TSTP Solution File: SCT174_5 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SCT174_5 : TPTP v8.2.0. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n020.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 02:47:22 EDT 2024

% Result   : Theorem 71.08s 57.06s
% Output   : Refutation 71.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  112
% Syntax   : Number of formulae    :  197 (  62 unt;  29 typ;   0 def)
%            Number of atoms       : 2063 ( 126 equ;   0 cnn)
%            Maximal formula atoms :   77 (  12 avg)
%            Number of connectives : 8940 (  68   ~;   8   |;  30   &;8640   @)
%                                         (  15 <=>; 179  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   30 (  13 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   31 (  31   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   31 (  29 usr;   8 con; 0-6 aty)
%            Number of variables   :  940 (   0   ^ 885   !;  13   ?; 940   :)
%                                         (  42  !>;   0  ?*;   0  @-;   0  @+)

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

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

thf(in_rel_type,type,
    in_rel: 
      !>[TA: $tType,TB: $tType] : ( ( fun @ ( product_prod @ TB @ TA ) @ bool ) > TB > TA > $o ) ).

thf(refl_type,type,
    refl: 
      !>[TA: $tType] : ( ( fun @ ( product_prod @ TA @ TA ) @ bool ) > $o ) ).

thf(order_215145569der_on_type,type,
    order_215145569der_on: 
      !>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ ( product_prod @ TA @ TA ) @ bool ) > $o ) ).

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

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

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

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

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

thf(product_prod_case_type,type,
    product_prod_case: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( fun @ ( fun @ TC @ ( fun @ TB @ TA ) ) @ ( fun @ ( 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(product_scomp_type,type,
    product_scomp: 
      !>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( fun @ TD @ ( product_prod @ TC @ TB ) ) > ( fun @ TC @ ( fun @ TB @ TA ) ) > ( fun @ TD @ TA ) ) ).

thf(id_on_type,type,
    id_on: 
      !>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ ( product_prod @ TA @ TA ) @ bool ) ) ).

thf(antisym_type,type,
    antisym: 
      !>[TA: $tType] : ( ( fun @ ( product_prod @ TA @ TA ) @ bool ) > $o ) ).

thf(inv_image_type,type,
    inv_image: 
      !>[TA: $tType,TB: $tType] : ( ( fun @ ( product_prod @ TB @ TB ) @ bool ) > ( fun @ TA @ TB ) > ( fun @ ( product_prod @ TA @ TA ) @ bool ) ) ).

thf(irrefl_type,type,
    irrefl: 
      !>[TA: $tType] : ( ( fun @ ( product_prod @ TA @ TA ) @ bool ) > $o ) ).

thf(single_valued_type,type,
    single_valued: 
      !>[TA: $tType,TB: $tType] : ( ( fun @ ( product_prod @ TB @ TA ) @ bool ) > $o ) ).

thf(total_on_type,type,
    total_on: 
      !>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ ( product_prod @ TA @ TA ) @ bool ) > $o ) ).

thf(trans_type,type,
    trans: 
      !>[TA: $tType] : ( ( fun @ ( product_prod @ TA @ TA ) @ bool ) > $o ) ).

thf(lex_prod_type,type,
    lex_prod: 
      !>[TA: $tType,TB: $tType] : ( ( fun @ ( product_prod @ TB @ TB ) @ bool ) > ( fun @ ( product_prod @ TA @ TA ) @ bool ) > ( fun @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ bool ) ) ).

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

thf(fFalse_type,type,
    fFalse: bool ).

thf(fTrue_type,type,
    fTrue: bool ).

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

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

thf(l_type,type,
    l: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ).

thf(x_type,type,
    x: arrow_411405190le_alt ).

thf(y_type,type,
    y: arrow_411405190le_alt ).

thf(17,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
         != ( aa @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_prod__cases4) ).

thf(142,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
         != ( aa @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(23,axiom,
    ! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
      ~ ! [B: TB,C: TA] :
          ( A
         != ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_prod_Oexhaust) ).

thf(157,plain,
    ! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
      ~ ! [B: TB,C: TA] :
          ( A
         != ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(26,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ TC] :
      ( ( aa @ TA @ TC @ ( aa @ TB @ ( fun @ TA @ TC ) @ ( product_curry @ TB @ TA @ TC @ C ) @ B ) @ A )
      = ( aa @ ( product_prod @ TB @ TA ) @ TC @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_curry__conv) ).

thf(166,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ TC] :
      ( ( aa @ TA @ TC @ ( aa @ TB @ ( fun @ TA @ TC ) @ ( product_curry @ TB @ TA @ TC @ C ) @ B ) @ A )
      = ( aa @ ( product_prod @ TB @ TA ) @ TC @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(61,axiom,
    ! [TA: $tType,A: fun @ TA @ bool] : ( trans @ TA @ ( id_on @ TA @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_trans__Id__on) ).

thf(286,plain,
    ! [TA: $tType,A: fun @ TA @ bool] : ( trans @ TA @ ( id_on @ TA @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(64,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( product_prod @ TB @ TC )] :
      ( ( product_scomp @ TA @ TB @ TC @ ( product_prod @ TB @ TC ) @ A @ ( product_Pair @ TB @ TC ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_scomp__Pair) ).

thf(299,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( product_prod @ TB @ TC )] :
      ( ( product_scomp @ TA @ TB @ TC @ ( product_prod @ TB @ TC ) @ A @ ( product_Pair @ TB @ TC ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(20,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 @ ( aa @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( aa @ TB @ ( fun @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ D ) @ ( aa @ ( product_prod @ TD @ TE ) @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TD @ TE ) @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) ) @ E ) @ ( aa @ TE @ ( product_prod @ TD @ TE ) @ ( aa @ TD @ ( fun @ TE @ ( product_prod @ TD @ TE ) ) @ ( 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_17_prod__induct5) ).

thf(150,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 @ ( aa @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( aa @ TB @ ( fun @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ D ) @ ( aa @ ( product_prod @ TD @ TE ) @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TD @ TE ) @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) ) @ E ) @ ( aa @ TE @ ( product_prod @ TD @ TE ) @ ( aa @ TD @ ( fun @ TE @ ( product_prod @ TD @ TE ) ) @ ( 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)],[20]) ).

thf(73,axiom,
    ! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool] :
      ( ! [B: TA,C: TB] :
          ( ( member @ ( product_prod @ TA @ TB ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ B ) @ C ) @ A )
         => ! [D: TB] :
              ( ( member @ ( product_prod @ TA @ TB ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ B ) @ D ) @ A )
             => ( C = D ) ) )
     => ( single_valued @ TA @ TB @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_single__valuedI) ).

