TSTP Solution File: ITP081^2 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ITP081^2 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n005.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 20 22:22:43 EDT 2024

% Result   : Theorem 77.22s 30.68s
% Output   : Refutation 77.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  308
% Syntax   : Number of formulae    :  573 ( 197 unt;  45 typ;   0 def)
%            Number of atoms       : 1613 ( 722 equ;   8 cnn)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives : 10501 ( 312   ~;  34   |; 134   &;9197   @)
%                                         (   0 <=>; 824  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   29 (  10 avg)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :  343 ( 343   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   48 (  45 usr;  20 con; 0-10 aty)
%            Number of variables   : 2273 (  24   ^2092   !; 122   ?;2273   :)
%                                         (  35  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(edgeD_type,type,
    edgeD: $tType ).

thf(node_type,type,
    node: $tType ).

thf(val_type,type,
    val: $tType ).

thf(g_type,type,
    g: $tType ).

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

thf(ord_type,type,
    ord: 
      !>[TA: $tType] : $o ).

thf(linorder_type,type,
    linorder: 
      !>[TA: $tType] : $o ).

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

thf(graph_1146196722h_path_type,type,
    graph_1146196722h_path: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > ( list @ TB ) ) > ( TC > $o ) > ( TC > TB > ( list @ ( product_prod @ TB @ TA ) ) ) > TC > ( list @ TB ) > $o ) ).

thf(graph_1661282752_path2_type,type,
    graph_1661282752_path2: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > ( list @ TB ) ) > ( TC > $o ) > ( TC > TB > ( list @ ( product_prod @ TB @ TA ) ) ) > TC > TB > ( list @ TB ) > TB > $o ) ).

thf(graph_1201503639essors_type,type,
    graph_1201503639essors: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > ( list @ ( product_prod @ TB @ TA ) ) ) > TC > TB > ( list @ TB ) ) ).

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

thf(butlast_type,type,
    butlast: 
      !>[TA: $tType] : ( ( list @ TA ) > ( list @ 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(tl_type,type,
    tl: 
      !>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) ) ).

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

thf(sSA_CFG_SSA_phiUses_type,type,
    sSA_CFG_SSA_phiUses: 
      !>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( TD > ( list @ TC ) ) > ( TD > TC > ( list @ ( product_prod @ TC @ TB ) ) ) > ( TD > ( product_prod @ TC @ TA ) > ( option @ ( list @ TA ) ) ) > TD > TC > ( set @ TA ) ) ).

thf(sSA_CF1081484811efNode_type,type,
    sSA_CF1081484811efNode: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > ( list @ TB ) ) > ( TC > TB > ( set @ TA ) ) > ( TC > ( product_prod @ TB @ TA ) > ( option @ ( list @ TA ) ) ) > TC > TA > TB ) ).

thf(sSA_CF1165125185phiArg_type,type,
    sSA_CF1165125185phiArg: 
      !>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > ( list @ TB ) ) > ( TC > TB > ( set @ TA ) ) > ( TC > ( product_prod @ TB @ TA ) > ( option @ ( list @ TA ) ) ) > TC > TA > TA > $o ) ).

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

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

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

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

thf(alpha_n_type,type,
    alpha_n: g > ( list @ node ) ).

thf(phi_r_type,type,
    phi_r: val ).

thf(defs_type,type,
    defs: g > node > ( set @ val ) ).

thf(g2_type,type,
    g2: g ).

thf(i_type,type,
    i: node ).

thf(inEdges_type,type,
    inEdges: g > node > ( list @ ( product_prod @ node @ edgeD ) ) ).

thf(invar_type,type,
    invar: g > $o ).

thf(m_type,type,
    m: node ).

thf(ms_type,type,
    ms: list @ node ).

thf(ms2_type,type,
    ms2: list @ node ).

thf(n_type,type,
    n: node ).

thf(ns_type,type,
    ns: list @ node ).

thf(phis_type,type,
    phis: g > ( product_prod @ node @ val ) > ( option @ ( list @ val ) ) ).

thf(pred_phi_r_type,type,
    pred_phi_r: node ).

thf(r_type,type,
    r: val ).

thf(ri_type,type,
    ri: list @ node ).

thf(rs_type,type,
    rs: list @ node ).

thf(rs2_type,type,
    rs2: list @ node ).

thf(s_type,type,
    s: val ).

thf(214,axiom,
    ! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( ( ( cons @ TA @ B @ ( nil @ TA ) )
          = ( append @ TA @ C @ A ) )
        = ( ( C
            = ( nil @ TA ) )
          & ( A
            = ( cons @ TA @ B @ ( nil @ TA ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_list__se__match_I4_J) ).

thf(1036,plain,
    ! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( ( ( cons @ TA @ B @ ( nil @ TA ) )
          = ( append @ TA @ C @ A ) )
        = ( ( C
            = ( nil @ TA ) )
          & ( A
            = ( cons @ TA @ B @ ( nil @ TA ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(211,axiom,
    ! [A: g,B: node] :
      ( ( ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ B )
       != ( nil @ node ) )
     => ( ( invar @ A )
       => ( member @ node @ B @ ( set2 @ node @ ( alpha_n @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_old_Osuccessor__in___092_060alpha_062n) ).

thf(1024,plain,
    ! [A: g,B: node] :
      ( ( ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ B )
       != ( nil @ node ) )
     => ( ( invar @ A )
       => ( member @ node @ B @ ( set2 @ node @ ( alpha_n @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(140,axiom,
    ! [A: g,B: node,C: list @ node,D: node,E: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( ( member @ node @ E @ ( set2 @ node @ C ) )
       => ~ ! [F: list @ node] :
              ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ F @ E )
             => ( ( prefix @ node @ F @ C )
               => ( member @ node @ E @ ( set2 @ node @ ( butlast @ node @ F ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_old_Opath2__prefix__ex) ).

thf(760,plain,
    ! [A: g,B: node,C: list @ node,D: node,E: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( ( member @ node @ E @ ( set2 @ node @ C ) )
       => ~ ! [F: list @ node] :
              ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ F @ E )
             => ( ( prefix @ node @ F @ C )
               => ( member @ node @ E @ ( set2 @ node @ ( butlast @ node @ F ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(27,axiom,
    ! [TA: $tType,A: list @ TA] : ( finite_finite @ TA @ ( set2 @ TA @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_List_Ofinite__set) ).

thf(347,plain,
    ! [TA: $tType,A: list @ TA] : ( finite_finite @ TA @ ( set2 @ TA @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(177,axiom,
    ! [TA: $tType,A: list @ TA,B: TA] :
      ( ( butlast @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_butlast__snoc) ).

thf(909,plain,
    ! [TA: $tType,A: list @ TA,B: TA] :
      ( ( butlast @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(74,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,F: list @ TA] :
            ( ( A @ E @ ( cons @ TA @ D @ F ) )
           => ( A @ ( cons @ TA @ D @ E ) @ F ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_revg_Oinduct) ).

thf(518,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,F: list @ TA] :
            ( ( A @ E @ ( cons @ TA @ D @ F ) )
           => ( A @ ( cons @ TA @ D @ E ) @ F ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(222,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: TA] :
      ( ( prefix @ TA @ A @ ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
      = ( ( A
          = ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
        | ( prefix @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_prefix__snoc) ).

thf(1083,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: TA] :
      ( ( prefix @ TA @ A @ ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
      = ( ( A
          = ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
        | ( prefix @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(245,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: TA,D: list @ TA] :
      ( ( ( append @ TA @ A @ B )
        = ( cons @ TA @ C @ D ) )
      = ( ( ( A
            = ( nil @ TA ) )
          & ( B
            = ( cons @ TA @ C @ D ) ) )
        | ? [E: list @ TA] :
            ( ( A
              = ( cons @ TA @ C @ E ) )
            & ( ( append @ TA @ E @ B )
              = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_append__eq__Cons__conv) ).

thf(1179,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: TA,D: list @ TA] :
      ( ( ( append @ TA @ A @ B )
        = ( cons @ TA @ C @ D ) )
      = ( ( ( A
            = ( nil @ TA ) )
          & ( B
            = ( cons @ TA @ C @ D ) ) )
        | ? [E: list @ TA] :
            ( ( A
              = ( cons @ TA @ C @ E ) )
            & ( ( append @ TA @ E @ B )
              = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(84,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/sandbox/benchmark/theBenchmark.p',fact_86_list__tail__coinc) ).

thf(555,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)],[84]) ).

thf(69,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( A = B )
     => ( suffix @ TA @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_suffix__order_Oeq__refl) ).

thf(481,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( A = B )
     => ( suffix @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(29,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,F: list @ TA] :
            ( ( A @ F @ E )
           => ( A @ ( cons @ TA @ D @ E ) @ F ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_splice_Oinduct) ).

thf(352,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,F: list @ TA] :
            ( ( A @ F @ E )
           => ( A @ ( cons @ TA @ D @ E ) @ F ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(16,axiom,
    ! [TA: $tType] :
      ( ( (=) @ ( list @ TA ) )
      = ( ^ [A: list @ TA,B: list @ TA] :
            ( ( suffix @ TA @ A @ B )
            & ( suffix @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_suffix__order_Oeq__iff) ).

thf(308,plain,
    ! [TA: $tType] :
      ( ( (=) @ ( list @ TA ) )
      = ( ^ [A: list @ TA,B: list @ TA] :
            ( ( suffix @ TA @ A @ B )
            & ( suffix @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(172,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: TA,D: list @ TA] :
      ( ( ( append @ TA @ A @ B )
        = ( cons @ TA @ C @ D ) )
     => ( ( ( A
            = ( nil @ TA ) )
         => ( B
           != ( cons @ TA @ C @ D ) ) )
       => ~ ! [E: list @ TA] :
              ( ( A
                = ( cons @ TA @ C @ E ) )
             => ( ( append @ TA @ E @ B )
               != D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_list__append__eq__Cons__cases) ).

thf(873,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: TA,D: list @ TA] :
      ( ( ( append @ TA @ A @ B )
        = ( cons @ TA @ C @ D ) )
     => ( ( ( A
            = ( nil @ TA ) )
         => ( B
           != ( cons @ TA @ C @ D ) ) )
       => ~ ! [E: list @ TA] :
              ( ( A
                = ( cons @ TA @ C @ E ) )
             => ( ( append @ TA @ E @ B )
               != D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(235,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( append @ TA @ ( nil @ TA ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_append_Oleft__neutral) ).

thf(1142,plain,
    ! [TA: $tType,A: list @ TA] :
      ( ( append @ TA @ ( nil @ TA ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(106,axiom,
    ! [A: g,B: node,C: list @ node,D: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( member @ node @ D @ ( set2 @ node @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_old_Opath2__last__in__ns) ).

thf(614,plain,
    ! [A: g,B: node,C: list @ node,D: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( member @ node @ D @ ( set2 @ node @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(243,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
      ( ( ( append @ TA @ A @ B )
        = ( append @ TA @ C @ D ) )
      = ( ? [E: list @ TA] :
            ( ( ( A
                = ( append @ TA @ C @ E ) )
              & ( ( append @ TA @ E @ B )
                = D ) )
            | ( ( ( append @ TA @ A @ E )
                = C )
              & ( B
                = ( append @ TA @ E @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_append__eq__append__conv2) ).

thf(1173,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
      ( ( ( append @ TA @ A @ B )
        = ( append @ TA @ C @ D ) )
      = ( ? [E: list @ TA] :
            ( ( ( A
                = ( append @ TA @ C @ E ) )
              & ( ( append @ TA @ E @ B )
                = D ) )
            | ( ( ( append @ TA @ A @ E )
                = C )
              & ( B
                = ( append @ TA @ E @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(255,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( ( ( tl @ TA @ A )
          = ( nil @ TA ) )
       => ~ ! [B: TA] :
              ( A
             != ( cons @ TA @ B @ ( nil @ TA ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_tl__obtain__elem) ).

thf(1233,plain,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( ( ( tl @ TA @ A )
          = ( nil @ TA ) )
       => ~ ! [B: TA] :
              ( A
             != ( cons @ TA @ B @ ( nil @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(120,axiom,
    ! [TA: $tType] :
      ( ( tl @ TA @ ( nil @ TA ) )
      = ( nil @ TA ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_list_Osel_I2_J) ).

thf(670,plain,
    ! [TA: $tType] :
      ( ( tl @ TA @ ( nil @ TA ) )
      = ( nil @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(203,axiom,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( member @ TA @ A @ ( set2 @ TA @ B ) )
     => ~ ! [C: list @ TA,D: list @ TA] :
            ( B
           != ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_in__set__list__format) ).

thf(1001,plain,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( member @ TA @ A @ ( set2 @ TA @ B ) )
     => ~ ! [C: list @ TA,D: list @ TA] :
            ( B
           != ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(11,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( suffix @ TA @ A @ B )
     => ( ( suffix @ TA @ B @ C )
       => ( suffix @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_suffix__order_Oorder_Otrans) ).

thf(288,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( suffix @ TA @ A @ B )
     => ( ( suffix @ TA @ B @ C )
       => ( suffix @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(253,axiom,
    ! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA] :
      ( ( ( cons @ TA @ A @ B )
        = ( append @ TA @ C @ D ) )
      = ( ( ( C
            = ( nil @ TA ) )
          & ( ( cons @ TA @ A @ B )
            = D ) )
        | ? [E: list @ TA] :
            ( ( ( cons @ TA @ A @ E )
              = C )
            & ( B
              = ( append @ TA @ E @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_Cons__eq__append__conv) ).

thf(1228,plain,
    ! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA] :
      ( ( ( cons @ TA @ A @ B )
        = ( append @ TA @ C @ D ) )
      = ( ( ( C
            = ( nil @ TA ) )
          & ( ( cons @ TA @ A @ B )
            = D ) )
        | ? [E: list @ TA] :
            ( ( ( cons @ TA @ A @ E )
              = C )
            & ( B
              = ( append @ TA @ E @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(159,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( suffix @ TA @ ( append @ TA @ A @ B ) @ B )
      = ( A
        = ( nil @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_same__suffix__nil) ).

thf(829,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( suffix @ TA @ ( append @ TA @ A @ B ) @ B )
      = ( A
        = ( nil @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(226,axiom,
    ! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
      ( ( ( append @ TA @ A @ ( cons @ TA @ B @ C ) )
        = ( cons @ TA @ D @ ( nil @ TA ) ) )
      = ( ( A
          = ( nil @ TA ) )
        & ( B = D )
        & ( C
          = ( nil @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_list__e__eq__lel_I2_J) ).

thf(1095,plain,
    ! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
      ( ( ( append @ TA @ A @ ( cons @ TA @ B @ C ) )
        = ( cons @ TA @ D @ ( nil @ TA ) ) )
      = ( ( A
          = ( nil @ TA ) )
        & ( B = D )
        & ( C
          = ( nil @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(218,axiom,
    ! [A: g,B: list @ node] :
      ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B )
     => ( ! [C: node] :
            ( ( B
              = ( cons @ node @ C @ ( nil @ node ) ) )
           => ( ( member @ node @ C @ ( set2 @ node @ ( alpha_n @ A ) ) )
             => ~ ( invar @ A ) ) )
       => ~ ! [C: list @ node,D: node] :
              ( ( B
                = ( cons @ node @ D @ C ) )
             => ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ C )
               => ~ ( member @ node @ D @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ ( hd @ node @ C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_old_Opath_Ocases) ).

thf(1055,plain,
    ! [A: g,B: list @ node] :
      ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B )
     => ( ! [C: node] :
            ( ( B
              = ( cons @ node @ C @ ( nil @ node ) ) )
           => ( ( member @ node @ C @ ( set2 @ node @ ( alpha_n @ A ) ) )
             => ~ ( invar @ A ) ) )
       => ~ ! [C: list @ node,D: node] :
              ( ( B
                = ( cons @ node @ D @ C ) )
             => ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ C )
               => ~ ( member @ node @ D @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ ( hd @ node @ C ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(88,axiom,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( member @ TA @ A @ ( set2 @ TA @ ( butlast @ TA @ B ) ) )
     => ( member @ TA @ A @ ( set2 @ TA @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_in__set__butlastD) ).

thf(570,plain,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( member @ TA @ A @ ( set2 @ TA @ ( butlast @ TA @ B ) ) )
     => ( member @ TA @ A @ ( set2 @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(263,axiom,
    ! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
      ( ~ ( member @ TA @ A @ ( set2 @ TA @ B ) )
     => ( ~ ( member @ TA @ A @ ( set2 @ TA @ C ) )
       => ( ( ( append @ TA @ B @ ( cons @ TA @ A @ C ) )
            = ( append @ TA @ D @ ( cons @ TA @ A @ E ) ) )
          = ( ( B = D )
            & ( C = E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_append__Cons__eq__iff) ).

thf(1264,plain,
    ! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
      ( ~ ( member @ TA @ A @ ( set2 @ TA @ B ) )
     => ( ~ ( member @ TA @ A @ ( set2 @ TA @ C ) )
       => ( ( ( append @ TA @ B @ ( cons @ TA @ A @ C ) )
            = ( append @ TA @ D @ ( cons @ TA @ A @ E ) ) )
          = ( ( B = D )
            & ( C = E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(26,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( linorder @ TB )
     => ! [A: ( TA > TB ) > ( list @ TA ) > $o,B: TA > TB,C: list @ TA] :
          ( ! [D: TA > TB,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
         => ( ! [D: TA > TB,E: TA,F: TA,G: list @ TA] :
                ( ( A @ D @ ( cons @ TA @ F @ G ) )
               => ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
           => ( ! [D: TA > TB] : ( A @ D @ ( nil @ TA ) )
             => ( A @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_arg__min__list_Oinduct) ).

thf(344,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( linorder @ TB )
     => ! [A: ( TA > TB ) > ( list @ TA ) > $o,B: TA > TB,C: list @ TA] :
          ( ! [D: TA > TB,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
         => ( ! [D: TA > TB,E: TA,F: TA,G: list @ TA] :
                ( ( A @ D @ ( cons @ TA @ F @ G ) )
               => ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
           => ( ! [D: TA > TB] : ( A @ D @ ( nil @ TA ) )
             => ( A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(189,axiom,
    ! [TA: $tType,A: list @ TA,B: TA > $o] :
      ( ? [C: TA] :
          ( ( member @ TA @ C @ ( set2 @ TA @ A ) )
          & ( B @ C ) )
     => ~ ! [C: list @ TA,D: TA] :
            ( ? [E: list @ TA] :
                ( A
                = ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
           => ( ( B @ D )
             => ~ ! [E: TA] :
                    ( ( member @ TA @ E @ ( set2 @ TA @ C ) )
                   => ~ ( B @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_split__list__first__propE) ).

