TSTP Solution File: ITP180^2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ITP180^2 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n009.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 : Sun May  5 07:05:02 EDT 2024

% Result   : Theorem 175.36s 25.47s
% Output   : Refutation 175.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :  206
% Syntax   : Number of formulae    :  224 (  16 unt; 202 typ;   0 def)
%            Number of atoms       :  479 (  20 equ;   0 cnn)
%            Maximal formula atoms :    3 (  21 avg)
%            Number of connectives :   24 (  12   ~;   6   |;   0   &;   0   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :  322 ( 317   >;   5   *;   0   +;   0  <<)
%            Number of symbols     :  203 ( 200 usr;  19 con; 0-8 aty)
%            Number of variables   :  492 (   0   ^  42   !;   0   ?; 492   :)
%                                         ( 450  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    set: $tType > $tType ).

thf(type_def_6,type,
    sTfun: ( $tType * $tType ) > $tType ).

thf(type_def_7,type,
    product_prod: ( $tType * $tType ) > $tType ).

thf(type_def_8,type,
    standard_Constant: $tType > $tType ).

thf(type_def_9,type,
    labeled_graph: ( $tType * $tType ) > $tType ).

thf(type_def_10,type,
    allegorical_term: $tType > $tType ).

thf(type_def_11,type,
    itself: $tType > $tType ).

thf(type_def_12,type,
    nat: $tType ).

thf(type_def_13,type,
    v2: $tType ).

thf(type_def_14,type,
    v: $tType ).

thf(func_def_0,type,
    standard_Constant: $tType > $tType ).

thf(func_def_1,type,
    allegorical_term: $tType > $tType ).

thf(func_def_2,type,
    labeled_graph: ( $tType * $tType ) > $tType ).

thf(func_def_3,type,
    product_prod: ( $tType * $tType ) > $tType ).

thf(func_def_4,type,
    set: $tType > $tType ).

thf(func_def_5,type,
    nat: $tType ).

thf(func_def_6,type,
    itself: $tType > $tType ).

thf(func_def_7,type,
    v: $tType ).

thf(func_def_8,type,
    v2: $tType ).

thf(func_def_9,type,
    bounded_lattice: 
      !>[X0: $tType] : $o ).

thf(func_def_10,type,
    type: 
      !>[X0: $tType] : $o ).

thf(func_def_11,type,
    bot: 
      !>[X0: $tType] : $o ).

thf(func_def_12,type,
    lattice: 
      !>[X0: $tType] : $o ).

thf(func_def_13,type,
    preorder: 
      !>[X0: $tType] : $o ).

thf(func_def_14,type,
    semilattice_sup: 
      !>[X0: $tType] : $o ).

thf(func_def_15,type,
    bounde1808546759up_bot: 
      !>[X0: $tType] : $o ).

thf(func_def_16,type,
    bNF_Gr: 
      !>[X0: $tType,X1: $tType] : ( set(X0) > ( X0 > X1 ) > set(product_prod(X0,X1)) ) ).

thf(func_def_17,type,
    comp: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 ) > ( X2 > X0 ) > X2 > X1 ) ).

thf(func_def_18,type,
    standard_S_Bot: 
      !>[X0: $tType] : standard_Constant(X0) ).

thf(func_def_19,type,
    standard_S_Const: 
      !>[X0: $tType] : ( X0 > standard_Constant(X0) ) ).

thf(func_def_20,type,
    standard_S_Top: 
      !>[X0: $tType] : standard_Constant(X0) ).

thf(func_def_21,type,
    getRel: 
      !>[X0: $tType,X1: $tType] : ( X0 > labeled_graph(X0,X1) > set(product_prod(X1,X1)) ) ).

thf(func_def_22,type,
    semantics: 
      !>[X0: $tType,X1: $tType] : ( labeled_graph(X0,X1) > allegorical_term(X0) > set(product_prod(X1,X1)) ) ).

thf(func_def_23,type,
    edge_preserving: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( set(product_prod(X0,X1)) > set(product_prod(X2,product_prod(X0,X0))) > set(product_prod(X2,product_prod(X1,X1))) > $o ) ).

thf(func_def_24,type,
    graph_homomorphism: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( labeled_graph(X0,X1) > labeled_graph(X0,X2) > set(product_prod(X1,X2)) > $o ) ).

thf(func_def_25,type,
    graph_union: 
      !>[X0: $tType,X1: $tType] : ( labeled_graph(X0,X1) > labeled_graph(X0,X1) > labeled_graph(X0,X1) ) ).

thf(func_def_26,type,
    labeled_LG: 
      !>[X0: $tType,X1: $tType] : ( set(product_prod(X0,product_prod(X1,X1))) > set(X1) > labeled_graph(X0,X1) ) ).

thf(func_def_27,type,
    labele1974067554_graph: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( set(product_prod(X0,product_prod(X1,X1))) > set(X1) > X2 ) > labeled_graph(X0,X1) > X2 ) ).

thf(func_def_28,type,
    labeled_edges: 
      !>[X0: $tType,X1: $tType] : ( labeled_graph(X0,X1) > set(product_prod(X0,product_prod(X1,X1))) ) ).

thf(func_def_29,type,
    labeled_vertices: 
      !>[X0: $tType,X1: $tType] : ( labeled_graph(X0,X1) > set(X1) ) ).

thf(func_def_30,type,
    map_graph: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( set(product_prod(X0,X1)) > labeled_graph(X2,X0) > labeled_graph(X2,X1) ) ).

thf(func_def_31,type,
    restrict: 
      !>[X0: $tType,X1: $tType] : ( labeled_graph(X0,X1) > labeled_graph(X0,X1) ) ).

thf(func_def_32,type,
    sup_sup: 
      !>[X0: $tType] : ( X0 > X0 > X0 ) ).

thf(func_def_33,type,
    bot_bot: 
      !>[X0: $tType] : X0 ).

thf(func_def_34,type,
    ord_less_eq: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(func_def_35,type,
    product_Pair: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > product_prod(X0,X1) ) ).

