TSTP Solution File: COM191^1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : COM191^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n016.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 147.60s 90.49s
% Output   : Refutation 148.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  268
% Syntax   : Number of formulae    :  487 ( 174 unt;  51 typ;   0 def)
%            Number of atoms       : 1495 ( 438 equ;   2 cnn)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives : 6529 ( 178   ~;  24   |; 162   &;5561   @)
%                                         (   0 <=>; 604  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   8 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :  246 ( 246   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   57 (  53 usr;  16 con; 0-6 aty)
%            Number of variables   : 1700 ( 118   ^1437   !; 110   ?;1700   :)
%                                         (  29  !>;   0  ?*;   0  @-;   6  @+)

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

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

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

thf(bNF_Greatest_shift_type,type,
    bNF_Greatest_shift: 
      !>[TA: $tType,TB: $tType] : ( ( ( list @ TB ) > TA ) > TB > ( list @ TB ) > TA ) ).

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

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

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

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

thf(gram_L1580978439le_Itr_type,type,
    gram_L1580978439le_Itr: ( set @ n ) > dtree > ( set @ n ) ).

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_L1333338417e_inFr_type,type,
    gram_L1333338417e_inFr: ( set @ n ) > dtree > t > $o ).

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_L250615845e_path_type,type,
    gram_L250615845e_path: ( n > dtree ) > ( list @ n ) > $o ).

thf(gram_L1918716148le_reg_type,type,
    gram_L1918716148le_reg: ( n > dtree ) > dtree > $o ).

thf(gram_L646766332egular_type,type,
    gram_L646766332egular: dtree > $o ).

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

thf(gram_L1283001940subtr2_type,type,
    gram_L1283001940subtr2: ( 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(coset_type,type,
    coset: 
      !>[TA: $tType] : ( ( list @ TA ) > ( set @ TA ) ) ).

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

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

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

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

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

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

thf(set2_type,type,
    set2: 
      !>[TA: $tType] : ( ( list @ TA ) > ( set @ TA ) ) ).

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

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

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

thf(ord_less_eq_type,type,
    ord_less_eq: 
      !>[TA: $tType] : ( TA > TA > $o ) ).

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

thf(insert2_type,type,
    insert2: 
      !>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).

thf(remove_type,type,
    remove: 
      !>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).

thf(the_elem_type,type,
    the_elem: 
      !>[TA: $tType] : ( ( set @ TA ) > TA ) ).

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_rec_sum_type,type,
    sum_rec_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(f_type,type,
    f: n > dtree ).

thf(nl_type,type,
    nl: list @ n ).

thf(ns_type,type,
    ns: set @ n ).

thf(nsa_type,type,
    nsa: set @ n ).

thf(tr_type,type,
    tr: dtree ).

thf(tr1_type,type,
    tr1: dtree ).

thf(tr1a_type,type,
    tr1a: dtree ).

thf(tr2_type,type,
    tr2: dtree ).

thf(tra_type,type,
    tra: dtree ).

thf(132,axiom,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( cons @ TA @ A @ B )
     != B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_not__Cons__self2) ).

thf(645,plain,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( cons @ TA @ A @ B )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(127,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
       => ( member @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_rev__subsetD) ).

thf(629,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
       => ( member @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(210,axiom,
    ! [A: set @ n,B: dtree,C: t,D: set @ n] :
      ( ( gram_L1333338417e_inFr @ A @ B @ C )
     => ( ( ord_less_eq @ ( set @ n ) @ A @ D )
       => ( gram_L1333338417e_inFr @ D @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_inFr__mono) ).

thf(941,plain,
    ! [A: set @ n,B: dtree,C: t,D: set @ n] :
      ( ( gram_L1333338417e_inFr @ A @ B @ C )
     => ( ( ord_less_eq @ ( set @ n ) @ A @ D )
       => ( gram_L1333338417e_inFr @ D @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(64,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_245_Inr__not__Inl) ).

thf(408,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)],[64]) ).

thf(20,axiom,
    ! [TA: $tType,A: TA,B: TA > $o] :
      ( ( insert2 @ TA @ A @ ( collect @ TA @ B ) )
      = ( collect @ TA
        @ ^ [C: TA] :
            ( ( C != A )
           => ( B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_insert__Collect) ).

thf(276,plain,
    ! [TA: $tType,A: TA,B: TA > $o] :
      ( ( insert2 @ TA @ A @ ( collect @ TA @ B ) )
      = ( collect @ TA
        @ ^ [C: TA] :
            ( ( C != A )
           => ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(157,axiom,
    ! [A: set @ n,B: dtree,C: dtree] :
      ( ( gram_L1283001940subtr2 @ A @ B @ C )
     => ( ( ( C = B )
         => ~ ( member @ n @ ( root @ B ) @ A ) )
       => ~ ( ( member @ n @ ( root @ B ) @ A )
           => ! [D: dtree] :
                ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ B ) @ ( cont @ D ) )
               => ~ ( gram_L1283001940subtr2 @ A @ D @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_subtr2_Ocases) ).

thf(741,plain,
    ! [A: set @ n,B: dtree,C: dtree] :
      ( ( gram_L1283001940subtr2 @ A @ B @ C )
     => ( ( ( C = B )
         => ~ ( member @ n @ ( root @ B ) @ A ) )
       => ~ ( ( member @ n @ ( root @ B ) @ A )
           => ! [D: dtree] :
                ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ B ) @ ( cont @ D ) )
               => ~ ( gram_L1283001940subtr2 @ A @ D @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(188,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_L1333338417e_inFr @ B @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_inFr_OBase) ).

thf(873,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_L1333338417e_inFr @ B @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(11,axiom,
    ! [TA: $tType] :
      ( ( (=) @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
            ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
            & ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_set__eq__subset) ).

thf(247,plain,
    ! [TA: $tType] :
      ( ( (=) @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
            ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
            & ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(55,axiom,
    member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ tr1a ) @ ( cont @ tra ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_tr1__tr) ).

thf(379,plain,
    member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ tr1a ) @ ( cont @ tra ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(183,axiom,
    ! [TA: $tType,A: TA,B: list @ TA] : ( member @ TA @ A @ ( set2 @ TA @ ( cons @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_list_Oset__intros_I1_J) ).

thf(861,plain,
    ! [TA: $tType,A: TA,B: list @ TA] : ( member @ TA @ A @ ( set2 @ TA @ ( cons @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(92,axiom,
    ! [TA: $tType,A: list @ TA,B: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ ( set2 @ TA @ A ) @ B )
      = ( ! [C: TA] :
            ( ( member @ TA @ C @ ( set2 @ TA @ A ) )
           => ( member @ TA @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_subset__code_I1_J) ).

thf(523,plain,
    ! [TA: $tType,A: list @ TA,B: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ ( set2 @ TA @ A ) @ B )
      = ( ! [C: TA] :
            ( ( member @ TA @ C @ ( set2 @ TA @ A ) )
           => ( member @ TA @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(159,axiom,
    ! [TA: $tType,A: set @ TA,B: TA > $o] :
      ( ord_less_eq @ ( set @ TA )
      @ ( collect @ TA
        @ ^ [C: TA] :
            ( ( member @ TA @ C @ A )
            & ( B @ C ) ) )
      @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_Collect__restrict) ).

thf(762,plain,
    ! [TA: $tType,A: set @ TA,B: TA > $o] :
      ( ord_less_eq @ ( set @ TA )
      @ ( collect @ TA
        @ ^ [C: TA] :
            ( ( member @ TA @ C @ A )
            & ( B @ C ) ) )
      @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(72,axiom,
    ! [A: set @ n,B: dtree,C: t] :
      ( ( gram_L805317441_inFr2 @ A @ B @ C )
     => ( ( ( member @ n @ ( root @ B ) @ A )
         => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ C ) @ ( cont @ B ) ) )
       => ~ ! [D: dtree,E: dtree,F: set @ n] :
              ( ( A
                = ( insert2 @ n @ ( root @ E ) @ F ) )
             => ( ( B = E )
               => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ D ) @ ( cont @ E ) )
                 => ~ ( gram_L805317441_inFr2 @ F @ D @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_inFr2_Ocases) ).

thf(440,plain,
    ! [A: set @ n,B: dtree,C: t] :
      ( ( gram_L805317441_inFr2 @ A @ B @ C )
     => ( ( ( member @ n @ ( root @ B ) @ A )
         => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ C ) @ ( cont @ B ) ) )
       => ~ ! [D: dtree,E: dtree,F: set @ n] :
              ( ( A
                = ( insert2 @ n @ ( root @ E ) @ F ) )
             => ( ( B = E )
               => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ D ) @ ( cont @ E ) )
                 => ~ ( gram_L805317441_inFr2 @ F @ D @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(136,axiom,
    ! [TA: $tType] :
      ( ( insert2 @ TA )
      = ( ^ [A: TA,B: set @ TA] :
            ( collect @ TA
            @ ^ [C: TA] :
                ( ( C = A )
                | ( member @ TA @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_insert__compr) ).

thf(655,plain,
    ! [TA: $tType] :
      ( ( insert2 @ TA )
      = ( ^ [A: TA,B: set @ TA] :
            ( collect @ TA
            @ ^ [C: TA] :
                ( ( C = A )
                | ( member @ TA @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(58,axiom,
    ! [A: n > dtree,B: dtree] :
      ( ( gram_L1918716148le_reg @ A @ B )
     => ( ( A @ ( root @ B ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_reg__root) ).

thf(385,plain,
    ! [A: n > dtree,B: dtree] :
      ( ( gram_L1918716148le_reg @ A @ B )
     => ( ( A @ ( root @ B ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(85,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_248_old_Osum_Odistinct_I2_J) ).

thf(500,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)],[85]) ).

thf(78,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_246_sumE) ).

thf(472,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)],[78]) ).

thf(170,axiom,
    ! [A: set @ n,B: dtree,C: dtree,D: set @ n] :
      ( ( gram_L716654942_subtr @ A @ B @ C )
     => ( ( ord_less_eq @ ( set @ n ) @ A @ D )
       => ( gram_L716654942_subtr @ D @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_subtr__mono) ).

thf(814,plain,
    ! [A: set @ n,B: dtree,C: dtree,D: set @ n] :
      ( ( gram_L716654942_subtr @ A @ B @ C )
     => ( ( ord_less_eq @ ( set @ n ) @ A @ D )
       => ( gram_L716654942_subtr @ D @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(145,axiom,
    ( gram_L250615845e_path
    = ( ^ [A: n > dtree,B: list @ n] :
          ( ? [C: n] :
              ( B
              = ( cons @ n @ C @ ( nil @ n ) ) )
          | ? [C: n,D: list @ n,E: n] :
              ( ( B
                = ( cons @ n @ E @ ( cons @ n @ C @ D ) ) )
              & ( gram_L250615845e_path @ A @ ( cons @ n @ C @ D ) )
              & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( A @ C ) ) @ ( cont @ ( A @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_path_Osimps) ).

thf(698,plain,
    ( gram_L250615845e_path
    = ( ^ [A: n > dtree,B: list @ n] :
          ( ? [C: n] :
              ( B
              = ( cons @ n @ C @ ( nil @ n ) ) )
          | ? [C: n,D: list @ n,E: n] :
              ( ( B
                = ( cons @ n @ E @ ( cons @ n @ C @ D ) ) )
              & ( gram_L250615845e_path @ A @ ( cons @ n @ C @ D ) )
              & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( A @ C ) ) @ ( cont @ ( A @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(212,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( member @ TA @ C @ A )
       => ( member @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_in__mono) ).

thf(945,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( member @ TA @ C @ A )
       => ( member @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(207,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: TA] :
      ( ( ~ ( member @ TA @ A @ B )
       => ( A = C ) )
     => ( member @ TA @ A @ ( insert2 @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_insertCI) ).

