Leo-III---1.8.0.THM-Ref.s

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : ITP015_7 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39

% Computer : n010.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 07:35:39 AM UTC 2026

% Result   : Theorem 33.46s 11.10s
% Output   : Refutation 33.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :  264
% Syntax   : Number of formulae    :  626 ( 404 unt;   0 typ;   2 def)
%            Number of atoms       : 1177 (1176 equ;   0 cnn)
%            Maximal formula atoms :   20 (   1 avg)
%            Number of connectives : 5854 ( 176   ~;  78   |; 183   &;5129   @)
%                                         (  62 <=>; 226  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   4 avg)
%            Number of types       :   13 (  13 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   57 (  55 usr;   5 con; 0-5 aty)
%            Number of variables   : 1464 (   2   ^;1438   !;  22   ?;1464   :)
%                                         (   0  !>;   0  ?*;   0  @-;   2  @+)

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_2Enum_2E0_2E0_decl,type,
    c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).

thf(c_2Earithmetic_2EDIV_2E2_decl,type,
    c_2Earithmetic_2EDIV_2E2: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Earithmetic_2EMOD_2E2_decl,type,
    c_2Earithmetic_2EMOD_2E2: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Earithmetic_2ENUMERAL_2E1_decl,type,
    c_2Earithmetic_2ENUMERAL_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2EbasicSize_2Ebool__size_2E1_decl,type,
    c_2EbasicSize_2Ebool__size_2E1: tyop_2Emin_2Ebool > tyop_2Enum_2Enum ).

thf(c_2EbasicSize_2Eone__size_2E1_decl,type,
    c_2EbasicSize_2Eone__size_2E1: tyop_2Eone_2Eone > tyop_2Enum_2Enum ).

thf(c_2Egcd_2Elcm_2E2_decl,type,
    c_2Egcd_2Elcm_2E2: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Enumpair_2Encons_2E2_decl,type,
    c_2Enumpair_2Encons_2E2: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Ebag_2EEMPTY__BAG_2E1_decl,type,
    c_2Ebag_2EEMPTY__BAG_2E1: 
      !>[TA: $tType] : ( TA > tyop_2Enum_2Enum ) ).

thf(c_2Estring_2Echar__size_2E1_decl,type,
    c_2Estring_2Echar__size_2E1: tyop_2Estring_2Echar > tyop_2Enum_2Enum ).

thf(c_2EternaryComparisons_2Eordering__size_2E1_decl,type,
    c_2EternaryComparisons_2Eordering__size_2E1: tyop_2EternaryComparisons_2Eordering > tyop_2Enum_2Enum ).

thf(c_2Einteger_2EABS_2E1_decl,type,
    c_2Einteger_2EABS_2E1: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).

thf(c_2Einteger_2ENum_2E1_decl,type,
    c_2Einteger_2ENum_2E1: tyop_2Einteger_2Eint > tyop_2Enum_2Enum ).

thf(c_2Einteger_2Eint__0_2E0_decl,type,
    c_2Einteger_2Eint__0_2E0: tyop_2Einteger_2Eint ).

thf(c_2Einteger_2Eint__add_2E2_decl,type,
    c_2Einteger_2Eint__add_2E2: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).

thf(c_2Einteger_2Eint__div_2E2_decl,type,
    c_2Einteger_2Eint__div_2E2: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).

thf(c_2Einteger_2Eint__exp_2E2_decl,type,
    c_2Einteger_2Eint__exp_2E2: tyop_2Einteger_2Eint > tyop_2Enum_2Enum > tyop_2Einteger_2Eint ).

thf(c_2Einteger_2Eint__le_2E2_decl,type,
    c_2Einteger_2Eint__le_2E2: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Emin_2Ebool ).

thf(c_2Einteger_2Eint__lt_2E2_decl,type,
    c_2Einteger_2Eint__lt_2E2: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Emin_2Ebool ).

thf(c_2Einteger_2Eint__mod_2E2_decl,type,
    c_2Einteger_2Eint__mod_2E2: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).

thf(c_2Einteger_2Eint__mul_2E2_decl,type,
    c_2Einteger_2Eint__mul_2E2: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).

thf(c_2Einteger_2Eint__neg_2E1_decl,type,
    c_2Einteger_2Eint__neg_2E1: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).

thf(c_2Einteger_2Eint__of__num_2E1_decl,type,
    c_2Einteger_2Eint__of__num_2E1: tyop_2Enum_2Enum > tyop_2Einteger_2Eint ).

thf(c_2Einteger_2Eint__quot_2E2_decl,type,
    c_2Einteger_2Eint__quot_2E2: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).

thf(c_2Einteger_2Eint__rem_2E2_decl,type,
    c_2Einteger_2Eint__rem_2E2: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).

thf(c_2Einteger_2Eint__sub_2E2_decl,type,
    c_2Einteger_2Eint__sub_2E2: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).

thf(c_2Ewords_2Ebit__count_2E1_decl,type,
    c_2Ewords_2Ebit__count_2E1: 
      !>[TA: $tType] : ( ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > tyop_2Enum_2Enum ) ).

thf(c_2Ewords_2Ebit__count__upto_2E2_decl,type,
    c_2Ewords_2Ebit__count__upto_2E2: 
      !>[TA: $tType] : ( tyop_2Enum_2Enum > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > tyop_2Enum_2Enum ) ).

thf(c_2Ewords_2En2w_2E1_decl,type,
    c_2Ewords_2En2w_2E1: 
      !>[TA: $tType] : ( tyop_2Enum_2Enum > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) ) ).

thf(c_2Ewords_2Esw2sw_2E1_decl,type,
    c_2Ewords_2Esw2sw_2E1: 
      !>[TA: $tType,TB: $tType] : ( ( TB @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) ) ).

thf(c_2Ewords_2Ew2n_2E1_decl,type,
    c_2Ewords_2Ew2n_2E1: 
      !>[TA: $tType] : ( ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > tyop_2Enum_2Enum ) ).

thf(c_2Ewords_2Ew2w_2E1_decl,type,
    c_2Ewords_2Ew2w_2E1: 
      !>[TA: $tType,TB: $tType] : ( ( TB @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) ) ).

thf(c_2Ewords_2Eword__2comp_2E1_decl,type,
    c_2Ewords_2Eword__2comp_2E1: 
      !>[TA: $tType] : ( ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) ) ).

thf(c_2Ewords_2Eword__L_2E0_decl,type,
    c_2Ewords_2Eword__L_2E0: 
      !>[TA: $tType] : ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) ).

thf(c_2Ewords_2Eword__abs_2E1_decl,type,
    c_2Ewords_2Eword__abs_2E1: 
      !>[TA: $tType] : ( ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) ) ).

thf(c_2Ewords_2Eword__add_2E2_decl,type,
    c_2Ewords_2Eword__add_2E2: 
      !>[TA: $tType] : ( ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) ) ).

thf(c_2Ewords_2Eword__bits_2E3_decl,type,
    c_2Ewords_2Eword__bits_2E3: 
      !>[TA: $tType] : ( tyop_2Enum_2Enum > tyop_2Enum_2Enum > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) ) ).

thf(c_2Ewords_2Eword__concat_2E2_decl,type,
    c_2Ewords_2Eword__concat_2E2: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > ( TB @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) ) ).

thf(c_2Ewords_2Eword__extract_2E3_decl,type,
    c_2Ewords_2Eword__extract_2E3: 
      !>[TA: $tType,TB: $tType] : ( tyop_2Enum_2Enum > tyop_2Enum_2Enum > ( TB @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) ) ).

thf(c_2Ewords_2Eword__mul_2E2_decl,type,
    c_2Ewords_2Eword__mul_2E2: 
      !>[TA: $tType] : ( ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) ) ).

thf(c_2Ewords_2Eword__reverse_2E1_decl,type,
    c_2Ewords_2Eword__reverse_2E1: 
      !>[TA: $tType] : ( ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) ) ).

thf(c_2Ewords_2Eword__slice_2E3_decl,type,
    c_2Ewords_2Eword__slice_2E3: 
      !>[TA: $tType] : ( tyop_2Enum_2Enum > tyop_2Enum_2Enum > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) ) ).

thf(c_2Ewords_2Eword__sub_2E2_decl,type,
    c_2Ewords_2Eword__sub_2E2: 
      !>[TA: $tType] : ( ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) ) ).

thf(c_2Ealignment_2Ealign_2E2_decl,type,
    c_2Ealignment_2Ealign_2E2: 
      !>[TA: $tType] : ( tyop_2Enum_2Enum > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) ) ).

thf(c_2Ebitstring_2Eshiftr_2E2_decl,type,
    c_2Ebitstring_2Eshiftr_2E2: ( tyop_2Emin_2Ebool @ tyop_2Elist_2Elist ) > tyop_2Enum_2Enum > ( tyop_2Emin_2Ebool @ tyop_2Elist_2Elist ) ).

thf(c_2Ebitstring_2Ev2w_2E1_decl,type,
    c_2Ebitstring_2Ev2w_2E1: 
      !>[TA: $tType] : ( ( tyop_2Emin_2Ebool @ tyop_2Elist_2Elist ) > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) ) ).

thf(c_2Esptree_2Espt__acc_2E2_decl,type,
    c_2Esptree_2Espt__acc_2E2: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Einteger__word_2Ei2w_2E1_decl,type,
    c_2Einteger__word_2Ei2w_2E1: 
      !>[TA: $tType] : ( tyop_2Einteger_2Eint > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) ) ).

thf(c_2Einteger__word_2Ew2i_2E1_decl,type,
    c_2Einteger__word_2Ew2i_2E1: 
      !>[TA: $tType] : ( ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > tyop_2Einteger_2Eint ) ).

thf(c_2Einteger__word_2Eword__sdiv_2E2_decl,type,
    c_2Einteger__word_2Eword__sdiv_2E2: 
      !>[TA: $tType] : ( ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) ) ).

thf(c_2Einteger__word_2Eword__smod_2E2_decl,type,
    c_2Einteger__word_2Eword__smod_2E2: 
      !>[TA: $tType] : ( ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) > ( TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) ) ) ).

thf(sk13_decl,type,
    sk13: tyop_2Einteger_2Eint > tyop_2Enum_2Enum ).

thf(sk14_decl,type,
    sk14: tyop_2Einteger_2Eint > tyop_2Enum_2Enum ).

thf(sk13_def,definition,
    ( sk13
    = ( ^ [A: tyop_2Einteger_2Eint] :
        @+[B: tyop_2Enum_2Enum] :
          ( ( B != c_2Enum_2E0_2E0 )
          & ( A
            = ( B @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ) ) ).

thf(sk14_def,definition,
    ( sk14
    = ( ^ [A: tyop_2Einteger_2Eint] :
        @+[B: tyop_2Enum_2Enum] :
          ( ( B != c_2Enum_2E0_2E0 )
          & ( A
            = ( B @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 ) ) ) ) ) ).

thf(149,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( TA @ c_2Ewords_2Ew2n_2E1 ) @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ ( TA @ c_2Ewords_2Ew2n_2E1 ) @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__mul_2E2 ) @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) )
      = ( B @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__mul__i2w__w2n) ).

thf(892,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( TA @ c_2Ewords_2Ew2n_2E1 ) @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ ( TA @ c_2Ewords_2Ew2n_2E1 ) @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__mul_2E2 ) @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) )
      = ( B @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(226,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__RID) ).

thf(1322,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(1,conjecture,
    ! [TA: $tType] :
      ( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) )
      = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger__word_2Ei2w__0) ).

thf(2,negated_conjecture,
    ~ ! [TA: $tType] :
        ( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) )
        = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(264,plain,
    ~ ! [TA: $tType] :
        ( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) )
        = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(265,plain,
    ( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( skt1 @ c_2Einteger__word_2Ei2w_2E1 ) )
   != ( c_2Enum_2E0_2E0 @ ( skt1 @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(cnf,[status(esa)],[264]) ).

thf(266,plain,
    ( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( skt1 @ c_2Einteger__word_2Ei2w_2E1 ) )
   != ( c_2Enum_2E0_2E0 @ ( skt1 @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(lifteq,[status(thm)],[265]) ).

thf(203,axiom,
    ( c_2Einteger_2Eint__0_2E0
    = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__0) ).

thf(1176,plain,
    ( c_2Einteger_2Eint__0_2E0
    = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(1177,plain,
    ( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 )
    = c_2Einteger_2Eint__0_2E0 ),
    inference(lifteq,[status(thm)],[1176]) ).

thf(1501,plain,
    ( ( c_2Einteger_2Eint__0_2E0 @ ( skt1 @ c_2Einteger__word_2Ei2w_2E1 ) )
   != ( c_2Enum_2E0_2E0 @ ( skt1 @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(rewrite,[status(thm)],[266,1177]) ).

thf(201,axiom,
    ! [TA: $tType] :
      ( ( TA @ c_2Ewords_2Eword__L_2E0 )
     != ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2ENOT__INT__MIN__ZERO) ).

thf(1166,plain,
    ! [TA: $tType] :
      ( ( TA @ c_2Ewords_2Eword__L_2E0 )
     != ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(1167,plain,
    ! [TA: $tType] :
      ( ( TA @ c_2Ewords_2Eword__L_2E0 )
     != ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(cnf,[status(esa)],[1166]) ).

thf(1168,plain,
    ! [TA: $tType] :
      ( ( TA @ c_2Ewords_2Eword__L_2E0 )
     != ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(lifteq,[status(thm)],[1167]) ).

thf(227,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( ( A @ c_2Einteger_2EABS_2E1 )
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
    <=> ( A
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__EQ0) ).

thf(1325,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( ( A
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
       => ( ( A @ c_2Einteger_2EABS_2E1 )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
      & ( ( ( A @ c_2Einteger_2EABS_2E1 )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
       => ( A
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(1326,plain,
    ( ! [A: tyop_2Einteger_2Eint] :
        ( ( A
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
       => ( ( A @ c_2Einteger_2EABS_2E1 )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
    & ! [A: tyop_2Einteger_2Eint] :
        ( ( ( A @ c_2Einteger_2EABS_2E1 )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
       => ( A
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ),
    inference(miniscope,[status(thm)],[1325]) ).

thf(1327,plain,
    ! [B: tyop_2Einteger_2Eint,A: tyop_2Einteger_2Eint] :
      ( ( ( ( B @ c_2Einteger_2EABS_2E1 )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
        | ( B
         != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
      & ( ( A
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
        | ( ( A @ c_2Einteger_2EABS_2E1 )
         != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ),
    inference(cnf,[status(esa)],[1326]) ).

thf(1329,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( ( A @ c_2Einteger_2EABS_2E1 )
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
      | ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    inference(cnfConj,[status(thm)],[1327]) ).

thf(1331,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( ( A @ c_2Einteger_2EABS_2E1 )
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
      | ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    inference(lifteq,[status(thm)],[1329]) ).

thf(1332,plain,
    ( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2EABS_2E1 )
    = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ),
    inference(simp,[status(thm)],[1331]) ).

thf(1559,plain,
    ( ( c_2Einteger_2Eint__0_2E0 @ c_2Einteger_2EABS_2E1 )
    = c_2Einteger_2Eint__0_2E0 ),
    inference(rewrite,[status(thm)],[1332,1177]) ).

thf(25,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__le_2E2 ) )
      = ( C @ ( B @ c_2Einteger_2Eint__le_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__LADD) ).

thf(333,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__le_2E2 ) )
      = ( C @ ( B @ c_2Einteger_2Eint__le_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(73,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( A @ ( B @ c_2Einteger_2Eint__add_2E2 ) @ ( C @ c_2Einteger_2Eint__mul_2E2 ) )
      = ( A @ ( C @ c_2Einteger_2Eint__mul_2E2 ) @ ( B @ ( C @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__add_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LDISTRIB) ).

thf(518,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( A @ ( B @ c_2Einteger_2Eint__add_2E2 ) @ ( C @ c_2Einteger_2Eint__mul_2E2 ) )
      = ( A @ ( C @ c_2Einteger_2Eint__mul_2E2 ) @ ( B @ ( C @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__add_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(66,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( TA @ c_2Ewords_2Ew2n_2E1 ) @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ ( TA @ c_2Ewords_2Ew2n_2E1 ) @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__add_2E2 ) @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) )
      = ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__add__i2w__w2n) ).

thf(468,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( TA @ c_2Ewords_2Ew2n_2E1 ) @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ ( TA @ c_2Ewords_2Ew2n_2E1 ) @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__add_2E2 ) @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) )
      = ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(69,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__neg_2E1 )
      = ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__add_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__ADD) ).

thf(481,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__neg_2E1 )
      = ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__add_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(235,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__mul_2E2 ) )
      = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__LZERO) ).

thf(1369,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__mul_2E2 ) )
      = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(206,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Enum_2E0_2E0 @ ( A @ c_2Egcd_2Elcm_2E2 ) )
        = c_2Enum_2E0_2E0 )
      & ( ( A @ ( c_2Enum_2E0_2E0 @ c_2Egcd_2Elcm_2E2 ) )
        = c_2Enum_2E0_2E0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Egcd_2ELCM__0) ).

thf(1185,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( ( c_2Enum_2E0_2E0 @ ( A @ c_2Egcd_2Elcm_2E2 ) )
        = c_2Enum_2E0_2E0 )
      & ( ( A @ ( c_2Enum_2E0_2E0 @ c_2Egcd_2Elcm_2E2 ) )
        = c_2Enum_2E0_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(1186,plain,
    ( ! [A: tyop_2Enum_2Enum] :
        ( ( c_2Enum_2E0_2E0 @ ( A @ c_2Egcd_2Elcm_2E2 ) )
        = c_2Enum_2E0_2E0 )
    & ! [A: tyop_2Enum_2Enum] :
        ( ( A @ ( c_2Enum_2E0_2E0 @ c_2Egcd_2Elcm_2E2 ) )
        = c_2Enum_2E0_2E0 ) ),
    inference(miniscope,[status(thm)],[1185]) ).

thf(1187,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( c_2Enum_2E0_2E0 @ ( B @ c_2Egcd_2Elcm_2E2 ) )
        = c_2Enum_2E0_2E0 )
      & ( ( A @ ( c_2Enum_2E0_2E0 @ c_2Egcd_2Elcm_2E2 ) )
        = c_2Enum_2E0_2E0 ) ),
    inference(cnf,[status(esa)],[1186]) ).

thf(1188,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( A @ ( c_2Enum_2E0_2E0 @ c_2Egcd_2Elcm_2E2 ) )
      = c_2Enum_2E0_2E0 ),
    inference(cnfConj,[status(thm)],[1187]) ).

thf(1190,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( A @ ( c_2Enum_2E0_2E0 @ c_2Egcd_2Elcm_2E2 ) )
      = c_2Enum_2E0_2E0 ),
    inference(lifteq,[status(thm)],[1188]) ).

thf(50,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( B != c_2Enum_2E0_2E0 )
     => ( ( B @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__div_2E2 ) )
        = ( B @ ( A @ c_2Earithmetic_2EDIV_2E2 ) @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIV) ).

thf(408,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( B != c_2Enum_2E0_2E0 )
     => ( ( B @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__div_2E2 ) )
        = ( B @ ( A @ c_2Earithmetic_2EDIV_2E2 ) @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(6,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
      = ( B @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__RMUL) ).