thf(949,plain,
    ! [TA: $tType,A: list @ TA,B: TA > $o] :
      ( ? [C: TA] :
          ( ( member @ TA @ C @ ( set2 @ TA @ A ) )
          & ( B @ C ) )
     => ~ ! [C: list @ TA,D: TA] :
            ( ? [E: list @ TA] :
                ( A
                = ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
           => ( ( B @ D )
             => ~ ! [E: TA] :
                    ( ( member @ TA @ E @ ( set2 @ TA @ C ) )
                   => ~ ( B @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(61,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( suffix @ TA @ A @ B )
     => ( ( suffix @ TA @ C @ B )
       => ( ( suffix @ TA @ A @ C )
          | ( suffix @ TA @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_suffix__same__cases) ).

thf(460,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( suffix @ TA @ A @ B )
     => ( ( suffix @ TA @ C @ B )
       => ( ( suffix @ TA @ A @ C )
          | ( suffix @ TA @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(186,axiom,
    ! [A: g,B: node,C: list @ node,D: node,E: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( ( member @ node @ E @ ( set2 @ node @ C ) )
       => ~ ! [F: list @ node] :
              ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ F @ E )
             => ! [G: list @ node] :
                  ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ E @ G @ D )
                 => ( C
                   != ( append @ node @ ( butlast @ node @ F ) @ G ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_old_Opath2__split__ex_H) ).

thf(934,plain,
    ! [A: g,B: node,C: list @ node,D: node,E: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( ( member @ node @ E @ ( set2 @ node @ C ) )
       => ~ ! [F: list @ node] :
              ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ F @ E )
             => ! [G: list @ node] :
                  ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ E @ G @ D )
                 => ( C
                   != ( append @ node @ ( butlast @ node @ F ) @ G ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(31,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( A = B )
     => ( ( suffix @ TA @ B @ C )
       => ( suffix @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_suffix__order_Oord__eq__le__trans) ).

thf(357,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( A = B )
     => ( ( suffix @ TA @ B @ C )
       => ( suffix @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(249,axiom,
    member @ node @ pred_phi_r @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_rs_H__props_I4_J) ).

thf(1191,plain,
    member @ node @ pred_phi_r @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(113,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( suffix @ TA @ A @ ( append @ TA @ B @ C ) )
      = ( ( suffix @ TA @ A @ C )
        | ? [D: list @ TA] :
            ( ( A
              = ( append @ TA @ D @ C ) )
            & ( suffix @ TA @ D @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_suffix__append) ).

thf(638,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( suffix @ TA @ A @ ( append @ TA @ B @ C ) )
      = ( ( suffix @ TA @ A @ C )
        | ? [D: list @ TA] :
            ( ( A
              = ( append @ TA @ D @ C ) )
            & ( suffix @ TA @ D @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(102,axiom,
    prefix @ node @ ms2 @ ms,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_ms_H__props_I2_J) ).

thf(606,plain,
    prefix @ node @ ms2 @ ms,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(143,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 @ ( append @ TB @ E @ ( cons @ TB @ D @ ( nil @ TB ) ) ) @ ( nil @ TA ) )
       => ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TB ) @ ( append @ TA @ E @ ( cons @ TA @ D @ ( nil @ TA ) ) ) )
         => ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
                ( ( A @ E @ G )
               => ( A @ ( append @ TB @ E @ ( cons @ TB @ D @ ( nil @ TB ) ) ) @ ( append @ TA @ G @ ( cons @ TA @ F @ ( nil @ TA ) ) ) ) )
           => ( A @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_rev__induct2_H) ).

thf(770,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 @ ( append @ TB @ E @ ( cons @ TB @ D @ ( nil @ TB ) ) ) @ ( nil @ TA ) )
       => ( ! [D: TA,E: list @ TA] : ( A @ ( nil @ TB ) @ ( append @ TA @ E @ ( cons @ TA @ D @ ( nil @ TA ) ) ) )
         => ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
                ( ( A @ E @ G )
               => ( A @ ( append @ TB @ E @ ( cons @ TB @ D @ ( nil @ TB ) ) ) @ ( append @ TA @ G @ ( cons @ TA @ F @ ( nil @ TA ) ) ) ) )
           => ( A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(57,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/sandbox/benchmark/theBenchmark.p',fact_119_set__ConsD) ).

thf(448,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)],[57]) ).

thf(19,axiom,
    ! [TA: $tType] :
      ( ( (=) @ ( list @ TA ) )
      = ( ^ [A: list @ TA,B: list @ TA] :
            ( ( suffix @ TA @ A @ B )
            & ( suffix @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_suffix__order_Oorder_Oeq__iff) ).

thf(316,plain,
    ! [TA: $tType] :
      ( ( (=) @ ( list @ TA ) )
      = ( ^ [A: list @ TA,B: list @ TA] :
            ( ( suffix @ TA @ A @ B )
            & ( suffix @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(149,axiom,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( member @ TA @ A @ ( set2 @ TA @ B ) )
     => ? [C: list @ TA,D: list @ TA] :
          ( B
          = ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_split__list) ).

thf(789,plain,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( member @ TA @ A @ ( set2 @ TA @ B ) )
     => ? [C: list @ TA,D: list @ TA] :
          ( B
          = ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(97,axiom,
    ! [A: g,B: node,C: list @ node,D: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( member @ node @ B @ ( set2 @ node @ ( alpha_n @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_old_Opath2__hd__in___092_060alpha_062n) ).

thf(591,plain,
    ! [A: g,B: node,C: list @ node,D: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( member @ node @ B @ ( set2 @ node @ ( alpha_n @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(55,axiom,
    ! [TA: $tType,A: TA,B: list @ TA,C: list @ TA] :
      ( ( suffix @ TA @ ( cons @ TA @ A @ B ) @ C )
     => ( suffix @ TA @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_suffix__ConsD) ).

thf(443,plain,
    ! [TA: $tType,A: TA,B: list @ TA,C: list @ TA] :
      ( ( suffix @ TA @ ( cons @ TA @ A @ B ) @ C )
     => ( suffix @ TA @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(21,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( suffix @ TA @ A @ ( nil @ TA ) )
     => ( A
        = ( nil @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_suffix__bot_Obot_Oextremum__uniqueI) ).

thf(321,plain,
    ! [TA: $tType,A: list @ TA] :
      ( ( suffix @ TA @ A @ ( nil @ TA ) )
     => ( A
        = ( nil @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(70,axiom,
    linorder @ $o,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder) ).

thf(485,plain,
    linorder @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(73,axiom,
    ! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
      ( ( A
        = ( cons @ TA @ B @ C ) )
     => ( A
       != ( nil @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_list_OdiscI) ).

thf(514,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(193,axiom,
    prefix @ node @ ri @ rs2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_ri__props_I4_J) ).

thf(966,plain,
    prefix @ node @ ri @ rs2,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(241,axiom,
    sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r @ r,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_assms_I10_J) ).

thf(1169,plain,
    sSA_CF1165125185phiArg @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r @ r,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(127,axiom,
    ! [A: g,B: node,C: list @ node,D: node,E: list @ node,F: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append @ node @ C @ ( cons @ node @ D @ E ) ) @ F )
     => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append @ node @ C @ ( cons @ node @ D @ ( nil @ node ) ) ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_old_Opath2__split_I1_J) ).

thf(692,plain,
    ! [A: g,B: node,C: list @ node,D: node,E: list @ node,F: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append @ node @ C @ ( cons @ node @ D @ E ) ) @ F )
     => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append @ node @ C @ ( cons @ node @ D @ ( nil @ node ) ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(13,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [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/sandbox/benchmark/theBenchmark.p',fact_90_strict__sorted_Oinduct) ).

thf(293,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [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)],[13]) ).

thf(169,axiom,
    ! [TA: $tType,A: TA,B: list @ TA,C: list @ TA] :
      ( ( append @ TA @ ( cons @ TA @ A @ B ) @ C )
      = ( cons @ TA @ A @ ( append @ TA @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_append__Cons) ).

thf(866,plain,
    ! [TA: $tType,A: TA,B: list @ TA,C: list @ TA] :
      ( ( append @ TA @ ( cons @ TA @ A @ B ) @ C )
      = ( cons @ TA @ A @ ( append @ TA @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(42,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( member @ TA @ ( hd @ TA @ A ) @ ( set2 @ TA @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_hd__in__set) ).

thf(396,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)],[42]) ).

thf(202,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( ( cons @ TA @ ( hd @ TA @ A ) @ ( tl @ TA @ A ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_list_Ocollapse) ).

thf(998,plain,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( ( cons @ TA @ ( hd @ TA @ A ) @ ( tl @ TA @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(48,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( suffix @ TA @ A @ B )
     => ( ( suffix @ TA @ B @ A )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_suffix__order_Odual__order_Oantisym) ).

thf(411,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( suffix @ TA @ A @ B )
     => ( ( suffix @ TA @ B @ A )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(1,conjecture,
    graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ( append @ node @ ns @ ( tl @ node @ ri ) ) @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ( append @ node @ ns @ ( tl @ node @ ri ) ) @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(265,plain,
    ~ ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ( append @ node @ ns @ ( tl @ node @ ri ) ) @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(101,axiom,
    ! [A: g,B: node,C: list @ node,D: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( B
        = ( hd @ node @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_old_Opath2__hd) ).

thf(602,plain,
    ! [A: g,B: node,C: list @ node,D: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( B
        = ( hd @ node @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(197,axiom,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( member @ TA @ A @ ( set2 @ TA @ B ) )
      = ( ? [C: list @ TA,D: list @ TA] :
            ( B
            = ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_in__set__conv__decomp) ).

thf(981,plain,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( member @ TA @ A @ ( set2 @ TA @ B ) )
      = ( ? [C: list @ TA,D: list @ TA] :
            ( B
            = ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(39,axiom,
    ! [TA: $tType,A: set @ TA,B: TA > $o] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ B ) )
      = ( ! [C: TA] :
            ( ( member @ TA @ C @ A )
           => ( B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_subset__Collect__conv) ).

thf(380,plain,
    ! [TA: $tType,A: set @ TA,B: TA > $o] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ B ) )
      = ( ! [C: TA] :
            ( ( member @ TA @ C @ A )
           => ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(123,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( ( hd @ TA @ ( append @ TA @ A @ B ) )
        = ( hd @ TA @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_hd__append2) ).

thf(678,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( ( hd @ TA @ ( append @ TA @ A @ B ) )
        = ( hd @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(116,axiom,
    member @ val @ r @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ g2 @ pred_phi_r ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_rs_H__props_I3_J) ).

thf(661,plain,
    member @ val @ r @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ g2 @ pred_phi_r ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(183,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: TA] :
      ( ( suffix @ TA @ A @ ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
      = ( ( A
          = ( nil @ TA ) )
        | ? [D: list @ TA] :
            ( ( A
              = ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
            & ( suffix @ TA @ D @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_suffix__snoc) ).

thf(925,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: TA] :
      ( ( suffix @ TA @ A @ ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
      = ( ( A
          = ( nil @ TA ) )
        | ? [D: list @ TA] :
            ( ( A
              = ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
            & ( suffix @ TA @ D @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(78,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/sandbox/benchmark/theBenchmark.p',fact_103_transpose_Ocases) ).

thf(534,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)],[78]) ).

thf(210,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( ( tl @ TA @ ( append @ TA @ A @ B ) )
        = ( append @ TA @ ( tl @ TA @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_tl__append2) ).

thf(1021,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( ( tl @ TA @ ( append @ TA @ A @ B ) )
        = ( append @ TA @ ( tl @ TA @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(216,axiom,
    ( ( i
     != ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
   => ( ( ( i
         != ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
       => ( m != i ) )
     => ~ ( ( i
           != ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
         => ( m = i ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11__092_060open_062_092_060And_062thesis_O_A_092_060lbrakk_062i_A_061_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_A_092_060Longrightarrow_062_Athesis_059_A_092_060lbrakk_062i_A_092_060noteq_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_059_Am_A_061_Ai_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_059_A_092_060lbrakk_062i_A_092_060noteq_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_059_Am_A_092_060noteq_062_Ai_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).

thf(1042,plain,
    ( ( i
     != ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
   => ( ( ( i
         != ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
       => ( m != i ) )
     => ~ ( ( i
           != ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
         => ( m = i ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(99,axiom,
    graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ s ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_assms_I8_J) ).

thf(598,plain,
    graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ s ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(41,axiom,
    ! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
      ( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
     => ( ! [D: list @ TA] : ( A @ D @ ( nil @ TA ) )
       => ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
              ( ( A @ E @ ( cons @ TA @ F @ G ) )
             => ( ( A @ ( cons @ TA @ D @ E ) @ G )
               => ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) ) )
         => ( A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_shuffles_Oinduct) ).

thf(392,plain,
    ! [TA: $tType,A: ( list @ TA ) > ( list @ TA ) > $o,B: list @ TA,C: list @ TA] :
      ( ! [D: list @ TA] : ( A @ ( nil @ TA ) @ D )
     => ( ! [D: list @ TA] : ( A @ D @ ( nil @ TA ) )
       => ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
              ( ( A @ E @ ( cons @ TA @ F @ G ) )
             => ( ( A @ ( cons @ TA @ D @ E ) @ G )
               => ( A @ ( cons @ TA @ D @ E ) @ ( cons @ TA @ F @ G ) ) ) )
         => ( A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(7,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( collect @ TA
        @ ^ [B: TA] : ( member @ TA @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).

thf(275,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( collect @ TA
        @ ^ [B: TA] : ( member @ TA @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(133,axiom,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( member @ TA @ A @ ( set2 @ TA @ B ) )
      = ( ? [C: list @ TA,D: list @ TA] :
            ( ( B
              = ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) )
            & ~ ( member @ TA @ A @ ( set2 @ TA @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_in__set__conv__decomp__first) ).

thf(729,plain,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( member @ TA @ A @ ( set2 @ TA @ B ) )
      = ( ? [C: list @ TA,D: list @ TA] :
            ( ( B
              = ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) )
            & ~ ( member @ TA @ A @ ( set2 @ TA @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(260,axiom,
    ! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
      ( ( suffix @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) @ ( append @ TA @ C @ ( cons @ TA @ D @ ( nil @ TA ) ) ) )
      = ( ( B = D )
        & ( suffix @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_snoc__suffix__snoc) ).

thf(1255,plain,
    ! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
      ( ( suffix @ TA @ ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) ) @ ( append @ TA @ C @ ( cons @ TA @ D @ ( nil @ TA ) ) ) )
      = ( ( B = D )
        & ( suffix @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(14,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( suffix @ TA @ A @ ( nil @ TA ) )
      = ( A
        = ( nil @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_suffix__Nil) ).

thf(302,plain,
    ! [TA: $tType,A: list @ TA] :
      ( ( suffix @ TA @ A @ ( nil @ TA ) )
      = ( A
        = ( nil @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(168,axiom,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( member @ TA @ A @ ( set2 @ TA @ B ) )
     => ? [C: list @ TA,D: list @ TA] :
          ( ( B
            = ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) )
          & ~ ( member @ TA @ A @ ( set2 @ TA @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_split__list__first) ).

thf(862,plain,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( member @ TA @ A @ ( set2 @ TA @ B ) )
     => ? [C: list @ TA,D: list @ TA] :
          ( ( B
            = ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) )
          & ~ ( member @ TA @ A @ ( set2 @ TA @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(28,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/sandbox/benchmark/theBenchmark.p',fact_101_remdups__adj_Ocases) ).

thf(349,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)],[28]) ).

thf(32,axiom,
    ! [TA: $tType] :
      ( ( ord @ TA )
     => ! [A: list @ TA] :
          ( ! [B: TA,C: list @ TA] :
              ( A
             != ( cons @ TA @ B @ C ) )
         => ( A
            = ( nil @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_min__list_Ocases) ).

thf(361,plain,
    ! [TA: $tType] :
      ( ( ord @ TA )
     => ! [A: list @ TA] :
          ( ! [B: TA,C: list @ TA] :
              ( A
             != ( cons @ TA @ B @ C ) )
         => ( A
            = ( nil @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(109,axiom,
    ! [A: g,B: node,C: list @ node,D: node,E: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( ( member @ node @ E @ ( set2 @ node @ C ) )
       => ~ ! [F: list @ node] :
              ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ F @ E )
             => ! [G: list @ node] :
                  ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ E @ G @ D )
                 => ( ( C
                      = ( append @ node @ F @ ( tl @ node @ G ) ) )
                   => ( C
                     != ( append @ node @ ( butlast @ node @ F ) @ G ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_old_Opath2__split__ex) ).

thf(625,plain,
    ! [A: g,B: node,C: list @ node,D: node,E: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( ( member @ node @ E @ ( set2 @ node @ C ) )
       => ~ ! [F: list @ node] :
              ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ F @ E )
             => ! [G: list @ node] :
                  ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ E @ G @ D )
                 => ( ( C
                      = ( append @ node @ F @ ( tl @ node @ G ) ) )
                   => ( C
                     != ( append @ node @ ( butlast @ node @ F ) @ G ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(118,axiom,
    ! [A: g] : ( invar @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_old_Oinvar) ).

thf(665,plain,
    ! [A: g] : ( invar @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(237,axiom,
    ! [TA: $tType,A: TA,B: TA,C: list @ TA,D: TA,E: TA,F: list @ TA] :
      ( ( ( cons @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) )
        = ( append @ TA @ C @ ( cons @ TA @ D @ ( cons @ TA @ E @ F ) ) ) )
      = ( ( C
          = ( nil @ TA ) )
        & ( A = D )
        & ( B = E )
        & ( F
          = ( nil @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_list__ee__eq__leel_I1_J) ).

thf(1159,plain,
    ! [TA: $tType,A: TA,B: TA,C: list @ TA,D: TA,E: TA,F: list @ TA] :
      ( ( ( cons @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) )
        = ( append @ TA @ C @ ( cons @ TA @ D @ ( cons @ TA @ E @ F ) ) ) )
      = ( ( C
          = ( nil @ TA ) )
        & ( A = D )
        & ( B = E )
        & ( F
          = ( nil @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(212,axiom,
    ! [TA: $tType,A: TA,B: list @ TA,C: list @ TA] :
      ( ( ( member @ TA @ A @ ( set2 @ TA @ ( butlast @ TA @ B ) ) )
        | ( member @ TA @ A @ ( set2 @ TA @ ( butlast @ TA @ C ) ) ) )
     => ( member @ TA @ A @ ( set2 @ TA @ ( butlast @ TA @ ( append @ TA @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_in__set__butlast__appendI) ).

