TSTP Solution File: ITP100^1 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ITP100^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n019.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 20 22:22:54 EDT 2024

% Result   : Theorem 21.24s 6.64s
% Output   : Refutation 22.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  416
% Syntax   : Number of formulae    :  749 ( 377 unt;  85 typ;   0 def)
%            Number of atoms       : 1645 (1292 equ;   0 cnn)
%            Maximal formula atoms :   13 (   2 avg)
%            Number of connectives : 6445 ( 384   ~;  91   |; 224   &;4914   @)
%                                         (   0 <=>; 832  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   29 (   6 avg)
%            Number of types       :   10 (   9 usr)
%            Number of type conns  :  737 ( 737   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   79 (  76 usr;   7 con; 0-3 aty)
%            Number of variables   : 2233 (  44   ^2041   !; 148   ?;2233   :)

% Comments : 
%------------------------------------------------------------------------------
thf(list_list_list_a_type,type,
    list_list_list_a: $tType ).

thf(set_list_list_a_type,type,
    set_list_list_a: $tType ).

thf(list_list_a_type,type,
    list_list_a: $tType ).

thf(set_list_a_type,type,
    set_list_a: $tType ).

thf(list_nat_type,type,
    list_nat: $tType ).

thf(list_a_type,type,
    list_a: $tType ).

thf(set_a_type,type,
    set_a: $tType ).

thf(nat_type,type,
    nat: $tType ).

thf(a_type,type,
    a: $tType ).

thf(bNF_Gr1972240547list_a_type,type,
    bNF_Gr1972240547list_a: set_list_list_a > list_a > set_list_list_a ).

thf(bNF_Greatest_Shift_a_type,type,
    bNF_Greatest_Shift_a: set_list_a > a > set_list_a ).

thf(bNF_Gr1046450207list_a_type,type,
    bNF_Gr1046450207list_a: set_list_list_a > list_list_a > set_list_a ).

thf(bNF_Greatest_Succ_a_type,type,
    bNF_Greatest_Succ_a: set_list_a > list_a > set_a ).

thf(if_list_a_type,type,
    if_list_a: $o > list_a > list_a > list_a ).

thf(list_ord_nat_type,type,
    list_ord_nat: ( nat > nat > $o ) > list_nat > $o ).

thf(list_strict_asc_nat_type,type,
    list_strict_asc_nat: list_nat > $o ).

thf(map2_a_a_a_type,type,
    map2_a_a_a: ( a > a > a ) > list_a > list_a > list_a ).

thf(listIn1753026346list_a_type,type,
    listIn1753026346list_a: list_list_a > ( nat > list_a ) > nat > list_a ).

thf(listIn1312259492pend_a_type,type,
    listIn1312259492pend_a: list_a > ( nat > a ) > nat > a ).

thf(append_list_a_type,type,
    append_list_a: list_list_a > list_list_a > list_list_a ).

thf(append_a_type,type,
    append_a: list_a > list_a > list_a ).

thf(bind_list_a_list_a_type,type,
    bind_list_a_list_a: list_list_a > ( list_a > list_list_a ) > list_list_a ).

thf(bind_list_a_a_type,type,
    bind_list_a_a: list_list_a > ( list_a > list_a ) > list_a ).

thf(bind_a_list_a_type,type,
    bind_a_list_a: list_a > ( a > list_list_a ) > list_list_a ).

thf(bind_a_a_type,type,
    bind_a_a: list_a > ( a > list_a ) > list_a ).

thf(butlast_list_a_type,type,
    butlast_list_a: list_list_a > list_list_a ).

thf(butlast_a_type,type,
    butlast_a: list_a > list_a ).

thf(concat_list_a_type,type,
    concat_list_a: list_list_list_a > list_list_a ).

thf(concat_a_type,type,
    concat_a: list_list_a > list_a ).

thf(distinct_adj_list_a_type,type,
    distinct_adj_list_a: list_list_a > $o ).

thf(distinct_adj_a_type,type,
    distinct_adj_a: list_a > $o ).

thf(foldr_769741863list_a_type,type,
    foldr_769741863list_a: ( list_list_a > list_list_a > list_list_a ) > list_list_list_a > list_list_a > list_list_a ).

thf(foldr_list_a_list_a_type,type,
    foldr_list_a_list_a: ( list_a > list_a > list_a ) > list_list_a > list_a > list_a ).

thf(insert_list_a_type,type,
    insert_list_a: list_a > list_list_a > list_list_a ).

thf(insert_a_type,type,
    insert_a: a > list_a > list_a ).

thf(last_list_a_type,type,
    last_list_a: list_list_a > list_a ).

thf(last_a_type,type,
    last_a: list_a > a ).

thf(cons_list_a_type,type,
    cons_list_a: list_a > list_list_a > list_list_a ).

thf(cons_a_type,type,
    cons_a: a > list_a > list_a ).

thf(nil_list_list_a_type,type,
    nil_list_list_a: list_list_list_a ).

thf(nil_list_a_type,type,
    nil_list_a: list_list_a ).

thf(nil_a_type,type,
    nil_a: list_a ).

thf(hd_list_list_a_type,type,
    hd_list_list_a: list_list_list_a > list_list_a ).

thf(hd_list_a_type,type,
    hd_list_a: list_list_a > list_a ).

thf(hd_a_type,type,
    hd_a: list_a > a ).

thf(tl_list_a_type,type,
    tl_list_a: list_list_a > list_list_a ).

thf(tl_a_type,type,
    tl_a: list_a > list_a ).

thf(list_ex1_list_a_type,type,
    list_ex1_list_a: ( list_a > $o ) > list_list_a > $o ).

thf(list_ex1_a_type,type,
    list_ex1_a: ( a > $o ) > list_a > $o ).

thf(listre1221556159list_a_type,type,
    listre1221556159list_a: ( list_a > list_a > $o ) > list_list_a > list_list_a > $o ).

thf(listrelp_list_a_a_type,type,
    listrelp_list_a_a: ( list_a > a > $o ) > list_list_a > list_a > $o ).

thf(listrelp_a_list_a_type,type,
    listrelp_a_list_a: ( a > list_a > $o ) > list_a > list_list_a > $o ).

thf(listrelp_a_a_type,type,
    listrelp_a_a: ( a > a > $o ) > list_a > list_a > $o ).

thf(map_ta982122357list_a_type,type,
    map_ta982122357list_a: ( list_a > list_a ) > list_list_a > list_list_a > list_list_a ).

thf(map_ta2002079599st_a_a_type,type,
    map_ta2002079599st_a_a: ( list_a > a ) > list_list_a > list_a > list_a ).

thf(map_ta41997947list_a_type,type,
    map_ta41997947list_a: ( a > list_a ) > list_a > list_list_a > list_list_a ).

thf(map_tailrec_rev_a_a_type,type,
    map_tailrec_rev_a_a: ( a > a ) > list_a > list_a > list_a ).

thf(maps_list_a_list_a_type,type,
    maps_list_a_list_a: ( list_a > list_list_a ) > list_list_a > list_list_a ).

thf(maps_list_a_a_type,type,
    maps_list_a_a: ( list_a > list_a ) > list_list_a > list_a ).

thf(maps_a_list_a_type,type,
    maps_a_list_a: ( a > list_list_a ) > list_a > list_list_a ).

thf(maps_a_a_type,type,
    maps_a_a: ( a > list_a ) > list_a > list_a ).

thf(member_list_a_type,type,
    member_list_a: list_list_a > list_a > $o ).

thf(member_a_type,type,
    member_a: list_a > a > $o ).

thf(lexordp_eq_list_a_type,type,
    lexordp_eq_list_a: ( list_a > list_a > $o ) > list_list_a > list_list_a > $o ).

thf(lexordp_eq_a_type,type,
    lexordp_eq_a: ( a > a > $o ) > list_a > list_a > $o ).

thf(product_lists_a_type,type,
    product_lists_a: list_list_a > list_list_a ).

thf(remdups_adj_a_type,type,
    remdups_adj_a: list_a > list_a ).

thf(rotate1_list_a_type,type,
    rotate1_list_a: list_list_a > list_list_a ).

thf(rotate1_a_type,type,
    rotate1_a: list_a > list_a ).

thf(shuffles_a_type,type,
    shuffles_a: list_a > list_a > set_list_a ).

thf(splice_list_a_type,type,
    splice_list_a: list_list_a > list_list_a > list_list_a ).

thf(splice_a_type,type,
    splice_a: list_a > list_a > list_a ).

thf(subseqs_a_type,type,
    subseqs_a: list_a > list_list_a ).

thf(successively_list_a_type,type,
    successively_list_a: ( list_a > list_a > $o ) > list_list_a > $o ).

thf(successively_a_type,type,
    successively_a: ( a > a > $o ) > list_a > $o ).

thf(size_size_list_a_type,type,
    size_size_list_a: list_a > nat ).

thf(ord_less_nat_type,type,
    ord_less_nat: nat > nat > $o ).

thf(collect_list_a_type,type,
    collect_list_a: ( list_a > $o ) > set_list_a ).

thf(collect_a_type,type,
    collect_a: ( a > $o ) > set_a ).

thf(member_list_list_a_type,type,
    member_list_list_a: list_list_a > set_list_list_a > $o ).

thf(member_list_a2_type,type,
    member_list_a2: list_a > set_list_a > $o ).

thf(member_a2_type,type,
    member_a2: a > set_a > $o ).

thf(f_type,type,
    f: nat > a ).

thf(x_type,type,
    x: a ).

thf(xs_type,type,
    xs: list_a ).

thf(116,axiom,
    ! [A: list_list_a,B: list_list_a] :
    ? [C: list_list_a,D: list_list_a,E: list_list_a] :
      ( ( A
        = ( append_list_a @ D @ C ) )
      & ( B
        = ( append_list_a @ E @ C ) )
      & ( ( D = nil_list_a )
        | ( E = nil_list_a )
        | ( ( last_list_a @ D )
         != ( last_list_a @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_longest__common__suffix) ).

thf(809,plain,
    ! [A: list_list_a,B: list_list_a] :
    ? [C: list_list_a,D: list_list_a,E: list_list_a] :
      ( ( A
        = ( append_list_a @ D @ C ) )
      & ( B
        = ( append_list_a @ E @ C ) )
      & ( ( D = nil_list_a )
        | ( E = nil_list_a )
        | ( ( last_list_a @ D )
         != ( last_list_a @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(229,axiom,
    ! [A: list_a,B: a] :
      ( ( ( A = nil_a )
       => ( ( butlast_a @ ( cons_a @ B @ A ) )
          = nil_a ) )
      & ( ( A != nil_a )
       => ( ( butlast_a @ ( cons_a @ B @ A ) )
          = ( cons_a @ B @ ( butlast_a @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_butlast_Osimps_I2_J) ).

thf(1337,plain,
    ! [A: list_a,B: a] :
      ( ( ( A = nil_a )
       => ( ( butlast_a @ ( cons_a @ B @ A ) )
          = nil_a ) )
      & ( ( A != nil_a )
       => ( ( butlast_a @ ( cons_a @ B @ A ) )
          = ( cons_a @ B @ ( butlast_a @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(162,axiom,
    ! [A: list_a,B: a,C: list_a] :
      ( ( ( append_a @ A @ ( cons_a @ B @ nil_a ) )
        = C )
      = ( ( C != nil_a )
        & ( ( butlast_a @ C )
          = A )
        & ( ( last_a @ C )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_snoc__eq__iff__butlast) ).

thf(1024,plain,
    ! [A: list_a,B: a,C: list_a] :
      ( ( ( append_a @ A @ ( cons_a @ B @ nil_a ) )
        = C )
      = ( ( C != nil_a )
        & ( ( butlast_a @ C )
          = A )
        & ( ( last_a @ C )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(194,axiom,
    ! [A: list_a] :
      ( ( nil_a
        = ( tl_a @ A ) )
      = ( ( A = nil_a )
        | ? [B: a] :
            ( A
            = ( cons_a @ B @ nil_a ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_Nil__tl) ).

thf(1168,plain,
    ! [A: list_a] :
      ( ( nil_a
        = ( tl_a @ A ) )
      = ( ( A = nil_a )
        | ? [B: a] :
            ( A
            = ( cons_a @ B @ nil_a ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(286,axiom,
    ! [A: list_a,B: list_a,C: list_a,D: list_a > list_a > list_a > $o] :
      ( ( ( size_size_list_a @ A )
        = ( size_size_list_a @ B ) )
     => ( ( ( size_size_list_a @ B )
          = ( size_size_list_a @ C ) )
       => ( ( D @ nil_a @ nil_a @ nil_a )
         => ( ! [E: a,F: list_a,G: a,H: list_a,I: a,J: list_a] :
                ( ( ( size_size_list_a @ F )
                  = ( size_size_list_a @ H ) )
               => ( ( ( size_size_list_a @ H )
                    = ( size_size_list_a @ J ) )
                 => ( ( D @ F @ H @ J )
                   => ( D @ ( cons_a @ E @ F ) @ ( cons_a @ G @ H ) @ ( cons_a @ I @ J ) ) ) ) )
           => ( D @ A @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_list__induct3) ).

thf(1633,plain,
    ! [A: list_a,B: list_a,C: list_a,D: list_a > list_a > list_a > $o] :
      ( ( ( size_size_list_a @ A )
        = ( size_size_list_a @ B ) )
     => ( ( ( size_size_list_a @ B )
          = ( size_size_list_a @ C ) )
       => ( ( D @ nil_a @ nil_a @ nil_a )
         => ( ! [E: a,F: list_a,G: a,H: list_a,I: a,J: list_a] :
                ( ( ( size_size_list_a @ F )
                  = ( size_size_list_a @ H ) )
               => ( ( ( size_size_list_a @ H )
                    = ( size_size_list_a @ J ) )
                 => ( ( D @ F @ H @ J )
                   => ( D @ ( cons_a @ E @ F ) @ ( cons_a @ G @ H ) @ ( cons_a @ I @ J ) ) ) ) )
           => ( D @ A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(270,axiom,
    ! [A: a > a,B: a,C: list_a,D: list_a] :
      ( ( map_tailrec_rev_a_a @ A @ ( cons_a @ B @ C ) @ D )
      = ( map_tailrec_rev_a_a @ A @ C @ ( cons_a @ ( A @ B ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_map__tailrec__rev_Osimps_I2_J) ).

thf(1559,plain,
    ! [A: a > a,B: a,C: list_a,D: list_a] :
      ( ( map_tailrec_rev_a_a @ A @ ( cons_a @ B @ C ) @ D )
      = ( map_tailrec_rev_a_a @ A @ C @ ( cons_a @ ( A @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(145,axiom,
    ! [A: list_list_a,B: list_list_a,C: list_list_a] :
      ( ( append_list_a @ ( append_list_a @ A @ B ) @ C )
      = ( append_list_a @ A @ ( append_list_a @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_append_Oassoc) ).

thf(941,plain,
    ! [A: list_list_a,B: list_list_a,C: list_list_a] :
      ( ( append_list_a @ ( append_list_a @ A @ B ) @ C )
      = ( append_list_a @ A @ ( append_list_a @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(51,axiom,
    ! [A: list_a,B: list_list_a,C: list_list_a,D: list_list_a,E: list_list_a] :
      ( ( ( cons_list_a @ A @ B )
        = C )
     => ( ( D
          = ( append_list_a @ B @ E ) )
       => ( ( cons_list_a @ A @ D )
          = ( append_list_a @ C @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_Cons__eq__appendI) ).

thf(481,plain,
    ! [A: list_a,B: list_list_a,C: list_list_a,D: list_list_a,E: list_list_a] :
      ( ( ( cons_list_a @ A @ B )
        = C )
     => ( ( D
          = ( append_list_a @ B @ E ) )
       => ( ( cons_list_a @ A @ D )
          = ( append_list_a @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(224,axiom,
    ! [A: list_a,B: list_a] :
      ( ( ( append_a @ A @ B )
        = B )
      = ( A = nil_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_append__self__conv2) ).

thf(1322,plain,
    ! [A: list_a,B: list_a] :
      ( ( ( append_a @ A @ B )
        = B )
      = ( A = nil_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(292,axiom,
    ! [A: a > a > $o] : ( listrelp_a_a @ A @ nil_a @ nil_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_listrelp_ONil) ).

thf(1665,plain,
    ! [A: a > a > $o] : ( listrelp_a_a @ A @ nil_a @ nil_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(1,conjecture,
    ( ( listIn1312259492pend_a @ ( cons_a @ x @ xs ) @ f )
    = ( listIn1312259492pend_a @ ( cons_a @ x @ nil_a ) @ ( listIn1312259492pend_a @ xs @ f ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ( ( listIn1312259492pend_a @ ( cons_a @ x @ xs ) @ f )
   != ( listIn1312259492pend_a @ ( cons_a @ x @ nil_a ) @ ( listIn1312259492pend_a @ xs @ f ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(333,plain,
    ( ( listIn1312259492pend_a @ ( cons_a @ x @ xs ) @ f )
   != ( listIn1312259492pend_a @ ( cons_a @ x @ nil_a ) @ ( listIn1312259492pend_a @ xs @ f ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(81,axiom,
    ! [A: list_a,B: list_list_a] :
      ( ( append_list_a @ ( cons_list_a @ A @ nil_list_a ) @ B )
      = ( cons_list_a @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_append__eq__Cons) ).

thf(628,plain,
    ! [A: list_a,B: list_list_a] :
      ( ( append_list_a @ ( cons_list_a @ A @ nil_list_a ) @ B )
      = ( cons_list_a @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(326,axiom,
    ! [A: a > a > $o,B: list_a] : ( lexordp_eq_a @ A @ nil_a @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_ord_Olexordp__eq_ONil) ).

thf(1855,plain,
    ! [A: a > a > $o,B: list_a] : ( lexordp_eq_a @ A @ nil_a @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(198,axiom,
    ! [A: list_a,B: list_a] :
      ( ( A != nil_a )
     => ( ( hd_a @ ( append_a @ A @ B ) )
        = ( hd_a @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_hd__append2) ).

thf(1211,plain,
    ! [A: list_a,B: list_a] :
      ( ( A != nil_a )
     => ( ( hd_a @ ( append_a @ A @ B ) )
        = ( hd_a @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(192,axiom,
    ! [A: list_a,B: a > a > a,C: a,D: list_a] :
      ( ( ( A = nil_a )
       => ( ( map2_a_a_a @ B @ A @ ( cons_a @ C @ D ) )
          = nil_a ) )
      & ( ( A != nil_a )
       => ( ( map2_a_a_a @ B @ A @ ( cons_a @ C @ D ) )
          = ( cons_a @ ( B @ ( hd_a @ A ) @ C ) @ ( map2_a_a_a @ B @ ( tl_a @ A ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_map2__Cons__if) ).

thf(1158,plain,
    ! [A: list_a,B: a > a > a,C: a,D: list_a] :
      ( ( ( A = nil_a )
       => ( ( map2_a_a_a @ B @ A @ ( cons_a @ C @ D ) )
          = nil_a ) )
      & ( ( A != nil_a )
       => ( ( map2_a_a_a @ B @ A @ ( cons_a @ C @ D ) )
          = ( cons_a @ ( B @ ( hd_a @ A ) @ C ) @ ( map2_a_a_a @ B @ ( tl_a @ A ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(240,axiom,
    ! [A: nat > a] :
      ( ( listIn1312259492pend_a @ nil_a @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_i__append__Nil) ).

thf(1406,plain,
    ! [A: nat > a] :
      ( ( listIn1312259492pend_a @ nil_a @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(297,axiom,
    ! [A: a] :
      ~ ( member_a @ nil_a @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_member__rec_I2_J) ).

thf(1692,plain,
    ! [A: a] :
      ~ ( member_a @ nil_a @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(257,axiom,
    ( listrelp_list_a_a
    = ( ^ [A: list_a > a > $o,B: list_list_a,C: list_a] :
          ( ( ( B = nil_list_a )
            & ( C = nil_a ) )
          | ? [D: list_a,E: a,F: list_list_a,G: list_a] :
              ( ( B
                = ( cons_list_a @ D @ F ) )
              & ( C
                = ( cons_a @ E @ G ) )
              & ( A @ D @ E )
              & ( listrelp_list_a_a @ A @ F @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_listrelp_Osimps) ).

thf(1486,plain,
    ( listrelp_list_a_a
    = ( ^ [A: list_a > a > $o,B: list_list_a,C: list_a] :
          ( ( ( B = nil_list_a )
            & ( C = nil_a ) )
          | ? [D: list_a,E: a,F: list_list_a,G: list_a] :
              ( ( B
                = ( cons_list_a @ D @ F ) )
              & ( C
                = ( cons_a @ E @ G ) )
              & ( A @ D @ E )
              & ( listrelp_list_a_a @ A @ F @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(311,axiom,
    ! [A: list_a] :
      ( ( A != nil_a )
     => ( ( cons_a @ ( hd_a @ A ) @ ( tl_a @ A ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_hd__Cons__tl) ).

thf(1750,plain,
    ! [A: list_a] :
      ( ( A != nil_a )
     => ( ( cons_a @ ( hd_a @ A ) @ ( tl_a @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(31,axiom,
    ! [A: set_list_list_a,B: list_a] :
      ( ( member_list_list_a @ nil_list_a @ A )
     => ( ( member_list_a2 @ B @ ( bNF_Gr1046450207list_a @ A @ nil_list_a ) )
       => ( member_list_list_a @ nil_list_a @ ( bNF_Gr1972240547list_a @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_empty__Shift) ).

thf(408,plain,
    ! [A: set_list_list_a,B: list_a] :
      ( ( member_list_list_a @ nil_list_a @ A )
     => ( ( member_list_a2 @ B @ ( bNF_Gr1046450207list_a @ A @ nil_list_a ) )
       => ( member_list_list_a @ nil_list_a @ ( bNF_Gr1972240547list_a @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(19,axiom,
    ! [A: list_a > list_a > $o,B: list_list_a] :
      ( ~ ( successively_list_a @ A @ B )
     => ~ ! [C: list_a,D: list_a,E: list_list_a] :
            ( ( B
              = ( cons_list_a @ C @ ( cons_list_a @ D @ E ) ) )
           => ( ( A @ C @ D )
              & ( successively_list_a @ A @ ( cons_list_a @ D @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_successively_Oelims_I3_J) ).

thf(379,plain,
    ! [A: list_a > list_a > $o,B: list_list_a] :
      ( ~ ( successively_list_a @ A @ B )
     => ~ ! [C: list_a,D: list_a,E: list_list_a] :
            ( ( B
              = ( cons_list_a @ C @ ( cons_list_a @ D @ E ) ) )
           => ( ( A @ C @ D )
              & ( successively_list_a @ A @ ( cons_list_a @ D @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(213,axiom,
    ! [A: list_a > a,B: list_a,C: list_list_a,D: list_a] :
      ( ( map_ta2002079599st_a_a @ A @ ( cons_list_a @ B @ C ) @ D )
      = ( map_ta2002079599st_a_a @ A @ C @ ( cons_a @ ( A @ B ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_map__tailrec__rev_Osimps_I2_J) ).

thf(1269,plain,
    ! [A: list_a > a,B: list_a,C: list_list_a,D: list_a] :
      ( ( map_ta2002079599st_a_a @ A @ ( cons_list_a @ B @ C ) @ D )
      = ( map_ta2002079599st_a_a @ A @ C @ ( cons_a @ ( A @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(318,axiom,
    ! [A: list_a,B: list_a,C: list_a] :
      ( ( member_list_a2 @ A @ ( shuffles_a @ B @ C ) )
     => ( ( ( A = B )
         => ( C != nil_a ) )
       => ( ( ( A = C )
           => ( B != nil_a ) )
         => ( ! [D: a,E: list_a] :
                ( ( B
                  = ( cons_a @ D @ E ) )
               => ! [F: a,G: list_a] :
                    ( ( A
                      = ( cons_a @ F @ G ) )
                   => ( ( D = F )
                     => ~ ( member_list_a2 @ G @ ( shuffles_a @ E @ C ) ) ) ) )
           => ~ ! [D: a,E: list_a] :
                  ( ( C
                    = ( cons_a @ D @ E ) )
                 => ! [F: a,G: list_a] :
                      ( ( A
                        = ( cons_a @ F @ G ) )
                     => ( ( D = F )
                       => ~ ( member_list_a2 @ G @ ( shuffles_a @ B @ E ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_shufflesE) ).

thf(1788,plain,
    ! [A: list_a,B: list_a,C: list_a] :
      ( ( member_list_a2 @ A @ ( shuffles_a @ B @ C ) )
     => ( ( ( A = B )
         => ( C != nil_a ) )
       => ( ( ( A = C )
           => ( B != nil_a ) )
         => ( ! [D: a,E: list_a] :
                ( ( B
                  = ( cons_a @ D @ E ) )
               => ! [F: a,G: list_a] :
                    ( ( A
                      = ( cons_a @ F @ G ) )
                   => ( ( D = F )
                     => ~ ( member_list_a2 @ G @ ( shuffles_a @ E @ C ) ) ) ) )
           => ~ ! [D: a,E: list_a] :
                  ( ( C
                    = ( cons_a @ D @ E ) )
                 => ! [F: a,G: list_a] :
                      ( ( A
                        = ( cons_a @ F @ G ) )
                     => ( ( D = F )
                       => ~ ( member_list_a2 @ G @ ( shuffles_a @ B @ E ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(21,axiom,
    ! [A: $o] :
      ( ( A = $true )
      | ( A = $false ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_If_001t__List__Olist_Itf__a_J_T) ).

thf(385,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(313,axiom,
    ! [A: a > a > $o,B: list_a] :
      ( ~ ( successively_a @ A @ B )
     => ~ ! [C: a,D: a,E: list_a] :
            ( ( B
              = ( cons_a @ C @ ( cons_a @ D @ E ) ) )
           => ( ( A @ C @ D )
              & ( successively_a @ A @ ( cons_a @ D @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_successively_Oelims_I3_J) ).

thf(1756,plain,
    ! [A: a > a > $o,B: list_a] :
      ( ~ ( successively_a @ A @ B )
     => ~ ! [C: a,D: a,E: list_a] :
            ( ( B
              = ( cons_a @ C @ ( cons_a @ D @ E ) ) )
           => ( ( A @ C @ D )
              & ( successively_a @ A @ ( cons_a @ D @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(56,axiom,
    ! [A: list_a > list_list_a] :
      ( ( maps_list_a_list_a @ A @ nil_list_a )
      = nil_list_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_maps__simps_I2_J) ).

thf(500,plain,
    ! [A: list_a > list_list_a] :
      ( ( maps_list_a_list_a @ A @ nil_list_a )
      = nil_list_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(331,axiom,
    ! [A: a,B: list_a] :
      ( ( rotate1_a @ ( cons_a @ A @ B ) )
      = ( append_a @ B @ ( cons_a @ A @ nil_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_rotate1_Osimps_I2_J) ).

thf(1872,plain,
    ! [A: a,B: list_a] :
      ( ( rotate1_a @ ( cons_a @ A @ B ) )
      = ( append_a @ B @ ( cons_a @ A @ nil_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(205,axiom,
    ! [A: a > a > $o,B: a,C: a,D: list_a,E: list_a] :
      ( ( A @ B @ C )
     => ( lexordp_eq_a @ A @ ( cons_a @ B @ D ) @ ( cons_a @ C @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_ord_Olexordp__eq_OCons) ).

thf(1233,plain,
    ! [A: a > a > $o,B: a,C: a,D: list_a,E: list_a] :
      ( ( A @ B @ C )
     => ( lexordp_eq_a @ A @ ( cons_a @ B @ D ) @ ( cons_a @ C @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(96,axiom,
    ! [A: list_list_a] :
      ( ( A != nil_list_a )
     => ~ ! [B: list_a,C: list_list_a] :
            ( A
           != ( cons_list_a @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_list_Oexhaust) ).

thf(698,plain,
    ! [A: list_list_a] :
      ( ( A != nil_list_a )
     => ~ ! [B: list_a,C: list_list_a] :
            ( A
           != ( cons_list_a @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(201,axiom,
    ! [A: a,B: list_a,C: list_a] :
      ( ( append_a @ ( cons_a @ A @ B ) @ C )
      = ( cons_a @ A @ ( append_a @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_append__Cons) ).

