TSTP Solution File: ITP015^7 by Leo-III---1.7.10

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : ITP015^7 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n014.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May  7 07:46:53 EDT 2024

% Result   : Theorem 28.76s 7.88s
% Output   : Refutation 29.70s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :  773
% Syntax   : Number of formulae    : 1533 ( 862 unt;  88 typ;   0 def)
%            Number of atoms       : 3977 (1974 equ;   0 cnn)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives : 14105 ( 430   ~; 229   |; 655   &;12181   @)
%                                         (   0 <=>; 610  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   5 avg)
%            Number of types       :   14 (  13 usr)
%            Number of type conns  :  198 ( 198   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   80 (  77 usr;  11 con; 0-5 aty)
%            Number of variables   : 3540 (   4   ^3413   !;  86   ?;3540   :)
%                                         (  37  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(tyop_2Emin_2Ebool_type,type,
    tyop_2Emin_2Ebool: $tType ).

thf(c_2Ebool_2E_2F_5C_type,type,
    c_2Ebool_2E_2F_5C: $o > $o > $o ).

thf(tyop_2Emin_2Eind_type,type,
    tyop_2Emin_2Eind: $tType ).

thf(c_2Ebool_2ECOND_type,type,
    c_2Ebool_2ECOND: 
      !>[TA: $tType] : ( $o > TA > TA > TA ) ).

thf(c_2Ebool_2EF_type,type,
    c_2Ebool_2EF: $o ).

thf(c_2Ebool_2ET_type,type,
    c_2Ebool_2ET: $o ).

thf(tyop_2Enum_2Enum_type,type,
    tyop_2Enum_2Enum: $tType ).

thf(c_2Enum_2E0_type,type,
    c_2Enum_2E0: tyop_2Enum_2Enum ).

thf(c_2Enum_2EABS__num_type,type,
    c_2Enum_2EABS__num: tyop_2Emin_2Eind > tyop_2Enum_2Enum ).

thf(c_2Enum_2EZERO__REP_type,type,
    c_2Enum_2EZERO__REP: tyop_2Emin_2Eind ).

thf(tyop_2Eone_2Eone_type,type,
    tyop_2Eone_2Eone: $tType ).

thf(c_2Eprim__rec_2E_3C_type,type,
    c_2Eprim__rec_2E_3C: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).

thf(c_2Earithmetic_2E_2A_type,type,
    c_2Earithmetic_2E_2A: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Earithmetic_2E_2D_type,type,
    c_2Earithmetic_2E_2D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Earithmetic_2E_3C_3D_type,type,
    c_2Earithmetic_2E_3C_3D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).

thf(c_2Earithmetic_2EABS__DIFF_type,type,
    c_2Earithmetic_2EABS__DIFF: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Earithmetic_2EDIV_type,type,
    c_2Earithmetic_2EDIV: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Earithmetic_2EMOD_type,type,
    c_2Earithmetic_2EMOD: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Earithmetic_2EMODEQ_type,type,
    c_2Earithmetic_2EMODEQ: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).

thf(c_2Earithmetic_2ENRC_type,type,
    c_2Earithmetic_2ENRC: 
      !>[TA: $tType] : ( ( TA > TA > $o ) > tyop_2Enum_2Enum > TA > TA > $o ) ).

thf(c_2Earithmetic_2ENUMERAL_type,type,
    c_2Earithmetic_2ENUMERAL: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2EbasicSize_2Ebool__size_type,type,
    c_2EbasicSize_2Ebool__size: $o > tyop_2Enum_2Enum ).

thf(c_2EbasicSize_2Eone__size_type,type,
    c_2EbasicSize_2Eone__size: tyop_2Eone_2Eone > tyop_2Enum_2Enum ).

thf(c_2Egcd_2Egcd_type,type,
    c_2Egcd_2Egcd: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Egcd_2Eis__gcd_type,type,
    c_2Egcd_2Eis__gcd: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).

thf(c_2Egcd_2Elcm_type,type,
    c_2Egcd_2Elcm: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Enumpair_2Encons_type,type,
    c_2Enumpair_2Encons: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(tyop_2Estring_2Echar_type,type,
    tyop_2Estring_2Echar: $tType ).

thf(c_2Estring_2Echar__size_type,type,
    c_2Estring_2Echar__size: tyop_2Estring_2Echar > tyop_2Enum_2Enum ).

thf(tyop_2EternaryComparisons_2Eordering_type,type,
    tyop_2EternaryComparisons_2Eordering: $tType ).

thf(c_2EternaryComparisons_2Eordering__size_type,type,
    c_2EternaryComparisons_2Eordering__size: tyop_2EternaryComparisons_2Eordering > tyop_2Enum_2Enum ).

thf(tyop_2Ehrat_2Ehrat_type,type,
    tyop_2Ehrat_2Ehrat: $tType ).

thf(tyop_2Einteger_2Eint_type,type,
    tyop_2Einteger_2Eint: $tType ).

thf(c_2Einteger_2EABS_type,type,
    c_2Einteger_2EABS: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).

thf(c_2Einteger_2ENum_type,type,
    c_2Einteger_2ENum: tyop_2Einteger_2Eint > tyop_2Enum_2Enum ).

thf(c_2Einteger_2Eint__0_type,type,
    c_2Einteger_2Eint__0: tyop_2Einteger_2Eint ).

thf(c_2Einteger_2Eint__add_type,type,
    c_2Einteger_2Eint__add: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).

thf(c_2Einteger_2Eint__div_type,type,
    c_2Einteger_2Eint__div: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).

thf(c_2Einteger_2Eint__divides_type,type,
    c_2Einteger_2Eint__divides: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > $o ).

thf(c_2Einteger_2Eint__exp_type,type,
    c_2Einteger_2Eint__exp: tyop_2Einteger_2Eint > tyop_2Enum_2Enum > tyop_2Einteger_2Eint ).

thf(c_2Einteger_2Eint__le_type,type,
    c_2Einteger_2Eint__le: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > $o ).

thf(c_2Einteger_2Eint__lt_type,type,
    c_2Einteger_2Eint__lt: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > $o ).

thf(c_2Einteger_2Eint__mod_type,type,
    c_2Einteger_2Eint__mod: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).

thf(c_2Einteger_2Eint__mul_type,type,
    c_2Einteger_2Eint__mul: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).

thf(c_2Einteger_2Eint__neg_type,type,
    c_2Einteger_2Eint__neg: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).

thf(c_2Einteger_2Eint__of__num_type,type,
    c_2Einteger_2Eint__of__num: tyop_2Enum_2Enum > tyop_2Einteger_2Eint ).

thf(c_2Einteger_2Eint__quot_type,type,
    c_2Einteger_2Eint__quot: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).

thf(c_2Einteger_2Eint__rem_type,type,
    c_2Einteger_2Eint__rem: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).

thf(c_2Einteger_2Eint__sub_type,type,
    c_2Einteger_2Eint__sub: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).

thf(tyop_2Equote_2Eindex_type,type,
    tyop_2Equote_2Eindex: $tType ).

thf(tyop_2Etoto_2Enum__dt_type,type,
    tyop_2Etoto_2Enum__dt: $tType ).

thf(c_2Ewords_2Ebit__count_type,type,
    c_2Ewords_2Ebit__count: 
      !>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > tyop_2Enum_2Enum ) ).

thf(c_2Ewords_2Ebit__count__upto_type,type,
    c_2Ewords_2Ebit__count__upto: 
      !>[TA: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ TA ) > tyop_2Enum_2Enum ) ).

thf(c_2Ewords_2En2w_type,type,
    c_2Ewords_2En2w: 
      !>[TA: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).

thf(c_2Ewords_2Esw2sw_type,type,
    c_2Ewords_2Esw2sw: 
      !>[TA: $tType,TB: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TB ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).

thf(c_2Ewords_2Ew2n_type,type,
    c_2Ewords_2Ew2n: 
      !>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > tyop_2Enum_2Enum ) ).

thf(c_2Ewords_2Ew2w_type,type,
    c_2Ewords_2Ew2w: 
      !>[TA: $tType,TB: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TB ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).

thf(c_2Ewords_2Eword__2comp_type,type,
    c_2Ewords_2Eword__2comp: 
      !>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).

thf(c_2Ewords_2Eword__L_type,type,
    c_2Ewords_2Eword__L: 
      !>[TA: $tType] : ( tyop_2Efcp_2Ecart @ $o @ TA ) ).

thf(c_2Ewords_2Eword__abs_type,type,
    c_2Ewords_2Eword__abs: 
      !>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).

thf(c_2Ewords_2Eword__add_type,type,
    c_2Ewords_2Eword__add: 
      !>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).

thf(c_2Ewords_2Eword__bit_type,type,
    c_2Ewords_2Eword__bit: 
      !>[TA: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ TA ) > $o ) ).

thf(c_2Ewords_2Eword__bits_type,type,
    c_2Ewords_2Eword__bits: 
      !>[TA: $tType] : ( tyop_2Enum_2Enum > tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).

thf(c_2Ewords_2Eword__concat_type,type,
    c_2Ewords_2Eword__concat: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TC ) > ( tyop_2Efcp_2Ecart @ $o @ TB ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).

thf(c_2Ewords_2Eword__extract_type,type,
    c_2Ewords_2Eword__extract: 
      !>[TA: $tType,TB: $tType] : ( tyop_2Enum_2Enum > tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ TB ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).

thf(c_2Ewords_2Eword__le_type,type,
    c_2Ewords_2Eword__le: 
      !>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) > $o ) ).

thf(c_2Ewords_2Eword__lo_type,type,
    c_2Ewords_2Eword__lo: 
      !>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) > $o ) ).

thf(c_2Ewords_2Eword__ls_type,type,
    c_2Ewords_2Eword__ls: 
      !>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) > $o ) ).

thf(c_2Ewords_2Eword__lt_type,type,
    c_2Ewords_2Eword__lt: 
      !>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) > $o ) ).

thf(c_2Ewords_2Eword__msb_type,type,
    c_2Ewords_2Eword__msb: 
      !>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > $o ) ).

thf(c_2Ewords_2Eword__mul_type,type,
    c_2Ewords_2Eword__mul: 
      !>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).

thf(c_2Ewords_2Eword__reverse_type,type,
    c_2Ewords_2Eword__reverse: 
      !>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).

thf(c_2Ewords_2Eword__slice_type,type,
    c_2Ewords_2Eword__slice: 
      !>[TA: $tType] : ( tyop_2Enum_2Enum > tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).

thf(c_2Ewords_2Eword__sub_type,type,
    c_2Ewords_2Eword__sub: 
      !>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).

thf(c_2Ealignment_2Ealign_type,type,
    c_2Ealignment_2Ealign: 
      !>[TA: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).

thf(c_2Ealignment_2Ealigned_type,type,
    c_2Ealignment_2Ealigned: 
      !>[TA: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ TA ) > $o ) ).

thf(c_2Ebitstring_2Eshiftr_type,type,
    c_2Ebitstring_2Eshiftr: ( tyop_2Elist_2Elist @ $o ) > tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ $o ) ).

thf(c_2Ebitstring_2Ev2w_type,type,
    c_2Ebitstring_2Ev2w: 
      !>[TA: $tType] : ( ( tyop_2Elist_2Elist @ $o ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).

thf(tyop_2Ehreal_2Ehreal_type,type,
    tyop_2Ehreal_2Ehreal: $tType ).

thf(c_2Esptree_2Espt__acc_type,type,
    c_2Esptree_2Espt__acc: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(tyop_2EDeepSyntax_2Edeep__form_type,type,
    tyop_2EDeepSyntax_2Edeep__form: $tType ).

thf(c_2Einteger__word_2Ei2w_type,type,
    c_2Einteger__word_2Ei2w: 
      !>[TA: $tType] : ( tyop_2Einteger_2Eint > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).

thf(c_2Einteger__word_2Ew2i_type,type,
    c_2Einteger__word_2Ew2i: 
      !>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > tyop_2Einteger_2Eint ) ).

thf(c_2Einteger__word_2Eword__sdiv_type,type,
    c_2Einteger__word_2Eword__sdiv: 
      !>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).

thf(c_2Einteger__word_2Eword__smod_type,type,
    c_2Einteger__word_2Eword__smod: 
      !>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).

thf(skt1_type,type,
    skt1: $tType ).

thf(sk32_type,type,
    sk32: $o ).

thf(sk33_type,type,
    sk33: $o ).

thf(223,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
     => ( ( c_2Earithmetic_2EMODEQ @ A @ C @ B )
        = ( ( c_2Earithmetic_2EMOD @ C @ A )
          = ( c_2Earithmetic_2EMOD @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMODEQ__NONZERO__MODEQUALITY) ).

thf(1665,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
     => ( ( c_2Earithmetic_2EMODEQ @ A @ C @ B )
        = ( ( c_2Earithmetic_2EMOD @ C @ A )
          = ( c_2Earithmetic_2EMOD @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(96,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ~ ( c_2Eprim__rec_2E_3C @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eprim__rec_2ELESS__REFL) ).

thf(1036,plain,
    ! [A: tyop_2Enum_2Enum] :
      ~ ( c_2Eprim__rec_2E_3C @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(366,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__ls @ TA @ A @ B )
      | ( c_2Ewords_2Eword__ls @ TA @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__EQ__CASES) ).

thf(2452,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__ls @ TA @ A @ B )
      | ( c_2Ewords_2Eword__ls @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(504,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ C ) @ ( c_2Einteger_2Eint__add @ B @ C ) )
      = ( c_2Einteger_2Eint__lt @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__RADD) ).

thf(2889,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ C ) @ ( c_2Einteger_2Eint__add @ B @ C ) )
      = ( c_2Einteger_2Eint__lt @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(467,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( A = B )
     => ~ ( c_2Ewords_2Eword__lo @ TA @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NOT__LOWER__EQ) ).

thf(2778,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( A = B )
     => ~ ( c_2Ewords_2Eword__lo @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(239,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__le @ TA @ A @ B )
        & ( c_2Ewords_2Eword__le @ TA @ B @ A ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__EQUAL__ANTISYM) ).

thf(1729,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__le @ TA @ A @ B )
        & ( c_2Ewords_2Eword__le @ TA @ B @ A ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(57,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2D @ B @ A ) @ ( c_2Earithmetic_2E_2D @ C @ A ) )
      = ( ( c_2Earithmetic_2E_3C_3D @ B @ A )
        | ( c_2Earithmetic_2E_3C_3D @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELE__SUB__RCANCEL) ).

thf(893,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2D @ B @ A ) @ ( c_2Earithmetic_2E_2D @ C @ A ) )
      = ( ( c_2Earithmetic_2E_3C_3D @ B @ A )
        | ( c_2Earithmetic_2E_3C_3D @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(151,axiom,
    ! [A: $o] :
      ( ( A
       => c_2Ebool_2EF )
      = ~ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CLAUSES__XF) ).

thf(1315,plain,
    ! [A: $o] :
      ( ( A
       => c_2Ebool_2EF )
      = ~ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(358,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__sub @ A @ B ) @ C )
        & ( c_2Einteger_2Eint__lt @ C @ A ) )
      = ( ? [D: tyop_2Einteger_2Eint] :
            ( ( C
              = ( c_2Einteger_2Eint__sub @ A @ D ) )
            & ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D )
            & ( c_2Einteger_2Eint__le @ D @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ein__subtractive__range) ).

thf(2427,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__sub @ A @ B ) @ C )
        & ( c_2Einteger_2Eint__lt @ C @ A ) )
      = ( ? [D: tyop_2Einteger_2Eint] :
            ( ( C
              = ( c_2Einteger_2Eint__sub @ A @ D ) )
            & ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D )
            & ( c_2Einteger_2Eint__le @ D @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(418,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__le @ A @ B )
        & ( c_2Einteger_2Eint__le @ C @ D ) )
     => ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ A @ C ) @ ( c_2Einteger_2Eint__add @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__ADD2) ).

thf(2612,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__le @ A @ B )
        & ( c_2Einteger_2Eint__le @ C @ D ) )
     => ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ A @ C ) @ ( c_2Einteger_2Eint__add @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(92,axiom,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2ECOND__CLAUSES__CF) ).

thf(1024,plain,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(133,axiom,
    ! [A: $o] :
      ( ( A
       => c_2Ebool_2EF )
     => ~ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__F) ).

thf(1168,plain,
    ! [A: $o] :
      ( ( A
       => c_2Ebool_2EF )
     => ~ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(317,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ A @ B )
     => ~ ( c_2Einteger_2Eint__lt @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__GT) ).

thf(2295,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ A @ B )
     => ~ ( c_2Einteger_2Eint__lt @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(321,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__lt @ A @ B )
        & ( c_2Einteger_2Eint__lt @ B @ C ) )
     => ( c_2Einteger_2Eint__lt @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__TRANS) ).

thf(2306,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__lt @ A @ B )
        & ( c_2Einteger_2Eint__lt @ B @ C ) )
     => ( c_2Einteger_2Eint__lt @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(22,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
     => ( ( c_2Earithmetic_2EDIV @ ( c_2Earithmetic_2E_2A @ B @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMULT__DIV) ).

thf(760,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
     => ( ( c_2Earithmetic_2EDIV @ ( c_2Earithmetic_2E_2A @ B @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(541,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__add @ A @ C )
        = ( c_2Einteger_2Eint__add @ B @ C ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__RADD) ).

thf(3008,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__add @ A @ C )
        = ( c_2Einteger_2Eint__add @ B @ C ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(273,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__neg @ B ) )
        = ( c_2Einteger_2Eint__divides @ A @ B ) )
      & ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__neg @ A ) @ B )
        = ( c_2Einteger_2Eint__divides @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__NEG) ).

thf(2131,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__neg @ B ) )
        = ( c_2Einteger_2Eint__divides @ A @ B ) )
      & ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__neg @ A ) @ B )
        = ( c_2Einteger_2Eint__divides @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(182,axiom,
    ! [TA: $tType,A: TA,B: TA] :
    ? [C: $o > TA] :
      ( ( ( C @ c_2Ebool_2ET )
        = A )
      & ( ( C @ c_2Ebool_2EF )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EboolAxiom) ).

thf(1454,plain,
    ! [TA: $tType,A: TA,B: TA] :
    ? [C: $o > TA] :
      ( ( ( C @ c_2Ebool_2ET )
        = A )
      & ( ( C @ c_2Ebool_2EF )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(396,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__mul @ B @ A )
      = ( c_2Einteger_2Eint__mul @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__COMM) ).

thf(2544,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__mul @ B @ A )
      = ( c_2Einteger_2Eint__mul @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(70,axiom,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_3C_3D @ B @ A )
     => ( ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2D @ A @ B ) )
        = ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2En2w @ TA @ A ) @ ( c_2Ewords_2En2w @ TA @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2En2w__sub) ).

thf(941,plain,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_3C_3D @ B @ A )
     => ( ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2D @ A @ B ) )
        = ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2En2w @ TA @ A ) @ ( c_2Ewords_2En2w @ TA @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(312,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A = B )
     => ( c_2Einteger_2Eint__le @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__IMP__LE) ).

thf(2280,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A = B )
     => ( c_2Einteger_2Eint__le @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(116,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__le @ TA @ A @ B )
      = ( c_2Einteger_2Eint__le @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger__word_2Ew2i @ TA @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2EWORD__LEi) ).

thf(1110,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__le @ TA @ A @ B )
      = ( c_2Einteger_2Eint__le @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger__word_2Ew2i @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(336,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ A ) @ A )
      = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__LINV) ).

thf(2363,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ A ) @ A )
      = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(294,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
      | ( c_2Ewords_2Eword__ls @ TA @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__CASES) ).

thf(2210,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
      | ( c_2Ewords_2Eword__ls @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(15,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__mul @ TA @ A @ B )
      = ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2A @ ( c_2Ewords_2Ew2n @ TA @ A ) @ ( c_2Ewords_2Ew2n @ TA @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__mul__def) ).

thf(730,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__mul @ TA @ A @ B )
      = ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2A @ ( c_2Ewords_2Ew2n @ TA @ A ) @ ( c_2Ewords_2Ew2n @ TA @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(615,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Ew2n @ TA @ A )
        = c_2Enum_2E0 )
      = ( A
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Ew2n__eq__0) ).

thf(3285,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Ew2n @ TA @ A )
        = c_2Enum_2E0 )
      = ( A
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

thf(434,axiom,
    ! [TA: $tType,A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Ewords_2Eword__add @ TA @ ( c_2Einteger__word_2Ei2w @ TA @ A ) @ ( c_2Einteger__word_2Ei2w @ TA @ B ) )
      = ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__add @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__i2w__add) ).

thf(2676,plain,
    ! [TA: $tType,A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Ewords_2Eword__add @ TA @ ( c_2Einteger__word_2Ei2w @ TA @ A ) @ ( c_2Einteger__word_2Ei2w @ TA @ B ) )
      = ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__add @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(574,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__add @ A @ B )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( A
        = ( c_2Einteger_2Eint__neg @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LNEG__UNIQ) ).

thf(3108,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__add @ A @ B )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( A
        = ( c_2Einteger_2Eint__neg @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(140,axiom,
    ! [A: $o] :
      ( ( c_2Ebool_2EF
        | A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EOR__CLAUSES__FX) ).

thf(1205,plain,
    ! [A: $o] :
      ( ( c_2Ebool_2EF
        | A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(227,axiom,
    ( ~ c_2Ebool_2EF = c_2Ebool_2ET ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2ENOT__CLAUSES__F) ).

thf(1692,plain,
    ( ~ c_2Ebool_2EF = c_2Ebool_2ET ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(98,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
        & ( c_2Earithmetic_2E_3C_3D @ B @ C ) )
     => ( c_2Earithmetic_2E_3C_3D @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__EQ__TRANS) ).

thf(1041,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
        & ( c_2Earithmetic_2E_3C_3D @ B @ C ) )
     => ( c_2Earithmetic_2E_3C_3D @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(134,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__le @ TA @ A @ B )
      = ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__OR__EQ) ).

thf(1173,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__le @ TA @ A @ B )
      = ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
        | ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(243,axiom,
    ! [A: $o,B: $o,C: $o,D: $o,E: $o] :
      ( ( ( A
         => ( C
           => B ) )
        & ( ~ A
         => ( E
           => D ) ) )
     => ( ( c_2Ebool_2ECOND @ $o @ A @ C @ E )
       => ( c_2Ebool_2ECOND @ $o @ A @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CONG__cond) ).

thf(1750,plain,
    ! [A: $o,B: $o,C: $o,D: $o,E: $o] :
      ( ( ( A
         => ( C
           => B ) )
        & ( ~ A
         => ( E
           => D ) ) )
     => ( ( c_2Ebool_2ECOND @ $o @ A @ C @ E )
       => ( c_2Ebool_2ECOND @ $o @ A @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(591,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__mul @ C @ B ) )
        = ( c_2Einteger_2Eint__divides @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2EINT__DIVIDES__LRMUL) ).

thf(3185,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__mul @ C @ B ) )
        = ( c_2Einteger_2Eint__divides @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(174,axiom,
    ! [TA: $tType,A: ( tyop_2Enum_2Enum > TA ) > tyop_2Enum_2Enum > TA] :
      ( ! [B: tyop_2Enum_2Enum > TA,C: tyop_2Enum_2Enum > TA,D: tyop_2Enum_2Enum] :
          ( ! [E: tyop_2Enum_2Enum] :
              ( ( c_2Eprim__rec_2E_3C @ E @ D )
             => ( ( B @ E )
                = ( C @ E ) ) )
         => ( ( A @ B @ D )
            = ( A @ C @ D ) ) )
     => ? [B: tyop_2Enum_2Enum > TA] :
        ! [C: tyop_2Enum_2Enum] :
          ( ( B @ C )
          = ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewellorder_2EWF__REC__num) ).

thf(1406,plain,
    ! [TA: $tType,A: ( tyop_2Enum_2Enum > TA ) > tyop_2Enum_2Enum > TA] :
      ( ! [B: tyop_2Enum_2Enum > TA,C: tyop_2Enum_2Enum > TA,D: tyop_2Enum_2Enum] :
          ( ! [E: tyop_2Enum_2Enum] :
              ( ( c_2Eprim__rec_2E_3C @ E @ D )
             => ( ( B @ E )
                = ( C @ E ) ) )
         => ( ( A @ B @ D )
            = ( A @ C @ D ) ) )
     => ? [B: tyop_2Enum_2Enum > TA] :
        ! [C: tyop_2Enum_2Enum] :
          ( ( B @ C )
          = ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(266,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Enum_2E0 = A )
      | ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__0__CASES) ).

thf(2104,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Enum_2E0 = A )
      | ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(422,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__mul @ C @ ( c_2Einteger_2Eint__mul @ B @ A ) )
      = ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__mul @ C @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__ASSOC) ).

thf(2622,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__mul @ C @ ( c_2Einteger_2Eint__mul @ B @ A ) )
      = ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__mul @ C @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(105,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ~ ( c_2Eprim__rec_2E_3C @ A @ c_2Enum_2E0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eprim__rec_2ENOT__LESS__0) ).

thf(1068,plain,
    ! [A: tyop_2Enum_2Enum] :
      ~ ( c_2Eprim__rec_2E_3C @ A @ c_2Enum_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(382,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
        & ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ C )
        & ( c_2Einteger_2Eint__lt @ A @ B )
        & ( c_2Einteger_2Eint__lt @ C @ D ) )
     => ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__mul @ A @ C ) @ ( c_2Einteger_2Eint__mul @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__MUL2) ).

thf(2495,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
        & ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ C )
        & ( c_2Einteger_2Eint__lt @ A @ B )
        & ( c_2Einteger_2Eint__lt @ C @ D ) )
     => ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__mul @ A @ C ) @ ( c_2Einteger_2Eint__mul @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(600,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Einteger__word_2Ew2i @ TA @ A )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( A
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Ew2i__eq__0) ).

thf(3230,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Einteger__word_2Ew2i @ TA @ A )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( A
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(347,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B )
        & ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) )
     => ( ( c_2Eprim__rec_2E_3C @ ( c_2Einteger_2ENum @ B ) @ ( c_2Einteger_2ENum @ A ) )
        = ( c_2Einteger_2Eint__lt @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2ENUM__LT) ).

thf(2395,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B )
        & ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) )
     => ( ( c_2Eprim__rec_2E_3C @ ( c_2Einteger_2ENum @ B ) @ ( c_2Einteger_2ENum @ A ) )
        = ( c_2Einteger_2Eint__lt @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(510,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum] :
      ( ( ( c_2Enumpair_2Encons @ B @ A )
        = ( c_2Enumpair_2Encons @ D @ C ) )
      = ( ( B = D )
        & ( A = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Encons__11) ).

thf(2908,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum] :
      ( ( ( c_2Enumpair_2Encons @ B @ A )
        = ( c_2Enumpair_2Encons @ D @ C ) )
      = ( ( B = D )
        & ( A = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(642,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD0) ).

thf(3377,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).

thf(391,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__add @ A @ B ) )
      = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ A ) @ ( c_2Einteger_2Eint__neg @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__ADD) ).

thf(2527,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__add @ A @ B ) )
      = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ A ) @ ( c_2Einteger_2Eint__neg @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(552,axiom,
    ! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( A @ ( c_2Einteger_2Eint__mod @ B @ C ) )
        = ( ? [D: tyop_2Einteger_2Eint,E: tyop_2Einteger_2Eint] :
              ( ( B
                = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ D @ C ) @ E ) )
              & ( ( ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
                  & ( c_2Einteger_2Eint__lt @ C @ E )
                  & ( c_2Einteger_2Eint__le @ E @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
                | ( ~ ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
                  & ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ E )
                  & ( c_2Einteger_2Eint__lt @ E @ C ) ) )
              & ( A @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__P) ).

thf(3040,plain,
    ! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( A @ ( c_2Einteger_2Eint__mod @ B @ C ) )
        = ( ? [D: tyop_2Einteger_2Eint,E: tyop_2Einteger_2Eint] :
              ( ( B
                = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ D @ C ) @ E ) )
              & ( ( ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
                  & ( c_2Einteger_2Eint__lt @ C @ E )
                  & ( c_2Einteger_2Eint__le @ E @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
                | ( ~ ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
                  & ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ E )
                  & ( c_2Einteger_2Eint__lt @ E @ C ) ) )
              & ( A @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(583,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__neg @ A )
        = ( c_2Einteger_2Eint__neg @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__NEG) ).

thf(3153,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__neg @ A )
        = ( c_2Einteger_2Eint__neg @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(268,axiom,
    ( ! [A: $o] :
        ( ( ~ ~ A )
        = A )
    & ( ~ c_2Ebool_2ET = c_2Ebool_2EF )
    & ( ~ c_2Ebool_2EF = c_2Ebool_2ET ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ENOT__CLAUSES) ).

thf(2114,plain,
    ( ( ~ c_2Ebool_2ET = c_2Ebool_2EF )
    & ( ~ c_2Ebool_2EF = c_2Ebool_2ET ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(125,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] : ( c_2Egcd_2Eis__gcd @ A @ B @ ( c_2Egcd_2Egcd @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EGCD__IS__GCD) ).

thf(1142,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] : ( c_2Egcd_2Eis__gcd @ A @ B @ ( c_2Egcd_2Egcd @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(52,axiom,
    ! [A: $o] :
      ( ( A
        & c_2Ebool_2ET )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EAND__CLAUSES__XT) ).

thf(876,plain,
    ! [A: $o] :
      ( ( A
        & c_2Ebool_2ET )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(877,plain,
    ( ( $true
      & c_2Ebool_2ET )
    = $true ),
    inference(instance,[status(thm)],[876]) ).

thf(878,plain,
    c_2Ebool_2ET,
    inference(simp,[status(thm)],[877]) ).

thf(680,axiom,
    ! [TA: $tType] :
      ~ ( c_2Ewords_2Eword__msb @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__0__POS) ).

thf(3498,plain,
    ! [TA: $tType] :
      ~ ( c_2Ewords_2Eword__msb @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).

thf(342,axiom,
    ! [TA: $tType] : ( c_2Ewords_2Eword__lo @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ ( c_2Ewords_2Eword__L @ TA ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EZERO__LO__INT__MIN) ).

thf(2380,plain,
    ! [TA: $tType] : ( c_2Ewords_2Eword__lo @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ ( c_2Ewords_2Eword__L @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(661,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__mod @ B @ A ) @ A )
        = ( c_2Einteger_2Eint__mod @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__MOD) ).

thf(3439,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__mod @ B @ A ) @ A )
        = ( c_2Einteger_2Eint__mod @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).

thf(631,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ? [B: tyop_2Enum_2Enum] :
          ( ( A
            = ( c_2Einteger_2Eint__of__num @ B ) )
          & ( B != c_2Enum_2E0 ) )
      | ? [B: tyop_2Enum_2Enum] :
          ( ( A
            = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ B ) ) )
          & ( B != c_2Enum_2E0 ) )
      | ( A
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NUM__CASES) ).

thf(3332,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ? [B: tyop_2Enum_2Enum] :
          ( ( A
            = ( c_2Einteger_2Eint__of__num @ B ) )
          & ( B != c_2Enum_2E0 ) )
      | ? [B: tyop_2Enum_2Enum] :
          ( ( A
            = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ B ) ) )
          & ( B != c_2Enum_2E0 ) )
      | ( A
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(663,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ! [A: tyop_2Enum_2Enum] : ( c_2Ealignment_2Ealigned @ TB @ A @ ( c_2Ewords_2En2w @ TB @ c_2Enum_2E0 ) )
      & ! [A: tyop_2Efcp_2Ecart @ $o @ TA] : ( c_2Ealignment_2Ealigned @ TA @ c_2Enum_2E0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ealignment_2Ealigned__0) ).

thf(3446,plain,
    ! [TA: $tType,TB: $tType] :
      ( ! [A: tyop_2Enum_2Enum] : ( c_2Ealignment_2Ealigned @ TB @ A @ ( c_2Ewords_2En2w @ TB @ c_2Enum_2E0 ) )
      & ! [A: tyop_2Efcp_2Ecart @ $o @ TA] : ( c_2Ealignment_2Ealigned @ TA @ c_2Enum_2E0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).

thf(607,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__mod @ A @ A )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__ID) ).

thf(3253,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__mod @ A @ A )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(674,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( c_2Ewords_2Ew2w @ TA @ TB @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
      = ( c_2Ewords_2En2w @ TB @ c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Ew2w__0) ).

thf(3481,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( c_2Ewords_2Ew2w @ TA @ TB @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
      = ( c_2Ewords_2En2w @ TB @ c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).

thf(624,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EABS__DIFF @ A @ B )
        = c_2Enum_2E0 )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EABS__DIFF__EQ__0) ).

thf(3313,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EABS__DIFF @ A @ B )
        = c_2Enum_2E0 )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(103,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ A )
        & ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ B ) )
     => ( ( c_2Ewords_2Eword__le @ TA @ A @ B )
        = ( c_2Ewords_2Eword__ls @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LE__EQ__LS) ).

thf(1063,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ A )
        & ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ B ) )
     => ( ( c_2Ewords_2Eword__le @ TA @ A @ B )
        = ( c_2Ewords_2Eword__ls @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(335,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__sub @ TA @ A @ B )
        = C )
      = ( A
        = ( c_2Ewords_2Eword__add @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__EQ__SUB__RADD) ).

thf(2360,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__sub @ TA @ A @ B )
        = C )
      = ( A
        = ( c_2Ewords_2Eword__add @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(233,axiom,
    ! [A: $o] :
      ( ( ( c_2Ebool_2ET = A )
        = A )
      & ( ( A = c_2Ebool_2ET )
        = A )
      & ( ( c_2Ebool_2EF = A )
        = ~ A )
      & ( ( A = c_2Ebool_2EF )
        = ~ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).

thf(1705,plain,
    ! [A: $o] :
      ( ( ( c_2Ebool_2ET = A )
        = A )
      & ( ( A = c_2Ebool_2ET )
        = A )
      & ( ( c_2Ebool_2EF = A )
        = ~ A )
      & ( ( A = c_2Ebool_2EF )
        = ~ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(544,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__neg @ A ) )
      = ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__NEGR) ).

thf(3017,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__neg @ A ) )
      = ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(638,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__2comp @ TA @ A )
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
      = ( A
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__EQ__0) ).

thf(3365,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__2comp @ TA @ A )
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
      = ( A
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(453,axiom,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__bits @ TA @ A @ B @ C )
      = ( c_2Ewords_2Eword__extract @ TA @ TA @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__BITS__EXTRACT) ).

thf(2740,plain,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__bits @ TA @ A @ B @ C )
      = ( c_2Ewords_2Eword__extract @ TA @ TA @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(10,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ C @ B ) )
      = ( ( B = c_2Enum_2E0 )
        | ( c_2Earithmetic_2E_3C_3D @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELE__MULT__RCANCEL) ).

thf(715,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ C @ B ) )
      = ( ( B = c_2Enum_2E0 )
        | ( c_2Earithmetic_2E_3C_3D @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(518,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__neg @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEGNEG) ).

thf(2933,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__neg @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(284,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__mod @ C @ A ) @ ( c_2Einteger_2Eint__mod @ B @ A ) ) @ A )
        = ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__sub @ C @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__SUB) ).

thf(2168,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__mod @ C @ A ) @ ( c_2Einteger_2Eint__mod @ B @ A ) ) @ A )
        = ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__sub @ C @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(6,axiom,
    ! [A: $o,B: $o] :
      ( ( c_2Ebool_2E_2F_5C @ A @ B )
      = ( A
        & B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_2F_5C) ).

thf(698,plain,
    ! [A: $o,B: $o] :
      ( ( c_2Ebool_2E_2F_5C @ A @ B )
      = ( A
        & B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(602,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__quot @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__QUOT__0) ).

thf(3236,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__quot @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(635,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__LID) ).

thf(3350,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(531,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__add @ A @ B ) @ ( c_2Einteger_2Eint__add @ C @ D ) )
      = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__sub @ A @ C ) @ ( c_2Einteger_2Eint__sub @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD2__SUB2) ).

thf(2972,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__add @ A @ B ) @ ( c_2Einteger_2Eint__add @ C @ D ) )
      = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__sub @ A @ C ) @ ( c_2Einteger_2Eint__sub @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(169,axiom,
    ! [A: tyop_2Enum_2Enum > $o] :
      ( ? [B: tyop_2Enum_2Enum] : ( A @ B )
     => ? [B: tyop_2Enum_2Enum] :
          ( ( A @ B )
          & ! [C: tyop_2Enum_2Enum] :
              ( ( c_2Eprim__rec_2E_3C @ C @ B )
             => ~ ( A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EWOP) ).

thf(1391,plain,
    ! [A: tyop_2Enum_2Enum > $o] :
      ( ? [B: tyop_2Enum_2Enum] : ( A @ B )
     => ? [B: tyop_2Enum_2Enum] :
          ( ( A @ B )
          & ! [C: tyop_2Enum_2Enum] :
              ( ( c_2Eprim__rec_2E_3C @ C @ B )
             => ~ ( A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(29,axiom,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Ewords_2Eword__mul @ TA @ ( c_2Ewords_2En2w @ TA @ A ) @ ( c_2Ewords_2En2w @ TA @ B ) )
      = ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__mul__n2w) ).

thf(782,plain,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Ewords_2Eword__mul @ TA @ ( c_2Ewords_2En2w @ TA @ A ) @ ( c_2Ewords_2En2w @ TA @ B ) )
      = ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(7,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
        & ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ B @ A ) @ C ) )
     => ( ( c_2Earithmetic_2EDIV @ ( c_2Earithmetic_2E_2D @ C @ ( c_2Earithmetic_2E_2A @ B @ A ) ) @ B )
        = ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2EDIV @ C @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EDIV__SUB) ).

thf(707,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
        & ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ B @ A ) @ C ) )
     => ( ( c_2Earithmetic_2EDIV @ ( c_2Earithmetic_2E_2D @ C @ ( c_2Earithmetic_2E_2A @ B @ A ) ) @ B )
        = ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2EDIV @ C @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(708,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
      | ~ ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ B @ A ) @ C )
      | ( ( c_2Earithmetic_2EDIV @ ( c_2Earithmetic_2E_2D @ C @ ( c_2Earithmetic_2E_2A @ B @ A ) ) @ B )
        = ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2EDIV @ C @ B ) @ A ) ) ),
    inference(cnf,[status(esa)],[707]) ).

thf(709,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EDIV @ ( c_2Earithmetic_2E_2D @ C @ ( c_2Earithmetic_2E_2A @ B @ A ) ) @ B )
        = ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2EDIV @ C @ B ) @ A ) )
      | ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
      | ~ ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ B @ A ) @ C ) ),
    inference(lifteq,[status(thm)],[708]) ).

thf(253,axiom,
    ! [A: $o] :
      ( ( c_2Ebool_2ET
        & A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EAND__CLAUSES__TX) ).

thf(2020,plain,
    ! [A: $o] :
      ( ( c_2Ebool_2ET
        & A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(503,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ C @ B ) )
     => ( ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__neg @ B ) )
       => ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ C ) @ A ) )
          = c_2Ebool_2EF ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ele__context__rwt2) ).

