TSTP Solution File: COM192^1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : COM192^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n007.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 20 19:09:20 EDT 2024

% Result   : Theorem 65.06s 39.73s
% Output   : Refutation 66.64s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  311
% Syntax   : Number of formulae    :  580 ( 229 unt;  44 typ;   0 def)
%            Number of atoms       : 1713 ( 625 equ;   2 cnn)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives : 8831 (  78   ~;   7   |;  94   &;8160   @)
%                                         (   0 <=>; 492  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   8 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :  615 ( 615   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   52 (  48 usr;  14 con; 0-7 aty)
%            Number of variables   : 2231 (  58   ^2073   !;  66   ?;2231   :)
%                                         (  34  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(dtree_type,type,
    dtree: $tType ).

thf(t_type,type,
    t: $tType ).

thf(n_type,type,
    n: $tType ).

thf(finite_finite_type,type,
    finite_finite: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(semiring_char_0_type,type,
    semiring_char_0: 
      !>[TA: $tType] : ( ( itself @ TA ) > $o ) ).

thf(node_type,type,
    node: n > ( set @ ( sum_sum @ t @ dtree ) ) > dtree ).

thf(cont_type,type,
    cont: dtree > ( set @ ( sum_sum @ t @ dtree ) ) ).

thf(corec_type,type,
    corec: 
      !>[TA: $tType] : ( ( TA > n ) > ( TA > ( set @ ( sum_sum @ t @ ( sum_sum @ dtree @ TA ) ) ) ) > TA > dtree ) ).

thf(root_type,type,
    root: dtree > n ).

thf(unfold_type,type,
    unfold: 
      !>[TA: $tType] : ( ( TA > n ) > ( TA > ( set @ ( sum_sum @ t @ TA ) ) ) > TA > dtree ) ).

thf(finite_finite2_type,type,
    finite_finite2: 
      !>[TA: $tType] : ( ( set @ TA ) > $o ) ).

thf(comp_type,type,
    comp: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB ) > ( TA > TC ) > TA > TB ) ).

thf(id_type,type,
    id: 
      !>[TA: $tType] : ( TA > TA ) ).

thf(inj_on_type,type,
    inj_on: 
      !>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > $o ) ).

thf(gram_L1451583624elle_H_type,type,
    gram_L1451583624elle_H: dtree > n > dtree ).

thf(gram_L1221482011le_H_c_type,type,
    gram_L1221482011le_H_c: dtree > n > ( set @ ( sum_sum @ t @ n ) ) ).

thf(gram_L1221482026le_H_r_type,type,
    gram_L1221482026le_H_r: dtree > n > n ).

thf(gram_L1451583635elle_S_type,type,
    gram_L1451583635elle_S: n > ( set @ ( sum_sum @ t @ n ) ) ).

thf(gram_L1231612515_deftr_type,type,
    gram_L1231612515_deftr: n > dtree ).

thf(gram_L1004374585hsubst_type,type,
    gram_L1004374585hsubst: dtree > dtree > dtree ).

thf(gram_L1905609002ubst_c_type,type,
    gram_L1905609002ubst_c: dtree > dtree > ( set @ ( sum_sum @ t @ dtree ) ) ).

thf(gram_L1905609017ubst_r_type,type,
    gram_L1905609017ubst_r: dtree > n ).

thf(gram_L805317441_inFr2_type,type,
    gram_L805317441_inFr2: ( set @ n ) > dtree > t > $o ).

thf(gram_L830233218_inItr_type,type,
    gram_L830233218_inItr: ( set @ n ) > dtree > n > $o ).

thf(gram_L315592705e_pick_type,type,
    gram_L315592705e_pick: dtree > n > dtree ).

thf(gram_L716654942_subtr_type,type,
    gram_L716654942_subtr: ( set @ n ) > dtree > dtree > $o ).

thf(gram_L1614515765ubtrOf_type,type,
    gram_L1614515765ubtrOf: dtree > n > dtree ).

thf(gram_L864798063lle_wf_type,type,
    gram_L864798063lle_wf: dtree > $o ).

thf(if_type,type,
    if: 
      !>[TA: $tType] : ( $o > TA > TA > TA ) ).

thf(top_top_type,type,
    top_top: 
      !>[TA: $tType] : TA ).

thf(type2_type,type,
    type2: 
      !>[TA: $tType] : ( itself @ TA ) ).

thf(collect_type,type,
    collect: 
      !>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).

thf(image_type,type,
    image: 
      !>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > ( set @ TA ) ) ).

thf(vimage_type,type,
    vimage: 
      !>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TA ) > ( set @ TB ) ) ).

thf(sum_Inl_type,type,
    sum_Inl: 
      !>[TA: $tType,TB: $tType] : ( TB > ( sum_sum @ TB @ TA ) ) ).

thf(sum_Inr_type,type,
    sum_Inr: 
      !>[TA: $tType,TB: $tType] : ( TB > ( sum_sum @ TA @ TB ) ) ).

thf(sum_map_sum_type,type,
    sum_map_sum: 
      !>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( TD > TC ) > ( TB > TA ) > ( sum_sum @ TD @ TB ) > ( sum_sum @ TC @ TA ) ) ).

thf(sum_rec_sum_type,type,
    sum_rec_sum: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB ) > ( TA > TB ) > ( sum_sum @ TC @ TA ) > TB ) ).

thf(sum_case_sum_type,type,
    sum_case_sum: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB ) > ( TA > TB ) > ( sum_sum @ TC @ TA ) > TB ) ).

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

thf(a_type,type,
    a: t ).

thf(n2_type,type,
    n2: n ).

thf(t_tr_type,type,
    t_tr: sum_sum @ t @ dtree ).

thf(tr0_type,type,
    tr0: dtree ).

thf(121,axiom,
    gram_L1905609017ubst_r = root,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_hsubst__r__def) ).

thf(645,plain,
    gram_L1905609017ubst_r = root,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(173,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: ( set @ TB ) > TB,B: TC > TB,C: TA > TC,D: set @ TA] :
      ( ( A @ ( image @ TC @ TB @ B @ ( image @ TA @ TC @ C @ D ) ) )
      = ( A @ ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ B @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_Inf_OINF__image) ).

thf(809,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: ( set @ TB ) > TB,B: TC > TB,C: TA > TC,D: set @ TA] :
      ( ( A @ ( image @ TC @ TB @ B @ ( image @ TA @ TC @ C @ D ) ) )
      = ( A @ ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ B @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(234,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: $o,B: TA > TB,C: TD > TC,D: sum_sum @ TA @ TD,E: TA] :
      ( ( A
       => ( ( sum_map_sum @ TA @ TB @ TD @ TC @ B @ C @ ( if @ ( sum_sum @ TA @ TD ) @ A @ D @ ( sum_Inl @ TA @ TD @ E ) ) )
          = ( sum_map_sum @ TA @ TB @ TD @ TC @ B @ C @ D ) ) )
      & ( ~ A
       => ( ( sum_map_sum @ TA @ TB @ TD @ TC @ B @ C @ ( if @ ( sum_sum @ TA @ TD ) @ A @ D @ ( sum_Inl @ TA @ TD @ E ) ) )
          = ( sum_Inl @ TB @ TC @ ( B @ E ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_map__sum__if__distrib__else_I1_J) ).

thf(1024,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: $o,B: TA > TB,C: TD > TC,D: sum_sum @ TA @ TD,E: TA] :
      ( ( A
       => ( ( sum_map_sum @ TA @ TB @ TD @ TC @ B @ C @ ( if @ ( sum_sum @ TA @ TD ) @ A @ D @ ( sum_Inl @ TA @ TD @ E ) ) )
          = ( sum_map_sum @ TA @ TB @ TD @ TC @ B @ C @ D ) ) )
      & ( ~ A
       => ( ( sum_map_sum @ TA @ TB @ TD @ TC @ B @ C @ ( if @ ( sum_sum @ TA @ TD ) @ A @ D @ ( sum_Inl @ TA @ TD @ E ) ) )
          = ( sum_Inl @ TB @ TC @ ( B @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(40,axiom,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
      ( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
     => ( ( member @ TB @ B @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) )
        = ( ? [C: TA] :
              ( ( B
                = ( A @ C ) )
              & ! [D: TA] :
                  ( ( B
                    = ( A @ D ) )
                 => ( D = C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_range__ex1__eq) ).

thf(365,plain,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
      ( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
     => ( ( member @ TB @ B @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) )
        = ( ? [C: TA] :
              ( ( B
                = ( A @ C ) )
              & ! [D: TA] :
                  ( ( B
                    = ( A @ D ) )
                 => ( D = C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(197,axiom,
    ( gram_L830233218_inItr
    = ( ^ [A: set @ n,B: dtree,C: n] :
          ( ? [D: dtree,E: set @ n] :
              ( ( A = E )
              & ( B = D )
              & ( C
                = ( root @ D ) )
              & ( member @ n @ ( root @ D ) @ E ) )
          | ? [D: dtree,E: set @ n,F: dtree,G: n] :
              ( ( A = E )
              & ( B = D )
              & ( C = G )
              & ( member @ n @ ( root @ D ) @ E )
              & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ F ) @ ( cont @ D ) )
              & ( gram_L830233218_inItr @ E @ F @ G ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_inItr_Osimps) ).

thf(893,plain,
    ( gram_L830233218_inItr
    = ( ^ [A: set @ n,B: dtree,C: n] :
          ( ? [D: dtree,E: set @ n] :
              ( ( A = E )
              & ( B = D )
              & ( C
                = ( root @ D ) )
              & ( member @ n @ ( root @ D ) @ E ) )
          | ? [D: dtree,E: set @ n,F: dtree,G: n] :
              ( ( A = E )
              & ( B = D )
              & ( C = G )
              & ( member @ n @ ( root @ D ) @ E )
              & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ F ) @ ( cont @ D ) )
              & ( gram_L830233218_inItr @ E @ F @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(215,axiom,
    ! [A: dtree,B: dtree] :
      ( ( ( root @ A )
       != ( root @ B ) )
     => ( ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ ( gram_L1004374585hsubst @ B @ A ) ) )
        = ( image @ dtree @ dtree @ ( gram_L1004374585hsubst @ B ) @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_Inr__cont__hsubst__neq) ).

thf(962,plain,
    ! [A: dtree,B: dtree] :
      ( ( ( root @ A )
       != ( root @ B ) )
     => ( ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ ( gram_L1004374585hsubst @ B @ A ) ) )
        = ( image @ dtree @ dtree @ ( gram_L1004374585hsubst @ B ) @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(209,axiom,
    ! [A: n] :
      ( ( gram_L1221482026le_H_r @ tr0 @ A )
      = ( root @ ( gram_L315592705e_pick @ tr0 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_H__r__def) ).

thf(941,plain,
    ! [A: n] :
      ( ( gram_L1221482026le_H_r @ tr0 @ A )
      = ( root @ ( gram_L315592705e_pick @ tr0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(128,axiom,
    ! [A: dtree,B: n] :
      ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ A @ B )
     => ( ( root @ ( gram_L1451583624elle_H @ A @ B ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_Gram__Lang__Mirabelle__ojxrtuoybn_Oroot__H) ).

thf(666,plain,
    ! [A: dtree,B: n] :
      ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ A @ B )
     => ( ( root @ ( gram_L1451583624elle_H @ A @ B ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(200,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TB > TC,B: TD > TB,C: TA > TB] :
      ( ( comp @ TB @ TC @ ( sum_sum @ TD @ TA ) @ A @ ( sum_case_sum @ TD @ TB @ TA @ B @ C ) )
      = ( sum_case_sum @ TD @ TC @ TA @ ( comp @ TB @ TC @ TD @ A @ B ) @ ( comp @ TB @ TC @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_o__case__sum) ).

thf(909,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TB > TC,B: TD > TB,C: TA > TB] :
      ( ( comp @ TB @ TC @ ( sum_sum @ TD @ TA ) @ A @ ( sum_case_sum @ TD @ TB @ TA @ B @ C ) )
      = ( sum_case_sum @ TD @ TC @ TA @ ( comp @ TB @ TC @ TD @ A @ B ) @ ( comp @ TB @ TC @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(29,axiom,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: TA > TB] :
      ( ! [C: TA] :
          ( ( A @ ( B @ C ) )
          = C )
     => ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
        = ( top_top @ ( set @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_surjI) ).

thf(333,plain,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: TA > TB] :
      ( ! [C: TA] :
          ( ( A @ ( B @ C ) )
          = C )
     => ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
        = ( top_top @ ( set @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(162,axiom,
    ( gram_L1221482026le_H_r
    = ( ^ [A: dtree,B: n] : ( root @ ( gram_L315592705e_pick @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_Gram__Lang__Mirabelle__ojxrtuoybn_OH__r__def) ).

thf(777,plain,
    ( gram_L1221482026le_H_r
    = ( ^ [A: dtree,B: n] : ( root @ ( gram_L315592705e_pick @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(96,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( collect @ TA
        @ ^ [B: TA] : ( member @ TA @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).

thf(555,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( collect @ TA
        @ ^ [B: TA] : ( member @ TA @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(134,axiom,
    ! [A: dtree,B: dtree,C: dtree] :
      ( ( gram_L864798063lle_wf @ A )
     => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ B ) @ ( cont @ A ) )
       => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ C ) @ ( cont @ A ) )
         => ( ( ( root @ B )
              = ( root @ C ) )
            = ( B = C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_wf__inj) ).

thf(683,plain,
    ! [A: dtree,B: dtree,C: dtree] :
      ( ( gram_L864798063lle_wf @ A )
     => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ B ) @ ( cont @ A ) )
       => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ C ) @ ( cont @ A ) )
         => ( ( ( root @ B )
              = ( root @ C ) )
            = ( B = C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(6,axiom,
    ! [TA: $tType,A: $o,B: TA] :
      ( ( A
        & ( top_top @ ( TA > $o ) @ B ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_top__conj_I2_J) ).

thf(276,plain,
    ! [TA: $tType,A: $o,B: TA] :
      ( ( A
        & ( top_top @ ( TA > $o ) @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(154,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TB > TA,C: set @ TA] :
      ( ( vimage @ TC @ TB @ A @ ( vimage @ TB @ TA @ B @ C ) )
      = ( vimage @ TC @ TA @ ( comp @ TB @ TA @ TC @ B @ A ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_set_Ocompositionality) ).

thf(741,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TB > TA,C: set @ TA] :
      ( ( vimage @ TC @ TB @ A @ ( vimage @ TB @ TA @ B @ C ) )
      = ( vimage @ TC @ TA @ ( comp @ TB @ TA @ TC @ B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(68,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > TC,B: TB > TC,C: TD > TC,D: sum_sum @ TA @ TB] :
      ( ( sum_case_sum @ ( sum_sum @ TA @ TB ) @ TC @ TD @ ( sum_case_sum @ TA @ TC @ TB @ A @ B ) @ C @ ( sum_Inl @ ( sum_sum @ TA @ TB ) @ TD @ D ) )
      = ( sum_case_sum @ TA @ TC @ TB @ A @ B @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_case__sum__step_I1_J) ).

thf(449,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > TC,B: TB > TC,C: TD > TC,D: sum_sum @ TA @ TB] :
      ( ( sum_case_sum @ ( sum_sum @ TA @ TB ) @ TC @ TD @ ( sum_case_sum @ TA @ TC @ TB @ A @ B ) @ C @ ( sum_Inl @ ( sum_sum @ TA @ TB ) @ TD @ D ) )
      = ( sum_case_sum @ TA @ TC @ TB @ A @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(110,axiom,
    ! [A: n] :
      ( ( gram_L864798063lle_wf @ tr0 )
     => ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ A )
       => ( gram_L864798063lle_wf @ ( gram_L315592705e_pick @ tr0 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_wf__pick) ).

thf(597,plain,
    ! [A: n] :
      ( ( gram_L864798063lle_wf @ tr0 )
     => ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ A )
       => ( gram_L864798063lle_wf @ ( gram_L315592705e_pick @ tr0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(1,conjecture,
    ( ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ ( comp @ n @ n @ dtree @ ( comp @ dtree @ n @ n @ root @ ( gram_L1451583624elle_H @ tr0 ) ) @ root ) @ t_tr )
    = ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root @ t_tr ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).

thf(2,negated_conjecture,
    ( ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ ( comp @ n @ n @ dtree @ ( comp @ dtree @ n @ n @ root @ ( gram_L1451583624elle_H @ tr0 ) ) @ root ) @ t_tr )
   != ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root @ t_tr ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(269,plain,
    ( ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ ( comp @ n @ n @ dtree @ ( comp @ dtree @ n @ n @ root @ ( gram_L1451583624elle_H @ tr0 ) ) @ root ) @ t_tr )
   != ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root @ t_tr ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(132,axiom,
    ! [A: dtree] :
      ( ( node @ ( root @ A ) @ ( cont @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_Node__root__cont) ).

thf(677,plain,
    ! [A: dtree] :
      ( ( node @ ( root @ A ) @ ( cont @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(250,axiom,
    ! [TA: $tType] :
      ( ( (=) @ TA )
      = ( ^ [A: TA,B: TA] :
          ? [C: TA] :
            ( ( member @ TA @ C @ ( top_top @ ( set @ TA ) ) )
            & ( ( id @ TA @ C )
              = A )
            & ( ( id @ TA @ C )
              = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_DEADID_Oin__rel) ).

thf(1078,plain,
    ! [TA: $tType] :
      ( ( (=) @ TA )
      = ( ^ [A: TA,B: TA] :
          ? [C: TA] :
            ( ( member @ TA @ C @ ( top_top @ ( set @ TA ) ) )
            & ( ( id @ TA @ C )
              = A )
            & ( ( id @ TA @ C )
              = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(47,axiom,
    ! [TA: $tType] :
      ( ( semiring_char_0 @ TA @ ( type2 @ TA ) )
     => ~ ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_infinite__UNIV__char__0) ).

thf(385,plain,
    ! [TA: $tType] :
      ( ( semiring_char_0 @ TA @ ( type2 @ TA ) )
     => ~ ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(94,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) )
     => ( ( finite_finite2 @ TB @ ( top_top @ ( set @ TB ) ) )
       => ( finite_finite2 @ ( product_prod @ TA @ TB ) @ ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_finite__Prod__UNIV) ).

thf(550,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) )
     => ( ( finite_finite2 @ TB @ ( top_top @ ( set @ TB ) ) )
       => ( finite_finite2 @ ( product_prod @ TA @ TB ) @ ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(168,axiom,
    ( gram_L1451583624elle_H
    = ( ^ [A: dtree] : ( unfold @ n @ ( gram_L1221482026le_H_r @ A ) @ ( gram_L1221482011le_H_c @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_Gram__Lang__Mirabelle__ojxrtuoybn_OH__def) ).

thf(797,plain,
    ( gram_L1451583624elle_H
    = ( ^ [A: dtree] : ( unfold @ n @ ( gram_L1221482026le_H_r @ A ) @ ( gram_L1221482011le_H_c @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(199,axiom,
    ! [A: set @ n,B: dtree,C: n] :
      ( ( gram_L830233218_inItr @ A @ B @ C )
     => ( ( ( C
            = ( root @ B ) )
         => ~ ( member @ n @ ( root @ B ) @ A ) )
       => ~ ( ( member @ n @ ( root @ B ) @ A )
           => ! [D: dtree] :
                ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ D ) @ ( cont @ B ) )
               => ~ ( gram_L830233218_inItr @ A @ D @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_inItr_Ocases) ).

thf(898,plain,
    ! [A: set @ n,B: dtree,C: n] :
      ( ( gram_L830233218_inItr @ A @ B @ C )
     => ( ( ( C
            = ( root @ B ) )
         => ~ ( member @ n @ ( root @ B ) @ A ) )
       => ~ ( ( member @ n @ ( root @ B ) @ A )
           => ! [D: dtree] :
                ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ D ) @ ( cont @ B ) )
               => ~ ( gram_L830233218_inItr @ A @ D @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(265,axiom,
    ! [A: n,B: dtree] :
      ( ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ A ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ B ) ) )
     => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( gram_L1614515765ubtrOf @ B @ A ) ) @ ( cont @ B ) )
        & ( ( root @ ( gram_L1614515765ubtrOf @ B @ A ) )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_subtrOf) ).

thf(1127,plain,
    ! [A: n,B: dtree] :
      ( ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ A ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ B ) ) )
     => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( gram_L1614515765ubtrOf @ B @ A ) ) @ ( cont @ B ) )
        & ( ( root @ ( gram_L1614515765ubtrOf @ B @ A ) )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(181,axiom,
    ! [A: dtree,B: dtree] :
      ( ( ( root @ A )
        = ( root @ B ) )
     => ( ( cont @ ( gram_L1004374585hsubst @ B @ A ) )
        = ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ dtree @ dtree @ ( id @ t ) @ ( gram_L1004374585hsubst @ B ) ) @ ( cont @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_cont__hsubst__eq) ).

thf(841,plain,
    ! [A: dtree,B: dtree] :
      ( ( ( root @ A )
        = ( root @ B ) )
     => ( ( cont @ ( gram_L1004374585hsubst @ B @ A ) )
        = ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ dtree @ dtree @ ( id @ t ) @ ( gram_L1004374585hsubst @ B ) ) @ ( cont @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(241,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: ( set @ TB ) > TB,B: TC > TB,C: TA > TC,D: set @ TA] :
      ( ( A @ ( image @ TC @ TB @ B @ ( image @ TA @ TC @ C @ D ) ) )
      = ( A @ ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ B @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_Sup_OSUP__image) ).

