TSTP Solution File: SCT223_5 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SCT223_5 : TPTP v8.2.0. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n032.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 02:47:32 EDT 2024

% Result   : Theorem 62.89s 35.18s
% Output   : Refutation 63.91s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  161
% Syntax   : Number of formulae    :  278 (  79 unt;  46 typ;   0 def)
%            Number of atoms       : 2650 ( 215 equ;   0 cnn)
%            Maximal formula atoms :  138 (  11 avg)
%            Number of connectives : 10747 ( 164   ~;  33   |;  91   &;10147   @)
%                                         (  36 <=>; 276  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   29 (  12 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :   52 (  52   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   48 (  46 usr;  17 con; 0-6 aty)
%            Number of variables   :  945 (   0   ^ 872   !;  33   ?; 945   :)
%                                         (  40  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(arrow_411405190le_alt_type,type,
    arrow_411405190le_alt: $tType ).

thf(arrow_159774573e_indi_type,type,
    arrow_159774573e_indi: $tType ).

thf(bool_type,type,
    bool: $tType ).

thf(arrow_1958449194le_IIA_type,type,
    arrow_1958449194le_IIA: ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) > $o ).

thf(arrow_1985332922le_Lin_type,type,
    arrow_1985332922le_Lin: fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ).

thf(arrow_610318064e_Prof_type,type,
    arrow_610318064e_Prof: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ).

thf(arrow_1158827142_above_type,type,
    arrow_1158827142_above: ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) > arrow_411405190le_alt > arrow_411405190le_alt > ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).

thf(arrow_319942042_below_type,type,
    arrow_319942042_below: fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) ).

thf(arrow_987702531ctator_type,type,
    arrow_987702531ctator: ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) > arrow_159774573e_indi > $o ).

thf(arrow_276188178_mkbot_type,type,
    arrow_276188178_mkbot: ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) > arrow_411405190le_alt > ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).

thf(arrow_424895264_mktop_type,type,
    arrow_424895264_mktop: ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) > arrow_411405190le_alt > ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).

thf(arrow_2069624013nimity_type,type,
    arrow_2069624013nimity: ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) > $o ).

thf(combb_type,type,
    combb: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ TB ) > ( fun @ TA @ TC ) > ( fun @ TA @ TB ) ) ).

thf(combc_type,type,
    combc: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > TB > ( fun @ TC @ TA ) ) ).

thf(combi_type,type,
    combi: 
      !>[TA: $tType] : ( fun @ TA @ TA ) ).

thf(combk_type,type,
    combk: 
      !>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ TB ) ) ).

thf(combs_type,type,
    combs: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( fun @ TC @ TB ) > ( fun @ TC @ TA ) ) ).

thf(pi_type,type,
    pi: 
      !>[TA: $tType,TB: $tType] : ( ( fun @ TB @ bool ) > ( fun @ TB @ ( fun @ TA @ bool ) ) > ( fun @ ( fun @ TB @ TA ) @ bool ) ) ).

thf(distinct_type,type,
    distinct: 
      !>[TA: $tType] : ( ( list @ TA ) > $o ) ).

thf(insert_type,type,
    insert: 
      !>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).

thf(lexord_type,type,
    lexord: 
      !>[TA: $tType] : ( ( fun @ ( product_prod @ TA @ TA ) @ bool ) > ( fun @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ bool ) ) ).

thf(cons_type,type,
    cons: 
      !>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).

thf(nil_type,type,
    nil: 
      !>[TA: $tType] : ( list @ TA ) ).

thf(list_case_type,type,
    list_case: 
      !>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ ( fun @ ( list @ TA ) @ TB ) ) > ( list @ TA ) > TB ) ).

thf(list_all_type,type,
    list_all: 
      !>[TA: $tType] : ( ( fun @ TA @ bool ) > ( list @ TA ) > $o ) ).

thf(list_ex1_type,type,
    list_ex1: 
      !>[TA: $tType] : ( ( fun @ TA @ bool ) > ( list @ TA ) > $o ) ).

thf(partition_type,type,
    partition: 
      !>[TA: $tType] : ( ( fun @ TA @ bool ) > ( list @ TA ) > ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) ) ).

thf(splice_type,type,
    splice: 
      !>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > ( list @ TA ) ) ).

thf(product_Pair_type,type,
    product_Pair: 
      !>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).

thf(product_curry_type,type,
    product_curry: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ ( product_prod @ TC @ TB ) @ TA ) > TC > TB > TA ) ).

thf(produc1605651328_split_type,type,
    produc1605651328_split: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( product_prod @ TC @ TB ) > TA ) ).

thf(product_prod_rec_type,type,
    product_prod_rec: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( product_prod @ TC @ TB ) > TA ) ).

thf(aa_type,type,
    aa: 
      !>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).

thf(fFalse_type,type,
    fFalse: bool ).

thf(fNot_type,type,
    fNot: fun @ bool @ bool ).

thf(fTrue_type,type,
    fTrue: bool ).

thf(fdisj_type,type,
    fdisj: fun @ bool @ ( fun @ bool @ bool ) ).

thf(fequal_type,type,
    fequal: 
      !>[TA: $tType] : ( TA > ( fun @ TA @ bool ) ) ).

thf(member_type,type,
    member: 
      !>[TA: $tType] : ( TA > ( fun @ TA @ bool ) > $o ) ).

thf(pp_type,type,
    pp: bool > $o ).

thf(f_type,type,
    f: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).

thf(p1_type,type,
    p1: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).

thf(p_type,type,
    p: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).

thf(a_type,type,
    a: arrow_411405190le_alt ).

thf(b_type,type,
    b: arrow_411405190le_alt ).

thf(c_type,type,
    c: arrow_411405190le_alt ).

thf(10,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( splice @ TA @ ( nil @ TA ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_splice_Osimps_I1_J) ).

thf(138,plain,
    ! [TA: $tType,A: list @ TA] :
      ( ( splice @ TA @ ( nil @ TA ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(99,axiom,
    ! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
      ( ! [C: TA] :
          ( ( aa @ TA @ TB @ B @ C )
          = ( aa @ TA @ TB @ A @ C ) )
     => ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ext) ).

thf(550,plain,
    ! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
      ( ! [C: TA] :
          ( ( aa @ TA @ TB @ B @ C )
          = ( aa @ TA @ TB @ A @ C ) )
     => ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(48,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
      ( ( aa @ TA @ TC @ ( combs @ TA @ TB @ TC @ C @ B ) @ A )
      = ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).

thf(301,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
      ( ( aa @ TA @ TC @ ( combs @ TA @ TB @ TC @ C @ B ) @ A )
      = ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(9,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( splice @ TA @ A @ ( nil @ TA ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_splice__Nil2) ).

thf(135,plain,
    ! [TA: $tType,A: list @ TA] :
      ( ( splice @ TA @ A @ ( nil @ TA ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(50,axiom,
    ! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
      ( ( C != B )
     => ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin )
       => ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( arrow_1158827142_above @ A @ C @ B ) @ arrow_1985332922le_Lin ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_above__Lin) ).

thf(308,plain,
    ! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
      ( ( C != B )
     => ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin )
       => ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( arrow_1158827142_above @ A @ C @ B ) @ arrow_1985332922le_Lin ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(33,axiom,
    ! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( fun @ ( list @ TA ) @ TB ),D: TB] :
      ( ( list_case @ TB @ TA @ D @ C @ ( cons @ TA @ B @ A ) )
      = ( aa @ ( list @ TA ) @ TB @ ( aa @ TA @ ( fun @ ( list @ TA ) @ TB ) @ C @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_list_Osimps_I5_J) ).

thf(247,plain,
    ! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( fun @ ( list @ TA ) @ TB ),D: TB] :
      ( ( list_case @ TB @ TA @ D @ C @ ( cons @ TA @ B @ A ) )
      = ( aa @ ( list @ TA ) @ TB @ ( aa @ TA @ ( fun @ ( list @ TA ) @ TB ) @ C @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(41,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
      ~ ! [B: TC,C: TB,D: TA] :
          ( A
         != ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_prod__cases3) ).