thf(2886,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ C @ B ) )
     => ( ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__neg @ B ) )
       => ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ C ) @ A ) )
          = c_2Ebool_2EF ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(43,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
        & ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ C ) )
     => ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2EDIV @ A @ B ) @ C )
        = ( c_2Earithmetic_2EDIV @ ( c_2Earithmetic_2EMOD @ A @ ( c_2Earithmetic_2E_2A @ B @ C ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EDIV__MOD__MOD__DIV) ).

thf(829,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
        & ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ C ) )
     => ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2EDIV @ A @ B ) @ C )
        = ( c_2Earithmetic_2EDIV @ ( c_2Earithmetic_2EMOD @ A @ ( c_2Earithmetic_2E_2A @ B @ C ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(113,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__mul @ TA @ A @ ( c_2Ewords_2Eword__mul @ TA @ B @ C ) )
      = ( c_2Ewords_2Eword__mul @ TA @ ( c_2Ewords_2Eword__mul @ TA @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__MULT__ASSOC) ).

thf(1095,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__mul @ TA @ A @ ( c_2Ewords_2Eword__mul @ TA @ B @ C ) )
      = ( c_2Ewords_2Eword__mul @ TA @ ( c_2Ewords_2Eword__mul @ TA @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(567,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( A
       != ( c_2Ewords_2Eword__L @ TA ) )
     => ( ( c_2Einteger__word_2Ew2i @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) )
        = ( c_2Einteger_2Eint__neg @ ( c_2Einteger__word_2Ew2i @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Ew2i__neg) ).

thf(3088,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( A
       != ( c_2Ewords_2Eword__L @ TA ) )
     => ( ( c_2Einteger__word_2Ew2i @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) )
        = ( c_2Einteger_2Eint__neg @ ( c_2Einteger__word_2Ew2i @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(58,axiom,
    ! [A: $o,B: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ A @ c_2Ebool_2ET @ B )
      = ( ~ A
       => B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2ECOND__CLAUSES__TT) ).

thf(896,plain,
    ! [A: $o,B: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ A @ c_2Ebool_2ET @ B )
      = ( ~ A
       => B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(897,plain,
    ( ( c_2Ebool_2ECOND @ $o @ $true @ c_2Ebool_2ET @ $true )
    = ( ~ $true
     => $true ) ),
    inference(instance,[status(thm)],[896]) ).

thf(898,plain,
    c_2Ebool_2ECOND @ $o @ $true @ c_2Ebool_2ET @ $true,
    inference(simp,[status(thm)],[897]) ).

thf(3777,plain,
    c_2Ebool_2ECOND @ $o @ $true @ $true @ $true,
    inference(rewrite,[status(thm)],[898,878]) ).

thf(204,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
        & ( c_2Earithmetic_2E_3C_3D @ A @ C ) )
     => ( ( ( c_2Earithmetic_2E_2D @ B @ A )
          = ( c_2Earithmetic_2E_2D @ C @ A ) )
        = ( B = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ECANCEL__SUB) ).

thf(1601,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
        & ( c_2Earithmetic_2E_3C_3D @ A @ C ) )
     => ( ( ( c_2Earithmetic_2E_2D @ B @ A )
          = ( c_2Earithmetic_2E_2D @ C @ A ) )
        = ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(168,axiom,
    ( ( c_2Ebool_2ET != c_2Ebool_2EF )
    & ( c_2Ebool_2EF != c_2Ebool_2ET ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EBOOL__EQ__DISTINCT) ).

thf(1386,plain,
    ( ( c_2Ebool_2ET != c_2Ebool_2EF )
    & ( c_2Ebool_2EF != c_2Ebool_2ET ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(669,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__mul @ A @ B )
        = ( c_2Einteger_2Eint__mul @ A @ C ) )
      = ( ( A
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        | ( B = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__LMUL) ).

thf(3466,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__mul @ A @ B )
        = ( c_2Einteger_2Eint__mul @ A @ C ) )
      = ( ( A
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        | ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).

thf(201,axiom,
    ! [A: $o,B: $o,C: $o,D: $o,E: $o] :
      ( ( ( C
         => B )
        & ( E
         => D ) )
     => ( ( c_2Ebool_2ECOND @ $o @ A @ C @ E )
       => ( c_2Ebool_2ECOND @ $o @ A @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CONG__cond__simple) ).

thf(1518,plain,
    ! [A: $o,B: $o,C: $o,D: $o,E: $o] :
      ( ( ( C
         => B )
        & ( E
         => D ) )
     => ( ( c_2Ebool_2ECOND @ $o @ A @ C @ E )
       => ( c_2Ebool_2ECOND @ $o @ A @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(232,axiom,
    ( c_2Ebool_2EF
    = ( ! [A: $o] : A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EF__DEF) ).

thf(1703,plain,
    ( c_2Ebool_2EF
    = ( ! [A: $o] : A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(212,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( B != c_2Enum_2E0 )
     => ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
        = ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIV) ).

thf(1628,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( B != c_2Enum_2E0 )
     => ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
        = ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(13,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
        & ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
        & ( c_2Earithmetic_2E_3C_3D @ C @ A ) )
     => ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2A @ B @ A ) @ C ) @ A )
        = ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ A @ C ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__TIMES__SUB) ).

thf(724,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
        & ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
        & ( c_2Earithmetic_2E_3C_3D @ C @ A ) )
     => ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2A @ B @ A ) @ C ) @ A )
        = ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ A @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(611,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__add @ TA @ A @ B )
        = A )
      = ( B
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__INV__0__EQ) ).

thf(3263,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__add @ TA @ A @ B )
        = A )
      = ( B
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(548,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
        & ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
     => ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__mul @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__MUL) ).

thf(3029,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
        & ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
     => ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__mul @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(177,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ~ ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
        & ( c_2Ewords_2Eword__lt @ TA @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__ANTISYM) ).

thf(1430,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ~ ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
        & ( c_2Ewords_2Eword__lt @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(479,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Esw2sw @ TA @ TA @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Esw2sw__id) ).

thf(2814,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Esw2sw @ TA @ TA @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(431,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ A ) @ ( c_2Einteger_2Eint__neg @ B ) )
      = ( c_2Einteger_2Eint__lt @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__NEG) ).

thf(2667,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ A ) @ ( c_2Einteger_2Eint__neg @ B ) )
      = ( c_2Einteger_2Eint__lt @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(30,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
      = ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL) ).

thf(785,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
      = ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(308,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__add @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger__word_2Ew2i @ TA @ B ) ) )
      = ( c_2Ewords_2Eword__add @ TA @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__add__i2w) ).

thf(2269,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__add @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger__word_2Ew2i @ TA @ B ) ) )
      = ( c_2Ewords_2Eword__add @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(679,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__add @ A @ B )
        = A )
      = ( B
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__RID__UNIQ) ).

thf(3495,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__add @ A @ B )
        = A )
      = ( B
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).

thf(558,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__lt @ c_2Einteger_2Eint__0 @ A )
        & ( c_2Einteger_2Eint__lt @ c_2Einteger_2Eint__0 @ B ) )
     => ( c_2Einteger_2Eint__lt @ c_2Einteger_2Eint__0 @ ( c_2Einteger_2Eint__mul @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__MUL) ).

thf(3061,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__lt @ c_2Einteger_2Eint__0 @ A )
        & ( c_2Einteger_2Eint__lt @ c_2Einteger_2Eint__0 @ B ) )
     => ( c_2Einteger_2Eint__lt @ c_2Einteger_2Eint__0 @ ( c_2Einteger_2Eint__mul @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(445,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__le @ A @ B )
        & ( c_2Einteger_2Eint__lt @ B @ C ) )
     => ( c_2Einteger_2Eint__lt @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LET__TRANS) ).

thf(2708,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__le @ A @ B )
        & ( c_2Einteger_2Eint__lt @ B @ C ) )
     => ( c_2Einteger_2Eint__lt @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(436,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__abs @ TA @ A )
      = ( c_2Ewords_2En2w @ TA @ ( c_2Einteger_2ENum @ ( c_2Einteger_2EABS @ ( c_2Einteger__word_2Ew2i @ TA @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__abs__w2i) ).

thf(2682,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__abs @ TA @ A )
      = ( c_2Ewords_2En2w @ TA @ ( c_2Einteger_2ENum @ ( c_2Einteger_2EABS @ ( c_2Einteger__word_2Ew2i @ TA @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(67,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EMODEQ @ A @ C @ B )
      = ( ( ( A = c_2Enum_2E0 )
          & ( C = B ) )
        | ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
          & ( ( c_2Earithmetic_2EMOD @ C @ A )
            = ( c_2Earithmetic_2EMOD @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMODEQ__THM) ).

thf(934,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EMODEQ @ A @ C @ B )
      = ( ( ( A = c_2Enum_2E0 )
          & ( C = B ) )
        | ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
          & ( ( c_2Earithmetic_2EMOD @ C @ A )
            = ( c_2Earithmetic_2EMOD @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(636,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
     => ? [B: tyop_2Enum_2Enum] :
          ( A
          = ( c_2Einteger_2Eint__of__num @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2ENUM__POSINT__EXISTS) ).

thf(3353,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
     => ? [B: tyop_2Enum_2Enum] :
          ( A
          = ( c_2Einteger_2Eint__of__num @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(553,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
        & ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
     => ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LET__ADD) ).

thf(3043,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
        & ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
     => ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(198,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ~ ( c_2Ewords_2Eword__lt @ TA @ A @ B )
        & ( A != B ) )
     => ( c_2Ewords_2Eword__lt @ TA @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__CASES__IMP) ).

thf(1511,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ~ ( c_2Ewords_2Eword__lt @ TA @ A @ B )
        & ( A != B ) )
     => ( c_2Ewords_2Eword__lt @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(701,plain,
    ( ( c_2Ebool_2E_2F_5C @ $true @ $false )
    = ( $true
      & $false ) ),
    inference(instance,[status(thm)],[698]) ).

thf(702,plain,
    ~ ( c_2Ebool_2E_2F_5C @ $true @ $false ),
    inference(simp,[status(thm)],[701]) ).

thf(19,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ B @ A )
        = ( c_2Earithmetic_2E_2A @ C @ A ) )
      = ( ( A = c_2Enum_2E0 )
        | ( B = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EEQ__MULT__RCANCEL) ).

thf(751,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ B @ A )
        = ( c_2Earithmetic_2E_2A @ C @ A ) )
      = ( ( A = c_2Enum_2E0 )
        | ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(652,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIV__0) ).

thf(3410,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).

thf(290,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ~ ( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
        & ( c_2Ewords_2Eword__ls @ TA @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__EQ__ANTISYM) ).

thf(2185,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ~ ( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
        & ( c_2Ewords_2Eword__ls @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(355,axiom,
    ! [TA: $tType] :
      ( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__L @ TA ) )
      = ( c_2Ewords_2Eword__L @ TA ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__L) ).

thf(2418,plain,
    ! [TA: $tType] :
      ( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__L @ TA ) )
      = ( c_2Ewords_2Eword__L @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(2419,plain,
    ! [TA: $tType] :
      ( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__L @ TA ) )
      = ( c_2Ewords_2Eword__L @ TA ) ),
    inference(cnf,[status(esa)],[2418]) ).

thf(2420,plain,
    ! [TA: $tType] :
      ( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__L @ TA ) )
      = ( c_2Ewords_2Eword__L @ TA ) ),
    inference(lifteq,[status(thm)],[2419]) ).

thf(439,axiom,
    ! [A: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__divides @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__REFL) ).

thf(2691,plain,
    ! [A: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__divides @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(571,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__lo @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) @ B )
      = ( ( B
         != ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
        & ( ( ( A
             != ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
            & ( c_2Ewords_2Eword__lo @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ B ) )
          | ( B
            = ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__LEFT__LO2) ).

thf(3099,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__lo @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) @ B )
      = ( ( B
         != ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
        & ( ( ( A
             != ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
            & ( c_2Ewords_2Eword__lo @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ B ) )
          | ( B
            = ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(447,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ A @ B )
      = ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2Eword__2comp @ TA @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__sub__def) ).

thf(2713,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ A @ B )
      = ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2Eword__2comp @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(199,axiom,
    ( c_2Ebool_2ET
    = ( ( ^ [A: $o] : A )
      = ( ^ [A: $o] : A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ET__DEF) ).

thf(1514,plain,
    c_2Ebool_2ET,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(463,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__neg @ A ) )
      = ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__GE0) ).

thf(2767,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__neg @ A ) )
      = ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(207,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2D @ c_2Enum_2E0 @ A )
        = c_2Enum_2E0 )
      & ( ( c_2Earithmetic_2E_2D @ A @ c_2Enum_2E0 )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ESUB__0) ).

thf(1609,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2D @ c_2Enum_2E0 @ A )
        = c_2Enum_2E0 )
      & ( ( c_2Earithmetic_2E_2D @ A @ c_2Enum_2E0 )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(160,axiom,
    ! [A: $o,B: $o,C: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ A @ B @ C )
      = ( ( A
          & B )
        | ( ~ A
          & C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__EXPAND__OR) ).

thf(1347,plain,
    ! [A: $o,B: $o,C: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ A @ B @ C )
      = ( ( A
          & B )
        | ( ~ A
          & C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(53,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__mul @ TA @ A @ B )
      = ( c_2Ewords_2Eword__mul @ TA @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__MULT__COMM) ).

thf(881,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__mul @ TA @ A @ B )
      = ( c_2Ewords_2Eword__mul @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(491,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ~ ( ( c_2Einteger_2Eint__lt @ A @ B )
        & ( c_2Einteger_2Eint__lt @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__ANTISYM) ).

thf(2852,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ~ ( ( c_2Einteger_2Eint__lt @ A @ B )
        & ( c_2Einteger_2Eint__lt @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(484,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) @ C )
      = ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__SUB__SYM) ).

thf(2829,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) @ C )
      = ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(86,axiom,
    ! [A: $o,B: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ A @ B @ c_2Ebool_2EF )
      = ( A
        & B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2ECOND__CLAUSES__FF) ).

thf(1000,plain,
    ! [A: $o,B: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ A @ B @ c_2Ebool_2EF )
      = ( A
        & B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(1003,plain,
    ( ( c_2Ebool_2ECOND @ $o @ $true @ $false @ c_2Ebool_2EF )
    = ( $true
      & $false ) ),
    inference(instance,[status(thm)],[1000]) ).

thf(1004,plain,
    ~ ( c_2Ebool_2ECOND @ $o @ $true @ $false @ c_2Ebool_2EF ),
    inference(simp,[status(thm)],[1003]) ).

thf(78,axiom,
    ! [A: $o] :
      ( c_2Ebool_2EF
     => A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2Efalse__imp) ).

thf(966,plain,
    ! [A: $o] :
      ( c_2Ebool_2EF
     => A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(969,plain,
    ( c_2Ebool_2EF
   => $false ),
    inference(instance,[status(thm)],[966]) ).

thf(970,plain,
    ~ c_2Ebool_2EF,
    inference(simp,[status(thm)],[969]) ).

thf(3840,plain,
    ~ ( c_2Ebool_2ECOND @ $o @ $true @ $false @ $false ),
    inference(rewrite,[status(thm)],[1004,970]) ).

thf(668,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__rem @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__REM0) ).

thf(3463,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__rem @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).

thf(641,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__mul @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__RZERO) ).

thf(3374,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__mul @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

thf(89,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__mul @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) @ C )
      = ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__mul @ TA @ A @ C ) @ ( c_2Ewords_2Eword__mul @ TA @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__RIGHT__ADD__DISTRIB) ).

thf(1013,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__mul @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) @ C )
      = ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__mul @ TA @ A @ C ) @ ( c_2Ewords_2Eword__mul @ TA @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(25,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Egcd_2Egcd @ ( c_2Earithmetic_2E_2A @ C @ A ) @ ( c_2Earithmetic_2E_2A @ C @ B ) )
      = ( c_2Earithmetic_2E_2A @ C @ ( c_2Egcd_2Egcd @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EGCD__COMMON__FACTOR) ).

thf(770,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Egcd_2Egcd @ ( c_2Earithmetic_2E_2A @ C @ A ) @ ( c_2Earithmetic_2E_2A @ C @ B ) )
      = ( c_2Earithmetic_2E_2A @ C @ ( c_2Egcd_2Egcd @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(543,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__le @ A @ B )
        & ( c_2Einteger_2Eint__le @ B @ A ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__ANTISYM) ).

thf(3014,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__le @ A @ B )
        & ( c_2Einteger_2Eint__le @ B @ A ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(389,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ A ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ B ) ) ) )
      = ( c_2Ewords_2Eword__mul @ TA @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__mul__i2w__w2n) ).

thf(2520,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ A ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ B ) ) ) )
      = ( c_2Ewords_2Eword__mul @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(345,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__divides @ A @ B )
     => ( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__add @ C @ B ) )
        = ( c_2Einteger_2Eint__divides @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__RADD) ).

thf(2388,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__divides @ A @ B )
     => ( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__add @ C @ B ) )
        = ( c_2Einteger_2Eint__divides @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(393,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__mul @ A @ B ) )
      & ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__mul @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__MUL) ).

thf(2533,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__mul @ A @ B ) )
      & ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__mul @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(176,axiom,
    ! [A: $o > $o] :
      ( ( ( A @ c_2Ebool_2ET )
        & ( A @ c_2Ebool_2EF ) )
     => ! [B: $o] : ( A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__INDUCT) ).

thf(1415,plain,
    ! [A: $o > $o] :
      ( ( ( A @ c_2Ebool_2ET )
        & ( A @ c_2Ebool_2EF ) )
     => ! [B: $o] : ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(420,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 )
        = ( c_2Einteger_2Eint__add @ C @ B ) )
     => ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ C @ A ) )
        = ( c_2Einteger_2Eint__le @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Eeq__context__rwt1) ).

thf(2616,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 )
        = ( c_2Einteger_2Eint__add @ C @ B ) )
     => ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ C @ A ) )
        = ( c_2Einteger_2Eint__le @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(472,axiom,
    ! [TA: $tType,TB: $tType,A: tyop_2Efcp_2Ecart @ $o @ TB] :
      ( ( c_2Ewords_2Ew2w @ TB @ TA @ A )
      = ( c_2Ewords_2En2w @ TA @ ( c_2Ewords_2Ew2n @ TB @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Ew2w__def) ).

thf(2794,plain,
    ! [TA: $tType,TB: $tType,A: tyop_2Efcp_2Ecart @ $o @ TB] :
      ( ( c_2Ewords_2Ew2w @ TB @ TA @ A )
      = ( c_2Ewords_2En2w @ TA @ ( c_2Ewords_2Ew2n @ TB @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(234,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
        & ( c_2Earithmetic_2E_3C_3D @ B @ C ) )
     => ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EDIV @ B @ A ) @ ( c_2Earithmetic_2EDIV @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EDIV__LE__MONOTONE) ).

thf(1714,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
        & ( c_2Earithmetic_2E_3C_3D @ B @ C ) )
     => ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EDIV @ B @ A ) @ ( c_2Earithmetic_2EDIV @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(537,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__add @ A @ B )
        = C )
      = ( B
        = ( c_2Einteger_2Eint__add @ C @ ( c_2Einteger_2Eint__neg @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Eeq__move__left__right) ).

thf(2996,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__add @ A @ B )
        = C )
      = ( B
        = ( c_2Einteger_2Eint__add @ C @ ( c_2Einteger_2Eint__neg @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(305,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ C @ B ) )
     => ( ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__neg @ A ) )
       => ( ( ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 )
            = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ C ) @ A ) )
          = c_2Ebool_2EF ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ele__context__rwt4) ).

thf(2259,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ C @ B ) )
     => ( ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__neg @ A ) )
       => ( ( ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 )
            = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ C ) @ A ) )
          = c_2Ebool_2EF ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(270,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ A @ B )
     => ( c_2Earithmetic_2E_3C_3D @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__IMP__LESS__OR__EQ) ).

thf(2122,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ A @ B )
     => ( c_2Earithmetic_2E_3C_3D @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(167,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ B )
        & ( c_2Ewords_2Eword__le @ TA @ B @ A ) )
     => ( ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) )
        & ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__LE) ).

thf(1383,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ B )
        & ( c_2Ewords_2Eword__le @ TA @ B @ A ) )
     => ( ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) )
        & ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(255,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__ls @ TA @ B @ A )
     => ( ( c_2Ewords_2Ew2n @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) )
        = ( c_2Earithmetic_2E_2D @ ( c_2Ewords_2Ew2n @ TA @ A ) @ ( c_2Ewords_2Ew2n @ TA @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__sub__w2n) ).

thf(2034,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__ls @ TA @ B @ A )
     => ( ( c_2Ewords_2Ew2n @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) )
        = ( c_2Earithmetic_2E_2D @ ( c_2Ewords_2Ew2n @ TA @ A ) @ ( c_2Ewords_2Ew2n @ TA @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(137,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2D @ A @ B ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ESUB__LESS__EQ) ).

thf(1183,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2D @ A @ B ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(59,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_3C_3D @ B @ A )
        & ( c_2Earithmetic_2E_3C_3D @ C @ A ) )
     => ( ( ( c_2Earithmetic_2E_2D @ A @ B )
          = ( c_2Earithmetic_2E_2D @ A @ C ) )
        = ( B = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ESUB__CANCEL) ).

thf(905,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_3C_3D @ B @ A )
        & ( c_2Earithmetic_2E_3C_3D @ C @ A ) )
     => ( ( ( c_2Earithmetic_2E_2D @ A @ B )
          = ( c_2Earithmetic_2E_2D @ A @ C ) )
        = ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(63,axiom,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2ECOND__CLAUSES__CT) ).

thf(924,plain,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(627,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Einteger_2Eint__exp @ A @ B )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( ( A
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        & ( B != c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EXP__EQ0) ).

thf(3322,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Einteger_2Eint__exp @ A @ B )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( ( A
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        & ( B != c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(617,axiom,
    ! [A: $o] :
      ( ( c_2EbasicSize_2Ebool__size @ A )
      = c_2Enum_2E0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EbasicSize_2Ebool__size__def) ).

thf(3291,plain,
    ! [A: $o] :
      ( ( c_2EbasicSize_2Ebool__size @ A )
      = c_2Enum_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(3293,plain,
    ( ( c_2EbasicSize_2Ebool__size @ $false )
    = c_2Enum_2E0 ),
    inference(instance,[status(thm)],[3291]) ).

thf(3295,plain,
    ( ( c_2EbasicSize_2Ebool__size @ $false )
    = c_2Enum_2E0 ),
    inference(lifteq,[status(thm)],[3293]) ).

thf(468,axiom,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ealignment_2Ealigned @ TA @ A @ B )
     => ( ( c_2Ealignment_2Ealign @ TA @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ealignment_2Ealign__aligned) ).

thf(2782,plain,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ealignment_2Ealigned @ TA @ A @ B )
     => ( ( c_2Ealignment_2Ealign @ TA @ A @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(665,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Einteger_2Eint__of__num @ A )
        = ( c_2Einteger_2Eint__of__num @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__INJ) ).

thf(3453,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Einteger_2Eint__of__num @ A )
        = ( c_2Einteger_2Eint__of__num @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).

thf(298,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ A @ B ) @ C ) )
      = ( c_2Einteger_2Eint__divides @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ejustify__divides3) ).

thf(2236,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ A @ B ) @ C ) )
      = ( c_2Einteger_2Eint__divides @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(501,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__ls @ TA @ B @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) )
      = ( ( B
          = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
        | ( A
          = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
        | ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__RIGHT__LS2) ).

thf(2880,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__ls @ TA @ B @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) )
      = ( ( B
          = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
        | ( A
          = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
        | ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(45,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2EABS @ A )
      = ( c_2Ebool_2ECOND @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( c_2Einteger_2Eint__neg @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS) ).

thf(834,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2EABS @ A )
      = ( c_2Ebool_2ECOND @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( c_2Einteger_2Eint__neg @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(129,axiom,
    ! [A: $o] :
      ( ( ~ A
        & A )
      = c_2Ebool_2EF ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2EAND__INV) ).

thf(1151,plain,
    ~ c_2Ebool_2EF,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(68,axiom,
    ! [A: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D @ c_2Enum_2E0 @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EZERO__LESS__EQ) ).

thf(937,plain,
    ! [A: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D @ c_2Enum_2E0 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(328,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint,E: tyop_2Enum_2Enum,F: tyop_2Einteger_2Eint,G: tyop_2Einteger_2Eint] :
      ( ( ( E
          = ( c_2Egcd_2Egcd @ B @ A ) )
        & ( ( c_2Einteger_2Eint__of__num @ E )
          = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ F @ ( c_2Einteger_2Eint__of__num @ B ) ) @ ( c_2Einteger_2Eint__mul @ G @ ( c_2Einteger_2Eint__of__num @ A ) ) ) )
        & ( E != c_2Enum_2E0 )
        & ( A != c_2Enum_2E0 )
        & ( B != c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ B ) @ C ) @ D ) )
        = ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__of__num @ E ) @ D )
          & ? [H: tyop_2Einteger_2Eint] :
              ( C
              = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ F ) @ ( c_2Einteger_2Eint__div @ D @ ( c_2Einteger_2Eint__of__num @ E ) ) ) @ ( c_2Einteger_2Eint__mul @ H @ ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Egcdthm2) ).

thf(2335,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint,E: tyop_2Enum_2Enum,F: tyop_2Einteger_2Eint,G: tyop_2Einteger_2Eint] :
      ( ( ( E
          = ( c_2Egcd_2Egcd @ B @ A ) )
        & ( ( c_2Einteger_2Eint__of__num @ E )
          = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ F @ ( c_2Einteger_2Eint__of__num @ B ) ) @ ( c_2Einteger_2Eint__mul @ G @ ( c_2Einteger_2Eint__of__num @ A ) ) ) )
        & ( E != c_2Enum_2E0 )
        & ( A != c_2Enum_2E0 )
        & ( B != c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ B ) @ C ) @ D ) )
        = ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__of__num @ E ) @ D )
          & ? [H: tyop_2Einteger_2Eint] :
              ( C
              = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ F ) @ ( c_2Einteger_2Eint__div @ D @ ( c_2Einteger_2Eint__of__num @ E ) ) ) @ ( c_2Einteger_2Eint__mul @ H @ ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ E ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(101,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( B != c_2Enum_2E0 )
     => ( ( c_2Einteger_2Eint__rem @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
        = ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EMOD @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__REM) ).

thf(1051,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( B != c_2Enum_2E0 )
     => ( ( c_2Einteger_2Eint__rem @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
        = ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EMOD @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(1007,plain,
    ( ( c_2Ebool_2ECOND @ $o @ $false @ $false @ c_2Ebool_2EF )
    = ( $false
      & $false ) ),
    inference(instance,[status(thm)],[1000]) ).

thf(1008,plain,
    ~ ( c_2Ebool_2ECOND @ $o @ $false @ $false @ c_2Ebool_2EF ),
    inference(simp,[status(thm)],[1007]) ).

thf(3851,plain,
    ~ ( c_2Ebool_2ECOND @ $o @ $false @ $false @ $false ),
    inference(rewrite,[status(thm)],[1008,970]) ).

thf(1,conjecture,
    ! [TA: $tType] :
      ( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Ei2w__0) ).

thf(2,negated_conjecture,
    ~ ! [TA: $tType] :
        ( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(687,plain,
    ~ ! [TA: $tType] :
        ( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(592,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__sub @ A @ B ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__SUB2) ).

thf(3189,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__sub @ A @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(494,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__add @ A @ B ) )
      = ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__ADDL) ).

thf(2861,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__add @ A @ B ) )
      = ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(683,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__of__num @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2ENUM__OF__INT) ).

thf(3505,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__of__num @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).

thf(629,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] : ( c_2Ewords_2Eword__ls @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__0__LS) ).

thf(3327,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] : ( c_2Ewords_2Eword__ls @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(598,axiom,
    ( c_2Enum_2E0
    = ( c_2Enum_2EABS__num @ c_2Enum_2EZERO__REP ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enum_2EZERO__DEF) ).

thf(3225,plain,
    ( c_2Enum_2E0
    = ( c_2Enum_2EABS__num @ c_2Enum_2EZERO__REP ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(3226,plain,
    ( ( c_2Enum_2EABS__num @ c_2Enum_2EZERO__REP )
    = c_2Enum_2E0 ),
    inference(lifteq,[status(thm)],[3225]) ).

thf(230,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
     => ( ( ( c_2Earithmetic_2EMOD @ A @ B )
          = A )
        = ( c_2Eprim__rec_2E_3C @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EX__MOD__Y__EQ__X) ).

thf(1697,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
     => ( ( ( c_2Earithmetic_2EMOD @ A @ B )
          = A )
        = ( c_2Eprim__rec_2E_3C @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(346,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__mul @ A @ B ) )
      = ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__LMUL) ).

thf(2392,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__mul @ A @ B ) )
      = ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(678,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EMODEQ @ c_2Enum_2E0 @ B @ A )
      = ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMODEQ__0__CONG) ).

thf(3492,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EMODEQ @ c_2Enum_2E0 @ B @ A )
      = ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).

thf(561,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ C )
     => ? [D: tyop_2Einteger_2Eint] :
          ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D )
          & ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__add @ B @ ( c_2Einteger_2Eint__mul @ D @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ecan__get__big) ).

thf(3068,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ C )
     => ? [D: tyop_2Einteger_2Eint] :
          ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D )
          & ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__add @ B @ ( c_2Einteger_2Eint__mul @ D @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(165,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__abs @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) )
      = ( c_2Ewords_2Eword__abs @ TA @ ( c_2Ewords_2Eword__sub @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__abs__diff) ).

thf(1377,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__abs @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) )
      = ( c_2Ewords_2Eword__abs @ TA @ ( c_2Ewords_2Eword__sub @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(4,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
     => ! [B: tyop_2Enum_2Enum] :
          ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ B @ A ) @ A )
          = c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__EQ__0) ).

thf(692,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
     => ! [B: tyop_2Enum_2Enum] :
          ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ B @ A ) @ A )
          = c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(292,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
        & ( c_2Ewords_2Eword__lo @ TA @ B @ C ) )
     => ( c_2Ewords_2Eword__lo @ TA @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__TRANS) ).

thf(2190,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
        & ( c_2Ewords_2Eword__lo @ TA @ B @ C ) )
     => ( c_2Ewords_2Eword__lo @ TA @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(655,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__mul @ A @ B )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( ( A
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        | ( B
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ENTIRE) ).

thf(3421,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__mul @ A @ B )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( ( A
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        | ( B
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).

thf(390,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
     => ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__mul @ A @ C ) )
        = ( c_2Einteger_2Eint__lt @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__MONO) ).

thf(2523,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
     => ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__mul @ A @ C ) )
        = ( c_2Einteger_2Eint__lt @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(392,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__sub @ A @ B ) @ C )
      = ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__add @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__SUB__RADD) ).

thf(2530,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__sub @ A @ B ) @ C )
      = ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__add @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(119,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ? [D: tyop_2Einteger_2Eint] :
          ( ( A
            = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ D @ B ) @ C ) )
          & ( c_2Ebool_2ECOND @ $o @ ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__lt @ B @ C ) @ ( c_2Einteger_2Eint__le @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ C ) @ ( c_2Einteger_2Eint__lt @ C @ B ) ) ) )
     => ( ( c_2Einteger_2Eint__mod @ A @ B )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__UNIQUE) ).

thf(1119,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ? [D: tyop_2Einteger_2Eint] :
          ( ( A
            = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ D @ B ) @ C ) )
          & ( c_2Ebool_2ECOND @ $o @ ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__lt @ B @ C ) @ ( c_2Einteger_2Eint__le @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ C ) @ ( c_2Einteger_2Eint__lt @ C @ B ) ) ) )
     => ( ( c_2Einteger_2Eint__mod @ A @ B )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(357,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__sub @ TA @ A @ B )
        = ( c_2Ewords_2Eword__sub @ TA @ C @ B ) )
      = ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LCANCEL__SUB) ).

thf(2424,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__sub @ TA @ A @ B )
        = ( c_2Ewords_2Eword__sub @ TA @ C @ B ) )
      = ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(170,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
     => ? [C: tyop_2Enum_2Enum] :
          ( A
          = ( c_2Earithmetic_2E_2D @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__EQUAL__DIFF) ).

thf(1394,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
     => ? [C: tyop_2Enum_2Enum] :
          ( A
          = ( c_2Earithmetic_2E_2D @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(465,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Einteger__word_2Ew2i @ TA @ A )
        = ( c_2Einteger__word_2Ew2i @ TA @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Ew2i__11) ).

thf(2772,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Einteger__word_2Ew2i @ TA @ A )
        = ( c_2Einteger__word_2Ew2i @ TA @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(85,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
     => ( c_2Earithmetic_2EMODEQ @ A @ A @ c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMODEQ__0) ).

thf(998,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
     => ( c_2Earithmetic_2EMODEQ @ A @ A @ c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(477,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Egcd_2Eis__gcd @ A @ B @ C )
      = ( c_2Egcd_2Eis__gcd @ B @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__SYM) ).

thf(2809,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Egcd_2Eis__gcd @ A @ B @ C )
      = ( c_2Egcd_2Eis__gcd @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(219,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ B @ A )
      = ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2E_2D @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ESUB__LESS__0) ).

thf(1651,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ B @ A )
      = ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2E_2D @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(570,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
        & ( c_2Ewords_2Eword__ls @ TA @ B @ C ) )
     => ( c_2Ewords_2Eword__lo @ TA @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__LOWER__EQ__TRANS) ).

thf(3097,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
        & ( c_2Ewords_2Eword__ls @ TA @ B @ C ) )
     => ( c_2Ewords_2Eword__lo @ TA @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(542,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__neg @ B ) )
      = ( c_2Einteger_2Eint__add @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__RNEG) ).

thf(3011,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__neg @ B ) )
      = ( c_2Einteger_2Eint__add @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(149,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ~ ( c_2Ewords_2Eword__lt @ TA @ A @ B ) )
      = ( c_2Ewords_2Eword__le @ TA @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NOT__LESS) ).

thf(1306,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ~ ( c_2Ewords_2Eword__lt @ TA @ A @ B ) )
      = ( c_2Ewords_2Eword__le @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(130,axiom,
    ! [A: $o,B: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ A @ B @ c_2Ebool_2ET )
      = ( A
       => B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2ECOND__CLAUSES__FT) ).

thf(1153,plain,
    ! [A: $o,B: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ A @ B @ c_2Ebool_2ET )
      = ( A
       => B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(38,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ C )
     => ( ( c_2Earithmetic_2E_3C_3D @ A @ ( c_2Earithmetic_2EDIV @ B @ C ) )
        = ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ A @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EX__LE__DIV) ).

thf(810,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ C )
     => ( ( c_2Earithmetic_2E_3C_3D @ A @ ( c_2Earithmetic_2EDIV @ B @ C ) )
        = ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ A @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(157,axiom,
    ! [TA: $tType,A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger__word_2Ei2w @ TA @ A )
      = ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ TA ) @ ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2En2w @ TA @ ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__neg @ A ) ) ) ) @ ( c_2Ewords_2En2w @ TA @ ( c_2Einteger_2ENum @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Ei2w__def) ).

thf(1338,plain,
    ! [TA: $tType,A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger__word_2Ei2w @ TA @ A )
      = ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ TA ) @ ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2En2w @ TA @ ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__neg @ A ) ) ) ) @ ( c_2Ewords_2En2w @ TA @ ( c_2Einteger_2ENum @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(263,axiom,
    ! [A: $o] :
      ( A
     => ( ~ A
       => c_2Ebool_2EF ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2EAND__INV__IMP) ).

thf(2093,plain,
    ! [A: $o] :
      ( A
     => ( ~ A
       => c_2Ebool_2EF ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(250,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( A = B )
      = ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
        & ( c_2Earithmetic_2E_3C_3D @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EEQ__LESS__EQ) ).

thf(2000,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( A = B )
      = ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
        & ( c_2Earithmetic_2E_3C_3D @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(107,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ A @ B )
      = ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
        & ( A != B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecardinal_2ELT__LE) ).

thf(1074,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ A @ B )
      = ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
        & ( A != B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(205,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
        & ( c_2Earithmetic_2E_3C_3D @ B @ A ) )
     => ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ A @ B ) @ B )
        = ( c_2Earithmetic_2EMOD @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ESUB__MOD) ).

thf(1604,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
        & ( c_2Earithmetic_2E_3C_3D @ B @ A ) )
     => ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ A @ B ) @ B )
        = ( c_2Earithmetic_2EMOD @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(664,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
      = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__LZERO) ).

thf(3450,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
      = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(682,axiom,
    ! [A: tyop_2Enum_2Enum] : ( c_2Egcd_2Eis__gcd @ A @ c_2Enum_2E0 @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__0R) ).

thf(3503,plain,
    ! [A: tyop_2Enum_2Enum] : ( c_2Egcd_2Eis__gcd @ A @ c_2Enum_2E0 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).

thf(667,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
     => ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__POS__NZ) ).

thf(3459,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
     => ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).

thf(509,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ? [B: tyop_2Enum_2Enum] :
          ( A
          = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2ENUM__NEGINT__EXISTS) ).

thf(2905,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ? [B: tyop_2Enum_2Enum] :
          ( A
          = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(9,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ A @ C )
        & ( c_2Eprim__rec_2E_3C @ B @ D ) )
     => ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebit_2ELESS__MULT__MONO2) ).

thf(713,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ A @ C )
        & ( c_2Eprim__rec_2E_3C @ B @ D ) )
     => ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(714,plain,
    ! [D: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ~ ( c_2Eprim__rec_2E_3C @ A @ C )
      | ~ ( c_2Eprim__rec_2E_3C @ B @ D )
      | ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ C @ D ) ) ),
    inference(cnf,[status(esa)],[713]) ).

thf(343,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ~ ( c_2Ewords_2Eword__ls @ TA @ A @ B ) )
      = ( c_2Ewords_2Eword__lo @ TA @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NOT__LOWER__EQUAL) ).

thf(2382,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ~ ( c_2Ewords_2Eword__ls @ TA @ A @ B ) )
      = ( c_2Ewords_2Eword__lo @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(34,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ A @ B )
      = ( c_2Earithmetic_2E_2A @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMULT__COMM) ).

thf(798,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ A @ B )
      = ( c_2Earithmetic_2E_2A @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(551,axiom,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ealignment_2Ealigned @ TA @ A @ B )
      = ( ( c_2Ealignment_2Ealign @ TA @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ealignment_2Ealigned__def) ).

thf(3037,plain,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ealignment_2Ealigned @ TA @ A @ B )
      = ( ( c_2Ealignment_2Ealign @ TA @ A @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(433,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ~ ( ( c_2Einteger_2Eint__le @ A @ B )
        & ( c_2Einteger_2Eint__lt @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LTE__ANTSYM) ).