thf(333,plain,
    ! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool] :
      ( ! [B: TA,C: TB] :
          ( ( member @ ( product_prod @ TA @ TB ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ B ) @ C ) @ A )
         => ! [D: TB] :
              ( ( member @ ( product_prod @ TA @ TB ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ B ) @ D ) @ A )
             => ( C = D ) ) )
     => ( single_valued @ TA @ TB @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(79,axiom,
    x != y,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(352,plain,
    x != y,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(29,axiom,
    ! [TA: $tType,TB: $tType,A: fun @ TB @ TA,B: fun @ ( product_prod @ TA @ TA ) @ bool,C: TB,D: TB] :
      ( ( member @ ( product_prod @ TB @ TB ) @ ( aa @ TB @ ( product_prod @ TB @ TB ) @ ( aa @ TB @ ( fun @ TB @ ( product_prod @ TB @ TB ) ) @ ( product_Pair @ TB @ TB ) @ D ) @ C ) @ ( inv_image @ TA @ TB @ B @ A ) )
    <=> ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ ( aa @ TB @ TA @ A @ D ) ) @ ( aa @ TB @ TA @ A @ C ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_in__inv__image) ).

thf(174,plain,
    ! [TA: $tType,TB: $tType,A: fun @ TB @ TA,B: fun @ ( product_prod @ TA @ TA ) @ bool,C: TB,D: TB] :
      ( ( ( member @ ( product_prod @ TB @ TB ) @ ( aa @ TB @ ( product_prod @ TB @ TB ) @ ( aa @ TB @ ( fun @ TB @ ( product_prod @ TB @ TB ) ) @ ( product_Pair @ TB @ TB ) @ D ) @ C ) @ ( inv_image @ TA @ TB @ B @ A ) )
       => ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ ( aa @ TB @ TA @ A @ D ) ) @ ( aa @ TB @ TA @ A @ C ) ) @ B ) )
      & ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ ( aa @ TB @ TA @ A @ D ) ) @ ( aa @ TB @ TA @ A @ C ) ) @ B )
       => ( member @ ( product_prod @ TB @ TB ) @ ( aa @ TB @ ( product_prod @ TB @ TB ) @ ( aa @ TB @ ( fun @ TB @ ( product_prod @ TB @ TB ) ) @ ( product_Pair @ TB @ TB ) @ D ) @ C ) @ ( inv_image @ TA @ TB @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(62,axiom,
    ! [TA: $tType,A: fun @ TA @ bool,B: TA,C: TA] :
      ( ( C = B )
     => ( ( member @ TA @ C @ A )
       => ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ B ) @ ( id_on @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_Id__on__eqI) ).

thf(288,plain,
    ! [TA: $tType,A: fun @ TA @ bool,B: TA,C: TA] :
      ( ( C = B )
     => ( ( member @ TA @ C @ A )
       => ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ B ) @ ( id_on @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(70,axiom,
    ! [TA: $tType,A: TA,B: TA,C: fun @ ( product_prod @ TA @ TA ) @ bool] :
      ( ( antisym @ TA @ C )
     => ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ A ) @ C )
       => ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ A ) @ B ) @ C )
         => ( B = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_antisymD) ).

thf(320,plain,
    ! [TA: $tType,A: TA,B: TA,C: fun @ ( product_prod @ TA @ TA ) @ bool] :
      ( ( antisym @ TA @ C )
     => ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ A ) @ C )
       => ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ A ) @ B ) @ C )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(35,axiom,
    ! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool] :
      ( ( order_215145569der_on @ TA @ B @ A )
    <=> ( ( trans @ TA @ A )
        & ( irrefl @ TA @ A )
        & ( total_on @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_strict__linear__order__on__def) ).

thf(189,plain,
    ! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool] :
      ( ( ( order_215145569der_on @ TA @ B @ A )
       => ( ( trans @ TA @ A )
          & ( irrefl @ TA @ A )
          & ( total_on @ TA @ B @ A ) ) )
      & ( ( ( trans @ TA @ A )
          & ( irrefl @ TA @ A )
          & ( total_on @ TA @ B @ A ) )
       => ( order_215145569der_on @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(21,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
         != ( aa @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ ( aa @ TF @ ( fun @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) ) @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B ) @ ( aa @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( aa @ TE @ ( fun @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ E ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ F ) @ G ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_prod__cases6) ).

thf(152,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
         != ( aa @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ ( aa @ TF @ ( fun @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) ) @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B ) @ ( aa @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( aa @ TE @ ( fun @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ E ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ F ) @ G ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(31,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
      ( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( product_curry @ TB @ TA @ bool @ C ) @ B ) @ A ) )
     => ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_curryE) ).

thf(179,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
      ( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( product_curry @ TB @ TA @ bool @ C ) @ B ) @ A ) )
     => ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(40,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ bool )] :
      ( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ B ) @ A ) )
     => ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_prod__caseI) ).

thf(211,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ bool )] :
      ( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ B ) @ A ) )
     => ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(50,axiom,
    ! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: product_prod @ TA @ TB] :
      ( ! [C: TA,D: TB] :
          ( ( B
            = ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) )
         => ( pp @ ( aa @ TB @ bool @ ( aa @ TA @ ( fun @ TB @ bool ) @ A @ C ) @ D ) ) )
     => ( pp @ ( aa @ ( product_prod @ TA @ TB ) @ bool @ ( aa @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( product_prod_case @ TA @ TB @ bool ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_splitI2) ).

thf(238,plain,
    ! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: product_prod @ TA @ TB] :
      ( ! [C: TA,D: TB] :
          ( ( B
            = ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ C ) @ D ) )
         => ( pp @ ( aa @ TB @ bool @ ( aa @ TA @ ( fun @ TB @ bool ) @ A @ C ) @ D ) ) )
     => ( pp @ ( aa @ ( product_prod @ TA @ TB ) @ bool @ ( aa @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ bool ) @ ( product_prod_case @ TA @ TB @ bool ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(19,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
         != ( aa @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( aa @ TE @ ( fun @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ D ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ E ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_prod__cases5) ).

thf(147,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
         != ( aa @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( aa @ TE @ ( fun @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ D ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ E ) @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(59,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA,B: fun @ TC @ ( fun @ TB @ TD ),C: fun @ TA @ ( product_prod @ TC @ TB )] :
      ( ( aa @ TA @ TD @ ( product_scomp @ TA @ TC @ TB @ TD @ C @ B ) @ A )
      = ( aa @ ( product_prod @ TC @ TB ) @ TD @ ( aa @ ( fun @ TC @ ( fun @ TB @ TD ) ) @ ( fun @ ( product_prod @ TC @ TB ) @ TD ) @ ( product_prod_case @ TC @ TB @ TD ) @ B ) @ ( aa @ TA @ ( product_prod @ TC @ TB ) @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_scomp__apply) ).

thf(280,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA,B: fun @ TC @ ( fun @ TB @ TD ),C: fun @ TA @ ( product_prod @ TC @ TB )] :
      ( ( aa @ TA @ TD @ ( product_scomp @ TA @ TC @ TB @ TD @ C @ B ) @ A )
      = ( aa @ ( product_prod @ TC @ TB ) @ TD @ ( aa @ ( fun @ TC @ ( fun @ TB @ TD ) ) @ ( fun @ ( product_prod @ TC @ TB ) @ TD ) @ ( product_prod_case @ TC @ TB @ TD ) @ B ) @ ( aa @ TA @ ( product_prod @ TC @ TB ) @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(44,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( fun @ TB @ TC ),B: product_prod @ TA @ TB,C: product_prod @ TA @ TB] :
      ( ( C = B )
     => ( ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ A ) @ C )
        = ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_split__weak__cong) ).