thf(1222,plain,
    ! [A: a,B: list_a,C: list_a] :
      ( ( append_a @ ( cons_a @ A @ B ) @ C )
      = ( cons_a @ A @ ( append_a @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(175,axiom,
    ! [A: a > list_a > $o,B: list_a,C: list_list_a,D: list_a > list_list_a > $o] :
      ( ( listrelp_a_list_a @ A @ B @ C )
     => ( ( D @ nil_a @ nil_list_a )
       => ( ! [E: a,F: list_a,G: list_a,H: list_list_a] :
              ( ( A @ E @ F )
             => ( ( listrelp_a_list_a @ A @ G @ H )
               => ( ( D @ G @ H )
                 => ( D @ ( cons_a @ E @ G ) @ ( cons_list_a @ F @ H ) ) ) ) )
         => ( D @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_listrelp_Oinducts) ).

thf(1063,plain,
    ! [A: a > list_a > $o,B: list_a,C: list_list_a,D: list_a > list_list_a > $o] :
      ( ( listrelp_a_list_a @ A @ B @ C )
     => ( ( D @ nil_a @ nil_list_a )
       => ( ! [E: a,F: list_a,G: list_a,H: list_list_a] :
              ( ( A @ E @ F )
             => ( ( listrelp_a_list_a @ A @ G @ H )
               => ( ( D @ G @ H )
                 => ( D @ ( cons_a @ E @ G ) @ ( cons_list_a @ F @ H ) ) ) ) )
         => ( D @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(5,axiom,
    ! [A: list_a,B: list_list_a] :
      ( ( distinct_adj_list_a @ ( cons_list_a @ A @ B ) )
     => ( distinct_adj_list_a @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_distinct__adj__ConsD) ).

thf(340,plain,
    ! [A: list_a,B: list_list_a] :
      ( ( distinct_adj_list_a @ ( cons_list_a @ A @ B ) )
     => ( distinct_adj_list_a @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(187,axiom,
    ! [A: a,B: list_a] :
      ( ( cons_a @ A @ ( tl_a @ ( remdups_adj_a @ ( cons_a @ A @ B ) ) ) )
      = ( remdups_adj_a @ ( cons_a @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_remdups__adj__Cons__alt) ).

thf(1127,plain,
    ! [A: a,B: list_a] :
      ( ( cons_a @ A @ ( tl_a @ ( remdups_adj_a @ ( cons_a @ A @ B ) ) ) )
      = ( remdups_adj_a @ ( cons_a @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(180,axiom,
    ! [A: list_a > $o,B: list_a] :
      ( ( A @ nil_a )
     => ( ! [C: a] : ( A @ ( cons_a @ C @ nil_a ) )
       => ( ! [C: a,D: a,E: list_a] :
              ( ( A @ E )
             => ( ( A @ ( cons_a @ D @ E ) )
               => ( A @ ( cons_a @ C @ ( cons_a @ D @ E ) ) ) ) )
         => ( A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_induct__list012) ).

thf(1095,plain,
    ! [A: list_a > $o,B: list_a] :
      ( ( A @ nil_a )
     => ( ! [C: a] : ( A @ ( cons_a @ C @ nil_a ) )
       => ( ! [C: a,D: a,E: list_a] :
              ( ( A @ E )
             => ( ( A @ ( cons_a @ D @ E ) )
               => ( A @ ( cons_a @ C @ ( cons_a @ D @ E ) ) ) ) )
         => ( A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(29,axiom,
    ! [A: list_a > list_a > $o,B: list_list_a,C: list_list_a] : ( lexordp_eq_list_a @ A @ B @ ( append_list_a @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_ord_Olexordp__eq__pref) ).

thf(404,plain,
    ! [A: list_a > list_a > $o,B: list_list_a,C: list_list_a] : ( lexordp_eq_list_a @ A @ B @ ( append_list_a @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(203,axiom,
    ! [A: list_a,B: list_a] :
      ( ( nil_a
        = ( append_a @ A @ B ) )
      = ( ( A = nil_a )
        & ( B = nil_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_Nil__is__append__conv) ).

thf(1228,plain,
    ! [A: list_a,B: list_a] :
      ( ( nil_a
        = ( append_a @ A @ B ) )
      = ( ( A = nil_a )
        & ( B = nil_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(256,axiom,
    ! [A: list_a] :
      ( ( A != nil_a )
     => ~ ! [B: list_a,C: a] :
            ( A
           != ( append_a @ B @ ( cons_a @ C @ nil_a ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_rev__exhaust) ).

thf(1482,plain,
    ! [A: list_a] :
      ( ( A != nil_a )
     => ~ ! [B: list_a,C: a] :
            ( A
           != ( append_a @ B @ ( cons_a @ C @ nil_a ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(23,axiom,
    ! [A: list_list_a,B: list_list_a] :
      ( ( distinct_adj_list_a @ ( append_list_a @ A @ B ) )
     => ( distinct_adj_list_a @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_distinct__adj__appendD1) ).

thf(389,plain,
    ! [A: list_list_a,B: list_list_a] :
      ( ( distinct_adj_list_a @ ( append_list_a @ A @ B ) )
     => ( distinct_adj_list_a @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(241,axiom,
    ! [A: a > a > $o,B: list_a,C: list_a,D: list_a > list_a > $o] :
      ( ( listrelp_a_a @ A @ B @ C )
     => ( ( D @ nil_a @ nil_a )
       => ( ! [E: a,F: a,G: list_a,H: list_a] :
              ( ( A @ E @ F )
             => ( ( listrelp_a_a @ A @ G @ H )
               => ( ( D @ G @ H )
                 => ( D @ ( cons_a @ E @ G ) @ ( cons_a @ F @ H ) ) ) ) )
         => ( D @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_listrelp_Oinducts) ).

thf(1409,plain,
    ! [A: a > a > $o,B: list_a,C: list_a,D: list_a > list_a > $o] :
      ( ( listrelp_a_a @ A @ B @ C )
     => ( ( D @ nil_a @ nil_a )
       => ( ! [E: a,F: a,G: list_a,H: list_a] :
              ( ( A @ E @ F )
             => ( ( listrelp_a_a @ A @ G @ H )
               => ( ( D @ G @ H )
                 => ( D @ ( cons_a @ E @ G ) @ ( cons_a @ F @ H ) ) ) ) )
         => ( D @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(216,axiom,
    ! [A: a,B: list_a] :
      ( ( cons_a @ A @ B )
     != B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_not__Cons__self2) ).

thf(1287,plain,
    ! [A: a,B: list_a] :
      ( ( cons_a @ A @ B )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(314,axiom,
    ! [A: a,B: list_a] :
      ( nil_a
     != ( cons_a @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_list_Odistinct_I1_J) ).

thf(1760,plain,
    ! [A: a,B: list_a] :
      ( nil_a
     != ( cons_a @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(98,axiom,
    ! [A: list_list_a > list_list_a > $o,B: list_list_a,C: list_list_a] :
      ( ! [D: list_list_a] : ( A @ nil_list_a @ D )
     => ( ! [D: list_a,E: list_list_a,F: list_list_a] :
            ( ( A @ F @ E )
           => ( A @ ( cons_list_a @ D @ E ) @ F ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_splice_Oinduct) ).

thf(719,plain,
    ! [A: list_list_a > list_list_a > $o,B: list_list_a,C: list_list_a] :
      ( ! [D: list_list_a] : ( A @ nil_list_a @ D )
     => ( ! [D: list_a,E: list_list_a,F: list_list_a] :
            ( ( A @ F @ E )
           => ( A @ ( cons_list_a @ D @ E ) @ F ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(97,axiom,
    ! [A: list_a > list_a > $o,B: list_list_a,C: list_list_a] :
      ( ( listre1221556159list_a @ A @ B @ C )
     => ( ( ( B = nil_list_a )
         => ( C != nil_list_a ) )
       => ~ ! [D: list_a,E: list_a,F: list_list_a] :
              ( ( B
                = ( cons_list_a @ D @ F ) )
             => ! [G: list_list_a] :
                  ( ( C
                    = ( cons_list_a @ E @ G ) )
                 => ( ( A @ D @ E )
                   => ~ ( listre1221556159list_a @ A @ F @ G ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_listrelp_Ocases) ).

thf(702,plain,
    ! [A: list_a > list_a > $o,B: list_list_a,C: list_list_a] :
      ( ( listre1221556159list_a @ A @ B @ C )
     => ( ( ( B = nil_list_a )
         => ( C != nil_list_a ) )
       => ~ ! [D: list_a,E: list_a,F: list_list_a] :
              ( ( B
                = ( cons_list_a @ D @ F ) )
             => ! [G: list_list_a] :
                  ( ( C
                    = ( cons_list_a @ E @ G ) )
                 => ( ( A @ D @ E )
                   => ~ ( listre1221556159list_a @ A @ F @ G ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(274,axiom,
    ! [A: list_a > list_a > $o,B: list_a,C: list_a] :
      ( ! [D: list_a] : ( A @ nil_a @ D )
     => ( ! [D: list_a] : ( A @ D @ nil_a )
       => ( ! [D: a,E: list_a,F: a,G: list_a] :
              ( ( A @ E @ ( cons_a @ F @ G ) )
             => ( ( A @ ( cons_a @ D @ E ) @ G )
               => ( A @ ( cons_a @ D @ E ) @ ( cons_a @ F @ G ) ) ) )
         => ( A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_shuffles_Oinduct) ).

thf(1577,plain,
    ! [A: list_a > list_a > $o,B: list_a,C: list_a] :
      ( ! [D: list_a] : ( A @ nil_a @ D )
     => ( ! [D: list_a] : ( A @ D @ nil_a )
       => ( ! [D: a,E: list_a,F: a,G: list_a] :
              ( ( A @ E @ ( cons_a @ F @ G ) )
             => ( ( A @ ( cons_a @ D @ E ) @ G )
               => ( A @ ( cons_a @ D @ E ) @ ( cons_a @ F @ G ) ) ) )
         => ( A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(143,axiom,
    ! [A: list_list_a,B: list_list_a] :
      ( ( A != nil_list_a )
     => ( ( tl_list_a @ ( append_list_a @ A @ B ) )
        = ( append_list_a @ ( tl_list_a @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_tl__append2) ).

thf(934,plain,
    ! [A: list_list_a,B: list_list_a] :
      ( ( A != nil_list_a )
     => ( ( tl_list_a @ ( append_list_a @ A @ B ) )
        = ( append_list_a @ ( tl_list_a @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(249,axiom,
    ! [A: a > list_a,B: a,C: list_a,D: list_list_a] :
      ( ( map_ta41997947list_a @ A @ ( cons_a @ B @ C ) @ D )
      = ( map_ta41997947list_a @ A @ C @ ( cons_list_a @ ( A @ B ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_map__tailrec__rev_Osimps_I2_J) ).

thf(1462,plain,
    ! [A: a > list_a,B: a,C: list_a,D: list_list_a] :
      ( ( map_ta41997947list_a @ A @ ( cons_a @ B @ C ) @ D )
      = ( map_ta41997947list_a @ A @ C @ ( cons_list_a @ ( A @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(328,axiom,
    ! [A: a,B: list_a,C: a,D: list_a] :
      ( ( ( cons_a @ A @ B )
        = ( cons_a @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_list_Oinject) ).

thf(1860,plain,
    ! [A: a,B: list_a,C: a,D: list_a] :
      ( ( ( cons_a @ A @ B )
        = ( cons_a @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(211,axiom,
    ! [A: list_a] :
      ( ( append_a @ nil_a @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_append_Oleft__neutral) ).

thf(1264,plain,
    ! [A: list_a] :
      ( ( append_a @ nil_a @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(67,axiom,
    ! [A: list_a > list_list_a] :
      ( ( bind_list_a_list_a @ nil_list_a @ A )
      = nil_list_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_bind__simps_I1_J) ).

thf(542,plain,
    ! [A: list_a > list_list_a] :
      ( ( bind_list_a_list_a @ nil_list_a @ A )
      = nil_list_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(47,axiom,
    ! [A: list_a,B: list_a] :
      ( ( distinct_adj_a @ ( append_a @ A @ B ) )
     => ( distinct_adj_a @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_distinct__adj__appendD2) ).

thf(460,plain,
    ! [A: list_a,B: list_a] :
      ( ( distinct_adj_a @ ( append_a @ A @ B ) )
     => ( distinct_adj_a @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(117,axiom,
    ! [A: list_a,B: list_a] :
      ( ( if_list_a @ $true @ A @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001t__List__Olist_Itf__a_J_T) ).

thf(817,plain,
    ! [A: list_a,B: list_a] :
      ( ( if_list_a @ $true @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(72,axiom,
    ! [A: list_a > list_a,B: list_list_a,C: list_list_a,D: list_list_a] :
      ( ( ( map_ta982122357list_a @ A @ B @ C )
        = D )
     => ( ( ( B = nil_list_a )
         => ( D != C ) )
       => ~ ! [E: list_a,F: list_list_a] :
              ( ( B
                = ( cons_list_a @ E @ F ) )
             => ( D
               != ( map_ta982122357list_a @ A @ F @ ( cons_list_a @ ( A @ E ) @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_map__tailrec__rev_Oelims) ).

thf(559,plain,
    ! [A: list_a > list_a,B: list_list_a,C: list_list_a,D: list_list_a] :
      ( ( ( map_ta982122357list_a @ A @ B @ C )
        = D )
     => ( ( ( B = nil_list_a )
         => ( D != C ) )
       => ~ ! [E: list_a,F: list_list_a] :
              ( ( B
                = ( cons_list_a @ E @ F ) )
             => ( D
               != ( map_ta982122357list_a @ A @ F @ ( cons_list_a @ ( A @ E ) @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(301,axiom,
    ! [A: a,B: list_a] :
      ( ( append_a @ ( cons_a @ A @ nil_a ) @ B )
      = ( cons_a @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_append__eq__Cons) ).

thf(1704,plain,
    ! [A: a,B: list_a] :
      ( ( append_a @ ( cons_a @ A @ nil_a ) @ B )
      = ( cons_a @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(75,axiom,
    ! [A: list_a] : ( distinct_adj_list_a @ ( cons_list_a @ A @ nil_list_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_distinct__adj__singleton) ).

thf(606,plain,
    ! [A: list_a] : ( distinct_adj_list_a @ ( cons_list_a @ A @ nil_list_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(34,axiom,
    ! [A: list_a,B: list_a,C: list_a] :
      ( ( append_a @ ( append_a @ A @ B ) @ C )
      = ( append_a @ A @ ( append_a @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_append__assoc) ).

thf(416,plain,
    ! [A: list_a,B: list_a,C: list_a] :
      ( ( append_a @ ( append_a @ A @ B ) @ C )
      = ( append_a @ A @ ( append_a @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(183,axiom,
    ! [A: a > a > $o,B: a,C: a,D: list_a,E: list_a] :
      ( ( A @ B @ C )
     => ( ( listrelp_a_a @ A @ D @ E )
       => ( listrelp_a_a @ A @ ( cons_a @ B @ D ) @ ( cons_a @ C @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_listrelp_OCons) ).

thf(1115,plain,
    ! [A: a > a > $o,B: a,C: a,D: list_a,E: list_a] :
      ( ( A @ B @ C )
     => ( ( listrelp_a_a @ A @ D @ E )
       => ( listrelp_a_a @ A @ ( cons_a @ B @ D ) @ ( cons_a @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(332,axiom,
    ! [A: a > a > $o,B: list_a,C: list_a] :
      ( ( lexordp_eq_a @ A @ B @ C )
     => ( ( B != nil_a )
       => ( ! [D: a] :
              ( ? [E: list_a] :
                  ( B
                  = ( cons_a @ D @ E ) )
             => ! [E: a] :
                  ( ? [F: list_a] :
                      ( C
                      = ( cons_a @ E @ F ) )
                 => ~ ( A @ D @ E ) ) )
         => ~ ! [D: a,E: a,F: list_a] :
                ( ( B
                  = ( cons_a @ D @ F ) )
               => ! [G: list_a] :
                    ( ( C
                      = ( cons_a @ E @ G ) )
                   => ( ~ ( A @ D @ E )
                     => ( ~ ( A @ E @ D )
                       => ~ ( lexordp_eq_a @ A @ F @ G ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_ord_Olexordp__eq_Ocases) ).

thf(1875,plain,
    ! [A: a > a > $o,B: list_a,C: list_a] :
      ( ( lexordp_eq_a @ A @ B @ C )
     => ( ( B != nil_a )
       => ( ! [D: a] :
              ( ? [E: list_a] :
                  ( B
                  = ( cons_a @ D @ E ) )
             => ! [E: a] :
                  ( ? [F: list_a] :
                      ( C
                      = ( cons_a @ E @ F ) )
                 => ~ ( A @ D @ E ) ) )
         => ~ ! [D: a,E: a,F: list_a] :
                ( ( B
                  = ( cons_a @ D @ F ) )
               => ! [G: list_a] :
                    ( ( C
                      = ( cons_a @ E @ G ) )
                   => ( ~ ( A @ D @ E )
                     => ( ~ ( A @ E @ D )
                       => ~ ( lexordp_eq_a @ A @ F @ G ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(85,axiom,
    ! [A: list_list_a,B: list_list_a] :
      ( ( ( A = nil_list_a )
       => ( ( last_list_a @ ( append_list_a @ B @ A ) )
          = ( last_list_a @ B ) ) )
      & ( ( A != nil_list_a )
       => ( ( last_list_a @ ( append_list_a @ B @ A ) )
          = ( last_list_a @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_last__append) ).

thf(638,plain,
    ! [A: list_list_a,B: list_list_a] :
      ( ( ( A = nil_list_a )
       => ( ( last_list_a @ ( append_list_a @ B @ A ) )
          = ( last_list_a @ B ) ) )
      & ( ( A != nil_list_a )
       => ( ( last_list_a @ ( append_list_a @ B @ A ) )
          = ( last_list_a @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(124,axiom,
    ! [A: list_list_a > $o,B: list_list_a] :
      ( ( A @ nil_list_a )
     => ( ! [C: list_a] : ( A @ ( cons_list_a @ C @ nil_list_a ) )
       => ( ! [C: list_a,D: list_a,E: list_list_a] :
              ( ( ( C = D )
               => ( A @ ( cons_list_a @ C @ E ) ) )
             => ( ( ( C != D )
                 => ( A @ ( cons_list_a @ D @ E ) ) )
               => ( A @ ( cons_list_a @ C @ ( cons_list_a @ D @ E ) ) ) ) )
         => ( A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_remdups__adj_Oinduct) ).

thf(853,plain,
    ! [A: list_list_a > $o,B: list_list_a] :
      ( ( A @ nil_list_a )
     => ( ! [C: list_a] : ( A @ ( cons_list_a @ C @ nil_list_a ) )
       => ( ! [C: list_a,D: list_a,E: list_list_a] :
              ( ( ( C = D )
               => ( A @ ( cons_list_a @ C @ E ) ) )
             => ( ( ( C != D )
                 => ( A @ ( cons_list_a @ D @ E ) ) )
               => ( A @ ( cons_list_a @ C @ ( cons_list_a @ D @ E ) ) ) ) )
         => ( A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(255,axiom,
    ! [A: list_a,B: list_a] :
      ( ( A
        = ( append_a @ A @ B ) )
      = ( B = nil_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_self__append__conv) ).

thf(1479,plain,
    ! [A: list_a,B: list_a] :
      ( ( A
        = ( append_a @ A @ B ) )
      = ( B = nil_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(282,axiom,
    ! [A: a > a > $o,B: list_a] :
      ( ( successively_a @ A @ B )
     => ( ( B != nil_a )
       => ( ! [C: a] :
              ( B
             != ( cons_a @ C @ nil_a ) )
         => ~ ! [C: a,D: a,E: list_a] :
                ( ( B
                  = ( cons_a @ C @ ( cons_a @ D @ E ) ) )
               => ~ ( ( A @ C @ D )
                    & ( successively_a @ A @ ( cons_a @ D @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_successively_Oelims_I2_J) ).

thf(1609,plain,
    ! [A: a > a > $o,B: list_a] :
      ( ( successively_a @ A @ B )
     => ( ( B != nil_a )
       => ( ! [C: a] :
              ( B
             != ( cons_a @ C @ nil_a ) )
         => ~ ! [C: a,D: a,E: list_a] :
                ( ( B
                  = ( cons_a @ C @ ( cons_a @ D @ E ) ) )
               => ~ ( ( A @ C @ D )
                    & ( successively_a @ A @ ( cons_a @ D @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(159,axiom,
    ! [A: list_a,B: set_list_a,C: a] :
      ( ( member_list_a2 @ A @ ( bNF_Greatest_Shift_a @ B @ C ) )
     => ( member_list_a2 @ ( cons_a @ C @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_ShiftD) ).

thf(1013,plain,
    ! [A: list_a,B: set_list_a,C: a] :
      ( ( member_list_a2 @ A @ ( bNF_Greatest_Shift_a @ B @ C ) )
     => ( member_list_a2 @ ( cons_a @ C @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(109,axiom,
    ! [A: list_list_a] :
      ( ( A != nil_list_a )
     => ( ( rotate1_list_a @ A )
        = ( append_list_a @ ( tl_list_a @ A ) @ ( cons_list_a @ ( hd_list_a @ A ) @ nil_list_a ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_rotate1__hd__tl) ).

thf(770,plain,
    ! [A: list_list_a] :
      ( ( A != nil_list_a )
     => ( ( rotate1_list_a @ A )
        = ( append_list_a @ ( tl_list_a @ A ) @ ( cons_list_a @ ( hd_list_a @ A ) @ nil_list_a ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(113,axiom,
    ( listre1221556159list_a
    = ( ^ [A: list_a > list_a > $o,B: list_list_a,C: list_list_a] :
          ( ( ( B = nil_list_a )
            & ( C = nil_list_a ) )
          | ? [D: list_a,E: list_a,F: list_list_a,G: list_list_a] :
              ( ( B
                = ( cons_list_a @ D @ F ) )
              & ( C
                = ( cons_list_a @ E @ G ) )
              & ( A @ D @ E )
              & ( listre1221556159list_a @ A @ F @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_listrelp_Osimps) ).

thf(789,plain,
    ( listre1221556159list_a
    = ( ^ [A: list_a > list_a > $o,B: list_list_a,C: list_list_a] :
          ( ( ( B = nil_list_a )
            & ( C = nil_list_a ) )
          | ? [D: list_a,E: list_a,F: list_list_a,G: list_list_a] :
              ( ( B
                = ( cons_list_a @ D @ F ) )
              & ( C
                = ( cons_list_a @ E @ G ) )
              & ( A @ D @ E )
              & ( listre1221556159list_a @ A @ F @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(42,axiom,
    ! [A: list_list_list_a] :
      ( ( A != nil_list_list_a )
     => ( ( ( hd_list_list_a @ A )
         != nil_list_a )
       => ( ( hd_list_a @ ( concat_list_a @ A ) )
          = ( hd_list_a @ ( hd_list_list_a @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_hd__concat) ).

thf(443,plain,
    ! [A: list_list_list_a] :
      ( ( A != nil_list_list_a )
     => ( ( ( hd_list_list_a @ A )
         != nil_list_a )
       => ( ( hd_list_a @ ( concat_list_a @ A ) )
          = ( hd_list_a @ ( hd_list_list_a @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(181,axiom,
    ! [A: a > a > $o,B: a] : ( successively_a @ A @ ( cons_a @ B @ nil_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_successively_Osimps_I2_J) ).

thf(1109,plain,
    ! [A: a > a > $o,B: a] : ( successively_a @ A @ ( cons_a @ B @ nil_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(18,axiom,
    ! [A: list_a,B: list_a,C: list_list_a] :
      ( ( distinct_adj_list_a @ ( cons_list_a @ A @ ( cons_list_a @ B @ C ) ) )
      = ( ( A != B )
        & ( distinct_adj_list_a @ ( cons_list_a @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_distinct__adj__Cons__Cons) ).

thf(376,plain,
    ! [A: list_a,B: list_a,C: list_list_a] :
      ( ( distinct_adj_list_a @ ( cons_list_a @ A @ ( cons_list_a @ B @ C ) ) )
      = ( ( A != B )
        & ( distinct_adj_list_a @ ( cons_list_a @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(79,axiom,
    ! [A: a > a > $o,B: list_a,C: list_a] : ( lexordp_eq_a @ A @ B @ ( append_a @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_ord_Olexordp__eq__pref) ).

thf(623,plain,
    ! [A: a > a > $o,B: list_a,C: list_a] : ( lexordp_eq_a @ A @ B @ ( append_a @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(296,axiom,
    ! [A: list_a > list_a > $o,B: list_a,C: list_a] :
      ( ( A @ nil_a @ nil_a )
     => ( ! [D: a,E: list_a] : ( A @ ( cons_a @ D @ E ) @ nil_a )
       => ( ! [D: a,E: list_a] : ( A @ nil_a @ ( cons_a @ D @ E ) )
         => ( ! [D: a,E: list_a,F: a,G: list_a] :
                ( ( A @ E @ G )
               => ( A @ ( cons_a @ D @ E ) @ ( cons_a @ F @ G ) ) )
           => ( A @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_list__induct2_H) ).

thf(1682,plain,
    ! [A: list_a > list_a > $o,B: list_a,C: list_a] :
      ( ( A @ nil_a @ nil_a )
     => ( ! [D: a,E: list_a] : ( A @ ( cons_a @ D @ E ) @ nil_a )
       => ( ! [D: a,E: list_a] : ( A @ nil_a @ ( cons_a @ D @ E ) )
         => ( ! [D: a,E: list_a,F: a,G: list_a] :
                ( ( A @ E @ G )
               => ( A @ ( cons_a @ D @ E ) @ ( cons_a @ F @ G ) ) )
           => ( A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(319,axiom,
    ! [A: list_a,B: list_a,C: list_a,D: a] :
      ( ( member_list_a2 @ A @ ( shuffles_a @ B @ C ) )
     => ( member_list_a2 @ ( cons_a @ D @ A ) @ ( shuffles_a @ B @ ( cons_a @ D @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_Cons__in__shuffles__rightI) ).

thf(1828,plain,
    ! [A: list_a,B: list_a,C: list_a,D: a] :
      ( ( member_list_a2 @ A @ ( shuffles_a @ B @ C ) )
     => ( member_list_a2 @ ( cons_a @ D @ A ) @ ( shuffles_a @ B @ ( cons_a @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(9,axiom,
    ! [A: list_a > list_a > $o,B: list_a,C: list_a,D: list_list_a] :
      ( ( successively_list_a @ A @ ( cons_list_a @ B @ ( cons_list_a @ C @ D ) ) )
      = ( ( A @ B @ C )
        & ( successively_list_a @ A @ ( cons_list_a @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_successively_Osimps_I3_J) ).

thf(353,plain,
    ! [A: list_a > list_a > $o,B: list_a,C: list_a,D: list_list_a] :
      ( ( successively_list_a @ A @ ( cons_list_a @ B @ ( cons_list_a @ C @ D ) ) )
      = ( ( A @ B @ C )
        & ( successively_list_a @ A @ ( cons_list_a @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(54,axiom,
    ! [A: list_a] :
      ( ( butlast_a @ ( tl_a @ A ) )
      = ( tl_a @ ( butlast_a @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_butlast__tl) ).

thf(492,plain,
    ! [A: list_a] :
      ( ( butlast_a @ ( tl_a @ A ) )
      = ( tl_a @ ( butlast_a @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(250,axiom,
    ! [A: list_a > a > $o] : ( listrelp_list_a_a @ A @ nil_list_a @ nil_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_listrelp_ONil) ).

thf(1465,plain,
    ! [A: list_a > a > $o] : ( listrelp_list_a_a @ A @ nil_list_a @ nil_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(228,axiom,
    ! [A: list_a] :
      ( ( ( tl_a @ A )
        = nil_a )
      = ( ( A = nil_a )
        | ? [B: a] :
            ( A
            = ( cons_a @ B @ nil_a ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_tl__Nil) ).

thf(1334,plain,
    ! [A: list_a] :
      ( ( ( tl_a @ A )
        = nil_a )
      = ( ( A = nil_a )
        | ? [B: a] :
            ( A
            = ( cons_a @ B @ nil_a ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(86,axiom,
    ! [A: list_a > list_a > $o,B: list_list_a,C: list_list_a,D: list_list_a > list_list_a > $o] :
      ( ( listre1221556159list_a @ A @ B @ C )
     => ( ( D @ nil_list_a @ nil_list_a )
       => ( ! [E: list_a,F: list_a,G: list_list_a,H: list_list_a] :
              ( ( A @ E @ F )
             => ( ( listre1221556159list_a @ A @ G @ H )
               => ( ( D @ G @ H )
                 => ( D @ ( cons_list_a @ E @ G ) @ ( cons_list_a @ F @ H ) ) ) ) )
         => ( D @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_listrelp_Oinducts) ).

