%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ITP051^2 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n003.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 22:22:25 EDT 2024

% Result   : Theorem 86.24s 28.68s
% Output   : Refutation 87.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   79
%            Number of leaves      :  324
% Syntax   : Number of formulae    : 1090 ( 366 unt;  50 typ;   0 def)
%            Number of atoms       : 3120 ( 576 equ;   4 cnn)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives : 9338 ( 459   ~; 310   |;  78   &;7858   @)
%                                         (   0 <=>; 633  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   76 (  16 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  : 7256 (7256   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   54 (  50 usr;  12 con; 0-5 aty)
%            Number of variables   : 8669 (  74   ^8486   !;  73   ?;8669   :)
%                                         (  36  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(nat_type,type,
    nat: $tType ).

thf(b_type,type,
    b: $tType ).

thf(a_type,type,
    a: $tType ).

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

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

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

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

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

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

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

thf(canoni770627133id_add_type,type,
    canoni770627133id_add: 
      !>[TA: $tType] : $o ).

thf(edmond2129202899alysis_type,type,
    edmond2129202899alysis: 
      !>[TA: $tType] : ( ( ( product_prod @ nat @ nat ) > TA ) > $o ) ).

thf(edmond115586663easure_type,type,
    edmond115586663easure: 
      !>[TA: $tType] : ( ( ( product_prod @ nat @ nat ) > TA ) > nat > nat > nat ) ).

thf(edmond1803015688pEdges_type,type,
    edmond1803015688pEdges: 
      !>[TA: $tType] : ( ( ( product_prod @ nat @ nat ) > TA ) > nat > nat > ( set @ ( product_prod @ nat @ nat ) ) ) ).

thf(edmond259086305sis_uE_type,type,
    edmond259086305sis_uE: 
      !>[TA: $tType] : ( ( ( product_prod @ nat @ nat ) > TA ) > ( set @ ( product_prod @ nat @ nat ) ) ) ).

thf(finite_card_type,type,
    finite_card: 
      !>[TA: $tType] : ( ( set @ TA ) > nat ) ).

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

thf(finite_Graph_type,type,
    finite_Graph: 
      !>[TA: $tType] : ( ( ( product_prod @ nat @ nat ) > TA ) > $o ) ).

thf(e_type,type,
    e: 
      !>[TA: $tType] : ( ( ( product_prod @ nat @ nat ) > TA ) > ( set @ ( product_prod @ nat @ nat ) ) ) ).

thf(v_type,type,
    v: 
      !>[TA: $tType] : ( ( ( product_prod @ nat @ nat ) > TA ) > ( set @ nat ) ) ).

thf(adjacent_nodes_type,type,
    adjacent_nodes: 
      !>[TA: $tType] : ( ( ( product_prod @ nat @ nat ) > TA ) > nat > ( set @ nat ) ) ).

thf(connected_type,type,
    connected: 
      !>[TA: $tType] : ( ( ( product_prod @ nat @ nat ) > TA ) > nat > nat > $o ) ).

thf(dist_type,type,
    dist: 
      !>[TA: $tType] : ( ( ( product_prod @ nat @ nat ) > TA ) > nat > nat > nat > $o ) ).

thf(incoming_type,type,
    incoming: 
      !>[TA: $tType] : ( ( ( product_prod @ nat @ nat ) > TA ) > ( set @ nat ) > ( set @ ( product_prod @ nat @ nat ) ) ) ).

thf(isPath_type,type,
    isPath: 
      !>[TA: $tType] : ( ( ( product_prod @ nat @ nat ) > TA ) > nat > ( list @ ( product_prod @ nat @ nat ) ) > nat > $o ) ).

thf(isShortestPath_type,type,
    isShortestPath: 
      !>[TA: $tType] : ( ( ( product_prod @ nat @ nat ) > TA ) > nat > ( list @ ( product_prod @ nat @ nat ) ) > nat > $o ) ).

thf(isSimplePath_type,type,
    isSimplePath: 
      !>[TA: $tType] : ( ( ( product_prod @ nat @ nat ) > TA ) > nat > ( list @ ( product_prod @ nat @ nat ) ) > nat > $o ) ).

thf(min_dist_type,type,
    min_dist: 
      !>[TA: $tType] : ( ( ( product_prod @ nat @ nat ) > TA ) > nat > nat > nat ) ).

thf(outgoing_type,type,
    outgoing: 
      !>[TA: $tType] : ( ( ( product_prod @ nat @ nat ) > TA ) > ( set @ nat ) > ( set @ ( product_prod @ nat @ nat ) ) ) ).

thf(reachableNodes_type,type,
    reachableNodes: 
      !>[TA: $tType] : ( ( ( product_prod @ nat @ nat ) > TA ) > nat > ( set @ nat ) ) ).

thf(zero_zero_type,type,
    zero_zero: 
      !>[TA: $tType] : TA ).

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

thf(size_size_type,type,
    size_size: 
      !>[TA: $tType] : ( TA > nat ) ).

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

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

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

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

thf(c_type,type,
    c: ( product_prod @ nat @ nat ) > a ).

thf(c2_type,type,
    c2: ( product_prod @ nat @ nat ) > b ).

thf(edges_type,type,
    edges: set @ ( product_prod @ nat @ nat ) ).

thf(p_type,type,
    p: list @ ( product_prod @ nat @ nat ) ).

thf(p2_type,type,
    p2: list @ ( product_prod @ nat @ nat ) ).

thf(s_type,type,
    s: nat ).

thf(t_type,type,
    t: nat ).

thf(sk1_type,type,
    sk1: list @ ( product_prod @ nat @ nat ) ).

thf(sk2_type,type,
    sk2: nat > nat > nat > nat > nat ).

thf(sk3_type,type,
    sk3: nat > nat > nat > nat > nat ).

thf(sk4_type,type,
    sk4: 
      !>[TA: $tType] : ( ( list @ TA ) > ( ( list @ TA ) > $o ) > ( list @ TA ) ) ).

thf(sk5_type,type,
    sk5: nat > nat > ( list @ ( product_prod @ nat @ nat ) ) ).

thf(sk44_type,type,
    sk44: 
      !>[TA: $tType] : ( TA > ( set @ TA ) > TA ) ).

thf(275,axiom,
    linordered_idom @ b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_1) ).

thf(977,plain,
    linordered_idom @ b,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(259,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( order @ TA ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Orderings_Oorder) ).

thf(953,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( order @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(954,plain,
    ! [TA: $tType] :
      ( ~ ( linordered_idom @ TA )
      | ( order @ TA ) ),
    inference(cnf,[status(esa)],[953]) ).

thf(1035,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
      | ( ( linordered_idom @ b )
       != ( linordered_idom @ TA ) ) ),
    inference(paramod_ordered,[status(thm)],[977,954]) ).

thf(1036,plain,
    order @ b,
    inference(pattern_uni,[status(thm)],[1035:[bind_type(TA,$thf( b ))]]) ).

thf(264,axiom,
    order @ nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_1) ).

thf(961,plain,
    order @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(261,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( order @ TA )
     => ( order @ ( TB > TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).

thf(957,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( order @ TA )
     => ( order @ ( TB > TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(958,plain,
    ! [TA: $tType,TB: $tType] :
      ( ~ ( order @ TB )
      | ( order @ ( TA > TB ) ) ),
    inference(cnf,[status(esa)],[957]) ).

thf(1075,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( order @ ( TA > TB ) )
      | ( ( order @ nat )
       != ( order @ TB ) ) ),
    inference(paramod_ordered,[status(thm)],[961,958]) ).

thf(1076,plain,
    ! [TA: $tType] : ( order @ ( TA > nat ) ),
    inference(pattern_uni,[status(thm)],[1075:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( nat ))]]) ).

thf(1086,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( order @ ( TB > TC ) )
      | ( ( order @ ( TA > nat ) )
       != ( order @ TC ) ) ),
    inference(paramod_ordered,[status(thm)],[1076,958]) ).

thf(1087,plain,
    ! [TA: $tType,TB: $tType] : ( order @ ( TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[1086:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TA > nat ))]]) ).

thf(1106,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
      ( ( order @ ( TC > TD ) )
      | ( ( order @ ( TB > TA > nat ) )
       != ( order @ TD ) ) ),
    inference(paramod_ordered,[status(thm)],[1087,958]) ).

thf(1107,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] : ( order @ ( TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[1106:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TB > TA > nat ))]]) ).

thf(1116,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
      ( ( order @ ( TD > TE ) )
      | ( ( order @ ( TC > TB > TA > nat ) )
       != ( order @ TE ) ) ),
    inference(paramod_ordered,[status(thm)],[1107,958]) ).

thf(1117,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( order @ ( TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[1116:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TC > TB > TA > nat ))]]) ).

thf(1131,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
      ( ( order @ ( TE > TF ) )
      | ( ( order @ ( TD > TC > TB > TA > nat ) )
       != ( order @ TF ) ) ),
    inference(paramod_ordered,[status(thm)],[1117,958]) ).

thf(1132,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] : ( order @ ( TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[1131:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TD > TC > TB > TA > nat ))]]) ).

thf(1162,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
      ( ( order @ ( TF > TG ) )
      | ( ( order @ ( TE > TD > TC > TB > TA > nat ) )
       != ( order @ TG ) ) ),
    inference(paramod_ordered,[status(thm)],[1132,958]) ).

thf(1163,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] : ( order @ ( TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[1162:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TE > TD > TC > TB > TA > nat ))]]) ).

thf(1173,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] :
      ( ( order @ ( TG > TH ) )
      | ( ( order @ ( TF > TE > TD > TC > TB > TA > nat ) )
       != ( order @ TH ) ) ),
    inference(paramod_ordered,[status(thm)],[1163,958]) ).

thf(1174,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] : ( order @ ( TG > TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[1173:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(1193,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] :
      ( ( order @ ( TH > TI ) )
      | ( ( order @ ( TG > TF > TE > TD > TC > TB > TA > nat ) )
       != ( order @ TI ) ) ),
    inference(paramod_ordered,[status(thm)],[1174,958]) ).

thf(1194,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] : ( order @ ( TH > TG > TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[1193:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(1204,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] :
      ( ( order @ ( TI > TJ ) )
      | ( ( order @ ( TH > TG > TF > TE > TD > TC > TB > TA > nat ) )
       != ( order @ TJ ) ) ),
    inference(paramod_ordered,[status(thm)],[1194,958]) ).

thf(1205,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] : ( order @ ( TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[1204:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(1638,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] :
      ( ( order @ ( TJ > TK ) )
      | ( ( order @ ( TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) )
       != ( order @ TK ) ) ),
    inference(paramod_ordered,[status(thm)],[1205,958]) ).

thf(1639,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] : ( order @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[1638:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(1755,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] :
      ( ( order @ ( TK > TL ) )
      | ( ( order @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) )
       != ( order @ TL ) ) ),
    inference(paramod_ordered,[status(thm)],[1639,958]) ).

thf(1756,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] : ( order @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[1755:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(1786,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] :
      ( ( order @ ( TL > TM ) )
      | ( ( order @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) )
       != ( order @ TM ) ) ),
    inference(paramod_ordered,[status(thm)],[1756,958]) ).

thf(1787,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] : ( order @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[1786:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(1862,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] :
      ( ( order @ ( TM > TN ) )
      | ( ( order @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) )
       != ( order @ TN ) ) ),
    inference(paramod_ordered,[status(thm)],[1787,958]) ).

thf(1863,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] : ( order @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[1862:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(1896,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] :
      ( ( order @ ( TN > TO ) )
      | ( ( order @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) )
       != ( order @ TO ) ) ),
    inference(paramod_ordered,[status(thm)],[1863,958]) ).

thf(1897,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] : ( order @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[1896:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(1995,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] :
      ( ( order @ ( TO > TP ) )
      | ( ( order @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) )
       != ( order @ TP ) ) ),
    inference(paramod_ordered,[status(thm)],[1897,958]) ).

thf(1996,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] : ( order @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[1995:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(2127,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] :
      ( ( order @ ( TP > TQ ) )
      | ( ( order @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) )
       != ( order @ TQ ) ) ),
    inference(paramod_ordered,[status(thm)],[1996,958]) ).

thf(2128,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] : ( order @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[2127:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(2208,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] :
      ( ( order @ ( TQ > TR ) )
      | ( ( order @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) )
       != ( order @ TR ) ) ),
    inference(paramod_ordered,[status(thm)],[2128,958]) ).

thf(2209,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] : ( order @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[2208:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(2233,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType] :
      ( ( order @ ( TR > TS ) )
      | ( ( order @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) )
       != ( order @ TS ) ) ),
    inference(paramod_ordered,[status(thm)],[2209,958]) ).

thf(2234,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] : ( order @ ( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[2233:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(2379,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType] :
      ( ( order @ ( TS > TT ) )
      | ( ( order @ ( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) )
       != ( order @ TT ) ) ),
    inference(paramod_ordered,[status(thm)],[2234,958]) ).

thf(2380,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType] : ( order @ ( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[2379:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(2685,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType] :
      ( ( order @ ( TT > TU ) )
      | ( ( order @ ( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) )
       != ( order @ TU ) ) ),
    inference(paramod_ordered,[status(thm)],[2380,958]) ).

thf(2686,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType] : ( order @ ( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[2685:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(2744,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType] :
      ( ( order @ ( TU > TV ) )
      | ( ( order @ ( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) )
       != ( order @ TV ) ) ),
    inference(paramod_ordered,[status(thm)],[2686,958]) ).

thf(2745,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType] : ( order @ ( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[2744:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(3127,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType] :
      ( ( order @ ( TV > TW ) )
      | ( ( order @ ( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) )
       != ( order @ TW ) ) ),
    inference(paramod_ordered,[status(thm)],[2745,958]) ).

thf(3128,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType] : ( order @ ( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[3127:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(3176,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType] :
      ( ( order @ ( TW > TX ) )
      | ( ( order @ ( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) )
       != ( order @ TX ) ) ),
    inference(paramod_ordered,[status(thm)],[3128,958]) ).

thf(3177,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType] : ( order @ ( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[3176:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(3225,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType] :
      ( ( order @ ( TX > TY ) )
      | ( ( order @ ( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) )
       != ( order @ TY ) ) ),
    inference(paramod_ordered,[status(thm)],[3177,958]) ).

thf(3226,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType] : ( order @ ( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[3225:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(3260,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType] :
      ( ( order @ ( TY > TZ ) )
      | ( ( order @ ( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) )
       != ( order @ TZ ) ) ),
    inference(paramod_ordered,[status(thm)],[3226,958]) ).

thf(3261,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType] : ( order @ ( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[3260:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(3379,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType] :
      ( ( order @ ( TZ > TZA ) )
      | ( ( order @ ( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) )
       != ( order @ TZA ) ) ),
    inference(paramod_ordered,[status(thm)],[3261,958]) ).

thf(3380,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType] : ( order @ ( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[3379:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(3507,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType] :
      ( ( order @ ( TZA > TZB ) )
      | ( ( order @ ( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) )
       != ( order @ TZB ) ) ),
    inference(paramod_ordered,[status(thm)],[3380,958]) ).

thf(3508,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType] : ( order @ ( TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[3507:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(3542,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType] :
      ( ( order @ ( TZB > TZC ) )
      | ( ( order @ ( TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) )
       != ( order @ TZC ) ) ),
    inference(paramod_ordered,[status(thm)],[3508,958]) ).

thf(3543,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType] : ( order @ ( TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[3542:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(3665,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType] :
      ( ( order @ ( TZC > TZD ) )
      | ( ( order @ ( TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) )
       != ( order @ TZD ) ) ),
    inference(paramod_ordered,[status(thm)],[3543,958]) ).

thf(3666,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType] : ( order @ ( TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[3665:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(3798,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType] :
      ( ( order @ ( TZD > TZE ) )
      | ( ( order @ ( TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) )
       != ( order @ TZE ) ) ),
    inference(paramod_ordered,[status(thm)],[3666,958]) ).

thf(3799,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType] : ( order @ ( TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[3798:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(3928,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType] :
      ( ( order @ ( TZE > TZF ) )
      | ( ( order @ ( TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) )
       != ( order @ TZF ) ) ),
    inference(paramod_ordered,[status(thm)],[3799,958]) ).

thf(3929,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType] : ( order @ ( TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[3928:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(3963,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType] :
      ( ( order @ ( TZF > TZG ) )
      | ( ( order @ ( TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) )
       != ( order @ TZG ) ) ),
    inference(paramod_ordered,[status(thm)],[3929,958]) ).

thf(3964,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType] : ( order @ ( TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[3963:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(4028,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType] :
      ( ( order @ ( TZG > TZH ) )
      | ( ( order @ ( TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) )
       != ( order @ TZH ) ) ),
    inference(paramod_ordered,[status(thm)],[3964,958]) ).

thf(4029,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType] : ( order @ ( TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[4028:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(4096,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType] :
      ( ( order @ ( TZH > TZI ) )
      | ( ( order @ ( TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) )
       != ( order @ TZI ) ) ),
    inference(paramod_ordered,[status(thm)],[4029,958]) ).

thf(4097,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType] : ( order @ ( TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[4096:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(4168,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType] :
      ( ( order @ ( TZI > TZJ ) )
      | ( ( order @ ( TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) )
       != ( order @ TZJ ) ) ),
    inference(paramod_ordered,[status(thm)],[4097,958]) ).

thf(4169,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType] : ( order @ ( TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[4168:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(31,axiom,
    ! [A: nat] :
      ( ( min_dist @ a @ c @ A @ A )
      = ( zero_zero @ nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_min__dist__z) ).

thf(333,plain,
    ! [A: nat] :
      ( ( min_dist @ a @ c @ A @ A )
      = ( zero_zero @ nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(230,axiom,
    ! [A: set @ nat] : ( ord_less_eq @ ( set @ ( product_prod @ nat @ nat ) ) @ ( outgoing @ a @ c @ A ) @ ( e @ a @ c ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_outgoing_H__edges) ).

thf(893,plain,
    ! [A: set @ nat] : ( ord_less_eq @ ( set @ ( product_prod @ nat @ nat ) ) @ ( outgoing @ a @ c @ A ) @ ( e @ a @ c ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(270,axiom,
    order @ $o,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_5) ).

thf(969,plain,
    order @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(1067,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( order @ ( TA > TB ) )
      | ( ( order @ $o )
       != ( order @ TB ) ) ),
    inference(paramod_ordered,[status(thm)],[969,958]) ).

thf(1068,plain,
    ! [TA: $tType] : ( order @ ( TA > $o ) ),
    inference(pattern_uni,[status(thm)],[1067:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( $o ))]]) ).

thf(1082,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( order @ ( TB > TC ) )
      | ( ( order @ ( TA > $o ) )
       != ( order @ TC ) ) ),
    inference(paramod_ordered,[status(thm)],[1068,958]) ).

thf(1083,plain,
    ! [TA: $tType,TB: $tType] : ( order @ ( TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[1082:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TA > $o ))]]) ).

thf(1102,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
      ( ( order @ ( TC > TD ) )
      | ( ( order @ ( TB > TA > $o ) )
       != ( order @ TD ) ) ),
    inference(paramod_ordered,[status(thm)],[1083,958]) ).

thf(1103,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] : ( order @ ( TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[1102:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TB > TA > $o ))]]) ).

thf(1112,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
      ( ( order @ ( TD > TE ) )
      | ( ( order @ ( TC > TB > TA > $o ) )
       != ( order @ TE ) ) ),
    inference(paramod_ordered,[status(thm)],[1103,958]) ).

thf(1113,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( order @ ( TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[1112:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TC > TB > TA > $o ))]]) ).

thf(1127,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
      ( ( order @ ( TE > TF ) )
      | ( ( order @ ( TD > TC > TB > TA > $o ) )
       != ( order @ TF ) ) ),
    inference(paramod_ordered,[status(thm)],[1113,958]) ).

thf(1128,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] : ( order @ ( TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[1127:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TD > TC > TB > TA > $o ))]]) ).

thf(1150,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
      ( ( order @ ( TF > TG ) )
      | ( ( order @ ( TE > TD > TC > TB > TA > $o ) )
       != ( order @ TG ) ) ),
    inference(paramod_ordered,[status(thm)],[1128,958]) ).

thf(1151,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] : ( order @ ( TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[1150:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TE > TD > TC > TB > TA > $o ))]]) ).

thf(1169,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] :
      ( ( order @ ( TG > TH ) )
      | ( ( order @ ( TF > TE > TD > TC > TB > TA > $o ) )
       != ( order @ TH ) ) ),
    inference(paramod_ordered,[status(thm)],[1151,958]) ).

thf(1170,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] : ( order @ ( TG > TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[1169:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(1189,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] :
      ( ( order @ ( TH > TI ) )
      | ( ( order @ ( TG > TF > TE > TD > TC > TB > TA > $o ) )
       != ( order @ TI ) ) ),
    inference(paramod_ordered,[status(thm)],[1170,958]) ).

thf(1190,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] : ( order @ ( TH > TG > TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[1189:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(1200,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] :
      ( ( order @ ( TI > TJ ) )
      | ( ( order @ ( TH > TG > TF > TE > TD > TC > TB > TA > $o ) )
       != ( order @ TJ ) ) ),
    inference(paramod_ordered,[status(thm)],[1190,958]) ).

thf(1201,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] : ( order @ ( TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[1200:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(1614,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] :
      ( ( order @ ( TJ > TK ) )
      | ( ( order @ ( TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) )
       != ( order @ TK ) ) ),
    inference(paramod_ordered,[status(thm)],[1201,958]) ).

thf(1615,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] : ( order @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[1614:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(1653,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] :
      ( ( order @ ( TK > TL ) )
      | ( ( order @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) )
       != ( order @ TL ) ) ),
    inference(paramod_ordered,[status(thm)],[1615,958]) ).

thf(1654,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] : ( order @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[1653:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(1776,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] :
      ( ( order @ ( TL > TM ) )
      | ( ( order @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) )
       != ( order @ TM ) ) ),
    inference(paramod_ordered,[status(thm)],[1654,958]) ).

thf(1777,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] : ( order @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[1776:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(1801,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] :
      ( ( order @ ( TM > TN ) )
      | ( ( order @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) )
       != ( order @ TN ) ) ),
    inference(paramod_ordered,[status(thm)],[1777,958]) ).

thf(1802,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] : ( order @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[1801:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(1886,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] :
      ( ( order @ ( TN > TO ) )
      | ( ( order @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) )
       != ( order @ TO ) ) ),
    inference(paramod_ordered,[status(thm)],[1802,958]) ).

thf(1887,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] : ( order @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[1886:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(1957,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] :
      ( ( order @ ( TO > TP ) )
      | ( ( order @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) )
       != ( order @ TP ) ) ),
    inference(paramod_ordered,[status(thm)],[1887,958]) ).

thf(1958,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] : ( order @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[1957:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(2117,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] :
      ( ( order @ ( TP > TQ ) )
      | ( ( order @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) )
       != ( order @ TQ ) ) ),
    inference(paramod_ordered,[status(thm)],[1958,958]) ).

thf(2118,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] : ( order @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[2117:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(2142,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] :
      ( ( order @ ( TQ > TR ) )
      | ( ( order @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) )
       != ( order @ TR ) ) ),
    inference(paramod_ordered,[status(thm)],[2118,958]) ).

thf(2143,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] : ( order @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[2142:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(2223,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType] :
      ( ( order @ ( TR > TS ) )
      | ( ( order @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) )
       != ( order @ TS ) ) ),
    inference(paramod_ordered,[status(thm)],[2143,958]) ).

thf(2224,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] : ( order @ ( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[2223:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(2369,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType] :
      ( ( order @ ( TS > TT ) )
      | ( ( order @ ( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) )
       != ( order @ TT ) ) ),
    inference(paramod_ordered,[status(thm)],[2224,958]) ).

thf(2370,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType] : ( order @ ( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[2369:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(2395,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType] :
      ( ( order @ ( TT > TU ) )
      | ( ( order @ ( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) )
       != ( order @ TU ) ) ),
    inference(paramod_ordered,[status(thm)],[2370,958]) ).

thf(2396,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType] : ( order @ ( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[2395:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(2734,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType] :
      ( ( order @ ( TU > TV ) )
      | ( ( order @ ( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) )
       != ( order @ TV ) ) ),
    inference(paramod_ordered,[status(thm)],[2396,958]) ).

thf(2735,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType] : ( order @ ( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[2734:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(3087,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType] :
      ( ( order @ ( TV > TW ) )
      | ( ( order @ ( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) )
       != ( order @ TW ) ) ),
    inference(paramod_ordered,[status(thm)],[2735,958]) ).

thf(3088,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType] : ( order @ ( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[3087:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(3162,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType] :
      ( ( order @ ( TW > TX ) )
      | ( ( order @ ( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) )
       != ( order @ TX ) ) ),
    inference(paramod_ordered,[status(thm)],[3088,958]) ).

thf(3163,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType] : ( order @ ( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[3162:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(3197,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType] :
      ( ( order @ ( TX > TY ) )
      | ( ( order @ ( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) )
       != ( order @ TY ) ) ),
    inference(paramod_ordered,[status(thm)],[3163,958]) ).

thf(3198,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType] : ( order @ ( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[3197:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(3246,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType] :
      ( ( order @ ( TY > TZ ) )
      | ( ( order @ ( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) )
       != ( order @ TZ ) ) ),
    inference(paramod_ordered,[status(thm)],[3198,958]) ).

thf(3247,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType] : ( order @ ( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[3246:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(3365,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType] :
      ( ( order @ ( TZ > TZA ) )
      | ( ( order @ ( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) )
       != ( order @ TZA ) ) ),
    inference(paramod_ordered,[status(thm)],[3247,958]) ).

thf(3366,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType] : ( order @ ( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[3365:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(3401,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType] :
      ( ( order @ ( TZA > TZB ) )
      | ( ( order @ ( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) )
       != ( order @ TZB ) ) ),
    inference(paramod_ordered,[status(thm)],[3366,958]) ).

thf(3402,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType] : ( order @ ( TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[3401:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(3528,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType] :
      ( ( order @ ( TZB > TZC ) )
      | ( ( order @ ( TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) )
       != ( order @ TZC ) ) ),
    inference(paramod_ordered,[status(thm)],[3402,958]) ).

thf(3529,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType] : ( order @ ( TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[3528:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(3651,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType] :
      ( ( order @ ( TZC > TZD ) )
      | ( ( order @ ( TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) )
       != ( order @ TZD ) ) ),
    inference(paramod_ordered,[status(thm)],[3529,958]) ).

thf(3652,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType] : ( order @ ( TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[3651:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(3784,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType] :
      ( ( order @ ( TZD > TZE ) )
      | ( ( order @ ( TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) )
       != ( order @ TZE ) ) ),
    inference(paramod_ordered,[status(thm)],[3652,958]) ).