thf(1046,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: ( set @ TB ) > TB,B: TC > TB,C: TA > TC,D: set @ TA] :
      ( ( A @ ( image @ TC @ TB @ B @ ( image @ TA @ TC @ C @ D ) ) )
      = ( A @ ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ B @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(24,axiom,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: set @ TA] :
      ( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
     => ( ( member @ TB @ ( A @ B ) @ ( image @ TA @ TB @ A @ C ) )
        = ( member @ TA @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_inj__image__mem__iff) ).

thf(320,plain,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: set @ TA] :
      ( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
     => ( ( member @ TB @ ( A @ B ) @ ( image @ TA @ TB @ A @ C ) )
        = ( member @ TA @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(65,axiom,
    ! [TA: $tType,TB: $tType,A: TB,B: TA] :
      ( ( sum_Inl @ TB @ TA @ A )
     != ( sum_Inr @ TA @ TB @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_sum_Odistinct_I1_J) ).

thf(436,plain,
    ! [TA: $tType,TB: $tType,A: TB,B: TA] :
      ( ( sum_Inl @ TB @ TA @ A )
     != ( sum_Inr @ TA @ TB @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(177,axiom,
    ! [TA: $tType,A: ( set @ TA ) > TA,B: set @ TA] :
      ( ( A @ ( image @ TA @ TA @ ( id @ TA ) @ B ) )
      = ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_Inf_OINF__id__eq) ).

thf(829,plain,
    ! [TA: $tType,A: ( set @ TA ) > TA,B: set @ TA] :
      ( ( A @ ( image @ TA @ TA @ ( id @ TA ) @ B ) )
      = ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(255,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: $o,B: TA > TC,C: TB > TD,D: TA,E: sum_sum @ TA @ TB] :
      ( ( A
       => ( ( sum_map_sum @ TA @ TC @ TB @ TD @ B @ C @ ( if @ ( sum_sum @ TA @ TB ) @ A @ ( sum_Inl @ TA @ TB @ D ) @ E ) )
          = ( sum_Inl @ TC @ TD @ ( B @ D ) ) ) )
      & ( ~ A
       => ( ( sum_map_sum @ TA @ TC @ TB @ TD @ B @ C @ ( if @ ( sum_sum @ TA @ TB ) @ A @ ( sum_Inl @ TA @ TB @ D ) @ E ) )
          = ( sum_map_sum @ TA @ TC @ TB @ TD @ B @ C @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_map__sum__if__distrib__then_I1_J) ).

thf(1095,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: $o,B: TA > TC,C: TB > TD,D: TA,E: sum_sum @ TA @ TB] :
      ( ( A
       => ( ( sum_map_sum @ TA @ TC @ TB @ TD @ B @ C @ ( if @ ( sum_sum @ TA @ TB ) @ A @ ( sum_Inl @ TA @ TB @ D ) @ E ) )
          = ( sum_Inl @ TC @ TD @ ( B @ D ) ) ) )
      & ( ~ A
       => ( ( sum_map_sum @ TA @ TC @ TB @ TD @ B @ C @ ( if @ ( sum_sum @ TA @ TB ) @ A @ ( sum_Inl @ TA @ TB @ D ) @ E ) )
          = ( sum_map_sum @ TA @ TC @ TB @ TD @ B @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(146,axiom,
    ! [A: dtree,B: dtree] :
      ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ A ) @ ( cont @ B ) )
     => ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ ( root @ A ) ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_root__prodOf) ).

thf(719,plain,
    ! [A: dtree,B: dtree] :
      ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ A ) @ ( cont @ B ) )
     => ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ ( root @ A ) ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(83,axiom,
    ! [A: n] : ( gram_L864798063lle_wf @ ( gram_L1231612515_deftr @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_wf__deftr) ).

thf(504,plain,
    ! [A: n] : ( gram_L864798063lle_wf @ ( gram_L1231612515_deftr @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(202,axiom,
    ! [A: dtree,B: set @ n,C: dtree] :
      ( ( gram_L864798063lle_wf @ A )
     => ( ( gram_L716654942_subtr @ B @ C @ A )
       => ( inj_on @ dtree @ n @ root @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_wf__subtr__inj__on) ).

thf(917,plain,
    ! [A: dtree,B: set @ n,C: dtree] :
      ( ( gram_L864798063lle_wf @ A )
     => ( ( gram_L716654942_subtr @ B @ C @ A )
       => ( inj_on @ dtree @ n @ root @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(170,axiom,
    ! [A: n] :
      ( ( root @ ( gram_L1451583624elle_H @ tr0 @ A ) )
      = ( root @ ( gram_L315592705e_pick @ tr0 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_root__H__pick) ).

thf(802,plain,
    ! [A: n] :
      ( ( root @ ( gram_L1451583624elle_H @ tr0 @ A ) )
      = ( root @ ( gram_L315592705e_pick @ tr0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(245,axiom,
    ! [TA: $tType] :
      ( ( id @ TA )
      = ( ^ [A: TA] : A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_id__apply) ).

thf(1059,plain,
    ! [TA: $tType] :
      ( ( id @ TA )
      = ( ^ [A: TA] : A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(107,axiom,
    ! [A: dtree,B: n] :
      ( ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ ( gram_L1451583624elle_H @ A @ B ) ) )
      = ( image @ dtree @ dtree @ ( comp @ n @ dtree @ dtree @ ( gram_L1451583624elle_H @ A ) @ root ) @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ ( gram_L315592705e_pick @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_Gram__Lang__Mirabelle__ojxrtuoybn_OInr__cont__H) ).

thf(587,plain,
    ! [A: dtree,B: n] :
      ( ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ ( gram_L1451583624elle_H @ A @ B ) ) )
      = ( image @ dtree @ dtree @ ( comp @ n @ dtree @ dtree @ ( gram_L1451583624elle_H @ A ) @ root ) @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ ( gram_L315592705e_pick @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(180,axiom,
    ! [A: dtree] :
      ( ( comp @ dtree @ n @ dtree @ root @ ( gram_L1004374585hsubst @ A ) )
      = root ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_root__o__subst) ).

thf(838,plain,
    ! [A: dtree] :
      ( ( comp @ dtree @ n @ dtree @ root @ ( gram_L1004374585hsubst @ A ) )
      = root ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(113,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TD > TC,B: TE > TD,C: TB > TC,D: TE > TB,E: TA > TE,F: TA > TB] :
      ( ( ( comp @ TD @ TC @ TE @ A @ B )
        = ( comp @ TB @ TC @ TE @ C @ D ) )
     => ( ( ( comp @ TE @ TB @ TA @ D @ E )
          = F )
       => ( ( comp @ TD @ TC @ TA @ A @ ( comp @ TE @ TD @ TA @ B @ E ) )
          = ( comp @ TB @ TC @ TA @ C @ F ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_rewriteL__comp__comp2) ).

thf(606,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TD > TC,B: TE > TD,C: TB > TC,D: TE > TB,E: TA > TE,F: TA > TB] :
      ( ( ( comp @ TD @ TC @ TE @ A @ B )
        = ( comp @ TB @ TC @ TE @ C @ D ) )
     => ( ( ( comp @ TE @ TB @ TA @ D @ E )
          = F )
       => ( ( comp @ TD @ TC @ TA @ A @ ( comp @ TE @ TD @ TA @ B @ E ) )
          = ( comp @ TB @ TC @ TA @ C @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(261,axiom,
    ! [TA: $tType,TB: $tType,A: TA > TB] :
      ( ( comp @ TB @ TB @ TA @ ( id @ TB ) @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_id__comp) ).

thf(1115,plain,
    ! [TA: $tType,TB: $tType,A: TA > TB] :
      ( ( comp @ TB @ TB @ TA @ ( id @ TB ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(12,axiom,
    finite_finite @ $o @ ( type2 @ $o ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Finite__Set_Ofinite_3) ).

thf(289,plain,
    finite_finite @ $o @ ( type2 @ $o ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(256,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > TB,B: TD > TC] :
      ( ( comp @ ( sum_sum @ TA @ TD ) @ ( sum_sum @ TB @ TC ) @ TA @ ( sum_map_sum @ TA @ TB @ TD @ TC @ A @ B ) @ ( sum_Inl @ TA @ TD ) )
      = ( comp @ TB @ ( sum_sum @ TB @ TC ) @ TA @ ( sum_Inl @ TB @ TC ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_map__sum__o__inj_I1_J) ).

thf(1100,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > TB,B: TD > TC] :
      ( ( comp @ ( sum_sum @ TA @ TD ) @ ( sum_sum @ TB @ TC ) @ TA @ ( sum_map_sum @ TA @ TB @ TD @ TC @ A @ B ) @ ( sum_Inl @ TA @ TD ) )
      = ( comp @ TB @ ( sum_sum @ TB @ TC ) @ TA @ ( sum_Inl @ TB @ TC ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(156,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA,B: set @ TC,C: TA > TB,D: TA > TB] :
      ( ( ( image @ TC @ TA @ A @ B )
        = ( top_top @ ( set @ TA ) ) )
     => ( ! [E: TC] :
            ( ( member @ TC @ E @ B )
           => ( ( comp @ TA @ TB @ TC @ C @ A @ E )
              = ( comp @ TA @ TB @ TC @ D @ A @ E ) ) )
       => ( C = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_surj__fun__eq) ).

thf(756,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA,B: set @ TC,C: TA > TB,D: TA > TB] :
      ( ( ( image @ TC @ TA @ A @ B )
        = ( top_top @ ( set @ TA ) ) )
     => ( ! [E: TC] :
            ( ( member @ TC @ E @ B )
           => ( ( comp @ TA @ TB @ TC @ C @ A @ E )
              = ( comp @ TA @ TB @ TC @ D @ A @ E ) ) )
       => ( C = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(267,axiom,
    ! [A: dtree,B: dtree] :
      ( ( gram_L864798063lle_wf @ A )
     => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ B ) @ ( cont @ A ) )
       => ( ( gram_L1614515765ubtrOf @ A @ ( root @ B ) )
          = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_subtrOf__root) ).

thf(1136,plain,
    ! [A: dtree,B: dtree] :
      ( ( gram_L864798063lle_wf @ A )
     => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ B ) @ ( cont @ A ) )
       => ( ( gram_L1614515765ubtrOf @ A @ ( root @ B ) )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(36,axiom,
    ! [TA: $tType,TB: $tType,A: TB,B: TB > TA,C: set @ TA] :
      ( ( member @ TB @ A @ ( vimage @ TB @ TA @ B @ C ) )
     => ( member @ TA @ ( B @ A ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_vimageD) ).

thf(353,plain,
    ! [TA: $tType,TB: $tType,A: TB,B: TB > TA,C: set @ TA] :
      ( ( member @ TB @ A @ ( vimage @ TB @ TA @ B @ C ) )
     => ( member @ TA @ ( B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(79,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TB,C: TA] :
      ( ( sum_case_sum @ TC @ TB @ TA @ A @ B @ ( sum_Inr @ TA @ TC @ C ) )
      = ( B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_old_Osum_Osimps_I6_J) ).

thf(480,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TB,C: TA] :
      ( ( sum_case_sum @ TC @ TB @ TA @ A @ B @ ( sum_Inr @ TA @ TC @ C ) )
      = ( B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(239,axiom,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: TA > TB,C: TA] :
      ( ( ( comp @ TB @ TA @ TA @ A @ B )
        = ( id @ TA ) )
     => ( ( A @ ( B @ C ) )
        = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_pointfree__idE) ).

thf(1040,plain,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: TA > TB,C: TA] :
      ( ( ( comp @ TB @ TA @ TA @ A @ B )
        = ( id @ TA ) )
     => ( ( A @ ( B @ C ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(259,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB > TA,C: set @ ( sum_sum @ TC @ TB )] :
      ( ( member @ ( sum_sum @ TC @ TA ) @ ( sum_Inr @ TA @ TC @ A ) @ ( image @ ( sum_sum @ TC @ TB ) @ ( sum_sum @ TC @ TA ) @ ( sum_map_sum @ TC @ TC @ TB @ TA @ ( id @ TC ) @ B ) @ C ) )
     => ? [D: TB] :
          ( ( member @ ( sum_sum @ TC @ TB ) @ ( sum_Inr @ TB @ TC @ D ) @ C )
          & ( ( B @ D )
            = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_Inr__oplus__elim) ).

thf(1109,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB > TA,C: set @ ( sum_sum @ TC @ TB )] :
      ( ( member @ ( sum_sum @ TC @ TA ) @ ( sum_Inr @ TA @ TC @ A ) @ ( image @ ( sum_sum @ TC @ TB ) @ ( sum_sum @ TC @ TA ) @ ( sum_map_sum @ TC @ TC @ TB @ TA @ ( id @ TC ) @ B ) @ C ) )
     => ? [D: TB] :
          ( ( member @ ( sum_sum @ TC @ TB ) @ ( sum_Inr @ TB @ TC @ D ) @ C )
          & ( ( B @ D )
            = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(34,axiom,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
      ( ( ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
        = ( top_top @ ( set @ TB ) ) )
     => ? [C: TA] :
          ( B
          = ( A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_surjD) ).

thf(348,plain,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
      ( ( ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
        = ( top_top @ ( set @ TB ) ) )
     => ? [C: TA] :
          ( B
          = ( A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(103,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TB > TA] :
      ( ( ( image @ TC @ TB @ A @ ( top_top @ ( set @ TC ) ) )
        = ( top_top @ ( set @ TB ) ) )
     => ( ( ( image @ TB @ TA @ B @ ( top_top @ ( set @ TB ) ) )
          = ( top_top @ ( set @ TA ) ) )
       => ( ( image @ TC @ TA @ ( comp @ TB @ TA @ TC @ B @ A ) @ ( top_top @ ( set @ TC ) ) )
          = ( top_top @ ( set @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_comp__surj) ).

thf(574,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TB > TA] :
      ( ( ( image @ TC @ TB @ A @ ( top_top @ ( set @ TC ) ) )
        = ( top_top @ ( set @ TB ) ) )
     => ( ( ( image @ TB @ TA @ B @ ( top_top @ ( set @ TB ) ) )
          = ( top_top @ ( set @ TA ) ) )
       => ( ( image @ TC @ TA @ ( comp @ TB @ TA @ TC @ B @ A ) @ ( top_top @ ( set @ TC ) ) )
          = ( top_top @ ( set @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(112,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: ( sum_sum @ TA @ TB ) > TC,B: TA > TC,C: sum_sum @ TA @ TB] :
      ( ( ( comp @ ( sum_sum @ TA @ TB ) @ TC @ TA @ A @ ( sum_Inl @ TA @ TB ) )
        = B )
     => ( ( A @ C )
        = ( sum_case_sum @ TA @ TC @ TB @ B @ ( comp @ ( sum_sum @ TA @ TB ) @ TC @ TB @ A @ ( sum_Inr @ TB @ TA ) ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_case__sum__expand__Inr) ).

thf(602,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: ( sum_sum @ TA @ TB ) > TC,B: TA > TC,C: sum_sum @ TA @ TB] :
      ( ( ( comp @ ( sum_sum @ TA @ TB ) @ TC @ TA @ A @ ( sum_Inl @ TA @ TB ) )
        = B )
     => ( ( A @ C )
        = ( sum_case_sum @ TA @ TC @ TB @ B @ ( comp @ ( sum_sum @ TA @ TB ) @ TC @ TB @ A @ ( sum_Inr @ TB @ TA ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(135,axiom,
    ! [A: dtree,B: n] :
      ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ A @ B )
     => ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ ( gram_L315592705e_pick @ A @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr__pick) ).

thf(687,plain,
    ! [A: dtree,B: n] :
      ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ A @ B )
     => ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ ( gram_L315592705e_pick @ A @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(15,axiom,
    ! [TA: $tType,A: TA,B: $o] :
      ( ( ( top_top @ ( TA > $o ) @ A )
        & B )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_top__conj_I1_J) ).

thf(293,plain,
    ! [TA: $tType,A: TA,B: $o] :
      ( ( ( top_top @ ( TA > $o ) @ A )
        & B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(161,axiom,
    ! [A: dtree,B: set @ n,C: t] :
      ( ( member @ n @ ( root @ A ) @ B )
     => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ C ) @ ( cont @ A ) )
       => ( gram_L805317441_inFr2 @ B @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_inFr2_OBase) ).

thf(774,plain,
    ! [A: dtree,B: set @ n,C: t] :
      ( ( member @ n @ ( root @ A ) @ B )
     => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ C ) @ ( cont @ A ) )
       => ( gram_L805317441_inFr2 @ B @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(51,axiom,
    ! [A: dtree,B: set @ n,C: dtree] :
      ( ( gram_L864798063lle_wf @ A )
     => ( ( gram_L716654942_subtr @ B @ C @ A )
       => ( gram_L864798063lle_wf @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_wf__subtr) ).

thf(396,plain,
    ! [A: dtree,B: set @ n,C: dtree] :
      ( ( gram_L864798063lle_wf @ A )
     => ( ( gram_L716654942_subtr @ B @ C @ A )
       => ( gram_L864798063lle_wf @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(62,axiom,
    ! [TA: $tType,TB: $tType,A: TA > TB] :
      ( ( vimage @ TA @ TB @ A @ ( top_top @ ( set @ TB ) ) )
      = ( top_top @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_vimage__UNIV) ).

thf(428,plain,
    ! [TA: $tType,TB: $tType,A: TA > TB] :
      ( ( vimage @ TA @ TB @ A @ ( top_top @ ( set @ TB ) ) )
      = ( top_top @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(194,axiom,
    ! [A: n,B: dtree] :
      ( ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ A ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ B ) ) )
     => ( ( root @ ( gram_L1614515765ubtrOf @ B @ A ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_root__subtrOf) ).

thf(877,plain,
    ! [A: n,B: dtree] :
      ( ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ A ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ B ) ) )
     => ( ( root @ ( gram_L1614515765ubtrOf @ B @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(137,axiom,
    ! [A: dtree,B: dtree] :
      ( ( ( root @ A )
        = ( root @ B ) )
     => ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L1004374585hsubst @ B @ A ) ) )
        = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_Inl__cont__hsubst__eq) ).

thf(692,plain,
    ! [A: dtree,B: dtree] :
      ( ( ( root @ A )
        = ( root @ B ) )
     => ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L1004374585hsubst @ B @ A ) ) )
        = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(20,axiom,
    ! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
      ( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
      = ( ? [D: TA] :
            ( ( member @ TA @ D @ C )
            & ( A
              = ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_image__iff) ).

thf(307,plain,
    ! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
      ( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
      = ( ? [D: TA] :
            ( ( member @ TA @ D @ C )
            & ( A
              = ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(14,axiom,
    ! [A: $o] :
      ( ( A = $true )
      | ( A = $false ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).

thf(292,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(69,axiom,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( if @ TA @ $false @ A @ B )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).

thf(452,plain,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( if @ TA @ $false @ A @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(203,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TB] :
      ( ( comp @ ( sum_sum @ TC @ TA ) @ TB @ TA @ ( sum_case_sum @ TC @ TB @ TA @ A @ B ) @ ( sum_Inr @ TA @ TC ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_case__sum__o__inj_I2_J) ).

thf(920,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TB] :
      ( ( comp @ ( sum_sum @ TC @ TA ) @ TB @ TA @ ( sum_case_sum @ TC @ TB @ TA @ A @ B ) @ ( sum_Inr @ TA @ TC ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(45,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: TA] :
      ( ( ( sum_Inr @ TA @ TB @ A )
        = ( sum_Inr @ TA @ TB @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_old_Osum_Oinject_I2_J) ).

thf(380,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: TA] :
      ( ( ( sum_Inr @ TA @ TB @ A )
        = ( sum_Inr @ TA @ TB @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(66,axiom,
    ! [TA: $tType] :
      ( ( finite_finite2 @ ( option @ TA ) @ ( top_top @ ( set @ ( option @ TA ) ) ) )
      = ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_finite__option__UNIV) ).

thf(439,plain,
    ! [TA: $tType] :
      ( ( finite_finite2 @ ( option @ TA ) @ ( top_top @ ( set @ ( option @ TA ) ) ) )
      = ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(157,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TD,C: TB > TC,D: TA > TB,E: TA] :
      ( ( ( comp @ TD @ TC @ TA @ A @ B )
        = ( comp @ TB @ TC @ TA @ C @ D ) )
     => ( ( A @ ( B @ E ) )
        = ( C @ ( D @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_comp__eq__dest) ).

thf(761,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TD,C: TB > TC,D: TA > TB,E: TA] :
      ( ( ( comp @ TD @ TC @ TA @ A @ B )
        = ( comp @ TB @ TC @ TA @ C @ D ) )
     => ( ( A @ ( B @ E ) )
        = ( C @ ( D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(90,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: TA] :
      ( ( ( sum_Inl @ TA @ TB @ A )
        = ( sum_Inl @ TA @ TB @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_Inl__inject) ).

thf(534,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: TA] :
      ( ( ( sum_Inl @ TA @ TB @ A )
        = ( sum_Inl @ TA @ TB @ B ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(145,axiom,
    ! [A: dtree,B: dtree] :
      ( ( gram_L864798063lle_wf @ A )
     => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ B ) @ ( cont @ A ) )
       => ? [C: n] :
            ( ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ C ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ A ) ) )
            & ( ( gram_L1614515765ubtrOf @ A @ C )
              = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_surj__subtrOf) ).