thf(930,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: TA] :
      ( ( ~ ( member @ TA @ A @ B )
       => ( A = C ) )
     => ( member @ TA @ A @ ( insert2 @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(175,axiom,
    ! [A: n > dtree,B: list @ n] :
      ( ( gram_L250615845e_path @ A @ B )
     => ? [C: list @ n] :
          ( ( gram_L250615845e_path @ A @ C )
          & ( ( hd @ n @ C )
            = ( hd @ n @ B ) )
          & ( ( last @ n @ C )
            = ( last @ n @ B ) )
          & ( ord_less_eq @ ( set @ n ) @ ( set2 @ n @ C ) @ ( set2 @ n @ B ) )
          & ( distinct @ n @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_path__distinct) ).

thf(829,plain,
    ! [A: n > dtree,B: list @ n] :
      ( ( gram_L250615845e_path @ A @ B )
     => ? [C: list @ n] :
          ( ( gram_L250615845e_path @ A @ C )
          & ( ( hd @ n @ C )
            = ( hd @ n @ B ) )
          & ( ( last @ n @ C )
            = ( last @ n @ B ) )
          & ( ord_less_eq @ ( set @ n ) @ ( set2 @ n @ C ) @ ( set2 @ n @ B ) )
          & ( distinct @ n @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(24,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
      = ( ! [C: TA] :
            ( ( A @ C )
           => ( B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_Collect__mono__iff) ).

thf(288,plain,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
      = ( ! [C: TA] :
            ( ( A @ C )
           => ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(104,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_43_old_Osum_Osimps_I8_J) ).

thf(565,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)],[104]) ).

thf(14,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_236_Inl__inject) ).

thf(257,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)],[14]) ).

thf(153,axiom,
    ! [TA: $tType] :
      ( ( insert @ TA )
      = ( ^ [A: TA,B: list @ TA] : ( if @ ( list @ TA ) @ ( member @ TA @ A @ ( set2 @ TA @ B ) ) @ B @ ( cons @ TA @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_List_Oinsert__def) ).

thf(719,plain,
    ! [TA: $tType] :
      ( ( insert @ TA )
      = ( ^ [A: TA,B: list @ TA] : ( if @ ( list @ TA ) @ ( member @ TA @ A @ ( set2 @ TA @ B ) ) @ B @ ( cons @ TA @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(46,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_83_subtr__inductL) ).

thf(344,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)],[46]) ).

thf(112,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
       => ( ord_less_eq @ ( set @ TA ) @ ( insert2 @ TA @ A @ C ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_insert__subsetI) ).

thf(587,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
       => ( ord_less_eq @ ( set @ TA ) @ ( insert2 @ TA @ A @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(123,axiom,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( nil @ TA )
     != ( cons @ TA @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_list_Odistinct_I1_J) ).

thf(619,plain,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( nil @ TA )
     != ( cons @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(99,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_81_subtr__StepL) ).

thf(542,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)],[99]) ).

thf(75,axiom,
    ( ( f @ ( hd @ n @ nl ) )
    = tr1a ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_f__nl) ).

thf(460,plain,
    ( ( f @ ( hd @ n @ nl ) )
    = tr1a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(187,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( bNF_Greatest_univ @ TA @ TB )
      = ( ^ [A: TA > TB,B: set @ TA] :
            ( A
            @ @+[C: TA] : ( member @ TA @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_univ__def) ).

thf(870,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( bNF_Greatest_univ @ TA @ TB )
      = ( ^ [A: TA > TB,B: set @ TA] :
            ( A
            @ @+[C: TA] : ( member @ TA @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(119,axiom,
    ! [A: dtree,B: set @ n,C: dtree,D: dtree] :
      ( ( member @ n @ ( root @ A ) @ B )
     => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ C ) @ ( cont @ A ) )
       => ( ( gram_L1283001940subtr2 @ B @ D @ C )
         => ( gram_L1283001940subtr2 @ B @ D @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_subtr2__StepR) ).

thf(606,plain,
    ! [A: dtree,B: set @ n,C: dtree,D: dtree] :
      ( ( member @ n @ ( root @ A ) @ B )
     => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ C ) @ ( cont @ A ) )
       => ( ( gram_L1283001940subtr2 @ B @ D @ C )
         => ( gram_L1283001940subtr2 @ B @ D @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(162,axiom,
    gram_L1918716148le_reg @ f @ tr1a,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_tr1) ).

thf(770,plain,
    gram_L1918716148le_reg @ f @ tr1a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(67,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_143_inItr_Oinducts) ).

thf(416,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)],[67]) ).

thf(39,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_227_sum_Oinject_I1_J) ).

thf(325,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)],[39]) ).

thf(171,axiom,
    ! [TA: $tType,A: set @ TA,B: list @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ ( coset @ TA @ B ) )
      = ( ! [C: TA] :
            ( ( member @ TA @ C @ ( set2 @ TA @ B ) )
           => ~ ( member @ TA @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_subset__code_I2_J) ).

thf(817,plain,
    ! [TA: $tType,A: set @ TA,B: list @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ ( coset @ TA @ B ) )
      = ( ! [C: TA] :
            ( ( member @ TA @ C @ ( set2 @ TA @ B ) )
           => ~ ( member @ TA @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(199,axiom,
    ! [TA: $tType] :
      ~ ( ord_less_eq @ ( set @ TA ) @ ( coset @ TA @ ( nil @ TA ) ) @ ( set2 @ TA @ ( nil @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_subset__code_I3_J) ).

thf(902,plain,
    ! [TA: $tType] :
      ~ ( ord_less_eq @ ( set @ TA ) @ ( coset @ TA @ ( nil @ TA ) ) @ ( set2 @ TA @ ( nil @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(82,axiom,
    ! [TA: $tType,TB: $tType,A: ( TB > TA ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA,C: list @ TB,D: list @ TA] :
      ( ! [E: TB > TA,F: list @ TA] : ( A @ E @ ( nil @ TB ) @ F )
     => ( ! [E: TB > TA,F: TB,G: list @ TB,H: list @ TA] :
            ( ( A @ E @ G @ ( cons @ TA @ ( E @ F ) @ H ) )
           => ( A @ E @ ( cons @ TB @ F @ G ) @ H ) )
       => ( A @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_map__tailrec__rev_Oinduct) ).

thf(492,plain,
    ! [TA: $tType,TB: $tType,A: ( TB > TA ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA,C: list @ TB,D: list @ TA] :
      ( ! [E: TB > TA,F: list @ TA] : ( A @ E @ ( nil @ TB ) @ F )
     => ( ! [E: TB > TA,F: TB,G: list @ TB,H: list @ TA] :
            ( ( A @ E @ G @ ( cons @ TA @ ( E @ F ) @ H ) )
           => ( A @ E @ ( cons @ TB @ F @ G ) @ H ) )
       => ( A @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(166,axiom,
    ! [A: set @ n,B: dtree,C: dtree] :
      ( ( gram_L1283001940subtr2 @ A @ B @ C )
     => ( member @ n @ ( root @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_subtr2__rootL__in) ).

thf(789,plain,
    ! [A: set @ n,B: dtree,C: dtree] :
      ( ( gram_L1283001940subtr2 @ A @ B @ C )
     => ( member @ n @ ( root @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(54,axiom,
    ! [A: n > dtree,B: n,C: list @ n,D: n] :
      ( ( gram_L250615845e_path @ A @ ( cons @ n @ B @ C ) )
     => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( A @ B ) ) @ ( cont @ ( A @ D ) ) )
       => ( gram_L250615845e_path @ A @ ( cons @ n @ D @ ( cons @ n @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_path_OInd) ).

thf(376,plain,
    ! [A: n > dtree,B: n,C: list @ n,D: n] :
      ( ( gram_L250615845e_path @ A @ ( cons @ n @ B @ C ) )
     => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( A @ B ) ) @ ( cont @ ( A @ D ) ) )
       => ( gram_L250615845e_path @ A @ ( cons @ n @ D @ ( cons @ n @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(8,axiom,
    ! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
      ( ( ord_less_eq @ ( set @ TA ) @ A
        @ ( collect @ TA
          @ ^ [D: TA] :
              ( ( B @ D )
              & ( C @ D ) ) ) )
      = ( ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ B ) )
        & ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_conj__subset__def) ).

thf(238,plain,
    ! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
      ( ( ord_less_eq @ ( set @ TA ) @ A
        @ ( collect @ TA
          @ ^ [D: TA] :
              ( ( B @ D )
              & ( C @ D ) ) ) )
      = ( ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ B ) )
        & ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(79,axiom,
    ! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
      ( ( A @ ( nil @ TA ) )
     => ( ! [C: TA,D: list @ TA] :
            ( ( A @ D )
           => ( A @ ( cons @ TA @ C @ D ) ) )
       => ( A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_list_Oinducts) ).

thf(475,plain,
    ! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
      ( ( A @ ( nil @ TA ) )
     => ( ! [C: TA,D: list @ TA] :
            ( ( A @ D )
           => ( A @ ( cons @ TA @ C @ D ) ) )
       => ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(204,axiom,
    ! [A: dtree,B: set @ n,C: t] :
      ( ~ ( member @ n @ ( root @ A ) @ B )
     => ~ ( gram_L1333338417e_inFr @ B @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_not__root__inFr) ).

thf(924,plain,
    ! [A: dtree,B: set @ n,C: t] :
      ( ~ ( member @ n @ ( root @ A ) @ B )
     => ~ ( gram_L1333338417e_inFr @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(26,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_subset__antisym) ).

thf(293,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(185,axiom,
    gram_L1918716148le_reg @ f @ tr,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_f) ).

thf(866,plain,
    gram_L1918716148le_reg @ f @ tr,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(73,axiom,
    ! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
      ( ( A
        = ( cons @ TA @ B @ C ) )
     => ( A
       != ( nil @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_list_OdiscI) ).

thf(453,plain,
    ! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
      ( ( A
        = ( cons @ TA @ B @ C ) )
     => ( A
       != ( nil @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(164,axiom,
    ! [A: set @ n,B: dtree,C: dtree,D: ( set @ n ) > dtree > dtree > $o] :
      ( ( gram_L1283001940subtr2 @ 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 )
             => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ E ) @ ( cont @ G ) )
               => ( ( gram_L1283001940subtr2 @ F @ G @ H )
                 => ( ( D @ F @ G @ H )
                   => ( D @ F @ E @ H ) ) ) ) )
         => ( D @ A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_subtr2_Oinducts) ).

thf(774,plain,
    ! [A: set @ n,B: dtree,C: dtree,D: ( set @ n ) > dtree > dtree > $o] :
      ( ( gram_L1283001940subtr2 @ 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 )
             => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ E ) @ ( cont @ G ) )
               => ( ( gram_L1283001940subtr2 @ F @ G @ H )
                 => ( ( D @ F @ G @ H )
                   => ( D @ F @ E @ H ) ) ) ) )
         => ( D @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(65,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ~ ( member @ TA @ C @ B )
       => ~ ( member @ TA @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_contra__subsetD) ).

thf(411,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ~ ( member @ TA @ C @ B )
       => ~ ( member @ TA @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(68,axiom,
    ! [TA: $tType,TB: $tType,A: TA,B: TA] :
      ( ( A != B )
     => ( ( sum_Inr @ TA @ TB @ A )
       != ( sum_Inr @ TA @ TB @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_not__arg__cong__Inr) ).

thf(428,plain,
    ! [TA: $tType,TB: $tType,A: TA,B: TA] :
      ( ( A != B )
     => ( ( sum_Inr @ TA @ TB @ A )
       != ( sum_Inr @ TA @ TB @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(62,axiom,
    ! [A: n > dtree,B: n,C: list @ n] :
      ( ( gram_L250615845e_path @ A @ ( cons @ n @ B @ C ) )
     => ( ( C
         != ( nil @ n ) )
       => ( gram_L250615845e_path @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_path__post) ).

thf(397,plain,
    ! [A: n > dtree,B: n,C: list @ n] :
      ( ( gram_L250615845e_path @ A @ ( cons @ n @ B @ C ) )
     => ( ( C
         != ( nil @ n ) )
       => ( gram_L250615845e_path @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(141,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ~ ( member @ TA @ A @ B )
     => ( ~ ( member @ TA @ A @ C )
       => ( ( ( insert2 @ TA @ A @ B )
            = ( insert2 @ TA @ A @ C ) )
          = ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_insert__ident) ).