thf(func_def_36,type,
    product_rec_prod: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > product_prod(X0,X1) > X2 ) ).

thf(func_def_37,type,
    field: 
      !>[X0: $tType] : ( set(product_prod(X0,X0)) > set(X0) ) ).

thf(func_def_38,type,
    id_on: 
      !>[X0: $tType] : ( set(X0) > set(product_prod(X0,X0)) ) ).

thf(func_def_39,type,
    total_on: 
      !>[X0: $tType] : ( set(X0) > set(product_prod(X0,X0)) > $o ) ).

thf(func_def_40,type,
    agree_on: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( labeled_graph(X0,X1) > set(product_prod(X1,X2)) > set(product_prod(X1,X2)) > $o ) ).

thf(func_def_41,type,
    consequence_graph: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( set(product_prod(labeled_graph(X0,X1),labeled_graph(X0,X1))) > labeled_graph(X0,X2) > $o ) ).

thf(func_def_42,type,
    extensible: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(labeled_graph(X0,X1),labeled_graph(X0,X1)) > labeled_graph(X0,X2) > set(product_prod(X1,X2)) > $o ) ).

thf(func_def_43,type,
    least: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( itself(X0) > set(product_prod(labeled_graph(X1,X2),labeled_graph(X1,X2))) > labeled_graph(X1,X3) > labeled_graph(X1,X3) > $o ) ).

thf(func_def_44,type,
    least_559130134_graph: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( itself(X0) > set(product_prod(labeled_graph(X1,X2),labeled_graph(X1,X2))) > labeled_graph(X1,X3) > labeled_graph(X1,X3) > $o ) ).

thf(func_def_45,type,
    maintained: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(labeled_graph(X0,X1),labeled_graph(X0,X1)) > labeled_graph(X0,X2) > $o ) ).

thf(func_def_46,type,
    collect: 
      !>[X0: $tType] : ( ( X0 > $o ) > set(X0) ) ).

thf(func_def_47,type,
    insert: 
      !>[X0: $tType] : ( X0 > set(X0) > set(X0) ) ).

thf(func_def_48,type,
    is_singleton: 
      !>[X0: $tType] : ( set(X0) > $o ) ).

thf(func_def_49,type,
    the_elem: 
      !>[X0: $tType] : ( set(X0) > X0 ) ).

thf(func_def_50,type,
    standa1138209853_rules: 
      !>[X0: $tType] : ( set(X0) > set(product_prod(labeled_graph(standard_Constant(X0),nat),labeled_graph(standard_Constant(X0),nat))) ) ).

thf(func_def_51,type,
    standa2002409347_rules: 
      !>[X0: $tType] : ( set(standard_Constant(X0)) > set(product_prod(labeled_graph(standard_Constant(X0),nat),labeled_graph(standard_Constant(X0),nat))) ) ).

thf(func_def_52,type,
    standa244753842y_rule: 
      !>[X0: $tType] : product_prod(labeled_graph(X0,nat),labeled_graph(X0,nat)) ).

thf(func_def_53,type,
    standa438229444_rules: 
      !>[X0: $tType] : ( set(X0) > set(standard_Constant(X0)) > set(product_prod(labeled_graph(standard_Constant(X0),nat),labeled_graph(standard_Constant(X0),nat))) ) ).

thf(func_def_54,type,
    standa400804411p_rule: 
      !>[X0: $tType] : ( X0 > product_prod(labeled_graph(X0,nat),labeled_graph(X0,nat)) ) ).

thf(func_def_55,type,
    member: 
      !>[X0: $tType] : ( X0 > set(X0) > $o ) ).

thf(func_def_56,type,
    c: set(v2) ).

thf(func_def_57,type,
    g: labeled_graph(standard_Constant(v2),v) ).

thf(func_def_58,type,
    l: set(standard_Constant(v2)) ).

thf(func_def_59,type,
    h: v > v ).

thf(func_def_60,type,
    m: v2 > v ).

thf(func_def_61,type,
    x: v ).

thf(func_def_62,type,
    xa: v2 ).

thf(func_def_63,type,
    y: v2 ).

thf(func_def_67,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(func_def_68,type,
    vNOT: $o > $o ).

thf(func_def_69,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_70,type,
    cCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).

thf(func_def_71,type,
    vIMP: $o > $o > $o ).

thf(func_def_72,type,
    vOR: $o > $o > $o ).

thf(func_def_73,type,
    vPI: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_74,type,
    sCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_75,type,
    iCOMB: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_76,type,
    vSIGMA: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_77,type,
    vAND: $o > $o > $o ).

thf(func_def_78,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_79,type,
    sP0: 
      !>[X0: $tType] : ( set(X0) > set(product_prod(X0,X0)) > $o ) ).

thf(func_def_80,type,
    sK1: v2 > v ).

thf(func_def_81,type,
    sK2: v ).

thf(func_def_82,type,
    sK3: v2 > v ).

thf(func_def_83,type,
    sK4: v2 > v ).

thf(func_def_84,type,
    sK5: 
      !>[X0: $tType] : ( set(X0) > X0 ) ).

thf(func_def_85,type,
    sK6: 
      !>[X0: $tType] : ( set(X0) > X0 ) ).

thf(func_def_86,type,
    sK7: 
      !>[X0: $tType] : ( set(X0) > X0 ) ).

thf(func_def_87,type,
    sK8: 
      !>[X0: $tType] : ( set(X0) > X0 ) ).

thf(func_def_88,type,
    sK9: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).

thf(func_def_89,type,
    sK10: 
      !>[X0: $tType] : ( set(X0) > set(X0) > X0 ) ).

thf(func_def_90,type,
    sK11: 
      !>[X0: $tType] : ( set(X0) > set(product_prod(X0,X0)) > X0 ) ).

thf(func_def_91,type,
    sK12: 
      !>[X0: $tType] : ( set(X0) > set(product_prod(X0,X0)) > X0 ) ).