thf(269,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
      ~ ! [B: TC,C: TB,D: TA] :
          ( A
         != ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(110,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ bool ),C: fun @ TA @ bool,D: fun @ TA @ TB] :
      ( ( member @ ( fun @ TA @ TB ) @ D @ ( pi @ TA @ TB @ C @ B ) )
     => ( ( member @ TA @ A @ C )
       => ( member @ TB @ ( aa @ TA @ TB @ D @ A ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_Pi__mem) ).

thf(597,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ bool ),C: fun @ TA @ bool,D: fun @ TA @ TB] :
      ( ( member @ ( fun @ TA @ TB ) @ D @ ( pi @ TA @ TB @ C @ B ) )
     => ( ( member @ TA @ A @ C )
       => ( member @ TB @ ( aa @ TA @ TB @ D @ A ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(70,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
      ( ( produc1605651328_split @ TC @ TA @ TB @ C @ ( product_Pair @ TC @ TA @ B @ A ) )
      = ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_internal__split__conv) ).

thf(389,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
      ( ( produc1605651328_split @ TC @ TA @ TB @ C @ ( product_Pair @ TC @ TA @ B @ A ) )
      = ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(22,axiom,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( distinct @ TA @ B )
     => ( distinct @ TA @ ( insert @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_distinct__insert) ).

thf(184,plain,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( distinct @ TA @ B )
     => ( distinct @ TA @ ( insert @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(84,axiom,
    ! [TA: $tType,TB: $tType,A: TB,B: TA] :
      ( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).

thf(504,plain,
    ! [TA: $tType,TB: $tType,A: TB,B: TA] :
      ( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(115,axiom,
    ! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
      ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( arrow_424895264_mktop @ B @ A ) )
    <=> ( ( D != A )
        & ( ( C = A )
         => ( D != C ) )
        & ( ( C != A )
         => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_in__mktop) ).

thf(619,plain,
    ! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
      ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( arrow_424895264_mktop @ B @ A ) )
       => ( ( D != A )
          & ( ( C = A )
           => ( D != C ) )
          & ( ( C != A )
           => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ B ) ) ) )
      & ( ( ( D != A )
          & ( ( C = A )
           => ( D != C ) )
          & ( ( C != A )
           => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ B ) ) )
       => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( arrow_424895264_mktop @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(4,axiom,
    arrow_2069624013nimity @ f,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_u) ).

thf(125,plain,
    arrow_2069624013nimity @ f,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(61,axiom,
    ! [TA: $tType,A: fun @ ( list @ TA ) @ bool,B: list @ TA] :
      ( ( B
       != ( nil @ TA ) )
     => ( ! [C: TA] : ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
       => ( ! [C: TA,D: list @ TA] :
              ( ( D
               != ( nil @ TA ) )
             => ( ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ D ) )
               => ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ ( cons @ TA @ C @ D ) ) ) ) )
         => ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_list__nonempty__induct) ).

thf(357,plain,
    ! [TA: $tType,A: fun @ ( list @ TA ) @ bool,B: list @ TA] :
      ( ( B
       != ( nil @ TA ) )
     => ( ! [C: TA] : ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
       => ( ! [C: TA,D: list @ TA] :
              ( ( D
               != ( nil @ TA ) )
             => ( ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ D ) )
               => ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ ( cons @ TA @ C @ D ) ) ) ) )
         => ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(15,axiom,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( B
     != ( cons @ TA @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_not__Cons__self) ).

thf(157,plain,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( B
     != ( cons @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(102,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
      ( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( product_Pair @ TB @ TA @ B @ A ) ) )
     => ( pp @ ( product_curry @ TB @ TA @ bool @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_curryI) ).

thf(559,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
      ( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( product_Pair @ TB @ TA @ B @ A ) ) )
     => ( pp @ ( product_curry @ TB @ TA @ bool @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(75,axiom,
    ! [A: arrow_159774573e_indi,B: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
      ( ( arrow_987702531ctator @ B @ A )
    <=> ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
          ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C @ arrow_610318064e_Prof )
         => ( ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ C )
            = ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_dictator__def) ).

thf(421,plain,
    ! [A: arrow_159774573e_indi,B: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
      ( ( ( arrow_987702531ctator @ B @ A )
       => ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
            ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C @ arrow_610318064e_Prof )
           => ( ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ C )
              = ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ A ) ) ) )
      & ( ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
            ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C @ arrow_610318064e_Prof )
           => ( ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ C )
              = ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ A ) ) )
       => ( arrow_987702531ctator @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(45,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( pp @ B )
      | ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).

thf(289,plain,
    ! [A: bool,B: bool] :
      ( ~ ( pp @ B )
      | ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(52,axiom,
    member @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ f @ ( pi @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_610318064e_Prof @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_1985332922le_Lin ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_assms_I1_J) ).

thf(321,plain,
    member @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ f @ ( pi @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_610318064e_Prof @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_1985332922le_Lin ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(59,axiom,
    a != b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096a_A_126_061_Ab_096) ).

thf(353,plain,
    a != b,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(73,axiom,
    ! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
      ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( arrow_276188178_mkbot @ B @ A ) )
    <=> ( ( C != A )
        & ( ( D = A )
         => ( D != C ) )
        & ( ( D != A )
         => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_in__mkbot) ).

thf(397,plain,
    ! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
      ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( arrow_276188178_mkbot @ B @ A ) )
       => ( ( C != A )
          & ( ( D = A )
           => ( D != C ) )
          & ( ( D != A )
           => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ B ) ) ) )
      & ( ( ( C != A )
          & ( ( D = A )
           => ( D != C ) )
          & ( ( D != A )
           => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ B ) ) )
       => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( arrow_276188178_mkbot @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(85,axiom,
    ! [A: arrow_159774573e_indi] :
      ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) )
    <=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_iff) ).

thf(507,plain,
    ! [A: arrow_159774573e_indi] :
      ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) )
       => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) ) )
      & ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) )
       => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(86,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
      ( ( ( product_Pair @ TB @ TA @ D @ C )
        = ( product_Pair @ TB @ TA @ B @ A ) )
    <=> ( ( D = B )
        & ( C = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_Pair__eq) ).

thf(512,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
      ( ( ( ( product_Pair @ TB @ TA @ D @ C )
          = ( product_Pair @ TB @ TA @ B @ A ) )
       => ( ( D = B )
          & ( C = A ) ) )
      & ( ( ( D = B )
          & ( C = A ) )
       => ( ( product_Pair @ TB @ TA @ D @ C )
          = ( product_Pair @ TB @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(93,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
      ( ( ( product_Pair @ TB @ TA @ D @ C )
        = ( product_Pair @ TB @ TA @ B @ A ) )
     => ~ ( ( D = B )
         => ( C != A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_Pair__inject) ).

thf(534,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
      ( ( ( product_Pair @ TB @ TA @ D @ C )
        = ( product_Pair @ TB @ TA @ B @ A ) )
     => ~ ( ( D = B )
         => ( C != A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(67,axiom,
    ! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: fun @ TA @ TB,C: fun @ TA @ bool] :
      ( ! [D: TA] :
          ( ( member @ TA @ D @ C )
         => ( member @ TB @ ( aa @ TA @ TB @ B @ D ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ A @ D ) ) )
     => ( member @ ( fun @ TA @ TB ) @ B @ ( pi @ TA @ TB @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Pi__I) ).

thf(380,plain,
    ! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: fun @ TA @ TB,C: fun @ TA @ bool] :
      ( ! [D: TA] :
          ( ( member @ TA @ D @ C )
         => ( member @ TB @ ( aa @ TA @ TB @ B @ D ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ A @ D ) ) )
     => ( member @ ( fun @ TA @ TB ) @ B @ ( pi @ TA @ TB @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(1,conjecture,
    ! [A: arrow_159774573e_indi] :
      ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) @ b ) @ a ) ) @ a ) @ c ) )
    <=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ! [A: arrow_159774573e_indi] :
        ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) @ b ) @ a ) ) @ a ) @ c ) )
      <=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(117,plain,
    ~ ! [A: arrow_159774573e_indi] :
        ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) @ b ) @ a ) ) @ a ) @ c ) )
         => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) )
        & ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) )
         => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) @ b ) @ a ) ) @ a ) @ c ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(56,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool] :
      ( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) ) )
     => ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_prod__induct6) ).