thf(646,plain,
    ! [A: list_a > list_a > $o,B: list_list_a,C: list_list_a,D: list_list_a > list_list_a > $o] :
      ( ( listre1221556159list_a @ A @ B @ C )
     => ( ( D @ nil_list_a @ nil_list_a )
       => ( ! [E: list_a,F: list_a,G: list_list_a,H: list_list_a] :
              ( ( A @ E @ F )
             => ( ( listre1221556159list_a @ A @ G @ H )
               => ( ( D @ G @ H )
                 => ( D @ ( cons_list_a @ E @ G ) @ ( cons_list_a @ F @ H ) ) ) ) )
         => ( D @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(161,axiom,
    ! [A: list_a > list_a > $o,B: list_a,C: list_a] :
      ( ! [D: list_a] : ( A @ nil_a @ D )
     => ( ! [D: a,E: list_a,F: list_a] :
            ( ( A @ F @ E )
           => ( A @ ( cons_a @ D @ E ) @ F ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_splice_Oinduct) ).

thf(1020,plain,
    ! [A: list_a > list_a > $o,B: list_a,C: list_a] :
      ( ! [D: list_a] : ( A @ nil_a @ D )
     => ( ! [D: a,E: list_a,F: list_a] :
            ( ( A @ F @ E )
           => ( A @ ( cons_a @ D @ E ) @ F ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(7,axiom,
    ! [A: list_list_a] :
      ( ( splice_list_a @ A @ nil_list_a )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_splice__Nil2) ).

thf(348,plain,
    ! [A: list_list_a] :
      ( ( splice_list_a @ A @ nil_list_a )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(94,axiom,
    ! [A: list_a > list_a,B: list_a,C: list_list_a,D: list_list_a] :
      ( ( map_ta982122357list_a @ A @ ( cons_list_a @ B @ C ) @ D )
      = ( map_ta982122357list_a @ A @ C @ ( cons_list_a @ ( A @ B ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_map__tailrec__rev_Osimps_I2_J) ).

thf(687,plain,
    ! [A: list_a > list_a,B: list_a,C: list_list_a,D: list_list_a] :
      ( ( map_ta982122357list_a @ A @ ( cons_list_a @ B @ C ) @ D )
      = ( map_ta982122357list_a @ A @ C @ ( cons_list_a @ ( A @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(128,axiom,
    ! [A: list_list_a,B: list_a,C: list_list_a,D: list_a] :
      ( ( ( append_list_a @ A @ ( cons_list_a @ B @ nil_list_a ) )
        = ( append_list_a @ C @ ( cons_list_a @ D @ nil_list_a ) ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_append1__eq__conv) ).

thf(877,plain,
    ! [A: list_list_a,B: list_a,C: list_list_a,D: list_a] :
      ( ( ( append_list_a @ A @ ( cons_list_a @ B @ nil_list_a ) )
        = ( append_list_a @ C @ ( cons_list_a @ D @ nil_list_a ) ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(148,axiom,
    ! [A: list_list_a,B: list_list_a] :
      ( ( concat_a @ ( append_list_a @ A @ B ) )
      = ( append_a @ ( concat_a @ A ) @ ( concat_a @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_concat__append) ).

thf(956,plain,
    ! [A: list_list_a,B: list_list_a] :
      ( ( concat_a @ ( append_list_a @ A @ B ) )
      = ( append_a @ ( concat_a @ A ) @ ( concat_a @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(26,axiom,
    ! [A: list_a > list_a > $o,B: list_list_a] :
      ( ( lexordp_eq_list_a @ A @ B @ nil_list_a )
      = ( B = nil_list_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_ord_Olexordp__eq__simps_I2_J) ).

thf(396,plain,
    ! [A: list_a > list_a > $o,B: list_list_a] :
      ( ( lexordp_eq_list_a @ A @ B @ nil_list_a )
      = ( B = nil_list_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(38,axiom,
    ! [A: ( list_a > list_a > $o ) > list_list_a > $o,B: list_a > list_a > $o,C: list_list_a] :
      ( ! [D: list_a > list_a > $o] : ( A @ D @ nil_list_a )
     => ( ! [D: list_a > list_a > $o,E: list_a] : ( A @ D @ ( cons_list_a @ E @ nil_list_a ) )
       => ( ! [D: list_a > list_a > $o,E: list_a,F: list_a,G: list_list_a] :
              ( ( A @ D @ ( cons_list_a @ F @ G ) )
             => ( A @ D @ ( cons_list_a @ E @ ( cons_list_a @ F @ G ) ) ) )
         => ( A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_successively_Oinduct) ).

thf(428,plain,
    ! [A: ( list_a > list_a > $o ) > list_list_a > $o,B: list_a > list_a > $o,C: list_list_a] :
      ( ! [D: list_a > list_a > $o] : ( A @ D @ nil_list_a )
     => ( ! [D: list_a > list_a > $o,E: list_a] : ( A @ D @ ( cons_list_a @ E @ nil_list_a ) )
       => ( ! [D: list_a > list_a > $o,E: list_a,F: list_a,G: list_list_a] :
              ( ( A @ D @ ( cons_list_a @ F @ G ) )
             => ( A @ D @ ( cons_list_a @ E @ ( cons_list_a @ F @ G ) ) ) )
         => ( A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(279,axiom,
    ! [A: a,B: list_a,C: a > list_list_a] :
      ( ( bind_a_list_a @ ( cons_a @ A @ B ) @ C )
      = ( append_list_a @ ( C @ A ) @ ( bind_a_list_a @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_bind__simps_I2_J) ).

thf(1600,plain,
    ! [A: a,B: list_a,C: a > list_list_a] :
      ( ( bind_a_list_a @ ( cons_a @ A @ B ) @ C )
      = ( append_list_a @ ( C @ A ) @ ( bind_a_list_a @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(208,axiom,
    ! [A: list_a,B: list_a,C: list_a > list_a > $o] :
      ( ( ( size_size_list_a @ A )
        = ( size_size_list_a @ B ) )
     => ( ( C @ nil_a @ nil_a )
       => ( ! [D: a,E: list_a,F: a,G: list_a] :
              ( ( ( size_size_list_a @ E )
                = ( size_size_list_a @ G ) )
             => ( ( C @ E @ G )
               => ( C @ ( cons_a @ D @ E ) @ ( cons_a @ F @ G ) ) ) )
         => ( C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_list__induct2) ).

thf(1242,plain,
    ! [A: list_a,B: list_a,C: list_a > list_a > $o] :
      ( ( ( size_size_list_a @ A )
        = ( size_size_list_a @ B ) )
     => ( ( C @ nil_a @ nil_a )
       => ( ! [D: a,E: list_a,F: a,G: list_a] :
              ( ( ( size_size_list_a @ E )
                = ( size_size_list_a @ G ) )
             => ( ( C @ E @ G )
               => ( C @ ( cons_a @ D @ E ) @ ( cons_a @ F @ G ) ) ) )
         => ( C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(199,axiom,
    ! [A: list_a > list_list_a > $o,B: list_a,C: list_list_a] :
      ( ( A @ nil_a @ nil_list_a )
     => ( ! [D: a,E: list_a] : ( A @ ( cons_a @ D @ E ) @ nil_list_a )
       => ( ! [D: list_a,E: list_list_a] : ( A @ nil_a @ ( cons_list_a @ D @ E ) )
         => ( ! [D: a,E: list_a,F: list_a,G: list_list_a] :
                ( ( A @ E @ G )
               => ( A @ ( cons_a @ D @ E ) @ ( cons_list_a @ F @ G ) ) )
           => ( A @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_list__induct2_H) ).

thf(1215,plain,
    ! [A: list_a > list_list_a > $o,B: list_a,C: list_list_a] :
      ( ( A @ nil_a @ nil_list_a )
     => ( ! [D: a,E: list_a] : ( A @ ( cons_a @ D @ E ) @ nil_list_a )
       => ( ! [D: list_a,E: list_list_a] : ( A @ nil_a @ ( cons_list_a @ D @ E ) )
         => ( ! [D: a,E: list_a,F: list_a,G: list_list_a] :
                ( ( A @ E @ G )
               => ( A @ ( cons_a @ D @ E ) @ ( cons_list_a @ F @ G ) ) )
           => ( A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(83,axiom,
    ! [A: a > a > $o,B: list_a] : ( lexordp_eq_a @ A @ B @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ord_Olexordp__eq__refl) ).

thf(634,plain,
    ! [A: a > a > $o,B: list_a] : ( lexordp_eq_a @ A @ B @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(32,axiom,
    ! [A: list_list_a] :
      ( ( splice_list_a @ nil_list_a @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_splice_Osimps_I1_J) ).

thf(411,plain,
    ! [A: list_list_a] :
      ( ( splice_list_a @ nil_list_a @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(230,axiom,
    ! [A: list_a,B: list_a] :
      ( ( A != nil_a )
     => ( ( tl_a @ ( append_a @ A @ B ) )
        = ( append_a @ ( tl_a @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_tl__append2) ).

thf(1345,plain,
    ! [A: list_a,B: list_a] :
      ( ( A != nil_a )
     => ( ( tl_a @ ( append_a @ A @ B ) )
        = ( append_a @ ( tl_a @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(329,axiom,
    ! [A: list_a,B: list_a] :
      ( ( A = nil_a )
     => ( ( last_a @ ( append_a @ B @ A ) )
        = ( last_a @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_last__appendL) ).

thf(1863,plain,
    ! [A: list_a,B: list_a] :
      ( ( A = nil_a )
     => ( ( last_a @ ( append_a @ B @ A ) )
        = ( last_a @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(91,axiom,
    ! [A: list_list_a] :
      ( ( A != nil_list_a )
      = ( ? [B: list_a,C: list_list_a] :
            ( A
            = ( cons_list_a @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_neq__Nil__conv) ).

thf(678,plain,
    ! [A: list_list_a] :
      ( ( A != nil_list_a )
      = ( ? [B: list_a,C: list_list_a] :
            ( A
            = ( cons_list_a @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(65,axiom,
    ! [A: list_a,B: list_a] :
      ( ( distinct_adj_a @ ( append_a @ A @ B ) )
     => ( distinct_adj_a @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_distinct__adj__appendD1) ).

thf(529,plain,
    ! [A: list_a,B: list_a] :
      ( ( distinct_adj_a @ ( append_a @ A @ B ) )
     => ( distinct_adj_a @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(190,axiom,
    ( ( subseqs_a @ nil_a )
    = ( cons_list_a @ nil_a @ nil_list_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_subseqs_Osimps_I1_J) ).

thf(1153,plain,
    ( ( subseqs_a @ nil_a )
    = ( cons_list_a @ nil_a @ nil_list_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(252,axiom,
    ! [A: a,B: list_a,C: a] :
      ( ( member_a @ ( cons_a @ A @ B ) @ C )
      = ( ( A = C )
        | ( member_a @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_member__rec_I1_J) ).

thf(1470,plain,
    ! [A: a,B: list_a,C: a] :
      ( ( member_a @ ( cons_a @ A @ B ) @ C )
      = ( ( A = C )
        | ( member_a @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(14,axiom,
    ! [A: list_a > list_a > $o,B: list_a,C: list_list_a,D: list_a,E: list_list_a] :
      ( ( lexordp_eq_list_a @ A @ ( cons_list_a @ B @ C ) @ ( cons_list_a @ D @ E ) )
      = ( ( A @ B @ D )
        | ( ~ ( A @ D @ B )
          & ( lexordp_eq_list_a @ A @ C @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_ord_Olexordp__eq__simps_I4_J) ).

thf(366,plain,
    ! [A: list_a > list_a > $o,B: list_a,C: list_list_a,D: list_a,E: list_list_a] :
      ( ( lexordp_eq_list_a @ A @ ( cons_list_a @ B @ C ) @ ( cons_list_a @ D @ E ) )
      = ( ( A @ B @ D )
        | ( ~ ( A @ D @ B )
          & ( lexordp_eq_list_a @ A @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(330,axiom,
    ! [A: list_a,B: list_a] :
      ( ( A != nil_a )
     => ( ( last_a @ ( append_a @ B @ A ) )
        = ( last_a @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_last__appendR) ).

thf(1868,plain,
    ! [A: list_a,B: list_a] :
      ( ( A != nil_a )
     => ( ( last_a @ ( append_a @ B @ A ) )
        = ( last_a @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(60,axiom,
    ! [A: ( list_a > list_a ) > list_list_a > list_list_a > $o,B: list_a > list_a,C: list_list_a,D: list_list_a] :
      ( ! [E: list_a > list_a,F: list_list_a] : ( A @ E @ nil_list_a @ F )
     => ( ! [E: list_a > list_a,F: list_a,G: list_list_a,H: list_list_a] :
            ( ( A @ E @ G @ ( cons_list_a @ ( E @ F ) @ H ) )
           => ( A @ E @ ( cons_list_a @ F @ G ) @ H ) )
       => ( A @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_map__tailrec__rev_Oinduct) ).

thf(512,plain,
    ! [A: ( list_a > list_a ) > list_list_a > list_list_a > $o,B: list_a > list_a,C: list_list_a,D: list_list_a] :
      ( ! [E: list_a > list_a,F: list_list_a] : ( A @ E @ nil_list_a @ F )
     => ( ! [E: list_a > list_a,F: list_a,G: list_list_a,H: list_list_a] :
            ( ( A @ E @ G @ ( cons_list_a @ ( E @ F ) @ H ) )
           => ( A @ E @ ( cons_list_a @ F @ G ) @ H ) )
       => ( A @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(41,axiom,
    ! [A: list_a,B: list_list_a] :
      ( ( cons_list_a @ A @ B )
     != B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_not__Cons__self2) ).

thf(439,plain,
    ! [A: list_a,B: list_list_a] :
      ( ( cons_list_a @ A @ B )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(169,axiom,
    ( ( rotate1_a @ nil_a )
    = nil_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_rotate1_Osimps_I1_J) ).

thf(1047,plain,
    ( ( rotate1_a @ nil_a )
    = nil_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(309,axiom,
    ! [A: a > a > $o,B: a,C: list_a] :
      ~ ( lexordp_eq_a @ A @ ( cons_a @ B @ C ) @ nil_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_ord_Olexordp__eq__simps_I3_J) ).

thf(1730,plain,
    ! [A: a > a > $o,B: a,C: list_a] :
      ~ ( lexordp_eq_a @ A @ ( cons_a @ B @ C ) @ nil_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(132,axiom,
    ! [A: list_a,B: list_a,C: list_a] :
      ( ( ( append_a @ A @ B )
        = ( append_a @ A @ C ) )
      = ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_same__append__eq) ).

thf(894,plain,
    ! [A: list_a,B: list_a,C: list_a] :
      ( ( ( append_a @ A @ B )
        = ( append_a @ A @ C ) )
      = ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(105,axiom,
    ! [A: list_list_a] :
      ( ( A != nil_list_a )
     => ( ( cons_list_a @ ( hd_list_a @ A ) @ ( tl_list_a @ A ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_list_Ocollapse) ).

thf(746,plain,
    ! [A: list_list_a] :
      ( ( A != nil_list_a )
     => ( ( cons_list_a @ ( hd_list_a @ A ) @ ( tl_list_a @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(232,axiom,
    ! [A: list_a > $o,B: list_a] :
      ( ( A @ nil_a )
     => ( ! [C: a] : ( A @ ( cons_a @ C @ nil_a ) )
       => ( ! [C: a,D: a,E: list_a] :
              ( ( ( C = D )
               => ( A @ ( cons_a @ C @ E ) ) )
             => ( ( ( C != D )
                 => ( A @ ( cons_a @ D @ E ) ) )
               => ( A @ ( cons_a @ C @ ( cons_a @ D @ E ) ) ) ) )
         => ( A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_remdups__adj_Oinduct) ).

thf(1355,plain,
    ! [A: list_a > $o,B: list_a] :
      ( ( A @ nil_a )
     => ( ! [C: a] : ( A @ ( cons_a @ C @ nil_a ) )
       => ( ! [C: a,D: a,E: list_a] :
              ( ( ( C = D )
               => ( A @ ( cons_a @ C @ E ) ) )
             => ( ( ( C != D )
                 => ( A @ ( cons_a @ D @ E ) ) )
               => ( A @ ( cons_a @ C @ ( cons_a @ D @ E ) ) ) ) )
         => ( A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(118,axiom,
    ! [A: list_a,B: list_list_a,C: list_list_a] :
      ( ( append_list_a @ ( cons_list_a @ A @ B ) @ C )
      = ( cons_list_a @ A @ ( append_list_a @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_append__Cons) ).

thf(820,plain,
    ! [A: list_a,B: list_list_a,C: list_list_a] :
      ( ( append_list_a @ ( cons_list_a @ A @ B ) @ C )
      = ( cons_list_a @ A @ ( append_list_a @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(24,axiom,
    distinct_adj_list_a @ nil_list_a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_distinct__adj__Nil) ).

thf(392,plain,
    distinct_adj_list_a @ nil_list_a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(167,axiom,
    ( lexordp_eq_a
    = ( ^ [A: a > a > $o,B: list_a,C: list_a] :
          ( ? [D: list_a] :
              ( ( B = nil_a )
              & ( C = D ) )
          | ? [D: a,E: a,F: list_a,G: list_a] :
              ( ( B
                = ( cons_a @ D @ F ) )
              & ( C
                = ( cons_a @ E @ G ) )
              & ( A @ D @ E ) )
          | ? [D: a,E: a,F: list_a,G: list_a] :
              ( ( B
                = ( cons_a @ D @ F ) )
              & ( C
                = ( cons_a @ E @ G ) )
              & ~ ( A @ D @ E )
              & ~ ( A @ E @ D )
              & ( lexordp_eq_a @ A @ F @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_ord_Olexordp__eq_Osimps) ).

thf(1042,plain,
    ( lexordp_eq_a
    = ( ^ [A: a > a > $o,B: list_a,C: list_a] :
          ( ? [D: list_a] :
              ( ( B = nil_a )
              & ( C = D ) )
          | ? [D: a,E: a,F: list_a,G: list_a] :
              ( ( B
                = ( cons_a @ D @ F ) )
              & ( C
                = ( cons_a @ E @ G ) )
              & ( A @ D @ E ) )
          | ? [D: a,E: a,F: list_a,G: list_a] :
              ( ( B
                = ( cons_a @ D @ F ) )
              & ( C
                = ( cons_a @ E @ G ) )
              & ~ ( A @ D @ E )
              & ~ ( A @ E @ D )
              & ( lexordp_eq_a @ A @ F @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(147,axiom,
    ! [A: list_list_a,B: list_list_a] :
      ( ( A != nil_list_a )
     => ( ( last_list_a @ ( append_list_a @ B @ A ) )
        = ( last_list_a @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_last__appendR) ).

thf(952,plain,
    ! [A: list_list_a,B: list_list_a] :
      ( ( A != nil_list_a )
     => ( ( last_list_a @ ( append_list_a @ B @ A ) )
        = ( last_list_a @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(136,axiom,
    ! [A: list_a,B: list_list_a] :
      ( ( hd_list_a @ ( cons_list_a @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_list_Osel_I1_J) ).

thf(916,plain,
    ! [A: list_a,B: list_list_a] :
      ( ( hd_list_a @ ( cons_list_a @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(122,axiom,
    ! [A: list_list_a,B: list_list_a] :
      ( ( ( append_list_a @ A @ B )
        = nil_list_a )
      = ( ( A = nil_list_a )
        & ( B = nil_list_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_append__is__Nil__conv) ).

thf(847,plain,
    ! [A: list_list_a,B: list_list_a] :
      ( ( ( append_list_a @ A @ B )
        = nil_list_a )
      = ( ( A = nil_list_a )
        & ( B = nil_list_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(80,axiom,
    ! [A: set_list_a] :
      ( ( collect_list_a
        @ ^ [B: list_a] : ( member_list_a2 @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_Collect__mem__eq) ).

thf(625,plain,
    ! [A: set_list_a] :
      ( ( collect_list_a
        @ ^ [B: list_a] : ( member_list_a2 @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(40,axiom,
    ! [A: list_list_a,B: list_list_a] :
      ( ( A = B )
     => ( A
        = ( append_list_a @ nil_list_a @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_eq__Nil__appendI) ).

thf(435,plain,
    ! [A: list_list_a,B: list_list_a] :
      ( ( A = B )
     => ( A
        = ( append_list_a @ nil_list_a @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(63,axiom,
    ! [A: list_list_a,B: list_list_a,C: nat > list_a] :
      ( ( listIn1753026346list_a @ A @ ( listIn1753026346list_a @ B @ C ) )
      = ( listIn1753026346list_a @ ( append_list_a @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_i__append__assoc) ).

thf(522,plain,
    ! [A: list_list_a,B: list_list_a,C: nat > list_a] :
      ( ( listIn1753026346list_a @ A @ ( listIn1753026346list_a @ B @ C ) )
      = ( listIn1753026346list_a @ ( append_list_a @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(197,axiom,
    distinct_adj_a @ nil_a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_distinct__adj__Nil) ).

thf(1210,plain,
    distinct_adj_a @ nil_a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(163,axiom,
    ! [A: a > list_list_a,B: a,C: list_a] :
      ( ( maps_a_list_a @ A @ ( cons_a @ B @ C ) )
      = ( append_list_a @ ( A @ B ) @ ( maps_a_list_a @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_maps__simps_I1_J) ).

thf(1027,plain,
    ! [A: a > list_list_a,B: a,C: list_a] :
      ( ( maps_a_list_a @ A @ ( cons_a @ B @ C ) )
      = ( append_list_a @ ( A @ B ) @ ( maps_a_list_a @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(108,axiom,
    ! [A: list_list_a,B: list_list_a,C: list_list_a] :
      ( ( ( splice_list_a @ A @ B )
        = C )
     => ( ( ( A = nil_list_a )
         => ( C != B ) )
       => ~ ! [D: list_a,E: list_list_a] :
              ( ( A
                = ( cons_list_a @ D @ E ) )
             => ( C
               != ( cons_list_a @ D @ ( splice_list_a @ B @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_splice_Oelims) ).

thf(757,plain,
    ! [A: list_list_a,B: list_list_a,C: list_list_a] :
      ( ( ( splice_list_a @ A @ B )
        = C )
     => ( ( ( A = nil_list_a )
         => ( C != B ) )
       => ~ ! [D: list_a,E: list_list_a] :
              ( ( A
                = ( cons_list_a @ D @ E ) )
             => ( C
               != ( cons_list_a @ D @ ( splice_list_a @ B @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(70,axiom,
    ! [A: list_list_a > list_list_a > $o,B: list_list_a,C: list_list_a] :
      ( ! [D: list_list_a] : ( A @ nil_list_a @ D )
     => ( ! [D: list_list_a] : ( A @ D @ nil_list_a )
       => ( ! [D: list_a,E: list_list_a,F: list_a,G: list_list_a] :
              ( ( A @ E @ ( cons_list_a @ F @ G ) )
             => ( ( A @ ( cons_list_a @ D @ E ) @ G )
               => ( A @ ( cons_list_a @ D @ E ) @ ( cons_list_a @ F @ G ) ) ) )
         => ( A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_shuffles_Oinduct) ).

thf(551,plain,
    ! [A: list_list_a > list_list_a > $o,B: list_list_a,C: list_list_a] :
      ( ! [D: list_list_a] : ( A @ nil_list_a @ D )
     => ( ! [D: list_list_a] : ( A @ D @ nil_list_a )
       => ( ! [D: list_a,E: list_list_a,F: list_a,G: list_list_a] :
              ( ( A @ E @ ( cons_list_a @ F @ G ) )
             => ( ( A @ ( cons_list_a @ D @ E ) @ G )
               => ( A @ ( cons_list_a @ D @ E ) @ ( cons_list_a @ F @ G ) ) ) )
         => ( A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(217,axiom,
    ! [A: list_a,B: list_a] :
    ? [C: list_a,D: list_a,E: list_a] :
      ( ( A
        = ( append_a @ D @ C ) )
      & ( B
        = ( append_a @ E @ C ) )
      & ( ( D = nil_a )
        | ( E = nil_a )
        | ( ( last_a @ D )
         != ( last_a @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_longest__common__suffix) ).

thf(1291,plain,
    ! [A: list_a,B: list_a] :
    ? [C: list_a,D: list_a,E: list_a] :
      ( ( A
        = ( append_a @ D @ C ) )
      & ( B
        = ( append_a @ E @ C ) )
      & ( ( D = nil_a )
        | ( E = nil_a )
        | ( ( last_a @ D )
         != ( last_a @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(62,axiom,
    ! [A: list_list_a] :
      ( ( nil_list_a
        = ( tl_list_a @ A ) )
      = ( ( A = nil_list_a )
        | ? [B: list_a] :
            ( A
            = ( cons_list_a @ B @ nil_list_a ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_Nil__tl) ).

thf(519,plain,
    ! [A: list_list_a] :
      ( ( nil_list_a
        = ( tl_list_a @ A ) )
      = ( ( A = nil_list_a )
        | ? [B: list_a] :
            ( A
            = ( cons_list_a @ B @ nil_list_a ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(178,axiom,
    ! [A: a > list_a,B: a,C: list_a] :
      ( ( maps_a_a @ A @ ( cons_a @ B @ C ) )
      = ( append_a @ ( A @ B ) @ ( maps_a_a @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_maps__simps_I1_J) ).

thf(1089,plain,
    ! [A: a > list_a,B: a,C: list_a] :
      ( ( maps_a_a @ A @ ( cons_a @ B @ C ) )
      = ( append_a @ ( A @ B ) @ ( maps_a_a @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(77,axiom,
    ! [A: list_list_a,B: list_a,C: list_list_a] :
      ( ( A
        = ( cons_list_a @ B @ C ) )
     => ( A != nil_list_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_list_OdiscI) ).

thf(615,plain,
    ! [A: list_list_a,B: list_a,C: list_list_a] :
      ( ( A
        = ( cons_list_a @ B @ C ) )
     => ( A != nil_list_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(226,axiom,
    ! [A: list_a,B: a] :
      ( ( last_a @ ( append_a @ A @ ( cons_a @ B @ nil_a ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_last__snoc) ).

thf(1328,plain,
    ! [A: list_a,B: a] :
      ( ( last_a @ ( append_a @ A @ ( cons_a @ B @ nil_a ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(185,axiom,
    ! [A: list_a,B: list_a,C: nat > a] :
      ( ( listIn1312259492pend_a @ A @ ( listIn1312259492pend_a @ B @ C ) )
      = ( listIn1312259492pend_a @ ( append_a @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_i__append__assoc) ).

thf(1121,plain,
    ! [A: list_a,B: list_a,C: nat > a] :
      ( ( listIn1312259492pend_a @ A @ ( listIn1312259492pend_a @ B @ C ) )
      = ( listIn1312259492pend_a @ ( append_a @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(182,axiom,
    ! [A: ( list_a > a ) > list_list_a > list_a > $o,B: list_a > a,C: list_list_a,D: list_a] :
      ( ! [E: list_a > a,F: list_a] : ( A @ E @ nil_list_a @ F )
     => ( ! [E: list_a > a,F: list_a,G: list_list_a,H: list_a] :
            ( ( A @ E @ G @ ( cons_a @ ( E @ F ) @ H ) )
           => ( A @ E @ ( cons_list_a @ F @ G ) @ H ) )
       => ( A @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_map__tailrec__rev_Oinduct) ).

thf(1111,plain,
    ! [A: ( list_a > a ) > list_list_a > list_a > $o,B: list_a > a,C: list_list_a,D: list_a] :
      ( ! [E: list_a > a,F: list_a] : ( A @ E @ nil_list_a @ F )
     => ( ! [E: list_a > a,F: list_a,G: list_list_a,H: list_a] :
            ( ( A @ E @ G @ ( cons_a @ ( E @ F ) @ H ) )
           => ( A @ E @ ( cons_list_a @ F @ G ) @ H ) )
       => ( A @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(267,axiom,
    ! [A: list_a > a,B: list_list_a,C: list_a,D: list_a] :
      ( ( ( map_ta2002079599st_a_a @ A @ B @ C )
        = D )
     => ( ( ( B = nil_list_a )
         => ( D != C ) )
       => ~ ! [E: list_a,F: list_list_a] :
              ( ( B
                = ( cons_list_a @ E @ F ) )
             => ( D
               != ( map_ta2002079599st_a_a @ A @ F @ ( cons_a @ ( A @ E ) @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_map__tailrec__rev_Oelims) ).