thf(687,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ~ ( member @ TA @ A @ B )
     => ( ~ ( member @ TA @ A @ C )
       => ( ( ( insert2 @ TA @ A @ B )
            = ( insert2 @ TA @ A @ C ) )
          = ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(17,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( A = B )
     => ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
         => ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_equalityE) ).

thf(265,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( A = B )
     => ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
         => ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(180,axiom,
    ! [A: dtree] :
      ( ( node @ ( root @ A ) @ ( cont @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_Node__root__cont) ).

thf(849,plain,
    ! [A: dtree] :
      ( ( node @ ( root @ A ) @ ( cont @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(32,axiom,
    gram_L1333338417e_inFr = gram_L805317441_inFr2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_inFr__inFr2) ).

thf(307,plain,
    gram_L1333338417e_inFr = gram_L805317441_inFr2,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(56,axiom,
    gram_L1905609017ubst_r = root,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_hsubst__r__def) ).

thf(380,plain,
    gram_L1905609017ubst_r = root,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(94,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_21_hsubst__c__def) ).

thf(529,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)],[94]) ).

thf(96,axiom,
    ( gram_L1580978439le_Itr
    = ( ^ [A: set @ n,B: dtree] : ( collect @ n @ ( gram_L830233218_inItr @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_Itr__def) ).

thf(534,plain,
    ( gram_L1580978439le_Itr
    = ( ^ [A: set @ n,B: dtree] : ( collect @ n @ ( gram_L830233218_inItr @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(151,axiom,
    ! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert2 @ TA @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_insertI1) ).

thf(714,plain,
    ! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert2 @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(89,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_152_inItr__subtr) ).

thf(512,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)],[89]) ).

thf(71,axiom,
    gram_L1918716148le_reg @ f @ tra,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_tr) ).

thf(439,plain,
    gram_L1918716148le_reg @ f @ tra,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(42,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ord_less_eq @ ( set @ TA ) @ A @ ( insert2 @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_subset__insertI2) ).

thf(334,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ord_less_eq @ ( set @ TA ) @ A @ ( insert2 @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(174,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_85_subtrOf__root) ).

thf(825,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)],[174]) ).

thf(215,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_78_subtr_OStep) ).

thf(952,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)],[215]) ).

thf(30,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( distinct @ TA @ ( union @ TA @ A @ B ) )
      = ( distinct @ TA @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_distinct__union) ).

thf(302,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( distinct @ TA @ ( union @ TA @ A @ B ) )
      = ( distinct @ TA @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(15,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_59_subtr__trans) ).

thf(260,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)],[15]) ).

thf(116,axiom,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( set2 @ TA @ ( cons @ TA @ A @ B ) )
      = ( insert2 @ TA @ A @ ( set2 @ TA @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_list_Osimps_I15_J) ).

thf(598,plain,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( set2 @ TA @ ( cons @ TA @ A @ B ) )
      = ( insert2 @ TA @ A @ ( set2 @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(172,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_153_inItr_OInd) ).

thf(820,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)],[172]) ).

thf(28,axiom,
    ! [TA: $tType,A: set @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( insert2 @ TA @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_subset__insertI) ).

thf(297,plain,
    ! [TA: $tType,A: set @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( insert2 @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(143,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_244_split__sum__ex) ).

thf(693,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)],[143]) ).

thf(19,axiom,
    gram_L716654942_subtr @ ns @ tr1 @ tr,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_n) ).

thf(275,plain,
    gram_L716654942_subtr @ ns @ tr1 @ tr,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(125,axiom,
    ( gram_L805317441_inFr2
    = ( ^ [A: set @ n,B: dtree,C: t] :
          ( ? [D: dtree,E: set @ n,F: t] :
              ( ( A = E )
              & ( B = D )
              & ( C = F )
              & ( member @ n @ ( root @ D ) @ E )
              & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ F ) @ ( cont @ D ) ) )
          | ? [D: dtree,E: dtree,F: set @ n,G: t] :
              ( ( A
                = ( insert2 @ n @ ( root @ E ) @ F ) )
              & ( B = E )
              & ( C = G )
              & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ D ) @ ( cont @ E ) )
              & ( gram_L805317441_inFr2 @ F @ D @ G ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_inFr2_Osimps) ).

thf(625,plain,
    ( gram_L805317441_inFr2
    = ( ^ [A: set @ n,B: dtree,C: t] :
          ( ? [D: dtree,E: set @ n,F: t] :
              ( ( A = E )
              & ( B = D )
              & ( C = F )
              & ( member @ n @ ( root @ D ) @ E )
              & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ F ) @ ( cont @ D ) ) )
          | ? [D: dtree,E: dtree,F: set @ n,G: t] :
              ( ( A
                = ( insert2 @ n @ ( root @ E ) @ F ) )
              & ( B = E )
              & ( C = G )
              & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ D ) @ ( cont @ E ) )
              & ( gram_L805317441_inFr2 @ F @ D @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(190,axiom,
    ! [A: set @ n,B: dtree,C: t] :
      ( ( gram_L1333338417e_inFr @ A @ B @ C )
     => ( member @ n @ ( root @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_inFr__root__in) ).

thf(879,plain,
    ! [A: set @ n,B: dtree,C: t] :
      ( ( gram_L1333338417e_inFr @ A @ B @ C )
     => ( member @ n @ ( root @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(181,axiom,
    ! [A: set @ n,B: dtree,C: t,D: set @ n] :
      ( ( gram_L805317441_inFr2 @ A @ B @ C )
     => ( ( ord_less_eq @ ( set @ n ) @ A @ D )
       => ( gram_L805317441_inFr2 @ D @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_inFr2__mono) ).

thf(852,plain,
    ! [A: set @ n,B: dtree,C: t,D: set @ n] :
      ( ( gram_L805317441_inFr2 @ A @ B @ C )
     => ( ( ord_less_eq @ ( set @ n ) @ A @ D )
       => ( gram_L805317441_inFr2 @ D @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(139,axiom,
    ( ( gram_L1918716148le_reg @ f @ tr1a )
   => ? [A: list @ n] :
        ( ( gram_L250615845e_path @ f @ A )
        & ( ( f @ ( hd @ n @ A ) )
          = tr1a )
        & ( ( f @ ( last @ n @ A ) )
          = tr2 )
        & ( ord_less_eq @ ( set @ n ) @ ( set2 @ n @ A ) @ nsa ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_Step_Ohyps_I3_J) ).

thf(665,plain,
    ( ( gram_L1918716148le_reg @ f @ tr1a )
   => ? [A: list @ n] :
        ( ( gram_L250615845e_path @ f @ A )
        & ( ( f @ ( hd @ n @ A ) )
          = tr1a )
        & ( ( f @ ( last @ n @ A ) )
          = tr2 )
        & ( ord_less_eq @ ( set @ n ) @ ( set2 @ n @ A ) @ nsa ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(110,axiom,
    gram_L250615845e_path @ f @ nl,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_nl) ).

thf(583,plain,
    gram_L250615845e_path @ f @ nl,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(194,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_148_inItr_OBase) ).

thf(889,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)],[194]) ).

thf(102,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
       => ( member @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_set__rev__mp) ).

thf(551,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
       => ( member @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(23,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(285,plain,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( if @ TA @ $true @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(5,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_229_old_Osum_Osimps_I7_J) ).

thf(229,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)],[5]) ).

thf(80,axiom,
    ! [TA: $tType,A: list @ TA,B: TA] :
      ( ( ( A
          = ( nil @ TA ) )
       => ( ( last @ TA @ ( cons @ TA @ B @ A ) )
          = B ) )
      & ( ( A
         != ( nil @ TA ) )
       => ( ( last @ TA @ ( cons @ TA @ B @ A ) )
          = ( last @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_last_Osimps) ).

thf(484,plain,
    ! [TA: $tType,A: list @ TA,B: TA] :
      ( ( ( A
          = ( nil @ TA ) )
       => ( ( last @ TA @ ( cons @ TA @ B @ A ) )
          = B ) )
      & ( ( A
         != ( nil @ TA ) )
       => ( ( last @ TA @ ( cons @ TA @ B @ A ) )
          = ( last @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(91,axiom,
    ! [A: n > dtree,B: list @ n] :
      ( ! [C: n] :
          ( ( root @ ( A @ C ) )
          = C )
     => ( ( gram_L250615845e_path @ A @ B )
       => ( gram_L716654942_subtr @ ( set2 @ n @ B ) @ ( A @ ( last @ n @ B ) ) @ ( A @ ( hd @ n @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_path__subtr) ).

thf(519,plain,
    ! [A: n > dtree,B: list @ n] :
      ( ! [C: n] :
          ( ( root @ ( A @ C ) )
          = C )
     => ( ( gram_L250615845e_path @ A @ B )
       => ( gram_L716654942_subtr @ ( set2 @ n @ B ) @ ( A @ ( last @ n @ B ) ) @ ( A @ ( hd @ n @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(36,axiom,
    ( gram_L646766332egular
    = ( ^ [A: dtree] :
        ? [B: n > dtree] : ( gram_L1918716148le_reg @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_regular__def) ).

thf(317,plain,
    ( gram_L646766332egular
    = ( ^ [A: dtree] :
        ? [B: n > dtree] : ( gram_L1918716148le_reg @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(59,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( bNF_Greatest_shift @ TA @ TB )
      = ( ^ [A: ( list @ TA ) > TB,B: TA,C: list @ TA] : ( A @ ( cons @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_shift__def) ).

thf(388,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( bNF_Greatest_shift @ TA @ TB )
      = ( ^ [A: ( list @ TA ) > TB,B: TA,C: list @ TA] : ( A @ ( cons @ TA @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(49,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ A
          @ ( collect @ TA
            @ ^ [D: TA] :
                ( ( member @ TA @ D @ B )
                & ( C @ D ) ) ) )
        = ( ! [D: TA] :
              ( ( member @ TA @ D @ A )
             => ( C @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_subset__Collect__iff) ).

thf(356,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ A
          @ ( collect @ TA
            @ ^ [D: TA] :
                ( ( member @ TA @ D @ B )
                & ( C @ D ) ) ) )
        = ( ! [D: TA] :
              ( ( member @ TA @ D @ A )
             => ( C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(40,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_62_wf__subtr) ).

thf(328,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)],[40]) ).

thf(192,axiom,
    ( gram_L1614515765ubtrOf
    = ( ^ [A: dtree,B: n] :
        @+[C: dtree] :
          ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ C ) @ ( cont @ A ) )
          & ( ( root @ C )
            = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_subtrOf__def) ).

thf(884,plain,
    ( gram_L1614515765ubtrOf
    = ( ^ [A: dtree,B: n] :
        @+[C: dtree] :
          ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ C ) @ ( cont @ A ) )
          & ( ( root @ C )
            = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(3,axiom,
    ! [A: $o] :
      ( ( A = $true )
      | ( A = $false ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).

thf(225,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(131,axiom,
    ! [TA: $tType,A: TA,B: TA,C: list @ TA] :
      ( ( distinct @ TA @ ( cons @ TA @ A @ ( cons @ TA @ B @ C ) ) )
      = ( ( A != B )
        & ( distinct @ TA @ ( cons @ TA @ A @ C ) )
        & ( distinct @ TA @ ( cons @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_distinct__length__2__or__more) ).

thf(642,plain,
    ! [TA: $tType,A: TA,B: TA,C: list @ TA] :
      ( ( distinct @ TA @ ( cons @ TA @ A @ ( cons @ TA @ B @ C ) ) )
      = ( ( A != B )
        & ( distinct @ TA @ ( cons @ TA @ A @ C ) )
        & ( distinct @ TA @ ( cons @ TA @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(93,axiom,
    ! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
      ( ( ( cons @ TA @ A @ B )
        = ( cons @ TA @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_list_Oinject) ).

thf(526,plain,
    ! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
      ( ( ( cons @ TA @ A @ B )
        = ( cons @ TA @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(148,axiom,
    ! [TA: $tType,A: TA,B: list @ TA,C: TA] :
      ( ( member @ TA @ A @ ( set2 @ TA @ B ) )
     => ( member @ TA @ A @ ( set2 @ TA @ ( cons @ TA @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_list_Oset__intros_I2_J) ).

