap(c_2Enumeral__bit_2EFDUB,V0f)),c_2Earithmetic_2EZERO) = c_2Earithmetic_2EZERO ) & ( ( ! [V1x] : ( mem(V1x,ty_2Enum_2Enum) => ( ap(ap(c_2Enumeral__bit_2EFDUB,ap(c_2Enumeral__bit_2EFDUB,V0f)),ap(c_2Enumeral__bit_2EiSUC,V1x)) = ap(ap(c_2Enumeral__bit_2EFDUB,V0f),ap(ap(c_2Enumeral__bit_2EFDUB,V0f),ap(c_2Enumeral__bit_2EiSUC,V1x))) ) ) ) & ( ( ! [V2x] : ( mem(V2x,ty_2Enum_2Enum) => ( ap(ap(c_2Enumeral__bit_2EFDUB,ap(c_2Enumeral__bit_2EFDUB,V0f)),ap(c_2Earithmetic_2EBIT1,V2x)) = ap(ap(c_2Enumeral__bit_2EFDUB,V0f),ap(ap(c_2Enumeral__bit_2EFDUB,V0f),ap(c_2Earithmetic_2EBIT1,V2x))) ) ) ) & ! [V3x] : ( mem(V3x,ty_2Enum_2Enum) => ( ap(ap(c_2Enumeral__bit_2EFDUB,ap(c_2Enumeral__bit_2EFDUB,V0f)),ap(c_2Earithmetic_2EBIT2,V3x)) = ap(ap(c_2Enumeral__bit_2EFDUB,V0f),ap(ap(c_2Enumeral__bit_2EFDUB,V0f),ap(c_2Earithmetic_2EBIT2,V3x))) ) ) ) ) ) ))).
fof(ax_thm_2Enumposrep_2El2n__def,axiom, ( ( ! [V0b] : ( mem(V0b,ty_2Enum_2Enum) => ( ap(ap(c_2Enumposrep_2El2n,V0b),c_2Elist_2ENIL(ty_2Enum_2Enum)) = c_2Enum_2E0 ) ) ) & ! [V1b] : ( mem(V1b,ty_2Enum_2Enum) => ! [V2h] : ( mem(V2h,ty_2Enum_2Enum) => ! [V3t] : ( mem(V3t,ty_2Elist_2Elist(ty_2Enum_2Enum)) => ( ap(ap(c_2Enumposrep_2El2n,V1b),ap(ap(c_2Elist_2ECONS(ty_2Enum_2Enum),V2h),V3t)) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EMOD,V2h),V1b)),ap(ap(c_2Earithmetic_2E_2A,V1b),ap(ap(c_2Enumposrep_2El2n,V1b),V3t))) ) ) ) ) )).
fof(conj_thm_2Enumposrep_2En2l__def,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ! [V1b] : ( mem(V1b,ty_2Enum_2Enum) => ( ap(ap(c_2Enumposrep_2En2l,V1b),V0n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Elist_2Elist(ty_2Enum_2Enum)),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Eprim__rec_2E_3C,V0n),V1b)),ap(ap(c_2Eprim__rec_2E_3C,V1b),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))),ap(ap(c_2Elist_2ECONS(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2EMOD,V0n),V1b)),c_2Elist_2ENIL(ty_2Enum_2Enum))),ap(ap(c_2Elist_2ECONS(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2EMOD,V0n),V1b)),ap(ap(c_2Enumposrep_2En2l,V1b),ap(ap(c_2Earithmetic_2EDIV,V0n),V1b)))) ) ) ))).
fof(conj_thm_2Enumposrep_2ELENGTH__n2l,lemma,(! [V0b] : ( mem(V0b,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0b)) => ( ap(c_2Elist_2ELENGTH(ty_2Enum_2Enum),ap(ap(c_2Enumposrep_2En2l,V0b),V1n)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1n),c_2Enum_2E0)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,ap(ap(c_2Elogroot_2ELOG,V0b),V1n))) ) ) ) ))).
fof(conj_thm_2Enumposrep_2EEL__n2l,lemma,(! [V0b] : ( mem(V0b,ty_2Enum_2Enum) => ! [V1x] : ( mem(V1x,ty_2Enum_2Enum) => ! [V2n] : ( mem(V2n,ty_2Enum_2Enum) => ( ( p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0b)) & p(ap(ap(c_2Eprim__rec_2E_3C,V1x),ap(c_2Elist_2ELENGTH(ty_2Enum_2Enum),ap(ap(c_2Enumposrep_2En2l,V0b),V2n)))) ) => ( ap(ap(c_2Elist_2EEL(ty_2Enum_2Enum),V1x),ap(ap(c_2Enumposrep_2En2l,V0b),V2n)) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2EDIV,V2n),ap(ap(c_2Earithmetic_2EEXP,V0b),V1x))),V0b) ) ) ) ) ))).