thf(1540,plain,
    ! [A: list_a > a,B: list_list_a,C: list_a,D: list_a] :
      ( ( ( map_ta2002079599st_a_a @ A @ B @ C )
        = D )
     => ( ( ( B = nil_list_a )
         => ( D != C ) )
       => ~ ! [E: list_a,F: list_list_a] :
              ( ( B
                = ( cons_list_a @ E @ F ) )
             => ( D
               != ( map_ta2002079599st_a_a @ A @ F @ ( cons_a @ ( A @ E ) @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(125,axiom,
    ! [A: list_a,B: list_list_a,C: list_a > list_list_a] :
      ( ( bind_list_a_list_a @ ( cons_list_a @ A @ B ) @ C )
      = ( append_list_a @ ( C @ A ) @ ( bind_list_a_list_a @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_bind__simps_I2_J) ).

thf(869,plain,
    ! [A: list_a,B: list_list_a,C: list_a > list_list_a] :
      ( ( bind_list_a_list_a @ ( cons_list_a @ A @ B ) @ C )
      = ( append_list_a @ ( C @ A ) @ ( bind_list_a_list_a @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(184,axiom,
    ! [A: list_list_a] :
      ( ( A != nil_list_a )
     => ( ( ( hd_list_a @ A )
         != nil_a )
       => ( ( hd_a @ ( concat_a @ A ) )
          = ( hd_a @ ( hd_list_a @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_hd__concat) ).

thf(1118,plain,
    ! [A: list_list_a] :
      ( ( A != nil_list_a )
     => ( ( ( hd_list_a @ A )
         != nil_a )
       => ( ( hd_a @ ( concat_a @ A ) )
          = ( hd_a @ ( hd_list_a @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(316,axiom,
    ! [A: a,B: list_a,C: a > list_a] :
      ( ( bind_a_a @ ( cons_a @ A @ B ) @ C )
      = ( append_a @ ( C @ A ) @ ( bind_a_a @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_bind__simps_I2_J) ).

thf(1772,plain,
    ! [A: a,B: list_a,C: a > list_a] :
      ( ( bind_a_a @ ( cons_a @ A @ B ) @ C )
      = ( append_a @ ( C @ A ) @ ( bind_a_a @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(209,axiom,
    ( ( product_lists_a @ nil_list_a )
    = ( cons_list_a @ nil_a @ nil_list_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_product__lists_Osimps_I1_J) ).

thf(1259,plain,
    ( ( product_lists_a @ nil_list_a )
    = ( cons_list_a @ nil_a @ nil_list_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(306,axiom,
    ! [A: a > a > $o,B: a,C: list_a] :
      ( ( successively_a @ A @ ( cons_a @ B @ C ) )
      = ( ( C = nil_a )
        | ( ( A @ B @ ( hd_a @ C ) )
          & ( successively_a @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_successively__Cons) ).

thf(1719,plain,
    ! [A: a > a > $o,B: a,C: list_a] :
      ( ( successively_a @ A @ ( cons_a @ B @ C ) )
      = ( ( C = nil_a )
        | ( ( A @ B @ ( hd_a @ C ) )
          & ( successively_a @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(10,axiom,
    ! [A: list_a > list_a > $o] : ( successively_list_a @ A @ nil_list_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_successively_Osimps_I1_J) ).

thf(356,plain,
    ! [A: list_a > list_a > $o] : ( successively_list_a @ A @ nil_list_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(276,axiom,
    ! [A: list_a > $o,B: list_a] :
      ( ( A @ nil_a )
     => ( ! [C: a,D: list_a] :
            ( ( A @ D )
           => ( A @ ( cons_a @ C @ D ) ) )
       => ( A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_list_Oinducts) ).

thf(1584,plain,
    ! [A: list_a > $o,B: list_a] :
      ( ( A @ nil_a )
     => ( ! [C: a,D: list_a] :
            ( ( A @ D )
           => ( A @ ( cons_a @ C @ D ) ) )
       => ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(53,axiom,
    ! [A: list_list_a] :
      ( ( A != nil_list_a )
     => ( ( cons_list_a @ ( hd_list_a @ A ) @ ( tl_list_a @ A ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_hd__Cons__tl) ).

thf(489,plain,
    ! [A: list_list_a] :
      ( ( A != nil_list_a )
     => ( ( cons_list_a @ ( hd_list_a @ A ) @ ( tl_list_a @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(191,axiom,
    ! [A: list_a] :
      ( ( A != nil_a )
      = ( ? [B: a,C: list_a] :
            ( A
            = ( cons_a @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_neq__Nil__conv) ).

thf(1155,plain,
    ! [A: list_a] :
      ( ( A != nil_a )
      = ( ? [B: a,C: list_a] :
            ( A
            = ( cons_a @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(25,axiom,
    ! [A: list_a,B: list_list_a,C: list_list_a] :
      ( ( splice_list_a @ ( cons_list_a @ A @ B ) @ C )
      = ( cons_list_a @ A @ ( splice_list_a @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_splice_Osimps_I2_J) ).

thf(393,plain,
    ! [A: list_a,B: list_list_a,C: list_list_a] :
      ( ( splice_list_a @ ( cons_list_a @ A @ B ) @ C )
      = ( cons_list_a @ A @ ( splice_list_a @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(247,axiom,
    ! [A: list_a,B: list_a > $o] :
      ( ( A != nil_a )
     => ( ! [C: a] : ( B @ ( cons_a @ C @ nil_a ) )
       => ( ! [C: a,D: list_a] :
              ( ( D != nil_a )
             => ( ( B @ D )
               => ( B @ ( cons_a @ C @ D ) ) ) )
         => ( B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_list__nonempty__induct) ).

thf(1451,plain,
    ! [A: list_a,B: list_a > $o] :
      ( ( A != nil_a )
     => ( ! [C: a] : ( B @ ( cons_a @ C @ nil_a ) )
       => ( ! [C: a,D: list_a] :
              ( ( D != nil_a )
             => ( ( B @ D )
               => ( B @ ( cons_a @ C @ D ) ) ) )
         => ( B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(235,axiom,
    ! [A: list_a,B: a,C: list_a,D: a] :
      ( ( ( append_a @ A @ ( cons_a @ B @ nil_a ) )
        = ( append_a @ C @ ( cons_a @ D @ nil_a ) ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_append1__eq__conv) ).

thf(1382,plain,
    ! [A: list_a,B: a,C: list_a,D: a] :
      ( ( ( append_a @ A @ ( cons_a @ B @ nil_a ) )
        = ( append_a @ C @ ( cons_a @ D @ nil_a ) ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(243,axiom,
    ! [A: a > a,B: list_a,C: list_a,D: list_a] :
      ( ( ( map_tailrec_rev_a_a @ A @ B @ C )
        = D )
     => ( ( ( B = nil_a )
         => ( D != C ) )
       => ~ ! [E: a,F: list_a] :
              ( ( B
                = ( cons_a @ E @ F ) )
             => ( D
               != ( map_tailrec_rev_a_a @ A @ F @ ( cons_a @ ( A @ E ) @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_map__tailrec__rev_Oelims) ).

thf(1429,plain,
    ! [A: a > a,B: list_a,C: list_a,D: list_a] :
      ( ( ( map_tailrec_rev_a_a @ A @ B @ C )
        = D )
     => ( ( ( B = nil_a )
         => ( D != C ) )
       => ~ ! [E: a,F: list_a] :
              ( ( B
                = ( cons_a @ E @ F ) )
             => ( D
               != ( map_tailrec_rev_a_a @ A @ F @ ( cons_a @ ( A @ E ) @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(112,axiom,
    ! [A: list_list_a > $o,B: list_list_a] :
      ( ( A @ nil_list_a )
     => ( ! [C: list_a,D: list_list_a] :
            ( ( A @ D )
           => ( A @ ( append_list_a @ D @ ( cons_list_a @ C @ nil_list_a ) ) ) )
       => ( A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_rev__induct) ).

thf(779,plain,
    ! [A: list_list_a > $o,B: list_list_a] :
      ( ( A @ nil_list_a )
     => ( ! [C: list_a,D: list_list_a] :
            ( ( A @ D )
           => ( A @ ( append_list_a @ D @ ( cons_list_a @ C @ nil_list_a ) ) ) )
       => ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(16,axiom,
    ! [A: list_a > list_a > $o,B: list_list_a] : ( lexordp_eq_list_a @ A @ nil_list_a @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_ord_Olexordp__eq_ONil) ).

thf(371,plain,
    ! [A: list_a > list_a > $o,B: list_list_a] : ( lexordp_eq_list_a @ A @ nil_list_a @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(57,axiom,
    ! [A: list_a > list_list_a,B: list_a,C: list_list_a] :
      ( ( maps_list_a_list_a @ A @ ( cons_list_a @ B @ C ) )
      = ( append_list_a @ ( A @ B ) @ ( maps_list_a_list_a @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_maps__simps_I1_J) ).

thf(503,plain,
    ! [A: list_a > list_list_a,B: list_a,C: list_list_a] :
      ( ( maps_list_a_list_a @ A @ ( cons_list_a @ B @ C ) )
      = ( append_list_a @ ( A @ B ) @ ( maps_list_a_list_a @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(320,axiom,
    ! [A: list_a,B: list_a] :
      ( ( ( append_a @ A @ B )
        = nil_a )
      = ( ( A = nil_a )
        & ( B = nil_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_append__is__Nil__conv) ).

thf(1831,plain,
    ! [A: list_a,B: list_a] :
      ( ( ( append_a @ A @ B )
        = nil_a )
      = ( ( A = nil_a )
        & ( B = nil_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(204,axiom,
    ! [A: a,B: set_list_a,C: list_a] :
      ( ( member_a2 @ A @ ( bNF_Greatest_Succ_a @ B @ C ) )
     => ( member_list_a2 @ ( append_a @ C @ ( cons_a @ A @ nil_a ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_SuccD) ).

thf(1231,plain,
    ! [A: a,B: set_list_a,C: list_a] :
      ( ( member_a2 @ A @ ( bNF_Greatest_Succ_a @ B @ C ) )
     => ( member_list_a2 @ ( append_a @ C @ ( cons_a @ A @ nil_a ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(174,axiom,
    ! [A: list_a] :
      ( ( splice_a @ A @ nil_a )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_splice__Nil2) ).

thf(1060,plain,
    ! [A: list_a] :
      ( ( splice_a @ A @ nil_a )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(46,axiom,
    ! [A: list_list_a,B: list_list_a] :
      ( ( nil_list_a
        = ( append_list_a @ A @ B ) )
      = ( ( A = nil_list_a )
        & ( B = nil_list_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_Nil__is__append__conv) ).

thf(457,plain,
    ! [A: list_list_a,B: list_list_a] :
      ( ( nil_list_a
        = ( append_list_a @ A @ B ) )
      = ( ( A = nil_list_a )
        & ( B = nil_list_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(327,axiom,
    ! [A: list_a,B: a,C: list_a] :
      ( ( remdups_adj_a @ ( append_a @ A @ ( cons_a @ B @ C ) ) )
      = ( append_a @ ( remdups_adj_a @ ( append_a @ A @ ( cons_a @ B @ nil_a ) ) ) @ ( tl_a @ ( remdups_adj_a @ ( cons_a @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_remdups__adj__append) ).

thf(1857,plain,
    ! [A: list_a,B: a,C: list_a] :
      ( ( remdups_adj_a @ ( append_a @ A @ ( cons_a @ B @ C ) ) )
      = ( append_a @ ( remdups_adj_a @ ( append_a @ A @ ( cons_a @ B @ nil_a ) ) ) @ ( tl_a @ ( remdups_adj_a @ ( cons_a @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(12,axiom,
    ! [A: list_list_a,B: list_list_a] :
      ( ( ( splice_list_a @ A @ B )
        = nil_list_a )
      = ( ( A = nil_list_a )
        & ( B = nil_list_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_split__Nil__iff) ).

thf(360,plain,
    ! [A: list_list_a,B: list_list_a] :
      ( ( ( splice_list_a @ A @ B )
        = nil_list_a )
      = ( ( A = nil_list_a )
        & ( B = nil_list_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(298,axiom,
    ! [A: a,B: list_a,C: list_a] :
      ( ( splice_a @ ( cons_a @ A @ B ) @ C )
      = ( cons_a @ A @ ( splice_a @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_splice_Osimps_I2_J) ).

thf(1695,plain,
    ! [A: a,B: list_a,C: list_a] :
      ( ( splice_a @ ( cons_a @ A @ B ) @ C )
      = ( cons_a @ A @ ( splice_a @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(90,axiom,
    ! [A: list_list_a,B: list_list_a] :
      ( ( A != nil_list_a )
     => ( ( hd_list_a @ ( append_list_a @ A @ B ) )
        = ( hd_list_a @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_hd__append2) ).

thf(674,plain,
    ! [A: list_list_a,B: list_list_a] :
      ( ( A != nil_list_a )
     => ( ( hd_list_a @ ( append_list_a @ A @ B ) )
        = ( hd_list_a @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(110,axiom,
    ! [A: list_a > list_a > $o,B: list_list_a,C: list_list_a] :
      ( ( successively_list_a @ A @ ( append_list_a @ B @ C ) )
      = ( ( successively_list_a @ A @ B )
        & ( successively_list_a @ A @ C )
        & ( ( B = nil_list_a )
          | ( C = nil_list_a )
          | ( A @ ( last_list_a @ B ) @ ( hd_list_a @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_successively__append__iff) ).

thf(773,plain,
    ! [A: list_a > list_a > $o,B: list_list_a,C: list_list_a] :
      ( ( successively_list_a @ A @ ( append_list_a @ B @ C ) )
      = ( ( successively_list_a @ A @ B )
        & ( successively_list_a @ A @ C )
        & ( ( B = nil_list_a )
          | ( C = nil_list_a )
          | ( A @ ( last_list_a @ B ) @ ( hd_list_a @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(140,axiom,
    ! [A: list_list_a] :
      ( ( A != nil_list_a )
     => ( ( append_list_a @ ( butlast_list_a @ A ) @ ( cons_list_a @ ( last_list_a @ A ) @ nil_list_a ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_append__butlast__last__id) ).

thf(926,plain,
    ! [A: list_list_a] :
      ( ( A != nil_list_a )
     => ( ( append_list_a @ ( butlast_list_a @ A ) @ ( cons_list_a @ ( last_list_a @ A ) @ nil_list_a ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(177,axiom,
    ! [A: a,B: list_a] :
      ( ( hd_a @ ( cons_a @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_list_Osel_I1_J) ).

thf(1086,plain,
    ! [A: a,B: list_a] :
      ( ( hd_a @ ( cons_a @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(144,axiom,
    ! [A: list_a,B: list_list_a,C: list_list_a,D: list_list_a] :
      ( ( ( cons_list_a @ A @ B )
        = ( append_list_a @ C @ D ) )
      = ( ( ( C = nil_list_a )
          & ( ( cons_list_a @ A @ B )
            = D ) )
        | ? [E: list_list_a] :
            ( ( ( cons_list_a @ A @ E )
              = C )
            & ( B
              = ( append_list_a @ E @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_Cons__eq__append__conv) ).

thf(938,plain,
    ! [A: list_a,B: list_list_a,C: list_list_a,D: list_list_a] :
      ( ( ( cons_list_a @ A @ B )
        = ( append_list_a @ C @ D ) )
      = ( ( ( C = nil_list_a )
          & ( ( cons_list_a @ A @ B )
            = D ) )
        | ? [E: list_list_a] :
            ( ( ( cons_list_a @ A @ E )
              = C )
            & ( B
              = ( append_list_a @ E @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(324,axiom,
    ! [A: list_a,B: list_a] :
      ( ( ( append_a @ A @ B )
        = A )
      = ( B = nil_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_append__self__conv) ).

thf(1846,plain,
    ! [A: list_a,B: list_a] :
      ( ( ( append_a @ A @ B )
        = A )
      = ( B = nil_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(172,axiom,
    ! [A: list_a,B: list_a,C: a > a > a,D: a,E: a] :
      ( ( ( size_size_list_a @ A )
        = ( size_size_list_a @ B ) )
     => ( ( map2_a_a_a @ C @ ( append_a @ A @ ( cons_a @ D @ nil_a ) ) @ ( append_a @ B @ ( cons_a @ E @ nil_a ) ) )
        = ( append_a @ ( map2_a_a_a @ C @ A @ B ) @ ( cons_a @ ( C @ D @ E ) @ nil_a ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_map2__snoc__snoc) ).

thf(1054,plain,
    ! [A: list_a,B: list_a,C: a > a > a,D: a,E: a] :
      ( ( ( size_size_list_a @ A )
        = ( size_size_list_a @ B ) )
     => ( ( map2_a_a_a @ C @ ( append_a @ A @ ( cons_a @ D @ nil_a ) ) @ ( append_a @ B @ ( cons_a @ E @ nil_a ) ) )
        = ( append_a @ ( map2_a_a_a @ C @ A @ B ) @ ( cons_a @ ( C @ D @ E ) @ nil_a ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(308,axiom,
    ! [A: a > a > a,B: a,C: list_a,D: a,E: list_a] :
      ( ( map2_a_a_a @ A @ ( cons_a @ B @ C ) @ ( cons_a @ D @ E ) )
      = ( cons_a @ ( A @ B @ D ) @ ( map2_a_a_a @ A @ C @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_map2__Cons__Cons) ).

thf(1727,plain,
    ! [A: a > a > a,B: a,C: list_a,D: a,E: list_a] :
      ( ( map2_a_a_a @ A @ ( cons_a @ B @ C ) @ ( cons_a @ D @ E ) )
      = ( cons_a @ ( A @ B @ D ) @ ( map2_a_a_a @ A @ C @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(315,axiom,
    ! [A: list_a,B: list_a] :
      ( ( ( A = nil_a )
       => ( ( butlast_a @ ( append_a @ B @ A ) )
          = ( butlast_a @ B ) ) )
      & ( ( A != nil_a )
       => ( ( butlast_a @ ( append_a @ B @ A ) )
          = ( append_a @ B @ ( butlast_a @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_butlast__append) ).

thf(1764,plain,
    ! [A: list_a,B: list_a] :
      ( ( ( A = nil_a )
       => ( ( butlast_a @ ( append_a @ B @ A ) )
          = ( butlast_a @ B ) ) )
      & ( ( A != nil_a )
       => ( ( butlast_a @ ( append_a @ B @ A ) )
          = ( append_a @ B @ ( butlast_a @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(37,axiom,
    ! [A: list_list_a,B: list_a,C: list_list_a] :
      ( ( ( append_list_a @ A @ ( cons_list_a @ B @ nil_list_a ) )
        = C )
      = ( ( C != nil_list_a )
        & ( ( butlast_list_a @ C )
          = A )
        & ( ( last_list_a @ C )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_snoc__eq__iff__butlast) ).

thf(425,plain,
    ! [A: list_list_a,B: list_a,C: list_list_a] :
      ( ( ( append_list_a @ A @ ( cons_list_a @ B @ nil_list_a ) )
        = C )
      = ( ( C != nil_list_a )
        & ( ( butlast_list_a @ C )
          = A )
        & ( ( last_list_a @ C )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(299,axiom,
    ! [A: list_a,B: list_a,C: a,D: list_a] :
      ( ( ( append_a @ A @ B )
        = ( cons_a @ C @ D ) )
      = ( ( ( A = nil_a )
          & ( B
            = ( cons_a @ C @ D ) ) )
        | ? [E: list_a] :
            ( ( A
              = ( cons_a @ C @ E ) )
            & ( ( append_a @ E @ B )
              = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_append__eq__Cons__conv) ).

thf(1698,plain,
    ! [A: list_a,B: list_a,C: a,D: list_a] :
      ( ( ( append_a @ A @ B )
        = ( cons_a @ C @ D ) )
      = ( ( ( A = nil_a )
          & ( B
            = ( cons_a @ C @ D ) ) )
        | ? [E: list_a] :
            ( ( A
              = ( cons_a @ C @ E ) )
            & ( ( append_a @ E @ B )
              = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(200,axiom,
    ! [A: list_a] :
      ( ( append_a @ A @ nil_a )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_append__Nil2) ).

thf(1219,plain,
    ! [A: list_a] :
      ( ( append_a @ A @ nil_a )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(234,axiom,
    ! [A: list_a,B: list_a] :
      ( ( ( A = nil_a )
       => ( ( last_a @ ( append_a @ B @ A ) )
          = ( last_a @ B ) ) )
      & ( ( A != nil_a )
       => ( ( last_a @ ( append_a @ B @ A ) )
          = ( last_a @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_last__append) ).

thf(1374,plain,
    ! [A: list_a,B: list_a] :
      ( ( ( A = nil_a )
       => ( ( last_a @ ( append_a @ B @ A ) )
          = ( last_a @ B ) ) )
      & ( ( A != nil_a )
       => ( ( last_a @ ( append_a @ B @ A ) )
          = ( last_a @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(152,axiom,
    ! [A: list_a > list_a > $o,B: list_list_a] :
      ( ( successively_list_a @ A @ B )
     => ( ( B != nil_list_a )
       => ( ! [C: list_a] :
              ( B
             != ( cons_list_a @ C @ nil_list_a ) )
         => ~ ! [C: list_a,D: list_a,E: list_list_a] :
                ( ( B
                  = ( cons_list_a @ C @ ( cons_list_a @ D @ E ) ) )
               => ~ ( ( A @ C @ D )
                    & ( successively_list_a @ A @ ( cons_list_a @ D @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_successively_Oelims_I2_J) ).

thf(975,plain,
    ! [A: list_a > list_a > $o,B: list_list_a] :
      ( ( successively_list_a @ A @ B )
     => ( ( B != nil_list_a )
       => ( ! [C: list_a] :
              ( B
             != ( cons_list_a @ C @ nil_list_a ) )
         => ~ ! [C: list_a,D: list_a,E: list_list_a] :
                ( ( B
                  = ( cons_list_a @ C @ ( cons_list_a @ D @ E ) ) )
               => ~ ( ( A @ C @ D )
                    & ( successively_list_a @ A @ ( cons_list_a @ D @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(157,axiom,
    ! [A: list_a,B: list_a > $o] :
      ( ( member_list_a2 @ A @ ( collect_list_a @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__Collect__eq) ).

thf(1007,plain,
    ! [A: list_a,B: list_a > $o] :
      ( ( member_list_a2 @ A @ ( collect_list_a @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(102,axiom,
    ! [A: list_a > list_a > $o,B: list_a,C: list_list_a] :
      ~ ( lexordp_eq_list_a @ A @ ( cons_list_a @ B @ C ) @ nil_list_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_ord_Olexordp__eq__simps_I3_J) ).

thf(732,plain,
    ! [A: list_a > list_a > $o,B: list_a,C: list_list_a] :
      ~ ( lexordp_eq_list_a @ A @ ( cons_list_a @ B @ C ) @ nil_list_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(237,axiom,
    ! [A: list_a,B: list_a] :
    ? [C: list_a,D: list_a,E: list_a] :
      ( ( A
        = ( append_a @ C @ D ) )
      & ( B
        = ( append_a @ C @ E ) )
      & ( ( D = nil_a )
        | ( E = nil_a )
        | ( ( hd_a @ D )
         != ( hd_a @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_longest__common__prefix) ).

thf(1388,plain,
    ! [A: list_a,B: list_a] :
    ? [C: list_a,D: list_a,E: list_a] :
      ( ( A
        = ( append_a @ C @ D ) )
      & ( B
        = ( append_a @ C @ E ) )
      & ( ( D = nil_a )
        | ( E = nil_a )
        | ( ( hd_a @ D )
         != ( hd_a @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(104,axiom,
    ! [A: list_list_a] :
      ( ( ( rotate1_list_a @ A )
        = nil_list_a )
      = ( A = nil_list_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_rotate1__is__Nil__conv) ).

thf(743,plain,
    ! [A: list_list_a] :
      ( ( ( rotate1_list_a @ A )
        = nil_list_a )
      = ( A = nil_list_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(265,axiom,
    ! [A: list_a] :
      ( ( A != nil_a )
     => ( ( append_a @ ( butlast_a @ A ) @ ( cons_a @ ( last_a @ A ) @ nil_a ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_append__butlast__last__id) ).

thf(1535,plain,
    ! [A: list_a] :
      ( ( A != nil_a )
     => ( ( append_a @ ( butlast_a @ A ) @ ( cons_a @ ( last_a @ A ) @ nil_a ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(300,axiom,
    ! [A: a] :
      ( ( insert_a @ A @ nil_a )
      = ( cons_a @ A @ nil_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_insert__Nil) ).

thf(1701,plain,
    ! [A: a] :
      ( ( insert_a @ A @ nil_a )
      = ( cons_a @ A @ nil_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(186,axiom,
    ! [A: list_a,B: a] :
      ( ( butlast_a @ ( append_a @ A @ ( cons_a @ B @ nil_a ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_butlast__snoc) ).

thf(1124,plain,
    ! [A: list_a,B: a] :
      ( ( butlast_a @ ( append_a @ A @ ( cons_a @ B @ nil_a ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(127,axiom,
    ( lexordp_eq_list_a
    = ( ^ [A: list_a > list_a > $o,B: list_list_a,C: list_list_a] :
          ( ? [D: list_list_a] :
              ( ( B = nil_list_a )
              & ( C = D ) )
          | ? [D: list_a,E: list_a,F: list_list_a,G: list_list_a] :
              ( ( B
                = ( cons_list_a @ D @ F ) )
              & ( C
                = ( cons_list_a @ E @ G ) )
              & ( A @ D @ E ) )
          | ? [D: list_a,E: list_a,F: list_list_a,G: list_list_a] :
              ( ( B
                = ( cons_list_a @ D @ F ) )
              & ( C
                = ( cons_list_a @ E @ G ) )
              & ~ ( A @ D @ E )
              & ~ ( A @ E @ D )
              & ( lexordp_eq_list_a @ A @ F @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_ord_Olexordp__eq_Osimps) ).

thf(875,plain,
    ( lexordp_eq_list_a
    = ( ^ [A: list_a > list_a > $o,B: list_list_a,C: list_list_a] :
          ( ? [D: list_list_a] :
              ( ( B = nil_list_a )
              & ( C = D ) )
          | ? [D: list_a,E: list_a,F: list_list_a,G: list_list_a] :
              ( ( B
                = ( cons_list_a @ D @ F ) )
              & ( C
                = ( cons_list_a @ E @ G ) )
              & ( A @ D @ E ) )
          | ? [D: list_a,E: list_a,F: list_list_a,G: list_list_a] :
              ( ( B
                = ( cons_list_a @ D @ F ) )
              & ( C
                = ( cons_list_a @ E @ G ) )
              & ~ ( A @ D @ E )
              & ~ ( A @ E @ D )
              & ( lexordp_eq_list_a @ A @ F @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(120,axiom,
    ! [A: list_a > list_a > $o,B: list_a] : ( successively_list_a @ A @ ( cons_list_a @ B @ nil_list_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_successively_Osimps_I2_J) ).

thf(826,plain,
    ! [A: list_a > list_a > $o,B: list_a] : ( successively_list_a @ A @ ( cons_list_a @ B @ nil_list_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(68,axiom,
    ! [A: list_list_a] :
      ( ( append_list_a @ A @ nil_list_a )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_append__Nil2) ).

thf(545,plain,
    ! [A: list_list_a] :
      ( ( append_list_a @ A @ nil_list_a )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(258,axiom,
    ! [A: a > a > $o,B: list_a,C: list_a,D: list_a > list_a > $o] :
      ( ( lexordp_eq_a @ A @ B @ C )
     => ( ! [E: list_a] : ( D @ nil_a @ E )
       => ( ! [E: a,F: a,G: list_a,H: list_a] :
              ( ( A @ E @ F )
             => ( D @ ( cons_a @ E @ G ) @ ( cons_a @ F @ H ) ) )
         => ( ! [E: a,F: a,G: list_a,H: list_a] :
                ( ~ ( A @ E @ F )
               => ( ~ ( A @ F @ E )
                 => ( ( lexordp_eq_a @ A @ G @ H )
                   => ( ( D @ G @ H )
                     => ( D @ ( cons_a @ E @ G ) @ ( cons_a @ F @ H ) ) ) ) ) )
           => ( D @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_ord_Olexordp__eq_Oinducts) ).