thf(3785,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType] : ( order @ ( TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[3784:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(3819,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType] :
      ( ( order @ ( TZE > TZF ) )
      | ( ( order @ ( TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) )
       != ( order @ TZF ) ) ),
    inference(paramod_ordered,[status(thm)],[3785,958]) ).

thf(3820,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType] : ( order @ ( TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[3819:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(3949,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType] :
      ( ( order @ ( TZF > TZG ) )
      | ( ( order @ ( TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) )
       != ( order @ TZG ) ) ),
    inference(paramod_ordered,[status(thm)],[3820,958]) ).

thf(3950,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType] : ( order @ ( TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[3949:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(4014,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType] :
      ( ( order @ ( TZG > TZH ) )
      | ( ( order @ ( TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) )
       != ( order @ TZH ) ) ),
    inference(paramod_ordered,[status(thm)],[3950,958]) ).

thf(4015,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType] : ( order @ ( TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[4014:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(254,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
      = ( ! [C: TA] :
            ( ( A @ C )
           => ( B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_Collect__mono__iff) ).

thf(941,plain,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
      = ( ! [C: TA] :
            ( ( A @ C )
           => ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(179,axiom,
    ( ( v @ b @ c2 )
    = ( v @ a @ c ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_Veq) ).

thf(776,plain,
    ( ( v @ b @ c2 )
    = ( v @ a @ c ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(777,plain,
    ( ( v @ b @ c2 )
    = ( v @ a @ c ) ),
    inference(lifteq,[status(thm)],[776]) ).

thf(137,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat] :
          ( ( min_dist @ TA @ A @ B @ B )
          = ( zero_zero @ nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_Graph_Omin__dist__z) ).

thf(666,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat] :
          ( ( min_dist @ TA @ A @ B @ B )
          = ( zero_zero @ nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(37,axiom,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( isPath @ b @ c2 @ A @ B @ C )
     => ( dist @ b @ c2 @ A @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_g_H_OisPath__distD) ).

thf(351,plain,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( isPath @ b @ c2 @ A @ B @ C )
     => ( dist @ b @ c2 @ A @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(352,plain,
    ! [C: nat,B: list @ ( product_prod @ nat @ nat ),A: nat] :
      ( ~ ( isPath @ b @ c2 @ A @ B @ C )
      | ( dist @ b @ c2 @ A @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ B ) @ C ) ),
    inference(cnf,[status(esa)],[351]) ).

thf(43,axiom,
    ! [A: nat] : ( dist @ b @ c2 @ A @ ( zero_zero @ nat ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_g_H_Odist__z) ).

thf(365,plain,
    ! [A: nat] : ( dist @ b @ c2 @ A @ ( zero_zero @ nat ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(83,axiom,
    ! [A: nat,B: nat] :
      ( ( A = B )
     => ( ord_less_eq @ nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_eq__imp__le) ).

thf(479,plain,
    ! [A: nat,B: nat] :
      ( ( A = B )
     => ( ord_less_eq @ nat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(274,axiom,
    linordered_idom @ a,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).

thf(976,plain,
    linordered_idom @ a,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(1037,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
      | ( ( linordered_idom @ a )
       != ( linordered_idom @ TA ) ) ),
    inference(paramod_ordered,[status(thm)],[976,954]) ).

thf(1038,plain,
    order @ a,
    inference(pattern_uni,[status(thm)],[1037:[bind_type(TA,$thf( a ))]]) ).

thf(1073,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( order @ ( TA > TB ) )
      | ( ( order @ a )
       != ( order @ TB ) ) ),
    inference(paramod_ordered,[status(thm)],[1038,958]) ).

thf(1074,plain,
    ! [TA: $tType] : ( order @ ( TA > a ) ),
    inference(pattern_uni,[status(thm)],[1073:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( a ))]]) ).

thf(1084,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( order @ ( TB > TC ) )
      | ( ( order @ ( TA > a ) )
       != ( order @ TC ) ) ),
    inference(paramod_ordered,[status(thm)],[1074,958]) ).

thf(1085,plain,
    ! [TA: $tType,TB: $tType] : ( order @ ( TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[1084:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TA > a ))]]) ).

thf(1104,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
      ( ( order @ ( TC > TD ) )
      | ( ( order @ ( TB > TA > a ) )
       != ( order @ TD ) ) ),
    inference(paramod_ordered,[status(thm)],[1085,958]) ).

thf(1105,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] : ( order @ ( TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[1104:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TB > TA > a ))]]) ).

thf(35,axiom,
    ! [A: nat,B: nat] :
      ( ( connected @ b @ c2 @ A @ B )
      = ( ? [C: nat] : ( dist @ b @ c2 @ A @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_g_H_Oconnected__by__dist) ).

thf(345,plain,
    ! [A: nat,B: nat] :
      ( ( connected @ b @ c2 @ A @ B )
      = ( ? [C: nat] : ( dist @ b @ c2 @ A @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(346,plain,
    ! [B: nat,A: nat] :
      ( ( connected @ b @ c2 @ A @ B )
      = ( ? [C: nat] : ( dist @ b @ c2 @ A @ C @ B ) ) ),
    inference(cnf,[status(esa)],[345]) ).

thf(347,plain,
    ! [B: nat,A: nat] :
      ( ( connected @ b @ c2 @ A @ B )
      = ( ? [C: nat] : ( dist @ b @ c2 @ A @ C @ B ) ) ),
    inference(lifteq,[status(thm)],[346]) ).

thf(1114,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
      ( ( order @ ( TD > TE ) )
      | ( ( order @ ( TC > TB > TA > a ) )
       != ( order @ TE ) ) ),
    inference(paramod_ordered,[status(thm)],[1105,958]) ).

thf(1115,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( order @ ( TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[1114:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TC > TB > TA > a ))]]) ).

thf(1129,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
      ( ( order @ ( TE > TF ) )
      | ( ( order @ ( TD > TC > TB > TA > a ) )
       != ( order @ TF ) ) ),
    inference(paramod_ordered,[status(thm)],[1115,958]) ).

thf(1130,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] : ( order @ ( TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[1129:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TD > TC > TB > TA > a ))]]) ).

thf(1160,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
      ( ( order @ ( TF > TG ) )
      | ( ( order @ ( TE > TD > TC > TB > TA > a ) )
       != ( order @ TG ) ) ),
    inference(paramod_ordered,[status(thm)],[1130,958]) ).

thf(1161,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] : ( order @ ( TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[1160:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TE > TD > TC > TB > TA > a ))]]) ).

thf(1171,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] :
      ( ( order @ ( TG > TH ) )
      | ( ( order @ ( TF > TE > TD > TC > TB > TA > a ) )
       != ( order @ TH ) ) ),
    inference(paramod_ordered,[status(thm)],[1161,958]) ).

thf(1172,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] : ( order @ ( TG > TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[1171:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TF > TE > TD > TC > TB > TA > a ))]]) ).

thf(1191,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] :
      ( ( order @ ( TH > TI ) )
      | ( ( order @ ( TG > TF > TE > TD > TC > TB > TA > a ) )
       != ( order @ TI ) ) ),
    inference(paramod_ordered,[status(thm)],[1172,958]) ).

thf(1192,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] : ( order @ ( TH > TG > TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[1191:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TG > TF > TE > TD > TC > TB > TA > a ))]]) ).

thf(1202,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] :
      ( ( order @ ( TI > TJ ) )
      | ( ( order @ ( TH > TG > TF > TE > TD > TC > TB > TA > a ) )
       != ( order @ TJ ) ) ),
    inference(paramod_ordered,[status(thm)],[1192,958]) ).

thf(1203,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] : ( order @ ( TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[1202:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TH > TG > TF > TE > TD > TC > TB > TA > a ))]]) ).

thf(1619,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] :
      ( ( order @ ( TJ > TK ) )
      | ( ( order @ ( TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) )
       != ( order @ TK ) ) ),
    inference(paramod_ordered,[status(thm)],[1203,958]) ).

thf(1620,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] : ( order @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[1619:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TI > TH > TG > TF > TE > TD > TC > TB > TA > a ))]]) ).

thf(1750,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] :
      ( ( order @ ( TK > TL ) )
      | ( ( order @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) )
       != ( order @ TL ) ) ),
    inference(paramod_ordered,[status(thm)],[1620,958]) ).

thf(1751,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] : ( order @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[1750:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ))]]) ).

thf(1781,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] :
      ( ( order @ ( TL > TM ) )
      | ( ( order @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) )
       != ( order @ TM ) ) ),
    inference(paramod_ordered,[status(thm)],[1751,958]) ).

thf(1782,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] : ( order @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[1781:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ))]]) ).

thf(1857,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] :
      ( ( order @ ( TM > TN ) )
      | ( ( order @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) )
       != ( order @ TN ) ) ),
    inference(paramod_ordered,[status(thm)],[1782,958]) ).

thf(1858,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] : ( order @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[1857:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ))]]) ).

thf(1891,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] :
      ( ( order @ ( TN > TO ) )
      | ( ( order @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) )
       != ( order @ TO ) ) ),
    inference(paramod_ordered,[status(thm)],[1858,958]) ).

thf(1892,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] : ( order @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[1891:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ))]]) ).

thf(1962,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] :
      ( ( order @ ( TO > TP ) )
      | ( ( order @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) )
       != ( order @ TP ) ) ),
    inference(paramod_ordered,[status(thm)],[1892,958]) ).

thf(1963,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] : ( order @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[1962:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ))]]) ).

thf(2122,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] :
      ( ( order @ ( TP > TQ ) )
      | ( ( order @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) )
       != ( order @ TQ ) ) ),
    inference(paramod_ordered,[status(thm)],[1963,958]) ).

thf(2123,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] : ( order @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[2122:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ))]]) ).

thf(2147,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] :
      ( ( order @ ( TQ > TR ) )
      | ( ( order @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) )
       != ( order @ TR ) ) ),
    inference(paramod_ordered,[status(thm)],[2123,958]) ).

thf(2148,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] : ( order @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[2147:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ))]]) ).

thf(2228,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType] :
      ( ( order @ ( TR > TS ) )
      | ( ( order @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) )
       != ( order @ TS ) ) ),
    inference(paramod_ordered,[status(thm)],[2148,958]) ).

thf(2229,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] : ( order @ ( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[2228:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ))]]) ).

thf(2374,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType] :
      ( ( order @ ( TS > TT ) )
      | ( ( order @ ( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) )
       != ( order @ TT ) ) ),
    inference(paramod_ordered,[status(thm)],[2229,958]) ).

thf(2375,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType] : ( order @ ( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[2374:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ))]]) ).

thf(2680,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType] :
      ( ( order @ ( TT > TU ) )
      | ( ( order @ ( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) )
       != ( order @ TU ) ) ),
    inference(paramod_ordered,[status(thm)],[2375,958]) ).

thf(2681,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType] : ( order @ ( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[2680:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ))]]) ).

thf(2739,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType] :
      ( ( order @ ( TU > TV ) )
      | ( ( order @ ( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) )
       != ( order @ TV ) ) ),
    inference(paramod_ordered,[status(thm)],[2681,958]) ).

thf(2740,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType] : ( order @ ( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[2739:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ))]]) ).

thf(3094,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType] :
      ( ( order @ ( TV > TW ) )
      | ( ( order @ ( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) )
       != ( order @ TW ) ) ),
    inference(paramod_ordered,[status(thm)],[2740,958]) ).

thf(3095,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType] : ( order @ ( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[3094:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ))]]) ).

thf(3169,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType] :
      ( ( order @ ( TW > TX ) )
      | ( ( order @ ( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) )
       != ( order @ TX ) ) ),
    inference(paramod_ordered,[status(thm)],[3095,958]) ).

thf(3170,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType] : ( order @ ( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[3169:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ))]]) ).

thf(3204,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType] :
      ( ( order @ ( TX > TY ) )
      | ( ( order @ ( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) )
       != ( order @ TY ) ) ),
    inference(paramod_ordered,[status(thm)],[3170,958]) ).

thf(3205,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType] : ( order @ ( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[3204:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ))]]) ).

thf(3253,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType] :
      ( ( order @ ( TY > TZ ) )
      | ( ( order @ ( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) )
       != ( order @ TZ ) ) ),
    inference(paramod_ordered,[status(thm)],[3205,958]) ).

thf(3254,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType] : ( order @ ( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[3253:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ))]]) ).

thf(3372,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType] :
      ( ( order @ ( TZ > TZA ) )
      | ( ( order @ ( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) )
       != ( order @ TZA ) ) ),
    inference(paramod_ordered,[status(thm)],[3254,958]) ).

thf(3373,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType] : ( order @ ( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[3372:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ))]]) ).

thf(3500,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType] :
      ( ( order @ ( TZA > TZB ) )
      | ( ( order @ ( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) )
       != ( order @ TZB ) ) ),
    inference(paramod_ordered,[status(thm)],[3373,958]) ).

thf(3501,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType] : ( order @ ( TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[3500:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ))]]) ).

thf(3535,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType] :
      ( ( order @ ( TZB > TZC ) )
      | ( ( order @ ( TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) )
       != ( order @ TZC ) ) ),
    inference(paramod_ordered,[status(thm)],[3501,958]) ).

thf(3536,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType] : ( order @ ( TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[3535:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ))]]) ).

thf(3658,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType] :
      ( ( order @ ( TZC > TZD ) )
      | ( ( order @ ( TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) )
       != ( order @ TZD ) ) ),
    inference(paramod_ordered,[status(thm)],[3536,958]) ).

thf(3659,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType] : ( order @ ( TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[3658:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ))]]) ).

thf(3791,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType] :
      ( ( order @ ( TZD > TZE ) )
      | ( ( order @ ( TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) )
       != ( order @ TZE ) ) ),
    inference(paramod_ordered,[status(thm)],[3659,958]) ).

thf(3792,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType] : ( order @ ( TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[3791:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ))]]) ).

thf(3826,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType] :
      ( ( order @ ( TZE > TZF ) )
      | ( ( order @ ( TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) )
       != ( order @ TZF ) ) ),
    inference(paramod_ordered,[status(thm)],[3792,958]) ).

thf(3827,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType] : ( order @ ( TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[3826:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ))]]) ).

thf(3956,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType] :
      ( ( order @ ( TZF > TZG ) )
      | ( ( order @ ( TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) )
       != ( order @ TZG ) ) ),
    inference(paramod_ordered,[status(thm)],[3827,958]) ).

thf(3957,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType] : ( order @ ( TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[3956:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ))]]) ).

thf(4021,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType] :
      ( ( order @ ( TZG > TZH ) )
      | ( ( order @ ( TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) )
       != ( order @ TZH ) ) ),
    inference(paramod_ordered,[status(thm)],[3957,958]) ).

thf(4022,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType] : ( order @ ( TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[4021:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ))]]) ).

thf(265,axiom,
    zero @ nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero) ).

thf(962,plain,
    zero @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(78,axiom,
    ! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_le0) ).

thf(468,plain,
    ! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(97,axiom,
    ! [A: nat > $o,B: nat] :
      ( ( A @ B )
     => ( ~ ( A @ ( zero_zero @ nat ) )
       => ? [C: nat] :
            ( ( ord_less_eq @ nat @ C @ B )
            & ! [D: nat] :
                ( ( ord_less @ nat @ D @ C )
               => ~ ( A @ D ) )
            & ( A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_ex__least__nat__le) ).

thf(523,plain,
    ! [A: nat > $o,B: nat] :
      ( ( A @ B )
     => ( ~ ( A @ ( zero_zero @ nat ) )
       => ? [C: nat] :
            ( ( ord_less_eq @ nat @ C @ B )
            & ! [D: nat] :
                ( ( ord_less @ nat @ D @ C )
               => ~ ( A @ D ) )
            & ( A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(4338,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType] :
      ( ( order @ ( TZJ > TZK ) )
      | ( ( order @ ( TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) )
       != ( order @ TZK ) ) ),
    inference(paramod_ordered,[status(thm)],[4169,958]) ).

thf(4339,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType] : ( order @ ( TZJ > TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[4338:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZJ )),bind_type(TZK,$thf( TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(1,conjecture,
    $false,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

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

thf(276,plain,
    ~ $false,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(1065,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( order @ ( TA > TB ) )
      | ( ( order @ b )
       != ( order @ TB ) ) ),
    inference(paramod_ordered,[status(thm)],[1036,958]) ).

thf(1066,plain,
    ! [TA: $tType] : ( order @ ( TA > b ) ),
    inference(pattern_uni,[status(thm)],[1065:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( b ))]]) ).

thf(1080,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( order @ ( TB > TC ) )
      | ( ( order @ ( TA > b ) )
       != ( order @ TC ) ) ),
    inference(paramod_ordered,[status(thm)],[1066,958]) ).

thf(1081,plain,
    ! [TA: $tType,TB: $tType] : ( order @ ( TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[1080:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TA > b ))]]) ).

thf(1100,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
      ( ( order @ ( TC > TD ) )
      | ( ( order @ ( TB > TA > b ) )
       != ( order @ TD ) ) ),
    inference(paramod_ordered,[status(thm)],[1081,958]) ).

thf(1101,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] : ( order @ ( TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[1100:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TB > TA > b ))]]) ).

thf(1110,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
      ( ( order @ ( TD > TE ) )
      | ( ( order @ ( TC > TB > TA > b ) )
       != ( order @ TE ) ) ),
    inference(paramod_ordered,[status(thm)],[1101,958]) ).

thf(1111,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( order @ ( TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[1110:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TC > TB > TA > b ))]]) ).

thf(1125,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
      ( ( order @ ( TE > TF ) )
      | ( ( order @ ( TD > TC > TB > TA > b ) )
       != ( order @ TF ) ) ),
    inference(paramod_ordered,[status(thm)],[1111,958]) ).

thf(1126,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] : ( order @ ( TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[1125:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TD > TC > TB > TA > b ))]]) ).

thf(1148,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
      ( ( order @ ( TF > TG ) )
      | ( ( order @ ( TE > TD > TC > TB > TA > b ) )
       != ( order @ TG ) ) ),
    inference(paramod_ordered,[status(thm)],[1126,958]) ).

thf(1149,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] : ( order @ ( TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[1148:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TE > TD > TC > TB > TA > b ))]]) ).

thf(1166,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] :
      ( ( order @ ( TG > TH ) )
      | ( ( order @ ( TF > TE > TD > TC > TB > TA > b ) )
       != ( order @ TH ) ) ),
    inference(paramod_ordered,[status(thm)],[1149,958]) ).

thf(1167,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] : ( order @ ( TG > TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[1166:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TF > TE > TD > TC > TB > TA > b ))]]) ).

thf(1187,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] :
      ( ( order @ ( TH > TI ) )
      | ( ( order @ ( TG > TF > TE > TD > TC > TB > TA > b ) )
       != ( order @ TI ) ) ),
    inference(paramod_ordered,[status(thm)],[1167,958]) ).

thf(1188,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] : ( order @ ( TH > TG > TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[1187:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TG > TF > TE > TD > TC > TB > TA > b ))]]) ).

thf(1197,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] :
      ( ( order @ ( TI > TJ ) )
      | ( ( order @ ( TH > TG > TF > TE > TD > TC > TB > TA > b ) )
       != ( order @ TJ ) ) ),
    inference(paramod_ordered,[status(thm)],[1188,958]) ).

thf(1198,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] : ( order @ ( TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[1197:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TH > TG > TF > TE > TD > TC > TB > TA > b ))]]) ).

thf(1609,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] :
      ( ( order @ ( TJ > TK ) )
      | ( ( order @ ( TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) )
       != ( order @ TK ) ) ),
    inference(paramod_ordered,[status(thm)],[1198,958]) ).

thf(1610,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] : ( order @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[1609:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TI > TH > TG > TF > TE > TD > TC > TB > TA > b ))]]) ).

thf(1648,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] :
      ( ( order @ ( TK > TL ) )
      | ( ( order @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) )
       != ( order @ TL ) ) ),
    inference(paramod_ordered,[status(thm)],[1610,958]) ).

thf(1649,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] : ( order @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[1648:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ))]]) ).

thf(1771,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] :
      ( ( order @ ( TL > TM ) )
      | ( ( order @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) )
       != ( order @ TM ) ) ),
    inference(paramod_ordered,[status(thm)],[1649,958]) ).

thf(1772,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] : ( order @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[1771:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ))]]) ).

thf(1796,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] :
      ( ( order @ ( TM > TN ) )
      | ( ( order @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) )
       != ( order @ TN ) ) ),
    inference(paramod_ordered,[status(thm)],[1772,958]) ).

thf(1797,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] : ( order @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[1796:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ))]]) ).

thf(1872,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] :
      ( ( order @ ( TN > TO ) )
      | ( ( order @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) )
       != ( order @ TO ) ) ),
    inference(paramod_ordered,[status(thm)],[1797,958]) ).

thf(1873,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] : ( order @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[1872:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ))]]) ).

thf(1952,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] :
      ( ( order @ ( TO > TP ) )
      | ( ( order @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) )
       != ( order @ TP ) ) ),
    inference(paramod_ordered,[status(thm)],[1873,958]) ).

thf(1953,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] : ( order @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[1952:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ))]]) ).

thf(2005,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] :
      ( ( order @ ( TP > TQ ) )
      | ( ( order @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) )
       != ( order @ TQ ) ) ),
    inference(paramod_ordered,[status(thm)],[1953,958]) ).

thf(2006,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] : ( order @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[2005:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ))]]) ).

thf(2137,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] :
      ( ( order @ ( TQ > TR ) )
      | ( ( order @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) )
       != ( order @ TR ) ) ),
    inference(paramod_ordered,[status(thm)],[2006,958]) ).

thf(2138,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] : ( order @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[2137:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ))]]) ).

thf(2218,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType] :
      ( ( order @ ( TR > TS ) )
      | ( ( order @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) )
       != ( order @ TS ) ) ),
    inference(paramod_ordered,[status(thm)],[2138,958]) ).

thf(2219,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] : ( order @ ( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[2218:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ))]]) ).

thf(2364,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType] :
      ( ( order @ ( TS > TT ) )
      | ( ( order @ ( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) )
       != ( order @ TT ) ) ),
    inference(paramod_ordered,[status(thm)],[2219,958]) ).

thf(2365,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType] : ( order @ ( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[2364:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ))]]) ).

thf(2390,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType] :
      ( ( order @ ( TT > TU ) )
      | ( ( order @ ( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) )
       != ( order @ TU ) ) ),
    inference(paramod_ordered,[status(thm)],[2365,958]) ).

thf(2391,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType] : ( order @ ( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[2390:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ))]]) ).

thf(2695,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType] :
      ( ( order @ ( TU > TV ) )
      | ( ( order @ ( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) )
       != ( order @ TV ) ) ),
    inference(paramod_ordered,[status(thm)],[2391,958]) ).

thf(2696,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType] : ( order @ ( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[2695:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ))]]) ).

thf(3080,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType] :
      ( ( order @ ( TV > TW ) )
      | ( ( order @ ( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) )
       != ( order @ TW ) ) ),
    inference(paramod_ordered,[status(thm)],[2696,958]) ).

thf(3081,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType] : ( order @ ( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[3080:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ))]]) ).

thf(3141,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType] :
      ( ( order @ ( TW > TX ) )
      | ( ( order @ ( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) )
       != ( order @ TX ) ) ),
    inference(paramod_ordered,[status(thm)],[3081,958]) ).

thf(3142,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType] : ( order @ ( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[3141:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ))]]) ).

thf(3190,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType] :
      ( ( order @ ( TX > TY ) )
      | ( ( order @ ( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) )
       != ( order @ TY ) ) ),
    inference(paramod_ordered,[status(thm)],[3142,958]) ).

thf(3191,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType] : ( order @ ( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[3190:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ))]]) ).

thf(3239,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType] :
      ( ( order @ ( TY > TZ ) )
      | ( ( order @ ( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) )
       != ( order @ TZ ) ) ),
    inference(paramod_ordered,[status(thm)],[3191,958]) ).

thf(3240,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType] : ( order @ ( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[3239:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ))]]) ).

thf(3358,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType] :
      ( ( order @ ( TZ > TZA ) )
      | ( ( order @ ( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) )
       != ( order @ TZA ) ) ),
    inference(paramod_ordered,[status(thm)],[3240,958]) ).

thf(3359,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType] : ( order @ ( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[3358:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ))]]) ).

thf(3394,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType] :
      ( ( order @ ( TZA > TZB ) )
      | ( ( order @ ( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) )
       != ( order @ TZB ) ) ),
    inference(paramod_ordered,[status(thm)],[3359,958]) ).

thf(3395,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType] : ( order @ ( TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[3394:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ))]]) ).

thf(3521,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType] :
      ( ( order @ ( TZB > TZC ) )
      | ( ( order @ ( TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) )
       != ( order @ TZC ) ) ),
    inference(paramod_ordered,[status(thm)],[3395,958]) ).

thf(3522,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType] : ( order @ ( TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[3521:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ))]]) ).

thf(3644,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType] :
      ( ( order @ ( TZC > TZD ) )
      | ( ( order @ ( TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) )
       != ( order @ TZD ) ) ),
    inference(paramod_ordered,[status(thm)],[3522,958]) ).

thf(3645,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType] : ( order @ ( TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[3644:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ))]]) ).

thf(3679,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType] :
      ( ( order @ ( TZD > TZE ) )
      | ( ( order @ ( TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) )
       != ( order @ TZE ) ) ),
    inference(paramod_ordered,[status(thm)],[3645,958]) ).

thf(3680,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType] : ( order @ ( TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[3679:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ))]]) ).

thf(3812,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType] :
      ( ( order @ ( TZE > TZF ) )
      | ( ( order @ ( TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) )
       != ( order @ TZF ) ) ),
    inference(paramod_ordered,[status(thm)],[3680,958]) ).

thf(3813,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType] : ( order @ ( TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[3812:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ))]]) ).

thf(165,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( dist @ a @ c @ A @ B @ C )
     => ( ord_less_eq @ nat @ ( min_dist @ a @ c @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_min__dist__minD) ).

thf(741,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( dist @ a @ c @ A @ B @ C )
     => ( ord_less_eq @ nat @ ( min_dist @ a @ c @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(212,axiom,
    ( ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( e @ a @ c ) )
   => ( finite_finite2 @ nat @ ( v @ a @ c ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_Efin__imp__Vfin) ).

thf(861,plain,
    ( ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( e @ a @ c ) )
   => ( finite_finite2 @ nat @ ( v @ a @ c ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(3942,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType] :
      ( ( order @ ( TZF > TZG ) )
      | ( ( order @ ( TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) )
       != ( order @ TZG ) ) ),
    inference(paramod_ordered,[status(thm)],[3813,958]) ).

thf(3943,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType] : ( order @ ( TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[3942:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ))]]) ).