thf(276,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
      = ( B @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(165,axiom,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( A @ ( TA @ c_2Ealignment_2Ealign_2E2 ) ) @ ( A @ ( TA @ c_2Ealignment_2Ealign_2E2 ) ) )
      = ( B @ ( A @ ( TA @ c_2Ealignment_2Ealign_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ealignment_2Ealign__align) ).

thf(994,plain,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( A @ ( TA @ c_2Ealignment_2Ealign_2E2 ) ) @ ( A @ ( TA @ c_2Ealignment_2Ealign_2E2 ) ) )
      = ( B @ ( A @ ( TA @ c_2Ealignment_2Ealign_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(241,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TB @ ( TA @ c_2Ewords_2Ew2w_2E1 ) ) )
      = ( c_2Enum_2E0_2E0 @ ( TB @ c_2Ewords_2En2w_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2Ew2w__0) ).

thf(1399,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TB @ ( TA @ c_2Ewords_2Ew2w_2E1 ) ) )
      = ( c_2Enum_2E0_2E0 @ ( TB @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(1400,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( c_2Enum_2E0_2E0 @ ( TB @ c_2Ewords_2En2w_2E1 ) @ ( TA @ ( TB @ c_2Ewords_2Ew2w_2E1 ) ) )
      = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(cnf,[status(esa)],[1399]) ).

thf(1401,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( c_2Enum_2E0_2E0 @ ( TB @ c_2Ewords_2En2w_2E1 ) @ ( TA @ ( TB @ c_2Ewords_2Ew2w_2E1 ) ) )
      = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(lifteq,[status(thm)],[1400]) ).

thf(245,axiom,
    ! [A: tyop_2Estring_2Echar] :
      ( ( A @ c_2Estring_2Echar__size_2E1 )
      = c_2Enum_2E0_2E0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Estring_2Echar__size__def) ).

thf(1420,plain,
    ! [A: tyop_2Estring_2Echar] :
      ( ( A @ c_2Estring_2Echar__size_2E1 )
      = c_2Enum_2E0_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(1421,plain,
    ! [A: tyop_2Estring_2Echar] :
      ( ( A @ c_2Estring_2Echar__size_2E1 )
      = c_2Enum_2E0_2E0 ),
    inference(cnf,[status(esa)],[1420]) ).

thf(1422,plain,
    ! [A: tyop_2Estring_2Echar] :
      ( ( A @ c_2Estring_2Echar__size_2E1 )
      = c_2Enum_2E0_2E0 ),
    inference(lifteq,[status(thm)],[1421]) ).

thf(3,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( TA @ c_2Ewords_2Eword__abs_2E1 ) )
      = ( A @ ( TA @ c_2Ewords_2Eword__abs_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2Eword__abs__neg) ).

thf(267,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( TA @ c_2Ewords_2Eword__abs_2E1 ) )
      = ( A @ ( TA @ c_2Ewords_2Eword__abs_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(268,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( TA @ c_2Ewords_2Eword__abs_2E1 ) )
      = ( A @ ( TA @ c_2Ewords_2Eword__abs_2E1 ) ) ),
    inference(cnf,[status(esa)],[267]) ).

thf(269,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( TA @ c_2Ewords_2Eword__abs_2E1 ) )
      = ( A @ ( TA @ c_2Ewords_2Eword__abs_2E1 ) ) ),
    inference(lifteq,[status(thm)],[268]) ).

thf(146,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ! [B: tyop_2Einteger_2Eint] :
          ( ( ( A @ ( B @ c_2Einteger_2Eint__rem_2E2 ) )
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
        <=> ? [C: tyop_2Einteger_2Eint] :
              ( B
              = ( A @ ( C @ c_2Einteger_2Eint__mul_2E2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__REM__EQ0) ).

thf(878,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ! [B: tyop_2Einteger_2Eint] :
          ( ( ? [C: tyop_2Einteger_2Eint] :
                ( B
                = ( A @ ( C @ c_2Einteger_2Eint__mul_2E2 ) ) )
           => ( ( A @ ( B @ c_2Einteger_2Eint__rem_2E2 ) )
              = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
          & ( ( ( A @ ( B @ c_2Einteger_2Eint__rem_2E2 ) )
              = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
           => ? [C: tyop_2Einteger_2Eint] :
                ( B
                = ( A @ ( C @ c_2Einteger_2Eint__mul_2E2 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(57,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( A @ ( A @ ( B @ c_2Einteger_2Eint__mod_2E2 ) @ ( A @ ( C @ c_2Einteger_2Eint__mod_2E2 ) @ c_2Einteger_2Eint__sub_2E2 ) @ c_2Einteger_2Eint__mod_2E2 ) )
        = ( A @ ( B @ ( C @ c_2Einteger_2Eint__sub_2E2 ) @ c_2Einteger_2Eint__mod_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__SUB) ).

thf(440,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( A @ ( A @ ( B @ c_2Einteger_2Eint__mod_2E2 ) @ ( A @ ( C @ c_2Einteger_2Eint__mod_2E2 ) @ c_2Einteger_2Eint__sub_2E2 ) @ c_2Einteger_2Eint__mod_2E2 ) )
        = ( A @ ( B @ ( C @ c_2Einteger_2Eint__sub_2E2 ) @ c_2Einteger_2Eint__mod_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(247,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2ENum_2E1 )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2ENUM__OF__INT) ).

thf(1426,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2ENum_2E1 )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(42,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( C @ ( B @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) )
      = ( A @ ( C @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) @ ( A @ ( B @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__RIGHT__SUB__DISTRIB) ).

thf(384,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( C @ ( B @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) )
      = ( A @ ( C @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) @ ( A @ ( B @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(195,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
      | ? [B: tyop_2Enum_2Enum] :
          ( ( B != c_2Enum_2E0_2E0 )
          & ( A
            = ( B @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 ) ) )
      | ? [B: tyop_2Enum_2Enum] :
          ( ( B != c_2Enum_2E0_2E0 )
          & ( A
            = ( B @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NUM__CASES) ).

thf(1137,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
      | ? [B: tyop_2Enum_2Enum] :
          ( ( B != c_2Enum_2E0_2E0 )
          & ( A
            = ( B @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 ) ) )
      | ? [B: tyop_2Enum_2Enum] :
          ( ( B != c_2Enum_2E0_2E0 )
          & ( A
            = ( B @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(78,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__neg_2E1 )
      = ( B @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__mul_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__LMUL) ).

thf(533,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__neg_2E1 )
      = ( B @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__mul_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(130,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
        = ( C @ ( A @ c_2Einteger_2Eint__add_2E2 ) ) )
    <=> ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__LADD) ).

thf(797,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( B = C )
       => ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
          = ( C @ ( A @ c_2Einteger_2Eint__add_2E2 ) ) ) )
      & ( ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
          = ( C @ ( A @ c_2Einteger_2Eint__add_2E2 ) ) )
       => ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(133,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( B @ ( B @ c_2Einteger_2Eint__mul_2E2 ) @ ( A @ ( A @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__add_2E2 ) )
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
    <=> ( ( B
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
        & ( A
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUMSQ) ).

thf(814,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( ( B
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
          & ( A
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
       => ( ( B @ ( B @ c_2Einteger_2Eint__mul_2E2 ) @ ( A @ ( A @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__add_2E2 ) )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
      & ( ( ( B @ ( B @ c_2Einteger_2Eint__mul_2E2 ) @ ( A @ ( A @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__add_2E2 ) )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
       => ( ( B
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
          & ( A
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(119,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
    <=> ( A
        = ( B @ c_2Einteger_2Eint__neg_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LNEG__UNIQ) ).

thf(747,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( A
          = ( B @ c_2Einteger_2Eint__neg_2E1 ) )
       => ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
      & ( ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
       => ( A
          = ( B @ c_2Einteger_2Eint__neg_2E1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(72,axiom,
    ( ! [A: tyop_2Einteger_2Eint] :
        ( ( ( A @ c_2Einteger_2Eint__neg_2E1 )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
      <=> ( A
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
    & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( ( A @ c_2Einteger_2Eint__of__num_2E1 )
          = ( B @ c_2Einteger_2Eint__of__num_2E1 ) )
      <=> ( A = B ) )
    & ! [A: tyop_2Einteger_2Eint] :
        ( ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__neg_2E1 )
        = A )
    & ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
        ( ( B
         != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
       => ( ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__rem_2E2 ) )
            = ( B @ ( A @ c_2Einteger_2Eint__rem_2E2 ) ) )
          & ( ( B @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__rem_2E2 ) )
            = ( B @ ( A @ c_2Einteger_2Eint__rem_2E2 ) @ c_2Einteger_2Eint__neg_2E1 ) ) ) )
    & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( B != c_2Enum_2E0_2E0 )
       => ( ( B @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__rem_2E2 ) )
          = ( B @ ( A @ c_2Earithmetic_2EMOD_2E2 ) @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__REM__CALCULATE) ).

thf(490,plain,
    ( ! [A: tyop_2Einteger_2Eint] :
        ( ( ( A
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
         => ( ( A @ c_2Einteger_2Eint__neg_2E1 )
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
        & ( ( ( A @ c_2Einteger_2Eint__neg_2E1 )
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
         => ( A
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ) )
    & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( ( A = B )
         => ( ( A @ c_2Einteger_2Eint__of__num_2E1 )
            = ( B @ c_2Einteger_2Eint__of__num_2E1 ) ) )
        & ( ( ( A @ c_2Einteger_2Eint__of__num_2E1 )
            = ( B @ c_2Einteger_2Eint__of__num_2E1 ) )
         => ( A = B ) ) )
    & ! [A: tyop_2Einteger_2Eint] :
        ( ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__neg_2E1 )
        = A )
    & ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
        ( ( B
         != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
       => ( ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__rem_2E2 ) )
            = ( B @ ( A @ c_2Einteger_2Eint__rem_2E2 ) ) )
          & ( ( B @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__rem_2E2 ) )
            = ( B @ ( A @ c_2Einteger_2Eint__rem_2E2 ) @ c_2Einteger_2Eint__neg_2E1 ) ) ) )
    & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( B != c_2Enum_2E0_2E0 )
       => ( ( B @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__rem_2E2 ) )
          = ( B @ ( A @ c_2Earithmetic_2EMOD_2E2 ) @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(491,plain,
    ( ! [A: tyop_2Einteger_2Eint] :
        ( ( A
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
       => ( ( A @ c_2Einteger_2Eint__neg_2E1 )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
    & ! [A: tyop_2Einteger_2Eint] :
        ( ( ( A @ c_2Einteger_2Eint__neg_2E1 )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
       => ( A
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
    & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( A = B )
       => ( ( A @ c_2Einteger_2Eint__of__num_2E1 )
          = ( B @ c_2Einteger_2Eint__of__num_2E1 ) ) )
    & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( ( A @ c_2Einteger_2Eint__of__num_2E1 )
          = ( B @ c_2Einteger_2Eint__of__num_2E1 ) )
       => ( A = B ) )
    & ! [A: tyop_2Einteger_2Eint] :
        ( ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__neg_2E1 )
        = A )
    & ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
        ( ( B
         != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
       => ( ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__rem_2E2 ) )
            = ( B @ ( A @ c_2Einteger_2Eint__rem_2E2 ) ) )
          & ( ( B @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__rem_2E2 ) )
            = ( B @ ( A @ c_2Einteger_2Eint__rem_2E2 ) @ c_2Einteger_2Eint__neg_2E1 ) ) ) )
    & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( B != c_2Enum_2E0_2E0 )
       => ( ( B @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__rem_2E2 ) )
          = ( B @ ( A @ c_2Earithmetic_2EMOD_2E2 ) @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ),
    inference(miniscope,[status(thm)],[490]) ).

thf(492,plain,
    ! [K: tyop_2Einteger_2Eint,J: tyop_2Einteger_2Eint,I: tyop_2Enum_2Enum,H: tyop_2Enum_2Enum,G: tyop_2Enum_2Enum,F: tyop_2Enum_2Enum,E: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( ( ( K @ c_2Einteger_2Eint__neg_2E1 )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
        | ( K
         != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
      & ( ( J
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
        | ( ( J @ c_2Einteger_2Eint__neg_2E1 )
         != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
      & ( ( ( H @ c_2Einteger_2Eint__of__num_2E1 )
          = ( I @ c_2Einteger_2Eint__of__num_2E1 ) )
        | ( H != I ) )
      & ( ( F = G )
        | ( ( F @ c_2Einteger_2Eint__of__num_2E1 )
         != ( G @ c_2Einteger_2Eint__of__num_2E1 ) ) )
      & ( ( E @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__neg_2E1 )
        = E )
      & ( ( ( D @ c_2Einteger_2Eint__neg_2E1 @ ( C @ c_2Einteger_2Eint__rem_2E2 ) )
          = ( D @ ( C @ c_2Einteger_2Eint__rem_2E2 ) ) )
        | ( D
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
      & ( ( ( D @ ( C @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__rem_2E2 ) )
          = ( D @ ( C @ c_2Einteger_2Eint__rem_2E2 ) @ c_2Einteger_2Eint__neg_2E1 ) )
        | ( D
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
      & ( ( ( B @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__rem_2E2 ) )
          = ( B @ ( A @ c_2Earithmetic_2EMOD_2E2 ) @ c_2Einteger_2Eint__of__num_2E1 ) )
        | ( B = c_2Enum_2E0_2E0 ) ) ),
    inference(cnf,[status(esa)],[491]) ).

thf(498,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( ( A @ c_2Einteger_2Eint__neg_2E1 )
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
      | ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    inference(cnfConj,[status(thm)],[492]) ).

thf(509,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( ( A @ c_2Einteger_2Eint__neg_2E1 )
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
      | ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    inference(lifteq,[status(thm)],[498]) ).

thf(510,plain,
    ( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 )
    = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ),
    inference(simp,[status(thm)],[509]) ).

thf(1507,plain,
    ( ( c_2Einteger_2Eint__0_2E0 @ c_2Einteger_2Eint__neg_2E1 )
    = c_2Einteger_2Eint__0_2E0 ),
    inference(rewrite,[status(thm)],[510,1177]) ).

thf(106,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A @ ( B @ c_2Einteger_2Eint__mul_2E2 ) )
      = ( B @ ( A @ c_2Einteger_2Eint__mul_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__COMM) ).

thf(670,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A @ ( B @ c_2Einteger_2Eint__mul_2E2 ) )
      = ( B @ ( A @ c_2Einteger_2Eint__mul_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(151,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
    <=> ( B
        = ( A @ c_2Einteger_2Eint__neg_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__RNEG__UNIQ) ).

thf(898,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( B
          = ( A @ c_2Einteger_2Eint__neg_2E1 ) )
       => ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
      & ( ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
       => ( B
          = ( A @ c_2Einteger_2Eint__neg_2E1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(125,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
      = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__LINV) ).

thf(782,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
      = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(10,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) @ c_2Einteger_2Eint__le_2E2 ) )
      = ( B @ ( C @ c_2Einteger_2Eint__add_2E2 ) @ ( A @ c_2Einteger_2Eint__le_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__SUB__RADD) ).

thf(288,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) @ c_2Einteger_2Eint__le_2E2 ) )
      = ( B @ ( C @ c_2Einteger_2Eint__add_2E2 ) @ ( A @ c_2Einteger_2Eint__le_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(233,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
        = B )
    <=> ( A
        = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__LID__UNIQ) ).

thf(1359,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( A
          = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) )
       => ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
          = B ) )
      & ( ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
          = B )
       => ( A
          = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(234,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ealignment_2Ealign_2E2 ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ealignment_2Ealign__0) ).

thf(1366,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ealignment_2Ealign_2E2 ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(138,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) @ ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__mul_2E2 ) )
      = ( B @ ( B @ c_2Einteger_2Eint__mul_2E2 ) @ ( A @ ( A @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__sub_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIFFSQ) ).

thf(841,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) @ ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__mul_2E2 ) )
      = ( B @ ( B @ c_2Einteger_2Eint__mul_2E2 ) @ ( A @ ( A @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__sub_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(53,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__SUB) ).

thf(417,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(117,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint] :
      ( ( ( B @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__sub_2E2 ) )
        = ( B @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__add_2E2 ) ) )
      & ( ( B @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__sub_2E2 ) )
        = ( B @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__add_2E2 ) ) )
      & ( ( B @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__sub_2E2 ) )
        = ( B @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__add_2E2 ) ) )
      & ( ( B @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__sub_2E2 ) )
        = ( B @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__add_2E2 ) ) )
      & ( ( C @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__sub_2E2 ) )
        = ( C @ c_2Einteger_2Eint__neg_2E1 ) )
      & ( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( C @ c_2Einteger_2Eint__sub_2E2 ) )
        = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__REDUCE) ).

thf(724,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint] :
      ( ( ( B @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__sub_2E2 ) )
        = ( B @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__add_2E2 ) ) )
      & ( ( B @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__sub_2E2 ) )
        = ( B @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__add_2E2 ) ) )
      & ( ( B @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__sub_2E2 ) )
        = ( B @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__add_2E2 ) ) )
      & ( ( B @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__sub_2E2 ) )
        = ( B @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Earithmetic_2ENUMERAL_2E1 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__add_2E2 ) ) )
      & ( ( C @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__sub_2E2 ) )
        = ( C @ c_2Einteger_2Eint__neg_2E1 ) )
      & ( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( C @ c_2Einteger_2Eint__sub_2E2 ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(88,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( A @ ( B @ c_2Einteger_2Eint__mul_2E2 ) @ ( C @ c_2Einteger_2Eint__mul_2E2 ) )
      = ( A @ ( B @ ( C @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__mul_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__ASSOC) ).

thf(570,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( A @ ( B @ c_2Einteger_2Eint__mul_2E2 ) @ ( C @ c_2Einteger_2Eint__mul_2E2 ) )
      = ( A @ ( B @ ( C @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__mul_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(126,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( B @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
      = ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB) ).

thf(785,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( B @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
      = ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(38,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( A @ ( B @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__NEG) ).

thf(372,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( A @ ( B @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(217,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( A @ ( A @ c_2Einteger_2Eint__rem_2E2 ) )
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__REM__ID) ).

thf(1279,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( A @ ( A @ c_2Einteger_2Eint__rem_2E2 ) )
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(33,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ c_2Einteger_2Eint__add_2E2 ) @ ( C @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__le_2E2 ) )
      = ( B @ ( A @ c_2Einteger_2Eint__le_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__RADD) ).

thf(357,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ c_2Einteger_2Eint__add_2E2 ) @ ( C @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__le_2E2 ) )
      = ( B @ ( A @ c_2Einteger_2Eint__le_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(256,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( A @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__quot_2E2 ) )
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__QUOT__0) ).

thf(1462,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( A @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__quot_2E2 ) )
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(81,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) @ ( A @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) @ c_2Einteger_2Eint__sub_2E2 ) @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) )
      = ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__sub__i2w) ).

thf(542,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) @ ( A @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) @ c_2Einteger_2Eint__sub_2E2 ) @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) )
      = ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(142,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( A
        = ( C @ ( B @ c_2Einteger_2Eint__add_2E2 ) ) )
    <=> ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
        = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eint__arith_2Eeq__move__left__left) ).