thf(221,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( fun @ TB @ TC ),B: product_prod @ TA @ TB,C: product_prod @ TA @ TB] :
      ( ( C = B )
     => ( ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ A ) @ C )
        = ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(10,axiom,
    ! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ ( product_prod @ TA @ TB ) @ bool] :
      ( ( in_rel @ TA @ TB @ C @ B @ A )
    <=> ( member @ ( product_prod @ TA @ TB ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ B ) @ A ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_in__rel__def) ).

thf(116,plain,
    ! [TA: $tType,TB: $tType,A: TB,B: TA,C: fun @ ( product_prod @ TA @ TB ) @ bool] :
      ( ( ( in_rel @ TA @ TB @ C @ B @ A )
       => ( member @ ( product_prod @ TA @ TB ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ B ) @ A ) @ C ) )
      & ( ( member @ ( product_prod @ TA @ TB ) @ ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ B ) @ A ) @ C )
       => ( in_rel @ TA @ TB @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(63,axiom,
    ! [TA: $tType,A: fun @ TA @ bool,B: TA,C: TA] :
      ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ B ) @ ( id_on @ TA @ A ) )
    <=> ( ( C = B )
        & ( member @ TA @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_Id__on__iff) ).

thf(292,plain,
    ! [TA: $tType,A: fun @ TA @ bool,B: TA,C: TA] :
      ( ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ B ) @ ( id_on @ TA @ A ) )
       => ( ( C = B )
          & ( member @ TA @ C @ A ) ) )
      & ( ( ( C = B )
          & ( member @ TA @ C @ A ) )
       => ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ B ) @ ( id_on @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(1,conjecture,
    $false,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_6) ).

thf(2,negated_conjecture,
    ~ $false,
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(85,plain,
    ~ $false,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(65,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( fun @ TC @ TB ),B: TA] :
      ( ( product_scomp @ TC @ TA @ TC @ TB @ ( aa @ TA @ ( fun @ TC @ ( product_prod @ TA @ TC ) ) @ ( product_Pair @ TA @ TC ) @ B ) @ A )
      = ( aa @ TA @ ( fun @ TC @ TB ) @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_Pair__scomp) ).

thf(302,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( fun @ TC @ TB ),B: TA] :
      ( ( product_scomp @ TC @ TA @ TC @ TB @ ( aa @ TA @ ( fun @ TC @ ( product_prod @ TA @ TC ) ) @ ( product_Pair @ TA @ TC ) @ B ) @ A )
      = ( aa @ TA @ ( fun @ TC @ TB ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(77,axiom,
    ~ ( pp @ fFalse ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).

thf(349,plain,
    ~ ( pp @ fFalse ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(24,axiom,
    ! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
      ~ ! [B: TB,C: TA] :
          ( A
         != ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_PairE) ).

thf(160,plain,
    ! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
      ~ ! [B: TB,C: TA] :
          ( A
         != ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(15,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
      ~ ! [B: TC,C: TB,D: TA] :
          ( A
         != ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ B ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_prod__cases3) ).

thf(137,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
      ~ ! [B: TC,C: TB,D: TA] :
          ( A
         != ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) ) @ B ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(47,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
      ( ( aa @ ( product_prod @ TC @ TA ) @ TB @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ TB ) @ ( product_prod_case @ TC @ TA @ TB ) @ C ) @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( 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_44_prod_Osimps_I2_J) ).

thf(229,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
      ( ( aa @ ( product_prod @ TC @ TA ) @ TB @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ TB ) @ ( product_prod_case @ TC @ TA @ TB ) @ C ) @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( 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)],[47]) ).

thf(37,axiom,
    ! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
    ? [B: TB,C: TA] :
      ( A
      = ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_surj__pair) ).

thf(197,plain,
    ! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
    ? [B: TB,C: TA] :
      ( A
      = ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(81,axiom,
    ! [A: arrow_411405190le_alt] :
      ~ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ A ) @ A ) @ l ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).

thf(356,plain,
    ! [A: arrow_411405190le_alt] :
      ~ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ A ) @ A ) @ l ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(27,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
      ( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) )
     => ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( product_curry @ TB @ TA @ bool @ C ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_curryI) ).

thf(169,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
      ( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) )
     => ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( product_curry @ TB @ TA @ bool @ C ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(8,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
      ( ( ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C )
        = ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) )
     => ~ ( ( D = B )
         => ( C != A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_Pair__inject) ).

thf(109,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
      ( ( ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C )
        = ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) )
     => ~ ( ( D = B )
         => ( C != A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(45,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ bool )] :
      ( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) )
     => ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_splitD) ).

thf(225,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ bool )] :
      ( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) )
     => ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(14,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
      ( ( product_prod_rec @ TC @ TA @ TB @ C @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( 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_11_prod_Orecs) ).

thf(134,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
      ( ( product_prod_rec @ TC @ TA @ TB @ C @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( 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)],[14]) ).

thf(75,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_72_ext) ).

thf(343,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)],[75]) ).

thf(7,axiom,
    ! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
      ( ! [B: TA,C: TA,D: TA] :
          ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ C ) @ A )
         => ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ D ) @ A )
           => ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ D ) @ A ) ) )
     => ( trans @ TA @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_transI) ).

thf(105,plain,
    ! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
      ( ! [B: TA,C: TA,D: TA] :
          ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ C ) @ A )
         => ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ D ) @ A )
           => ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ D ) @ A ) ) )
     => ( trans @ TA @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(57,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ TB,B: fun @ TA @ ( fun @ TB @ TC ),C: fun @ TA @ ( fun @ TB @ TC ),D: product_prod @ TA @ TB] :
      ( ! [E: TA,F: TB] :
          ( ( ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ E ) @ F )
            = D )
         => ( ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ E ) @ F )
            = ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ B @ E ) @ F ) ) )
     => ( ( A = D )
       => ( ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ C ) @ A )
          = ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_split__cong) ).

thf(266,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ TB,B: fun @ TA @ ( fun @ TB @ TC ),C: fun @ TA @ ( fun @ TB @ TC ),D: product_prod @ TA @ TB] :
      ( ! [E: TA,F: TB] :
          ( ( ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ E ) @ F )
            = D )
         => ( ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ E ) @ F )
            = ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ B @ E ) @ F ) ) )
     => ( ( A = D )
       => ( ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ C ) @ A )
          = ( aa @ ( product_prod @ TA @ TB ) @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(68,axiom,
    ! [TA: $tType,A: fun @ TA @ bool] : ( antisym @ TA @ ( id_on @ TA @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_antisym__Id__on) ).

thf(311,plain,
    ! [TA: $tType,A: fun @ TA @ bool] : ( antisym @ TA @ ( id_on @ TA @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(69,axiom,
    ! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
      ( ( antisym @ TA @ A )
    <=> ! [B: TA,C: TA] :
          ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ C ) @ A )
         => ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ B ) @ A )
           => ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_antisym__def) ).