thf(func_def_92,type,
    sK13: 
      !>[X0: $tType] : ( set(X0) > X0 > set(X0) ) ).

thf(func_def_93,type,
    sK14: 
      !>[X0: $tType] : ( set(X0) > X0 > set(X0) ) ).

thf(func_def_94,type,
    sK15: 
      !>[X0: $tType] : ( set(X0) > product_prod(X0,X0) > X0 ) ).

thf(func_def_95,type,
    sK16: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).

thf(func_def_96,type,
    sK17: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).

thf(func_def_97,type,
    sK18: 
      !>[X0: $tType,X1: $tType] : ( labeled_graph(X0,X1) > set(product_prod(X0,product_prod(X1,X1))) ) ).

thf(func_def_98,type,
    sK19: 
      !>[X0: $tType,X1: $tType] : ( labeled_graph(X0,X1) > set(X1) ) ).

thf(func_def_99,type,
    sK20: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).

thf(func_def_100,type,
    sK21: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).

thf(func_def_101,type,
    sK22: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > X1 ) ).

thf(func_def_102,type,
    sK23: 
      !>[X0: $tType,X1: $tType] : ( ( product_prod(X1,X0) > $o ) > X1 ) ).

thf(func_def_103,type,
    sK24: 
      !>[X0: $tType,X1: $tType] : ( ( product_prod(X1,X0) > $o ) > X0 ) ).

thf(func_def_104,type,
    sK25: 
      !>[X0: $tType,X1: $tType] : ( ( product_prod(X1,X0) > $o ) > X1 ) ).

thf(func_def_105,type,
    sK26: 
      !>[X0: $tType,X1: $tType] : ( ( product_prod(X1,X0) > $o ) > X0 ) ).

thf(func_def_106,type,
    sK27: 
      !>[X0: $tType,X1: $tType] : ( ( labeled_graph(X1,X0) > $o ) > set(product_prod(X1,product_prod(X0,X0))) ) ).

thf(func_def_107,type,
    sK28: 
      !>[X0: $tType,X1: $tType] : ( ( labeled_graph(X1,X0) > $o ) > set(X0) ) ).

thf(func_def_108,type,
    sK29: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X0 ) ).

thf(func_def_109,type,
    sK30: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X1 ) ).

thf(func_def_110,type,
    sK31: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X2 ) ).

thf(func_def_111,type,
    sK32: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X2,product_prod(X1,X0)) > $o ) > X2 ) ).

thf(func_def_112,type,
    sK33: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X2,product_prod(X1,X0)) > $o ) > X1 ) ).

thf(func_def_113,type,
    sK34: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X2,product_prod(X1,X0)) > $o ) > X0 ) ).

thf(func_def_114,type,
    sK35: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X0 ) ).

thf(func_def_115,type,
    sK36: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X1 ) ).

thf(func_def_116,type,
    sK37: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X2 ) ).

thf(func_def_117,type,
    sK38: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X3 ) ).

thf(func_def_118,type,
    sK39: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > labeled_graph(X2,X1) > X1 ) ).

thf(func_def_119,type,
    sK40: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( labeled_graph(X2,X0) > labeled_graph(X2,X1) > labeled_graph(X2,X0) > set(product_prod(X0,X1)) ) ).

thf(func_def_120,type,
    sK41: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( set(product_prod(X2,product_prod(X1,X1))) > ( X0 > X1 ) > labeled_graph(X2,X0) > X2 ) ).

thf(func_def_121,type,
    sK42: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( set(product_prod(X2,product_prod(X1,X1))) > ( X0 > X1 ) > labeled_graph(X2,X0) > X0 ) ).

thf(func_def_122,type,
    sK43: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( set(product_prod(X2,product_prod(X1,X1))) > ( X0 > X1 ) > labeled_graph(X2,X0) > X0 ) ).

thf(func_def_123,type,
    sK44: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o ) > X3 ) ).

thf(func_def_124,type,
    sK45: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o ) > X2 ) ).

thf(func_def_125,type,
    sK46: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o ) > X1 ) ).

thf(func_def_126,type,
    sK47: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o ) > X0 ) ).

thf(func_def_127,type,
    sK48: 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X0 ) > labeled_graph(X1,X0) > X0 ) ).

thf(func_def_128,type,
    sK49: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X0 ) ).

thf(func_def_129,type,
    sK50: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X1 ) ).

thf(func_def_130,type,
    sK51: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X2 ) ).

thf(func_def_131,type,
    sK52: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X3 ) ).

thf(func_def_132,type,
    sK53: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X4 ) ).

thf(func_def_133,type,
    sK54: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( ( product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o ) > X4 ) ).

thf(func_def_134,type,
    sK55: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( ( product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o ) > X3 ) ).

thf(func_def_135,type,
    sK56: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( ( product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o ) > X2 ) ).

thf(func_def_136,type,
    sK57: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( ( product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o ) > X1 ) ).

thf(func_def_137,type,
    sK58: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( ( product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o ) > X0 ) ).

thf(func_def_138,type,
    sK59: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X0 ) ).

thf(func_def_139,type,
    sK60: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X1 ) ).

thf(func_def_140,type,
    sK61: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X2 ) ).

thf(func_def_141,type,
    sK62: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X3 ) ).

thf(func_def_142,type,
    sK63: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X4 ) ).

thf(func_def_143,type,
    sK64: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X5 ) ).

thf(func_def_144,type,
    sK65: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X0 ) > ( X0 > X1 ) > labeled_graph(X2,X1) > X1 ) ).

thf(func_def_145,type,
    sK66: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( ( product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o ) > X5 ) ).

thf(func_def_146,type,
    sK67: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( ( product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o ) > X4 ) ).

thf(func_def_147,type,
    sK68: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( ( product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o ) > X3 ) ).

thf(func_def_148,type,
    sK69: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( ( product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o ) > X2 ) ).

thf(func_def_149,type,
    sK70: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( ( product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o ) > X1 ) ).