thf(706,plain,
    ! [TA: $tType,A: TA,B: list @ TA,C: TA] :
      ( ( member @ TA @ A @ ( set2 @ TA @ B ) )
     => ( member @ TA @ A @ ( set2 @ TA @ ( cons @ TA @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(74,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_243_split__sum__all) ).

thf(457,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)],[74]) ).

thf(86,axiom,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( distinct @ TA @ ( cons @ TA @ A @ B ) )
      = ( ~ ( member @ TA @ A @ ( set2 @ TA @ B ) )
        & ( distinct @ TA @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_distinct_Osimps_I2_J) ).

thf(503,plain,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( distinct @ TA @ ( cons @ TA @ A @ B ) )
      = ( ~ ( member @ TA @ A @ ( set2 @ TA @ B ) )
        & ( distinct @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(124,axiom,
    ! [TA: $tType,A: list @ ( list @ TA )] :
      ( ! [B: list @ TA] :
          ( ( member @ ( list @ TA ) @ B @ ( set2 @ ( list @ TA ) @ A ) )
         => ( distinct @ TA @ B ) )
     => ( distinct @ ( list @ TA ) @ ( product_lists @ TA @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_distinct__product__lists) ).

thf(622,plain,
    ! [TA: $tType,A: list @ ( list @ TA )] :
      ( ! [B: list @ TA] :
          ( ( member @ ( list @ TA ) @ B @ ( set2 @ ( list @ TA ) @ A ) )
         => ( distinct @ TA @ B ) )
     => ( distinct @ ( list @ TA ) @ ( product_lists @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(176,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_68_subtr__rootL__in) ).

thf(837,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)],[176]) ).

thf(10,axiom,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( set2 @ TA @ ( insert @ TA @ A @ B ) )
      = ( insert2 @ TA @ A @ ( set2 @ TA @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_List_Oset__insert) ).

thf(244,plain,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( set2 @ TA @ ( insert @ TA @ A @ B ) )
      = ( insert2 @ TA @ A @ ( set2 @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(167,axiom,
    ! [TA: $tType,A: TA,B: TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( remove @ TA @ B @ C ) )
      = ( ( member @ TA @ A @ C )
        & ( A != B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_member__remove) ).

thf(792,plain,
    ! [TA: $tType,A: TA,B: TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( remove @ TA @ B @ C ) )
      = ( ( member @ TA @ A @ C )
        & ( A != B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(209,axiom,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( member @ TA @ A @ ( set2 @ TA @ B ) )
     => ( ( insert @ TA @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_in__set__insert) ).

thf(938,plain,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( member @ TA @ A @ ( set2 @ TA @ B ) )
     => ( ( insert @ TA @ A @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(129,axiom,
    ! [A: set @ n,B: dtree,C: dtree] :
      ( ( gram_L1283001940subtr2 @ A @ B @ C )
     => ( member @ n @ ( root @ C ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_subtr2__rootR__in) ).

thf(633,plain,
    ! [A: set @ n,B: dtree,C: dtree] :
      ( ( gram_L1283001940subtr2 @ A @ B @ C )
     => ( member @ n @ ( root @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(34,axiom,
    ! [TA: $tType,A: TA,B: TA,C: set @ TA] :
      ( ( insert2 @ TA @ A @ ( insert2 @ TA @ B @ C ) )
      = ( insert2 @ TA @ B @ ( insert2 @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_insert__commute) ).

thf(311,plain,
    ! [TA: $tType,A: TA,B: TA,C: set @ TA] :
      ( ( insert2 @ TA @ A @ ( insert2 @ TA @ B @ C ) )
      = ( insert2 @ TA @ B @ ( insert2 @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(203,axiom,
    ! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
      ( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
     => ( ! [D: TA,E: list @ TA] : ( A @ ( cons @ TA @ D @ E ) @ ( nil @ TA ) )
       => ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
              ( ( A @ E @ G )
             => ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
         => ( A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_splice_Oinduct) ).

thf(921,plain,
    ! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
      ( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
     => ( ! [D: TA,E: list @ TA] : ( A @ ( cons @ TA @ D @ E ) @ ( nil @ TA ) )
       => ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
              ( ( A @ E @ G )
             => ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
         => ( A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(138,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( ! [B: TA] :
            ( A
           != ( cons @ TA @ B @ ( nil @ TA ) ) )
       => ~ ! [B: TA,C: TA,D: list @ TA] :
              ( A
             != ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_remdups__adj_Ocases) ).

thf(662,plain,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( ! [B: TA] :
            ( A
           != ( cons @ TA @ B @ ( nil @ TA ) ) )
       => ~ ! [B: TA,C: TA,D: list @ TA] :
              ( A
             != ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(21,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ! [C: TA] :
          ( ( A @ C )
         => ( B @ C ) )
     => ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_Collect__mono) ).

thf(279,plain,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ! [C: TA] :
          ( ( A @ C )
         => ( B @ C ) )
     => ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(107,axiom,
    ! [A: set @ n,B: dtree,C: t] :
      ( ( gram_L1333338417e_inFr @ A @ B @ C )
     => ? [D: dtree] :
          ( ( gram_L716654942_subtr @ A @ D @ B )
          & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ C ) @ ( cont @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_inFr__subtr) ).

thf(573,plain,
    ! [A: set @ n,B: dtree,C: t] :
      ( ( gram_L1333338417e_inFr @ A @ B @ C )
     => ? [D: dtree] :
          ( ( gram_L716654942_subtr @ A @ D @ B )
          & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ C ) @ ( cont @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(27,axiom,
    gram_L716654942_subtr @ nsa @ tr2 @ tr1a,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_tr2__tr1) ).

thf(296,plain,
    gram_L716654942_subtr @ nsa @ tr2 @ tr1a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(117,axiom,
    ! [TA: $tType] :
      ( ( ord_less_eq @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
          ! [C: TA] :
            ( ( member @ TA @ C @ A )
           => ( member @ TA @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_subset__eq) ).

thf(601,plain,
    ! [TA: $tType] :
      ( ( ord_less_eq @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
          ! [C: TA] :
            ( ( member @ TA @ C @ A )
           => ( member @ TA @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(111,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_17_sum_Oinject_I2_J) ).

thf(584,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)],[111]) ).

thf(200,axiom,
    ! [A: set @ n,B: dtree,C: t,D: dtree] :
      ( ( gram_L1333338417e_inFr @ A @ B @ C )
     => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ B ) @ ( cont @ D ) )
       => ( gram_L1333338417e_inFr @ ( insert2 @ n @ ( root @ D ) @ A ) @ D @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_inFr__Ind__minus) ).

thf(904,plain,
    ! [A: set @ n,B: dtree,C: t,D: dtree] :
      ( ( gram_L1333338417e_inFr @ A @ B @ C )
     => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ B ) @ ( cont @ D ) )
       => ( gram_L1333338417e_inFr @ ( insert2 @ n @ ( root @ D ) @ A ) @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(178,axiom,
    ! [TA: $tType,A: list @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ ( set2 @ TA @ A ) @ ( set2 @ TA @ ( cons @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_set__subset__Cons) ).

thf(843,plain,
    ! [TA: $tType,A: list @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ ( set2 @ TA @ A ) @ ( set2 @ TA @ ( cons @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(150,axiom,
    ! [TA: $tType,A: list @ TA,B: TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( ( last @ TA @ ( cons @ TA @ B @ A ) )
        = ( last @ TA @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_last__ConsR) ).

thf(711,plain,
    ! [TA: $tType,A: list @ TA,B: TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( ( last @ TA @ ( cons @ TA @ B @ A ) )
        = ( last @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(25,axiom,
    ! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_subset__refl) ).

thf(291,plain,
    ! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(100,axiom,
    ! [A: n > dtree,B: dtree,C: dtree] :
      ( ( gram_L1918716148le_reg @ A @ B )
     => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ C ) @ ( cont @ B ) )
       => ( gram_L1918716148le_reg @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_reg__Inr__cont) ).

thf(545,plain,
    ! [A: n > dtree,B: dtree,C: dtree] :
      ( ( gram_L1918716148le_reg @ A @ B )
     => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ C ) @ ( cont @ B ) )
       => ( gram_L1918716148le_reg @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(66,axiom,
    ! [TA: $tType] :
      ( ( product_lists @ TA @ ( nil @ ( list @ TA ) ) )
      = ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_product__lists_Osimps_I1_J) ).

thf(413,plain,
    ! [TA: $tType] :
      ( ( product_lists @ TA @ ( nil @ ( list @ TA ) ) )
      = ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(60,axiom,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ? [C: set @ TA] :
          ( ( B
            = ( insert2 @ TA @ A @ C ) )
          & ~ ( member @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_mk__disjoint__insert) ).

thf(391,plain,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ? [C: set @ TA] :
          ( ( B
            = ( insert2 @ TA @ A @ C ) )
          & ~ ( member @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(57,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ~ ! [B: TA,C: list @ TA] :
            ( A
           != ( cons @ TA @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_list_Oexhaust) ).

thf(382,plain,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ~ ! [B: TA,C: list @ TA] :
            ( A
           != ( cons @ TA @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(213,axiom,
    ! [TA: $tType,A: TA,B: TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( insert2 @ TA @ B @ C ) )
      = ( ( A = B )
        | ( member @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_insert__iff) ).

thf(947,plain,
    ! [TA: $tType,A: TA,B: TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( insert2 @ TA @ B @ C ) )
      = ( ( A = B )
        | ( member @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(140,axiom,
    ! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
      ( ( A @ ( nil @ TA ) )
     => ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
       => ( ! [C: TA,D: TA,E: list @ TA] :
              ( ( ( C = D )
               => ( A @ ( cons @ TA @ C @ E ) ) )
             => ( ( ( C != D )
                 => ( A @ ( cons @ TA @ D @ E ) ) )
               => ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
         => ( A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_remdups__adj_Oinduct) ).

thf(672,plain,
    ! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
      ( ( A @ ( nil @ TA ) )
     => ( ! [C: TA] : ( A @ ( cons @ TA @ C @ ( nil @ TA ) ) )
       => ( ! [C: TA,D: TA,E: list @ TA] :
              ( ( ( C = D )
               => ( A @ ( cons @ TA @ C @ E ) ) )
             => ( ( ( C != D )
                 => ( A @ ( cons @ TA @ D @ E ) ) )
               => ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
         => ( A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(1,conjecture,
    ( ? [A: n] :
        ( ( cons @ n @ ( root @ tra ) @ nl )
        = ( cons @ n @ A @ ( nil @ n ) ) )
    | ? [A: n,B: list @ n,C: n] :
        ( ( ( cons @ n @ ( root @ tra ) @ nl )
          = ( cons @ n @ C @ ( cons @ n @ A @ B ) ) )
        & ( gram_L250615845e_path @ f @ ( cons @ n @ A @ B ) )
        & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( f @ A ) ) @ ( cont @ ( f @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ( ? [A: n] :
          ( ( cons @ n @ ( root @ tra ) @ nl )
          = ( cons @ n @ A @ ( nil @ n ) ) )
      | ? [A: n,B: list @ n,C: n] :
          ( ( ( cons @ n @ ( root @ tra ) @ nl )
            = ( cons @ n @ C @ ( cons @ n @ A @ B ) ) )
          & ( gram_L250615845e_path @ f @ ( cons @ n @ A @ B ) )
          & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( f @ A ) ) @ ( cont @ ( f @ C ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(219,plain,
    ~ ( ? [A: n] :
          ( ( cons @ n @ ( root @ tra ) @ nl )
          = ( cons @ n @ A @ ( nil @ n ) ) )
      | ? [A: n,B: list @ n,C: n] :
          ( ( ( cons @ n @ ( root @ tra ) @ nl )
            = ( cons @ n @ C @ ( cons @ n @ A @ B ) ) )
          & ( gram_L250615845e_path @ f @ ( cons @ n @ A @ B ) )
          & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( f @ A ) ) @ ( cont @ ( f @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(155,axiom,
    ! [A: n,B: set @ ( sum_sum @ t @ dtree )] :
      ( ( root @ ( node @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_root__Node) ).