thf(4007,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType] :
      ( ( order @ ( TZG > TZH ) )
      | ( ( order @ ( TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) )
       != ( order @ TZH ) ) ),
    inference(paramod_ordered,[status(thm)],[3943,958]) ).

thf(4008,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType] : ( order @ ( TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[4007:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ))]]) ).

thf(4042,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType] :
      ( ( order @ ( TZH > TZI ) )
      | ( ( order @ ( TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) )
       != ( order @ TZI ) ) ),
    inference(paramod_ordered,[status(thm)],[4008,958]) ).

thf(4043,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType] : ( order @ ( TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[4042:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ))]]) ).

thf(220,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: nat,B: ( product_prod @ nat @ nat ) > TA] :
          ( ( member @ nat @ A @ ( v @ TA @ B ) )
         => ( ord_less_eq @ ( set @ nat ) @ ( reachableNodes @ TA @ B @ A ) @ ( v @ TA @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_Graph_Oreachable__ss__V) ).

thf(873,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: nat,B: ( product_prod @ nat @ nat ) > TA] :
          ( ( member @ nat @ A @ ( v @ TA @ B ) )
         => ( ord_less_eq @ ( set @ nat ) @ ( reachableNodes @ TA @ B @ A ) @ ( v @ TA @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(72,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( dist @ b @ c2 @ A @ B @ C )
     => ( ord_less_eq @ nat @ ( min_dist @ b @ c2 @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_g_H_Omin__dist__minD) ).

thf(449,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( dist @ b @ c2 @ A @ B @ C )
     => ( ord_less_eq @ nat @ ( min_dist @ b @ c2 @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(94,axiom,
    ! [A: nat,B: nat] :
      ( ( ( ord_less @ nat @ A @ B )
        | ( A = B ) )
     => ( ord_less_eq @ nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_less__or__eq__imp__le) ).

thf(511,plain,
    ! [A: nat,B: nat] :
      ( ( ( ord_less @ nat @ A @ B )
        | ( A = B ) )
     => ( ord_less_eq @ nat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(203,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: set @ TA,B: TA] :
          ( ( finite_finite2 @ TA @ A )
         => ( ( member @ TA @ B @ A )
           => ? [C: TA] :
                ( ( member @ TA @ C @ A )
                & ( ord_less_eq @ TA @ C @ B )
                & ! [D: TA] :
                    ( ( member @ TA @ D @ A )
                   => ( ( ord_less_eq @ TA @ D @ C )
                     => ( C = D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_finite__has__minimal2) ).

thf(839,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: set @ TA,B: TA] :
          ( ( finite_finite2 @ TA @ A )
         => ( ( member @ TA @ B @ A )
           => ? [C: TA] :
                ( ( member @ TA @ C @ A )
                & ( ord_less_eq @ TA @ C @ B )
                & ! [D: TA] :
                    ( ( member @ TA @ D @ A )
                   => ( ( ord_less_eq @ TA @ D @ C )
                     => ( C = D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(842,plain,
    ! [TA: $tType,C: TA,B: TA,A: set @ TA] :
      ( ~ ( order @ TA )
      | ~ ( finite_finite2 @ TA @ A )
      | ~ ( member @ TA @ B @ A )
      | ~ ( member @ TA @ C @ A )
      | ~ ( ord_less_eq @ TA @ C @ ( sk44 @ TA @ B @ A ) )
      | ( ( sk44 @ TA @ B @ A )
        = C ) ),
    inference(cnf,[status(esa)],[839]) ).

thf(843,plain,
    ! [TA: $tType,C: TA,B: TA,A: set @ TA] :
      ( ( ( sk44 @ TA @ B @ A )
        = C )
      | ~ ( order @ TA )
      | ~ ( finite_finite2 @ TA @ A )
      | ~ ( member @ TA @ B @ A )
      | ~ ( member @ TA @ C @ A )
      | ~ ( ord_less_eq @ TA @ C @ ( sk44 @ TA @ B @ A ) ) ),
    inference(lifteq,[status(thm)],[842]) ).

thf(8,axiom,
    ord_less @ nat @ ( min_dist @ b @ c2 @ s @ t ) @ ( min_dist @ a @ c @ s @ t ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_SHORTER) ).

thf(284,plain,
    ord_less @ nat @ ( min_dist @ b @ c2 @ s @ t ) @ ( min_dist @ a @ c @ s @ t ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(58,axiom,
    ! [A: nat] :
      ~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_less__nat__zero__code) ).

thf(403,plain,
    ! [A: nat] :
      ~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(404,plain,
    ~ ? [A: nat] : ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
    inference(miniscope,[status(thm)],[403]) ).

thf(405,plain,
    ! [A: nat] :
      ~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
    inference(cnf,[status(esa)],[404]) ).

thf(1012,plain,
    ! [A: nat] :
      ( ( ord_less @ nat @ ( min_dist @ b @ c2 @ s @ t ) @ ( min_dist @ a @ c @ s @ t ) )
     != ( ord_less @ nat @ A @ ( zero_zero @ nat ) ) ),
    inference(paramod_ordered,[status(thm)],[284,405]) ).

thf(1013,plain,
    ! [A: nat] :
      ( ( ( min_dist @ b @ c2 @ s @ t )
       != A )
      | ( ( min_dist @ a @ c @ s @ t )
       != ( zero_zero @ nat ) ) ),
    inference(simp,[status(thm)],[1012]) ).

thf(1015,plain,
    ( ( min_dist @ a @ c @ s @ t )
   != ( zero_zero @ nat ) ),
    inference(simp,[status(thm)],[1013]) ).

thf(1464,plain,
    ! [C: ( product_prod @ nat @ nat ) > a,B: ( product_prod @ nat @ nat ) > a,A: set @ ( ( product_prod @ nat @ nat ) > a )] :
      ( ~ ( order @ ( ( product_prod @ nat @ nat ) > a ) )
      | ~ ( finite_finite2 @ ( ( product_prod @ nat @ nat ) > a ) @ A )
      | ~ ( member @ ( ( product_prod @ nat @ nat ) > a ) @ B @ A )
      | ~ ( member @ ( ( product_prod @ nat @ nat ) > a ) @ C @ A )
      | ~ ( ord_less_eq @ ( ( product_prod @ nat @ nat ) > a ) @ C @ ( sk44 @ ( ( product_prod @ nat @ nat ) > a ) @ B @ A ) )
      | ( ( min_dist @ a @ ( sk44 @ ( ( product_prod @ nat @ nat ) > a ) @ B @ A ) @ s @ t )
       != ( zero_zero @ nat ) )
      | ( C != c ) ),
    inference(paramod_ordered,[status(thm)],[843,1015]) ).

thf(1465,plain,
    ! [B: ( product_prod @ nat @ nat ) > a,A: set @ ( ( product_prod @ nat @ nat ) > a )] :
      ( ~ ( order @ ( ( product_prod @ nat @ nat ) > a ) )
      | ~ ( finite_finite2 @ ( ( product_prod @ nat @ nat ) > a ) @ A )
      | ~ ( member @ ( ( product_prod @ nat @ nat ) > a ) @ B @ A )
      | ~ ( member @ ( ( product_prod @ nat @ nat ) > a ) @ c @ A )
      | ~ ( ord_less_eq @ ( ( product_prod @ nat @ nat ) > a ) @ c @ ( sk44 @ ( ( product_prod @ nat @ nat ) > a ) @ B @ A ) )
      | ( ( min_dist @ a @ ( sk44 @ ( ( product_prod @ nat @ nat ) > a ) @ B @ A ) @ s @ t )
       != ( zero_zero @ nat ) ) ),
    inference(pattern_uni,[status(thm)],[1464:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( c ))]]) ).

thf(1655,plain,
    ! [B: ( product_prod @ nat @ nat ) > a,A: set @ ( ( product_prod @ nat @ nat ) > a )] :
      ( ~ $true
      | ~ ( finite_finite2 @ ( ( product_prod @ nat @ nat ) > a ) @ A )
      | ~ ( member @ ( ( product_prod @ nat @ nat ) > a ) @ B @ A )
      | ~ ( member @ ( ( product_prod @ nat @ nat ) > a ) @ c @ A )
      | ~ ( ord_less_eq @ ( ( product_prod @ nat @ nat ) > a ) @ c @ ( sk44 @ ( ( product_prod @ nat @ nat ) > a ) @ B @ A ) )
      | ( ( min_dist @ a @ ( sk44 @ ( ( product_prod @ nat @ nat ) > a ) @ B @ A ) @ s @ t )
       != ( zero_zero @ nat ) ) ),
    inference(rewrite,[status(thm)],[1465,1074]) ).

thf(1656,plain,
    ! [B: ( product_prod @ nat @ nat ) > a,A: set @ ( ( product_prod @ nat @ nat ) > a )] :
      ( ~ ( finite_finite2 @ ( ( product_prod @ nat @ nat ) > a ) @ A )
      | ~ ( member @ ( ( product_prod @ nat @ nat ) > a ) @ B @ A )
      | ~ ( member @ ( ( product_prod @ nat @ nat ) > a ) @ c @ A )
      | ~ ( ord_less_eq @ ( ( product_prod @ nat @ nat ) > a ) @ c @ ( sk44 @ ( ( product_prod @ nat @ nat ) > a ) @ B @ A ) )
      | ( ( min_dist @ a @ ( sk44 @ ( ( product_prod @ nat @ nat ) > a ) @ B @ A ) @ s @ t )
       != ( zero_zero @ nat ) ) ),
    inference(simp,[status(thm)],[1655]) ).

thf(1690,plain,
    ! [B: ( product_prod @ nat @ nat ) > a,A: set @ ( ( product_prod @ nat @ nat ) > a )] :
      ( ~ ( finite_finite2 @ ( ( product_prod @ nat @ nat ) > a ) @ A )
      | ~ ( member @ ( ( product_prod @ nat @ nat ) > a ) @ B @ A )
      | ~ ( ord_less_eq @ ( ( product_prod @ nat @ nat ) > a ) @ c @ ( sk44 @ ( ( product_prod @ nat @ nat ) > a ) @ B @ A ) )
      | ( ( min_dist @ a @ ( sk44 @ ( ( product_prod @ nat @ nat ) > a ) @ B @ A ) @ s @ t )
       != ( zero_zero @ nat ) )
      | ( ( member @ ( ( product_prod @ nat @ nat ) > a ) @ c @ A )
       != ( member @ ( ( product_prod @ nat @ nat ) > a ) @ B @ A ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[1656]) ).

thf(1692,plain,
    ! [A: set @ ( ( product_prod @ nat @ nat ) > a )] :
      ( ~ ( finite_finite2 @ ( ( product_prod @ nat @ nat ) > a ) @ A )
      | ~ ( member @ ( ( product_prod @ nat @ nat ) > a ) @ c @ A )
      | ~ ( ord_less_eq @ ( ( product_prod @ nat @ nat ) > a ) @ c @ ( sk44 @ ( ( product_prod @ nat @ nat ) > a ) @ c @ A ) )
      | ( ( min_dist @ a @ ( sk44 @ ( ( product_prod @ nat @ nat ) > a ) @ c @ A ) @ s @ t )
       != ( zero_zero @ nat ) ) ),
    inference(pattern_uni,[status(thm)],[1690:[bind(A,$thf( A )),bind(B,$thf( c ))]]) ).

thf(141,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat] :
          ( ( connected @ TA @ A @ B @ C )
         => ( ( member @ nat @ C @ ( v @ TA @ A ) )
            = ( member @ nat @ B @ ( v @ TA @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_Graph_Oconnected__inV__iff) ).

thf(677,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat] :
          ( ( connected @ TA @ A @ B @ C )
         => ( ( member @ nat @ C @ ( v @ TA @ A ) )
            = ( member @ nat @ B @ ( v @ TA @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(268,axiom,
    ! [TA: $tType] : ( order @ ( set @ TA ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_3) ).

thf(966,plain,
    ! [TA: $tType] : ( order @ ( set @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(967,plain,
    ! [TA: $tType] : ( order @ ( set @ TA ) ),
    inference(cnf,[status(esa)],[966]) ).

thf(1077,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] :
      ( ( order @ ( TB > TC ) )
      | ( ( order @ ( set @ TA ) )
       != ( order @ TC ) ) ),
    inference(paramod_ordered,[status(thm)],[967,958]) ).

thf(1078,plain,
    ! [TA: $tType,TB: $tType] : ( order @ ( TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[1077:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( set @ TA ))]]) ).

thf(4089,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType] :
      ( ( order @ ( TZH > TZI ) )
      | ( ( order @ ( TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) )
       != ( order @ TZI ) ) ),
    inference(paramod_ordered,[status(thm)],[4022,958]) ).

thf(4090,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType] : ( order @ ( TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[4089:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ))]]) ).

thf(188,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: list @ ( product_prod @ nat @ nat ),D: nat] :
          ( ( isPath @ TA @ A @ B @ C @ D )
         => ? [E: list @ ( product_prod @ nat @ nat )] : ( isSimplePath @ TA @ A @ B @ E @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_Graph_OisSPath__pathLE) ).

thf(797,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: list @ ( product_prod @ nat @ nat ),D: nat] :
          ( ( isPath @ TA @ A @ B @ C @ D )
         => ? [E: list @ ( product_prod @ nat @ nat )] : ( isSimplePath @ TA @ A @ B @ E @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(80,axiom,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA )
     => ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_zero__le) ).

thf(472,plain,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA )
     => ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(1088,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
      ( ( order @ ( TC > TD ) )
      | ( ( order @ ( TB > ( set @ TA ) ) )
       != ( order @ TD ) ) ),
    inference(paramod_ordered,[status(thm)],[1078,958]) ).

thf(1089,plain,
    ! [TA: $tType,TB: $tType,TC: $tType] : ( order @ ( TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[1088:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TB > ( set @ TA ) ))]]) ).

thf(1108,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
      ( ( order @ ( TD > TE ) )
      | ( ( order @ ( TC > TB > ( set @ TA ) ) )
       != ( order @ TE ) ) ),
    inference(paramod_ordered,[status(thm)],[1089,958]) ).

thf(1109,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( order @ ( TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[1108:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TC > TB > ( set @ TA ) ))]]) ).

thf(1118,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
      ( ( order @ ( TE > TF ) )
      | ( ( order @ ( TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TF ) ) ),
    inference(paramod_ordered,[status(thm)],[1109,958]) ).

thf(1119,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] : ( order @ ( TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[1118:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TD > TC > TB > ( set @ TA ) ))]]) ).

thf(1146,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
      ( ( order @ ( TF > TG ) )
      | ( ( order @ ( TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TG ) ) ),
    inference(paramod_ordered,[status(thm)],[1119,958]) ).

thf(1147,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] : ( order @ ( TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[1146:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(1164,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] :
      ( ( order @ ( TG > TH ) )
      | ( ( order @ ( TF > TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TH ) ) ),
    inference(paramod_ordered,[status(thm)],[1147,958]) ).

thf(1165,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] : ( order @ ( TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[1164:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(1185,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] :
      ( ( order @ ( TH > TI ) )
      | ( ( order @ ( TG > TF > TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TI ) ) ),
    inference(paramod_ordered,[status(thm)],[1165,958]) ).

thf(1186,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] : ( order @ ( TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[1185:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(1195,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] :
      ( ( order @ ( TI > TJ ) )
      | ( ( order @ ( TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TJ ) ) ),
    inference(paramod_ordered,[status(thm)],[1186,958]) ).

thf(1196,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] : ( order @ ( TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[1195:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(1206,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] :
      ( ( order @ ( TJ > TK ) )
      | ( ( order @ ( TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TK ) ) ),
    inference(paramod_ordered,[status(thm)],[1196,958]) ).

thf(1207,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] : ( order @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[1206:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(1643,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] :
      ( ( order @ ( TK > TL ) )
      | ( ( order @ ( TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TL ) ) ),
    inference(paramod_ordered,[status(thm)],[1207,958]) ).

thf(1644,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] : ( order @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[1643:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(1760,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] :
      ( ( order @ ( TL > TM ) )
      | ( ( order @ ( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TM ) ) ),
    inference(paramod_ordered,[status(thm)],[1644,958]) ).

thf(1761,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] : ( order @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[1760:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(249,axiom,
    ord_less_eq @ ( set @ ( product_prod @ nat @ nat ) ) @ edges @ ( e @ a @ c ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246__092_060open_062edges_A_092_060subseteq_062_AE_092_060close_062) ).

thf(930,plain,
    ord_less_eq @ ( set @ ( product_prod @ nat @ nat ) ) @ edges @ ( e @ a @ c ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(1791,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] :
      ( ( order @ ( TM > TN ) )
      | ( ( order @ ( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TN ) ) ),
    inference(paramod_ordered,[status(thm)],[1761,958]) ).

thf(1792,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] : ( order @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[1791:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(1867,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] :
      ( ( order @ ( TN > TO ) )
      | ( ( order @ ( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TO ) ) ),
    inference(paramod_ordered,[status(thm)],[1792,958]) ).

thf(1868,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] : ( order @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[1867:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(1947,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] :
      ( ( order @ ( TO > TP ) )
      | ( ( order @ ( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TP ) ) ),
    inference(paramod_ordered,[status(thm)],[1868,958]) ).

thf(1948,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] : ( order @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[1947:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(2000,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] :
      ( ( order @ ( TP > TQ ) )
      | ( ( order @ ( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TQ ) ) ),
    inference(paramod_ordered,[status(thm)],[1948,958]) ).

thf(2001,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] : ( order @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[2000:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(2132,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] :
      ( ( order @ ( TQ > TR ) )
      | ( ( order @ ( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TR ) ) ),
    inference(paramod_ordered,[status(thm)],[2001,958]) ).

thf(2133,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] : ( order @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[2132:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(2213,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType] :
      ( ( order @ ( TR > TS ) )
      | ( ( order @ ( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TS ) ) ),
    inference(paramod_ordered,[status(thm)],[2133,958]) ).

thf(2214,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] : ( order @ ( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[2213:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(2238,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType] :
      ( ( order @ ( TS > TT ) )
      | ( ( order @ ( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TT ) ) ),
    inference(paramod_ordered,[status(thm)],[2214,958]) ).

thf(2239,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType] : ( order @ ( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[2238:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(2385,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType] :
      ( ( order @ ( TT > TU ) )
      | ( ( order @ ( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TU ) ) ),
    inference(paramod_ordered,[status(thm)],[2239,958]) ).

thf(2386,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType] : ( order @ ( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[2385:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(2690,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType] :
      ( ( order @ ( TU > TV ) )
      | ( ( order @ ( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TV ) ) ),
    inference(paramod_ordered,[status(thm)],[2386,958]) ).

thf(2691,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType] : ( order @ ( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[2690:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(3073,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType] :
      ( ( order @ ( TV > TW ) )
      | ( ( order @ ( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TW ) ) ),
    inference(paramod_ordered,[status(thm)],[2691,958]) ).

thf(3074,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType] : ( order @ ( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[3073:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(3134,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType] :
      ( ( order @ ( TW > TX ) )
      | ( ( order @ ( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TX ) ) ),
    inference(paramod_ordered,[status(thm)],[3074,958]) ).

thf(3135,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType] : ( order @ ( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[3134:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(233,axiom,
    ( ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( e @ b @ c2 ) )
   => ( finite_finite2 @ nat @ ( v @ b @ c2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_g_H_OEfin__imp__Vfin) ).

thf(898,plain,
    ( ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( e @ b @ c2 ) )
   => ( finite_finite2 @ nat @ ( v @ b @ c2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(258,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( zero @ TA ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Ozero) ).

thf(951,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( zero @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(952,plain,
    ! [TA: $tType] :
      ( ~ ( linordered_idom @ TA )
      | ( zero @ TA ) ),
    inference(cnf,[status(esa)],[951]) ).

thf(1000,plain,
    ! [TA: $tType] :
      ( ( zero @ TA )
      | ( ( linordered_idom @ b )
       != ( linordered_idom @ TA ) ) ),
    inference(paramod_ordered,[status(thm)],[977,952]) ).

thf(1001,plain,
    zero @ b,
    inference(pattern_uni,[status(thm)],[1000:[bind_type(TA,$thf( b ))]]) ).

thf(182,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( ( isSimplePath @ TA )
        = ( isSimplePath @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_Graph_OisSimplePath_Ocong) ).

thf(782,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(152,axiom,
    ord_less_eq @ nat @ ( finite_card @ ( product_prod @ nat @ nat ) @ ( edmond1803015688pEdges @ a @ c @ s @ t ) ) @ ( finite_card @ ( product_prod @ nat @ nat ) @ ( edmond259086305sis_uE @ a @ c ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_card__spEdges__le) ).

thf(709,plain,
    ord_less_eq @ nat @ ( finite_card @ ( product_prod @ nat @ nat ) @ ( edmond1803015688pEdges @ a @ c @ s @ t ) ) @ ( finite_card @ ( product_prod @ nat @ nat ) @ ( edmond259086305sis_uE @ a @ c ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(12,axiom,
    finite_Graph @ a @ c,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_Finite__Graph__axioms) ).

thf(288,plain,
    finite_Graph @ a @ c,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(21,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA] :
          ( ( edmond2129202899alysis @ TA @ A )
         => ( finite_Graph @ TA @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_ek__analysis_Oaxioms) ).

thf(301,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA] :
          ( ( edmond2129202899alysis @ TA @ A )
         => ( finite_Graph @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(27,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( connected @ b @ c2 @ A @ B )
     => ( ( ( min_dist @ b @ c2 @ A @ B )
          = C )
       => ( ( ord_less @ nat @ D @ C )
         => ? [E: nat] :
              ( ( connected @ b @ c2 @ A @ E )
              & ( ( min_dist @ b @ c2 @ A @ E )
                = D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_g_H_Omin__dist__less) ).

thf(320,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( connected @ b @ c2 @ A @ B )
     => ( ( ( min_dist @ b @ c2 @ A @ B )
          = C )
       => ( ( ord_less @ nat @ D @ C )
         => ? [E: nat] :
              ( ( connected @ b @ c2 @ A @ E )
              & ( ( min_dist @ b @ c2 @ A @ E )
                = D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(69,axiom,
    ! [A: nat,B: nat] :
      ( ( connected @ b @ c2 @ A @ B )
     => ~ ! [C: list @ ( product_prod @ nat @ nat )] :
            ~ ( isShortestPath @ b @ c2 @ A @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_g_H_Oobtain__shortest__path) ).

thf(436,plain,
    ! [A: nat,B: nat] :
      ( ( connected @ b @ c2 @ A @ B )
     => ~ ! [C: list @ ( product_prod @ nat @ nat )] :
            ~ ( isShortestPath @ b @ c2 @ A @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(226,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat] :
          ( ( edmond2129202899alysis @ TA @ A )
         => ( ord_less_eq @ ( set @ ( product_prod @ nat @ nat ) ) @ ( edmond1803015688pEdges @ TA @ A @ B @ C ) @ ( e @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_ek__analysis_OspEdges__ss__E) ).

thf(885,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat] :
          ( ( edmond2129202899alysis @ TA @ A )
         => ( ord_less_eq @ ( set @ ( product_prod @ nat @ nat ) ) @ ( edmond1803015688pEdges @ TA @ A @ B @ C ) @ ( e @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(158,axiom,
    ! [A: nat,B: nat] :
      ( ( connected @ b @ c2 @ A @ B )
     => ( ( member @ nat @ B @ ( v @ b @ c2 ) )
        = ( member @ nat @ A @ ( v @ b @ c2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_g_H_Oconnected__inV__iff) ).

thf(724,plain,
    ! [A: nat,B: nat] :
      ( ( connected @ b @ c2 @ A @ B )
     => ( ( member @ nat @ B @ ( v @ b @ c2 ) )
        = ( member @ nat @ A @ ( v @ b @ c2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(184,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ~ ( finite_finite2 @ TA @ A )
       => ~ ( finite_finite2 @ TA @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_infinite__super) ).

thf(785,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ~ ( finite_finite2 @ TA @ A )
       => ~ ( finite_finite2 @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(34,axiom,
    ! [A: nat,B: nat] :
      ( ( connected @ a @ c @ A @ B )
     => ( ( member @ nat @ B @ ( v @ a @ c ) )
        = ( member @ nat @ A @ ( v @ a @ c ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_connected__inV__iff) ).

thf(342,plain,
    ! [A: nat,B: nat] :
      ( ( connected @ a @ c @ A @ B )
     => ( ( member @ nat @ B @ ( v @ a @ c ) )
        = ( member @ nat @ A @ ( v @ a @ c ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(343,plain,
    ! [B: nat,A: nat] :
      ( ~ ( connected @ a @ c @ A @ B )
      | ( ( member @ nat @ B @ ( v @ a @ c ) )
        = ( member @ nat @ A @ ( v @ a @ c ) ) ) ),
    inference(cnf,[status(esa)],[342]) ).

thf(344,plain,
    ! [B: nat,A: nat] :
      ( ( ( member @ nat @ B @ ( v @ a @ c ) )
        = ( member @ nat @ A @ ( v @ a @ c ) ) )
      | ~ ( connected @ a @ c @ A @ B ) ),
    inference(lifteq,[status(thm)],[343]) ).

thf(100,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat,D: nat] :
          ( ( dist @ TA @ A @ B @ C @ D )
         => ( ! [E: nat] :
                ( ( dist @ TA @ A @ B @ E @ D )
               => ( ord_less_eq @ nat @ C @ E ) )
           => ( ( min_dist @ TA @ A @ B @ D )
              = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_Graph_Omin__distI__eq) ).

thf(542,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat,D: nat] :
          ( ( dist @ TA @ A @ B @ C @ D )
         => ( ! [E: nat] :
                ( ( dist @ TA @ A @ B @ E @ D )
               => ( ord_less_eq @ nat @ C @ E ) )
           => ( ( min_dist @ TA @ A @ B @ D )
              = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(53,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA] :
          ( ( edmond2129202899alysis @ TA @ A )
         => ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( edmond259086305sis_uE @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_ek__analysis_Ofinite__uE) ).

thf(389,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA] :
          ( ( edmond2129202899alysis @ TA @ A )
         => ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( edmond259086305sis_uE @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(251,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_subset__antisym) ).

thf(934,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(39,axiom,
    ! [A: nat,B: nat] :
      ( ( connected @ b @ c2 @ A @ B )
     => ( dist @ b @ c2 @ A @ ( min_dist @ b @ c2 @ A @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_g_H_Omin__dist__is__dist) ).

thf(356,plain,
    ! [A: nat,B: nat] :
      ( ( connected @ b @ c2 @ A @ B )
     => ( dist @ b @ c2 @ A @ ( min_dist @ b @ c2 @ A @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(357,plain,
    ! [B: nat,A: nat] :
      ( ~ ( connected @ b @ c2 @ A @ B )
      | ( dist @ b @ c2 @ A @ ( min_dist @ b @ c2 @ A @ B ) @ B ) ),
    inference(cnf,[status(esa)],[356]) ).