fof(conj_thm_2Enumposrep_2En2l__BOUND,lemma,(! [V0b] : ( mem(V0b,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0b)) => p(ap(ap(c_2Elist_2EEVERY(ty_2Enum_2Enum),ap(c_2Earithmetic_2E_3E,V0b)),ap(ap(c_2Enumposrep_2En2l,V0b),V1n))) ) ) ))).
fof(conj_thm_2Enumposrep_2El2n__pow2__compute,lemma,(( ( ! [V0p] : ( mem(V0p,ty_2Enum_2Enum) => ( ap(ap(c_2Enumposrep_2El2n,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0p)),c_2Elist_2ENIL(ty_2Enum_2Enum)) = c_2Enum_2E0 ) ) ) & ! [V1p] : ( mem(V1p,ty_2Enum_2Enum) => ! [V2h] : ( mem(V2h,ty_2Enum_2Enum) => ! [V3t] : ( mem(V3t,ty_2Elist_2Elist(ty_2Enum_2Enum)) => ( ap(ap(c_2Enumposrep_2El2n,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1p)),ap(ap(c_2Elist_2ECONS(ty_2Enum_2Enum),V2h),V3t)) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Ebit_2EMOD__2EXP,V1p),V2h)),ap(ap(c_2Ebit_2ETIMES__2EXP,V1p),ap(ap(c_2Enumposrep_2El2n,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1p)),V3t))) ) ) ) ) ))).
fof(conj_thm_2Enumposrep_2En2l__pow2__compute,lemma,(! [V0p] : ( mem(V0p,ty_2Enum_2Enum) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0p)) => ( ap(ap(c_2Enumposrep_2En2l,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0p)),V1n) = ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Elist_2Elist(ty_2Enum_2Enum)),ap(c_2Epair_2EUNCURRY(ty_2Enum_2Enum,ty_2Enum_2Enum,ty_2Elist_2Elist(ty_2Enum_2Enum)),f820(V0p))),ap(ap(c_2Ebit_2EDIVMOD__2EXP,V0p),V1n)) ) ) ) ))).
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(ax_thm_2Epatricia__casts_2ESKIP1__def,axiom, ! [V0c] : ( mem(V0c,ty_2Estring_2Echar) => ! [V1s] : ( mem(V1s,ty_2Elist_2Elist(ty_2Estring_2Echar)) => ( ap(c_2Epatricia__casts_2ESKIP1,ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),V0c),V1s)) = V1s ) ) )).
fof(ax_thm_2Epatricia__casts_2Estring__to__num__def,axiom, ! [V0s] : ( mem(V0s,ty_2Elist_2Elist(ty_2Estring_2Echar)) => ( ap(c_2Epatricia__casts_2Estring__to__num,V0s) = ap(ap(ap(c_2EASCIInumbers_2Es2n,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))),c_2Estring_2EORD),ap(ap(c_2Elist_2ECONS(ty_2Estring_2Echar),ap(c_2Estring_2ECHR,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0s)) ) )).
fof(ax_thm_2Epatricia__casts_2Enum__to__string__def,axiom, ! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ap(c_2Epatricia__casts_2Enum__to__string,V0n) = ap(c_2Epatricia__casts_2ESKIP1,ap(ap(ap(c_2EASCIInumbers_2En2s,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))),c_2Estring_2ECHR),V0n)) ) )).
fof(conj_thm_2Epatricia__casts_2EIMAGE__string__to__num,lemma,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( ( ( V0n = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) | ( p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))),V0n)) & ( ap(ap(c_2Earithmetic_2EDIV,V0n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))),ap(ap(c_2Elogroot_2ELOG,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))),V0n))) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) ) ) ) <=> p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V0n),ap(ap(c_2Epred__set_2EIMAGE(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Enum_2Enum),c_2Epatricia__casts_2Estring__to__num),c_2Epred__set_2EUNIV(ty_2Elist_2Elist(ty_2Estring_2Echar))))) ) ))).
fof(conj_thm_2Eprim__rec_2EPRE,lemma,(( ( ap(c_2Eprim__rec_2EPRE,c_2Enum_2E0) = c_2Enum_2E0 ) & ! [V0m] : ( mem(V0m,ty_2Enum_2Enum) => ( ap(c_2Eprim__rec_2EPRE,ap(c_2Enum_2ESUC,V0m)) = V0m ) ) ))).