thf(714,plain,
    ! [A: dtree,B: dtree] :
      ( ( gram_L864798063lle_wf @ A )
     => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ B ) @ ( cont @ A ) )
       => ? [C: n] :
            ( ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ C ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ A ) ) )
            & ( ( gram_L1614515765ubtrOf @ A @ C )
              = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(244,axiom,
    ( ( gram_L1451583624elle_H @ tr0 )
    = ( unfold @ n @ ( gram_L1221482026le_H_r @ tr0 ) @ ( gram_L1221482011le_H_c @ tr0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_H__def) ).

thf(1057,plain,
    ( ( gram_L1451583624elle_H @ tr0 )
    = ( unfold @ n @ ( gram_L1221482026le_H_r @ tr0 ) @ ( gram_L1221482011le_H_c @ tr0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(18,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( finite_finite @ TB @ ( type2 @ TB ) )
        & ( finite_finite @ TA @ ( type2 @ TA ) ) )
     => ( finite_finite @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Finite__Set_Ofinite) ).

thf(302,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( finite_finite @ TB @ ( type2 @ TB ) )
        & ( finite_finite @ TA @ ( type2 @ TA ) ) )
     => ( finite_finite @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(189,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: TA > TB,D: TA] :
      ( ( ( comp @ TC @ TB @ TA @ A @ B )
        = ( comp @ TB @ TB @ TA @ ( id @ TB ) @ C ) )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_comp__eq__id__dest) ).

thf(862,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: TA > TB,D: TA] :
      ( ( ( comp @ TC @ TB @ TA @ A @ B )
        = ( comp @ TB @ TB @ TA @ ( id @ TB ) @ C ) )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(55,axiom,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
      ( ( ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
        = ( top_top @ ( set @ TB ) ) )
     => ~ ! [C: TA] :
            ( B
           != ( A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_surjE) ).

thf(407,plain,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
      ( ( ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
        = ( top_top @ ( set @ TB ) ) )
     => ~ ! [C: TA] :
            ( B
           != ( A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(5,axiom,
    $true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(275,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(150,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: TA > TB,D: TA] :
      ( ( ( comp @ TC @ TB @ TA @ A @ B )
        = C )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_comp__eq__dest__lhs) ).

thf(729,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: TA > TB,D: TA] :
      ( ( ( comp @ TC @ TB @ TA @ A @ B )
        = C )
     => ( ( A @ ( B @ D ) )
        = ( C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(74,axiom,
    ! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA] :
      ( ( A
        = ( B @ C ) )
     => ( member @ TB @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_range__eqI) ).

thf(467,plain,
    ! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA] :
      ( ( A
        = ( B @ C ) )
     => ( member @ TB @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(100,axiom,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TA] :
      ( ( finite_finite2 @ TB @ ( vimage @ TB @ TA @ A @ B ) )
     => ( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
          = ( top_top @ ( set @ TA ) ) )
       => ( finite_finite2 @ TA @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_finite__vimageD) ).

thf(566,plain,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TA] :
      ( ( finite_finite2 @ TB @ ( vimage @ TB @ TA @ A @ B ) )
     => ( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
          = ( top_top @ ( set @ TA ) ) )
       => ( finite_finite2 @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(236,axiom,
    ( t_tr
    = ( sum_Inl @ t @ dtree @ a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).

thf(1032,plain,
    ( t_tr
    = ( sum_Inl @ t @ dtree @ a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(39,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: TA > TB] :
      ( ( member @ TA @ A @ B )
     => ( ( C
          = ( D @ A ) )
       => ( member @ TB @ C @ ( image @ TA @ TB @ D @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_rev__image__eqI) ).

thf(361,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: TA > TB] :
      ( ( member @ TA @ A @ B )
     => ( ( C
          = ( D @ A ) )
       => ( member @ TB @ C @ ( image @ TA @ TB @ D @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(106,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TB,B: TA > TD,C: TA > TB,D: TB > TC] :
      ( ( ( comp @ TD @ TB @ TA @ A @ B )
        = C )
     => ( ( comp @ TD @ TC @ TA @ ( comp @ TB @ TC @ TD @ D @ A ) @ B )
        = ( comp @ TB @ TC @ TA @ D @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_rewriteR__comp__comp) ).

thf(583,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TB,B: TA > TD,C: TA > TB,D: TB > TC] :
      ( ( ( comp @ TD @ TB @ TA @ A @ B )
        = C )
     => ( ( comp @ TD @ TC @ TA @ ( comp @ TB @ TC @ TD @ D @ A ) @ B )
        = ( comp @ TB @ TC @ TA @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(72,axiom,
    ! [TA: $tType,A: TA > TA] :
      ( ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) )
     => ( ( inj_on @ TA @ TA @ A @ ( top_top @ ( set @ TA ) ) )
       => ( ( image @ TA @ TA @ A @ ( top_top @ ( set @ TA ) ) )
          = ( top_top @ ( set @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_finite__UNIV__inj__surj) ).

thf(461,plain,
    ! [TA: $tType,A: TA > TA] :
      ( ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) )
     => ( ( inj_on @ TA @ TA @ A @ ( top_top @ ( set @ TA ) ) )
       => ( ( image @ TA @ TA @ A @ ( top_top @ ( set @ TA ) ) )
          = ( top_top @ ( set @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(219,axiom,
    ! [A: dtree,B: n,C: dtree] :
      ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ A @ B )
     => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ C @ ( gram_L1451583624elle_H @ A @ B ) )
       => ? [D: n] :
            ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ A @ D )
            & ( C
              = ( gram_L1451583624elle_H @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr__H) ).

thf(974,plain,
    ! [A: dtree,B: n,C: dtree] :
      ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ A @ B )
     => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ C @ ( gram_L1451583624elle_H @ A @ B ) )
       => ? [D: n] :
            ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ A @ D )
            & ( C
              = ( gram_L1451583624elle_H @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(230,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( comp @ TB @ TB @ TA @ ( id @ TB ) )
      = ( id @ ( TA > TB ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_fun_Omap__id0) ).

thf(1012,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( comp @ TB @ TB @ TA @ ( id @ TB ) )
      = ( id @ ( TA > TB ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(10,axiom,
    ! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_top1I) ).

thf(285,plain,
    ! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(258,axiom,
    ! [A: dtree,B: dtree] :
      ( ( gram_L864798063lle_wf @ A )
     => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ B ) @ ( cont @ A ) )
       => ( gram_L864798063lle_wf @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_wf__cont) ).

thf(1106,plain,
    ! [A: dtree,B: dtree] :
      ( ( gram_L864798063lle_wf @ A )
     => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ B ) @ ( cont @ A ) )
       => ( gram_L864798063lle_wf @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(23,axiom,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
      ( ( inj_on @ TA @ TB @ A @ B )
     => ( ( finite_finite2 @ TB @ ( image @ TA @ TB @ A @ B ) )
        = ( finite_finite2 @ TA @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_finite__image__iff) ).

thf(317,plain,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
      ( ( inj_on @ TA @ TB @ A @ B )
     => ( ( finite_finite2 @ TB @ ( image @ TA @ TB @ A @ B ) )
        = ( finite_finite2 @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(123,axiom,
    ! [A: n] :
      ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ A )
     => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ ( gram_L315592705e_pick @ tr0 @ A ) @ tr0 )
        & ( ( root @ ( gram_L315592705e_pick @ tr0 @ A ) )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_pick) ).

thf(650,plain,
    ! [A: n] :
      ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ A )
     => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ ( gram_L315592705e_pick @ tr0 @ A ) @ tr0 )
        & ( ( root @ ( gram_L315592705e_pick @ tr0 @ A ) )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(263,axiom,
    ! [TA: $tType,A: ( set @ TA ) > TA,B: set @ TA] :
      ( ( A @ ( image @ TA @ TA @ ( id @ TA ) @ B ) )
      = ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_Sup_OSUP__id__eq) ).

thf(1121,plain,
    ! [TA: $tType,A: ( set @ TA ) > TA,B: set @ TA] :
      ( ( A @ ( image @ TA @ TA @ ( id @ TA ) @ B ) )
      = ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(228,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TB,C: TA] :
      ( ( sum_map_sum @ TD @ TC @ TA @ TB @ A @ B @ ( sum_Inr @ TA @ TD @ C ) )
      = ( sum_Inr @ TB @ TC @ ( B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_map__sum_Osimps_I2_J) ).

thf(1006,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TB,C: TA] :
      ( ( sum_map_sum @ TD @ TC @ TA @ TB @ A @ B @ ( sum_Inr @ TA @ TD @ C ) )
      = ( sum_Inr @ TB @ TC @ ( B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(191,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC,B: set @ TA,C: TC > TB] :
      ( ( inj_on @ TA @ TC @ A @ B )
     => ( ( inj_on @ TC @ TB @ C @ ( image @ TA @ TC @ A @ B ) )
        = ( inj_on @ TA @ TB @ ( comp @ TC @ TB @ TA @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_comp__inj__on__iff) ).

thf(869,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC,B: set @ TA,C: TC > TB] :
      ( ( inj_on @ TA @ TC @ A @ B )
     => ( ( inj_on @ TC @ TB @ C @ ( image @ TA @ TC @ A @ B ) )
        = ( inj_on @ TA @ TB @ ( comp @ TC @ TB @ TA @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(114,axiom,
    ! [A: set @ n,B: dtree,C: dtree] :
      ( ( gram_L716654942_subtr @ A @ B @ C )
     => ( member @ n @ ( root @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_subtr__rootL__in) ).

thf(610,plain,
    ! [A: set @ n,B: dtree,C: dtree] :
      ( ( gram_L716654942_subtr @ A @ B @ C )
     => ( member @ n @ ( root @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(82,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TB,C: TC > TB,D: TA > TB] :
      ( ( ( sum_case_sum @ TC @ TB @ TA @ A @ B )
        = ( sum_case_sum @ TC @ TB @ TA @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_case__sum__inject) ).

thf(499,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TB,C: TC > TB,D: TA > TB] :
      ( ( ( sum_case_sum @ TC @ TB @ TA @ A @ B )
        = ( sum_case_sum @ TC @ TB @ TA @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(223,axiom,
    ! [TA: $tType,TB: $tType,A: sum_sum @ TA @ TB] :
      ( ( sum_map_sum @ TA @ TA @ TB @ TB @ ( id @ TA ) @ ( id @ TB ) @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_sum_Omap__id) ).

thf(989,plain,
    ! [TA: $tType,TB: $tType,A: sum_sum @ TA @ TB] :
      ( ( sum_map_sum @ TA @ TA @ TB @ TB @ ( id @ TA ) @ ( id @ TB ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(139,axiom,
    ! [A: dtree,B: dtree] :
      ( ( ( root @ A )
       != ( root @ B ) )
     => ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L1004374585hsubst @ B @ A ) ) )
        = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_Inl__cont__hsubst__neq) ).

thf(697,plain,
    ! [A: dtree,B: dtree] :
      ( ( ( root @ A )
       != ( root @ B ) )
     => ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L1004374585hsubst @ B @ A ) ) )
        = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(253,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( comp @ TA @ TB @ TC )
      = ( ^ [A: TA > TB,B: TC > TA,C: TC] : ( A @ ( B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_comp__apply) ).

thf(1089,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( comp @ TA @ TB @ TC )
      = ( ^ [A: TA > TB,B: TC > TA,C: TC] : ( A @ ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(59,axiom,
    ! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_UNIV__I) ).

thf(420,plain,
    ! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(262,axiom,
    ! [A: dtree,B: n] :
      ( ( gram_L864798063lle_wf @ A )
     => ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ A @ B )
       => ( gram_L864798063lle_wf @ ( gram_L315592705e_pick @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_Gram__Lang__Mirabelle__ojxrtuoybn_Owf__pick) ).

thf(1118,plain,
    ! [A: dtree,B: n] :
      ( ( gram_L864798063lle_wf @ A )
     => ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ A @ B )
       => ( gram_L864798063lle_wf @ ( gram_L315592705e_pick @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(31,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TB,C: TA] :
      ( ( sum_rec_sum @ TC @ TB @ TA @ A @ B @ ( sum_Inr @ TA @ TC @ C ) )
      = ( B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_old_Osum_Osimps_I8_J) ).

thf(339,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TB,C: TA] :
      ( ( sum_rec_sum @ TC @ TB @ TA @ A @ B @ ( sum_Inr @ TA @ TC @ C ) )
      = ( B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(91,axiom,
    ! [TA: $tType,TB: $tType,A: set @ ( sum_sum @ TA @ TB ),B: set @ ( sum_sum @ TA @ TB )] :
      ( ( ( vimage @ TA @ ( sum_sum @ TA @ TB ) @ ( sum_Inl @ TA @ TB ) @ A )
        = ( vimage @ TA @ ( sum_sum @ TA @ TB ) @ ( sum_Inl @ TA @ TB ) @ B ) )
     => ( ( ( vimage @ TB @ ( sum_sum @ TA @ TB ) @ ( sum_Inr @ TB @ TA ) @ A )
          = ( vimage @ TB @ ( sum_sum @ TA @ TB ) @ ( sum_Inr @ TB @ TA ) @ B ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_Inl__Inr__image__cong) ).

thf(537,plain,
    ! [TA: $tType,TB: $tType,A: set @ ( sum_sum @ TA @ TB ),B: set @ ( sum_sum @ TA @ TB )] :
      ( ( ( vimage @ TA @ ( sum_sum @ TA @ TB ) @ ( sum_Inl @ TA @ TB ) @ A )
        = ( vimage @ TA @ ( sum_sum @ TA @ TB ) @ ( sum_Inl @ TA @ TB ) @ B ) )
     => ( ( ( vimage @ TB @ ( sum_sum @ TA @ TB ) @ ( sum_Inr @ TB @ TA ) @ A )
          = ( vimage @ TB @ ( sum_sum @ TA @ TB ) @ ( sum_Inr @ TB @ TA ) @ B ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(129,axiom,
    ! [A: dtree,B: dtree] :
      ( ( ( root @ A )
        = ( root @ B ) )
     => ( ( gram_L1004374585hsubst @ B @ A )
        = ( gram_L1004374585hsubst @ B @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_hsubst__eq) ).

thf(669,plain,
    ! [A: dtree,B: dtree] :
      ( ( ( root @ A )
        = ( root @ B ) )
     => ( ( gram_L1004374585hsubst @ B @ A )
        = ( gram_L1004374585hsubst @ B @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(77,axiom,
    ! [TA: $tType] :
      ( ( finite_finite @ TA @ ( type2 @ TA ) )
     => ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_finite__UNIV) ).

thf(476,plain,
    ! [TA: $tType] :
      ( ( finite_finite @ TA @ ( type2 @ TA ) )
     => ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(120,axiom,
    ! [A: dtree,B: dtree] :
      ( ( ( root @ A )
        = ( root @ B ) )
     => ( ( ( cont @ A )
          = ( cont @ B ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_dtree__cong) ).

thf(642,plain,
    ! [A: dtree,B: dtree] :
      ( ( ( root @ A )
        = ( root @ B ) )
     => ( ( ( cont @ A )
          = ( cont @ B ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(108,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TB > TC,C: TB > TC] :
      ( ! [D: TB] :
          ( ( member @ TB @ D @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) )
         => ( ( B @ D )
            = ( C @ D ) ) )
     => ( ( comp @ TB @ TC @ TA @ B @ A )
        = ( comp @ TB @ TC @ TA @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_fun_Omap__cong0) ).

thf(590,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TB > TC,C: TB > TC] :
      ( ! [D: TB] :
          ( ( member @ TB @ D @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) )
         => ( ( B @ D )
            = ( C @ D ) ) )
     => ( ( comp @ TB @ TC @ TA @ B @ A )
        = ( comp @ TB @ TC @ TA @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(93,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: TA] :
      ( ( ( sum_Inr @ TA @ TB @ A )
        = ( sum_Inr @ TA @ TB @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_Inr__inject) ).

thf(547,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: TA] :
      ( ( ( sum_Inr @ TA @ TB @ A )
        = ( sum_Inr @ TA @ TB @ B ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(142,axiom,
    ! [A: dtree,B: set @ n] :
      ( ( member @ n @ ( root @ A ) @ B )
     => ( gram_L716654942_subtr @ B @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_subtr_ORefl) ).

thf(706,plain,
    ! [A: dtree,B: set @ n] :
      ( ( member @ n @ ( root @ A ) @ B )
     => ( gram_L716654942_subtr @ B @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(27,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TC > TB,C: TA] :
      ( ( sum_case_sum @ TA @ TB @ TC @ A @ B @ ( sum_Inl @ TA @ TC @ C ) )
      = ( A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_old_Osum_Osimps_I5_J) ).

thf(328,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TC > TB,C: TA] :
      ( ( sum_case_sum @ TA @ TB @ TC @ A @ B @ ( sum_Inl @ TA @ TC @ C ) )
      = ( A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(75,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: TA] :
      ( ( ( sum_Inl @ TA @ TB @ A )
        = ( sum_Inl @ TA @ TB @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_sum_Oinject_I1_J) ).

thf(471,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: TA] :
      ( ( ( sum_Inl @ TA @ TB @ A )
        = ( sum_Inl @ TA @ TB @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(50,axiom,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
      ( ! [D: TB] :
          ( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
         => ( C @ D ) )
     => ! [D: TA] :
          ( ( member @ TA @ D @ B )
         => ( C @ ( A @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_ball__imageD) ).

thf(393,plain,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
      ( ! [D: TB] :
          ( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
         => ( C @ D ) )
     => ! [D: TA] :
          ( ( member @ TA @ D @ B )
         => ( C @ ( A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(122,axiom,
    ! [A: dtree,B: set @ n,C: dtree,D: dtree] :
      ( ( member @ n @ ( root @ A ) @ B )
     => ( ( gram_L716654942_subtr @ B @ C @ D )
       => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ D ) @ ( cont @ A ) )
         => ( gram_L716654942_subtr @ B @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_subtr_OStep) ).

thf(647,plain,
    ! [A: dtree,B: set @ n,C: dtree,D: dtree] :
      ( ( member @ n @ ( root @ A ) @ B )
     => ( ( gram_L716654942_subtr @ B @ C @ D )
       => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ D ) @ ( cont @ A ) )
         => ( gram_L716654942_subtr @ B @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(153,axiom,
    ! [A: n] :
      ( ( gram_L1221482011le_H_c @ tr0 @ A )
      = ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ ( gram_L315592705e_pick @ tr0 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_H__c__def) ).

thf(738,plain,
    ! [A: n] :
      ( ( gram_L1221482011le_H_c @ tr0 @ A )
      = ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ ( gram_L315592705e_pick @ tr0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(147,axiom,
    ! [A: set @ n,B: dtree,C: dtree] :
      ( ( gram_L716654942_subtr @ A @ B @ C )
     => ( member @ n @ ( root @ C ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_subtr__rootR__in) ).

thf(721,plain,
    ! [A: set @ n,B: dtree,C: dtree] :
      ( ( gram_L716654942_subtr @ A @ B @ C )
     => ( member @ n @ ( root @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(227,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE > TD,B: TA > TE,C: TB > TD,D: TA > TB,E: TD > TC,F: TB > TC] :
      ( ( ( comp @ TE @ TD @ TA @ A @ B )
        = ( comp @ TB @ TD @ TA @ C @ D ) )
     => ( ( ( comp @ TD @ TC @ TB @ E @ C )
          = F )
       => ( ( comp @ TE @ TC @ TA @ ( comp @ TD @ TC @ TE @ E @ A ) @ B )
          = ( comp @ TB @ TC @ TA @ F @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_rewriteR__comp__comp2) ).

thf(1002,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE > TD,B: TA > TE,C: TB > TD,D: TA > TB,E: TD > TC,F: TB > TC] :
      ( ( ( comp @ TE @ TD @ TA @ A @ B )
        = ( comp @ TB @ TD @ TA @ C @ D ) )
     => ( ( ( comp @ TD @ TC @ TB @ E @ C )
          = F )
       => ( ( comp @ TE @ TC @ TA @ ( comp @ TD @ TC @ TE @ E @ A ) @ B )
          = ( comp @ TB @ TC @ TA @ F @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(101,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( '!' @ ( sum_sum @ TA @ TB ) )
      = ( ^ [A: ( sum_sum @ TA @ TB ) > $o] :
            ( ! [B: TA] : ( A @ ( sum_Inl @ TA @ TB @ B ) )
            & ! [B: TB] : ( A @ ( sum_Inr @ TB @ TA @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_split__sum__all) ).

thf(569,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( '!' @ ( sum_sum @ TA @ TB ) )
      = ( ^ [A: ( sum_sum @ TA @ TB ) > $o] :
            ( ! [B: TA] : ( A @ ( sum_Inl @ TA @ TB @ B ) )
            & ! [B: TB] : ( A @ ( sum_Inr @ TB @ TA @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(163,axiom,
    ! [A: dtree,B: n] : ( finite_finite2 @ ( sum_sum @ t @ n ) @ ( gram_L1221482011le_H_c @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_Gram__Lang__Mirabelle__ojxrtuoybn_Ofinite__H__c) ).

thf(779,plain,
    ! [A: dtree,B: n] : ( finite_finite2 @ ( sum_sum @ t @ n ) @ ( gram_L1221482011le_H_c @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(42,axiom,
    ! [TA: $tType,TB: $tType,A: sum_sum @ TB @ TA] :
      ( ! [B: TB] :
          ( A
         != ( sum_Inl @ TB @ TA @ B ) )
     => ~ ! [B: TA] :
            ( A
           != ( sum_Inr @ TA @ TB @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_sumE) ).