thf(func_def_150,type,
    sK71: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( ( product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o ) > X0 ) ).

thf(func_def_151,type,
    sK72: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( labeled_graph(X3,X2) > labeled_graph(X3,X2) > set(product_prod(labeled_graph(X3,X1),labeled_graph(X3,X1))) > labeled_graph(X3,X0) ) ).

thf(func_def_152,type,
    sK73: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( set(product_prod(labeled_graph(X3,X1),labeled_graph(X3,X1))) > labeled_graph(X3,X2) > labeled_graph(X3,X2) > labeled_graph(X3,X0) ) ).

thf(func_def_153,type,
    sK74: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X0 ) ).

thf(func_def_154,type,
    sK75: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X1 ) ).

thf(func_def_155,type,
    sK76: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X2 ) ).

thf(func_def_156,type,
    sK77: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X3 ) ).

thf(func_def_157,type,
    sK78: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X4 ) ).

thf(func_def_158,type,
    sK79: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X5 ) ).

thf(func_def_159,type,
    sK80: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X6 ) ).

thf(func_def_160,type,
    sK81: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( ( product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o ) > X6 ) ).

thf(func_def_161,type,
    sK82: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( ( product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o ) > X5 ) ).

thf(func_def_162,type,
    sK83: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( ( product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o ) > X4 ) ).

thf(func_def_163,type,
    sK84: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( ( product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o ) > X3 ) ).

thf(func_def_164,type,
    sK85: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( ( product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o ) > X2 ) ).

thf(func_def_165,type,
    sK86: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( ( product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o ) > X1 ) ).

thf(func_def_166,type,
    sK87: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( ( product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o ) > X0 ) ).

thf(func_def_167,type,
    sK88: v2 > v ).

thf(func_def_168,type,
    sK89: 
      !>[X0: $tType] : ( X0 > set(X0) > X0 > set(X0) > set(X0) ) ).

thf(func_def_169,type,
    sK90: 
      !>[X0: $tType] : ( set(X0) > ( X0 > $o ) > X0 ) ).

thf(func_def_170,type,
    sK91: 
      !>[X0: $tType] : ( set(X0) > ( X0 > $o ) > X0 ) ).

thf(func_def_171,type,
    sK92: 
      !>[X0: $tType] : ( set(X0) > ( X0 > $o ) > set(X0) > X0 ) ).

thf(func_def_172,type,
    sK93: 
      !>[X0: $tType] : ( set(X0) > ( X0 > $o ) > set(X0) > X0 ) ).

thf(func_def_173,type,
    sK94: 
      !>[X0: $tType] : ( set(X0) > ( X0 > $o ) > X0 ) ).

thf(func_def_174,type,
    sK95: 
      !>[X0: $tType] : ( set(X0) > ( X0 > $o ) > X0 ) ).

thf(func_def_175,type,
    sK96: 
      !>[X0: $tType] : ( set(X0) > X0 ) ).

thf(func_def_176,type,
    sK97: 
      !>[X0: $tType] : ( set(X0) > X0 ) ).

thf(func_def_177,type,
    sK98: 
      !>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).

thf(func_def_178,type,
    sK99: 
      !>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).

thf(func_def_179,type,
    sK100: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_180,type,
    sK101: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_181,type,
    sK102: 
      !>[X0: $tType] : ( set(X0) > X0 ) ).

thf(func_def_182,type,
    sK103: 
      !>[X0: $tType] : ( set(X0) > X0 ) ).

thf(func_def_183,type,
    sK104: v2 ).

thf(func_def_184,type,
    sK105: v2 ).

thf(func_def_185,type,
    sK106: v2 ).

thf(func_def_186,type,
    sK107: v2 ).

thf(func_def_187,type,
    sK108: v2 ).

thf(func_def_188,type,
    sK109: 
      !>[X0: $tType] : ( set(X0) > X0 ) ).

thf(func_def_189,type,
    sK110: 
      !>[X0: $tType] : ( set(X0) > X0 ) ).

thf(func_def_190,type,
    sK111: v2 ).

thf(func_def_191,type,
    sK112: v2 ).

thf(func_def_192,type,
    sK113: v2 ).

thf(func_def_193,type,
    sK114: v2 ).

thf(func_def_194,type,
    sK115: v2 ).

thf(f477955,plain,
    $false,
    inference(subsumption_resolution,[],[f477949,f1344]) ).

thf(f1344,plain,
    vAPP(set(product_prod(v,v)),$o,vAPP(labeled_graph(standard_Constant(v2),v),sTfun(set(product_prod(v,v)),$o),vAPP(labeled_graph(standard_Constant(v2),v),sTfun(labeled_graph(standard_Constant(v2),v),sTfun(set(product_prod(v,v)),$o)),graph_homomorphism(standard_Constant(v2),v,v),vAPP(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v),vAPP(set(product_prod(v,v)),sTfun(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v)),map_graph(v,v,standard_Constant(v2)),vAPP(sTfun(v,v),set(product_prod(v,v)),vAPP(set(v),sTfun(sTfun(v,v),set(product_prod(v,v))),bNF_Gr(v,v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),g)),h)),g)),g),vAPP(set(v),set(product_prod(v,v)),id_on(v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),vAPP(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v),vAPP(set(product_prod(v,v)),sTfun(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v)),map_graph(v,v,standard_Constant(v2)),vAPP(sTfun(v,v),set(product_prod(v,v)),vAPP(set(v),sTfun(sTfun(v,v),set(product_prod(v,v))),bNF_Gr(v,v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),g)),h)),g)))) = $true,
    inference(cnf_transformation,[],[f707]) ).