thf(257,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( type @ TA ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___HOL_Otype) ).

thf(949,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( type @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(207,axiom,
    ! [A: nat] :
      ( ( member @ nat @ A @ ( v @ a @ c ) )
     => ( ord_less_eq @ ( set @ nat ) @ ( reachableNodes @ a @ c @ A ) @ ( v @ a @ c ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_reachable__ss__V) ).

thf(853,plain,
    ! [A: nat] :
      ( ( member @ nat @ A @ ( v @ a @ c ) )
     => ( ord_less_eq @ ( set @ nat ) @ ( reachableNodes @ a @ c @ A ) @ ( v @ a @ c ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(4110,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType] :
      ( ( order @ ( TZI > TZJ ) )
      | ( ( order @ ( TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) )
       != ( order @ TZJ ) ) ),
    inference(paramod_ordered,[status(thm)],[4043,958]) ).

thf(4111,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType] : ( order @ ( TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[4110:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ))]]) ).

thf(4269,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType] :
      ( ( order @ ( TZJ > TZK ) )
      | ( ( order @ ( TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) )
       != ( order @ TZK ) ) ),
    inference(paramod_ordered,[status(thm)],[4111,958]) ).

thf(4270,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType] : ( order @ ( TZJ > TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[4269:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZJ )),bind_type(TZK,$thf( TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ))]]) ).

thf(4352,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType] :
      ( ( order @ ( TZK > TZL ) )
      | ( ( order @ ( TZJ > TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) )
       != ( order @ TZL ) ) ),
    inference(paramod_ordered,[status(thm)],[4270,958]) ).

thf(4353,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType] : ( order @ ( TZK > TZJ > TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ) ),
    inference(pattern_uni,[status(thm)],[4352:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZJ )),bind_type(TZK,$thf( TZK )),bind_type(TZL,$thf( TZJ > TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > b ))]]) ).

thf(217,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( ( reachableNodes @ TA )
        = ( reachableNodes @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_Graph_OreachableNodes_Ocong) ).

thf(870,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(224,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA] :
          ( ( finite_Graph @ TA @ A )
         => ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( e @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_Finite__Graph_Ofinite__E) ).

thf(881,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA] :
          ( ( finite_Graph @ TA @ A )
         => ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( e @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(13,axiom,
    ord_less @ nat @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p ) @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10__092_060open_062length_Ap_A_060_Alength_Ap_H_092_060close_062) ).

thf(289,plain,
    ord_less @ nat @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p ) @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(24,axiom,
    ~ ! [A: list @ ( product_prod @ nat @ nat )] :
        ( ( isPath @ b @ c2 @ s @ A @ t )
       => ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ A )
         != ( min_dist @ b @ c2 @ s @ t ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062p_H_O_A_092_060lbrakk_062g_H_OisPath_As_Ap_H_At_059_Alength_Ap_H_A_061_Ag_H_Omin__dist_As_At_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).

thf(306,plain,
    ~ ! [A: list @ ( product_prod @ nat @ nat )] :
        ( ( isPath @ b @ c2 @ s @ A @ t )
       => ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ A )
         != ( min_dist @ b @ c2 @ s @ t ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(307,plain,
    ~ ! [A: list @ ( product_prod @ nat @ nat )] :
        ( ( isPath @ b @ c2 @ s @ A @ t )
       => ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ A )
         != ( min_dist @ b @ c2 @ s @ t ) ) ),
    inference(polarity_switch,[status(thm)],[306]) ).

thf(308,plain,
    ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ sk1 )
    = ( min_dist @ b @ c2 @ s @ t ) ),
    inference(cnf,[status(esa)],[307]) ).

thf(310,plain,
    ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ sk1 )
    = ( min_dist @ b @ c2 @ s @ t ) ),
    inference(lifteq,[status(thm)],[308]) ).

thf(5,axiom,
    ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p2 )
    = ( min_dist @ b @ c2 @ s @ t ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_LENP_H) ).

thf(280,plain,
    ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p2 )
    = ( min_dist @ b @ c2 @ s @ t ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(281,plain,
    ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p2 )
    = ( min_dist @ b @ c2 @ s @ t ) ),
    inference(lifteq,[status(thm)],[280]) ).

thf(107,axiom,
    ! [A: nat] :
      ~ ( ord_less @ nat @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_less__not__refl) ).

thf(566,plain,
    ! [A: nat] :
      ~ ( ord_less @ nat @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(567,plain,
    ~ ? [A: nat] : ( ord_less @ nat @ A @ A ),
    inference(miniscope,[status(thm)],[566]) ).

thf(568,plain,
    ! [A: nat] :
      ~ ( ord_less @ nat @ A @ A ),
    inference(cnf,[status(esa)],[567]) ).

thf(1011,plain,
    ! [A: nat] :
      ( ( ord_less @ nat @ ( min_dist @ b @ c2 @ s @ t ) @ ( min_dist @ a @ c @ s @ t ) )
     != ( ord_less @ nat @ A @ A ) ),
    inference(paramod_ordered,[status(thm)],[284,568]) ).

thf(1014,plain,
    ! [A: nat] :
      ( ( ( min_dist @ b @ c2 @ s @ t )
       != A )
      | ( ( min_dist @ a @ c @ s @ t )
       != A ) ),
    inference(simp,[status(thm)],[1011]) ).

thf(1016,plain,
    ( ( min_dist @ a @ c @ s @ t )
   != ( min_dist @ b @ c2 @ s @ t ) ),
    inference(simp,[status(thm)],[1014]) ).

thf(1137,plain,
    ( ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p2 )
     != ( min_dist @ a @ c @ s @ t ) )
    | ( ( min_dist @ b @ c2 @ s @ t )
     != ( min_dist @ b @ c2 @ s @ t ) ) ),
    inference(paramod_ordered,[status(thm)],[281,1016]) ).

thf(1138,plain,
    ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p2 )
   != ( min_dist @ a @ c @ s @ t ) ),
    inference(pattern_uni,[status(thm)],[1137:[]]) ).

thf(1813,plain,
    ( ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ sk1 )
     != ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p2 ) )
    | ( ( min_dist @ b @ c2 @ s @ t )
     != ( min_dist @ a @ c @ s @ t ) ) ),
    inference(paramod_ordered,[status(thm)],[310,1138]) ).

thf(1847,plain,
    ( ( sk1 != p2 )
    | ( ( min_dist @ b @ c2 @ s @ t )
     != ( min_dist @ a @ c @ s @ t ) ) ),
    inference(simp,[status(thm)],[1813]) ).

thf(195,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( ( finite_Graph @ TA )
        = ( ^ [A: ( product_prod @ nat @ nat ) > TA] : ( finite_finite2 @ nat @ ( v @ TA @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_Finite__Graph__def) ).

thf(817,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( ( finite_Graph @ TA )
        = ( ^ [A: ( product_prod @ nat @ nat ) > TA] : ( finite_finite2 @ nat @ ( v @ TA @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(236,axiom,
    ( ( finite_finite2 @ nat @ ( v @ b @ c2 ) )
   => ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( e @ b @ c2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_g_H_OVfin__imp__Efin) ).

thf(902,plain,
    ( ( finite_finite2 @ nat @ ( v @ b @ c2 ) )
   => ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( e @ b @ c2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(3183,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType] :
      ( ( order @ ( TX > TY ) )
      | ( ( order @ ( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TY ) ) ),
    inference(paramod_ordered,[status(thm)],[3135,958]) ).

thf(3184,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType] : ( order @ ( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[3183:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(3232,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType] :
      ( ( order @ ( TY > TZ ) )
      | ( ( order @ ( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TZ ) ) ),
    inference(paramod_ordered,[status(thm)],[3184,958]) ).

thf(3233,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType] : ( order @ ( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[3232:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(3267,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType] :
      ( ( order @ ( TZ > TZA ) )
      | ( ( order @ ( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TZA ) ) ),
    inference(paramod_ordered,[status(thm)],[3233,958]) ).

thf(3268,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType] : ( order @ ( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[3267:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(3387,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType] :
      ( ( order @ ( TZA > TZB ) )
      | ( ( order @ ( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TZB ) ) ),
    inference(paramod_ordered,[status(thm)],[3268,958]) ).

thf(3388,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType] : ( order @ ( TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[3387:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(3514,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType] :
      ( ( order @ ( TZB > TZC ) )
      | ( ( order @ ( TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TZC ) ) ),
    inference(paramod_ordered,[status(thm)],[3388,958]) ).

thf(3515,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType] : ( order @ ( TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[3514:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(3637,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType] :
      ( ( order @ ( TZC > TZD ) )
      | ( ( order @ ( TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TZD ) ) ),
    inference(paramod_ordered,[status(thm)],[3515,958]) ).

thf(3638,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType] : ( order @ ( TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[3637:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(121,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( ( dist @ TA )
        = ( dist @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_Graph_Odist_Ocong) ).

thf(606,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(321,plain,
    ! [A: nat,B: nat] :
      ( ( connected @ b @ c2 @ A @ B )
     => ! [C: nat] :
          ( ( ( min_dist @ b @ c2 @ A @ B )
            = C )
         => ! [D: nat] :
              ( ( ord_less @ nat @ D @ C )
             => ? [E: nat] :
                  ( ( connected @ b @ c2 @ A @ E )
                  & ( ( min_dist @ b @ c2 @ A @ E )
                    = D ) ) ) ) ),
    inference(miniscope,[status(thm)],[320]) ).

thf(322,plain,
    ! [D: nat,C: nat,B: nat,A: nat] :
      ( ~ ( connected @ b @ c2 @ A @ B )
      | ( ( min_dist @ b @ c2 @ A @ B )
       != C )
      | ~ ( ord_less @ nat @ D @ C )
      | ( connected @ b @ c2 @ A @ ( sk3 @ D @ C @ B @ A ) ) ),
    inference(cnf,[status(esa)],[321]) ).

thf(324,plain,
    ! [D: nat,C: nat,B: nat,A: nat] :
      ( ( ( min_dist @ b @ c2 @ A @ B )
       != C )
      | ~ ( connected @ b @ c2 @ A @ B )
      | ~ ( ord_less @ nat @ D @ C )
      | ( connected @ b @ c2 @ A @ ( sk3 @ D @ C @ B @ A ) ) ),
    inference(lifteq,[status(thm)],[322]) ).

thf(325,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ~ ( connected @ b @ c2 @ A @ B )
      | ~ ( ord_less @ nat @ C @ ( min_dist @ b @ c2 @ A @ B ) )
      | ( connected @ b @ c2 @ A @ ( sk3 @ C @ ( min_dist @ b @ c2 @ A @ B ) @ B @ A ) ) ),
    inference(simp,[status(thm)],[324]) ).

thf(247,axiom,
    ! [A: set @ nat] :
      ( ( finite_finite2 @ nat @ ( v @ b @ c2 ) )
     => ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( outgoing @ b @ c2 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_g_H_Ofinite__outgoing_H) ).

thf(924,plain,
    ! [A: set @ nat] :
      ( ( finite_finite2 @ nat @ ( v @ b @ c2 ) )
     => ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( outgoing @ b @ c2 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(186,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( finite_finite2 @ TA @ A )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
       => ( ( ( finite_card @ TA @ B )
            = ( finite_card @ TA @ A ) )
         => ( B = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_card__subset__eq) ).

thf(789,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( finite_finite2 @ TA @ A )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
       => ( ( ( finite_card @ TA @ B )
            = ( finite_card @ TA @ A ) )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(201,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( ( isShortestPath @ TA )
        = ( ^ [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: list @ ( product_prod @ nat @ nat ),D: nat] :
              ( ( isSimplePath @ TA @ A @ B @ C @ D )
              & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ C )
                = ( min_dist @ TA @ A @ B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_Graph_OisShortestPath__alt) ).

thf(834,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( ( isShortestPath @ TA )
        = ( ^ [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: list @ ( product_prod @ nat @ nat ),D: nat] :
              ( ( isSimplePath @ TA @ A @ B @ C @ D )
              & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ C )
                = ( min_dist @ TA @ A @ B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(4161,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType] :
      ( ( order @ ( TZI > TZJ ) )
      | ( ( order @ ( TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) )
       != ( order @ TZJ ) ) ),
    inference(paramod_ordered,[status(thm)],[4090,958]) ).

thf(4162,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType] : ( order @ ( TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[4161:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ))]]) ).

thf(4049,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType] :
      ( ( order @ ( TZH > TZI ) )
      | ( ( order @ ( TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) )
       != ( order @ TZI ) ) ),
    inference(paramod_ordered,[status(thm)],[4015,958]) ).

thf(4050,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType] : ( order @ ( TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[4049:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(252,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ! [C: TA] :
          ( ( member @ TA @ C @ A )
         => ( member @ TA @ C @ B ) )
     => ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_subsetI) ).

thf(937,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ! [C: TA] :
          ( ( member @ TA @ C @ A )
         => ( member @ TA @ C @ B ) )
     => ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(4,axiom,
    ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p )
    = ( min_dist @ a @ c @ s @ t ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_LENP) ).

thf(278,plain,
    ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p )
    = ( min_dist @ a @ c @ s @ t ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(279,plain,
    ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p )
    = ( min_dist @ a @ c @ s @ t ) ),
    inference(lifteq,[status(thm)],[278]) ).

thf(1019,plain,
    ( ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p )
     != ( zero_zero @ nat ) )
    | ( ( min_dist @ a @ c @ s @ t )
     != ( min_dist @ a @ c @ s @ t ) ) ),
    inference(paramod_ordered,[status(thm)],[279,1015]) ).

thf(1020,plain,
    ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p )
   != ( zero_zero @ nat ) ),
    inference(pattern_uni,[status(thm)],[1019:[]]) ).

thf(36,axiom,
    ! [A: nat,B: nat] :
      ( ( connected @ a @ c @ A @ B )
     => ~ ! [C: list @ ( product_prod @ nat @ nat )] :
            ~ ( isShortestPath @ a @ c @ A @ C @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_obtain__shortest__path) ).

thf(348,plain,
    ! [A: nat,B: nat] :
      ( ( connected @ a @ c @ A @ B )
     => ~ ! [C: list @ ( product_prod @ nat @ nat )] :
            ~ ( isShortestPath @ a @ c @ A @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(38,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( dist @ b @ c2 @ A @ B @ C )
      = ( ? [D: list @ ( product_prod @ nat @ nat )] :
            ( ( isPath @ b @ c2 @ A @ D @ C )
            & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ D )
              = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_g_H_Odist__def) ).

thf(353,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( dist @ b @ c2 @ A @ B @ C )
      = ( ? [D: list @ ( product_prod @ nat @ nat )] :
            ( ( isPath @ b @ c2 @ A @ D @ C )
            & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ D )
              = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(118,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( ( min_dist @ TA )
        = ( min_dist @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_Graph_Omin__dist_Ocong) ).

thf(602,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(1047,plain,
    ! [A: nat] :
      ( ( ord_less @ nat @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p ) @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p2 ) )
     != ( ord_less @ nat @ A @ ( zero_zero @ nat ) ) ),
    inference(paramod_ordered,[status(thm)],[289,405]) ).

thf(1049,plain,
    ! [A: nat] :
      ( ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p )
       != A )
      | ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p2 )
       != ( zero_zero @ nat ) ) ),
    inference(simp,[status(thm)],[1047]) ).

thf(1053,plain,
    ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p2 )
   != ( zero_zero @ nat ) ),
    inference(simp,[status(thm)],[1049]) ).

thf(1055,plain,
    ( ( ( min_dist @ b @ c2 @ s @ t )
     != ( zero_zero @ nat ) )
    | ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p2 )
     != ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p2 ) ) ),
    inference(paramod_ordered,[status(thm)],[281,1053]) ).

thf(1056,plain,
    ( ( min_dist @ b @ c2 @ s @ t )
   != ( zero_zero @ nat ) ),
    inference(pattern_uni,[status(thm)],[1055:[]]) ).

thf(1842,plain,
    ( ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ sk1 )
     != ( zero_zero @ nat ) )
    | ( ( min_dist @ b @ c2 @ s @ t )
     != ( min_dist @ b @ c2 @ s @ t ) ) ),
    inference(paramod_ordered,[status(thm)],[310,1056]) ).

thf(1843,plain,
    ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ sk1 )
   != ( zero_zero @ nat ) ),
    inference(pattern_uni,[status(thm)],[1842:[]]) ).

thf(162,axiom,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( isShortestPath @ a @ c @ A @ B @ C )
     => ( isSimplePath @ a @ c @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_shortestPath__is__simple) ).

thf(734,plain,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( isShortestPath @ a @ c @ A @ B @ C )
     => ( isSimplePath @ a @ c @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(16,axiom,
    connected @ b @ c2 @ s @ t,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_CONN2) ).

thf(293,plain,
    connected @ b @ c2 @ s @ t,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(215,axiom,
    ! [A: nat] : ( finite_finite2 @ nat @ ( adjacent_nodes @ a @ c @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_adjacent__nodes__finite) ).

thf(866,plain,
    ! [A: nat] : ( finite_finite2 @ nat @ ( adjacent_nodes @ a @ c @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(205,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: list @ ( product_prod @ nat @ nat ),D: nat] :
          ( ( finite_Graph @ TA @ A )
         => ( ( member @ nat @ B @ ( v @ TA @ A ) )
           => ( ( isSimplePath @ TA @ A @ B @ C @ D )
             => ( ord_less @ nat @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ C ) @ ( finite_card @ nat @ ( v @ TA @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_Finite__Graph_OsimplePath__length__less__V) ).

thf(849,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: list @ ( product_prod @ nat @ nat ),D: nat] :
          ( ( finite_Graph @ TA @ A )
         => ( ( member @ nat @ B @ ( v @ TA @ A ) )
           => ( ( isSimplePath @ TA @ A @ B @ C @ D )
             => ( ord_less @ nat @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ C ) @ ( finite_card @ nat @ ( v @ TA @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(92,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less @ nat @ A @ B )
     => ( ord_less_eq @ nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_less__imp__le__nat) ).

thf(507,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less @ nat @ A @ B )
     => ( ord_less_eq @ nat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(26,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( connected @ a @ c @ A @ B )
     => ( ( ( min_dist @ a @ c @ A @ B )
          = C )
       => ( ( ord_less @ nat @ D @ C )
         => ? [E: nat] :
              ( ( connected @ a @ c @ A @ E )
              & ( ( min_dist @ a @ c @ A @ E )
                = D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_min__dist__less) ).

thf(312,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( connected @ a @ c @ A @ B )
     => ( ( ( min_dist @ a @ c @ A @ B )
          = C )
       => ( ( ord_less @ nat @ D @ C )
         => ? [E: nat] :
              ( ( connected @ a @ c @ A @ E )
              & ( ( min_dist @ a @ c @ A @ E )
                = D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(56,axiom,
    ! [TA: $tType,A: nat] :
    ? [B: list @ TA] :
      ( ( size_size @ ( list @ TA ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_Ex__list__of__length) ).

thf(397,plain,
    ! [TA: $tType,A: nat] :
    ? [B: list @ TA] :
      ( ( size_size @ ( list @ TA ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(145,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat] :
          ( ( connected @ TA @ A @ B @ C )
         => ~ ! [D: list @ ( product_prod @ nat @ nat )] :
                ~ ( isShortestPath @ TA @ A @ B @ D @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_Graph_Oobtain__shortest__path) ).

thf(687,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat] :
          ( ( connected @ TA @ A @ B @ C )
         => ~ ! [D: list @ ( product_prod @ nat @ nat )] :
                ~ ( isShortestPath @ TA @ A @ B @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(222,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA] :
          ( ( finite_finite2 @ nat @ ( v @ TA @ A ) )
         => ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( e @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_Graph_OVfin__imp__Efin) ).

thf(877,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA] :
          ( ( finite_finite2 @ nat @ ( v @ TA @ A ) )
         => ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( e @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(147,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat,D: nat,E: nat] :
          ( ( connected @ TA @ A @ B @ C )
         => ( ( ( min_dist @ TA @ A @ B @ C )
              = D )
           => ( ( ord_less @ nat @ E @ D )
             => ? [F: nat] :
                  ( ( connected @ TA @ A @ B @ F )
                  & ( ( min_dist @ TA @ A @ B @ F )
                    = E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_Graph_Omin__dist__less) ).

thf(692,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat,D: nat,E: nat] :
          ( ( connected @ TA @ A @ B @ C )
         => ( ( ( min_dist @ TA @ A @ B @ C )
              = D )
           => ( ( ord_less @ nat @ E @ D )
             => ? [F: nat] :
                  ( ( connected @ TA @ A @ B @ F )
                  & ( ( min_dist @ TA @ A @ B @ F )
                    = E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(178,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( dist @ a @ c @ A @ B @ C )
     => ( connected @ a @ c @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_connected__distI) ).

thf(774,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( dist @ a @ c @ A @ B @ C )
     => ( connected @ a @ c @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(15,axiom,
    isShortestPath @ a @ c @ s @ p @ t,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_SP) ).

thf(292,plain,
    isShortestPath @ a @ c @ s @ p @ t,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(245,axiom,
    ! [A: set @ nat] : ( ord_less_eq @ ( set @ ( product_prod @ nat @ nat ) ) @ ( incoming @ b @ c2 @ A ) @ ( e @ b @ c2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_g_H_Oincoming_H__edges) ).

thf(920,plain,
    ! [A: set @ nat] : ( ord_less_eq @ ( set @ ( product_prod @ nat @ nat ) ) @ ( incoming @ b @ c2 @ A ) @ ( e @ b @ c2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(50,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(380,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)],[50]) ).

thf(70,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( connected @ b @ c2 @ A @ B )
     => ( ( ord_less_eq @ nat @ C @ ( min_dist @ b @ c2 @ A @ B ) )
       => ? [D: nat] :
            ( ( connected @ b @ c2 @ A @ D )
            & ( ( min_dist @ b @ c2 @ A @ D )
              = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_g_H_Omin__dist__le) ).

thf(439,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( connected @ b @ c2 @ A @ B )
     => ( ( ord_less_eq @ nat @ C @ ( min_dist @ b @ c2 @ A @ B ) )
       => ? [D: nat] :
            ( ( connected @ b @ c2 @ A @ D )
            & ( ( min_dist @ b @ c2 @ A @ D )
              = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(172,axiom,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( member @ nat @ A @ ( v @ b @ c2 ) )
     => ( ( isShortestPath @ b @ c2 @ A @ B @ C )
       => ( ord_less @ nat @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ B ) @ ( finite_card @ nat @ ( v @ b @ c2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_g_H_OisShortestPath__length__less__V) ).

thf(761,plain,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( member @ nat @ A @ ( v @ b @ c2 ) )
     => ( ( isShortestPath @ b @ c2 @ A @ B @ C )
       => ( ord_less @ nat @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ B ) @ ( finite_card @ nat @ ( v @ b @ c2 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(194,axiom,
    ! [TA: $tType,A: set @ TA,B: nat] :
      ( ! [C: set @ TA] :
          ( ( ord_less_eq @ ( set @ TA ) @ C @ A )
         => ( ( finite_finite2 @ TA @ C )
           => ( ord_less_eq @ nat @ ( finite_card @ TA @ C ) @ B ) ) )
     => ( ( finite_finite2 @ TA @ A )
        & ( ord_less_eq @ nat @ ( finite_card @ TA @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_finite__if__finite__subsets__card__bdd) ).

thf(810,plain,
    ! [TA: $tType,A: set @ TA,B: nat] :
      ( ! [C: set @ TA] :
          ( ( ord_less_eq @ ( set @ TA ) @ C @ A )
         => ( ( finite_finite2 @ TA @ C )
           => ( ord_less_eq @ nat @ ( finite_card @ TA @ C ) @ B ) ) )
     => ( ( finite_finite2 @ TA @ A )
        & ( ord_less_eq @ nat @ ( finite_card @ TA @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(155,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( finite_card @ TA @ A ) )
     => ( finite_finite2 @ TA @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_card__ge__0__finite) ).

thf(714,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( finite_card @ TA @ A ) )
     => ( finite_finite2 @ TA @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(239,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( ( incoming @ TA )
        = ( incoming @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_Graph_Oincoming_H_Ocong) ).

thf(910,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(180,axiom,
    ! [A: nat] : ( ord_less_eq @ ( set @ nat ) @ ( adjacent_nodes @ b @ c2 @ A ) @ ( v @ b @ c2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_g_H_Oadjacent__nodes__ss__V) ).

thf(778,plain,
    ! [A: nat] : ( ord_less_eq @ ( set @ nat ) @ ( adjacent_nodes @ b @ c2 @ A ) @ ( v @ b @ c2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(302,plain,
    ! [TA: $tType,A: ( product_prod @ nat @ nat ) > TA] :
      ( ~ ( linordered_idom @ TA )
      | ~ ( edmond2129202899alysis @ TA @ A )
      | ( finite_Graph @ TA @ A ) ),
    inference(cnf,[status(esa)],[301]) ).

thf(66,axiom,
    ! [A: nat,B: nat] :
      ( ( connected @ a @ c @ A @ B )
      = ( ? [C: list @ ( product_prod @ nat @ nat )] : ( isPath @ a @ c @ A @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_connected__def) ).

thf(429,plain,
    ! [A: nat,B: nat] :
      ( ( connected @ a @ c @ A @ B )
      = ( ? [C: list @ ( product_prod @ nat @ nat )] : ( isPath @ a @ c @ A @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(4283,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType] :
      ( ( order @ ( TZJ > TZK ) )
      | ( ( order @ ( TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) )
       != ( order @ TZK ) ) ),
    inference(paramod_ordered,[status(thm)],[4162,958]) ).

thf(4284,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType] : ( order @ ( TZJ > TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[4283:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZJ )),bind_type(TZK,$thf( TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ))]]) ).

thf(160,axiom,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( isPath @ a @ c @ A @ B @ C )
     => ? [D: list @ ( product_prod @ nat @ nat )] : ( isSimplePath @ a @ c @ A @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_isSPath__pathLE) ).

thf(729,plain,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( isPath @ a @ c @ A @ B @ C )
     => ? [D: list @ ( product_prod @ nat @ nat )] : ( isSimplePath @ a @ c @ A @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(196,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA] :
          ( ( finite_finite2 @ nat @ ( v @ TA @ A ) )
         => ( finite_Graph @ TA @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_Finite__Graph_Ointro) ).

thf(820,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA] :
          ( ( finite_finite2 @ nat @ ( v @ TA @ A ) )
         => ( finite_Graph @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(131,axiom,
    ! [A: nat] :
      ~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_not__less0) ).

thf(630,plain,
    ! [A: nat] :
      ~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(243,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: set @ nat] :
          ( ( finite_finite2 @ nat @ ( v @ TA @ A ) )
         => ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( outgoing @ TA @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_Graph_Ofinite__outgoing_H) ).