thf(334,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool] :
      ( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) ) )
     => ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(37,axiom,
    ! [TA: $tType,TB: $tType,A: TB,B: fun @ TA @ bool,C: fun @ TB @ bool,D: fun @ TB @ TA] :
      ( ( member @ ( fun @ TB @ TA ) @ D @ ( pi @ TB @ TA @ C @ ( combk @ ( fun @ TA @ bool ) @ TB @ B ) ) )
     => ( ( member @ TB @ A @ C )
       => ( member @ TA @ ( aa @ TB @ TA @ D @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_funcset__mem) ).

thf(260,plain,
    ! [TA: $tType,TB: $tType,A: TB,B: fun @ TA @ bool,C: fun @ TB @ bool,D: fun @ TB @ TA] :
      ( ( member @ ( fun @ TB @ TA ) @ D @ ( pi @ TB @ TA @ C @ ( combk @ ( fun @ TA @ bool ) @ TB @ B ) ) )
     => ( ( member @ TB @ A @ C )
       => ( member @ TA @ ( aa @ TB @ TA @ D @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(16,axiom,
    ! [TA: $tType,A: fun @ TA @ bool] :
      ~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_list__ex1__simps_I1_J) ).

thf(160,plain,
    ! [TA: $tType,A: fun @ TA @ bool] :
      ~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(103,axiom,
    ! [TA: $tType,A: list @ TA,B: TA,C: fun @ TA @ bool] :
      ( ( list_ex1 @ TA @ C @ ( cons @ TA @ B @ A ) )
    <=> ( ( ( pp @ ( aa @ TA @ bool @ C @ B ) )
         => ( list_all @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fdisj @ ( combb @ bool @ bool @ TA @ fNot @ C ) ) @ ( fequal @ TA @ B ) ) @ A ) )
        & ( ~ ( pp @ ( aa @ TA @ bool @ C @ B ) )
         => ( list_ex1 @ TA @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_list__ex1__simps_I2_J) ).

thf(561,plain,
    ! [TA: $tType,A: list @ TA,B: TA,C: fun @ TA @ bool] :
      ( ( ( list_ex1 @ TA @ C @ ( cons @ TA @ B @ A ) )
       => ( ( ( pp @ ( aa @ TA @ bool @ C @ B ) )
           => ( list_all @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fdisj @ ( combb @ bool @ bool @ TA @ fNot @ C ) ) @ ( fequal @ TA @ B ) ) @ A ) )
          & ( ~ ( pp @ ( aa @ TA @ bool @ C @ B ) )
           => ( list_ex1 @ TA @ C @ A ) ) ) )
      & ( ( ( ( pp @ ( aa @ TA @ bool @ C @ B ) )
           => ( list_all @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fdisj @ ( combb @ bool @ bool @ TA @ fNot @ C ) ) @ ( fequal @ TA @ B ) ) @ A ) )
          & ( ~ ( pp @ ( aa @ TA @ bool @ C @ B ) )
           => ( list_ex1 @ TA @ C @ A ) ) )
       => ( list_ex1 @ TA @ C @ ( cons @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(71,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: fun @ ( product_prod @ TB @ TA ) @ TC,B: TB,C: TA] :
      ( ( product_curry @ TB @ TA @ TC @ A @ B @ C )
      = ( aa @ ( product_prod @ TB @ TA ) @ TC @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_curry__def) ).

thf(392,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: fun @ ( product_prod @ TB @ TA ) @ TC,B: TB,C: TA] :
      ( ( product_curry @ TB @ TA @ TC @ A @ B @ C )
      = ( aa @ ( product_prod @ TB @ TA ) @ TC @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(18,axiom,
    ! [TA: $tType,A: list @ TA,B: TA,C: TA] :
      ( ( distinct @ TA @ ( cons @ TA @ C @ ( cons @ TA @ B @ A ) ) )
    <=> ( ( C != B )
        & ( distinct @ TA @ ( cons @ TA @ C @ A ) )
        & ( distinct @ TA @ ( cons @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_distinct__length__2__or__more) ).

thf(165,plain,
    ! [TA: $tType,A: list @ TA,B: TA,C: TA] :
      ( ( ( distinct @ TA @ ( cons @ TA @ C @ ( cons @ TA @ B @ A ) ) )
       => ( ( C != B )
          & ( distinct @ TA @ ( cons @ TA @ C @ A ) )
          & ( distinct @ TA @ ( cons @ TA @ B @ A ) ) ) )
      & ( ( ( C != B )
          & ( distinct @ TA @ ( cons @ TA @ C @ A ) )
          & ( distinct @ TA @ ( cons @ TA @ B @ A ) ) )
       => ( distinct @ TA @ ( cons @ TA @ C @ ( cons @ TA @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(88,axiom,
    ! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
      ( ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
    <=> ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_split__paired__All) ).

thf(522,plain,
    ! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
      ( ( ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
       => ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) )
      & ( ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) )
       => ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(80,axiom,
    ! [A: bool] :
      ( ( pp @ A )
      | ( pp @ ( aa @ bool @ bool @ fNot @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).

thf(461,plain,
    ! [A: bool] :
      ( ( pp @ A )
      | ( pp @ ( aa @ bool @ bool @ fNot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(54,axiom,
    ! [TA: $tType,A: TA] :
      ( ( aa @ TA @ TA @ ( combi @ TA ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).

thf(324,plain,
    ! [TA: $tType,A: TA] :
      ( ( aa @ TA @ TA @ ( combi @ TA ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(60,axiom,
    member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) @ b ) @ a ) ) @ a ) @ c ) @ arrow_610318064e_Prof,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11__096_I_Fp_O_Abelow_A_Ibelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_J_A_058_AProf_096) ).

thf(356,plain,
    member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) @ b ) @ a ) ) @ a ) @ c ) @ arrow_610318064e_Prof,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(11,axiom,
    ! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
      ( ( ( cons @ TA @ D @ C )
        = ( cons @ TA @ B @ A ) )
    <=> ( ( D = B )
        & ( C = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_list_Oinject) ).

thf(141,plain,
    ! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
      ( ( ( ( cons @ TA @ D @ C )
          = ( cons @ TA @ B @ A ) )
       => ( ( D = B )
          & ( C = A ) ) )
      & ( ( ( D = B )
          & ( C = A ) )
       => ( ( cons @ TA @ D @ C )
          = ( cons @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(58,axiom,
    ! [A: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt,F: arrow_411405190le_alt] :
      ( ( F != E )
     => ( ( D != C )
       => ( ( F != C )
         => ( ( E != D )
           => ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
             => ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A @ arrow_610318064e_Prof )
               => ( ! [G: arrow_159774573e_indi] :
                      ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ G ) )
                    <=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ G ) ) )
                 => ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) )
                  <=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23__C2_C) ).

thf(339,plain,
    ! [A: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt,F: arrow_411405190le_alt] :
      ( ( F != E )
     => ( ( D != C )
       => ( ( F != C )
         => ( ( E != D )
           => ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
             => ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A @ arrow_610318064e_Prof )
               => ( ! [G: arrow_159774573e_indi] :
                      ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ G ) )
                       => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ G ) ) )
                      & ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ G ) )
                       => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ G ) ) ) )
                 => ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) )
                     => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) ) )
                    & ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) )
                     => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(26,axiom,
    ! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
      ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
     => ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C )
       => ~ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_Lin__irrefl) ).

thf(193,plain,
    ! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
      ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
     => ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C )
       => ~ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(89,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool] :
      ( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) ) )
     => ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_prod__induct5) ).