thf(f707,plain,
    vAPP(set(product_prod(v,v)),$o,vAPP(labeled_graph(standard_Constant(v2),v),sTfun(set(product_prod(v,v)),$o),vAPP(labeled_graph(standard_Constant(v2),v),sTfun(labeled_graph(standard_Constant(v2),v),sTfun(set(product_prod(v,v)),$o)),graph_homomorphism(standard_Constant(v2),v,v),vAPP(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v),vAPP(set(product_prod(v,v)),sTfun(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v)),map_graph(v,v,standard_Constant(v2)),vAPP(sTfun(v,v),set(product_prod(v,v)),vAPP(set(v),sTfun(sTfun(v,v),set(product_prod(v,v))),bNF_Gr(v,v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),g)),h)),g)),g),vAPP(set(v),set(product_prod(v,v)),id_on(v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),vAPP(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v),vAPP(set(product_prod(v,v)),sTfun(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v)),map_graph(v,v,standard_Constant(v2)),vAPP(sTfun(v,v),set(product_prod(v,v)),vAPP(set(v),sTfun(sTfun(v,v),set(product_prod(v,v))),bNF_Gr(v,v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),g)),h)),g)))) = $true,
    inference(fool_elimination,[],[f706]) ).

thf(f706,plain,
    vAPP(set(product_prod(v,v)),$o,vAPP(labeled_graph(standard_Constant(v2),v),sTfun(set(product_prod(v,v)),$o),vAPP(labeled_graph(standard_Constant(v2),v),sTfun(labeled_graph(standard_Constant(v2),v),sTfun(set(product_prod(v,v)),$o)),graph_homomorphism(standard_Constant(v2),v,v),vAPP(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v),vAPP(set(product_prod(v,v)),sTfun(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v)),map_graph(v,v,standard_Constant(v2)),vAPP(sTfun(v,v),set(product_prod(v,v)),vAPP(set(v),sTfun(sTfun(v,v),set(product_prod(v,v))),bNF_Gr(v,v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),g)),h)),g)),g),vAPP(set(v),set(product_prod(v,v)),id_on(v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),vAPP(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v),vAPP(set(product_prod(v,v)),sTfun(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v)),map_graph(v,v,standard_Constant(v2)),vAPP(sTfun(v,v),set(product_prod(v,v)),vAPP(set(v),sTfun(sTfun(v,v),set(product_prod(v,v))),bNF_Gr(v,v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),g)),h)),g)))),
    inference(rectify,[],[f9]) ).

thf(f9,axiom,
    vAPP(set(product_prod(v,v)),$o,vAPP(labeled_graph(standard_Constant(v2),v),sTfun(set(product_prod(v,v)),$o),vAPP(labeled_graph(standard_Constant(v2),v),sTfun(labeled_graph(standard_Constant(v2),v),sTfun(set(product_prod(v,v)),$o)),graph_homomorphism(standard_Constant(v2),v,v),vAPP(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v),vAPP(set(product_prod(v,v)),sTfun(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v)),map_graph(v,v,standard_Constant(v2)),vAPP(sTfun(v,v),set(product_prod(v,v)),vAPP(set(v),sTfun(sTfun(v,v),set(product_prod(v,v))),bNF_Gr(v,v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),g)),h)),g)),g),vAPP(set(v),set(product_prod(v,v)),id_on(v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),vAPP(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v),vAPP(set(product_prod(v,v)),sTfun(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v)),map_graph(v,v,standard_Constant(v2)),vAPP(sTfun(v,v),set(product_prod(v,v)),vAPP(set(v),sTfun(sTfun(v,v),set(product_prod(v,v))),bNF_Gr(v,v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),g)),h)),g)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_h_I3_J) ).

thf(f477949,plain,
    vAPP(set(product_prod(v,v)),$o,vAPP(labeled_graph(standard_Constant(v2),v),sTfun(set(product_prod(v,v)),$o),vAPP(labeled_graph(standard_Constant(v2),v),sTfun(labeled_graph(standard_Constant(v2),v),sTfun(set(product_prod(v,v)),$o)),graph_homomorphism(standard_Constant(v2),v,v),vAPP(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v),vAPP(set(product_prod(v,v)),sTfun(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v)),map_graph(v,v,standard_Constant(v2)),vAPP(sTfun(v,v),set(product_prod(v,v)),vAPP(set(v),sTfun(sTfun(v,v),set(product_prod(v,v))),bNF_Gr(v,v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),g)),h)),g)),g),vAPP(set(v),set(product_prod(v,v)),id_on(v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),vAPP(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v),vAPP(set(product_prod(v,v)),sTfun(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v)),map_graph(v,v,standard_Constant(v2)),vAPP(sTfun(v,v),set(product_prod(v,v)),vAPP(set(v),sTfun(sTfun(v,v),set(product_prod(v,v))),bNF_Gr(v,v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),g)),h)),g)))) != $true,
    inference(unit_resulting_resolution,[],[f1342,f1041,f1303]) ).

thf(f1303,plain,
    ! [X1: $tType,X0: $tType,X2: X0,X3: X0,X6: labeled_graph(X1,X0),X4: X1,X5: labeled_graph(X1,X0)] :
      ( ( $true != vAPP(set(product_prod(X0,X0)),$o,vAPP(labeled_graph(X1,X0),sTfun(set(product_prod(X0,X0)),$o),vAPP(labeled_graph(X1,X0),sTfun(labeled_graph(X1,X0),sTfun(set(product_prod(X0,X0)),$o)),graph_homomorphism(X1,X0,X0),X5),X6),vAPP(set(X0),set(product_prod(X0,X0)),id_on(X0),vAPP(labeled_graph(X1,X0),set(X0),labeled_vertices(X1,X0),X5))) )
      | ( $true = vAPP(set(product_prod(X0,X0)),$o,vAPP(product_prod(X0,X0),sTfun(set(product_prod(X0,X0)),$o),member(product_prod(X0,X0)),vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3)),vAPP(labeled_graph(X1,X0),set(product_prod(X0,X0)),vAPP(X1,sTfun(labeled_graph(X1,X0),set(product_prod(X0,X0))),getRel(X1,X0),X4),X6)) )
      | ( $true != vAPP(set(product_prod(X0,X0)),$o,vAPP(product_prod(X0,X0),sTfun(set(product_prod(X0,X0)),$o),member(product_prod(X0,X0)),vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3)),vAPP(labeled_graph(X1,X0),set(product_prod(X0,X0)),vAPP(X1,sTfun(labeled_graph(X1,X0),set(product_prod(X0,X0))),getRel(X1,X0),X4),X5)) ) ),
    inference(cnf_transformation,[],[f930]) ).