thf(916,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: set @ nat] :
          ( ( finite_finite2 @ nat @ ( v @ TA @ A ) )
         => ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( outgoing @ TA @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(1046,plain,
    ! [A: nat] :
      ( ( ord_less @ nat @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p ) @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p2 ) )
     != ( ord_less @ nat @ A @ A ) ),
    inference(paramod_ordered,[status(thm)],[289,568]) ).

thf(1048,plain,
    ! [A: nat] :
      ( ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p )
       != A )
      | ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p2 )
       != A ) ),
    inference(simp,[status(thm)],[1046]) ).

thf(1052,plain,
    ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p2 )
   != ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p ) ),
    inference(simp,[status(thm)],[1048]) ).

thf(1060,plain,
    ( ( ( min_dist @ b @ c2 @ s @ t )
     != ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p ) )
    | ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p2 )
     != ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p2 ) ) ),
    inference(paramod_ordered,[status(thm)],[281,1052]) ).

thf(1061,plain,
    ( ( min_dist @ b @ c2 @ s @ t )
   != ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p ) ),
    inference(pattern_uni,[status(thm)],[1060:[]]) ).

thf(1836,plain,
    ( ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ sk1 )
     != ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p ) )
    | ( ( min_dist @ b @ c2 @ s @ t )
     != ( min_dist @ b @ c2 @ s @ t ) ) ),
    inference(paramod_ordered,[status(thm)],[310,1061]) ).

thf(1837,plain,
    ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ sk1 )
   != ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p ) ),
    inference(pattern_uni,[status(thm)],[1836:[]]) ).

thf(4154,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType] :
      ( ( order @ ( TZI > TZJ ) )
      | ( ( order @ ( TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) )
       != ( order @ TZJ ) ) ),
    inference(paramod_ordered,[status(thm)],[4050,958]) ).

thf(4155,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType] : ( order @ ( TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[4154:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(28,axiom,
    ! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
      ( ! [C: list @ TA] :
          ( ! [D: list @ TA] :
              ( ( ord_less @ nat @ ( size_size @ ( list @ TA ) @ D ) @ ( size_size @ ( list @ TA ) @ C ) )
             => ( A @ D ) )
         => ( A @ C ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_length__induct) ).

thf(328,plain,
    ! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
      ( ! [C: list @ TA] :
          ( ! [D: list @ TA] :
              ( ( ord_less @ nat @ ( size_size @ ( list @ TA ) @ D ) @ ( size_size @ ( list @ TA ) @ C ) )
             => ( A @ D ) )
         => ( A @ C ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(329,plain,
    ! [TA: $tType,C: list @ TA,B: list @ TA,A: ( list @ TA ) > $o] :
      ( ~ ( ord_less @ nat @ ( size_size @ ( list @ TA ) @ C ) @ ( size_size @ ( list @ TA ) @ ( sk4 @ TA @ B @ A ) ) )
      | ( A @ C )
      | ( A @ B ) ),
    inference(cnf,[status(esa)],[328]) ).

thf(200,axiom,
    ! [TA: $tType,A: set @ TA,B: ( set @ TA ) > $o] :
      ( ( finite_finite2 @ TA @ A )
     => ( ! [C: set @ TA] :
            ( ( finite_finite2 @ TA @ C )
           => ( ! [D: set @ TA] :
                  ( ( ord_less @ ( set @ TA ) @ D @ C )
                 => ( B @ D ) )
             => ( B @ C ) ) )
       => ( B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_finite__psubset__induct) ).

thf(830,plain,
    ! [TA: $tType,A: set @ TA,B: ( set @ TA ) > $o] :
      ( ( finite_finite2 @ TA @ A )
     => ( ! [C: set @ TA] :
            ( ( finite_finite2 @ TA @ C )
           => ( ! [D: set @ TA] :
                  ( ( ord_less @ ( set @ TA ) @ D @ C )
                 => ( B @ D ) )
             => ( B @ C ) ) )
       => ( B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(228,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat] :
          ( ( finite_Graph @ TA @ A )
         => ( finite_finite2 @ nat @ ( adjacent_nodes @ TA @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_Finite__Graph_Oadjacent__nodes__finite) ).

thf(889,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat] :
          ( ( finite_Graph @ TA @ A )
         => ( finite_finite2 @ nat @ ( adjacent_nodes @ TA @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(143,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat,D: nat] :
          ( ( dist @ TA @ A @ B @ C @ D )
         => ( connected @ TA @ A @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_Graph_Oconnected__distI) ).

thf(682,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat,D: nat] :
          ( ( dist @ TA @ A @ B @ C @ D )
         => ( connected @ TA @ A @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(153,axiom,
    ord_less_eq @ nat @ ( finite_card @ ( product_prod @ nat @ nat ) @ ( edmond1803015688pEdges @ b @ c2 @ s @ t ) ) @ ( finite_card @ ( product_prod @ nat @ nat ) @ ( edmond259086305sis_uE @ b @ c2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_g_H_Ocard__spEdges__le) ).

thf(710,plain,
    ord_less_eq @ nat @ ( finite_card @ ( product_prod @ nat @ nat ) @ ( edmond1803015688pEdges @ b @ c2 @ s @ t ) ) @ ( finite_card @ ( product_prod @ nat @ nat ) @ ( edmond259086305sis_uE @ b @ c2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(74,axiom,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( isShortestPath @ a @ c @ A @ B @ C )
      = ( ( isPath @ a @ c @ A @ B @ C )
        & ! [D: list @ ( product_prod @ nat @ nat )] :
            ( ( isPath @ a @ c @ A @ D @ C )
           => ( ord_less_eq @ nat @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ B ) @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_isShortestPath__def) ).

thf(456,plain,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( isShortestPath @ a @ c @ A @ B @ C )
      = ( ( isPath @ a @ c @ A @ B @ C )
        & ! [D: list @ ( product_prod @ nat @ nat )] :
            ( ( isPath @ a @ c @ A @ D @ C )
           => ( ord_less_eq @ nat @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ B ) @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(9,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( ( edmond259086305sis_uE @ TA )
        = ( edmond259086305sis_uE @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_ek__analysis__defs_OuE_Ocong) ).

thf(285,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(223,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA] :
          ( ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( e @ TA @ A ) )
         => ( finite_Graph @ TA @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_Graph_OFinite__Graph__EI) ).

thf(879,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA] :
          ( ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( e @ TA @ A ) )
         => ( finite_Graph @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(3672,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType] :
      ( ( order @ ( TZD > TZE ) )
      | ( ( order @ ( TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TZE ) ) ),
    inference(paramod_ordered,[status(thm)],[3638,958]) ).

thf(3673,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType] : ( order @ ( TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[3672:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(3805,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType] :
      ( ( order @ ( TZE > TZF ) )
      | ( ( order @ ( TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TZF ) ) ),
    inference(paramod_ordered,[status(thm)],[3673,958]) ).

thf(3806,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType] : ( order @ ( TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[3805:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(3935,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType] :
      ( ( order @ ( TZF > TZG ) )
      | ( ( order @ ( TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TZG ) ) ),
    inference(paramod_ordered,[status(thm)],[3806,958]) ).

thf(3936,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType] : ( order @ ( TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[3935:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(3970,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType] :
      ( ( order @ ( TZG > TZH ) )
      | ( ( order @ ( TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TZH ) ) ),
    inference(paramod_ordered,[status(thm)],[3936,958]) ).

thf(3971,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType] : ( order @ ( TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[3970:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(4035,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType] :
      ( ( order @ ( TZH > TZI ) )
      | ( ( order @ ( TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TZI ) ) ),
    inference(paramod_ordered,[status(thm)],[3971,958]) ).

thf(4036,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType] : ( order @ ( TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[4035:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(4103,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType] :
      ( ( order @ ( TZI > TZJ ) )
      | ( ( order @ ( TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TZJ ) ) ),
    inference(paramod_ordered,[status(thm)],[4036,958]) ).

thf(4104,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType] : ( order @ ( TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[4103:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(102,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( ( isShortestPath @ TA )
        = ( ^ [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: list @ ( product_prod @ nat @ nat ),D: nat] :
              ( ( isPath @ TA @ A @ B @ C @ D )
              & ! [E: list @ ( product_prod @ nat @ nat )] :
                  ( ( isPath @ TA @ A @ B @ E @ D )
                 => ( ord_less_eq @ nat @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ C ) @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_Graph_OisShortestPath__def) ).

thf(551,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( ( isShortestPath @ TA )
        = ( ^ [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: list @ ( product_prod @ nat @ nat ),D: nat] :
              ( ( isPath @ TA @ A @ B @ C @ D )
              & ! [E: list @ ( product_prod @ nat @ nat )] :
                  ( ( isPath @ TA @ A @ B @ E @ D )
                 => ( ord_less_eq @ nat @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ C ) @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(273,axiom,
    ! [TA: $tType,TB: $tType] : ( size @ ( product_prod @ TB @ TA ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Nat_Osize_8) ).

thf(974,plain,
    ! [TA: $tType,TB: $tType] : ( size @ ( product_prod @ TB @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(96,axiom,
    ! [A: nat > nat,B: nat,C: nat] :
      ( ! [D: nat,E: nat] :
          ( ( ord_less @ nat @ D @ E )
         => ( ord_less @ nat @ ( A @ D ) @ ( A @ E ) ) )
     => ( ( ord_less_eq @ nat @ B @ C )
       => ( ord_less_eq @ nat @ ( A @ B ) @ ( A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_less__mono__imp__le__mono) ).

thf(519,plain,
    ! [A: nat > nat,B: nat,C: nat] :
      ( ! [D: nat,E: nat] :
          ( ( ord_less @ nat @ D @ E )
         => ( ord_less @ nat @ ( A @ D ) @ ( A @ E ) ) )
     => ( ( ord_less_eq @ nat @ B @ C )
       => ( ord_less_eq @ nat @ ( A @ B ) @ ( A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(126,axiom,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA )
     => ! [A: TA] :
          ~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_not__less__zero) ).

thf(615,plain,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA )
     => ! [A: TA] :
          ~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(114,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
      ( ! [D: TA] :
          ( ~ ( A @ D )
         => ? [E: TA] :
              ( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
              & ~ ( A @ E ) ) )
     => ( A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_infinite__descent__measure) ).

thf(593,plain,
    ! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
      ( ! [D: TA] :
          ( ~ ( A @ D )
         => ? [E: TA] :
              ( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
              & ~ ( A @ E ) ) )
     => ( A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(124,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: list @ ( product_prod @ nat @ nat ),D: nat] :
          ( ( finite_Graph @ TA @ A )
         => ( ( member @ nat @ B @ ( v @ TA @ A ) )
           => ( ( isShortestPath @ TA @ A @ B @ C @ D )
             => ( ord_less @ nat @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ C ) @ ( finite_card @ nat @ ( v @ TA @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_Finite__Graph_OisShortestPath__length__less__V) ).

thf(610,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: list @ ( product_prod @ nat @ nat ),D: nat] :
          ( ( finite_Graph @ TA @ A )
         => ( ( member @ nat @ B @ ( v @ TA @ A ) )
           => ( ( isShortestPath @ TA @ A @ B @ C @ D )
             => ( ord_less @ nat @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ C ) @ ( finite_card @ nat @ ( v @ TA @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(183,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( finite_finite2 @ TA @ B )
       => ( finite_finite2 @ TA @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_finite__subset) ).

thf(783,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( finite_finite2 @ TA @ B )
       => ( finite_finite2 @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(313,plain,
    ! [A: nat,B: nat] :
      ( ( connected @ a @ c @ A @ B )
     => ! [C: nat] :
          ( ( ( min_dist @ a @ c @ A @ B )
            = C )
         => ! [D: nat] :
              ( ( ord_less @ nat @ D @ C )
             => ? [E: nat] :
                  ( ( connected @ a @ c @ A @ E )
                  & ( ( min_dist @ a @ c @ A @ E )
                    = D ) ) ) ) ),
    inference(miniscope,[status(thm)],[312]) ).

thf(314,plain,
    ! [D: nat,C: nat,B: nat,A: nat] :
      ( ~ ( connected @ a @ c @ A @ B )
      | ( ( min_dist @ a @ c @ A @ B )
       != C )
      | ~ ( ord_less @ nat @ D @ C )
      | ( connected @ a @ c @ A @ ( sk2 @ D @ C @ B @ A ) ) ),
    inference(cnf,[status(esa)],[313]) ).

thf(316,plain,
    ! [D: nat,C: nat,B: nat,A: nat] :
      ( ( ( min_dist @ a @ c @ A @ B )
       != C )
      | ~ ( connected @ a @ c @ A @ B )
      | ~ ( ord_less @ nat @ D @ C )
      | ( connected @ a @ c @ A @ ( sk2 @ D @ C @ B @ A ) ) ),
    inference(lifteq,[status(thm)],[314]) ).

thf(317,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ~ ( connected @ a @ c @ A @ B )
      | ~ ( ord_less @ nat @ C @ ( min_dist @ a @ c @ A @ B ) )
      | ( connected @ a @ c @ A @ ( sk2 @ C @ ( min_dist @ a @ c @ A @ B ) @ B @ A ) ) ),
    inference(simp,[status(thm)],[316]) ).

thf(89,axiom,
    ! [A: nat] :
      ( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
      = ( A
        = ( zero_zero @ nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_bot__nat__0_Oextremum__unique) ).

thf(499,plain,
    ! [A: nat] :
      ( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
      = ( A
        = ( zero_zero @ nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(209,axiom,
    ord_less_eq @ ( set @ ( product_prod @ nat @ nat ) ) @ ( edmond1803015688pEdges @ a @ c @ s @ t ) @ ( e @ a @ c ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_spEdges__ss__E) ).

thf(857,plain,
    ord_less_eq @ ( set @ ( product_prod @ nat @ nat ) ) @ ( edmond1803015688pEdges @ a @ c @ s @ t ) @ ( e @ a @ c ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(4262,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType] :
      ( ( order @ ( TZJ > TZK ) )
      | ( ( order @ ( TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TZK ) ) ),
    inference(paramod_ordered,[status(thm)],[4104,958]) ).

thf(4263,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType] : ( order @ ( TZJ > TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[4262:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZJ )),bind_type(TZK,$thf( TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(86,axiom,
    ! [A: nat > $o,B: nat,C: nat] :
      ( ( A @ B )
     => ( ! [D: nat] :
            ( ( A @ D )
           => ( ord_less_eq @ nat @ D @ C ) )
       => ? [D: nat] :
            ( ( A @ D )
            & ! [E: nat] :
                ( ( A @ E )
               => ( ord_less_eq @ nat @ E @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_Nat_Oex__has__greatest__nat) ).

thf(488,plain,
    ! [A: nat > $o,B: nat,C: nat] :
      ( ( A @ B )
     => ( ! [D: nat] :
            ( ( A @ D )
           => ( ord_less_eq @ nat @ D @ C ) )
       => ? [D: nat] :
            ( ( A @ D )
            & ! [E: nat] :
                ( ( A @ E )
               => ( ord_less_eq @ nat @ E @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(33,axiom,
    ! [A: nat,B: nat] :
      ( ( connected @ b @ c2 @ A @ B )
      = ( ? [C: list @ ( product_prod @ nat @ nat )] : ( isPath @ b @ c2 @ A @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_g_H_Oconnected__def) ).

thf(339,plain,
    ! [A: nat,B: nat] :
      ( ( connected @ b @ c2 @ A @ B )
      = ( ? [C: list @ ( product_prod @ nat @ nat )] : ( isPath @ b @ c2 @ A @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(138,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat] : ( dist @ TA @ A @ B @ ( zero_zero @ nat ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_Graph_Odist__z) ).

thf(669,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat] : ( dist @ TA @ A @ B @ ( zero_zero @ nat ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(271,axiom,
    ! [TA: $tType] : ( size @ ( list @ TA ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_List_Olist___Nat_Osize_6) ).

thf(970,plain,
    ! [TA: $tType] : ( size @ ( list @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(101,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat,D: nat > $o] :
          ( ( connected @ TA @ A @ B @ C )
         => ( ! [E: nat] :
                ( ( dist @ TA @ A @ B @ E @ C )
               => ( ! [F: nat] :
                      ( ( dist @ TA @ A @ B @ F @ C )
                     => ( ord_less_eq @ nat @ E @ F ) )
                 => ( D @ E ) ) )
           => ( D @ ( min_dist @ TA @ A @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_Graph_Omin__distI2) ).

thf(547,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat,D: nat > $o] :
          ( ( connected @ TA @ A @ B @ C )
         => ( ! [E: nat] :
                ( ( dist @ TA @ A @ B @ E @ C )
               => ( ! [F: nat] :
                      ( ( dist @ TA @ A @ B @ F @ C )
                     => ( ord_less_eq @ nat @ E @ F ) )
                 => ( D @ E ) ) )
           => ( D @ ( min_dist @ TA @ A @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(151,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ~ ( finite_finite2 @ TA @ A )
     => ( ( finite_card @ TA @ A )
        = ( zero_zero @ nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_card_Oinfinite) ).

thf(706,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ~ ( finite_finite2 @ TA @ A )
     => ( ( finite_card @ TA @ A )
        = ( zero_zero @ nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(103,axiom,
    ! [TA: $tType] :
      ( ( zero @ TA )
     => ! [A: TA] :
          ( ( ( zero_zero @ TA )
            = A )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_zero__reorient) ).

thf(554,plain,
    ! [TA: $tType] :
      ( ( zero @ TA )
     => ! [A: TA] :
          ( ( ( zero_zero @ TA )
            = A )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(169,axiom,
    ! [A: nat,B: nat] :
      ( ( connected @ a @ c @ A @ B )
     => ( dist @ a @ c @ A @ ( min_dist @ a @ c @ A @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_min__dist__is__dist) ).

thf(753,plain,
    ! [A: nat,B: nat] :
      ( ( connected @ a @ c @ A @ B )
     => ( dist @ a @ c @ A @ ( min_dist @ a @ c @ A @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(235,axiom,
    finite_finite2 @ ( product_prod @ nat @ nat ) @ ( e @ b @ c2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_g_H_Ofinite__E) ).

thf(901,plain,
    finite_finite2 @ ( product_prod @ nat @ nat ) @ ( e @ b @ c2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(82,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ( ( ord_less_eq @ nat @ B @ C )
       => ( ord_less_eq @ nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_le__trans) ).

thf(476,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ( ( ord_less_eq @ nat @ B @ C )
       => ( ord_less_eq @ nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(113,axiom,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ~ ( ord_less @ nat @ A @ B )
       => ( ord_less @ nat @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_linorder__neqE__nat) ).

thf(590,plain,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ~ ( ord_less @ nat @ A @ B )
       => ( ord_less @ nat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(202,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat] :
          ( ( edmond2129202899alysis @ TA @ A )
         => ( ord_less_eq @ nat @ ( finite_card @ ( product_prod @ nat @ nat ) @ ( edmond1803015688pEdges @ TA @ A @ B @ C ) ) @ ( finite_card @ ( product_prod @ nat @ nat ) @ ( edmond259086305sis_uE @ TA @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_ek__analysis_Ocard__spEdges__le) ).

thf(837,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat] :
          ( ( edmond2129202899alysis @ TA @ A )
         => ( ord_less_eq @ nat @ ( finite_card @ ( product_prod @ nat @ nat ) @ ( edmond1803015688pEdges @ TA @ A @ B @ C ) ) @ ( finite_card @ ( product_prod @ nat @ nat ) @ ( edmond259086305sis_uE @ TA @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(55,axiom,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( ( size_size @ ( list @ TA ) @ A )
       != ( size_size @ ( list @ TA ) @ B ) )
     => ( A != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_neq__if__length__neq) ).

thf(393,plain,
    ! [TA: $tType,A: list @ TA,B: list @ TA] :
      ( ( ( size_size @ ( list @ TA ) @ A )
       != ( size_size @ ( list @ TA ) @ B ) )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(950,plain,
    ! [TA: $tType] :
      ( ~ ( linordered_idom @ TA )
      | ( type @ TA ) ),
    inference(cnf,[status(esa)],[949]) ).

thf(984,plain,
    ! [TA: $tType] :
      ( ( type @ TA )
      | ( ( linordered_idom @ b )
       != ( linordered_idom @ TA ) ) ),
    inference(paramod_ordered,[status(thm)],[977,950]) ).

thf(985,plain,
    type @ b,
    inference(pattern_uni,[status(thm)],[984:[bind_type(TA,$thf( b ))]]) ).

thf(149,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: list @ ( product_prod @ nat @ nat ),D: nat] :
          ( ( isPath @ TA @ A @ B @ C @ D )
         => ( dist @ TA @ A @ B @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_Graph_OisPath__distD) ).

thf(701,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: list @ ( product_prod @ nat @ nat ),D: nat] :
          ( ( isPath @ TA @ A @ B @ C @ D )
         => ( dist @ TA @ A @ B @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(164,axiom,
    ! [TA: $tType] :
      ( ( finite_finite @ TA )
     => ( ( finite_finite2 @ TA )
        = ( ^ [A: set @ TA] : $true ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_finite__code) ).

thf(738,plain,
    ! [TA: $tType] :
      ( ( finite_finite @ TA )
     => ( ( finite_finite2 @ TA )
        = ( ^ [A: set @ TA] : $true ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(240,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( ( outgoing @ TA )
        = ( outgoing @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_Graph_Ooutgoing_H_Ocong) ).

thf(911,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(47,axiom,
    ! [A: nat,B: nat] :
      ( ( connected @ b @ c2 @ A @ B )
     => ( ( ( min_dist @ b @ c2 @ A @ B )
          = ( zero_zero @ nat ) )
        = ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_g_H_Omin__dist__z__iff) ).

thf(371,plain,
    ! [A: nat,B: nat] :
      ( ( connected @ b @ c2 @ A @ B )
     => ( ( ( min_dist @ b @ c2 @ A @ B )
          = ( zero_zero @ nat ) )
        = ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(157,axiom,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( isShortestPath @ b @ c2 @ A @ B @ C )
      = ( ( isSimplePath @ b @ c2 @ A @ B @ C )
        & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ B )
          = ( min_dist @ b @ c2 @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_g_H_OisShortestPath__alt) ).

thf(721,plain,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( isShortestPath @ b @ c2 @ A @ B @ C )
      = ( ( isSimplePath @ b @ c2 @ A @ B @ C )
        & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ B )
          = ( min_dist @ b @ c2 @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(108,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less @ nat @ A @ B )
     => ( B != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_less__not__refl2) ).

thf(569,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less @ nat @ A @ B )
     => ( B != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(187,axiom,
    ! [TA: $tType,A: set @ TA,B: nat] :
      ( ~ ( finite_finite2 @ TA @ A )
     => ? [C: set @ TA] :
          ( ( finite_finite2 @ TA @ C )
          & ( ( finite_card @ TA @ C )
            = B )
          & ( ord_less_eq @ ( set @ TA ) @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_infinite__arbitrarily__large) ).

thf(792,plain,
    ! [TA: $tType,A: set @ TA,B: nat] :
      ( ~ ( finite_finite2 @ TA @ A )
     => ? [C: set @ TA] :
          ( ( finite_finite2 @ TA @ C )
          & ( ( finite_card @ TA @ C )
            = B )
          & ( ord_less_eq @ ( set @ TA ) @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(192,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( finite_finite2 @ TA @ A )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
       => ( ord_less_eq @ nat @ ( finite_card @ TA @ B ) @ ( finite_card @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_card__mono) ).

thf(805,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( finite_finite2 @ TA @ A )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
       => ( ord_less_eq @ nat @ ( finite_card @ TA @ B ) @ ( finite_card @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(25,axiom,
    connected @ a @ c @ s @ t,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_CONN) ).

thf(311,plain,
    connected @ a @ c @ s @ t,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(140,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( ( connected @ TA )
        = ( ^ [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat] :
            ? [D: list @ ( product_prod @ nat @ nat )] : ( isPath @ TA @ A @ B @ D @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_Graph_Oconnected__def) ).

thf(674,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( ( connected @ TA )
        = ( ^ [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat] :
            ? [D: list @ ( product_prod @ nat @ nat )] : ( isPath @ TA @ A @ B @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(132,axiom,
    ! [A: nat] :
      ~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_less__zeroE) ).

thf(633,plain,
    ! [A: nat] :
      ~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(41,axiom,
    ! [A: nat] : ( connected @ a @ c @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_connected__refl) ).

thf(360,plain,
    ! [A: nat] : ( connected @ a @ c @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(19,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( ( edmond2129202899alysis @ TA )
        = ( finite_Graph @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_ek__analysis__def) ).

thf(296,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( ( edmond2129202899alysis @ TA )
        = ( finite_Graph @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(297,plain,
    ! [TA: $tType] :
      ( ~ ( linordered_idom @ TA )
      | ( ( edmond2129202899alysis @ TA )
        = ( finite_Graph @ TA ) ) ),
    inference(cnf,[status(esa)],[296]) ).

thf(298,plain,
    ! [TA: $tType] :
      ( ( ( finite_Graph @ TA )
        = ( edmond2129202899alysis @ TA ) )
      | ~ ( linordered_idom @ TA ) ),
    inference(lifteq,[status(thm)],[297]) ).

thf(61,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( ( isShortestPath @ TA )
        = ( ^ [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: list @ ( product_prod @ nat @ nat ),D: nat] :
              ( ( isPath @ TA @ A @ B @ C @ D )
              & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ C )
                = ( min_dist @ TA @ A @ B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_Graph_OisShortestPath__min__dist__def) ).

thf(412,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( ( isShortestPath @ TA )
        = ( ^ [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: list @ ( product_prod @ nat @ nat ),D: nat] :
              ( ( isPath @ TA @ A @ B @ C @ D )
              & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ C )
                = ( min_dist @ TA @ A @ B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(168,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( dist @ a @ c @ A @ B @ C )
      = ( ? [D: list @ ( product_prod @ nat @ nat )] :
            ( ( isPath @ a @ c @ A @ D @ C )
            & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ D )
              = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_dist__def) ).

thf(750,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( dist @ a @ c @ A @ B @ C )
      = ( ? [D: list @ ( product_prod @ nat @ nat )] :
            ( ( isPath @ a @ c @ A @ D @ C )
            & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ D )
              = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(198,axiom,
    ! [TA: $tType] :
      ( ( finite_finite @ TA )
     => ! [A: set @ TA] : ( finite_finite2 @ TA @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_finite) ).

thf(824,plain,
    ! [TA: $tType] :
      ( ( finite_finite @ TA )
     => ! [A: set @ TA] : ( finite_finite2 @ TA @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(71,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( dist @ b @ c2 @ A @ B @ C )
     => ( ! [D: nat] :
            ( ( dist @ b @ c2 @ A @ D @ C )
           => ( ord_less_eq @ nat @ B @ D ) )
       => ( ( min_dist @ b @ c2 @ A @ C )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_g_H_Omin__distI__eq) ).