thf(2673,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ~ ( ( c_2Einteger_2Eint__le @ A @ B )
        & ( c_2Einteger_2Eint__lt @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(444,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ A ) )
      = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__RINV) ).

thf(2705,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ A ) )
      = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(111,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
        & ( c_2Ewords_2Eword__lt @ TA @ B @ C ) )
     => ( c_2Ewords_2Eword__lt @ TA @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__TRANS) ).

thf(1091,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
        & ( c_2Ewords_2Eword__lt @ TA @ B @ C ) )
     => ( c_2Ewords_2Eword__lt @ TA @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(302,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A = B )
      = ( ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ B ) )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Eeq__move__all__left) ).

thf(2249,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A = B )
      = ( ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ B ) )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(102,axiom,
    ! [A: $o > $o] :
      ( ( ! [B: $o] : ( A @ B ) )
      = ( ( A @ c_2Ebool_2ET )
        & ( A @ c_2Ebool_2EF ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EFORALL__BOOL) ).

thf(1054,plain,
    ! [A: $o > $o] :
      ( ( ! [B: $o] : ( A @ B ) )
      = ( ( A @ c_2Ebool_2ET )
        & ( A @ c_2Ebool_2EF ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(1059,plain,
    ( ( ! [A: $o] : A )
    = ( c_2Ebool_2ET
      & c_2Ebool_2EF ) ),
    inference(instance,[status(thm)],[1054]) ).

thf(1061,plain,
    ( ( c_2Ebool_2ET
      & c_2Ebool_2EF )
    = ( ! [A: $o] : A ) ),
    inference(lifteq,[status(thm)],[1059]) ).

thf(3865,plain,
    ( ( $true
      & $false )
    = ( ! [A: $o] : A ) ),
    inference(rewrite,[status(thm)],[1061,970,878]) ).

thf(3866,plain,
    ~ ! [A: $o] : A,
    inference(simp,[status(thm)],[3865]) ).

thf(3867,plain,
    ~ sk33,
    inference(cnf,[status(esa)],[3866]) ).

thf(277,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) )
      = ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ ( c_2Ewords_2Eword__2comp @ TA @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__ADD) ).

thf(2147,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) )
      = ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ ( c_2Ewords_2Eword__2comp @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(603,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ A @ A )
      = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__REFL) ).

thf(3239,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ A @ A )
      = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).

thf(606,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2EABS @ A )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( A
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__EQ0) ).

thf(3250,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2EABS @ A )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( A
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(594,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A = B )
      | ( c_2Einteger_2Eint__lt @ A @ B )
      | ( c_2Einteger_2Eint__lt @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__TOTAL) ).

thf(3207,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A = B )
      | ( c_2Einteger_2Eint__lt @ A @ B )
      | ( c_2Einteger_2Eint__lt @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(899,plain,
    ( ( c_2Ebool_2ECOND @ $o @ $true @ c_2Ebool_2ET @ $false )
    = ( ~ $true
     => $false ) ),
    inference(instance,[status(thm)],[896]) ).

thf(900,plain,
    c_2Ebool_2ECOND @ $o @ $true @ c_2Ebool_2ET @ $false,
    inference(simp,[status(thm)],[899]) ).

thf(3778,plain,
    c_2Ebool_2ECOND @ $o @ $true @ $true @ $false,
    inference(rewrite,[status(thm)],[900,878]) ).

thf(145,axiom,
    ! [TA: $tType,TB: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Efcp_2Ecart @ $o @ TB] :
      ( ( c_2Eprim__rec_2E_3C @ A @ B )
     => ( ( c_2Ewords_2Eword__extract @ TB @ TA @ A @ B @ C )
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__EXTRACT__ZERO) ).

thf(1223,plain,
    ! [TA: $tType,TB: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Efcp_2Ecart @ $o @ TB] :
      ( ( c_2Eprim__rec_2E_3C @ A @ B )
     => ( ( c_2Ewords_2Eword__extract @ TB @ TA @ A @ B @ C )
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(610,axiom,
    ! [A: tyop_2Enum_2Enum] : ( c_2Egcd_2Eis__gcd @ c_2Enum_2E0 @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__0L) ).

thf(3261,plain,
    ! [A: tyop_2Enum_2Enum] : ( c_2Egcd_2Eis__gcd @ c_2Enum_2E0 @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(77,axiom,
    ! [A: $o,B: $o] :
      ( ( ~ ( ~ B
            | A )
       => c_2Ebool_2EF )
      = ( B
       => ( ~ A
         => c_2Ebool_2EF ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2EOR__DUAL3) ).

thf(957,plain,
    ! [A: $o,B: $o] :
      ( ( ~ ( ~ B
            | A )
       => c_2Ebool_2EF )
      = ( B
       => ( ~ A
         => c_2Ebool_2EF ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(75,axiom,
    ! [TA: $tType,TB: $tType,A: tyop_2Efcp_2Ecart @ $o @ TB] : ( c_2Earithmetic_2E_3C_3D @ ( c_2Ewords_2Ew2n @ TA @ ( c_2Ewords_2Ew2w @ TB @ TA @ A ) ) @ ( c_2Ewords_2Ew2n @ TB @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Ew2n__w2w__le) ).

thf(952,plain,
    ! [TA: $tType,TB: $tType,A: tyop_2Efcp_2Ecart @ $o @ TB] : ( c_2Earithmetic_2E_3C_3D @ ( c_2Ewords_2Ew2n @ TA @ ( c_2Ewords_2Ew2w @ TB @ TA @ A ) ) @ ( c_2Ewords_2Ew2n @ TB @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(395,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B )
     => ? [C: tyop_2Einteger_2Eint] :
          ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__mul @ C @ B ) ) )
          & ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__mul @ C @ B ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Esubtract__to__small) ).

thf(2541,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B )
     => ? [C: tyop_2Einteger_2Eint] :
          ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__mul @ C @ B ) ) )
          & ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__mul @ C @ B ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(601,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger__word_2Ew2i @ TA @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Ei2w__w2i) ).

thf(3233,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger__word_2Ew2i @ TA @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(640,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( c_2Ewords_2Eword__concat @ TC @ TB @ TA @ ( c_2Ewords_2En2w @ TC @ c_2Enum_2E0 ) @ ( c_2Ewords_2En2w @ TB @ c_2Enum_2E0 ) )
      = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__concat__0__0) ).

thf(3371,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( c_2Ewords_2Eword__concat @ TC @ TB @ TA @ ( c_2Ewords_2En2w @ TC @ c_2Enum_2E0 ) @ ( c_2Ewords_2En2w @ TB @ c_2Enum_2E0 ) )
      = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(31,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ C @ B ) )
      = ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
        & ( c_2Eprim__rec_2E_3C @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELT__MULT__RCANCEL) ).

thf(788,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ C @ B ) )
      = ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
        & ( c_2Eprim__rec_2E_3C @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(209,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
      | ( c_2Earithmetic_2E_3C_3D @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecardinal_2ELE__CASES) ).

thf(1619,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
      | ( c_2Earithmetic_2E_3C_3D @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(278,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Einteger__word_2Eword__smod @ TA @ A @ B )
      = ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__mod @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger__word_2Ew2i @ TA @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__smod__def) ).

thf(2150,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Einteger__word_2Eword__smod @ TA @ A @ B )
      = ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__mod @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger__word_2Ew2i @ TA @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(613,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ A @ A )
      = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__REFL) ).

thf(3269,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ A @ A )
      = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(403,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ B @ ( c_2Einteger_2Eint__sub @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__ADD2) ).

thf(2565,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ B @ ( c_2Einteger_2Eint__sub @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(498,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__ls @ TA @ A @ B )
        & ( c_2Ewords_2Eword__lo @ TA @ B @ C ) )
     => ( c_2Ewords_2Eword__lo @ TA @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__EQ__LOWER__TRANS) ).

thf(2872,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__ls @ TA @ A @ B )
        & ( c_2Ewords_2Eword__lo @ TA @ B @ C ) )
     => ( c_2Ewords_2Eword__lo @ TA @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(211,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ? [D: tyop_2Einteger_2Eint] :
          ( ( A
            = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ C @ B ) @ D ) )
          & ( c_2Ebool_2ECOND @ $o @ ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__lt @ B @ D ) @ ( c_2Einteger_2Eint__le @ D @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D ) @ ( c_2Einteger_2Eint__lt @ D @ B ) ) ) )
     => ( ( c_2Einteger_2Eint__div @ A @ B )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIV__UNIQUE) ).

thf(1624,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ? [D: tyop_2Einteger_2Eint] :
          ( ( A
            = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ C @ B ) @ D ) )
          & ( c_2Ebool_2ECOND @ $o @ ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__lt @ B @ D ) @ ( c_2Einteger_2Eint__le @ D @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D ) @ ( c_2Einteger_2Eint__lt @ D @ B ) ) ) )
     => ( ( c_2Einteger_2Eint__div @ A @ B )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(417,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__ls @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) @ B )
      = ( ( A
          = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
        | ( ( B
           != ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
          & ( ( c_2Ewords_2Eword__lo @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ B )
            | ( B
              = ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__LEFT__LS2) ).

thf(2609,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__ls @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) @ B )
      = ( ( A
          = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
        | ( ( B
           != ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
          & ( ( c_2Ewords_2Eword__lo @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ B )
            | ( B
              = ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(288,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ A @ B )
      = ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__CALCULATE) ).

thf(2179,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ A @ B )
      = ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(141,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ~ ( c_2Ewords_2Eword__le @ TA @ A @ B ) )
      = ( c_2Ewords_2Eword__lt @ TA @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NOT__LESS__EQUAL) ).

thf(1210,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ~ ( c_2Ewords_2Eword__le @ TA @ A @ B ) )
      = ( c_2Ewords_2Eword__lt @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(21,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ C )
     => ( ( ( c_2Earithmetic_2E_2A @ C @ B )
          = A )
        = ( ( B
            = ( c_2Earithmetic_2EDIV @ A @ C ) )
          & ( ( c_2Earithmetic_2EMOD @ A @ C )
            = c_2Enum_2E0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMULT__EQ__DIV) ).

thf(757,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ C )
     => ( ( ( c_2Earithmetic_2E_2A @ C @ B )
          = A )
        = ( ( B
            = ( c_2Earithmetic_2EDIV @ A @ C ) )
          & ( ( c_2Earithmetic_2EMOD @ A @ C )
            = c_2Enum_2E0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(214,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__mul @ TA @ ( c_2Ewords_2Eword__sub @ TA @ B @ C ) @ A )
      = ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__mul @ TA @ B @ A ) @ ( c_2Ewords_2Eword__mul @ TA @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__RIGHT__SUB__DISTRIB) ).

thf(1634,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__mul @ TA @ ( c_2Ewords_2Eword__sub @ TA @ B @ C ) @ A )
      = ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__mul @ TA @ B @ A ) @ ( c_2Ewords_2Eword__mul @ TA @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(8,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
        & ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
        & ( c_2Eprim__rec_2E_3C @ C @ ( c_2Earithmetic_2E_2A @ B @ A ) ) )
     => ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2A @ B @ A ) @ C ) @ A )
        = ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ A @ ( c_2Earithmetic_2EMOD @ C @ A ) ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EMOD__COMPLEMENT) ).

thf(710,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
        & ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
        & ( c_2Eprim__rec_2E_3C @ C @ ( c_2Earithmetic_2E_2A @ B @ A ) ) )
     => ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2A @ B @ A ) @ C ) @ A )
        = ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ A @ ( c_2Earithmetic_2EMOD @ C @ A ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(80,axiom,
    ! [A: $o] :
      ( ( c_2Ebool_2ET
        | A )
      = c_2Ebool_2ET ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EOR__CLAUSES__TX) ).

thf(974,plain,
    ! [A: $o] :
      ( ( c_2Ebool_2ET
        | A )
      = c_2Ebool_2ET ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(526,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger__word_2Ew2i @ TA @ B ) ) )
      = ( c_2Ewords_2Eword__mul @ TA @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__mul__i2w) ).

thf(2958,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger__word_2Ew2i @ TA @ B ) ) )
      = ( c_2Ewords_2Eword__mul @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(622,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EABS__DIFF @ A @ A )
      = c_2Enum_2E0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EABS__DIFF__EQS) ).

thf(3307,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EABS__DIFF @ A @ A )
      = c_2Enum_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(424,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( A
        = ( c_2Ewords_2Eword__sub @ TA @ B @ C ) )
      = ( ( c_2Ewords_2Eword__add @ TA @ A @ C )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__EQ__SUB__LADD) ).

thf(2628,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( A
        = ( c_2Ewords_2Eword__sub @ TA @ B @ C ) )
      = ( ( c_2Ewords_2Eword__add @ TA @ A @ C )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(432,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ A @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) )
      = ( c_2Ewords_2Eword__2comp @ TA @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__SUB3) ).

thf(2670,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ A @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) )
      = ( c_2Ewords_2Eword__2comp @ TA @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(360,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Earithmetic_2E_3C_3D @ B @ A )
        & ( C
         != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
     => ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__exp @ C @ A ) @ ( c_2Einteger_2Eint__exp @ C @ B ) )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EXP__MOD) ).

thf(2433,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Earithmetic_2E_3C_3D @ B @ A )
        & ( C
         != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
     => ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__exp @ C @ A ) @ ( c_2Einteger_2Eint__exp @ C @ B ) )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(375,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__lt @ A @ B )
        & ( c_2Einteger_2Eint__le @ B @ C ) )
     => ( c_2Einteger_2Eint__lt @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LTE__TRANS) ).

thf(2477,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__lt @ A @ B )
        & ( c_2Einteger_2Eint__le @ B @ C ) )
     => ( c_2Einteger_2Eint__lt @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(483,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ~ ( c_2Einteger_2Eint__lt @ A @ c_2Einteger_2Eint__0 )
     => ? [B: tyop_2Enum_2Enum] :
          ( A
          = ( c_2Einteger_2Eint__of__num @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2ENUM__POSINT__EX) ).

thf(2826,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ~ ( c_2Einteger_2Eint__lt @ A @ c_2Einteger_2Eint__0 )
     => ? [B: tyop_2Enum_2Enum] :
          ( A
          = ( c_2Einteger_2Eint__of__num @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(481,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__mul @ A @ B ) )
      = ( c_2Einteger_2Eint__mul @ A @ ( c_2Einteger_2Eint__neg @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__RMUL) ).

thf(2820,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__mul @ A @ B ) )
      = ( c_2Einteger_2Eint__mul @ A @ ( c_2Einteger_2Eint__neg @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(3499,plain,
    ! [TA: $tType] :
      ~ ( c_2Ewords_2Eword__msb @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
    inference(cnf,[status(esa)],[3498]) ).

thf(560,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Einteger_2EABS @ ( c_2Einteger_2Eint__of__num @ A ) )
      = ( c_2Einteger_2Eint__of__num @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__NUM) ).

thf(3065,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Einteger_2EABS @ ( c_2Einteger_2Eint__of__num @ A ) )
      = ( c_2Einteger_2Eint__of__num @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(109,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Egcd_2Egcd @ c_2Enum_2E0 @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EGCD__0L) ).

thf(1079,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Egcd_2Egcd @ c_2Enum_2E0 @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(93,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
        & ( c_2Egcd_2Eis__gcd @ A @ ( c_2Earithmetic_2E_2D @ B @ A ) @ C ) )
     => ( c_2Egcd_2Eis__gcd @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__MINUS__R) ).

thf(1027,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
        & ( c_2Egcd_2Eis__gcd @ A @ ( c_2Earithmetic_2E_2D @ B @ A ) @ C ) )
     => ( c_2Egcd_2Eis__gcd @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(397,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__mul @ A @ C ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ A @ D ) @ B ) )
      = ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__mul @ A @ C ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ A @ D ) @ B ) )
        & ( c_2Einteger_2Eint__divides @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ejustify__divides2) ).

thf(2547,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__mul @ A @ C ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ A @ D ) @ B ) )
      = ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__mul @ A @ C ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ A @ D ) @ B ) )
        & ( c_2Einteger_2Eint__divides @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(381,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ C ) ) )
      = ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ B @ C ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__ADDNEG) ).

thf(2492,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ C ) ) )
      = ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ B @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(5,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ A @ B )
      = ( c_2Earithmetic_2E_2A @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMULT__SYM) ).

thf(695,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ A @ B )
      = ( c_2Earithmetic_2E_2A @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(696,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ A @ B )
      = ( c_2Earithmetic_2E_2A @ B @ A ) ),
    inference(cnf,[status(esa)],[695]) ).

thf(697,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ A @ B )
      = ( c_2Earithmetic_2E_2A @ B @ A ) ),
    inference(lifteq,[status(thm)],[696]) ).

thf(51,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ A @ B )
        & ( c_2Eprim__rec_2E_3C @ B @ C ) )
     => ( c_2Eprim__rec_2E_3C @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__TRANS) ).

thf(874,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ A @ B )
        & ( c_2Eprim__rec_2E_3C @ B @ C ) )
     => ( c_2Eprim__rec_2E_3C @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(653,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Ebit__count__upto @ TA @ c_2Enum_2E0 @ A )
      = c_2Enum_2E0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Ebit__count__upto__0) ).

thf(3413,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Ebit__count__upto @ TA @ c_2Enum_2E0 @ A )
      = c_2Enum_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).

thf(535,axiom,
    ! [A: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2EABS @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__POS) ).

thf(2990,plain,
    ! [A: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2EABS @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(437,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ~ ( c_2Ewords_2Eword__lo @ TA @ A @ B ) )
      = ( c_2Ewords_2Eword__ls @ TA @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NOT__LOWER) ).

thf(2685,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ~ ( c_2Ewords_2Eword__lo @ TA @ A @ B ) )
      = ( c_2Ewords_2Eword__ls @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(506,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
     => ( ( c_2Einteger_2Eint__lt @ B @ C )
        = ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__mul @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Elt__justify__multiplication) ).

thf(2895,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
     => ( ( c_2Einteger_2Eint__lt @ B @ C )
        = ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__mul @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(154,axiom,
    ! [A: $o] :
      ( A
     => c_2Ebool_2ET ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2Etrue__imp) ).

thf(1328,plain,
    ! [A: $o] :
      ( A
     => c_2Ebool_2ET ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(194,axiom,
    ! [A: $o] :
      ( ~ A
     => ( A
       => c_2Ebool_2EF ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EF__IMP) ).

thf(1498,plain,
    ! [A: $o] :
      ( ~ A
     => ( A
       => c_2Ebool_2EF ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(686,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__add @ TA @ A @ B )
        = A )
      = ( B
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__RID__UNIQ) ).

thf(3518,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__add @ TA @ A @ B )
        = A )
      = ( B
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).

thf(425,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ~ ( c_2Ewords_2Eword__msb @ TA @ A )
     => ( ( A
          = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
        | ( c_2Ewords_2Eword__msb @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2ETWO__COMP__POS) ).

thf(2631,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ~ ( c_2Ewords_2Eword__msb @ TA @ A )
     => ( ( A
          = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
        | ( c_2Ewords_2Eword__msb @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(82,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__abs @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) )
      = ( c_2Ewords_2Eword__abs @ TA @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__abs__neg) ).

thf(989,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__abs @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) )
      = ( c_2Ewords_2Eword__abs @ TA @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(171,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ A )
        & ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ B ) )
     => ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
        = ( c_2Ewords_2Eword__lo @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LT__EQ__LO) ).

thf(1397,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ A )
        & ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ B ) )
     => ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
        = ( c_2Ewords_2Eword__lo @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(573,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ A @ ( c_2Ewords_2Eword__sub @ TA @ B @ C ) )
      = ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__SUB) ).

thf(3105,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ A @ ( c_2Ewords_2Eword__sub @ TA @ B @ C ) )
      = ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(319,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__add @ TA @ A @ B )
        = ( c_2Ewords_2Eword__add @ TA @ A @ C ) )
      = ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__EQ__ADD__LCANCEL) ).

thf(2300,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__add @ TA @ A @ B )
        = ( c_2Ewords_2Eword__add @ TA @ A @ C ) )
      = ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(341,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ A ) @ ( c_2Einteger_2Eint__neg @ B ) )
      = ( c_2Einteger_2Eint__mul @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__MUL2) ).

thf(2377,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ A ) @ ( c_2Einteger_2Eint__neg @ B ) )
      = ( c_2Einteger_2Eint__mul @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(73,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ~ ( c_2Eprim__rec_2E_3C @ A @ B ) )
      = ( c_2Earithmetic_2E_3C_3D @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ENOT__LESS) ).

thf(948,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ~ ( c_2Eprim__rec_2E_3C @ A @ B ) )
      = ( c_2Earithmetic_2E_3C_3D @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(572,axiom,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ealignment_2Ealign @ TA @ A @ ( c_2Ealignment_2Ealign @ TA @ A @ B ) )
      = ( c_2Ealignment_2Ealign @ TA @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ealignment_2Ealign__align) ).

thf(3102,plain,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ealignment_2Ealign @ TA @ A @ ( c_2Ealignment_2Ealign @ TA @ A @ B ) )
      = ( c_2Ealignment_2Ealign @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(225,axiom,
    ! [A: $o,B: $o,C: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ A @ B @ C )
      = ( ( ~ A
          | B )
        & ( A
          | C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__EXPAND) ).

thf(1672,plain,
    ! [A: $o,B: $o,C: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ A @ B @ C )
      = ( ( ~ A
          | B )
        & ( A
          | C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(124,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Einteger_2Eint,E: tyop_2Enum_2Enum,F: tyop_2Einteger_2Eint,G: tyop_2Einteger_2Eint,H: tyop_2Einteger_2Eint,I: tyop_2Einteger_2Eint,J: tyop_2Enum_2Enum] :
      ( ( ( J
          = ( c_2Egcd_2Egcd @ ( c_2Earithmetic_2E_2A @ E @ A ) @ ( c_2Earithmetic_2E_2A @ C @ B ) ) )
        & ( ( c_2Einteger_2Eint__of__num @ J )
          = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__mul @ G @ ( c_2Einteger_2Eint__of__num @ E ) ) @ ( c_2Einteger_2Eint__of__num @ A ) ) @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__mul @ H @ ( c_2Einteger_2Eint__of__num @ C ) ) @ ( c_2Einteger_2Eint__of__num @ B ) ) ) )
        & ( A != c_2Enum_2E0 )
        & ( B != c_2Enum_2E0 )
        & ( C != c_2Enum_2E0 )
        & ( E != c_2Enum_2E0 ) )
     => ( ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ C ) @ I ) @ D ) )
          & ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__of__num @ B ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ E ) @ I ) @ F ) ) )
        = ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ J ) @ I ) @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__mul @ F @ ( c_2Einteger_2Eint__of__num @ A ) ) @ G ) ) @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__mul @ D @ ( c_2Einteger_2Eint__of__num @ B ) ) @ H ) ) )
          & ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__of__num @ J ) @ ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ C ) @ F ) @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ E ) @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ecooper__lemma__1) ).

thf(1138,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Einteger_2Eint,E: tyop_2Enum_2Enum,F: tyop_2Einteger_2Eint,G: tyop_2Einteger_2Eint,H: tyop_2Einteger_2Eint,I: tyop_2Einteger_2Eint,J: tyop_2Enum_2Enum] :
      ( ( ( J
          = ( c_2Egcd_2Egcd @ ( c_2Earithmetic_2E_2A @ E @ A ) @ ( c_2Earithmetic_2E_2A @ C @ B ) ) )
        & ( ( c_2Einteger_2Eint__of__num @ J )
          = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__mul @ G @ ( c_2Einteger_2Eint__of__num @ E ) ) @ ( c_2Einteger_2Eint__of__num @ A ) ) @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__mul @ H @ ( c_2Einteger_2Eint__of__num @ C ) ) @ ( c_2Einteger_2Eint__of__num @ B ) ) ) )
        & ( A != c_2Enum_2E0 )
        & ( B != c_2Enum_2E0 )
        & ( C != c_2Enum_2E0 )
        & ( E != c_2Enum_2E0 ) )
     => ( ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ C ) @ I ) @ D ) )
          & ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__of__num @ B ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ E ) @ I ) @ F ) ) )
        = ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ J ) @ I ) @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__mul @ F @ ( c_2Einteger_2Eint__of__num @ A ) ) @ G ) ) @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__mul @ D @ ( c_2Einteger_2Eint__of__num @ B ) ) @ H ) ) )
          & ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__of__num @ J ) @ ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ C ) @ F ) @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ E ) @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(451,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__sub @ A @ B ) )
      = ( c_2Einteger_2Eint__sub @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__SUB) ).

thf(2724,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__sub @ A @ B ) )
      = ( c_2Einteger_2Eint__sub @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(236,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ~ ( ( c_2Eprim__rec_2E_3C @ A @ B )
        & ( c_2Eprim__rec_2E_3C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__ANTISYM) ).

thf(1719,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ~ ( ( c_2Eprim__rec_2E_3C @ A @ B )
        & ( c_2Eprim__rec_2E_3C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(493,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__SUB) ).

thf(2858,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(54,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
      = ( c_2Eprim__rec_2E_3C @ ( c_2Ewords_2Ew2n @ TA @ A ) @ ( c_2Ewords_2Ew2n @ TA @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LO) ).

thf(884,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
      = ( c_2Eprim__rec_2E_3C @ ( c_2Ewords_2Ew2n @ TA @ A ) @ ( c_2Ewords_2Ew2n @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(500,axiom,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__slice @ TA @ A @ c_2Enum_2E0 @ B )
      = ( c_2Ewords_2Eword__bits @ TA @ A @ c_2Enum_2E0 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SLICE__BITS__THM) ).

thf(2877,plain,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__slice @ TA @ A @ c_2Enum_2E0 @ B )
      = ( c_2Ewords_2Eword__bits @ TA @ A @ c_2Enum_2E0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(110,axiom,
    ! [A: $o,B: $o] :
      ( ( ~ ( B
            | A )
       => c_2Ebool_2EF )
      = ( ~ B
       => ( ~ A
         => c_2Ebool_2EF ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2EOR__DUAL) ).

thf(1082,plain,
    ! [A: $o,B: $o] :
      ( ( ~ ( B
            | A )
       => c_2Ebool_2EF )
      = ( ~ B
       => ( ~ A
         => c_2Ebool_2EF ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(569,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__mul @ A @ ( c_2Einteger_2Eint__sub @ B @ C ) )
      = ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__mul @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__LDISTRIB) ).

thf(3094,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__mul @ A @ ( c_2Einteger_2Eint__sub @ B @ C ) )
      = ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__mul @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(231,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__mul @ TA @ A @ B ) )
      = ( c_2Ewords_2Eword__mul @ TA @ A @ ( c_2Ewords_2Eword__2comp @ TA @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__RMUL) ).

thf(1700,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__mul @ TA @ A @ B ) )
      = ( c_2Ewords_2Eword__mul @ TA @ A @ ( c_2Ewords_2Eword__2comp @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(285,axiom,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Efcp_2Ecart @ $o @ TA] : ( c_2Ealignment_2Ealigned @ TA @ A @ ( c_2Ealignment_2Ealign @ TA @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ealignment_2Ealigned__align) ).

thf(2172,plain,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Efcp_2Ecart @ $o @ TA] : ( c_2Ealignment_2Ealigned @ TA @ A @ ( c_2Ealignment_2Ealign @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(90,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
     => ( ( c_2Earithmetic_2EMOD @ c_2Enum_2E0 @ A )
        = c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EZERO__MOD) ).

thf(1016,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
     => ( ( c_2Earithmetic_2EMOD @ c_2Enum_2E0 @ A )
        = c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(705,plain,
    ( ( c_2Ebool_2E_2F_5C @ $false @ $false )
    = ( $false
      & $false ) ),
    inference(instance,[status(thm)],[698]) ).

thf(706,plain,
    ~ ( c_2Ebool_2E_2F_5C @ $false @ $false ),
    inference(simp,[status(thm)],[705]) ).

thf(369,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ A @ B )
      | ( c_2Einteger_2Eint__le @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__TOTAL) ).

thf(2460,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ A @ B )
      | ( c_2Einteger_2Eint__le @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(192,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_3C_3D @ B @ A )
        & ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B ) )
     => ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2EDIV @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebit_2EDIV__GT0) ).

thf(1493,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_3C_3D @ B @ A )
        & ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B ) )
     => ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2EDIV @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(651,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
    ? [B: tyop_2Einteger_2Eint] :
      ( A
      = ( c_2Einteger__word_2Ei2w @ TA @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Eint__word__nchotomy) ).

thf(3407,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
    ? [B: tyop_2Einteger_2Eint] :
      ( A
      = ( c_2Einteger__word_2Ei2w @ TA @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).

thf(402,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint] :
      ( ( B != c_2Enum_2E0 )
     => ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ B ) @ C ) )
        = ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Eelim__lt__coeffs1) ).

thf(2561,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint] :
      ( ( B != c_2Enum_2E0 )
     => ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ B ) @ C ) )
        = ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(595,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__le @ A @ B )
        & ( c_2Einteger_2Eint__le @ B @ C ) )
     => ( c_2Einteger_2Eint__le @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__TRANS) ).

thf(3210,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__le @ A @ B )
        & ( c_2Einteger_2Eint__le @ B @ C ) )
     => ( c_2Einteger_2Eint__le @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(533,axiom,
    ! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ! [D: tyop_2Einteger_2Eint] :
            ( ( A @ D )
           => ( A @ ( c_2Einteger_2Eint__sub @ D @ B ) ) )
        & ( A @ C ) )
     => ! [D: tyop_2Einteger_2Eint] :
          ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D )
         => ( A @ ( c_2Einteger_2Eint__sub @ C @ ( c_2Einteger_2Eint__mul @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Etop__and__lessers) ).

thf(2978,plain,
    ! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ! [D: tyop_2Einteger_2Eint] :
            ( ( A @ D )
           => ( A @ ( c_2Einteger_2Eint__sub @ D @ B ) ) )
        & ( A @ C ) )
     => ! [D: tyop_2Einteger_2Eint] :
          ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D )
         => ( A @ ( c_2Einteger_2Eint__sub @ C @ ( c_2Einteger_2Eint__mul @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(97,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
        & ( c_2Earithmetic_2E_3C_3D @ B @ A ) )
     => ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2D @ A @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ESUB__LESS) ).

thf(1039,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
        & ( c_2Earithmetic_2E_3C_3D @ B @ A ) )
     => ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2D @ A @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(325,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__divides @ A @ B )
        & ( c_2Einteger_2Eint__divides @ B @ C ) )
     => ( c_2Einteger_2Eint__divides @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__TRANS) ).

thf(2317,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__divides @ A @ B )
        & ( c_2Einteger_2Eint__divides @ B @ C ) )
     => ( c_2Einteger_2Eint__divides @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(3292,plain,
    ( ( c_2EbasicSize_2Ebool__size @ $true )
    = c_2Enum_2E0 ),
    inference(instance,[status(thm)],[3291]) ).

thf(3294,plain,
    ( ( c_2EbasicSize_2Ebool__size @ $true )
    = c_2Enum_2E0 ),
    inference(lifteq,[status(thm)],[3292]) ).

thf(384,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2Eword__sub @ TA @ B @ A ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__ADD2) ).

thf(2504,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2Eword__sub @ TA @ B @ A ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(181,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__lt @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ B )
        & ( c_2Ewords_2Eword__lt @ TA @ B @ A ) )
     => ( ( c_2Ewords_2Eword__lt @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) )
        & ( c_2Ewords_2Eword__lt @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__LT) ).

thf(1451,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__lt @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ B )
        & ( c_2Ewords_2Eword__lt @ TA @ B @ A ) )
     => ( ( c_2Ewords_2Eword__lt @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) )
        & ( c_2Ewords_2Eword__lt @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(379,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__sub @ A @ B ) )
      = ( c_2Einteger_2Eint__lt @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__LT) ).

thf(2487,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__sub @ A @ B ) )
      = ( c_2Einteger_2Eint__lt @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(300,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ B @ A )
      = ( c_2Einteger_2Eint__add @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__COMM) ).

thf(2243,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ B @ A )
      = ( c_2Einteger_2Eint__add @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(371,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      | ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
      | ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__neg @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__NEGTOTAL) ).

thf(2465,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      | ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
      | ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__neg @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(61,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum > $o] :
      ( ( ( C @ B )
        & ! [D: tyop_2Enum_2Enum] :
            ( ( c_2Eprim__rec_2E_3C @ D @ B )
           => ~ ( C @ D ) )
        & ( C @ A )
        & ! [D: tyop_2Enum_2Enum] :
            ( ( c_2Eprim__rec_2E_3C @ D @ A )
           => ~ ( C @ D ) ) )
     => ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2ETemporal__Logic_2EWELL__ORDER__UNIQUE) ).

thf(911,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum > $o] :
      ( ( ( C @ B )
        & ! [D: tyop_2Enum_2Enum] :
            ( ( c_2Eprim__rec_2E_3C @ D @ B )
           => ~ ( C @ D ) )
        & ( C @ A )
        & ! [D: tyop_2Enum_2Enum] :
            ( ( c_2Eprim__rec_2E_3C @ D @ A )
           => ~ ( C @ D ) ) )
     => ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(576,axiom,
    ( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( B != c_2Enum_2E0 )
       => ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
          = ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EMOD @ A @ B ) ) ) )
    & ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
        ( ( B
         != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
       => ( ( c_2Einteger_2Eint__mod @ A @ ( c_2Einteger_2Eint__neg @ B ) )
          = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__neg @ A ) @ B ) ) ) )
    & ! [A: tyop_2Einteger_2Eint] :
        ( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__neg @ A ) )
        = A )
    & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( ( c_2Einteger_2Eint__of__num @ A )
          = ( c_2Einteger_2Eint__of__num @ B ) )
        = ( A = B ) )
    & ! [A: tyop_2Einteger_2Eint] :
        ( ( ( c_2Einteger_2Eint__neg @ A )
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = ( A
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__CALCULATE) ).

thf(3115,plain,
    ( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( B != c_2Enum_2E0 )
       => ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
          = ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EMOD @ A @ B ) ) ) )
    & ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
        ( ( B
         != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
       => ( ( c_2Einteger_2Eint__mod @ A @ ( c_2Einteger_2Eint__neg @ B ) )
          = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__neg @ A ) @ B ) ) ) )
    & ! [A: tyop_2Einteger_2Eint] :
        ( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__neg @ A ) )
        = A )
    & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( ( c_2Einteger_2Eint__of__num @ A )
          = ( c_2Einteger_2Eint__of__num @ B ) )
        = ( A = B ) )
    & ! [A: tyop_2Einteger_2Eint] :
        ( ( ( c_2Einteger_2Eint__neg @ A )
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = ( A
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(260,axiom,
    ! [A: $o] :
      ( ( c_2Ebool_2EF
        & A )
      = c_2Ebool_2EF ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EAND__CLAUSES__FX) ).

thf(2052,plain,
    ! [A: $o] :
      ( ( c_2Ebool_2EF
        & A )
      = c_2Ebool_2EF ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(309,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__neg @ A ) @ B )
      = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__add @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__LNEG) ).

thf(2272,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__neg @ A ) @ B )
      = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__add @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(46,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum,E: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EMODEQ @ E @ D @ C )
     => ( ( c_2Earithmetic_2EMODEQ @ E @ B @ A )
       => ( c_2Earithmetic_2EMODEQ @ E @ ( c_2Earithmetic_2E_2A @ D @ B ) @ ( c_2Earithmetic_2E_2A @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMODEQ__MULT__CONG) ).

thf(837,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum,E: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EMODEQ @ E @ D @ C )
     => ( ( c_2Earithmetic_2EMODEQ @ E @ B @ A )
       => ( c_2Earithmetic_2EMODEQ @ E @ ( c_2Earithmetic_2E_2A @ D @ B ) @ ( c_2Earithmetic_2E_2A @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(604,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Enumpair_2Encons @ B @ A )
     != c_2Enum_2E0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Encons__not__nnil) ).

thf(3242,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Enumpair_2Encons @ B @ A )
     != c_2Enum_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(279,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ B @ A ) )
     => ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ B ) @ ( c_2Einteger_2Eint__neg @ A ) ) )
        = ( ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 )
          = ( c_2Einteger_2Eint__add @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ele__context__rwt5) ).

thf(2153,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ B @ A ) )
     => ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ B ) @ ( c_2Einteger_2Eint__neg @ A ) ) )
        = ( ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 )
          = ( c_2Einteger_2Eint__add @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(244,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ A @ B )
      | ( c_2Earithmetic_2E_3C_3D @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__CASES) ).

thf(1831,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ A @ B )
      | ( c_2Earithmetic_2E_3C_3D @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(383,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( ( c_2Einteger_2EABS @ A )
          = B )
        = ( ( ( A = B )
            & ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
          | ( ( A
              = ( c_2Einteger_2Eint__neg @ B ) )
            & ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) ) ) )
      & ( ( B
          = ( c_2Einteger_2EABS @ A ) )
        = ( ( ( A = B )
            & ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
          | ( ( A
              = ( c_2Einteger_2Eint__neg @ B ) )
            & ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__EQ) ).

thf(2497,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( ( c_2Einteger_2EABS @ A )
          = B )
        = ( ( ( A = B )
            & ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
          | ( ( A
              = ( c_2Einteger_2Eint__neg @ B ) )
            & ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) ) ) )
      & ( ( B
          = ( c_2Einteger_2EABS @ A ) )
        = ( ( ( A = B )
            & ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
          | ( ( A
              = ( c_2Einteger_2Eint__neg @ B ) )
            & ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(12,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
        & ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ C ) )
     => ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2EMOD @ B @ C ) )
        = ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__COMMON__FACTOR) ).

thf(721,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
        & ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ C ) )
     => ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2EMOD @ B @ C ) )
        = ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(28,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2E_2A @ B @ C ) )
      = ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2E_2A @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMULT__ASSOC) ).

thf(779,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2E_2A @ B @ C ) )
      = ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2E_2A @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(563,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__add @ TA @ A @ B )
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
      = ( A
        = ( c_2Ewords_2Eword__2comp @ TA @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUM__ZERO) ).

thf(3074,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__add @ TA @ A @ B )
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
      = ( A
        = ( c_2Ewords_2Eword__2comp @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(540,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( c_2Ewords_2Eword__lt @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Ew2i__lt__0) ).

thf(3005,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( c_2Ewords_2Eword__lt @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(566,axiom,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ealignment_2Ealigned @ TA @ A @ C )
     => ( ( ( c_2Ealignment_2Ealigned @ TA @ A @ ( c_2Ewords_2Eword__add @ TA @ B @ C ) )
          = ( c_2Ealignment_2Ealigned @ TA @ A @ B ) )
        & ( ( c_2Ealignment_2Ealigned @ TA @ A @ ( c_2Ewords_2Eword__sub @ TA @ B @ C ) )
          = ( c_2Ealignment_2Ealigned @ TA @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ealignment_2Ealigned__add__sub) ).