thf(736,plain,
    ! [A: n,B: set @ ( sum_sum @ t @ dtree )] :
      ( ( root @ ( node @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(122,axiom,
    ! [A: set @ n,B: dtree,C: n,D: set @ n] :
      ( ( gram_L830233218_inItr @ A @ B @ C )
     => ( ( ord_less_eq @ ( set @ n ) @ A @ D )
       => ( gram_L830233218_inItr @ D @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_inItr__mono) ).

thf(616,plain,
    ! [A: set @ n,B: dtree,C: n,D: set @ n] :
      ( ( gram_L830233218_inItr @ A @ B @ C )
     => ( ( ord_less_eq @ ( set @ n ) @ A @ D )
       => ( gram_L830233218_inItr @ D @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(184,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_230_obj__sumE) ).

thf(863,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)],[184]) ).

thf(160,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_53_inFr2__Ind) ).

thf(764,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)],[160]) ).

thf(118,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_80_subtr_Osimps) ).

thf(604,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)],[118]) ).

thf(88,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_L1283001940subtr2 @ B @ C @ D )
         => ( gram_L1283001940subtr2 @ B @ A @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_subtr2_OStep) ).

thf(509,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_L1283001940subtr2 @ B @ C @ D )
         => ( gram_L1283001940subtr2 @ B @ A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(134,axiom,
    ! [TA: $tType,A: TA,B: TA > $o] :
      ( ( member @ TA @ A @ ( collect @ TA @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_mem__Collect__eq) ).

thf(649,plain,
    ! [TA: $tType,A: TA,B: TA > $o] :
      ( ( member @ TA @ A @ ( collect @ TA @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(70,axiom,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( member @ TA @ A @ ( set2 @ TA @ B ) )
     => ( ! [C: list @ TA] :
            ( B
           != ( cons @ TA @ A @ C ) )
       => ~ ! [C: TA,D: list @ TA] :
              ( ( B
                = ( cons @ TA @ C @ D ) )
             => ~ ( member @ TA @ A @ ( set2 @ TA @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_list_Oset__cases) ).

thf(434,plain,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( member @ TA @ A @ ( set2 @ TA @ B ) )
     => ( ! [C: list @ TA] :
            ( B
           != ( cons @ TA @ A @ C ) )
       => ~ ! [C: TA,D: list @ TA] :
              ( ( B
                = ( cons @ TA @ C @ D ) )
             => ~ ( member @ TA @ A @ ( set2 @ TA @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(128,axiom,
    ! [TA: $tType,A: TA] : ( distinct @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_distinct__singleton) ).

thf(631,plain,
    ! [TA: $tType,A: TA] : ( distinct @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(51,axiom,
    ! [TA: $tType,A: TA,B: TA,C: list @ TA] :
      ( ( member @ TA @ A @ ( set2 @ TA @ ( cons @ TA @ B @ C ) ) )
     => ( ( A = B )
        | ( member @ TA @ A @ ( set2 @ TA @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_set__ConsD) ).

thf(367,plain,
    ! [TA: $tType,A: TA,B: TA,C: list @ TA] :
      ( ( member @ TA @ A @ ( set2 @ TA @ ( cons @ TA @ B @ C ) ) )
     => ( ( A = B )
        | ( member @ TA @ A @ ( set2 @ TA @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(120,axiom,
    ! [TA: $tType,A: TA] :
      ( ( the_elem @ TA @ ( set2 @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_the__elem__set) ).

thf(609,plain,
    ! [TA: $tType,A: TA] :
      ( ( the_elem @ TA @ ( set2 @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(146,axiom,
    ! [TA: $tType,A: TA,B: TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( insert2 @ TA @ B @ C ) )
     => ( ( A != B )
       => ( member @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_insertE) ).

thf(700,plain,
    ! [TA: $tType,A: TA,B: TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( insert2 @ TA @ B @ C ) )
     => ( ( A != B )
       => ( member @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(196,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( member @ TA @ C @ A )
       => ( member @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_subsetD) ).

thf(895,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( member @ TA @ C @ A )
       => ( member @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(76,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: TA] :
      ( ( member @ TA @ A @ B )
     => ( member @ TA @ A @ ( insert2 @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_insertI2) ).

thf(462,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: TA] :
      ( ( member @ TA @ A @ B )
     => ( member @ TA @ A @ ( insert2 @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(217,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_241_old_Osum_Oinducts) ).

thf(959,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)],[217]) ).

thf(29,axiom,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( remove @ TA @ A @ ( coset @ TA @ B ) )
      = ( coset @ TA @ ( insert @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_remove__code_I2_J) ).

thf(299,plain,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( remove @ TA @ A @ ( coset @ TA @ B ) )
      = ( coset @ TA @ ( insert @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(4,axiom,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( distinct @ TA @ ( insert @ TA @ A @ B ) )
      = ( distinct @ TA @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_distinct__insert) ).

thf(226,plain,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( distinct @ TA @ ( insert @ TA @ A @ B ) )
      = ( distinct @ TA @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(69,axiom,
    ! [TA: $tType] :
      ( ( sublists @ TA @ ( nil @ TA ) )
      = ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_sublists_Osimps_I1_J) ).

thf(431,plain,
    ! [TA: $tType] :
      ( ( sublists @ TA @ ( nil @ TA ) )
      = ( cons @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ ( list @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(9,axiom,
    ! [A: dtree,B: set @ n,C: dtree] :
      ( ( gram_L646766332egular @ A )
     => ( ( gram_L716654942_subtr @ B @ C @ A )
       => ( gram_L646766332egular @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_regular__subtr) ).

thf(241,plain,
    ! [A: dtree,B: set @ n,C: dtree] :
      ( ( gram_L646766332egular @ A )
     => ( ( gram_L716654942_subtr @ B @ C @ A )
       => ( gram_L646766332egular @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(137,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_52_wf__inj) ).

thf(658,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)],[137]) ).

thf(154,axiom,
    ! [A: set @ n,B: dtree,C: t,D: ( set @ n ) > dtree > t > $o] :
      ( ( gram_L805317441_inFr2 @ A @ B @ C )
     => ( ! [E: dtree,F: set @ n,G: t] :
            ( ( member @ n @ ( root @ E ) @ F )
           => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ G ) @ ( cont @ E ) )
             => ( D @ F @ E @ G ) ) )
       => ( ! [E: dtree,F: dtree,G: set @ n,H: t] :
              ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ E ) @ ( cont @ F ) )
             => ( ( gram_L805317441_inFr2 @ G @ E @ H )
               => ( ( D @ G @ E @ H )
                 => ( D @ ( insert2 @ n @ ( root @ F ) @ G ) @ F @ H ) ) ) )
         => ( D @ A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_inFr2_Oinducts) ).

thf(722,plain,
    ! [A: set @ n,B: dtree,C: t,D: ( set @ n ) > dtree > t > $o] :
      ( ( gram_L805317441_inFr2 @ A @ B @ C )
     => ( ! [E: dtree,F: set @ n,G: t] :
            ( ( member @ n @ ( root @ E ) @ F )
           => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ G ) @ ( cont @ E ) )
             => ( D @ F @ E @ G ) ) )
       => ( ! [E: dtree,F: dtree,G: set @ n,H: t] :
              ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ E ) @ ( cont @ F ) )
             => ( ( gram_L805317441_inFr2 @ G @ E @ H )
               => ( ( D @ G @ E @ H )
                 => ( D @ ( insert2 @ n @ ( root @ F ) @ G ) @ F @ H ) ) ) )
         => ( D @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(81,axiom,
    ( ( f @ ( last @ n @ nl ) )
    = tr2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_last__nl) ).

thf(490,plain,
    ( ( f @ ( last @ n @ nl ) )
    = tr2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(113,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ord_less_eq @ ( TA > $o )
        @ ^ [C: TA] : ( member @ TA @ C @ A )
        @ ^ [C: TA] : ( member @ TA @ C @ B ) )
      = ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_pred__subset__eq) ).

thf(589,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ord_less_eq @ ( TA > $o )
        @ ^ [C: TA] : ( member @ TA @ C @ A )
        @ ^ [C: TA] : ( member @ TA @ C @ B ) )
      = ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(168,axiom,
    ! [A: set @ n,B: dtree,C: t,D: ( set @ n ) > dtree > t > $o] :
      ( ( gram_L1333338417e_inFr @ A @ B @ C )
     => ( ! [E: dtree,F: set @ n,G: t] :
            ( ( member @ n @ ( root @ E ) @ F )
           => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ G ) @ ( cont @ E ) )
             => ( D @ F @ E @ G ) ) )
       => ( ! [E: dtree,F: set @ n,G: dtree,H: t] :
              ( ( member @ n @ ( root @ E ) @ F )
             => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ G ) @ ( cont @ E ) )
               => ( ( gram_L1333338417e_inFr @ F @ G @ H )
                 => ( ( D @ F @ G @ H )
                   => ( D @ F @ E @ H ) ) ) ) )
         => ( D @ A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_inFr_Oinducts) ).

thf(795,plain,
    ! [A: set @ n,B: dtree,C: t,D: ( set @ n ) > dtree > t > $o] :
      ( ( gram_L1333338417e_inFr @ A @ B @ C )
     => ( ! [E: dtree,F: set @ n,G: t] :
            ( ( member @ n @ ( root @ E ) @ F )
           => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ G ) @ ( cont @ E ) )
             => ( D @ F @ E @ G ) ) )
       => ( ! [E: dtree,F: set @ n,G: dtree,H: t] :
              ( ( member @ n @ ( root @ E ) @ F )
             => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ G ) @ ( cont @ E ) )
               => ( ( gram_L1333338417e_inFr @ F @ G @ H )
                 => ( ( D @ F @ G @ H )
                   => ( D @ F @ E @ H ) ) ) ) )
         => ( D @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(101,axiom,
    ! [A: dtree,B: dtree] :
      ( ( ( root @ A )
        = ( root @ B ) )
     => ( ( ( cont @ A )
          = ( cont @ B ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_dtree__cong) ).

thf(548,plain,
    ! [A: dtree,B: dtree] :
      ( ( ( root @ A )
        = ( root @ B ) )
     => ( ( ( cont @ A )
          = ( cont @ B ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(205,axiom,
    ( gram_L646766332egular
    = ( ^ [A: dtree] :
        ? [B: n > dtree] :
          ( ( gram_L1918716148le_reg @ B @ A )
          & ! [C: n] :
              ( ( root @ ( B @ C ) )
              = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_regular__def2) ).

thf(927,plain,
    ( gram_L646766332egular
    = ( ^ [A: dtree] :
        ? [B: n > dtree] :
          ( ( gram_L1918716148le_reg @ B @ A )
          & ! [C: n] :
              ( ( root @ ( B @ C ) )
              = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(133,axiom,
    gram_L1918716148le_reg @ f @ tra,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_Step_Oprems) ).

thf(648,plain,
    gram_L1918716148le_reg @ f @ tra,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(169,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( member @ TA @ C @ A )
       => ( member @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_subsetCE) ).

thf(812,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( member @ TA @ C @ A )
       => ( member @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(90,axiom,
    ! [A: dtree,B: set @ n,C: dtree,D: t] :
      ( ( member @ n @ ( root @ A ) @ B )
     => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ C ) @ ( cont @ A ) )
       => ( ( gram_L1333338417e_inFr @ B @ C @ D )
         => ( gram_L1333338417e_inFr @ B @ A @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_inFr_OInd) ).

thf(516,plain,
    ! [A: dtree,B: set @ n,C: dtree,D: t] :
      ( ( member @ n @ ( root @ A ) @ B )
     => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ C ) @ ( cont @ A ) )
       => ( ( gram_L1333338417e_inFr @ B @ C @ D )
         => ( gram_L1333338417e_inFr @ B @ A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(45,axiom,
    ! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
      ( ( A @ B )
     => ( ( ord_less_eq @ ( TA > $o ) @ A @ C )
       => ( C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_rev__predicate1D) ).

thf(342,plain,
    ! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
      ( ( A @ B )
     => ( ( ord_less_eq @ ( TA > $o ) @ A @ C )
       => ( C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(103,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_82_subtr_Oinducts) ).

thf(553,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)],[103]) ).

thf(173,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_69_subtr__rootR__in) ).