thf(444,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( dist @ b @ c2 @ A @ B @ C )
     => ( ! [D: nat] :
            ( ( dist @ b @ c2 @ A @ D @ C )
           => ( ord_less_eq @ nat @ B @ D ) )
       => ( ( min_dist @ b @ c2 @ A @ C )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(117,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( ( v @ TA )
        = ( v @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_Graph_OV_Ocong) ).

thf(601,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(109,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less @ nat @ A @ B )
     => ( A != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_less__not__refl3) ).

thf(573,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less @ nat @ A @ B )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(146,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat] :
          ( ( connected @ TA @ A @ B @ C )
         => ( ( ( min_dist @ TA @ A @ B @ C )
              = ( zero_zero @ nat ) )
            = ( C = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_Graph_Omin__dist__z__iff) ).

thf(689,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat] :
          ( ( connected @ TA @ A @ B @ C )
         => ( ( ( min_dist @ TA @ A @ B @ C )
              = ( zero_zero @ nat ) )
            = ( C = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(64,axiom,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( member @ nat @ A @ ( v @ a @ c ) )
     => ( ( isShortestPath @ a @ c @ A @ B @ C )
       => ( ord_less @ nat @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ B ) @ ( finite_card @ nat @ ( v @ a @ c ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_isShortestPath__length__less__V) ).

thf(423,plain,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( member @ nat @ A @ ( v @ a @ c ) )
     => ( ( isShortestPath @ a @ c @ A @ B @ C )
       => ( ord_less @ nat @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ B ) @ ( finite_card @ nat @ ( v @ a @ c ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(177,axiom,
    ! [A: nat] : ( dist @ a @ c @ A @ ( zero_zero @ nat ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_dist__z) ).

thf(772,plain,
    ! [A: nat] : ( dist @ a @ c @ A @ ( zero_zero @ nat ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(10,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( ( edmond1803015688pEdges @ TA )
        = ( edmond1803015688pEdges @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_ek__analysis__defs_OspEdges_Ocong) ).

thf(286,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(166,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( dist @ a @ c @ A @ B @ C )
     => ( ! [D: nat] :
            ( ( dist @ a @ c @ A @ D @ C )
           => ( ord_less_eq @ nat @ B @ D ) )
       => ( ( min_dist @ a @ c @ A @ C )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_min__distI__eq) ).

thf(743,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( dist @ a @ c @ A @ B @ C )
     => ( ! [D: nat] :
            ( ( dist @ a @ c @ A @ D @ C )
           => ( ord_less_eq @ nat @ B @ D ) )
       => ( ( min_dist @ a @ c @ A @ C )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(14,axiom,
    ( ( edmond259086305sis_uE @ b @ c2 )
    = ( edmond259086305sis_uE @ a @ c ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_uE__eq) ).

thf(290,plain,
    ( ( edmond259086305sis_uE @ b @ c2 )
    = ( edmond259086305sis_uE @ a @ c ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(291,plain,
    ( ( edmond259086305sis_uE @ b @ c2 )
    = ( edmond259086305sis_uE @ a @ c ) ),
    inference(lifteq,[status(thm)],[290]) ).

thf(237,axiom,
    ! [A: set @ nat] :
      ( ( finite_finite2 @ nat @ ( v @ a @ c ) )
     => ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( outgoing @ a @ c @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_finite__outgoing_H) ).

thf(904,plain,
    ! [A: set @ nat] :
      ( ( finite_finite2 @ nat @ ( v @ a @ c ) )
     => ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( outgoing @ a @ c @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(975,plain,
    ! [TA: $tType,TB: $tType] : ( size @ ( product_prod @ TA @ TB ) ),
    inference(cnf,[status(esa)],[974]) ).

thf(221,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA] :
          ( ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( e @ TA @ A ) )
         => ( finite_finite2 @ nat @ ( v @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_Graph_OEfin__imp__Vfin) ).

thf(875,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA] :
          ( ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( e @ TA @ A ) )
         => ( finite_finite2 @ nat @ ( v @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(199,axiom,
    ! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB > $o] :
      ( ( finite_finite2 @ TA @ A )
     => ( ! [C: TA] :
            ( ( member @ TA @ C @ A )
           => ? [D: TB] : ( B @ C @ D ) )
       => ? [C: TA > TB] :
          ! [D: TA] :
            ( ( member @ TA @ D @ A )
           => ( B @ D @ ( C @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_finite__set__choice) ).

thf(826,plain,
    ! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB > $o] :
      ( ( finite_finite2 @ TA @ A )
     => ( ! [C: TA] :
            ( ( member @ TA @ C @ A )
           => ? [D: TB] : ( B @ C @ D ) )
       => ? [C: TA > TB] :
          ! [D: TA] :
            ( ( member @ TA @ D @ A )
           => ( B @ D @ ( C @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(110,axiom,
    ! [A: nat] :
      ~ ( ord_less @ nat @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_less__irrefl__nat) ).

thf(577,plain,
    ! [A: nat] :
      ~ ( ord_less @ nat @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(154,axiom,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( member @ nat @ A @ ( v @ a @ c ) )
     => ( ( isSimplePath @ a @ c @ A @ B @ C )
       => ( ord_less @ nat @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ B ) @ ( finite_card @ nat @ ( v @ a @ c ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_simplePath__length__less__V) ).

thf(711,plain,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( member @ nat @ A @ ( v @ a @ c ) )
     => ( ( isSimplePath @ a @ c @ A @ B @ C )
       => ( ord_less @ nat @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ B ) @ ( finite_card @ nat @ ( v @ a @ c ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(54,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat] :
          ( ( edmond2129202899alysis @ TA @ A )
         => ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( edmond1803015688pEdges @ TA @ A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_ek__analysis_Ofinite__spEdges) ).

thf(391,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat] :
          ( ( edmond2129202899alysis @ TA @ A )
         => ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( edmond1803015688pEdges @ TA @ A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(185,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( finite_finite2 @ TA @ A )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
       => ( finite_finite2 @ TA @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_rev__finite__subset) ).

thf(787,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( finite_finite2 @ TA @ A )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
       => ( finite_finite2 @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(334,plain,
    ! [A: nat] :
      ( ( min_dist @ a @ c @ A @ A )
      = ( zero_zero @ nat ) ),
    inference(cnf,[status(esa)],[333]) ).

thf(335,plain,
    ! [A: nat] :
      ( ( min_dist @ a @ c @ A @ A )
      = ( zero_zero @ nat ) ),
    inference(lifteq,[status(thm)],[334]) ).

thf(256,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
       => ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_subset__trans) ).

thf(947,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
       => ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(99,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat,D: nat] :
          ( ( dist @ TA @ A @ B @ C @ D )
         => ( ord_less_eq @ nat @ ( min_dist @ TA @ A @ B @ D ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_Graph_Omin__dist__minD) ).

thf(540,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat,D: nat] :
          ( ( dist @ TA @ A @ B @ C @ D )
         => ( ord_less_eq @ nat @ ( min_dist @ TA @ A @ B @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(1058,plain,
    p2 != p,
    inference(simp,[status(thm)],[1052]) ).

thf(349,plain,
    ! [A: nat,B: nat] :
      ( ( connected @ a @ c @ A @ B )
     => ~ ~ ? [C: list @ ( product_prod @ nat @ nat )] : ( isShortestPath @ a @ c @ A @ C @ B ) ),
    inference(miniscope,[status(thm)],[348]) ).

thf(350,plain,
    ! [B: nat,A: nat] :
      ( ~ ( connected @ a @ c @ A @ B )
      | ( isShortestPath @ a @ c @ A @ ( sk5 @ B @ A ) @ B ) ),
    inference(cnf,[status(esa)],[349]) ).

thf(163,axiom,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( isShortestPath @ b @ c2 @ A @ B @ C )
     => ( isSimplePath @ b @ c2 @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_g_H_OshortestPath__is__simple) ).

thf(736,plain,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( isShortestPath @ b @ c2 @ A @ B @ C )
     => ( isSimplePath @ b @ c2 @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(49,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(377,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( collect @ TA
        @ ^ [B: TA] : ( member @ TA @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(213,axiom,
    finite_finite2 @ ( product_prod @ nat @ nat ) @ ( e @ a @ c ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_finite__E) ).

thf(863,plain,
    finite_finite2 @ ( product_prod @ nat @ nat ) @ ( e @ a @ c ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(173,axiom,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( isShortestPath @ a @ c @ A @ B @ C )
      = ( ( isSimplePath @ a @ c @ A @ B @ C )
        & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ B )
          = ( min_dist @ a @ c @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_isShortestPath__alt) ).

thf(764,plain,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( isShortestPath @ a @ c @ A @ B @ C )
      = ( ( isSimplePath @ a @ c @ A @ B @ C )
        & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ B )
          = ( min_dist @ a @ c @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(120,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat] : ( connected @ TA @ A @ B @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_Graph_Oconnected__refl) ).

thf(604,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat] : ( connected @ TA @ A @ B @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(234,axiom,
    ord_less_eq @ ( set @ ( product_prod @ nat @ nat ) ) @ ( edmond1803015688pEdges @ b @ c2 @ s @ t ) @ ( e @ b @ c2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_g_H_OspEdges__ss__E) ).

thf(900,plain,
    ord_less_eq @ ( set @ ( product_prod @ nat @ nat ) ) @ ( edmond1803015688pEdges @ b @ c2 @ s @ t ) @ ( e @ b @ c2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(59,axiom,
    ! [A: nat] :
      ( ( A
       != ( zero_zero @ nat ) )
      = ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_neq0__conv) ).

thf(406,plain,
    ! [A: nat] :
      ( ( A
       != ( zero_zero @ nat ) )
      = ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(42,axiom,
    ! [A: nat,B: nat] :
      ( ( dist @ b @ c2 @ A @ ( zero_zero @ nat ) @ B )
      = ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_g_H_Odist__z__iff) ).

thf(362,plain,
    ! [A: nat,B: nat] :
      ( ( dist @ b @ c2 @ A @ ( zero_zero @ nat ) @ B )
      = ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(73,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( connected @ a @ c @ A @ B )
     => ( ( ord_less_eq @ nat @ C @ ( min_dist @ a @ c @ A @ B ) )
       => ? [D: nat] :
            ( ( connected @ a @ c @ A @ D )
            & ( ( min_dist @ a @ c @ A @ D )
              = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_min__dist__le) ).

thf(451,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( connected @ a @ c @ A @ B )
     => ( ( ord_less_eq @ nat @ C @ ( min_dist @ a @ c @ A @ B ) )
       => ? [D: nat] :
            ( ( connected @ a @ c @ A @ D )
            & ( ( min_dist @ a @ c @ A @ D )
              = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(93,axiom,
    ( ( ord_less_eq @ nat )
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less @ nat @ A @ B )
          | ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_le__eq__less__or__eq) ).

thf(509,plain,
    ( ( ord_less_eq @ nat )
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less @ nat @ A @ B )
          | ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(68,axiom,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( isShortestPath @ b @ c2 @ A @ B @ C )
     => ( isPath @ b @ c2 @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_g_H_OshortestPath__is__path) ).

thf(434,plain,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( isShortestPath @ b @ c2 @ A @ B @ C )
     => ( isPath @ b @ c2 @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(616,plain,
    ! [TA: $tType,A: TA] :
      ( ~ ( canoni770627133id_add @ TA )
      | ~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
    inference(cnf,[status(esa)],[615]) ).

thf(22,axiom,
    ( ~ ( connected @ b @ c2 @ s @ t )
   => ( ord_less @ nat @ ( edmond115586663easure @ b @ c2 @ s @ t ) @ ( edmond115586663easure @ a @ c @ s @ t ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19__092_060open_062_092_060not_062_Ag_H_Oconnected_As_At_A_092_060Longrightarrow_062_Ag_H_OekMeasure_A_060_AekMeasure_092_060close_062) ).

thf(303,plain,
    ( ~ ( connected @ b @ c2 @ s @ t )
   => ( ord_less @ nat @ ( edmond115586663easure @ b @ c2 @ s @ t ) @ ( edmond115586663easure @ a @ c @ s @ t ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(4429,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType] :
      ( ( order @ ( TZK > TZL ) )
      | ( ( order @ ( TZJ > TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) )
       != ( order @ TZL ) ) ),
    inference(paramod_ordered,[status(thm)],[4284,958]) ).

thf(4430,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType] : ( order @ ( TZK > TZJ > TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ) ),
    inference(pattern_uni,[status(thm)],[4429:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZJ )),bind_type(TZK,$thf( TZK )),bind_type(TZL,$thf( TZJ > TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > a ))]]) ).

thf(87,axiom,
    ! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_less__eq__nat_Osimps_I1_J) ).

thf(494,plain,
    ! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(171,axiom,
    ! [A: nat,B: nat] :
      ( ( member @ nat @ A @ ( v @ b @ c2 ) )
     => ( ( connected @ b @ c2 @ A @ B )
       => ( ord_less @ nat @ ( min_dist @ b @ c2 @ A @ B ) @ ( finite_card @ nat @ ( v @ b @ c2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_g_H_Omin__dist__less__V) ).

thf(758,plain,
    ! [A: nat,B: nat] :
      ( ( member @ nat @ A @ ( v @ b @ c2 ) )
     => ( ( connected @ b @ c2 @ A @ B )
       => ( ord_less @ nat @ ( min_dist @ b @ c2 @ A @ B ) @ ( finite_card @ nat @ ( v @ b @ c2 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(189,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: list @ ( product_prod @ nat @ nat ),D: nat] :
          ( ( isShortestPath @ TA @ A @ B @ C @ D )
         => ( isSimplePath @ TA @ A @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_Graph_OshortestPath__is__simple) ).

thf(799,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: list @ ( product_prod @ nat @ nat ),D: nat] :
          ( ( isShortestPath @ TA @ A @ B @ C @ D )
         => ( isSimplePath @ TA @ A @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(84,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ( ( ord_less_eq @ nat @ B @ A )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_le__antisym) ).

thf(483,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ( ( ord_less_eq @ nat @ B @ A )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(231,axiom,
    ord_less_eq @ ( set @ ( product_prod @ nat @ nat ) ) @ ( e @ b @ c2 ) @ ( edmond259086305sis_uE @ b @ c2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_g_H_OE__ss__uE) ).

thf(895,plain,
    ord_less_eq @ ( set @ ( product_prod @ nat @ nat ) ) @ ( e @ b @ c2 ) @ ( edmond259086305sis_uE @ b @ c2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(176,axiom,
    ! [A: nat,B: nat] :
      ( ( dist @ a @ c @ A @ ( zero_zero @ nat ) @ B )
      = ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_dist__z__iff) ).

thf(769,plain,
    ! [A: nat,B: nat] :
      ( ( dist @ a @ c @ A @ ( zero_zero @ nat ) @ B )
      = ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(330,plain,
    ! [TA: $tType,B: list @ TA,A: ( list @ TA ) > $o] :
      ( ~ ( A @ ( sk4 @ TA @ B @ A ) )
      | ( A @ B ) ),
    inference(cnf,[status(esa)],[328]) ).

thf(210,axiom,
    ord_less_eq @ ( set @ ( product_prod @ nat @ nat ) ) @ ( e @ a @ c ) @ ( edmond259086305sis_uE @ a @ c ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_E__ss__uE) ).

thf(858,plain,
    ord_less_eq @ ( set @ ( product_prod @ nat @ nat ) ) @ ( e @ a @ c ) @ ( edmond259086305sis_uE @ a @ c ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(44,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( dist @ b @ c2 @ A @ B @ C )
     => ( connected @ b @ c2 @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_g_H_Oconnected__distI) ).

thf(367,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( dist @ b @ c2 @ A @ B @ C )
     => ( connected @ b @ c2 @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(4276,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType] :
      ( ( order @ ( TZJ > TZK ) )
      | ( ( order @ ( TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) )
       != ( order @ TZK ) ) ),
    inference(paramod_ordered,[status(thm)],[4155,958]) ).

thf(4277,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType] : ( order @ ( TZJ > TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[4276:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZJ )),bind_type(TZK,$thf( TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(128,axiom,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA )
     => ! [A: TA] :
          ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
          = ( A
           != ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_zero__less__iff__neq__zero) ).

thf(621,plain,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA )
     => ! [A: TA] :
          ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
          = ( A
           != ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(267,axiom,
    ! [TA: $tType] :
      ( ( finite_finite @ TA )
     => ( finite_finite @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Finite__Set_Ofinite_2) ).

thf(964,plain,
    ! [TA: $tType] :
      ( ( finite_finite @ TA )
     => ( finite_finite @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(76,axiom,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( isShortestPath @ b @ c2 @ A @ B @ C )
      = ( ( isPath @ b @ c2 @ A @ B @ C )
        & ! [D: list @ ( product_prod @ nat @ nat )] :
            ( ( isPath @ b @ c2 @ A @ D @ C )
           => ( ord_less_eq @ nat @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ B ) @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_g_H_OisShortestPath__def) ).

thf(462,plain,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( isShortestPath @ b @ c2 @ A @ B @ C )
      = ( ( isPath @ b @ c2 @ A @ B @ C )
        & ! [D: list @ ( product_prod @ nat @ nat )] :
            ( ( isPath @ b @ c2 @ A @ D @ C )
           => ( ord_less_eq @ nat @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ B ) @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(241,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: set @ nat] : ( ord_less_eq @ ( set @ ( product_prod @ nat @ nat ) ) @ ( outgoing @ TA @ A @ B ) @ ( e @ TA @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_Graph_Ooutgoing_H__edges) ).

thf(912,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: set @ nat] : ( ord_less_eq @ ( set @ ( product_prod @ nat @ nat ) ) @ ( outgoing @ TA @ A @ B ) @ ( e @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(262,axiom,
    canoni770627133id_add @ nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).

thf(959,plain,
    canoni770627133id_add @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(175,axiom,
    finite_finite2 @ nat @ ( v @ a @ c ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_finite__V) ).

thf(768,plain,
    finite_finite2 @ nat @ ( v @ a @ c ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(133,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less @ nat @ A @ B )
     => ( B
       != ( zero_zero @ nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_gr__implies__not0) ).

thf(636,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less @ nat @ A @ B )
     => ( B
       != ( zero_zero @ nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(181,axiom,
    ! [A: nat] : ( ord_less_eq @ ( set @ nat ) @ ( adjacent_nodes @ a @ c @ A ) @ ( v @ a @ c ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_adjacent__nodes__ss__V) ).

thf(780,plain,
    ! [A: nat] : ( ord_less_eq @ ( set @ nat ) @ ( adjacent_nodes @ a @ c @ A ) @ ( v @ a @ c ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(123,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat] :
          ( ( finite_Graph @ TA @ A )
         => ( ( member @ nat @ B @ ( v @ TA @ A ) )
           => ( ( connected @ TA @ A @ B @ C )
             => ( ord_less @ nat @ ( min_dist @ TA @ A @ B @ C ) @ ( finite_card @ nat @ ( v @ TA @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_Finite__Graph_Omin__dist__less__V) ).

thf(608,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat] :
          ( ( finite_Graph @ TA @ A )
         => ( ( member @ nat @ B @ ( v @ TA @ A ) )
           => ( ( connected @ TA @ A @ B @ C )
             => ( ord_less @ nat @ ( min_dist @ TA @ A @ B @ C ) @ ( finite_card @ nat @ ( v @ TA @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(20,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA] :
          ( ( finite_Graph @ TA @ A )
         => ( edmond2129202899alysis @ TA @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_ek__analysis_Ointro) ).

thf(299,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA] :
          ( ( finite_Graph @ TA @ A )
         => ( edmond2129202899alysis @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(206,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( finite_finite2 @ TA @ A )
     => ( ( ord_less @ ( set @ TA ) @ B @ A )
       => ( ord_less @ nat @ ( finite_card @ TA @ B ) @ ( finite_card @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_psubset__card__mono) ).

thf(851,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( finite_finite2 @ TA @ A )
     => ( ( ord_less @ ( set @ TA ) @ B @ A )
       => ( ord_less @ nat @ ( finite_card @ TA @ B ) @ ( finite_card @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(91,axiom,
    ( ( ord_less @ nat )
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_eq @ nat @ A @ B )
          & ( A != B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_nat__less__le) ).

thf(505,plain,
    ( ( ord_less @ nat )
    = ( ^ [A: nat,B: nat] :
          ( ( ord_less_eq @ nat @ A @ B )
          & ( A != B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(246,axiom,
    ! [A: set @ nat] : ( ord_less_eq @ ( set @ ( product_prod @ nat @ nat ) ) @ ( outgoing @ b @ c2 @ A ) @ ( e @ b @ c2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_g_H_Ooutgoing_H__edges) ).

thf(922,plain,
    ! [A: set @ nat] : ( ord_less_eq @ ( set @ ( product_prod @ nat @ nat ) ) @ ( outgoing @ b @ c2 @ A ) @ ( e @ b @ c2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(2498,plain,
    ! [TA: $tType,B: list @ TA,A: list @ TA] :
      ( ~ ( ord_less @ nat @ ( size_size @ ( list @ TA ) @ B )
          @ ( size_size @ ( list @ TA )
            @ ( sk4 @ TA @ A
              @ ^ [C: list @ TA] : $false ) ) )
      | $false
      | $false ),
    inference(prim_subst,[status(thm)],[329:[bind(A,$thf( ^ [D: list @ TA] : $false ))]]) ).

thf(2620,plain,
    ! [TA: $tType,B: list @ TA,A: list @ TA] :
      ~ ( ord_less @ nat @ ( size_size @ ( list @ TA ) @ B )
        @ ( size_size @ ( list @ TA )
          @ ( sk4 @ TA @ A
            @ ^ [C: list @ TA] : $false ) ) ),
    inference(simp,[status(thm)],[2498]) ).

thf(216,axiom,
    ( ( finite_finite2 @ nat @ ( v @ a @ c ) )
   => ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( e @ a @ c ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_Vfin__imp__Efin) ).

thf(868,plain,
    ( ( finite_finite2 @ nat @ ( v @ a @ c ) )
   => ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( e @ a @ c ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(225,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA] :
          ( ( edmond2129202899alysis @ TA @ A )
         => ( ord_less_eq @ ( set @ ( product_prod @ nat @ nat ) ) @ ( e @ TA @ A ) @ ( edmond259086305sis_uE @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_ek__analysis_OE__ss__uE) ).

thf(883,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA] :
          ( ( edmond2129202899alysis @ TA @ A )
         => ( ord_less_eq @ ( set @ ( product_prod @ nat @ nat ) ) @ ( e @ TA @ A ) @ ( edmond259086305sis_uE @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(106,axiom,
    ! [A: nat,B: nat] :
      ( ( A != B )
      = ( ( ord_less @ nat @ A @ B )
        | ( ord_less @ nat @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_nat__neq__iff) ).

thf(563,plain,
    ! [A: nat,B: nat] :
      ( ( A != B )
      = ( ( ord_less @ nat @ A @ B )
        | ( ord_less @ nat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(255,axiom,
    ! [TA: $tType] :
      ( ( (=) @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
            ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
            & ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_set__eq__subset) ).

thf(944,plain,
    ! [TA: $tType] :
      ( ( (=) @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
            ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
            & ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(269,axiom,
    finite_finite @ $o,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Finite__Set_Ofinite_4) ).

thf(968,plain,
    finite_finite @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(65,axiom,
    ! [A: nat,B: nat] :
      ( ( member @ nat @ A @ ( v @ a @ c ) )
     => ( ( connected @ a @ c @ A @ B )
       => ( ord_less @ nat @ ( min_dist @ a @ c @ A @ B ) @ ( finite_card @ nat @ ( v @ a @ c ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_min__dist__less__V) ).

thf(426,plain,
    ! [A: nat,B: nat] :
      ( ( member @ nat @ A @ ( v @ a @ c ) )
     => ( ( connected @ a @ c @ A @ B )
       => ( ord_less @ nat @ ( min_dist @ a @ c @ A @ B ) @ ( finite_card @ nat @ ( v @ a @ c ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(142,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: list @ ( product_prod @ nat @ nat ),D: nat] :
          ( ( isShortestPath @ TA @ A @ B @ C @ D )
         => ( isPath @ TA @ A @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_Graph_OshortestPath__is__path) ).

thf(680,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: list @ ( product_prod @ nat @ nat ),D: nat] :
          ( ( isShortestPath @ TA @ A @ B @ C @ D )
         => ( isPath @ TA @ A @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(248,axiom,
    ! [A: set @ nat] :
      ( ( finite_finite2 @ nat @ ( v @ b @ c2 ) )
     => ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( incoming @ b @ c2 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_g_H_Ofinite__incoming_H) ).

thf(927,plain,
    ! [A: set @ nat] :
      ( ( finite_finite2 @ nat @ ( v @ b @ c2 ) )
     => ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( incoming @ b @ c2 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(48,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(374,plain,
    ! [TA: $tType,A: TA,B: TA > $o] :
      ( ( member @ TA @ A @ ( collect @ TA @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(127,axiom,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( B
           != ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_gr__implies__not__zero) ).

thf(617,plain,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less @ TA @ A @ B )
         => ( B
           != ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(95,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ( ( A != B )
       => ( ord_less @ nat @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_le__neq__implies__less) ).

thf(516,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
     => ( ( A != B )
       => ( ord_less @ nat @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(354,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ( dist @ b @ c2 @ A @ B @ C )
      = ( ? [D: list @ ( product_prod @ nat @ nat )] :
            ( ( isPath @ b @ c2 @ A @ D @ C )
            & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ D )
              = B ) ) ) ),
    inference(cnf,[status(esa)],[353]) ).

thf(355,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ( dist @ b @ c2 @ A @ B @ C )
      = ( ? [D: list @ ( product_prod @ nat @ nat )] :
            ( ( isPath @ b @ c2 @ A @ D @ C )
            & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ D )
              = B ) ) ) ),
    inference(lifteq,[status(thm)],[354]) ).

thf(134,axiom,
    ! [A: nat > $o,B: nat] :
      ( ( A @ ( zero_zero @ nat ) )
     => ( ! [C: nat] :
            ( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
           => ( ~ ( A @ C )
             => ? [D: nat] :
                  ( ( ord_less @ nat @ D @ C )
                  & ~ ( A @ D ) ) ) )
       => ( A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_infinite__descent0) ).

thf(640,plain,
    ! [A: nat > $o,B: nat] :
      ( ( A @ ( zero_zero @ nat ) )
     => ( ! [C: nat] :
            ( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
           => ( ~ ( A @ C )
             => ? [D: nat] :
                  ( ( ord_less @ nat @ D @ C )
                  & ~ ( A @ D ) ) ) )
       => ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(18,axiom,
    isPath @ b @ c2 @ s @ p2 @ t,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_P_H) ).