thf(3083,plain,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ealignment_2Ealigned @ TA @ A @ C )
     => ( ( ( c_2Ealignment_2Ealigned @ TA @ A @ ( c_2Ewords_2Eword__add @ TA @ B @ C ) )
          = ( c_2Ealignment_2Ealigned @ TA @ A @ B ) )
        & ( ( c_2Ealignment_2Ealigned @ TA @ A @ ( c_2Ewords_2Eword__sub @ TA @ B @ C ) )
          = ( c_2Ealignment_2Ealigned @ TA @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(586,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ A @ B )
      = ( ( c_2Einteger_2Eint__le @ A @ B )
        & ( A != B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__LE) ).

thf(3162,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ A @ B )
      = ( ( c_2Einteger_2Eint__le @ A @ B )
        & ( A != B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(581,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ! [B: tyop_2Einteger_2Eint] :
          ( ( c_2Einteger_2Eint__rem @ ( c_2Einteger_2Eint__mul @ B @ A ) @ A )
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__REM__COMMON__FACTOR) ).

thf(3147,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ! [B: tyop_2Einteger_2Eint] :
          ( ( c_2Einteger_2Eint__rem @ ( c_2Einteger_2Eint__mul @ B @ A ) @ A )
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(155,axiom,
    ! [TA: $tType,TB: $tType,A: $o,B: TB > TA,C: TB > TA] :
      ( ( ^ [D: TB] : ( c_2Ebool_2ECOND @ TA @ A @ ( B @ D ) @ ( C @ D ) ) )
      = ( c_2Ebool_2ECOND @ ( TB > TA ) @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__ABS) ).

thf(1333,plain,
    ! [TA: $tType,TB: $tType,A: $o,B: TB > TA,C: TB > TA] :
      ( ( ^ [D: TB] : ( c_2Ebool_2ECOND @ TA @ A @ ( B @ D ) @ ( C @ D ) ) )
      = ( c_2Ebool_2ECOND @ ( TB > TA ) @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(426,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__ls @ TA @ A @ B )
      = ( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__OR__EQ) ).

thf(2634,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__ls @ TA @ A @ B )
      = ( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
        | ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(470,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__of__num @ ( c_2Einteger_2ENum @ A ) )
        = A )
      = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__OF__NUM) ).

thf(2788,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__of__num @ ( c_2Einteger_2ENum @ A ) )
        = A )
      = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(516,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( B
         != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        & ( ( c_2Einteger_2Eint__mod @ A @ B )
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
     => ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__mul @ C @ A ) @ B )
        = ( c_2Einteger_2Eint__mul @ C @ ( c_2Einteger_2Eint__div @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__DIV) ).

thf(2926,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( B
         != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        & ( ( c_2Einteger_2Eint__mod @ A @ B )
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
     => ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__mul @ C @ A ) @ B )
        = ( c_2Einteger_2Eint__mul @ C @ ( c_2Einteger_2Eint__div @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(139,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) )
      = ( A = c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ENOT__LT__ZERO__EQ__ZERO) ).

thf(1202,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) )
      = ( A = c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(229,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_3C_3D @ B @ A )
        & ( c_2Egcd_2Eis__gcd @ ( c_2Earithmetic_2E_2D @ A @ B ) @ B @ C ) )
     => ( c_2Egcd_2Eis__gcd @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__MINUS__L) ).

thf(1695,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_3C_3D @ B @ A )
        & ( c_2Egcd_2Eis__gcd @ ( c_2Earithmetic_2E_2D @ A @ B ) @ B @ C ) )
     => ( c_2Egcd_2Eis__gcd @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(456,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__add @ A @ B ) )
      = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__ADDR) ).

thf(2748,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__add @ A @ B ) )
      = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(528,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__divides @ A @ B )
     => ( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__add @ B @ C ) )
        = ( c_2Einteger_2Eint__divides @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__LADD) ).

thf(2963,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__divides @ A @ B )
     => ( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__add @ B @ C ) )
        = ( c_2Einteger_2Eint__divides @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(106,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
      = ( c_2Eprim__rec_2E_3C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT) ).

thf(1071,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
      = ( c_2Eprim__rec_2E_3C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(200,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
      = ( A != c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecardinal_2ELT__NZ) ).

thf(1515,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
      = ( A != c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(684,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EABS__DIFF @ A @ c_2Enum_2E0 )
        = A )
      & ( ( c_2Earithmetic_2EABS__DIFF @ c_2Enum_2E0 @ A )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EABS__DIFF__ZERO) ).

thf(3508,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EABS__DIFF @ A @ c_2Enum_2E0 )
        = A )
      & ( ( c_2Earithmetic_2EABS__DIFF @ c_2Enum_2E0 @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).

thf(208,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__mul @ TA @ A @ ( c_2Ewords_2Eword__add @ TA @ B @ C ) )
      = ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__mul @ TA @ A @ B ) @ ( c_2Ewords_2Eword__mul @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LEFT__ADD__DISTRIB) ).

thf(1616,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__mul @ TA @ A @ ( c_2Ewords_2Eword__add @ TA @ B @ C ) )
      = ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__mul @ TA @ A @ B ) @ ( c_2Ewords_2Eword__mul @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(138,axiom,
    ! [A: $o,B: $o,C: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ A @ B @ C )
      = ( ( A
         => B )
        & ( ~ A
         => C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__EXPAND__IMP) ).

thf(1185,plain,
    ! [A: $o,B: $o,C: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ A @ B @ C )
      = ( ( A
         => B )
        & ( ~ A
         => C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(11,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ A @ c_2Enum_2E0 )
      = c_2Enum_2E0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMULT__0) ).

thf(718,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ A @ c_2Enum_2E0 )
      = c_2Enum_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(240,axiom,
    ! [TA: $tType,A: $o,B: $o,C: TA,D: TA,E: TA,F: TA] :
      ( ( ( A = B )
        & ( B
         => ( C = D ) )
        & ( ~ B
         => ( E = F ) ) )
     => ( ( c_2Ebool_2ECOND @ TA @ A @ C @ E )
        = ( c_2Ebool_2ECOND @ TA @ B @ D @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__case__CONG) ).

thf(1732,plain,
    ! [TA: $tType,A: $o,B: $o,C: TA,D: TA,E: TA,F: TA] :
      ( ( ( A = B )
        & ( B
         => ( C = D ) )
        & ( ~ B
         => ( E = F ) ) )
     => ( ( c_2Ebool_2ECOND @ TA @ A @ C @ E )
        = ( c_2Ebool_2ECOND @ TA @ B @ D @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(938,plain,
    ! [A: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D @ c_2Enum_2E0 @ A ),
    inference(cnf,[status(esa)],[937]) ).

thf(443,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2EABS @ ( c_2Einteger_2Eint__neg @ A ) )
      = ( c_2Einteger_2EABS @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__NEG) ).

thf(2702,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2EABS @ ( c_2Einteger_2Eint__neg @ A ) )
      = ( c_2Einteger_2EABS @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(461,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ B ) @ ( c_2Einteger_2Eint__add @ A @ C ) )
      = ( c_2Einteger_2Eint__lt @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__LADD) ).

thf(2761,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ B ) @ ( c_2Einteger_2Eint__add @ A @ C ) )
      = ( c_2Einteger_2Eint__lt @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(502,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__add @ A @ B )
        = ( c_2Einteger_2Eint__add @ A @ C ) )
      = ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__LADD) ).

thf(2883,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__add @ A @ B )
        = ( c_2Einteger_2Eint__add @ A @ C ) )
      = ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(62,axiom,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
     => ( ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2D @ A @ B ) )
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2En2w__sub__eq__0) ).

thf(921,plain,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
     => ( ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2D @ A @ B ) )
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(261,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_3C_3D @ B @ A )
     => ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
        = ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2E_2D @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB) ).

thf(2057,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_3C_3D @ B @ A )
     => ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
        = ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2E_2D @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(26,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__exp @ ( c_2Einteger_2Eint__exp @ C @ B ) @ A )
      = ( c_2Einteger_2Eint__exp @ C @ ( c_2Earithmetic_2E_2A @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EXP__MULTIPLY__EXPONENTS) ).

thf(773,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__exp @ ( c_2Einteger_2Eint__exp @ C @ B ) @ A )
      = ( c_2Einteger_2Eint__exp @ C @ ( c_2Earithmetic_2E_2A @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(33,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
     => ( ( ( c_2Earithmetic_2EMOD @ B @ A )
          = c_2Enum_2E0 )
        = ( ? [C: tyop_2Enum_2Enum] :
              ( B
              = ( c_2Earithmetic_2E_2A @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__EQ__0__DIVISOR) ).

thf(794,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
     => ( ( ( c_2Earithmetic_2EMOD @ B @ A )
          = c_2Enum_2E0 )
        = ( ? [C: tyop_2Enum_2Enum] :
              ( B
              = ( c_2Earithmetic_2E_2A @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(238,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
      | ( c_2Earithmetic_2E_3C_3D @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__EQ__CASES) ).

thf(1727,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
      | ( c_2Earithmetic_2E_3C_3D @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(400,axiom,
    ! [A: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__mul @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__SQUARE) ).

thf(2556,plain,
    ! [A: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__mul @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(310,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__sub @ A @ B )
        = C )
      = ( A
        = ( c_2Einteger_2Eint__add @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__SUB__RADD) ).

thf(2275,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__sub @ A @ B )
        = C )
      = ( A
        = ( c_2Einteger_2Eint__add @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(410,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__neg @ A ) @ A )
      = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__NEGL) ).

thf(2585,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__neg @ A ) @ A )
      = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(405,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__add @ A @ B ) )
      = ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__ADDR) ).

thf(2570,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__add @ A @ B ) )
      = ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(415,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__ADD) ).

thf(2602,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(147,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ~ ( c_2Ewords_2Eword__lt @ TA @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__REFL) ).

thf(1301,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ~ ( c_2Ewords_2Eword__lt @ TA @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(575,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
     => ( ( c_2Einteger_2Eint__divides @ B @ C )
        = ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__mul @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ejustify__divides) ).

thf(3111,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
     => ( ( c_2Einteger_2Eint__divides @ B @ C )
        = ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__mul @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(164,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( A = B )
      | ( c_2Eprim__rec_2E_3C @ A @ B )
      | ( c_2Eprim__rec_2E_3C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__LESS__CASES) ).

thf(1374,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( A = B )
      | ( c_2Eprim__rec_2E_3C @ A @ B )
      | ( c_2Eprim__rec_2E_3C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(519,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ A @ B )
      = ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2Eint__sub) ).

thf(2936,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ A @ B )
      = ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(218,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( B != c_2Enum_2E0 )
     => ( ( c_2Einteger_2Eint__quot @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
        = ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__QUOT) ).

thf(1648,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( B != c_2Enum_2E0 )
     => ( ( c_2Einteger_2Eint__quot @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
        = ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(353,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Enum_2Enum] :
      ( ( ~ ( c_2Ewords_2Eword__msb @ TA @ A )
        & ( c_2Einteger_2Eint__lt @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) ) )
     => ( c_2Eprim__rec_2E_3C @ ( c_2Ewords_2Ew2n @ TA @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Ew2i__w2n__pos) ).

thf(2413,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Enum_2Enum] :
      ( ( ~ ( c_2Ewords_2Eword__msb @ TA @ A )
        & ( c_2Einteger_2Eint__lt @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) ) )
     => ( c_2Eprim__rec_2E_3C @ ( c_2Ewords_2Ew2n @ TA @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(577,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__sub @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger__word_2Ew2i @ TA @ B ) ) )
      = ( c_2Ewords_2Eword__sub @ TA @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__sub__i2w) ).

thf(3130,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__sub @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger__word_2Ew2i @ TA @ B ) ) )
      = ( c_2Ewords_2Eword__sub @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(127,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__mul @ TA @ A @ B ) )
      = ( c_2Ewords_2Eword__mul @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__LMUL) ).

thf(1146,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__mul @ TA @ A @ B ) )
      = ( c_2Ewords_2Eword__mul @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(316,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ A ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__LT0) ).

thf(2292,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ A ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(677,axiom,
    ( c_2Einteger_2Eint__0
    = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__0) ).

thf(3490,plain,
    ( c_2Einteger_2Eint__0
    = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).

thf(3491,plain,
    ( ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 )
    = c_2Einteger_2Eint__0 ),
    inference(lifteq,[status(thm)],[3490]) ).

thf(189,axiom,
    ! [A: $o] :
      ( ( ~ A
       => c_2Ebool_2EF )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2ENOT__ELIM2) ).

thf(1483,plain,
    ! [A: $o] :
      ( ( ~ A
       => c_2Ebool_2EF )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(213,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2D @ C @ B ) @ ( c_2Earithmetic_2E_2D @ C @ A ) )
      = ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
        | ( c_2Earithmetic_2E_3C_3D @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELE__SUB__LCANCEL) ).

thf(1631,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2D @ C @ B ) @ ( c_2Earithmetic_2E_2D @ C @ A ) )
      = ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
        | ( c_2Earithmetic_2E_3C_3D @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(16,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2E_2A @ A @ B ) )
      = ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
        & ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EZERO__LESS__MULT) ).

thf(733,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2E_2A @ A @ B ) )
      = ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
        & ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(245,axiom,
    c_2Ebool_2ET,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).

thf(1833,plain,
    c_2Ebool_2ET,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(452,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2EABS @ A ) @ B )
        = ( ( c_2Einteger_2Eint__lt @ A @ B )
          & ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ B ) @ A ) ) )
      & ( ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2EABS @ A ) )
        = ( ( c_2Einteger_2Eint__lt @ B @ A )
          | ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__neg @ B ) ) ) )
      & ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2EABS @ A ) ) @ B )
        = ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ B ) @ A )
          | ( c_2Einteger_2Eint__lt @ A @ B ) ) )
      & ( ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2EABS @ A ) ) )
        = ( ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__neg @ B ) )
          & ( c_2Einteger_2Eint__lt @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__LT) ).

thf(2727,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2EABS @ A ) @ B )
        = ( ( c_2Einteger_2Eint__lt @ A @ B )
          & ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ B ) @ A ) ) )
      & ( ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2EABS @ A ) )
        = ( ( c_2Einteger_2Eint__lt @ B @ A )
          | ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__neg @ B ) ) ) )
      & ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2EABS @ A ) ) @ B )
        = ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ B ) @ A )
          | ( c_2Einteger_2Eint__lt @ A @ B ) ) )
      & ( ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2EABS @ A ) ) )
        = ( ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__neg @ B ) )
          & ( c_2Einteger_2Eint__lt @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(259,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( A = B )
     => ~ ( c_2Eprim__rec_2E_3C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eprim__rec_2ENOT__LESS__EQ) ).

thf(2048,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( A = B )
     => ~ ( c_2Eprim__rec_2E_3C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(471,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EABS__DIFF @ A @ B )
      = ( c_2Earithmetic_2EABS__DIFF @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EABS__DIFF__SYM) ).

thf(2791,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EABS__DIFF @ A @ B )
      = ( c_2Earithmetic_2EABS__DIFF @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(490,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__sub @ TA @ B @ A ) )
      = ( c_2Ewords_2Eword__sub @ TA @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__SUB) ).

thf(2849,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__sub @ TA @ B @ A ) )
      = ( c_2Ewords_2Eword__sub @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(671,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__RZERO) ).

thf(3472,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).

thf(614,axiom,
    ( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( ( c_2Einteger_2Eint__of__num @ A )
          = ( c_2Einteger_2Eint__of__num @ B ) )
        = ( A = B ) )
    & ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
        ( ( ( c_2Einteger_2Eint__neg @ A )
          = ( c_2Einteger_2Eint__neg @ B ) )
        = ( A = B ) )
    & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( ( ( c_2Einteger_2Eint__of__num @ A )
            = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ B ) ) )
          = ( ( A = c_2Enum_2E0 )
            & ( B = c_2Enum_2E0 ) ) )
        & ( ( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ A ) )
            = ( c_2Einteger_2Eint__of__num @ B ) )
          = ( ( A = c_2Enum_2E0 )
            & ( B = c_2Enum_2E0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__CALCULATE) ).

thf(3272,plain,
    ( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( ( c_2Einteger_2Eint__of__num @ A )
          = ( c_2Einteger_2Eint__of__num @ B ) )
        = ( A = B ) )
    & ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
        ( ( ( c_2Einteger_2Eint__neg @ A )
          = ( c_2Einteger_2Eint__neg @ B ) )
        = ( A = B ) )
    & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( ( ( c_2Einteger_2Eint__of__num @ A )
            = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ B ) ) )
          = ( ( A = c_2Enum_2E0 )
            & ( B = c_2Enum_2E0 ) ) )
        & ( ( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ A ) )
            = ( c_2Einteger_2Eint__of__num @ B ) )
          = ( ( A = c_2Enum_2E0 )
            & ( B = c_2Enum_2E0 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(42,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
        & ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) )
     => ! [C: tyop_2Enum_2Enum] :
          ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2EMOD @ C @ ( c_2Earithmetic_2E_2A @ B @ A ) ) @ B )
          = ( c_2Earithmetic_2EMOD @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__MULT__MOD) ).

thf(826,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
        & ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) )
     => ! [C: tyop_2Enum_2Enum] :
          ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2EMOD @ C @ ( c_2Earithmetic_2E_2A @ B @ A ) ) @ B )
          = ( c_2Earithmetic_2EMOD @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(476,axiom,
    ! [TA: $tType,TB: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Elist_2Elist @ $o] :
      ( ( c_2Ewords_2Eword__extract @ TB @ TA @ A @ B @ ( c_2Ebitstring_2Ev2w @ TB @ C ) )
      = ( c_2Ewords_2Ew2w @ TB @ TA @ ( c_2Ewords_2Eword__bits @ TB @ A @ B @ ( c_2Ebitstring_2Ev2w @ TB @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebitstring_2Eword__extract__v2w) ).

thf(2806,plain,
    ! [TA: $tType,TB: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Elist_2Elist @ $o] :
      ( ( c_2Ewords_2Eword__extract @ TB @ TA @ A @ B @ ( c_2Ebitstring_2Ev2w @ TB @ C ) )
      = ( c_2Ewords_2Ew2w @ TB @ TA @ ( c_2Ewords_2Eword__bits @ TB @ A @ B @ ( c_2Ebitstring_2Ev2w @ TB @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(173,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__le @ TA @ A @ B )
      = ( ( ( ( c_2Ewords_2Eword__msb @ TA @ A )
            = ( c_2Ewords_2Eword__msb @ TA @ B ) )
          & ( c_2Earithmetic_2E_3C_3D @ ( c_2Ewords_2Ew2n @ TA @ A ) @ ( c_2Ewords_2Ew2n @ TA @ B ) ) )
        | ( ( c_2Ewords_2Eword__msb @ TA @ A )
          & ~ ( c_2Ewords_2Eword__msb @ TA @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LE) ).

thf(1403,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__le @ TA @ A @ B )
      = ( ( ( ( c_2Ewords_2Eword__msb @ TA @ A )
            = ( c_2Ewords_2Eword__msb @ TA @ B ) )
          & ( c_2Earithmetic_2E_3C_3D @ ( c_2Ewords_2Ew2n @ TA @ A ) @ ( c_2Ewords_2Ew2n @ TA @ B ) ) )
        | ( ( c_2Ewords_2Eword__msb @ TA @ A )
          & ~ ( c_2Ewords_2Eword__msb @ TA @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(348,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ A @ B )
      = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ B @ ( c_2Einteger_2Eint__neg @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ele__move__all__right) ).

thf(2398,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ A @ B )
      = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ B @ ( c_2Einteger_2Eint__neg @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(448,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__mul @ C @ ( c_2Einteger_2Eint__add @ B @ A ) )
      = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ C @ B ) @ ( c_2Einteger_2Eint__mul @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LDISTRIB) ).

thf(2716,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__mul @ C @ ( c_2Einteger_2Eint__add @ B @ A ) )
      = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ C @ B ) @ ( c_2Einteger_2Eint__mul @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(120,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ~ ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
        & ( c_2Ewords_2Eword__le @ TA @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__EQ__ANTISYM) ).

thf(1124,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ~ ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
        & ( c_2Ewords_2Eword__le @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(530,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
        & ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
     => ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__ADD) ).

thf(2970,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
        & ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
     => ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(693,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
      | ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ B @ A ) @ A )
        = c_2Enum_2E0 ) ),
    inference(cnf,[status(esa)],[692]) ).

thf(694,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ B @ A ) @ A )
        = c_2Enum_2E0 )
      | ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) ),
    inference(lifteq,[status(thm)],[693]) ).

thf(626,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__mul @ A @ C )
        = ( c_2Einteger_2Eint__mul @ B @ C ) )
      = ( ( C
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__RMUL) ).

thf(3319,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__mul @ A @ C )
        = ( c_2Einteger_2Eint__mul @ B @ C ) )
      = ( ( C
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        | ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(612,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__neg @ A )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( A
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__EQ0) ).

thf(3266,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__neg @ A )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( A
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

thf(252,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( A = B )
     => ~ ( c_2Ewords_2Eword__lt @ TA @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NOT__LESS__EQ) ).

thf(2016,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( A = B )
     => ~ ( c_2Ewords_2Eword__lt @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(387,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ C )
     => ? [D: tyop_2Einteger_2Eint] :
          ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D )
          & ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__sub @ B @ ( c_2Einteger_2Eint__mul @ D @ C ) ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ecan__get__small) ).

thf(2514,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ C )
     => ? [D: tyop_2Einteger_2Eint] :
          ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D )
          & ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__sub @ B @ ( c_2Einteger_2Eint__mul @ D @ C ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(404,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
        & ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
     => ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__ADD) ).

thf(2568,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
        & ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
     => ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(650,axiom,
    ! [A: tyop_2Eone_2Eone] :
      ( ( c_2EbasicSize_2Eone__size @ A )
      = c_2Enum_2E0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EbasicSize_2Eone__size__def) ).

thf(3404,plain,
    ! [A: tyop_2Eone_2Eone] :
      ( ( c_2EbasicSize_2Eone__size @ A )
      = c_2Enum_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).

thf(480,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__add @ A @ B )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( B
        = ( c_2Einteger_2Eint__neg @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__RNEG__UNIQ) ).

thf(2817,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__add @ A @ B )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( B
        = ( c_2Einteger_2Eint__neg @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(146,axiom,
    ! [A: $o,B: $o,C: $o,D: $o,E: $o] :
      ( ( C
       => B )
     => ( ( A
         => D )
       => ( ( c_2Ebool_2ECOND @ $o @ E @ C @ A )
         => ( c_2Ebool_2ECOND @ $o @ E @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EMONO__COND) ).

thf(1226,plain,
    ! [A: $o,B: $o,C: $o,D: $o,E: $o] :
      ( ( C
       => B )
     => ( ( A
         => D )
       => ( ( c_2Ebool_2ECOND @ $o @ E @ C @ A )
         => ( c_2Ebool_2ECOND @ $o @ E @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(190,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Earithmetic_2E_3C_3D @ B @ A )
        & ( C
         != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
     => ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__exp @ C @ A ) @ ( c_2Einteger_2Eint__exp @ C @ B ) )
        = ( c_2Einteger_2Eint__exp @ C @ ( c_2Earithmetic_2E_2D @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EXP__SUBTRACT__EXPONENTS) ).

thf(1488,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Earithmetic_2E_3C_3D @ B @ A )
        & ( C
         != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
     => ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__exp @ C @ A ) @ ( c_2Einteger_2Eint__exp @ C @ B ) )
        = ( c_2Einteger_2Eint__exp @ C @ ( c_2Earithmetic_2E_2D @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(195,axiom,
    ! [TA: $tType,A: TA] :
      ( ( A = A )
      = c_2Ebool_2ET ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EREFL__CLAUSE) ).

thf(1503,plain,
    c_2Ebool_2ET,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(539,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__add @ B @ C ) )
      = ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ B ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Elt__move__left__left) ).

thf(3002,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__add @ B @ C ) )
      = ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(676,axiom,
    ! [TA: $tType,TB: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Ewords_2Eword__extract @ TA @ TB @ A @ B @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
      = ( c_2Ewords_2En2w @ TB @ c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__EXTRACT__ZERO2) ).

thf(3487,plain,
    ! [TA: $tType,TB: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Ewords_2Eword__extract @ TA @ TB @ A @ B @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
      = ( c_2Ewords_2En2w @ TB @ c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).

thf(654,axiom,
    ( ! [A: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
    & ! [A: tyop_2Einteger_2Eint] :
        ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
        = ( A
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__0) ).

thf(3416,plain,
    ( ! [A: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
    & ! [A: tyop_2Einteger_2Eint] :
        ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
        = ( A
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).

thf(703,plain,
    ( ( c_2Ebool_2E_2F_5C @ $false @ $true )
    = ( $false
      & $true ) ),
    inference(instance,[status(thm)],[698]) ).

thf(704,plain,
    ~ ( c_2Ebool_2E_2F_5C @ $false @ $true ),
    inference(simp,[status(thm)],[703]) ).

thf(620,axiom,
    ! [TA: $tType] :
      ( ( c_2Ewords_2Eword__L @ TA )
     != ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2ENOT__INT__MIN__ZERO) ).

thf(3302,plain,
    ! [TA: $tType] :
      ( ( c_2Ewords_2Eword__L @ TA )
     != ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(3303,plain,
    ! [TA: $tType] :
      ( ( c_2Ewords_2Eword__L @ TA )
     != ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
    inference(cnf,[status(esa)],[3302]) ).

thf(3304,plain,
    ! [TA: $tType] :
      ( ( c_2Ewords_2Eword__L @ TA )
     != ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
    inference(lifteq,[status(thm)],[3303]) ).

thf(546,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ C @ B ) )
     => ( ( c_2Einteger_2Eint__le @ B @ A )
       => ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ C @ A ) )
          = c_2Ebool_2ET ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ele__context__rwt1) ).

thf(3023,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ C @ B ) )
     => ( ( c_2Einteger_2Eint__le @ B @ A )
       => ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ C @ A ) )
          = c_2Ebool_2ET ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(224,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
      = ( ( ( ( c_2Ewords_2Eword__msb @ TA @ A )
            = ( c_2Ewords_2Eword__msb @ TA @ B ) )
          & ( c_2Eprim__rec_2E_3C @ ( c_2Ewords_2Ew2n @ TA @ A ) @ ( c_2Ewords_2Ew2n @ TA @ B ) ) )
        | ( ( c_2Ewords_2Eword__msb @ TA @ A )
          & ~ ( c_2Ewords_2Eword__msb @ TA @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LT) ).

thf(1669,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
      = ( ( ( ( c_2Ewords_2Eword__msb @ TA @ A )
            = ( c_2Ewords_2Eword__msb @ TA @ B ) )
          & ( c_2Eprim__rec_2E_3C @ ( c_2Ewords_2Ew2n @ TA @ A ) @ ( c_2Ewords_2Ew2n @ TA @ B ) ) )
        | ( ( c_2Ewords_2Eword__msb @ TA @ A )
          & ~ ( c_2Ewords_2Eword__msb @ TA @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(322,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) @ C )
      = ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2Eword__sub @ TA @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__SUB__ASSOC) ).

thf(2308,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) @ C )
      = ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2Eword__sub @ TA @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(163,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
     => ! [B: tyop_2Enum_2Enum] :
          ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2EMOD @ B @ A ) @ A )
          = ( c_2Earithmetic_2EMOD @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__MOD) ).

thf(1371,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
     => ! [B: tyop_2Enum_2Enum] :
          ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2EMOD @ B @ A ) @ A )
          = ( c_2Earithmetic_2EMOD @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(564,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ A @ B )
      = ( ~ ( c_2Einteger_2Eint__lt @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2Eint__le) ).

thf(3077,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ A @ B )
      = ( ~ ( c_2Einteger_2Eint__lt @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(460,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EMODEQ @ A @ B @ C )
        & ( c_2Earithmetic_2EMODEQ @ A @ C @ D ) )
     => ( c_2Earithmetic_2EMODEQ @ A @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMODEQ__TRANS) ).

thf(2759,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EMODEQ @ A @ B @ C )
        & ( c_2Earithmetic_2EMODEQ @ A @ C @ D ) )
     => ( c_2Earithmetic_2EMODEQ @ A @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(660,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__ls @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
      = ( A
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LS__word__0) ).

thf(3436,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__ls @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
      = ( A
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).

thf(368,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__sub @ A @ B ) @ A )
      = ( c_2Einteger_2Eint__neg @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__SUB) ).

thf(2457,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__sub @ A @ B ) @ A )
      = ( c_2Einteger_2Eint__neg @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(36,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2E_2D @ A @ B ) @ C )
      = ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2A @ A @ C ) @ ( c_2Earithmetic_2E_2A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ERIGHT__SUB__DISTRIB) ).

thf(804,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2E_2D @ A @ B ) @ C )
      = ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2A @ A @ C ) @ ( c_2Earithmetic_2E_2A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(568,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__sub @ B @ C ) )
      = ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__add @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2EINT__SUB__SUB3) ).

thf(3091,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__sub @ B @ C ) )
      = ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__add @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(184,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ A @ B )
     => ( ( c_2Earithmetic_2EDIV @ A @ B )
        = c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__DIV__EQ__ZERO) ).

thf(1464,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ A @ B )
     => ( ( c_2Earithmetic_2EDIV @ A @ B )
        = c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(374,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ A )
      = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__LINV) ).

thf(2474,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ A )
      = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(326,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ A @ B )
      = ( ( c_2Einteger_2Eint__lt @ A @ B )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__LT) ).

thf(2319,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ A @ B )
      = ( ( c_2Einteger_2Eint__lt @ A @ B )
        | ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(406,axiom,
    ! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( A @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2E_2D @ B @ C ) ) )
      = ( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ C ) @ ( c_2Einteger_2Eint__of__num @ B ) )
          & ( A @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__of__num @ B ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ C ) ) ) ) )
        | ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ B ) @ ( c_2Einteger_2Eint__of__num @ C ) )
          & ( A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2EHO__SUB__ELIM) ).

thf(2573,plain,
    ! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( A @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2E_2D @ B @ C ) ) )
      = ( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ C ) @ ( c_2Einteger_2Eint__of__num @ B ) )
          & ( A @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__of__num @ B ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ C ) ) ) ) )
        | ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ B ) @ ( c_2Einteger_2Eint__of__num @ C ) )
          & ( A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(688,plain,
    ( ( c_2Einteger__word_2Ei2w @ skt1 @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
   != ( c_2Ewords_2En2w @ skt1 @ c_2Enum_2E0 ) ),
    inference(cnf,[status(esa)],[687]) ).

thf(689,plain,
    ( ( c_2Einteger__word_2Ei2w @ skt1 @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
   != ( c_2Ewords_2En2w @ skt1 @ c_2Enum_2E0 ) ),
    inference(lifteq,[status(thm)],[688]) ).

thf(3719,plain,
    ( ( c_2Einteger__word_2Ei2w @ skt1 @ c_2Einteger_2Eint__0 )
   != ( c_2Ewords_2En2w @ skt1 @ c_2Enum_2E0 ) ),
    inference(rewrite,[status(thm)],[689,3491]) ).

thf(331,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
     => ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ A @ C ) @ B ) )
        = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ C @ ( c_2Einteger_2Eint__div @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Eelim__le__coeffs) ).

thf(2346,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
     => ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ A @ C ) @ B ) )
        = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ C @ ( c_2Einteger_2Eint__div @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(323,axiom,
    ! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( A @ ( c_2Einteger_2Eint__div @ B @ C ) )
        = ( ? [D: tyop_2Einteger_2Eint,E: tyop_2Einteger_2Eint] :
              ( ( B
                = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ D @ C ) @ E ) )
              & ( ( ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
                  & ( c_2Einteger_2Eint__lt @ C @ E )
                  & ( c_2Einteger_2Eint__le @ E @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
                | ( ~ ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
                  & ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ E )
                  & ( c_2Einteger_2Eint__lt @ E @ C ) ) )
              & ( A @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIV__P) ).

thf(2311,plain,
    ! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( A @ ( c_2Einteger_2Eint__div @ B @ C ) )
        = ( ? [D: tyop_2Einteger_2Eint,E: tyop_2Einteger_2Eint] :
              ( ( B
                = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ D @ C ) @ E ) )
              & ( ( ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
                  & ( c_2Einteger_2Eint__lt @ C @ E )
                  & ( c_2Einteger_2Eint__le @ E @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
                | ( ~ ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
                  & ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ E )
                  & ( c_2Einteger_2Eint__lt @ E @ C ) ) )
              & ( A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(269,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Egcd_2Egcd @ A @ B )
      = ( c_2Egcd_2Egcd @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EGCD__SYM) ).

thf(2119,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Egcd_2Egcd @ A @ B )
      = ( c_2Egcd_2Egcd @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(435,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EABS__DIFF @ A @ B )
      = ( c_2Earithmetic_2EABS__DIFF @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EABS__DIFF__COMM) ).

thf(2679,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EABS__DIFF @ A @ B )
      = ( c_2Earithmetic_2EABS__DIFF @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(394,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( A
        = ( c_2Einteger_2Eint__sub @ B @ C ) )
      = ( ( c_2Einteger_2Eint__add @ A @ C )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__SUB__LADD) ).

thf(2538,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( A
        = ( c_2Einteger_2Eint__sub @ B @ C ) )
      = ( ( c_2Einteger_2Eint__add @ A @ C )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(427,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2EABS @ A ) )
      = ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__0LT) ).

thf(2637,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2EABS @ A ) )
      = ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(88,axiom,
    ! [A: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__EQ__REFL) ).

thf(1011,plain,
    ! [A: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(685,axiom,
    ! [A: tyop_2Einteger_2Eint > $o] :
      ( ( ! [B: tyop_2Enum_2Enum] : ( A @ ( c_2Einteger_2Eint__of__num @ B ) ) )
      = ( ! [B: tyop_2Einteger_2Eint] :
            ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B )
           => ( A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2EINT__NUM__FORALL) ).

thf(3515,plain,
    ! [A: tyop_2Einteger_2Eint > $o] :
      ( ( ! [B: tyop_2Enum_2Enum] : ( A @ ( c_2Einteger_2Eint__of__num @ B ) ) )
      = ( ! [B: tyop_2Einteger_2Eint] :
            ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B )
           => ( A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).

thf(313,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ B ) @ C )
      = ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__sub @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__ADD__SUB) ).

thf(2284,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ B ) @ C )
      = ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__sub @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(301,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( A
        = ( c_2Einteger_2Eint__add @ B @ C ) )
      = ( ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ B ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Eeq__move__left__left) ).

thf(2246,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( A
        = ( c_2Einteger_2Eint__add @ B @ C ) )
      = ( ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ B ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(487,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__mul @ A @ A ) )
      = ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__POASQ) ).

thf(2839,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__mul @ A @ A ) )
      = ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(522,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
      = ( c_2Einteger_2Eint__neg @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__LZERO) ).

thf(2945,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
      = ( c_2Einteger_2Eint__neg @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(99,axiom,
    ! [A: $o] :
      ( ~ A
     => ( A = c_2Ebool_2EF ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2EEQF__Imp1) ).

thf(1043,plain,
    ! [A: $o] :
      ( ~ A
     => ( A = c_2Ebool_2EF ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(681,axiom,
    ! [A: tyop_2Estring_2Echar] :
      ( ( c_2Estring_2Echar__size @ A )
      = c_2Enum_2E0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Estring_2Echar__size__def) ).

thf(3500,plain,
    ! [A: tyop_2Estring_2Echar] :
      ( ( c_2Estring_2Echar__size @ A )
      = c_2Enum_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).

thf(1704,plain,
    ( c_2Ebool_2EF
    = ( ! [A: $o] : A ) ),
    inference(lifteq,[status(thm)],[1703]) ).

thf(3585,plain,
    ~ ! [A: $o] : A,
    inference(rewrite,[status(thm)],[1704,970]) ).

thf(3586,plain,
    ~ sk32,
    inference(cnf,[status(esa)],[3585]) ).

thf(386,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
     => ( A != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__NOT__EQ) ).

thf(2510,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(23,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
     => ! [B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
          ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2EMOD @ B @ A ) @ ( c_2Earithmetic_2EMOD @ C @ A ) ) @ A )
          = ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ B @ C ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__TIMES2) ).

thf(764,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
     => ! [B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
          ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2EMOD @ B @ A ) @ ( c_2Earithmetic_2EMOD @ C @ A ) ) @ A )
          = ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ B @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(81,axiom,
    ! [A: $o] :
      ( ( ( c_2Ebool_2ET
         => A )
        = A )
      & ( ( A
         => c_2Ebool_2ET )
        = c_2Ebool_2ET )
      & ( ( c_2Ebool_2EF
         => A )
        = c_2Ebool_2ET )
      & ( ( A
         => A )
        = c_2Ebool_2ET )
      & ( ( A
         => c_2Ebool_2EF )
        = ~ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__CLAUSES) ).

thf(979,plain,
    ! [A: $o] :
      ( ( ( c_2Ebool_2ET
         => A )
        = A )
      & ( ( A
         => c_2Ebool_2ET )
        = c_2Ebool_2ET )
      & ( ( c_2Ebool_2EF
         => A )
        = c_2Ebool_2ET )
      & c_2Ebool_2ET
      & ( ( A
         => c_2Ebool_2EF )
        = ~ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(354,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__sub @ A @ B ) @ C )
      = ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__add @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__SUB__RADD) ).

thf(2415,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__sub @ A @ B ) @ C )
      = ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__add @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(534,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ B ) @ A )
      = ( c_2Ewords_2Eword__sub @ TA @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB) ).

thf(2987,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ B ) @ A )
      = ( c_2Ewords_2Eword__sub @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(901,plain,
    ( ( c_2Ebool_2ECOND @ $o @ $false @ c_2Ebool_2ET @ $true )
    = ( ~ $false
     => $true ) ),
    inference(instance,[status(thm)],[896]) ).

thf(902,plain,
    c_2Ebool_2ECOND @ $o @ $false @ c_2Ebool_2ET @ $true,
    inference(simp,[status(thm)],[901]) ).

thf(3779,plain,
    c_2Ebool_2ECOND @ $o @ $false @ $true @ $true,
    inference(rewrite,[status(thm)],[902,878]) ).

thf(100,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
    ? [C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ C @ ( c_2Einteger_2Eint__of__num @ A ) ) @ ( c_2Einteger_2Eint__mul @ D @ ( c_2Einteger_2Eint__of__num @ B ) ) )
      = ( c_2Einteger_2Eint__of__num @ ( c_2Egcd_2Egcd @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2EINT__LINEAR__GCD) ).

thf(1048,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
    ? [C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ C @ ( c_2Einteger_2Eint__of__num @ A ) ) @ ( c_2Einteger_2Eint__mul @ D @ ( c_2Einteger_2Eint__of__num @ B ) ) )
      = ( c_2Einteger_2Eint__of__num @ ( c_2Egcd_2Egcd @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(17,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ A @ C ) )
      = ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
        & ( c_2Eprim__rec_2E_3C @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELT__MULT__LCANCEL) ).

thf(736,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ A @ C ) )
      = ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
        & ( c_2Eprim__rec_2E_3C @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(237,axiom,
    ! [A: $o] :
      ( ( A
        | c_2Ebool_2EF )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EOR__CLAUSES__XF) ).