thf(526,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool] :
      ( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) ) )
     => ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(107,axiom,
    ! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: list @ TA] :
      ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ ( nil @ TA ) ) @ ( lexord @ TA @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_lexord__Nil__right) ).

thf(590,plain,
    ! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: list @ TA] :
      ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ ( nil @ TA ) ) @ ( lexord @ TA @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(98,axiom,
    ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ c ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) @ b ) @ a ) ) )
  <=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) @ b ) @ a ) ) @ a ) @ c ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_bc) ).

thf(547,plain,
    ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ c ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) @ b ) @ a ) ) )
     => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) @ b ) @ a ) ) @ a ) @ c ) ) ) )
    & ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) @ b ) @ a ) ) @ a ) @ c ) ) )
     => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ c ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) @ b ) @ a ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(32,axiom,
    ! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
      ( ( E != D )
     => ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
       => ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ ( arrow_1158827142_above @ C @ E @ D ) )
        <=> ( ( B != A )
            & ( ( B = D )
             => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ E @ A ) @ C ) )
            & ( ( B != D )
             => ( ( ( A = D )
                 => ( ( B = E )
                    | ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ E ) @ C ) ) )
                & ( ( A != D )
                 => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_in__above) ).

thf(212,plain,
    ! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
      ( ( E != D )
     => ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
       => ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ ( arrow_1158827142_above @ C @ E @ D ) )
           => ( ( B != A )
              & ( ( B = D )
               => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ E @ A ) @ C ) )
              & ( ( B != D )
               => ( ( ( A = D )
                   => ( ( B = E )
                      | ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ E ) @ C ) ) )
                  & ( ( A != D )
                   => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C ) ) ) ) ) )
          & ( ( ( B != A )
              & ( ( B = D )
               => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ E @ A ) @ C ) )
              & ( ( B != D )
               => ( ( ( A = D )
                   => ( ( B = E )
                      | ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ E ) @ C ) ) )
                  & ( ( A != D )
                   => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C ) ) ) ) )
           => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ ( arrow_1158827142_above @ C @ E @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(78,axiom,
    ! [TA: $tType,A: list @ TA,B: fun @ ( product_prod @ TA @ TA ) @ bool] :
      ( ! [C: TA] :
          ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ C ) @ B )
     => ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ A ) @ ( lexord @ TA @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_lexord__irreflexive) ).

thf(457,plain,
    ! [TA: $tType,A: list @ TA,B: fun @ ( product_prod @ TA @ TA ) @ bool] :
      ( ! [C: TA] :
          ~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ C ) @ B )
     => ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ A ) @ ( lexord @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(19,axiom,
    ! [TA: $tType,A: list @ TA,B: TA] :
      ( ( cons @ TA @ B @ A )
     != A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_not__Cons__self2) ).

thf(173,plain,
    ! [TA: $tType,A: list @ TA,B: TA] :
      ( ( cons @ TA @ B @ A )
     != A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(8,axiom,
    arrow_1958449194le_IIA @ f,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_assms_I3_J) ).

thf(134,plain,
    arrow_1958449194le_IIA @ f,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(6,axiom,
    ! [TA: $tType,A: list @ TA,B: TA] :
      ( ( nil @ TA )
     != ( cons @ TA @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_list_Osimps_I2_J) ).

thf(128,plain,
    ! [TA: $tType,A: list @ TA,B: TA] :
      ( ( nil @ TA )
     != ( cons @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(40,axiom,
    ! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: fun @ TB @ TA,C: fun @ TB @ bool] :
      ( ! [D: TB] :
          ( ( member @ TB @ D @ C )
         => ( member @ TA @ ( aa @ TB @ TA @ B @ D ) @ A ) )
     => ( member @ ( fun @ TB @ TA ) @ B @ ( pi @ TB @ TA @ C @ ( combk @ ( fun @ TA @ bool ) @ TB @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_funcsetI) ).

thf(266,plain,
    ! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: fun @ TB @ TA,C: fun @ TB @ bool] :
      ( ! [D: TB] :
          ( ( member @ TB @ D @ C )
         => ( member @ TA @ ( aa @ TB @ TA @ B @ D ) @ A ) )
     => ( member @ ( fun @ TB @ TA ) @ B @ ( pi @ TB @ TA @ C @ ( combk @ ( fun @ TA @ bool ) @ TB @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(51,axiom,
    ! [A: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt,F: arrow_411405190le_alt] :
      ( ( F != E )
     => ( ( D != C )
       => ( ( F != C )
         => ( ( E != D )
           => ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
             => ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A @ arrow_610318064e_Prof )
               => ( ! [G: arrow_159774573e_indi] :
                      ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ G ) )
                    <=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ G ) ) )
                 => ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) )
                   => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22__C1_C) ).

thf(311,plain,
    ! [A: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt,F: arrow_411405190le_alt] :
      ( ( F != E )
     => ( ( D != C )
       => ( ( F != C )
         => ( ( E != D )
           => ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
             => ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A @ arrow_610318064e_Prof )
               => ( ! [G: arrow_159774573e_indi] :
                      ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ G ) )
                       => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ G ) ) )
                      & ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ G ) )
                       => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ G ) ) ) )
                 => ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) )
                   => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(76,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
      ~ ! [B: TD,C: TC,D: TB,E: TA] :
          ( A
         != ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_prod__cases4) ).

thf(430,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
      ~ ! [B: TD,C: TC,D: TB,E: TA] :
          ( A
         != ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(105,axiom,
    ! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: fun @ ( product_prod @ TA @ TB ) @ bool] :
      ( ! [C: TA,D: TB] :
          ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B )
        <=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_pred__equals__eq2) ).

thf(573,plain,
    ! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: fun @ ( product_prod @ TA @ TB ) @ bool] :
      ( ( ! [C: TA,D: TB] :
            ( ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B )
             => ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
            & ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
             => ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: TA,D: TB] :
            ( ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B )
             => ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
            & ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
             => ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(47,axiom,
    ! [A: arrow_159774573e_indi] :
      ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) )
    <=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ c ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_096) ).

thf(296,plain,
    ! [A: arrow_159774573e_indi] :
      ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) )
       => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ c ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) )
      & ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ c ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) )
       => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(12,axiom,
    ! [TA: $tType,A: fun @ TA @ bool] : ( list_all @ TA @ A @ ( nil @ TA ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_list__all__simps_I2_J) ).

thf(149,plain,
    ! [TA: $tType,A: fun @ TA @ bool] : ( list_all @ TA @ A @ ( nil @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(65,axiom,
    ! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
      ( ( C != B )
     => ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin )
       => ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ A ) @ C ) @ B ) @ arrow_1985332922le_Lin ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_below__Lin) ).

thf(375,plain,
    ! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
      ( ( C != B )
     => ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin )
       => ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ A ) @ C ) @ B ) @ arrow_1985332922le_Lin ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(20,axiom,
    ~ ( pp @ fFalse ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).

thf(176,plain,
    ~ ( pp @ fFalse ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(44,axiom,
    ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ p ) )
  <=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ c ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_ab) ).

thf(286,plain,
    ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ p ) )
     => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ c ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) ) )
    & ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ c ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) )
     => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ p ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(46,axiom,
    ! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
      ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
     => ( ( B != A )
       => ( ~ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C )
        <=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ A @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_notin__Lin__iff) ).

thf(291,plain,
    ! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
      ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
     => ( ( B != A )
       => ( ( ~ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C )
           => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ A @ B ) @ C ) )
          & ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ A @ B ) @ C )
           => ~ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(97,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) )
      | ( pp @ B )
      | ( pp @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).

thf(545,plain,
    ! [A: bool,B: bool] :
      ( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) )
      | ( pp @ B )
      | ( pp @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(116,axiom,
    ! [TA: $tType,A: TA,B: TA] :
      ( ~ ( pp @ ( aa @ TA @ bool @ ( fequal @ TA @ B ) @ A ) )
      | ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).