thf(853,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
          = C )
       => ( A
          = ( C @ ( B @ c_2Einteger_2Eint__add_2E2 ) ) ) )
      & ( ( A
          = ( C @ ( B @ c_2Einteger_2Eint__add_2E2 ) ) )
       => ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
          = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(196,axiom,
    ! [A: tyop_2Eone_2Eone] :
      ( ( A @ c_2EbasicSize_2Eone__size_2E1 )
      = c_2Enum_2E0_2E0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EbasicSize_2Eone__size__def) ).

thf(1147,plain,
    ! [A: tyop_2Eone_2Eone] :
      ( ( A @ c_2EbasicSize_2Eone__size_2E1 )
      = c_2Enum_2E0_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(212,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) )
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__0) ).

thf(1247,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( A = B )
       => ( ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
      & ( ( ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(159,axiom,
    ! [TA: $tType,TB: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Emin_2Ebool @ tyop_2Elist_2Elist] :
      ( ( C @ ( TB @ c_2Ebitstring_2Ev2w_2E1 ) @ ( B @ ( A @ ( TA @ ( TB @ c_2Ewords_2Eword__extract_2E3 ) ) ) ) )
      = ( C @ ( TB @ c_2Ebitstring_2Ev2w_2E1 ) @ ( B @ ( A @ ( TB @ c_2Ewords_2Eword__bits_2E3 ) ) ) @ ( TA @ ( TB @ c_2Ewords_2Ew2w_2E1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebitstring_2Eword__extract__v2w) ).

thf(969,plain,
    ! [TA: $tType,TB: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Emin_2Ebool @ tyop_2Elist_2Elist] :
      ( ( C @ ( TB @ c_2Ebitstring_2Ev2w_2E1 ) @ ( B @ ( A @ ( TA @ ( TB @ c_2Ewords_2Eword__extract_2E3 ) ) ) ) )
      = ( C @ ( TB @ c_2Ebitstring_2Ev2w_2E1 ) @ ( B @ ( A @ ( TB @ c_2Ewords_2Eword__bits_2E3 ) ) ) @ ( TA @ ( TB @ c_2Ewords_2Ew2w_2E1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(123,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( A
        = ( C @ ( B @ c_2Einteger_2Eint__add_2E2 ) ) )
    <=> ( ( C @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eint__arith_2Eeq__move__right__left) ).

thf(770,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( ( C @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
          = B )
       => ( A
          = ( C @ ( B @ c_2Einteger_2Eint__add_2E2 ) ) ) )
      & ( ( A
          = ( C @ ( B @ c_2Einteger_2Eint__add_2E2 ) ) )
       => ( ( C @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(189,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__mul_2E2 ) )
      = ( C @ ( B @ c_2Einteger_2Eint__mul_2E2 ) @ ( C @ ( A @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__add_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__RDISTRIB) ).

thf(1115,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__mul_2E2 ) )
      = ( C @ ( B @ c_2Einteger_2Eint__mul_2E2 ) @ ( C @ ( A @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__add_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(263,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
        = A )
    <=> ( B
        = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__RID__UNIQ) ).

thf(1494,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( B
          = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) )
       => ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
          = A ) )
      & ( ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
          = A )
       => ( B
          = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(184,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = ( B @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__SUB3) ).

thf(1100,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = ( B @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(209,axiom,
    ! [TA: $tType] :
      ( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Ew2n_2E1 ) )
      = c_2Enum_2E0_2E0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2Eword__0__n2w) ).

thf(1232,plain,
    ! [TA: $tType] :
      ( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Ew2n_2E1 ) )
      = c_2Enum_2E0_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(257,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__add_2E2 ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__LID) ).

thf(1465,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__add_2E2 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(252,axiom,
    ! [TA: $tType] :
      ( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) )
      = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__0__w2i) ).

thf(1450,plain,
    ! [TA: $tType] :
      ( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) )
      = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(101,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
        = C )
    <=> ( A
        = ( B @ ( C @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__EQ__SUB) ).

thf(646,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( A
          = ( B @ ( C @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) )
       => ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
          = C ) )
      & ( ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
          = C )
       => ( A
          = ( B @ ( C @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(136,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( A @ ( TA @ c_2Einteger__word_2Eword__smod_2E2 ) ) )
      = ( B @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) @ ( A @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) @ c_2Einteger_2Eint__mod_2E2 ) @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__smod__def) ).

thf(834,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( A @ ( TA @ c_2Einteger__word_2Eword__smod_2E2 ) ) )
      = ( B @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) @ ( A @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) @ c_2Einteger_2Eint__mod_2E2 ) @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(30,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( B @ ( C @ c_2Einteger_2Eint__sub_2E2 ) @ ( A @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__ADD__SUB) ).

thf(348,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( B @ ( C @ c_2Einteger_2Eint__sub_2E2 ) @ ( A @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(187,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( C @ ( B @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = ( B @ ( C @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__SUB) ).

thf(1109,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( C @ ( B @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = ( B @ ( C @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(21,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ ( B @ c_2Einteger_2Eint__le_2E2 ) )
      = ( A @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__le_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__ADDL) ).

thf(321,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ ( B @ c_2Einteger_2Eint__le_2E2 ) )
      = ( A @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__le_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(122,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( A @ ( B @ ( A @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__div_2E2 ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIV__LMUL) ).

thf(766,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( A @ ( B @ ( A @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__div_2E2 ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(251,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( c_2Enum_2E0_2E0 @ ( TB @ c_2Ewords_2En2w_2E1 ) @ ( TA @ ( TB @ c_2Ewords_2Esw2sw_2E1 ) ) )
      = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2Esw2sw__0) ).

thf(1447,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( c_2Enum_2E0_2E0 @ ( TB @ c_2Ewords_2En2w_2E1 ) @ ( TA @ ( TB @ c_2Ewords_2Esw2sw_2E1 ) ) )
      = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(61,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ c_2Einteger_2EABS_2E1 @ ( A @ c_2Einteger_2EABS_2E1 @ c_2Einteger_2Eint__mul_2E2 ) )
      = ( B @ ( A @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2EABS_2E1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__MUL) ).

thf(453,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ c_2Einteger_2EABS_2E1 @ ( A @ c_2Einteger_2EABS_2E1 @ c_2Einteger_2Eint__mul_2E2 ) )
      = ( B @ ( A @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2EABS_2E1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(46,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ c_2Einteger_2Eint__sub_2E2 ) @ ( A @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( B @ ( C @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__SUB__LADD) ).

thf(396,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ c_2Einteger_2Eint__sub_2E2 ) @ ( A @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( B @ ( C @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(104,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
        = ( C @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) )
    <=> ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__EQ__ADD__LCANCEL) ).

thf(660,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( B = C )
       => ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
          = ( C @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) ) )
      & ( ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
          = ( C @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) )
       => ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(243,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( A @ ( TA @ c_2Ewords_2Ew2n_2E1 ) )
        = c_2Enum_2E0_2E0 )
    <=> ( A
        = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2Ew2n__eq__0) ).

thf(1405,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( A
          = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) )
       => ( ( A @ ( TA @ c_2Ewords_2Ew2n_2E1 ) )
          = c_2Enum_2E0_2E0 ) )
      & ( ( ( A @ ( TA @ c_2Ewords_2Ew2n_2E1 ) )
          = c_2Enum_2E0_2E0 )
       => ( A
          = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(202,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
        = A )
    <=> ( B
        = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__INV__0__EQ) ).

thf(1169,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( B
          = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) )
       => ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
          = A ) )
      & ( ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
          = A )
       => ( B
          = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(110,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
        = C )
    <=> ( B
        = ( A @ c_2Einteger_2Eint__neg_2E1 @ ( C @ c_2Einteger_2Eint__add_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eint__arith_2Eeq__move__left__right) ).

thf(687,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( B
          = ( A @ c_2Einteger_2Eint__neg_2E1 @ ( C @ c_2Einteger_2Eint__add_2E2 ) ) )
       => ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
          = C ) )
      & ( ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
          = C )
       => ( B
          = ( A @ c_2Einteger_2Eint__neg_2E1 @ ( C @ c_2Einteger_2Eint__add_2E2 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(51,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__add_2E2 ) )
      = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__LINV) ).

thf(411,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__add_2E2 ) )
      = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(163,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) @ ( A @ c_2Einteger_2Eint__sub_2E2 ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__SUB2) ).

thf(988,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) @ ( A @ c_2Einteger_2Eint__sub_2E2 ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(76,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( TA @ ( TA @ c_2Ewords_2Esw2sw_2E1 ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2Esw2sw__id) ).

thf(527,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( TA @ ( TA @ c_2Ewords_2Esw2sw_2E1 ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(18,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( A @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__LT0) ).

thf(312,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( A @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(153,axiom,
    ( ! [A: tyop_2Einteger_2Eint] :
        ( ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__neg_2E1 )
        = A )
    & ! [A: tyop_2Einteger_2Eint] :
        ( ( ( A @ c_2Einteger_2Eint__neg_2E1 )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
      <=> ( A
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
    & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( ( A @ c_2Einteger_2Eint__of__num_2E1 )
          = ( B @ c_2Einteger_2Eint__of__num_2E1 ) )
      <=> ( A = B ) )
    & ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
        ( ( B
         != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
       => ( ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__quot_2E2 ) )
            = ( B @ ( A @ c_2Einteger_2Eint__quot_2E2 ) @ c_2Einteger_2Eint__neg_2E1 ) )
          & ( ( B @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__quot_2E2 ) )
            = ( B @ ( A @ c_2Einteger_2Eint__quot_2E2 ) @ c_2Einteger_2Eint__neg_2E1 ) ) ) )
    & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( B != c_2Enum_2E0_2E0 )
       => ( ( B @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__quot_2E2 ) )
          = ( B @ ( A @ c_2Earithmetic_2EDIV_2E2 ) @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__QUOT__CALCULATE) ).

thf(920,plain,
    ( ! [A: tyop_2Einteger_2Eint] :
        ( ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__neg_2E1 )
        = A )
    & ! [A: tyop_2Einteger_2Eint] :
        ( ( ( A
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
         => ( ( A @ c_2Einteger_2Eint__neg_2E1 )
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
        & ( ( ( A @ c_2Einteger_2Eint__neg_2E1 )
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
         => ( A
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ) )
    & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( ( A = B )
         => ( ( A @ c_2Einteger_2Eint__of__num_2E1 )
            = ( B @ c_2Einteger_2Eint__of__num_2E1 ) ) )
        & ( ( ( A @ c_2Einteger_2Eint__of__num_2E1 )
            = ( B @ c_2Einteger_2Eint__of__num_2E1 ) )
         => ( A = B ) ) )
    & ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
        ( ( B
         != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
       => ( ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__quot_2E2 ) )
            = ( B @ ( A @ c_2Einteger_2Eint__quot_2E2 ) @ c_2Einteger_2Eint__neg_2E1 ) )
          & ( ( B @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__quot_2E2 ) )
            = ( B @ ( A @ c_2Einteger_2Eint__quot_2E2 ) @ c_2Einteger_2Eint__neg_2E1 ) ) ) )
    & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( B != c_2Enum_2E0_2E0 )
       => ( ( B @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__quot_2E2 ) )
          = ( B @ ( A @ c_2Earithmetic_2EDIV_2E2 ) @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(223,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
    ? [B: tyop_2Enum_2Enum] :
      ( A
      = ( B @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2Eword__nchotomy) ).

thf(1306,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
    ? [B: tyop_2Enum_2Enum] :
      ( A
      = ( B @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(198,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__sub_2E2 ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__RZERO) ).

thf(1153,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__sub_2E2 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(132,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( ( B @ ( A @ c_2Einteger_2Eint__rem_2E2 ) )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
        & ( B
         != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
     => ( ( B @ ( A @ ( C @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__quot_2E2 ) )
        = ( B @ ( A @ c_2Einteger_2Eint__quot_2E2 ) @ ( C @ c_2Einteger_2Eint__mul_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__QUOT) ).

thf(810,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( ( B @ ( A @ c_2Einteger_2Eint__rem_2E2 ) )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
        & ( B
         != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
     => ( ( B @ ( A @ ( C @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__quot_2E2 ) )
        = ( B @ ( A @ c_2Einteger_2Eint__quot_2E2 ) @ ( C @ c_2Einteger_2Eint__mul_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(41,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( C @ ( B @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) )
      = ( C @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LEFT__SUB__DISTRIB) ).

thf(381,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( C @ ( B @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) )
      = ( C @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(36,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ ( A @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( B @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__ADDR) ).

thf(366,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ ( A @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( B @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(225,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Enum_2Enum] :
      ( ( ( B @ ( A @ c_2Einteger_2Eint__exp_2E2 ) )
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
    <=> ( ( B != c_2Enum_2E0_2E0 )
        & ( A
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EXP__EQ0) ).

thf(1311,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Enum_2Enum] :
      ( ( ( ( B != c_2Enum_2E0_2E0 )
          & ( A
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
       => ( ( B @ ( A @ c_2Einteger_2Eint__exp_2E2 ) )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
      & ( ( ( B @ ( A @ c_2Einteger_2Eint__exp_2E2 ) )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
       => ( ( B != c_2Enum_2E0_2E0 )
          & ( A
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(175,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__LZERO) ).

thf(1047,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(4,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A @ c_2Einteger_2Eint__neg_2E1 @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__GT0) ).

thf(270,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A @ c_2Einteger_2Eint__neg_2E1 @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(528,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( TA @ ( TA @ c_2Ewords_2Esw2sw_2E1 ) ) )
      = A ),
    inference(cnf,[status(esa)],[527]) ).

thf(529,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( TA @ ( TA @ c_2Ewords_2Esw2sw_2E1 ) ) )
      = A ),
    inference(lifteq,[status(thm)],[528]) ).

thf(157,axiom,
    ! [TA: $tType,TB: $tType,A: TB @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( TA @ ( TB @ c_2Ewords_2Ew2w_2E1 ) ) )
      = ( A @ ( TB @ c_2Ewords_2Ew2n_2E1 ) @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2Ew2w__def) ).

thf(957,plain,
    ! [TA: $tType,TB: $tType,A: TB @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( TA @ ( TB @ c_2Ewords_2Ew2w_2E1 ) ) )
      = ( A @ ( TB @ c_2Ewords_2Ew2n_2E1 ) @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(181,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__sub_2E2 ) )
      = ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__neg_2E1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__LNEG) ).

thf(1091,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__sub_2E2 ) )
      = ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__neg_2E1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(213,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( A @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__mod_2E2 ) )
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD0) ).

thf(1255,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( A @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__mod_2E2 ) )
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(143,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
        = ( C @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) )
    <=> ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__RCANCEL__SUB) ).

thf(862,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( B = C )
       => ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
          = ( C @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) ) )
      & ( ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
          = ( C @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) )
       => ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(1312,plain,
    ( ! [A: tyop_2Einteger_2Eint,B: tyop_2Enum_2Enum] :
        ( ( ( B != c_2Enum_2E0_2E0 )
          & ( A
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
       => ( ( B @ ( A @ c_2Einteger_2Eint__exp_2E2 ) )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
    & ! [A: tyop_2Einteger_2Eint,B: tyop_2Enum_2Enum] :
        ( ( ( B @ ( A @ c_2Einteger_2Eint__exp_2E2 ) )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
       => ( ( B != c_2Enum_2E0_2E0 )
          & ( A
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ) ),
    inference(miniscope,[status(thm)],[1311]) ).

thf(1313,plain,
    ! [D: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint,B: tyop_2Enum_2Enum,A: tyop_2Einteger_2Eint] :
      ( ( ( ( D @ ( C @ c_2Einteger_2Eint__exp_2E2 ) )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
        | ( D = c_2Enum_2E0_2E0 )
        | ( C
         != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
      & ( ( B != c_2Enum_2E0_2E0 )
        | ( ( B @ ( A @ c_2Einteger_2Eint__exp_2E2 ) )
         != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
      & ( ( A
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
        | ( ( B @ ( A @ c_2Einteger_2Eint__exp_2E2 ) )
         != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ),
    inference(cnf,[status(esa)],[1312]) ).

thf(1315,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Einteger_2Eint] :
      ( ( B != c_2Enum_2E0_2E0 )
      | ( ( B @ ( A @ c_2Einteger_2Eint__exp_2E2 ) )
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    inference(cnfConj,[status(thm)],[1313]) ).

thf(1318,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Einteger_2Eint] :
      ( ( B != c_2Enum_2E0_2E0 )
      | ( ( B @ ( A @ c_2Einteger_2Eint__exp_2E2 ) )
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    inference(lifteq,[status(thm)],[1315]) ).

thf(1319,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Enum_2E0_2E0 @ ( A @ c_2Einteger_2Eint__exp_2E2 ) )
     != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ),
    inference(simp,[status(thm)],[1318]) ).

thf(1502,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Enum_2E0_2E0 @ ( A @ c_2Einteger_2Eint__exp_2E2 ) )
     != c_2Einteger_2Eint__0_2E0 ),
    inference(rewrite,[status(thm)],[1319,1177]) ).

thf(262,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
        = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) )
    <=> ( A
        = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__EQ__0) ).

thf(1487,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( A
          = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) )
       => ( ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
          = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ) )
      & ( ( ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
          = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) )
       => ( A
          = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(13,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( B @ ( C @ c_2Einteger_2Eint__add_2E2 ) @ ( A @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__SUB__RADD) ).

thf(297,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( B @ ( C @ c_2Einteger_2Eint__add_2E2 ) @ ( A @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(127,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( C @ ( A @ ( C @ ( B @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__mod_2E2 ) )
        = ( C @ ( A @ c_2Einteger_2Eint__mod_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__ADD__MULTIPLES) ).

thf(788,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( C @ ( A @ ( C @ ( B @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__mod_2E2 ) )
        = ( C @ ( A @ c_2Einteger_2Eint__mod_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(211,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( B = C )
      <=> ( ( B @ ( A @ c_2Einteger_2Eint__mul_2E2 ) )
          = ( C @ ( A @ c_2Einteger_2Eint__mul_2E2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__LMUL2) ).

thf(1238,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( ( ( B @ ( A @ c_2Einteger_2Eint__mul_2E2 ) )
            = ( C @ ( A @ c_2Einteger_2Eint__mul_2E2 ) ) )
         => ( B = C ) )
        & ( ( B = C )
         => ( ( B @ ( A @ c_2Einteger_2Eint__mul_2E2 ) )
            = ( C @ ( A @ c_2Einteger_2Eint__mul_2E2 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(246,axiom,
    ! [A: tyop_2Emin_2Ebool] :
      ( ( A @ c_2EbasicSize_2Ebool__size_2E1 )
      = c_2Enum_2E0_2E0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EbasicSize_2Ebool__size__def) ).

thf(1423,plain,
    ! [A: tyop_2Emin_2Ebool] :
      ( ( A @ c_2EbasicSize_2Ebool__size_2E1 )
      = c_2Enum_2E0_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(204,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( ( C @ ( A @ c_2Einteger_2Eint__mul_2E2 ) )
          = ( C @ ( B @ c_2Einteger_2Eint__mul_2E2 ) ) )
        & ( C
         != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__RMUL__IMP) ).