thf(1027,plain,
    ! [TA: $tType,A: TA,B: list @ TA,C: list @ TA] :
      ( ( ( member @ TA @ A @ ( set2 @ TA @ ( butlast @ TA @ B ) ) )
        | ( member @ TA @ A @ ( set2 @ TA @ ( butlast @ TA @ C ) ) ) )
     => ( member @ TA @ A @ ( set2 @ TA @ ( butlast @ TA @ ( append @ TA @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(232,axiom,
    linorder @ node,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_1) ).

thf(1128,plain,
    linorder @ node,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(131,axiom,
    ! [TA: $tType,A: TA,B: list @ TA,C: TA] :
      ( ( member @ TA @ A @ ( set2 @ TA @ B ) )
     => ( ( member @ TA @ C @ ( set2 @ TA @ B ) )
       => ( ( ( A = C )
           => ! [D: list @ TA,E: list @ TA] :
                ( B
               != ( append @ TA @ D @ ( cons @ TA @ C @ E ) ) ) )
         => ( ( ( A != C )
             => ! [D: list @ TA,E: list @ TA,F: list @ TA] :
                  ( B
                 != ( append @ TA @ D @ ( cons @ TA @ A @ ( append @ TA @ E @ ( cons @ TA @ C @ F ) ) ) ) ) )
           => ~ ( ( A != C )
               => ! [D: list @ TA,E: list @ TA,F: list @ TA] :
                    ( B
                   != ( append @ TA @ D @ ( cons @ TA @ C @ ( append @ TA @ E @ ( cons @ TA @ A @ F ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_xy__in__set__cases) ).

thf(710,plain,
    ! [TA: $tType,A: TA,B: list @ TA,C: TA] :
      ( ( member @ TA @ A @ ( set2 @ TA @ B ) )
     => ( ( member @ TA @ C @ ( set2 @ TA @ B ) )
       => ( ( ( A = C )
           => ! [D: list @ TA,E: list @ TA] :
                ( B
               != ( append @ TA @ D @ ( cons @ TA @ C @ E ) ) ) )
         => ( ( ( A != C )
             => ! [D: list @ TA,E: list @ TA,F: list @ TA] :
                  ( B
                 != ( append @ TA @ D @ ( cons @ TA @ A @ ( append @ TA @ E @ ( cons @ TA @ C @ F ) ) ) ) ) )
           => ~ ( ( A != C )
               => ! [D: list @ TA,E: list @ TA,F: list @ TA] :
                    ( B
                   != ( append @ TA @ D @ ( cons @ TA @ C @ ( append @ TA @ E @ ( cons @ TA @ A @ F ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(22,axiom,
    ! [TA: $tType,A: list @ TA,B: TA] :
      ( ( ( A
          = ( nil @ TA ) )
       => ( ( butlast @ TA @ ( cons @ TA @ B @ A ) )
          = ( nil @ TA ) ) )
      & ( ( A
         != ( nil @ TA ) )
       => ( ( butlast @ TA @ ( cons @ TA @ B @ A ) )
          = ( cons @ TA @ B @ ( butlast @ TA @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_butlast_Osimps_I2_J) ).

thf(324,plain,
    ! [TA: $tType,A: list @ TA,B: TA] :
      ( ( ( A
          = ( nil @ TA ) )
       => ( ( butlast @ TA @ ( cons @ TA @ B @ A ) )
          = ( nil @ TA ) ) )
      & ( ( A
         != ( nil @ TA ) )
       => ( ( butlast @ TA @ ( cons @ TA @ B @ A ) )
          = ( cons @ TA @ B @ ( butlast @ TA @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(207,axiom,
    ! [A: g,B: node,C: list @ node] :
      ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons @ node @ B @ C ) )
     => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons @ node @ B @ ( nil @ node ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_old_Opath__hd) ).

thf(1012,plain,
    ! [A: g,B: node,C: list @ node] :
      ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons @ node @ B @ C ) )
     => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons @ node @ B @ ( nil @ node ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(10,axiom,
    ! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
      ( ( prefix @ TA @ ( cons @ TA @ A @ B ) @ ( cons @ TA @ C @ D ) )
      = ( ( A = C )
        & ( prefix @ TA @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_Cons__prefix__Cons) ).

thf(285,plain,
    ! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
      ( ( prefix @ TA @ ( cons @ TA @ A @ B ) @ ( cons @ TA @ C @ D ) )
      = ( ( A = C )
        & ( prefix @ TA @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(180,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( ( ( append @ TA @ A @ B )
          = ( cons @ TA @ C @ ( nil @ TA ) ) )
        = ( ( A
            = ( cons @ TA @ C @ ( nil @ TA ) ) )
          & ( B
            = ( nil @ TA ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_list__se__match_I1_J) ).

thf(916,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( ( ( append @ TA @ A @ B )
          = ( cons @ TA @ C @ ( nil @ TA ) ) )
        = ( ( A
            = ( cons @ TA @ C @ ( nil @ TA ) ) )
          & ( B
            = ( nil @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(64,axiom,
    ! [TA: $tType,A: list @ TA] : ( prefix @ TA @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_prefix__order_Odual__order_Orefl) ).

thf(467,plain,
    ! [TA: $tType,A: list @ TA] : ( prefix @ TA @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(224,axiom,
    ! [A: g,B: node,C: node] :
      ~ ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( nil @ node ) @ C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_old_Opath2__not__Nil2) ).

thf(1089,plain,
    ! [A: g,B: node,C: node] :
      ~ ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( nil @ node ) @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(209,axiom,
    ! [A: g,B: list @ node] :
      ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B )
     => ( B
       != ( nil @ node ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_old_Opath__not__Nil) ).

thf(1017,plain,
    ! [A: g,B: list @ node] :
      ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B )
     => ( B
       != ( nil @ node ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(45,axiom,
    ! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
      ( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
     => ( ! [D: TA > TA > $o,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
       => ( ! [D: TA > TA > $o,E: TA,F: TA,G: list @ TA] :
              ( ( A @ D @ ( cons @ TA @ F @ G ) )
             => ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
         => ( A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_successively_Oinduct) ).

thf(403,plain,
    ! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
      ( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
     => ( ! [D: TA > TA > $o,E: TA] : ( A @ D @ ( cons @ TA @ E @ ( nil @ TA ) ) )
       => ( ! [D: TA > TA > $o,E: TA,F: TA,G: list @ TA] :
              ( ( A @ D @ ( cons @ TA @ F @ G ) )
             => ( A @ D @ ( cons @ TA @ E @ ( cons @ TA @ F @ G ) ) ) )
         => ( A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(205,axiom,
    ( ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r )
   != ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__092_060open_062defNode_Ag_A_092_060phi_062_092_060_094sub_062r_A_092_060noteq_062_AdefNode_Ag_Ar_092_060close_062) ).

thf(1006,plain,
    ( ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r )
   != ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(170,axiom,
    ! [A: g,B: node,C: list @ node,D: node,E: list @ node,F: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( ( prefix @ node @ ( append @ node @ E @ ( cons @ node @ F @ ( nil @ node ) ) ) @ C )
       => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append @ node @ E @ ( cons @ node @ F @ ( nil @ node ) ) ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_old_Opath2__prefix) ).

thf(869,plain,
    ! [A: g,B: node,C: list @ node,D: node,E: list @ node,F: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( ( prefix @ node @ ( append @ node @ E @ ( cons @ node @ F @ ( nil @ node ) ) ) @ C )
       => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append @ node @ E @ ( cons @ node @ F @ ( nil @ node ) ) ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(199,axiom,
    ! [A: g,B: node,C: list @ node,D: node,E: list @ node,F: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ F )
       => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append @ node @ C @ ( tl @ node @ E ) ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_old_Opath2__app) ).

thf(989,plain,
    ! [A: g,B: node,C: list @ node,D: node,E: list @ node,F: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ F )
       => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append @ node @ C @ ( tl @ node @ E ) ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(229,axiom,
    ! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
      ( ( ( cons @ TA @ A @ ( nil @ TA ) )
        = ( append @ TA @ B @ ( cons @ TA @ C @ D ) ) )
      = ( ( B
          = ( nil @ TA ) )
        & ( C = A )
        & ( D
          = ( nil @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_list__e__eq__lel_I1_J) ).

thf(1111,plain,
    ! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
      ( ( ( cons @ TA @ A @ ( nil @ TA ) )
        = ( append @ TA @ B @ ( cons @ TA @ C @ D ) ) )
      = ( ( B
          = ( nil @ TA ) )
        & ( C = A )
        & ( D
          = ( nil @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(252,axiom,
    graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ ri @ i,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_ri__props_I1_J) ).

thf(1227,plain,
    graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ ri @ i,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(246,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ~ ! [B: list @ TA,C: TA] :
            ( A
           != ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_rev__exhaust) ).

thf(1182,plain,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ~ ! [B: list @ TA,C: TA] :
            ( A
           != ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(79,axiom,
    ! [TA: $tType] :
      ( ( (=) @ ( list @ TA ) )
      = ( ^ [A: list @ TA,B: list @ TA] :
            ( ( prefix @ TA @ A @ B )
            & ( prefix @ TA @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_prefix__order_Oeq__iff) ).

thf(537,plain,
    ! [TA: $tType] :
      ( ( (=) @ ( list @ TA ) )
      = ( ^ [A: list @ TA,B: list @ TA] :
            ( ( prefix @ TA @ A @ B )
            & ( prefix @ TA @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(67,axiom,
    ! [TA: $tType,A: list @ TA] : ( prefix @ TA @ ( nil @ TA ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_prefix__code_I1_J) ).

thf(476,plain,
    ! [TA: $tType,A: list @ TA] : ( prefix @ TA @ ( nil @ TA ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(76,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,F: list @ TA] :
            ( ( A @ E @ F )
           => ( A @ ( cons @ TB @ D @ E ) @ F ) )
       => ( ! [D: TA,E: list @ TB,F: list @ TA] :
              ( ( A @ E @ F )
             => ( A @ E @ ( cons @ TA @ D @ F ) ) )
         => ( A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_list__2pre__induct) ).

thf(526,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,F: list @ TA] :
            ( ( A @ E @ F )
           => ( A @ ( cons @ TB @ D @ E ) @ F ) )
       => ( ! [D: TA,E: list @ TB,F: list @ TA] :
              ( ( A @ E @ F )
             => ( A @ E @ ( cons @ TA @ D @ F ) ) )
         => ( A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(112,axiom,
    graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms2 @ i,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_ms_H__props_I1_J) ).

thf(637,plain,
    graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms2 @ i,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(215,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( ( nil @ TA )
        = ( append @ TA @ A @ B ) )
      = ( ( A
          = ( nil @ TA ) )
        & ( B
          = ( nil @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_Nil__is__append__conv) ).

thf(1039,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( ( nil @ TA )
        = ( append @ TA @ A @ B ) )
      = ( ( A
          = ( nil @ TA ) )
        & ( B
          = ( nil @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(108,axiom,
    ! [TA: $tType] :
      ( ( append @ TA @ ( nil @ TA ) )
      = ( ^ [A: list @ TA] : A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_empty__append__eq__id) ).

thf(622,plain,
    ! [TA: $tType] :
      ( ( append @ TA @ ( nil @ TA ) )
      = ( ^ [A: list @ TA] : A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(230,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( prefix @ TA @ ( append @ TA @ A @ B ) @ A )
      = ( B
        = ( nil @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_same__prefix__nil) ).

thf(1114,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( prefix @ TA @ ( append @ TA @ A @ B ) @ A )
      = ( B
        = ( nil @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(254,axiom,
    ! [A: g,B: node] : ( finite_finite @ val @ ( defs @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_defs__finite) ).

thf(1231,plain,
    ! [A: g,B: node] : ( finite_finite @ val @ ( defs @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(250,axiom,
    ! [TA: $tType,A: list @ TA,B: TA > $o] :
      ( ? [C: TA] :
          ( ( member @ TA @ C @ ( set2 @ TA @ A ) )
          & ( B @ C ) )
     => ~ ! [C: list @ TA,D: TA,E: list @ TA] :
            ( ( A
              = ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
           => ( ( B @ D )
             => ~ ! [F: TA] :
                    ( ( member @ TA @ F @ ( set2 @ TA @ E ) )
                   => ~ ( B @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_split__list__last__propE) ).

thf(1192,plain,
    ! [TA: $tType,A: list @ TA,B: TA > $o] :
      ( ? [C: TA] :
          ( ( member @ TA @ C @ ( set2 @ TA @ A ) )
          & ( B @ C ) )
     => ~ ! [C: list @ TA,D: TA,E: list @ TA] :
            ( ( A
              = ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
           => ( ( B @ D )
             => ~ ! [F: TA] :
                    ( ( member @ TA @ F @ ( set2 @ TA @ E ) )
                   => ~ ( B @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(60,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/sandbox/benchmark/theBenchmark.p',fact_43_list_Oinject) ).

thf(457,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)],[60]) ).

thf(198,axiom,
    ! [A: g,B: node,C: list @ node,D: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( C
       != ( nil @ node ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_old_Opath2__not__Nil) ).

thf(984,plain,
    ! [A: g,B: node,C: list @ node,D: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( C
       != ( nil @ node ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(146,axiom,
    ! [TA: $tType,A: list @ TA,B: TA > $o] :
      ( ? [C: TA] :
          ( ( member @ TA @ C @ ( set2 @ TA @ A ) )
          & ( B @ C ) )
     => ? [C: list @ TA,D: TA] :
          ( ? [E: list @ TA] :
              ( A
              = ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
          & ( B @ D )
          & ! [E: TA] :
              ( ( member @ TA @ E @ ( set2 @ TA @ C ) )
             => ~ ( B @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_split__list__first__prop) ).

thf(779,plain,
    ! [TA: $tType,A: list @ TA,B: TA > $o] :
      ( ? [C: TA] :
          ( ( member @ TA @ C @ ( set2 @ TA @ A ) )
          & ( B @ C ) )
     => ? [C: list @ TA,D: TA] :
          ( ? [E: list @ TA] :
              ( A
              = ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
          & ( B @ D )
          & ! [E: TA] :
              ( ( member @ TA @ E @ ( set2 @ TA @ C ) )
             => ~ ( B @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(150,axiom,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( member @ TA @ A @ ( set2 @ TA @ B ) )
     => ? [C: list @ TA,D: list @ TA] :
          ( ( B
            = ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) )
          & ~ ( member @ TA @ A @ ( set2 @ TA @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_split__list__last) ).

thf(792,plain,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( member @ TA @ A @ ( set2 @ TA @ B ) )
     => ? [C: list @ TA,D: list @ TA] :
          ( ( B
            = ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) )
          & ~ ( member @ TA @ A @ ( set2 @ TA @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(223,axiom,
    ! [TA: $tType,A: list @ TA,B: set @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( ( ord_less_eq @ ( set @ TA ) @ ( set2 @ TA @ A ) @ B )
       => ( ord_less_eq @ ( set @ TA ) @ ( set2 @ TA @ ( tl @ TA @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_tl__subset) ).

thf(1086,plain,
    ! [TA: $tType,A: list @ TA,B: set @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( ( ord_less_eq @ ( set @ TA ) @ ( set2 @ TA @ A ) @ B )
       => ( ord_less_eq @ ( set @ TA ) @ ( set2 @ TA @ ( tl @ TA @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(3,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TA )
     => ( ord @ ( TB > TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).

thf(266,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TA )
     => ( ord @ ( TB > TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(110,axiom,
    ( rs2
    = ( append @ node @ rs @ ( cons @ node @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) @ ( nil @ node ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_rs__def) ).

thf(633,plain,
    ( rs2
    = ( append @ node @ rs @ ( cons @ node @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) @ ( nil @ node ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(153,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( A
        = ( append @ TA @ B @ A ) )
      = ( B
        = ( nil @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_self__append__conv2) ).

thf(805,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( A
        = ( append @ TA @ B @ A ) )
      = ( B
        = ( nil @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(17,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
      = ( ? [B: TA,C: list @ TA] :
            ( A
            = ( cons @ TA @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_neq__Nil__conv) ).

thf(311,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)],[17]) ).

thf(141,axiom,
    ! [A: g,B: list @ node,C: node] :
      ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B )
     => ( ( member @ node @ C @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ ( hd @ node @ B ) ) ) )
       => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons @ node @ C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_old_OCons__path) ).

thf(765,plain,
    ! [A: g,B: list @ node,C: node] :
      ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B )
     => ( ( member @ node @ C @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ ( hd @ node @ B ) ) ) )
       => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons @ node @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(242,axiom,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( tl @ TA @ ( cons @ TA @ A @ B ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_list_Osel_I3_J) ).

thf(1170,plain,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( tl @ TA @ ( cons @ TA @ A @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(247,axiom,
    ! [A: g,B: list @ node,C: node,D: list @ node] :
      ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( append @ node @ B @ ( cons @ node @ C @ D ) ) )
     => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( append @ node @ B @ ( cons @ node @ C @ ( nil @ node ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_old_Opath__split_I1_J) ).

thf(1185,plain,
    ! [A: g,B: list @ node,C: node,D: list @ node] :
      ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( append @ node @ B @ ( cons @ node @ C @ D ) ) )
     => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( append @ node @ B @ ( cons @ node @ C @ ( nil @ node ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(117,axiom,
    ! [TA: $tType,A: list @ TA,B: TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( ( member @ TA @ B @ ( set2 @ TA @ ( tl @ TA @ A ) ) )
       => ( member @ TA @ B @ ( set2 @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_list_Oset__sel_I2_J) ).

thf(662,plain,
    ! [TA: $tType,A: list @ TA,B: TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( ( member @ TA @ B @ ( set2 @ TA @ ( tl @ TA @ A ) ) )
       => ( member @ TA @ B @ ( set2 @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(144,axiom,
    ! [A: node,B: g,C: node] :
      ( ( member @ node @ A @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ B @ C ) ) )
     => ( ( invar @ B )
       => ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_old_Opredecessor__is__node) ).

thf(773,plain,
    ! [A: node,B: g,C: node] :
      ( ( member @ node @ A @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ B @ C ) ) )
     => ( ( invar @ B )
       => ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(95,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( finite_finite @ TA @ A )
     => ? [B: list @ TA] :
          ( ( set2 @ TA @ B )
          = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_finite__list) ).