thf(1722,plain,
    ! [A: $o] :
      ( ( A
        | c_2Ebool_2EF )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(126,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
        & ( c_2Eprim__rec_2E_3C @ B @ C ) )
     => ( c_2Eprim__rec_2E_3C @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__EQ__LESS__TRANS) ).

thf(1144,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
        & ( c_2Eprim__rec_2E_3C @ B @ C ) )
     => ( c_2Eprim__rec_2E_3C @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(597,axiom,
    ! [TA: $tType] :
      ( ! [A: tyop_2Efcp_2Ecart @ $o @ TA] :
          ( ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
          = A )
      & ! [A: tyop_2Efcp_2Ecart @ $o @ TA] :
          ( ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ A )
          = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__0) ).

thf(3219,plain,
    ! [TA: $tType] :
      ( ! [A: tyop_2Efcp_2Ecart @ $o @ TA] :
          ( ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
          = A )
      & ! [A: tyop_2Efcp_2Ecart @ $o @ TA] :
          ( ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ A )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(289,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ! [B: tyop_2Einteger_2Eint] :
          ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__mul @ B @ A ) @ A )
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__COMMON__FACTOR) ).

thf(2182,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ! [B: tyop_2Einteger_2Eint] :
          ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__mul @ B @ A ) @ A )
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(416,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__divides @ A @ B )
     => ( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__sub @ B @ C ) )
        = ( c_2Einteger_2Eint__divides @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__LSUB) ).

thf(2605,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__divides @ A @ B )
     => ( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__sub @ B @ C ) )
        = ( c_2Einteger_2Eint__divides @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(40,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2A @ B @ A ) @ B )
        = ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
          & ( A = c_2Enum_2E0 ) ) )
      & ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2A @ B @ A ) @ A )
        = ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
          & ( B = c_2Enum_2E0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELT__MULT__CANCEL__RBARE) ).

thf(816,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2A @ B @ A ) @ B )
        = ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
          & ( A = c_2Enum_2E0 ) ) )
      & ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2A @ B @ A ) @ A )
        = ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
          & ( B = c_2Enum_2E0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(131,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
      = ( c_2Einteger_2Eint__lt @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger__word_2Ew2i @ TA @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2EWORD__LTi) ).

thf(1162,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
      = ( c_2Einteger_2Eint__lt @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger__word_2Ew2i @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(587,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__add @ A @ B ) @ ( c_2Einteger_2Eint__sub @ A @ B ) )
      = ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__mul @ A @ A ) @ ( c_2Einteger_2Eint__mul @ B @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIFFSQ) ).

thf(3165,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__add @ A @ B ) @ ( c_2Einteger_2Eint__sub @ A @ B ) )
      = ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__mul @ A @ A ) @ ( c_2Einteger_2Eint__mul @ B @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(159,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__quot @ A @ B )
        = ( c_2Ebool_2ECOND @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) @ ( c_2Ebool_2ECOND @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ ( c_2Einteger_2ENum @ A ) @ ( c_2Einteger_2ENum @ B ) ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__neg @ A ) ) @ ( c_2Einteger_2ENum @ B ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ ( c_2Einteger_2ENum @ A ) @ ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__neg @ B ) ) ) ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__neg @ A ) ) @ ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__neg @ B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2Eint__quot) ).

thf(1344,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__quot @ A @ B )
        = ( c_2Ebool_2ECOND @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) @ ( c_2Ebool_2ECOND @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ ( c_2Einteger_2ENum @ A ) @ ( c_2Einteger_2ENum @ B ) ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__neg @ A ) ) @ ( c_2Einteger_2ENum @ B ) ) ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ ( c_2Einteger_2ENum @ A ) @ ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__neg @ B ) ) ) ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__neg @ A ) ) @ ( c_2Einteger_2ENum @ ( c_2Einteger_2Eint__neg @ B ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(303,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__sub @ C @ A ) @ B )
      = ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__add @ C @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Emove__sub) ).

thf(2252,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__sub @ C @ A ) @ B )
      = ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__add @ C @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(56,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
     => ( ( c_2Earithmetic_2EDIV @ c_2Enum_2E0 @ A )
        = c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EZERO__DIV) ).

thf(890,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
     => ( ( c_2Earithmetic_2EDIV @ c_2Enum_2E0 @ A )
        = c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(666,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Ebit__count @ TA @ A )
        = c_2Enum_2E0 )
      = ( A
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Ebit__count__is__zero) ).

thf(3456,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Ebit__count @ TA @ A )
        = c_2Enum_2E0 )
      = ( A
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).

thf(254,axiom,
    ! [A: $o,B: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ A @ c_2Ebool_2EF @ B )
      = ( ~ A
        & B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2ECOND__CLAUSES__TF) ).

thf(2025,plain,
    ! [A: $o,B: $o] :
      ( ( c_2Ebool_2ECOND @ $o @ A @ c_2Ebool_2EF @ B )
      = ( ~ A
        & B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(478,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
      | ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__neg @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__NEGTOTAL) ).

thf(2812,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
      | ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__neg @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(578,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ A @ ( c_2Ewords_2Eword__add @ TA @ B @ C ) )
      = ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__PLUS) ).

thf(3133,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ A @ ( c_2Ewords_2Eword__add @ TA @ B @ C ) )
      = ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(556,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2Eword__add @ TA @ B @ C ) )
      = ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__ASSOC) ).

thf(3055,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2Eword__add @ TA @ B @ C ) )
      = ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(324,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__sub @ A @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__ADD) ).

thf(2314,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__sub @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(330,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( A = B )
      | ( c_2Ewords_2Eword__lo @ TA @ A @ B )
      | ( c_2Ewords_2Eword__lo @ TA @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__LOWER__CASES) ).

thf(2343,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( A = B )
      | ( c_2Ewords_2Eword__lo @ TA @ A @ B )
      | ( c_2Ewords_2Eword__lo @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(423,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__neg @ A ) @ ( c_2Einteger_2Eint__neg @ B ) )
      = ( c_2Einteger_2Eint__sub @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__NEG2) ).

thf(2625,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__neg @ A ) @ ( c_2Einteger_2Eint__neg @ B ) )
      = ( c_2Einteger_2Eint__sub @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(364,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ A @ C ) @ ( c_2Einteger_2Eint__add @ B @ C ) )
      = ( c_2Einteger_2Eint__le @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__RADD) ).

thf(2446,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ A @ C ) @ ( c_2Einteger_2Eint__add @ B @ C ) )
      = ( c_2Einteger_2Eint__le @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(459,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__lt @ A @ B )
        & ( c_2Einteger_2Eint__lt @ C @ D ) )
     => ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ C ) @ ( c_2Einteger_2Eint__add @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__ADD2) ).

thf(2757,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__lt @ A @ B )
        & ( c_2Einteger_2Eint__lt @ C @ D ) )
     => ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ C ) @ ( c_2Einteger_2Eint__add @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(593,axiom,
    ( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( B != c_2Enum_2E0 )
       => ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
          = ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ A @ B ) ) ) )
    & ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
        ( ( B
         != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
       => ( ( c_2Einteger_2Eint__div @ A @ ( c_2Einteger_2Eint__neg @ B ) )
          = ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__neg @ A ) @ B ) ) )
    & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( ( c_2Einteger_2Eint__of__num @ A )
          = ( c_2Einteger_2Eint__of__num @ B ) )
        = ( A = B ) )
    & ! [A: tyop_2Einteger_2Eint] :
        ( ( ( c_2Einteger_2Eint__neg @ A )
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = ( A
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
    & ! [A: tyop_2Einteger_2Eint] :
        ( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__neg @ A ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIV__CALCULATE) ).

thf(3192,plain,
    ( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( B != c_2Enum_2E0 )
       => ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
          = ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ A @ B ) ) ) )
    & ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
        ( ( B
         != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
       => ( ( c_2Einteger_2Eint__div @ A @ ( c_2Einteger_2Eint__neg @ B ) )
          = ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__neg @ A ) @ B ) ) )
    & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( ( c_2Einteger_2Eint__of__num @ A )
          = ( c_2Einteger_2Eint__of__num @ B ) )
        = ( A = B ) )
    & ! [A: tyop_2Einteger_2Eint] :
        ( ( ( c_2Einteger_2Eint__neg @ A )
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = ( A
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
    & ! [A: tyop_2Einteger_2Eint] :
        ( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__neg @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(699,plain,
    ( ( c_2Ebool_2E_2F_5C @ $true @ $true )
    = ( $true
      & $true ) ),
    inference(instance,[status(thm)],[698]) ).

thf(700,plain,
    c_2Ebool_2E_2F_5C @ $true @ $true,
    inference(simp,[status(thm)],[699]) ).

thf(550,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ~ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2EABS @ A ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__LT0) ).

thf(3034,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ~ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2EABS @ A ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(352,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__divides @ A @ B )
      = ( ? [C: tyop_2Einteger_2Eint] :
            ( ( c_2Einteger_2Eint__mul @ C @ A )
            = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES) ).

thf(2410,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__divides @ A @ B )
      = ( ? [C: tyop_2Einteger_2Eint] :
            ( ( c_2Einteger_2Eint__mul @ C @ A )
            = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(515,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B )
     => ? [C: tyop_2Einteger_2Eint] :
          ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__mul @ C @ B ) ) )
          & ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__mul @ C @ B ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Eadd__to__great) ).

thf(2923,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B )
     => ? [C: tyop_2Einteger_2Eint] :
          ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__mul @ C @ B ) ) )
          & ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__mul @ C @ B ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(153,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
    ? [B: tyop_2Elist_2Elist @ $o] :
      ( A
      = ( c_2Ebitstring_2Ev2w @ TA @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebitstring_2Ebitstring__nchotomy) ).

thf(1325,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
    ? [B: tyop_2Elist_2Elist @ $o] :
      ( A
      = ( c_2Ebitstring_2Ev2w @ TA @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(469,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
        & ( c_2Einteger_2Eint__lt @ A @ B ) )
     => ( ( c_2Einteger_2Eint__mod @ A @ B )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LESS__MOD) ).

thf(2785,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
        & ( c_2Einteger_2Eint__lt @ A @ B ) )
     => ( ( c_2Einteger_2Eint__mod @ A @ B )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(94,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ A @ B )
     => ( A != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eprim__rec_2ELESS__NOT__EQ) ).

thf(1029,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ A @ B )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(128,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
     => ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EMOD @ A @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebit_2EMOD__LEQ) ).

thf(1149,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
     => ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EMOD @ A @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(499,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ~ ( ( c_2Einteger_2Eint__lt @ A @ B )
        & ( c_2Einteger_2Eint__le @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LET__ANTISYM) ).

thf(2874,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ~ ( ( c_2Einteger_2Eint__lt @ A @ B )
        & ( c_2Einteger_2Eint__le @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(311,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
        & ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
     => ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LTE__ADD) ).

thf(2278,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
        & ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
     => ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(399,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Egcd_2Elcm @ B @ A )
      = ( c_2Egcd_2Elcm @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2ELCM__COMM) ).

thf(2553,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Egcd_2Elcm @ B @ A )
      = ( c_2Egcd_2Elcm @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(582,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ~ ( c_2Einteger_2Eint__lt @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__REFL) ).

thf(3150,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ~ ( c_2Einteger_2Eint__lt @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(488,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( B
         != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        & ( ( c_2Einteger_2Eint__rem @ A @ B )
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
     => ( ( c_2Einteger_2Eint__quot @ ( c_2Einteger_2Eint__mul @ C @ A ) @ B )
        = ( c_2Einteger_2Eint__mul @ C @ ( c_2Einteger_2Eint__quot @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__QUOT) ).

thf(2842,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( B
         != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        & ( ( c_2Einteger_2Eint__rem @ A @ B )
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
     => ( ( c_2Einteger_2Eint__quot @ ( c_2Einteger_2Eint__mul @ C @ A ) @ B )
        = ( c_2Einteger_2Eint__mul @ C @ ( c_2Einteger_2Eint__quot @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(446,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ B ) ) @ C )
      = ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__add @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__ADDNEG2) ).

thf(2710,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ B ) ) @ C )
      = ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__add @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(511,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ B ) @ C )
      = ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__add @ C @ ( c_2Einteger_2Eint__neg @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Elt__move__left__right) ).

thf(2911,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ B ) @ C )
      = ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__add @ C @ ( c_2Einteger_2Eint__neg @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(247,axiom,
    ! [TA: $tType,A: $o,B: TA] :
      ( ( c_2Ebool_2ECOND @ TA @ A @ B @ B )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2ECOND__CLAUSES__ID) ).

thf(1841,plain,
    ! [TA: $tType,A: $o,B: TA] :
      ( ( c_2Ebool_2ECOND @ TA @ A @ B @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(332,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__add @ TA @ B @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__SUB2) ).

thf(2350,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__add @ TA @ B @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(349,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ B @ A )
      = ( c_2Einteger_2Eint__add @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__SYM) ).

thf(2401,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ B @ A )
      = ( c_2Einteger_2Eint__add @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(295,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Ew2w @ TA @ TA @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Ew2w__id) ).

thf(2212,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Ew2w @ TA @ TA @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(104,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__lt @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ B )
        & ( c_2Ewords_2Eword__lt @ TA @ B @ A ) )
     => ( c_2Ewords_2Eword__lt @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LT__SUB__UPPER) ).

thf(1066,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__lt @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ B )
        & ( c_2Ewords_2Eword__lt @ TA @ B @ A ) )
     => ( c_2Ewords_2Eword__lt @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(216,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ~ ( c_2Earithmetic_2E_3C_3D @ A @ B ) )
      = ( c_2Eprim__rec_2E_3C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ENOT__LESS__EQUAL) ).

thf(1643,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ~ ( c_2Earithmetic_2E_3C_3D @ A @ B ) )
      = ( c_2Eprim__rec_2E_3C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(135,axiom,
    ! [A: $o] :
      ( c_2Ebool_2EF
     => A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EFALSITY) ).

thf(1176,plain,
    ! [A: $o] :
      ( c_2Ebool_2EF
     => A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(623,axiom,
    ! [A: tyop_2Einteger_2Eint > $o] :
      ( ( ? [B: tyop_2Enum_2Enum] : ( A @ ( c_2Einteger_2Eint__of__num @ B ) ) )
      = ( ? [B: tyop_2Einteger_2Eint] :
            ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B )
            & ( A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2EINT__NUM__EXISTS) ).

thf(3310,plain,
    ! [A: tyop_2Einteger_2Eint > $o] :
      ( ( ? [B: tyop_2Enum_2Enum] : ( A @ ( c_2Einteger_2Eint__of__num @ B ) ) )
      = ( ? [B: tyop_2Einteger_2Eint] :
            ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B )
            & ( A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

thf(265,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
     => ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EMOD @ B @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__LESS__EQ) ).

thf(2101,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
     => ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EMOD @ B @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(320,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__add @ A @ B ) )
      = ( c_2Einteger_2Eint__neg @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__SUB2) ).

thf(2303,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__add @ A @ B ) )
      = ( c_2Einteger_2Eint__neg @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(589,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ B )
      = ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__LNEG) ).

thf(3178,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ B )
      = ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(496,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__add @ A @ B ) @ C )
      = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ A @ C ) @ ( c_2Einteger_2Eint__mul @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__RDISTRIB) ).

thf(2867,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__add @ A @ B ) @ C )
      = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ A @ C ) @ ( c_2Einteger_2Eint__mul @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(464,axiom,
    ! [TA: $tType] : ( c_2Ewords_2Eword__msb @ TA @ ( c_2Ewords_2Eword__L @ TA ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__L__NEG) ).

thf(2770,plain,
    ! [TA: $tType] : ( c_2Ewords_2Eword__msb @ TA @ ( c_2Ewords_2Eword__L @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(142,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
      = ( ( c_2Eprim__rec_2E_3C @ A @ B )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__OR__EQ) ).

thf(1213,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
      = ( ( c_2Eprim__rec_2E_3C @ A @ B )
        | ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(486,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__mul @ A @ B ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIV__LMUL) ).

thf(2835,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__mul @ A @ B ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(398,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__neg @ A ) @ B )
        = ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__sub @ B @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__NEG__NUMERATOR) ).

thf(2550,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__neg @ A ) @ B )
        = ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__sub @ B @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(377,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__rem @ A @ B )
        = ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__quot @ A @ B ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2Eint__rem) ).

thf(2481,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__rem @ A @ B )
        = ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__quot @ A @ B ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(585,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__NEG) ).

thf(3159,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(338,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__sub @ TA @ B @ A ) @ B )
      = ( c_2Ewords_2Eword__2comp @ TA @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__SUB3) ).

thf(2369,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__sub @ TA @ B @ A ) @ B )
      = ( c_2Ewords_2Eword__2comp @ TA @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(117,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ~ ( c_2Eprim__rec_2E_3C @ A @ B )
        & ( A != B ) )
     => ( c_2Eprim__rec_2E_3C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__CASES__IMP) ).

thf(1113,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ~ ( c_2Eprim__rec_2E_3C @ A @ B )
        & ( A != B ) )
     => ( c_2Eprim__rec_2E_3C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(473,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__neg @ A ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__LE0) ).

thf(2797,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__neg @ A ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(179,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
        = ( c_2Eprim__rec_2E_3C @ A @ B ) )
      & ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ A ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ B ) ) )
        = ( c_2Eprim__rec_2E_3C @ B @ A ) )
      & ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ A ) ) @ ( c_2Einteger_2Eint__of__num @ B ) )
        = ( ( A != c_2Enum_2E0 )
          | ( B != c_2Enum_2E0 ) ) )
      & ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ B ) ) )
        = c_2Ebool_2EF ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__CALCULATE) ).

thf(1435,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
        = ( c_2Eprim__rec_2E_3C @ A @ B ) )
      & ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ A ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ B ) ) )
        = ( c_2Eprim__rec_2E_3C @ B @ A ) )
      & ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ A ) ) @ ( c_2Einteger_2Eint__of__num @ B ) )
        = ( ( A != c_2Enum_2E0 )
          | ( B != c_2Enum_2E0 ) ) )
      & ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ B ) ) )
        = c_2Ebool_2EF ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(187,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
        & ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) )
     => ( ( c_2Earithmetic_2E_3C_3D @ B @ ( c_2Egcd_2Elcm @ B @ A ) )
        & ( c_2Earithmetic_2E_3C_3D @ B @ ( c_2Egcd_2Elcm @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2ELCM__LE) ).

thf(1477,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
        & ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) )
     => ( ( c_2Earithmetic_2E_3C_3D @ B @ ( c_2Egcd_2Elcm @ B @ A ) )
        & ( c_2Earithmetic_2E_3C_3D @ B @ ( c_2Egcd_2Elcm @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(628,axiom,
    ! [A: tyop_2Enum_2Enum] : ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__of__num @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__POS) ).

thf(3325,plain,
    ! [A: tyop_2Enum_2Enum] : ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__of__num @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

thf(161,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
     => ( ( c_2Earithmetic_2EMODEQ @ A @ C @ B )
       => ( ( c_2Earithmetic_2EMOD @ C @ A )
          = ( c_2Earithmetic_2EMOD @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMODEQ__INTRO__CONG) ).

thf(1364,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
     => ( ( c_2Earithmetic_2EMODEQ @ A @ C @ B )
       => ( ( c_2Earithmetic_2EMOD @ C @ A )
          = ( c_2Earithmetic_2EMOD @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(529,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ~ ( c_2Einteger_2Eint__le @ A @ B ) )
      = ( c_2Einteger_2Eint__lt @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NOT__LE) ).

thf(2967,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ~ ( c_2Einteger_2Eint__le @ A @ B ) )
      = ( c_2Einteger_2Eint__lt @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(538,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2EABS @ A ) @ ( c_2Einteger_2EABS @ B ) )
      = ( c_2Einteger_2EABS @ ( c_2Einteger_2Eint__mul @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__MUL) ).

thf(2999,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2EABS @ A ) @ ( c_2Einteger_2EABS @ B ) )
      = ( c_2Einteger_2EABS @ ( c_2Einteger_2Eint__mul @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(280,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__msb @ TA @ A )
      = ( c_2Ewords_2Eword__ls @ TA @ ( c_2Ewords_2Eword__L @ TA ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__MSB__INT__MIN__LS) ).

thf(2156,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__msb @ TA @ A )
      = ( c_2Ewords_2Eword__ls @ TA @ ( c_2Ewords_2Eword__L @ TA ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(228,axiom,
    c_2Ebool_2ET,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebag_2Emlt__UNION__EMPTY__EQN) ).

thf(1694,plain,
    c_2Ebool_2ET,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(440,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__msb @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2Eword__L @ TA ) ) )
      = ( ~ ( c_2Ewords_2Eword__msb @ TA @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__msb__add__word__L) ).

thf(2693,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__msb @ TA @ ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2Eword__L @ TA ) ) )
      = ( ~ ( c_2Ewords_2Eword__msb @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(643,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__RID) ).

thf(3380,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(299,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( A != c_2Enum_2E0 )
     => ( ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ A ) @ B )
          = C )
        = ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__of__num @ A ) @ C )
          & ( B
            = ( c_2Einteger_2Eint__div @ C @ ( c_2Einteger_2Eint__of__num @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Eelim__eq__coeffs) ).

thf(2239,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( A != c_2Enum_2E0 )
     => ( ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ A ) @ B )
          = C )
        = ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__of__num @ A ) @ C )
          & ( B
            = ( c_2Einteger_2Eint__div @ C @ ( c_2Einteger_2Eint__of__num @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(524,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ? [D: tyop_2Einteger_2Eint] :
          ( ( A
            = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ C @ B ) @ D ) )
          & ( c_2Ebool_2ECOND @ $o @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D ) @ ( c_2Einteger_2Eint__le @ D @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
          & ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2EABS @ D ) @ ( c_2Einteger_2EABS @ B ) ) )
     => ( ( c_2Einteger_2Eint__quot @ A @ B )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__QUOT__UNIQUE) ).

thf(2952,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ? [D: tyop_2Einteger_2Eint] :
          ( ( A
            = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ C @ B ) @ D ) )
          & ( c_2Ebool_2ECOND @ $o @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D ) @ ( c_2Einteger_2Eint__le @ D @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
          & ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2EABS @ D ) @ ( c_2Einteger_2EABS @ B ) ) )
     => ( ( c_2Einteger_2Eint__quot @ A @ B )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(657,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Einteger_2Eint__of__num @ A )
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__of__num @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__NZ) ).

thf(3427,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Einteger_2Eint__of__num @ A )
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__of__num @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).

thf(267,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ! [B: tyop_2Einteger_2Eint] :
          ( ( B
            = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__div @ B @ A ) @ A ) @ ( c_2Einteger_2Eint__mod @ B @ A ) ) )
          & ( c_2Ebool_2ECOND @ $o @ ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__mod @ B @ A ) ) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__mod @ B @ A ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__mod @ B @ A ) ) @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__mod @ B @ A ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVISION) ).

thf(2107,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ! [B: tyop_2Einteger_2Eint] :
          ( ( B
            = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__div @ B @ A ) @ A ) @ ( c_2Einteger_2Eint__mod @ B @ A ) ) )
          & ( c_2Ebool_2ECOND @ $o @ ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__mod @ B @ A ) ) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__mod @ B @ A ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__mod @ B @ A ) ) @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__mod @ B @ A ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(71,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
      | ( c_2Ewords_2Eword__le @ TA @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__CASES) ).

thf(944,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
      | ( c_2Ewords_2Eword__le @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(185,axiom,
    ! [A: $o] :
      ( ( A
       => c_2Ebool_2ET )
      = c_2Ebool_2ET ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CLAUSES__XT) ).

thf(1467,plain,
    ! [A: $o] :
      ( ( A
       => c_2Ebool_2ET )
      = c_2Ebool_2ET ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(647,axiom,
    ! [A: tyop_2Elist_2Elist @ $o] :
      ( ( c_2Ebitstring_2Eshiftr @ A @ c_2Enum_2E0 )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebitstring_2Eshiftr__0) ).

thf(3395,plain,
    ! [A: tyop_2Elist_2Elist @ $o] :
      ( ( c_2Ebitstring_2Eshiftr @ A @ c_2Enum_2E0 )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).

thf(373,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__div @ A @ ( c_2Einteger_2Eint__neg @ B ) )
        = ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__neg @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIV__NEG) ).

thf(2471,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__div @ A @ ( c_2Einteger_2Eint__neg @ B ) )
        = ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__neg @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(271,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Einteger__word_2Eword__sdiv @ TA @ A @ B )
      = ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__div @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger__word_2Ew2i @ TA @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__sdiv__def) ).

thf(2124,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Einteger__word_2Eword__sdiv @ TA @ A @ B )
      = ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__div @ ( c_2Einteger__word_2Ew2i @ TA @ A ) @ ( c_2Einteger__word_2Ew2i @ TA @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(365,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__add @ A @ B ) @ A )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__SUB) ).

thf(2449,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__add @ A @ B ) @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(555,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__mul @ A @ B ) )
        = ( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
            & ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
          | ( ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
            & ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) )
      & ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = ( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
            & ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
          | ( ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
            & ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__SIGN__CASES) ).

thf(3048,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__mul @ A @ B ) )
        = ( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
            & ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
          | ( ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
            & ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) )
      & ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = ( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
            & ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
          | ( ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
            & ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(69,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] : ( c_2Ewords_2Eword__le @ TA @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__EQ__REFL) ).

thf(939,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] : ( c_2Ewords_2Eword__le @ TA @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(186,axiom,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
        = A )
      & ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CLAUSES) ).

thf(1472,plain,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
        = A )
      & ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(489,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ! [B: tyop_2Einteger_2Eint] :
          ( ( ( c_2Einteger_2Eint__mod @ B @ A )
            = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
          = ( ? [C: tyop_2Einteger_2Eint] :
                ( B
                = ( c_2Einteger_2Eint__mul @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__EQ0) ).

thf(2846,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ! [B: tyop_2Einteger_2Eint] :
          ( ( ( c_2Einteger_2Eint__mod @ B @ A )
            = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
          = ( ? [C: tyop_2Einteger_2Eint] :
                ( B
                = ( c_2Einteger_2Eint__mul @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(20,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
        & ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ B @ A ) @ C ) )
     => ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ C @ ( c_2Earithmetic_2E_2A @ B @ A ) ) @ B )
        = ( c_2Earithmetic_2EMOD @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__SUB) ).

thf(754,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
        & ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ B @ A ) @ C ) )
     => ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ C @ ( c_2Earithmetic_2E_2A @ B @ A ) ) @ B )
        = ( c_2Earithmetic_2EMOD @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(507,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ A @ A ) @ ( c_2Einteger_2Eint__mul @ B @ B ) )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( ( A
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        & ( B
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUMSQ) ).

thf(2899,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ A @ A ) @ ( c_2Einteger_2Eint__mul @ B @ B ) )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( ( A
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        & ( B
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(409,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ C @ B ) )
     => ( ( c_2Einteger_2Eint__lt @ B @ A )
       => ( ( ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 )
            = ( c_2Einteger_2Eint__add @ C @ A ) )
          = c_2Ebool_2EF ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ele__context__rwt3) ).

thf(2582,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ C @ B ) )
     => ( ( c_2Einteger_2Eint__lt @ B @ A )
       => ( ( ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 )
            = ( c_2Einteger_2Eint__add @ C @ A ) )
          = c_2Ebool_2EF ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(512,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__sub @ A @ B ) @ C )
      = ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__mul @ A @ C ) @ ( c_2Einteger_2Eint__mul @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__RDISTRIB) ).

thf(2914,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__sub @ A @ B ) @ C )
      = ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__mul @ A @ C ) @ ( c_2Einteger_2Eint__mul @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(549,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ B @ ( c_2Einteger_2Eint__add @ A @ B ) )
      = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__ADDL) ).

thf(3031,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ B @ ( c_2Einteger_2Eint__add @ A @ B ) )
      = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(222,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__abs @ TA @ ( c_2Ewords_2Eword__abs @ TA @ A ) )
      = ( c_2Ewords_2Eword__abs @ TA @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__abs__word__abs) ).

thf(1662,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__abs @ TA @ ( c_2Ewords_2Eword__abs @ TA @ A ) )
      = ( c_2Ewords_2Eword__abs @ TA @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(419,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
     => ( c_2Ewords_2Eword__ls @ TA @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__IMP__LOWER__OR__EQ) ).

thf(2614,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
     => ( c_2Ewords_2Eword__ls @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(64,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
     => ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2EMOD @ A @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__LESS) ).

thf(927,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
     => ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2EMOD @ A @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(256,axiom,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Eprim__rec_2E_3C @ A @ B )
     => ( ( c_2Ewords_2Eword__slice @ TA @ A @ B @ C )
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SLICE__ZERO) ).

thf(2037,plain,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Eprim__rec_2E_3C @ A @ B )
     => ( ( c_2Ewords_2Eword__slice @ TA @ A @ B @ C )
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(136,axiom,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Eprim__rec_2E_3C @ A @ B )
        & ( c_2Ealignment_2Ealigned @ TA @ B @ C ) )
     => ( c_2Ealignment_2Ealigned @ TA @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ealignment_2Ealigned__imp) ).

thf(1181,plain,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Eprim__rec_2E_3C @ A @ B )
        & ( c_2Ealignment_2Ealigned @ TA @ B @ C ) )
     => ( c_2Ealignment_2Ealigned @ TA @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(41,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2E_2D @ A @ B ) )
      = ( c_2Ebool_2ECOND @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2EINT__NUM__SUB) ).

thf(823,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2E_2D @ A @ B ) )
      = ( c_2Ebool_2ECOND @ tyop_2Einteger_2Eint @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(521,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2EABS @ ( c_2Einteger_2EABS @ A ) )
      = ( c_2Einteger_2EABS @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__ABS) ).

thf(2942,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2EABS @ ( c_2Einteger_2EABS @ A ) )
      = ( c_2Einteger_2EABS @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(711,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
      | ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
      | ~ ( c_2Eprim__rec_2E_3C @ C @ ( c_2Earithmetic_2E_2A @ B @ A ) )
      | ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2A @ B @ A ) @ C ) @ A )
        = ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ A @ ( c_2Earithmetic_2EMOD @ C @ A ) ) @ A ) ) ),
    inference(cnf,[status(esa)],[710]) ).

thf(712,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2A @ B @ A ) @ C ) @ A )
        = ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2D @ A @ ( c_2Earithmetic_2EMOD @ C @ A ) ) @ A ) )
      | ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
      | ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
      | ~ ( c_2Eprim__rec_2E_3C @ C @ ( c_2Earithmetic_2E_2A @ B @ A ) ) ),
    inference(lifteq,[status(thm)],[711]) ).

thf(79,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2D @ A @ B )
        = A )
      = ( ( A = c_2Enum_2E0 )
        | ( B = c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ESUB__EQ__EQ__0) ).

thf(971,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2D @ A @ B )
        = A )
      = ( ( A = c_2Enum_2E0 )
        | ( B = c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(411,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__lo @ TA @ A @ ( c_2Ewords_2Eword__2comp @ TA @ B ) )
      = ( ( B
         != ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
        & ( ( A
            = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
          | ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__NEG__RIGHT) ).

thf(2588,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__lo @ TA @ A @ ( c_2Ewords_2Eword__2comp @ TA @ B ) )
      = ( ( B
         != ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
        & ( ( A
            = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
          | ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(76,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Egcd_2Egcd @ A @ B )
        = c_2Enum_2E0 )
      = ( ( A = c_2Enum_2E0 )
        & ( B = c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EGCD__EQ__0) ).

thf(954,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Egcd_2Egcd @ A @ B )
        = c_2Enum_2E0 )
      = ( ( A = c_2Enum_2E0 )
        & ( B = c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(18,axiom,
    ( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
        = ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2E_2A @ A @ B ) ) )
    & ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
        ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ A ) @ B )
        = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__mul @ A @ B ) ) )
    & ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
        ( ( c_2Einteger_2Eint__mul @ A @ ( c_2Einteger_2Eint__neg @ B ) )
        = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__mul @ A @ B ) ) )
    & ! [A: tyop_2Einteger_2Eint] :
        ( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__neg @ A ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__CALCULATE) ).

thf(739,plain,
    ( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
        = ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2E_2A @ A @ B ) ) )
    & ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
        ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ A ) @ B )
        = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__mul @ A @ B ) ) )
    & ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
        ( ( c_2Einteger_2Eint__mul @ A @ ( c_2Einteger_2Eint__neg @ B ) )
        = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__mul @ A @ B ) ) )
    & ! [A: tyop_2Einteger_2Eint] :
        ( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__neg @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(162,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Egcd_2Egcd @ A @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EGCD__REF) ).

thf(1368,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Egcd_2Egcd @ A @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(114,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > TA] :
    ? [C: TA > TA] :
    ! [D: TA] :
      ( ( C @ D )
      = ( c_2Ebool_2ECOND @ TA @ ( A @ D ) @ D @ ( C @ ( B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewhile_2EITERATION) ).

thf(1098,plain,
    ! [TA: $tType,A: TA > $o,B: TA > TA] :
    ? [C: TA > TA] :
    ! [D: TA] :
      ( ( C @ D )
      = ( c_2Ebool_2ECOND @ TA @ ( A @ D ) @ D @ ( C @ ( B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(27,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( c_2Ebool_2ECOND @ $o @ ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__mod @ A @ B ) ) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__mod @ A @ B ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__mod @ A @ B ) ) @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__mod @ A @ B ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__BOUNDS) ).

thf(776,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( c_2Ebool_2ECOND @ $o @ ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__lt @ B @ ( c_2Einteger_2Eint__mod @ A @ B ) ) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__mod @ A @ B ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) @ ( c_2Ebool_2E_2F_5C @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__mod @ A @ B ) ) @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__mod @ A @ B ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(242,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ A ) @ B )
     => ( c_2Earithmetic_2E_3C_3D @ A @ ( c_2Einteger_2ENum @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2ELE__NUM__OF__INT) ).

thf(1748,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ A ) @ B )
     => ( c_2Earithmetic_2E_3C_3D @ A @ ( c_2Einteger_2ENum @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(3,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_3C_3D @ A @ C )
        & ( c_2Earithmetic_2E_3C_3D @ B @ D ) )
     => ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__MONO__MULT2) ).

thf(690,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_3C_3D @ A @ C )
        & ( c_2Earithmetic_2E_3C_3D @ B @ D ) )
     => ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(203,axiom,
    ! [TA: $tType,A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Ewords_2Eword__mul @ TA @ ( c_2Einteger__word_2Ei2w @ TA @ A ) @ ( c_2Einteger__word_2Ei2w @ TA @ B ) )
      = ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__mul @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__i2w__mul) ).

thf(1598,plain,
    ! [TA: $tType,A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Ewords_2Eword__mul @ TA @ ( c_2Einteger__word_2Ei2w @ TA @ A ) @ ( c_2Einteger__word_2Ei2w @ TA @ B ) )
      = ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__mul @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(262,axiom,
    ! [A: $o,B: $o,C: $o,D: $o] :
      ( ( D
        = ( c_2Ebool_2ECOND @ $o @ C @ B @ A ) )
      = ( ( D
          | C
          | ~ A )
        & ( D
          | ~ B
          | ~ C )
        & ( D
          | ~ B
          | ~ A )
        & ( ~ C
          | B
          | ~ D )
        & ( C
          | A
          | ~ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2Edc__cond) ).

thf(2060,plain,
    ! [A: $o,B: $o,C: $o,D: $o] :
      ( ( D
        = ( c_2Ebool_2ECOND @ $o @ C @ B @ A ) )
      = ( ( D
          | C
          | ~ A )
        & ( D
          | ~ B
          | ~ C )
        & ( D
          | ~ B
          | ~ A )
        & ( ~ C
          | B
          | ~ D )
        & ( C
          | A
          | ~ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(172,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Egcd_2Egcd @ A @ c_2Enum_2E0 )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EGCD__0R) ).

thf(1400,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Egcd_2Egcd @ A @ c_2Enum_2E0 )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(293,axiom,
    ( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( B != c_2Enum_2E0 )
       => ( ( c_2Einteger_2Eint__rem @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
          = ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EMOD @ A @ B ) ) ) )
    & ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
        ( ( B
         != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
       => ( ( ( c_2Einteger_2Eint__rem @ ( c_2Einteger_2Eint__neg @ A ) @ B )
            = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__rem @ A @ B ) ) )
          & ( ( c_2Einteger_2Eint__rem @ A @ ( c_2Einteger_2Eint__neg @ B ) )
            = ( c_2Einteger_2Eint__rem @ A @ B ) ) ) )
    & ! [A: tyop_2Einteger_2Eint] :
        ( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__neg @ A ) )
        = A )
    & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( ( c_2Einteger_2Eint__of__num @ A )
          = ( c_2Einteger_2Eint__of__num @ B ) )
        = ( A = B ) )
    & ! [A: tyop_2Einteger_2Eint] :
        ( ( ( c_2Einteger_2Eint__neg @ A )
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = ( A
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__REM__CALCULATE) ).

thf(2192,plain,
    ( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( B != c_2Enum_2E0 )
       => ( ( c_2Einteger_2Eint__rem @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
          = ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EMOD @ A @ B ) ) ) )
    & ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
        ( ( B
         != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
       => ( ( ( c_2Einteger_2Eint__rem @ ( c_2Einteger_2Eint__neg @ A ) @ B )
            = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__rem @ A @ B ) ) )
          & ( ( c_2Einteger_2Eint__rem @ A @ ( c_2Einteger_2Eint__neg @ B ) )
            = ( c_2Einteger_2Eint__rem @ A @ B ) ) ) )
    & ! [A: tyop_2Einteger_2Eint] :
        ( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__neg @ A ) )
        = A )
    & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( ( c_2Einteger_2Eint__of__num @ A )
          = ( c_2Einteger_2Eint__of__num @ B ) )
        = ( A = B ) )
    & ! [A: tyop_2Einteger_2Eint] :
        ( ( ( c_2Einteger_2Eint__neg @ A )
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = ( A
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(55,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
      = ( c_2Earithmetic_2E_3C_3D @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE) ).

thf(887,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
      = ( c_2Earithmetic_2E_3C_3D @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(351,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( B
         != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        & ( ( c_2Einteger_2Eint__mod @ A @ B )
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
     => ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__div @ A @ B ) @ B )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIV__MUL__ID) ).

thf(2407,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( B
         != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        & ( ( c_2Einteger_2Eint__mod @ A @ B )
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
     => ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__div @ A @ B ) @ B )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(557,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2EABS @ A )
        = A )
      = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__EQ__ID) ).

thf(3058,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2EABS @ A )
        = A )
      = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(565,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ A @ B )
      = ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ B @ ( c_2Einteger_2Eint__neg @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Elt__move__all__right) ).

thf(3080,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ A @ B )
      = ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ B @ ( c_2Einteger_2Eint__neg @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(605,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( C
         != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        & ( ( c_2Einteger_2Eint__mul @ A @ C )
          = ( c_2Einteger_2Eint__mul @ B @ C ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__RMUL__IMP) ).