thf(313,plain,
    ! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
      ( ( ( antisym @ TA @ A )
       => ! [B: TA,C: TA] :
            ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ C ) @ A )
           => ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ B ) @ A )
             => ( B = C ) ) ) )
      & ( ! [B: TA,C: TA] :
            ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ C ) @ A )
           => ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ B ) @ A )
             => ( B = C ) ) )
       => ( antisym @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(32,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
      ( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( product_curry @ TB @ TA @ bool @ C ) @ B ) @ A ) )
     => ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_curryD) ).

thf(181,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
      ( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( product_curry @ TB @ TA @ bool @ C ) @ B ) @ A ) )
     => ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(3,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 @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_split__paired__All) ).

thf(86,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 @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) ) )
      & ( ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( 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)],[3]) ).

thf(83,axiom,
    member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ y ) @ x ) @ l,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).

thf(362,plain,
    member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ y ) @ x ) @ l,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(5,axiom,
    ! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
      ( ( trans @ TA @ A )
    <=> ! [B: TA,C: TA,D: TA] :
          ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ C ) @ A )
         => ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ D ) @ A )
           => ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ D ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_trans__def) ).

thf(98,plain,
    ! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
      ( ( ( trans @ TA @ A )
       => ! [B: TA,C: TA,D: TA] :
            ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ C ) @ A )
           => ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ D ) @ A )
             => ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ D ) @ A ) ) ) )
      & ( ! [B: TA,C: TA,D: TA] :
            ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ C ) @ A )
           => ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ D ) @ A )
             => ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ D ) @ A ) ) )
       => ( trans @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(6,axiom,
    ! [TA: $tType,A: TA,B: TA,C: TA,D: fun @ ( product_prod @ TA @ TA ) @ bool] :
      ( ( trans @ TA @ D )
     => ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ B ) @ D )
       => ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ A ) @ D )
         => ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_transD) ).

thf(103,plain,
    ! [TA: $tType,A: TA,B: TA,C: TA,D: fun @ ( product_prod @ TA @ TA ) @ bool] :
      ( ( trans @ TA @ D )
     => ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ B ) @ D )
       => ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ A ) @ D )
         => ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(71,axiom,
    ! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
      ( ( single_valued @ TB @ TA @ A )
    <=> ! [B: TB,C: TA] :
          ( ( member @ ( product_prod @ TB @ TA ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) @ A )
         => ! [D: TA] :
              ( ( member @ ( product_prod @ TB @ TA ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ D ) @ A )
             => ( C = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_single__valued__def) ).

thf(323,plain,
    ! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
      ( ( ( single_valued @ TB @ TA @ A )
       => ! [B: TB,C: TA] :
            ( ( member @ ( product_prod @ TB @ TA ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) @ A )
           => ! [D: TA] :
                ( ( member @ ( product_prod @ TB @ TA ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ D ) @ A )
               => ( C = D ) ) ) )
      & ( ! [B: TB,C: TA] :
            ( ( member @ ( product_prod @ TB @ TA ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) @ A )
           => ! [D: TA] :
                ( ( member @ ( product_prod @ TB @ TA ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ D ) @ A )
               => ( C = D ) ) )
       => ( single_valued @ TB @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(16,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 @ ( aa @ ( product_prod @ TB @ TC ) @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ TC ) @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) ) @ C ) @ ( aa @ TC @ ( product_prod @ TB @ TC ) @ ( aa @ TB @ ( fun @ TC @ ( product_prod @ TB @ TC ) ) @ ( 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_13_prod__induct3) ).

thf(140,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 @ ( aa @ ( product_prod @ TB @ TC ) @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ TC ) @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) ) @ C ) @ ( aa @ TC @ ( product_prod @ TB @ TC ) @ ( aa @ TB @ ( fun @ TC @ ( product_prod @ TB @ TC ) ) @ ( 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)],[16]) ).

thf(41,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ ( fun @ TC @ bool ) ),D: TC] :
      ( ( member @ TC @ D @ ( aa @ TA @ ( fun @ TC @ bool ) @ ( aa @ TB @ ( fun @ TA @ ( fun @ TC @ bool ) ) @ C @ B ) @ A ) )
     => ( member @ TC @ D @ ( aa @ ( product_prod @ TB @ TA ) @ ( fun @ TC @ bool ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ ( fun @ TC @ bool ) ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ ( fun @ TC @ bool ) ) @ ( product_prod_case @ TB @ TA @ ( fun @ TC @ bool ) ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_mem__splitI) ).

thf(213,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ ( fun @ TC @ bool ) ),D: TC] :
      ( ( member @ TC @ D @ ( aa @ TA @ ( fun @ TC @ bool ) @ ( aa @ TB @ ( fun @ TA @ ( fun @ TC @ bool ) ) @ C @ B ) @ A ) )
     => ( member @ TC @ D @ ( aa @ ( product_prod @ TB @ TA ) @ ( fun @ TC @ bool ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ ( fun @ TC @ bool ) ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ ( fun @ TC @ bool ) ) @ ( product_prod_case @ TB @ TA @ ( fun @ TC @ bool ) ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(22,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 @ ( aa @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( aa @ TB @ ( fun @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ D ) @ ( aa @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ E ) @ ( aa @ ( product_prod @ TE @ TF ) @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TE @ TF ) @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) ) @ F ) @ ( aa @ TF @ ( product_prod @ TE @ TF ) @ ( aa @ TE @ ( fun @ TF @ ( product_prod @ TE @ TF ) ) @ ( 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_19_prod__induct6) ).

thf(155,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 @ ( aa @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( aa @ TB @ ( fun @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ D ) @ ( aa @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( aa @ TC @ ( fun @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ E ) @ ( aa @ ( product_prod @ TE @ TF ) @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ ( aa @ TD @ ( fun @ ( product_prod @ TE @ TF ) @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) ) @ F ) @ ( aa @ TF @ ( product_prod @ TE @ TF ) @ ( aa @ TE @ ( fun @ TF @ ( product_prod @ TE @ TF ) ) @ ( 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)],[22]) ).

thf(72,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: TA,C: TB,D: fun @ ( product_prod @ TB @ TA ) @ bool] :
      ( ( single_valued @ TB @ TA @ D )
     => ( ( member @ ( product_prod @ TB @ TA ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ C ) @ B ) @ D )
       => ( ( member @ ( product_prod @ TB @ TA ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ C ) @ A ) @ D )
         => ( B = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_single__valuedD) ).

thf(330,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: TA,C: TB,D: fun @ ( product_prod @ TB @ TA ) @ bool] :
      ( ( single_valued @ TB @ TA @ D )
     => ( ( member @ ( product_prod @ TB @ TA ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ C ) @ B ) @ D )
       => ( ( member @ ( product_prod @ TB @ TA ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ C ) @ A ) @ D )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(39,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ bool )] :
      ( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ B ) @ A ) )
     => ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_splitI) ).

thf(209,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ TB @ ( fun @ TA @ bool )] :
      ( ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ C @ B ) @ A ) )
     => ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ C ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(12,axiom,
    ! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
      ( ( refl @ TA @ A )
    <=> ! [B: TA] : ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_Nitpick_Orefl_H__def) ).

thf(123,plain,
    ! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
      ( ( ( refl @ TA @ A )
       => ! [B: TA] : ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ B ) @ A ) )
      & ( ! [B: TA] : ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ B ) @ A )
       => ( refl @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(80,axiom,
    trans @ arrow_411405190le_alt @ l,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).