thf(586,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( finite_finite @ TA @ A )
     => ? [B: list @ TA] :
          ( ( set2 @ TA @ B )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(176,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
      = ( ? [B: list @ TA,C: TA] :
            ( A
            = ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_neq__Nil__rev__conv) ).

thf(906,plain,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
      = ( ? [B: list @ TA,C: TA] :
            ( A
            = ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(259,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( A
        = ( append @ TA @ B @ C ) )
     => ( suffix @ TA @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_suffixI) ).

thf(1251,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( A
        = ( append @ TA @ B @ C ) )
     => ( suffix @ TA @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(51,axiom,
    ! [TA: $tType,A: list @ TA] : ( prefix @ TA @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_prefix__order_Oorder__refl) ).

thf(425,plain,
    ! [TA: $tType,A: list @ TA] : ( prefix @ TA @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(53,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ~ ! [B: TA,C: list @ TA] :
            ( A
           != ( cons @ TA @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_list_Oexhaust) ).

thf(430,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)],[53]) ).

thf(157,axiom,
    ! [TA: $tType,A: list @ TA,B: TA > $o] :
      ( ( ? [C: TA] :
            ( ( member @ TA @ C @ ( set2 @ TA @ A ) )
            & ( B @ C ) ) )
      = ( ? [C: list @ TA,D: TA,E: list @ TA] :
            ( ( A
              = ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
            & ( B @ D )
            & ! [F: TA] :
                ( ( member @ TA @ F @ ( set2 @ TA @ E ) )
               => ~ ( B @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_split__list__last__prop__iff) ).

thf(824,plain,
    ! [TA: $tType,A: list @ TA,B: TA > $o] :
      ( ( ? [C: TA] :
            ( ( member @ TA @ C @ ( set2 @ TA @ A ) )
            & ( B @ C ) ) )
      = ( ? [C: list @ TA,D: TA,E: list @ TA] :
            ( ( A
              = ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
            & ( B @ D )
            & ! [F: TA] :
                ( ( member @ TA @ F @ ( set2 @ TA @ E ) )
               => ~ ( B @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(166,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( append @ TA @ ( append @ TA @ A @ B ) @ C )
      = ( append @ TA @ A @ ( append @ TA @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_append_Oassoc) ).

thf(856,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( append @ TA @ ( append @ TA @ A @ B ) @ C )
      = ( append @ TA @ A @ ( append @ TA @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(37,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( prefix @ TA @ A @ B )
     => ( ( prefix @ TA @ B @ A )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_prefix__order_Oantisym) ).

thf(375,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( prefix @ TA @ A @ B )
     => ( ( prefix @ TA @ B @ A )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(94,axiom,
    ! [TA: $tType,A: list @ TA] : ( suffix @ TA @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_suffix__order_Oorder__refl) ).

thf(584,plain,
    ! [TA: $tType,A: list @ TA] : ( suffix @ TA @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(175,axiom,
    ! [A: node,B: g] :
      ( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
     => ( ( invar @ B )
       => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ B @ A @ ( cons @ node @ A @ ( nil @ node ) ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_old_Oempty__path2) ).

thf(904,plain,
    ! [A: node,B: g] :
      ( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
     => ( ( invar @ B )
       => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ B @ A @ ( cons @ node @ A @ ( nil @ node ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(50,axiom,
    ! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
      ( ( suffix @ TA @ ( cons @ TA @ A @ B ) @ ( cons @ TA @ C @ D ) )
     => ( suffix @ TA @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_suffix__ConsD2) ).

thf(423,plain,
    ! [TA: $tType,A: TA,B: list @ TA,C: TA,D: list @ TA] :
      ( ( suffix @ TA @ ( cons @ TA @ A @ B ) @ ( cons @ TA @ C @ D ) )
     => ( suffix @ TA @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(134,axiom,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( A
       != ( hd @ TA @ B ) )
     => ( ( member @ TA @ A @ ( set2 @ TA @ B ) )
       => ( member @ TA @ A @ ( set2 @ TA @ ( tl @ TA @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_not__hd__in__tl) ).

thf(732,plain,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( A
       != ( hd @ TA @ B ) )
     => ( ( member @ TA @ A @ ( set2 @ TA @ B ) )
       => ( member @ TA @ A @ ( set2 @ TA @ ( tl @ TA @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(91,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ( ord @ TA ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Orderings_Olinorder___Orderings_Oord) ).

thf(577,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ( ord @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(92,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/sandbox/benchmark/theBenchmark.p',fact_248_set__subset__Cons) ).

thf(579,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)],[92]) ).

thf(82,axiom,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( hd @ TA @ ( cons @ TA @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_list_Osel_I1_J) ).

thf(545,plain,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( hd @ TA @ ( cons @ TA @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(114,axiom,
    ! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: list @ TA,E: TA,F: list @ TA] :
      ( ( ( append @ TA @ A @ ( cons @ TA @ B @ C ) )
        = ( append @ TA @ D @ ( cons @ TA @ E @ F ) ) )
     => ( ! [G: list @ TA] :
            ( ( A
              = ( append @ TA @ D @ ( cons @ TA @ E @ G ) ) )
           => ( F
             != ( append @ TA @ G @ ( cons @ TA @ B @ C ) ) ) )
       => ( ( ( D = A )
           => ( ( E = B )
             => ( F != C ) ) )
         => ~ ! [G: list @ TA] :
                ( ( D
                  = ( append @ TA @ A @ ( cons @ TA @ B @ G ) ) )
               => ( C
                 != ( append @ TA @ G @ ( cons @ TA @ E @ F ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_list__match__lel__lel) ).

thf(641,plain,
    ! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: list @ TA,E: TA,F: list @ TA] :
      ( ( ( append @ TA @ A @ ( cons @ TA @ B @ C ) )
        = ( append @ TA @ D @ ( cons @ TA @ E @ F ) ) )
     => ( ! [G: list @ TA] :
            ( ( A
              = ( append @ TA @ D @ ( cons @ TA @ E @ G ) ) )
           => ( F
             != ( append @ TA @ G @ ( cons @ TA @ B @ C ) ) ) )
       => ( ( ( D = A )
           => ( ( E = B )
             => ( F != C ) ) )
         => ~ ! [G: list @ TA] :
                ( ( D
                  = ( append @ TA @ A @ ( cons @ TA @ B @ G ) ) )
               => ( C
                 != ( append @ TA @ G @ ( cons @ TA @ E @ F ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(234,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( suffix @ TA @ A @ B )
     => ~ ! [C: list @ TA] :
            ( B
           != ( append @ TA @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_suffixE) ).

thf(1139,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( suffix @ TA @ A @ B )
     => ~ ! [C: list @ TA] :
            ( B
           != ( append @ TA @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(56,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/sandbox/benchmark/theBenchmark.p',fact_93_map__tailrec__rev_Oinduct) ).

thf(445,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)],[56]) ).

thf(89,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( suffix @ TA @ A @ B )
     => ( ( suffix @ TA @ B @ A )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_suffix__order_Oantisym) ).

thf(572,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( suffix @ TA @ A @ B )
     => ( ( suffix @ TA @ B @ A )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(225,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( prefix @ TA @ ( append @ TA @ A @ B ) @ ( append @ TA @ A @ C ) )
      = ( prefix @ TA @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_same__prefix__prefix) ).

thf(1092,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( prefix @ TA @ ( append @ TA @ A @ B ) @ ( append @ TA @ A @ C ) )
      = ( prefix @ TA @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(181,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( ( ( append @ TA @ B @ A )
          = ( cons @ TA @ C @ ( nil @ TA ) ) )
        = ( ( B
            = ( nil @ TA ) )
          & ( A
            = ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_list__se__match_I2_J) ).

thf(919,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( ( ( append @ TA @ B @ A )
          = ( cons @ TA @ C @ ( nil @ TA ) ) )
        = ( ( B
            = ( nil @ TA ) )
          & ( A
            = ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(80,axiom,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( cons @ TA @ A @ B )
     != B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_not__Cons__self2) ).

thf(540,plain,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( cons @ TA @ A @ B )
     != B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(261,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( append @ TA @ ( append @ TA @ A @ B ) @ C )
      = ( append @ TA @ A @ ( append @ TA @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_append__assoc) ).

thf(1258,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( append @ TA @ ( append @ TA @ A @ B ) @ C )
      = ( append @ TA @ A @ ( append @ TA @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(129,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( ( cons @ TA @ ( hd @ TA @ A ) @ ( tl @ TA @ A ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_hd__Cons__tl) ).

thf(704,plain,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( ( cons @ TA @ ( hd @ TA @ A ) @ ( tl @ TA @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(46,axiom,
    ! [TA: $tType] :
      ( ( (=) @ ( list @ TA ) )
      = ( ^ [A: list @ TA,B: list @ TA] :
            ( ( suffix @ TA @ B @ A )
            & ( suffix @ TA @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_suffix__order_Odual__order_Oeq__iff) ).

thf(406,plain,
    ! [TA: $tType] :
      ( ( (=) @ ( list @ TA ) )
      = ( ^ [A: list @ TA,B: list @ TA] :
            ( ( suffix @ TA @ B @ A )
            & ( suffix @ TA @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(124,axiom,
    ! [A: g,B: node,C: list @ node,D: node,E: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( ( member @ node @ D @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ E ) ) )
       => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append @ node @ C @ ( cons @ node @ E @ ( nil @ node ) ) ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_old_Opath2__snoc) ).

thf(681,plain,
    ! [A: g,B: node,C: list @ node,D: node,E: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( ( member @ node @ D @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ E ) ) )
       => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append @ node @ C @ ( cons @ node @ E @ ( nil @ node ) ) ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(136,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( butlast @ TA @ ( tl @ TA @ A ) )
      = ( tl @ TA @ ( butlast @ TA @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_butlast__tl) ).

thf(737,plain,
    ! [TA: $tType,A: list @ TA] :
      ( ( butlast @ TA @ ( tl @ TA @ A ) )
      = ( tl @ TA @ ( butlast @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(107,axiom,
    ~ ! [A: node,B: list @ node] :
        ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ B @ A )
       => ( ( member @ node @ A @ ( set2 @ node @ ms ) )
         => ( ! [C: node] :
                ( ( member @ node @ C @ ( set2 @ node @ ( butlast @ node @ B ) ) )
               => ~ ( member @ node @ C @ ( set2 @ node @ ms ) ) )
           => ~ ( prefix @ node @ B @ rs2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062i_Ari_O_A_092_060lbrakk_062g_A_092_060turnstile_062_AdefNode_Ag_Ar_Nri_092_060rightarrow_062i_059_Ai_A_092_060in_062_Aset_Ams_059_A_092_060forall_062n_092_060in_062set_A_Ibutlast_Ari_J_O_An_A_092_060notin_062_Aset_Ams_059_Aprefix_Ari_Ars_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).

thf(616,plain,
    ~ ! [A: node,B: list @ node] :
        ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ B @ A )
       => ( ( member @ node @ A @ ( set2 @ node @ ms ) )
         => ( ! [C: node] :
                ( ( member @ node @ C @ ( set2 @ node @ ( butlast @ node @ B ) ) )
               => ~ ( member @ node @ C @ ( set2 @ node @ ms ) ) )
           => ~ ( prefix @ node @ B @ rs2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(5,axiom,
    ord @ $o,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_2) ).

thf(271,plain,
    ord @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(100,axiom,
    ! [A: g,B: node,C: list @ node,D: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( member @ node @ B @ ( set2 @ node @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_old_Opath2__hd__in__ns) ).

thf(599,plain,
    ! [A: g,B: node,C: list @ node,D: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( member @ node @ B @ ( set2 @ node @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(147,axiom,
    ! [TA: $tType,A: list @ TA] : ( suffix @ TA @ ( tl @ TA @ A ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_suffix__tl) ).

thf(784,plain,
    ! [TA: $tType,A: list @ TA] : ( suffix @ TA @ ( tl @ TA @ A ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(231,axiom,
    ! [A: g,B: node,C: list @ node,D: node,E: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( ( member @ node @ E @ ( set2 @ node @ C ) )
       => ~ ! [F: list @ node,G: list @ node,H: list @ node] :
              ( ( C
                = ( append @ node @ F @ ( append @ node @ G @ H ) ) )
             => ( ( prefix @ node @ ( append @ node @ F @ ( cons @ node @ E @ ( nil @ node ) ) ) @ C )
               => ( ( suffix @ node @ ( cons @ node @ E @ H ) @ C )
                 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append @ node @ F @ ( cons @ node @ E @ ( nil @ node ) ) ) @ E )
                   => ( ~ ( member @ node @ E @ ( set2 @ node @ F ) )
                     => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ E @ G @ E )
                       => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ E @ ( cons @ node @ E @ H ) @ D )
                         => ( member @ node @ E @ ( set2 @ node @ H ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_old_Opath2__split__first__last) ).

thf(1117,plain,
    ! [A: g,B: node,C: list @ node,D: node,E: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( ( member @ node @ E @ ( set2 @ node @ C ) )
       => ~ ! [F: list @ node,G: list @ node,H: list @ node] :
              ( ( C
                = ( append @ node @ F @ ( append @ node @ G @ H ) ) )
             => ( ( prefix @ node @ ( append @ node @ F @ ( cons @ node @ E @ ( nil @ node ) ) ) @ C )
               => ( ( suffix @ node @ ( cons @ node @ E @ H ) @ C )
                 => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append @ node @ F @ ( cons @ node @ E @ ( nil @ node ) ) ) @ E )
                   => ( ~ ( member @ node @ E @ ( set2 @ node @ F ) )
                     => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ E @ G @ E )
                       => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ E @ ( cons @ node @ E @ H ) @ D )
                         => ( member @ node @ E @ ( set2 @ node @ H ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(58,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/sandbox/benchmark/theBenchmark.p',fact_109_list__induct2_H) ).

thf(451,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)],[58]) ).

thf(87,axiom,
    ! [TA: $tType] :
      ( ( butlast @ TA @ ( nil @ TA ) )
      = ( nil @ TA ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_butlast_Osimps_I1_J) ).

thf(567,plain,
    ! [TA: $tType] :
      ( ( butlast @ TA @ ( nil @ TA ) )
      = ( nil @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(139,axiom,
    ! [A: node] :
      ( ( member @ node @ A @ ( set2 @ node @ ( butlast @ node @ ri ) ) )
     => ~ ( member @ node @ A @ ( set2 @ node @ ms ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_ri__props_I3_J) ).

thf(758,plain,
    ! [A: node] :
      ( ( member @ node @ A @ ( set2 @ node @ ( butlast @ node @ ri ) ) )
     => ~ ( member @ node @ A @ ( set2 @ node @ ms ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(34,axiom,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( nil @ TA )
     != ( cons @ TA @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_list_Odistinct_I1_J) ).

thf(367,plain,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( nil @ TA )
     != ( cons @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(104,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( append @ TA @ A @ ( nil @ TA ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_append_Oright__neutral) ).

thf(609,plain,
    ! [TA: $tType,A: list @ TA] :
      ( ( append @ TA @ A @ ( nil @ TA ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(98,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( A = B )
     => ( A
        = ( append @ TA @ ( nil @ TA ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_eq__Nil__appendI) ).

thf(594,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( A = B )
     => ( A
        = ( append @ TA @ ( nil @ TA ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(163,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( ( tl @ TA @ A )
        = ( nil @ TA ) )
      = ( ( A
          = ( nil @ TA ) )
        | ? [B: TA] :
            ( A
            = ( cons @ TA @ B @ ( nil @ TA ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_tl__Nil) ).

thf(848,plain,
    ! [TA: $tType,A: list @ TA] :
      ( ( ( tl @ TA @ A )
        = ( nil @ TA ) )
      = ( ( A
          = ( nil @ TA ) )
        | ? [B: TA] :
            ( A
            = ( cons @ TA @ B @ ( nil @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(192,axiom,
    ~ ( member @ node @ i @ ( set2 @ node @ ( butlast @ node @ ms2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_ms_H__props_I3_J) ).

thf(964,plain,
    ~ ( member @ node @ i @ ( set2 @ node @ ( butlast @ node @ ms2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(179,axiom,
    linorder @ val,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).

thf(915,plain,
    linorder @ val,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(23,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( prefix @ TA @ A @ B )
     => ( ( prefix @ TA @ C @ B )
       => ( ( prefix @ TA @ A @ C )
          | ( prefix @ TA @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_prefix__same__cases) ).

thf(330,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( prefix @ TA @ A @ B )
     => ( ( prefix @ TA @ C @ B )
       => ( ( prefix @ TA @ A @ C )
          | ( prefix @ TA @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(62,axiom,
    ! [TA: $tType,TB: $tType,A: ( TB > TA > $o ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA > $o,C: list @ TB,D: list @ TA] :
      ( ! [E: TB > TA > $o] : ( A @ E @ ( nil @ TB ) @ ( nil @ TA ) )
     => ( ! [E: TB > TA > $o,F: TB,G: list @ TB,H: TA,I: list @ TA] :
            ( ( A @ E @ G @ I )
           => ( A @ E @ ( cons @ TB @ F @ G ) @ ( cons @ TA @ H @ I ) ) )
       => ( ! [E: TB > TA > $o,F: TB,G: list @ TB] : ( A @ E @ ( cons @ TB @ F @ G ) @ ( nil @ TA ) )
         => ( ! [E: TB > TA > $o,F: TA,G: list @ TA] : ( A @ E @ ( nil @ TB ) @ ( cons @ TA @ F @ G ) )
           => ( A @ B @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_list__all__zip_Oinduct) ).

thf(462,plain,
    ! [TA: $tType,TB: $tType,A: ( TB > TA > $o ) > ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA > $o,C: list @ TB,D: list @ TA] :
      ( ! [E: TB > TA > $o] : ( A @ E @ ( nil @ TB ) @ ( nil @ TA ) )
     => ( ! [E: TB > TA > $o,F: TB,G: list @ TB,H: TA,I: list @ TA] :
            ( ( A @ E @ G @ I )
           => ( A @ E @ ( cons @ TB @ F @ G ) @ ( cons @ TA @ H @ I ) ) )
       => ( ! [E: TB > TA > $o,F: TB,G: list @ TB] : ( A @ E @ ( cons @ TB @ F @ G ) @ ( nil @ TA ) )
         => ( ! [E: TB > TA > $o,F: TA,G: list @ TA] : ( A @ E @ ( nil @ TB ) @ ( cons @ TA @ F @ G ) )
           => ( A @ B @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(152,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( ( A
          = ( nil @ TA ) )
       => ( ( butlast @ TA @ ( append @ TA @ B @ A ) )
          = ( butlast @ TA @ B ) ) )
      & ( ( A
         != ( nil @ TA ) )
       => ( ( butlast @ TA @ ( append @ TA @ B @ A ) )
          = ( append @ TA @ B @ ( butlast @ TA @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_butlast__append) ).