thf(823,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)],[173]) ).

thf(95,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_71_inFr2__root__in) ).

thf(531,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)],[95]) ).

thf(211,axiom,
    ord_less_eq @ ( set @ n ) @ ( set2 @ n @ nl ) @ nsa,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_set) ).

thf(944,plain,
    ord_less_eq @ ( set @ n ) @ ( set2 @ n @ nl ) @ nsa,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(142,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ~ ( member @ TA @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ ( insert2 @ TA @ A @ C ) )
        = ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_subset__insert) ).

thf(690,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ~ ( member @ TA @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ ( insert2 @ TA @ A @ C ) )
        = ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(22,axiom,
    ! [A: set @ n,B: dtree,C: dtree,D: dtree] :
      ( ( gram_L1283001940subtr2 @ A @ B @ C )
     => ( ( gram_L1283001940subtr2 @ A @ C @ D )
       => ( gram_L1283001940subtr2 @ A @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_subtr2__trans) ).

thf(282,plain,
    ! [A: set @ n,B: dtree,C: dtree,D: dtree] :
      ( ( gram_L1283001940subtr2 @ A @ B @ C )
     => ( ( gram_L1283001940subtr2 @ A @ C @ D )
       => ( gram_L1283001940subtr2 @ A @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(156,axiom,
    ( gram_L1918716148le_reg
    = ( ^ [A: n > dtree,B: dtree] :
        ! [C: set @ n,D: dtree] :
          ( ( gram_L716654942_subtr @ C @ D @ B )
         => ( D
            = ( A @ ( root @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_reg__def2) ).

thf(739,plain,
    ( gram_L1918716148le_reg
    = ( ^ [A: n > dtree,B: dtree] :
        ! [C: set @ n,D: dtree] :
          ( ( gram_L716654942_subtr @ C @ D @ B )
         => ( D
            = ( A @ ( root @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(16,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
      ( ( ord_less_eq @ ( TA > $o ) @ A @ B )
     => ( ( A @ C )
       => ( B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_predicate1D) ).

thf(263,plain,
    ! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
      ( ( ord_less_eq @ ( TA > $o ) @ A @ B )
     => ( ( A @ C )
       => ( B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(109,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_18_old_Osum_Oinject_I2_J) ).

thf(580,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)],[109]) ).

thf(182,axiom,
    ! [A: n > dtree,B: list @ n,C: ( list @ n ) > $o] :
      ( ( gram_L250615845e_path @ A @ B )
     => ( ! [D: n] : ( C @ ( cons @ n @ D @ ( nil @ n ) ) )
       => ( ! [D: n,E: list @ n,F: n] :
              ( ( gram_L250615845e_path @ A @ ( cons @ n @ D @ E ) )
             => ( ( C @ ( cons @ n @ D @ E ) )
               => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( A @ D ) ) @ ( cont @ ( A @ F ) ) )
                 => ( C @ ( cons @ n @ F @ ( cons @ n @ D @ E ) ) ) ) ) )
         => ( C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_path_Oinducts) ).

thf(855,plain,
    ! [A: n > dtree,B: list @ n,C: ( list @ n ) > $o] :
      ( ( gram_L250615845e_path @ A @ B )
     => ( ! [D: n] : ( C @ ( cons @ n @ D @ ( nil @ n ) ) )
       => ( ! [D: n,E: list @ n,F: n] :
              ( ( gram_L250615845e_path @ A @ ( cons @ n @ D @ E ) )
             => ( ( C @ ( cons @ n @ D @ E ) )
               => ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( A @ D ) ) @ ( cont @ ( A @ F ) ) )
                 => ( C @ ( cons @ n @ F @ ( cons @ n @ D @ E ) ) ) ) ) )
         => ( C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(41,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_150_subtr__inItr) ).

thf(331,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)],[41]) ).

thf(52,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
      ( ~ ( member @ TA @ A @ B )
     => ( ~ ( member @ TA @ C @ D )
       => ( ( ( insert2 @ TA @ A @ B )
            = ( insert2 @ TA @ C @ D ) )
          = ( ( ( A = C )
             => ( B = D ) )
            & ( ( A != C )
             => ? [E: set @ TA] :
                  ( ( B
                    = ( insert2 @ TA @ C @ E ) )
                  & ~ ( member @ TA @ C @ E )
                  & ( D
                    = ( insert2 @ TA @ A @ E ) )
                  & ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_insert__eq__iff) ).

thf(370,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
      ( ~ ( member @ TA @ A @ B )
     => ( ~ ( member @ TA @ C @ D )
       => ( ( ( insert2 @ TA @ A @ B )
            = ( insert2 @ TA @ C @ D ) )
          = ( ( ( A = C )
             => ( B = D ) )
            & ( ( A != C )
             => ? [E: set @ TA] :
                  ( ( B
                    = ( insert2 @ TA @ C @ E ) )
                  & ~ ( member @ TA @ C @ E )
                  & ( D
                    = ( insert2 @ TA @ A @ E ) )
                  & ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(177,axiom,
    ! [TA: $tType,A: list @ ( list @ TA )] :
      ( ( A
       != ( nil @ ( list @ TA ) ) )
     => ( ! [B: list @ ( list @ TA )] :
            ( A
           != ( cons @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
       => ~ ! [B: TA,C: list @ TA,D: list @ ( list @ TA )] :
              ( A
             != ( cons @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_transpose_Ocases) ).

thf(840,plain,
    ! [TA: $tType,A: list @ ( list @ TA )] :
      ( ( A
       != ( nil @ ( list @ TA ) ) )
     => ( ! [B: list @ ( list @ TA )] :
            ( A
           != ( cons @ ( list @ TA ) @ ( nil @ TA ) @ B ) )
       => ~ ! [B: TA,C: list @ TA,D: list @ ( list @ TA )] :
              ( A
             != ( cons @ ( list @ TA ) @ ( cons @ TA @ B @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(44,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( A = B )
     => ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_equalityD2) ).

thf(338,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( A = B )
     => ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(108,axiom,
    ! [TA: $tType,A: list @ TA,B: TA] :
      ( ( A
        = ( nil @ TA ) )
     => ( ( last @ TA @ ( cons @ TA @ B @ A ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_last__ConsL) ).

thf(576,plain,
    ! [TA: $tType,A: list @ TA,B: TA] :
      ( ( A
        = ( nil @ TA ) )
     => ( ( last @ TA @ ( cons @ TA @ B @ A ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(50,axiom,
    ! [A: n > dtree,B: list @ n] :
      ( ( gram_L250615845e_path @ A @ B )
     => ( ! [C: n] :
            ( B
           != ( cons @ n @ C @ ( nil @ n ) ) )
       => ~ ! [C: n,D: list @ n,E: n] :
              ( ( B
                = ( cons @ n @ E @ ( cons @ n @ C @ D ) ) )
             => ( ( gram_L250615845e_path @ A @ ( cons @ n @ C @ D ) )
               => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( A @ C ) ) @ ( cont @ ( A @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_path_Ocases) ).

thf(359,plain,
    ! [A: n > dtree,B: list @ n] :
      ( ( gram_L250615845e_path @ A @ B )
     => ( ! [C: n] :
            ( B
           != ( cons @ n @ C @ ( nil @ n ) ) )
       => ~ ! [C: n,D: list @ n,E: n] :
              ( ( B
                = ( cons @ n @ E @ ( cons @ n @ C @ D ) ) )
             => ( ( gram_L250615845e_path @ A @ ( cons @ n @ C @ D ) )
               => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ ( A @ C ) ) @ ( cont @ ( A @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(201,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_154_inItr_Ocases) ).

thf(907,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)],[201]) ).

thf(43,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ord_less_eq @ ( set @ TA ) @ ( insert2 @ TA @ C @ A ) @ ( insert2 @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_insert__mono) ).

thf(336,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ord_less_eq @ ( set @ TA ) @ ( insert2 @ TA @ C @ A ) @ ( insert2 @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(147,axiom,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ( ( insert2 @ TA @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_insert__absorb) ).

thf(703,plain,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ( ( insert2 @ TA @ A @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(35,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(314,plain,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( if @ TA @ $false @ A @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(106,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_144_inItr_Osimps) ).

thf(571,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)],[106]) ).

thf(115,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_149_inItr__root__in) ).

thf(595,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)],[115]) ).

thf(121,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o,D: TA > $o] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ! [E: TA] :
            ( ( member @ TA @ E @ A )
           => ( ( C @ E )
             => ( D @ E ) ) )
       => ( ord_less_eq @ ( set @ TA )
          @ ( collect @ TA
            @ ^ [E: TA] :
                ( ( member @ TA @ E @ A )
                & ( C @ E ) ) )
          @ ( collect @ TA
            @ ^ [E: TA] :
                ( ( member @ TA @ E @ B )
                & ( D @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_subset__CollectI) ).

thf(612,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o,D: TA > $o] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ! [E: TA] :
            ( ( member @ TA @ E @ A )
           => ( ( C @ E )
             => ( D @ E ) ) )
       => ( ord_less_eq @ ( set @ TA )
          @ ( collect @ TA
            @ ^ [E: TA] :
                ( ( member @ TA @ E @ A )
                & ( C @ E ) ) )
          @ ( collect @ TA
            @ ^ [E: TA] :
                ( ( member @ TA @ E @ B )
                & ( D @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(84,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ ( insert2 @ TA @ A @ B ) @ C )
      = ( ( member @ TA @ A @ C )
        & ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_insert__subset) ).

thf(497,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ ( insert2 @ TA @ A @ B ) @ C )
      = ( ( member @ TA @ A @ C )
        & ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(189,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_249_sum_Odistinct_I1_J) ).

thf(876,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)],[189]) ).

thf(179,axiom,
    ! [A: n > dtree,B: list @ n] :
      ( ( gram_L250615845e_path @ A @ B )
     => ( B
       != ( nil @ n ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_path__NE) ).

thf(845,plain,
    ! [A: n > dtree,B: list @ n] :
      ( ( gram_L250615845e_path @ A @ B )
     => ( B
       != ( nil @ n ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(12,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( A = B )
     => ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_equalityD1) ).

thf(250,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( A = B )
     => ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(126,axiom,
    ! [TA: $tType] : ( distinct @ TA @ ( nil @ TA ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_distinct_Osimps_I1_J) ).

thf(627,plain,
    ! [TA: $tType] : ( distinct @ TA @ ( nil @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(98,axiom,
    ! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
      ( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
     => ( ! [D: TB,E: list @ TB] : ( A @ ( cons @ TB @ D @ E ) @ ( nil @ TA ) )
       => ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TB ) @ ( cons @ TA @ D @ E ) )
         => ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
                ( ( A @ E @ G )
               => ( A @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
           => ( A @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_list__induct2_H) ).

thf(539,plain,
    ! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: list @ TB,C: list @ TA] :
      ( ( A @ ( nil @ TB ) @ ( nil @ TA ) )
     => ( ! [D: TB,E: list @ TB] : ( A @ ( cons @ TB @ D @ E ) @ ( nil @ TA ) )
       => ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TB ) @ ( cons @ TA @ D @ E ) )
         => ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
                ( ( A @ E @ G )
               => ( A @ ( cons @ TB @ D @ E ) @ ( cons @ TA @ F @ G ) ) )
           => ( A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(83,axiom,
    ! [A: n > dtree,B: n] : ( gram_L250615845e_path @ A @ ( cons @ n @ B @ ( nil @ n ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_path_OBase) ).

thf(495,plain,
    ! [A: n > dtree,B: n] : ( gram_L250615845e_path @ A @ ( cons @ n @ B @ ( nil @ n ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(195,axiom,
    ! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
      ( ? [D: TA] :
          ( ( member @ TA @ D @ A )
          & ( B @ D ) )
     => ( ! [D: TA] :
            ( ( ( member @ TA @ D @ A )
              & ( B @ D ) )
           => ( C @ D ) )
       => ( C
          @ @+[D: TA] :
              ( ( member @ TA @ D @ A )
              & ( B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_someI2__bex) ).