thf(1178,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( ( C @ ( A @ c_2Einteger_2Eint__mul_2E2 ) )
          = ( C @ ( B @ c_2Einteger_2Eint__mul_2E2 ) ) )
        & ( C
         != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(220,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( A @ ( B @ c_2Enumpair_2Encons_2E2 ) )
     != c_2Enum_2E0_2E0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Enumpair_2Encons__not__nnil) ).

thf(1296,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( A @ ( B @ c_2Enumpair_2Encons_2E2 ) )
     != c_2Enum_2E0_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(148,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
      = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__RINV) ).

thf(889,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
      = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(200,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( A @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) )
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
    <=> ( A
        = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger__word_2Ew2i__eq__0) ).

thf(1159,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( A
          = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) )
       => ( ( A @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
      & ( ( ( A @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
       => ( A
          = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(84,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__mul_2E2 ) )
      = ( B @ ( A @ c_2Einteger_2Eint__mul_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__MUL2) ).

thf(551,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__mul_2E2 ) )
      = ( B @ ( A @ c_2Einteger_2Eint__mul_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(240,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( A @ ( B @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
        = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__EQ__SUB__ZERO) ).

thf(1392,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( B = A )
       => ( ( A @ ( B @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
          = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ) )
      & ( ( ( A @ ( B @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
          = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(114,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( B @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
        = A )
    <=> ( B
        = ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__EQ) ).

thf(710,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( B
          = ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) ) )
       => ( ( B @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
          = A ) )
      & ( ( ( B @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
          = A )
       => ( B
          = ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(62,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ ( A @ c_2Einteger_2Eint__sub_2E2 ) )
      = ( B @ c_2Einteger_2Eint__neg_2E1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__SUB2) ).

thf(456,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ ( A @ c_2Einteger_2Eint__sub_2E2 ) )
      = ( B @ c_2Einteger_2Eint__neg_2E1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(22,axiom,
    ! [TA: $tType,A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) @ ( A @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) )
      = ( B @ ( A @ c_2Einteger_2Eint__mul_2E2 ) @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__i2w__mul) ).

thf(324,plain,
    ! [TA: $tType,A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) @ ( A @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) )
      = ( B @ ( A @ c_2Einteger_2Eint__mul_2E2 ) @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(140,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( TA @ c_2Ewords_2Ew2n_2E1 ) @ ( TA @ c_2Ewords_2En2w_2E1 ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2En2w__w2n) ).

thf(847,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( TA @ c_2Ewords_2Ew2n_2E1 ) @ ( TA @ c_2Ewords_2En2w_2E1 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(70,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__SUB2) ).

thf(484,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(9,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ c_2Einteger_2Eint__add_2E2 ) @ ( A @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( C @ ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eint__arith_2Elt__move__left__left) ).

thf(285,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ c_2Einteger_2Eint__add_2E2 ) @ ( A @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( C @ ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(186,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( C @ ( B @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
      = ( C @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__TRIANGLE) ).

thf(1106,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( C @ ( B @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
      = ( C @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(242,axiom,
    ! [TA: $tType,TB: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( B @ ( A @ ( TB @ ( TA @ c_2Ewords_2Eword__extract_2E3 ) ) ) ) )
      = ( c_2Enum_2E0_2E0 @ ( TB @ c_2Ewords_2En2w_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__EXTRACT__ZERO2) ).

thf(1402,plain,
    ! [TA: $tType,TB: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( B @ ( A @ ( TB @ ( TA @ c_2Ewords_2Eword__extract_2E3 ) ) ) ) )
      = ( c_2Enum_2E0_2E0 @ ( TB @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(1233,plain,
    ! [TA: $tType] :
      ( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Ew2n_2E1 ) )
      = c_2Enum_2E0_2E0 ),
    inference(cnf,[status(esa)],[1232]) ).

thf(1234,plain,
    ! [TA: $tType] :
      ( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Ew2n_2E1 ) )
      = c_2Enum_2E0_2E0 ),
    inference(lifteq,[status(thm)],[1233]) ).

thf(154,axiom,
    ! [TA: $tType] :
      ( ( TA @ c_2Ewords_2Eword__L_2E0 @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
      = ( TA @ c_2Ewords_2Eword__L_2E0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__L) ).

thf(948,plain,
    ! [TA: $tType] :
      ( ( TA @ c_2Ewords_2Eword__L_2E0 @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
      = ( TA @ c_2Ewords_2Eword__L_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(94,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__quot_2E2 ) )
          = ( B @ ( A @ c_2Einteger_2Eint__quot_2E2 ) @ c_2Einteger_2Eint__neg_2E1 ) )
        & ( ( B @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__quot_2E2 ) )
          = ( B @ ( A @ c_2Einteger_2Eint__quot_2E2 ) @ c_2Einteger_2Eint__neg_2E1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__QUOT__NEG) ).

thf(615,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__quot_2E2 ) )
          = ( B @ ( A @ c_2Einteger_2Eint__quot_2E2 ) @ c_2Einteger_2Eint__neg_2E1 ) )
        & ( ( B @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__quot_2E2 ) )
          = ( B @ ( A @ c_2Einteger_2Eint__quot_2E2 ) @ c_2Einteger_2Eint__neg_2E1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(1424,plain,
    ! [A: tyop_2Emin_2Ebool] :
      ( ( A @ c_2EbasicSize_2Ebool__size_2E1 )
      = c_2Enum_2E0_2E0 ),
    inference(cnf,[status(esa)],[1423]) ).

thf(1425,plain,
    ! [A: tyop_2Emin_2Ebool] :
      ( ( A @ c_2EbasicSize_2Ebool__size_2E1 )
      = c_2Enum_2E0_2E0 ),
    inference(lifteq,[status(thm)],[1424]) ).

thf(144,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__neg_2E1 )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEGNEG) ).

thf(869,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__neg_2E1 )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(237,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A @ ( A @ c_2Einteger_2Eint__sub_2E2 ) )
      = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__REFL) ).

thf(1375,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A @ ( A @ c_2Einteger_2Eint__sub_2E2 ) )
      = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(191,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( C @ ( B @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
      = ( C @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__ASSOC) ).

thf(1121,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( C @ ( B @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
      = ( C @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(54,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( A @ ( B @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__SUB3) ).

thf(420,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( A @ ( B @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(190,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A @ c_2Einteger_2EABS_2E1 @ c_2Einteger_2EABS_2E1 )
      = ( A @ c_2Einteger_2EABS_2E1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__ABS) ).

thf(1118,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A @ c_2Einteger_2EABS_2E1 @ c_2Einteger_2EABS_2E1 )
      = ( A @ c_2Einteger_2EABS_2E1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(27,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__le_2E2 ) )
      = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__le_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__NEGR) ).

thf(339,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__le_2E2 ) )
      = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__le_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(85,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( A @ c_2Einteger_2Eint__neg_2E1 )
        = ( B @ c_2Einteger_2Eint__neg_2E1 ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__NEG) ).

thf(554,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( A = B )
       => ( ( A @ c_2Einteger_2Eint__neg_2E1 )
          = ( B @ c_2Einteger_2Eint__neg_2E1 ) ) )
      & ( ( ( A @ c_2Einteger_2Eint__neg_2E1 )
          = ( B @ c_2Einteger_2Eint__neg_2E1 ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(205,axiom,
    ! [TA: $tType,A: TA] :
      ( ( A @ ( TA @ c_2Ebag_2EEMPTY__BAG_2E1 ) )
      = c_2Enum_2E0_2E0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebag_2EEMPTY__BAG__alt) ).

thf(1182,plain,
    ! [TA: $tType,A: TA] :
      ( ( A @ ( TA @ c_2Ebag_2EEMPTY__BAG_2E1 ) )
      = c_2Enum_2E0_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(255,axiom,
    ! [TA: $tType] :
      ( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__reverse_2E1 ) )
      = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2Eword__reverse__0) ).

thf(1459,plain,
    ! [TA: $tType] :
      ( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__reverse_2E1 ) )
      = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(1460,plain,
    ! [TA: $tType] :
      ( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__reverse_2E1 ) )
      = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(cnf,[status(esa)],[1459]) ).

thf(1461,plain,
    ! [TA: $tType] :
      ( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__reverse_2E1 ) )
      = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(lifteq,[status(thm)],[1460]) ).

thf(75,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( TA @ ( TA @ c_2Ewords_2Ew2w_2E1 ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2Ew2w__id) ).

thf(524,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( TA @ ( TA @ c_2Ewords_2Ew2w_2E1 ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(525,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( TA @ ( TA @ c_2Ewords_2Ew2w_2E1 ) ) )
      = A ),
    inference(cnf,[status(esa)],[524]) ).

thf(526,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( TA @ ( TA @ c_2Ewords_2Ew2w_2E1 ) ) )
      = A ),
    inference(lifteq,[status(thm)],[525]) ).

thf(98,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( B @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
      = ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__SUB) ).

thf(637,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( B @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
      = ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(250,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( A @ ( TA @ c_2Ewords_2Ebit__count_2E1 ) )
        = c_2Enum_2E0_2E0 )
    <=> ( A
        = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2Ebit__count__is__zero) ).

thf(1440,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( A
          = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) )
       => ( ( A @ ( TA @ c_2Ewords_2Ebit__count_2E1 ) )
          = c_2Enum_2E0_2E0 ) )
      & ( ( ( A @ ( TA @ c_2Ewords_2Ebit__count_2E1 ) )
          = c_2Enum_2E0_2E0 )
       => ( A
          = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(1441,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( ( A @ ( TA @ c_2Ewords_2Ebit__count_2E1 ) )
          = c_2Enum_2E0_2E0 )
        | ( A
         != ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ) )
      & ( ( A
          = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) )
        | ( ( A @ ( TA @ c_2Ewords_2Ebit__count_2E1 ) )
         != c_2Enum_2E0_2E0 ) ) ),
    inference(cnf,[status(esa)],[1440]) ).

thf(1443,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( A @ ( TA @ c_2Ewords_2Ebit__count_2E1 ) )
        = c_2Enum_2E0_2E0 )
      | ( A
       != ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ) ),
    inference(cnfConj,[status(thm)],[1441]) ).

thf(1445,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( A @ ( TA @ c_2Ewords_2Ebit__count_2E1 ) )
        = c_2Enum_2E0_2E0 )
      | ( A
       != ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ) ),
    inference(lifteq,[status(thm)],[1443]) ).

thf(1446,plain,
    ! [TA: $tType] :
      ( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Ebit__count_2E1 ) )
      = c_2Enum_2E0_2E0 ),
    inference(simp,[status(thm)],[1445]) ).

thf(5,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__le_2E2 ) )
      = ( A @ ( B @ c_2Einteger_2Eint__le_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__LE) ).

thf(273,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__le_2E2 ) )
      = ( A @ ( B @ c_2Einteger_2Eint__le_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(274,plain,
    ! [B: tyop_2Einteger_2Eint,A: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__le_2E2 ) )
      = ( A @ ( B @ c_2Einteger_2Eint__le_2E2 ) ) ),
    inference(cnf,[status(esa)],[273]) ).

thf(275,plain,
    ! [B: tyop_2Einteger_2Eint,A: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__le_2E2 ) )
      = ( A @ ( B @ c_2Einteger_2Eint__le_2E2 ) ) ),
    inference(lifteq,[status(thm)],[274]) ).

thf(1567,plain,
    ! [B: tyop_2Einteger_2Eint,A: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) @ ( c_2Einteger_2Eint__0_2E0 @ c_2Einteger_2Eint__le_2E2 ) )
      = ( A @ ( B @ c_2Einteger_2Eint__le_2E2 ) ) ),
    inference(rewrite,[status(thm)],[275,1177]) ).

thf(67,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( A @ ( TA @ c_2Ewords_2Ew2n_2E1 ) )
        = ( B @ ( TA @ c_2Ewords_2Ew2n_2E1 ) ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2Ew2n__11) ).

thf(471,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( A = B )
       => ( ( A @ ( TA @ c_2Ewords_2Ew2n_2E1 ) )
          = ( B @ ( TA @ c_2Ewords_2Ew2n_2E1 ) ) ) )
      & ( ( ( A @ ( TA @ c_2Ewords_2Ew2n_2E1 ) )
          = ( B @ ( TA @ c_2Ewords_2Ew2n_2E1 ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(137,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( ( B @ ( A @ c_2Einteger_2Eint__mod_2E2 ) )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
        & ( B
         != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
     => ( ( B @ ( A @ ( C @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__div_2E2 ) )
        = ( B @ ( A @ c_2Einteger_2Eint__div_2E2 ) @ ( C @ c_2Einteger_2Eint__mul_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__DIV) ).

thf(837,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( ( B @ ( A @ c_2Einteger_2Eint__mod_2E2 ) )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
        & ( B
         != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
     => ( ( B @ ( A @ ( C @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__div_2E2 ) )
        = ( B @ ( A @ c_2Einteger_2Eint__div_2E2 ) @ ( C @ c_2Einteger_2Eint__mul_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(45,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ c_2Einteger_2Eint__sub_2E2 ) @ ( A @ c_2Einteger_2Eint__le_2E2 ) )
      = ( B @ ( C @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__le_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__SUB__LADD) ).

thf(393,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ c_2Einteger_2Eint__sub_2E2 ) @ ( A @ c_2Einteger_2Eint__le_2E2 ) )
      = ( B @ ( C @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__le_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(166,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ c_2Einteger_2Eint__sub_2E2 ) @ ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) @ c_2Einteger_2Eint__add_2E2 ) )
      = ( C @ ( A @ c_2Einteger_2Eint__sub_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__TRIANGLE) ).

thf(997,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ c_2Einteger_2Eint__sub_2E2 ) @ ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) @ c_2Einteger_2Eint__add_2E2 ) )
      = ( C @ ( A @ c_2Einteger_2Eint__sub_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(1189,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Enum_2E0_2E0 @ ( A @ c_2Egcd_2Elcm_2E2 ) )
      = c_2Enum_2E0_2E0 ),
    inference(cnfConj,[status(thm)],[1187]) ).

thf(1191,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Enum_2E0_2E0 @ ( A @ c_2Egcd_2Elcm_2E2 ) )
      = c_2Enum_2E0_2E0 ),
    inference(lifteq,[status(thm)],[1189]) ).

thf(1192,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( c_2Enum_2E0_2E0 @ ( A @ c_2Egcd_2Elcm_2E2 ) )
      = c_2Enum_2E0_2E0 ),
    inference(simp,[status(thm)],[1191]) ).

thf(176,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__div_2E2 ) )
        = ( B @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__div_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIV__NEG) ).

thf(1050,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__div_2E2 ) )
        = ( B @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__div_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(162,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint] :
      ( ( B != c_2Enum_2E0_2E0 )
     => ( ( C @ ( B @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__mul_2E2 ) @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) )
        = ( C @ ( B @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__div_2E2 ) @ c_2Einteger_2Eint__lt_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eint__arith_2Eelim__lt__coeffs1) ).

thf(984,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Einteger_2Eint] :
      ( ( B != c_2Enum_2E0_2E0 )
     => ( ( C @ ( B @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__mul_2E2 ) @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) )
        = ( C @ ( B @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__div_2E2 ) @ c_2Einteger_2Eint__lt_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(116,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__LNEG) ).

thf(721,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(248,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( c_2Enum_2E0_2E0 @ ( TB @ c_2Ewords_2En2w_2E1 ) @ ( c_2Enum_2E0_2E0 @ ( TC @ c_2Ewords_2En2w_2E1 ) @ ( TA @ ( TB @ ( TC @ c_2Ewords_2Eword__concat_2E2 ) ) ) ) )
      = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2Eword__concat__0__0) ).

thf(1429,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( c_2Enum_2E0_2E0 @ ( TB @ c_2Ewords_2En2w_2E1 ) @ ( c_2Enum_2E0_2E0 @ ( TC @ c_2Ewords_2En2w_2E1 ) @ ( TA @ ( TB @ ( TC @ c_2Ewords_2Eword__concat_2E2 ) ) ) ) )
      = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(124,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2EABS_2E1 )
      = ( A @ c_2Einteger_2EABS_2E1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__NEG) ).

thf(779,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2EABS_2E1 )
      = ( A @ c_2Einteger_2EABS_2E1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(197,axiom,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__bits_2E3 ) ) ) )
      = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__BITS__ZERO2) ).

thf(1150,plain,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__bits_2E3 ) ) ) )
      = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(259,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( A @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__rem_2E2 ) )
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__REM0) ).

thf(1478,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( A @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__rem_2E2 ) )
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(271,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A @ c_2Einteger_2Eint__neg_2E1 @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    inference(cnf,[status(esa)],[270]) ).

thf(272,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A @ c_2Einteger_2Eint__neg_2E1 @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    inference(lifteq,[status(thm)],[271]) ).

thf(1530,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A @ c_2Einteger_2Eint__neg_2E1 @ ( c_2Einteger_2Eint__0_2E0 @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( c_2Einteger_2Eint__0_2E0 @ ( A @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    inference(rewrite,[status(thm)],[272,1177]) ).

thf(254,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__REFL) ).

thf(1456,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(193,axiom,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( c_2Enum_2E0_2E0 @ ( A @ ( TA @ c_2Ewords_2Eword__slice_2E3 ) ) ) )
      = ( B @ ( c_2Enum_2E0_2E0 @ ( A @ ( TA @ c_2Ewords_2Eword__bits_2E3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SLICE__BITS__THM) ).

thf(1131,plain,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( c_2Enum_2E0_2E0 @ ( A @ ( TA @ c_2Ewords_2Eword__slice_2E3 ) ) ) )
      = ( B @ ( c_2Enum_2E0_2E0 @ ( A @ ( TA @ c_2Ewords_2Eword__bits_2E3 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(102,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ c_2Einteger_2Eint__sub_2E2 ) @ ( A @ c_2Einteger_2Eint__mul_2E2 ) )
      = ( C @ ( A @ c_2Einteger_2Eint__mul_2E2 ) @ ( B @ ( A @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__sub_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__LDISTRIB) ).

thf(654,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ c_2Einteger_2Eint__sub_2E2 ) @ ( A @ c_2Einteger_2Eint__mul_2E2 ) )
      = ( C @ ( A @ c_2Einteger_2Eint__mul_2E2 ) @ ( B @ ( A @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__sub_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(228,axiom,
    ! [TA: $tType] :
      ( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
      = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__0) ).

thf(1333,plain,
    ! [TA: $tType] :
      ( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
      = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(34,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( C @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) )
      = ( C @ ( B @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) @ ( C @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__RIGHT__ADD__DISTRIB) ).

thf(360,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( C @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) )
      = ( C @ ( B @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) @ ( C @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(103,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( B @ ( A @ c_2Einteger_2Eint__rem_2E2 ) )
        = ( B @ ( B @ ( A @ c_2Einteger_2Eint__quot_2E2 ) @ c_2Einteger_2Eint__mul_2E2 ) @ ( A @ c_2Einteger_2Eint__sub_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2Eint__rem) ).

thf(657,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( B @ ( A @ c_2Einteger_2Eint__rem_2E2 ) )
        = ( B @ ( B @ ( A @ c_2Einteger_2Eint__quot_2E2 ) @ c_2Einteger_2Eint__mul_2E2 ) @ ( A @ c_2Einteger_2Eint__sub_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(77,axiom,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( C @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__bits_2E3 ) ) ) )
      = ( C @ ( B @ ( A @ ( TA @ ( TA @ c_2Ewords_2Eword__extract_2E3 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__BITS__EXTRACT) ).