thf(641,plain,
    ! [TA: $tType,A: TA,B: TA] :
      ( ~ ( pp @ ( aa @ TA @ bool @ ( fequal @ TA @ B ) @ A ) )
      | ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(82,axiom,
    ! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
      ( ( E != D )
     => ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
       => ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ C ) @ E ) @ D ) )
        <=> ( ( B != A )
            & ( ( A = E )
             => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ D ) @ C ) )
            & ( ( A != E )
             => ( ( ( B = E )
                 => ( ( A = D )
                    | ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ A ) @ C ) ) )
                & ( ( B != E )
                 => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_in__below) ).

thf(466,plain,
    ! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
      ( ( E != D )
     => ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
       => ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ C ) @ E ) @ D ) )
           => ( ( B != A )
              & ( ( A = E )
               => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ D ) @ C ) )
              & ( ( A != E )
               => ( ( ( B = E )
                   => ( ( A = D )
                      | ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ A ) @ C ) ) )
                  & ( ( B != E )
                   => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C ) ) ) ) ) )
          & ( ( ( B != A )
              & ( ( A = E )
               => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ D ) @ C ) )
              & ( ( A != E )
               => ( ( ( B = E )
                   => ( ( A = D )
                      | ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ A ) @ C ) ) )
                  & ( ( B != E )
                   => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C ) ) ) ) )
           => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ C ) @ E ) @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(95,axiom,
    ! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: fun @ TA @ TB,C: fun @ TA @ bool] :
      ( ! [D: TA] :
          ( ( member @ TA @ D @ C )
         => ( member @ TB @ ( aa @ TA @ TB @ B @ D ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ A @ D ) ) )
     => ( member @ ( fun @ TA @ TB ) @ B @ ( pi @ TA @ TB @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_Pi__I_H) ).

thf(540,plain,
    ! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: fun @ TA @ TB,C: fun @ TA @ bool] :
      ( ! [D: TA] :
          ( ( member @ TA @ D @ C )
         => ( member @ TB @ ( aa @ TA @ TB @ B @ D ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ A @ D ) ) )
     => ( member @ ( fun @ TA @ TB ) @ B @ ( pi @ TA @ TB @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(24,axiom,
    ! [TA: $tType,A: TA] :
      ( ( insert @ TA @ A @ ( nil @ TA ) )
      = ( cons @ TA @ A @ ( nil @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_insert__Nil) ).

thf(187,plain,
    ! [TA: $tType,A: TA] :
      ( ( insert @ TA @ A @ ( nil @ TA ) )
      = ( cons @ TA @ A @ ( nil @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(74,axiom,
    ? [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] : ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_linear__alt) ).

thf(419,plain,
    ? [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] : ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(111,axiom,
    member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) @ b ) @ a ) @ arrow_610318064e_Prof,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10__096_I_Fp_O_Abelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_A_058_AProf_096) ).

thf(599,plain,
    member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) @ b ) @ a ) @ arrow_610318064e_Prof,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(63,axiom,
    ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ c ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) )
  <=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ c ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) @ b ) @ a ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_ac) ).

thf(367,plain,
    ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ c ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) )
     => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ c ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) @ b ) @ a ) ) ) )
    & ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ c ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) @ b ) @ a ) ) )
     => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ c ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(87,axiom,
    ! [TA: $tType,A: fun @ TA @ bool] : ( member @ ( fun @ TA @ TA ) @ ( combi @ TA ) @ ( pi @ TA @ TA @ A @ ( combk @ ( fun @ TA @ bool ) @ TA @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_funcset__id) ).

thf(520,plain,
    ! [TA: $tType,A: fun @ TA @ bool] : ( member @ ( fun @ TA @ TA ) @ ( combi @ TA ) @ ( pi @ TA @ TA @ A @ ( combk @ ( fun @ TA @ bool ) @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(30,axiom,
    member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ p1 @ arrow_610318064e_Prof,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21__096P_H_A_058_AProf_096) ).

thf(209,plain,
    member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ p1 @ arrow_610318064e_Prof,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(3,axiom,
    ! [TA: $tType,A: TA] : ( distinct @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_distinct__singleton) ).

thf(123,plain,
    ! [TA: $tType,A: TA] : ( distinct @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(100,axiom,
    ! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
      ~ ! [B: TB,C: TA] :
          ( A
         != ( product_Pair @ TB @ TA @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_prod_Oexhaust) ).

thf(553,plain,
    ! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
      ~ ! [B: TB,C: TA] :
          ( A
         != ( product_Pair @ TB @ TA @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(17,axiom,
    ! [TA: $tType,A: list @ TA,B: TA] :
      ( ( cons @ TA @ B @ A )
     != ( nil @ TA ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_list_Osimps_I3_J) ).

thf(162,plain,
    ! [TA: $tType,A: list @ TA,B: TA] :
      ( ( cons @ TA @ B @ A )
     != ( nil @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(91,axiom,
    member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ p @ arrow_610318064e_Prof,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096P_A_058_AProf_096) ).

thf(531,plain,
    member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ p @ arrow_610318064e_Prof,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(55,axiom,
    ! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: fun @ TA @ TB,C: fun @ TA @ TB,D: fun @ TA @ bool] :
      ( ! [E: TA] :
          ( ( member @ TA @ E @ D )
         => ( ( aa @ TA @ TB @ C @ E )
            = ( aa @ TA @ TB @ B @ E ) ) )
     => ( ( member @ ( fun @ TA @ TB ) @ C @ ( pi @ TA @ TB @ D @ A ) )
      <=> ( member @ ( fun @ TA @ TB ) @ B @ ( pi @ TA @ TB @ D @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_Pi__cong) ).

thf(327,plain,
    ! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: fun @ TA @ TB,C: fun @ TA @ TB,D: fun @ TA @ bool] :
      ( ! [E: TA] :
          ( ( member @ TA @ E @ D )
         => ( ( aa @ TA @ TB @ C @ E )
            = ( aa @ TA @ TB @ B @ E ) ) )
     => ( ( ( member @ ( fun @ TA @ TB ) @ C @ ( pi @ TA @ TB @ D @ A ) )
         => ( member @ ( fun @ TA @ TB ) @ B @ ( pi @ TA @ TB @ D @ A ) ) )
        & ( ( member @ ( fun @ TA @ TB ) @ B @ ( pi @ TA @ TB @ D @ A ) )
         => ( member @ ( fun @ TA @ TB ) @ C @ ( pi @ TA @ TB @ D @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(39,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
      ~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
          ( A
         != ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_prod__cases6) ).

thf(263,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
      ~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
          ( A
         != ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(28,axiom,
    ! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: list @ TA,C: TA,D: list @ TA,E: TA] :
      ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ E @ D ) @ ( cons @ TA @ C @ B ) ) @ ( lexord @ TA @ A ) )
    <=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ C ) @ A )
        | ( ( E = C )
          & ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ D @ B ) @ ( lexord @ TA @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_lexord__cons__cons) ).

thf(199,plain,
    ! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: list @ TA,C: TA,D: list @ TA,E: TA] :
      ( ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ E @ D ) @ ( cons @ TA @ C @ B ) ) @ ( lexord @ TA @ A ) )
       => ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ C ) @ A )
          | ( ( E = C )
            & ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ D @ B ) @ ( lexord @ TA @ A ) ) ) ) )
      & ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ C ) @ A )
          | ( ( E = C )
            & ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ D @ B ) @ ( lexord @ TA @ A ) ) ) )
       => ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ E @ D ) @ ( cons @ TA @ C @ B ) ) @ ( lexord @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(64,axiom,
    ! [A: arrow_159774573e_indi] :
      ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ c ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) )
    <=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ c ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) @ b ) @ a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_096) ).

thf(370,plain,
    ! [A: arrow_159774573e_indi] :
      ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ c ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) )
       => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ c ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) @ b ) @ a ) ) )
      & ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ c ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) @ b ) @ a ) )
       => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ c ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(81,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ TC] :
      ( ( product_curry @ TB @ TA @ TC @ C @ B @ A )
      = ( aa @ ( product_prod @ TB @ TA ) @ TC @ C @ ( product_Pair @ TB @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_curry__conv) ).