thf(1488,plain,
    ! [A: a > a > $o,B: list_a,C: list_a,D: list_a > list_a > $o] :
      ( ( lexordp_eq_a @ A @ B @ C )
     => ( ! [E: list_a] : ( D @ nil_a @ E )
       => ( ! [E: a,F: a,G: list_a,H: list_a] :
              ( ( A @ E @ F )
             => ( D @ ( cons_a @ E @ G ) @ ( cons_a @ F @ H ) ) )
         => ( ! [E: a,F: a,G: list_a,H: list_a] :
                ( ~ ( A @ E @ F )
               => ( ~ ( A @ F @ E )
                 => ( ( lexordp_eq_a @ A @ G @ H )
                   => ( ( D @ G @ H )
                     => ( D @ ( cons_a @ E @ G ) @ ( cons_a @ F @ H ) ) ) ) ) )
           => ( D @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(73,axiom,
    ! [A: list_a > list_a > $o,B: list_list_a,C: list_list_a] :
      ( ( lexordp_eq_list_a @ A @ B @ C )
     => ( ( B != nil_list_a )
       => ( ! [D: list_a] :
              ( ? [E: list_list_a] :
                  ( B
                  = ( cons_list_a @ D @ E ) )
             => ! [E: list_a] :
                  ( ? [F: list_list_a] :
                      ( C
                      = ( cons_list_a @ E @ F ) )
                 => ~ ( A @ D @ E ) ) )
         => ~ ! [D: list_a,E: list_a,F: list_list_a] :
                ( ( B
                  = ( cons_list_a @ D @ F ) )
               => ! [G: list_list_a] :
                    ( ( C
                      = ( cons_list_a @ E @ G ) )
                   => ( ~ ( A @ D @ E )
                     => ( ~ ( A @ E @ D )
                       => ~ ( lexordp_eq_list_a @ A @ F @ G ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_ord_Olexordp__eq_Ocases) ).

thf(572,plain,
    ! [A: list_a > list_a > $o,B: list_list_a,C: list_list_a] :
      ( ( lexordp_eq_list_a @ A @ B @ C )
     => ( ( B != nil_list_a )
       => ( ! [D: list_a] :
              ( ? [E: list_list_a] :
                  ( B
                  = ( cons_list_a @ D @ E ) )
             => ! [E: list_a] :
                  ( ? [F: list_list_a] :
                      ( C
                      = ( cons_list_a @ E @ F ) )
                 => ~ ( A @ D @ E ) ) )
         => ~ ! [D: list_a,E: list_a,F: list_list_a] :
                ( ( B
                  = ( cons_list_a @ D @ F ) )
               => ! [G: list_list_a] :
                    ( ( C
                      = ( cons_list_a @ E @ G ) )
                   => ( ~ ( A @ D @ E )
                     => ( ~ ( A @ E @ D )
                       => ~ ( lexordp_eq_list_a @ A @ F @ G ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(302,axiom,
    ! [A: list_a,B: a,C: a] :
      ( ( remdups_adj_a @ ( append_a @ A @ ( cons_a @ B @ ( cons_a @ C @ nil_a ) ) ) )
      = ( append_a @ ( remdups_adj_a @ ( append_a @ A @ ( cons_a @ B @ nil_a ) ) ) @ ( if_list_a @ ( B = C ) @ nil_a @ ( cons_a @ C @ nil_a ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_remdups__adj__append__two) ).

thf(1707,plain,
    ! [A: list_a,B: a,C: a] :
      ( ( remdups_adj_a @ ( append_a @ A @ ( cons_a @ B @ ( cons_a @ C @ nil_a ) ) ) )
      = ( append_a @ ( remdups_adj_a @ ( append_a @ A @ ( cons_a @ B @ nil_a ) ) ) @ ( if_list_a @ ( B = C ) @ nil_a @ ( cons_a @ C @ nil_a ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(233,axiom,
    ! [A: a,B: list_a,C: list_a,D: list_a] :
      ( ( member_list_a2 @ ( cons_a @ A @ B ) @ ( shuffles_a @ C @ D ) )
      = ( ( ( C != nil_a )
          & ( ( hd_a @ C )
            = A )
          & ( member_list_a2 @ B @ ( shuffles_a @ ( tl_a @ C ) @ D ) ) )
        | ( ( D != nil_a )
          & ( ( hd_a @ D )
            = A )
          & ( member_list_a2 @ B @ ( shuffles_a @ C @ ( tl_a @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_Cons__in__shuffles__iff) ).

thf(1371,plain,
    ! [A: a,B: list_a,C: list_a,D: list_a] :
      ( ( member_list_a2 @ ( cons_a @ A @ B ) @ ( shuffles_a @ C @ D ) )
      = ( ( ( C != nil_a )
          & ( ( hd_a @ C )
            = A )
          & ( member_list_a2 @ B @ ( shuffles_a @ ( tl_a @ C ) @ D ) ) )
        | ( ( D != nil_a )
          & ( ( hd_a @ D )
            = A )
          & ( member_list_a2 @ B @ ( shuffles_a @ C @ ( tl_a @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(220,axiom,
    ! [A: a > a > $o] : ( successively_a @ A @ nil_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_successively_Osimps_I1_J) ).

thf(1312,plain,
    ! [A: a > a > $o] : ( successively_a @ A @ nil_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(310,axiom,
    ! [A: a > list_a > $o,B: list_a,C: list_list_a] :
      ( ( listrelp_a_list_a @ A @ B @ C )
     => ( ( ( B = nil_a )
         => ( C != nil_list_a ) )
       => ~ ! [D: a,E: list_a,F: list_a] :
              ( ( B
                = ( cons_a @ D @ F ) )
             => ! [G: list_list_a] :
                  ( ( C
                    = ( cons_list_a @ E @ G ) )
                 => ( ( A @ D @ E )
                   => ~ ( listrelp_a_list_a @ A @ F @ G ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_listrelp_Ocases) ).

thf(1733,plain,
    ! [A: a > list_a > $o,B: list_a,C: list_list_a] :
      ( ( listrelp_a_list_a @ A @ B @ C )
     => ( ( ( B = nil_a )
         => ( C != nil_list_a ) )
       => ~ ! [D: a,E: list_a,F: list_a] :
              ( ( B
                = ( cons_a @ D @ F ) )
             => ! [G: list_list_a] :
                  ( ( C
                    = ( cons_list_a @ E @ G ) )
                 => ( ( A @ D @ E )
                   => ~ ( listrelp_a_list_a @ A @ F @ G ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(173,axiom,
    ( ( remdups_adj_a @ nil_a )
    = nil_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_remdups__adj_Osimps_I1_J) ).

thf(1058,plain,
    ( ( remdups_adj_a @ nil_a )
    = nil_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(207,axiom,
    ! [A: list_a] :
      ( ( append_a @ A @ nil_a )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_append_Oright__neutral) ).

thf(1239,plain,
    ! [A: list_a] :
      ( ( append_a @ A @ nil_a )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(179,axiom,
    ! [A: list_a,B: list_a] :
      ( ( member_list_a2 @ nil_a @ ( shuffles_a @ A @ B ) )
      = ( ( A = nil_a )
        & ( B = nil_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_Nil__in__shuffles) ).

thf(1092,plain,
    ! [A: list_a,B: list_a] :
      ( ( member_list_a2 @ nil_a @ ( shuffles_a @ A @ B ) )
      = ( ( A = nil_a )
        & ( B = nil_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(3,axiom,
    ! [A: list_list_a,B: set_list_list_a,C: list_a] :
      ( ( member_list_list_a @ A @ ( bNF_Gr1972240547list_a @ B @ C ) )
     => ( member_list_list_a @ ( cons_list_a @ C @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_ShiftD) ).

thf(335,plain,
    ! [A: list_list_a,B: set_list_list_a,C: list_a] :
      ( ( member_list_list_a @ A @ ( bNF_Gr1972240547list_a @ B @ C ) )
     => ( member_list_list_a @ ( cons_list_a @ C @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(137,axiom,
    ! [A: list_a] :
      ~ ( member_list_a @ nil_list_a @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_member__rec_I2_J) ).

thf(919,plain,
    ! [A: list_a] :
      ~ ( member_list_a @ nil_list_a @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(92,axiom,
    ! [A: list_a,B: list_a,C: list_a] :
      ( ( ( append_a @ A @ B )
        = ( append_a @ C @ B ) )
      = ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_append__same__eq) ).

thf(681,plain,
    ! [A: list_a,B: list_a,C: list_a] :
      ( ( ( append_a @ A @ B )
        = ( append_a @ C @ B ) )
      = ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(35,axiom,
    ! [A: list_list_a,B: list_list_a] :
      ( ( distinct_adj_list_a @ ( append_list_a @ A @ B ) )
      = ( ( distinct_adj_list_a @ A )
        & ( distinct_adj_list_a @ B )
        & ( ( A = nil_list_a )
          | ( B = nil_list_a )
          | ( ( last_list_a @ A )
           != ( hd_list_a @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_distinct__adj__append__iff) ).

thf(419,plain,
    ! [A: list_list_a,B: list_list_a] :
      ( ( distinct_adj_list_a @ ( append_list_a @ A @ B ) )
      = ( ( distinct_adj_list_a @ A )
        & ( distinct_adj_list_a @ B )
        & ( ( A = nil_list_a )
          | ( B = nil_list_a )
          | ( ( last_list_a @ A )
           != ( hd_list_a @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(263,axiom,
    ! [A: a > a > $o,B: a,C: a,D: list_a,E: list_a] :
      ( ~ ( A @ B @ C )
     => ( ~ ( A @ C @ B )
       => ( ( lexordp_eq_a @ A @ D @ E )
         => ( lexordp_eq_a @ A @ ( cons_a @ B @ D ) @ ( cons_a @ C @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_ord_Olexordp__eq_OCons__eq) ).

thf(1524,plain,
    ! [A: a > a > $o,B: a,C: a,D: list_a,E: list_a] :
      ( ~ ( A @ B @ C )
     => ( ~ ( A @ C @ B )
       => ( ( lexordp_eq_a @ A @ D @ E )
         => ( lexordp_eq_a @ A @ ( cons_a @ B @ D ) @ ( cons_a @ C @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(231,axiom,
    ! [A: list_a > a > $o,B: list_list_a,C: list_a,D: list_list_a > list_a > $o] :
      ( ( listrelp_list_a_a @ A @ B @ C )
     => ( ( D @ nil_list_a @ nil_a )
       => ( ! [E: list_a,F: a,G: list_list_a,H: list_a] :
              ( ( A @ E @ F )
             => ( ( listrelp_list_a_a @ A @ G @ H )
               => ( ( D @ G @ H )
                 => ( D @ ( cons_list_a @ E @ G ) @ ( cons_a @ F @ H ) ) ) ) )
         => ( D @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_listrelp_Oinducts) ).

thf(1349,plain,
    ! [A: list_a > a > $o,B: list_list_a,C: list_a,D: list_list_a > list_a > $o] :
      ( ( listrelp_list_a_a @ A @ B @ C )
     => ( ( D @ nil_list_a @ nil_a )
       => ( ! [E: list_a,F: a,G: list_list_a,H: list_a] :
              ( ( A @ E @ F )
             => ( ( listrelp_list_a_a @ A @ G @ H )
               => ( ( D @ G @ H )
                 => ( D @ ( cons_list_a @ E @ G ) @ ( cons_a @ F @ H ) ) ) ) )
         => ( D @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(155,axiom,
    ! [A: list_list_a] :
      ( ( append_list_a @ A @ nil_list_a )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_append_Oright__neutral) ).

thf(996,plain,
    ! [A: list_list_a] :
      ( ( append_list_a @ A @ nil_list_a )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(280,axiom,
    ! [A: a > list_a] :
      ( ( maps_a_a @ A @ nil_a )
      = nil_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_maps__simps_I2_J) ).

thf(1603,plain,
    ! [A: a > list_a] :
      ( ( maps_a_a @ A @ nil_a )
      = nil_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(44,axiom,
    ! [A: list_a,B: list_a,C: list_a,D: list_a] :
      ( ( ( append_a @ A @ B )
        = ( append_a @ C @ D ) )
      = ( ? [E: list_a] :
            ( ( ( A
                = ( append_a @ C @ E ) )
              & ( ( append_a @ E @ B )
                = D ) )
            | ( ( ( append_a @ A @ E )
                = C )
              & ( B
                = ( append_a @ E @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_append__eq__append__conv2) ).

thf(451,plain,
    ! [A: list_a,B: list_a,C: list_a,D: list_a] :
      ( ( ( append_a @ A @ B )
        = ( append_a @ C @ D ) )
      = ( ? [E: list_a] :
            ( ( ( A
                = ( append_a @ C @ E ) )
              & ( ( append_a @ E @ B )
                = D ) )
            | ( ( ( append_a @ A @ E )
                = C )
              & ( B
                = ( append_a @ E @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(307,axiom,
    ! [A: list_a,B: a] :
      ( ( A = nil_a )
     => ( ( last_a @ ( cons_a @ B @ A ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_last__ConsL) ).

thf(1722,plain,
    ! [A: list_a,B: a] :
      ( ( A = nil_a )
     => ( ( last_a @ ( cons_a @ B @ A ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(134,axiom,
    ! [A: list_a > list_a > $o,B: list_list_a,C: list_list_a,D: list_list_a > list_list_a > $o] :
      ( ( lexordp_eq_list_a @ A @ B @ C )
     => ( ! [E: list_list_a] : ( D @ nil_list_a @ E )
       => ( ! [E: list_a,F: list_a,G: list_list_a,H: list_list_a] :
              ( ( A @ E @ F )
             => ( D @ ( cons_list_a @ E @ G ) @ ( cons_list_a @ F @ H ) ) )
         => ( ! [E: list_a,F: list_a,G: list_list_a,H: list_list_a] :
                ( ~ ( A @ E @ F )
               => ( ~ ( A @ F @ E )
                 => ( ( lexordp_eq_list_a @ A @ G @ H )
                   => ( ( D @ G @ H )
                     => ( D @ ( cons_list_a @ E @ G ) @ ( cons_list_a @ F @ H ) ) ) ) ) )
           => ( D @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_ord_Olexordp__eq_Oinducts) ).

thf(900,plain,
    ! [A: list_a > list_a > $o,B: list_list_a,C: list_list_a,D: list_list_a > list_list_a > $o] :
      ( ( lexordp_eq_list_a @ A @ B @ C )
     => ( ! [E: list_list_a] : ( D @ nil_list_a @ E )
       => ( ! [E: list_a,F: list_a,G: list_list_a,H: list_list_a] :
              ( ( A @ E @ F )
             => ( D @ ( cons_list_a @ E @ G ) @ ( cons_list_a @ F @ H ) ) )
         => ( ! [E: list_a,F: list_a,G: list_list_a,H: list_list_a] :
                ( ~ ( A @ E @ F )
               => ( ~ ( A @ F @ E )
                 => ( ( lexordp_eq_list_a @ A @ G @ H )
                   => ( ( D @ G @ H )
                     => ( D @ ( cons_list_a @ E @ G ) @ ( cons_list_a @ F @ H ) ) ) ) ) )
           => ( D @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(30,axiom,
    ! [A: list_list_a,B: list_list_a] :
      ( ( distinct_adj_list_a @ ( append_list_a @ A @ B ) )
     => ( distinct_adj_list_a @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_distinct__adj__appendD2) ).

thf(406,plain,
    ! [A: list_list_a,B: list_list_a] :
      ( ( distinct_adj_list_a @ ( append_list_a @ A @ B ) )
     => ( distinct_adj_list_a @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(59,axiom,
    ! [A: list_a,B: list_list_a] :
      ( ( concat_a @ ( cons_list_a @ A @ B ) )
      = ( append_a @ A @ ( concat_a @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_concat_Osimps_I2_J) ).

thf(509,plain,
    ! [A: list_a,B: list_list_a] :
      ( ( concat_a @ ( cons_list_a @ A @ B ) )
      = ( append_a @ A @ ( concat_a @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(129,axiom,
    ! [A: list_a,B: set_list_list_a,C: list_list_a] :
      ( ( member_list_a2 @ A @ ( bNF_Gr1046450207list_a @ B @ C ) )
     => ( member_list_list_a @ ( append_list_a @ C @ ( cons_list_a @ A @ nil_list_a ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_SuccD) ).

thf(880,plain,
    ! [A: list_a,B: set_list_list_a,C: list_list_a] :
      ( ( member_list_a2 @ A @ ( bNF_Gr1046450207list_a @ B @ C ) )
     => ( member_list_list_a @ ( append_list_a @ C @ ( cons_list_a @ A @ nil_list_a ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(293,axiom,
    ! [A: list_a] :
      ( ( ( remdups_adj_a @ A )
        = nil_a )
      = ( A = nil_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_remdups__adj__Nil__iff) ).

thf(1667,plain,
    ! [A: list_a] :
      ( ( ( remdups_adj_a @ A )
        = nil_a )
      = ( A = nil_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(82,axiom,
    ! [A: list_a,B: list_list_a,C: list_a] :
      ( ( member_list_a @ ( cons_list_a @ A @ B ) @ C )
      = ( ( A = C )
        | ( member_list_a @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_member__rec_I1_J) ).

thf(631,plain,
    ! [A: list_a,B: list_list_a,C: list_a] :
      ( ( member_list_a @ ( cons_list_a @ A @ B ) @ C )
      = ( ( A = C )
        | ( member_list_a @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(100,axiom,
    ( concat_list_a
    = ( ^ [A: list_list_list_a] : ( foldr_769741863list_a @ append_list_a @ A @ nil_list_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_concat__conv__foldr) ).

thf(726,plain,
    ( concat_list_a
    = ( ^ [A: list_list_list_a] : ( foldr_769741863list_a @ append_list_a @ A @ nil_list_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(150,axiom,
    ! [A: list_list_a,B: list_list_a] :
    ? [C: list_list_a,D: list_list_a,E: list_list_a] :
      ( ( A
        = ( append_list_a @ C @ D ) )
      & ( B
        = ( append_list_a @ C @ E ) )
      & ( ( D = nil_list_a )
        | ( E = nil_list_a )
        | ( ( hd_list_a @ D )
         != ( hd_list_a @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_longest__common__prefix) ).

thf(964,plain,
    ! [A: list_list_a,B: list_list_a] :
    ? [C: list_list_a,D: list_list_a,E: list_list_a] :
      ( ( A
        = ( append_list_a @ C @ D ) )
      & ( B
        = ( append_list_a @ C @ E ) )
      & ( ( D = nil_list_a )
        | ( E = nil_list_a )
        | ( ( hd_list_a @ D )
         != ( hd_list_a @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(269,axiom,
    ! [A: list_a] :
      ( ( splice_a @ nil_a @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_splice_Osimps_I1_J) ).

thf(1556,plain,
    ! [A: list_a] :
      ( ( splice_a @ nil_a @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(322,axiom,
    ! [A: a,B: a,C: list_a] :
      ( ( distinct_adj_a @ ( cons_a @ A @ ( cons_a @ B @ C ) ) )
      = ( ( A != B )
        & ( distinct_adj_a @ ( cons_a @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_distinct__adj__Cons__Cons) ).

thf(1838,plain,
    ! [A: a,B: a,C: list_a] :
      ( ( distinct_adj_a @ ( cons_a @ A @ ( cons_a @ B @ C ) ) )
      = ( ( A != B )
        & ( distinct_adj_a @ ( cons_a @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(225,axiom,
    ! [A: a] :
      ( ( remdups_adj_a @ ( cons_a @ A @ nil_a ) )
      = ( cons_a @ A @ nil_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_remdups__adj_Osimps_I2_J) ).

thf(1325,plain,
    ! [A: a] :
      ( ( remdups_adj_a @ ( cons_a @ A @ nil_a ) )
      = ( cons_a @ A @ nil_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(48,axiom,
    ! [A: list_list_a,B: list_list_a] :
      ( ( A
        = ( append_list_a @ A @ B ) )
      = ( B = nil_list_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_self__append__conv) ).

thf(462,plain,
    ! [A: list_list_a,B: list_list_a] :
      ( ( A
        = ( append_list_a @ A @ B ) )
      = ( B = nil_list_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(142,axiom,
    ( ( rotate1_list_a @ nil_list_a )
    = nil_list_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_rotate1_Osimps_I1_J) ).

thf(932,plain,
    ( ( rotate1_list_a @ nil_list_a )
    = nil_list_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(153,axiom,
    ! [A: list_a,B: list_a,C: list_a] :
      ( ( append_a @ ( append_a @ A @ B ) @ C )
      = ( append_a @ A @ ( append_a @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_append_Oassoc) ).

thf(983,plain,
    ! [A: list_a,B: list_a,C: list_a] :
      ( ( append_a @ ( append_a @ A @ B ) @ C )
      = ( append_a @ A @ ( append_a @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(27,axiom,
    ( ( tl_list_a @ nil_list_a )
    = nil_list_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_list_Osel_I2_J) ).

thf(399,plain,
    ( ( tl_list_a @ nil_list_a )
    = nil_list_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(277,axiom,
    ! [A: a > a > $o,B: list_a] :
      ( ( lexordp_eq_a @ A @ B @ nil_a )
      = ( B = nil_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_ord_Olexordp__eq__simps_I2_J) ).

thf(1594,plain,
    ! [A: a > a > $o,B: list_a] :
      ( ( lexordp_eq_a @ A @ B @ nil_a )
      = ( B = nil_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(149,axiom,
    ! [A: list_a,B: list_a,C: list_a,D: list_a,E: list_a] :
      ( ( ( append_a @ A @ B )
        = C )
     => ( ( D
          = ( append_a @ B @ E ) )
       => ( ( append_a @ A @ D )
          = ( append_a @ C @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_append__eq__appendI) ).

thf(959,plain,
    ! [A: list_a,B: list_a,C: list_a,D: list_a,E: list_a] :
      ( ( ( append_a @ A @ B )
        = C )
     => ( ( D
          = ( append_a @ B @ E ) )
       => ( ( append_a @ A @ D )
          = ( append_a @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(287,axiom,
    ! [A: a > a > $o,B: list_a,C: list_a] :
      ( ( successively_a @ A @ ( append_a @ B @ C ) )
      = ( ( successively_a @ A @ B )
        & ( successively_a @ A @ C )
        & ( ( B = nil_a )
          | ( C = nil_a )
          | ( A @ ( last_a @ B ) @ ( hd_a @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_successively__append__iff) ).

thf(1643,plain,
    ! [A: a > a > $o,B: list_a,C: list_a] :
      ( ( successively_a @ A @ ( append_a @ B @ C ) )
      = ( ( successively_a @ A @ B )
        & ( successively_a @ A @ C )
        & ( ( B = nil_a )
          | ( C = nil_a )
          | ( A @ ( last_a @ B ) @ ( hd_a @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(160,axiom,
    ! [A: list_a,B: a,C: list_a] :
      ( ( A
        = ( cons_a @ B @ C ) )
     => ( A != nil_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_list_OdiscI) ).

thf(1015,plain,
    ! [A: list_a,B: a,C: list_a] :
      ( ( A
        = ( cons_a @ B @ C ) )
     => ( A != nil_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(76,axiom,
    ! [A: list_list_a,B: list_a,C: list_a] :
      ( ( ( concat_a @ A )
        = ( append_a @ B @ C ) )
     => ( ( A != nil_list_a )
       => ? [D: list_list_a,E: list_a,F: list_a,G: list_list_a] :
            ( ( A
              = ( append_list_a @ D @ ( cons_list_a @ ( append_a @ E @ F ) @ G ) ) )
            & ( B
              = ( append_a @ ( concat_a @ D ) @ E ) )
            & ( C
              = ( append_a @ F @ ( concat_a @ G ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_concat__eq__appendD) ).

thf(608,plain,
    ! [A: list_list_a,B: list_a,C: list_a] :
      ( ( ( concat_a @ A )
        = ( append_a @ B @ C ) )
     => ( ( A != nil_list_a )
       => ? [D: list_list_a,E: list_a,F: list_a,G: list_list_a] :
            ( ( A
              = ( append_list_a @ D @ ( cons_list_a @ ( append_a @ E @ F ) @ G ) ) )
            & ( B
              = ( append_a @ ( concat_a @ D ) @ E ) )
            & ( C
              = ( append_a @ F @ ( concat_a @ G ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(154,axiom,
    ! [A: list_list_a > $o,B: list_list_a] :
      ( ( A @ nil_list_a )
     => ( ! [C: list_a,D: list_list_a] :
            ( ( A @ D )
           => ( A @ ( cons_list_a @ C @ D ) ) )
       => ( A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_list_Oinducts) ).

thf(986,plain,
    ! [A: list_list_a > $o,B: list_list_a] :
      ( ( A @ nil_list_a )
     => ( ! [C: list_a,D: list_list_a] :
            ( ( A @ D )
           => ( A @ ( cons_list_a @ C @ D ) ) )
       => ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(317,axiom,
    ! [A: list_a,B: list_a,C: list_a] :
      ( ( ( splice_a @ A @ B )
        = C )
     => ( ( ( A = nil_a )
         => ( C != B ) )
       => ~ ! [D: a,E: list_a] :
              ( ( A
                = ( cons_a @ D @ E ) )
             => ( C
               != ( cons_a @ D @ ( splice_a @ B @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_splice_Oelims) ).

thf(1775,plain,
    ! [A: list_a,B: list_a,C: list_a] :
      ( ( ( splice_a @ A @ B )
        = C )
     => ( ( ( A = nil_a )
         => ( C != B ) )
       => ~ ! [D: a,E: list_a] :
              ( ( A
                = ( cons_a @ D @ E ) )
             => ( C
               != ( cons_a @ D @ ( splice_a @ B @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(138,axiom,
    lexordp_eq_a = lexordp_eq_a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_ord_Olexordp__eq_Ocong) ).

thf(922,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(271,axiom,
    ! [A: list_list_a,B: list_a,C: list_a] :
      ( ( ( concat_a @ A )
        = ( append_a @ B @ C ) )
      = ( ( ( A = nil_list_a )
         => ( ( B = nil_a )
            & ( C = nil_a ) ) )
        & ( ( A != nil_list_a )
         => ? [D: list_list_a,E: list_a,F: list_a,G: list_list_a] :
              ( ( A
                = ( append_list_a @ D @ ( cons_list_a @ ( append_a @ E @ F ) @ G ) ) )
              & ( B
                = ( append_a @ ( concat_a @ D ) @ E ) )
              & ( C
                = ( append_a @ F @ ( concat_a @ G ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_concat__eq__append__conv) ).

thf(1562,plain,
    ! [A: list_list_a,B: list_a,C: list_a] :
      ( ( ( concat_a @ A )
        = ( append_a @ B @ C ) )
      = ( ( ( A = nil_list_a )
         => ( ( B = nil_a )
            & ( C = nil_a ) ) )
        & ( ( A != nil_list_a )
         => ? [D: list_list_a,E: list_a,F: list_a,G: list_list_a] :
              ( ( A
                = ( append_list_a @ D @ ( cons_list_a @ ( append_a @ E @ F ) @ G ) ) )
              & ( B
                = ( append_a @ ( concat_a @ D ) @ E ) )
              & ( C
                = ( append_a @ F @ ( concat_a @ G ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(135,axiom,
    ! [A: list_list_a] :
      ( ( A != nil_list_a )
     => ( ! [B: list_a] :
            ( A
           != ( cons_list_a @ B @ nil_list_a ) )
       => ~ ! [B: list_a,C: list_a,D: list_list_a] :
              ( A
             != ( cons_list_a @ B @ ( cons_list_a @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_remdups__adj_Ocases) ).

thf(912,plain,
    ! [A: list_list_a] :
      ( ( A != nil_list_a )
     => ( ! [B: list_a] :
            ( A
           != ( cons_list_a @ B @ nil_list_a ) )
       => ~ ! [B: list_a,C: list_a,D: list_list_a] :
              ( A
             != ( cons_list_a @ B @ ( cons_list_a @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(195,axiom,
    ! [A: list_a > a > $o,B: list_list_a,C: list_a] :
      ( ( listrelp_list_a_a @ A @ B @ C )
     => ( ( ( B = nil_list_a )
         => ( C != nil_a ) )
       => ~ ! [D: list_a,E: a,F: list_list_a] :
              ( ( B
                = ( cons_list_a @ D @ F ) )
             => ! [G: list_a] :
                  ( ( C
                    = ( cons_a @ E @ G ) )
                 => ( ( A @ D @ E )
                   => ~ ( listrelp_list_a_a @ A @ F @ G ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_listrelp_Ocases) ).

thf(1171,plain,
    ! [A: list_a > a > $o,B: list_list_a,C: list_a] :
      ( ( listrelp_list_a_a @ A @ B @ C )
     => ( ( ( B = nil_list_a )
         => ( C != nil_a ) )
       => ~ ! [D: list_a,E: a,F: list_list_a] :
              ( ( B
                = ( cons_list_a @ D @ F ) )
             => ! [G: list_a] :
                  ( ( C
                    = ( cons_a @ E @ G ) )
                 => ( ( A @ D @ E )
                   => ~ ( listrelp_list_a_a @ A @ F @ G ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(323,axiom,
    ! [A: list_a,B: list_a] :
      ( ( A = nil_a )
     => ( ( B = nil_a )
       => ( member_list_a2 @ nil_a @ ( shuffles_a @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_Nil__in__shufflesI) ).