thf(3246,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( C
         != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        & ( ( c_2Einteger_2Eint__mul @ A @ C )
          = ( c_2Einteger_2Eint__mul @ B @ C ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(716,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ C @ B ) )
      = ( ( B = c_2Enum_2E0 )
        | ( c_2Earithmetic_2E_3C_3D @ A @ C ) ) ),
    inference(cnf,[status(esa)],[715]) ).

thf(717,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ C @ B ) )
      = ( ( B = c_2Enum_2E0 )
        | ( c_2Earithmetic_2E_3C_3D @ A @ C ) ) ),
    inference(lifteq,[status(thm)],[716]) ).

thf(633,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__sub @ A @ B )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__0) ).

thf(3344,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__sub @ A @ B )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).

thf(327,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2EABS @ A ) @ B )
        = ( ( c_2Einteger_2Eint__le @ A @ B )
          & ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__neg @ B ) @ A ) ) )
      & ( ( c_2Einteger_2Eint__le @ B @ ( c_2Einteger_2EABS @ A ) )
        = ( ( c_2Einteger_2Eint__le @ B @ A )
          | ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__neg @ B ) ) ) )
      & ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2EABS @ A ) ) @ B )
        = ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__neg @ B ) @ A )
          | ( c_2Einteger_2Eint__le @ A @ B ) ) )
      & ( ( c_2Einteger_2Eint__le @ B @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2EABS @ A ) ) )
        = ( ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__neg @ B ) )
          & ( c_2Einteger_2Eint__le @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__LE) ).

thf(2322,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2EABS @ A ) @ B )
        = ( ( c_2Einteger_2Eint__le @ A @ B )
          & ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__neg @ B ) @ A ) ) )
      & ( ( c_2Einteger_2Eint__le @ B @ ( c_2Einteger_2EABS @ A ) )
        = ( ( c_2Einteger_2Eint__le @ B @ A )
          | ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__neg @ B ) ) ) )
      & ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2EABS @ A ) ) @ B )
        = ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__neg @ B ) @ A )
          | ( c_2Einteger_2Eint__le @ A @ B ) ) )
      & ( ( c_2Einteger_2Eint__le @ B @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2EABS @ A ) ) )
        = ( ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__neg @ B ) )
          & ( c_2Einteger_2Eint__le @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(630,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
    ? [B: tyop_2Enum_2Enum] :
      ( A
      = ( c_2Ewords_2En2w @ TA @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__nchotomy) ).

thf(3329,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
    ? [B: tyop_2Enum_2Enum] :
      ( A
      = ( c_2Ewords_2En2w @ TA @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(156,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
        & ( c_2Ewords_2Eword__le @ TA @ B @ C ) )
     => ( c_2Ewords_2Eword__lt @ TA @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__LESS__EQ__TRANS) ).

thf(1336,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
        & ( c_2Ewords_2Eword__le @ TA @ B @ C ) )
     => ( c_2Ewords_2Eword__lt @ TA @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(372,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__sub @ B @ C ) )
      = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__SUB__LADD) ).

thf(2468,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__sub @ B @ C ) )
      = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(235,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( A = B )
      | ( c_2Ewords_2Eword__lt @ TA @ A @ B )
      | ( c_2Ewords_2Eword__lt @ TA @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__LESS__CASES) ).

thf(1716,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( A = B )
      | ( c_2Ewords_2Eword__lt @ TA @ A @ B )
      | ( c_2Ewords_2Eword__lt @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(367,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( c_2Einteger_2Eint__le @ ( c_2Einteger_2EABS @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__quot @ A @ B ) @ B ) ) @ ( c_2Einteger_2EABS @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__QUOT) ).

thf(2454,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( c_2Einteger_2Eint__le @ ( c_2Einteger_2EABS @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__quot @ A @ B ) @ B ) ) @ ( c_2Einteger_2EABS @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(621,axiom,
    ( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
    = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__0) ).

thf(3305,plain,
    ( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
    = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(178,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__mul @ TA @ A @ ( c_2Ewords_2Eword__sub @ TA @ B @ C ) )
      = ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__mul @ TA @ A @ B ) @ ( c_2Ewords_2Eword__mul @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LEFT__SUB__DISTRIB) ).

thf(1432,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__mul @ TA @ A @ ( c_2Ewords_2Eword__sub @ TA @ B @ C ) )
      = ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__mul @ TA @ A @ B ) @ ( c_2Ewords_2Eword__mul @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(283,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__divides @ A @ B )
     => ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__mul @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__LMUL) ).

thf(2165,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__divides @ A @ B )
     => ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__mul @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(215,axiom,
    ! [A: $o] :
      ( ( c_2Ebool_2EF
       => A )
      = c_2Ebool_2ET ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CLAUSES__FX) ).

thf(1637,plain,
    ! [A: $o] :
      ( ( c_2Ebool_2EF
       => A )
      = c_2Ebool_2ET ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(438,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
      = ( ( ( c_2Ewords_2Eword__ls @ TA @ ( c_2Ewords_2Eword__L @ TA ) @ A )
          & ( ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__L @ TA ) )
            | ( c_2Ewords_2Eword__lo @ TA @ A @ B ) ) )
        | ( ( c_2Ewords_2Eword__lo @ TA @ A @ ( c_2Ewords_2Eword__L @ TA ) )
          & ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__L @ TA ) )
          & ( c_2Ewords_2Eword__lo @ TA @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LT__LO) ).

thf(2688,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
      = ( ( ( c_2Ewords_2Eword__ls @ TA @ ( c_2Ewords_2Eword__L @ TA ) @ A )
          & ( ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__L @ TA ) )
            | ( c_2Ewords_2Eword__lo @ TA @ A @ B ) ) )
        | ( ( c_2Ewords_2Eword__lo @ TA @ A @ ( c_2Ewords_2Eword__L @ TA ) )
          & ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__L @ TA ) )
          & ( c_2Ewords_2Eword__lo @ TA @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(559,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ A @ B )
      | ( c_2Einteger_2Eint__lt @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LET__TOTAL) ).

thf(3063,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ A @ B )
      | ( c_2Einteger_2Eint__lt @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(514,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EMODEQ @ C @ B @ A )
      = ( c_2Earithmetic_2EMODEQ @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMODEQ__SYM) ).

thf(2920,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2EMODEQ @ C @ B @ A )
      = ( c_2Earithmetic_2EMODEQ @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(32,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2E_2D @ A @ B ) )
      = ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2A @ C @ A ) @ ( c_2Earithmetic_2E_2A @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELEFT__SUB__DISTRIB) ).

thf(791,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2E_2D @ A @ B ) )
      = ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2A @ C @ A ) @ ( c_2Earithmetic_2E_2A @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(672,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( A
         != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        & ( ( c_2Einteger_2Eint__mul @ A @ B )
          = ( c_2Einteger_2Eint__mul @ A @ C ) ) )
     => ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__LMUL__IMP) ).

thf(3475,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( A
         != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        & ( ( c_2Einteger_2Eint__mul @ A @ B )
          = ( c_2Einteger_2Eint__mul @ A @ C ) ) )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).

thf(547,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ C @ ( c_2Einteger_2Eint__add @ B @ A ) )
      = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__add @ C @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__ASSOC) ).

thf(3026,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ C @ ( c_2Einteger_2Eint__add @ B @ A ) )
      = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__add @ C @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(74,axiom,
    ! [A: $o] :
      ( ( A
       => A )
      = c_2Ebool_2ET ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CLAUSES__XX) ).

thf(951,plain,
    c_2Ebool_2ET,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(414,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ! [B: tyop_2Einteger_2Eint] :
          ( ( ( c_2Einteger_2Eint__rem @ B @ A )
            = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
          = ( ? [C: tyop_2Einteger_2Eint] :
                ( B
                = ( c_2Einteger_2Eint__mul @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__REM__EQ0) ).

thf(2599,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ! [B: tyop_2Einteger_2Eint] :
          ( ( ( c_2Einteger_2Eint__rem @ B @ A )
            = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
          = ( ? [C: tyop_2Einteger_2Eint] :
                ( B
                = ( c_2Einteger_2Eint__mul @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(523,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2EABS @ C ) @ ( c_2Einteger_2EABS @ B ) )
        & ( c_2Ebool_2ECOND @ $o @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ C ) @ ( c_2Einteger_2Eint__le @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
        & ? [D: tyop_2Einteger_2Eint] :
            ( A
            = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ D @ B ) @ C ) ) )
     => ( ( c_2Einteger_2Eint__rem @ A @ B )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__REM__UNIQUE) ).

thf(2948,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2EABS @ C ) @ ( c_2Einteger_2EABS @ B ) )
        & ( c_2Ebool_2ECOND @ $o @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ C ) @ ( c_2Einteger_2Eint__le @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
        & ? [D: tyop_2Einteger_2Eint] :
            ( A
            = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ D @ B ) @ C ) ) )
     => ( ( c_2Einteger_2Eint__rem @ A @ B )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(249,axiom,
    ! [A: $o > $o > $o] :
      ( ( ( A @ c_2Ebool_2ET @ c_2Ebool_2ET )
        & ( A @ c_2Ebool_2EF @ c_2Ebool_2EF )
        & ( A @ c_2Ebool_2ET @ c_2Ebool_2EF )
        & ( A @ c_2Ebool_2EF @ c_2Ebool_2ET ) )
     => ! [B: $o,C: $o] : ( A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EternaryComparisons_2Ebool__compare__ind) ).

thf(1849,plain,
    ! [A: $o > $o > $o] :
      ( ( ( A @ c_2Ebool_2ET @ c_2Ebool_2ET )
        & ( A @ c_2Ebool_2EF @ c_2Ebool_2EF )
        & ( A @ c_2Ebool_2ET @ c_2Ebool_2EF )
        & ( A @ c_2Ebool_2EF @ c_2Ebool_2ET ) )
     => ! [B: $o,C: $o] : ( A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(401,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 )
        = ( c_2Einteger_2Eint__add @ C @ B ) )
     => ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ C ) @ A ) )
        = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__neg @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Eeq__context__rwt2) ).

thf(2558,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 )
        = ( c_2Einteger_2Eint__add @ C @ B ) )
     => ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ C ) @ A ) )
        = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__neg @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(536,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
     => ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__mul @ A @ C ) )
        = ( c_2Einteger_2Eint__le @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__MONO) ).

thf(2992,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
     => ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__mul @ A @ C ) )
        = ( c_2Einteger_2Eint__le @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(637,axiom,
    ! [A: tyop_2Enum_2Enum > $o] :
      ( ( ( A @ c_2Enum_2E0 )
        & ! [B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
            ( ( A @ C )
           => ( A @ ( c_2Enumpair_2Encons @ B @ C ) ) ) )
     => ! [B: tyop_2Enum_2Enum] : ( A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Enlist__ind) ).

thf(3356,plain,
    ! [A: tyop_2Enum_2Enum > $o] :
      ( ( ( A @ c_2Enum_2E0 )
        & ! [B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
            ( ( A @ C )
           => ( A @ ( c_2Enumpair_2Encons @ B @ C ) ) ) )
     => ! [B: tyop_2Enum_2Enum] : ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(450,axiom,
    ! [A: tyop_2Enum_2Enum] : ( c_2Egcd_2Eis__gcd @ A @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__REF) ).

thf(2722,plain,
    ! [A: tyop_2Enum_2Enum] : ( c_2Egcd_2Eis__gcd @ A @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(520,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ A @ B ) @ ( c_2Einteger_2Eint__add @ A @ C ) )
      = ( c_2Einteger_2Eint__le @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__LADD) ).

thf(2939,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ A @ B ) @ ( c_2Einteger_2Eint__add @ A @ C ) )
      = ( c_2Einteger_2Eint__le @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(562,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ A @ ( c_2Ewords_2Eword__2comp @ TA @ B ) )
      = ( c_2Ewords_2Eword__add @ TA @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__RNEG) ).

thf(3071,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ A @ ( c_2Ewords_2Eword__2comp @ TA @ B ) )
      = ( c_2Ewords_2Eword__add @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(584,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ A @ B )
      = ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ B ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Elt__move__all__left) ).

thf(3156,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ A @ B )
      = ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ B ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(648,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Esptree_2Espt__acc @ c_2Enum_2E0 @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esptree_2Espt__acc__0) ).

thf(3398,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Esptree_2Espt__acc @ c_2Enum_2E0 @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).

thf(616,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ealignment_2Ealign @ TA @ c_2Enum_2E0 @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ealignment_2Ealign__0) ).

thf(3288,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ealignment_2Ealign @ TA @ c_2Enum_2E0 @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(144,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__le @ TA @ A @ B )
        & ( c_2Ewords_2Eword__lt @ TA @ B @ C ) )
     => ( c_2Ewords_2Eword__lt @ TA @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__EQ__LESS__TRANS) ).

thf(1221,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__le @ TA @ A @ B )
        & ( c_2Ewords_2Eword__lt @ TA @ B @ C ) )
     => ( c_2Ewords_2Eword__lt @ TA @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(532,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__mul @ B @ A )
      = ( c_2Einteger_2Eint__mul @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__SYM) ).

thf(2975,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__mul @ B @ A )
      = ( c_2Einteger_2Eint__mul @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(334,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__mod @ A @ ( c_2Einteger_2Eint__neg @ B ) )
        = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__neg @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__NEG) ).

thf(2357,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__mod @ A @ ( c_2Einteger_2Eint__neg @ B ) )
        = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__neg @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(276,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__ls @ TA @ A @ B )
        & ( c_2Ewords_2Eword__ls @ TA @ B @ C ) )
     => ( c_2Ewords_2Eword__ls @ TA @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__EQ__TRANS) ).

thf(2145,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__ls @ TA @ A @ B )
        & ( c_2Ewords_2Eword__ls @ TA @ B @ C ) )
     => ( c_2Ewords_2Eword__ls @ TA @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(408,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum] :
      ( ( ( c_2Egcd_2Eis__gcd @ A @ B @ C )
        & ( c_2Egcd_2Eis__gcd @ A @ B @ D ) )
     => ( C = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__UNIQUE) ).

thf(2579,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum] :
      ( ( ( c_2Egcd_2Eis__gcd @ A @ B @ C )
        & ( c_2Egcd_2Eis__gcd @ A @ B @ D ) )
     => ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(49,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_3C_3D @ B @ ( c_2Earithmetic_2E_2A @ B @ A ) )
        = ( ( B = c_2Enum_2E0 )
          | ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) ) )
      & ( ( c_2Earithmetic_2E_3C_3D @ B @ ( c_2Earithmetic_2E_2A @ A @ B ) )
        = ( ( B = c_2Enum_2E0 )
          | ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELE__MULT__CANCEL__LBARE) ).

thf(864,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_3C_3D @ B @ ( c_2Earithmetic_2E_2A @ B @ A ) )
        = ( ( B = c_2Enum_2E0 )
          | ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) ) )
      & ( ( c_2Earithmetic_2E_3C_3D @ B @ ( c_2Earithmetic_2E_2A @ A @ B ) )
        = ( ( B = c_2Enum_2E0 )
          | ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(14,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ A @ C ) )
      = ( ( A = c_2Enum_2E0 )
        | ( c_2Earithmetic_2E_3C_3D @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELE__MULT__LCANCEL) ).

thf(727,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ A @ C ) )
      = ( ( A = c_2Enum_2E0 )
        | ( c_2Earithmetic_2E_3C_3D @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(645,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( B = C )
        = ( ( c_2Einteger_2Eint__mul @ A @ B )
          = ( c_2Einteger_2Eint__mul @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__LMUL2) ).

thf(3388,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( B = C )
        = ( ( c_2Einteger_2Eint__mul @ A @ B )
          = ( c_2Einteger_2Eint__mul @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(196,axiom,
    ! [A: tyop_2Enum_2Enum > $o] :
      ( ! [B: tyop_2Enum_2Enum] :
          ( ! [C: tyop_2Enum_2Enum] :
              ( ( c_2Eprim__rec_2E_3C @ C @ B )
             => ( A @ C ) )
         => ( A @ B ) )
     => ! [B: tyop_2Enum_2Enum] : ( A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ECOMPLETE__INDUCTION) ).

thf(1504,plain,
    ! [A: tyop_2Enum_2Enum > $o] :
      ( ! [B: tyop_2Enum_2Enum] :
          ( ! [C: tyop_2Enum_2Enum] :
              ( ( c_2Eprim__rec_2E_3C @ C @ B )
             => ( A @ C ) )
         => ( A @ B ) )
     => ! [B: tyop_2Enum_2Enum] : ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(608,axiom,
    ! [A: tyop_2EternaryComparisons_2Eordering] :
      ( ( c_2EternaryComparisons_2Eordering__size @ A )
      = c_2Enum_2E0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EternaryComparisons_2Eordering__size__def) ).

thf(3256,plain,
    ! [A: tyop_2EternaryComparisons_2Eordering] :
      ( ( c_2EternaryComparisons_2Eordering__size @ A )
      = c_2Enum_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(505,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__add @ B @ C ) )
      = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ C ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ele__move__right__left) ).

thf(2892,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ A @ ( c_2Einteger_2Eint__add @ B @ C ) )
      = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ C ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(588,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ! [B: tyop_2Einteger_2Eint] :
          ( ( B
            = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__quot @ B @ A ) @ A ) @ ( c_2Einteger_2Eint__rem @ B @ A ) ) )
          & ( c_2Ebool_2ECOND @ $o @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__rem @ B @ A ) ) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__rem @ B @ A ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
          & ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2EABS @ ( c_2Einteger_2Eint__rem @ B @ A ) ) @ ( c_2Einteger_2EABS @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__REMQUOT) ).

thf(3168,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ! [B: tyop_2Einteger_2Eint] :
          ( ( B
            = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__quot @ B @ A ) @ A ) @ ( c_2Einteger_2Eint__rem @ B @ A ) ) )
          & ( c_2Ebool_2ECOND @ $o @ ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__rem @ B @ A ) ) @ ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__rem @ B @ A ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
          & ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2EABS @ ( c_2Einteger_2Eint__rem @ B @ A ) ) @ ( c_2Einteger_2EABS @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(48,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__mul @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      & ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ C )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      & ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) )
        = ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ) )
      & ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) )
        = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ) ) )
      & ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) )
        = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ) ) )
      & ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) )
        = ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__REDUCE) ).

thf(845,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__mul @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      & ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ C )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      & ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) )
        = ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ) )
      & ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) )
        = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ) ) )
      & ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) )
        = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ) ) )
      & ( ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) )
        = ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(673,axiom,
    ! [TA: $tType] :
      ( ( c_2Ewords_2Ew2n @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
      = c_2Enum_2E0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__0__n2w) ).

thf(3478,plain,
    ! [TA: $tType] :
      ( ( c_2Ewords_2Ew2n @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
      = c_2Enum_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).

thf(659,axiom,
    ! [TA: $tType] :
      ( ( c_2Einteger__word_2Ew2i @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
      = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__0__w2i) ).

thf(3433,plain,
    ! [TA: $tType] :
      ( ( c_2Einteger__word_2Ew2i @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
      = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).

thf(376,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] : ( c_2Ewords_2Eword__ls @ TA @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__EQ__REFL) ).

thf(2479,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] : ( c_2Ewords_2Eword__ls @ TA @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(649,axiom,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Ewords_2Eword__slice @ TA @ B @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
      = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SLICE__ZERO2) ).

thf(3401,plain,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Ewords_2Eword__slice @ TA @ B @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
      = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(66,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ A @ B )
      | ( c_2Eprim__rec_2E_3C @ B @ A )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecardinal_2ELT__CASES) ).

thf(931,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ A @ B )
      | ( c_2Eprim__rec_2E_3C @ B @ A )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(441,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__lo @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ B )
      = ( ( B
         != ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
        & ( ( A
            = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
          | ( c_2Ewords_2Eword__lo @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__NEG__LEFT) ).

thf(2696,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__lo @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ B )
      = ( ( B
         != ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
        & ( ( A
            = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
          | ( c_2Ewords_2Eword__lo @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(497,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ B @ C )
     => ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ B ) @ ( c_2Einteger_2Eint__add @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__LADD__IMP) ).

thf(2870,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ B @ C )
     => ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ B ) @ ( c_2Einteger_2Eint__add @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(246,axiom,
    ! [A: $o] :
      ( ( A = c_2Ebool_2ET )
      | ( A = c_2Ebool_2EF ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EBOOL__CASES__AX) ).

thf(1834,plain,
    ! [A: $o] :
      ( ( A = c_2Ebool_2ET )
      | ( A = c_2Ebool_2EF ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(248,axiom,
    ! [A: $o] :
      ( ( c_2Ebool_2ET
       => A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EIMP__CLAUSES__TX) ).

thf(1844,plain,
    ! [A: $o] :
      ( ( c_2Ebool_2ET
       => A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(296,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2EABS @ A ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( A
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__LE0) ).

thf(2215,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2EABS @ A ) @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
      = ( A
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(143,axiom,
    ! [A: $o] :
      ( ( ~ A
       => c_2Ebool_2EF )
     => ( ( A
         => c_2Ebool_2EF )
       => c_2Ebool_2EF ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2EAND__INV2) ).

thf(1216,plain,
    ! [A: $o] :
      ( ( ~ A
       => c_2Ebool_2EF )
     => ( ( A
         => c_2Ebool_2EF )
       => c_2Ebool_2EF ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(121,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__msb @ TA @ A )
      = ( c_2Ewords_2Eword__lt @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__msb__neg) ).

thf(1126,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__msb @ TA @ A )
      = ( c_2Ewords_2Eword__lt @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(429,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( C
         != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        & ( ( ( c_2Einteger_2Eint__mod @ A @ C )
            = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
          | ( ( c_2Einteger_2Eint__mod @ B @ C )
            = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) )
     => ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__add @ A @ B ) @ C )
        = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__div @ A @ C ) @ ( c_2Einteger_2Eint__div @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__DIV) ).

thf(2643,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( C
         != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        & ( ( ( c_2Einteger_2Eint__mod @ A @ C )
            = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
          | ( ( c_2Einteger_2Eint__mod @ B @ C )
            = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) )
     => ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__add @ A @ B ) @ C )
        = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__div @ A @ C ) @ ( c_2Einteger_2Eint__div @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(466,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ A @ A ) )
      = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__DOUBLE) ).

thf(2775,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__add @ A @ A ) )
      = ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(183,axiom,
    ! [A: $o] :
      ( ( A
       => c_2Ebool_2EF )
      = ( A = c_2Ebool_2EF ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__F__EQ__F) ).

thf(1459,plain,
    ! [A: $o] :
      ( ( A
       => c_2Ebool_2EF )
      = ( A = c_2Ebool_2EF ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(258,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ B @ A )
     => ( ( c_2Earithmetic_2EMOD @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__MOD) ).

thf(2045,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ B @ A )
     => ( ( c_2Earithmetic_2EMOD @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(220,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( A != c_2Enum_2E0 )
      = ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ENOT__ZERO__LT__ZERO) ).

thf(1654,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( A != c_2Enum_2E0 )
      = ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(175,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( B != c_2Enum_2E0 )
     => ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
        = ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EMOD @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD) ).

thf(1412,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( B != c_2Enum_2E0 )
     => ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
        = ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EMOD @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(454,axiom,
    ! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( A @ ( c_2Einteger_2Eint__div @ B @ C ) )
        = ( ! [D: tyop_2Einteger_2Eint,E: tyop_2Einteger_2Eint] :
              ( ( ( B
                  = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ D @ C ) @ E ) )
                & ( ( ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
                    & ( c_2Einteger_2Eint__lt @ C @ E )
                    & ( c_2Einteger_2Eint__le @ E @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
                  | ( ~ ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
                    & ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ E )
                    & ( c_2Einteger_2Eint__lt @ E @ C ) ) ) )
             => ( A @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIV__FORALL__P) ).

thf(2743,plain,
    ! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( A @ ( c_2Einteger_2Eint__div @ B @ C ) )
        = ( ! [D: tyop_2Einteger_2Eint,E: tyop_2Einteger_2Eint] :
              ( ( ( B
                  = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ D @ C ) @ E ) )
                & ( ( ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
                    & ( c_2Einteger_2Eint__lt @ C @ E )
                    & ( c_2Einteger_2Eint__le @ E @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
                  | ( ~ ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
                    & ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ E )
                    & ( c_2Einteger_2Eint__lt @ E @ C ) ) ) )
             => ( A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(180,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2D @ C @ B ) @ ( c_2Earithmetic_2E_2D @ C @ A ) )
      = ( ( c_2Eprim__rec_2E_3C @ A @ B )
        & ( c_2Eprim__rec_2E_3C @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELT__SUB__LCANCEL) ).

thf(1448,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2D @ C @ B ) @ ( c_2Earithmetic_2E_2D @ C @ A ) )
      = ( ( c_2Eprim__rec_2E_3C @ A @ B )
        & ( c_2Eprim__rec_2E_3C @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(380,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__le @ A @ B )
        & ( c_2Einteger_2Eint__lt @ C @ D ) )
     => ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ C ) @ ( c_2Einteger_2Eint__add @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LET__ADD2) ).

thf(2490,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__le @ A @ B )
        & ( c_2Einteger_2Eint__lt @ C @ D ) )
     => ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ C ) @ ( c_2Einteger_2Eint__add @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(291,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ A @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__SUB2) ).

thf(2187,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ A @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(412,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__2comp @ TA @ B )
        = A )
      = ( B
        = ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__EQ) ).

thf(2591,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__2comp @ TA @ B )
        = A )
      = ( B
        = ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(286,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__mod @ A @ B )
        = ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__div @ A @ B ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2Eint__mod) ).

thf(2174,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__mod @ A @ B )
        = ( c_2Einteger_2Eint__sub @ A @ ( c_2Einteger_2Eint__mul @ ( c_2Einteger_2Eint__div @ A @ B ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(492,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__sub @ TA @ A @ B )
        = ( c_2Ewords_2Eword__sub @ TA @ A @ C ) )
      = ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__RCANCEL__SUB) ).

thf(2855,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__sub @ TA @ A @ B )
        = ( c_2Ewords_2Eword__sub @ TA @ A @ C ) )
      = ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(315,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
        & ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
     => ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__mul @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Epositive__product__implication) ).

thf(2290,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
        & ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ B ) )
     => ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__mul @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(197,axiom,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: $o,C: TB,D: TB] :
      ( ( A @ ( c_2Ebool_2ECOND @ TB @ B @ C @ D ) )
      = ( c_2Ebool_2ECOND @ TA @ B @ ( A @ C ) @ ( A @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__RAND) ).

thf(1508,plain,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: $o,C: TB,D: TB] :
      ( ( A @ ( c_2Ebool_2ECOND @ TB @ B @ C @ D ) )
      = ( c_2Ebool_2ECOND @ TA @ B @ ( A @ C ) @ ( A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(644,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ! [A: tyop_2Efcp_2Ecart @ $o @ TB] :
          ( ( c_2Ewords_2Eword__lo @ TB @ ( c_2Ewords_2En2w @ TB @ c_2Enum_2E0 ) @ A )
          = ( A
           != ( c_2Ewords_2En2w @ TB @ c_2Enum_2E0 ) ) )
      & ! [A: tyop_2Efcp_2Ecart @ $o @ TA] :
          ~ ( c_2Ewords_2Eword__lo @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LO__word__0) ).

thf(3383,plain,
    ! [TA: $tType,TB: $tType] :
      ( ! [A: tyop_2Efcp_2Ecart @ $o @ TB] :
          ( ( c_2Ewords_2Eword__lo @ TB @ ( c_2Ewords_2En2w @ TB @ c_2Enum_2E0 ) @ A )
          = ( A
           != ( c_2Ewords_2En2w @ TB @ c_2Enum_2E0 ) ) )
      & ! [A: tyop_2Efcp_2Ecart @ $o @ TA] :
          ~ ( c_2Ewords_2Eword__lo @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).

thf(482,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ~ ( c_2Einteger_2Eint__lt @ A @ B ) )
      = ( c_2Einteger_2Eint__le @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NOT__LT) ).

thf(2823,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ~ ( c_2Einteger_2Eint__lt @ A @ B ) )
      = ( c_2Einteger_2Eint__le @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(241,axiom,
    ! [TA: $tType,A: $o,B: TA] :
      ( ( c_2Ebool_2ECOND @ TA @ A @ B @ B )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__case__ID) ).

thf(1745,plain,
    ! [TA: $tType,A: $o,B: TA] :
      ( ( c_2Ebool_2ECOND @ TA @ A @ B @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(462,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2En2w @ TA @ ( c_2Ewords_2Ew2n @ TA @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2En2w__w2n) ).

thf(2764,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2En2w @ TA @ ( c_2Ewords_2Ew2n @ TA @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(903,plain,
    ( ( c_2Ebool_2ECOND @ $o @ $false @ c_2Ebool_2ET @ $false )
    = ( ~ $false
     => $false ) ),
    inference(instance,[status(thm)],[896]) ).

thf(904,plain,
    ~ ( c_2Ebool_2ECOND @ $o @ $false @ c_2Ebool_2ET @ $false ),
    inference(simp,[status(thm)],[903]) ).

thf(3780,plain,
    ~ ( c_2Ebool_2ECOND @ $o @ $false @ $true @ $false ),
    inference(rewrite,[status(thm)],[904,878]) ).

thf(217,axiom,
    ( ~ c_2Ebool_2ET = c_2Ebool_2EF ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2ENOT__CLAUSES__T) ).

thf(1646,plain,
    ( ~ c_2Ebool_2ET = c_2Ebool_2EF ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(363,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__le @ TA @ A @ B )
      = ( ( ( c_2Ewords_2Eword__ls @ TA @ ( c_2Ewords_2Eword__L @ TA ) @ A )
          & ( ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__L @ TA ) )
            | ( c_2Ewords_2Eword__ls @ TA @ A @ B ) ) )
        | ( ( c_2Ewords_2Eword__lo @ TA @ A @ ( c_2Ewords_2Eword__L @ TA ) )
          & ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__L @ TA ) )
          & ( c_2Ewords_2Eword__ls @ TA @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LE__LS) ).

thf(2443,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__le @ TA @ A @ B )
      = ( ( ( c_2Ewords_2Eword__ls @ TA @ ( c_2Ewords_2Eword__L @ TA ) @ A )
          & ( ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__L @ TA ) )
            | ( c_2Ewords_2Eword__ls @ TA @ A @ B ) ) )
        | ( ( c_2Ewords_2Eword__lo @ TA @ A @ ( c_2Ewords_2Eword__L @ TA ) )
          & ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__L @ TA ) )
          & ( c_2Ewords_2Eword__ls @ TA @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(39,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
        & ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B ) )
     => ! [C: tyop_2Enum_2Enum] :
          ( ( c_2Earithmetic_2EDIV @ ( c_2Earithmetic_2EDIV @ C @ A ) @ B )
          = ( c_2Earithmetic_2EDIV @ C @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EDIV__DIV__DIV__MULT) ).

thf(813,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
        & ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B ) )
     => ! [C: tyop_2Enum_2Enum] :
          ( ( c_2Earithmetic_2EDIV @ ( c_2Earithmetic_2EDIV @ C @ A ) @ B )
          = ( c_2Earithmetic_2EDIV @ C @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(413,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( ( c_2Einteger_2Eint__quot @ ( c_2Einteger_2Eint__neg @ A ) @ B )
          = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__quot @ A @ B ) ) )
        & ( ( c_2Einteger_2Eint__quot @ A @ ( c_2Einteger_2Eint__neg @ B ) )
          = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__quot @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__QUOT__NEG) ).

thf(2594,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( ( c_2Einteger_2Eint__quot @ ( c_2Einteger_2Eint__neg @ A ) @ B )
          = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__quot @ A @ B ) ) )
        & ( ( c_2Einteger_2Eint__quot @ A @ ( c_2Einteger_2Eint__neg @ B ) )
          = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__quot @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(158,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2D @ B @ A ) @ ( c_2Earithmetic_2E_2D @ C @ A ) )
      = ( ( c_2Eprim__rec_2E_3C @ B @ C )
        & ( c_2Eprim__rec_2E_3C @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELT__SUB__RCANCEL) ).

thf(1341,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2D @ B @ A ) @ ( c_2Earithmetic_2E_2D @ C @ A ) )
      = ( ( c_2Eprim__rec_2E_3C @ B @ C )
        & ( c_2Eprim__rec_2E_3C @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(264,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__abs @ TA @ A )
      = ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ TA ) @ ( c_2Ewords_2Eword__lt @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__abs__def) ).

thf(2098,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__abs @ TA @ A )
      = ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ TA ) @ ( c_2Ewords_2Eword__lt @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(675,axiom,
    ! [TA: $tType] :
      ( ( c_2Ewords_2Eword__reverse @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
      = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__reverse__0) ).

thf(3484,plain,
    ! [TA: $tType] :
      ( ( c_2Ewords_2Eword__reverse @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
      = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).

thf(72,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__le @ TA @ A @ B )
      | ( c_2Ewords_2Eword__le @ TA @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__EQ__CASES) ).

thf(946,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__le @ TA @ A @ B )
      | ( c_2Ewords_2Eword__le @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(115,axiom,
    ! [A: $o,B: $o] :
      ( ( ~ ( B
            | A )
       => c_2Ebool_2EF )
      = ( ( B
         => c_2Ebool_2EF )
       => ( ~ A
         => c_2Ebool_2EF ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2EOR__DUAL2) ).

thf(1101,plain,
    ! [A: $o,B: $o] :
      ( ( ~ ( B
            | A )
       => c_2Ebool_2EF )
      = ( ( B
         => c_2Ebool_2EF )
       => ( ~ A
         => c_2Ebool_2EF ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(579,axiom,
    ! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ! [D: tyop_2Einteger_2Eint] :
            ( ( A @ D )
           => ( A @ ( c_2Einteger_2Eint__add @ D @ B ) ) )
        & ( A @ C ) )
     => ! [D: tyop_2Einteger_2Eint] :
          ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D )
         => ( A @ ( c_2Einteger_2Eint__add @ C @ ( c_2Einteger_2Eint__mul @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ebot__and__greaters) ).

thf(3136,plain,
    ! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ! [D: tyop_2Einteger_2Eint] :
            ( ( A @ D )
           => ( A @ ( c_2Einteger_2Eint__add @ D @ B ) ) )
        & ( A @ C ) )
     => ! [D: tyop_2Einteger_2Eint] :
          ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D )
         => ( A @ ( c_2Einteger_2Eint__add @ C @ ( c_2Einteger_2Eint__mul @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(639,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( A = c_2Enum_2E0 )
      | ? [B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
          ( A
          = ( c_2Enumpair_2Encons @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Enlist__cases) ).

thf(3368,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( A = c_2Enum_2E0 )
      | ? [B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
          ( A
          = ( c_2Enumpair_2Encons @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(84,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
        & ( c_2Earithmetic_2E_3C_3D @ B @ A ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__EQUAL__ANTISYM) ).

thf(995,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
        & ( c_2Earithmetic_2E_3C_3D @ B @ A ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(306,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( A
        = ( c_2Einteger_2Eint__add @ B @ C ) )
      = ( ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ C ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Eeq__move__right__left) ).

thf(2262,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( A
        = ( c_2Einteger_2Eint__add @ B @ C ) )
      = ( ( c_2Einteger_2Eint__add @ A @ ( c_2Einteger_2Eint__neg @ C ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(226,axiom,
    ! [TA: $tType,A: $o,B: TA] :
      ( ( c_2Ebool_2ECOND @ TA @ A @ B @ B )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__ID) ).

thf(1689,plain,
    ! [TA: $tType,A: $o,B: TA] :
      ( ( c_2Ebool_2ECOND @ TA @ A @ B @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(590,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mod @ C @ A ) @ ( c_2Einteger_2Eint__mod @ B @ A ) ) @ A )
        = ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__add @ C @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__PLUS) ).

thf(3181,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mod @ C @ A ) @ ( c_2Einteger_2Eint__mod @ B @ A ) ) @ A )
        = ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__add @ C @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(370,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( A
         != ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
        & ( A
         != ( c_2Ewords_2Eword__L @ TA ) ) )
     => ( ( ~ ( c_2Ewords_2Eword__msb @ TA @ A ) )
        = ( c_2Ewords_2Eword__msb @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2ETWO__COMP__POS__NEG) ).

thf(2462,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( A
         != ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
        & ( A
         != ( c_2Ewords_2Eword__L @ TA ) ) )
     => ( ( ~ ( c_2Ewords_2Eword__msb @ TA @ A ) )
        = ( c_2Ewords_2Eword__msb @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(65,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
     => ! [B: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EDIV @ B @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EDIV__LESS__EQ) ).

thf(929,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
     => ! [B: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2EDIV @ B @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(407,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Ew2n @ TA @ A )
        = ( c_2Ewords_2Ew2n @ TA @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Ew2n__11) ).

thf(2576,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Ew2n @ TA @ A )
        = ( c_2Ewords_2Ew2n @ TA @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(206,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ A @ B )
        & ( c_2Earithmetic_2E_3C_3D @ B @ C ) )
     => ( c_2Eprim__rec_2E_3C @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__LESS__EQ__TRANS) ).

thf(1607,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ A @ B )
        & ( c_2Earithmetic_2E_3C_3D @ B @ C ) )
     => ( c_2Eprim__rec_2E_3C @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(508,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ A @ B )
      = ( ( c_2Einteger_2Eint__lt @ A @ B )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__CALCULATE) ).

thf(2902,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ A @ B )
      = ( ( c_2Einteger_2Eint__lt @ A @ B )
        | ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(44,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
        & ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B ) )
     => ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__MULT2) ).

thf(832,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
        & ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B ) )
     => ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(150,axiom,
    ! [TA: $tType] :
      ( ! [A: TA,B: TA] :
          ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
          = A )
      & ! [A: TA,B: TA] :
          ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
          = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__case__thm) ).

thf(1309,plain,
    ! [TA: $tType] :
      ( ! [A: TA,B: TA] :
          ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
          = A )
      & ! [A: TA,B: TA] :
          ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
          = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(513,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A = B )
      = ( ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 )
        = ( c_2Einteger_2Eint__add @ B @ ( c_2Einteger_2Eint__neg @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Eeq__move__all__right) ).

thf(2917,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A = B )
      = ( ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 )
        = ( c_2Einteger_2Eint__add @ B @ ( c_2Einteger_2Eint__neg @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(356,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2EABS @ B )
        = ( c_2Einteger_2EABS @ A ) )
      = ( ( B = A )
        | ( B
          = ( c_2Einteger_2Eint__neg @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__EQ__ABS) ).

thf(2421,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2EABS @ B )
        = ( c_2Einteger_2EABS @ A ) )
      = ( ( B = A )
        | ( B
          = ( c_2Einteger_2Eint__neg @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(525,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EMODEQ @ A @ B @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMODEQ__REFL) ).

thf(2956,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EMODEQ @ A @ B @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(191,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
     => ( c_2Ewords_2Eword__le @ TA @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__IMP__LESS__OR__EQ) ).