thf(891,plain,
    ! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
      ( ? [D: TA] :
          ( ( member @ TA @ D @ A )
          & ( B @ D ) )
     => ( ! [D: TA] :
            ( ( ( member @ TA @ D @ A )
              & ( B @ D ) )
           => ( C @ D ) )
       => ( C
          @ @+[D: TA] :
              ( ( member @ TA @ D @ A )
              & ( B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(163,axiom,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ~ ( member @ TA @ A @ ( set2 @ TA @ B ) )
     => ( ( insert @ TA @ A @ B )
        = ( cons @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_not__in__set__insert) ).

thf(771,plain,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ~ ( member @ TA @ A @ ( set2 @ TA @ B ) )
     => ( ( insert @ TA @ A @ B )
        = ( cons @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(218,axiom,
    ! [TA: $tType] :
      ( ( ord_less_eq @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
          ! [C: TA] :
            ( ( member @ TA @ C @ A )
           => ( member @ TA @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_subset__iff) ).

thf(961,plain,
    ! [TA: $tType] :
      ( ( ord_less_eq @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
          ! [C: TA] :
            ( ( member @ TA @ C @ A )
           => ( member @ TA @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(37,axiom,
    ! [A: n > dtree,B: dtree,C: set @ n,D: dtree] :
      ( ( gram_L1918716148le_reg @ A @ B )
     => ( ( gram_L716654942_subtr @ C @ D @ B )
       => ( gram_L1918716148le_reg @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_reg__subtr) ).

thf(319,plain,
    ! [A: n > dtree,B: dtree,C: set @ n,D: dtree] :
      ( ( gram_L1918716148le_reg @ A @ B )
     => ( ( gram_L716654942_subtr @ C @ D @ B )
       => ( gram_L1918716148le_reg @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(165,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( collect @ TA
        @ ^ [B: TA] : ( member @ TA @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_Collect__mem__eq) ).

thf(786,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( collect @ TA
        @ ^ [B: TA] : ( member @ TA @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(135,axiom,
    ! [A: set @ n,B: dtree,C: dtree,D: set @ n] :
      ( ( gram_L1283001940subtr2 @ A @ B @ C )
     => ( ( ord_less_eq @ ( set @ n ) @ A @ D )
       => ( gram_L1283001940subtr2 @ D @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_subtr2__mono) ).

thf(652,plain,
    ! [A: set @ n,B: dtree,C: dtree,D: set @ n] :
      ( ( gram_L1283001940subtr2 @ A @ B @ C )
     => ( ( ord_less_eq @ ( set @ n ) @ A @ D )
       => ( gram_L1283001940subtr2 @ D @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(47,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_77_wf__cont) ).

thf(351,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)],[47]) ).

thf(105,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
      = ( ? [B: TA,C: list @ TA] :
            ( A
            = ( cons @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_neq__Nil__conv) ).

thf(568,plain,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
      = ( ? [B: TA,C: list @ TA] :
            ( A
            = ( cons @ TA @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(7,axiom,
    ! [A: set @ n,B: dtree,C: t,D: dtree] :
      ( ( gram_L1333338417e_inFr @ A @ B @ C )
     => ( ( gram_L716654942_subtr @ A @ B @ D )
       => ( gram_L1333338417e_inFr @ A @ D @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_subtr__inFr) ).

thf(235,plain,
    ! [A: set @ n,B: dtree,C: t,D: dtree] :
      ( ( gram_L1333338417e_inFr @ A @ B @ C )
     => ( ( gram_L716654942_subtr @ A @ B @ D )
       => ( gram_L1333338417e_inFr @ A @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(206,axiom,
    member @ n @ ( root @ tra ) @ nsa,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_rtr) ).

thf(929,plain,
    member @ n @ ( root @ tra ) @ nsa,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(18,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ! [C: TA] :
          ( ( A @ C )
         => ( B @ C ) )
     => ( ord_less_eq @ ( TA > $o ) @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_predicate1I) ).

thf(272,plain,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ! [C: TA] :
          ( ( A @ C )
         => ( B @ C ) )
     => ( ord_less_eq @ ( TA > $o ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(198,axiom,
    ! [TA: $tType] :
      ( ( ord_less_eq @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
            ( ord_less_eq @ ( TA > $o )
            @ ^ [C: TA] : ( member @ TA @ C @ A )
            @ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_less__eq__set__def) ).

thf(899,plain,
    ! [TA: $tType] :
      ( ( ord_less_eq @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
            ( ord_less_eq @ ( TA > $o )
            @ ^ [C: TA] : ( member @ TA @ C @ A )
            @ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(97,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_33_Inr__inject) ).

thf(536,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)],[97]) ).

thf(152,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( member @ TA @ ( hd @ TA @ A ) @ ( set2 @ TA @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_hd__in__set) ).

thf(716,plain,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( member @ TA @ ( hd @ TA @ A ) @ ( set2 @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(158,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_79_subtr_Ocases) ).

thf(752,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)],[158]) ).

thf(214,axiom,
    ( gram_L1333338417e_inFr
    = ( ^ [A: set @ n,B: dtree,C: t] :
          ( ? [D: dtree,E: set @ n,F: t] :
              ( ( A = E )
              & ( B = D )
              & ( C = F )
              & ( member @ n @ ( root @ D ) @ E )
              & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ F ) @ ( cont @ D ) ) )
          | ? [D: dtree,E: set @ n,F: dtree,G: t] :
              ( ( A = E )
              & ( B = D )
              & ( C = G )
              & ( member @ n @ ( root @ D ) @ E )
              & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ F ) @ ( cont @ D ) )
              & ( gram_L1333338417e_inFr @ E @ F @ G ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_inFr_Osimps) ).

thf(950,plain,
    ( gram_L1333338417e_inFr
    = ( ^ [A: set @ n,B: dtree,C: t] :
          ( ? [D: dtree,E: set @ n,F: t] :
              ( ( A = E )
              & ( B = D )
              & ( C = F )
              & ( member @ n @ ( root @ D ) @ E )
              & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ F ) @ ( cont @ D ) ) )
          | ? [D: dtree,E: set @ n,F: dtree,G: t] :
              ( ( A = E )
              & ( B = D )
              & ( C = G )
              & ( member @ n @ ( root @ D ) @ E )
              & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ F ) @ ( cont @ D ) )
              & ( gram_L1333338417e_inFr @ E @ F @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(186,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( member @ TA @ ( last @ TA @ A ) @ ( set2 @ TA @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_last__in__set) ).

thf(867,plain,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( member @ TA @ ( last @ TA @ A ) @ ( set2 @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(53,axiom,
    ! [TA: $tType,A: TA] :
      ( ( insert @ TA @ A @ ( nil @ TA ) )
      = ( cons @ TA @ A @ ( nil @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_insert__Nil) ).

thf(373,plain,
    ! [TA: $tType,A: TA] :
      ( ( insert @ TA @ A @ ( nil @ TA ) )
      = ( cons @ TA @ A @ ( nil @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(31,axiom,
    gram_L716654942_subtr = gram_L1283001940subtr2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_subtr__subtr2) ).

thf(305,plain,
    gram_L716654942_subtr = gram_L1283001940subtr2,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(202,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ! [C: TA] :
          ( ( member @ TA @ C @ A )
         => ( member @ TA @ C @ B ) )
     => ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_subsetI) ).

thf(918,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ! [C: TA] :
          ( ( member @ TA @ C @ A )
         => ( member @ TA @ C @ B ) )
     => ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(87,axiom,
    ! [A: dtree,B: dtree,C: set @ n,D: t] :
      ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ A ) @ ( cont @ B ) )
     => ( ( gram_L805317441_inFr2 @ C @ A @ D )
       => ( gram_L805317441_inFr2 @ ( insert2 @ n @ ( root @ B ) @ C ) @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_inFr2_OInd) ).

thf(506,plain,
    ! [A: dtree,B: dtree,C: set @ n,D: t] :
      ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ A ) @ ( cont @ B ) )
     => ( ( gram_L805317441_inFr2 @ C @ A @ D )
       => ( gram_L805317441_inFr2 @ ( insert2 @ n @ ( root @ B ) @ C ) @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(63,axiom,
    ! [A: set @ n,B: dtree,C: t] :
      ( ( gram_L1333338417e_inFr @ A @ B @ C )
     => ( ( ( member @ n @ ( root @ B ) @ A )
         => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ C ) @ ( cont @ B ) ) )
       => ~ ( ( member @ n @ ( root @ B ) @ A )
           => ! [D: dtree] :
                ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ D ) @ ( cont @ B ) )
               => ~ ( gram_L1333338417e_inFr @ A @ D @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_inFr_Ocases) ).

thf(400,plain,
    ! [A: set @ n,B: dtree,C: t] :
      ( ( gram_L1333338417e_inFr @ A @ B @ C )
     => ( ( ( member @ n @ ( root @ B ) @ A )
         => ~ ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inl @ t @ dtree @ C ) @ ( cont @ B ) ) )
       => ~ ( ( member @ n @ ( root @ B ) @ A )
           => ! [D: dtree] :
                ( ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ D ) @ ( cont @ B ) )
               => ~ ( gram_L1333338417e_inFr @ A @ D @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(130,axiom,
    ! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
      ( ( A
       != ( nil @ TA ) )
     => ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
       => ( ! [C: TA,D: list @ TA] :
              ( ( D
               != ( nil @ TA ) )
             => ( ( B @ D )
               => ( B @ ( cons @ TA @ C @ D ) ) ) )
         => ( B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_list__nonempty__induct) ).

thf(635,plain,
    ! [TA: $tType,A: list @ TA,B: ( list @ TA ) > $o] :
      ( ( A
       != ( nil @ TA ) )
     => ( ! [C: TA] : ( B @ ( cons @ TA @ C @ ( nil @ TA ) ) )
       => ( ! [C: TA,D: list @ TA] :
              ( ( D
               != ( nil @ TA ) )
             => ( ( B @ D )
               => ( B @ ( cons @ TA @ C @ D ) ) ) )
         => ( B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(144,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( member @ TA @ C @ A )
       => ( member @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_set__mp) ).

thf(696,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( member @ TA @ C @ A )
       => ( member @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(216,axiom,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ~ ! [C: set @ TA] :
            ( ( B
              = ( insert2 @ TA @ A @ C ) )
           => ( member @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_Set_Oset__insert) ).

thf(955,plain,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ~ ! [C: set @ TA] :
            ( ( B
              = ( insert2 @ TA @ A @ C ) )
           => ( member @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(193,axiom,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( hd @ TA @ ( cons @ TA @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_list_Osel_I1_J) ).

thf(886,plain,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( hd @ TA @ ( cons @ TA @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(197,axiom,
    ! [A: dtree,B: set @ n] :
      ( ( member @ n @ ( root @ A ) @ B )
     => ( gram_L1283001940subtr2 @ B @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_subtr2_ORefl) ).

thf(897,plain,
    ! [A: dtree,B: set @ n] :
      ( ( member @ n @ ( root @ A ) @ B )
     => ( gram_L1283001940subtr2 @ B @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(161,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_242_old_Osum_Oexhaust) ).

thf(767,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)],[161]) ).

thf(61,axiom,
    ( gram_L1283001940subtr2
    = ( ^ [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 = D )
              & ( C = G )
              & ( member @ n @ ( root @ D ) @ E )
              & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ D ) @ ( cont @ F ) )
              & ( gram_L1283001940subtr2 @ E @ F @ G ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_subtr2_Osimps) ).

thf(395,plain,
    ( gram_L1283001940subtr2
    = ( ^ [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 = D )
              & ( C = G )
              & ( member @ n @ ( root @ D ) @ E )
              & ( member @ ( sum_sum @ t @ dtree ) @ ( sum_Inr @ dtree @ t @ D ) @ ( cont @ F ) )
              & ( gram_L1283001940subtr2 @ E @ F @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(77,axiom,
    ~ ! [A: list @ n] :
        ( ( gram_L250615845e_path @ f @ A )
       => ( ( ( f @ ( hd @ n @ A ) )
            = tr1a )
         => ( ( ( f @ ( last @ n @ A ) )
              = tr2 )
           => ~ ( ord_less_eq @ ( set @ n ) @ ( set2 @ n @ A ) @ nsa ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062nl_O_A_092_060lbrakk_062path_Af_Anl_059_Af_A_Ihd_Anl_J_A_061_Atr1_059_Af_A_Ilast_Anl_J_A_061_Atr2_059_Aset_Anl_A_092_060subseteq_062_Ans_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).