thf(1841,plain,
    ! [A: list_a,B: list_a] :
      ( ( A = nil_a )
     => ( ( B = nil_a )
       => ( member_list_a2 @ nil_a @ ( shuffles_a @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(238,axiom,
    ! [A: list_a,B: a] :
      ( ( ( A = nil_a )
       => ( ( last_a @ ( cons_a @ B @ A ) )
          = B ) )
      & ( ( A != nil_a )
       => ( ( last_a @ ( cons_a @ B @ A ) )
          = ( last_a @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_last_Osimps) ).

thf(1396,plain,
    ! [A: list_a,B: a] :
      ( ( ( A = nil_a )
       => ( ( last_a @ ( cons_a @ B @ A ) )
          = B ) )
      & ( ( A != nil_a )
       => ( ( last_a @ ( cons_a @ B @ A ) )
          = ( last_a @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(84,axiom,
    ! [A: list_list_a,B: list_a,C: set_list_list_a] :
      ( ( member_list_list_a @ ( append_list_a @ A @ ( cons_list_a @ B @ nil_list_a ) ) @ C )
     => ( member_list_a2 @ B @ ( bNF_Gr1046450207list_a @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_SuccI) ).

thf(636,plain,
    ! [A: list_list_a,B: list_a,C: set_list_list_a] :
      ( ( member_list_list_a @ ( append_list_a @ A @ ( cons_list_a @ B @ nil_list_a ) ) @ C )
     => ( member_list_a2 @ B @ ( bNF_Gr1046450207list_a @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(168,axiom,
    ! [A: a > list_list_a] :
      ( ( maps_a_list_a @ A @ nil_a )
      = nil_list_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_maps__simps_I2_J) ).

thf(1044,plain,
    ! [A: a > list_list_a] :
      ( ( maps_a_list_a @ A @ nil_a )
      = nil_list_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(50,axiom,
    ! [A: list_list_a,B: list_a] :
      ( ( ( A = nil_list_a )
       => ( ( butlast_list_a @ ( cons_list_a @ B @ A ) )
          = nil_list_a ) )
      & ( ( A != nil_list_a )
       => ( ( butlast_list_a @ ( cons_list_a @ B @ A ) )
          = ( cons_list_a @ B @ ( butlast_list_a @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_butlast_Osimps_I2_J) ).

thf(473,plain,
    ! [A: list_list_a,B: list_a] :
      ( ( ( A = nil_list_a )
       => ( ( butlast_list_a @ ( cons_list_a @ B @ A ) )
          = nil_list_a ) )
      & ( ( A != nil_list_a )
       => ( ( butlast_list_a @ ( cons_list_a @ B @ A ) )
          = ( cons_list_a @ B @ ( butlast_list_a @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(165,axiom,
    ! [A: list_a,B: a > a > a,C: a,D: list_a] :
      ( ( A != nil_a )
     => ( ( map2_a_a_a @ B @ A @ ( cons_a @ C @ D ) )
        = ( cons_a @ ( B @ ( hd_a @ A ) @ C ) @ ( map2_a_a_a @ B @ ( tl_a @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_map2__Cons__not__empty) ).

thf(1034,plain,
    ! [A: list_a,B: a > a > a,C: a,D: list_a] :
      ( ( A != nil_a )
     => ( ( map2_a_a_a @ B @ A @ ( cons_a @ C @ D ) )
        = ( cons_a @ ( B @ ( hd_a @ A ) @ C ) @ ( map2_a_a_a @ B @ ( tl_a @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(291,axiom,
    ! [A: a > a > $o,B: a,C: list_a,D: a,E: list_a] :
      ( ( lexordp_eq_a @ A @ ( cons_a @ B @ C ) @ ( cons_a @ D @ E ) )
      = ( ( A @ B @ D )
        | ( ~ ( A @ D @ B )
          & ( lexordp_eq_a @ A @ C @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_ord_Olexordp__eq__simps_I4_J) ).

thf(1662,plain,
    ! [A: a > a > $o,B: a,C: list_a,D: a,E: list_a] :
      ( ( lexordp_eq_a @ A @ ( cons_a @ B @ C ) @ ( cons_a @ D @ E ) )
      = ( ( A @ B @ D )
        | ( ~ ( A @ D @ B )
          & ( lexordp_eq_a @ A @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(193,axiom,
    ( concat_a
    = ( ^ [A: list_list_a] : ( foldr_list_a_list_a @ append_a @ A @ nil_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_concat__conv__foldr) ).

thf(1166,plain,
    ( concat_a
    = ( ^ [A: list_list_a] : ( foldr_list_a_list_a @ append_a @ A @ nil_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(146,axiom,
    ! [A: list_list_a,B: list_list_a > $o] :
      ( ( A != nil_list_a )
     => ( ! [C: list_a] : ( B @ ( cons_list_a @ C @ nil_list_a ) )
       => ( ! [C: list_a,D: list_list_a] :
              ( ( D != nil_list_a )
             => ( ( B @ D )
               => ( B @ ( cons_list_a @ C @ D ) ) ) )
         => ( B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_list__nonempty__induct) ).

thf(944,plain,
    ! [A: list_list_a,B: list_list_a > $o] :
      ( ( A != nil_list_a )
     => ( ! [C: list_a] : ( B @ ( cons_list_a @ C @ nil_list_a ) )
       => ( ! [C: list_a,D: list_list_a] :
              ( ( D != nil_list_a )
             => ( ( B @ D )
               => ( B @ ( cons_list_a @ C @ D ) ) ) )
         => ( B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(251,axiom,
    ! [A: set_list_a,B: a] :
      ( ( member_list_a2 @ nil_a @ A )
     => ( ( member_a2 @ B @ ( bNF_Greatest_Succ_a @ A @ nil_a ) )
       => ( member_list_a2 @ nil_a @ ( bNF_Greatest_Shift_a @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_empty__Shift) ).

thf(1467,plain,
    ! [A: set_list_a,B: a] :
      ( ( member_list_a2 @ nil_a @ A )
     => ( ( member_a2 @ B @ ( bNF_Greatest_Succ_a @ A @ nil_a ) )
       => ( member_list_a2 @ nil_a @ ( bNF_Greatest_Shift_a @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(115,axiom,
    ! [A: list_list_a > $o,B: list_list_a] :
      ( ( A @ nil_list_a )
     => ( ! [C: list_a] : ( A @ ( cons_list_a @ C @ nil_list_a ) )
       => ( ! [C: list_a,D: list_a,E: list_list_a] :
              ( ( A @ E )
             => ( ( A @ ( cons_list_a @ D @ E ) )
               => ( A @ ( cons_list_a @ C @ ( cons_list_a @ D @ E ) ) ) ) )
         => ( A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_induct__list012) ).

thf(795,plain,
    ! [A: list_list_a > $o,B: list_list_a] :
      ( ( A @ nil_list_a )
     => ( ! [C: list_a] : ( A @ ( cons_list_a @ C @ nil_list_a ) )
       => ( ! [C: list_a,D: list_a,E: list_list_a] :
              ( ( A @ E )
             => ( ( A @ ( cons_list_a @ D @ E ) )
               => ( A @ ( cons_list_a @ C @ ( cons_list_a @ D @ E ) ) ) ) )
         => ( A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(69,axiom,
    ! [A: list_list_a,B: list_list_a] :
      ( ( ( append_list_a @ A @ B )
        = B )
      = ( A = nil_list_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_append__self__conv2) ).

thf(548,plain,
    ! [A: list_list_a,B: list_list_a] :
      ( ( ( append_list_a @ A @ B )
        = B )
      = ( A = nil_list_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(189,axiom,
    ! [A: a > a > $o,B: list_a,C: $o] :
      ( ( ( successively_a @ A @ B )
        = C )
     => ( ( ( B = nil_a )
         => ~ C )
       => ( ( ? [D: a] :
                ( B
                = ( cons_a @ D @ nil_a ) )
           => ~ C )
         => ~ ! [D: a,E: a,F: list_a] :
                ( ( B
                  = ( cons_a @ D @ ( cons_a @ E @ F ) ) )
               => ( C
                  = ( ~ ( ( A @ D @ E )
                        & ( successively_a @ A @ ( cons_a @ E @ F ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_successively_Oelims_I1_J) ).

thf(1134,plain,
    ! [A: a > a > $o,B: list_a,C: $o] :
      ( ( ( successively_a @ A @ B )
        = C )
     => ( ( ( B = nil_a )
         => ~ C )
       => ( ( ? [D: a] :
                ( B
                = ( cons_a @ D @ nil_a ) )
           => ~ C )
         => ~ ! [D: a,E: a,F: list_a] :
                ( ( B
                  = ( cons_a @ D @ ( cons_a @ E @ F ) ) )
               => ( C
                  = ( ~ ( ( A @ D @ E )
                        & ( successively_a @ A @ ( cons_a @ E @ F ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(106,axiom,
    ! [A: list_a > list_a,B: list_a,C: list_list_a] :
      ( ( maps_list_a_a @ A @ ( cons_list_a @ B @ C ) )
      = ( append_a @ ( A @ B ) @ ( maps_list_a_a @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_maps__simps_I1_J) ).

thf(749,plain,
    ! [A: list_a > list_a,B: list_a,C: list_list_a] :
      ( ( maps_list_a_a @ A @ ( cons_list_a @ B @ C ) )
      = ( append_a @ ( A @ B ) @ ( maps_list_a_a @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(61,axiom,
    ! [A: list_list_a,B: list_a] :
      ( ( last_list_a @ ( append_list_a @ A @ ( cons_list_a @ B @ nil_list_a ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_last__snoc) ).

thf(516,plain,
    ! [A: list_list_a,B: list_a] :
      ( ( last_list_a @ ( append_list_a @ A @ ( cons_list_a @ B @ nil_list_a ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(6,axiom,
    ! [A: list_list_a] :
      ( ( ( A = nil_list_a )
        | ( ( tl_list_a @ A )
         != nil_list_a ) )
     => ( ( last_list_a @ ( tl_list_a @ A ) )
        = ( last_list_a @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_last__tl) ).

thf(342,plain,
    ! [A: list_list_a] :
      ( ( ( A = nil_list_a )
        | ( ( tl_list_a @ A )
         != nil_list_a ) )
     => ( ( last_list_a @ ( tl_list_a @ A ) )
        = ( last_list_a @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(119,axiom,
    ! [A: list_a > $o] :
      ~ ( list_ex1_list_a @ A @ nil_list_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_list__ex1__simps_I1_J) ).

thf(823,plain,
    ! [A: list_a > $o] :
      ~ ( list_ex1_list_a @ A @ nil_list_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(170,axiom,
    ! [A: set_list_a,B: a,C: list_a] :
      ( ( bNF_Greatest_Succ_a @ ( bNF_Greatest_Shift_a @ A @ B ) @ C )
      = ( bNF_Greatest_Succ_a @ A @ ( cons_a @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_Succ__Shift) ).

thf(1049,plain,
    ! [A: set_list_a,B: a,C: list_a] :
      ( ( bNF_Greatest_Succ_a @ ( bNF_Greatest_Shift_a @ A @ B ) @ C )
      = ( bNF_Greatest_Succ_a @ A @ ( cons_a @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(111,axiom,
    ! [A: set_a] :
      ( ( collect_a
        @ ^ [B: a] : ( member_a2 @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_Collect__mem__eq) ).

thf(776,plain,
    ! [A: set_a] :
      ( ( collect_a
        @ ^ [B: a] : ( member_a2 @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(64,axiom,
    ! [A: list_list_a,B: list_a] :
      ( ( A != nil_list_a )
     => ( ( last_list_a @ ( cons_list_a @ B @ A ) )
        = ( last_list_a @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_last__ConsR) ).

thf(525,plain,
    ! [A: list_list_a,B: list_a] :
      ( ( A != nil_list_a )
     => ( ( last_list_a @ ( cons_list_a @ B @ A ) )
        = ( last_list_a @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(95,axiom,
    ! [A: list_list_a,B: list_list_a] :
      ( ( ( A = nil_list_a )
       => ( ( butlast_list_a @ ( append_list_a @ B @ A ) )
          = ( butlast_list_a @ B ) ) )
      & ( ( A != nil_list_a )
       => ( ( butlast_list_a @ ( append_list_a @ B @ A ) )
          = ( append_list_a @ B @ ( butlast_list_a @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_butlast__append) ).

thf(690,plain,
    ! [A: list_list_a,B: list_list_a] :
      ( ( ( A = nil_list_a )
       => ( ( butlast_list_a @ ( append_list_a @ B @ A ) )
          = ( butlast_list_a @ B ) ) )
      & ( ( A != nil_list_a )
       => ( ( butlast_list_a @ ( append_list_a @ B @ A ) )
          = ( append_list_a @ B @ ( butlast_list_a @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(126,axiom,
    ! [A: list_list_a,B: list_list_a,C: list_list_a] :
      ( ( ( append_list_a @ A @ B )
        = ( append_list_a @ A @ C ) )
      = ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_same__append__eq) ).

thf(872,plain,
    ! [A: list_list_a,B: list_list_a,C: list_list_a] :
      ( ( ( append_list_a @ A @ B )
        = ( append_list_a @ A @ C ) )
      = ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(202,axiom,
    ! [A: list_a] :
      ( ( append_a @ nil_a @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_append__Nil) ).

thf(1225,plain,
    ! [A: list_a] :
      ( ( append_a @ nil_a @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(33,axiom,
    ( list_strict_asc_nat
    = ( list_ord_nat @ ord_less_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_list__strict__asc__def) ).

thf(414,plain,
    ( list_strict_asc_nat
    = ( list_ord_nat @ ord_less_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(312,axiom,
    ! [A: list_a,B: list_a] :
      ( ( distinct_adj_a @ ( append_a @ A @ B ) )
      = ( ( distinct_adj_a @ A )
        & ( distinct_adj_a @ B )
        & ( ( A = nil_a )
          | ( B = nil_a )
          | ( ( last_a @ A )
           != ( hd_a @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_distinct__adj__append__iff) ).

thf(1753,plain,
    ! [A: list_a,B: list_a] :
      ( ( distinct_adj_a @ ( append_a @ A @ B ) )
      = ( ( distinct_adj_a @ A )
        & ( distinct_adj_a @ B )
        & ( ( A = nil_a )
          | ( B = nil_a )
          | ( ( last_a @ A )
           != ( hd_a @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(212,axiom,
    ( listrelp_a_list_a
    = ( ^ [A: a > list_a > $o,B: list_a,C: list_list_a] :
          ( ( ( B = nil_a )
            & ( C = nil_list_a ) )
          | ? [D: a,E: list_a,F: list_a,G: list_list_a] :
              ( ( B
                = ( cons_a @ D @ F ) )
              & ( C
                = ( cons_list_a @ E @ G ) )
              & ( A @ D @ E )
              & ( listrelp_a_list_a @ A @ F @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_listrelp_Osimps) ).

thf(1267,plain,
    ( listrelp_a_list_a
    = ( ^ [A: a > list_a > $o,B: list_a,C: list_list_a] :
          ( ( ( B = nil_a )
            & ( C = nil_list_a ) )
          | ? [D: a,E: list_a,F: list_a,G: list_list_a] :
              ( ( B
                = ( cons_a @ D @ F ) )
              & ( C
                = ( cons_list_a @ E @ G ) )
              & ( A @ D @ E )
              & ( listrelp_a_list_a @ A @ F @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(305,axiom,
    ! [A: a > a,B: list_a] :
      ( ( map_tailrec_rev_a_a @ A @ nil_a @ B )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_map__tailrec__rev_Osimps_I1_J) ).

thf(1716,plain,
    ! [A: a > a,B: list_a] :
      ( ( map_tailrec_rev_a_a @ A @ nil_a @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(114,axiom,
    ! [A: ( list_a > list_a > $o ) > list_list_a > $o,B: list_a > list_a > $o,C: list_list_a] :
      ( ! [D: list_a > list_a > $o] : ( A @ D @ nil_list_a )
     => ( ! [D: list_a > list_a > $o,E: list_a,F: list_list_a] :
            ( ( A @ D @ F )
           => ( A @ D @ ( cons_list_a @ E @ F ) ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_sorted__wrt_Oinduct) ).

thf(791,plain,
    ! [A: ( list_a > list_a > $o ) > list_list_a > $o,B: list_a > list_a > $o,C: list_list_a] :
      ( ! [D: list_a > list_a > $o] : ( A @ D @ nil_list_a )
     => ( ! [D: list_a > list_a > $o,E: list_a,F: list_list_a] :
            ( ( A @ D @ F )
           => ( A @ D @ ( cons_list_a @ E @ F ) ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(196,axiom,
    ! [A: list_a,B: list_a] :
      ( ( ( remdups_adj_a @ A )
        = B )
     => ( ( ( A = nil_a )
         => ( B != nil_a ) )
       => ( ! [C: a] :
              ( ( A
                = ( cons_a @ C @ nil_a ) )
             => ( B
               != ( cons_a @ C @ nil_a ) ) )
         => ~ ! [C: a,D: a,E: list_a] :
                ( ( A
                  = ( cons_a @ C @ ( cons_a @ D @ E ) ) )
               => ~ ( ( ( C = D )
                     => ( B
                        = ( remdups_adj_a @ ( cons_a @ C @ E ) ) ) )
                    & ( ( C != D )
                     => ( B
                        = ( cons_a @ C @ ( remdups_adj_a @ ( cons_a @ D @ E ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_remdups__adj_Oelims) ).

thf(1188,plain,
    ! [A: list_a,B: list_a] :
      ( ( ( remdups_adj_a @ A )
        = B )
     => ( ( ( A = nil_a )
         => ( B != nil_a ) )
       => ( ! [C: a] :
              ( ( A
                = ( cons_a @ C @ nil_a ) )
             => ( B
               != ( cons_a @ C @ nil_a ) ) )
         => ~ ! [C: a,D: a,E: list_a] :
                ( ( A
                  = ( cons_a @ C @ ( cons_a @ D @ E ) ) )
               => ~ ( ( ( C = D )
                     => ( B
                        = ( remdups_adj_a @ ( cons_a @ C @ E ) ) ) )
                    & ( ( C != D )
                     => ( B
                        = ( cons_a @ C @ ( remdups_adj_a @ ( cons_a @ D @ E ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(166,axiom,
    ! [A: list_list_a > list_a > $o,B: list_list_a,C: list_a] :
      ( ( A @ nil_list_a @ nil_a )
     => ( ! [D: list_a,E: list_list_a] : ( A @ ( cons_list_a @ D @ E ) @ nil_a )
       => ( ! [D: a,E: list_a] : ( A @ nil_list_a @ ( cons_a @ D @ E ) )
         => ( ! [D: list_a,E: list_list_a,F: a,G: list_a] :
                ( ( A @ E @ G )
               => ( A @ ( cons_list_a @ D @ E ) @ ( cons_a @ F @ G ) ) )
           => ( A @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_list__induct2_H) ).

thf(1038,plain,
    ! [A: list_list_a > list_a > $o,B: list_list_a,C: list_a] :
      ( ( A @ nil_list_a @ nil_a )
     => ( ! [D: list_a,E: list_list_a] : ( A @ ( cons_list_a @ D @ E ) @ nil_a )
       => ( ! [D: a,E: list_a] : ( A @ nil_list_a @ ( cons_a @ D @ E ) )
         => ( ! [D: list_a,E: list_list_a,F: a,G: list_a] :
                ( ( A @ E @ G )
               => ( A @ ( cons_list_a @ D @ E ) @ ( cons_a @ F @ G ) ) )
           => ( A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(222,axiom,
    ! [A: a,B: list_a,C: list_a,D: list_a] :
      ( ( ( cons_a @ A @ B )
        = ( append_a @ C @ D ) )
      = ( ( ( C = nil_a )
          & ( ( cons_a @ A @ B )
            = D ) )
        | ? [E: list_a] :
            ( ( ( cons_a @ A @ E )
              = C )
            & ( B
              = ( append_a @ E @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_Cons__eq__append__conv) ).

thf(1317,plain,
    ! [A: a,B: list_a,C: list_a,D: list_a] :
      ( ( ( cons_a @ A @ B )
        = ( append_a @ C @ D ) )
      = ( ( ( C = nil_a )
          & ( ( cons_a @ A @ B )
            = D ) )
        | ? [E: list_a] :
            ( ( ( cons_a @ A @ E )
              = C )
            & ( B
              = ( append_a @ E @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(266,axiom,
    ( ( tl_a @ nil_a )
    = nil_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_list_Osel_I2_J) ).

thf(1538,plain,
    ( ( tl_a @ nil_a )
    = nil_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(295,axiom,
    ! [A: list_a] :
      ( ( A != nil_a )
     => ( ( rotate1_a @ A )
        = ( append_a @ ( tl_a @ A ) @ ( cons_a @ ( hd_a @ A ) @ nil_a ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_rotate1__hd__tl) ).

thf(1679,plain,
    ! [A: list_a] :
      ( ( A != nil_a )
     => ( ( rotate1_a @ A )
        = ( append_a @ ( tl_a @ A ) @ ( cons_a @ ( hd_a @ A ) @ nil_a ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(188,axiom,
    ! [A: list_a,B: list_a] :
      ( ( A = B )
     => ( A
        = ( append_a @ nil_a @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_eq__Nil__appendI) ).

thf(1130,plain,
    ! [A: list_a,B: list_a] :
      ( ( A = B )
     => ( A
        = ( append_a @ nil_a @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(215,axiom,
    ! [A: a,B: list_a] :
      ( ( distinct_adj_a @ ( cons_a @ A @ B ) )
     => ( distinct_adj_a @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_distinct__adj__ConsD) ).

thf(1285,plain,
    ! [A: a,B: list_a] :
      ( ( distinct_adj_a @ ( cons_a @ A @ B ) )
     => ( distinct_adj_a @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(239,axiom,
    ! [A: a] : ( distinct_adj_a @ ( cons_a @ A @ nil_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_distinct__adj__singleton) ).

thf(1404,plain,
    ! [A: a] : ( distinct_adj_a @ ( cons_a @ A @ nil_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(325,axiom,
    ! [A: list_a] :
      ( ( ( A = nil_a )
        | ( ( tl_a @ A )
         != nil_a ) )
     => ( ( last_a @ ( tl_a @ A ) )
        = ( last_a @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_last__tl) ).

thf(1849,plain,
    ! [A: list_a] :
      ( ( ( A = nil_a )
        | ( ( tl_a @ A )
         != nil_a ) )
     => ( ( last_a @ ( tl_a @ A ) )
        = ( last_a @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(171,axiom,
    ( ( concat_a @ nil_list_a )
    = nil_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_concat_Osimps_I1_J) ).

thf(1052,plain,
    ( ( concat_a @ nil_list_a )
    = nil_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(242,axiom,
    ! [A: list_a,B: a,C: set_list_a] :
      ( ( member_list_a2 @ ( append_a @ A @ ( cons_a @ B @ nil_a ) ) @ C )
     => ( member_a2 @ B @ ( bNF_Greatest_Succ_a @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_SuccI) ).

thf(1427,plain,
    ! [A: list_a,B: a,C: set_list_a] :
      ( ( member_list_a2 @ ( append_a @ A @ ( cons_a @ B @ nil_a ) ) @ C )
     => ( member_a2 @ B @ ( bNF_Greatest_Succ_a @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(260,axiom,
    ! [A: ( a > a > $o ) > list_a > $o,B: a > a > $o,C: list_a] :
      ( ! [D: a > a > $o] : ( A @ D @ nil_a )
     => ( ! [D: a > a > $o,E: a,F: list_a] :
            ( ( A @ D @ F )
           => ( A @ D @ ( cons_a @ E @ F ) ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_sorted__wrt_Oinduct) ).

thf(1504,plain,
    ! [A: ( a > a > $o ) > list_a > $o,B: a > a > $o,C: list_a] :
      ( ! [D: a > a > $o] : ( A @ D @ nil_a )
     => ( ! [D: a > a > $o,E: a,F: list_a] :
            ( ( A @ D @ F )
           => ( A @ D @ ( cons_a @ E @ F ) ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(22,axiom,
    ! [A: list_a > list_a > $o,B: list_a,C: list_a,D: list_list_a,E: list_list_a] :
      ( ( A @ B @ C )
     => ( ( listre1221556159list_a @ A @ D @ E )
       => ( listre1221556159list_a @ A @ ( cons_list_a @ B @ D ) @ ( cons_list_a @ C @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_listrelp_OCons) ).

thf(386,plain,
    ! [A: list_a > list_a > $o,B: list_a,C: list_a,D: list_list_a,E: list_list_a] :
      ( ( A @ B @ C )
     => ( ( listre1221556159list_a @ A @ D @ E )
       => ( listre1221556159list_a @ A @ ( cons_list_a @ B @ D ) @ ( cons_list_a @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(294,axiom,
    ! [A: list_a,B: list_a] :
      ( ( ( A = nil_a )
        | ( B = nil_a )
        | ( ( last_a @ A )
         != ( hd_a @ B ) ) )
     => ( ( remdups_adj_a @ ( append_a @ A @ B ) )
        = ( append_a @ ( remdups_adj_a @ A ) @ ( remdups_adj_a @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_remdups__adj__append_H) ).

thf(1670,plain,
    ! [A: list_a,B: list_a] :
      ( ( ( A = nil_a )
        | ( B = nil_a )
        | ( ( last_a @ A )
         != ( hd_a @ B ) ) )
     => ( ( remdups_adj_a @ ( append_a @ A @ B ) )
        = ( append_a @ ( remdups_adj_a @ A ) @ ( remdups_adj_a @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(43,axiom,
    ! [A: list_list_a,B: list_a] :
      ( ( A = nil_list_a )
     => ( ( last_list_a @ ( cons_list_a @ B @ A ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_last__ConsL) ).

thf(446,plain,
    ! [A: list_list_a,B: list_a] :
      ( ( A = nil_list_a )
     => ( ( last_list_a @ ( cons_list_a @ B @ A ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(214,axiom,
    ! [A: a > list_a,B: list_a,C: list_list_a,D: list_list_a] :
      ( ( ( map_ta41997947list_a @ A @ B @ C )
        = D )
     => ( ( ( B = nil_a )
         => ( D != C ) )
       => ~ ! [E: a,F: list_a] :
              ( ( B
                = ( cons_a @ E @ F ) )
             => ( D
               != ( map_ta41997947list_a @ A @ F @ ( cons_list_a @ ( A @ E ) @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_map__tailrec__rev_Oelims) ).

thf(1272,plain,
    ! [A: a > list_a,B: list_a,C: list_list_a,D: list_list_a] :
      ( ( ( map_ta41997947list_a @ A @ B @ C )
        = D )
     => ( ( ( B = nil_a )
         => ( D != C ) )
       => ~ ! [E: a,F: list_a] :
              ( ( B
                = ( cons_a @ E @ F ) )
             => ( D
               != ( map_ta41997947list_a @ A @ F @ ( cons_list_a @ ( A @ E ) @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(283,axiom,
    ! [A: list_a,B: list_a] :
      ( ( ( A = nil_a )
       => ( ( hd_a @ ( append_a @ A @ B ) )
          = ( hd_a @ B ) ) )
      & ( ( A != nil_a )
       => ( ( hd_a @ ( append_a @ A @ B ) )
          = ( hd_a @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_hd__append) ).

thf(1617,plain,
    ! [A: list_a,B: list_a] :
      ( ( ( A = nil_a )
       => ( ( hd_a @ ( append_a @ A @ B ) )
          = ( hd_a @ B ) ) )
      & ( ( A != nil_a )
       => ( ( hd_a @ ( append_a @ A @ B ) )
          = ( hd_a @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(49,axiom,
    ! [A: list_list_a,B: list_list_a] :
      ( ( ( A = nil_list_a )
       => ( ( hd_list_a @ ( append_list_a @ A @ B ) )
          = ( hd_list_a @ B ) ) )
      & ( ( A != nil_list_a )
       => ( ( hd_list_a @ ( append_list_a @ A @ B ) )
          = ( hd_list_a @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_hd__append) ).

thf(465,plain,
    ! [A: list_list_a,B: list_list_a] :
      ( ( ( A = nil_list_a )
       => ( ( hd_list_a @ ( append_list_a @ A @ B ) )
          = ( hd_list_a @ B ) ) )
      & ( ( A != nil_list_a )
       => ( ( hd_list_a @ ( append_list_a @ A @ B ) )
          = ( hd_list_a @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(248,axiom,
    ! [A: a > list_a] :
      ( ( bind_a_a @ nil_a @ A )
      = nil_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_bind__simps_I1_J) ).