thf(463,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ TC] :
      ( ( product_curry @ TB @ TA @ TC @ C @ B @ A )
      = ( aa @ ( product_prod @ TB @ TA ) @ TC @ C @ ( product_Pair @ TB @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(57,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
      ( ( aa @ TA @ TC @ ( combb @ TB @ TC @ TA @ C @ B ) @ A )
      = ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).

thf(336,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
      ( ( aa @ TA @ TC @ ( combb @ TB @ TC @ TA @ C @ B ) @ A )
      = ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(114,axiom,
    ! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: list @ TA] :
      ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ B ) @ ( lexord @ TA @ A ) )
    <=> ? [C: TA,D: list @ TA] :
          ( B
          = ( cons @ TA @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_lexord__Nil__left) ).

thf(613,plain,
    ! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: list @ TA] :
      ( ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ B ) @ ( lexord @ TA @ A ) )
       => ? [C: TA,D: list @ TA] :
            ( B
            = ( cons @ TA @ C @ D ) ) )
      & ( ? [C: TA,D: list @ TA] :
            ( B
            = ( cons @ TA @ C @ D ) )
       => ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ B ) @ ( lexord @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(14,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ~ ! [B: TA,C: list @ TA] :
            ( A
           != ( cons @ TA @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_list_Oexhaust) ).

thf(154,plain,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ~ ! [B: TA,C: list @ TA] :
            ( A
           != ( cons @ TA @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(112,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: fun @ ( product_prod @ TA @ TA ) @ bool] :
      ( ! [D: TA,E: TA] :
          ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ C )
          | ( D = E )
          | ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ D ) @ C ) )
     => ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ A ) @ ( lexord @ TA @ C ) )
        | ( B = A )
        | ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( lexord @ TA @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_lexord__linear) ).

thf(600,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: fun @ ( product_prod @ TA @ TA ) @ bool] :
      ( ! [D: TA,E: TA] :
          ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ C )
          | ( D = E )
          | ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ D ) @ C ) )
     => ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ A ) @ ( lexord @ TA @ C ) )
        | ( B = A )
        | ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( lexord @ TA @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(69,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
      ( ( aa @ TC @ TB @ ( combc @ TC @ TA @ TB @ C @ B ) @ A )
      = ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).

thf(386,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
      ( ( aa @ TC @ TB @ ( combc @ TC @ TA @ TB @ C @ B ) @ A )
      = ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(109,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ bool ),C: fun @ TA @ bool,D: fun @ TA @ TB] :
      ( ( member @ ( fun @ TA @ TB ) @ D @ ( pi @ TA @ TB @ C @ B ) )
     => ( ~ ( member @ TB @ ( aa @ TA @ TB @ D @ A ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ B @ A ) )
       => ~ ( member @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_PiE) ).

thf(595,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ bool ),C: fun @ TA @ bool,D: fun @ TA @ TB] :
      ( ( member @ ( fun @ TA @ TB ) @ D @ ( pi @ TA @ TB @ C @ B ) )
     => ( ~ ( member @ TB @ ( aa @ TA @ TB @ D @ A ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ B @ A ) )
       => ~ ( member @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(34,axiom,
    ! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
      ( ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
    <=> ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_split__paired__Ex) ).

thf(250,plain,
    ! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
      ( ( ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
       => ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) )
      & ( ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) )
       => ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(101,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
      ~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
          ( A
         != ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_prod__cases5) ).

thf(556,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
      ~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
          ( A
         != ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(94,axiom,
    distinct @ arrow_411405190le_alt @ ( cons @ arrow_411405190le_alt @ a @ ( cons @ arrow_411405190le_alt @ b @ ( cons @ arrow_411405190le_alt @ c @ ( nil @ arrow_411405190le_alt ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_dist) ).

thf(539,plain,
    distinct @ arrow_411405190le_alt @ ( cons @ arrow_411405190le_alt @ a @ ( cons @ arrow_411405190le_alt @ b @ ( cons @ arrow_411405190le_alt @ c @ ( nil @ arrow_411405190le_alt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(106,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool] :
      ( ! [C: TA,D: TB,E: TC,F: TD] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) ) )
     => ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_prod__induct4) ).

thf(588,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool] :
      ( ! [C: TA,D: TB,E: TC,F: TD] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) ) )
     => ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(49,axiom,
    ! [TA: $tType,A: list @ TA,B: TA,C: fun @ TA @ bool] :
      ( ( list_all @ TA @ C @ ( cons @ TA @ B @ A ) )
    <=> ( ( pp @ ( aa @ TA @ bool @ C @ B ) )
        & ( list_all @ TA @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_list__all__simps_I1_J) ).

thf(304,plain,
    ! [TA: $tType,A: list @ TA,B: TA,C: fun @ TA @ bool] :
      ( ( ( list_all @ TA @ C @ ( cons @ TA @ B @ A ) )
       => ( ( pp @ ( aa @ TA @ bool @ C @ B ) )
          & ( list_all @ TA @ C @ A ) ) )
      & ( ( ( pp @ ( aa @ TA @ bool @ C @ B ) )
          & ( list_all @ TA @ C @ A ) )
       => ( list_all @ TA @ C @ ( cons @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(36,axiom,
    ! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
      ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ arrow_1985332922le_Lin )
     => ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( arrow_276188178_mkbot @ B @ A ) @ arrow_1985332922le_Lin ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_mkbot__Lin) ).

thf(258,plain,
    ! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
      ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ arrow_1985332922le_Lin )
     => ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( arrow_276188178_mkbot @ B @ A ) @ arrow_1985332922le_Lin ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(23,axiom,
    pp @ fTrue,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).

thf(186,plain,
    pp @ fTrue,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(104,axiom,
    ! [A: arrow_159774573e_indi] :
      ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ c ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) @ b ) @ a ) )
    <=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) @ b ) @ a ) ) @ a ) @ c ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__096ALL_Ai_O_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_092_060_094esub_062_Aa_J_096) ).

thf(568,plain,
    ! [A: arrow_159774573e_indi] :
      ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ c ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) @ b ) @ a ) )
       => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) @ b ) @ a ) ) @ a ) @ c ) ) )
      & ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) @ b ) @ a ) ) @ a ) @ c ) )
       => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ c ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) @ b ) @ a ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(66,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
      ( ( pp @ ( product_curry @ TB @ TA @ bool @ C @ B @ A ) )
     => ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( product_Pair @ TB @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_curryD) ).

thf(378,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
      ( ( pp @ ( product_curry @ TB @ TA @ bool @ C @ B @ A ) )
     => ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( product_Pair @ TB @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(77,axiom,
    ! [A: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
      ( ( arrow_1958449194le_IIA @ A )
    <=> ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
          ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
         => ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
              ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C @ arrow_610318064e_Prof )
             => ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
                  ( ! [F: arrow_159774573e_indi] :
                      ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) )
                    <=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ F ) ) )
                 => ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) )
                  <=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_IIA__def) ).

thf(433,plain,
    ! [A: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
      ( ( ( arrow_1958449194le_IIA @ A )
       => ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
            ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
           => ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
                ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C @ arrow_610318064e_Prof )
               => ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
                    ( ! [F: arrow_159774573e_indi] :
                        ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) )
                         => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ F ) ) )
                        & ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ F ) )
                         => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) ) ) )
                   => ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) )
                       => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ C ) ) )
                      & ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ C ) )
                       => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) ) ) ) ) ) )
      & ( ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
            ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
           => ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
                ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C @ arrow_610318064e_Prof )
               => ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
                    ( ! [F: arrow_159774573e_indi] :
                        ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) )
                         => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ F ) ) )
                        & ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ F ) )
                         => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) ) ) )
                   => ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) )
                       => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ C ) ) )
                      & ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ C ) )
                       => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) ) ) ) ) )
       => ( arrow_1958449194le_IIA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(29,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ ( product_prod @ TB @ TC ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool] :
      ( ! [C: TA,D: TB,E: TC] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) ) )
     => ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_prod__induct3) ).