thf(1491,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
     => ( c_2Ewords_2Eword__le @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(430,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__sub @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = C )
      & ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ C )
        = ( c_2Einteger_2Eint__neg @ C ) )
      & ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) )
        = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) ) )
      & ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) )
        = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) ) )
      & ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) )
        = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) )
      & ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) )
        = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__REDUCE) ).

thf(2648,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__sub @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = C )
      & ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ C )
        = ( c_2Einteger_2Eint__neg @ C ) )
      & ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) )
        = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) ) )
      & ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) )
        = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) ) )
      & ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) )
        = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) )
      & ( ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) )
        = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ A ) ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2ENUMERAL @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(658,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__rem @ A @ A )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__REM__ID) ).

thf(3430,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__rem @ A @ A )
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).

thf(108,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
     => ( c_2Earithmetic_2EMODEQ @ B @ ( c_2Earithmetic_2EMOD @ A @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMODEQ__MOD) ).

thf(1077,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B )
     => ( c_2Earithmetic_2EMODEQ @ B @ ( c_2Earithmetic_2EMOD @ A @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(282,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) )
      = ( ( A
         != ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
        & ( ( B
            = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
          | ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__RIGHT__LO2) ).

thf(2162,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__add @ TA @ A @ B ) )
      = ( ( A
         != ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
        & ( ( B
            = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
          | ( c_2Ewords_2Eword__lo @ TA @ B @ ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(340,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__sub @ A @ B ) @ ( c_2Einteger_2Eint__sub @ B @ C ) )
      = ( c_2Einteger_2Eint__sub @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__TRIANGLE) ).

thf(2374,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__sub @ A @ B ) @ ( c_2Einteger_2Eint__sub @ B @ C ) )
      = ( c_2Einteger_2Eint__sub @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(314,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__neg @ A ) )
      = ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__GT0) ).

thf(2287,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__neg @ A ) )
      = ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(388,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ~ ( c_2Ewords_2Eword__lo @ TA @ A @ B )
        & ( A != B ) )
     => ( c_2Ewords_2Eword__lo @ TA @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__CASES__IMP) ).

thf(2517,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ~ ( c_2Ewords_2Eword__lo @ TA @ A @ B )
        & ( A != B ) )
     => ( c_2Ewords_2Eword__lo @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(344,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ ( c_2Ewords_2Eword__2comp @ TA @ B ) )
      = ( c_2Ewords_2Eword__sub @ TA @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__NEG) ).

thf(2385,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) @ ( c_2Ewords_2Eword__2comp @ TA @ B ) )
      = ( c_2Ewords_2Eword__sub @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(304,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
     => ( ( B = C )
        = ( ( c_2Einteger_2Eint__mul @ A @ B )
          = ( c_2Einteger_2Eint__mul @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Eeq__justify__multiplication) ).

thf(2255,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ A )
     => ( ( B = C )
        = ( ( c_2Einteger_2Eint__mul @ A @ B )
          = ( c_2Einteger_2Eint__mul @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(449,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__add @ TA @ A @ B )
        = ( c_2Ewords_2Eword__add @ TA @ C @ B ) )
      = ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__EQ__ADD__RCANCEL) ).

thf(2719,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__add @ TA @ A @ B )
        = ( c_2Ewords_2Eword__add @ TA @ C @ B ) )
      = ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(148,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2D @ A @ A )
      = c_2Enum_2E0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ESUB__EQUAL__0) ).

thf(1303,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2D @ A @ A )
      = c_2Enum_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(188,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ~ ( ( c_2Eprim__rec_2E_3C @ A @ B )
        & ( c_2Earithmetic_2E_3C_3D @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__EQ__ANTISYM) ).

thf(1480,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ~ ( ( c_2Eprim__rec_2E_3C @ A @ B )
        & ( c_2Earithmetic_2E_3C_3D @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(670,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
        = ( c_2Einteger_2Eint__neg @ A ) )
      = ( A
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__SAME__EQ) ).

thf(3469,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
        = ( c_2Einteger_2Eint__neg @ A ) )
      = ( A
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).

thf(118,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Einteger__word_2Ew2i @ TA @ A )
      = ( c_2Ebool_2ECOND @ tyop_2Einteger_2Eint @ ( c_2Ewords_2Eword__msb @ TA @ A ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Ew2i__def) ).

thf(1116,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Einteger__word_2Ew2i @ TA @ A )
      = ( c_2Ebool_2ECOND @ tyop_2Einteger_2Eint @ ( c_2Ewords_2Eword__msb @ TA @ A ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ A ) ) ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(251,axiom,
    ! [TA: $tType,A: $o,B: $o,C: TA,D: TA,E: TA,F: TA] :
      ( ( ( A = B )
        & ( B
         => ( C = D ) )
        & ( ~ B
         => ( E = F ) ) )
     => ( ( c_2Ebool_2ECOND @ TA @ A @ C @ E )
        = ( c_2Ebool_2ECOND @ TA @ B @ D @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CONG) ).

thf(2003,plain,
    ! [TA: $tType,A: $o,B: $o,C: TA,D: TA,E: TA,F: TA] :
      ( ( ( A = B )
        & ( B
         => ( C = D ) )
        & ( ~ B
         => ( E = F ) ) )
     => ( ( c_2Ebool_2ECOND @ TA @ A @ C @ E )
        = ( c_2Ebool_2ECOND @ TA @ B @ D @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(275,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__divides @ A @ B )
     => ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__mul @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__RMUL) ).

thf(2142,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__divides @ A @ B )
     => ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__mul @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(517,axiom,
    ! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( A @ ( c_2Einteger_2Eint__mod @ B @ C ) )
        = ( ! [D: tyop_2Einteger_2Eint,E: tyop_2Einteger_2Eint] :
              ( ( ( B
                  = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ D @ C ) @ E ) )
                & ( ( ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
                    & ( c_2Einteger_2Eint__lt @ C @ E )
                    & ( c_2Einteger_2Eint__le @ E @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
                  | ( ~ ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
                    & ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ E )
                    & ( c_2Einteger_2Eint__lt @ E @ C ) ) ) )
             => ( A @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__FORALL__P) ).

thf(2930,plain,
    ! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( A @ ( c_2Einteger_2Eint__mod @ B @ C ) )
        = ( ! [D: tyop_2Einteger_2Eint,E: tyop_2Einteger_2Eint] :
              ( ( ( B
                  = ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ D @ C ) @ E ) )
                & ( ( ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
                    & ( c_2Einteger_2Eint__lt @ C @ E )
                    & ( c_2Einteger_2Eint__le @ E @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
                  | ( ~ ( c_2Einteger_2Eint__lt @ C @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
                    & ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ E )
                    & ( c_2Einteger_2Eint__lt @ E @ C ) ) ) )
             => ( A @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(297,axiom,
    ( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( B != c_2Enum_2E0 )
       => ( ( c_2Einteger_2Eint__quot @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
          = ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ A @ B ) ) ) )
    & ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
        ( ( B
         != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
       => ( ( ( c_2Einteger_2Eint__quot @ ( c_2Einteger_2Eint__neg @ A ) @ B )
            = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__quot @ A @ B ) ) )
          & ( ( c_2Einteger_2Eint__quot @ A @ ( c_2Einteger_2Eint__neg @ B ) )
            = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__quot @ A @ B ) ) ) ) )
    & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( ( c_2Einteger_2Eint__of__num @ A )
          = ( c_2Einteger_2Eint__of__num @ B ) )
        = ( A = B ) )
    & ! [A: tyop_2Einteger_2Eint] :
        ( ( ( c_2Einteger_2Eint__neg @ A )
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = ( A
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
    & ! [A: tyop_2Einteger_2Eint] :
        ( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__neg @ A ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__QUOT__CALCULATE) ).

thf(2218,plain,
    ( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( B != c_2Enum_2E0 )
       => ( ( c_2Einteger_2Eint__quot @ ( c_2Einteger_2Eint__of__num @ A ) @ ( c_2Einteger_2Eint__of__num @ B ) )
          = ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EDIV @ A @ B ) ) ) )
    & ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
        ( ( B
         != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
       => ( ( ( c_2Einteger_2Eint__quot @ ( c_2Einteger_2Eint__neg @ A ) @ B )
            = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__quot @ A @ B ) ) )
          & ( ( c_2Einteger_2Eint__quot @ A @ ( c_2Einteger_2Eint__neg @ B ) )
            = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__quot @ A @ B ) ) ) ) )
    & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( ( c_2Einteger_2Eint__of__num @ A )
          = ( c_2Einteger_2Eint__of__num @ B ) )
        = ( A = B ) )
    & ! [A: tyop_2Einteger_2Eint] :
        ( ( ( c_2Einteger_2Eint__neg @ A )
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
        = ( A
          = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
    & ! [A: tyop_2Einteger_2Eint] :
        ( ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__neg @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(123,axiom,
    ! [A: $o] :
      ( ~ A
     => ( A = c_2Ebool_2EF ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ENOT__F) ).

thf(1133,plain,
    ! [A: $o] :
      ( ~ A
     => ( A = c_2Ebool_2EF ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(202,axiom,
    ! [A: $o] :
      ( ( ( c_2Ebool_2ET
          & A )
        = A )
      & ( ( A
          & c_2Ebool_2ET )
        = A )
      & ( ( c_2Ebool_2EF
          & A )
        = c_2Ebool_2EF )
      & ( ( A
          & c_2Ebool_2EF )
        = c_2Ebool_2EF )
      & ( ( A
          & A )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EAND__CLAUSES) ).

thf(1593,plain,
    ! [A: $o] :
      ( ( ( c_2Ebool_2ET
          & A )
        = A )
      & ( ( A
          & c_2Ebool_2ET )
        = A )
      & ( ( c_2Ebool_2EF
          & A )
        = c_2Ebool_2EF )
      & ( ( A
          & c_2Ebool_2EF )
        = c_2Ebool_2EF ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(166,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__ls @ TA @ A @ B )
      = ( c_2Earithmetic_2E_3C_3D @ ( c_2Ewords_2Ew2n @ TA @ A ) @ ( c_2Ewords_2Ew2n @ TA @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LS) ).

thf(1380,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__ls @ TA @ A @ B )
      = ( c_2Earithmetic_2E_3C_3D @ ( c_2Ewords_2Ew2n @ TA @ A ) @ ( c_2Ewords_2Ew2n @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(580,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ A @ B )
      | ( c_2Einteger_2Eint__le @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LTE__TOTAL) ).

thf(3145,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ A @ B )
      | ( c_2Einteger_2Eint__le @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(35,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ A @ B )
        = c_2Enum_2E0 )
      = ( ( A = c_2Enum_2E0 )
        | ( B = c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EMULT__EQ__0) ).

thf(801,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ A @ B )
        = c_2Enum_2E0 )
      = ( ( A = c_2Enum_2E0 )
        | ( B = c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(193,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2ENUMERAL @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ENUMERAL__DEF) ).

thf(1495,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2ENUMERAL @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(221,axiom,
    ! [A: $o] :
      ( ( A
        | c_2Ebool_2ET )
      = c_2Ebool_2ET ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EOR__CLAUSES__XT) ).

thf(1657,plain,
    ! [A: $o] :
      ( ( A
        | c_2Ebool_2ET )
      = c_2Ebool_2ET ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(634,axiom,
    ! [TA: $tType,A: TA > TA > $o,B: TA,C: TA] :
      ( ( c_2Earithmetic_2ENRC @ TA @ A @ c_2Enum_2E0 @ B @ C )
      = ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ENRC__0) ).

thf(3347,plain,
    ! [TA: $tType,A: TA > TA > $o,B: TA,C: TA] :
      ( ( c_2Earithmetic_2ENRC @ TA @ A @ c_2Enum_2E0 @ B @ C )
      = ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(37,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ C )
     => ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2EDIV @ B @ C ) @ A )
        = ( c_2Eprim__rec_2E_3C @ B @ ( c_2Earithmetic_2E_2A @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EDIV__LT__X) ).

thf(807,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ C )
     => ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2EDIV @ B @ C ) @ A )
        = ( c_2Eprim__rec_2E_3C @ B @ ( c_2Earithmetic_2E_2A @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(455,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ~ ( c_2Ewords_2Eword__lo @ TA @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__REFL) ).

thf(2746,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ~ ( c_2Ewords_2Eword__lo @ TA @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(24,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
     => ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ A @ C ) @ ( c_2Earithmetic_2E_2A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__MONO__MULT) ).

thf(767,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_3C_3D @ A @ B )
     => ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ A @ C ) @ ( c_2Earithmetic_2E_2A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(337,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__add @ TA @ A @ B )
      = ( c_2Ewords_2Eword__add @ TA @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__COMM) ).

thf(2366,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__add @ TA @ A @ B )
      = ( c_2Ewords_2Eword__add @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(350,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__neg @ A ) @ ( c_2Einteger_2Eint__neg @ B ) )
      = ( c_2Einteger_2Eint__le @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__NEG) ).

thf(2404,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__neg @ A ) @ ( c_2Einteger_2Eint__neg @ B ) )
      = ( c_2Einteger_2Eint__le @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(257,axiom,
    ! [A: $o] :
      ( ( A
        & c_2Ebool_2EF )
      = c_2Ebool_2EF ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EConseqConv_2EAND__CLAUSES__XF) ).

thf(2040,plain,
    ! [A: $o] :
      ( ( A
        & c_2Ebool_2EF )
      = c_2Ebool_2EF ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(554,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) @ ( c_2Ewords_2Eword__sub @ TA @ B @ C ) )
      = ( c_2Ewords_2Eword__sub @ TA @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__TRIANGLE) ).

thf(3045,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2Eword__sub @ TA @ A @ B ) @ ( c_2Ewords_2Eword__sub @ TA @ B @ C ) )
      = ( c_2Ewords_2Eword__sub @ TA @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(457,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__lt @ A @ C )
        & ( c_2Einteger_2Eint__le @ C @ ( c_2Einteger_2Eint__add @ A @ B ) ) )
      = ( ? [D: tyop_2Einteger_2Eint] :
            ( ( C
              = ( c_2Einteger_2Eint__add @ A @ D ) )
            & ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D )
            & ( c_2Einteger_2Eint__le @ D @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Ein__additive__range) ).

thf(2751,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__lt @ A @ C )
        & ( c_2Einteger_2Eint__le @ C @ ( c_2Einteger_2Eint__add @ A @ B ) ) )
      = ( ? [D: tyop_2Einteger_2Eint] :
            ( ( C
              = ( c_2Einteger_2Eint__add @ A @ D ) )
            & ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ D )
            & ( c_2Einteger_2Eint__le @ D @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(474,axiom,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__bits @ TA @ A @ B @ ( c_2Ewords_2Eword__slice @ TA @ A @ B @ C ) )
      = ( c_2Ewords_2Eword__bits @ TA @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__BITS__SLICE__THM) ).

thf(2800,plain,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__bits @ TA @ A @ B @ ( c_2Ewords_2Eword__slice @ TA @ A @ B @ C ) )
      = ( c_2Ewords_2Eword__bits @ TA @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(95,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_3C_3D @ A @ c_2Enum_2E0 )
      = ( A = c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__EQ__0) ).

thf(1033,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_3C_3D @ A @ c_2Enum_2E0 )
      = ( A = c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(527,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ~ ( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
        & ( c_2Ewords_2Eword__lo @ TA @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__ANTISYM) ).

thf(2961,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ~ ( ( c_2Ewords_2Eword__lo @ TA @ A @ B )
        & ( c_2Ewords_2Eword__lo @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(421,axiom,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ealignment_2Ealigned @ TA @ A @ B )
        & ( c_2Ealignment_2Ealigned @ TA @ A @ C ) )
     => ( ( c_2Ealignment_2Ealigned @ TA @ A @ ( c_2Ewords_2Eword__add @ TA @ B @ C ) )
        & ( c_2Ealignment_2Ealigned @ TA @ A @ ( c_2Ewords_2Eword__sub @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ealignment_2Ealigned__add__sub__cor) ).

thf(2619,plain,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ealignment_2Ealigned @ TA @ A @ B )
        & ( c_2Ealignment_2Ealigned @ TA @ A @ C ) )
     => ( ( c_2Ealignment_2Ealigned @ TA @ A @ ( c_2Ewords_2Eword__add @ TA @ B @ C ) )
        & ( c_2Ealignment_2Ealigned @ TA @ A @ ( c_2Ewords_2Eword__sub @ TA @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(656,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__RZERO) ).

thf(3424,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).

thf(719,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ A @ c_2Enum_2E0 )
      = c_2Enum_2E0 ),
    inference(cnf,[status(esa)],[718]) ).

thf(720,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Earithmetic_2E_2A @ A @ c_2Enum_2E0 )
      = c_2Enum_2E0 ),
    inference(lifteq,[status(thm)],[719]) ).

thf(329,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ B @ C ) @ A ) @ C )
        = ( c_2Einteger_2Eint__mod @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__ADD__MULTIPLES) ).

thf(2340,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__mod @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__mul @ B @ C ) @ A ) @ C )
        = ( c_2Einteger_2Eint__mod @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(132,axiom,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Eprim__rec_2E_3C @ A @ B )
     => ( ( c_2Ewords_2Eword__bits @ TA @ A @ B @ C )
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__BITS__ZERO) ).

thf(1165,plain,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Eprim__rec_2E_3C @ A @ B )
     => ( ( c_2Ewords_2Eword__bits @ TA @ A @ B @ C )
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(272,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__mul @ A @ C ) )
        = ( c_2Einteger_2Eint__divides @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__MUL__BOTH) ).

thf(2127,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__divides @ ( c_2Einteger_2Eint__mul @ A @ B ) @ ( c_2Einteger_2Eint__mul @ A @ C ) )
        = ( c_2Einteger_2Eint__divides @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(281,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ A )
      = ( c_2Ewords_2Eword__2comp @ TA @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__LZERO) ).

thf(2159,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) @ A )
      = ( c_2Ewords_2Eword__2comp @ TA @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(122,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
     => ( A != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__NOT__EQ) ).

thf(1129,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__lt @ TA @ A @ B )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(359,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2Eword__2comp @ TA @ A ) )
      = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__RINV) ).

thf(2430,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2Eword__2comp @ TA @ A ) )
      = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(475,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__neg @ A )
        = B )
      = ( A
        = ( c_2Einteger_2Eint__neg @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__EQ) ).

thf(2803,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__neg @ A )
        = B )
      = ( A
        = ( c_2Einteger_2Eint__neg @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(609,axiom,
    ! [TA: $tType,A: tyop_2Enum_2Enum] :
      ~ ( c_2Ewords_2Eword__bit @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__bit__0) ).

thf(3259,plain,
    ! [TA: $tType,A: tyop_2Enum_2Enum] :
      ~ ( c_2Ewords_2Eword__bit @ TA @ A @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(385,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__divides @ A @ B )
      = ( ( ( ( c_2Einteger_2Eint__mod @ B @ A )
            = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
          & ( A
           != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
        | ( ( A
            = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
          & ( B
            = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__MOD0) ).

thf(2507,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__divides @ A @ B )
      = ( ( ( ( c_2Einteger_2Eint__mod @ B @ A )
            = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
          & ( A
           != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) )
        | ( ( A
            = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
          & ( B
            = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(646,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( A != c_2Enum_2E0 )
     => ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__of__num @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NZ__IMP__LT) ).

thf(3392,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( A != c_2Enum_2E0 )
     => ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__of__num @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).

thf(495,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__sub @ A @ B ) )
      = ( c_2Einteger_2Eint__le @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__LE) ).

thf(2864,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__le @ ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) @ ( c_2Einteger_2Eint__sub @ A @ B ) )
      = ( c_2Einteger_2Eint__le @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(691,plain,
    ! [D: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ~ ( c_2Earithmetic_2E_3C_3D @ A @ C )
      | ~ ( c_2Earithmetic_2E_3C_3D @ B @ D )
      | ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ C @ D ) ) ),
    inference(cnf,[status(esa)],[690]) ).

thf(50,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ A @ B )
        = ( c_2Earithmetic_2E_2A @ A @ C ) )
      = ( ( A = c_2Enum_2E0 )
        | ( B = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2EEQ__MULT__LCANCEL) ).

thf(871,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2A @ A @ B )
        = ( c_2Earithmetic_2E_2A @ A @ C ) )
      = ( ( A = c_2Enum_2E0 )
        | ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(210,axiom,
    ! [A: tyop_2Enum_2Enum > $o] :
      ( ( ? [B: tyop_2Enum_2Enum] : ( A @ B ) )
      = ( ? [B: tyop_2Enum_2Enum] :
            ( ( A @ B )
            & ! [C: tyop_2Enum_2Enum] :
                ( ( c_2Eprim__rec_2E_3C @ C @ B )
               => ~ ( A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2ETemporal__Logic_2EWELL__ORDER) ).

thf(1621,plain,
    ! [A: tyop_2Enum_2Enum > $o] :
      ( ( ? [B: tyop_2Enum_2Enum] : ( A @ B ) )
      = ( ? [B: tyop_2Enum_2Enum] :
            ( ( A @ B )
            & ! [C: tyop_2Enum_2Enum] :
                ( ( c_2Eprim__rec_2E_3C @ C @ B )
               => ~ ( A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(339,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__lt @ A @ B )
        & ( c_2Einteger_2Eint__le @ C @ D ) )
     => ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ C ) @ ( c_2Einteger_2Eint__add @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LTE__ADD2) ).

thf(2372,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__lt @ A @ B )
        & ( c_2Einteger_2Eint__le @ C @ D ) )
     => ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ C ) @ ( c_2Einteger_2Eint__add @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(112,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__le @ TA @ A @ B )
        & ( c_2Ewords_2Eword__le @ TA @ B @ C ) )
     => ( c_2Ewords_2Eword__le @ TA @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LESS__EQ__TRANS) ).

thf(1093,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__le @ TA @ A @ B )
        & ( c_2Ewords_2Eword__le @ TA @ B @ C ) )
     => ( c_2Ewords_2Eword__le @ TA @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(333,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ A @ B )
     => ( A != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__IMP__NE) ).

thf(2353,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ A @ B )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(47,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
          ( ( c_2Ewords_2Eword__mul @ TB @ ( c_2Ewords_2En2w @ TB @ A ) @ ( c_2Ewords_2Eword__2comp @ TB @ ( c_2Ewords_2En2w @ TB @ B ) ) )
          = ( c_2Ewords_2Eword__2comp @ TB @ ( c_2Ewords_2En2w @ TB @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ) )
      & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
          ( ( c_2Ewords_2Eword__mul @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2En2w @ TA @ A ) ) @ ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2En2w @ TA @ B ) ) )
          = ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LITERAL__MULT) ).

thf(839,plain,
    ! [TA: $tType,TB: $tType] :
      ( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
          ( ( c_2Ewords_2Eword__mul @ TB @ ( c_2Ewords_2En2w @ TB @ A ) @ ( c_2Ewords_2Eword__2comp @ TB @ ( c_2Ewords_2En2w @ TB @ B ) ) )
          = ( c_2Ewords_2Eword__2comp @ TB @ ( c_2Ewords_2En2w @ TB @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ) )
      & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
          ( ( c_2Ewords_2Eword__mul @ TA @ ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2En2w @ TA @ A ) ) @ ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2En2w @ TA @ B ) ) )
          = ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2A @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(307,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__divides @ A @ B )
     => ( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__sub @ C @ B ) )
        = ( c_2Einteger_2Eint__divides @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__RSUB) ).

thf(2265,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__divides @ A @ B )
     => ( ( c_2Einteger_2Eint__divides @ A @ ( c_2Einteger_2Eint__sub @ C @ B ) )
        = ( c_2Einteger_2Eint__divides @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(91,axiom,
    ! [A: $o] :
      ( ( ( c_2Ebool_2ET
          | A )
        = c_2Ebool_2ET )
      & ( ( A
          | c_2Ebool_2ET )
        = c_2Ebool_2ET )
      & ( ( c_2Ebool_2EF
          | A )
        = A )
      & ( ( A
          | c_2Ebool_2EF )
        = A )
      & ( ( A
          | A )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EOR__CLAUSES) ).

thf(1019,plain,
    ! [A: $o] :
      ( ( ( c_2Ebool_2ET
          | A )
        = c_2Ebool_2ET )
      & ( ( A
          | c_2Ebool_2ET )
        = c_2Ebool_2ET )
      & ( ( c_2Ebool_2EF
          | A )
        = A )
      & ( ( A
          | c_2Ebool_2EF )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(60,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2D @ A @ B )
        = c_2Enum_2E0 )
      = ( c_2Earithmetic_2E_3C_3D @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ESUB__EQ__0) ).

thf(908,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2E_2D @ A @ B )
        = c_2Enum_2E0 )
      = ( c_2Earithmetic_2E_3C_3D @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(83,axiom,
    ! [TA: $tType,TB: $tType,A: $o,B: TB > TA,C: TB > TA,D: TB] :
      ( ( c_2Ebool_2ECOND @ ( TB > TA ) @ A @ B @ C @ D )
      = ( c_2Ebool_2ECOND @ TA @ A @ ( B @ D ) @ ( C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__RATOR) ).

thf(992,plain,
    ! [TA: $tType,TB: $tType,A: $o,B: TB > TA,C: TB > TA,D: TB] :
      ( ( c_2Ebool_2ECOND @ ( TB > TA ) @ A @ B @ C @ D )
      = ( c_2Ebool_2ECOND @ TA @ A @ ( B @ D ) @ ( C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(722,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
      | ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ C )
      | ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2EMOD @ B @ C ) )
        = ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ A @ C ) ) ) ),
    inference(cnf,[status(esa)],[721]) ).

thf(723,plain,
    ! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ A @ B ) @ ( c_2Earithmetic_2E_2A @ A @ C ) )
        = ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2EMOD @ B @ C ) ) )
      | ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A )
      | ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ C ) ),
    inference(lifteq,[status(thm)],[722]) ).

thf(545,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__ls @ TA @ A @ B )
        & ( c_2Ewords_2Eword__ls @ TA @ B @ A ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LOWER__EQUAL__ANTISYM) ).

thf(3020,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__ls @ TA @ A @ B )
        & ( c_2Ewords_2Eword__ls @ TA @ B @ A ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(378,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ A ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ B ) ) ) )
      = ( c_2Ewords_2Eword__add @ TA @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__add__i2w__w2n) ).

thf(2484,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__add @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ A ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ B ) ) ) )
      = ( c_2Ewords_2Eword__add @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(442,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__2comp @ TA @ A )
        = ( c_2Ewords_2Eword__2comp @ TA @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__EQ__NEG) ).

thf(2699,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__2comp @ TA @ A )
        = ( c_2Ewords_2Eword__2comp @ TA @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(274,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__mul @ B @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIV__RMUL) ).

thf(2138,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( c_2Einteger_2Eint__div @ ( c_2Einteger_2Eint__mul @ B @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(632,axiom,
    ! [TA: $tType] :
      ( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
      = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__0) ).

thf(3341,plain,
    ! [TA: $tType] :
      ( ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
      = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(458,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__add @ TA @ A @ B )
        = C )
      = ( A
        = ( c_2Ewords_2Eword__sub @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__EQ__SUB) ).

thf(2754,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA,C: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__add @ TA @ A @ B )
        = C )
      = ( A
        = ( c_2Ewords_2Eword__sub @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(428,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__sub @ B @ C ) )
      = ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__SUB__LADD) ).

thf(2640,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ A @ ( c_2Einteger_2Eint__sub @ B @ C ) )
      = ( c_2Einteger_2Eint__lt @ ( c_2Einteger_2Eint__add @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(152,axiom,
    ! [A: $o] :
      ( A
     => ( A = c_2Ebool_2ET ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esat_2EEQT__Imp1) ).

thf(1320,plain,
    ! [A: $o] :
      ( A
     => ( A = c_2Ebool_2ET ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(599,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__add @ A @ B )
        = B )
      = ( A
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__LID__UNIQ) ).

thf(3227,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( c_2Einteger_2Eint__add @ A @ B )
        = B )
      = ( A
        = ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(485,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ A ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ B ) ) ) )
      = ( c_2Ewords_2Eword__sub @ TA @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__sub__i2w__w2n) ).

thf(2832,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( c_2Einteger__word_2Ei2w @ TA @ ( c_2Einteger_2Eint__sub @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ A ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Ewords_2Ew2n @ TA @ B ) ) ) )
      = ( c_2Ewords_2Eword__sub @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(361,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ A @ B )
     => ( c_2Einteger_2Eint__le @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__IMP__LE) ).

thf(2436,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__lt @ A @ B )
     => ( c_2Einteger_2Eint__le @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(625,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__sub @ TA @ B @ A )
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
      = ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__EQ__SUB__ZERO) ).

thf(3316,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__sub @ TA @ B @ A )
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
      = ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(1156,plain,
    ( ( c_2Ebool_2ECOND @ $o @ $true @ $false @ c_2Ebool_2ET )
    = ( $true
     => $false ) ),
    inference(instance,[status(thm)],[1153]) ).

thf(1157,plain,
    ~ ( c_2Ebool_2ECOND @ $o @ $true @ $false @ c_2Ebool_2ET ),
    inference(simp,[status(thm)],[1156]) ).

thf(3933,plain,
    ~ ( c_2Ebool_2ECOND @ $o @ $true @ $false @ $true ),
    inference(rewrite,[status(thm)],[1157,878]) ).

thf(618,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__add @ TA @ A @ B )
        = B )
      = ( A
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__LID__UNIQ) ).

thf(3296,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
      ( ( ( c_2Ewords_2Eword__add @ TA @ A @ B )
        = B )
      = ( A
        = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

thf(287,axiom,
    ! [A: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__le @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__REFL) ).

thf(2177,plain,
    ! [A: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__le @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(2771,plain,
    ! [TA: $tType] : ( c_2Ewords_2Eword__msb @ TA @ ( c_2Ewords_2Eword__L @ TA ) ),
    inference(cnf,[status(esa)],[2770]) ).

thf(596,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Egcd_2Elcm @ c_2Enum_2E0 @ A )
        = c_2Enum_2E0 )
      & ( ( c_2Egcd_2Elcm @ A @ c_2Enum_2E0 )
        = c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2ELCM__0) ).

thf(3212,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Egcd_2Elcm @ c_2Enum_2E0 @ A )
        = c_2Enum_2E0 )
      & ( ( c_2Egcd_2Elcm @ A @ c_2Enum_2E0 )
        = c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(619,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( c_2Ewords_2Esw2sw @ TB @ TA @ ( c_2Ewords_2En2w @ TB @ c_2Enum_2E0 ) )
      = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Esw2sw__0) ).

thf(3299,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( c_2Ewords_2Esw2sw @ TB @ TA @ ( c_2Ewords_2En2w @ TB @ c_2Enum_2E0 ) )
      = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(87,axiom,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] : ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2Eword__L @ TA ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__L__LESS__EQ) ).

thf(1009,plain,
    ! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA] : ( c_2Ewords_2Eword__le @ TA @ ( c_2Ewords_2Eword__L @ TA ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(362,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( ( c_2Einteger_2Eint__rem @ ( c_2Einteger_2Eint__neg @ A ) @ B )
          = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__rem @ A @ B ) ) )
        & ( ( c_2Einteger_2Eint__rem @ A @ ( c_2Einteger_2Eint__neg @ B ) )
          = ( c_2Einteger_2Eint__rem @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__REM__NEG) ).

thf(2438,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Einteger_2Eint__of__num @ c_2Enum_2E0 ) )
     => ( ( ( c_2Einteger_2Eint__rem @ ( c_2Einteger_2Eint__neg @ A ) @ B )
          = ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__rem @ A @ B ) ) )
        & ( ( c_2Einteger_2Eint__rem @ A @ ( c_2Einteger_2Eint__neg @ B ) )
          = ( c_2Einteger_2Eint__rem @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(318,axiom,
    ! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Einteger_2Eint] :
      ( ( ? [C: tyop_2Einteger_2Eint] : ( A @ ( c_2Einteger_2Eint__mul @ B @ C ) ) )
      = ( ? [C: tyop_2Einteger_2Eint] :
            ( ( A @ C )
            & ( c_2Einteger_2Eint__divides @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eint__arith_2Elcm__eliminate) ).

thf(2297,plain,
    ! [A: tyop_2Einteger_2Eint > $o,B: tyop_2Einteger_2Eint] :
      ( ( ? [C: tyop_2Einteger_2Eint] : ( A @ ( c_2Einteger_2Eint__mul @ B @ C ) ) )
      = ( ? [C: tyop_2Einteger_2Eint] :
            ( ( A @ C )
            & ( c_2Einteger_2Eint__divides @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(662,axiom,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Ewords_2Eword__bits @ TA @ A @ B @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
      = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__BITS__ZERO2) ).