thf(799,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( ( A
          = ( nil @ TA ) )
       => ( ( butlast @ TA @ ( append @ TA @ B @ A ) )
          = ( butlast @ TA @ B ) ) )
      & ( ( A
         != ( nil @ TA ) )
       => ( ( butlast @ TA @ ( append @ TA @ B @ A ) )
          = ( append @ TA @ B @ ( butlast @ TA @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(238,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( ( append @ TA @ A @ B )
        = ( nil @ TA ) )
      = ( ( A
          = ( nil @ TA ) )
        & ( B
          = ( nil @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_append__is__Nil__conv) ).

thf(1162,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( ( append @ TA @ A @ B )
        = ( nil @ TA ) )
      = ( ( A
          = ( nil @ TA ) )
        & ( B
          = ( nil @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(132,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( ( append @ TA @ A @ B )
        = ( append @ TA @ A @ C ) )
      = ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_same__append__eq) ).

thf(726,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( ( append @ TA @ A @ B )
        = ( append @ TA @ A @ C ) )
      = ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(43,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( suffix @ TA @ A @ B )
     => ( ord_less_eq @ ( set @ TA ) @ ( set2 @ TA @ A ) @ ( set2 @ TA @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_set__mono__suffix) ).

thf(399,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( suffix @ TA @ A @ B )
     => ( ord_less_eq @ ( set @ TA ) @ ( set2 @ TA @ A ) @ ( set2 @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(8,axiom,
    ! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA,D: list @ TA] :
      ( ! [E: TA > TA > $o,F: TA,G: list @ TA,H: TA,I: list @ TA] :
          ( ( ( E @ F @ H )
           => ( A @ E @ G @ ( cons @ TA @ H @ I ) ) )
         => ( ( ~ ( E @ F @ H )
             => ( A @ E @ ( cons @ TA @ F @ G ) @ I ) )
           => ( A @ E @ ( cons @ TA @ F @ G ) @ ( cons @ TA @ H @ I ) ) ) )
     => ( ! [E: TA > TA > $o,F: list @ TA] : ( A @ E @ F @ ( nil @ TA ) )
       => ( ! [E: TA > TA > $o,F: TA,G: list @ TA] : ( A @ E @ ( nil @ TA ) @ ( cons @ TA @ F @ G ) )
         => ( A @ B @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_mergesort__by__rel__merge_Oinduct) ).

thf(278,plain,
    ! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA,D: list @ TA] :
      ( ! [E: TA > TA > $o,F: TA,G: list @ TA,H: TA,I: list @ TA] :
          ( ( ( E @ F @ H )
           => ( A @ E @ G @ ( cons @ TA @ H @ I ) ) )
         => ( ( ~ ( E @ F @ H )
             => ( A @ E @ ( cons @ TA @ F @ G ) @ I ) )
           => ( A @ E @ ( cons @ TA @ F @ G ) @ ( cons @ TA @ H @ I ) ) ) )
     => ( ! [E: TA > TA > $o,F: list @ TA] : ( A @ E @ F @ ( nil @ TA ) )
       => ( ! [E: TA > TA > $o,F: TA,G: list @ TA] : ( A @ E @ ( nil @ TA ) @ ( cons @ TA @ F @ G ) )
         => ( A @ B @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(208,axiom,
    ~ ( member @ node @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set2 @ node @ ( tl @ node @ rs ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_rs_H__loopfree) ).

thf(1015,plain,
    ~ ( member @ node @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set2 @ node @ ( tl @ node @ rs ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(244,axiom,
    ! [TA: $tType,A: list @ TA,B: TA,C: TA,D: list @ TA,E: TA,F: TA] :
      ( ( ( append @ TA @ A @ ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) )
        = ( cons @ TA @ E @ ( cons @ TA @ F @ ( nil @ TA ) ) ) )
      = ( ( A
          = ( nil @ TA ) )
        & ( E = B )
        & ( F = C )
        & ( D
          = ( nil @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_list__ee__eq__leel_I2_J) ).

thf(1176,plain,
    ! [TA: $tType,A: list @ TA,B: TA,C: TA,D: list @ TA,E: TA,F: TA] :
      ( ( ( append @ TA @ A @ ( cons @ TA @ B @ ( cons @ TA @ C @ D ) ) )
        = ( cons @ TA @ E @ ( cons @ TA @ F @ ( nil @ TA ) ) ) )
      = ( ( A
          = ( nil @ TA ) )
        & ( E = B )
        & ( F = C )
        & ( D
          = ( nil @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(164,axiom,
    ! [A: g,B: list @ node,C: node,D: node] :
      ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( append @ node @ B @ ( cons @ node @ C @ ( nil @ node ) ) ) )
     => ( ( member @ node @ C @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ D ) ) )
       => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( append @ node @ B @ ( cons @ node @ C @ ( cons @ node @ D @ ( nil @ node ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_old_Opath__snoc) ).

thf(851,plain,
    ! [A: g,B: list @ node,C: node,D: node] :
      ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( append @ node @ B @ ( cons @ node @ C @ ( nil @ node ) ) ) )
     => ( ( member @ node @ C @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ D ) ) )
       => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( append @ node @ B @ ( cons @ node @ C @ ( cons @ node @ D @ ( nil @ node ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(182,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( append @ TA @ A @ ( nil @ TA ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_append__Nil2) ).

thf(922,plain,
    ! [TA: $tType,A: list @ TA] :
      ( ( append @ TA @ A @ ( nil @ TA ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(115,axiom,
    ! [TA: $tType,A: list @ TA,B: TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( ( ( B
            = ( hd @ TA @ A ) )
          | ( member @ TA @ B @ ( set2 @ TA @ ( tl @ TA @ A ) ) ) )
        = ( member @ TA @ B @ ( set2 @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_in__hd__or__tl__conv) ).

thf(658,plain,
    ! [TA: $tType,A: list @ TA,B: TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( ( ( B
            = ( hd @ TA @ A ) )
          | ( member @ TA @ B @ ( set2 @ TA @ ( tl @ TA @ A ) ) ) )
        = ( member @ TA @ B @ ( set2 @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(178,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( append @ TA @ ( nil @ TA ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_append__Nil) ).

thf(912,plain,
    ! [TA: $tType,A: list @ TA] :
      ( ( append @ TA @ ( nil @ TA ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(75,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/sandbox/benchmark/theBenchmark.p',fact_118_list_Oset__cases) ).

thf(521,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)],[75]) ).

thf(142,axiom,
    ! [A: node,B: g,C: node] :
      ( ( member @ node @ A @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ B @ C ) ) )
     => ( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
       => ( ( invar @ B )
         => ( member @ node @ C @ ( set2 @ node @ ( alpha_n @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_old_Osuccessor__is__node) ).

thf(768,plain,
    ! [A: node,B: g,C: node] :
      ( ( member @ node @ A @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ B @ C ) ) )
     => ( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
       => ( ( invar @ B )
         => ( member @ node @ C @ ( set2 @ node @ ( alpha_n @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(158,axiom,
    ! [A: g,B: node,C: list @ node,D: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( member @ node @ D @ ( set2 @ node @ ( alpha_n @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_old_Opath2__tl__in___092_060alpha_062n) ).

thf(827,plain,
    ! [A: g,B: node,C: list @ node,D: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( member @ node @ D @ ( set2 @ node @ ( alpha_n @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(128,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( ( A
          = ( nil @ TA ) )
        = ( B
          = ( nil @ TA ) ) )
     => ( ( ( A
           != ( nil @ TA ) )
         => ( ( B
             != ( nil @ TA ) )
           => ( ( ( hd @ TA @ A )
                = ( hd @ TA @ B ) )
              & ( ( tl @ TA @ A )
                = ( tl @ TA @ B ) ) ) ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_list_Oexpand) ).

thf(695,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( ( A
          = ( nil @ TA ) )
        = ( B
          = ( nil @ TA ) ) )
     => ( ( ( A
           != ( nil @ TA ) )
         => ( ( B
             != ( nil @ TA ) )
           => ( ( ( hd @ TA @ A )
                = ( hd @ TA @ B ) )
              & ( ( tl @ TA @ A )
                = ( tl @ TA @ B ) ) ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(257,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( A
        = ( cons @ TA @ ( hd @ TA @ A ) @ ( tl @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_list_Oexhaust__sel) ).

thf(1245,plain,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( A
        = ( cons @ TA @ ( hd @ TA @ A ) @ ( tl @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(240,axiom,
    ! [A: g,B: list @ node] :
      ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B )
      = ( ? [C: node] :
            ( ( B
              = ( cons @ node @ C @ ( nil @ node ) ) )
            & ( member @ node @ C @ ( set2 @ node @ ( alpha_n @ A ) ) )
            & ( invar @ A ) )
        | ? [C: list @ node,D: node] :
            ( ( B
              = ( cons @ node @ D @ C ) )
            & ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ C )
            & ( member @ node @ D @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ ( hd @ node @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_old_Opath_Osimps) ).

thf(1166,plain,
    ! [A: g,B: list @ node] :
      ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B )
      = ( ? [C: node] :
            ( ( B
              = ( cons @ node @ C @ ( nil @ node ) ) )
            & ( member @ node @ C @ ( set2 @ node @ ( alpha_n @ A ) ) )
            & ( invar @ A ) )
        | ? [C: list @ node,D: node] :
            ( ( B
              = ( cons @ node @ D @ C ) )
            & ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ C )
            & ( member @ node @ D @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ ( hd @ node @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(96,axiom,
    ~ ( member @ node @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set2 @ node @ ( tl @ node @ rs2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_rs__props_I3_J) ).

thf(589,plain,
    ~ ( member @ node @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set2 @ node @ ( tl @ node @ rs2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(77,axiom,
    ! [TA: $tType,A: list @ TA,B: set @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( ( ord_less_eq @ ( set @ TA ) @ ( set2 @ TA @ A ) @ B )
       => ( ord_less_eq @ ( set @ TA ) @ ( set2 @ TA @ ( butlast @ TA @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_butlast__subset) ).

thf(531,plain,
    ! [TA: $tType,A: list @ TA,B: set @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( ( ord_less_eq @ ( set @ TA ) @ ( set2 @ TA @ A ) @ B )
       => ( ord_less_eq @ ( set @ TA ) @ ( set2 @ TA @ ( butlast @ TA @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(83,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/sandbox/benchmark/theBenchmark.p',fact_94_list__nonempty__induct) ).

thf(548,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)],[83]) ).

thf(221,axiom,
    ( i
    = ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_ri__is__valid) ).

thf(1081,plain,
    ( i
    = ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(25,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/sandbox/benchmark/theBenchmark.p',fact_121_list_Oset__intros_I2_J) ).

thf(342,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)],[25]) ).

thf(236,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: ( list @ TA ) > ( list @ TA ) > $o] :
      ( ~ ( suffix @ TA @ A @ B )
     => ( ! [D: TA,E: list @ TA] : ( C @ ( append @ TA @ E @ ( cons @ TA @ D @ ( nil @ TA ) ) ) @ ( nil @ TA ) )
       => ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
              ( ( D != F )
             => ( C @ ( append @ TA @ E @ ( cons @ TA @ D @ ( nil @ TA ) ) ) @ ( append @ TA @ G @ ( cons @ TA @ F @ ( nil @ TA ) ) ) ) )
         => ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
                ( ( D = F )
               => ( ~ ( suffix @ TA @ E @ G )
                 => ( ( C @ E @ G )
                   => ( C @ ( append @ TA @ E @ ( cons @ TA @ D @ ( nil @ TA ) ) ) @ ( append @ TA @ G @ ( cons @ TA @ F @ ( nil @ TA ) ) ) ) ) ) )
           => ( C @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_not__suffix__induct) ).

thf(1145,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: ( list @ TA ) > ( list @ TA ) > $o] :
      ( ~ ( suffix @ TA @ A @ B )
     => ( ! [D: TA,E: list @ TA] : ( C @ ( append @ TA @ E @ ( cons @ TA @ D @ ( nil @ TA ) ) ) @ ( nil @ TA ) )
       => ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
              ( ( D != F )
             => ( C @ ( append @ TA @ E @ ( cons @ TA @ D @ ( nil @ TA ) ) ) @ ( append @ TA @ G @ ( cons @ TA @ F @ ( nil @ TA ) ) ) ) )
         => ( ! [D: TA,E: list @ TA,F: TA,G: list @ TA] :
                ( ( D = F )
               => ( ~ ( suffix @ TA @ E @ G )
                 => ( ( C @ E @ G )
                   => ( C @ ( append @ TA @ E @ ( cons @ TA @ D @ ( nil @ TA ) ) ) @ ( append @ TA @ G @ ( cons @ TA @ F @ ( nil @ TA ) ) ) ) ) ) )
           => ( C @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(30,axiom,
    ! [TA: $tType] : ( ord @ ( set @ TA ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_1) ).

thf(355,plain,
    ! [TA: $tType] : ( ord @ ( set @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(138,axiom,
    ! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
      ( ( ( cons @ TA @ A @ B )
        = C )
     => ( ( D
          = ( append @ TA @ B @ E ) )
       => ( ( cons @ TA @ A @ D )
          = ( append @ TA @ C @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_Cons__eq__appendI) ).

thf(754,plain,
    ! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
      ( ( ( cons @ TA @ A @ B )
        = C )
     => ( ( D
          = ( append @ TA @ B @ E ) )
       => ( ( cons @ TA @ A @ D )
          = ( append @ TA @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(66,axiom,
    ! [TA: $tType,TB: $tType,TC: $tType,A: ( TC > TA > TB ) > ( list @ TC ) > ( list @ TA ) > $o,B: TC > TA > TB,C: list @ TC,D: list @ TA] :
      ( ! [E: TC > TA > TB] : ( A @ E @ ( nil @ TC ) @ ( nil @ TA ) )
     => ( ! [E: TC > TA > TB,F: TC,G: list @ TC,H: TA,I: list @ TA] :
            ( ( A @ E @ G @ I )
           => ( A @ E @ ( cons @ TC @ F @ G ) @ ( cons @ TA @ H @ I ) ) )
       => ( ! [E: TC > TA > TB,F: TC,G: list @ TC] : ( A @ E @ ( cons @ TC @ F @ G ) @ ( nil @ TA ) )
         => ( ! [E: TC > TA > TB,F: TA,G: list @ TA] : ( A @ E @ ( nil @ TC ) @ ( cons @ TA @ F @ G ) )
           => ( A @ B @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_zipf_Oinduct) ).

thf(473,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,A: ( TC > TA > TB ) > ( list @ TC ) > ( list @ TA ) > $o,B: TC > TA > TB,C: list @ TC,D: list @ TA] :
      ( ! [E: TC > TA > TB] : ( A @ E @ ( nil @ TC ) @ ( nil @ TA ) )
     => ( ! [E: TC > TA > TB,F: TC,G: list @ TC,H: TA,I: list @ TA] :
            ( ( A @ E @ G @ I )
           => ( A @ E @ ( cons @ TC @ F @ G ) @ ( cons @ TA @ H @ I ) ) )
       => ( ! [E: TC > TA > TB,F: TC,G: list @ TC] : ( A @ E @ ( cons @ TC @ F @ G ) @ ( nil @ TA ) )
         => ( ! [E: TC > TA > TB,F: TA,G: list @ TA] : ( A @ E @ ( nil @ TC ) @ ( cons @ TA @ F @ G ) )
           => ( A @ B @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(220,axiom,
    ! [TA: $tType,A: list @ TA,B: TA > $o] :
      ( ? [C: TA] :
          ( ( member @ TA @ C @ ( set2 @ TA @ A ) )
          & ( B @ C ) )
     => ? [C: list @ TA,D: TA,E: list @ TA] :
          ( ( A
            = ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
          & ( B @ D )
          & ! [F: TA] :
              ( ( member @ TA @ F @ ( set2 @ TA @ E ) )
             => ~ ( B @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_split__list__last__prop) ).

thf(1076,plain,
    ! [TA: $tType,A: list @ TA,B: TA > $o] :
      ( ? [C: TA] :
          ( ( member @ TA @ C @ ( set2 @ TA @ A ) )
          & ( B @ C ) )
     => ? [C: list @ TA,D: TA,E: list @ TA] :
          ( ( A
            = ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
          & ( B @ D )
          & ! [F: TA] :
              ( ( member @ TA @ F @ ( set2 @ TA @ E ) )
             => ~ ( B @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(145,axiom,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( member @ TA @ A @ ( set2 @ TA @ B ) )
      = ( ? [C: list @ TA,D: list @ TA] :
            ( ( B
              = ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) )
            & ~ ( member @ TA @ A @ ( set2 @ TA @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_in__set__conv__decomp__last) ).

thf(776,plain,
    ! [TA: $tType,A: TA,B: list @ TA] :
      ( ( member @ TA @ A @ ( set2 @ TA @ B ) )
      = ( ? [C: list @ TA,D: list @ TA] :
            ( ( B
              = ( append @ TA @ C @ ( cons @ TA @ A @ D ) ) )
            & ~ ( member @ TA @ A @ ( set2 @ TA @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(9,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( suffix @ TA @ A @ B )
     => ( ( suffix @ TA @ B @ A )
        = ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_suffix__order_Oantisym__conv) ).

thf(282,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( suffix @ TA @ A @ B )
     => ( ( suffix @ TA @ B @ A )
        = ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(130,axiom,
    ! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
      ( ( ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) )
        = ( append @ TA @ C @ ( cons @ TA @ D @ ( nil @ TA ) ) ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_append1__eq__conv) ).

thf(707,plain,
    ! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
      ( ( ( append @ TA @ A @ ( cons @ TA @ B @ ( nil @ TA ) ) )
        = ( append @ TA @ C @ ( cons @ TA @ D @ ( nil @ TA ) ) ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(190,axiom,
    ! [A: g,B: node,C: list @ node,D: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ B )
     => ( ( member @ node @ D @ ( set2 @ node @ C ) )
       => ~ ! [E: list @ node] :
              ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ E @ B )
             => ( ( member @ node @ D @ ( set2 @ node @ E ) )
               => ( ~ ( member @ node @ B @ ( set2 @ node @ ( tl @ node @ ( butlast @ node @ E ) ) ) )
                 => ~ ( ord_less_eq @ ( set @ node ) @ ( set2 @ node @ E ) @ ( set2 @ node @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_old_Opath2__simple__loop) ).