thf(371,plain,
    ! [TA: $tType,TB: $tType,A: sum_sum @ TB @ TA] :
      ( ! [B: TB] :
          ( A
         != ( sum_Inl @ TB @ TA @ B ) )
     => ~ ! [B: TA] :
            ( A
           != ( sum_Inr @ TA @ TB @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(266,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: $o,B: TA > TC,C: TB > TD,D: TB,E: sum_sum @ TA @ TB] :
      ( ( A
       => ( ( sum_map_sum @ TA @ TC @ TB @ TD @ B @ C @ ( if @ ( sum_sum @ TA @ TB ) @ A @ ( sum_Inr @ TB @ TA @ D ) @ E ) )
          = ( sum_Inr @ TD @ TC @ ( C @ D ) ) ) )
      & ( ~ A
       => ( ( sum_map_sum @ TA @ TC @ TB @ TD @ B @ C @ ( if @ ( sum_sum @ TA @ TB ) @ A @ ( sum_Inr @ TB @ TA @ D ) @ E ) )
          = ( sum_map_sum @ TA @ TC @ TB @ TD @ B @ C @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_map__sum__if__distrib__then_I2_J) ).

thf(1131,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: $o,B: TA > TC,C: TB > TD,D: TB,E: sum_sum @ TA @ TB] :
      ( ( A
       => ( ( sum_map_sum @ TA @ TC @ TB @ TD @ B @ C @ ( if @ ( sum_sum @ TA @ TB ) @ A @ ( sum_Inr @ TB @ TA @ D ) @ E ) )
          = ( sum_Inr @ TD @ TC @ ( C @ D ) ) ) )
      & ( ~ A
       => ( ( sum_map_sum @ TA @ TC @ TB @ TD @ B @ C @ ( if @ ( sum_sum @ TA @ TB ) @ A @ ( sum_Inr @ TB @ TA @ D ) @ E ) )
          = ( sum_map_sum @ TA @ TC @ TB @ TD @ B @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(124,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TC > TD,B: TB > TC,C: TA > TB] :
      ( ( comp @ TB @ TD @ TA @ ( comp @ TC @ TD @ TB @ A @ B ) @ C )
      = ( comp @ TC @ TD @ TA @ A @ ( comp @ TB @ TC @ TA @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_comp__assoc) ).

thf(654,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TC > TD,B: TB > TC,C: TA > TB] :
      ( ( comp @ TB @ TD @ TA @ ( comp @ TC @ TD @ TB @ A @ B ) @ C )
      = ( comp @ TC @ TD @ TA @ A @ ( comp @ TB @ TC @ TA @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(208,axiom,
    ! [TA: $tType,A: TA > TA] :
      ( ( ! [B: TA] :
            ( ( A @ B )
            = B ) )
      = ( A
        = ( id @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_eq__id__iff) ).

thf(938,plain,
    ! [TA: $tType,A: TA > TA] :
      ( ( ! [B: TA] :
            ( ( A @ B )
            = B ) )
      = ( A
        = ( id @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(117,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB] :
      ( ( image @ TA @ TC @ ( comp @ TB @ TC @ TA @ A @ B ) @ ( top_top @ ( set @ TA ) ) )
      = ( image @ TB @ TC @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_fun_Oset__map) ).

thf(633,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB] :
      ( ( image @ TA @ TC @ ( comp @ TB @ TC @ TA @ A @ B ) @ ( top_top @ ( set @ TA ) ) )
      = ( image @ TB @ TC @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(171,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE > TB,B: TA > TE,C: TA,D: TD > TB,E: TA > TD,F: TB > TC] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ C ) ) )
     => ( ( comp @ TE @ TC @ TA @ ( comp @ TB @ TC @ TE @ F @ A ) @ B @ C )
        = ( comp @ TD @ TC @ TA @ ( comp @ TB @ TC @ TD @ F @ D ) @ E @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_type__copy__map__cong0) ).

thf(805,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE > TB,B: TA > TE,C: TA,D: TD > TB,E: TA > TD,F: TB > TC] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ C ) ) )
     => ( ( comp @ TE @ TC @ TA @ ( comp @ TB @ TC @ TE @ F @ A ) @ B @ C )
        = ( comp @ TD @ TC @ TA @ ( comp @ TB @ TC @ TD @ F @ D ) @ E @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(125,axiom,
    ( gram_L1231612515_deftr
    = ( unfold @ n @ ( id @ n ) @ gram_L1451583635elle_S ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_deftr__def) ).

thf(657,plain,
    ( gram_L1231612515_deftr
    = ( unfold @ n @ ( id @ n ) @ gram_L1451583635elle_S ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(97,axiom,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
      ( ( finite_finite2 @ TB @ ( image @ TA @ TB @ A @ B ) )
     => ( ( inj_on @ TA @ TB @ A @ B )
       => ( finite_finite2 @ TA @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_finite__imageD) ).

thf(558,plain,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
      ( ( finite_finite2 @ TB @ ( image @ TA @ TB @ A @ B ) )
     => ( ( inj_on @ TA @ TB @ A @ B )
       => ( finite_finite2 @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(131,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TB] :
      ( ( comp @ ( sum_sum @ TD @ TA ) @ ( sum_sum @ TC @ TB ) @ TA @ ( sum_map_sum @ TD @ TC @ TA @ TB @ A @ B ) @ ( sum_Inr @ TA @ TD ) )
      = ( comp @ TB @ ( sum_sum @ TC @ TB ) @ TA @ ( sum_Inr @ TB @ TC ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_map__sum__o__inj_I2_J) ).

thf(674,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TB] :
      ( ( comp @ ( sum_sum @ TD @ TA ) @ ( sum_sum @ TC @ TB ) @ TA @ ( sum_map_sum @ TD @ TC @ TA @ TB @ A @ B ) @ ( sum_Inr @ TA @ TD ) )
      = ( comp @ TB @ ( sum_sum @ TC @ TB ) @ TA @ ( sum_Inr @ TB @ TC ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(205,axiom,
    ! [TA: $tType] :
      ( ( image @ TA @ TA @ ( id @ TA ) )
      = ( id @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_image__id) ).

thf(926,plain,
    ! [TA: $tType] :
      ( ( image @ TA @ TA @ ( id @ TA ) )
      = ( id @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(216,axiom,
    ! [TA: $tType,TB: $tType,A: TA > TB] :
      ( ( comp @ TA @ TB @ TA @ A @ ( id @ TA ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_comp__id) ).

thf(965,plain,
    ! [TA: $tType,TB: $tType,A: TA > TB] :
      ( ( comp @ TA @ TB @ TA @ A @ ( id @ TA ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(61,axiom,
    ! [TA: $tType,TB: $tType,A: TB,B: TA] :
      ( ( sum_Inr @ TB @ TA @ A )
     != ( sum_Inl @ TA @ TB @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_Inr__not__Inl) ).

thf(425,plain,
    ! [TA: $tType,TB: $tType,A: TB,B: TA] :
      ( ( sum_Inr @ TB @ TA @ A )
     != ( sum_Inl @ TA @ TB @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(85,axiom,
    ! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB > $o] :
      ( ( finite_finite2 @ TA @ A )
     => ( ! [C: TA] :
            ( ( member @ TA @ C @ A )
           => ? [D: TB] : ( B @ C @ D ) )
       => ? [C: TA > TB] :
          ! [D: TA] :
            ( ( member @ TA @ D @ A )
           => ( B @ D @ ( C @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_finite__set__choice) ).

thf(513,plain,
    ! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB > $o] :
      ( ( finite_finite2 @ TA @ A )
     => ( ! [C: TA] :
            ( ( member @ TA @ C @ A )
           => ? [D: TB] : ( B @ C @ D ) )
       => ? [C: TA > TB] :
          ! [D: TA] :
            ( ( member @ TA @ D @ A )
           => ( B @ D @ ( C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(257,axiom,
    ! [A: set @ n,B: dtree,C: t,D: dtree] :
      ( ( gram_L805317441_inFr2 @ A @ B @ C )
     => ( ( member @ n @ ( root @ D ) @ A )
       => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ B ) @ ( cont @ D ) )
         => ( gram_L805317441_inFr2 @ A @ D @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_inFr2__Ind) ).

thf(1103,plain,
    ! [A: set @ n,B: dtree,C: t,D: dtree] :
      ( ( gram_L805317441_inFr2 @ A @ B @ C )
     => ( ( member @ n @ ( root @ D ) @ A )
       => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ B ) @ ( cont @ D ) )
         => ( gram_L805317441_inFr2 @ A @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(175,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB > TC,C: set @ ( sum_sum @ TA @ TB )] :
      ( ( member @ ( sum_sum @ TA @ TC ) @ ( sum_Inl @ TA @ TC @ A ) @ ( image @ ( sum_sum @ TA @ TB ) @ ( sum_sum @ TA @ TC ) @ ( sum_map_sum @ TA @ TA @ TB @ TC @ ( id @ TA ) @ B ) @ C ) )
     => ( member @ ( sum_sum @ TA @ TB ) @ ( sum_Inl @ TA @ TB @ A ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_Inl__oplus__elim) ).

thf(824,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB > TC,C: set @ ( sum_sum @ TA @ TB )] :
      ( ( member @ ( sum_sum @ TA @ TC ) @ ( sum_Inl @ TA @ TC @ A ) @ ( image @ ( sum_sum @ TA @ TB ) @ ( sum_sum @ TA @ TC ) @ ( sum_map_sum @ TA @ TA @ TB @ TC @ ( id @ TA ) @ B ) @ C ) )
     => ( member @ ( sum_sum @ TA @ TB ) @ ( sum_Inl @ TA @ TB @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(187,axiom,
    ! [A: dtree,B: n] :
      ( ( cont @ ( gram_L1451583624elle_H @ A @ B ) )
      = ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ dtree @ dtree @ ( id @ t ) @ ( comp @ n @ dtree @ dtree @ ( gram_L1451583624elle_H @ A ) @ root ) ) @ ( cont @ ( gram_L315592705e_pick @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_Gram__Lang__Mirabelle__ojxrtuoybn_Ocont__H) ).

thf(856,plain,
    ! [A: dtree,B: n] :
      ( ( cont @ ( gram_L1451583624elle_H @ A @ B ) )
      = ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ dtree @ dtree @ ( id @ t ) @ ( comp @ n @ dtree @ dtree @ ( gram_L1451583624elle_H @ A ) @ root ) ) @ ( cont @ ( gram_L315592705e_pick @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(7,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( finite_finite @ TB @ ( type2 @ TB ) )
        & ( finite_finite @ TA @ ( type2 @ TA ) ) )
     => ( finite_finite @ ( sum_sum @ TB @ TA ) @ ( type2 @ ( sum_sum @ TB @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Sum__Type_Osum___Finite__Set_Ofinite_5) ).

thf(279,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( finite_finite @ TB @ ( type2 @ TB ) )
        & ( finite_finite @ TA @ ( type2 @ TA ) ) )
     => ( finite_finite @ ( sum_sum @ TB @ TA ) @ ( type2 @ ( sum_sum @ TB @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(151,axiom,
    ! [A: dtree,B: dtree] :
      ( ( root @ ( gram_L1004374585hsubst @ A @ B ) )
      = ( root @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_root__hsubst) ).

thf(733,plain,
    ! [A: dtree,B: dtree] :
      ( ( root @ ( gram_L1004374585hsubst @ A @ B ) )
      = ( root @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(136,axiom,
    ! [A: dtree,B: n] :
      ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ A @ B )
     => ( ( root @ ( gram_L315592705e_pick @ A @ B ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_Gram__Lang__Mirabelle__ojxrtuoybn_Oroot__pick) ).

thf(689,plain,
    ! [A: dtree,B: n] :
      ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ A @ B )
     => ( ( root @ ( gram_L315592705e_pick @ A @ B ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(16,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ! [C: TA] :
          ( ( A @ C )
          = ( B @ C ) )
     => ( ( collect @ TA @ A )
        = ( collect @ TA @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Collect__cong) ).

thf(296,plain,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ! [C: TA] :
          ( ( A @ C )
          = ( B @ C ) )
     => ( ( collect @ TA @ A )
        = ( collect @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(53,axiom,
    ! [TA: $tType,TB: $tType,A: TB,B: TA] :
      ( ( sum_Inr @ TB @ TA @ A )
     != ( sum_Inl @ TA @ TB @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_old_Osum_Odistinct_I2_J) ).

thf(402,plain,
    ! [TA: $tType,TB: $tType,A: TB,B: TA] :
      ( ( sum_Inr @ TB @ TA @ A )
     != ( sum_Inl @ TA @ TB @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(57,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: $o,B: TC > TB,C: TA > TB,D: TC,E: TA] :
      ( ( A
       => ( ( sum_case_sum @ TC @ TB @ TA @ B @ C @ ( if @ ( sum_sum @ TC @ TA ) @ A @ ( sum_Inl @ TC @ TA @ D ) @ ( sum_Inr @ TA @ TC @ E ) ) )
          = ( B @ D ) ) )
      & ( ~ A
       => ( ( sum_case_sum @ TC @ TB @ TA @ B @ C @ ( if @ ( sum_sum @ TC @ TA ) @ A @ ( sum_Inl @ TC @ TA @ D ) @ ( sum_Inr @ TA @ TC @ E ) ) )
          = ( C @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_case__sum__if) ).

thf(413,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: $o,B: TC > TB,C: TA > TB,D: TC,E: TA] :
      ( ( A
       => ( ( sum_case_sum @ TC @ TB @ TA @ B @ C @ ( if @ ( sum_sum @ TC @ TA ) @ A @ ( sum_Inl @ TC @ TA @ D ) @ ( sum_Inr @ TA @ TC @ E ) ) )
          = ( B @ D ) ) )
      & ( ~ A
       => ( ( sum_case_sum @ TC @ TB @ TA @ B @ C @ ( if @ ( sum_sum @ TC @ TA ) @ A @ ( sum_Inl @ TC @ TA @ D ) @ ( sum_Inr @ TA @ TC @ E ) ) )
          = ( C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(193,axiom,
    ! [A: dtree,B: set @ n] :
      ( ( member @ n @ ( root @ A ) @ B )
     => ( gram_L830233218_inItr @ B @ A @ ( root @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_inItr_OBase) ).

thf(875,plain,
    ! [A: dtree,B: set @ n] :
      ( ( member @ n @ ( root @ A ) @ B )
     => ( gram_L830233218_inItr @ B @ A @ ( root @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(176,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TD,C: TB > TC,D: TA > TB] :
      ( ( ( comp @ TD @ TC @ TA @ A @ B )
        = ( comp @ TB @ TC @ TA @ C @ D ) )
     => ! [E: TA] :
          ( ( A @ ( B @ E ) )
          = ( C @ ( D @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_comp__eq__elim) ).

thf(826,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TD,C: TB > TC,D: TA > TB] :
      ( ( ( comp @ TD @ TC @ TA @ A @ B )
        = ( comp @ TB @ TC @ TA @ C @ D ) )
     => ! [E: TA] :
          ( ( A @ ( B @ E ) )
          = ( C @ ( D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(104,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TC > TD,B: TF > TE,C: TA > TC,D: TB > TF,E: sum_sum @ TA @ TB] :
      ( ( sum_map_sum @ TC @ TD @ TF @ TE @ A @ B @ ( sum_map_sum @ TA @ TC @ TB @ TF @ C @ D @ E ) )
      = ( sum_map_sum @ TA @ TD @ TB @ TE @ ( comp @ TC @ TD @ TA @ A @ C ) @ ( comp @ TF @ TE @ TB @ B @ D ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_map__sum_Ocompositionality) ).

thf(577,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TC > TD,B: TF > TE,C: TA > TC,D: TB > TF,E: sum_sum @ TA @ TB] :
      ( ( sum_map_sum @ TC @ TD @ TF @ TE @ A @ B @ ( sum_map_sum @ TA @ TC @ TB @ TF @ C @ D @ E ) )
      = ( sum_map_sum @ TA @ TD @ TB @ TE @ ( comp @ TC @ TD @ TA @ A @ C ) @ ( comp @ TF @ TE @ TB @ B @ D ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(144,axiom,
    ! [TA: $tType] :
      ( ( id @ TA )
      = ( ^ [A: TA] : A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_id__def) ).

thf(711,plain,
    ! [TA: $tType] :
      ( ( id @ TA )
      = ( ^ [A: TA] : A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(264,axiom,
    ! [TA: $tType,A: TA > ( set @ ( sum_sum @ t @ ( sum_sum @ dtree @ TA ) ) ),B: TA,C: TA > n] :
      ( ( finite_finite2 @ ( sum_sum @ t @ ( sum_sum @ dtree @ TA ) ) @ ( A @ B ) )
     => ( ( cont @ ( corec @ TA @ C @ A @ B ) )
        = ( image @ ( sum_sum @ t @ ( sum_sum @ dtree @ TA ) ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ ( sum_sum @ dtree @ TA ) @ dtree @ ( id @ t ) @ ( sum_case_sum @ dtree @ dtree @ TA @ ( id @ dtree ) @ ( corec @ TA @ C @ A ) ) ) @ ( A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_corec_I2_J) ).

thf(1124,plain,
    ! [TA: $tType,A: TA > ( set @ ( sum_sum @ t @ ( sum_sum @ dtree @ TA ) ) ),B: TA,C: TA > n] :
      ( ( finite_finite2 @ ( sum_sum @ t @ ( sum_sum @ dtree @ TA ) ) @ ( A @ B ) )
     => ( ( cont @ ( corec @ TA @ C @ A @ B ) )
        = ( image @ ( sum_sum @ t @ ( sum_sum @ dtree @ TA ) ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ ( sum_sum @ dtree @ TA ) @ dtree @ ( id @ t ) @ ( sum_case_sum @ dtree @ dtree @ TA @ ( id @ dtree ) @ ( corec @ TA @ C @ A ) ) ) @ ( A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(8,axiom,
    ! [TA: $tType] :
      ( ( finite_finite @ TA @ ( type2 @ TA ) )
     => ( finite_finite @ ( option @ TA ) @ ( type2 @ ( option @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Option_Ooption___Finite__Set_Ofinite_6) ).

thf(281,plain,
    ! [TA: $tType] :
      ( ( finite_finite @ TA @ ( type2 @ TA ) )
     => ( finite_finite @ ( option @ TA ) @ ( type2 @ ( option @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(102,axiom,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: TA] : ( member @ TB @ ( A @ B ) @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_rangeI) ).

thf(572,plain,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: TA] : ( member @ TB @ ( A @ B ) @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(166,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TC,C: sum_sum @ TA @ TB] :
      ( ( comp @ ( sum_sum @ TC @ TB ) @ TC @ ( sum_sum @ TA @ TB ) @ ( sum_case_sum @ TC @ TC @ TB @ ( id @ TC ) @ A ) @ ( sum_map_sum @ TA @ TC @ TB @ TB @ B @ ( id @ TB ) ) @ C )
      = ( sum_case_sum @ TA @ TC @ TB @ ( comp @ TA @ TC @ TA @ B @ ( id @ TA ) ) @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_case__sum__o__map__sum__id) ).

thf(787,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TC,C: sum_sum @ TA @ TB] :
      ( ( comp @ ( sum_sum @ TC @ TB ) @ TC @ ( sum_sum @ TA @ TB ) @ ( sum_case_sum @ TC @ TC @ TB @ ( id @ TC ) @ A ) @ ( sum_map_sum @ TA @ TC @ TB @ TB @ B @ ( id @ TB ) ) @ C )
      = ( sum_case_sum @ TA @ TC @ TB @ ( comp @ TA @ TC @ TA @ B @ ( id @ TA ) ) @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(254,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( sum_map_sum @ TA @ TA @ TB @ TB @ ( id @ TA ) @ ( id @ TB ) )
      = ( id @ ( sum_sum @ TA @ TB ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_sum_Omap__id0) ).

thf(1092,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( sum_map_sum @ TA @ TA @ TB @ TB @ ( id @ TA ) @ ( id @ TB ) )
      = ( id @ ( sum_sum @ TA @ TB ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(211,axiom,
    ! [A: set @ ( sum_sum @ t @ dtree ),B: set @ ( sum_sum @ t @ dtree ),C: n,D: n] :
      ( ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ A )
     => ( ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ B )
       => ( ( ( node @ C @ A )
            = ( node @ D @ B ) )
          = ( ( C = D )
            & ( A = B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_dtree__simps) ).

thf(947,plain,
    ! [A: set @ ( sum_sum @ t @ dtree ),B: set @ ( sum_sum @ t @ dtree ),C: n,D: n] :
      ( ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ A )
     => ( ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ B )
       => ( ( ( node @ C @ A )
            = ( node @ D @ B ) )
          = ( ( C = D )
            & ( A = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(92,axiom,
    ! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB,E: ( set @ TB ) > TB] :
      ( ( A = B )
     => ( ! [F: TA] :
            ( ( member @ TA @ F @ B )
           => ( ( C @ F )
              = ( D @ F ) ) )
       => ( ( E @ ( image @ TA @ TB @ C @ A ) )
          = ( E @ ( image @ TA @ TB @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_Sup_OSUP__cong) ).