thf(207,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ ( product_prod @ TB @ TC ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool] :
      ( ! [C: TA,D: TB,E: TC] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) ) )
     => ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(42,axiom,
    ! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
      ( ( B != A )
     => ? [C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
          ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
          & ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_complete__Lin) ).

thf(272,plain,
    ! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
      ( ( B != A )
     => ? [C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
          ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
          & ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(68,axiom,
    ! [TA: $tType,A: fun @ TA @ bool] :
      ( ( partition @ TA @ A @ ( nil @ TA ) )
      = ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_partition_Osimps_I1_J) ).

thf(383,plain,
    ! [TA: $tType,A: fun @ TA @ bool] :
      ( ( partition @ TA @ A @ ( nil @ TA ) )
      = ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(13,axiom,
    ! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
      ( ( splice @ TA @ ( cons @ TA @ D @ C ) @ ( cons @ TA @ B @ A ) )
      = ( cons @ TA @ D @ ( cons @ TA @ B @ ( splice @ TA @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_splice_Osimps_I3_J) ).

thf(151,plain,
    ! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
      ( ( splice @ TA @ ( cons @ TA @ D @ C ) @ ( cons @ TA @ B @ A ) )
      = ( cons @ TA @ D @ ( cons @ TA @ B @ ( splice @ TA @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(38,axiom,
    member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) @ arrow_610318064e_Prof,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14__096_I_Fp_O_Abelow_A_IP_Ap_J_Ac_Ab_J_A_058_AProf_096) ).

thf(262,plain,
    member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) @ arrow_610318064e_Prof,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(25,axiom,
    ! [TA: $tType,A: list @ TA,B: TA] :
      ( ( splice @ TA @ ( cons @ TA @ B @ A ) @ ( nil @ TA ) )
      = ( cons @ TA @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_splice_Osimps_I2_J) ).

thf(190,plain,
    ! [TA: $tType,A: list @ TA,B: TA] :
      ( ( splice @ TA @ ( cons @ TA @ B @ A ) @ ( nil @ TA ) )
      = ( cons @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(31,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
      ( ( pp @ ( product_curry @ TB @ TA @ bool @ C @ B @ A ) )
     => ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( product_Pair @ TB @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_curryE) ).

thf(210,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
      ( ( pp @ ( product_curry @ TB @ TA @ bool @ C @ B @ A ) )
     => ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( product_Pair @ TB @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(5,axiom,
    ! [TA: $tType] : ( distinct @ TA @ ( nil @ TA ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_distinct_Osimps_I1_J) ).

thf(126,plain,
    ! [TA: $tType] : ( distinct @ TA @ ( nil @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(27,axiom,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( B != A )
      | ( pp @ ( aa @ TA @ bool @ ( fequal @ TA @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).

thf(195,plain,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( B != A )
      | ( pp @ ( aa @ TA @ bool @ ( fequal @ TA @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(92,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( pp @ B )
      | ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).

thf(532,plain,
    ! [A: bool,B: bool] :
      ( ~ ( pp @ B )
      | ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(72,axiom,
    ? [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: arrow_411405190le_alt] : ( distinct @ arrow_411405190le_alt @ ( cons @ arrow_411405190le_alt @ A @ ( cons @ arrow_411405190le_alt @ B @ ( cons @ arrow_411405190le_alt @ C @ ( nil @ arrow_411405190le_alt ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_alt3) ).

thf(395,plain,
    ? [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: arrow_411405190le_alt] : ( distinct @ arrow_411405190le_alt @ ( cons @ arrow_411405190le_alt @ A @ ( cons @ arrow_411405190le_alt @ B @ ( cons @ arrow_411405190le_alt @ C @ ( nil @ arrow_411405190le_alt ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(90,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
      ( ( product_prod_rec @ TC @ TA @ TB @ C @ ( product_Pair @ TC @ TA @ B @ A ) )
      = ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_prod_Orecs) ).

thf(528,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
      ( ( product_prod_rec @ TC @ TA @ TB @ C @ ( product_Pair @ TC @ TA @ B @ A ) )
      = ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(79,axiom,
    ! [A: bool] :
      ( ~ ( pp @ ( aa @ bool @ bool @ fNot @ A ) )
      | ~ ( pp @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).

thf(459,plain,
    ! [A: bool] :
      ( ~ ( pp @ ( aa @ bool @ bool @ fNot @ A ) )
      | ~ ( pp @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(7,axiom,
    ! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ ( list @ TB ) @ TA ),B: TA] :
      ( ( list_case @ TA @ TB @ B @ A @ ( nil @ TB ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_list_Osimps_I4_J) ).

thf(131,plain,
    ! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ ( list @ TB ) @ TA ),B: TA] :
      ( ( list_case @ TA @ TB @ B @ A @ ( nil @ TB ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(21,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
    <=> ? [B: TA,C: list @ TA] :
          ( A
          = ( cons @ TA @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_neq__Nil__conv) ).

thf(178,plain,
    ! [TA: $tType,A: list @ TA] :
      ( ( ( A
         != ( nil @ TA ) )
       => ? [B: TA,C: list @ TA] :
            ( A
            = ( cons @ TA @ B @ C ) ) )
      & ( ? [B: TA,C: list @ TA] :
            ( A
            = ( cons @ TA @ B @ C ) )
       => ( A
         != ( nil @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(43,axiom,
    ! [A: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
      ( ( arrow_2069624013nimity @ A )
    <=> ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
          ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
         => ! [C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
              ( ! [E: arrow_159774573e_indi] : ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ E ) )
             => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_unanimity__def) ).

thf(277,plain,
    ! [A: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
      ( ( ( arrow_2069624013nimity @ A )
       => ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
            ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
           => ! [C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
                ( ! [E: arrow_159774573e_indi] : ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ E ) )
               => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) ) ) )
      & ( ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
            ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
           => ! [C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
                ( ! [E: arrow_159774573e_indi] : ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ E ) )
               => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) ) )
       => ( arrow_2069624013nimity @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(83,axiom,
    ! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
      ( ( B != A )
     => ? [C: arrow_411405190le_alt] : ( distinct @ arrow_411405190le_alt @ ( cons @ arrow_411405190le_alt @ B @ ( cons @ arrow_411405190le_alt @ A @ ( cons @ arrow_411405190le_alt @ C @ ( nil @ arrow_411405190le_alt ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_third__alt) ).

thf(501,plain,
    ! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
      ( ( B != A )
     => ? [C: arrow_411405190le_alt] : ( distinct @ arrow_411405190le_alt @ ( cons @ arrow_411405190le_alt @ B @ ( cons @ arrow_411405190le_alt @ A @ ( cons @ arrow_411405190le_alt @ C @ ( nil @ arrow_411405190le_alt ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(113,axiom,
    ! [A: arrow_159774573e_indi,B: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
      ( ( member @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ ( pi @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_610318064e_Prof @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_1985332922le_Lin ) ) )
     => ( ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
            ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C @ arrow_610318064e_Prof )
           => ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
                ( ( D != E )
               => ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ A ) )
                 => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ C ) ) ) ) )
       => ( arrow_987702531ctator @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_dictatorI) ).

thf(607,plain,
    ! [A: arrow_159774573e_indi,B: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
      ( ( member @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ ( pi @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_610318064e_Prof @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_1985332922le_Lin ) ) )
     => ( ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
            ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C @ arrow_610318064e_Prof )
           => ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
                ( ( D != E )
               => ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ A ) )
                 => ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ C ) ) ) ) )
       => ( arrow_987702531ctator @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(35,axiom,
    ~ ! [A: arrow_411405190le_alt] :
        ~ ( distinct @ arrow_411405190le_alt @ ( cons @ arrow_411405190le_alt @ a @ ( cons @ arrow_411405190le_alt @ b @ ( cons @ arrow_411405190le_alt @ A @ ( nil @ arrow_411405190le_alt ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7__096_B_Bthesis_O_A_I_B_Bc_O_Adistinct_A_091a_M_Ab_M_Ac_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).