thf(f930,plain,
    ! [X0: $tType,X1: $tType,X2: X0,X3: X0,X4: X1,X5: labeled_graph(X1,X0),X6: labeled_graph(X1,X0)] :
      ( ( $true = vAPP(set(product_prod(X0,X0)),$o,vAPP(product_prod(X0,X0),sTfun(set(product_prod(X0,X0)),$o),member(product_prod(X0,X0)),vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3)),vAPP(labeled_graph(X1,X0),set(product_prod(X0,X0)),vAPP(X1,sTfun(labeled_graph(X1,X0),set(product_prod(X0,X0))),getRel(X1,X0),X4),X6)) )
      | ( $true != vAPP(set(product_prod(X0,X0)),$o,vAPP(labeled_graph(X1,X0),sTfun(set(product_prod(X0,X0)),$o),vAPP(labeled_graph(X1,X0),sTfun(labeled_graph(X1,X0),sTfun(set(product_prod(X0,X0)),$o)),graph_homomorphism(X1,X0,X0),X5),X6),vAPP(set(X0),set(product_prod(X0,X0)),id_on(X0),vAPP(labeled_graph(X1,X0),set(X0),labeled_vertices(X1,X0),X5))) )
      | ( $true != vAPP(set(product_prod(X0,X0)),$o,vAPP(product_prod(X0,X0),sTfun(set(product_prod(X0,X0)),$o),member(product_prod(X0,X0)),vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3)),vAPP(labeled_graph(X1,X0),set(product_prod(X0,X0)),vAPP(X1,sTfun(labeled_graph(X1,X0),set(product_prod(X0,X0))),getRel(X1,X0),X4),X5)) ) ),
    inference(flattening,[],[f929]) ).

thf(f929,plain,
    ! [X0: $tType,X1: $tType,X2: X0,X3: X0,X4: X1,X5: labeled_graph(X1,X0),X6: labeled_graph(X1,X0)] :
      ( ( $true = vAPP(set(product_prod(X0,X0)),$o,vAPP(product_prod(X0,X0),sTfun(set(product_prod(X0,X0)),$o),member(product_prod(X0,X0)),vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3)),vAPP(labeled_graph(X1,X0),set(product_prod(X0,X0)),vAPP(X1,sTfun(labeled_graph(X1,X0),set(product_prod(X0,X0))),getRel(X1,X0),X4),X6)) )
      | ( $true != vAPP(set(product_prod(X0,X0)),$o,vAPP(labeled_graph(X1,X0),sTfun(set(product_prod(X0,X0)),$o),vAPP(labeled_graph(X1,X0),sTfun(labeled_graph(X1,X0),sTfun(set(product_prod(X0,X0)),$o)),graph_homomorphism(X1,X0,X0),X5),X6),vAPP(set(X0),set(product_prod(X0,X0)),id_on(X0),vAPP(labeled_graph(X1,X0),set(X0),labeled_vertices(X1,X0),X5))) )
      | ( $true != vAPP(set(product_prod(X0,X0)),$o,vAPP(product_prod(X0,X0),sTfun(set(product_prod(X0,X0)),$o),member(product_prod(X0,X0)),vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3)),vAPP(labeled_graph(X1,X0),set(product_prod(X0,X0)),vAPP(X1,sTfun(labeled_graph(X1,X0),set(product_prod(X0,X0))),getRel(X1,X0),X4),X5)) ) ),
    inference(ennf_transformation,[],[f639]) ).

thf(f639,plain,
    ! [X0: $tType,X1: $tType,X2: X0,X3: X0,X4: X1,X5: labeled_graph(X1,X0),X6: labeled_graph(X1,X0)] :
      ( ( $true = vAPP(set(product_prod(X0,X0)),$o,vAPP(product_prod(X0,X0),sTfun(set(product_prod(X0,X0)),$o),member(product_prod(X0,X0)),vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3)),vAPP(labeled_graph(X1,X0),set(product_prod(X0,X0)),vAPP(X1,sTfun(labeled_graph(X1,X0),set(product_prod(X0,X0))),getRel(X1,X0),X4),X5)) )
     => ( ( $true = vAPP(set(product_prod(X0,X0)),$o,vAPP(labeled_graph(X1,X0),sTfun(set(product_prod(X0,X0)),$o),vAPP(labeled_graph(X1,X0),sTfun(labeled_graph(X1,X0),sTfun(set(product_prod(X0,X0)),$o)),graph_homomorphism(X1,X0,X0),X5),X6),vAPP(set(X0),set(product_prod(X0,X0)),id_on(X0),vAPP(labeled_graph(X1,X0),set(X0),labeled_vertices(X1,X0),X5))) )
       => ( $true = vAPP(set(product_prod(X0,X0)),$o,vAPP(product_prod(X0,X0),sTfun(set(product_prod(X0,X0)),$o),member(product_prod(X0,X0)),vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3)),vAPP(labeled_graph(X1,X0),set(product_prod(X0,X0)),vAPP(X1,sTfun(labeled_graph(X1,X0),set(product_prod(X0,X0))),getRel(X1,X0),X4),X6)) ) ) ),
    inference(fool_elimination,[],[f638]) ).