thf(540,plain,
    ! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB,E: ( set @ TB ) > TB] :
      ( ( A = B )
     => ( ! [F: TA] :
            ( ( member @ TA @ F @ B )
           => ( ( C @ F )
              = ( D @ F ) ) )
       => ( ( E @ ( image @ TA @ TB @ C @ A ) )
          = ( E @ ( image @ TA @ TB @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(130,axiom,
    ! [A: n] :
      ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ A )
     => ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ ( gram_L315592705e_pick @ tr0 @ A ) @ tr0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_subtr__pick) ).

thf(672,plain,
    ! [A: n] :
      ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ A )
     => ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ ( gram_L315592705e_pick @ tr0 @ A ) @ tr0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(165,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TC > TD,B: TF > TE,C: TA > TC,D: TB > TF,E: sum_sum @ TA @ TB] :
      ( ( sum_map_sum @ TC @ TD @ TF @ TE @ A @ B @ ( sum_map_sum @ TA @ TC @ TB @ TF @ C @ D @ E ) )
      = ( sum_map_sum @ TA @ TD @ TB @ TE @ ( comp @ TC @ TD @ TA @ A @ C ) @ ( comp @ TF @ TE @ TB @ B @ D ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_sum_Omap__comp) ).

thf(784,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TC > TD,B: TF > TE,C: TA > TC,D: TB > TF,E: sum_sum @ TA @ TB] :
      ( ( sum_map_sum @ TC @ TD @ TF @ TE @ A @ B @ ( sum_map_sum @ TA @ TC @ TB @ TF @ C @ D @ E ) )
      = ( sum_map_sum @ TA @ TD @ TB @ TE @ ( comp @ TC @ TD @ TA @ A @ C ) @ ( comp @ TF @ TE @ TB @ B @ D ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(152,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC,B: set @ TA,C: TC > TB] :
      ( ( inj_on @ TA @ TC @ A @ B )
     => ( ( inj_on @ TC @ TB @ C @ ( image @ TA @ TC @ A @ B ) )
       => ( inj_on @ TA @ TB @ ( comp @ TC @ TB @ TA @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_comp__inj__on) ).

thf(736,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC,B: set @ TA,C: TC > TB] :
      ( ( inj_on @ TA @ TC @ A @ B )
     => ( ( inj_on @ TC @ TB @ C @ ( image @ TA @ TC @ A @ B ) )
       => ( inj_on @ TA @ TB @ ( comp @ TC @ TB @ TA @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(44,axiom,
    ! [A: dtree,B: dtree] :
      ( ( gram_L864798063lle_wf @ A )
     => ( ( gram_L864798063lle_wf @ B )
       => ( gram_L864798063lle_wf @ ( gram_L1004374585hsubst @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_wf__hsubst) ).

thf(377,plain,
    ! [A: dtree,B: dtree] :
      ( ( gram_L864798063lle_wf @ A )
     => ( ( gram_L864798063lle_wf @ B )
       => ( gram_L864798063lle_wf @ ( gram_L1004374585hsubst @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(3,axiom,
    $true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).

thf(271,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(158,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TB > TD,C: TA > TB] :
      ( ( comp @ TD @ TC @ TA @ A @ ( comp @ TB @ TD @ TA @ B @ C ) )
      = ( comp @ TB @ TC @ TA @ ( comp @ TD @ TC @ TB @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_fun_Omap__comp) ).

thf(764,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TB > TD,C: TA > TB] :
      ( ( comp @ TD @ TC @ TA @ A @ ( comp @ TB @ TD @ TA @ B @ C ) )
      = ( comp @ TB @ TC @ TA @ ( comp @ TD @ TC @ TB @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(220,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: set @ TA] :
      ( ( image @ TC @ TB @ A @ ( image @ TA @ TC @ B @ C ) )
      = ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_image__comp) ).

thf(979,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: set @ TA] :
      ( ( image @ TC @ TB @ A @ ( image @ TA @ TC @ B @ C ) )
      = ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(195,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB > TC,C: set @ ( sum_sum @ TA @ TB )] :
      ( ( member @ ( sum_sum @ TA @ TC ) @ ( sum_Inl @ TA @ TC @ A ) @ ( image @ ( sum_sum @ TA @ TB ) @ ( sum_sum @ TA @ TC ) @ ( sum_map_sum @ TA @ TA @ TB @ TC @ ( id @ TA ) @ B ) @ C ) )
      = ( member @ ( sum_sum @ TA @ TB ) @ ( sum_Inl @ TA @ TB @ A ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_Inl__oplus__iff) ).

thf(880,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB > TC,C: set @ ( sum_sum @ TA @ TB )] :
      ( ( member @ ( sum_sum @ TA @ TC ) @ ( sum_Inl @ TA @ TC @ A ) @ ( image @ ( sum_sum @ TA @ TB ) @ ( sum_sum @ TA @ TC ) @ ( sum_map_sum @ TA @ TA @ TB @ TC @ ( id @ TA ) @ B ) @ C ) )
      = ( member @ ( sum_sum @ TA @ TB ) @ ( sum_Inl @ TA @ TB @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(240,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TB > TA,C: set @ TA] :
      ( ( vimage @ TC @ TB @ A @ ( vimage @ TB @ TA @ B @ C ) )
      = ( vimage @ TC @ TA @ ( comp @ TB @ TA @ TC @ B @ A ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_vimage__comp) ).

thf(1043,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TB > TA,C: set @ TA] :
      ( ( vimage @ TC @ TB @ A @ ( vimage @ TB @ TA @ B @ C ) )
      = ( vimage @ TC @ TA @ ( comp @ TB @ TA @ TC @ B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(64,axiom,
    ! [TA: $tType,TB: $tType,A: ( sum_sum @ TA @ TB ) > $o,B: sum_sum @ TA @ TB] :
      ( ! [C: TA] : ( A @ ( sum_Inl @ TA @ TB @ C ) )
     => ( ! [C: TB] : ( A @ ( sum_Inr @ TB @ TA @ C ) )
       => ( A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_old_Osum_Oinducts) ).

thf(434,plain,
    ! [TA: $tType,TB: $tType,A: ( sum_sum @ TA @ TB ) > $o,B: sum_sum @ TA @ TB] :
      ( ! [C: TA] : ( A @ ( sum_Inl @ TA @ TB @ C ) )
     => ( ! [C: TB] : ( A @ ( sum_Inr @ TB @ TA @ C ) )
       => ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(48,axiom,
    ! [TA: $tType,TB: $tType,A: TB,B: TA] :
      ( ( sum_Inl @ TB @ TA @ A )
     != ( sum_Inr @ TA @ TB @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_Inl__Inr__False) ).

thf(387,plain,
    ! [TA: $tType,TB: $tType,A: TB,B: TA] :
      ( ( sum_Inl @ TB @ TA @ A )
     != ( sum_Inr @ TA @ TB @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(116,axiom,
    ( ( comp @ dtree @ n @ n @ root @ gram_L1231612515_deftr )
    = ( id @ n ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_root__o__deftr) ).

thf(631,plain,
    ( ( comp @ dtree @ n @ n @ root @ gram_L1231612515_deftr )
    = ( id @ n ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(25,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( finite_finite2 @ ( sum_sum @ TB @ TA ) @ ( top_top @ ( set @ ( sum_sum @ TB @ TA ) ) ) )
      = ( ( finite_finite2 @ TB @ ( top_top @ ( set @ TB ) ) )
        & ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_finite__Plus__UNIV__iff) ).

thf(323,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( finite_finite2 @ ( sum_sum @ TB @ TA ) @ ( top_top @ ( set @ ( sum_sum @ TB @ TA ) ) ) )
      = ( ( finite_finite2 @ TB @ ( top_top @ ( set @ TB ) ) )
        & ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(80,axiom,
    ! [TA: $tType,TB: $tType,A: TB,B: TA] :
      ( ( sum_Inr @ TB @ TA @ A )
     != ( sum_Inl @ TA @ TB @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_Inr__Inl__False) ).

thf(483,plain,
    ! [TA: $tType,TB: $tType,A: TB,B: TA] :
      ( ( sum_Inr @ TB @ TA @ A )
     != ( sum_Inl @ TA @ TB @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(233,axiom,
    ! [A: dtree] : ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ ( cont @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_finite__cont) ).

thf(1022,plain,
    ! [A: dtree] : ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ ( cont @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(33,axiom,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
      ( ? [D: TB] :
          ( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
          & ( C @ D ) )
     => ? [D: TA] :
          ( ( member @ TA @ D @ B )
          & ( C @ ( A @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_bex__imageD) ).

thf(345,plain,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
      ( ? [D: TB] :
          ( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
          & ( C @ D ) )
     => ? [D: TA] :
          ( ( member @ TA @ D @ B )
          & ( C @ ( A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(95,axiom,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( if @ TA @ $true @ A @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).

thf(552,plain,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( if @ TA @ $true @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(169,axiom,
    ! [A: set @ n,B: dtree,C: n] :
      ( ( gram_L830233218_inItr @ A @ B @ C )
     => ( member @ n @ ( root @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_inItr__root__in) ).

thf(799,plain,
    ! [A: set @ n,B: dtree,C: n] :
      ( ( gram_L830233218_inItr @ A @ B @ C )
     => ( member @ n @ ( root @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(149,axiom,
    ! [TA: $tType,A: TA > n,B: TA > ( set @ ( sum_sum @ t @ TA ) ),C: TA] :
      ( ( root @ ( unfold @ TA @ A @ B @ C ) )
      = ( A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_unfold_I1_J) ).

thf(726,plain,
    ! [TA: $tType,A: TA > n,B: TA > ( set @ ( sum_sum @ t @ TA ) ),C: TA] :
      ( ( root @ ( unfold @ TA @ A @ B @ C ) )
      = ( A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(184,axiom,
    ! [A: dtree,B: dtree] : ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ ( gram_L1905609002ubst_c @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_finite__hsubst__c) ).

thf(848,plain,
    ! [A: dtree,B: dtree] : ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ ( gram_L1905609002ubst_c @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(140,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > TB,B: TD > TC,C: TA] :
      ( ( sum_map_sum @ TA @ TB @ TD @ TC @ A @ B @ ( sum_Inl @ TA @ TD @ C ) )
      = ( sum_Inl @ TB @ TC @ ( A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_map__sum_Osimps_I1_J) ).

thf(700,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > TB,B: TD > TC,C: TA] :
      ( ( sum_map_sum @ TA @ TB @ TD @ TC @ A @ B @ ( sum_Inl @ TA @ TD @ C ) )
      = ( sum_Inl @ TB @ TC @ ( A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(87,axiom,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: TA,D: set @ TA] :
      ( ( ( A @ B )
        = C )
     => ( ( member @ TA @ C @ D )
       => ( member @ TB @ B @ ( vimage @ TB @ TA @ A @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_vimageI) ).

thf(520,plain,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: TA,D: set @ TA] :
      ( ( ( A @ B )
        = C )
     => ( ( member @ TA @ C @ D )
       => ( member @ TB @ B @ ( vimage @ TB @ TA @ A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(235,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TE > TD,B: TB > TC,C: TF > TE,D: TA > TB] :
      ( ( comp @ ( sum_sum @ TE @ TB ) @ ( sum_sum @ TD @ TC ) @ ( sum_sum @ TF @ TA ) @ ( sum_map_sum @ TE @ TD @ TB @ TC @ A @ B ) @ ( sum_map_sum @ TF @ TE @ TA @ TB @ C @ D ) )
      = ( sum_map_sum @ TF @ TD @ TA @ TC @ ( comp @ TE @ TD @ TF @ A @ C ) @ ( comp @ TB @ TC @ TA @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_map__sum_Ocomp) ).

thf(1029,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TE > TD,B: TB > TC,C: TF > TE,D: TA > TB] :
      ( ( comp @ ( sum_sum @ TE @ TB ) @ ( sum_sum @ TD @ TC ) @ ( sum_sum @ TF @ TA ) @ ( sum_map_sum @ TE @ TD @ TB @ TC @ A @ B ) @ ( sum_map_sum @ TF @ TE @ TA @ TB @ C @ D ) )
      = ( sum_map_sum @ TF @ TD @ TA @ TC @ ( comp @ TE @ TD @ TF @ A @ C ) @ ( comp @ TB @ TC @ TA @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(198,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: set @ ( sum_sum @ TA @ TB )] :
      ( ( vimage @ TA @ ( sum_sum @ TA @ TC ) @ ( sum_Inl @ TA @ TC ) @ ( image @ ( sum_sum @ TA @ TB ) @ ( sum_sum @ TA @ TC ) @ ( sum_map_sum @ TA @ TA @ TB @ TC @ ( id @ TA ) @ A ) @ B ) )
      = ( vimage @ TA @ ( sum_sum @ TA @ TB ) @ ( sum_Inl @ TA @ TB ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_Inl__m__oplus) ).

thf(895,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: set @ ( sum_sum @ TA @ TB )] :
      ( ( vimage @ TA @ ( sum_sum @ TA @ TC ) @ ( sum_Inl @ TA @ TC ) @ ( image @ ( sum_sum @ TA @ TB ) @ ( sum_sum @ TA @ TC ) @ ( sum_map_sum @ TA @ TA @ TB @ TC @ ( id @ TA ) @ A ) @ B ) )
      = ( vimage @ TA @ ( sum_sum @ TA @ TB ) @ ( sum_Inl @ TA @ TB ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(201,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: $o,B: TD > TC,C: TA > TB,D: sum_sum @ TD @ TA,E: TA] :
      ( ( A
       => ( ( sum_map_sum @ TD @ TC @ TA @ TB @ B @ C @ ( if @ ( sum_sum @ TD @ TA ) @ A @ D @ ( sum_Inr @ TA @ TD @ E ) ) )
          = ( sum_map_sum @ TD @ TC @ TA @ TB @ B @ C @ D ) ) )
      & ( ~ A
       => ( ( sum_map_sum @ TD @ TC @ TA @ TB @ B @ C @ ( if @ ( sum_sum @ TD @ TA ) @ A @ D @ ( sum_Inr @ TA @ TD @ E ) ) )
          = ( sum_Inr @ TB @ TC @ ( C @ E ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_map__sum__if__distrib__else_I2_J) ).

thf(912,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: $o,B: TD > TC,C: TA > TB,D: sum_sum @ TD @ TA,E: TA] :
      ( ( A
       => ( ( sum_map_sum @ TD @ TC @ TA @ TB @ B @ C @ ( if @ ( sum_sum @ TD @ TA ) @ A @ D @ ( sum_Inr @ TA @ TD @ E ) ) )
          = ( sum_map_sum @ TD @ TC @ TA @ TB @ B @ C @ D ) ) )
      & ( ~ A
       => ( ( sum_map_sum @ TD @ TC @ TA @ TB @ B @ C @ ( if @ ( sum_sum @ TD @ TA ) @ A @ D @ ( sum_Inr @ TA @ TD @ E ) ) )
          = ( sum_Inr @ TB @ TC @ ( C @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(52,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( '?' @ ( sum_sum @ TA @ TB ) )
      = ( ^ [A: ( sum_sum @ TA @ TB ) > $o] :
            ( ? [B: TA] : ( A @ ( sum_Inl @ TA @ TB @ B ) )
            | ? [B: TB] : ( A @ ( sum_Inr @ TB @ TA @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_split__sum__ex) ).

thf(399,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( '?' @ ( sum_sum @ TA @ TB ) )
      = ( ^ [A: ( sum_sum @ TA @ TB ) > $o] :
            ( ? [B: TA] : ( A @ ( sum_Inl @ TA @ TB @ B ) )
            | ? [B: TB] : ( A @ ( sum_Inr @ TB @ TA @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(214,axiom,
    ! [A: dtree,B: set @ n,C: dtree,D: n] :
      ( ( member @ n @ ( root @ A ) @ B )
     => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ C ) @ ( cont @ A ) )
       => ( ( gram_L830233218_inItr @ B @ C @ D )
         => ( gram_L830233218_inItr @ B @ A @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_inItr_OInd) ).

thf(959,plain,
    ! [A: dtree,B: set @ n,C: dtree,D: n] :
      ( ( member @ n @ ( root @ A ) @ B )
     => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ C ) @ ( cont @ A ) )
       => ( ( gram_L830233218_inItr @ B @ C @ D )
         => ( gram_L830233218_inItr @ B @ A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(248,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: set @ TD,C: TA > TC,D: set @ TA,E: TC > TB] :
      ( ( ( image @ TD @ TC @ A @ B )
        = ( image @ TA @ TC @ C @ D ) )
     => ( ( image @ TD @ TB @ ( comp @ TC @ TB @ TD @ E @ A ) @ B )
        = ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ E @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_image__eq__imp__comp) ).

thf(1066,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: set @ TD,C: TA > TC,D: set @ TA,E: TC > TB] :
      ( ( ( image @ TD @ TC @ A @ B )
        = ( image @ TA @ TC @ C @ D ) )
     => ( ( image @ TD @ TB @ ( comp @ TC @ TB @ TD @ E @ A ) @ B )
        = ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ E @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(231,axiom,
    ! [TA: $tType,TB: $tType,A: TA > TB] :
      ( ( comp @ TB @ TB @ TA @ ( id @ TB ) @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_fun_Omap__id) ).

thf(1015,plain,
    ! [TA: $tType,TB: $tType,A: TA > TB] :
      ( ( comp @ TB @ TB @ TA @ ( id @ TB ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(222,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TD > TC,B: TB > TC,C: TE > TD,D: TA > TB] :
      ( ( comp @ ( sum_sum @ TD @ TB ) @ TC @ ( sum_sum @ TE @ TA ) @ ( sum_case_sum @ TD @ TC @ TB @ A @ B ) @ ( sum_map_sum @ TE @ TD @ TA @ TB @ C @ D ) )
      = ( sum_case_sum @ TE @ TC @ TA @ ( comp @ TD @ TC @ TE @ A @ C ) @ ( comp @ TB @ TC @ TA @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_case__sum__o__map__sum) ).

thf(986,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TD > TC,B: TB > TC,C: TE > TD,D: TA > TB] :
      ( ( comp @ ( sum_sum @ TD @ TB ) @ TC @ ( sum_sum @ TE @ TA ) @ ( sum_case_sum @ TD @ TC @ TB @ A @ B ) @ ( sum_map_sum @ TE @ TD @ TA @ TB @ C @ D ) )
      = ( sum_case_sum @ TE @ TC @ TA @ ( comp @ TD @ TC @ TE @ A @ C ) @ ( comp @ TB @ TC @ TA @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(17,axiom,
    ! [TA: $tType] :
      ( ( finite_finite @ TA @ ( type2 @ TA ) )
     => ( ( finite_finite2 @ TA )
        = ( ^ [A: set @ TA] : $true ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_finite__code) ).

thf(299,plain,
    ! [TA: $tType] :
      ( ( finite_finite @ TA @ ( type2 @ TA ) )
     => ( ( finite_finite2 @ TA )
        = ( ^ [A: set @ TA] : $true ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(63,axiom,
    ! [TA: $tType] :
      ( ( finite_finite2 @ ( set @ TA ) @ ( top_top @ ( set @ ( set @ TA ) ) ) )
      = ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_Finite__Set_Ofinite__set) ).

thf(431,plain,
    ! [TA: $tType] :
      ( ( finite_finite2 @ ( set @ TA ) @ ( top_top @ ( set @ ( set @ TA ) ) ) )
      = ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(118,axiom,
    ! [A: n,B: set @ ( sum_sum @ t @ dtree )] :
      ( ( root @ ( node @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_root__Node) ).

thf(636,plain,
    ! [A: n,B: set @ ( sum_sum @ t @ dtree )] :
      ( ( root @ ( node @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(138,axiom,
    ( gram_L1221482011le_H_c
    = ( ^ [A: dtree,B: n] : ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ ( gram_L315592705e_pick @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_Gram__Lang__Mirabelle__ojxrtuoybn_OH__c__def) ).

thf(695,plain,
    ( gram_L1221482011le_H_c
    = ( ^ [A: dtree,B: n] : ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ ( gram_L315592705e_pick @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(70,axiom,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TA] :
      ( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
        = ( top_top @ ( set @ TA ) ) )
     => ( ( image @ TB @ TA @ A @ ( vimage @ TB @ TA @ A @ B ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_surj__image__vimage__eq) ).

thf(455,plain,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TA] :
      ( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
        = ( top_top @ ( set @ TA ) ) )
     => ( ( image @ TB @ TA @ A @ ( vimage @ TB @ TA @ A @ B ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(196,axiom,
    ! [A: set @ n,B: dtree,C: dtree] :
      ( ( gram_L716654942_subtr @ A @ B @ C )
     => ( ( ( C = B )
         => ~ ( member @ n @ ( root @ B ) @ A ) )
       => ~ ( ( member @ n @ ( root @ C ) @ A )
           => ! [D: dtree] :
                ( ( gram_L716654942_subtr @ A @ B @ D )
               => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ D ) @ ( cont @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_subtr_Ocases) ).

thf(883,plain,
    ! [A: set @ n,B: dtree,C: dtree] :
      ( ( gram_L716654942_subtr @ A @ B @ C )
     => ( ( ( C = B )
         => ~ ( member @ n @ ( root @ B ) @ A ) )
       => ~ ( ( member @ n @ ( root @ C ) @ A )
           => ! [D: dtree] :
                ( ( gram_L716654942_subtr @ A @ B @ D )
               => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ D ) @ ( cont @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(260,axiom,
    ( gram_L1905609002ubst_c
    = ( ^ [A: dtree,B: dtree] :
          ( if @ ( set @ ( sum_sum @ t @ dtree ) )
          @ ( ( root @ B )
            = ( root @ A ) )
          @ ( cont @ A )
          @ ( cont @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_hsubst__c__def) ).