thf(530,plain,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( C @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__bits_2E3 ) ) ) )
      = ( C @ ( B @ ( A @ ( TA @ ( TA @ c_2Ewords_2Eword__extract_2E3 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(129,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = ( A @ ( B @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__NEG) ).

thf(794,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = ( A @ ( B @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(115,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) @ ( B @ c_2Einteger_2Eint__add_2E2 ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__ADD2) ).

thf(718,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) @ ( B @ c_2Einteger_2Eint__add_2E2 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(152,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum] :
      ( ( ( A @ ( B @ c_2Enumpair_2Encons_2E2 ) )
        = ( C @ ( D @ c_2Enumpair_2Encons_2E2 ) ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Enumpair_2Encons__11) ).

thf(906,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum] :
      ( ( ( ( A = C )
          & ( B = D ) )
       => ( ( A @ ( B @ c_2Enumpair_2Encons_2E2 ) )
          = ( C @ ( D @ c_2Enumpair_2Encons_2E2 ) ) ) )
      & ( ( ( A @ ( B @ c_2Enumpair_2Encons_2E2 ) )
          = ( C @ ( D @ c_2Enumpair_2Encons_2E2 ) ) )
       => ( ( A = C )
          & ( B = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(1138,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( ( A
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
        | ( ( A @ sk14 )
         != c_2Enum_2E0_2E0 )
        | ( ( A @ sk13 )
         != c_2Enum_2E0_2E0 ) )
      & ( ( A
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
        | ( A
          = ( A @ sk14 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 ) )
        | ( ( A @ sk13 )
         != c_2Enum_2E0_2E0 ) )
      & ( ( A
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
        | ( ( A @ sk14 )
         != c_2Enum_2E0_2E0 )
        | ( A
          = ( A @ sk13 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
      & ( ( A
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
        | ( A
          = ( A @ sk14 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 ) )
        | ( A
          = ( A @ sk13 @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ),
    inference(cnf,[status(esa)],[1137]) ).

thf(1142,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
      | ( ( A @ sk14 )
       != c_2Enum_2E0_2E0 )
      | ( ( A @ sk13 )
       != c_2Enum_2E0_2E0 ) ),
    inference(cnfConj,[status(thm)],[1138]) ).

thf(1146,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
      | ( ( A @ sk14 )
       != c_2Enum_2E0_2E0 )
      | ( ( A @ sk13 )
       != c_2Enum_2E0_2E0 ) ),
    inference(lifteq,[status(thm)],[1142]) ).

thf(1510,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A = c_2Einteger_2Eint__0_2E0 )
      | ( ( A @ sk14 )
       != c_2Enum_2E0_2E0 )
      | ( ( A @ sk13 )
       != c_2Enum_2E0_2E0 ) ),
    inference(rewrite,[status(thm)],[1146,1177]) ).

thf(185,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 )
        = ( B @ ( C @ c_2Einteger_2Eint__add_2E2 ) ) )
     => ( ( A @ ( C @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__add_2E2 ) @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__le_2E2 ) )
        = ( A @ ( B @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__le_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eint__arith_2Eeq__context__rwt2) ).

thf(1103,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 )
        = ( B @ ( C @ c_2Einteger_2Eint__add_2E2 ) ) )
     => ( ( A @ ( C @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__add_2E2 ) @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__le_2E2 ) )
        = ( A @ ( B @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__le_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(134,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( C @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = ( C @ ( B @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__SUB__ASSOC) ).

thf(824,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( C @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = ( C @ ( B @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(7,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ ( A @ c_2Einteger_2Eint__le_2E2 ) )
      = ( B @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__le_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__ADDR) ).

thf(279,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ ( A @ c_2Einteger_2Eint__le_2E2 ) )
      = ( B @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__le_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(89,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ ( C @ c_2Einteger_2Eint__sub_2E2 ) @ c_2Einteger_2Eint__add_2E2 ) )
      = ( A @ ( B @ ( C @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__sub_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eint__arith_2Emove__sub) ).

thf(573,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ ( C @ c_2Einteger_2Eint__sub_2E2 ) @ c_2Einteger_2Eint__add_2E2 ) )
      = ( A @ ( B @ ( C @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__sub_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(58,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) )
      = ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__add_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__CALCULATE) ).

thf(444,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) )
      = ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__add_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(236,axiom,
    ! [A: tyop_2EternaryComparisons_2Eordering] :
      ( ( A @ c_2EternaryComparisons_2Eordering__size_2E1 )
      = c_2Enum_2E0_2E0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EternaryComparisons_2Eordering__size__def) ).

thf(1372,plain,
    ! [A: tyop_2EternaryComparisons_2Eordering] :
      ( ( A @ c_2EternaryComparisons_2Eordering__size_2E1 )
      = c_2Enum_2E0_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(1373,plain,
    ! [A: tyop_2EternaryComparisons_2Eordering] :
      ( ( A @ c_2EternaryComparisons_2Eordering__size_2E1 )
      = c_2Enum_2E0_2E0 ),
    inference(cnf,[status(esa)],[1372]) ).

thf(1374,plain,
    ! [A: tyop_2EternaryComparisons_2Eordering] :
      ( ( A @ c_2EternaryComparisons_2Eordering__size_2E1 )
      = c_2Enum_2E0_2E0 ),
    inference(lifteq,[status(thm)],[1373]) ).

thf(39,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
      = ( B @ ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__LMUL) ).

thf(375,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
      = ( B @ ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(91,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ! [B: tyop_2Einteger_2Eint] :
          ( ( ( A @ ( B @ c_2Einteger_2Eint__mod_2E2 ) )
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
        <=> ? [C: tyop_2Einteger_2Eint] :
              ( B
              = ( A @ ( C @ c_2Einteger_2Eint__mul_2E2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__EQ0) ).

thf(601,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ! [B: tyop_2Einteger_2Eint] :
          ( ( ? [C: tyop_2Einteger_2Eint] :
                ( B
                = ( A @ ( C @ c_2Einteger_2Eint__mul_2E2 ) ) )
           => ( ( A @ ( B @ c_2Einteger_2Eint__mod_2E2 ) )
              = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
          & ( ( ( A @ ( B @ c_2Einteger_2Eint__mod_2E2 ) )
              = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
           => ? [C: tyop_2Einteger_2Eint] :
                ( B
                = ( A @ ( C @ c_2Einteger_2Eint__mul_2E2 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(161,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( A
        = ( C @ ( B @ c_2Einteger_2Eint__sub_2E2 ) ) )
    <=> ( ( C @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__SUB__LADD) ).

thf(975,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( ( C @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
          = B )
       => ( A
          = ( C @ ( B @ c_2Einteger_2Eint__sub_2E2 ) ) ) )
      & ( ( A
          = ( C @ ( B @ c_2Einteger_2Eint__sub_2E2 ) ) )
       => ( ( C @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(55,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( B @ c_2Einteger_2EABS_2E1 )
        = ( A @ c_2Einteger_2EABS_2E1 ) )
    <=> ( ( B
          = ( A @ c_2Einteger_2Eint__neg_2E1 ) )
        | ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__EQ__ABS) ).

thf(423,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( ( B
            = ( A @ c_2Einteger_2Eint__neg_2E1 ) )
          | ( B = A ) )
       => ( ( B @ c_2Einteger_2EABS_2E1 )
          = ( A @ c_2Einteger_2EABS_2E1 ) ) )
      & ( ( ( B @ c_2Einteger_2EABS_2E1 )
          = ( A @ c_2Einteger_2EABS_2E1 ) )
       => ( ( B
            = ( A @ c_2Einteger_2Eint__neg_2E1 ) )
          | ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(48,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ ( B @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( A @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__ADDL) ).

thf(402,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ ( B @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( A @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(11,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ ( B @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( A @ ( C @ ( B @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__ADDNEG) ).

thf(291,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ ( B @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( A @ ( C @ ( B @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(192,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
        = ( B @ ( C @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) )
    <=> ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LCANCEL__SUB) ).

thf(1124,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( A = C )
       => ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
          = ( B @ ( C @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) ) )
      & ( ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
          = ( B @ ( C @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) )
       => ( A = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(82,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
      = ( A @ ( B @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__COMM) ).

thf(545,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
      = ( A @ ( B @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(214,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( A @ ( c_2Enum_2E0_2E0 @ c_2Esptree_2Espt__acc_2E2 ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esptree_2Espt__acc__0) ).

thf(1258,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( A @ ( c_2Enum_2E0_2E0 @ c_2Esptree_2Espt__acc_2E2 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(232,axiom,
    ! [A: tyop_2Emin_2Ebool @ tyop_2Elist_2Elist] :
      ( ( c_2Enum_2E0_2E0 @ ( A @ c_2Ebitstring_2Eshiftr_2E2 ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebitstring_2Eshiftr__0) ).

thf(1356,plain,
    ! [A: tyop_2Emin_2Ebool @ tyop_2Elist_2Elist] :
      ( ( c_2Enum_2E0_2E0 @ ( A @ c_2Ebitstring_2Eshiftr_2E2 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(218,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( B @ ( A @ c_2Einteger_2Eint__mul_2E2 ) )
        = ( C @ ( A @ c_2Einteger_2Eint__mul_2E2 ) ) )
    <=> ( ( B = C )
        | ( A
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__LMUL) ).

thf(1282,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( ( B = C )
          | ( A
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
       => ( ( B @ ( A @ c_2Einteger_2Eint__mul_2E2 ) )
          = ( C @ ( A @ c_2Einteger_2Eint__mul_2E2 ) ) ) )
      & ( ( ( B @ ( A @ c_2Einteger_2Eint__mul_2E2 ) )
          = ( C @ ( A @ c_2Einteger_2Eint__mul_2E2 ) ) )
       => ( ( B = C )
          | ( A
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(1523,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__0_2E0 != c_2Einteger_2Eint__0_2E0 )
      | ( ( A @ ( skt1 @ c_2Einteger__word_2Ei2w_2E1 ) )
       != ( c_2Enum_2E0_2E0 @ ( skt1 @ c_2Ewords_2En2w_2E1 ) ) )
      | ( ( A @ sk14 )
       != c_2Enum_2E0_2E0 )
      | ( ( A @ sk13 )
       != c_2Enum_2E0_2E0 ) ),
    inference(paramod_ordered,[status(thm)],[1510,1501]) ).

thf(1524,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( ( A @ ( skt1 @ c_2Einteger__word_2Ei2w_2E1 ) )
       != ( c_2Enum_2E0_2E0 @ ( skt1 @ c_2Ewords_2En2w_2E1 ) ) )
      | ( ( A @ sk14 )
       != c_2Enum_2E0_2E0 )
      | ( ( A @ sk13 )
       != c_2Enum_2E0_2E0 ) ),
    inference(pattern_uni,[status(thm)],[1523:[]]) ).

thf(87,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A
       != ( TA @ c_2Ewords_2Eword__L_2E0 ) )
     => ( ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) )
        = ( A @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) @ c_2Einteger_2Eint__neg_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger__word_2Ew2i__neg) ).

thf(567,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A
       != ( TA @ c_2Ewords_2Eword__L_2E0 ) )
     => ( ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) )
        = ( A @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) @ c_2Einteger_2Eint__neg_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(20,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( B != c_2Enum_2E0_2E0 )
     => ( ( B @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__mod_2E2 ) )
        = ( B @ ( A @ c_2Earithmetic_2EMOD_2E2 ) @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD) ).

thf(318,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( B != c_2Enum_2E0_2E0 )
     => ( ( B @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__mod_2E2 ) )
        = ( B @ ( A @ c_2Earithmetic_2EMOD_2E2 ) @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(56,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__rem_2E2 ) )
          = ( B @ ( A @ c_2Einteger_2Eint__rem_2E2 ) ) )
        & ( ( B @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__rem_2E2 ) )
          = ( B @ ( A @ c_2Einteger_2Eint__rem_2E2 ) @ c_2Einteger_2Eint__neg_2E1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__REM__NEG) ).

thf(434,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__rem_2E2 ) )
          = ( B @ ( A @ c_2Einteger_2Eint__rem_2E2 ) ) )
        & ( ( B @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__rem_2E2 ) )
          = ( B @ ( A @ c_2Einteger_2Eint__rem_2E2 ) @ c_2Einteger_2Eint__neg_2E1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(15,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( A @ c_2Earithmetic_2ENUMERAL_2E1 )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2ENUMERAL__DEF) ).

thf(303,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( A @ c_2Earithmetic_2ENUMERAL_2E1 )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(43,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( C @ ( B @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__LADD) ).

thf(387,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( C @ ( B @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(29,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ c_2Einteger_2Eint__add_2E2 ) @ ( A @ c_2Einteger_2Eint__le_2E2 ) )
      = ( B @ ( C @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__le_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eint__arith_2Ele__move__right__left) ).

thf(345,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ c_2Einteger_2Eint__add_2E2 ) @ ( A @ c_2Einteger_2Eint__le_2E2 ) )
      = ( B @ ( C @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__le_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(92,axiom,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( C @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__slice_2E3 ) ) ) @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__bits_2E3 ) ) ) )
      = ( C @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__bits_2E3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__BITS__SLICE__THM) ).

thf(609,plain,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( C @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__slice_2E3 ) ) ) @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__bits_2E3 ) ) ) )
      = ( C @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__bits_2E3 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(95,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__sub_2E2 ) )
      = ( A @ c_2Einteger_2Eint__neg_2E1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__LZERO) ).

thf(621,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__sub_2E2 ) )
      = ( A @ c_2Einteger_2Eint__neg_2E1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(112,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
        = ( B @ ( C @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) )
    <=> ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__EQ__ADD__RCANCEL) ).

thf(700,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( A = C )
       => ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
          = ( B @ ( C @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) ) )
      & ( ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
          = ( B @ ( C @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) )
       => ( A = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(150,axiom,
    ! [TA: $tType,A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) @ ( A @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
      = ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__i2w__add) ).

thf(895,plain,
    ! [TA: $tType,A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) @ ( A @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
      = ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(1148,plain,
    ! [A: tyop_2Eone_2Eone] :
      ( ( A @ c_2EbasicSize_2Eone__size_2E1 )
      = c_2Enum_2E0_2E0 ),
    inference(cnf,[status(esa)],[1147]) ).

thf(1149,plain,
    ! [A: tyop_2Eone_2Eone] :
      ( ( A @ c_2EbasicSize_2Eone__size_2E1 )
      = c_2Enum_2E0_2E0 ),
    inference(lifteq,[status(thm)],[1148]) ).

thf(230,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( ( A @ c_2Einteger_2Eint__neg_2E1 )
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
    <=> ( A
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__EQ0) ).

thf(1344,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( ( A
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
       => ( ( A @ c_2Einteger_2Eint__neg_2E1 )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
      & ( ( ( A @ c_2Einteger_2Eint__neg_2E1 )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
       => ( A
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(170,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__NEG) ).

thf(1022,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(219,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__RZERO) ).

thf(1293,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(24,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( C @ ( B @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) )
      = ( C @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__MULT__ASSOC) ).

thf(330,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( C @ ( B @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) )
      = ( C @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(64,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( A @ ( TA @ c_2Einteger__word_2Eword__sdiv_2E2 ) ) )
      = ( B @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) @ ( A @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) @ c_2Einteger_2Eint__div_2E2 ) @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__sdiv__def) ).

thf(462,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( A @ ( TA @ c_2Einteger__word_2Eword__sdiv_2E2 ) ) )
      = ( B @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) @ ( A @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) @ c_2Einteger_2Eint__div_2E2 ) @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(188,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2EABS_2E1 )
      = ( A @ c_2Einteger_2Eint__of__num_2E1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ABS__NUM) ).

thf(1112,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2EABS_2E1 )
      = ( A @ c_2Einteger_2Eint__of__num_2E1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(239,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( C @ ( A @ c_2Einteger_2Eint__mul_2E2 ) )
        = ( C @ ( B @ c_2Einteger_2Eint__mul_2E2 ) ) )
    <=> ( ( A = B )
        | ( C
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__RMUL) ).

thf(1381,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( ( A = B )
          | ( C
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
       => ( ( C @ ( A @ c_2Einteger_2Eint__mul_2E2 ) )
          = ( C @ ( B @ c_2Einteger_2Eint__mul_2E2 ) ) ) )
      & ( ( ( C @ ( A @ c_2Einteger_2Eint__mul_2E2 ) )
          = ( C @ ( B @ c_2Einteger_2Eint__mul_2E2 ) ) )
       => ( ( A = B )
          | ( C
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(74,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( ( B @ ( A @ c_2Einteger_2Eint__mod_2E2 ) )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
        & ( B
         != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
     => ( ( B @ ( B @ ( A @ c_2Einteger_2Eint__div_2E2 ) @ c_2Einteger_2Eint__mul_2E2 ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIV__MUL__ID) ).

thf(521,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( ( B @ ( A @ c_2Einteger_2Eint__mod_2E2 ) )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
        & ( B
         != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
     => ( ( B @ ( B @ ( A @ c_2Einteger_2Eint__div_2E2 ) @ c_2Einteger_2Eint__mul_2E2 ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(47,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__le_2E2 ) )
      = ( A @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__le_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__NEGL) ).

thf(399,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__le_2E2 ) )
      = ( A @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__le_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(135,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
        = ( B @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__EQ__NEG) ).

thf(827,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( A = B )
       => ( ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
          = ( B @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) ) ) )
      & ( ( ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
          = ( B @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(174,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) @ c_2Einteger_2Eint__neg_2E1 )
      = ( A @ ( B @ c_2Einteger_2Eint__sub_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__SUB) ).

thf(1044,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) @ c_2Einteger_2Eint__neg_2E1 )
      = ( A @ ( B @ c_2Einteger_2Eint__sub_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(16,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( B != c_2Enum_2E0_2E0 )
     => ( ( B @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__rem_2E2 ) )
        = ( B @ ( A @ c_2Earithmetic_2EMOD_2E2 ) @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__REM) ).

thf(306,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( B != c_2Enum_2E0_2E0 )
     => ( ( B @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__rem_2E2 ) )
        = ( B @ ( A @ c_2Earithmetic_2EMOD_2E2 ) @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(167,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A = B )
    <=> ( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 )
        = ( A @ c_2Einteger_2Eint__neg_2E1 @ ( B @ c_2Einteger_2Eint__add_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eint__arith_2Eeq__move__all__right) ).

thf(1000,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 )
          = ( A @ c_2Einteger_2Eint__neg_2E1 @ ( B @ c_2Einteger_2Eint__add_2E2 ) ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 )
          = ( A @ c_2Einteger_2Eint__neg_2E1 @ ( B @ c_2Einteger_2Eint__add_2E2 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(277,plain,
    ! [TA: $tType,B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
      = ( B @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) ) ),
    inference(cnf,[status(esa)],[276]) ).

thf(278,plain,
    ! [TA: $tType,B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) )
      = ( B @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) ) ),
    inference(lifteq,[status(thm)],[277]) ).