thf(954,plain,
    ! [A: g,B: node,C: list @ node,D: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ B )
     => ( ( member @ node @ D @ ( set2 @ node @ C ) )
       => ~ ! [E: list @ node] :
              ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ E @ B )
             => ( ( member @ node @ D @ ( set2 @ node @ E ) )
               => ( ~ ( member @ node @ B @ ( set2 @ node @ ( tl @ node @ ( butlast @ node @ E ) ) ) )
                 => ~ ( ord_less_eq @ ( set @ node ) @ ( set2 @ node @ E ) @ ( set2 @ node @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(264,axiom,
    ! [TA: $tType,A: list @ TA,B: TA > $o] :
      ( ? [C: TA] :
          ( ( member @ TA @ C @ ( set2 @ TA @ A ) )
          & ( B @ C ) )
     => ? [C: list @ TA,D: TA] :
          ( ? [E: list @ TA] :
              ( A
              = ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
          & ( B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_split__list__prop) ).

thf(1267,plain,
    ! [TA: $tType,A: list @ TA,B: TA > $o] :
      ( ? [C: TA] :
          ( ( member @ TA @ C @ ( set2 @ TA @ A ) )
          & ( B @ C ) )
     => ? [C: list @ TA,D: TA] :
          ( ? [E: list @ TA] :
              ( A
              = ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
          & ( B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(47,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( prefix @ TA @ A @ B )
     => ( ord_less_eq @ ( set @ TA ) @ ( set2 @ TA @ A ) @ ( set2 @ TA @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_set__mono__prefix) ).

thf(409,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( prefix @ TA @ A @ B )
     => ( ord_less_eq @ ( set @ TA ) @ ( set2 @ TA @ A ) @ ( set2 @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(227,axiom,
    ! [A: g,B: node,C: list @ node,D: node,E: node > ( list @ node ) > node > $o] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( ( ( member @ node @ B @ ( set2 @ node @ ( alpha_n @ A ) ) )
         => ( E @ B @ ( cons @ node @ B @ ( nil @ node ) ) @ B ) )
       => ( ! [F: list @ node,G: node,H: node] :
              ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ F @ G )
             => ( ( E @ B @ F @ G )
               => ( ( member @ node @ G @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ H ) ) )
                 => ( E @ B @ ( append @ node @ F @ ( cons @ node @ H @ ( nil @ node ) ) ) @ H ) ) ) )
         => ( E @ B @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_old_Opath2__rev__induct) ).

thf(1098,plain,
    ! [A: g,B: node,C: list @ node,D: node,E: node > ( list @ node ) > node > $o] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( ( ( member @ node @ B @ ( set2 @ node @ ( alpha_n @ A ) ) )
         => ( E @ B @ ( cons @ node @ B @ ( nil @ node ) ) @ B ) )
       => ( ! [F: list @ node,G: node,H: node] :
              ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ F @ G )
             => ( ( E @ B @ F @ G )
               => ( ( member @ node @ G @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ H ) ) )
                 => ( E @ B @ ( append @ node @ F @ ( cons @ node @ H @ ( nil @ node ) ) ) @ H ) ) ) )
         => ( E @ B @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(219,axiom,
    ! [A: g,B: node,C: list @ node,D: node,E: node > $o] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( ? [F: node] :
            ( ( member @ node @ F @ ( set2 @ node @ C ) )
            & ( E @ F ) )
       => ~ ! [F: node,G: list @ node] :
              ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ F @ G @ D )
             => ( ( E @ F )
               => ( ! [H: node] :
                      ( ( member @ node @ H @ ( set2 @ node @ ( tl @ node @ G ) ) )
                     => ~ ( E @ H ) )
                 => ~ ( suffix @ node @ G @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_old_Opath2__split__last__prop) ).

thf(1070,plain,
    ! [A: g,B: node,C: list @ node,D: node,E: node > $o] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( ? [F: node] :
            ( ( member @ node @ F @ ( set2 @ node @ C ) )
            & ( E @ F ) )
       => ~ ! [F: node,G: list @ node] :
              ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ F @ G @ D )
             => ( ( E @ F )
               => ( ! [H: node] :
                      ( ( member @ node @ H @ ( set2 @ node @ ( tl @ node @ G ) ) )
                     => ~ ( E @ H ) )
                 => ~ ( suffix @ node @ G @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(171,axiom,
    graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs @ pred_phi_r,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_rs_H__props_I1_J) ).

thf(872,plain,
    graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs @ pred_phi_r,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(49,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/sandbox/benchmark/theBenchmark.p',fact_111_list_Oinducts) ).

thf(414,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)],[49]) ).

thf(195,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 @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ) )
         => ( B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_rev__nonempty__induct) ).

thf(971,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 @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ) )
         => ( B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(121,axiom,
    ! [A: g,B: list @ node,C: node] :
      ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B )
     => ( ( member @ node @ C @ ( set2 @ node @ B ) )
       => ( member @ node @ C @ ( set2 @ node @ ( alpha_n @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_old_Opath__in___092_060alpha_062n) ).

thf(673,plain,
    ! [A: g,B: list @ node,C: node] :
      ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B )
     => ( ( member @ node @ C @ ( set2 @ node @ B ) )
       => ( member @ node @ C @ ( set2 @ node @ ( alpha_n @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(248,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( ( nil @ TA )
        = ( tl @ TA @ A ) )
      = ( ( A
          = ( nil @ TA ) )
        | ? [B: TA] :
            ( A
            = ( cons @ TA @ B @ ( nil @ TA ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_Nil__tl) ).

thf(1188,plain,
    ! [TA: $tType,A: list @ TA] :
      ( ( ( nil @ TA )
        = ( tl @ TA @ A ) )
      = ( ( A
          = ( nil @ TA ) )
        | ? [B: TA] :
            ( A
            = ( cons @ TA @ B @ ( nil @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(35,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( suffix @ TA @ A @ ( nil @ TA ) )
      = ( A
        = ( nil @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_suffix__bot_Obot_Oextremum__unique) ).

thf(370,plain,
    ! [TA: $tType,A: list @ TA] :
      ( ( suffix @ TA @ A @ ( nil @ TA ) )
      = ( A
        = ( nil @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(154,axiom,
    ~ ! [A: list @ node] :
        ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ A @ i )
       => ( ( prefix @ node @ A @ ms )
         => ( member @ node @ i @ ( set2 @ node @ ( butlast @ node @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062ms_H_O_A_092_060lbrakk_062g_A_092_060turnstile_062_Am_Nms_H_092_060rightarrow_062i_059_Aprefix_Ams_H_Ams_059_Ai_A_092_060notin_062_Aset_A_Ibutlast_Ams_H_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).

thf(808,plain,
    ~ ! [A: list @ node] :
        ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ A @ i )
       => ( ( prefix @ node @ A @ ms )
         => ( member @ node @ i @ ( set2 @ node @ ( butlast @ node @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(217,axiom,
    ! [TA: $tType,A: list @ TA,B: TA > $o] :
      ( ( ? [C: TA] :
            ( ( member @ TA @ C @ ( set2 @ TA @ A ) )
            & ( B @ C ) ) )
      = ( ? [C: list @ TA,D: TA] :
            ( ? [E: list @ TA] :
                ( A
                = ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
            & ( B @ D )
            & ! [E: TA] :
                ( ( member @ TA @ E @ ( set2 @ TA @ C ) )
               => ~ ( B @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_split__list__first__prop__iff) ).

thf(1052,plain,
    ! [TA: $tType,A: list @ TA,B: TA > $o] :
      ( ( ? [C: TA] :
            ( ( member @ TA @ C @ ( set2 @ TA @ A ) )
            & ( B @ C ) ) )
      = ( ? [C: list @ TA,D: TA] :
            ( ? [E: list @ TA] :
                ( A
                = ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
            & ( B @ D )
            & ! [E: TA] :
                ( ( member @ TA @ E @ ( set2 @ TA @ C ) )
               => ~ ( B @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(196,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( ( append @ TA @ A @ B )
        = B )
      = ( A
        = ( nil @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_append__self__conv2) ).

thf(978,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( ( append @ TA @ A @ B )
        = B )
      = ( A
        = ( nil @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(18,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( suffix @ TA @ A @ B )
     => ( ( suffix @ TA @ B @ C )
       => ( suffix @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_suffix__order_Oorder__trans) ).

thf(314,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( suffix @ TA @ A @ B )
     => ( ( suffix @ TA @ B @ C )
       => ( suffix @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(105,axiom,
    ! [A: g,B: node,C: list @ node,D: node,E: list @ node,F: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append @ node @ C @ ( cons @ node @ D @ E ) ) @ F )
     => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ D @ ( cons @ node @ D @ E ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_old_Opath2__split_I2_J) ).

thf(612,plain,
    ! [A: g,B: node,C: list @ node,D: node,E: list @ node,F: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append @ node @ C @ ( cons @ node @ D @ E ) ) @ F )
     => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ D @ ( cons @ node @ D @ E ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(167,axiom,
    r != phi_r,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_False) ).

thf(859,plain,
    r != phi_r,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(63,axiom,
    ! [TA: $tType,A: list @ TA] : ( suffix @ TA @ ( nil @ TA ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_Nil__suffix) ).

thf(465,plain,
    ! [TA: $tType,A: list @ TA] : ( suffix @ TA @ ( nil @ TA ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(185,axiom,
    ! [A: g,B: node,C: list @ node,D: node,E: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( ( member @ node @ E @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ B ) ) )
       => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ E @ ( cons @ node @ E @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_old_OCons__path2) ).

thf(931,plain,
    ! [A: g,B: node,C: list @ node,D: node,E: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( ( member @ node @ E @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ B ) ) )
       => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ E @ ( cons @ node @ E @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(174,axiom,
    graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_rs__props_I1_J) ).

thf(903,plain,
    graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs2 @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ phi_r ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(93,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ~ ! [B: TA,C: list @ TA] :
            ( A
           != ( cons @ TA @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_neq__NilE) ).

thf(581,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)],[93]) ).

thf(228,axiom,
    ! [A: g,B: list @ node] :
      ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B )
     => ( invar @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_old_Opath__invar) ).

thf(1108,plain,
    ! [A: g,B: list @ node] :
      ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B )
     => ( invar @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(155,axiom,
    ! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
      ( ( A @ ( nil @ TA ) )
     => ( ! [C: TA,D: list @ TA] :
            ( ( A @ D )
           => ( A @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) )
       => ( A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_rev__induct) ).

thf(813,plain,
    ! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
      ( ( A @ ( nil @ TA ) )
     => ( ! [C: TA,D: list @ TA] :
            ( ( A @ D )
           => ( A @ ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) )
       => ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(20,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( suffix @ TA @ A @ B )
     => ( ( suffix @ TA @ C @ A )
       => ( suffix @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_suffix__order_Odual__order_Otrans) ).

thf(319,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( suffix @ TA @ A @ B )
     => ( ( suffix @ TA @ C @ A )
       => ( suffix @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(188,axiom,
    ! [TA: $tType] :
      ( ( suffix @ TA )
      = ( ^ [A: list @ TA,B: list @ TA] :
          ? [C: list @ TA] :
            ( B
            = ( append @ TA @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_Sublist_Osuffix__def) ).

thf(946,plain,
    ! [TA: $tType] :
      ( ( suffix @ TA )
      = ( ^ [A: list @ TA,B: list @ TA] :
          ? [C: list @ TA] :
            ( B
            = ( append @ TA @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(44,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: TA] :
      ( ( suffix @ TA @ A @ B )
     => ( suffix @ TA @ A @ ( cons @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_suffix__ConsI) ).

thf(401,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: TA] :
      ( ( suffix @ TA @ A @ B )
     => ( suffix @ TA @ A @ ( cons @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(148,axiom,
    ! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
      ( ( ( butlast @ TA @ A )
        = ( cons @ TA @ B @ C ) )
      = ( ? [D: TA] :
            ( A
            = ( cons @ TA @ B @ ( append @ TA @ C @ ( cons @ TA @ D @ ( nil @ TA ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_butlast__eq__cons__conv) ).

thf(786,plain,
    ! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
      ( ( ( butlast @ TA @ A )
        = ( cons @ TA @ B @ C ) )
      = ( ? [D: TA] :
            ( A
            = ( cons @ TA @ B @ ( append @ TA @ C @ ( cons @ TA @ D @ ( nil @ TA ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(201,axiom,
    ! [A: g,B: node,C: list @ node,D: node,E: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( ( member @ node @ E @ ( set2 @ node @ C ) )
       => ( member @ node @ E @ ( set2 @ node @ ( alpha_n @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_old_Opath2__in___092_060alpha_062n) ).

thf(995,plain,
    ! [A: g,B: node,C: list @ node,D: node,E: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( ( member @ node @ E @ ( set2 @ node @ C ) )
       => ( member @ node @ E @ ( set2 @ node @ ( alpha_n @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(213,axiom,
    ! [A: g,B: node,C: list @ node,D: node,E: node > $o] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( ? [F: node] :
            ( ( member @ node @ F @ ( set2 @ node @ C ) )
            & ( E @ F ) )
       => ~ ! [F: node,G: list @ node] :
              ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ G @ F )
             => ( ( E @ F )
               => ( ! [H: node] :
                      ( ( member @ node @ H @ ( set2 @ node @ ( butlast @ node @ G ) ) )
                     => ~ ( E @ H ) )
                 => ~ ( prefix @ node @ G @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_old_Opath2__split__first__prop) ).

thf(1030,plain,
    ! [A: g,B: node,C: list @ node,D: node,E: node > $o] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( ? [F: node] :
            ( ( member @ node @ F @ ( set2 @ node @ C ) )
            & ( E @ F ) )
       => ~ ! [F: node,G: list @ node] :
              ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ G @ F )
             => ( ( E @ F )
               => ( ! [H: node] :
                      ( ( member @ node @ H @ ( set2 @ node @ ( butlast @ node @ G ) ) )
                     => ~ ( E @ H ) )
                 => ~ ( prefix @ node @ G @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(54,axiom,
    ! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA > $o,C: list @ TB,D: list @ TA] :
      ( ! [E: list @ TB] : ( A @ E @ ( nil @ TA ) )
     => ( ! [E: list @ TA] : ( A @ ( nil @ TB ) @ E )
       => ( ! [E: TB,F: list @ TB,G: TA,H: list @ TA] :
              ( ( B @ E @ G )
             => ( ( A @ F @ ( cons @ TA @ G @ H ) )
               => ( A @ ( cons @ TB @ E @ F ) @ ( cons @ TA @ G @ H ) ) ) )
         => ( ! [E: TB,F: list @ TB,G: TA,H: list @ TA] :
                ( ~ ( B @ E @ G )
               => ( ( A @ ( cons @ TB @ E @ F ) @ H )
                 => ( A @ ( cons @ TB @ E @ F ) @ ( cons @ TA @ G @ H ) ) ) )
           => ( A @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_mergesort__by__rel__merge__induct) ).

thf(433,plain,
    ! [TA: $tType,TB: $tType,A: ( list @ TB ) > ( list @ TA ) > $o,B: TB > TA > $o,C: list @ TB,D: list @ TA] :
      ( ! [E: list @ TB] : ( A @ E @ ( nil @ TA ) )
     => ( ! [E: list @ TA] : ( A @ ( nil @ TB ) @ E )
       => ( ! [E: TB,F: list @ TB,G: TA,H: list @ TA] :
              ( ( B @ E @ G )
             => ( ( A @ F @ ( cons @ TA @ G @ H ) )
               => ( A @ ( cons @ TB @ E @ F ) @ ( cons @ TA @ G @ H ) ) ) )
         => ( ! [E: TB,F: list @ TB,G: TA,H: list @ TA] :
                ( ~ ( B @ E @ G )
               => ( ( A @ ( cons @ TB @ E @ F ) @ H )
                 => ( A @ ( cons @ TB @ E @ F ) @ ( cons @ TA @ G @ H ) ) ) )
           => ( A @ C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(119,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( ( append @ TA @ A @ B )
        = ( append @ TA @ C @ B ) )
      = ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_append__same__eq) ).

thf(667,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( ( append @ TA @ A @ B )
        = ( append @ TA @ C @ B ) )
      = ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(68,axiom,
    ! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
      ( ( suffix @ TA @ A @ ( cons @ TA @ B @ C ) )
      = ( ( A
          = ( cons @ TA @ B @ C ) )
        | ( suffix @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_suffix__Cons) ).

thf(478,plain,
    ! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
      ( ( suffix @ TA @ A @ ( cons @ TA @ B @ C ) )
      = ( ( A
          = ( cons @ TA @ B @ C ) )
        | ( suffix @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(6,axiom,
    ! [TA: $tType,A: TA,B: TA > $o] :
      ( ( member @ TA @ A @ ( collect @ TA @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).

thf(272,plain,
    ! [TA: $tType,A: TA,B: TA > $o] :
      ( ( member @ TA @ A @ ( collect @ TA @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(40,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] :
              ( ( A @ E )
             => ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) )
         => ( A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_list__induct__first2) ).

thf(383,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] :
              ( ( A @ E )
             => ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) )
         => ( A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(12,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( suffix @ TA @ A @ B )
     => ( ( suffix @ TA @ B @ A )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_suffix__order_Oorder_Oantisym) ).

thf(290,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( suffix @ TA @ A @ B )
     => ( ( suffix @ TA @ B @ A )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(38,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ( type @ TA ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Orderings_Olinorder___HOL_Otype) ).

thf(378,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ( type @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(160,axiom,
    ! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( ( ( cons @ TA @ B @ ( nil @ TA ) )
          = ( append @ TA @ A @ C ) )
        = ( ( A
            = ( cons @ TA @ B @ ( nil @ TA ) ) )
          & ( C
            = ( nil @ TA ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_list__se__match_I3_J) ).

thf(832,plain,
    ! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( ( ( cons @ TA @ B @ ( nil @ TA ) )
          = ( append @ TA @ A @ C ) )
        = ( ( A
            = ( cons @ TA @ B @ ( nil @ TA ) ) )
          & ( C
            = ( nil @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(125,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
    ? [C: list @ TA,D: list @ TA,E: list @ TA] :
      ( ( A
        = ( append @ TA @ C @ D ) )
      & ( B
        = ( append @ TA @ C @ E ) )
      & ( ( D
          = ( nil @ TA ) )
        | ( E
          = ( nil @ TA ) )
        | ( ( hd @ TA @ D )
         != ( hd @ TA @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_longest__common__prefix) ).