thf(1113,plain,
    ( gram_L1905609002ubst_c
    = ( ^ [A: dtree,B: dtree] :
          ( if @ ( set @ ( sum_sum @ t @ dtree ) )
          @ ( ( root @ B )
            = ( root @ A ) )
          @ ( cont @ A )
          @ ( cont @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(99,axiom,
    ! [A: set @ n,B: dtree,C: n,D: dtree] :
      ( ( gram_L830233218_inItr @ A @ B @ C )
     => ( ( gram_L716654942_subtr @ A @ B @ D )
       => ( gram_L830233218_inItr @ A @ D @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_subtr__inItr) ).

thf(563,plain,
    ! [A: set @ n,B: dtree,C: n,D: dtree] :
      ( ( gram_L830233218_inItr @ A @ B @ C )
     => ( ( gram_L716654942_subtr @ A @ B @ D )
       => ( gram_L830233218_inItr @ A @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(237,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( comp @ TA @ TB @ TC )
      = ( ^ [A: TA > TB,B: TC > TA,C: TC] : ( A @ ( B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_comp__def) ).

thf(1034,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( comp @ TA @ TB @ TC )
      = ( ^ [A: TA > TB,B: TC > TA,C: TC] : ( A @ ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(133,axiom,
    ! [A: n] :
      ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ A )
     => ( ( root @ ( gram_L1451583624elle_H @ tr0 @ A ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_root__H) ).

thf(680,plain,
    ! [A: n] :
      ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ A )
     => ( ( root @ ( gram_L1451583624elle_H @ tr0 @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(43,axiom,
    ! [TA: $tType,TB: $tType,A: sum_sum @ TB @ TA] :
      ( ! [B: TB] :
          ( A
         != ( sum_Inl @ TB @ TA @ B ) )
     => ~ ! [B: TA] :
            ( A
           != ( sum_Inr @ TA @ TB @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_old_Osum_Oexhaust) ).

thf(374,plain,
    ! [TA: $tType,TB: $tType,A: sum_sum @ TB @ TA] :
      ( ! [B: TB] :
          ( A
         != ( sum_Inl @ TB @ TA @ B ) )
     => ~ ! [B: TA] :
            ( A
           != ( sum_Inr @ TA @ TB @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(174,axiom,
    ! [A: set @ n,B: dtree,C: dtree,D: ( set @ n ) > dtree > dtree > $o] :
      ( ( gram_L716654942_subtr @ A @ B @ C )
     => ( ! [E: dtree,F: set @ n] :
            ( ( member @ n @ ( root @ E ) @ F )
           => ( D @ F @ E @ E ) )
       => ( ! [E: dtree,F: set @ n,G: dtree,H: dtree] :
              ( ( member @ n @ ( root @ E ) @ F )
             => ( ( gram_L716654942_subtr @ F @ G @ H )
               => ( ( D @ F @ G @ H )
                 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ H ) @ ( cont @ E ) )
                   => ( D @ F @ G @ E ) ) ) ) )
         => ( D @ A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_subtr_Oinducts) ).

thf(812,plain,
    ! [A: set @ n,B: dtree,C: dtree,D: ( set @ n ) > dtree > dtree > $o] :
      ( ( gram_L716654942_subtr @ A @ B @ C )
     => ( ! [E: dtree,F: set @ n] :
            ( ( member @ n @ ( root @ E ) @ F )
           => ( D @ F @ E @ E ) )
       => ( ! [E: dtree,F: set @ n,G: dtree,H: dtree] :
              ( ( member @ n @ ( root @ E ) @ F )
             => ( ( gram_L716654942_subtr @ F @ G @ H )
               => ( ( D @ F @ G @ H )
                 => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ H ) @ ( cont @ E ) )
                   => ( D @ F @ G @ E ) ) ) ) )
         => ( D @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(251,axiom,
    ! [TA: $tType,A: TA > n,B: TA > ( set @ ( sum_sum @ t @ ( sum_sum @ dtree @ TA ) ) ),C: TA] :
      ( ( root @ ( corec @ TA @ A @ B @ C ) )
      = ( A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_corec_I1_J) ).

thf(1081,plain,
    ! [TA: $tType,A: TA > n,B: TA > ( set @ ( sum_sum @ t @ ( sum_sum @ dtree @ TA ) ) ),C: TA] :
      ( ( root @ ( corec @ TA @ A @ B @ C ) )
      = ( A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(32,axiom,
    ! [TA: $tType] :
      ( ( top_top @ ( TA > $o ) )
      = ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_top__empty__eq) ).

thf(342,plain,
    ! [TA: $tType] :
      ( ( top_top @ ( TA > $o ) )
      = ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(232,axiom,
    ! [A: set @ n,B: dtree,C: n] :
      ( ( gram_L716654942_subtr @ A @ B @ ( gram_L1231612515_deftr @ C ) )
     => ( B
        = ( gram_L1231612515_deftr @ ( root @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_subtr__deftr) ).

thf(1018,plain,
    ! [A: set @ n,B: dtree,C: n] :
      ( ( gram_L716654942_subtr @ A @ B @ ( gram_L1231612515_deftr @ C ) )
     => ( B
        = ( gram_L1231612515_deftr @ ( root @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(37,axiom,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
      ( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
     => ( ( ( image @ TA @ TB @ A @ B )
          = ( image @ TA @ TB @ A @ C ) )
        = ( B = C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_inj__image__eq__iff) ).

thf(355,plain,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
      ( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
     => ( ( ( image @ TA @ TB @ A @ B )
          = ( image @ TA @ TB @ A @ C ) )
        = ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(242,axiom,
    ! [A: n] :
      ( ( cont @ ( gram_L1451583624elle_H @ tr0 @ A ) )
      = ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ dtree @ dtree @ ( id @ t ) @ ( comp @ n @ dtree @ dtree @ ( gram_L1451583624elle_H @ tr0 ) @ root ) ) @ ( cont @ ( gram_L315592705e_pick @ tr0 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_cont__H) ).

thf(1049,plain,
    ! [A: n] :
      ( ( cont @ ( gram_L1451583624elle_H @ tr0 @ A ) )
      = ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ dtree @ dtree @ ( id @ t ) @ ( comp @ n @ dtree @ dtree @ ( gram_L1451583624elle_H @ tr0 ) @ root ) ) @ ( cont @ ( gram_L315592705e_pick @ tr0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(89,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: TA] :
      ( ( ( sum_Inl @ TA @ TB @ A )
        = ( sum_Inl @ TA @ TB @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_old_Osum_Oinject_I1_J) ).

thf(531,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: TA] :
      ( ( ( sum_Inl @ TA @ TB @ A )
        = ( sum_Inl @ TA @ TB @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(210,axiom,
    ! [A: n] :
      ( ( root @ ( gram_L1231612515_deftr @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_root__deftr) ).

thf(944,plain,
    ! [A: n] :
      ( ( root @ ( gram_L1231612515_deftr @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(217,axiom,
    ! [A: set @ n,B: dtree,C: n] :
      ( ( gram_L830233218_inItr @ A @ B @ C )
     => ? [D: dtree] :
          ( ( gram_L716654942_subtr @ A @ D @ B )
          & ( ( root @ D )
            = C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_inItr__subtr) ).

thf(968,plain,
    ! [A: set @ n,B: dtree,C: n] :
      ( ( gram_L830233218_inItr @ A @ B @ C )
     => ? [D: dtree] :
          ( ( gram_L716654942_subtr @ A @ D @ B )
          & ( ( root @ D )
            = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(71,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ! [B: TA] : ( member @ TA @ B @ A )
     => ( ( top_top @ ( set @ TA ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_UNIV__eq__I) ).

thf(458,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ! [B: TA] : ( member @ TA @ B @ A )
     => ( ( top_top @ ( set @ TA ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(105,axiom,
    ! [TA: $tType] :
      ( ( vimage @ TA @ TA @ ( id @ TA ) )
      = ( id @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_vimage__id) ).

thf(580,plain,
    ! [TA: $tType] :
      ( ( vimage @ TA @ TA @ ( id @ TA ) )
      = ( id @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(192,axiom,
    ! [A: dtree,B: n] :
      ( ( root @ ( gram_L1451583624elle_H @ A @ B ) )
      = ( root @ ( gram_L315592705e_pick @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_Gram__Lang__Mirabelle__ojxrtuoybn_Oroot__H__pick) ).

thf(872,plain,
    ! [A: dtree,B: n] :
      ( ( root @ ( gram_L1451583624elle_H @ A @ B ) )
      = ( root @ ( gram_L315592705e_pick @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(213,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TB > TA,C: sum_sum @ TD @ TB,D: TA] :
      ( ( ( sum_map_sum @ TD @ TC @ TB @ TA @ A @ B @ C )
        = ( sum_Inr @ TA @ TC @ D ) )
     => ? [E: TB] :
          ( ( C
            = ( sum_Inr @ TB @ TD @ E ) )
          & ( ( B @ E )
            = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_map__sum__InrD) ).

thf(954,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TB > TA,C: sum_sum @ TD @ TB,D: TA] :
      ( ( ( sum_map_sum @ TD @ TC @ TB @ TA @ A @ B @ C )
        = ( sum_Inr @ TA @ TC @ D ) )
     => ? [E: TB] :
          ( ( C
            = ( sum_Inr @ TB @ TD @ E ) )
          & ( ( B @ E )
            = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(21,axiom,
    ! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA,D: set @ TA] :
      ( ( A
        = ( B @ C ) )
     => ( ( member @ TA @ C @ D )
       => ( member @ TB @ A @ ( image @ TA @ TB @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_image__eqI) ).

thf(310,plain,
    ! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA,D: set @ TA] :
      ( ( A
        = ( B @ C ) )
     => ( ( member @ TA @ C @ D )
       => ( member @ TB @ A @ ( image @ TA @ TB @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(28,axiom,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: set @ TA] :
      ( ( member @ TA @ ( A @ B ) @ C )
     => ( member @ TB @ B @ ( vimage @ TB @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_vimageI2) ).

thf(331,plain,
    ! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: set @ TA] :
      ( ( member @ TA @ ( A @ B ) @ C )
     => ( member @ TB @ B @ ( vimage @ TB @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(212,axiom,
    ! [A: n] :
      ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ A )
     => ( ( root @ ( gram_L315592705e_pick @ tr0 @ A ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_root__pick) ).

thf(951,plain,
    ! [A: n] :
      ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ A )
     => ( ( root @ ( gram_L315592705e_pick @ tr0 @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(172,axiom,
    gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ n2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n) ).

thf(808,plain,
    gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ n2,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(155,axiom,
    ! [A: set @ n,B: dtree,C: n,D: ( set @ n ) > dtree > n > $o] :
      ( ( gram_L830233218_inItr @ A @ B @ C )
     => ( ! [E: dtree,F: set @ n] :
            ( ( member @ n @ ( root @ E ) @ F )
           => ( D @ F @ E @ ( root @ E ) ) )
       => ( ! [E: dtree,F: set @ n,G: dtree,H: n] :
              ( ( member @ n @ ( root @ E ) @ F )
             => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ G ) @ ( cont @ E ) )
               => ( ( gram_L830233218_inItr @ F @ G @ H )
                 => ( ( D @ F @ G @ H )
                   => ( D @ F @ E @ H ) ) ) ) )
         => ( D @ A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_inItr_Oinducts) ).

thf(744,plain,
    ! [A: set @ n,B: dtree,C: n,D: ( set @ n ) > dtree > n > $o] :
      ( ( gram_L830233218_inItr @ A @ B @ C )
     => ( ! [E: dtree,F: set @ n] :
            ( ( member @ n @ ( root @ E ) @ F )
           => ( D @ F @ E @ ( root @ E ) ) )
       => ( ! [E: dtree,F: set @ n,G: dtree,H: n] :
              ( ( member @ n @ ( root @ E ) @ F )
             => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ G ) @ ( cont @ E ) )
               => ( ( gram_L830233218_inItr @ F @ G @ H )
                 => ( ( D @ F @ G @ H )
                   => ( D @ F @ E @ H ) ) ) ) )
         => ( D @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(30,axiom,
    ! [TA: $tType,TB: $tType,A: TB > $o,B: TA > TB,C: TA > $o] :
      ( ! [D: TA] :
          ( ( A @ ( B @ D ) )
          = ( C @ D ) )
     => ( ( vimage @ TA @ TB @ B @ ( collect @ TB @ A ) )
        = ( collect @ TA @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_vimage__Collect) ).

thf(336,plain,
    ! [TA: $tType,TB: $tType,A: TB > $o,B: TA > TB,C: TA > $o] :
      ( ! [D: TA] :
          ( ( A @ ( B @ D ) )
          = ( C @ D ) )
     => ( ( vimage @ TA @ TB @ B @ ( collect @ TB @ A ) )
        = ( collect @ TA @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(141,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: set @ ( sum_sum @ TA @ TB )] :
      ( ( vimage @ TC @ ( sum_sum @ TA @ TC ) @ ( sum_Inr @ TC @ TA ) @ ( image @ ( sum_sum @ TA @ TB ) @ ( sum_sum @ TA @ TC ) @ ( sum_map_sum @ TA @ TA @ TB @ TC @ ( id @ TA ) @ A ) @ B ) )
      = ( image @ TB @ TC @ A @ ( vimage @ TB @ ( sum_sum @ TA @ TB ) @ ( sum_Inr @ TB @ TA ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_Inr__m__oplus) ).

thf(703,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: set @ ( sum_sum @ TA @ TB )] :
      ( ( vimage @ TC @ ( sum_sum @ TA @ TC ) @ ( sum_Inr @ TC @ TA ) @ ( image @ ( sum_sum @ TA @ TB ) @ ( sum_sum @ TA @ TC ) @ ( sum_map_sum @ TA @ TA @ TB @ TC @ ( id @ TA ) @ A ) @ B ) )
      = ( image @ TB @ TC @ A @ ( vimage @ TB @ ( sum_sum @ TA @ TB ) @ ( sum_Inr @ TB @ TA ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(115,axiom,
    ! [A: dtree,B: dtree,C: dtree > dtree > $o] :
      ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ A @ B )
     => ( ! [D: dtree] : ( C @ D @ D )
       => ( ! [D: dtree,E: dtree,F: dtree] :
              ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ D ) @ ( cont @ E ) )
             => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ E @ F )
               => ( ( C @ E @ F )
                 => ( C @ D @ F ) ) ) )
         => ( C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_subtr__UNIV__inductL) ).

thf(613,plain,
    ! [A: dtree,B: dtree,C: dtree > dtree > $o] :
      ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ A @ B )
     => ( ! [D: dtree] : ( C @ D @ D )
       => ( ! [D: dtree,E: dtree,F: dtree] :
              ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ D ) @ ( cont @ E ) )
             => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ E @ F )
               => ( ( C @ E @ F )
                 => ( C @ D @ F ) ) ) )
         => ( C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(111,axiom,
    ! [A: n] : ( finite_finite2 @ ( sum_sum @ t @ n ) @ ( gram_L1451583635elle_S @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_finite__S) ).

thf(600,plain,
    ! [A: n] : ( finite_finite2 @ ( sum_sum @ t @ n ) @ ( gram_L1451583635elle_S @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(243,axiom,
    ! [A: dtree] :
      ~ ! [B: n,C: set @ ( sum_sum @ t @ dtree )] :
          ( ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ C )
         => ( A
           != ( node @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_dtree__cases) ).

thf(1052,plain,
    ! [A: dtree] :
      ~ ! [B: n,C: set @ ( sum_sum @ t @ dtree )] :
          ( ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ C )
         => ( A
           != ( node @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(268,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TC > TB] :
      ( ( comp @ ( sum_sum @ TA @ TC ) @ TB @ TA @ ( sum_case_sum @ TA @ TB @ TC @ A @ B ) @ ( sum_Inl @ TA @ TC ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_case__sum__o__inj_I1_J) ).

thf(1140,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TC > TB] :
      ( ( comp @ ( sum_sum @ TA @ TC ) @ TB @ TA @ ( sum_case_sum @ TA @ TB @ TC @ A @ B ) @ ( sum_Inl @ TA @ TC ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(22,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: TA] :
      ( ( ( sum_Inr @ TA @ TB @ A )
        = ( sum_Inr @ TA @ TB @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_sum_Oinject_I2_J) ).

thf(314,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: TA] :
      ( ( ( sum_Inr @ TA @ TB @ A )
        = ( sum_Inr @ TA @ TB @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(109,axiom,
    ( gram_L716654942_subtr
    = ( ^ [A: set @ n,B: dtree,C: dtree] :
          ( ? [D: dtree,E: set @ n] :
              ( ( A = E )
              & ( B = D )
              & ( C = D )
              & ( member @ n @ ( root @ D ) @ E ) )
          | ? [D: dtree,E: set @ n,F: dtree,G: dtree] :
              ( ( A = E )
              & ( B = F )
              & ( C = D )
              & ( member @ n @ ( root @ D ) @ E )
              & ( gram_L716654942_subtr @ E @ F @ G )
              & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ G ) @ ( cont @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_subtr_Osimps) ).

thf(595,plain,
    ( gram_L716654942_subtr
    = ( ^ [A: set @ n,B: dtree,C: dtree] :
          ( ? [D: dtree,E: set @ n] :
              ( ( A = E )
              & ( B = D )
              & ( C = D )
              & ( member @ n @ ( root @ D ) @ E ) )
          | ? [D: dtree,E: set @ n,F: dtree,G: dtree] :
              ( ( A = E )
              & ( B = F )
              & ( C = D )
              & ( member @ n @ ( root @ D ) @ E )
              & ( gram_L716654942_subtr @ E @ F @ G )
              & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ G ) @ ( cont @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(188,axiom,
    ! [A: n] :
      ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L1451583624elle_H @ tr0 @ A ) ) )
      = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L315592705e_pick @ tr0 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_Inl__cont__H) ).

thf(859,plain,
    ! [A: n] :
      ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L1451583624elle_H @ tr0 @ A ) ) )
      = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L315592705e_pick @ tr0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(183,axiom,
    ! [TA: $tType] :
      ( ( image @ TA @ TA @ ( id @ TA ) @ ( top_top @ ( set @ TA ) ) )
      = ( top_top @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_surj__id) ).

thf(845,plain,
    ! [TA: $tType] :
      ( ( image @ TA @ TA @ ( id @ TA ) @ ( top_top @ ( set @ TA ) ) )
      = ( top_top @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(252,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TB > TA,B: TD > TC,C: sum_sum @ TB @ TD,D: TA] :
      ( ( ( sum_map_sum @ TB @ TA @ TD @ TC @ A @ B @ C )
        = ( sum_Inl @ TA @ TC @ D ) )
     => ? [E: TB] :
          ( ( C
            = ( sum_Inl @ TB @ TD @ E ) )
          & ( ( A @ E )
            = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_map__sum__InlD) ).

thf(1084,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TB > TA,B: TD > TC,C: sum_sum @ TB @ TD,D: TA] :
      ( ( ( sum_map_sum @ TB @ TA @ TD @ TC @ A @ B @ C )
        = ( sum_Inl @ TA @ TC @ D ) )
     => ? [E: TB] :
          ( ( C
            = ( sum_Inl @ TB @ TD @ E ) )
          & ( ( A @ E )
            = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(207,axiom,
    ! [A: set @ n,B: dtree,C: dtree,D: ( set @ n ) > dtree > dtree > $o] :
      ( ( gram_L716654942_subtr @ A @ B @ C )
     => ( ! [E: set @ n,F: dtree] : ( D @ E @ F @ F )
       => ( ! [E: set @ n,F: dtree,G: dtree,H: dtree] :
              ( ( member @ n @ ( root @ F ) @ E )
             => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ F ) @ ( cont @ G ) )
               => ( ( gram_L716654942_subtr @ E @ G @ H )
                 => ( ( D @ E @ G @ H )
                   => ( D @ E @ F @ H ) ) ) ) )
         => ( D @ A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_subtr__inductL) ).

thf(931,plain,
    ! [A: set @ n,B: dtree,C: dtree,D: ( set @ n ) > dtree > dtree > $o] :
      ( ( gram_L716654942_subtr @ A @ B @ C )
     => ( ! [E: set @ n,F: dtree] : ( D @ E @ F @ F )
       => ( ! [E: set @ n,F: dtree,G: dtree,H: dtree] :
              ( ( member @ n @ ( root @ F ) @ E )
             => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ F ) @ ( cont @ G ) )
               => ( ( gram_L716654942_subtr @ E @ G @ H )
                 => ( ( D @ E @ G @ H )
                   => ( D @ E @ F @ H ) ) ) ) )
         => ( D @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(88,axiom,
    ! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
      ( ( A = B )
     => ( ! [E: TA] :
            ( ( member @ TA @ E @ B )
           => ( ( C @ E )
              = ( D @ E ) ) )
       => ( ( image @ TA @ TB @ C @ A )
          = ( image @ TA @ TB @ D @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_image__cong) ).