thf(254,plain,
    ~ ! [A: arrow_411405190le_alt] :
        ~ ( distinct @ arrow_411405190le_alt @ ( cons @ arrow_411405190le_alt @ a @ ( cons @ arrow_411405190le_alt @ b @ ( cons @ arrow_411405190le_alt @ A @ ( nil @ arrow_411405190le_alt ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(53,axiom,
    ! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
      ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ arrow_1985332922le_Lin )
     => ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( arrow_424895264_mktop @ B @ A ) @ arrow_1985332922le_Lin ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_mktop__Lin) ).

thf(322,plain,
    ! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
      ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ arrow_1985332922le_Lin )
     => ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( arrow_424895264_mktop @ B @ A ) @ arrow_1985332922le_Lin ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(96,axiom,
    ! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
      ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin )
     => ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combk @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_159774573e_indi @ A ) @ arrow_610318064e_Prof ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_const__Lin__Prof) ).

thf(543,plain,
    ! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
      ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin )
     => ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combk @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_159774573e_indi @ A ) @ arrow_610318064e_Prof ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(108,axiom,
    ! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
      ~ ! [B: TB,C: TA] :
          ( A
         != ( product_Pair @ TB @ TA @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_PairE) ).

thf(592,plain,
    ! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
      ~ ! [B: TB,C: TA] :
          ( A
         != ( product_Pair @ TB @ TA @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(62,axiom,
    ! [TA: $tType,A: fun @ TA @ bool,B: TA] :
      ( ( member @ TA @ B @ A )
    <=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__def) ).

thf(364,plain,
    ! [TA: $tType,A: fun @ TA @ bool,B: TA] :
      ( ( ( member @ TA @ B @ A )
       => ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
      & ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
       => ( member @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(644,plain,
    $false,
    inference(e,[status(thm)],[138,550,301,135,308,247,269,597,389,184,504,619,125,357,157,559,421,289,321,353,397,507,512,534,380,117,334,260,160,561,392,165,522,461,324,356,141,339,193,526,590,547,212,457,173,134,128,266,311,430,573,296,149,375,176,286,291,545,641,466,540,187,419,599,367,520,209,123,553,162,531,327,263,199,370,463,336,613,154,600,386,595,250,556,539,588,304,258,186,568,378,433,207,272,383,151,262,190,210,126,195,532,395,528,459,131,178,277,501,607,254,322,543,592,364]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : SCT223_5 : TPTP v8.2.0. Released v6.0.0.
% 0.12/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n032.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Mon May 20 00:00:54 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 1.27/1.17  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.22/1.53  % [INFO] 	 Parsing done (352ms). 
% 2.43/1.54  % [INFO] 	 Running in sequential loop mode. 
% 3.57/2.00  % [INFO] 	 eprover registered as external prover. 
% 3.57/2.01  % [INFO] 	 cvc4 registered as external prover. 
% 3.57/2.01  % [INFO] 	 Scanning for conjecture ... 
% 4.28/2.28  % [INFO] 	 Found a conjecture (or negated_conjecture) and 114 axioms. Running axiom selection ... 
% 4.84/2.44  % [INFO] 	 Axiom selection finished. Selected 114 axioms (removed 0 axioms). 
% 5.88/2.72  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 5.88/2.75  % [INFO] 	 Type checking passed. 
% 5.88/2.76  % [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 ... 
% 62.89/35.17  % External prover 'e' found a proof!
% 62.89/35.17  % [INFO] 	 Killing All external provers ... 
% 62.89/35.17  % Time passed: 34624ms (effective reasoning time: 33625ms)
% 62.89/35.17  % 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)>
% 62.89/35.18  % Axioms used in derivation (114): help_fdisj_1_1_U, fact_42_above__Lin, fact_94_list__all__simps_I2_J, fact_60_alt3, fact_20_assms_I3_J, fact_78_prod__induct3, fact_91_list__ex1__simps_I2_J, fact_64_splice_Osimps_I2_J, help_COMBS_1_1_U, fact_15_ab, fact_18_in__below, fact_1__096a_A_126_061_Ab_096, fact_92_lexord__cons__cons, fact_29_notin__Lin__iff, fact_57_funcsetI, fact_83_internal__split__conv, fact_95_lexord__Nil__right, help_COMBI_1_1_U, fact_23__C2_C, fact_3_iff, fact_70_prod__induct6, fact_62_Pi__cong, fact_50_list_Oexhaust, fact_21__096P_H_A_058_AProf_096, fact_38_in__above, fact_69_list_Osimps_I5_J, fact_9_Pair__eq, fact_11__096_I_Fp_O_Abelow_A_Ibelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_J_A_058_AProf_096, fact_8_split__paired__All, fact_5__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_096, fact_71_prod__cases6, fact_82_prod_Oexhaust, help_fNot_2_1_U, fact_32_distinct_Osimps_I1_J, fact_67_splice__Nil2, help_fNot_1_1_U, fact_73_prod__cases5, fact_39_prod_Orecs, fact_25_const__Lin__Prof, fact_52_funcset__mem, fact_14__096_I_Fp_O_Abelow_A_IP_Ap_J_Ac_Ab_J_A_058_AProf_096, fact_34_split__paired__Ex, fact_44_list_Osimps_I2_J, fact_77_prod__induct4, fact_51_Pi__mem, fact_43_list_Osimps_I3_J, fact_12_in__mkbot, fact_87_curryD, fact_80_pred__equals__eq2, help_COMBB_1_1_U, fact_93_list__all__simps_I1_J, fact_99_partition_Osimps_I1_J, fact_97_lexord__irreflexive, fact_45_distinct__length__2__or__more, fact_98_lexord__linear, fact_89_list__ex1__simps_I1_J, fact_85_curryI, fact_90_list__nonempty__induct, fact_10__096_I_Fp_O_Abelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_A_058_AProf_096, fact_55_Pi__I, fact_41_not__Cons__self, fact_35_distinct__singleton, fact_30_below__Lin, fact_36_complete__Lin, fact_74_prod__cases4, fact_46_unanimity__def, help_fequal_1_1_T, fact_17_bc, fact_24_assms_I1_J, fact_47_IIA__def, fact_22__C1_C, fact_59_distinct__insert, fact_88_curry__def, fact_76_mem__def, fact_4__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_096, fact_2_dist, fact_0__096P_A_058_AProf_096, fact_54_dictator__def, help_fdisj_2_1_U, help_COMBK_1_1_U, fact_58_insert__Nil, fact_7__096_B_Bthesis_O_A_I_B_Bc_O_Adistinct_A_091a_M_Ab_M_Ac_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_31_Pair__inject, fact_84_curry__conv, fact_53_funcset__id, help_COMBC_1_1_U, fact_56_neq__Nil__conv, help_fequal_2_1_T, fact_48_dictatorI, fact_26_mkbot__Lin, fact_68_splice_Osimps_I1_J, fact_79_prod__cases3, fact_16_ac, fact_27_mktop__Lin, help_fdisj_3_1_U, fact_37_list_Oinject, fact_49_PiE, fact_72_prod__induct5, fact_86_curryE, help_pp_1_1_U, fact_40_not__Cons__self2, fact_66_splice_Osimps_I3_J, fact_65_list_Osimps_I4_J, fact_81_PairE, fact_13_in__mktop, fact_75_ext, fact_6__096ALL_Ai_O_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_092_060_094esub_062_Aa_J_096, help_pp_2_1_U, fact_19_u, fact_61_linear__alt, fact_28_Lin__irrefl, fact_33_third__alt, fact_63_Pi__I_H, fact_96_lexord__Nil__left
% 62.89/35.18  % No. of inferences in proof: 232
% 62.89/35.18  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 34624 ms resp. 33625 ms w/o parsing
% 63.91/35.40  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 63.91/35.40  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------