thf(464,plain,
    ~ ! [A: list @ n] :
        ( ( gram_L250615845e_path @ f @ A )
       => ( ( ( f @ ( hd @ n @ A ) )
            = tr1a )
         => ( ( ( f @ ( last @ n @ A ) )
              = tr2 )
           => ~ ( ord_less_eq @ ( set @ n ) @ ( set2 @ n @ A ) @ nsa ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(13,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_46_Collect__cong) ).

thf(254,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)],[13]) ).

thf(38,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_228_old_Osum_Oinject_I1_J) ).

thf(322,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)],[38]) ).

thf(48,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_67_subtr_ORefl) ).

thf(354,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)],[48]) ).

thf(208,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( member @ TA @ ( hd @ TA @ A ) @ ( set2 @ TA @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_list_Oset__sel_I1_J) ).

thf(935,plain,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( member @ TA @ ( hd @ TA @ A ) @ ( set2 @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(33,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
       => ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_subset__trans) ).

thf(309,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
       => ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(114,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_247_old_Osum_Odistinct_I1_J) ).

thf(592,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)],[114]) ).

thf(191,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA,D: TA > $o] :
      ( ( member @ TA @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B
          @ ( collect @ TA
            @ ^ [E: TA] :
                ( ( member @ TA @ E @ C )
                & ( D @ E ) ) ) )
       => ( D @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_prop__restrict) ).

thf(882,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA,D: TA > $o] :
      ( ( member @ TA @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B
          @ ( collect @ TA
            @ ^ [E: TA] :
                ( ( member @ TA @ E @ C )
                & ( D @ E ) ) ) )
       => ( D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(149,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_251_inFr2_OBase) ).

thf(708,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)],[149]) ).

thf(6,axiom,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( insert2 @ TA @ A @ ( insert2 @ TA @ A @ B ) )
      = ( insert2 @ TA @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_insert__absorb2) ).

thf(232,plain,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( insert2 @ TA @ A @ ( insert2 @ TA @ A @ B ) )
      = ( insert2 @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(969,plain,
    $false,
    inference(cvc4,[status(thm)],[645,629,941,408,276,741,873,247,379,861,523,762,440,655,385,500,472,814,698,945,930,829,288,565,257,719,344,587,619,542,460,870,606,770,416,325,817,902,492,789,376,238,475,924,293,866,453,774,411,428,397,687,265,849,307,380,529,534,714,512,439,334,825,952,302,260,598,820,297,693,275,625,879,852,665,583,889,551,285,229,484,519,317,388,356,328,884,225,642,526,706,457,503,622,837,244,792,938,633,311,921,662,279,573,296,601,584,904,843,711,291,545,413,391,382,947,672,219,736,616,863,764,604,509,649,434,631,367,609,700,895,462,959,299,226,431,241,658,722,490,589,795,548,927,648,812,516,342,553,823,531,944,690,282,739,263,580,855,331,370,840,338,576,359,907,336,703,314,571,595,612,497,876,845,250,627,539,495,891,771,961,319,786,652,351,568,235,929,272,899,536,716,752,950,867,373,305,918,506,400,635,696,955,886,897,767,395,464,254,322,354,935,309,592,882,708,232]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12  % Problem  : COM191^1 : TPTP v8.2.0. Released v7.0.0.
% 0.05/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.35  % Computer : n016.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Sun May 19 10:20:24 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.95/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.79/1.15  % [INFO] 	 Parsing done (291ms). 
% 1.79/1.16  % [INFO] 	 Running in sequential loop mode. 
% 2.58/1.40  % [INFO] 	 eprover registered as external prover. 
% 2.58/1.41  % [INFO] 	 cvc4 registered as external prover. 
% 2.58/1.41  % [INFO] 	 Scanning for conjecture ... 
% 2.79/1.52  % [INFO] 	 Found a conjecture (or negated_conjecture) and 268 axioms. Running axiom selection ... 
% 3.08/1.62  % [INFO] 	 Axiom selection finished. Selected 216 axioms (removed 52 axioms). 
% 3.79/1.79  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 3.79/1.80  % [INFO] 	 Type checking passed. 
% 3.99/1.81  % [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 ... 
% 147.60/90.48  % External prover 'cvc4' found a proof!
% 147.60/90.49  % [INFO] 	 Killing All external provers ... 
% 147.60/90.49  % Time passed: 89977ms (effective reasoning time: 89324ms)
% 147.60/90.49  % 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)>
% 147.60/90.49  % Axioms used in derivation (216): fact_210_insert__ident, fact_40_list__induct2_H, fact_147_predicate1D, fact_144_inItr_Osimps, fact_230_obj__sumE, fact_34_map__tailrec__rev_Oinduct, fact_183_Collect__restrict, fact_42__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062nl_O_A_092_060lbrakk_062path_Af_Anl_059_Af_A_Ihd_Anl_J_A_061_Atr1_059_Af_A_Ilast_Anl_J_A_061_Atr2_059_Aset_Anl_A_092_060subseteq_062_Ans_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_1_tr, fact_54_Step_Ohyps_I3_J, fact_78_subtr_OStep, fact_238_inFr__root__in, fact_63_list_Oset__intros_I2_J, fact_219_subtr2__rootL__in, fact_195_insertCI, fact_17_sum_Oinject_I2_J, fact_191_inFr2_OInd, fact_92_the__elem__set, fact_251_inFr2_OBase, fact_66_list_Oset__cases, fact_242_old_Osum_Oexhaust, fact_4_f, fact_130_equalityD2, fact_24_list_Oexhaust, fact_68_subtr__rootL__in, fact_143_inItr_Oinducts, fact_222_subtr2__StepR, fact_98_distinct_Osimps_I2_J, fact_239_inFr__subtr, fact_129_equalityD1, fact_182_member__remove, fact_50_set, fact_19_list_Oinject, fact_61_inFr2__mono, fact_236_Inl__inject, fact_79_subtr_Ocases, fact_252_inFr_OInd, fact_85_subtrOf__root, fact_241_old_Osum_Oinducts, fact_228_old_Osum_Oinject_I1_J, fact_84_regular__def, fact_139_Collect__mono__iff, fact_244_split__sum__ex, fact_35_list__nonempty__induct, fact_140_distinct__union, fact_6_rtr, fact_237_not__root__inFr, fact_148_inItr_OBase, fact_131_set__rev__mp, fact_135_Collect__mono, fact_154_inItr_Ocases, fact_232_subtr__inFr, fact_82_subtr_Oinducts, fact_231_inFr__mono, fact_138_contra__subsetD, fact_73_hd__in__set, fact_65_set__ConsD, fact_199_insert__subsetI, fact_7_tr1, fact_5_f__nl, fact_10_path_OBase, fact_215_insert__compr, fact_59_subtr__trans, fact_220_subtr2__rootR__in, fact_74_last__in__set, fact_250_inFr__inFr2, fact_153_inItr_OInd, fact_77_wf__cont, fact_137_set__eq__subset, fact_234_inFr_Osimps, fact_2_tr1__tr, fact_253_inFr2_Oinducts, fact_180_conj__subset__def, fact_87_subsetI, fact_91_product__lists_Osimps_I1_J, fact_25_list_Oinducts, fact_62_wf__subtr, fact_235_inFr_Ocases, fact_141_subtrOf__def, fact_184_subset__Collect__iff, fact_162_someI2__bex, fact_240_inFr_OBase, help_If_1_1_T, fact_190_univ__def, fact_81_subtr__StepL, fact_26_neq__Nil__conv, fact_133_rev__subsetD, fact_37_remdups__adj_Ocases, fact_21_hsubst__c__def, fact_216_insert__Collect, fact_127_equalityE, fact_134_subset__refl, fact_245_Inr__not__Inl, fact_33_Inr__inject, fact_145_predicate1I, fact_13_path_Osimps, fact_93_distinct__product__lists, fact_20_dtree__cong, fact_36_remdups__adj_Oinduct, fact_41_n, fact_52_wf__inj, fact_3_nl, fact_15_last__nl, fact_53_inFr2__Ind, fact_189_shift__def, fact_196_insert__subset, fact_56_subset__code_I1_J, fact_60_subtr__mono, fact_225_inFr__Ind__minus, fact_71_inFr2__root__in, fact_192_subtr2_OStep, fact_14_path_Oinducts, fact_9_path_OInd, fact_69_subtr__rootR__in, fact_207_insert__commute, fact_86_subset__antisym, fact_226_inFr2_Ocases, fact_227_sum_Oinject_I1_J, fact_202_subset__insert, fact_29_last__ConsL, fact_181_prop__restrict, fact_168_subset__code_I3_J, fact_90_path__distinct, fact_213_insertI1, fact_132_subset__iff, fact_152_inItr__subtr, fact_169_subset__code_I2_J, fact_198_List_Oset__insert, fact_76_reg__def2, fact_171_Itr__def, fact_12_path_Ocases, fact_193_insert__absorb2, fact_218_subtr2_ORefl, fact_51_Step_Oprems, fact_197_list_Osimps_I15_J, help_If_3_1_T, fact_8_path__NE, fact_211_Set_Oset__insert, fact_246_sumE, fact_177_List_Oinsert__def, fact_30_last_Osimps, fact_188_not__arg__cong__Inr, fact_64_list_Oset__intros_I1_J, fact_173_in__set__insert, help_If_2_1_T, fact_149_inItr__root__in, fact_150_subtr__inItr, fact_89_sublists_Osimps_I1_J, fact_94_less__eq__set__def, fact_203_subset__insertI, fact_18_old_Osum_Oinject_I2_J, fact_11_path__post, fact_212_insertI2, fact_125_subsetD, fact_80_subtr_Osimps, fact_83_subtr__inductL, fact_45_Collect__mem__eq, fact_247_old_Osum_Odistinct_I1_J, fact_151_inItr__mono, fact_39_splice_Oinduct, fact_166_pred__subset__eq, fact_179_remove__code_I2_J, fact_58_regular__subtr, fact_224_subtr2_Ocases, fact_233_inFr_Oinducts, fact_57_set__subset__Cons, fact_221_subtr2_Oinducts, fact_175_insert__Nil, fact_49_regular__def2, fact_206_mk__disjoint__insert, fact_128_subset__eq, fact_95_distinct__length__2__or__more, fact_146_rev__predicate1D, fact_174_distinct__insert, fact_126_subsetCE, fact_229_old_Osum_Osimps_I7_J, fact_0_reg__root, fact_214_insertE, fact_27_tr2__tr1, fact_205_subtr2__trans, fact_70_reg__subtr, fact_96_distinct_Osimps_I1_J, fact_97_distinct__singleton, fact_194_insert__iff, fact_72_list_Oset__sel_I1_J, fact_67_subtr_ORefl, fact_28_last__ConsR, fact_204_subset__insertI2, fact_208_insert__eq__iff, fact_75_path__subtr, fact_55_root__Node, fact_254_inFr2_Osimps, fact_32_not__Cons__self2, fact_23_list_OdiscI, fact_43_old_Osum_Osimps_I8_J, fact_48_Node__root__cont, fact_223_subtr2_Osimps, fact_136_subset__trans, fact_249_sum_Odistinct_I1_J, fact_200_subtr2__mono, fact_22_list_Odistinct_I1_J, fact_201_insert__mono, fact_16_reg__Inr__cont, fact_209_insert__absorb, fact_44_mem__Collect__eq, fact_248_old_Osum_Odistinct_I2_J, fact_31_list_Osel_I1_J, fact_142_hsubst__r__def, fact_243_split__sum__all, fact_185_subset__CollectI, fact_217_subtr__subtr2, fact_124_in__mono, fact_172_not__in__set__insert, fact_46_Collect__cong, fact_123_set__mp, fact_38_transpose_Ocases
% 147.60/90.49  % No. of inferences in proof: 436
% 147.60/90.49  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 89977 ms resp. 89324 ms w/o parsing
% 148.48/90.67  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 148.48/90.67  % [INFO] 	 Killing All external provers ... 
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