thf(524,plain,
    ! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
      ( ( A = B )
     => ( ! [E: TA] :
            ( ( member @ TA @ E @ B )
           => ( ( C @ E )
              = ( D @ E ) ) )
       => ( ( image @ TA @ TB @ C @ A )
          = ( image @ TA @ TB @ D @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(160,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TB,B: TA > TD,C: TA,D: TC > TB,E: TA > TC] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ C ) ) )
     => ( ( comp @ TD @ TB @ TA @ A @ B @ C )
        = ( comp @ TC @ TB @ TA @ D @ E @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_comp__apply__eq) ).

thf(771,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TB,B: TA > TD,C: TA,D: TC > TB,E: TA > TC] :
      ( ( ( A @ ( B @ C ) )
        = ( D @ ( E @ C ) ) )
     => ( ( comp @ TD @ TB @ TA @ A @ B @ C )
        = ( comp @ TC @ TB @ TA @ D @ E @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(41,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TC > TB,C: TA] :
      ( ( sum_rec_sum @ TA @ TB @ TC @ A @ B @ ( sum_Inl @ TA @ TC @ C ) )
      = ( A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_old_Osum_Osimps_I7_J) ).

thf(368,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TC > TB,C: TA] :
      ( ( sum_rec_sum @ TA @ TB @ TC @ A @ B @ ( sum_Inl @ TA @ TC @ C ) )
      = ( A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(182,axiom,
    finite_finite2 @ n @ ( top_top @ ( set @ n ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_finite__N) ).

thf(844,plain,
    finite_finite2 @ n @ ( top_top @ ( set @ n ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(86,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TC,C: TB > TC,D: sum_sum @ TA @ TB] :
      ( ( sum_case_sum @ TD @ TC @ ( sum_sum @ TA @ TB ) @ A @ ( sum_case_sum @ TA @ TC @ TB @ B @ C ) @ ( sum_Inr @ ( sum_sum @ TA @ TB ) @ TD @ D ) )
      = ( sum_case_sum @ TA @ TC @ TB @ B @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_case__sum__step_I2_J) ).

thf(517,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TC,C: TB > TC,D: sum_sum @ TA @ TB] :
      ( ( sum_case_sum @ TD @ TC @ ( sum_sum @ TA @ TB ) @ A @ ( sum_case_sum @ TA @ TC @ TB @ B @ C ) @ ( sum_Inr @ ( sum_sum @ TA @ TB ) @ TD @ D ) )
      = ( sum_case_sum @ TA @ TC @ TB @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(19,axiom,
    ! [TA: $tType,A: TA,B: TA > $o] :
      ( ( member @ TA @ A @ ( collect @ TA @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).

thf(304,plain,
    ! [TA: $tType,A: TA,B: TA > $o] :
      ( ( member @ TA @ A @ ( collect @ TA @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(246,axiom,
    ! [A: dtree,B: dtree] :
      ( ( ( root @ A )
        = ( root @ B ) )
     => ( ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ ( gram_L1004374585hsubst @ B @ A ) ) )
        = ( image @ dtree @ dtree @ ( gram_L1004374585hsubst @ B ) @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_Inr__cont__hsubst__eq) ).

thf(1062,plain,
    ! [A: dtree,B: dtree] :
      ( ( ( root @ A )
        = ( root @ B ) )
     => ( ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ ( gram_L1004374585hsubst @ B @ A ) ) )
        = ( image @ dtree @ dtree @ ( gram_L1004374585hsubst @ B ) @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(35,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
      ( ( member @ TA @ A @ B )
     => ( member @ TB @ ( C @ A ) @ ( image @ TA @ TB @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_imageI) ).

thf(351,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
      ( ( member @ TA @ A @ B )
     => ( member @ TB @ ( C @ A ) @ ( image @ TA @ TB @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(49,axiom,
    ! [TA: $tType,TB: $tType,A: sum_sum @ TB @ TA] :
      ( ! [B: TB] :
          ( A
         != ( sum_Inl @ TB @ TA @ B ) )
     => ~ ! [B: TA] :
            ( A
           != ( sum_Inr @ TA @ TB @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_obj__sumE) ).

thf(390,plain,
    ! [TA: $tType,TB: $tType,A: sum_sum @ TB @ TA] :
      ( ! [B: TB] :
          ( A
         != ( sum_Inl @ TB @ TA @ B ) )
     => ~ ! [B: TA] :
            ( A
           != ( sum_Inr @ TA @ TB @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(58,axiom,
    ! [TA: $tType] :
    ? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_UNIV__witness) ).

thf(418,plain,
    ! [TA: $tType] :
    ? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(164,axiom,
    ! [A: set @ n,B: dtree,C: t] :
      ( ( gram_L805317441_inFr2 @ A @ B @ C )
     => ( member @ n @ ( root @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_inFr2__root__in) ).

thf(781,plain,
    ! [A: set @ n,B: dtree,C: t] :
      ( ( gram_L805317441_inFr2 @ A @ B @ C )
     => ( member @ n @ ( root @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(225,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: ( sum_sum @ TA @ TB ) > TC,B: TA > TC] :
      ( ( ( comp @ ( sum_sum @ TA @ TB ) @ TC @ TA @ A @ ( sum_Inl @ TA @ TB ) )
        = B )
     => ( ( sum_case_sum @ TA @ TC @ TB @ B @ ( comp @ ( sum_sum @ TA @ TB ) @ TC @ TB @ A @ ( sum_Inr @ TB @ TA ) ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_case__sum__expand__Inr__pointfree) ).

thf(995,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: ( sum_sum @ TA @ TB ) > TC,B: TA > TC] :
      ( ( ( comp @ ( sum_sum @ TA @ TB ) @ TC @ TA @ A @ ( sum_Inl @ TA @ TB ) )
        = B )
     => ( ( sum_case_sum @ TA @ TC @ TB @ B @ ( comp @ ( sum_sum @ TA @ TB ) @ TC @ TB @ A @ ( sum_Inr @ TB @ TA ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(13,axiom,
    ! [TA: $tType] :
      ( ( finite_finite @ TA @ ( type2 @ TA ) )
     => ( finite_finite @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Finite__Set_Ofinite_1) ).

thf(290,plain,
    ! [TA: $tType] :
      ( ( finite_finite @ TA @ ( type2 @ TA ) )
     => ( finite_finite @ ( set @ TA ) @ ( type2 @ ( set @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(206,axiom,
    ! [A: n,B: dtree] :
      ( ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ A ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ B ) ) )
     => ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( gram_L1614515765ubtrOf @ B @ A ) ) @ ( cont @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_Inr__subtrOf) ).

thf(929,plain,
    ! [A: n,B: dtree] :
      ( ( member @ ( sum_sum @ t @ n ) @ ( sum_Inr @ n @ t @ A ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ B ) ) )
     => ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( gram_L1614515765ubtrOf @ B @ A ) ) @ ( cont @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(78,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( finite_finite2 @ ( TB > TA ) @ ( top_top @ ( set @ ( TB > TA ) ) ) )
     => ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_finite__fun__UNIVD2) ).

thf(478,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( finite_finite2 @ ( TB > TA ) @ ( top_top @ ( set @ ( TB > TA ) ) ) )
     => ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(4,axiom,
    ! [TA: $tType] :
      ( ( top_top @ ( set @ TA ) )
      = ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_top__set__def) ).

thf(272,plain,
    ! [TA: $tType] :
      ( ( top_top @ ( set @ TA ) )
      = ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(46,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ~ ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) )
     => ( ( finite_finite2 @ TA @ A )
       => ? [B: TA] :
            ~ ( member @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_ex__new__if__finite) ).

thf(383,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ~ ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) )
     => ( ( finite_finite2 @ TA @ A )
       => ? [B: TA] :
            ~ ( member @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(178,axiom,
    ! [A: n] :
      ( ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ ( gram_L1451583624elle_H @ tr0 @ A ) ) )
      = ( image @ dtree @ dtree @ ( comp @ n @ dtree @ dtree @ ( gram_L1451583624elle_H @ tr0 ) @ root ) @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ ( gram_L315592705e_pick @ tr0 @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_Inr__cont__H) ).

thf(832,plain,
    ! [A: n] :
      ( ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ ( gram_L1451583624elle_H @ tr0 @ A ) ) )
      = ( image @ dtree @ dtree @ ( comp @ n @ dtree @ dtree @ ( gram_L1451583624elle_H @ tr0 ) @ root ) @ ( vimage @ dtree @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t ) @ ( cont @ ( gram_L315592705e_pick @ tr0 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(11,axiom,
    ! [TA: $tType] :
      ( ( finite_finite @ TA @ ( type2 @ TA ) )
     => ! [A: set @ TA] : ( finite_finite2 @ TA @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_finite) ).

thf(287,plain,
    ! [TA: $tType] :
      ( ( finite_finite @ TA @ ( type2 @ TA ) )
     => ! [A: set @ TA] : ( finite_finite2 @ TA @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(226,axiom,
    ! [A: n] :
      ( ( cont @ ( gram_L1231612515_deftr @ A ) )
      = ( image @ ( sum_sum @ t @ n ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ n @ dtree @ ( id @ t ) @ gram_L1231612515_deftr ) @ ( gram_L1451583635elle_S @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_cont__deftr) ).

thf(999,plain,
    ! [A: n] :
      ( ( cont @ ( gram_L1231612515_deftr @ A ) )
      = ( image @ ( sum_sum @ t @ n ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ n @ dtree @ ( id @ t ) @ gram_L1231612515_deftr ) @ ( gram_L1451583635elle_S @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(56,axiom,
    ! [TA: $tType,TB: $tType,A: TB,B: TB > TA,C: set @ TA] :
      ( ( member @ TB @ A @ ( vimage @ TB @ TA @ B @ C ) )
      = ( member @ TA @ ( B @ A ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_vimage__eq) ).

thf(410,plain,
    ! [TA: $tType,TB: $tType,A: TB,B: TB > TA,C: set @ TA] :
      ( ( member @ TB @ A @ ( vimage @ TB @ TA @ B @ C ) )
      = ( member @ TA @ ( B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(179,axiom,
    ! [A: dtree,B: n] :
      ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L1451583624elle_H @ A @ B ) ) )
      = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L315592705e_pick @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_Gram__Lang__Mirabelle__ojxrtuoybn_OInl__cont__H) ).

thf(835,plain,
    ! [A: dtree,B: n] :
      ( ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L1451583624elle_H @ A @ B ) ) )
      = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ ( gram_L315592705e_pick @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(54,axiom,
    ! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_iso__tuple__UNIV__I) ).

thf(405,plain,
    ! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(186,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: set @ TA] :
      ( ( inj_on @ TA @ TC @ ( comp @ TB @ TC @ TA @ A @ B ) @ C )
     => ( inj_on @ TB @ TC @ A @ ( image @ TA @ TB @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_inj__on__imageI) ).

thf(854,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: set @ TA] :
      ( ( inj_on @ TA @ TC @ ( comp @ TB @ TC @ TA @ A @ B ) @ C )
     => ( inj_on @ TB @ TC @ A @ ( image @ TA @ TB @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(190,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: ( sum_sum @ TA @ TB ) > TC,B: TA > TC,C: TB > TC] :
      ( ( ( comp @ ( sum_sum @ TA @ TB ) @ TC @ TA @ A @ ( sum_Inl @ TA @ TB ) )
        = B )
     => ( ( C
          = ( comp @ ( sum_sum @ TA @ TB ) @ TC @ TB @ A @ ( sum_Inr @ TB @ TA ) ) )
        = ( ( sum_case_sum @ TA @ TC @ TB @ B @ C )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_case__sum__expand__Inr_H) ).

thf(865,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: ( sum_sum @ TA @ TB ) > TC,B: TA > TC,C: TB > TC] :
      ( ( ( comp @ ( sum_sum @ TA @ TB ) @ TC @ TA @ A @ ( sum_Inl @ TA @ TB ) )
        = B )
     => ( ( C
          = ( comp @ ( sum_sum @ TA @ TB ) @ TC @ TB @ A @ ( sum_Inr @ TB @ TA ) ) )
        = ( ( sum_case_sum @ TA @ TC @ TB @ B @ C )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(60,axiom,
    ! [A: set @ n,B: dtree,C: dtree,D: dtree] :
      ( ( gram_L716654942_subtr @ A @ B @ C )
     => ( ( gram_L716654942_subtr @ A @ C @ D )
       => ( gram_L716654942_subtr @ A @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_subtr__trans) ).

thf(422,plain,
    ! [A: set @ n,B: dtree,C: dtree,D: dtree] :
      ( ( gram_L716654942_subtr @ A @ B @ C )
     => ( ( gram_L716654942_subtr @ A @ C @ D )
       => ( gram_L716654942_subtr @ A @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(167,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TA > TB,C: TB > TC,D: TB > TC] :
      ( ( A = B )
     => ( ! [E: TB] :
            ( ( member @ TB @ E @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) )
           => ( ( C @ E )
              = ( D @ E ) ) )
       => ( ( comp @ TB @ TC @ TA @ C @ A )
          = ( comp @ TB @ TC @ TA @ D @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_fun_Omap__cong) ).

thf(790,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TA > TB,C: TB > TC,D: TB > TC] :
      ( ( A = B )
     => ( ! [E: TB] :
            ( ( member @ TB @ E @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) )
           => ( ( C @ E )
              = ( D @ E ) ) )
       => ( ( comp @ TB @ TC @ TA @ C @ A )
          = ( comp @ TB @ TC @ TA @ D @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(26,axiom,
    ! [TA: $tType,TB: $tType,A: TB,B: TB > TA,C: set @ TA] :
      ( ( member @ TB @ A @ ( vimage @ TB @ TA @ B @ C ) )
     => ( member @ TA @ ( B @ A ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_vimageE) ).

thf(326,plain,
    ! [TA: $tType,TB: $tType,A: TB,B: TB > TA,C: set @ TA] :
      ( ( member @ TB @ A @ ( vimage @ TB @ TA @ B @ C ) )
     => ( member @ TA @ ( B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(84,axiom,
    ! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB,E: ( set @ TB ) > TB] :
      ( ( A = B )
     => ( ! [F: TA] :
            ( ( member @ TA @ F @ B )
           => ( ( C @ F )
              = ( D @ F ) ) )
       => ( ( E @ ( image @ TA @ TB @ C @ A ) )
          = ( E @ ( image @ TA @ TB @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_Inf_OINF__cong) ).

thf(506,plain,
    ! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB,E: ( set @ TB ) > TB] :
      ( ( A = B )
     => ( ! [F: TA] :
            ( ( member @ TA @ F @ B )
           => ( ( C @ F )
              = ( D @ F ) ) )
       => ( ( E @ ( image @ TA @ TB @ C @ A ) )
          = ( E @ ( image @ TA @ TB @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(38,axiom,
    ! [TA: $tType,TB: $tType,A: TB > TA] :
      ( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
        = ( top_top @ ( set @ TA ) ) )
      = ( ! [B: TA] :
          ? [C: TB] :
            ( B
            = ( A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_surj__def) ).

thf(358,plain,
    ! [TA: $tType,TB: $tType,A: TB > TA] :
      ( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
        = ( top_top @ ( set @ TA ) ) )
      = ( ! [B: TA] :
          ? [C: TB] :
            ( B
            = ( A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(127,axiom,
    ! [A: n] : ( finite_finite2 @ ( sum_sum @ t @ n ) @ ( gram_L1221482011le_H_c @ tr0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_finite__H__c) ).

thf(664,plain,
    ! [A: n] : ( finite_finite2 @ ( sum_sum @ t @ n ) @ ( gram_L1221482011le_H_c @ tr0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(247,axiom,
    member @ ( sum_sum @ t @ dtree ) @ t_tr @ ( cont @ ( gram_L315592705e_pick @ tr0 @ n2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_t__tr) ).

thf(1065,plain,
    member @ ( sum_sum @ t @ dtree ) @ t_tr @ ( cont @ ( gram_L315592705e_pick @ tr0 @ n2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(9,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( finite_finite @ TB @ ( type2 @ TB ) )
        & ( finite_finite @ TA @ ( type2 @ TA ) ) )
     => ( finite_finite @ ( product_prod @ TB @ TA ) @ ( type2 @ ( product_prod @ TB @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Finite__Set_Ofinite_7) ).

thf(283,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( finite_finite @ TB @ ( type2 @ TB ) )
        & ( finite_finite @ TA @ ( type2 @ TA ) ) )
     => ( finite_finite @ ( product_prod @ TB @ TA ) @ ( type2 @ ( product_prod @ TB @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(76,axiom,
    ! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB] :
      ( ( finite_finite2 @ TA @ A )
     => ( finite_finite2 @ TB @ ( image @ TA @ TB @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_finite__imageI) ).

thf(474,plain,
    ! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB] :
      ( ( finite_finite2 @ TA @ A )
     => ( finite_finite2 @ TB @ ( image @ TA @ TB @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(159,axiom,
    ! [A: set @ ( sum_sum @ t @ dtree ),B: n] :
      ( ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ A )
     => ( ( cont @ ( node @ B @ A ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_cont__Node) ).

thf(767,plain,
    ! [A: set @ ( sum_sum @ t @ dtree ),B: n] :
      ( ( finite_finite2 @ ( sum_sum @ t @ dtree ) @ A )
     => ( ( cont @ ( node @ B @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(73,axiom,
    ! [TA: $tType,TB: $tType,A: TB,B: TA] :
      ( ( sum_Inl @ TB @ TA @ A )
     != ( sum_Inr @ TA @ TB @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_old_Osum_Odistinct_I1_J) ).

thf(464,plain,
    ! [TA: $tType,TB: $tType,A: TB,B: TA] :
      ( ( sum_Inl @ TB @ TA @ A )
     != ( sum_Inr @ TA @ TB @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(224,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TB > TC] :
      ( ( comp @ ( set @ TB ) @ ( set @ TA ) @ ( set @ TC ) @ ( vimage @ TA @ TB @ A ) @ ( vimage @ TB @ TC @ B ) )
      = ( vimage @ TA @ TC @ ( comp @ TB @ TC @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_set_Ocomp) ).

thf(992,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TB > TC] :
      ( ( comp @ ( set @ TB ) @ ( set @ TA ) @ ( set @ TC ) @ ( vimage @ TA @ TB @ A ) @ ( vimage @ TB @ TC @ B ) )
      = ( vimage @ TA @ TC @ ( comp @ TB @ TC @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(148,axiom,
    ! [A: dtree,B: set @ n,C: dtree,D: dtree] :
      ( ( member @ n @ ( root @ A ) @ B )
     => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ A ) @ ( cont @ C ) )
       => ( ( gram_L716654942_subtr @ B @ C @ D )
         => ( gram_L716654942_subtr @ B @ A @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_subtr__StepL) ).

thf(723,plain,
    ! [A: dtree,B: set @ n,C: dtree,D: dtree] :
      ( ( member @ n @ ( root @ A ) @ B )
     => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ A ) @ ( cont @ C ) )
       => ( ( gram_L716654942_subtr @ B @ C @ D )
         => ( gram_L716654942_subtr @ B @ A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(185,axiom,
    ! [A: dtree,B: n] :
      ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ A @ B )
     => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ ( gram_L315592705e_pick @ A @ B ) @ A )
        & ( ( root @ ( gram_L315592705e_pick @ A @ B ) )
          = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_Gram__Lang__Mirabelle__ojxrtuoybn_Opick) ).

thf(850,plain,
    ! [A: dtree,B: n] :
      ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ A @ B )
     => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ ( gram_L315592705e_pick @ A @ B ) @ A )
        & ( ( root @ ( gram_L315592705e_pick @ A @ B ) )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(221,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TB > TD,C: TB > TC,D: TA > TB] :
      ( ( ( comp @ TD @ TC @ TB @ A @ B )
        = C )
     => ( ( comp @ TD @ TC @ TA @ A @ ( comp @ TB @ TD @ TA @ B @ D ) )
        = ( comp @ TB @ TC @ TA @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_rewriteL__comp__comp) ).

thf(982,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TB > TD,C: TB > TC,D: TA > TB] :
      ( ( ( comp @ TD @ TC @ TB @ A @ B )
        = C )
     => ( ( comp @ TD @ TC @ TA @ A @ ( comp @ TB @ TD @ TA @ B @ D ) )
        = ( comp @ TB @ TC @ TA @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(67,axiom,
    ! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: TA > TA] :
      ( ! [D: TA] :
          ( ( member @ TA @ D @ A )
         => ! [E: TA] :
              ( ( member @ TA @ E @ A )
             => ( ( ( B @ ( C @ D ) )
                  = ( B @ ( C @ E ) ) )
                = ( ( B @ D )
                  = ( B @ E ) ) ) ) )
     => ( ( inj_on @ TA @ TA @ C @ A )
       => ( ( inj_on @ TA @ TB @ B @ ( image @ TA @ TA @ C @ A ) )
          = ( inj_on @ TA @ TB @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_inj__on__image__iff) ).

thf(442,plain,
    ! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: TA > TA] :
      ( ! [D: TA] :
          ( ( member @ TA @ D @ A )
         => ! [E: TA] :
              ( ( member @ TA @ E @ A )
             => ( ( ( B @ ( C @ D ) )
                  = ( B @ ( C @ E ) ) )
                = ( ( B @ D )
                  = ( B @ E ) ) ) ) )
     => ( ( inj_on @ TA @ TA @ C @ A )
       => ( ( inj_on @ TA @ TB @ B @ ( image @ TA @ TA @ C @ A ) )
          = ( inj_on @ TA @ TB @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(81,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: ( sum_sum @ TC @ TB ) > TA,C: $o] :
      ( ! [D: TC] :
          ( ( A
            = ( B @ ( sum_Inl @ TC @ TB @ D ) ) )
         => C )
     => ( ! [D: TB] :
            ( ( A
              = ( B @ ( sum_Inr @ TB @ TC @ D ) ) )
           => C )
       => ! [D: sum_sum @ TC @ TB] :
            ( ( A
              = ( B @ D ) )
           => C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_obj__sumE__f) ).