thf(355,plain,
    trans @ arrow_411405190le_alt @ l,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(36,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ TB] :
      ( ( product_apfst @ TC @ TB @ TA @ C @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ B ) @ A ) )
      = ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ ( aa @ TC @ TB @ C @ B ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_apfst__conv) ).

thf(194,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ TB] :
      ( ( product_apfst @ TC @ TB @ TA @ C @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ B ) @ A ) )
      = ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ ( aa @ TC @ TB @ C @ B ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(18,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 @ ( aa @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ TD ) @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ ( aa @ TB @ ( fun @ ( product_prod @ TC @ TD ) @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) ) @ D ) @ ( aa @ TD @ ( product_prod @ TC @ TD ) @ ( aa @ TC @ ( fun @ TD @ ( product_prod @ TC @ TD ) ) @ ( 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_15_prod__induct4) ).

thf(145,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 @ ( aa @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ ( aa @ TA @ ( fun @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ C ) @ ( aa @ ( product_prod @ TC @ TD ) @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ ( aa @ TB @ ( fun @ ( product_prod @ TC @ TD ) @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) ) @ D ) @ ( aa @ TD @ ( product_prod @ TC @ TD ) @ ( aa @ TC @ ( fun @ TD @ ( product_prod @ TC @ TD ) ) @ ( 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)],[18]) ).

thf(30,axiom,
    ! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ ( product_prod @ TB @ TB ) @ bool] :
      ( ( trans @ TB @ B )
     => ( trans @ TA @ ( inv_image @ TB @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_trans__inv__image) ).

thf(177,plain,
    ! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ ( product_prod @ TB @ TB ) @ bool] :
      ( ( trans @ TB @ B )
     => ( trans @ TA @ ( inv_image @ TB @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(74,axiom,
    ! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
      ( ! [B: TA,C: TA] :
          ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ C ) @ A )
         => ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ B ) @ A )
           => ( B = C ) ) )
     => ( antisym @ TA @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_antisymI) ).

thf(338,plain,
    ! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
      ( ! [B: TA,C: TA] :
          ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ C ) @ A )
         => ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ B ) @ A )
           => ( B = C ) ) )
     => ( antisym @ TA @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(82,axiom,
    ! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
      ( ( A != B )
     => ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ A ) @ B ) @ l )
        | ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) @ l ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).

thf(359,plain,
    ! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
      ( ( A != B )
     => ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ A ) @ B ) @ l )
        | ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ B ) @ A ) @ l ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(53,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ),C: product_prod @ TC @ TB] :
      ( ! [D: TC,E: TB] :
          ( ( ( aa @ TB @ ( product_prod @ TC @ TB ) @ ( aa @ TC @ ( fun @ TB @ ( product_prod @ TC @ TB ) ) @ ( product_Pair @ TC @ TB ) @ D ) @ E )
            = C )
         => ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( aa @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ B @ D ) @ E ) @ A ) ) )
     => ( pp @ ( aa @ TA @ bool @ ( aa @ ( product_prod @ TC @ TB ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( product_prod @ TC @ TB ) @ ( fun @ TA @ bool ) ) @ ( product_prod_case @ TC @ TB @ ( fun @ TA @ bool ) ) @ B ) @ C ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_splitI2_H) ).

thf(250,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ),C: product_prod @ TC @ TB] :
      ( ! [D: TC,E: TB] :
          ( ( ( aa @ TB @ ( product_prod @ TC @ TB ) @ ( aa @ TC @ ( fun @ TB @ ( product_prod @ TC @ TB ) ) @ ( product_Pair @ TC @ TB ) @ D ) @ E )
            = C )
         => ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ ( aa @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ B @ D ) @ E ) @ A ) ) )
     => ( pp @ ( aa @ TA @ bool @ ( aa @ ( product_prod @ TC @ TB ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TC @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( product_prod @ TC @ TB ) @ ( fun @ TA @ bool ) ) @ ( product_prod_case @ TC @ TB @ ( fun @ TA @ bool ) ) @ B ) @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(84,axiom,
    member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ x ) @ y ) @ l,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_5) ).

thf(363,plain,
    member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ x ) @ y ) @ l,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(43,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TA @ TB,B: fun @ TA @ TD,C: fun @ TB @ TC] :
      ( ( product_apsnd @ TB @ TC @ TD @ C @ ( product_apfst @ TA @ TD @ TB @ B @ A ) )
      = ( product_apfst @ TA @ TD @ TC @ B @ ( product_apsnd @ TB @ TC @ TA @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_apsnd__apfst__commute) ).

thf(218,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TA @ TB,B: fun @ TA @ TD,C: fun @ TB @ TC] :
      ( ( product_apsnd @ TB @ TC @ TD @ C @ ( product_apfst @ TA @ TD @ TB @ B @ A ) )
      = ( product_apfst @ TA @ TD @ TC @ B @ ( product_apsnd @ TB @ TC @ TA @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(55,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: product_prod @ TB @ TC,C: fun @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) )] :
      ( ( pp @ ( aa @ TA @ bool @ ( aa @ ( product_prod @ TB @ TC ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( product_prod @ TB @ TC ) @ ( fun @ TA @ bool ) ) @ ( product_prod_case @ TB @ TC @ ( fun @ TA @ bool ) ) @ C ) @ B ) @ A ) )
     => ~ ! [D: TB,E: TC] :
            ( ( B
              = ( aa @ TC @ ( product_prod @ TB @ TC ) @ ( aa @ TB @ ( fun @ TC @ ( product_prod @ TB @ TC ) ) @ ( product_Pair @ TB @ TC ) @ D ) @ E ) )
           => ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TC @ ( fun @ TA @ bool ) @ ( aa @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) ) @ C @ D ) @ E ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_splitE_H) ).

thf(258,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: product_prod @ TB @ TC,C: fun @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) )] :
      ( ( pp @ ( aa @ TA @ bool @ ( aa @ ( product_prod @ TB @ TC ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( product_prod @ TB @ TC ) @ ( fun @ TA @ bool ) ) @ ( product_prod_case @ TB @ TC @ ( fun @ TA @ bool ) ) @ C ) @ B ) @ A ) )
     => ~ ! [D: TB,E: TC] :
            ( ( B
              = ( aa @ TC @ ( product_prod @ TB @ TC ) @ ( aa @ TB @ ( fun @ TC @ ( product_prod @ TB @ TC ) ) @ ( product_Pair @ TB @ TC ) @ D ) @ E ) )
           => ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TC @ ( fun @ TA @ bool ) @ ( aa @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) ) @ C @ D ) @ E ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(78,axiom,
    pp @ fTrue,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).

thf(351,plain,
    pp @ fTrue,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(34,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TA @ TB] :
      ( ( product_apsnd @ TA @ TB @ TC @ C @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ B ) @ A ) )
      = ( aa @ TB @ ( product_prod @ TC @ TB ) @ ( aa @ TC @ ( fun @ TB @ ( product_prod @ TC @ TB ) ) @ ( product_Pair @ TC @ TB ) @ B ) @ ( aa @ TA @ TB @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_apsnd__conv) ).