thf(1518,plain,
    ! [B: tyop_2Einteger_2Eint,A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ ( B @ c_2Einteger_2Eint__exp_2E2 ) ) )
      | ( c_2Einteger_2Eint__0_2E0 != c_2Einteger_2Eint__0_2E0 )
      | ( ( A @ sk14 )
       != c_2Enum_2E0_2E0 )
      | ( ( A @ sk13 )
       != c_2Enum_2E0_2E0 ) ),
    inference(paramod_ordered,[status(thm)],[1510,1502]) ).

thf(1519,plain,
    ! [B: tyop_2Einteger_2Eint,A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ ( B @ c_2Einteger_2Eint__exp_2E2 ) ) )
      | ( ( A @ sk14 )
       != c_2Enum_2E0_2E0 )
      | ( ( A @ sk13 )
       != c_2Enum_2E0_2E0 ) ),
    inference(simp,[status(thm)],[1518]) ).

thf(1520,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( ( c_2Enum_2E0_2E0 @ ( A @ c_2Einteger_2Eint__exp_2E2 ) @ sk14 )
       != c_2Enum_2E0_2E0 )
      | ( ( c_2Enum_2E0_2E0 @ ( A @ c_2Einteger_2Eint__exp_2E2 ) @ sk13 )
       != c_2Enum_2E0_2E0 ) ),
    inference(pattern_uni,[status(thm)],[1519:[bind(A,$thf( c_2Enum_2E0_2E0 @ ( C @ c_2Einteger_2Eint__exp_2E2 ) )),bind(B,$thf( C ))]]) ).

thf(1528,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( ( c_2Enum_2E0_2E0 @ ( A @ c_2Einteger_2Eint__exp_2E2 ) @ sk14 )
       != c_2Enum_2E0_2E0 )
      | ( ( c_2Enum_2E0_2E0 @ ( A @ c_2Einteger_2Eint__exp_2E2 ) @ sk13 )
       != c_2Enum_2E0_2E0 ) ),
    inference(simp,[status(thm)],[1520]) ).

thf(172,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
      = ( B @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__ADD) ).

thf(1034,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
      = ( B @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(83,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__sub_2E2 ) )
      = ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__RNEG) ).

thf(548,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__sub_2E2 ) )
      = ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(179,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( A @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) )
        = ( B @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger__word_2Ew2i__11) ).

thf(1081,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( A = B )
       => ( ( A @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) )
          = ( B @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) ) ) )
      & ( ( ( A @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) )
          = ( B @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(28,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) )
      = ( A @ ( B @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__MULT__COMM) ).

thf(342,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) )
      = ( A @ ( B @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(169,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( A @ ( A @ ( B @ c_2Einteger_2Eint__mod_2E2 ) @ ( A @ ( C @ c_2Einteger_2Eint__mod_2E2 ) @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__mod_2E2 ) )
        = ( A @ ( B @ ( C @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__mod_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__PLUS) ).

thf(1018,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( A @ ( A @ ( B @ c_2Einteger_2Eint__mod_2E2 ) @ ( A @ ( C @ c_2Einteger_2Eint__mod_2E2 ) @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__mod_2E2 ) )
        = ( A @ ( B @ ( C @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__mod_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(194,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ! [B: tyop_2Einteger_2Eint] :
          ( ( A @ ( A @ ( B @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__mod_2E2 ) )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__COMMON__FACTOR) ).

thf(1134,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ! [B: tyop_2Einteger_2Eint] :
          ( ( A @ ( A @ ( B @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__mod_2E2 ) )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(71,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
      = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__RINV) ).

thf(487,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
      = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(99,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( C @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = ( B @ ( C @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__SUB__SYM) ).

thf(640,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( C @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = ( B @ ( C @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(171,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) )
        = C )
    <=> ( A
        = ( B @ ( C @ c_2Einteger_2Eint__add_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__SUB__RADD) ).

thf(1025,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( A
          = ( B @ ( C @ c_2Einteger_2Eint__add_2E2 ) ) )
       => ( ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) )
          = C ) )
      & ( ( ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) )
          = C )
       => ( A
          = ( B @ ( C @ c_2Einteger_2Eint__add_2E2 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(145,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( ( ( C @ ( B @ c_2Einteger_2Eint__mod_2E2 ) )
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
          | ( ( C @ ( A @ c_2Einteger_2Eint__mod_2E2 ) )
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
        & ( C
         != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
     => ( ( C @ ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__div_2E2 ) )
        = ( C @ ( B @ c_2Einteger_2Eint__div_2E2 ) @ ( C @ ( A @ c_2Einteger_2Eint__div_2E2 ) @ c_2Einteger_2Eint__add_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__DIV) ).

thf(872,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( ( ( C @ ( B @ c_2Einteger_2Eint__mod_2E2 ) )
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
          | ( ( C @ ( A @ c_2Einteger_2Eint__mod_2E2 ) )
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
        & ( C
         != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
     => ( ( C @ ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__div_2E2 ) )
        = ( C @ ( B @ c_2Einteger_2Eint__div_2E2 ) @ ( C @ ( A @ c_2Einteger_2Eint__div_2E2 ) @ c_2Einteger_2Eint__add_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(113,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__sub_2E2 ) )
      = ( A @ ( B @ c_2Einteger_2Eint__sub_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__NEG2) ).

thf(707,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__sub_2E2 ) )
      = ( A @ ( B @ c_2Einteger_2Eint__sub_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(52,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ! [B: tyop_2Einteger_2Eint] :
          ( ( A @ ( A @ ( B @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__rem_2E2 ) )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__REM__COMMON__FACTOR) ).

thf(414,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ! [B: tyop_2Einteger_2Eint] :
          ( ( A @ ( A @ ( B @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__rem_2E2 ) )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(23,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ c_2Einteger_2Eint__add_2E2 ) @ ( C @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( B @ ( A @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__RADD) ).

thf(327,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ c_2Einteger_2Eint__add_2E2 ) @ ( C @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( B @ ( A @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(156,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__RNEG) ).

thf(954,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(261,axiom,
    ! [A: tyop_2Enum_2Enum] :
      ( ? [B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
          ( A
          = ( C @ ( B @ c_2Enumpair_2Encons_2E2 ) ) )
      | ( A = c_2Enum_2E0_2E0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Enumpair_2Enlist__cases) ).

thf(1484,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ? [B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
          ( A
          = ( C @ ( B @ c_2Enumpair_2Encons_2E2 ) ) )
      | ( A = c_2Enum_2E0_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(8,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
    ? [B: tyop_2Emin_2Ebool @ tyop_2Elist_2Elist] :
      ( A
      = ( B @ ( TA @ c_2Ebitstring_2Ev2w_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebitstring_2Ebitstring__nchotomy) ).

thf(282,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
    ? [B: tyop_2Emin_2Ebool @ tyop_2Elist_2Elist] :
      ( A
      = ( B @ ( TA @ c_2Ebitstring_2Ev2w_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(199,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
    ? [B: tyop_2Einteger_2Eint] :
      ( A
      = ( B @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger__word_2Eint__word__nchotomy) ).

thf(1156,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
    ? [B: tyop_2Einteger_2Eint] :
      ( A
      = ( B @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(177,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( A @ ( B @ c_2Einteger_2Eint__add_2E2 ) @ ( C @ c_2Einteger_2Eint__add_2E2 ) )
      = ( A @ ( B @ ( C @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__add_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__ASSOC) ).

thf(1053,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( A @ ( B @ c_2Einteger_2Eint__add_2E2 ) @ ( C @ c_2Einteger_2Eint__add_2E2 ) )
      = ( A @ ( B @ ( C @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__add_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(107,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) @ c_2Einteger_2Eint__mul_2E2 ) )
      = ( C @ ( B @ c_2Einteger_2Eint__mul_2E2 ) @ ( C @ ( A @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__sub_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__RDISTRIB) ).

thf(673,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) @ c_2Einteger_2Eint__mul_2E2 ) )
      = ( C @ ( B @ c_2Einteger_2Eint__mul_2E2 ) @ ( C @ ( A @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__sub_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(249,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
        = ( A @ c_2Einteger_2Eint__neg_2E1 ) )
    <=> ( A
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__SAME__EQ) ).

thf(1432,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( ( A
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
       => ( A
          = ( A @ c_2Einteger_2Eint__neg_2E1 ) ) )
      & ( ( A
          = ( A @ c_2Einteger_2Eint__neg_2E1 ) )
       => ( A
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(221,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger__word_2Ei2w__w2i) ).

thf(1300,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(128,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A @ ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) @ c_2Einteger_2Eint__sub_2E2 ) )
      = ( B @ c_2Einteger_2Eint__neg_2E1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__SUB) ).

thf(791,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A @ ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) @ c_2Einteger_2Eint__sub_2E2 ) )
      = ( B @ c_2Einteger_2Eint__neg_2E1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(210,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( A @ ( A @ c_2Einteger_2Eint__mod_2E2 ) )
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__ID) ).

thf(1235,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( A @ ( A @ c_2Einteger_2Eint__mod_2E2 ) )
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(90,axiom,
    ( ! [A: tyop_2Einteger_2Eint] :
        ( ( ( A @ c_2Einteger_2Eint__neg_2E1 )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
      <=> ( A
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
    & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( ( A @ c_2Einteger_2Eint__of__num_2E1 )
          = ( B @ c_2Einteger_2Eint__of__num_2E1 ) )
      <=> ( A = B ) )
    & ! [A: tyop_2Einteger_2Eint] :
        ( ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__neg_2E1 )
        = A )
    & ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
        ( ( B
         != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
       => ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__mod_2E2 ) )
          = ( B @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__mod_2E2 ) @ c_2Einteger_2Eint__neg_2E1 ) ) )
    & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( B != c_2Enum_2E0_2E0 )
       => ( ( B @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__mod_2E2 ) )
          = ( B @ ( A @ c_2Earithmetic_2EMOD_2E2 ) @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__CALCULATE) ).

thf(576,plain,
    ( ! [A: tyop_2Einteger_2Eint] :
        ( ( ( A
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
         => ( ( A @ c_2Einteger_2Eint__neg_2E1 )
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
        & ( ( ( A @ c_2Einteger_2Eint__neg_2E1 )
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
         => ( A
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ) )
    & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( ( A = B )
         => ( ( A @ c_2Einteger_2Eint__of__num_2E1 )
            = ( B @ c_2Einteger_2Eint__of__num_2E1 ) ) )
        & ( ( ( A @ c_2Einteger_2Eint__of__num_2E1 )
            = ( B @ c_2Einteger_2Eint__of__num_2E1 ) )
         => ( A = B ) ) )
    & ! [A: tyop_2Einteger_2Eint] :
        ( ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__neg_2E1 )
        = A )
    & ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
        ( ( B
         != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
       => ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__mod_2E2 ) )
          = ( B @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__mod_2E2 ) @ c_2Einteger_2Eint__neg_2E1 ) ) )
    & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( B != c_2Enum_2E0_2E0 )
       => ( ( B @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__mod_2E2 ) )
          = ( B @ ( A @ c_2Earithmetic_2EMOD_2E2 ) @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(155,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ c_2Einteger_2Eint__sub_2E2 ) @ ( A @ c_2Einteger_2Eint__sub_2E2 ) )
      = ( B @ ( C @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__sub_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eint__arith_2EINT__SUB__SUB3) ).

thf(951,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ c_2Einteger_2Eint__sub_2E2 ) @ ( A @ c_2Einteger_2Eint__sub_2E2 ) )
      = ( B @ ( C @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__sub_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(229,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
        = B )
    <=> ( A
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__LID__UNIQ) ).

thf(1336,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( A
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
       => ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
          = B ) )
      & ( ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
          = B )
       => ( A
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(100,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) @ c_2Einteger_2Eint__add_2E2 ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__ADD) ).

thf(643,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) @ c_2Einteger_2Eint__add_2E2 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(118,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( A @ c_2Einteger_2Eint__neg_2E1 @ ( B @ c_2Einteger_2Eint__add_2E2 ) @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eint__arith_2Elt__move__all__right) ).

thf(744,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( A @ c_2Einteger_2Eint__neg_2E1 @ ( B @ c_2Einteger_2Eint__add_2E2 ) @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(26,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__le_2E2 ) )
      = ( A @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__le_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__DOUBLE) ).

thf(336,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__le_2E2 ) )
      = ( A @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__le_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(182,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__mod_2E2 ) )
        = ( B @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__mod_2E2 ) @ c_2Einteger_2Eint__neg_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__NEG) ).

thf(1094,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__mod_2E2 ) )
        = ( B @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__mod_2E2 ) @ c_2Einteger_2Eint__neg_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(93,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
      ( ( D @ ( C @ c_2Einteger_2Eint__add_2E2 ) @ ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__sub_2E2 ) )
      = ( D @ ( B @ c_2Einteger_2Eint__sub_2E2 ) @ ( C @ ( A @ c_2Einteger_2Eint__sub_2E2 ) @ c_2Einteger_2Eint__add_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD2__SUB2) ).

thf(612,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint,D: tyop_2Einteger_2Eint] :
      ( ( D @ ( C @ c_2Einteger_2Eint__add_2E2 ) @ ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__sub_2E2 ) )
      = ( D @ ( B @ c_2Einteger_2Eint__sub_2E2 ) @ ( C @ ( A @ c_2Einteger_2Eint__sub_2E2 ) @ c_2Einteger_2Eint__add_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(164,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eint__arith_2Elt__move__all__left) ).

thf(991,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(280,plain,
    ! [B: tyop_2Einteger_2Eint,A: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ ( A @ c_2Einteger_2Eint__le_2E2 ) )
      = ( B @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__le_2E2 ) ) ),
    inference(cnf,[status(esa)],[279]) ).

thf(281,plain,
    ! [B: tyop_2Einteger_2Eint,A: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ ( A @ c_2Einteger_2Eint__le_2E2 ) )
      = ( B @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__le_2E2 ) ) ),
    inference(lifteq,[status(thm)],[280]) ).

thf(1617,plain,
    ! [B: tyop_2Einteger_2Eint,A: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ ( A @ c_2Einteger_2Eint__le_2E2 ) )
      = ( B @ ( c_2Einteger_2Eint__0_2E0 @ c_2Einteger_2Eint__le_2E2 ) ) ),
    inference(rewrite,[status(thm)],[281,1177]) ).

thf(65,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__neg_2E1 )
      = ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__mul_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__RMUL) ).

thf(465,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__neg_2E1 )
      = ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__mul_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(97,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( C @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
        = ( C @ ( B @ c_2Einteger_2Eint__add_2E2 ) ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__RADD) ).

thf(627,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( A = B )
       => ( ( C @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
          = ( C @ ( B @ c_2Einteger_2Eint__add_2E2 ) ) ) )
      & ( ( ( C @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
          = ( C @ ( B @ c_2Einteger_2Eint__add_2E2 ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(60,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( B @ ( A @ c_2Einteger_2Eint__mod_2E2 ) )
        = ( B @ ( B @ ( A @ c_2Einteger_2Eint__div_2E2 ) @ c_2Einteger_2Eint__mul_2E2 ) @ ( A @ c_2Einteger_2Eint__sub_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2Eint__mod) ).

thf(450,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( B @ ( A @ c_2Einteger_2Eint__mod_2E2 ) )
        = ( B @ ( B @ ( A @ c_2Einteger_2Eint__div_2E2 ) @ c_2Einteger_2Eint__mul_2E2 ) @ ( A @ c_2Einteger_2Eint__sub_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(35,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 )
        = ( B @ ( C @ c_2Einteger_2Eint__add_2E2 ) ) )
     => ( ( A @ ( C @ c_2Einteger_2Eint__add_2E2 ) @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__le_2E2 ) )
        = ( A @ ( B @ c_2Einteger_2Eint__le_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eint__arith_2Eeq__context__rwt1) ).

thf(363,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 )
        = ( B @ ( C @ c_2Einteger_2Eint__add_2E2 ) ) )
     => ( ( A @ ( C @ c_2Einteger_2Eint__add_2E2 ) @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__le_2E2 ) )
        = ( A @ ( B @ c_2Einteger_2Eint__le_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(80,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__ADD) ).

thf(539,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(244,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
        = A )
    <=> ( B
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__RID__UNIQ) ).

thf(1412,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( B
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
       => ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
          = A ) )
      & ( ( ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
          = A )
       => ( B
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(1516,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Einteger_2Eint__0_2E0 != c_2Einteger_2Eint__0_2E0 )
      | ( ( A @ c_2Einteger_2Eint__neg_2E1 )
        = c_2Einteger_2Eint__0_2E0 )
      | ( ( A @ sk14 )
       != c_2Enum_2E0_2E0 )
      | ( ( A @ sk13 )
       != c_2Enum_2E0_2E0 ) ),
    inference(paramod_ordered,[status(thm)],[1510,1507]) ).

thf(1517,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( ( A @ c_2Einteger_2Eint__neg_2E1 )
        = c_2Einteger_2Eint__0_2E0 )
      | ( ( A @ sk14 )
       != c_2Enum_2E0_2E0 )
      | ( ( A @ sk13 )
       != c_2Enum_2E0_2E0 ) ),
    inference(pattern_uni,[status(thm)],[1516:[]]) ).

thf(139,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( TA @ c_2Ewords_2Eword__abs_2E1 ) )
      = ( A @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) @ c_2Einteger_2EABS_2E1 @ c_2Einteger_2ENum_2E1 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__abs__w2i) ).

thf(844,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( TA @ c_2Ewords_2Eword__abs_2E1 ) )
      = ( A @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) @ c_2Einteger_2EABS_2E1 @ c_2Einteger_2ENum_2E1 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(253,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( ( B @ ( A @ c_2Einteger_2Eint__mul_2E2 ) )
          = ( C @ ( A @ c_2Einteger_2Eint__mul_2E2 ) ) )
        & ( A
         != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
     => ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__LMUL__IMP) ).

thf(1453,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( ( ( B @ ( A @ c_2Einteger_2Eint__mul_2E2 ) )
          = ( C @ ( A @ c_2Einteger_2Eint__mul_2E2 ) ) )
        & ( A
         != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(260,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2Ebit__count__upto_2E2 ) ) )
      = c_2Enum_2E0_2E0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2Ebit__count__upto__0) ).

thf(1481,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2Ebit__count__upto_2E2 ) ) )
      = c_2Enum_2E0_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(31,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( A @ c_2Einteger_2Eint__neg_2E1 @ ( C @ c_2Einteger_2Eint__add_2E2 ) @ ( B @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eint__arith_2Elt__move__left__right) ).

thf(351,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( A @ c_2Einteger_2Eint__neg_2E1 @ ( C @ c_2Einteger_2Eint__add_2E2 ) @ ( B @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(44,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( TA @ c_2Ewords_2Eword__abs_2E1 ) @ ( TA @ c_2Ewords_2Eword__abs_2E1 ) )
      = ( A @ ( TA @ c_2Ewords_2Eword__abs_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2Eword__abs__word__abs) ).

thf(390,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( TA @ c_2Ewords_2Eword__abs_2E1 ) @ ( TA @ c_2Ewords_2Eword__abs_2E1 ) )
      = ( A @ ( TA @ c_2Ewords_2Eword__abs_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(40,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__abs_2E1 ) )
      = ( A @ ( B @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__abs_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2Eword__abs__diff) ).