thf(3443,plain,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Ewords_2Eword__bits @ TA @ A @ B @ ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) )
      = ( c_2Ewords_2En2w @ TA @ c_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(3959,plain,
    $false,
    inference(e,[status(thm)],[1665,1036,2452,2889,2778,1729,893,1315,2427,2612,1024,1168,2295,2306,760,3008,2131,1454,2544,941,2280,1110,2363,2210,730,3285,2676,3108,1205,1692,1041,1173,1750,3185,1406,2104,2622,1068,2495,3230,2395,2908,3377,2527,3040,3153,2114,1142,878,3498,2380,3439,3332,3446,3253,3481,3313,1063,2360,1705,3017,3365,2740,715,2933,2168,698,3236,3350,2972,1391,782,709,2020,2886,829,1095,3088,3777,1601,1386,3466,1518,1703,1628,724,3263,3029,1430,2814,2667,785,2269,3495,3061,2708,2682,934,3353,3043,1511,702,751,3410,2185,2420,2691,3099,2713,1514,2767,1609,1347,881,2852,2829,3840,3463,3374,1013,770,3014,2520,2388,2533,1415,2616,2794,1714,2996,2259,2122,1383,2034,1183,905,924,3322,3295,2782,3453,2236,2880,834,1151,937,2335,966,1051,3851,687,3189,2861,3505,3327,3226,1697,2392,3492,3068,1377,692,2190,3421,2523,2530,1119,2424,1394,2772,998,2809,1651,3097,3011,1306,1153,810,1338,2093,2000,1074,1604,3450,3503,3459,2905,714,2382,798,3037,2673,2705,1091,2249,3867,2147,3239,3250,3207,3778,1223,3261,957,952,2541,3233,3371,788,1619,2150,3269,2565,2872,1624,2609,2179,1210,757,1634,710,974,2958,3307,2628,2670,2433,2477,2826,2820,3499,3065,1079,1027,2547,2492,697,874,3413,2990,2685,2895,1328,1498,3518,2631,989,1397,3105,2300,2377,948,3102,1672,1138,2724,1719,2858,884,2877,1082,3094,1700,2172,1016,706,2460,1493,3407,2561,3210,2978,1039,970,2317,3294,2504,1451,2487,2243,2465,911,3115,2052,2272,837,3242,2153,1831,2497,721,779,3074,3005,3083,3162,3147,1333,2634,2788,2926,1202,1695,2748,2963,1071,1515,3508,1616,1185,718,1732,938,3225,2702,2761,2883,921,2057,1054,773,794,1727,2556,2275,2585,2570,2602,1301,3111,1374,2936,1648,2413,3130,1146,2292,3491,1483,1631,733,1833,2727,2048,2791,2849,3472,3272,826,2806,1403,2398,2716,1124,2970,694,3319,3266,2016,2514,2568,3404,2817,1226,1488,1503,713,3002,3487,3416,704,3304,3302,3023,1669,2308,1371,3077,2759,3436,2457,804,3091,1464,2474,2319,2573,3719,2346,2311,2119,2679,2538,2637,1011,3515,2284,2246,2839,2945,1043,3500,3586,2510,764,979,2415,2987,3779,1048,736,1722,1144,3219,2182,2605,816,1162,3165,1344,2252,890,3456,2025,2812,3133,3055,2314,2343,2625,2446,2757,3192,700,3034,2410,2923,1325,2785,1029,1149,2874,2278,2553,3150,2842,2710,2911,1841,2350,2401,2212,1066,1643,1176,3310,2101,2303,3178,2867,2770,2418,1213,2835,2550,695,2481,3159,2369,1113,2797,1000,1435,1477,3325,1364,2967,2999,2156,1694,2693,3490,3380,2239,2952,3427,2107,944,1467,3395,2471,2124,2449,3048,939,1472,2846,754,2899,2582,2914,3031,1662,2614,927,2037,1181,823,2942,712,971,2588,954,739,1368,1098,776,1748,690,1598,2060,1400,707,2192,887,2407,3058,3080,3246,717,3344,2322,3329,1336,2468,1716,2454,3305,1432,2165,1637,2688,3063,2920,791,3475,3026,951,2599,2948,1849,2558,2992,3356,2722,2939,3071,3156,876,3398,3288,1221,2975,2357,2145,2579,864,727,3388,1504,3256,2892,3168,845,3478,3433,2479,3401,931,2696,2870,1834,1844,2215,1216,1126,2643,2775,1459,2045,1654,1412,2743,1448,2490,2187,2591,2174,2855,2290,1508,3383,2823,1745,2764,3780,1646,2443,813,2594,1341,896,2098,3484,946,1101,3136,3368,995,2262,1689,3181,2462,929,2576,1607,2902,832,1309,2917,2421,2956,1491,2648,3430,1077,2162,2374,2287,2517,2385,2255,3291,2719,1303,1480,3469,1116,2003,2142,2930,2218,1133,1593,1380,3145,801,1495,1657,3347,807,2746,767,2366,2404,2040,3045,2751,2800,1033,2961,2619,3424,720,2340,1165,2127,2159,1129,2430,2803,3259,2507,3392,2864,691,871,1621,2372,1093,2353,839,2265,1019,908,992,723,3020,2484,2699,2138,3341,2754,2640,1320,3227,2832,2436,3316,3933,3296,2177,2771,3212,3299,1009,2438,2297,3443]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : ITP015^7 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.12/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n014.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Mon May  6 14:28:10 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.98/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 4.83/2.08  % [INFO] 	 Parsing done (1218ms). 
% 4.83/2.10  % [INFO] 	 Running in sequential loop mode. 
% 5.31/2.29  % [INFO] 	 eprover registered as external prover. 
% 5.31/2.29  % [INFO] 	 cvc4 registered as external prover. 
% 5.31/2.29  % [INFO] 	 Scanning for conjecture ... 
% 6.97/2.79  % [INFO] 	 Found a conjecture and 10012 axioms. Running axiom selection ... 
% 8.79/3.31  % [INFO] 	 Axiom selection finished. Selected 684 axioms (removed 9328 axioms). 
% 9.57/3.55  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 9.57/3.57  % [INFO] 	 Type checking passed. 
% 9.57/3.57  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 28.76/7.88  % External prover 'e' found a proof!
% 28.76/7.88  % [INFO] 	 Killing All external provers ... 
% 28.76/7.88  % Time passed: 7342ms (effective reasoning time: 5780ms)
% 28.76/7.88  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 28.76/7.88  % Axioms used in derivation (684): thm_2Ewords_2Eword__sub__w2n, thm_2Einteger_2EINT__NEG__RMUL, thm_2Ewords_2EWORD__NEG__EQ, thm_2Eint__arith_2Elt__justify__multiplication, thm_2Ebool_2EBOOL__CASES__AX, thm_2Einteger_2EINT__LT__SUB__LADD, thm_2Ewords_2EWORD__LESS__REFL, thm_2Ewords_2Ew2w__0, thm_2Ewords_2EWORD__SLICE__ZERO2, thm_2Ewords_2EWORD__ADD__RIGHT__LO2, thm_2Ewords_2EWORD__ADD__RIGHT__LS2, thm_2Egcd_2EIS__GCD__MINUS__L, thm_2Einteger_2EINT__LT__LE, thm_2Ewords_2EWORD__ADD__ASSOC, thm_2Einteger_2EINT__SUB__LT, thm_2Ewellorder_2EWF__REC__num, thm_2EConseqConv_2EOR__CLAUSES__FX, thm_2Einteger_2EINT__LE__LADD, thm_2Earithmetic_2EABS__DIFF__EQS, thm_2Einteger_2EINT__LT__MONO, thm_2Einteger_2EINT__RNEG__UNIQ, thm_2Ewords_2EWORD__MULT__ASSOC, thm_2Einteger_2EINT__LT__MUL2, thm_2Einteger_2EINT__ABS__ABS, thm_2Einteger_2EINT__ADD__DIV, thm_2Ewords_2EWORD__LOWER__CASES__IMP, thm_2Eint__arith_2Ejustify__divides2, thm_2Einteger_2EINT__MOD0, thm_2Eint__arith_2Epositive__product__implication, thm_2Eint__arith_2Ele__move__right__left, thm_2Einteger_2EINT__LE__ADD2, thm_2Einteger_2EINT__DIVIDES__MUL, thm_2Eint__arith_2EINT__LINEAR__GCD, thm_2Earithmetic_2ESUB__CANCEL, thm_2Ewords_2EWORD__NOT__LESS, thm_2Einteger_2Eint__sub, thm_2Earithmetic_2EABS__DIFF__EQ__0, thm_2Einteger_2EINT__ADD__LID__UNIQ, thm_2Ewords_2EWORD__LESS__EQ__LESS__TRANS, thm_2Ebool_2ECOND__ABS, thm_2Ebool_2ENOT__CLAUSES, thm_2Ewords_2EWORD__LOWER__OR__EQ, thm_2Ecardinal_2ELT__NZ, thm_2Earithmetic_2ELESS__LESS__EQ__TRANS, thm_2Einteger_2EINT__DIVIDES__MOD0, thm_2EternaryComparisons_2Ebool__compare__ind, thm_2Einteger_2EINT__MUL__REDUCE, thm_2Ewords_2EWORD__LESS__EQ__TRANS, thm_2Eint__arith_2Ele__context__rwt3, thm_2Einteger_2EINT__LT__NEG, thm_2Einteger_2EINT__NEG__GE0, thm_2Einteger_2EINT__LE__RADD, thm_2Einteger_2EINT__ADD__ASSOC, thm_2Ebool_2Ebool__INDUCT, thm_2Earithmetic_2ENOT__ZERO__LT__ZERO, thm_2Einteger_2EINT__DIV__RMUL, thm_2Earithmetic_2EDIV__MOD__MOD__DIV, thm_2Einteger_2EINT__LESS__MOD, thm_2Eint__arith_2Ebot__and__greaters, thm_2Einteger_2EINT__NZ__IMP__LT, thm_2Ebool_2EIMP__F__EQ__F, thm_2Einteger_2EINT__NEG__SUB, thm_2Earithmetic_2ECOMPLETE__INDUCTION, thm_2Earithmetic_2ESUB__EQ__EQ__0, thm_2Einteger_2EINT__LE__ADDR, thm_2Einteger_2EINT__SUB__REDUCE, thm_2EConseqConv_2EIMP__CLAUSES__XF, thm_2Ewords_2Ebit__count__upto__0, thm_2Einteger_2EINT__MOD__UNIQUE, thm_2Esat_2ENOT__ELIM2, thm_2Eint__arith_2EINT__NUM__EXISTS, thm_2Einteger_2EINT__SUB__LE, thm_2Esat_2EAND__INV__IMP, thm_2Ewords_2EWORD__LOWER__NOT__EQ, thm_2Ewords_2EWORD__ADD__COMM, thm_2Ewords_2Eword__sub__def, thm_2Esat_2EOR__DUAL3, thm_2Ewords_2EWORD__LEFT__ADD__DISTRIB, thm_2Einteger_2ENUM__NEGINT__EXISTS, thm_2Einteger_2EINT__SUB__CALCULATE, thm_2Egcd_2EIS__GCD__UNIQUE, thm_2Ewords_2EWORD__0__LS, thm_2Einteger_2EINT__MOD__SUB, thm_2Ebool_2EREFL__CLAUSE, thm_2Einteger_2EINT__QUOT__NEG, thm_2Einteger__word_2Eint__word__nchotomy, thm_2Einteger_2EINT__OF__NUM, thm_2Ealignment_2Ealigned__def, thm_2Einteger_2EINT__LTE__ADD2, thm_2Ewords_2EWORD__ADD__LEFT__LO2, thm_2Ewords_2EWORD__LESS__NEG__LEFT, thm_2Enumpair_2Enlist__cases, thm_2Ealignment_2Ealigned__add__sub, thm_2Ewords_2EWORD__LOWER__CASES, thm_2Earithmetic_2ELESS__CASES, thm_2Ebool_2ECOND__RAND, thm_2Einteger_2EINT__ABS__LT, thm_2Eint__arith_2Eadd__to__great, thm_2Ewords_2ETWO__COMP__POS, thm_2Einteger_2EINT__LE__REFL, thm_2Earithmetic_2EMOD__MULT__MOD, thm_2Ewords_2EWORD__LOWER__EQ__LOWER__TRANS, thm_2Ewords_2EWORD__LO__word__0, thm_2Einteger_2EINT__REM__UNIQUE, thm_2Einteger_2EINT__DIV, thm_2Earithmetic_2ELESS__TRANS, thm_2Einteger_2EINT__EQ__NEG, thm_2Ewords_2EWORD__NEG__LMUL, thm_2Ewords_2EWORD__ADD__SUB__SYM, thm_2Eint__arith_2Ein__subtractive__range, thm_2Ebool_2EEQ__CLAUSES, thm_2Earithmetic_2EMODEQ__REFL, thm_2Einteger_2EINT__ABS__MUL, thm_2Ewords_2EWORD__LE, thm_2Ewords_2EWORD__LOWER__TRANS, thm_2Einteger_2EINT__ABS__POS, thm_2Einteger__word_2Eword__sdiv__def, thm_2Earithmetic_2EMULT__ASSOC, thm_2Ewords_2EWORD__EXTRACT__ZERO2, thm_2Einteger_2EINT__NOT__LT, thm_2Einteger_2EINT__LE__SQUARE, thm_2Earithmetic_2ELE__MULT__LCANCEL, thm_2Earithmetic_2ESUB__EQUAL__0, thm_2Ewords_2EWORD__NEG__L, thm_2Einteger_2EINT__LT__ADD, thm_2Egcd_2EGCD__0R, thm_2Eint__arith_2Ele__move__all__right, thm_2Einteger_2EINT__SUMSQ, thm_2Einteger_2EINT__LE__ADDL, thm_2Einteger_2EINT__REM__CALCULATE, thm_2Eint__arith_2Elcm__eliminate, thm_2Einteger_2EINT__ABS__NUM, thm_2Egcd_2EGCD__SYM, thm_2Ewords_2EWORD__LOWER__LOWER__CASES, thm_2Einteger_2EINT__LE__SUB__LADD, thm_2Einteger_2EINT__SUB__NEG2, thm_2Einteger_2EINT__MOD__PLUS, thm_2Enum_2EZERO__DEF, thm_2Eint__arith_2Ecooper__lemma__1, thm_2Earithmetic_2EMULT__SYM, thm_2Einteger_2EINT__DIVIDES__MUL__BOTH, thm_2Einteger_2EINT__DIVIDES__LSUB, thm_2Ecardinal_2ELE__CASES, thm_2Earithmetic_2ELE__MULT__RCANCEL, thm_2Einteger_2EINT__EQ__LMUL__IMP, thm_2Einteger_2EINT__MUL__DIV, thm_2Ewords_2EWORD__ADD__INV__0__EQ, thm_2EConseqConv_2ENOT__CLAUSES__T, thm_2Einteger_2EINT__DIVIDES__REFL, thm_2EConseqConv_2EIMP__CONG__cond__simple, thm_2Einteger_2EINT__DIV__LMUL, thm_2EConseqConv_2EAND__CLAUSES__TX, thm_2Ewords_2Eword__mul__n2w, thm_2Einteger_2EINT__DIVIDES__0, thm_2Einteger__word_2Eword__smod__def, thm_2Einteger_2EINT__SUB__REFL, thm_2Ewords_2Eword__0__n2w, thm_2Einteger_2EINT__QUOT, thm_2Einteger_2EINT__NOT__LE, thm_2Earithmetic_2EDIV__LE__MONOTONE, thm_2Earithmetic_2ELT__SUB__RCANCEL, thm_2Ewords_2Esw2sw__0, thm_2EConseqConv_2EIMP__CLAUSES__XX, thm_2Ebool_2EIMP__F, thm_2Ewords_2EWORD__SUB__REFL, thm_2Egcd_2ELCM__COMM, thm_2Ewords_2EWORD__EQ__ADD__RCANCEL, thm_2Einteger_2EINT__DIVIDES__RADD, thm_2Earithmetic_2ERIGHT__SUB__DISTRIB, thm_2Earithmetic_2ESUB__EQ__0, thm_2Einteger_2EINT__MOD__MOD, thm_2Einteger_2EINT__LE__SUB__RADD, thm_2Einteger_2EINT__EXP__SUBTRACT__EXPONENTS, thm_2Ewords_2EWORD__LOWER__EQ__TRANS, thm_2Ewords_2EWORD__LS__word__0, thm_2Einteger_2EINT__SUB__TRIANGLE, thm_2Einteger_2EINT__MUL__SYM, thm_2Ewords_2En2w__w2n, thm_2Eint__arith_2EHO__SUB__ELIM, thm_2Einteger__word_2Eword__0__w2i, thm_2Einteger_2EINT__ADD__LINV, thm_2Ewords_2EWORD__LITERAL__MULT, thm_2Einteger_2EINT__DIVIDES__RSUB, thm_2Einteger_2EINT__LT__LADD, thm_2Einteger_2EINT__POS, thm_2Einteger_2EINT__SUB__SUB2, thm_2Einteger_2EINT__DIVIDES, thm_2Einteger_2EINT__MUL__COMM, thm_2Ewords_2ETWO__COMP__POS__NEG, thm_2Ewords_2EWORD__LOWER__EQUAL__ANTISYM, thm_2Eint__arith_2Eeq__justify__multiplication, thm_2Einteger_2EINT__ABS__EQ__ABS, thm_2EConseqConv_2Efalse__imp, thm_2Ewords_2EWORD__L__LESS__EQ, thm_2Einteger_2EINT__LE__MUL, thm_2Earithmetic_2EMULT__0, thm_2Einteger_2EINT__LE__TOTAL, thm_2Einteger_2EINT__MUL, thm_2Einteger_2EINT__ADD__SUB2, thm_2Einteger_2EINT__ABS__NEG, thm_2Earithmetic_2EMOD__MOD, thm_2Einteger__word_2Eword__mul__i2w, thm_2Einteger_2EINT__SUB__0, thm_2Earithmetic_2EMODEQ__MOD, thm_2Einteger_2EINT__LT__GT, thm_2Ewords_2EWORD__LESS__LESS__EQ__TRANS, thm_2Einteger_2EINT__NEG__LT0, thm_2Ewords_2Eword__abs__def, thm_2Ewords_2EWORD__ADD__SUB__ASSOC, thm_2Ewords_2EWORD__ADD__LINV, thm_2Ewords_2EWORD__LT__EQ__LO, thm_2Einteger_2EINT__LT__RADD, thm_2Einteger_2EINT__DIVIDES__RMUL, thm_2Einteger_2EINT__EXP__EQ0, thm_2Eint__arith_2Eelim__le__coeffs, thm_2Einteger_2EINT__DIV__UNIQUE, thm_2Ewords_2EWORD__LESS__TRANS, thm_2Eint__arith_2Ele__context__rwt4, thm_2Eint__arith_2Elt__move__all__right, thm_2Einteger__word_2Ew2i__eq__0, thm_2Earithmetic_2ENOT__LT__ZERO__EQ__ZERO, thm_2Earithmetic_2ELESS__ANTISYM, thm_2Egcd_2EGCD__COMMON__FACTOR, thm_2Ewords_2EWORD__SUB__PLUS, thm_2Einteger_2EINT__LE__DOUBLE, thm_2Einteger_2EINT__LE__TRANS, thm_2Ewords_2EWORD__NEG__ADD, thm_2Einteger__word_2Ei2w__w2i, thm_2Ebool_2EFALSITY, thm_2Einteger_2EINT__LE, thm_2Einteger_2EINT__ABS__EQ__ID, thm_2Einteger_2EINT__REMQUOT, thm_2Einteger_2EINT__NEG__LE0, thm_2Einteger__word_2Eword__sub__i2w, thm_2Earithmetic_2ELESS__EQ__REFL, thm_2Einteger_2EINT__LT__LADD__IMP, thm_2Ewords_2EWORD__ADD__SUB2, thm_2EConseqConv_2ECOND__CLAUSES__FT, thm_2Ewords_2EWORD__LESS__IMP__LESS__OR__EQ, thm_2Ebitstring_2Eword__extract__v2w, thm_2Einteger__word_2Ew2i__neg, thm_2Earithmetic_2EABS__DIFF__SYM, thm_2Einteger_2EINT__SUB__RNEG, thm_2Ewords_2EWORD__NEG__SUB, thm_2Ewords_2Ew2n__11, thm_2Einteger_2EINT__LE__NEGL, thm_2Ewords_2EWORD__LESS__LESS__CASES, thm_2Earithmetic_2EMODEQ__TRANS, thm_2Ecardinal_2ELT__LE, thm_2Eint__arith_2EINT__SUB__SUB3, thm_2Ewords_2EWORD__ADD__RINV, thm_2Earithmetic_2ELESS__MONO__MULT2, thm_2Einteger_2EINT__ENTIRE, thm_2EternaryComparisons_2Eordering__size__def, thm_2Einteger_2EINT__LTE__TRANS, thm_2Eint__arith_2Elt__move__left__left, thm_2EbasicSize_2Eone__size__def, thm_2Earithmetic_2EX__LE__DIV, thm_2Ewords_2EWORD__LT__LO, thm_2Earithmetic_2ESUB__0, thm_2Einteger_2EINT__LET__ADD2, thm_2Einteger_2EINT__LT__ADDR, thm_2Ewords_2Eword__msb__add__word__L, thm_2Ewords_2Eword__nchotomy, thm_2Einteger__word_2Eword__add__i2w, thm_2Einteger_2EINT__DIVIDES__LMUL, thm_2Einteger_2EINT__LT__ADD2, thm_2Ealignment_2Ealign__0, thm_2Ewords_2EWORD__EQ__NEG, thm_2Ebag_2Emlt__UNION__EMPTY__EQN, thm_2Einteger_2EINT__LT__ANTISYM, thm_2Ewords_2EWORD__EQ__SUB__LADD, thm_2Einteger_2EINT__LE__CALCULATE, thm_2EConseqConv_2ECOND__CLAUSES__FF, thm_2Einteger_2EINT__INJ, thm_2Ebool_2Ebool__case__CONG, thm_2Ewords_2EWORD__EQ__SUB__ZERO, thm_2Ebool_2ECOND__CLAUSES, thm_2Einteger_2EINT__EQ__RMUL__IMP, thm_2Ewords_2En2w__sub, thm_2Egcd_2ELCM__0, thm_2Einteger_2EINT__LT__TOTAL, thm_2Ewords_2EWORD__LOWER__EQ__CASES, thm_2Ewords_2EWORD__EQ__ADD__LCANCEL, thm_2Ewords_2EWORD__SUB, thm_2Ewords_2EWORD__SLICE__BITS__THM, thm_2Earithmetic_2EX__MOD__Y__EQ__X, thm_2Einteger_2EINT__QUOT__0, thm_2Earithmetic_2EZERO__LESS__MULT, thm_2Earithmetic_2EMODEQ__0, thm_2Ewords_2Eword__abs__diff, thm_2Einteger_2EINT__NEG__SAME__EQ, thm_2Earithmetic_2ENRC__0, thm_2Earithmetic_2ELESS__EQ__0, thm_2Ewords_2EWORD__SUB__TRIANGLE, thm_2Earithmetic_2ENOT__LESS__EQUAL, thm_2Einteger_2EINT__ADD__LID, thm_2Ewords_2EWORD__LCANCEL__SUB, thm_2Ewords_2EWORD__LOWER__REFL, thm_2Einteger__word_2Eword__sub__i2w__w2n, thm_2Earithmetic_2ELESS__OR__EQ, thm_2Enumpair_2Encons__not__nnil, thm_2Einteger__word_2Eword__i2w__mul, thm_2Earithmetic_2EDIV__LESS__EQ, thm_2Ewords_2Ew2w__def, thm_2Einteger_2EINT__ADD__RID__UNIQ, thm_2Einteger_2EINT__SUB, thm_2Egcd_2EIS__GCD__REF, thm_2Ewords_2EWORD__BITS__ZERO2, thm_2Einteger_2EINT__LT__NEGTOTAL, thm_2Ewords_2EMOD__COMPLEMENT, thm_2Ebool_2ECOND__EXPAND, thm_2Einteger_2EINT__DIVIDES__NEG, thm_2Einteger_2ENUM__LT, thm_2Einteger_2EINT__NEGNEG, thm_2Ebool_2ECOND__CONG, thm_2Ebitstring_2Eshiftr__0, thm_2Ebit_2EDIV__GT0, thm_2Eint__arith_2Eeq__move__right__left, thm_2Eint__arith_2Emove__sub, thm_2Ewords_2EWORD__LESS__EQ__REFL, thm_2Earithmetic_2ELT__MULT__CANCEL__RBARE, thm_2Estring_2Echar__size__def, thm_2Eprim__rec_2ELESS__NOT__EQ, thm_2Earithmetic_2ELESS__EQ__CASES, thm_2Ewords_2Eword__abs__neg, thm_2Ewords_2Eword__mul__def, thm_2Einteger_2EINT__EQ__IMP__LE, thm_2EConseqConv_2ECOND__CLAUSES__ID, thm_2Ewords_2EWORD__NOT__LESS__EQ, thm_2Einteger__word_2Eword__mul__i2w__w2n, thm_2Earithmetic_2ELE__MULT__CANCEL__LBARE, thm_2Einteger_2EINT__MOD__P, thm_2Ewords_2EWORD__NOT__LESS__EQUAL, thm_2Earithmetic_2EABS__DIFF__COMM, thm_2Ewords_2EWORD__LESS__CASES__IMP, thm_2ETemporal__Logic_2EWELL__ORDER, thm_2Einteger_2Eint__mod, thm_2Ebool_2ECOND__ID, thm_2Einteger_2EINT__EQ__CALCULATE, thm_2Einteger_2EINT__NEG__0, thm_2Einteger_2EINT__NEG__EQ, thm_2Eint__arith_2Eeq__context__rwt1, thm_2Earithmetic_2EMODEQ__THM, thm_2Einteger_2EINT__MOD__NEG__NUMERATOR, thm_2Ewords_2EWORD__RIGHT__SUB__DISTRIB, thm_2Einteger_2EINT__DIVIDES__TRANS, thm_2Einteger_2EINT__LT__IMP__LE, thm_2Ewords_2EWORD__EXTRACT__ZERO, thm_2Einteger_2EINT__ADD2__SUB2, thm_2Ebool_2ETRUTH, thm_2Einteger_2EINT__NEG__MUL2, thm_2Ebool_2ENOT__F, thm_2Earithmetic_2EMODEQ__SYM, thm_2Einteger_2EINT__DIVIDES__LADD, thm_2Ewords_2EWORD__LESS__CASES, thm_2Einteger_2EINT__ADD__COMM, thm_2Einteger_2EINT__LT__IMP__NE, thm_2Ebool_2EFORALL__BOOL, thm_2Ewords_2EWORD__SUB__LT, thm_2Ebool_2EIMP__CLAUSES, thm_2Earithmetic_2EABS__DIFF__ZERO, thm_2Earithmetic_2EMODEQ__NONZERO__MODEQUALITY, thm_2Egcd_2EGCD__IS__GCD, thm_2Ewords_2EWORD__SUB__LNEG, thm_2Earithmetic_2ELESS__EQUAL__ANTISYM, thm_2Earithmetic_2ELESS__EQ__TRANS, thm_2EConseqConv_2EIMP__CLAUSES__TX, thm_2EConseqConv_2EAND__CLAUSES__XF, thm_2Ebit_2ELESS__MULT__MONO2, thm_2Ewords_2Eword__reverse__0, thm_2Einteger__word_2Eword__i2w__add, thm_2Eint__arith_2Eeq__move__left__right, thm_2Einteger_2EINT__SUB__RDISTRIB, thm_2Einteger_2EINT__ABS__LE0, thm_2Earithmetic_2ELT__MULT__LCANCEL, thm_2Ewords_2EWORD__SUB__LE, thm_2Ebool_2EF__IMP, thm_2Einteger_2EINT__LDISTRIB, thm_2Ebool_2ECOND__EXPAND__OR, thm_2Einteger_2EINT__DIV__MUL__ID, thm_2Ewords_2EWORD__LEFT__SUB__DISTRIB, thm_2Ebool_2EboolAxiom, thm_2Einteger_2EINT__MOD__NEG, thm_2Eint__arith_2EINT__NUM__SUB, thm_2Einteger_2EINT__DIV__FORALL__P, thm_2Earithmetic_2EDIV__DIV__DIV__MULT, thm_2Ewords_2EWORD__LOWER__IMP__LOWER__OR__EQ, thm_2Earithmetic_2ESUB__LESS, thm_2EConseqConv_2ECOND__CLAUSES__CT, thm_2Einteger_2EINT__SUB__LDISTRIB, thm_2Eint__arith_2Ejustify__divides, thm_2EConseqConv_2EIMP__CLAUSES__XT, thm_2Einteger_2EINT__LT__MUL, thm_2Einteger_2EINT__LE__MONO, thm_2Ebool_2EMONO__COND, thm_2Earithmetic_2ELESS__IMP__LESS__OR__EQ, thm_2Eprim__rec_2ENOT__LESS__0, thm_2Earithmetic_2ESUB__MOD, thm_2Einteger_2EINT__MUL__ASSOC, thm_2Ebit_2EMOD__LEQ, thm_2Ewords_2EWORD__LOWER__EQ__REFL, thm_2Ewords_2EWORD__LESS__EQ__CASES, thm_2Earithmetic_2EWOP, thm_2Ewords_2EWORD__ADD__SUB3, thm_2Ealignment_2Ealigned__0, thm_2Ewords_2EWORD__BITS__SLICE__THM, thm_2Earithmetic_2ESUB__LESS__0, thm_2Einteger_2ENUM__POSINT__EXISTS, thm_2Ewords_2EWORD__LE__EQ__LS, thm_2Einteger__word_2Ew2i__def, thm_2EConseqConv_2ECOND__CLAUSES__TF, thm_2Einteger__word_2Eword__abs__w2i, thm_2Einteger_2ENUM__POSINT__EX, thm_2Ealignment_2Ealigned__imp, thm_2Einteger_2EINT__ABS__0LT, thm_2Einteger_2EINT__MUL__RZERO, thm_2Einteger_2EINT__ADD__RID, thm_2Einteger_2EINT__MOD__ADD__MULTIPLES, thm_2Ewords_2EWORD__LT__SUB__UPPER, thm_2Ewords_2EWORD__LESS__ANTISYM, thm_2Ewords_2EWORD__NEG__NEG, thm_2Einteger_2EINT__REM__NEG, thm_2Ewords_2En2w__sub__eq__0, thm_2Ebool_2ET__DEF, thm_2Eint__arith_2Ele__context__rwt5, thm_2Einteger_2EINT__LE__NEGR, thm_2Ewords_2Ew2w__id, thm_2Esat_2Edc__cond, thm_2Earithmetic_2EEQ__LESS__EQ, thm_2Ewords_2Eword__abs__word__abs, thm_2Ealignment_2Ealign__align, thm_2Ewords_2EWORD__LOWER__ANTISYM, thm_2Earithmetic_2EMOD__EQ__0__DIVISOR, thm_2EbasicSize_2Ebool__size__def, thm_2EConseqConv_2EAND__CLAUSES__FX, thm_2Earithmetic_2ELESS__DIV__EQ__ZERO, thm_2Egcd_2EIS__GCD__SYM, thm_2Einteger_2EINT__LT__CALCULATE, thm_2Ewords_2ENOT__INT__MIN__ZERO, thm_2Einteger_2EINT__LE__NEGTOTAL, thm_2Ewords_2EWORD__LS, thm_2Esat_2EAND__INV2, thm_2Earithmetic_2EMULT__COMM, thm_2Einteger_2EINT__LE__NEG, thm_2Ebool_2EF__DEF, thm_2Einteger_2EINT__POS__NZ, thm_2Earithmetic_2EMOD__SUB, thm_2Esat_2EOR__DUAL, thm_2Einteger_2EINT__REM__ID, thm_2Earithmetic_2EMOD__LESS__EQ, thm_2Einteger_2Eint__le, thm_2Ewhile_2EITERATION, thm_2Ewords_2EWORD__ADD__RID__UNIQ, thm_2Ewords_2Esw2sw__id, thm_2Ewords_2EWORD__EQ__SUB__RADD, thm_2Ebitstring_2Ebitstring__nchotomy, thm_2EConseqConv_2EOR__CLAUSES__XT, thm_2Earithmetic_2EMOD__TIMES2, thm_2Earithmetic_2EZERO__LESS__EQ, thm_2Ebool_2ECOND__RATOR, thm_2Earithmetic_2ENOT__LESS, thm_2Einteger_2EINT__MOD__BOUNDS, thm_2Einteger_2ELE__NUM__OF__INT, thm_2Einteger_2EINT__RDISTRIB, thm_2Earithmetic_2EEQ__MULT__LCANCEL, thm_2Earithmetic_2EDIV__LT__X, thm_2Earithmetic_2EMODEQ__0__CONG, thm_2Ealignment_2Ealigned__add__sub__cor, thm_2Ewords_2EWORD__MULT__COMM, thm_2Einteger_2EINT__LT__ADDL, thm_2Einteger_2EINT__REM, thm_2Eint__arith_2Elt__move__all__left, thm_2Einteger_2EINT__LET__ADD, thm_2Einteger_2EINT__ADD__RINV, thm_2Eint__arith_2Ele__context__rwt1, thm_2Einteger_2EINT__MOD__CALCULATE, thm_2Einteger_2EINT__SUB__LZERO, thm_2Ewords_2EWORD__SUB__SUB3, thm_2Einteger_2EINT__EQ__LMUL2, thm_2Ewords_2EWORD__NEG__EQ__0, thm_2Eint__arith_2Eeq__move__left__left, thm_2Ewords_2EWORD__0__POS, thm_2Einteger_2EINT__NUM__CASES, thm_2Ewords_2EWORD__LOWER__LOWER__EQ__TRANS, thm_2Ewords_2EWORD__ADD__LEFT__LS2, thm_2Einteger_2EINT__MUL__LZERO, thm_2Earithmetic_2ELESS__LESS__CASES, thm_2Einteger_2EINT__0, thm_2Earithmetic_2ELESS__EQ__LESS__TRANS, thm_2Ebool_2Ebool__case__ID, thm_2Einteger_2EINT__MOD__EQ0, thm_2Einteger_2EINT__ABS, thm_2Eint__arith_2Eeq__move__all__right, thm_2Einteger_2EINT__REM__COMMON__FACTOR, thm_2EConseqConv_2EOR__CLAUSES__XF, thm_2Einteger_2EINT__MOD__ID, thm_2Ewords_2EWORD__NEG__RMUL, thm_2Einteger_2EINT__LE__LT, thm_2EConseqConv_2Etrue__imp, thm_2Ewords_2EWORD__LESS__OR__EQ, thm_2Earithmetic_2ELESS__0__CASES, thm_2EConseqConv_2ENOT__CLAUSES__F, thm_2Earithmetic_2EMODEQ__MULT__CONG, thm_2Esat_2EEQF__Imp1, thm_2Einteger_2EINT__SUB__ADD, thm_2Einteger_2EINT__EQ__RADD, thm_2Earithmetic_2EMOD__LESS, thm_2Ewords_2EWORD__ADD__SUB, thm_2Einteger_2EINT__LET__TOTAL, thm_2Enumpair_2Encons__11, thm_2Einteger_2EINT__MUL__SIGN__CASES, thm_2Earithmetic_2EEQ__MULT__RCANCEL, thm_2Ebool_2EOR__CLAUSES, thm_2Einteger_2EINT__LTE__TOTAL, thm_2Eint__arith_2EINT__DIVIDES__LRMUL, thm_2Einteger_2EINT__LTE__ADD, thm_2Ewords_2Eword__msb__neg, thm_2Eprim__rec_2ENOT__LESS__EQ, thm_2Egcd_2EGCD__EQ__0, thm_2Einteger_2EINT__LT__NZ, thm_2Einteger__word_2EWORD__LTi, thm_2Ewords_2EWORD__BITS__EXTRACT, thm_2Earithmetic_2ELE__SUB__RCANCEL, thm_2Earithmetic_2EMODEQ__INTRO__CONG, thm_2Einteger_2EINT__SUB__LNEG, thm_2Ewords_2EWORD__SUB__LZERO, thm_2Earithmetic_2EMULT__EQ__0, thm_2Ewords_2EWORD__LO, thm_2Einteger_2EINT__MUL__QUOT, thm_2Einteger_2EINT__LT__ADDNEG, thm_2Einteger_2EINT__NEG__LMUL, thm_2Earithmetic_2EMOD__EQ__0, thm_2Earithmetic_2ELESS__MOD, thm_2Ewords_2EWORD__NOT__LOWER__EQ, thm_2EConseqConv_2ECOND__CLAUSES__TT, thm_2Einteger_2EINT__LT__TRANS, thm_2Einteger_2EINT__ABS__EQ, thm_2Einteger_2EINT__NEG__ADD, thm_2Einteger_2EINT__LT__REFL, thm_2Einteger_2EINT__LE__ANTISYM, thm_2Einteger__word_2EWORD__LEi, thm_2Ewords_2EWORD__LESS__EQUAL__ANTISYM, thm_2Eint__arith_2Eelim__eq__coeffs, thm_2Einteger__word_2Eword__add__i2w__w2n, thm_2Earithmetic_2ENUMERAL__DEF, thm_2Ewords_2EWORD__LESS__NEG__RIGHT, thm_2Ewords_2EWORD__ADD__EQ__SUB, thm_2Einteger__word_2Ew2i__lt__0, thm_2Eint__arith_2Egcdthm2, thm_2Einteger_2EINT__QUOT__UNIQUE, thm_2Ewords_2EWORD__ADD__LID__UNIQ, thm_2Eint__arith_2Ecan__get__small, thm_2EConseqConv_2EAND__CLAUSES__XT, thm_2Einteger_2EINT__ABS__LT0, thm_2Ewords_2EWORD__SUB__SUB, thm_2EConseqConv_2EOR__CLAUSES__TX, thm_2Eint__arith_2Eeq__context__rwt2, thm_2Ewords_2EWORD__SUB__RNEG, thm_2Earithmetic_2ESUB__LESS__EQ, thm_2Egcd_2EIS__GCD__MINUS__R, thm_2Ebool_2ECOND__EXPAND__IMP, thm_2Eint__arith_2Esubtract__to__small, thm_2Einteger_2EINT__LNEG__UNIQ, thm_2Eprim__rec_2ELESS__REFL, thm_2Einteger_2EINT__NEG__EQ0, thm_2Earithmetic_2ELT__SUB__LCANCEL, thm_2Ewords_2EWORD__SUB__ADD, thm_2Einteger_2EINT__LET__ANTISYM, thm_2Eint__arith_2Eeq__move__all__left, thm_2Ewords_2Ew2n__w2w__le, thm_2Einteger_2EINT__EQ__LMUL, thm_2Earithmetic_2EDIV__SUB, thm_2Ewords_2EWORD__RCANCEL__SUB, thm_2Einteger_2EINT__REM__EQ0, thm_2Earithmetic_2ELESS__EQ__ANTISYM, thm_2Ealignment_2Ealign__aligned, thm_2Ewords_2EWORD__ADD__0, thm_2EConseqConv_2EIMP__CLAUSES__FX, thm_2Einteger_2EINT__ADD__SYM, thm_2Ewords_2EWORD__BITS__ZERO, thm_2Eint__arith_2Etop__and__lessers, thm_2Ewords_2EWORD__SUB__SUB2, thm_2Einteger_2EINT__MOD__COMMON__FACTOR, thm_2Earithmetic_2ELE__SUB__LCANCEL, thm_2Einteger_2EINT__EQ__SUB__RADD, thm_2Einteger_2EINT__ADD__SUB, thm_2Ewords_2Eword__concat__0__0, thm_2Ebool_2EAND__CLAUSES, thm_2Einteger_2EINT__LT__ADDNEG2, thm_2Einteger_2EINT__DIVISION, thm_2Ecardinal_2ELT__CASES, thm_2Einteger_2EINT__ABS__LE, thm_2Einteger_2EINT__POASQ, thm_2Einteger_2EINT__EQ__SUB__LADD, thm_2Earithmetic_2ELESS__EQUAL__DIFF, thm_2Einteger_2EINT__LTE__ANTSYM, thm_2Eint__arith_2Ele__context__rwt2, thm_2Einteger_2EINT__LE__ADD, thm_2Ewords_2EWORD__NOT__LOWER__EQUAL, thm_2Ewords_2Ebit__count__is__zero, thm_2Earithmetic_2EMOD__TIMES__SUB, thm_2Eint__arith_2Eelim__lt__coeffs1, thm_2Eint__arith_2Ecan__get__big, thm_2Einteger_2EINT__ABS__EQ0, thm_2Ewords_2EWORD__LE__LS, thm_2Esat_2EOR__DUAL2, thm_2Einteger__word_2Ew2i__w2n__pos, thm_2Ewords_2EWORD__LOWER__EQ__ANTISYM, logicdef_2E_2F_5C, thm_2Ewords_2EWORD__MSB__INT__MIN__LS, thm_2Einteger_2EINT__EXP__MULTIPLY__EXPONENTS, thm_2Einteger__word_2Ei2w__def, thm_2Egcd_2EIS__GCD__0R, thm_2Esat_2EEQT__Imp1, thm_2Ewords_2EWORD__SUB__ADD2, thm_2Einteger_2EINT__ABS__QUOT, thm_2Ewords_2EWORD__RIGHT__ADD__DISTRIB, thm_2Ewords_2EWORD__LESS__NOT__EQ, thm_2Ewords_2EWORD__LESS__EQ__ANTISYM, thm_2Einteger_2EINT__SUB__SUB, thm_2Einteger_2EINT__EXP__MOD, thm_2Ewords_2Ew2n__eq__0, thm_2Earithmetic_2ELESS__MONO__MULT, thm_2Earithmetic_2ECANCEL__SUB, thm_2ETemporal__Logic_2EWELL__ORDER__UNIQUE, thm_2Earithmetic_2EMULT__EQ__DIV, thm_2Earithmetic_2EZERO__MOD, thm_2Earithmetic_2EMULT__DIV, thm_2Earithmetic_2ELEFT__SUB__DISTRIB, thm_2EConseqConv_2ECOND__CLAUSES__CF, thm_2Einteger_2EINT__DIV__NEG, thm_2Einteger_2EINT__EQ__LADD, thm_2Earithmetic_2ELESS__MULT2, thm_2Earithmetic_2EMOD__COMMON__FACTOR, thm_2Eint__arith_2EINT__NUM__FORALL, thm_2Einteger_2EINT__QUOT__CALCULATE, thm_2Ewords_2Eword__bit__0, thm_2Einteger_2EINT__LT__SUB__RADD, thm_2Egcd_2ELCM__LE, thm_2Egcd_2EGCD__0L, thm_2Ewords_2EWORD__NEG__0, thm_2Einteger_2EINT__SUB__RZERO, thm_2Earithmetic_2EZERO__DIV, thm_2Einteger_2ENUM__OF__INT, thm_2Ewords_2EWORD__LT, thm_2Eint__arith_2Ejustify__divides3, thm_2Einteger_2EINT__DIV__0, thm_2Ebool_2Ebool__case__thm, thm_2Einteger_2EINT__LT, thm_2Ewords_2EWORD__SUB__RZERO, thm_2Egcd_2EGCD__REF, thm_2Enumpair_2Enlist__ind, thm_2Eint__arith_2Ein__additive__range, thm_2Einteger_2EINT__DIV__P, thm_2Einteger_2EINT__EQ__RMUL, thm_2Eint__arith_2Elt__move__left__right, thm_2Einteger_2EINT__REM0, thm_2Egcd_2EIS__GCD__0L, thm_2Esptree_2Espt__acc__0, thm_2Earithmetic_2ELESS__CASES__IMP, thm_2Ebool_2EBOOL__EQ__DISTINCT, thm_2Einteger_2EINT__NEG__GT0, thm_2Ewords_2EZERO__LO__INT__MIN, thm_2Ewords_2EWORD__SUM__ZERO, thm_2Ealignment_2Ealigned__align, thm_2Einteger_2EINT__LET__TRANS, thm_2Einteger_2EINT__MUL__CALCULATE, thm_2Einteger_2EINT__SUB__ADD2, thm_2Esat_2EAND__INV, thm_2EConseqConv_2EIMP__CONG__cond, thm_2Einteger_2EINT__MOD, thm_2Einteger_2EINT__MOD__FORALL__P, thm_2Einteger_2EINT__DIV__CALCULATE, thm_2Earithmetic_2ELT__MULT__RCANCEL, thm_2Ewords_2EWORD__SUB__NEG, thm_2Ewords_2EWORD__L__NEG, thm_2Einteger__word_2Ew2i__11, thm_2Einteger_2Eint__rem, thm_2Einteger_2EINT__DIFFSQ, thm_2Einteger_2Eint__quot, thm_2Ewords_2EWORD__SLICE__ZERO, thm_2Ewords_2EWORD__NOT__LOWER, thm_2Einteger_2EINT__LT__ADD__SUB
% 28.76/7.88  % No. of inferences in proof: 1445
% 28.76/7.88  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 7342 ms resp. 5780 ms w/o parsing
% 29.70/8.13  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 29.70/8.14  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------