thf(f638,plain,
    ! [X0: $tType,X1: $tType,X2: X0,X3: X0,X4: X1,X5: labeled_graph(X1,X0),X6: labeled_graph(X1,X0)] :
      ( vAPP(set(product_prod(X0,X0)),$o,vAPP(product_prod(X0,X0),sTfun(set(product_prod(X0,X0)),$o),member(product_prod(X0,X0)),vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3)),vAPP(labeled_graph(X1,X0),set(product_prod(X0,X0)),vAPP(X1,sTfun(labeled_graph(X1,X0),set(product_prod(X0,X0))),getRel(X1,X0),X4),X5))
     => ( vAPP(set(product_prod(X0,X0)),$o,vAPP(labeled_graph(X1,X0),sTfun(set(product_prod(X0,X0)),$o),vAPP(labeled_graph(X1,X0),sTfun(labeled_graph(X1,X0),sTfun(set(product_prod(X0,X0)),$o)),graph_homomorphism(X1,X0,X0),X5),X6),vAPP(set(X0),set(product_prod(X0,X0)),id_on(X0),vAPP(labeled_graph(X1,X0),set(X0),labeled_vertices(X1,X0),X5)))
       => vAPP(set(product_prod(X0,X0)),$o,vAPP(product_prod(X0,X0),sTfun(set(product_prod(X0,X0)),$o),member(product_prod(X0,X0)),vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X3)),vAPP(labeled_graph(X1,X0),set(product_prod(X0,X0)),vAPP(X1,sTfun(labeled_graph(X1,X0),set(product_prod(X0,X0))),getRel(X1,X0),X4),X6)) ) ),
    inference(rectify,[],[f30]) ).

thf(f30,axiom,
    ! [X0: $tType,X1: $tType,X25: X0,X26: X0,X27: X1,X28: labeled_graph(X1,X0),X36: labeled_graph(X1,X0)] :
      ( vAPP(set(product_prod(X0,X0)),$o,vAPP(product_prod(X0,X0),sTfun(set(product_prod(X0,X0)),$o),member(product_prod(X0,X0)),vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X25),X26)),vAPP(labeled_graph(X1,X0),set(product_prod(X0,X0)),vAPP(X1,sTfun(labeled_graph(X1,X0),set(product_prod(X0,X0))),getRel(X1,X0),X27),X28))
     => ( vAPP(set(product_prod(X0,X0)),$o,vAPP(labeled_graph(X1,X0),sTfun(set(product_prod(X0,X0)),$o),vAPP(labeled_graph(X1,X0),sTfun(labeled_graph(X1,X0),sTfun(set(product_prod(X0,X0)),$o)),graph_homomorphism(X1,X0,X0),X28),X36),vAPP(set(X0),set(product_prod(X0,X0)),id_on(X0),vAPP(labeled_graph(X1,X0),set(X0),labeled_vertices(X1,X0),X28)))
       => vAPP(set(product_prod(X0,X0)),$o,vAPP(product_prod(X0,X0),sTfun(set(product_prod(X0,X0)),$o),member(product_prod(X0,X0)),vAPP(X0,product_prod(X0,X0),vAPP(X0,sTfun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X25),X26)),vAPP(labeled_graph(X1,X0),set(product_prod(X0,X0)),vAPP(X1,sTfun(labeled_graph(X1,X0),set(product_prod(X0,X0))),getRel(X1,X0),X27),X36)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_getRel__subgraph) ).

thf(f1041,plain,
    vAPP(set(product_prod(v,v)),$o,vAPP(product_prod(v,v),sTfun(set(product_prod(v,v)),$o),member(product_prod(v,v)),vAPP(v,product_prod(v,v),vAPP(v,sTfun(v,product_prod(v,v)),product_Pair(v,v),vAPP(v2,v,m,xa)),vAPP(v2,v,m,xa))),vAPP(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v)),vAPP(standard_Constant(v2),sTfun(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v))),getRel(standard_Constant(v2),v),vAPP(v2,standard_Constant(v2),standard_S_Const(v2),y)),g)) != $true,
    inference(cnf_transformation,[],[f708]) ).

thf(f708,plain,
    vAPP(set(product_prod(v,v)),$o,vAPP(product_prod(v,v),sTfun(set(product_prod(v,v)),$o),member(product_prod(v,v)),vAPP(v,product_prod(v,v),vAPP(v,sTfun(v,product_prod(v,v)),product_Pair(v,v),vAPP(v2,v,m,xa)),vAPP(v2,v,m,xa))),vAPP(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v)),vAPP(standard_Constant(v2),sTfun(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v))),getRel(standard_Constant(v2),v),vAPP(v2,standard_Constant(v2),standard_S_Const(v2),y)),g)) != $true,
    inference(flattening,[],[f284]) ).

thf(f284,plain,
    vAPP(set(product_prod(v,v)),$o,vAPP(product_prod(v,v),sTfun(set(product_prod(v,v)),$o),member(product_prod(v,v)),vAPP(v,product_prod(v,v),vAPP(v,sTfun(v,product_prod(v,v)),product_Pair(v,v),vAPP(v2,v,m,xa)),vAPP(v2,v,m,xa))),vAPP(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v)),vAPP(standard_Constant(v2),sTfun(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v))),getRel(standard_Constant(v2),v),vAPP(v2,standard_Constant(v2),standard_S_Const(v2),y)),g)) != $true,
    inference(fool_elimination,[],[f283]) ).

thf(f283,plain,
    ~ vAPP(set(product_prod(v,v)),$o,vAPP(product_prod(v,v),sTfun(set(product_prod(v,v)),$o),member(product_prod(v,v)),vAPP(v,product_prod(v,v),vAPP(v,sTfun(v,product_prod(v,v)),product_Pair(v,v),vAPP(v2,v,m,xa)),vAPP(v2,v,m,xa))),vAPP(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v)),vAPP(standard_Constant(v2),sTfun(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v))),getRel(standard_Constant(v2),v),vAPP(v2,standard_Constant(v2),standard_S_Const(v2),y)),g)),
    inference(rectify,[],[f280]) ).

thf(f280,negated_conjecture,
    ~ vAPP(set(product_prod(v,v)),$o,vAPP(product_prod(v,v),sTfun(set(product_prod(v,v)),$o),member(product_prod(v,v)),vAPP(v,product_prod(v,v),vAPP(v,sTfun(v,product_prod(v,v)),product_Pair(v,v),vAPP(v2,v,m,xa)),vAPP(v2,v,m,xa))),vAPP(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v)),vAPP(standard_Constant(v2),sTfun(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v))),getRel(standard_Constant(v2),v),vAPP(v2,standard_Constant(v2),standard_S_Const(v2),y)),g)),
    inference(negated_conjecture,[],[f279]) ).