thf(378,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__abs_2E1 ) )
      = ( A @ ( B @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__abs_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(105,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( B @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__mod_2E2 ) )
        = ( B @ ( A @ ( B @ c_2Einteger_2Eint__sub_2E2 ) @ c_2Einteger_2Eint__mod_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__NEG__NUMERATOR) ).

thf(667,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( B @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__mod_2E2 ) )
        = ( B @ ( A @ ( B @ c_2Einteger_2Eint__sub_2E2 ) @ c_2Einteger_2Eint__mod_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(207,axiom,
    ( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( ( ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 )
            = ( B @ c_2Einteger_2Eint__of__num_2E1 ) )
        <=> ( ( B = c_2Enum_2E0_2E0 )
            & ( A = c_2Enum_2E0_2E0 ) ) )
        & ( ( ( A @ c_2Einteger_2Eint__of__num_2E1 )
            = ( B @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 ) )
        <=> ( ( B = c_2Enum_2E0_2E0 )
            & ( A = c_2Enum_2E0_2E0 ) ) ) )
    & ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
        ( ( ( A @ c_2Einteger_2Eint__neg_2E1 )
          = ( B @ c_2Einteger_2Eint__neg_2E1 ) )
      <=> ( A = B ) )
    & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( ( A @ c_2Einteger_2Eint__of__num_2E1 )
          = ( B @ c_2Einteger_2Eint__of__num_2E1 ) )
      <=> ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__CALCULATE) ).

thf(1193,plain,
    ( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( ( ( B = c_2Enum_2E0_2E0 )
            & ( A = c_2Enum_2E0_2E0 ) )
         => ( ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 )
            = ( B @ c_2Einteger_2Eint__of__num_2E1 ) ) )
        & ( ( ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 )
            = ( B @ c_2Einteger_2Eint__of__num_2E1 ) )
         => ( ( B = c_2Enum_2E0_2E0 )
            & ( A = c_2Enum_2E0_2E0 ) ) )
        & ( ( ( B = c_2Enum_2E0_2E0 )
            & ( A = c_2Enum_2E0_2E0 ) )
         => ( ( A @ c_2Einteger_2Eint__of__num_2E1 )
            = ( B @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 ) ) )
        & ( ( ( A @ c_2Einteger_2Eint__of__num_2E1 )
            = ( B @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 ) )
         => ( ( B = c_2Enum_2E0_2E0 )
            & ( A = c_2Enum_2E0_2E0 ) ) ) )
    & ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
        ( ( ( A = B )
         => ( ( A @ c_2Einteger_2Eint__neg_2E1 )
            = ( B @ c_2Einteger_2Eint__neg_2E1 ) ) )
        & ( ( ( A @ c_2Einteger_2Eint__neg_2E1 )
            = ( B @ c_2Einteger_2Eint__neg_2E1 ) )
         => ( A = B ) ) )
    & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( ( A = B )
         => ( ( A @ c_2Einteger_2Eint__of__num_2E1 )
            = ( B @ c_2Einteger_2Eint__of__num_2E1 ) ) )
        & ( ( ( A @ c_2Einteger_2Eint__of__num_2E1 )
            = ( B @ c_2Einteger_2Eint__of__num_2E1 ) )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(68,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( A @ ( B @ c_2Egcd_2Elcm_2E2 ) )
      = ( B @ ( A @ c_2Egcd_2Elcm_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Egcd_2ELCM__COMM) ).

thf(478,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( A @ ( B @ c_2Egcd_2Elcm_2E2 ) )
      = ( B @ ( A @ c_2Egcd_2Elcm_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(121,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = ( B @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2Eword__sub__def) ).

thf(763,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = ( B @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(109,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) @ ( A @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) @ c_2Einteger_2Eint__add_2E2 ) @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) )
      = ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__add__i2w) ).

thf(684,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) @ ( A @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) @ c_2Einteger_2Eint__add_2E2 ) @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) )
      = ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(224,axiom,
    ( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 )
    = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__0) ).

thf(1309,plain,
    ( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__neg_2E1 )
    = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(79,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( C @ ( B @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = ( C @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__PLUS) ).

thf(536,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( C @ ( B @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = ( C @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(14,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__le_2E2 ) )
      = ( A @ ( B @ c_2Einteger_2Eint__le_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LE__NEG) ).

thf(300,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__le_2E2 ) )
      = ( A @ ( B @ c_2Einteger_2Eint__le_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(59,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( A @ ( B @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__SUB2) ).

thf(447,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( A @ ( B @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(19,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( B @ ( C @ c_2Einteger_2Eint__add_2E2 ) @ ( A @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__ADDNEG2) ).

thf(315,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint,C: tyop_2Einteger_2Eint] :
      ( ( C @ ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( B @ ( C @ c_2Einteger_2Eint__add_2E2 ) @ ( A @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(208,axiom,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( A @ ( B @ ( TA @ c_2Ewords_2Eword__slice_2E3 ) ) ) )
      = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SLICE__ZERO2) ).

thf(1229,plain,
    ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( A @ ( B @ ( TA @ c_2Ewords_2Eword__slice_2E3 ) ) ) )
      = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(1160,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( ( A @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
        | ( A
         != ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ) )
      & ( ( A
          = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) )
        | ( ( A @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) )
         != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ),
    inference(cnf,[status(esa)],[1159]) ).

thf(1162,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( A @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) )
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
      | ( A
       != ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ) ),
    inference(cnfConj,[status(thm)],[1160]) ).

thf(1164,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( A @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) )
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
      | ( A
       != ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ) ),
    inference(lifteq,[status(thm)],[1162]) ).

thf(1165,plain,
    ! [TA: $tType] :
      ( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 )
      = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) ) ),
    inference(simp,[status(thm)],[1164]) ).

thf(1546,plain,
    ! [TA: $tType] :
      ( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) )
      = c_2Einteger_2Eint__0_2E0 ),
    inference(rewrite,[status(thm)],[1165,1177]) ).

thf(49,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__le_2E2 ) )
      = ( A @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__le_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__LE0) ).

thf(405,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__le_2E2 ) )
      = ( A @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__le_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(222,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__mul_2E2 ) )
      = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__RZERO) ).

thf(1303,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__mul_2E2 ) )
      = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(949,plain,
    ! [TA: $tType] :
      ( ( TA @ c_2Ewords_2Eword__L_2E0 @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
      = ( TA @ c_2Ewords_2Eword__L_2E0 ) ),
    inference(cnf,[status(esa)],[948]) ).

thf(950,plain,
    ! [TA: $tType] :
      ( ( TA @ c_2Ewords_2Eword__L_2E0 @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
      = ( TA @ c_2Ewords_2Eword__L_2E0 ) ),
    inference(lifteq,[status(thm)],[949]) ).

thf(183,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A @ ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__sub_2E2 ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__SUB) ).

thf(1097,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A @ ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) @ c_2Einteger_2Eint__sub_2E2 ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(86,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A @ ( B @ c_2Einteger_2Eint__add_2E2 ) )
      = ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__SYM) ).

thf(564,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A @ ( B @ c_2Einteger_2Eint__add_2E2 ) )
      = ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(304,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( A @ c_2Earithmetic_2ENUMERAL_2E1 )
      = A ),
    inference(cnf,[status(esa)],[303]) ).

thf(305,plain,
    ! [A: tyop_2Enum_2Enum] :
      ( ( A @ c_2Earithmetic_2ENUMERAL_2E1 )
      = A ),
    inference(lifteq,[status(thm)],[304]) ).

thf(12,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( A @ ( B @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__LT) ).

thf(294,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__lt_2E2 ) )
      = ( A @ ( B @ c_2Einteger_2Eint__lt_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(131,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A @ ( B @ c_2Einteger_2Eint__add_2E2 ) )
      = ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__COMM) ).

thf(807,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A @ ( B @ c_2Einteger_2Eint__add_2E2 ) )
      = ( B @ ( A @ c_2Einteger_2Eint__add_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(1334,plain,
    ! [TA: $tType] :
      ( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
      = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(cnf,[status(esa)],[1333]) ).

thf(1335,plain,
    ! [TA: $tType] :
      ( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) )
      = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(lifteq,[status(thm)],[1334]) ).

thf(178,axiom,
    ( ! [A: tyop_2Einteger_2Eint] :
        ( ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__neg_2E1 )
        = A )
    & ! [A: tyop_2Einteger_2Eint] :
        ( ( ( A @ c_2Einteger_2Eint__neg_2E1 )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
      <=> ( A
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
    & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( ( A @ c_2Einteger_2Eint__of__num_2E1 )
          = ( B @ c_2Einteger_2Eint__of__num_2E1 ) )
      <=> ( A = B ) )
    & ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
        ( ( B
         != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
       => ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__div_2E2 ) )
          = ( B @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__div_2E2 ) ) ) )
    & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( B != c_2Enum_2E0_2E0 )
       => ( ( B @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__div_2E2 ) )
          = ( B @ ( A @ c_2Earithmetic_2EDIV_2E2 ) @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIV__CALCULATE) ).

thf(1056,plain,
    ( ! [A: tyop_2Einteger_2Eint] :
        ( ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__neg_2E1 )
        = A )
    & ! [A: tyop_2Einteger_2Eint] :
        ( ( ( A
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
         => ( ( A @ c_2Einteger_2Eint__neg_2E1 )
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
        & ( ( ( A @ c_2Einteger_2Eint__neg_2E1 )
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
         => ( A
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ) )
    & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( ( A = B )
         => ( ( A @ c_2Einteger_2Eint__of__num_2E1 )
            = ( B @ c_2Einteger_2Eint__of__num_2E1 ) ) )
        & ( ( ( A @ c_2Einteger_2Eint__of__num_2E1 )
            = ( B @ c_2Einteger_2Eint__of__num_2E1 ) )
         => ( A = B ) ) )
    & ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
        ( ( B
         != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
       => ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__div_2E2 ) )
          = ( B @ ( A @ c_2Einteger_2Eint__neg_2E1 @ c_2Einteger_2Eint__div_2E2 ) ) ) )
    & ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( B != c_2Enum_2E0_2E0 )
       => ( ( B @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__div_2E2 ) )
          = ( B @ ( A @ c_2Earithmetic_2EDIV_2E2 ) @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(158,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( A @ c_2Einteger_2Eint__neg_2E1 )
        = B )
    <=> ( A
        = ( B @ c_2Einteger_2Eint__neg_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__EQ) ).

thf(960,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( A
          = ( B @ c_2Einteger_2Eint__neg_2E1 ) )
       => ( ( A @ c_2Einteger_2Eint__neg_2E1 )
          = B ) )
      & ( ( ( A @ c_2Einteger_2Eint__neg_2E1 )
          = B )
       => ( A
          = ( B @ c_2Einteger_2Eint__neg_2E1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(111,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( A @ ( A @ ( B @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__div_2E2 ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIV__RMUL) ).

thf(696,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( A @ ( A @ ( B @ c_2Einteger_2Eint__mul_2E2 ) @ c_2Einteger_2Eint__div_2E2 ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(147,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( TA @ c_2Ewords_2Ew2n_2E1 ) @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ ( TA @ c_2Ewords_2Ew2n_2E1 ) @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__sub_2E2 ) @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) )
      = ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__sub__i2w__w2n) ).

thf(886,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( TA @ c_2Ewords_2Ew2n_2E1 ) @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ ( TA @ c_2Ewords_2Ew2n_2E1 ) @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__sub_2E2 ) @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) )
      = ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(96,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A @ ( B @ c_2Einteger_2Eint__mul_2E2 ) )
      = ( B @ ( A @ c_2Einteger_2Eint__mul_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__SYM) ).

thf(624,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A @ ( B @ c_2Einteger_2Eint__mul_2E2 ) )
      = ( B @ ( A @ c_2Einteger_2Eint__mul_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(231,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( A @ ( A @ ( B @ c_2Einteger_2Eint__mod_2E2 ) @ c_2Einteger_2Eint__mod_2E2 ) )
        = ( A @ ( B @ c_2Einteger_2Eint__mod_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MOD__MOD) ).

thf(1352,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( A @ ( A @ ( B @ c_2Einteger_2Eint__mod_2E2 ) @ c_2Einteger_2Eint__mod_2E2 ) )
        = ( A @ ( B @ c_2Einteger_2Eint__mod_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(215,axiom,
    ! [TA: $tType] :
      ( ! [A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
          ( ( A @ ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
          = A )
      & ! [A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
          ( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
          = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__ADD__0) ).

thf(1261,plain,
    ! [TA: $tType] :
      ( ! [A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
          ( ( A @ ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
          = A )
      & ! [A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
          ( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(216,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( B @ ( A @ c_2Einteger_2Eint__mul_2E2 ) )
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
    <=> ( ( B
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
        | ( A
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ENTIRE) ).

thf(1268,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( ( B
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
          | ( A
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
       => ( ( B @ ( A @ c_2Einteger_2Eint__mul_2E2 ) )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) )
      & ( ( ( B @ ( A @ c_2Einteger_2Eint__mul_2E2 ) )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
       => ( ( B
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
          | ( A
            = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(238,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( A @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__div_2E2 ) )
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIV__0) ).

thf(1378,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A
       != ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
     => ( ( A @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__div_2E2 ) )
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(63,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) @ ( A @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) @ c_2Einteger_2Eint__mul_2E2 ) @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) )
      = ( B @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger__word_2Eword__mul__i2w) ).

thf(459,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( B @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) @ ( A @ ( TA @ c_2Einteger__word_2Ew2i_2E1 ) @ c_2Einteger_2Eint__mul_2E2 ) @ ( TA @ c_2Einteger__word_2Ei2w_2E1 ) )
      = ( B @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(141,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) )
      = ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__add_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2Eint__sub) ).

thf(850,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__sub_2E2 ) )
      = ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__add_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(1430,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( c_2Enum_2E0_2E0 @ ( TB @ c_2Ewords_2En2w_2E1 ) @ ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TC @ ( TB @ ( TA @ c_2Ewords_2Eword__concat_2E2 ) ) ) ) )
      = ( c_2Enum_2E0_2E0 @ ( TC @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(cnf,[status(esa)],[1429]) ).

thf(1431,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( c_2Enum_2E0_2E0 @ ( TB @ c_2Ewords_2En2w_2E1 ) @ ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TC @ ( TB @ ( TA @ c_2Ewords_2Eword__concat_2E2 ) ) ) ) )
      = ( c_2Enum_2E0_2E0 @ ( TC @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(lifteq,[status(thm)],[1430]) ).

thf(1297,plain,
    ~ ? [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
        ( ( A @ ( B @ c_2Enumpair_2Encons_2E2 ) )
        = c_2Enum_2E0_2E0 ),
    inference(miniscope,[status(thm)],[1296]) ).

thf(1298,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( A @ ( B @ c_2Enumpair_2Encons_2E2 ) )
     != c_2Enum_2E0_2E0 ),
    inference(cnf,[status(esa)],[1297]) ).

thf(1299,plain,
    ! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
      ( ( A @ ( B @ c_2Enumpair_2Encons_2E2 ) )
     != c_2Enum_2E0_2E0 ),
    inference(lifteq,[status(thm)],[1298]) ).

thf(37,axiom,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A @ c_2Einteger_2Eint__neg_2E1 @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__le_2E2 ) )
      = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__le_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__GE0) ).

thf(369,plain,
    ! [A: tyop_2Einteger_2Eint] :
      ( ( A @ c_2Einteger_2Eint__neg_2E1 @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__le_2E2 ) )
      = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__le_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(32,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( C @ ( B @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) )
      = ( C @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LEFT__ADD__DISTRIB) ).

thf(354,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( C @ ( B @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) )
      = ( C @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) @ ( B @ ( A @ ( TA @ c_2Ewords_2Eword__mul_2E2 ) ) @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(168,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( A = B )
    <=> ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
        = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eint__arith_2Eeq__move__all__left) ).

thf(1009,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( B @ c_2Einteger_2Eint__neg_2E1 @ ( A @ c_2Einteger_2Eint__add_2E2 ) )
          = ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(1183,plain,
    ! [TA: $tType,A: TA] :
      ( ( A @ ( TA @ c_2Ebag_2EEMPTY__BAG_2E1 ) )
      = c_2Enum_2E0_2E0 ),
    inference(cnf,[status(esa)],[1182]) ).

thf(1184,plain,
    ! [TA: $tType,A: TA] :
      ( ( A @ ( TA @ c_2Ebag_2EEMPTY__BAG_2E1 ) )
      = c_2Enum_2E0_2E0 ),
    inference(lifteq,[status(thm)],[1183]) ).

thf(17,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( B != c_2Enum_2E0_2E0 )
     => ( ( B @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__quot_2E2 ) )
        = ( B @ ( A @ c_2Earithmetic_2EDIV_2E2 ) @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__QUOT) ).

thf(309,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( B != c_2Enum_2E0_2E0 )
     => ( ( B @ c_2Einteger_2Eint__of__num_2E1 @ ( A @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__quot_2E2 ) )
        = ( B @ ( A @ c_2Earithmetic_2EDIV_2E2 ) @ c_2Einteger_2Eint__of__num_2E1 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(173,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
        = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) )
    <=> ( A
        = ( B @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUM__ZERO) ).

thf(1037,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( A
          = ( B @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) ) )
       => ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
          = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) ) )
      & ( ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
          = ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) ) )
       => ( A
          = ( B @ ( TA @ c_2Ewords_2Eword__2comp_2E1 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(180,axiom,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__le_2E2 ) )
      = ( A @ c_2Einteger_2Eint__neg_2E1 @ ( B @ c_2Einteger_2Eint__add_2E2 ) @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__le_2E2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eint__arith_2Ele__move__all__right) ).

thf(1088,plain,
    ! [A: tyop_2Einteger_2Eint,B: tyop_2Einteger_2Eint] :
      ( ( B @ ( A @ c_2Einteger_2Eint__le_2E2 ) )
      = ( A @ c_2Einteger_2Eint__neg_2E1 @ ( B @ c_2Einteger_2Eint__add_2E2 ) @ ( c_2Enum_2E0_2E0 @ c_2Einteger_2Eint__of__num_2E1 @ c_2Einteger_2Eint__le_2E2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(1448,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TB @ ( TA @ c_2Ewords_2Esw2sw_2E1 ) ) )
      = ( c_2Enum_2E0_2E0 @ ( TB @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(cnf,[status(esa)],[1447]) ).

thf(1449,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( c_2Enum_2E0_2E0 @ ( TA @ c_2Ewords_2En2w_2E1 ) @ ( TB @ ( TA @ c_2Ewords_2Esw2sw_2E1 ) ) )
      = ( c_2Enum_2E0_2E0 @ ( TB @ c_2Ewords_2En2w_2E1 ) ) ),
    inference(lifteq,[status(thm)],[1448]) ).

thf(258,axiom,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( A @ c_2Einteger_2Eint__of__num_2E1 )
        = ( B @ c_2Einteger_2Eint__of__num_2E1 ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__INJ) ).

thf(1468,plain,
    ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
      ( ( ( A = B )
       => ( ( A @ c_2Einteger_2Eint__of__num_2E1 )
          = ( B @ c_2Einteger_2Eint__of__num_2E1 ) ) )
      & ( ( ( A @ c_2Einteger_2Eint__of__num_2E1 )
          = ( B @ c_2Einteger_2Eint__of__num_2E1 ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(160,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( B @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__SUB__ADD2) ).