thf(186,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TA @ TB] :
      ( ( product_apsnd @ TA @ TB @ TC @ C @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ B ) @ A ) )
      = ( aa @ TB @ ( product_prod @ TC @ TB ) @ ( aa @ TC @ ( fun @ TB @ ( product_prod @ TC @ TB ) ) @ ( product_Pair @ TC @ TB ) @ B ) @ ( aa @ TA @ TB @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(9,axiom,
    ! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ ( product_prod @ TB @ TB ) @ bool] :
      ( ( trans @ TB @ B )
     => ( ( trans @ TA @ A )
       => ( trans @ ( product_prod @ TB @ TA ) @ ( lex_prod @ TB @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_trans__lex__prod) ).

thf(114,plain,
    ! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ ( product_prod @ TB @ TB ) @ bool] :
      ( ( trans @ TB @ B )
     => ( ( trans @ TA @ A )
       => ( trans @ ( product_prod @ TB @ TA ) @ ( lex_prod @ TB @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(28,axiom,
    ! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
      ( ( irrefl @ TA @ A )
    <=> ! [B: TA] :
          ~ ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_irrefl__def) ).

thf(171,plain,
    ! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool] :
      ( ( ( irrefl @ TA @ A )
       => ! [B: TA] :
            ~ ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ B ) @ A ) )
      & ( ! [B: TA] :
            ~ ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ B ) @ B ) @ A )
       => ( irrefl @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(11,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 @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_split__paired__Ex) ).

thf(119,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 @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) ) )
      & ( ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( 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)],[11]) ).

thf(76,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_73_mem__def) ).

thf(346,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)],[76]) ).

thf(49,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: fun @ ( product_prod @ TA @ TB ) @ TC] :
      ( ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ ( product_curry @ TA @ TB @ TC @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_split__curry) ).

thf(235,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: fun @ ( product_prod @ TA @ TB ) @ TC] :
      ( ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ ( product_curry @ TA @ TB @ TC @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(52,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( fun @ TB @ ( fun @ TC @ bool ) ),B: TC,C: product_prod @ TA @ TB] :
      ( ! [D: TA,E: TB] :
          ( ( C
            = ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ D ) @ E ) )
         => ( member @ TC @ B @ ( aa @ TB @ ( fun @ TC @ bool ) @ ( aa @ TA @ ( fun @ TB @ ( fun @ TC @ bool ) ) @ A @ D ) @ E ) ) )
     => ( member @ TC @ B @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ TC @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ ( fun @ TC @ bool ) ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ ( fun @ TC @ bool ) ) @ ( product_prod_case @ TA @ TB @ ( fun @ TC @ bool ) ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_mem__splitI2) ).

thf(246,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( fun @ TB @ ( fun @ TC @ bool ) ),B: TC,C: product_prod @ TA @ TB] :
      ( ! [D: TA,E: TB] :
          ( ( C
            = ( aa @ TB @ ( product_prod @ TA @ TB ) @ ( aa @ TA @ ( fun @ TB @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ TA @ TB ) @ D ) @ E ) )
         => ( member @ TC @ B @ ( aa @ TB @ ( fun @ TC @ bool ) @ ( aa @ TA @ ( fun @ TB @ ( fun @ TC @ bool ) ) @ A @ D ) @ E ) ) )
     => ( member @ TC @ B @ ( aa @ ( product_prod @ TA @ TB ) @ ( fun @ TC @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ ( fun @ TC @ bool ) ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ ( fun @ TC @ bool ) ) @ ( product_prod_case @ TA @ TB @ ( fun @ TC @ bool ) ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(56,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ TA,B: fun @ TC @ ( fun @ TA @ TB ),C: fun @ TB @ bool] :
      ( ( pp @ ( aa @ TB @ bool @ C @ ( aa @ ( product_prod @ TC @ TA ) @ TB @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ TB ) @ ( product_prod_case @ TC @ TA @ TB ) @ B ) @ A ) ) )
     => ~ ! [D: TC,E: TA] :
            ( ( A
              = ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ D ) @ E ) )
           => ~ ( pp @ ( aa @ TB @ bool @ C @ ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ B @ D ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_splitE2) ).

thf(262,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ TA,B: fun @ TC @ ( fun @ TA @ TB ),C: fun @ TB @ bool] :
      ( ( pp @ ( aa @ TB @ bool @ C @ ( aa @ ( product_prod @ TC @ TA ) @ TB @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ TB ) @ ( product_prod_case @ TC @ TA @ TB ) @ B ) @ A ) ) )
     => ~ ! [D: TC,E: TA] :
            ( ( A
              = ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ D ) @ E ) )
           => ~ ( pp @ ( aa @ TB @ bool @ C @ ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ B @ D ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(33,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( produc1605651328_split @ TA @ TB @ TC )
      = ( product_prod_case @ TA @ TB @ TC ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_internal__split__def) ).

thf(183,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( produc1605651328_split @ TA @ TB @ TC )
      = ( product_prod_case @ TA @ TB @ TC ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(58,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ TA,B: fun @ TC @ TB,C: product_prod @ TB @ TA] :
      ( ( C
        = ( product_apfst @ TC @ TB @ TA @ B @ A ) )
     => ~ ! [D: TC,E: TA] :
            ( ( A
              = ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ D ) @ E ) )
           => ( C
             != ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ ( aa @ TC @ TB @ B @ D ) ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_apfst__convE) ).

thf(273,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ TA,B: fun @ TC @ TB,C: product_prod @ TB @ TA] :
      ( ( C
        = ( product_apfst @ TC @ TB @ TA @ B @ A ) )
     => ~ ! [D: TC,E: TA] :
            ( ( A
              = ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ D ) @ E ) )
           => ( C
             != ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ ( aa @ TC @ TB @ B @ D ) ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(66,axiom,
    ! [TA: $tType,A: fun @ TA @ bool,B: product_prod @ TA @ TA] :
      ( ( member @ ( product_prod @ TA @ TA ) @ B @ ( id_on @ TA @ A ) )
     => ~ ! [C: TA] :
            ( ( member @ TA @ C @ A )
           => ( B
             != ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_Id__onE) ).

thf(305,plain,
    ! [TA: $tType,A: fun @ TA @ bool,B: product_prod @ TA @ TA] :
      ( ( member @ ( product_prod @ TA @ TA ) @ B @ ( id_on @ TA @ A ) )
     => ~ ! [C: TA] :
            ( ( member @ TA @ C @ A )
           => ( B
             != ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(51,axiom,
    ! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA,B: fun @ TB @ ( fun @ TA @ bool )] :
      ( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ B ) @ A ) )
     => ~ ! [C: TB,D: TA] :
            ( ( A
              = ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ C ) @ D ) )
           => ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ B @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_splitE) ).