thf(1459,plain,
    ! [A: a > list_a] :
      ( ( bind_a_a @ nil_a @ A )
      = nil_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(268,axiom,
    ! [A: list_a,B: list_a] :
      ( ( ( splice_a @ A @ B )
        = nil_a )
      = ( ( A = nil_a )
        & ( B = nil_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_split__Nil__iff) ).

thf(1553,plain,
    ! [A: list_a,B: list_a] :
      ( ( ( splice_a @ A @ B )
        = nil_a )
      = ( ( A = nil_a )
        & ( B = nil_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(89,axiom,
    ! [A: list_a > list_a > list_a,B: list_list_a,C: list_list_a,D: list_a] :
      ( ( foldr_list_a_list_a @ A @ ( append_list_a @ B @ C ) @ D )
      = ( foldr_list_a_list_a @ A @ B @ ( foldr_list_a_list_a @ A @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_foldr__append) ).

thf(671,plain,
    ! [A: list_a > list_a > list_a,B: list_list_a,C: list_list_a,D: list_a] :
      ( ( foldr_list_a_list_a @ A @ ( append_list_a @ B @ C ) @ D )
      = ( foldr_list_a_list_a @ A @ B @ ( foldr_list_a_list_a @ A @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(321,axiom,
    ! [A: list_list_a] :
      ( ( A != nil_list_a )
     => ( ! [B: list_list_a] :
            ( A
           != ( cons_list_a @ nil_a @ B ) )
       => ~ ! [B: a,C: list_a,D: list_list_a] :
              ( A
             != ( cons_list_a @ ( cons_a @ B @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_transpose_Ocases) ).

thf(1834,plain,
    ! [A: list_list_a] :
      ( ( A != nil_list_a )
     => ( ! [B: list_list_a] :
            ( A
           != ( cons_list_a @ nil_a @ B ) )
       => ~ ! [B: a,C: list_a,D: list_list_a] :
              ( A
             != ( cons_list_a @ ( cons_a @ B @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(131,axiom,
    ! [A: list_list_a] :
      ( ( append_list_a @ nil_list_a @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_append_Oleft__neutral) ).

thf(891,plain,
    ! [A: list_list_a] :
      ( ( append_list_a @ nil_list_a @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(246,axiom,
    ! [A: a > list_a > $o,B: a,C: list_a,D: list_a,E: list_list_a] :
      ( ( A @ B @ C )
     => ( ( listrelp_a_list_a @ A @ D @ E )
       => ( listrelp_a_list_a @ A @ ( cons_a @ B @ D ) @ ( cons_list_a @ C @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_listrelp_OCons) ).

thf(1448,plain,
    ! [A: a > list_a > $o,B: a,C: list_a,D: list_a,E: list_list_a] :
      ( ( A @ B @ C )
     => ( ( listrelp_a_list_a @ A @ D @ E )
       => ( listrelp_a_list_a @ A @ ( cons_a @ B @ D ) @ ( cons_list_a @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(13,axiom,
    ! [A: list_a > list_a > $o,B: list_a,C: list_a,D: list_list_a,E: list_list_a] :
      ( ( A @ B @ C )
     => ( lexordp_eq_list_a @ A @ ( cons_list_a @ B @ D ) @ ( cons_list_a @ C @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_ord_Olexordp__eq_OCons) ).

thf(363,plain,
    ! [A: list_a > list_a > $o,B: list_a,C: list_a,D: list_list_a,E: list_list_a] :
      ( ( A @ B @ C )
     => ( lexordp_eq_list_a @ A @ ( cons_list_a @ B @ D ) @ ( cons_list_a @ C @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(71,axiom,
    ! [A: list_a,B: list_list_a,C: list_a > list_a] :
      ( ( bind_list_a_a @ ( cons_list_a @ A @ B ) @ C )
      = ( append_a @ ( C @ A ) @ ( bind_list_a_a @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_bind__simps_I2_J) ).

thf(556,plain,
    ! [A: list_a,B: list_list_a,C: list_a > list_a] :
      ( ( bind_list_a_a @ ( cons_list_a @ A @ B ) @ C )
      = ( append_a @ ( C @ A ) @ ( bind_list_a_a @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(55,axiom,
    ! [A: list_list_a,B: list_list_a,C: list_list_a,D: list_list_a,E: list_list_a] :
      ( ( ( append_list_a @ A @ B )
        = C )
     => ( ( D
          = ( append_list_a @ B @ E ) )
       => ( ( append_list_a @ A @ D )
          = ( append_list_a @ C @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_append__eq__appendI) ).

thf(495,plain,
    ! [A: list_list_a,B: list_list_a,C: list_list_a,D: list_list_a,E: list_list_a] :
      ( ( ( append_list_a @ A @ B )
        = C )
     => ( ( D
          = ( append_list_a @ B @ E ) )
       => ( ( append_list_a @ A @ D )
          = ( append_list_a @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(289,axiom,
    ! [A: list_a] :
      ( ( A != nil_a )
     => ( ( cons_a @ ( hd_a @ A ) @ ( tl_a @ A ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_list_Ocollapse) ).

thf(1654,plain,
    ! [A: list_a] :
      ( ( A != nil_a )
     => ( ( cons_a @ ( hd_a @ A ) @ ( tl_a @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(158,axiom,
    ! [A: a > a > $o,B: a,C: a,D: list_a] :
      ( ( successively_a @ A @ ( cons_a @ B @ ( cons_a @ C @ D ) ) )
      = ( ( A @ B @ C )
        & ( successively_a @ A @ ( cons_a @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_successively_Osimps_I3_J) ).

thf(1010,plain,
    ! [A: a > a > $o,B: a,C: a,D: list_a] :
      ( ( successively_a @ A @ ( cons_a @ B @ ( cons_a @ C @ D ) ) )
      = ( ( A @ B @ C )
        & ( successively_a @ A @ ( cons_a @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(273,axiom,
    ! [A: a > a > $o,B: list_a] : ( lexordp_eq_a @ A @ nil_a @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_ord_Olexordp__eq__simps_I1_J) ).

thf(1575,plain,
    ! [A: a > a > $o,B: list_a] : ( lexordp_eq_a @ A @ nil_a @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(288,axiom,
    ! [A: list_a,B: list_a > $o] :
      ( ( A != nil_a )
     => ( ! [C: a] : ( B @ ( cons_a @ C @ nil_a ) )
       => ( ! [C: a,D: list_a] :
              ( ( D != nil_a )
             => ( ( B @ D )
               => ( B @ ( append_a @ D @ ( cons_a @ C @ nil_a ) ) ) ) )
         => ( B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_rev__nonempty__induct) ).

thf(1646,plain,
    ! [A: list_a,B: list_a > $o] :
      ( ( A != nil_a )
     => ( ! [C: a] : ( B @ ( cons_a @ C @ nil_a ) )
       => ( ! [C: a,D: list_a] :
              ( ( D != nil_a )
             => ( ( B @ D )
               => ( B @ ( append_a @ D @ ( cons_a @ C @ nil_a ) ) ) ) )
         => ( B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(236,axiom,
    ! [A: list_a > list_a] :
      ( ( maps_list_a_a @ A @ nil_list_a )
      = nil_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_maps__simps_I2_J) ).

thf(1385,plain,
    ! [A: list_a > list_a] :
      ( ( maps_list_a_a @ A @ nil_list_a )
      = nil_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(254,axiom,
    ! [A: list_a,B: list_a] :
      ( ( A
        = ( append_a @ B @ A ) )
      = ( B = nil_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_self__append__conv2) ).

thf(1476,plain,
    ! [A: list_a,B: list_a] :
      ( ( A
        = ( append_a @ B @ A ) )
      = ( B = nil_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(261,axiom,
    ! [A: list_a] :
      ( ( A != nil_a )
     => ( ! [B: a] :
            ( A
           != ( cons_a @ B @ nil_a ) )
       => ~ ! [B: a,C: a,D: list_a] :
              ( A
             != ( cons_a @ B @ ( cons_a @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_remdups__adj_Ocases) ).

thf(1508,plain,
    ! [A: list_a] :
      ( ( A != nil_a )
     => ( ! [B: a] :
            ( A
           != ( cons_a @ B @ nil_a ) )
       => ~ ! [B: a,C: a,D: list_a] :
              ( A
             != ( cons_a @ B @ ( cons_a @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(8,axiom,
    ! [A: list_a > list_a > $o,B: list_list_a] : ( lexordp_eq_list_a @ A @ nil_list_a @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_ord_Olexordp__eq__simps_I1_J) ).

thf(351,plain,
    ! [A: list_a > list_a > $o,B: list_list_a] : ( lexordp_eq_list_a @ A @ nil_list_a @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(285,axiom,
    ! [A: ( a > a > $o ) > list_a > $o,B: a > a > $o,C: list_a] :
      ( ! [D: a > a > $o] : ( A @ D @ nil_a )
     => ( ! [D: a > a > $o,E: a] : ( A @ D @ ( cons_a @ E @ nil_a ) )
       => ( ! [D: a > a > $o,E: a,F: a,G: list_a] :
              ( ( A @ D @ ( cons_a @ F @ G ) )
             => ( A @ D @ ( cons_a @ E @ ( cons_a @ F @ G ) ) ) )
         => ( A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_successively_Oinduct) ).

thf(1629,plain,
    ! [A: ( a > a > $o ) > list_a > $o,B: a > a > $o,C: list_a] :
      ( ! [D: a > a > $o] : ( A @ D @ nil_a )
     => ( ! [D: a > a > $o,E: a] : ( A @ D @ ( cons_a @ E @ nil_a ) )
       => ( ! [D: a > a > $o,E: a,F: a,G: list_a] :
              ( ( A @ D @ ( cons_a @ F @ G ) )
             => ( A @ D @ ( cons_a @ E @ ( cons_a @ F @ G ) ) ) )
         => ( A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(28,axiom,
    ! [A: list_a > list_a > $o,B: list_a,C: list_a,D: list_list_a,E: list_list_a] :
      ( ~ ( A @ B @ C )
     => ( ~ ( A @ C @ B )
       => ( ( lexordp_eq_list_a @ A @ D @ E )
         => ( lexordp_eq_list_a @ A @ ( cons_list_a @ B @ D ) @ ( cons_list_a @ C @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_ord_Olexordp__eq_OCons__eq) ).

thf(401,plain,
    ! [A: list_a > list_a > $o,B: list_a,C: list_a,D: list_list_a,E: list_list_a] :
      ( ~ ( A @ B @ C )
     => ( ~ ( A @ C @ B )
       => ( ( lexordp_eq_list_a @ A @ D @ E )
         => ( lexordp_eq_list_a @ A @ ( cons_list_a @ B @ D ) @ ( cons_list_a @ C @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(164,axiom,
    ! [A: nat,B: list_a] :
      ( ( ord_less_nat @ A @ ( size_size_list_a @ B ) )
     => ( B != nil_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_length__greater__imp__not__empty) ).

thf(1030,plain,
    ! [A: nat,B: list_a] :
      ( ( ord_less_nat @ A @ ( size_size_list_a @ B ) )
     => ( B != nil_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(88,axiom,
    ! [A: list_list_a] :
      ( ( A != nil_list_a )
     => ~ ! [B: list_list_a,C: list_a] :
            ( A
           != ( append_list_a @ B @ ( cons_list_a @ C @ nil_list_a ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_rev__exhaust) ).

thf(667,plain,
    ! [A: list_list_a] :
      ( ( A != nil_list_a )
     => ~ ! [B: list_list_a,C: list_a] :
            ( A
           != ( append_list_a @ B @ ( cons_list_a @ C @ nil_list_a ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(141,axiom,
    ! [A: list_list_a] :
      ( ( ( tl_list_a @ A )
        = nil_list_a )
      = ( ( A = nil_list_a )
        | ? [B: list_a] :
            ( A
            = ( cons_list_a @ B @ nil_list_a ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_tl__Nil) ).

thf(929,plain,
    ! [A: list_list_a] :
      ( ( ( tl_list_a @ A )
        = nil_list_a )
      = ( ( A = nil_list_a )
        | ? [B: list_a] :
            ( A
            = ( cons_list_a @ B @ nil_list_a ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(219,axiom,
    ! [A: ( a > a ) > list_a > list_a > $o,B: a > a,C: list_a,D: list_a] :
      ( ! [E: a > a,F: list_a] : ( A @ E @ nil_a @ F )
     => ( ! [E: a > a,F: a,G: list_a,H: list_a] :
            ( ( A @ E @ G @ ( cons_a @ ( E @ F ) @ H ) )
           => ( A @ E @ ( cons_a @ F @ G ) @ H ) )
       => ( A @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_map__tailrec__rev_Oinduct) ).

thf(1308,plain,
    ! [A: ( a > a ) > list_a > list_a > $o,B: a > a,C: list_a,D: list_a] :
      ( ! [E: a > a,F: list_a] : ( A @ E @ nil_a @ F )
     => ( ! [E: a > a,F: a,G: list_a,H: list_a] :
            ( ( A @ E @ G @ ( cons_a @ ( E @ F ) @ H ) )
           => ( A @ E @ ( cons_a @ F @ G ) @ H ) )
       => ( A @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(20,axiom,
    ( ( butlast_list_a @ nil_list_a )
    = nil_list_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_butlast_Osimps_I1_J) ).

thf(383,plain,
    ( ( butlast_list_a @ nil_list_a )
    = nil_list_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(93,axiom,
    ! [A: list_list_a] :
      ( ( append_list_a @ nil_list_a @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_append__Nil) ).

thf(684,plain,
    ! [A: list_list_a] :
      ( ( append_list_a @ nil_list_a @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(245,axiom,
    ! [A: ( a > list_a ) > list_a > list_list_a > $o,B: a > list_a,C: list_a,D: list_list_a] :
      ( ! [E: a > list_a,F: list_list_a] : ( A @ E @ nil_a @ F )
     => ( ! [E: a > list_a,F: a,G: list_a,H: list_list_a] :
            ( ( A @ E @ G @ ( cons_list_a @ ( E @ F ) @ H ) )
           => ( A @ E @ ( cons_a @ F @ G ) @ H ) )
       => ( A @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_map__tailrec__rev_Oinduct) ).

thf(1444,plain,
    ! [A: ( a > list_a ) > list_a > list_list_a > $o,B: a > list_a,C: list_a,D: list_list_a] :
      ( ! [E: a > list_a,F: list_list_a] : ( A @ E @ nil_a @ F )
     => ( ! [E: a > list_a,F: a,G: list_a,H: list_list_a] :
            ( ( A @ E @ G @ ( cons_list_a @ ( E @ F ) @ H ) )
           => ( A @ E @ ( cons_a @ F @ G ) @ H ) )
       => ( A @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(244,axiom,
    ( ( butlast_a @ nil_a )
    = nil_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_butlast_Osimps_I1_J) ).

thf(1442,plain,
    ( ( butlast_a @ nil_a )
    = nil_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(107,axiom,
    ! [A: list_list_a,B: list_list_a] :
      ( ( A = nil_list_a )
     => ( ( last_list_a @ ( append_list_a @ B @ A ) )
        = ( last_list_a @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_last__appendL) ).

thf(752,plain,
    ! [A: list_list_a,B: list_list_a] :
      ( ( A = nil_list_a )
     => ( ( last_list_a @ ( append_list_a @ B @ A ) )
        = ( last_list_a @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(262,axiom,
    ! [A: list_a,B: list_a,C: list_a,D: list_a,E: list_a > list_a > list_a > list_a > $o] :
      ( ( ( size_size_list_a @ A )
        = ( size_size_list_a @ B ) )
     => ( ( ( size_size_list_a @ B )
          = ( size_size_list_a @ C ) )
       => ( ( ( size_size_list_a @ C )
            = ( size_size_list_a @ D ) )
         => ( ( E @ nil_a @ nil_a @ nil_a @ nil_a )
           => ( ! [F: a,G: list_a,H: a,I: list_a,J: a,K: list_a,L: a,M: list_a] :
                  ( ( ( size_size_list_a @ G )
                    = ( size_size_list_a @ I ) )
                 => ( ( ( size_size_list_a @ I )
                      = ( size_size_list_a @ K ) )
                   => ( ( ( size_size_list_a @ K )
                        = ( size_size_list_a @ M ) )
                     => ( ( E @ G @ I @ K @ M )
                       => ( E @ ( cons_a @ F @ G ) @ ( cons_a @ H @ I ) @ ( cons_a @ J @ K ) @ ( cons_a @ L @ M ) ) ) ) ) )
             => ( E @ A @ B @ C @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_list__induct4) ).

thf(1512,plain,
    ! [A: list_a,B: list_a,C: list_a,D: list_a,E: list_a > list_a > list_a > list_a > $o] :
      ( ( ( size_size_list_a @ A )
        = ( size_size_list_a @ B ) )
     => ( ( ( size_size_list_a @ B )
          = ( size_size_list_a @ C ) )
       => ( ( ( size_size_list_a @ C )
            = ( size_size_list_a @ D ) )
         => ( ( E @ nil_a @ nil_a @ nil_a @ nil_a )
           => ( ! [F: a,G: list_a,H: a,I: list_a,J: a,K: list_a,L: a,M: list_a] :
                  ( ( ( size_size_list_a @ G )
                    = ( size_size_list_a @ I ) )
                 => ( ( ( size_size_list_a @ I )
                      = ( size_size_list_a @ K ) )
                   => ( ( ( size_size_list_a @ K )
                        = ( size_size_list_a @ M ) )
                     => ( ( E @ G @ I @ K @ M )
                       => ( E @ ( cons_a @ F @ G ) @ ( cons_a @ H @ I ) @ ( cons_a @ J @ K ) @ ( cons_a @ L @ M ) ) ) ) ) )
             => ( E @ A @ B @ C @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(39,axiom,
    ! [A: nat > list_a] :
      ( ( listIn1753026346list_a @ nil_list_a @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_i__append__Nil) ).

thf(432,plain,
    ! [A: nat > list_a] :
      ( ( listIn1753026346list_a @ nil_list_a @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(284,axiom,
    ! [A: list_a,B: a] :
      ( ( A != nil_a )
     => ( ( last_a @ ( cons_a @ B @ A ) )
        = ( last_a @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_last__ConsR) ).

thf(1625,plain,
    ! [A: list_a,B: a] :
      ( ( A != nil_a )
     => ( ( last_a @ ( cons_a @ B @ A ) )
        = ( last_a @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(264,axiom,
    ! [A: a,B: a,C: list_a] :
      ( ( ( A = B )
       => ( ( remdups_adj_a @ ( cons_a @ A @ ( cons_a @ B @ C ) ) )
          = ( remdups_adj_a @ ( cons_a @ A @ C ) ) ) )
      & ( ( A != B )
       => ( ( remdups_adj_a @ ( cons_a @ A @ ( cons_a @ B @ C ) ) )
          = ( cons_a @ A @ ( remdups_adj_a @ ( cons_a @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_remdups__adj_Osimps_I3_J) ).

thf(1527,plain,
    ! [A: a,B: a,C: list_a] :
      ( ( ( A = B )
       => ( ( remdups_adj_a @ ( cons_a @ A @ ( cons_a @ B @ C ) ) )
          = ( remdups_adj_a @ ( cons_a @ A @ C ) ) ) )
      & ( ( A != B )
       => ( ( remdups_adj_a @ ( cons_a @ A @ ( cons_a @ B @ C ) ) )
          = ( cons_a @ A @ ( remdups_adj_a @ ( cons_a @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(36,axiom,
    ! [A: list_a,B: list_a] :
      ( ( if_list_a @ $false @ A @ B )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__List__Olist_Itf__a_J_T) ).

thf(422,plain,
    ! [A: list_a,B: list_a] :
      ( ( if_list_a @ $false @ A @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(103,axiom,
    ! [A: list_list_a,B: list_a] :
      ( ( ( A = nil_list_a )
       => ( ( last_list_a @ ( cons_list_a @ B @ A ) )
          = B ) )
      & ( ( A != nil_list_a )
       => ( ( last_list_a @ ( cons_list_a @ B @ A ) )
          = ( last_list_a @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_last_Osimps) ).

thf(735,plain,
    ! [A: list_list_a,B: list_a] :
      ( ( ( A = nil_list_a )
       => ( ( last_list_a @ ( cons_list_a @ B @ A ) )
          = B ) )
      & ( ( A != nil_list_a )
       => ( ( last_list_a @ ( cons_list_a @ B @ A ) )
          = ( last_list_a @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(156,axiom,
    ! [A: list_list_a,B: list_list_a > $o] :
      ( ( A != nil_list_a )
     => ( ! [C: list_a] : ( B @ ( cons_list_a @ C @ nil_list_a ) )
       => ( ! [C: list_a,D: list_list_a] :
              ( ( D != nil_list_a )
             => ( ( B @ D )
               => ( B @ ( append_list_a @ D @ ( cons_list_a @ C @ nil_list_a ) ) ) ) )
         => ( B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_rev__nonempty__induct) ).

thf(999,plain,
    ! [A: list_list_a,B: list_list_a > $o] :
      ( ( A != nil_list_a )
     => ( ! [C: list_a] : ( B @ ( cons_list_a @ C @ nil_list_a ) )
       => ( ! [C: list_a,D: list_list_a] :
              ( ( D != nil_list_a )
             => ( ( B @ D )
               => ( B @ ( append_list_a @ D @ ( cons_list_a @ C @ nil_list_a ) ) ) ) )
         => ( B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(78,axiom,
    ! [A: list_list_a,B: list_list_a,C: list_list_a] :
      ( ( ( append_list_a @ A @ B )
        = ( append_list_a @ C @ B ) )
      = ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_append__same__eq) ).

thf(620,plain,
    ! [A: list_list_a,B: list_list_a,C: list_list_a] :
      ( ( ( append_list_a @ A @ B )
        = ( append_list_a @ C @ B ) )
      = ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(17,axiom,
    ! [A: list_a,B: list_list_a] :
      ( ( tl_list_a @ ( cons_list_a @ A @ B ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_list_Osel_I3_J) ).

thf(373,plain,
    ! [A: list_a,B: list_list_a] :
      ( ( tl_list_a @ ( cons_list_a @ A @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(74,axiom,
    ! [A: list_list_a,B: list_list_a] :
      ( ( A
        = ( append_list_a @ B @ A ) )
      = ( B = nil_list_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_self__append__conv2) ).

thf(603,plain,
    ! [A: list_list_a,B: list_list_a] :
      ( ( A
        = ( append_list_a @ B @ A ) )
      = ( B = nil_list_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(221,axiom,
    ! [A: a,B: list_a] :
      ( ( tl_a @ ( cons_a @ A @ B ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_list_Osel_I3_J) ).

thf(1314,plain,
    ! [A: a,B: list_a] :
      ( ( tl_a @ ( cons_a @ A @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(290,axiom,
    ! [A: a,B: list_a,C: list_a,D: list_a,E: list_a] :
      ( ( ( cons_a @ A @ B )
        = C )
     => ( ( D
          = ( append_a @ B @ E ) )
       => ( ( cons_a @ A @ D )
          = ( append_a @ C @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_Cons__eq__appendI) ).

thf(1657,plain,
    ! [A: a,B: list_a,C: list_a,D: list_a,E: list_a] :
      ( ( ( cons_a @ A @ B )
        = C )
     => ( ( D
          = ( append_a @ B @ E ) )
       => ( ( cons_a @ A @ D )
          = ( append_a @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(58,axiom,
    ! [A: a,B: a > $o] :
      ( ( member_a2 @ A @ ( collect_a @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_mem__Collect__eq) ).

thf(506,plain,
    ! [A: a,B: a > $o] :
      ( ( member_a2 @ A @ ( collect_a @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(11,axiom,
    ( ( concat_list_a @ nil_list_list_a )
    = nil_list_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_concat_Osimps_I1_J) ).

thf(358,plain,
    ( ( concat_list_a @ nil_list_list_a )
    = nil_list_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(133,axiom,
    ! [A: list_list_a,B: list_list_a,C: list_list_a] :
      ( ( append_list_a @ ( append_list_a @ A @ B ) @ C )
      = ( append_list_a @ A @ ( append_list_a @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_append__assoc) ).

thf(897,plain,
    ! [A: list_list_a,B: list_list_a,C: list_list_a] :
      ( ( append_list_a @ ( append_list_a @ A @ B ) @ C )
      = ( append_list_a @ A @ ( append_list_a @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(87,axiom,
    ! [A: list_a] :
      ( ( insert_list_a @ A @ nil_list_a )
      = ( cons_list_a @ A @ nil_list_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_insert__Nil) ).

thf(664,plain,
    ! [A: list_a] :
      ( ( insert_list_a @ A @ nil_list_a )
      = ( cons_list_a @ A @ nil_list_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(303,axiom,
    ! [A: list_a > a > $o,B: list_a,C: a,D: list_list_a,E: list_a] :
      ( ( A @ B @ C )
     => ( ( listrelp_list_a_a @ A @ D @ E )
       => ( listrelp_list_a_a @ A @ ( cons_list_a @ B @ D ) @ ( cons_a @ C @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_listrelp_OCons) ).

thf(1710,plain,
    ! [A: list_a > a > $o,B: list_a,C: a,D: list_list_a,E: list_a] :
      ( ( A @ B @ C )
     => ( ( listrelp_list_a_a @ A @ D @ E )
       => ( listrelp_list_a_a @ A @ ( cons_list_a @ B @ D ) @ ( cons_a @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(121,axiom,
    ! [A: list_a > list_a > $o,B: list_list_a,C: $o] :
      ( ( ( successively_list_a @ A @ B )
        = C )
     => ( ( ( B = nil_list_a )
         => ~ C )
       => ( ( ? [D: list_a] :
                ( B
                = ( cons_list_a @ D @ nil_list_a ) )
           => ~ C )
         => ~ ! [D: list_a,E: list_a,F: list_list_a] :
                ( ( B
                  = ( cons_list_a @ D @ ( cons_list_a @ E @ F ) ) )
               => ( C
                  = ( ~ ( ( A @ D @ E )
                        & ( successively_list_a @ A @ ( cons_list_a @ E @ F ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_successively_Oelims_I1_J) ).

thf(828,plain,
    ! [A: list_a > list_a > $o,B: list_list_a,C: $o] :
      ( ( ( successively_list_a @ A @ B )
        = C )
     => ( ( ( B = nil_list_a )
         => ~ C )
       => ( ( ? [D: list_a] :
                ( B
                = ( cons_list_a @ D @ nil_list_a ) )
           => ~ C )
         => ~ ! [D: list_a,E: list_a,F: list_list_a] :
                ( ( B
                  = ( cons_list_a @ D @ ( cons_list_a @ E @ F ) ) )
               => ( C
                  = ( ~ ( ( A @ D @ E )
                        & ( successively_list_a @ A @ ( cons_list_a @ E @ F ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(253,axiom,
    ! [A: a > $o] :
      ~ ( list_ex1_a @ A @ nil_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_list__ex1__simps_I1_J) ).

thf(1473,plain,
    ! [A: a > $o] :
      ~ ( list_ex1_a @ A @ nil_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(66,axiom,
    ! [A: list_list_a > list_list_a > $o,B: list_list_a,C: list_list_a] :
      ( ( A @ nil_list_a @ nil_list_a )
     => ( ! [D: list_a,E: list_list_a] : ( A @ ( cons_list_a @ D @ E ) @ nil_list_a )
       => ( ! [D: list_a,E: list_list_a] : ( A @ nil_list_a @ ( cons_list_a @ D @ E ) )
         => ( ! [D: list_a,E: list_list_a,F: list_a,G: list_list_a] :
                ( ( A @ E @ G )
               => ( A @ ( cons_list_a @ D @ E ) @ ( cons_list_a @ F @ G ) ) )
           => ( A @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_list__induct2_H) ).

thf(532,plain,
    ! [A: list_list_a > list_list_a > $o,B: list_list_a,C: list_list_a] :
      ( ( A @ nil_list_a @ nil_list_a )
     => ( ! [D: list_a,E: list_list_a] : ( A @ ( cons_list_a @ D @ E ) @ nil_list_a )
       => ( ! [D: list_a,E: list_list_a] : ( A @ nil_list_a @ ( cons_list_a @ D @ E ) )
         => ( ! [D: list_a,E: list_list_a,F: list_a,G: list_list_a] :
                ( ( A @ E @ G )
               => ( A @ ( cons_list_a @ D @ E ) @ ( cons_list_a @ F @ G ) ) )
           => ( A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(101,axiom,
    ! [A: list_a,B: list_list_a] :
      ( nil_list_a
     != ( cons_list_a @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_list_Odistinct_I1_J) ).