thf(295,plain,
    isPath @ b @ c2 @ s @ p2 @ t,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(219,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( ( e @ TA )
        = ( e @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_Graph_OE_Ocong) ).

thf(872,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(227,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat] : ( ord_less_eq @ ( set @ nat ) @ ( adjacent_nodes @ TA @ A @ B ) @ ( v @ TA @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_Graph_Oadjacent__nodes__ss__V) ).

thf(887,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat] : ( ord_less_eq @ ( set @ nat ) @ ( adjacent_nodes @ TA @ A @ B ) @ ( v @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(971,plain,
    ! [TA: $tType] : ( size @ ( list @ TA ) ),
    inference(cnf,[status(esa)],[970]) ).

thf(323,plain,
    ! [D: nat,C: nat,B: nat,A: nat] :
      ( ~ ( connected @ b @ c2 @ A @ B )
      | ( ( min_dist @ b @ c2 @ A @ B )
       != C )
      | ~ ( ord_less @ nat @ D @ C )
      | ( ( min_dist @ b @ c2 @ A @ ( sk3 @ D @ C @ B @ A ) )
        = D ) ),
    inference(cnf,[status(esa)],[321]) ).

thf(326,plain,
    ! [D: nat,C: nat,B: nat,A: nat] :
      ( ( ( min_dist @ b @ c2 @ A @ B )
       != C )
      | ( ( min_dist @ b @ c2 @ A @ ( sk3 @ D @ C @ B @ A ) )
        = D )
      | ~ ( connected @ b @ c2 @ A @ B )
      | ~ ( ord_less @ nat @ D @ C ) ),
    inference(lifteq,[status(thm)],[323]) ).

thf(327,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ( ( min_dist @ b @ c2 @ A @ ( sk3 @ C @ ( min_dist @ b @ c2 @ A @ B ) @ B @ A ) )
        = C )
      | ~ ( connected @ b @ c2 @ A @ B )
      | ~ ( ord_less @ nat @ C @ ( min_dist @ b @ c2 @ A @ B ) ) ),
    inference(simp,[status(thm)],[326]) ).

thf(60,axiom,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA )
     => ! [A: TA] :
          ( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_not__gr__zero) ).

thf(409,plain,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA )
     => ! [A: TA] :
          ( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(104,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( wellorder @ TB )
     => ! [A: TA > TB,B: TA > $o,C: TA] :
          ( ! [D: TA] :
              ( ! [E: TA] :
                  ( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
                 => ( B @ E ) )
             => ( B @ D ) )
         => ( B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_measure__induct) ).

thf(557,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( wellorder @ TB )
     => ! [A: TA > TB,B: TA > $o,C: TA] :
          ( ! [D: TA] :
              ( ! [E: TA] :
                  ( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
                 => ( B @ E ) )
             => ( B @ D ) )
         => ( B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(1002,plain,
    ! [TA: $tType] :
      ( ( zero @ TA )
      | ( ( linordered_idom @ a )
       != ( linordered_idom @ TA ) ) ),
    inference(paramod_ordered,[status(thm)],[976,952]) ).

thf(1003,plain,
    zero @ a,
    inference(pattern_uni,[status(thm)],[1002:[bind_type(TA,$thf( a ))]]) ).

thf(111,axiom,
    ! [A: nat > $o,B: nat] :
      ( ! [C: nat] :
          ( ! [D: nat] :
              ( ( ord_less @ nat @ D @ C )
             => ( A @ D ) )
         => ( A @ C ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_nat__less__induct) ).

thf(580,plain,
    ! [A: nat > $o,B: nat] :
      ( ! [C: nat] :
          ( ! [D: nat] :
              ( ( ord_less @ nat @ D @ C )
             => ( A @ D ) )
         => ( A @ C ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(208,axiom,
    ! [A: nat] :
      ( ( member @ nat @ A @ ( v @ b @ c2 ) )
     => ( ord_less_eq @ ( set @ nat ) @ ( reachableNodes @ b @ c2 @ A ) @ ( v @ b @ c2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_g_H_Oreachable__ss__V) ).

thf(855,plain,
    ! [A: nat] :
      ( ( member @ nat @ A @ ( v @ b @ c2 ) )
     => ( ord_less_eq @ ( set @ nat ) @ ( reachableNodes @ b @ c2 @ A ) @ ( v @ b @ c2 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(6,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( ( edmond115586663easure @ TA )
        = ( edmond115586663easure @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_ek__analysis__defs_OekMeasure_Ocong) ).

thf(282,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(4436,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType] :
      ( ( order @ ( TZK > TZL ) )
      | ( ( order @ ( TZJ > TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) )
       != ( order @ TZL ) ) ),
    inference(paramod_ordered,[status(thm)],[4339,958]) ).

thf(4437,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType] : ( order @ ( TZK > TZJ > TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ) ),
    inference(pattern_uni,[status(thm)],[4436:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZJ )),bind_type(TZK,$thf( TZK )),bind_type(TZL,$thf( TZJ > TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > nat ))]]) ).

thf(4345,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType] :
      ( ( order @ ( TZK > TZL ) )
      | ( ( order @ ( TZJ > TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) )
       != ( order @ TZL ) ) ),
    inference(paramod_ordered,[status(thm)],[4263,958]) ).

thf(4346,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType] : ( order @ ( TZK > TZJ > TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ) ),
    inference(pattern_uni,[status(thm)],[4345:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZJ )),bind_type(TZK,$thf( TZK )),bind_type(TZL,$thf( TZJ > TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > ( set @ TA ) ))]]) ).

thf(3302,plain,
    ! [A: nat] :
      ( ( min_dist @ a @ c @ A @ A )
     != ( min_dist @ a @ c @ s @ t ) ),
    inference(paramod_ordered,[status(thm)],[335,1015]) ).

thf(3335,plain,
    ! [A: nat] :
      ( ( c != c )
      | ( A != s )
      | ( A != t ) ),
    inference(simp,[status(thm)],[3302]) ).

thf(3344,plain,
    t != s,
    inference(simp,[status(thm)],[3335]) ).

thf(90,axiom,
    ! [A: nat] :
      ( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
     => ( A
        = ( zero_zero @ nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_bot__nat__0_Oextremum__uniqueI) ).

thf(502,plain,
    ! [A: nat] :
      ( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
     => ( A
        = ( zero_zero @ nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(32,axiom,
    ! [A: nat] :
      ( ( min_dist @ b @ c2 @ A @ A )
      = ( zero_zero @ nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_g_H_Omin__dist__z) ).

thf(336,plain,
    ! [A: nat] :
      ( ( min_dist @ b @ c2 @ A @ A )
      = ( zero_zero @ nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(337,plain,
    ! [A: nat] :
      ( ( min_dist @ b @ c2 @ A @ A )
      = ( zero_zero @ nat ) ),
    inference(cnf,[status(esa)],[336]) ).

thf(338,plain,
    ! [A: nat] :
      ( ( min_dist @ b @ c2 @ A @ A )
      = ( zero_zero @ nat ) ),
    inference(lifteq,[status(thm)],[337]) ).

thf(238,axiom,
    ! [A: set @ nat] :
      ( ( finite_finite2 @ nat @ ( v @ a @ c ) )
     => ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( incoming @ a @ c @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_finite__incoming_H) ).

thf(907,plain,
    ! [A: set @ nat] :
      ( ( finite_finite2 @ nat @ ( v @ a @ c ) )
     => ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( incoming @ a @ c @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(29,axiom,
    finite_finite2 @ ( product_prod @ nat @ nat ) @ ( edmond1803015688pEdges @ a @ c @ s @ t ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_finite__spEdges) ).

thf(331,plain,
    finite_finite2 @ ( product_prod @ nat @ nat ) @ ( edmond1803015688pEdges @ a @ c @ s @ t ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(112,axiom,
    ! [A: nat > $o,B: nat] :
      ( ! [C: nat] :
          ( ~ ( A @ C )
         => ? [D: nat] :
              ( ( ord_less @ nat @ D @ C )
              & ~ ( A @ D ) ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_infinite__descent) ).

thf(585,plain,
    ! [A: nat > $o,B: nat] :
      ( ! [C: nat] :
          ( ~ ( A @ C )
         => ? [D: nat] :
              ( ( ord_less @ nat @ D @ C )
              & ~ ( A @ D ) ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(46,axiom,
    finite_finite2 @ ( product_prod @ nat @ nat ) @ ( edmond259086305sis_uE @ a @ c ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_finite__uE) ).

thf(370,plain,
    finite_finite2 @ ( product_prod @ nat @ nat ) @ ( edmond259086305sis_uE @ a @ c ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(79,axiom,
    ! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_bot__nat__0_Oextremum) ).

thf(470,plain,
    ! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(40,axiom,
    ! [A: nat] : ( connected @ b @ c2 @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_g_H_Oconnected__refl) ).

thf(358,plain,
    ! [A: nat] : ( connected @ b @ c2 @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(359,plain,
    ! [A: nat] : ( connected @ b @ c2 @ A @ A ),
    inference(cnf,[status(esa)],[358]) ).

thf(150,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( ( dist @ TA )
        = ( ^ [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat,D: nat] :
            ? [E: list @ ( product_prod @ nat @ nat )] :
              ( ( isPath @ TA @ A @ B @ E @ D )
              & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ E )
                = C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_Graph_Odist__def) ).

thf(703,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( ( dist @ TA )
        = ( ^ [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat,D: nat] :
            ? [E: list @ ( product_prod @ nat @ nat )] :
              ( ( isPath @ TA @ A @ B @ E @ D )
              & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ E )
                = C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(4132,plain,
    ! [TA: $tType,B: list @ TA,A: list @ TA] :
      ( ~ ( ord_less @ nat @ ( min_dist @ b @ c2 @ s @ t )
          @ ( size_size @ ( list @ TA )
            @ ( sk4 @ TA @ A
              @ ^ [C: list @ TA] : $false ) ) )
      | ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p2 )
       != ( size_size @ ( list @ TA ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[281,2620]) ).

thf(4133,plain,
    ! [A: list @ ( product_prod @ nat @ nat )] :
      ~ ( ord_less @ nat @ ( min_dist @ b @ c2 @ s @ t )
        @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) )
          @ ( sk4 @ ( product_prod @ nat @ nat ) @ A
            @ ^ [B: list @ ( product_prod @ nat @ nat )] : $false ) ) ),
    inference(pattern_uni,[status(thm)],[4132:[bind(A,$thf( A )),bind(B,$thf( p2 )),bind_type(TA,$thf( product_prod @ nat @ nat ))]]) ).

thf(116,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( ( isPath @ TA )
        = ( isPath @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_Graph_OisPath_Ocong) ).

thf(600,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(214,axiom,
    ! [A: nat] : ( finite_finite2 @ nat @ ( adjacent_nodes @ b @ c2 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_g_H_Oadjacent__nodes__finite) ).

thf(864,plain,
    ! [A: nat] : ( finite_finite2 @ nat @ ( adjacent_nodes @ b @ c2 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(52,axiom,
    ! [A: nat,B: nat] :
      ( ( connected @ a @ c @ A @ B )
     => ( ( ( min_dist @ a @ c @ A @ B )
          = ( zero_zero @ nat ) )
        = ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_min__dist__z__iff) ).

thf(386,plain,
    ! [A: nat,B: nat] :
      ( ( connected @ a @ c @ A @ B )
     => ( ( ( min_dist @ a @ c @ A @ B )
          = ( zero_zero @ nat ) )
        = ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(125,axiom,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA )
     => ! [A: TA] :
          ( ( A
           != ( zero_zero @ TA ) )
         => ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_gr__zeroI) ).

thf(612,plain,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA )
     => ! [A: TA] :
          ( ( A
           != ( zero_zero @ TA ) )
         => ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(211,axiom,
    ( ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( e @ a @ c ) )
   => ( finite_Graph @ a @ c ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_Finite__Graph__EI) ).

thf(859,plain,
    ( ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( e @ a @ c ) )
   => ( finite_Graph @ a @ c ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(1835,plain,
    ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ sk1 )
   != ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p ) ),
    inference(paramod_ordered,[status(thm)],[310,1061]) ).

thf(1849,plain,
    sk1 != p,
    inference(simp,[status(thm)],[1835]) ).

thf(135,axiom,
    ! [A: nat] :
      ~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_bot__nat__0_Oextremum__strict) ).

thf(656,plain,
    ! [A: nat] :
      ~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(159,axiom,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( isPath @ b @ c2 @ A @ B @ C )
     => ? [D: list @ ( product_prod @ nat @ nat )] : ( isSimplePath @ b @ c2 @ A @ D @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_g_H_OisSPath__pathLE) ).

thf(727,plain,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( isPath @ b @ c2 @ A @ B @ C )
     => ? [D: list @ ( product_prod @ nat @ nat )] : ( isSimplePath @ b @ c2 @ A @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(77,axiom,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_le__zero__eq) ).

thf(465,plain,
    ! [TA: $tType] :
      ( ( canoni770627133id_add @ TA )
     => ! [A: TA] :
          ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
          = ( A
            = ( zero_zero @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(130,axiom,
    ! [A: nat] :
      ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
      = ( A
        = ( zero_zero @ nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_not__gr0) ).

thf(627,plain,
    ! [A: nat] :
      ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
      = ( A
        = ( zero_zero @ nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(250,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( A != B )
       => ( ord_less @ ( set @ TA ) @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_psubsetI) ).

thf(931,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( A != B )
       => ( ord_less @ ( set @ TA ) @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(139,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat] :
          ( ( dist @ TA @ A @ B @ ( zero_zero @ nat ) @ C )
          = ( C = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_Graph_Odist__z__iff) ).

thf(671,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat] :
          ( ( dist @ TA @ A @ B @ ( zero_zero @ nat ) @ C )
          = ( C = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(204,axiom,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: set @ TA,B: TA] :
          ( ( finite_finite2 @ TA @ A )
         => ( ( member @ TA @ B @ A )
           => ? [C: TA] :
                ( ( member @ TA @ C @ A )
                & ( ord_less_eq @ TA @ B @ C )
                & ! [D: TA] :
                    ( ( member @ TA @ D @ A )
                   => ( ( ord_less_eq @ TA @ C @ D )
                     => ( C = D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_finite__has__maximal2) ).

thf(844,plain,
    ! [TA: $tType] :
      ( ( order @ TA )
     => ! [A: set @ TA,B: TA] :
          ( ( finite_finite2 @ TA @ A )
         => ( ( member @ TA @ B @ A )
           => ? [C: TA] :
                ( ( member @ TA @ C @ A )
                & ( ord_less_eq @ TA @ B @ C )
                & ! [D: TA] :
                    ( ( member @ TA @ D @ A )
                   => ( ( ord_less_eq @ TA @ C @ D )
                     => ( C = D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(229,axiom,
    ! [A: set @ nat] : ( ord_less_eq @ ( set @ ( product_prod @ nat @ nat ) ) @ ( incoming @ a @ c @ A ) @ ( e @ a @ c ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_incoming_H__edges) ).

thf(891,plain,
    ! [A: set @ nat] : ( ord_less_eq @ ( set @ ( product_prod @ nat @ nat ) ) @ ( incoming @ a @ c @ A ) @ ( e @ a @ c ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(4120,plain,
    ! [TA: $tType,B: list @ TA,A: list @ TA] :
      ( ~ ( ord_less @ nat @ ( min_dist @ a @ c @ s @ t )
          @ ( size_size @ ( list @ TA )
            @ ( sk4 @ TA @ A
              @ ^ [C: list @ TA] : $false ) ) )
      | ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p )
       != ( size_size @ ( list @ TA ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[279,2620]) ).

thf(4121,plain,
    ! [A: list @ ( product_prod @ nat @ nat )] :
      ~ ( ord_less @ nat @ ( min_dist @ a @ c @ s @ t )
        @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) )
          @ ( sk4 @ ( product_prod @ nat @ nat ) @ A
            @ ^ [B: list @ ( product_prod @ nat @ nat )] : $false ) ) ),
    inference(pattern_uni,[status(thm)],[4120:[bind(A,$thf( A )),bind(B,$thf( p )),bind_type(TA,$thf( product_prod @ nat @ nat ))]]) ).

thf(148,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat] :
          ( ( connected @ TA @ A @ B @ C )
         => ( dist @ TA @ A @ B @ ( min_dist @ TA @ A @ B @ C ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_Graph_Omin__dist__is__dist) ).

thf(699,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat] :
          ( ( connected @ TA @ A @ B @ C )
         => ( dist @ TA @ A @ B @ ( min_dist @ TA @ A @ B @ C ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(266,axiom,
    size @ nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Nat_Osize) ).

thf(963,plain,
    size @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(315,plain,
    ! [D: nat,C: nat,B: nat,A: nat] :
      ( ~ ( connected @ a @ c @ A @ B )
      | ( ( min_dist @ a @ c @ A @ B )
       != C )
      | ~ ( ord_less @ nat @ D @ C )
      | ( ( min_dist @ a @ c @ A @ ( sk2 @ D @ C @ B @ A ) )
        = D ) ),
    inference(cnf,[status(esa)],[313]) ).

thf(318,plain,
    ! [D: nat,C: nat,B: nat,A: nat] :
      ( ( ( min_dist @ a @ c @ A @ B )
       != C )
      | ( ( min_dist @ a @ c @ A @ ( sk2 @ D @ C @ B @ A ) )
        = D )
      | ~ ( connected @ a @ c @ A @ B )
      | ~ ( ord_less @ nat @ D @ C ) ),
    inference(lifteq,[status(thm)],[315]) ).

thf(319,plain,
    ! [C: nat,B: nat,A: nat] :
      ( ( ( min_dist @ a @ c @ A @ ( sk2 @ C @ ( min_dist @ a @ c @ A @ B ) @ B @ A ) )
        = C )
      | ~ ( connected @ a @ c @ A @ B )
      | ~ ( ord_less @ nat @ C @ ( min_dist @ a @ c @ A @ B ) ) ),
    inference(simp,[status(thm)],[318]) ).

thf(232,axiom,
    ( ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( e @ b @ c2 ) )
   => ( finite_Graph @ b @ c2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_g_H_OFinite__Graph__EI) ).

thf(896,plain,
    ( ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( e @ b @ c2 ) )
   => ( finite_Graph @ b @ c2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(167,axiom,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( isPath @ a @ c @ A @ B @ C )
     => ( dist @ a @ c @ A @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_isPath__distD) ).

thf(748,plain,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( isPath @ a @ c @ A @ B @ C )
     => ( dist @ a @ c @ A @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(945,plain,
    ! [TA: $tType] :
      ( ( (=) @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
            ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
            & ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
    inference(cnf,[status(esa)],[944]) ).

thf(946,plain,
    ! [TA: $tType] :
      ( ( ^ [A: set @ TA,B: set @ TA] :
            ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
            & ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) )
      = ( (=) @ ( set @ TA ) ) ),
    inference(lifteq,[status(thm)],[945]) ).

thf(161,axiom,
    ! [A: nat,B: nat] :
      ( ( connected @ a @ c @ A @ B )
      = ( ? [C: nat] : ( dist @ a @ c @ A @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_connected__by__dist) ).

thf(731,plain,
    ! [A: nat,B: nat] :
      ( ( connected @ a @ c @ A @ B )
      = ( ? [C: nat] : ( dist @ a @ c @ A @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(63,axiom,
    ! [A: nat,B: nat,C: nat > $o] :
      ( ( connected @ b @ c2 @ A @ B )
     => ( ! [D: nat] :
            ( ( dist @ b @ c2 @ A @ D @ B )
           => ( ! [E: nat] :
                  ( ( dist @ b @ c2 @ A @ E @ B )
                 => ( ord_less_eq @ nat @ D @ E ) )
             => ( C @ D ) ) )
       => ( C @ ( min_dist @ b @ c2 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_g_H_Omin__distI2) ).

thf(418,plain,
    ! [A: nat,B: nat,C: nat > $o] :
      ( ( connected @ b @ c2 @ A @ B )
     => ( ! [D: nat] :
            ( ( dist @ b @ c2 @ A @ D @ B )
           => ( ! [E: nat] :
                  ( ( dist @ b @ c2 @ A @ E @ B )
                 => ( ord_less_eq @ nat @ D @ E ) )
             => ( C @ D ) ) )
       => ( C @ ( min_dist @ b @ c2 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(510,plain,
    ( ( ^ [A: nat,B: nat] :
          ( ( ord_less @ nat @ A @ B )
          | ( A = B ) ) )
    = ( ord_less_eq @ nat ) ),
    inference(lifteq,[status(thm)],[509]) ).

thf(51,axiom,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: TA > TB] :
      ( ! [C: TA] :
          ( ( A @ C )
          = ( B @ C ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_ext) ).

thf(383,plain,
    ! [TA: $tType,TB: $tType,A: TA > TB,B: TA > TB] :
      ( ! [C: TA] :
          ( ( A @ C )
          = ( B @ C ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(144,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( ( connected @ TA )
        = ( ^ [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat] :
            ? [D: nat] : ( dist @ TA @ A @ B @ D @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_Graph_Oconnected__by__dist) ).

thf(684,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( ( connected @ TA )
        = ( ^ [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat] :
            ? [D: nat] : ( dist @ TA @ A @ B @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(98,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat,D: nat] :
          ( ( connected @ TA @ A @ B @ C )
         => ( ( ord_less_eq @ nat @ D @ ( min_dist @ TA @ A @ B @ C ) )
           => ? [E: nat] :
                ( ( connected @ TA @ A @ B @ E )
                & ( ( min_dist @ TA @ A @ B @ E )
                  = D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_Graph_Omin__dist__le) ).

thf(536,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: nat,C: nat,D: nat] :
          ( ( connected @ TA @ A @ B @ C )
         => ( ( ord_less_eq @ nat @ D @ ( min_dist @ TA @ A @ B @ C ) )
           => ? [E: nat] :
                ( ( connected @ TA @ A @ B @ E )
                & ( ( min_dist @ TA @ A @ B @ E )
                  = D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(242,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: set @ nat] : ( ord_less_eq @ ( set @ ( product_prod @ nat @ nat ) ) @ ( incoming @ TA @ A @ B ) @ ( e @ TA @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_Graph_Oincoming_H__edges) ).

thf(914,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: set @ nat] : ( ord_less_eq @ ( set @ ( product_prod @ nat @ nat ) ) @ ( incoming @ TA @ A @ B ) @ ( e @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(156,axiom,
    ! [A: nat,B: nat,C: nat > $o] :
      ( ( connected @ a @ c @ A @ B )
     => ( ! [D: nat] :
            ( ( dist @ a @ c @ A @ D @ B )
           => ( ! [E: nat] :
                  ( ( dist @ a @ c @ A @ E @ B )
                 => ( ord_less_eq @ nat @ D @ E ) )
             => ( C @ D ) ) )
       => ( C @ ( min_dist @ a @ c @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_min__distI2) ).

thf(716,plain,
    ! [A: nat,B: nat,C: nat > $o] :
      ( ( connected @ a @ c @ A @ B )
     => ( ! [D: nat] :
            ( ( dist @ a @ c @ A @ D @ B )
           => ( ! [E: nat] :
                  ( ( dist @ a @ c @ A @ E @ B )
                 => ( ord_less_eq @ nat @ D @ E ) )
             => ( C @ D ) ) )
       => ( C @ ( min_dist @ a @ c @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(11,axiom,
    finite_Graph @ b @ c2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_g_H_OFinite__Graph__axioms) ).

thf(287,plain,
    finite_Graph @ b @ c2,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(300,plain,
    ! [TA: $tType,A: ( product_prod @ nat @ nat ) > TA] :
      ( ~ ( linordered_idom @ TA )
      | ~ ( finite_Graph @ TA @ A )
      | ( edmond2129202899alysis @ TA @ A ) ),
    inference(cnf,[status(esa)],[299]) ).

thf(67,axiom,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( isShortestPath @ a @ c @ A @ B @ C )
     => ( isPath @ a @ c @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_shortestPath__is__path) ).

thf(432,plain,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( isShortestPath @ a @ c @ A @ B @ C )
     => ( isPath @ a @ c @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(119,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( ( connected @ TA )
        = ( connected @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_Graph_Oconnected_Ocong) ).

thf(603,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(23,axiom,
    dist @ b @ c2 @ s @ ( min_dist @ b @ c2 @ s @ t ) @ t,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20__092_060open_062g_H_Odist_As_A_Ig_H_Omin__dist_As_At_J_At_092_060close_062) ).

thf(305,plain,
    dist @ b @ c2 @ s @ ( min_dist @ b @ c2 @ s @ t ) @ t,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(57,axiom,
    ! [A: nat] :
      ( ( A
       != ( zero_zero @ nat ) )
      = ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_bot__nat__0_Onot__eq__extremum) ).

thf(400,plain,
    ! [A: nat] :
      ( ( A
       != ( zero_zero @ nat ) )
      = ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(263,axiom,
    wellorder @ nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Owellorder) ).

thf(960,plain,
    wellorder @ nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(260,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( finite_finite @ TB )
        & ( finite_finite @ TA ) )
     => ( finite_finite @ ( TB > TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Finite__Set_Ofinite) ).

thf(955,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( finite_finite @ TB )
        & ( finite_finite @ TA ) )
     => ( finite_finite @ ( TB > TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(7,axiom,
    edmond2129202899alysis @ b @ c2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_g_H_Oek__analysis__axioms) ).

thf(283,plain,
    edmond2129202899alysis @ b @ c2,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(62,axiom,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( isShortestPath @ b @ c2 @ A @ B @ C )
      = ( ( isPath @ b @ c2 @ A @ B @ C )
        & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ B )
          = ( min_dist @ b @ c2 @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_g_H_OisShortestPath__min__dist__def) ).

thf(415,plain,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( isShortestPath @ b @ c2 @ A @ B @ C )
      = ( ( isPath @ b @ c2 @ A @ B @ C )
        & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ B )
          = ( min_dist @ b @ c2 @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(17,axiom,
    member @ nat @ s @ ( v @ a @ c ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_SV) ).

thf(294,plain,
    member @ nat @ s @ ( v @ a @ c ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(244,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: set @ nat] :
          ( ( finite_finite2 @ nat @ ( v @ TA @ A ) )
         => ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( incoming @ TA @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_Graph_Ofinite__incoming_H) ).

thf(918,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA,B: set @ nat] :
          ( ( finite_finite2 @ nat @ ( v @ TA @ A ) )
         => ( finite_finite2 @ ( product_prod @ nat @ nat ) @ ( incoming @ TA @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(190,axiom,
    ! [TA: $tType,A: set @ ( list @ TA )] :
      ( ( finite_finite2 @ ( list @ TA ) @ A )
     => ? [B: nat] :
        ! [C: list @ TA] :
          ( ( member @ ( list @ TA ) @ C @ A )
         => ( ord_less @ nat @ ( size_size @ ( list @ TA ) @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_finite__maxlen) ).