thf(684,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
    ? [C: list @ TA,D: list @ TA,E: list @ TA] :
      ( ( A
        = ( append @ TA @ C @ D ) )
      & ( B
        = ( append @ TA @ C @ E ) )
      & ( ( D
          = ( nil @ TA ) )
        | ( E
          = ( nil @ TA ) )
        | ( ( hd @ TA @ D )
         != ( hd @ TA @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(194,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
      ( ( ( append @ TA @ A @ B )
        = C )
     => ( ( D
          = ( append @ TA @ B @ E ) )
       => ( ( append @ TA @ A @ D )
          = ( append @ TA @ C @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_append__eq__appendI) ).

thf(967,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
      ( ( ( append @ TA @ A @ B )
        = C )
     => ( ( D
          = ( append @ TA @ B @ E ) )
       => ( ( append @ TA @ A @ D )
          = ( append @ TA @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(161,axiom,
    ! [TA: $tType,A: list @ TA,B: TA > $o] :
      ( ? [C: TA] :
          ( ( member @ TA @ C @ ( set2 @ TA @ A ) )
          & ( B @ C ) )
     => ~ ! [C: list @ TA,D: TA] :
            ( ? [E: list @ TA] :
                ( A
                = ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
           => ~ ( B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_split__list__propE) ).

thf(835,plain,
    ! [TA: $tType,A: list @ TA,B: TA > $o] :
      ( ? [C: TA] :
          ( ( member @ TA @ C @ ( set2 @ TA @ A ) )
          & ( B @ C ) )
     => ~ ! [C: list @ TA,D: TA] :
            ( ? [E: list @ TA] :
                ( A
                = ( append @ TA @ C @ ( cons @ TA @ D @ E ) ) )
           => ~ ( B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(165,axiom,
    ! [A: g,B: node,C: list @ node,D: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( hd @ node @ C ) @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_old_Opath2__forget__hd) ).

thf(854,plain,
    ! [A: g,B: node,C: list @ node,D: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( hd @ node @ C ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(258,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ~ ! [B: list @ TA,C: TA] :
            ( A
           != ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_neq__Nil__revE) ).

thf(1248,plain,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ~ ! [B: list @ TA,C: TA] :
            ( A
           != ( append @ TA @ B @ ( cons @ TA @ C @ ( nil @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(36,axiom,
    ! [TA: $tType,A: TA,B: list @ TA] : ( member @ TA @ A @ ( set2 @ TA @ ( cons @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_list_Oset__intros_I1_J) ).

thf(373,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)],[36]) ).

thf(135,axiom,
    ! [A: node,B: g] :
      ( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
     => ( finite_finite @ val @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_phiUses__finite) ).

thf(735,plain,
    ! [A: node,B: g] :
      ( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
     => ( finite_finite @ val @ ( sSA_CFG_SSA_phiUses @ g @ node @ edgeD @ val @ alpha_n @ inEdges @ phis @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(86,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( prefix @ TA @ A @ ( nil @ TA ) )
      = ( A
        = ( nil @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_prefix__Nil) ).

thf(564,plain,
    ! [TA: $tType,A: list @ TA] :
      ( ( prefix @ TA @ A @ ( nil @ TA ) )
      = ( A
        = ( nil @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(15,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( A
       != ( nil @ TA ) )
     => ( member @ TA @ ( hd @ TA @ A ) @ ( set2 @ TA @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_list_Oset__sel_I1_J) ).

thf(305,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)],[15]) ).

thf(4,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ! [C: TA] :
          ( ( A @ C )
          = ( B @ C ) )
     => ( ( collect @ TA @ A )
        = ( collect @ TA @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_Collect__cong) ).

thf(268,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)],[4]) ).

thf(251,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ~ ( suffix @ TA @ A @ B )
     => ( ( ( A
           != ( nil @ TA ) )
         => ( B
           != ( nil @ TA ) ) )
       => ( ! [C: TA,D: list @ TA] :
              ( ( A
                = ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
             => ! [E: TA,F: list @ TA] :
                  ( ( B
                    = ( append @ TA @ F @ ( cons @ TA @ E @ ( nil @ TA ) ) ) )
                 => ( ( E = C )
                   => ( suffix @ TA @ D @ F ) ) ) )
         => ~ ! [C: TA] :
                ( ? [D: list @ TA] :
                    ( A
                    = ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
               => ! [D: TA] :
                    ( ? [E: list @ TA] :
                        ( B
                        = ( append @ TA @ E @ ( cons @ TA @ D @ ( nil @ TA ) ) ) )
                   => ( D = C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_not__suffix__cases) ).

thf(1197,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ~ ( suffix @ TA @ A @ B )
     => ( ( ( A
           != ( nil @ TA ) )
         => ( B
           != ( nil @ TA ) ) )
       => ( ! [C: TA,D: list @ TA] :
              ( ( A
                = ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
             => ! [E: TA,F: list @ TA] :
                  ( ( B
                    = ( append @ TA @ F @ ( cons @ TA @ E @ ( nil @ TA ) ) ) )
                 => ( ( E = C )
                   => ( suffix @ TA @ D @ F ) ) ) )
         => ~ ! [C: TA] :
                ( ? [D: list @ TA] :
                    ( A
                    = ( append @ TA @ D @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
               => ! [D: TA] :
                    ( ? [E: list @ TA] :
                        ( B
                        = ( append @ TA @ E @ ( cons @ TA @ D @ ( nil @ TA ) ) ) )
                   => ( D = C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(239,axiom,
    graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_assms_I7_J) ).

thf(1165,plain,
    graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF1081484811efNode @ g @ node @ val @ alpha_n @ defs @ phis @ g2 @ r ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(151,axiom,
    ! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
      ( ( ( butlast @ TA @ A )
        = ( cons @ TA @ B @ C ) )
     => ~ ! [D: TA] :
            ( A
           != ( cons @ TA @ B @ ( append @ TA @ C @ ( cons @ TA @ D @ ( nil @ TA ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_butlast__eq__consE) ).

thf(796,plain,
    ! [TA: $tType,A: list @ TA,B: TA,C: list @ TA] :
      ( ( ( butlast @ TA @ A )
        = ( cons @ TA @ B @ C ) )
     => ~ ! [D: TA] :
            ( A
           != ( cons @ TA @ B @ ( append @ TA @ C @ ( cons @ TA @ D @ ( nil @ TA ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(184,axiom,
    ! [A: g,B: node,C: list @ node,D: node,E: list @ node,F: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ F )
       => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append @ node @ ( butlast @ node @ C ) @ E ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_old_Opath2__app_H) ).

thf(928,plain,
    ! [A: g,B: node,C: list @ node,D: node,E: list @ node,F: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ D @ E @ F )
       => ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ ( append @ node @ ( butlast @ node @ C ) @ E ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(191,axiom,
    ! [A: g,B: node,C: node,D: list @ node,E: list @ node] :
      ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons @ node @ B @ ( cons @ node @ C @ D ) ) )
     => ( ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons @ node @ C @ D ) )
         => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons @ node @ C @ E ) ) )
       => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons @ node @ B @ ( cons @ node @ C @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_old_Opath__by__tail) ).

thf(960,plain,
    ! [A: g,B: node,C: node,D: list @ node,E: list @ node] :
      ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons @ node @ B @ ( cons @ node @ C @ D ) ) )
     => ( ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons @ node @ C @ D ) )
         => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons @ node @ C @ E ) ) )
       => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons @ node @ B @ ( cons @ node @ C @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(111,axiom,
    ! [A: g,B: list @ node,C: node,D: list @ node] :
      ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( append @ node @ B @ ( cons @ node @ C @ D ) ) )
     => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons @ node @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_old_Opath__split_I2_J) ).

thf(635,plain,
    ! [A: g,B: list @ node,C: node,D: list @ node] :
      ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( append @ node @ B @ ( cons @ node @ C @ D ) ) )
     => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( cons @ node @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(162,axiom,
    ! [A: g,B: node,C: list @ node,D: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( ( ( C
            = ( cons @ node @ B @ ( nil @ node ) ) )
         => ( D != B ) )
       => ~ ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( hd @ node @ ( tl @ node @ C ) ) @ ( tl @ node @ C ) @ D )
           => ~ ( member @ node @ B @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ ( hd @ node @ ( tl @ node @ C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_old_Opath2__cases) ).

thf(839,plain,
    ! [A: g,B: node,C: list @ node,D: node] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( ( ( C
            = ( cons @ node @ B @ ( nil @ node ) ) )
         => ( D != B ) )
       => ~ ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ ( hd @ node @ ( tl @ node @ C ) ) @ ( tl @ node @ C ) @ D )
           => ~ ( member @ node @ B @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ ( hd @ node @ ( tl @ node @ C ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(137,axiom,
    ! [A: g,B: list @ node,C: ( list @ node ) > $o] :
      ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B )
     => ( ! [D: node] :
            ( ( member @ node @ D @ ( set2 @ node @ ( alpha_n @ A ) ) )
           => ( ( invar @ A )
             => ( C @ ( cons @ node @ D @ ( nil @ node ) ) ) ) )
       => ( ! [D: list @ node,E: node] :
              ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ D )
             => ( ( C @ D )
               => ( ( member @ node @ E @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ ( hd @ node @ D ) ) ) )
                 => ( C @ ( cons @ node @ E @ D ) ) ) ) )
         => ( C @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_old_Opath_Oinducts) ).

thf(740,plain,
    ! [A: g,B: list @ node,C: ( list @ node ) > $o] :
      ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B )
     => ( ! [D: node] :
            ( ( member @ node @ D @ ( set2 @ node @ ( alpha_n @ A ) ) )
           => ( ( invar @ A )
             => ( C @ ( cons @ node @ D @ ( nil @ node ) ) ) ) )
       => ( ! [D: list @ node,E: node] :
              ( ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ D )
             => ( ( C @ D )
               => ( ( member @ node @ E @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ ( hd @ node @ D ) ) ) )
                 => ( C @ ( cons @ node @ E @ D ) ) ) ) )
         => ( C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(256,axiom,
    ! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA] :
      ( ( ( cons @ TA @ A @ B )
        = ( append @ TA @ C @ D ) )
     => ( ( ( C
            = ( nil @ TA ) )
         => ( D
           != ( cons @ TA @ A @ B ) ) )
       => ~ ! [E: list @ TA] :
              ( ( C
                = ( cons @ TA @ A @ E ) )
             => ( ( append @ TA @ E @ D )
               != B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_list__Cons__eq__append__cases) ).

thf(1236,plain,
    ! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: list @ TA] :
      ( ( ( cons @ TA @ A @ B )
        = ( append @ TA @ C @ D ) )
     => ( ( ( C
            = ( nil @ TA ) )
         => ( D
           != ( cons @ TA @ A @ B ) ) )
       => ~ ! [E: list @ TA] :
              ( ( C
                = ( cons @ TA @ A @ E ) )
             => ( ( append @ TA @ E @ D )
               != B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(262,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( ( append @ TA @ A @ B )
        = A )
      = ( B
        = ( nil @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_append__self__conv) ).

thf(1261,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( ( append @ TA @ A @ B )
        = A )
      = ( B
        = ( nil @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(90,axiom,
    ! [TA: $tType,A: list @ TA] : ( suffix @ TA @ ( nil @ TA ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_suffix__bot_Obot_Oextremum) ).

thf(575,plain,
    ! [TA: $tType,A: list @ TA] : ( suffix @ TA @ ( nil @ TA ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(52,axiom,
    ! [TA: $tType,A: list @ TA] :
      ( ( prefix @ TA @ A @ ( nil @ TA ) )
      = ( A
        = ( nil @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_prefix__bot_Obot_Oextremum__unique) ).

thf(427,plain,
    ! [TA: $tType,A: list @ TA] :
      ( ( prefix @ TA @ A @ ( nil @ TA ) )
      = ( A
        = ( nil @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(200,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( A
        = ( append @ TA @ A @ B ) )
      = ( B
        = ( nil @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_self__append__conv) ).

thf(992,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( A
        = ( append @ TA @ A @ B ) )
      = ( B
        = ( nil @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(156,axiom,
    ! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: TA] :
      ( ( member @ TA @ A @ ( set2 @ TA @ B ) )
     => ( member @ TA @ A @ ( set2 @ TA @ ( tl @ TA @ ( append @ TA @ C @ ( cons @ TA @ D @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_old_Oelem__set__implies__elem__tl__app__cons) ).

thf(822,plain,
    ! [TA: $tType,A: TA,B: list @ TA,C: list @ TA,D: TA] :
      ( ( member @ TA @ A @ ( set2 @ TA @ B ) )
     => ( member @ TA @ A @ ( set2 @ TA @ ( tl @ TA @ ( append @ TA @ C @ ( cons @ TA @ D @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(204,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( suffix @ TA @ ( append @ TA @ A @ B ) @ C )
     => ( suffix @ TA @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_suffix__appendD) ).

thf(1004,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( suffix @ TA @ ( append @ TA @ A @ B ) @ C )
     => ( suffix @ TA @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(126,axiom,
    member @ node @ i @ ( set2 @ node @ ms ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_ri__props_I2_J) ).

thf(691,plain,
    member @ node @ i @ ( set2 @ node @ ms ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(72,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] :
              ( ( A @ E )
             => ( ( A @ ( cons @ TA @ D @ E ) )
               => ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
         => ( A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_induct__list012) ).

thf(501,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] :
              ( ( A @ E )
             => ( ( A @ ( cons @ TA @ D @ E ) )
               => ( A @ ( cons @ TA @ C @ ( cons @ TA @ D @ E ) ) ) ) )
         => ( A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(103,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( suffix @ TA @ A @ B )
     => ( suffix @ TA @ A @ ( append @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_suffix__appendI) ).

thf(607,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( suffix @ TA @ A @ B )
     => ( suffix @ TA @ A @ ( append @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(24,axiom,
    ! [TA: $tType] :
      ( ( ord @ TA )
     => ! [A: ( list @ TA ) > $o,B: list @ TA] :
          ( ! [C: TA,D: list @ TA] :
              ( ! [E: TA,F: list @ TA] :
                  ( ( D
                    = ( cons @ TA @ E @ F ) )
                 => ( A @ D ) )
             => ( A @ ( cons @ TA @ C @ D ) ) )
         => ( ( A @ ( nil @ TA ) )
           => ( A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_min__list_Oinduct) ).

thf(332,plain,
    ! [TA: $tType] :
      ( ( ord @ TA )
     => ! [A: ( list @ TA ) > $o,B: list @ TA] :
          ( ! [C: TA,D: list @ TA] :
              ( ! [E: TA,F: list @ TA] :
                  ( ( D
                    = ( cons @ TA @ E @ F ) )
                 => ( A @ D ) )
             => ( A @ ( cons @ TA @ C @ D ) ) )
         => ( ( A @ ( nil @ TA ) )
           => ( A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(233,axiom,
    ! [A: g,B: node,C: list @ node,D: node,E: node > ( list @ node ) > node > $o] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( ( ( invar @ A )
         => ( E @ D @ ( cons @ node @ D @ ( nil @ node ) ) @ D ) )
       => ( ! [F: list @ node,G: node,H: node] :
              ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ H @ F @ D )
             => ( ( E @ H @ F @ D )
               => ( ( member @ node @ G @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ H ) ) )
                 => ( E @ G @ ( cons @ node @ G @ F ) @ D ) ) ) )
         => ( E @ B @ C @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_old_Opath2__induct) ).

thf(1129,plain,
    ! [A: g,B: node,C: list @ node,D: node,E: node > ( list @ node ) > node > $o] :
      ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ B @ C @ D )
     => ( ( ( invar @ A )
         => ( E @ D @ ( cons @ node @ D @ ( nil @ node ) ) @ D ) )
       => ( ! [F: list @ node,G: node,H: node] :
              ( ( graph_1661282752_path2 @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ A @ H @ F @ D )
             => ( ( E @ H @ F @ D )
               => ( ( member @ node @ G @ ( set2 @ node @ ( graph_1201503639essors @ g @ node @ edgeD @ inEdges @ A @ H ) ) )
                 => ( E @ G @ ( cons @ node @ G @ F ) @ D ) ) ) )
         => ( E @ B @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(71,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/sandbox/benchmark/theBenchmark.p',fact_99_remdups__adj_Oinduct) ).

thf(486,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)],[71]) ).

thf(206,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( suffix @ TA @ ( append @ TA @ A @ B ) @ ( append @ TA @ C @ B ) )
      = ( suffix @ TA @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_same__suffix__suffix) ).

thf(1009,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( suffix @ TA @ ( append @ TA @ A @ B ) @ ( append @ TA @ C @ B ) )
      = ( suffix @ TA @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(81,axiom,
    ! [TA: $tType,A: list @ TA] : ( suffix @ TA @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_suffix__order_Odual__order_Orefl) ).

thf(543,plain,
    ! [TA: $tType,A: list @ TA] : ( suffix @ TA @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(85,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( suffix @ TA @ A @ B )
     => ( ( B = C )
       => ( suffix @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_suffix__order_Oord__le__eq__trans) ).

thf(560,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
      ( ( suffix @ TA @ A @ B )
     => ( ( B = C )
       => ( suffix @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(122,axiom,
    ! [A: node,B: g] :
      ( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
     => ( ( invar @ B )
       => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ B @ ( cons @ node @ A @ ( nil @ node ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_old_Oempty__path) ).

thf(676,plain,
    ! [A: node,B: g] :
      ( ( member @ node @ A @ ( set2 @ node @ ( alpha_n @ B ) ) )
     => ( ( invar @ B )
       => ( graph_1146196722h_path @ g @ node @ edgeD @ alpha_n @ invar @ inEdges @ B @ ( cons @ node @ A @ ( nil @ node ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(59,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/sandbox/benchmark/theBenchmark.p',fact_238_subset__code_I1_J) ).

thf(454,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)],[59]) ).

thf(33,axiom,
    ! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
      ( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
     => ( ! [D: TA > TA > $o,E: TA,F: list @ TA] :
            ( ( A @ D @ F )
           => ( A @ D @ ( cons @ TA @ E @ F ) ) )
       => ( A @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_sorted__wrt_Oinduct) ).