thf(728,plain,
    ! [A: list_a,B: list_list_a] :
      ( nil_list_a
     != ( cons_list_a @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(206,axiom,
    ! [A: list_a,B: list_a,C: list_a,D: a] :
      ( ( member_list_a2 @ A @ ( shuffles_a @ B @ C ) )
     => ( member_list_a2 @ ( cons_a @ D @ A ) @ ( shuffles_a @ ( cons_a @ D @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_Cons__in__shuffles__leftI) ).

thf(1236,plain,
    ! [A: list_a,B: list_a,C: list_a,D: a] :
      ( ( member_list_a2 @ A @ ( shuffles_a @ B @ C ) )
     => ( member_list_a2 @ ( cons_a @ D @ A ) @ ( shuffles_a @ ( cons_a @ D @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(210,axiom,
    ! [A: a,B: list_a] :
      ( ( distinct_adj_a @ ( cons_a @ A @ B ) )
      = ( ( B = nil_a )
        | ( ( A
           != ( hd_a @ B ) )
          & ( distinct_adj_a @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_distinct__adj__Cons) ).

thf(1261,plain,
    ! [A: a,B: list_a] :
      ( ( distinct_adj_a @ ( cons_a @ A @ B ) )
      = ( ( B = nil_a )
        | ( ( A
           != ( hd_a @ B ) )
          & ( distinct_adj_a @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(275,axiom,
    ! [A: a > list_a > $o] : ( listrelp_a_list_a @ A @ nil_a @ nil_list_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_listrelp_ONil) ).

thf(1582,plain,
    ! [A: a > list_a > $o] : ( listrelp_a_list_a @ A @ nil_a @ nil_list_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(278,axiom,
    ! [A: a > list_list_a] :
      ( ( bind_a_list_a @ nil_a @ A )
      = nil_list_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_bind__simps_I1_J) ).

thf(1597,plain,
    ! [A: a > list_list_a] :
      ( ( bind_a_list_a @ nil_a @ A )
      = nil_list_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(218,axiom,
    ! [A: list_a,B: list_a] :
      ( ( ( A = nil_a )
        = ( B = nil_a ) )
     => ( ( ( A != nil_a )
         => ( ( B != nil_a )
           => ( ( ( hd_a @ A )
                = ( hd_a @ B ) )
              & ( ( tl_a @ A )
                = ( tl_a @ B ) ) ) ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_list_Oexpand) ).

thf(1299,plain,
    ! [A: list_a,B: list_a] :
      ( ( ( A = nil_a )
        = ( B = nil_a ) )
     => ( ( ( A != nil_a )
         => ( ( B != nil_a )
           => ( ( ( hd_a @ A )
                = ( hd_a @ B ) )
              & ( ( tl_a @ A )
                = ( tl_a @ B ) ) ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(15,axiom,
    ! [A: list_a > list_a > $o] : ( listre1221556159list_a @ A @ nil_list_a @ nil_list_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_listrelp_ONil) ).

thf(369,plain,
    ! [A: list_a > list_a > $o] : ( listre1221556159list_a @ A @ nil_list_a @ nil_list_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(259,axiom,
    ! [A: list_a] :
      ( ( A != nil_a )
     => ~ ! [B: a,C: list_a] :
            ( A
           != ( cons_a @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_list_Oexhaust) ).

thf(1500,plain,
    ! [A: list_a] :
      ( ( A != nil_a )
     => ~ ! [B: a,C: list_a] :
            ( A
           != ( cons_a @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(99,axiom,
    ! [A: list_list_a,B: list_list_a] :
      ( ( ( append_list_a @ A @ B )
        = A )
      = ( B = nil_list_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_append__self__conv) ).

thf(723,plain,
    ! [A: list_list_a,B: list_list_a] :
      ( ( ( append_list_a @ A @ B )
        = A )
      = ( B = nil_list_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(123,axiom,
    ! [A: list_list_a,B: list_list_a,C: list_a,D: list_list_a] :
      ( ( ( append_list_a @ A @ B )
        = ( cons_list_a @ C @ D ) )
      = ( ( ( A = nil_list_a )
          & ( B
            = ( cons_list_a @ C @ D ) ) )
        | ? [E: list_list_a] :
            ( ( A
              = ( cons_list_a @ C @ E ) )
            & ( ( append_list_a @ E @ B )
              = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_append__eq__Cons__conv) ).

thf(850,plain,
    ! [A: list_list_a,B: list_list_a,C: list_a,D: list_list_a] :
      ( ( ( append_list_a @ A @ B )
        = ( cons_list_a @ C @ D ) )
      = ( ( ( A = nil_list_a )
          & ( B
            = ( cons_list_a @ C @ D ) ) )
        | ? [E: list_list_a] :
            ( ( A
              = ( cons_list_a @ C @ E ) )
            & ( ( append_list_a @ E @ B )
              = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(304,axiom,
    ! [A: list_a > list_a] :
      ( ( bind_list_a_a @ nil_list_a @ A )
      = nil_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_bind__simps_I1_J) ).

thf(1713,plain,
    ! [A: list_a > list_a] :
      ( ( bind_list_a_a @ nil_list_a @ A )
      = nil_a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(52,axiom,
    ! [A: list_list_a,B: list_a] :
      ( ( butlast_list_a @ ( append_list_a @ A @ ( cons_list_a @ B @ nil_list_a ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_butlast__snoc) ).

thf(486,plain,
    ! [A: list_list_a,B: list_a] :
      ( ( butlast_list_a @ ( append_list_a @ A @ ( cons_list_a @ B @ nil_list_a ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(223,axiom,
    ( listrelp_a_a
    = ( ^ [A: a > a > $o,B: list_a,C: list_a] :
          ( ( ( B = nil_a )
            & ( C = nil_a ) )
          | ? [D: a,E: a,F: list_a,G: list_a] :
              ( ( B
                = ( cons_a @ D @ F ) )
              & ( C
                = ( cons_a @ E @ G ) )
              & ( A @ D @ E )
              & ( listrelp_a_a @ A @ F @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_listrelp_Osimps) ).

thf(1320,plain,
    ( listrelp_a_a
    = ( ^ [A: a > a > $o,B: list_a,C: list_a] :
          ( ( ( B = nil_a )
            & ( C = nil_a ) )
          | ? [D: a,E: a,F: list_a,G: list_a] :
              ( ( B
                = ( cons_a @ D @ F ) )
              & ( C
                = ( cons_a @ E @ G ) )
              & ( A @ D @ E )
              & ( listrelp_a_a @ A @ F @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(4,axiom,
    ! [A: set_list_list_a,B: list_a,C: list_list_a] :
      ( ( bNF_Gr1046450207list_a @ ( bNF_Gr1972240547list_a @ A @ B ) @ C )
      = ( bNF_Gr1046450207list_a @ A @ ( cons_list_a @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_Succ__Shift) ).

thf(337,plain,
    ! [A: set_list_list_a,B: list_a,C: list_list_a] :
      ( ( bNF_Gr1046450207list_a @ ( bNF_Gr1972240547list_a @ A @ B ) @ C )
      = ( bNF_Gr1046450207list_a @ A @ ( cons_list_a @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(139,axiom,
    ! [A: list_list_a,B: list_list_a,C: list_list_a,D: list_list_a] :
      ( ( ( append_list_a @ A @ B )
        = ( append_list_a @ C @ D ) )
      = ( ? [E: list_list_a] :
            ( ( ( A
                = ( append_list_a @ C @ E ) )
              & ( ( append_list_a @ E @ B )
                = D ) )
            | ( ( ( append_list_a @ A @ E )
                = C )
              & ( B
                = ( append_list_a @ E @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_append__eq__append__conv2) ).

thf(923,plain,
    ! [A: list_list_a,B: list_list_a,C: list_list_a,D: list_list_a] :
      ( ( ( append_list_a @ A @ B )
        = ( append_list_a @ C @ D ) )
      = ( ? [E: list_list_a] :
            ( ( ( A
                = ( append_list_a @ C @ E ) )
              & ( ( append_list_a @ E @ B )
                = D ) )
            | ( ( ( append_list_a @ A @ E )
                = C )
              & ( B
                = ( append_list_a @ E @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(272,axiom,
    ! [A: list_a > $o,B: list_a] :
      ( ( A @ nil_a )
     => ( ! [C: a,D: list_a] :
            ( ( A @ D )
           => ( A @ ( append_a @ D @ ( cons_a @ C @ nil_a ) ) ) )
       => ( A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_rev__induct) ).

thf(1565,plain,
    ! [A: list_a > $o,B: list_a] :
      ( ( A @ nil_a )
     => ( ! [C: a,D: list_a] :
            ( ( A @ D )
           => ( A @ ( append_a @ D @ ( cons_a @ C @ nil_a ) ) ) )
       => ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(130,axiom,
    ! [A: list_list_a,B: list_list_a] :
      ( ( ( A = nil_list_a )
        = ( B = nil_list_a ) )
     => ( ( ( A != nil_list_a )
         => ( ( B != nil_list_a )
           => ( ( ( hd_list_a @ A )
                = ( hd_list_a @ B ) )
              & ( ( tl_list_a @ A )
                = ( tl_list_a @ B ) ) ) ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_list_Oexpand) ).

thf(882,plain,
    ! [A: list_list_a,B: list_list_a] :
      ( ( ( A = nil_list_a )
        = ( B = nil_list_a ) )
     => ( ( ( A != nil_list_a )
         => ( ( B != nil_list_a )
           => ( ( ( hd_list_a @ A )
                = ( hd_list_a @ B ) )
              & ( ( tl_list_a @ A )
                = ( tl_list_a @ B ) ) ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(151,axiom,
    ! [A: list_a,B: list_list_a,C: list_a,D: list_list_a] :
      ( ( ( cons_list_a @ A @ B )
        = ( cons_list_a @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_list_Oinject) ).

thf(972,plain,
    ! [A: list_a,B: list_list_a,C: list_a,D: list_list_a] :
      ( ( ( cons_list_a @ A @ B )
        = ( cons_list_a @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(227,axiom,
    ! [A: list_a] :
      ( ( ( rotate1_a @ A )
        = nil_a )
      = ( A = nil_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_rotate1__is__Nil__conv) ).

thf(1331,plain,
    ! [A: list_a] :
      ( ( ( rotate1_a @ A )
        = nil_a )
      = ( A = nil_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(281,axiom,
    ! [A: list_a] :
      ( ( A != nil_a )
     => ( A
        = ( cons_a @ ( hd_a @ A ) @ ( tl_a @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_list_Oexhaust__sel) ).

thf(1606,plain,
    ! [A: list_a] :
      ( ( A != nil_a )
     => ( A
        = ( cons_a @ ( hd_a @ A ) @ ( tl_a @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(45,axiom,
    ! [A: list_a,B: list_list_a] :
      ( ( rotate1_list_a @ ( cons_list_a @ A @ B ) )
      = ( append_list_a @ B @ ( cons_list_a @ A @ nil_list_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_rotate1_Osimps_I2_J) ).

thf(454,plain,
    ! [A: list_a,B: list_list_a] :
      ( ( rotate1_list_a @ ( cons_list_a @ A @ B ) )
      = ( append_list_a @ B @ ( cons_list_a @ A @ nil_list_a ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(176,axiom,
    ! [A: a > a > $o,B: list_a,C: list_a] :
      ( ( listrelp_a_a @ A @ B @ C )
     => ( ( ( B = nil_a )
         => ( C != nil_a ) )
       => ~ ! [D: a,E: a,F: list_a] :
              ( ( B
                = ( cons_a @ D @ F ) )
             => ! [G: list_a] :
                  ( ( C
                    = ( cons_a @ E @ G ) )
                 => ( ( A @ D @ E )
                   => ~ ( listrelp_a_a @ A @ F @ G ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_listrelp_Ocases) ).

thf(1069,plain,
    ! [A: a > a > $o,B: list_a,C: list_a] :
      ( ( listrelp_a_a @ A @ B @ C )
     => ( ( ( B = nil_a )
         => ( C != nil_a ) )
       => ~ ! [D: a,E: a,F: list_a] :
              ( ( B
                = ( cons_a @ D @ F ) )
             => ! [G: list_a] :
                  ( ( C
                    = ( cons_a @ E @ G ) )
                 => ( ( A @ D @ E )
                   => ~ ( listrelp_a_a @ A @ F @ G ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(1906,plain,
    $false,
    inference(e,[status(thm)],[809,1337,1024,1168,1633,1559,941,481,1322,1665,333,628,1855,1211,1158,1406,1692,1486,1750,408,379,1269,1788,385,1756,500,1872,1233,698,1222,1063,340,1127,1095,404,1228,1482,389,1409,1287,1760,719,702,1577,934,1462,1860,1264,542,460,817,559,1704,606,416,1115,1875,638,853,1479,1609,1013,770,789,443,1109,376,623,1682,1828,353,492,1465,1334,646,1020,348,687,877,956,396,428,1600,1242,1215,634,411,1345,1863,678,529,1153,1470,366,1868,512,439,1047,1730,894,746,1355,820,392,1042,952,916,847,625,435,522,1210,1027,757,551,1291,519,1089,615,1328,1121,1111,1540,869,1118,1772,1259,1719,356,1584,489,1155,393,1451,1382,1429,779,371,503,1831,1231,1060,457,1857,360,1695,674,773,926,1086,938,1846,1054,1727,1764,425,1698,1219,1374,975,1007,732,1388,743,1535,1701,1124,875,826,545,1488,572,1707,1371,1312,1733,1058,1239,1092,335,919,681,419,1524,1349,996,1603,451,1722,900,406,509,880,1667,631,726,964,1556,1838,1325,462,932,983,399,1594,959,1643,1015,608,986,1775,922,1562,912,1171,1841,1396,636,1044,473,1034,1662,1166,944,1467,795,548,1134,749,516,342,823,1049,776,525,690,872,1225,414,1753,1267,1716,791,1188,1038,1317,1538,1679,1130,1285,1404,1849,1052,1427,1504,386,1670,446,1272,1617,465,1459,1553,671,1834,891,1448,363,556,495,1654,1010,1575,1646,1385,1476,1508,351,1629,401,1030,667,929,1308,383,684,1444,1442,752,1512,432,1625,1527,422,735,999,620,373,603,1314,1657,506,358,897,664,1710,828,1473,532,728,1236,1261,1582,1597,1299,369,1500,723,850,1713,486,1320,337,923,1565,882,972,1331,1606,454,1069]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ITP100^1 : TPTP v8.2.0. Released v7.5.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n019.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Sat May 18 18:07:24 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.82/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.86/1.12  % [INFO] 	 Parsing done (270ms). 
% 1.86/1.13  % [INFO] 	 Running in sequential loop mode. 
% 2.61/1.34  % [INFO] 	 eprover registered as external prover. 
% 2.61/1.34  % [INFO] 	 cvc4 registered as external prover. 
% 2.61/1.34  % [INFO] 	 Scanning for conjecture ... 
% 2.71/1.44  % [INFO] 	 Found a conjecture (or negated_conjecture) and 355 axioms. Running axiom selection ... 
% 3.06/1.53  % [INFO] 	 Axiom selection finished. Selected 330 axioms (removed 25 axioms). 
% 3.77/1.73  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 4.08/1.75  % [INFO] 	 Type checking passed. 
% 4.08/1.75  % [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 ... 
% 21.24/6.64  % External prover 'e' found a proof!
% 21.24/6.64  % [INFO] 	 Killing All external provers ... 
% 21.24/6.64  % Time passed: 6116ms (effective reasoning time: 5504ms)
% 21.24/6.64  % 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)>
% 21.24/6.64  % Axioms used in derivation (330): fact_277_distinct__adj__append__iff, fact_84_ord_Olexordp__eq_ONil, fact_57_listrelp_Oinducts, fact_180_Cons__eq__append__conv, fact_147_split__Nil__iff, fact_131_append_Oright__neutral, fact_3_list_Oinject, fact_162_Cons__eq__appendI, fact_279_rotate1__hd__tl, fact_182_rev__exhaust, fact_319_successively_Osimps_I2_J, fact_296_successively_Oelims_I3_J, fact_311_tl__Nil, fact_303_distinct__adj__appendD2, fact_83_ord_Olexordp__eq_OCons__eq, fact_322_successively_Oelims_I2_J, fact_264_hd__concat, fact_99_ord_Olexordp__eq_Ocases, fact_170_ord_Olexordp__eq__pref, fact_197_butlast__snoc, fact_10_list_Oinducts, fact_214_append__butlast__last__id, fact_20_induct__list012, fact_52_bind__simps_I1_J, fact_47_map__tailrec__rev_Oelims, fact_198_butlast__snoc, fact_299_successively_Osimps_I1_J, fact_137_self__append__conv2, fact_18_splice_Oinduct, fact_45_list__ex1__simps_I1_J, fact_95_map__tailrec__rev_Osimps_I2_J, fact_169_ord_Olexordp__eq__pref, fact_350_list__induct3, fact_50_ord_Olexordp__eq__simps_I3_J, fact_124_append__same__eq, fact_263_hd__concat, fact_250_concat__conv__foldr, fact_42_insert__Nil, fact_205_rotate1__is__Nil__conv, fact_71_ord_Olexordp__eq__simps_I2_J, fact_225_last__ConsR, fact_2_list_Oinject, fact_291_list_Osel_I3_J, fact_11_list_Oinducts, fact_305_distinct__adj__Nil, fact_139_append__self__conv2, fact_16_list__induct2_H, fact_43_insert__Nil, fact_344_remdups__adj_Osimps_I1_J, fact_163_append_Oleft__neutral, fact_246_empty__Shift, fact_72_ord_Olexordp__eq__simps_I1_J, fact_330_map2__Cons__not__empty, fact_130_append_Oright__neutral, fact_174_splice_Osimps_I1_J, fact_63_listrelp_Osimps, fact_181_rev__exhaust, fact_318_successively_Osimps_I2_J, fact_157_append__eq__appendI, fact_167_eq__Nil__appendI, fact_178_append__eq__Cons__conv, fact_240_maps__simps_I2_J, fact_226_last__ConsR, fact_101_ord_Olexordp__eq_Osimps, fact_314_list_Oexpand, fact_88_listrelp_OCons, fact_79_Collect__mem__eq, fact_64_listrelp_Ocases, fact_190_maps__simps_I1_J, fact_341_remdups__adj__Cons__alt, fact_21_induct__list012, fact_241_maps__simps_I2_J, fact_34_remdups__adj_Oinduct, fact_59_listrelp_Oinducts, fact_36_sorted__wrt_Oinduct, fact_128_append_Oassoc, fact_35_remdups__adj_Oinduct, fact_331_Nil__in__shuffles, fact_306_distinct__adj__Nil, help_If_3_1_If_001t__List__Olist_Itf__a_J_T, fact_96_map__tailrec__rev_Osimps_I2_J, fact_308_distinct__adj__ConsD, fact_237_butlast__append, fact_165_append__Nil, fact_74_ord_Olexordp__eq_Ocong, fact_230_longest__common__suffix, fact_202_SuccI, fact_340_remdups__adj__Nil__iff, fact_125_append__same__eq, fact_106_product__lists_Osimps_I1_J, fact_142_append__self__conv, fact_135_Nil__is__append__conv, fact_100_ord_Olexordp__eq_Ocases, fact_153_append1__eq__conv, fact_86_listrelp_OCons, fact_286_tl__append2, fact_313_Nil__tl, help_If_2_1_If_001t__List__Olist_Itf__a_J_T, fact_70_ord_Olexordp__eq__simps_I2_J, fact_65_listrelp_Ocases, fact_239_maps__simps_I2_J, fact_176_rev__nonempty__induct, fact_69_ord_Olexordp__eq__simps_I4_J, fact_349_list__induct2, fact_347_map2__snoc__snoc, fact_6_list_OdiscI, fact_134_Nil__is__append__conv, fact_60_listrelp_Osimps, fact_199_last__snoc, fact_323_successively_Oelims_I2_J, fact_191_maps__simps_I1_J, fact_27_map__tailrec__rev_Oinduct, fact_320_successively_Oelims_I1_J, fact_337_map2__Cons__if, fact_62_listrelp_Osimps, fact_229_longest__common__suffix, fact_13_neq__Nil__conv, fact_332_shufflesE, fact_112_member__rec_I2_J, fact_196_rotate1_Osimps_I2_J, fact_94_map__tailrec__rev_Osimps_I2_J, fact_56_listrelp_Oinducts, fact_259_hd__append2, fact_12_neq__Nil__conv, fact_175_rev__nonempty__induct, fact_342_remdups__adj_Oelims, fact_206_rotate1__is__Nil__conv, fact_23_shuffles_Oinduct, fact_194_concat__eq__append__conv, fact_268_longest__common__prefix, fact_192_maps__simps_I1_J, fact_97_map__tailrec__rev_Osimps_I2_J, fact_102_ord_Olexordp__eq_Osimps, fact_307_distinct__adj__ConsD, fact_9_list_Oexhaust, fact_129_append_Oassoc, fact_140_self__append__conv, fact_227_last__append, fact_338_remdups__adj__append_H, fact_251_foldr__append, fact_37_sorted__wrt_Oinduct, fact_315_list_Oexpand, help_If_1_1_If_001t__List__Olist_Itf__a_J_T, fact_5_list_Odistinct_I1_J, fact_108_subseqs_Osimps_I1_J, fact_127_append__assoc, fact_265_hd__append, fact_183_rev__induct, fact_81_ord_Olexordp__eq_OCons, fact_317_last__tl, fact_66_listrelp_Ocases, fact_151_i__append__assoc, fact_351_list__induct4, fact_204_SuccD, fact_288_hd__Cons__tl, fact_160_append__Cons, fact_123_same__append__eq, fact_25_not__Cons__self2, fact_266_hd__append, fact_328_distinct__adj__Cons, fact_30_list__nonempty__induct, fact_33_successively_Oinduct, fact_54_bind__simps_I1_J, fact_168_eq__Nil__appendI, fact_334_Cons__in__shuffles__leftI, fact_300_successively_Osimps_I1_J, fact_14_list__induct2_H, fact_98_map__tailrec__rev_Osimps_I1_J, fact_262_list_Osel_I1_J, fact_267_longest__common__prefix, fact_345_remdups__adj_Osimps_I3_J, fact_92_listrelp_ONil, fact_336_Nil__in__shufflesI, fact_224_last__ConsL, fact_171_splice_Osimps_I2_J, fact_143_append__self__conv, fact_41_transpose_Ocases, fact_210_last__appendR, fact_289_list_Ocollapse, fact_343_remdups__adj_Osimps_I2_J, fact_244_concat__eq__appendD, fact_177_append__eq__Cons__conv, fact_220_rotate1_Osimps_I1_J, fact_19_splice_Oinduct, fact_46_map__tailrec__rev_Oelims, fact_258_hd__append2, fact_213_append__butlast__last__id, fact_295_successively_Oelims_I3_J, fact_61_listrelp_Osimps, fact_132_append__is__Nil__conv, fact_179_Cons__eq__append__conv, fact_324_distinct__adj__singleton, fact_245_empty__Shift, fact_302_distinct__adj__appendD1, fact_242_maps__simps_I2_J, fact_310_tl__Nil, fact_346_remdups__adj__append__two, fact_116_splice_Oelims, fact_119_bind__simps_I2_J, fact_24_not__Cons__self2, fact_149_splice__Nil2, fact_285_tl__append2, fact_113_member__rec_I2_J, fact_212_concat__append, fact_133_append__is__Nil__conv, fact_321_successively_Oelims_I1_J, fact_78_Collect__mem__eq, fact_26_map__tailrec__rev_Oinduct, fact_80_ord_Olexordp__eq_OCons, fact_4_list_Odistinct_I1_J, fact_15_list__induct2_H, fact_145_append__Nil2, fact_7_list_OdiscI, fact_121_bind__simps_I2_J, fact_126_append__assoc, fact_215_butlast_Osimps_I1_J, fact_294_list_Osel_I2_J, fact_326_list_Oexhaust__sel, fact_207_last__appendL, fact_283_distinct__adj__Cons__Cons, fact_195_rotate1_Osimps_I2_J, fact_1_i__append__Nil, fact_185_append__eq__Cons, fact_218_snoc__eq__iff__butlast, fact_44_list__ex1__simps_I1_J, fact_152_append1__eq__conv, fact_327_successively__Cons, fact_232_butlast_Osimps_I2_J, fact_223_last__ConsL, fact_201_SuccI, fact_236_concat_Osimps_I2_J, fact_55_bind__simps_I1_J, fact_73_ord_Olexordp__eq__simps_I1_J, fact_155_append__eq__append__conv2, fact_254_list__strict__asc__def, fact_17_list__induct2_H, fact_38_remdups__adj_Ocases, fact_67_listrelp_Ocases, fact_233_concat_Osimps_I1_J, fact_217_snoc__eq__iff__butlast, fact_247_Succ__Shift, fact_91_listrelp_ONil, fact_120_bind__simps_I2_J, fact_280_rotate1__hd__tl, fact_141_self__append__conv, fact_76_mem__Collect__eq, fact_31_list__nonempty__induct, fact_203_SuccD, fact_118_bind__simps_I2_J, fact_103_ord_Olexordp__eq_Oinducts, fact_297_successively_Osimps_I3_J, fact_252_ShiftD, fact_216_butlast_Osimps_I1_J, fact_158_append__eq__appendI, fact_82_ord_Olexordp__eq_OCons__eq, fact_261_list_Osel_I1_J, fact_166_append__Nil, fact_173_splice_Osimps_I1_J, fact_348_length__greater__imp__not__empty, fact_222_last_Osimps, fact_156_append__eq__append__conv2, fact_298_successively_Osimps_I3_J, fact_172_splice_Osimps_I2_J, fact_228_last__append, fact_253_ShiftD, fact_144_append__Nil2, fact_312_Nil__tl, fact_39_remdups__adj_Ocases, fact_208_last__appendL, fact_249_concat__conv__foldr, fact_316_last__tl, fact_32_successively_Oinduct, fact_329_Cons__in__shuffles__iff, fact_29_map__tailrec__rev_Oinduct, fact_104_ord_Olexordp__eq_Oinducts, fact_28_map__tailrec__rev_Oinduct, fact_122_same__append__eq, fact_248_Succ__Shift, fact_209_last__appendR, fact_146_split__Nil__iff, fact_77_mem__Collect__eq, fact_117_splice_Oelims, fact_282_successively__append__iff, fact_184_rev__induct, fact_164_append_Oleft__neutral, fact_87_listrelp_OCons, fact_231_butlast_Osimps_I2_J, fact_304_distinct__adj__appendD2, fact_281_successively__append__iff, fact_8_list_Oexhaust, fact_234_concat_Osimps_I1_J, fact_325_distinct__adj__singleton, fact_219_rotate1_Osimps_I1_J, fact_278_distinct__adj__append__iff, fact_53_bind__simps_I1_J, fact_115_member__rec_I1_J, fact_309_butlast__tl, fact_221_last_Osimps, fact_238_butlast__append, fact_85_ord_Olexordp__eq_ONil, fact_75_ord_Olexordp__eq__refl, fact_58_listrelp_Oinducts, fact_150_i__append__assoc, fact_301_distinct__adj__appendD1, fact_51_ord_Olexordp__eq__simps_I3_J, fact_189_maps__simps_I1_J, fact_335_Cons__in__shuffles__rightI, fact_200_last__snoc, fact_49_map__tailrec__rev_Oelims, fact_68_ord_Olexordp__eq__simps_I4_J, fact_293_list_Osel_I2_J, fact_290_list_Ocollapse, fact_339_remdups__adj__append, fact_136_self__append__conv2, fact_148_splice__Nil2, fact_89_listrelp_OCons, fact_161_Cons__eq__appendI, fact_292_list_Osel_I3_J, fact_90_listrelp_ONil, fact_287_hd__Cons__tl, fact_186_append__eq__Cons, fact_138_append__self__conv2, fact_159_append__Cons, fact_93_listrelp_ONil, fact_48_map__tailrec__rev_Oelims, fact_22_shuffles_Oinduct, fact_333_map2__Cons__Cons, fact_0_i__append__Nil, fact_114_member__rec_I1_J, fact_284_distinct__adj__Cons__Cons
% 21.24/6.64  % No. of inferences in proof: 664
% 21.24/6.64  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6116 ms resp. 5504 ms w/o parsing
% 22.19/6.82  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 22.19/6.82  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------