thf(801,plain,
    ! [TA: $tType,A: set @ ( list @ TA )] :
      ( ( finite_finite2 @ ( list @ TA ) @ A )
     => ? [B: nat] :
        ! [C: list @ TA] :
          ( ( member @ ( list @ TA ) @ C @ A )
         => ( ord_less @ nat @ ( size_size @ ( list @ TA ) @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(340,plain,
    ! [B: nat,A: nat] :
      ( ( connected @ b @ c2 @ A @ B )
      = ( ? [C: list @ ( product_prod @ nat @ nat )] : ( isPath @ b @ c2 @ A @ C @ B ) ) ),
    inference(cnf,[status(esa)],[339]) ).

thf(341,plain,
    ! [B: nat,A: nat] :
      ( ( connected @ b @ c2 @ A @ B )
      = ( ? [C: list @ ( product_prod @ nat @ nat )] : ( isPath @ b @ c2 @ A @ C @ B ) ) ),
    inference(lifteq,[status(thm)],[340]) ).

thf(1815,plain,
    ( ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ sk1 )
     != ( min_dist @ a @ c @ s @ t ) )
    | ( ( min_dist @ b @ c2 @ s @ t )
     != ( min_dist @ b @ c2 @ s @ t ) ) ),
    inference(paramod_ordered,[status(thm)],[310,1016]) ).

thf(1816,plain,
    ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ sk1 )
   != ( min_dist @ a @ c @ s @ t ) ),
    inference(pattern_uni,[status(thm)],[1815:[]]) ).

thf(193,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( finite_finite2 @ TA @ A )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
       => ( ( ord_less_eq @ nat @ ( finite_card @ TA @ A ) @ ( finite_card @ TA @ B ) )
         => ( B = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_card__seteq) ).

thf(807,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( finite_finite2 @ TA @ A )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
       => ( ( ord_less_eq @ nat @ ( finite_card @ TA @ A ) @ ( finite_card @ TA @ B ) )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(81,axiom,
    ! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_le__refl) ).

thf(474,plain,
    ! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(174,axiom,
    finite_finite2 @ nat @ ( v @ b @ c2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_g_H_Ofinite__V) ).

thf(767,plain,
    finite_finite2 @ nat @ ( v @ b @ c2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(986,plain,
    ! [TA: $tType] :
      ( ( type @ TA )
      | ( ( linordered_idom @ a )
       != ( linordered_idom @ TA ) ) ),
    inference(paramod_ordered,[status(thm)],[976,950]) ).

thf(987,plain,
    type @ a,
    inference(pattern_uni,[status(thm)],[986:[bind_type(TA,$thf( a ))]]) ).

thf(115,axiom,
    ! [TA: $tType] :
      ( ( size @ TA )
     => ! [A: TA,B: TA] :
          ( ( ( size_size @ TA @ A )
           != ( size_size @ TA @ B ) )
         => ( A != B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_size__neq__size__imp__neq) ).

thf(596,plain,
    ! [TA: $tType] :
      ( ( size @ TA )
     => ! [A: TA,B: TA] :
          ( ( ( size_size @ TA @ A )
           != ( size_size @ TA @ B ) )
         => ( A != B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(75,axiom,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( isShortestPath @ a @ c @ A @ B @ C )
      = ( ( isPath @ a @ c @ A @ B @ C )
        & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ B )
          = ( min_dist @ a @ c @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_isShortestPath__min__dist__def) ).

thf(459,plain,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( isShortestPath @ a @ c @ A @ B @ C )
      = ( ( isPath @ a @ c @ A @ B @ C )
        & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ B )
          = ( min_dist @ a @ c @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(197,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA] :
          ( ( finite_Graph @ TA @ A )
         => ( finite_finite2 @ nat @ ( v @ TA @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_Finite__Graph_Ofinite__V) ).

thf(822,plain,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ! [A: ( product_prod @ nat @ nat ) > TA] :
          ( ( finite_Graph @ TA @ A )
         => ( finite_finite2 @ nat @ ( v @ TA @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(3,axiom,
    edmond2129202899alysis @ a @ c,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_ek__analysis__axioms) ).

thf(277,plain,
    edmond2129202899alysis @ a @ c,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(2698,plain,
    ( ( sk1 != p2 )
    | ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p )
     != ( min_dist @ b @ c2 @ s @ t ) )
    | ( ( min_dist @ a @ c @ s @ t )
     != ( min_dist @ a @ c @ s @ t ) ) ),
    inference(paramod_ordered,[status(thm)],[279,1847]) ).

thf(2699,plain,
    ( ( sk1 != p2 )
    | ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p )
     != ( min_dist @ b @ c2 @ s @ t ) ) ),
    inference(pattern_uni,[status(thm)],[2698:[]]) ).

thf(218,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( ( adjacent_nodes @ TA )
        = ( adjacent_nodes @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_Graph_Oadjacent__nodes_Ocong) ).

thf(871,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(129,axiom,
    ! [A: nat] :
      ( ( A
       != ( zero_zero @ nat ) )
     => ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_gr0I) ).

thf(624,plain,
    ! [A: nat] :
      ( ( A
       != ( zero_zero @ nat ) )
     => ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(30,axiom,
    finite_finite2 @ ( product_prod @ nat @ nat ) @ ( edmond1803015688pEdges @ b @ c2 @ s @ t ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_g_H_Ofinite__spEdges) ).

thf(332,plain,
    finite_finite2 @ ( product_prod @ nat @ nat ) @ ( edmond1803015688pEdges @ b @ c2 @ s @ t ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(45,axiom,
    finite_finite2 @ ( product_prod @ nat @ nat ) @ ( edmond259086305sis_uE @ b @ c2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_g_H_Ofinite__uE) ).

thf(369,plain,
    finite_finite2 @ ( product_prod @ nat @ nat ) @ ( edmond259086305sis_uE @ b @ c2 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(122,axiom,
    ! [TA: $tType] :
      ( ( linordered_idom @ TA )
     => ( ( isShortestPath @ TA )
        = ( isShortestPath @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_Graph_OisShortestPath_Ocong) ).

thf(607,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(85,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
      | ( ord_less_eq @ nat @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_nat__le__linear) ).

thf(486,plain,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq @ nat @ A @ B )
      | ( ord_less_eq @ nat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(253,axiom,
    ord_less_eq @ ( set @ ( product_prod @ nat @ nat ) ) @ edges @ ( set2 @ ( product_prod @ nat @ nat ) @ p ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_SP__EDGES) ).

thf(940,plain,
    ord_less_eq @ ( set @ ( product_prod @ nat @ nat ) ) @ edges @ ( set2 @ ( product_prod @ nat @ nat ) @ p ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(105,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( wellorder @ TB )
     => ! [A: TA > TB,B: TA > $o,C: TA] :
          ( ! [D: TA] :
              ( ! [E: TA] :
                  ( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
                 => ( B @ E ) )
             => ( B @ D ) )
         => ( B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_measure__induct__rule) ).

thf(560,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( wellorder @ TB )
     => ! [A: TA > TB,B: TA > $o,C: TA] :
          ( ! [D: TA] :
              ( ! [E: TA] :
                  ( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
                 => ( B @ E ) )
             => ( B @ D ) )
         => ( B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(88,axiom,
    ! [A: nat] :
      ( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
      = ( A
        = ( zero_zero @ nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_le__0__eq) ).

thf(496,plain,
    ! [A: nat] :
      ( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
      = ( A
        = ( zero_zero @ nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(272,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( finite_finite @ TB )
        & ( finite_finite @ TA ) )
     => ( finite_finite @ ( product_prod @ TB @ TA ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Finite__Set_Ofinite_7) ).

thf(972,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( finite_finite @ TB )
        & ( finite_finite @ TA ) )
     => ( finite_finite @ ( product_prod @ TB @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(191,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( finite_finite2 @ TA @ A )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
       => ( ( ord_less @ nat @ ( finite_card @ TA @ B ) @ ( finite_card @ TA @ A ) )
         => ( ord_less @ ( set @ TA ) @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_card__psubset) ).

thf(803,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( finite_finite2 @ TA @ A )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
       => ( ( ord_less @ nat @ ( finite_card @ TA @ B ) @ ( finite_card @ TA @ A ) )
         => ( ord_less @ ( set @ TA ) @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(309,plain,
    isPath @ b @ c2 @ s @ sk1 @ t,
    inference(cnf,[status(esa)],[307]) ).

thf(136,axiom,
    ! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
      ( ! [D: TA] :
          ( ( ( A @ D )
            = ( zero_zero @ nat ) )
         => ( B @ D ) )
     => ( ! [D: TA] :
            ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( A @ D ) )
           => ( ~ ( B @ D )
             => ? [E: TA] :
                  ( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
                  & ~ ( B @ E ) ) ) )
       => ( B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_infinite__descent0__measure) ).

thf(659,plain,
    ! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
      ( ! [D: TA] :
          ( ( ( A @ D )
            = ( zero_zero @ nat ) )
         => ( B @ D ) )
     => ( ! [D: TA] :
            ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( A @ D ) )
           => ( ~ ( B @ D )
             => ? [E: TA] :
                  ( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
                  & ~ ( B @ E ) ) ) )
       => ( B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(4422,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType] :
      ( ( order @ ( TZK > TZL ) )
      | ( ( order @ ( TZJ > TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) )
       != ( order @ TZL ) ) ),
    inference(paramod_ordered,[status(thm)],[4277,958]) ).

thf(4423,plain,
    ! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType] : ( order @ ( TZK > TZJ > TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ) ),
    inference(pattern_uni,[status(thm)],[4422:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZJ )),bind_type(TZK,$thf( TZK )),bind_type(TZL,$thf( TZJ > TZI > TZH > TZG > TZF > TZE > TZD > TZC > TZB > TZA > TZ > TY > TX > TW > TV > TU > TT > TS > TR > TQ > TP > TO > TN > TM > TL > TK > TJ > TI > TH > TG > TF > TE > TD > TC > TB > TA > $o ))]]) ).

thf(170,axiom,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( member @ nat @ A @ ( v @ b @ c2 ) )
     => ( ( isSimplePath @ b @ c2 @ A @ B @ C )
       => ( ord_less @ nat @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ B ) @ ( finite_card @ nat @ ( v @ b @ c2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_g_H_OsimplePath__length__less__V) ).

thf(755,plain,
    ! [A: nat,B: list @ ( product_prod @ nat @ nat ),C: nat] :
      ( ( member @ nat @ A @ ( v @ b @ c2 ) )
     => ( ( isSimplePath @ b @ c2 @ A @ B @ C )
       => ( ord_less @ nat @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ B ) @ ( finite_card @ nat @ ( v @ b @ c2 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(4833,plain,
    $false,
    inference(e,[status(thm)],[1036,4169,333,893,4015,941,777,666,352,365,1190,479,1105,347,3666,4022,1083,962,468,977,523,4339,276,1068,3813,741,3402,861,3680,4043,873,1205,449,511,2380,1692,677,1078,4090,2686,1756,2740,797,472,1761,930,3135,4097,1196,898,1001,1782,782,709,288,301,320,436,1887,885,3088,724,1792,2735,785,344,1132,542,3820,389,934,357,949,2745,853,1892,4353,1147,870,881,289,1963,1847,817,2691,902,3638,1087,969,606,284,4270,1115,325,3268,4008,924,789,1109,3163,834,4162,1858,4050,1151,937,1020,348,353,966,602,1843,280,734,293,866,849,507,312,3184,397,687,877,692,1119,774,3226,1201,1863,1074,292,920,380,439,761,2118,810,1163,714,1868,910,3827,778,952,302,429,4284,729,2396,3261,957,1174,2133,1751,820,3233,630,916,1837,4155,329,830,889,1787,1656,682,710,456,285,3191,566,3198,879,4104,551,1128,3799,974,519,1089,3254,1953,615,1111,403,593,610,783,1772,317,1138,356,3205,499,857,4263,328,488,339,669,1644,970,547,706,554,753,901,476,1016,1207,590,837,393,985,701,2681,738,1192,911,3074,371,2370,2006,721,569,3247,792,805,311,1170,674,4036,953,1996,633,360,3508,1167,298,412,2001,750,2391,1103,824,279,444,601,573,3792,689,296,3536,423,1615,3240,843,772,1620,286,3081,743,291,958,281,904,975,875,826,577,711,391,3964,787,335,1897,947,2148,540,1058,1107,350,3170,1194,2229,2214,1117,736,377,863,764,604,900,406,3957,3515,362,451,509,434,616,303,4430,494,758,799,483,895,3971,769,330,345,858,367,4277,621,1149,964,462,1061,912,1198,2365,959,768,636,780,1015,608,306,299,3142,851,505,922,3380,1066,278,2620,868,883,3806,1113,563,1076,3522,1948,2239,1873,1203,944,2234,1081,342,968,426,3936,3395,680,927,374,617,516,1958,355,776,640,295,872,887,971,2143,327,3659,954,2386,409,310,557,1003,580,855,282,2375,1053,4437,4346,2224,3344,502,338,951,1130,3095,907,331,1188,1186,1038,585,370,2219,2128,1085,470,3359,359,336,703,4133,600,1052,864,386,1797,3943,612,3366,4111,859,1849,3652,656,1802,3388,727,465,627,1649,931,2696,671,976,1654,1126,844,3929,891,2209,4121,699,961,963,319,1639,351,3501,896,748,946,1101,731,418,568,510,1777,3529,383,684,3645,536,290,914,716,1161,287,2123,300,3785,432,967,950,3373,405,603,305,4029,1056,400,960,1165,955,283,415,294,918,801,341,1816,358,807,3177,1172,474,767,3673,1610,987,3543,596,459,822,277,2699,871,624,839,3128,332,369,607,2138,486,940,560,496,972,803,3950,309,659,4423,755]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : ITP051^2 : TPTP v8.2.0. Released v7.5.0.
% 0.06/0.14  % Command  : run_Leo-III %s %d
% 0.15/0.35  % Computer : n003.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Sat May 18 18:25:39 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.95/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.82/1.08  % [INFO] 	 Parsing done (216ms). 
% 1.82/1.09  % [INFO] 	 Running in sequential loop mode. 
% 2.52/1.30  % [INFO] 	 eprover registered as external prover. 
% 2.52/1.30  % [INFO] 	 cvc4 registered as external prover. 
% 2.52/1.31  % [INFO] 	 Scanning for conjecture ... 
% 2.76/1.39  % [INFO] 	 Found a conjecture (or negated_conjecture) and 273 axioms. Running axiom selection ... 
% 2.76/1.42  % [INFO] 	 Axiom selection finished. Selected 273 axioms (removed 0 axioms). 
% 3.40/1.58  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 3.40/1.60  % [INFO] 	 Type checking passed. 
% 3.40/1.60  % [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 ... 
% 86.24/28.67  % External prover 'e' found a proof!
% 86.24/28.67  % [INFO] 	 Killing All external provers ... 
% 86.24/28.67  % Time passed: 28124ms (effective reasoning time: 27578ms)
% 86.24/28.67  % 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)>
% 86.24/28.68  % Axioms used in derivation (273): fact_9_Finite__Graph__axioms, fact_91_less__or__eq__imp__le, fact_102_measure__induct__rule, fact_206_spEdges__ss__E, fact_57_not__gr__zero, fact_106_less__not__refl3, fact_12_SP, fact_167_g_H_OsimplePath__length__less__V, fact_186_Graph_OshortestPath__is__simple, fact_144_Graph_Omin__dist__less, fact_80_eq__imp__le, fact_207_E__ss__uE, fact_238_Graph_Ooutgoing_H__edges, fact_171_g_H_Ofinite__V, fact_62_min__dist__less__V, tfree_0, tcon_fun___Finite__Set_Ofinite, fact_191_finite__if__finite__subsets__card__bdd, fact_169_g_H_OisShortestPath__length__less__V, fact_35_g_H_Odist__def, fact_236_Graph_Oincoming_H_Ocong, fact_93_less__mono__imp__le__mono, fact_130_gr__implies__not0, fact_60_g_H_Omin__distI2, tcon_Nat_Onat___Nat_Osize, fact_72_isShortestPath__min__dist__def, fact_73_g_H_OisShortestPath__def, fact_121_Finite__Graph_OisShortestPath__length__less__V, fact_56_neq0__conv, fact_38_connected__refl, fact_176_Veq, fact_0_ek__analysis__axioms, fact_86_bot__nat__0_Oextremum__unique, fact_155_g_H_Oconnected__inV__iff, fact_82_nat__le__linear, fact_221_Finite__Graph_Ofinite__E, fact_134_Graph_Omin__dist__z, fact_235_finite__incoming_H, fact_240_Graph_Ofinite__outgoing_H, fact_61_isShortestPath__length__less__V, fact_52_neq__if__length__neq, fact_253_subset__trans, fact_179_Graph_OisSimplePath_Ocong, fact_33_obtain__shortest__path, fact_170_isShortestPath__alt, fact_76_bot__nat__0_Oextremum, fact_212_adjacent__nodes__finite, fact_51_ek__analysis_Ofinite__spEdges, fact_58_Graph_OisShortestPath__min__dist__def, fact_7_ek__analysis__defs_OspEdges_Ocong, fact_203_psubset__card__mono, fact_183_card__subset__eq, tcon_HOL_Obool___Orderings_Oorder_5, fact_88_nat__less__le, fact_44_g_H_Omin__dist__z__iff, fact_228_g_H_OE__ss__uE, tcon_Set_Oset___Orderings_Oorder_3, fact_128_not__less0, fact_143_Graph_Omin__dist__z__iff, fact_68_g_H_Omin__distI__eq, fact_147_Graph_Odist__def, fact_142_Graph_Oobtain__shortest__path, fact_249_subsetI, fact_30_g_H_Oconnected__def, fact_182_rev__finite__subset, fact_83_Nat_Oex__has__greatest__nat, subcl_Rings_Olinordered__idom___Groups_Ozero, fact_123_not__less__zero, fact_97_Graph_Omin__distI__eq, fact_40_g_H_Odist__z, fact_113_Graph_OisPath_Ocong, fact_14_SV, tcon_HOL_Obool___Finite__Set_Ofinite_4, fact_251_Collect__mono__iff, fact_122_gr__zeroI, fact_215_Graph_Oadjacent__nodes_Ocong, fact_71_isShortestPath__def, fact_187_finite__maxlen, fact_96_Graph_Omin__dist__minD, fact_111_infinite__descent__measure, fact_165_dist__def, fact_190_card__seteq, fact_158_connected__by__dist, fact_229_g_H_OFinite__Graph__EI, fact_116_Graph_Oconnected_Ocong, fact_90_le__eq__less__or__eq, fact_200_finite__has__minimal2, subcl_Rings_Olinordered__idom___HOL_Otype, fact_87_bot__nat__0_Oextremum__uniqueI, fact_199_ek__analysis_Ocard__spEdges__le, tcon_Product__Type_Oprod___Finite__Set_Ofinite_7, fact_110_linorder__neqE__nat, fact_132_bot__nat__0_Oextremum__strict, subcl_Rings_Olinordered__idom___Orderings_Oorder, fact_133_infinite__descent0__measure, fact_208_Finite__Graph__EI, fact_42_g_H_Ofinite__uE, fact_15_P_H, fact_46_Collect__mem__eq, fact_89_less__imp__le__nat, fact_136_Graph_Odist__z__iff, fact_21__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062p_H_O_A_092_060lbrakk_062g_H_OisPath_As_Ap_H_At_059_Alength_Ap_H_A_061_Ag_H_Omin__dist_As_At_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_209_Efin__imp__Vfin, fact_225_Finite__Graph_Oadjacent__nodes__finite, fact_244_g_H_Ofinite__outgoing_H, fact_175_connected__distI, fact_193_Finite__Graph_Ointro, fact_64_shortestPath__is__path, fact_2_LENP_H, fact_108_nat__less__induct, fact_230_g_H_OEfin__imp__Vfin, fact_139_Graph_OshortestPath__is__path, fact_246__092_060open_062edges_A_092_060subseteq_062_AE_092_060close_062, fact_188_card__psubset, fact_137_Graph_Oconnected__def, fact_105_less__not__refl2, fact_8_g_H_OFinite__Graph__axioms, fact_159_shortestPath__is__simple, fact_11_uE__eq, fact_66_g_H_Oobtain__shortest__path, fact_177_g_H_Oadjacent__nodes__ss__V, fact_219_Graph_OVfin__imp__Efin, fact_195_finite, fact_218_Graph_OEfin__imp__Vfin, fact_124_gr__implies__not__zero, fact_164_isPath__distD, fact_189_card__mono, fact_4_g_H_Oek__analysis__axioms, fact_75_le0, fact_146_Graph_OisPath__distD, fact_156_g_H_OisSPath__pathLE, fact_173_dist__z__iff, fact_205_g_H_Oreachable__ss__V, tcon_Nat_Onat___Orderings_Owellorder, fact_81_le__antisym, fact_39_g_H_Odist__z__iff, fact_49_min__dist__z__iff, fact_232_g_H_Ofinite__E, fact_28_min__dist__z, tcon_Nat_Onat___Groups_Ozero, fact_125_zero__less__iff__neq__zero, fact_184_infinite__arbitrarily__large, fact_94_ex__least__nat__le, fact_50_ek__analysis_Ofinite__uE, fact_138_Graph_Oconnected__inV__iff, fact_84_less__eq__nat_Osimps_I1_J, fact_77_zero__le, fact_45_mem__Collect__eq, fact_233_g_H_OVfin__imp__Efin, fact_148_card_Oinfinite, fact_24_g_H_Omin__dist__less, fact_210_finite__E, fact_192_Finite__Graph__def, fact_95_Graph_Omin__dist__le, fact_67_g_H_Omin__dist__le, fact_181_infinite__super, fact_115_Graph_Omin__dist_Ocong, fact_223_ek__analysis_OspEdges__ss__E, fact_214_Graph_OreachableNodes_Ocong, fact_154_g_H_OisShortestPath__alt, fact_129_less__zeroE, fact_226_incoming_H__edges, fact_163_min__distI__eq, fact_25_length__induct, fact_10__092_060open_062length_Ap_A_060_Alength_Ap_H_092_060close_062, fact_178_adjacent__nodes__ss__V, fact_32_g_H_Oconnected__by__dist, fact_53_Ex__list__of__length, fact_242_g_H_Oincoming_H__edges, fact_120_Finite__Graph_Omin__dist__less__V, fact_216_Graph_OE_Ocong, fact_161_finite__code, fact_3_ek__analysis__defs_OekMeasure_Ocong, fact_234_finite__outgoing_H, fact_20__092_060open_062g_H_Odist_As_A_Ig_H_Omin__dist_As_At_J_At_092_060close_062, fact_47_Collect__cong, fact_202_Finite__Graph_OsimplePath__length__less__V, tcon_Product__Type_Oprod___Nat_Osize_8, fact_59_g_H_OisShortestPath__min__dist__def, fact_101_measure__induct, fact_63_connected__def, fact_54_bot__nat__0_Onot__eq__extremum, fact_13_CONN2, fact_6_ek__analysis__defs_OuE_Ocong, fact_99_Graph_OisShortestPath__def, fact_69_g_H_Omin__dist__minD, fact_103_nat__neq__iff, fact_131_infinite__descent0, fact_43_finite__uE, fact_252_set__eq__subset, fact_5_SHORTER, fact_152_card__ge__0__finite, fact_204_reachable__ss__V, fact_19__092_060open_062_092_060not_062_Ag_H_Oconnected_As_At_A_092_060Longrightarrow_062_Ag_H_OekMeasure_A_060_AekMeasure_092_060close_062, fact_197_finite__psubset__induct, fact_127_not__gr0, fact_151_simplePath__length__less__V, fact_1_LENP, fact_112_size__neq__size__imp__neq, fact_27_g_H_Ofinite__spEdges, fact_227_outgoing_H__edges, tfree_1, fact_36_g_H_Omin__dist__is__dist, fact_18_ek__analysis_Oaxioms, fact_23_min__dist__less, fact_149_card__spEdges__le, fact_109_infinite__descent, fact_211_g_H_Oadjacent__nodes__finite, fact_107_less__irrefl__nat, fact_153_min__distI2, fact_201_finite__has__maximal2, fact_100_zero__reorient, fact_41_g_H_Oconnected__distI, fact_174_dist__z, fact_168_g_H_Omin__dist__less__V, fact_114_Graph_OV_Ocong, tcon_fun___Orderings_Oorder, fact_104_less__not__refl, fact_237_Graph_Ooutgoing_H_Ocong, fact_85_le__0__eq, fact_245_g_H_Ofinite__incoming_H, fact_239_Graph_Oincoming_H__edges, fact_126_gr0I, fact_220_Graph_OFinite__Graph__EI, fact_247_psubsetI, fact_17_ek__analysis_Ointro, fact_79_le__trans, fact_250_SP__EDGES, fact_118_Graph_Odist_Ocong, tcon_Nat_Onat___Orderings_Oorder_1, fact_48_ext, fact_231_g_H_OspEdges__ss__E, tcon_List_Olist___Nat_Osize_6, fact_65_g_H_OshortestPath__is__path, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, fact_26_finite__spEdges, fact_55_less__nat__zero__code, fact_78_le__refl, tcon_Set_Oset___Finite__Set_Ofinite_2, fact_172_finite__V, fact_29_g_H_Omin__dist__z, fact_37_g_H_Oconnected__refl, fact_140_Graph_Oconnected__distI, fact_98_Graph_Omin__distI2, fact_241_Graph_Ofinite__incoming_H, fact_222_ek__analysis_OE__ss__uE, fact_74_le__zero__eq, fact_157_isSPath__pathLE, fact_145_Graph_Omin__dist__is__dist, fact_217_Graph_Oreachable__ss__V, fact_16_ek__analysis__def, fact_119_Graph_OisShortestPath_Ocong, fact_196_finite__set__choice, fact_162_min__dist__minD, fact_70_min__dist__le, fact_185_Graph_OisSPath__pathLE, fact_180_finite__subset, fact_224_Graph_Oadjacent__nodes__ss__V, fact_141_Graph_Oconnected__by__dist, fact_117_Graph_Oconnected__refl, fact_135_Graph_Odist__z, fact_92_le__neq__implies__less, fact_31_connected__inV__iff, fact_22_CONN, fact_194_Finite__Graph_Ofinite__V, fact_198_Graph_OisShortestPath__alt, fact_213_Vfin__imp__Efin, fact_248_subset__antisym, fact_150_g_H_Ocard__spEdges__le, fact_166_min__dist__is__dist, fact_34_g_H_OisPath__distD, fact_160_g_H_OshortestPath__is__simple, fact_243_g_H_Ooutgoing_H__edges
% 86.24/28.68  % No. of inferences in proof: 1040
% 86.24/28.68  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 28124 ms resp. 27578 ms w/o parsing
% 87.25/28.88  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 87.25/28.89  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------