thf(486,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: ( sum_sum @ TC @ TB ) > TA,C: $o] :
      ( ! [D: TC] :
          ( ( A
            = ( B @ ( sum_Inl @ TC @ TB @ D ) ) )
         => C )
     => ( ! [D: TB] :
            ( ( A
              = ( B @ ( sum_Inr @ TB @ TC @ D ) ) )
           => C )
       => ! [D: sum_sum @ TC @ TB] :
            ( ( A
              = ( B @ D ) )
           => C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(229,axiom,
    ! [TA: $tType,A: TA > ( set @ ( sum_sum @ t @ TA ) ),B: TA,C: TA > n] :
      ( ( finite_finite2 @ ( sum_sum @ t @ TA ) @ ( A @ B ) )
     => ( ( cont @ ( unfold @ TA @ C @ A @ B ) )
        = ( image @ ( sum_sum @ t @ TA ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ TA @ dtree @ ( id @ t ) @ ( unfold @ TA @ C @ A ) ) @ ( A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_unfold_I2_J) ).

thf(1009,plain,
    ! [TA: $tType,A: TA > ( set @ ( sum_sum @ t @ TA ) ),B: TA,C: TA > n] :
      ( ( finite_finite2 @ ( sum_sum @ t @ TA ) @ ( A @ B ) )
     => ( ( cont @ ( unfold @ TA @ C @ A @ B ) )
        = ( image @ ( sum_sum @ t @ TA ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ TA @ dtree @ ( id @ t ) @ ( unfold @ TA @ C @ A ) ) @ ( A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(204,axiom,
    ! [A: dtree,B: dtree] :
      ( ( ( root @ A )
       != ( root @ B ) )
     => ( ( cont @ ( gram_L1004374585hsubst @ B @ A ) )
        = ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ dtree @ dtree @ ( id @ t ) @ ( gram_L1004374585hsubst @ B ) ) @ ( cont @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_cont__hsubst__neq) ).

thf(923,plain,
    ! [A: dtree,B: dtree] :
      ( ( ( root @ A )
       != ( root @ B ) )
     => ( ( cont @ ( gram_L1004374585hsubst @ B @ A ) )
        = ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ dtree ) @ ( sum_map_sum @ t @ t @ dtree @ dtree @ ( id @ t ) @ ( gram_L1004374585hsubst @ B ) ) @ ( cont @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(126,axiom,
    ! [A: n,B: dtree] :
      ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ A )
     => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ B @ ( gram_L1451583624elle_H @ tr0 @ A ) )
       => ? [C: n] :
            ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ C )
            & ( B
              = ( gram_L1451583624elle_H @ tr0 @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_subtr__H) ).

thf(659,plain,
    ! [A: n,B: dtree] :
      ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ A )
     => ( ( gram_L716654942_subtr @ ( top_top @ ( set @ n ) ) @ B @ ( gram_L1451583624elle_H @ tr0 @ A ) )
       => ? [C: n] :
            ( ( gram_L830233218_inItr @ ( top_top @ ( set @ n ) ) @ tr0 @ C )
            & ( B
              = ( gram_L1451583624elle_H @ tr0 @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(119,axiom,
    ! [A: dtree] :
      ( ( vimage @ t @ ( sum_sum @ t @ n ) @ ( sum_Inl @ t @ n ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ A ) ) )
      = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_Inl__prodOf) ).

thf(639,plain,
    ! [A: dtree] :
      ( ( vimage @ t @ ( sum_sum @ t @ n ) @ ( sum_Inl @ t @ n ) @ ( image @ ( sum_sum @ t @ dtree ) @ ( sum_sum @ t @ n ) @ ( sum_map_sum @ t @ t @ dtree @ n @ ( id @ t ) @ root ) @ ( cont @ A ) ) )
      = ( vimage @ t @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree ) @ ( cont @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(249,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TA > TB,C: TB > TC,D: TB > TC] :
      ( ! [E: TB,F: TB] :
          ( ( member @ TB @ E @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) )
         => ( ( member @ TB @ F @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) )
           => ( ( ( C @ E )
                = ( D @ F ) )
             => ( E = F ) ) ) )
     => ( ( ( comp @ TB @ TC @ TA @ C @ A )
          = ( comp @ TB @ TC @ TA @ D @ B ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_fun_Oinj__map__strong) ).

thf(1069,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TA > TB,C: TB > TC,D: TB > TC] :
      ( ! [E: TB,F: TB] :
          ( ( member @ TB @ E @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) )
         => ( ( member @ TB @ F @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) )
           => ( ( ( C @ E )
                = ( D @ F ) )
             => ( E = F ) ) ) )
     => ( ( ( comp @ TB @ TC @ TA @ C @ A )
          = ( comp @ TB @ TC @ TA @ D @ B ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(143,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TC > TD,B: TE > TD,C: TA > TC,D: TB > TE,E: sum_sum @ TA @ TB] :
      ( ( sum_case_sum @ TC @ TD @ TE @ A @ B @ ( sum_map_sum @ TA @ TC @ TB @ TE @ C @ D @ E ) )
      = ( sum_case_sum @ TA @ TD @ TB @ ( comp @ TC @ TD @ TA @ A @ C ) @ ( comp @ TE @ TD @ TB @ B @ D ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_case__sum__map__sum) ).

thf(708,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TC > TD,B: TE > TD,C: TA > TC,D: TB > TE,E: sum_sum @ TA @ TB] :
      ( ( sum_case_sum @ TC @ TD @ TE @ A @ B @ ( sum_map_sum @ TA @ TC @ TB @ TE @ C @ D @ E ) )
      = ( sum_case_sum @ TA @ TD @ TB @ ( comp @ TC @ TD @ TA @ A @ C ) @ ( comp @ TE @ TD @ TB @ B @ D ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(218,axiom,
    ( gram_L1004374585hsubst
    = ( ^ [A: dtree] : ( unfold @ dtree @ gram_L1905609017ubst_r @ ( gram_L1905609002ubst_c @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_hsubst__def) ).

thf(972,plain,
    ( gram_L1004374585hsubst
    = ( ^ [A: dtree] : ( unfold @ dtree @ gram_L1905609017ubst_r @ ( gram_L1905609002ubst_c @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(238,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA > TC,C: set @ ( sum_sum @ TB @ TA )] :
      ( ( member @ ( sum_sum @ TB @ TC ) @ ( sum_Inr @ TC @ TB @ A ) @ ( image @ ( sum_sum @ TB @ TA ) @ ( sum_sum @ TB @ TC ) @ ( sum_map_sum @ TB @ TB @ TA @ TC @ ( id @ TB ) @ B ) @ C ) )
      = ( ? [D: TA] :
            ( ( member @ ( sum_sum @ TB @ TA ) @ ( sum_Inr @ TA @ TB @ D ) @ C )
            & ( ( B @ D )
              = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_Inr__oplus__iff) ).

thf(1037,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA > TC,C: set @ ( sum_sum @ TB @ TA )] :
      ( ( member @ ( sum_sum @ TB @ TC ) @ ( sum_Inr @ TC @ TB @ A ) @ ( image @ ( sum_sum @ TB @ TA ) @ ( sum_sum @ TB @ TC ) @ ( sum_map_sum @ TB @ TB @ TA @ TC @ ( id @ TB ) @ B ) @ C ) )
      = ( ? [D: TA] :
            ( ( member @ ( sum_sum @ TB @ TA ) @ ( sum_Inr @ TA @ TB @ D ) @ C )
            & ( ( B @ D )
              = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(98,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( finite_finite2 @ ( product_prod @ TB @ TA ) @ ( top_top @ ( set @ ( product_prod @ TB @ TA ) ) ) )
      = ( ( finite_finite2 @ TB @ ( top_top @ ( set @ TB ) ) )
        & ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_finite__prod) ).

thf(560,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( finite_finite2 @ ( product_prod @ TB @ TA ) @ ( top_top @ ( set @ ( product_prod @ TB @ TA ) ) ) )
      = ( ( finite_finite2 @ TB @ ( top_top @ ( set @ TB ) ) )
        & ( finite_finite2 @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(1144,plain,
    $false,
    inference(e,[status(thm)],[645,809,1024,365,893,962,941,666,909,333,777,555,683,276,741,449,597,269,677,1078,385,550,797,898,1127,841,1046,320,436,829,1095,719,504,917,802,1059,587,838,606,1115,289,1100,756,1136,353,480,1040,1109,348,574,602,687,293,774,396,428,877,692,307,292,452,920,380,439,761,534,714,1057,302,862,407,275,729,467,566,1032,361,583,461,974,1012,285,1106,317,650,1121,1006,869,610,499,989,697,1089,420,1118,339,537,669,476,642,590,547,706,328,471,393,647,738,721,1002,569,779,371,1131,654,938,633,805,657,558,674,926,965,425,513,1103,824,856,279,733,689,296,402,413,875,826,577,711,1124,281,572,787,1092,947,540,672,784,736,377,271,764,979,880,1043,434,387,631,323,483,1022,345,552,799,726,848,700,520,1029,895,912,399,959,1066,1015,986,299,431,636,695,455,883,1113,563,1034,680,374,812,1081,342,1018,355,1049,531,944,968,458,580,872,954,310,331,951,808,744,336,703,613,600,1052,1140,314,595,859,845,1084,931,524,771,368,844,517,304,1062,351,390,418,781,995,290,929,478,272,383,832,287,999,410,835,405,854,865,422,790,326,506,358,664,1065,283,474,767,464,992,723,850,982,442,486,1009,923,659,639,1069,708,972,1037,560]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : COM192^1 : TPTP v8.2.0. Released v7.0.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n007.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Sun May 19 10:36:39 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 1.18/1.10  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 2.34/1.53  % [INFO] 	 Parsing done (419ms). 
% 2.59/1.54  % [INFO] 	 Running in sequential loop mode. 
% 3.72/1.96  % [INFO] 	 eprover registered as external prover. 
% 3.72/1.97  % [INFO] 	 cvc4 registered as external prover. 
% 3.72/1.97  % [INFO] 	 Scanning for conjecture ... 
% 4.22/2.16  % [INFO] 	 Found a conjecture (or negated_conjecture) and 271 axioms. Running axiom selection ... 
% 4.78/2.33  % [INFO] 	 Axiom selection finished. Selected 266 axioms (removed 5 axioms). 
% 6.25/2.72  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 6.25/2.75  % [INFO] 	 Type checking passed. 
% 6.25/2.75  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 9.84/3.70  % [INFO] 	 [Domain constraints] Detected constraint on $o 
% 9.84/3.70  % [INFO] 	 [Domain constraints] dom($o) ⊆ {$true} 
% 65.06/39.72  % External prover 'e' found a proof!
% 65.06/39.73  % [INFO] 	 Killing All external provers ... 
% 65.06/39.73  % Time passed: 39198ms (effective reasoning time: 38179ms)
% 65.06/39.73  % 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)>
% 65.06/39.73  % Axioms used in derivation (266): fact_210_Inr__inject, fact_218_case__sum__o__inj_I2_J, fact_81_rangeI, fact_161_vimageI, fact_7_Gram__Lang__Mirabelle__ojxrtuoybn_Oroot__pick, fact_179_case__sum__map__sum, fact_131_finite__hsubst__c, fact_86_top__set__def, fact_120_finite__option__UNIV, fact_253_inj__on__imageI, fact_213_map__sum__InrD, fact_97_rewriteL__comp__comp, tcon_fun___Finite__Set_Ofinite, fact_139_finite__prod, fact_116_unfold_I2_J, fact_195_Inr__cont__hsubst__neq, fact_34_comp__eq__elim, fact_55_sum_Omap__id0, fact_44_Gram__Lang__Mirabelle__ojxrtuoybn_Opick, fact_98_rewriteR__comp__comp, fact_51_comp__eq__id__dest, fact_191_Inr__Inl__False, fact_127_finite__cont, fact_164_Inl__m__oplus, fact_3_root__pick, fact_28_subtr__inItr, fact_247_finite__image__iff, fact_174_set_Ocompositionality, fact_204_Inr__not__Inl, fact_1_root__H__pick, fact_53_sum_Omap__comp, fact_165_Inl__cont__hsubst__neq, fact_99_rewriteL__comp__comp2, fact_30_UNIV__witness, fact_70_root__deftr, fact_234_case__sum__expand__Inr__pointfree, fact_73_image__iff, fact_252_comp__inj__on, fact_146_dtree__simps, fact_180_finite__vimageD, fact_54_map__sum_Ocomp, fact_241_subtrOf__root, fact_150_hsubst__r__def, fact_227_subtr__inductL, fact_95_Gram__Lang__Mirabelle__ojxrtuoybn_OH__def, fact_25_subtr__rootR__in, fact_125_root__hsubst, fact_17_subtr__pick, fact_248_finite__imageD, fact_186_corec_I2_J, fact_147_cont__Node, fact_193_old_Osum_Osimps_I8_J, fact_214_map__sum_Osimps_I2_J, fact_122_cont__hsubst__neq, fact_65_map__sum__InlD, fact_203_split__sum__ex, fact_246_inj__on__image__iff, fact_140_Finite__Set_Ofinite__set, fact_201_old_Osum_Oexhaust, fact_224_subtr_Osimps, fact_56_sum_Omap__id, fact_101_Gram__Lang__Mirabelle__ojxrtuoybn_OH__c__def, fact_153_Sup_OSUP__image, fact_138_finite__Prod__UNIV, fact_251_inj__image__mem__iff, fact_137_finite__fun__UNIVD2, fact_173_old_Osum_Osimps_I5_J, fact_207_old_Osum_Odistinct_I2_J, fact_190_Inr__cont__H, fact_102_subtr__deftr, fact_117_Gram__Lang__Mirabelle__ojxrtuoybn_Ofinite__H__c, fact_126_root__o__subst, fact_110_hsubst__c__def, fact_144_DEADID_Oin__rel, fact_35_comp__eq__dest, fact_91_fun_Oinj__map__strong, fact_212_map__sum__if__distrib__then_I2_J, fact_229_inItr_Ocases, fact_87_comp__surj, fact_200_old_Osum_Oinducts, fact_5_root__H, fact_41_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr__pick, fact_59_root__o__deftr, fact_24_subtr__trans, fact_205_sumE, fact_29_inItr__subtr, fact_12_pick, fact_141_hsubst__def, fact_46_Collect__mem__eq, fact_148_dtree__cases, fact_249_range__ex1__eq, fact_64_map__sum__o__inj_I1_J, fact_106_finite__H__c, fact_168_case__sum__inject, fact_176_set_Ocomp, tcon_Product__Type_Oprod___Finite__Set_Ofinite_7, fact_167_case__sum__step_I1_J, fact_90_fun_Omap__cong0, fact_172_vimageD, fact_175_vimage__comp, fact_123_cont__hsubst__eq, fact_243_subtrOf, fact_69_image__id, fact_114_top__conj_I1_J, fact_238_map__sum__o__inj_I2_J, fact_89_fun_Omap__cong, fact_237_inFr2__Ind, fact_14_id__comp, fact_154_Sup_OSUP__cong, help_If_1_1_T, fact_233_case__sum__expand__Inr_H, fact_113_top__conj_I2_J, conj_2, fact_132_finite, fact_100_rewriteR__comp__comp2, fact_185_Inl__prodOf, fact_239_root__subtrOf, fact_39_id__def, fact_129_hsubst__eq, fact_222_subtr_OStep, fact_49_Gram__Lang__Mirabelle__ojxrtuoybn_OH__r__def, fact_79_surjE, fact_88_fun_Oset__map, fact_244_obj__sumE, fact_33_comp__eq__dest__lhs, fact_115_finite__S, fact_58_H__def, fact_206_old_Osum_Odistinct_I1_J, fact_184_case__sum__o__map__sum, fact_63_old_Osum_Osimps_I7_J, fact_250_inj__image__eq__iff, fact_9_Gram__Lang__Mirabelle__ojxrtuoybn_Oroot__H__pick, fact_216_case__sum__if, fact_198_case__sum__step_I2_J, tcon_Option_Ooption___Finite__Set_Ofinite_6, fact_45_mem__Collect__eq, fact_22_UNIV__I, fact_177_surj__image__vimage__eq, fact_211_map__sum__if__distrib__else_I2_J, fact_85_image__eq__imp__comp, fact_76_ball__imageD, fact_118_Gram__Lang__Mirabelle__ojxrtuoybn_Ocont__H, fact_109_dtree__cong, fact_189_old_Osum_Oinject_I2_J, fact_111_top1I, fact_236_subtr__UNIV__inductL, fact_235_corec_I1_J, fact_240_surj__subtrOf, fact_104_deftr__def, fact_32_fun_Omap__comp, fact_8_inItr_OBase, fact_183_Gram__Lang__Mirabelle__ojxrtuoybn_OInl__cont__H, tcon_HOL_Obool___Finite__Set_Ofinite_3, fact_68_image__eqI, fact_133_finite__set__choice, fact_208_sum_Odistinct_I1_J, fact_232_case__sum__expand__Inr, fact_94_wf__deftr, fact_194_wf__inj, fact_84_image__comp, fact_72_imageI, fact_27_subtr_ORefl, fact_6_Gram__Lang__Mirabelle__ojxrtuoybn_Oroot__H, fact_37_comp__def, fact_149_type__copy__map__cong0, fact_159_inFr2_OBase, fact_47_Collect__cong, fact_92_surj__id, fact_202_split__sum__all, fact_82_surj__def, fact_83_range__eqI, fact_93_Inl__oplus__elim, help_If_2_1_T, fact_219_root__prodOf, fact_155_Inf_OINF__cong, fact_152_Inf_OINF__id__eq, fact_134_finite__UNIV, help_If_3_1_T, fact_31_UNIV__eq__I, fact_217_wf__cont, fact_221_Inr__oplus__elim, fact_254_comp__inj__on__iff, fact_50_fun_Omap__id0, fact_96_comp__apply__eq, fact_228_inItr_OInd, fact_57_map__sum_Osimps_I1_J, fact_80_surjI, fact_182_o__case__sum, fact_128_finite__N, fact_157_Inl__cont__H, fact_21_comp__apply, fact_15_fun_Omap__id, fact_105_surj__fun__eq, fact_119_finite__Plus__UNIV__iff, fact_223_subtr_Ocases, conj_1, fact_209_obj__sumE__f, fact_103_pointfree__idE, fact_142_top__empty__eq, fact_130_wf__hsubst, fact_19_old_Osum_Oinject_I1_J, fact_192_Inl__Inr__False, fact_108_cont__H, fact_215_Inl__Inr__image__cong, fact_199_old_Osum_Osimps_I6_J, fact_77_rev__image__eqI, fact_156_Inf_OINF__image, fact_42_Gram__Lang__Mirabelle__ojxrtuoybn_Osubtr__H, fact_245_wf__subtr__inj__on, fact_135_infinite__UNIV__char__0, tcon_Set_Oset___Finite__Set_Ofinite_1, fact_13_comp__id, fact_171_vimageE, fact_107_unfold_I1_J, fact_181_case__sum__o__inj_I1_J, fact_36_comp__assoc, fact_75_image__cong, fact_20_id__apply, fact_43_Gram__Lang__Mirabelle__ojxrtuoybn_Owf__pick, fact_169_vimage__Collect, fact_60_iso__tuple__UNIV__I, fact_121_finite__imageI, fact_166_Inl__cont__hsubst__eq, fact_26_subtr__rootL__in, fact_170_vimageI2, fact_158_case__sum__o__map__sum__id, fact_52_map__sum_Ocompositionality, fact_136_ex__new__if__finite, fact_197_Inr__oplus__iff, fact_67_map__sum__if__distrib__else_I1_J, fact_242_Inr__subtrOf, tcon_Sum__Type_Osum___Finite__Set_Ofinite_5, fact_112_cont__deftr, fact_4_H__r__def, fact_196_Inr__cont__hsubst__eq, fact_62_H__c__def, fact_225_subtr__StepL, fact_188_sum_Oinject_I2_J, fact_23_wf__subtr, fact_124_finite__code, fact_220_Gram__Lang__Mirabelle__ojxrtuoybn_OInr__cont__H, fact_160_vimage__eq, fact_178_inFr2__root__in, fact_78_surjD, fact_145_root__Node, fact_40_Inl__inject, conj_0, fact_163_vimage__id, fact_143_Node__root__cont, fact_11_wf__pick, fact_0_n, fact_74_bex__imageD, fact_151_Sup_OSUP__id__eq, fact_230_inItr_Osimps, fact_255_finite__UNIV__inj__surj, fact_66_map__sum__if__distrib__then_I1_J, fact_10_inItr__root__in, fact_18_sum_Oinject_I1_J, fact_2_t__tr, fact_71_Inl__oplus__iff, fact_162_vimage__UNIV, fact_187_Inr__m__oplus, fact_38_eq__id__iff, fact_231_inItr_Oinducts, fact_16_subtr__H, fact_226_subtr_Oinducts
% 65.06/39.73  % No. of inferences in proof: 536
% 65.06/39.73  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 39198 ms resp. 38179 ms w/o parsing
% 66.64/40.05  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 66.64/40.05  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------