thf(242,plain,
    ! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA,B: fun @ TB @ ( fun @ TA @ bool )] :
      ( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ ( product_prod @ TB @ TA ) @ bool ) @ ( product_prod_case @ TB @ TA @ bool ) @ B ) @ A ) )
     => ~ ! [C: TB,D: TA] :
            ( ( A
              = ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ C ) @ D ) )
           => ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TB @ ( fun @ TA @ bool ) @ B @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(13,axiom,
    ! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ ( product_prod @ TB @ TB ) @ bool,C: TA,D: TB,E: TA,F: TB] :
      ( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ F ) @ E ) ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C ) ) @ ( lex_prod @ TB @ TA @ B @ A ) )
    <=> ( ( member @ ( product_prod @ TB @ TB ) @ ( aa @ TB @ ( product_prod @ TB @ TB ) @ ( aa @ TB @ ( fun @ TB @ ( product_prod @ TB @ TB ) ) @ ( product_Pair @ TB @ TB ) @ F ) @ D ) @ B )
        | ( ( F = D )
          & ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ E ) @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_in__lex__prod) ).

thf(126,plain,
    ! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ ( product_prod @ TB @ TB ) @ bool,C: TA,D: TB,E: TA,F: TB] :
      ( ( ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ F ) @ E ) ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C ) ) @ ( lex_prod @ TB @ TA @ B @ A ) )
       => ( ( member @ ( product_prod @ TB @ TB ) @ ( aa @ TB @ ( product_prod @ TB @ TB ) @ ( aa @ TB @ ( fun @ TB @ ( product_prod @ TB @ TB ) ) @ ( product_Pair @ TB @ TB ) @ F ) @ D ) @ B )
          | ( ( F = D )
            & ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ E ) @ C ) @ A ) ) ) )
      & ( ( ( member @ ( product_prod @ TB @ TB ) @ ( aa @ TB @ ( product_prod @ TB @ TB ) @ ( aa @ TB @ ( fun @ TB @ ( product_prod @ TB @ TB ) ) @ ( product_Pair @ TB @ TB ) @ F ) @ D ) @ B )
          | ( ( F = D )
            & ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ E ) @ C ) @ A ) ) )
       => ( member @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( aa @ ( product_prod @ TB @ TA ) @ ( fun @ ( product_prod @ TB @ TA ) @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) ) @ ( product_Pair @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ F ) @ E ) ) @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C ) ) @ ( lex_prod @ TB @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(60,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: fun @ TC @ ( fun @ TB @ TD ),B: fun @ TA @ ( product_prod @ TC @ TB ),C: TA] :
      ( ( aa @ TA @ TD @ ( product_scomp @ TA @ TC @ TB @ TD @ B @ A ) @ C )
      = ( aa @ ( product_prod @ TC @ TB ) @ TD @ ( aa @ ( fun @ TC @ ( fun @ TB @ TD ) ) @ ( fun @ ( product_prod @ TC @ TB ) @ TD ) @ ( product_prod_case @ TC @ TB @ TD ) @ A ) @ ( aa @ TA @ ( product_prod @ TC @ TB ) @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_scomp__def) ).

thf(283,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: fun @ TC @ ( fun @ TB @ TD ),B: fun @ TA @ ( product_prod @ TC @ TB ),C: TA] :
      ( ( aa @ TA @ TD @ ( product_scomp @ TA @ TC @ TB @ TD @ B @ A ) @ C )
      = ( aa @ ( product_prod @ TC @ TB ) @ TD @ ( aa @ ( fun @ TC @ ( fun @ TB @ TD ) ) @ ( fun @ ( product_prod @ TC @ TB ) @ TD ) @ ( product_prod_case @ TC @ TB @ TD ) @ A ) @ ( aa @ TA @ ( product_prod @ TC @ TB ) @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(25,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
      ( ( aa @ ( product_prod @ TC @ TA ) @ TB @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ TB ) @ ( produc1605651328_split @ TC @ TA @ TB ) @ C ) @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( 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_22_internal__split__conv) ).

thf(163,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
      ( ( aa @ ( product_prod @ TC @ TA ) @ TB @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ TB ) @ ( produc1605651328_split @ TC @ TA @ TB ) @ C ) @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( 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)],[25]) ).

thf(38,axiom,
    ! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool] :
      ( ( total_on @ TA @ B @ A )
    <=> ! [C: TA] :
          ( ( member @ TA @ C @ B )
         => ! [D: TA] :
              ( ( member @ TA @ D @ B )
             => ( ( C != D )
               => ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ D ) @ A )
                  | ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ D ) @ C ) @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_total__on__def) ).

thf(200,plain,
    ! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: fun @ TA @ bool] :
      ( ( ( total_on @ TA @ B @ A )
       => ! [C: TA] :
            ( ( member @ TA @ C @ B )
           => ! [D: TA] :
                ( ( member @ TA @ D @ B )
               => ( ( C != D )
                 => ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ D ) @ A )
                    | ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ D ) @ C ) @ A ) ) ) ) ) )
      & ( ! [C: TA] :
            ( ( member @ TA @ C @ B )
           => ! [D: TA] :
                ( ( member @ TA @ D @ B )
               => ( ( C != D )
                 => ( ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ C ) @ D ) @ A )
                    | ( member @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( product_prod @ TA @ TA ) @ ( aa @ TA @ ( fun @ TA @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TA @ TA ) @ D ) @ C ) @ A ) ) ) ) )
       => ( total_on @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(4,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
      ( ( ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C )
        = ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) )
    <=> ( ( D = B )
        & ( C = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_Pair__eq) ).

thf(90,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
      ( ( ( ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C )
          = ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) )
       => ( ( D = B )
          & ( C = A ) ) )
      & ( ( ( D = B )
          & ( C = A ) )
       => ( ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C )
          = ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(67,axiom,
    ! [TA: $tType,A: fun @ TA @ bool] : ( single_valued @ TA @ TA @ ( id_on @ TA @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_single__valued__Id__on) ).

thf(309,plain,
    ! [TA: $tType,A: fun @ TA @ bool] : ( single_valued @ TA @ TA @ ( id_on @ TA @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(42,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
      ( ( aa @ ( product_prod @ TC @ TA ) @ TB @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ TB ) @ ( product_prod_case @ TC @ TA @ TB ) @ C ) @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( 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_split__conv) ).

thf(215,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
      ( ( aa @ ( product_prod @ TC @ TA ) @ TB @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ TB ) @ ( product_prod_case @ TC @ TA @ TB ) @ C ) @ ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( 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)],[42]) ).

thf(48,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( fun @ TB @ TC )] :
      ( ( product_curry @ TA @ TB @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_curry__split) ).

thf(232,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: fun @ TA @ ( fun @ TB @ TC )] :
      ( ( product_curry @ TA @ TB @ TC @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( product_prod @ TA @ TB ) @ TC ) @ ( product_prod_case @ TA @ TB @ TC ) @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(54,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ TA,B: fun @ TC @ ( fun @ TA @ ( fun @ TB @ bool ) ),C: TB] :
      ( ( member @ TB @ C @ ( aa @ ( product_prod @ TC @ TA ) @ ( fun @ TB @ bool ) @ ( aa @ ( fun @ TC @ ( fun @ TA @ ( fun @ TB @ bool ) ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ ( fun @ TB @ bool ) ) @ ( product_prod_case @ TC @ TA @ ( fun @ TB @ bool ) ) @ B ) @ A ) )
     => ~ ! [D: TC,E: TA] :
            ( ( A
              = ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ D ) @ E ) )
           => ~ ( member @ TB @ C @ ( aa @ TA @ ( fun @ TB @ bool ) @ ( aa @ TC @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ B @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_mem__splitE) ).