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(conj_thm_2Erich__list_2EMAP__REVERSE,lemma,( ! [A_27a]: ( ne(A_27a) =>  ! [A_27b]: ( ne(A_27b) => ! [V0f] : ( mem(V0f,arr(A_27a,A_27b)) => ! [V1l] : ( mem(V1l,ty_2Elist_2Elist(A_27a)) => ( ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),ap(c_2Elist_2EREVERSE(A_27a),V1l)) = ap(c_2Elist_2EREVERSE(A_27b),ap(ap(c_2Elist_2EMAP(A_27a,A_27b),V0f),V1l)) ) ) ))))).
fof(conj_thm_2Erich__list_2EEL__PRE__LENGTH,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0l] : ( mem(V0l,ty_2Elist_2Elist(A_27a)) => ( ( ~~ ( V0l = c_2Elist_2ENIL(A_27a) ) ) => ( ap(ap(c_2Elist_2EEL(A_27a),ap(c_2Eprim__rec_2EPRE,ap(c_2Elist_2ELENGTH(A_27a),V0l))),V0l) = ap(c_2Elist_2ELAST(A_27a),V0l) ) ) )))).
fof(conj_thm_2Erich__list_2EEVERY__REVERSE,lemma,( ! [A_27a]: ( ne(A_27a) => ! [V0P] : ( mem(V0P,arr(A_27a,bool)) => ! [V1l] : ( mem(V1l,ty_2Elist_2Elist(A_27a)) => ( p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),ap(c_2Elist_2EREVERSE(A_27a),V1l))) <=> p(ap(ap(c_2Elist_2EEVERY(A_27a),V0P),V1l)) ) ) )))).
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_2Estring_2ECHR__11,lemma,(! [V0r] : ( mem(V0r,ty_2Enum_2Enum) => ! [V1r_27] : ( mem(V1r_27,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,V0r),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))))) => ( p(ap(ap(c_2Eprim__rec_2E_3C,V1r_27),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))))) => ( ( ap(c_2Estring_2ECHR,V0r) = ap(c_2Estring_2ECHR,V1r_27) ) <=> ( V0r = V1r_27 ) ) ) ) ) ))).
fof(conj_thm_2Estring_2EORD__CHR__RWT,lemma,(! [V0r] : ( mem(V0r,ty_2Enum_2Enum) => ( p(ap(ap(c_2Eprim__rec_2E_3C,V0r),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))))) => ( ap(c_2Estring_2EORD,ap(c_2Estring_2ECHR,V0r)) = V0r ) ) ))).
fof(conj_thm_2Estring_2EORD__CHR__COMPUTE,lemma,(! [V0_3E_20255] : ( mem(V0_3E_20255,bool) => ! [V1n] : ( mem(V1n,ty_2Enum_2Enum) => ( ap(c_2Estring_2EORD,ap(c_2Estring_2ECHR,V1n)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))))),V1n),ap(ap(ap(c_2Ecombin_2EFAIL(arr(ty_2Estring_2Echar,ty_2Enum_2Enum),bool),c_2Estring_2EORD),V0_3E_20255),ap(c_2Estring_2ECHR,V1n))) ) ) ))).
fof(conj_thm_2Estring_2Eranged__char__nchotomy,lemma,(! [V0c] : ( mem(V0c,ty_2Estring_2Echar) => ? [V1n] : ( mem(V1n,ty_2Enum_2Enum) & ( ( V0c = ap(c_2Estring_2ECHR,V1n) ) & p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))))) ) ) ))).
fof(conj_thm_2Epatricia__casts_2Estring__to__num__num__to__string,conjecture,(! [V0n] : ( mem(V0n,ty_2Enum_2Enum) => ( p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V0n),ap(ap(c_2Epred__set_2EIMAGE(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Enum_2Enum),c_2Epatricia__casts_2Estring__to__num),c_2Epred__set_2EUNIV(ty_2Elist_2Elist(ty_2Estring_2Echar))))) => ( ap(c_2Epatricia__casts_2Estring__to__num,ap(c_2Epatricia__casts_2Enum__to__string,V0n)) = V0n ) ) ))).