thf(364,plain,
    ! [TA: $tType,A: ( TA > TA > $o ) > ( list @ TA ) > $o,B: TA > TA > $o,C: list @ TA] :
      ( ! [D: TA > TA > $o] : ( A @ D @ ( nil @ TA ) )
     => ( ! [D: TA > TA > $o,E: TA,F: list @ TA] :
            ( ( A @ D @ F )
           => ( A @ D @ ( cons @ TA @ E @ F ) ) )
       => ( A @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(173,axiom,
    ! [TA: $tType,TB: $tType,A: list @ TB,B: list @ TA,C: ( list @ TB ) > ( list @ TA ) > $o] :
      ( ( A
       != ( nil @ TB ) )
     => ( ( B
         != ( nil @ TA ) )
       => ( ! [D: TB,E: TA] : ( C @ ( cons @ TB @ D @ ( nil @ TB ) ) @ ( cons @ TA @ E @ ( nil @ TA ) ) )
         => ( ! [D: TB,E: list @ TB,F: TA] :
                ( ( E
                 != ( nil @ TB ) )
               => ( C @ ( append @ TB @ E @ ( cons @ TB @ D @ ( nil @ TB ) ) ) @ ( cons @ TA @ F @ ( nil @ TA ) ) ) )
           => ( ! [D: TB,E: TA,F: list @ TA] :
                  ( ( F
                   != ( nil @ TA ) )
                 => ( C @ ( cons @ TB @ D @ ( nil @ TB ) ) @ ( append @ TA @ F @ ( cons @ TA @ E @ ( nil @ TA ) ) ) ) )
             => ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
                    ( ( C @ E @ G )
                   => ( ( E
                       != ( nil @ TB ) )
                     => ( ( G
                         != ( nil @ TA ) )
                       => ( C @ ( append @ TB @ E @ ( cons @ TB @ D @ ( nil @ TB ) ) ) @ ( append @ TA @ G @ ( cons @ TA @ F @ ( nil @ TA ) ) ) ) ) ) )
               => ( C @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_rev__nonempty__induct2_H) ).

thf(882,plain,
    ! [TA: $tType,TB: $tType,A: list @ TB,B: list @ TA,C: ( list @ TB ) > ( list @ TA ) > $o] :
      ( ( A
       != ( nil @ TB ) )
     => ( ( B
         != ( nil @ TA ) )
       => ( ! [D: TB,E: TA] : ( C @ ( cons @ TB @ D @ ( nil @ TB ) ) @ ( cons @ TA @ E @ ( nil @ TA ) ) )
         => ( ! [D: TB,E: list @ TB,F: TA] :
                ( ( E
                 != ( nil @ TB ) )
               => ( C @ ( append @ TB @ E @ ( cons @ TB @ D @ ( nil @ TB ) ) ) @ ( cons @ TA @ F @ ( nil @ TA ) ) ) )
           => ( ! [D: TB,E: TA,F: list @ TA] :
                  ( ( F
                   != ( nil @ TA ) )
                 => ( C @ ( cons @ TB @ D @ ( nil @ TB ) ) @ ( append @ TA @ F @ ( cons @ TA @ E @ ( nil @ TA ) ) ) ) )
             => ( ! [D: TB,E: list @ TB,F: TA,G: list @ TA] :
                    ( ( C @ E @ G )
                   => ( ( E
                       != ( nil @ TB ) )
                     => ( ( G
                         != ( nil @ TA ) )
                       => ( C @ ( append @ TB @ E @ ( cons @ TB @ D @ ( nil @ TB ) ) ) @ ( append @ TA @ G @ ( cons @ TA @ F @ ( nil @ TA ) ) ) ) ) ) )
               => ( C @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(65,axiom,
    ! [TA: $tType] :
      ( ( ord @ TA )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( A = B )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ( C = D )
             => ( ord_less_eq @ TA @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_ord__eq__le__eq__trans) ).

thf(469,plain,
    ! [TA: $tType] :
      ( ( ord @ TA )
     => ! [A: TA,B: TA,C: TA,D: TA] :
          ( ( A = B )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ( C = D )
             => ( ord_less_eq @ TA @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(187,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( ( A
          = ( nil @ TA ) )
       => ( ( hd @ TA @ ( append @ TA @ A @ B ) )
          = ( hd @ TA @ B ) ) )
      & ( ( A
         != ( nil @ TA ) )
       => ( ( hd @ TA @ ( append @ TA @ A @ B ) )
          = ( hd @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_hd__append) ).

thf(940,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( ( A
          = ( nil @ TA ) )
       => ( ( hd @ TA @ ( append @ TA @ A @ B ) )
          = ( hd @ TA @ B ) ) )
      & ( ( A
         != ( nil @ TA ) )
       => ( ( hd @ TA @ ( append @ TA @ A @ B ) )
          = ( hd @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(1271,plain,
    $false,
    inference(cvc4,[status(thm)],[1036,1024,760,347,909,518,1083,1179,555,481,352,308,873,1142,614,1173,1233,670,1001,288,1228,829,1095,1055,570,1264,344,949,460,934,357,1191,638,606,770,448,316,789,591,443,321,485,514,966,1169,692,293,866,396,998,411,265,602,981,380,678,661,925,534,1021,1042,598,392,275,729,1255,302,862,349,361,625,665,1159,1027,1128,710,324,1012,285,916,467,1089,1017,403,1006,869,989,1111,1227,1182,537,476,526,637,1039,622,1114,1231,1192,457,984,779,792,1086,266,633,805,311,765,1170,1185,662,773,586,906,1251,425,430,824,856,375,584,904,423,732,577,579,545,641,1139,445,572,1092,919,540,1258,704,406,681,737,616,271,599,784,1117,451,567,758,367,609,594,848,964,915,330,462,799,1162,726,399,278,1015,1176,851,922,658,912,521,768,827,695,1245,1166,589,531,548,1081,342,1145,355,754,473,1076,776,282,707,954,1267,409,1098,1070,872,414,971,673,1188,370,808,1052,978,314,612,859,465,931,903,581,1108,813,319,946,401,786,995,1030,433,667,478,272,383,290,378,832,684,967,835,854,1248,373,735,564,305,268,1197,1165,796,928,960,635,839,740,1236,1261,575,427,992,822,1004,691,501,607,332,1129,486,1009,543,560,676,454,364,882,469,940]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : ITP081^2 : TPTP v8.2.0. Released v7.5.0.
% 0.06/0.13  % Command  : run_Leo-III %s %d
% 0.13/0.34  % Computer : n005.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sat May 18 16:29:54 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 1.06/0.99  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.20/1.38  % [INFO] 	 Parsing done (390ms). 
% 2.20/1.40  % [INFO] 	 Running in sequential loop mode. 
% 3.33/1.78  % [INFO] 	 eprover registered as external prover. 
% 3.33/1.78  % [INFO] 	 cvc4 registered as external prover. 
% 3.33/1.79  % [INFO] 	 Scanning for conjecture ... 
% 3.69/1.97  % [INFO] 	 Found a conjecture (or negated_conjecture) and 263 axioms. Running axiom selection ... 
% 4.40/2.14  % [INFO] 	 Axiom selection finished. Selected 262 axioms (removed 1 axioms). 
% 5.96/2.57  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 6.17/2.60  % [INFO] 	 Type checking passed. 
% 6.17/2.60  % [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 ... 
% 77.22/30.68  % External prover 'cvc4' found a proof!
% 77.22/30.68  % [INFO] 	 Killing All external provers ... 
% 77.22/30.68  % Time passed: 30183ms (effective reasoning time: 29275ms)
% 77.22/30.68  % 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)>
% 77.22/30.68  % Axioms used in derivation (262): fact_23_old_Opath2__split_I1_J, fact_12_old_Opath2__split_I2_J, fact_125_eq__Nil__appendI, fact_157_split__list, fact_26_rs__def, fact_81_butlast_Osimps_I2_J, fact_74_butlast__snoc, fact_3_assms_I7_J, tcon_Set_Oset___Orderings_Oord_1, fact_218_suffix__append, fact_216_suffixI, tfree_0, fact_206_subset__Collect__conv, fact_200_list_Ocollapse, fact_224_suffix__order_Oantisym, fact_37_list__se__match_I2_J, fact_145_split__list__first__propE, fact_223_suffix__order_Oeq__iff, fact_211_suffix__Cons, fact_129_list_Osel_I2_J, fact_113_zipf_Oinduct, fact_82_butlast__append, fact_66_old_Opath2__prefix__ex, fact_219_suffix__appendD, fact_135_Cons__eq__append__conv, fact_50_append__same__eq, fact_7_rs_H__props_I1_J, fact_179_old_Opath__split_I2_J, fact_221_suffix__tl, fact_230_suffix__order_Oorder_Oantisym, fact_246_list_Oexpand, fact_175_old_Opath__not__Nil, fact_65_old_Opath2__split__ex_H, fact_83_in__set__butlast__appendI, fact_60_self__append__conv2, fact_253_prefix__order_Oeq__iff, fact_68_old_Opath2__induct, fact_188_same__suffix__suffix, fact_144_in__set__conv__decomp__last, fact_34_list__e__eq__lel_I1_J, fact_121_list_Oset__intros_I2_J, fact_97_arg__min__list_Oinduct, fact_40_list__ee__eq__leel_I1_J, fact_119_set__ConsD, tcon_fun___Orderings_Oord, fact_80_butlast__tl, fact_165_old_Opath2__simple__loop, fact_15_rs_H__props_I3_J, fact_196_hd__append2, fact_170_defs__finite, fact_28_old_Oempty__path2, fact_44_append_Oassoc, fact_108_splice_Oinduct, fact_59_append__self__conv2, fact_38_list__se__match_I1_J, fact_30_rs_H__props_I4_J, tcon_HOL_Obool___Orderings_Olinorder, fact_235_suffix__order_Odual__order_Oantisym, fact_18_old_Opath2__in___092_060alpha_062n, fact_128_list_Osel_I3_J, fact_19_old_Oelem__set__implies__elem__tl__app__cons, fact_155_split__list__prop, fact_95_list__all__zip_Oinduct, fact_212_suffix__bot_Obot_Oextremum__uniqueI, fact_51_same__append__eq, fact_5_old_Opath2__app, fact_236_list_Osel_I1_J, fact_27_ri__props_I4_J, fact_63_empty__append__eq__id, fact_150_in__set__conv__decomp, fact_215_suffixE, fact_228_suffix__order_Oantisym__conv, fact_103_transpose_Ocases, fact_89_append__eq__append__conv2, fact_239_set__mono__prefix, fact_244_not__suffix__cases, fact_152_split__list__propE, fact_114_revg_Oinduct, fact_46_Collect__mem__eq, fact_43_list_Oinject, fact_76__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062i_Ari_O_A_092_060lbrakk_062g_A_092_060turnstile_062_AdefNode_Ag_Ar_Nri_092_060rightarrow_062i_059_Ai_A_092_060in_062_Aset_Ams_059_A_092_060forall_062n_092_060in_062set_A_Ibutlast_Ari_J_O_An_A_092_060notin_062_Aset_Ams_059_Aprefix_Ari_Ars_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_69_old_Opath2__split__ex, fact_161_list_Oset__sel_I2_J, fact_16_old_Opath2__hd__in___092_060alpha_062n, fact_93_map__tailrec__rev_Oinduct, fact_194_old_Opath_Ocases, fact_22_old_Opath2__last__in__ns, fact_101_remdups__adj_Ocases, fact_92_mergesort__by__rel__merge_Oinduct, fact_100_sorted__wrt_Oinduct, fact_78_butlast_Osimps_I1_J, fact_88_append__eq__appendI, fact_153_split__list__first, fact_202_old_Opath__invar, fact_35_list__se__match_I4_J, fact_73_append1__eq__conv, fact_159_tl__Nil, fact_209_suffix__ConsI, fact_62_append__is__Nil__conv, fact_111_list_Oinducts, fact_130_list__append__eq__Cons__cases, fact_109_list__induct2_H, fact_210_suffix__ConsD, fact_156_split__list__last, fact_229_suffix__order_Oorder_Oeq__iff, fact_149_in__set__list__format, fact_49_append__assoc, fact_75__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062ms_H_O_A_092_060lbrakk_062g_A_092_060turnstile_062_Am_Nms_H_092_060rightarrow_062i_059_Aprefix_Ams_H_Ams_059_Ai_A_092_060notin_062_Aset_A_Ibutlast_Ams_H_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_67_old_Opath2__split__first__prop, fact_110_neq__Nil__conv, fact_9_rs__props_I1_J, fact_213_suffix__bot_Obot_Oextremum, fact_141_split__list__first__prop__iff, fact_208_suffix__ConsD2, fact_41_ms_H__props_I2_J, fact_84_butlast__eq__cons__conv, fact_126_append__Nil, fact_177_old_Opath2__forget__hd, fact_137_rev__induct2_H, fact_193_old_Opath_Oinducts, fact_147_split__list__first__prop, fact_2_old_Oinvar, fact_10_ms_H__props_I1_J, fact_116_neq__NilE, fact_102_list__2pre__induct, fact_181_Cons__prefix__Cons, fact_192_old_Opath_Osimps, fact_21_old_Opath2__tl__in___092_060alpha_062n, fact_227_suffix__order_Oorder__trans, fact_87_not__Cons__self2, fact_162_prefix__snoc, fact_45_mem__Collect__eq, fact_226_suffix__order_Oorder_Otrans, fact_189_old_Oempty__path, fact_232_suffix__order_Oord__le__eq__trans, fact_163_old_Opath2__split__first__last, fact_254_prefix__order_Oantisym, fact_140_rev__induct, fact_53_old_Osuccessor__is__node, fact_134_append__eq__Cons__conv, fact_186_suffix__Nil, fact_54_old_Osuccessor__in___092_060alpha_062n, fact_77_old_OCons__path2, fact_241_hd__in__set, fact_169_old_Opath2__split__last__prop, fact_56_append__Nil2, fact_117_list_Odistinct_I1_J, fact_24_rs__props_I3_J, fact_124_list__match__lel__lel, fact_29_ms_H__props_I3_J, fact_85_butlast__eq__consE, fact_222_suffix__same__cases, fact_178_old_Opath__hd, fact_217_Sublist_Osuffix__def, fact_71_old_Opath2__rev__induct, fact_233_suffix__order_Odual__order_Otrans, fact_47_Collect__cong, fact_136_neq__Nil__rev__conv, fact_225_suffix__order_Oeq__refl, fact_231_suffix__order_Oord__eq__le__trans, fact_183_prefix__Nil, fact_1_ri__is__valid, fact_199_hd__Cons__tl, fact_154_xy__in__set__cases, fact_58_self__append__conv, subcl_Orderings_Olinorder___Orderings_Oord, fact_112_list_Oexhaust, fact_207_ord__eq__le__eq__trans, fact_167_old_Opath__snoc, fact_61_Nil__is__append__conv, fact_106_min__list_Ocases, fact_36_list__se__match_I3_J, fact_99_remdups__adj_Oinduct, fact_8_assms_I10_J, fact_172_prefix__order_Odual__order_Orefl, fact_168_phiUses__finite, fact_90_strict__sorted_Oinduct, fact_249_list_Oexhaust__sel, fact_57_append__self__conv, fact_248_set__subset__Cons, fact_42_ri__props_I3_J, fact_148_split__list__last__prop, fact_220_suffix__appendI, fact_171_prefix__order_Oorder__refl, fact_139_rev__exhaust, fact_4_ri__props_I1_J, fact_204_old_Opath__by__tail, fact_173_suffix__order_Oorder__refl, fact_131_list__Cons__eq__append__cases, fact_105_min__list_Oinduct, fact_55_old_Opath2__app_H, fact_70_old_Opath2__prefix, fact_107_induct__list012, fact_198_snoc__suffix__snoc, fact_164_same__prefix__nil, fact_52_old_Opredecessor__is__node, fact_243_longest__common__prefix, fact_72_old_Opath2__snoc, tfree_1, fact_205_set__mono__suffix, fact_118_list_Oset__cases, fact_182_prefix__code_I1_J, fact_195_same__suffix__nil, fact_94_list__nonempty__induct, fact_142_split__list__last__prop__iff, fact_14_old_Opath2__not__Nil2, fact_160_Nil__tl, fact_238_subset__code_I1_J, fact_86_list__tail__coinc, fact_133_rev__nonempty__induct, fact_252_prefix__same__cases, fact_122_Cons__eq__appendI, fact_127_append_Oleft__neutral, fact_0_False, fact_6__092_060open_062defNode_Ag_A_092_060phi_062_092_060_094sub_062r_A_092_060noteq_062_AdefNode_Ag_Ar_092_060close_062, fact_32_tl__append2, fact_11__092_060open_062_092_060And_062thesis_O_A_092_060lbrakk_062i_A_061_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_A_092_060Longrightarrow_062_Athesis_059_A_092_060lbrakk_062i_A_092_060noteq_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_059_Am_A_061_Ai_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_059_A_092_060lbrakk_062i_A_092_060noteq_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_059_Am_A_092_060noteq_062_Ai_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_104_shuffles_Oinduct, fact_237_finite__list, fact_39_list__ee__eq__leel_I2_J, fact_190_old_Opath__split_I1_J, fact_120_list_Oset__intros_I1_J, fact_180_List_Ofinite__set, fact_33_list__e__eq__lel_I2_J, fact_123_append__Cons, fact_247_not__hd__in__tl, fact_166_old_Opath2__cases, fact_214_Nil__suffix, fact_25_rs_H__loopfree, fact_64_append_Oright__neutral, fact_132_rev__nonempty__induct2_H, fact_187_same__prefix__prefix, fact_250_tl__subset, fact_31_assms_I8_J, subcl_Orderings_Olinorder___HOL_Otype, fact_234_suffix__order_Odual__order_Oeq__iff, fact_91_mergesort__by__rel__merge__induct, fact_191_old_OCons__path, fact_176_old_Opath2__hd, fact_96_successively_Oinduct, fact_98_list__induct__first2, fact_13_old_Opath2__not__Nil, fact_245_not__suffix__induct, fact_242_hd__append, fact_185_suffix__bot_Obot_Oextremum__unique, fact_79_in__set__butlastD, fact_174_suffix__order_Odual__order_Orefl, fact_20_ri__props_I2_J, fact_138_neq__Nil__revE, fact_184_prefix__bot_Obot_Oextremum__unique, tcon_HOL_Obool___Orderings_Oord_2, fact_146_split__list__last__propE, fact_203_old_Opath__in___092_060alpha_062n, fact_240_list_Oset__sel_I1_J, fact_17_old_Opath2__hd__in__ns, fact_143_in__set__conv__decomp__first, fact_115_list_OdiscI, fact_158_tl__obtain__elem, fact_197_suffix__snoc, fact_251_butlast__subset, fact_201_in__hd__or__tl__conv, fact_151_append__Cons__eq__iff
% 77.22/30.68  % No. of inferences in proof: 528
% 77.22/30.68  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 30183 ms resp. 29275 ms w/o parsing
% 77.89/30.87  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 77.89/30.87  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------