thf(254,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ TA,B: fun @ TC @ ( fun @ TA @ ( fun @ TB @ bool ) ),C: TB] :
      ( ( member @ TB @ C @ ( aa @ ( product_prod @ TC @ TA ) @ ( fun @ TB @ bool ) @ ( aa @ ( fun @ TC @ ( fun @ TA @ ( fun @ TB @ bool ) ) ) @ ( fun @ ( product_prod @ TC @ TA ) @ ( fun @ TB @ bool ) ) @ ( product_prod_case @ TC @ TA @ ( fun @ TB @ bool ) ) @ B ) @ A ) )
     => ~ ! [D: TC,E: TA] :
            ( ( A
              = ( aa @ TA @ ( product_prod @ TC @ TA ) @ ( aa @ TC @ ( fun @ TA @ ( product_prod @ TC @ TA ) ) @ ( product_Pair @ TC @ TA ) @ D ) @ E ) )
           => ~ ( member @ TB @ C @ ( aa @ TA @ ( fun @ TB @ bool ) @ ( aa @ TC @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ B @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(46,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB,D: fun @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) )] :
      ( ( pp @ ( aa @ TA @ bool @ ( aa @ ( product_prod @ TB @ TC ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( product_prod @ TB @ TC ) @ ( fun @ TA @ bool ) ) @ ( product_prod_case @ TB @ TC @ ( fun @ TA @ bool ) ) @ D ) @ ( aa @ TC @ ( product_prod @ TB @ TC ) @ ( aa @ TB @ ( fun @ TC @ ( product_prod @ TB @ TC ) ) @ ( product_Pair @ TB @ TC ) @ C ) @ B ) ) @ A ) )
     => ( pp @ ( aa @ TA @ bool @ ( aa @ TC @ ( fun @ TA @ bool ) @ ( aa @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) ) @ D @ C ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_splitD_H) ).

thf(227,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB,D: fun @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) )] :
      ( ( pp @ ( aa @ TA @ bool @ ( aa @ ( product_prod @ TB @ TC ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( product_prod @ TB @ TC ) @ ( fun @ TA @ bool ) ) @ ( product_prod_case @ TB @ TC @ ( fun @ TA @ bool ) ) @ D ) @ ( aa @ TC @ ( product_prod @ TB @ TC ) @ ( aa @ TB @ ( fun @ TC @ ( product_prod @ TB @ TC ) ) @ ( product_Pair @ TB @ TC ) @ C ) @ B ) ) @ A ) )
     => ( pp @ ( aa @ TA @ bool @ ( aa @ TC @ ( fun @ TA @ bool ) @ ( aa @ TB @ ( fun @ TC @ ( fun @ TA @ bool ) ) @ D @ C ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(364,plain,
    $false,
    inference(cvc4,[status(thm)],[142,157,166,286,299,150,333,352,174,288,320,189,152,179,211,238,147,280,221,116,292,85,302,349,160,137,229,197,356,169,109,225,134,343,105,266,311,313,181,86,362,98,103,323,140,213,155,330,209,123,355,194,145,177,338,359,250,363,218,258,351,186,114,171,119,346,235,246,262,183,273,305,242,126,283,163,200,90,309,215,232,254,227]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SCT174_5 : TPTP v8.2.0. Released v6.0.0.
% 0.16/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n020.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Mon May 20 00:19:24 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.96/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.62/1.12  % [INFO] 	 Parsing done (210ms). 
% 1.62/1.13  % [INFO] 	 Running in sequential loop mode. 
% 2.36/1.35  % [INFO] 	 eprover registered as external prover. 
% 2.36/1.35  % [INFO] 	 cvc4 registered as external prover. 
% 2.36/1.35  % [INFO] 	 Scanning for conjecture ... 
% 2.77/1.45  % [INFO] 	 Found a conjecture (or negated_conjecture) and 82 axioms. Running axiom selection ... 
% 2.86/1.47  % [INFO] 	 Axiom selection finished. Selected 82 axioms (removed 0 axioms). 
% 3.40/1.64  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 3.40/1.67  % [INFO] 	 Type checking passed. 
% 3.40/1.67  % [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 ... 
% 71.08/57.06  % External prover 'cvc4' found a proof!
% 71.08/57.06  % [INFO] 	 Killing All external provers ... 
% 71.08/57.06  % Time passed: 56545ms (effective reasoning time: 55921ms)
% 71.08/57.06  % 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)>
% 71.08/57.06  % Axioms used in derivation (82): fact_17_prod__induct5, fact_37_prod__caseI, fact_29_curryD, fact_24_curryI, fact_66_antisym__def, fact_38_mem__splitI, fact_52_splitE_H, fact_12_prod__cases3, fact_5_Pair__inject, fact_35_total__on__def, fact_21_PairE, fact_14_prod__cases4, fact_69_single__valuedD, fact_19_prod__induct6, fact_68_single__valued__def, fact_62_Pair__scomp, conj_3, fact_51_mem__splitE, fact_11_prod_Orecs, fact_54_split__cong, fact_13_prod__induct3, fact_23_curry__conv, fact_46_split__curry, fact_28_curryE, fact_60_Id__on__iff, fact_47_splitI2, fact_6_trans__lex__prod, fact_73_mem__def, fact_50_splitI2_H, fact_22_internal__split__conv, fact_9_Nitpick_Orefl_H__def, fact_26_in__inv__image, fact_48_splitE, conj_2, fact_10_in__lex__prod, fact_20_prod_Oexhaust, fact_49_mem__splitI2, fact_55_apfst__convE, fact_45_curry__split, fact_0_split__paired__All, fact_34_surj__pair, fact_61_scomp__Pair, fact_8_split__paired__Ex, fact_27_trans__inv__image, fact_63_Id__onE, fact_72_ext, fact_4_transI, fact_16_prod__cases5, fact_44_prod_Osimps_I2_J, fact_15_prod__induct4, fact_57_scomp__def, fact_56_scomp__apply, conj_1, fact_71_antisymI, fact_43_splitD_H, fact_33_apfst__conv, fact_3_transD, fact_7_in__rel__def, fact_39_split__conv, fact_70_single__valuedI, fact_25_irrefl__def, fact_36_splitI, fact_42_splitD, fact_59_Id__on__eqI, fact_65_antisym__Id__on, help_pp_1_1_U, conj_4, fact_67_antisymD, fact_41_split__weak__cong, fact_53_splitE2, fact_58_trans__Id__on, conj_5, fact_64_single__valued__Id__on, conj_0, fact_30_internal__split__def, fact_32_strict__linear__order__on__def, help_pp_2_1_U, fact_40_apsnd__apfst__commute, fact_1_Pair__eq, fact_2_trans__def, fact_18_prod__cases6, fact_31_apsnd__conv
% 71.08/57.06  % No. of inferences in proof: 168
% 71.08/57.06  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 56545 ms resp. 55921 ms w/o parsing
% 71.53/57.23  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 71.53/57.23  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------