thf(972,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A @ ( B @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(120,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
        = C )
    <=> ( A
        = ( B @ ( C @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__EQ__SUB__RADD) ).

thf(755,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( A
          = ( B @ ( C @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) )
       => ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
          = C ) )
      & ( ( ( B @ ( A @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) )
          = C )
       => ( A
          = ( B @ ( C @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(108,axiom,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( A
        = ( C @ ( B @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) )
    <=> ( ( C @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__EQ__SUB__LADD) ).

thf(676,plain,
    ! [TA: $tType,A: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),B: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ),C: TA @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart )] :
      ( ( ( ( C @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
          = B )
       => ( A
          = ( C @ ( B @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) ) )
      & ( ( A
          = ( C @ ( B @ ( TA @ c_2Ewords_2Eword__sub_2E2 ) ) ) )
       => ( ( C @ ( A @ ( TA @ c_2Ewords_2Eword__add_2E2 ) ) )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(1734,plain,
    $false,
    inference(e,[status(thm)],[892,1322,1501,1168,1559,333,518,468,481,1369,1190,408,276,994,1401,1422,269,878,440,1426,384,1137,533,797,814,747,1507,670,898,782,288,1359,1366,841,417,724,570,785,372,1279,357,1462,542,853,1147,1247,969,770,1115,1494,1100,1232,1465,1450,646,834,348,1109,321,766,1447,453,396,660,1405,1169,687,411,988,527,312,920,1306,1153,810,381,366,1311,1047,270,529,957,1091,1255,862,1502,1487,297,788,1238,1423,1178,1296,889,1159,551,1392,710,456,324,847,484,285,1106,1402,1234,948,615,1425,869,1375,1121,420,1118,339,554,1182,1461,526,637,1446,1567,471,837,393,997,1192,1050,984,721,1429,779,1150,1478,1530,1456,1131,654,1333,360,657,530,1185,794,718,906,1510,1103,824,264,279,573,444,1374,375,601,975,423,402,291,1124,545,1258,1356,1282,1524,567,318,434,303,387,345,609,621,700,1325,895,1149,1344,1022,1293,330,462,1112,1177,1381,521,399,827,1044,1176,306,1000,267,278,1528,1034,490,1166,548,1420,1081,342,1018,1134,487,640,1025,872,707,414,327,954,1484,282,1156,1053,673,1432,1300,791,1235,576,951,1336,643,744,336,1094,1372,612,991,1617,465,627,450,1459,363,539,524,1412,1517,844,1453,1481,351,390,378,667,1440,1193,478,763,684,1309,536,300,447,315,1229,1546,405,1303,273,950,1097,564,305,294,807,1335,1056,960,696,886,624,1352,1261,1268,1378,459,850,1431,1299,1399,369,354,1009,1184,309,1037,1088,1449,1468,972,755,676]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : ITP015_7 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.08  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/0.41  % Computer : n010.cluster.edu
% 0.15/0.41  % Model    : x86_64 x86_64
% 0.15/0.41  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41  % Memory   : 8046.5625MB
% 0.15/0.41  % OS       : Linux 6.8.0-71-generic
% 0.15/0.41  % CPULimit : 300
% 0.15/0.41  % WCLimit  : 300
% 0.15/0.41  % DateTime : Fri Sep 25 17:22:48 UTC 2026
% 0.15/0.41  % CPUTime  : 
% 0.15/0.41  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.71/0.70  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 11.11/3.92  % [INFO] 	 Parsing done (3208ms). 
% 11.11/3.95  % [INFO] 	 Running in sequential loop mode. 
% 11.83/4.31  % [INFO] 	 eprover registered as external prover. 
% 11.83/4.32  % [INFO] 	 Scanning for conjecture ... 
% 18.20/6.30  % [INFO] 	 Found a conjecture (or negated_conjecture) and 19035 axioms. Running axiom selection ... 
% 19.93/7.28  % [INFO] 	 Axiom selection finished. Selected 261 axioms (removed 18774 axioms). 
% 20.50/7.48  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 20.84/7.50  % [INFO] 	 Type checking passed. 
% 20.84/7.51  % [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 ... 
% 33.46/11.09  % External prover 'e' found a proof!
% 33.46/11.09  % [INFO] 	 Killing All external provers ... 
% 33.46/11.09  % Time passed: 10598ms (effective reasoning time: 7141ms)
% 33.46/11.10  % 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)>
% 33.46/11.10  % Axioms used in derivation (261): thm_2Einteger_2EINT__NEG__RMUL, thm_2Ewords_2EWORD__NEG__EQ, thm_2Einteger_2EINT__LT__SUB__LADD, thm_2Ewords_2Ew2w__0, thm_2Ewords_2EWORD__ADD__ASSOC, thm_2Ewords_2EWORD__SLICE__ZERO2, thm_2Einteger_2EINT__SUB__LT, thm_2Einteger_2EINT__LE__LADD, thm_2Einteger_2Eint__sub, thm_2Einteger_2EINT__RNEG__UNIQ, thm_2Ewords_2EWORD__MULT__ASSOC, thm_2Einteger_2EINT__ADD__LID__UNIQ, thm_2Einteger_2EINT__ABS__ABS, thm_2Einteger_2EINT__ADD__DIV, thm_2Einteger_2EINT__MOD0, thm_2Eint__arith_2Ele__move__right__left, thm_2Einteger_2EINT__LT__NEG, thm_2Einteger_2EINT__NEG__GE0, thm_2Einteger_2EINT__LE__RADD, thm_2Einteger_2EINT__ADD__ASSOC, thm_2Einteger_2EINT__DIV__RMUL, thm_2Ewords_2Ebit__count__upto__0, thm_2Einteger_2EINT__NEG__SUB, thm_2Einteger_2EINT__SUB__LE, thm_2Einteger_2EINT__LE__ADDR, thm_2Einteger_2EINT__SUB__REDUCE, thm_2Ewords_2EWORD__ADD__COMM, thm_2Enumpair_2Enlist__cases, thm_2Ewords_2Eword__sub__def, thm_2Ewords_2EWORD__LEFT__ADD__DISTRIB, thm_2Einteger_2EINT__SUB__CALCULATE, thm_2Einteger_2EINT__MOD__SUB, thm_2Einteger_2EINT__QUOT__NEG, thm_2Einteger__word_2Eint__word__nchotomy, thm_2Einteger_2EINT__ABS__MUL, thm_2Einteger_2EINT__DIV, thm_2Einteger__word_2Eword__sdiv__def, thm_2Einteger_2EINT__EQ__NEG, thm_2Ewords_2EWORD__EXTRACT__ZERO2, thm_2Ewords_2EWORD__NEG__LMUL, thm_2Ewords_2EWORD__ADD__SUB__SYM, thm_2Einteger_2EINT__REM__CALCULATE, thm_2Einteger_2EINT__ABS__NUM, thm_2Einteger_2EINT__LE__SUB__LADD, thm_2Ewords_2EWORD__NEG__L, thm_2Eint__arith_2Ele__move__all__right, thm_2Einteger_2EINT__SUMSQ, thm_2Einteger_2EINT__LE__ADDL, thm_2Einteger_2EINT__SUB__NEG2, thm_2Einteger_2EINT__MOD__PLUS, thm_2Einteger__word_2Eword__smod__def, thm_2Einteger_2EINT__EQ__LMUL__IMP, thm_2Einteger_2EINT__MUL__DIV, thm_2Ewords_2EWORD__ADD__INV__0__EQ, thm_2Einteger_2EINT__QUOT, thm_2Einteger_2EINT__DIV__LMUL, thm_2Einteger_2EINT__SUB__REFL, thm_2Ewords_2Eword__0__n2w, thm_2Einteger_2EINT__MOD__MOD, thm_2Ewords_2Esw2sw__0, thm_2Ewords_2EWORD__SUB__REFL, thm_2Egcd_2ELCM__COMM, thm_2Ewords_2EWORD__EQ__ADD__RCANCEL, thm_2Einteger_2EINT__LE__SUB__RADD, thm_2Einteger_2EINT__SUB__TRIANGLE, thm_2Einteger_2EINT__MUL__SYM, thm_2Ewords_2En2w__w2n, thm_2Einteger_2EINT__SUB__SUB2, thm_2Einteger__word_2Eword__0__w2i, thm_2Einteger_2EINT__ADD__LINV, thm_2Einteger_2EINT__MUL__COMM, thm_2Einteger_2EINT__ABS__EQ__ABS, thm_2Einteger_2EINT__LT__LADD, thm_2Einteger_2EINT__ADD__SUB2, thm_2Einteger_2EINT__ABS__NEG, thm_2Einteger_2EINT__EXP__EQ0, thm_2Einteger__word_2Eword__mul__i2w, thm_2Einteger_2EINT__SUB__0, thm_2Einteger_2EINT__NEG__LT0, thm_2Ewords_2EWORD__ADD__SUB__ASSOC, thm_2Eint__arith_2Elt__move__all__right, thm_2Ewords_2EWORD__ADD__LINV, thm_2Einteger_2EINT__LT__RADD, thm_2Einteger__word_2Ew2i__eq__0, thm_2Ewords_2EWORD__ADD__SUB2, thm_2Ewords_2EWORD__SUB__PLUS, thm_2Einteger_2EINT__LE__DOUBLE, thm_2Ewords_2EWORD__NEG__ADD, thm_2Einteger__word_2Ei2w__w2i, thm_2Einteger_2EINT__NEG__LE0, thm_2Ebitstring_2Eword__extract__v2w, thm_2Einteger__word_2Eword__sub__i2w, thm_2Einteger__word_2Ew2i__neg, thm_2Einteger_2EINT__SUB__RNEG, thm_2Eint__arith_2Elt__move__left__left, thm_2EbasicSize_2Eone__size__def, thm_2Ewords_2EWORD__NEG__SUB, thm_2Ewords_2Ew2n__11, thm_2Einteger_2EINT__LE__NEGL, thm_2Einteger_2EINT__LT__ADDR, thm_2Eint__arith_2EINT__SUB__SUB3, thm_2Ewords_2EWORD__ADD__RINV, thm_2Einteger_2EINT__ENTIRE, thm_2EternaryComparisons_2Eordering__size__def, thm_2Ewords_2Eword__nchotomy, thm_2Einteger__word_2Eword__add__i2w, thm_2Ealignment_2Ealign__0, thm_2Ewords_2EWORD__EQ__NEG, thm_2Ewords_2EWORD__EQ__SUB__LADD, thm_2Egcd_2ELCM__0, thm_2Einteger_2EINT__INJ, thm_2Ewords_2EWORD__SLICE__BITS__THM, thm_2Ewords_2EWORD__EQ__SUB__ZERO, thm_2Einteger_2EINT__QUOT__0, thm_2Einteger_2EINT__EQ__RMUL__IMP, thm_2Ewords_2EWORD__EQ__ADD__LCANCEL, thm_2Ewords_2EWORD__SUB, thm_2Ewords_2Eword__abs__diff, thm_2Einteger_2EINT__NEG__SAME__EQ, thm_2Ewords_2EWORD__SUB__TRIANGLE, thm_2Enumpair_2Encons__not__nnil, thm_2Einteger__word_2Eword__i2w__mul, thm_2Einteger_2EINT__ADD__LID, thm_2Ewords_2EWORD__BITS__ZERO2, thm_2Ewords_2EWORD__LCANCEL__SUB, thm_2Einteger__word_2Eword__sub__i2w__w2n, thm_2Ewords_2Ew2w__def, thm_2Einteger_2EINT__ADD__RID__UNIQ, thm_2Ewords_2Eword__abs__neg, thm_2Einteger_2EINT__NEGNEG, thm_2Ebitstring_2Eshiftr__0, thm_2Einteger__word_2Eword__mul__i2w__w2n, thm_2Eint__arith_2Eeq__move__right__left, thm_2Eint__arith_2Emove__sub, thm_2Estring_2Echar__size__def, thm_2Einteger_2Eint__mod, thm_2Einteger_2EINT__EQ__CALCULATE, thm_2Einteger_2EINT__NEG__0, thm_2Einteger_2EINT__NEG__EQ, thm_2Eint__arith_2Eeq__context__rwt1, thm_2Einteger_2EINT__MOD__NEG__NUMERATOR, thm_2Ewords_2EWORD__RIGHT__SUB__DISTRIB, thm_2Einteger_2EINT__ADD__COMM, thm_2Ewords_2EWORD__SUB__LNEG, thm_2Einteger_2EINT__ADD2__SUB2, thm_2Einteger_2EINT__NEG__MUL2, thm_2Einteger_2EINT__LDISTRIB, thm_2Ewords_2Eword__reverse__0, thm_2Einteger__word_2Eword__i2w__add, thm_2Einteger_2EINT__MOD__NEG, thm_2Eint__arith_2Eeq__move__left__right, thm_2Einteger_2EINT__SUB__RDISTRIB, thm_2Einteger_2EINT__DIV__MUL__ID, thm_2Ewords_2EWORD__LEFT__SUB__DISTRIB, thm_2Einteger_2EINT__SUB__LDISTRIB, thm_2Einteger_2EINT__MUL__ASSOC, thm_2Ewords_2EWORD__ADD__SUB3, thm_2Ewords_2EWORD__BITS__SLICE__THM, thm_2Einteger_2EINT__MUL__RZERO, thm_2Ewords_2EWORD__NEG__NEG, thm_2Einteger_2EINT__REM__NEG, thm_2Einteger_2EINT__LE__NEGR, thm_2Ewords_2Ew2w__id, thm_2Ewords_2Eword__abs__word__abs, thm_2Einteger__word_2Eword__abs__w2i, thm_2Einteger_2EINT__ADD__RID, thm_2Einteger_2EINT__MOD__ADD__MULTIPLES, thm_2Ealignment_2Ealign__align, thm_2Einteger_2EINT__LE__NEG, thm_2EbasicSize_2Ebool__size__def, thm_2Einteger_2EINT__REM__ID, thm_2Ewords_2ENOT__INT__MIN__ZERO, thm_2Ewords_2EWORD__ADD__RID__UNIQ, thm_2Ewords_2Esw2sw__id, thm_2Ewords_2EWORD__EQ__SUB__RADD, thm_2Ebitstring_2Ebitstring__nchotomy, thm_2Einteger_2EINT__RDISTRIB, thm_2Einteger_2EINT__NUM__CASES, thm_2Ewords_2EWORD__MULT__COMM, thm_2Einteger_2EINT__LT__ADDL, thm_2Einteger_2EINT__REM, thm_2Eint__arith_2Elt__move__all__left, thm_2Einteger_2EINT__ADD__RINV, thm_2Einteger_2EINT__MOD__CALCULATE, thm_2Einteger_2EINT__SUB__LZERO, thm_2Ewords_2EWORD__SUB__SUB3, thm_2Einteger_2EINT__EQ__LMUL2, thm_2Eint__arith_2Eeq__move__left__left, thm_2Ewords_2EWORD__NEG__EQ__0, thm_2Einteger_2EINT__MUL__LZERO, thm_2Einteger_2EINT__0, thm_2Einteger_2EINT__MOD__EQ0, thm_2Eint__arith_2Eeq__move__all__right, thm_2Einteger_2EINT__REM__COMMON__FACTOR, thm_2Einteger_2EINT__MOD__ID, thm_2Einteger_2EINT__SUB__ADD, thm_2Ewords_2EWORD__NEG__RMUL, thm_2Einteger_2EINT__EQ__RADD, thm_2Ewords_2EWORD__BITS__EXTRACT, thm_2Ewords_2EWORD__ADD__SUB, thm_2Enumpair_2Encons__11, thm_2Einteger_2EINT__SUB__LNEG, thm_2Ewords_2EWORD__SUB__LZERO, thm_2Einteger_2EINT__MUL__QUOT, thm_2Einteger_2EINT__LT__ADDNEG, thm_2Einteger_2EINT__NEG__LMUL, thm_2Ebag_2EEMPTY__BAG__alt, thm_2Einteger_2EINT__NEG__ADD, thm_2Einteger__word_2Eword__add__i2w__w2n, thm_2Earithmetic_2ENUMERAL__DEF, thm_2Ewords_2EWORD__ADD__EQ__SUB, thm_2Ewords_2EWORD__ADD__LID__UNIQ, thm_2Einteger_2EINT__LNEG__UNIQ, thm_2Ewords_2EWORD__SUB__SUB, thm_2Eint__arith_2Eeq__context__rwt2, thm_2Ewords_2EWORD__SUB__RNEG, thm_2Einteger_2EINT__ADD__SYM, thm_2Einteger_2EINT__NEG__EQ0, thm_2Ewords_2EWORD__SUB__ADD, thm_2Eint__arith_2Eeq__move__all__left, thm_2Einteger_2EINT__EQ__LMUL, thm_2Ewords_2EWORD__RCANCEL__SUB, thm_2Einteger_2EINT__REM__EQ0, thm_2Ewords_2EWORD__ADD__0, thm_2Einteger_2EINT__LT__ADDNEG2, thm_2Ewords_2EWORD__SUB__SUB2, thm_2Einteger_2EINT__MOD__COMMON__FACTOR, thm_2Einteger_2EINT__EQ__SUB__RADD, thm_2Einteger_2EINT__EQ__SUB__LADD, thm_2Einteger_2EINT__ADD__SUB, thm_2Ewords_2Eword__concat__0__0, thm_2Ewords_2EWORD__SUB__ADD2, thm_2Ewords_2Ebit__count__is__zero, thm_2Ewords_2EWORD__RIGHT__ADD__DISTRIB, thm_2Eint__arith_2Eelim__lt__coeffs1, thm_2Einteger_2EINT__ABS__EQ0, thm_2Einteger_2EINT__SUB__SUB, thm_2Ewords_2Ew2n__eq__0, thm_2Einteger_2EINT__DIV__NEG, thm_2Einteger_2EINT__EQ__LADD, thm_2Einteger_2EINT__QUOT__CALCULATE, thm_2Einteger_2EINT__LT__SUB__RADD, thm_2Ewords_2EWORD__NEG__0, thm_2Einteger_2EINT__SUB__RZERO, thm_2Einteger_2ENUM__OF__INT, thm_2Einteger_2EINT__DIV__0, thm_2Ewords_2EWORD__SUB__RZERO, thm_2Einteger_2EINT__EQ__RMUL, thm_2Eint__arith_2Elt__move__left__right, thm_2Einteger_2EINT__REM0, thm_2Einteger_2EINT__MOD, thm_2Esptree_2Espt__acc__0, thm_2Einteger_2EINT__DIV__CALCULATE, thm_2Einteger_2EINT__NEG__GT0, thm_2Ewords_2EWORD__SUM__ZERO, thm_2Einteger_2EINT__SUB__ADD2, thm_2Einteger_2EINT__LT__ADD__SUB, thm_2Ewords_2EWORD__SUB__NEG, thm_2Einteger__word_2Ew2i__11, thm_2Einteger_2Eint__rem, thm_2Einteger_2EINT__DIFFSQ
% 33.46/11.10  % No. of inferences in proof: 624
% 33.46/11.10  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10598 ms resp. 7141 ms w/o parsing
% 33.80/11.36  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 33.80/11.37  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------