thf(f279,conjecture,
    vAPP(set(product_prod(v,v)),$o,vAPP(product_prod(v,v),sTfun(set(product_prod(v,v)),$o),member(product_prod(v,v)),vAPP(v,product_prod(v,v),vAPP(v,sTfun(v,product_prod(v,v)),product_Pair(v,v),vAPP(v2,v,m,xa)),vAPP(v2,v,m,xa))),vAPP(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v)),vAPP(standard_Constant(v2),sTfun(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v))),getRel(standard_Constant(v2),v),vAPP(v2,standard_Constant(v2),standard_S_Const(v2),y)),g)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(f1342,plain,
    vAPP(set(product_prod(v,v)),$o,vAPP(product_prod(v,v),sTfun(set(product_prod(v,v)),$o),member(product_prod(v,v)),vAPP(v,product_prod(v,v),vAPP(v,sTfun(v,product_prod(v,v)),product_Pair(v,v),vAPP(v2,v,m,xa)),vAPP(v2,v,m,xa))),vAPP(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v)),vAPP(standard_Constant(v2),sTfun(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v))),getRel(standard_Constant(v2),v),vAPP(v2,standard_Constant(v2),standard_S_Const(v2),y)),vAPP(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v),vAPP(set(product_prod(v,v)),sTfun(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v)),map_graph(v,v,standard_Constant(v2)),vAPP(sTfun(v,v),set(product_prod(v,v)),vAPP(set(v),sTfun(sTfun(v,v),set(product_prod(v,v))),bNF_Gr(v,v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),g)),h)),g))) = $true,
    inference(cnf_transformation,[],[f703]) ).

thf(f703,plain,
    vAPP(set(product_prod(v,v)),$o,vAPP(product_prod(v,v),sTfun(set(product_prod(v,v)),$o),member(product_prod(v,v)),vAPP(v,product_prod(v,v),vAPP(v,sTfun(v,product_prod(v,v)),product_Pair(v,v),vAPP(v2,v,m,xa)),vAPP(v2,v,m,xa))),vAPP(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v)),vAPP(standard_Constant(v2),sTfun(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v))),getRel(standard_Constant(v2),v),vAPP(v2,standard_Constant(v2),standard_S_Const(v2),y)),vAPP(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v),vAPP(set(product_prod(v,v)),sTfun(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v)),map_graph(v,v,standard_Constant(v2)),vAPP(sTfun(v,v),set(product_prod(v,v)),vAPP(set(v),sTfun(sTfun(v,v),set(product_prod(v,v))),bNF_Gr(v,v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),g)),h)),g))) = $true,
    inference(fool_elimination,[],[f702]) ).

thf(f702,plain,
    vAPP(set(product_prod(v,v)),$o,vAPP(product_prod(v,v),sTfun(set(product_prod(v,v)),$o),member(product_prod(v,v)),vAPP(v,product_prod(v,v),vAPP(v,sTfun(v,product_prod(v,v)),product_Pair(v,v),vAPP(v2,v,m,xa)),vAPP(v2,v,m,xa))),vAPP(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v)),vAPP(standard_Constant(v2),sTfun(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v))),getRel(standard_Constant(v2),v),vAPP(v2,standard_Constant(v2),standard_S_Const(v2),y)),vAPP(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v),vAPP(set(product_prod(v,v)),sTfun(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v)),map_graph(v,v,standard_Constant(v2)),vAPP(sTfun(v,v),set(product_prod(v,v)),vAPP(set(v),sTfun(sTfun(v,v),set(product_prod(v,v))),bNF_Gr(v,v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),g)),h)),g))),
    inference(rectify,[],[f7]) ).

thf(f7,axiom,
    vAPP(set(product_prod(v,v)),$o,vAPP(product_prod(v,v),sTfun(set(product_prod(v,v)),$o),member(product_prod(v,v)),vAPP(v,product_prod(v,v),vAPP(v,sTfun(v,product_prod(v,v)),product_Pair(v,v),vAPP(v2,v,m,xa)),vAPP(v2,v,m,xa))),vAPP(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v)),vAPP(standard_Constant(v2),sTfun(labeled_graph(standard_Constant(v2),v),set(product_prod(v,v))),getRel(standard_Constant(v2),v),vAPP(v2,standard_Constant(v2),standard_S_Const(v2),y)),vAPP(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v),vAPP(set(product_prod(v,v)),sTfun(labeled_graph(standard_Constant(v2),v),labeled_graph(standard_Constant(v2),v)),map_graph(v,v,standard_Constant(v2)),vAPP(sTfun(v,v),set(product_prod(v,v)),vAPP(set(v),sTfun(sTfun(v,v),set(product_prod(v,v))),bNF_Gr(v,v),vAPP(labeled_graph(standard_Constant(v2),v),set(v),labeled_vertices(standard_Constant(v2),v),g)),h)),g))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6__092_060open_062_Im_Ax_M_Am_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ay_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : ITP180^2 : TPTP v8.1.2. Released v7.5.0.
% 0.10/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.33  % Computer : n009.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Fri May  3 19:18:53 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.12/0.33  % (24382)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.37  % (24385)WARNING: value z3 for option sas not known
% 0.17/0.37  % (24384)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.17/0.37  % (24383)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.17/0.37  % (24386)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.17/0.37  % (24385)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.17/0.37  % (24387)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.17/0.37  % (24388)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.17/0.37  % (24389)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.17/0.41  % (24389)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.17/0.42  % Exception at run slice level
% 0.17/0.42  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.42  % Exception at run slice level
% 0.17/0.42  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.43  % Exception at run slice level
% 0.17/0.43  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.43  % (24391)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.17/0.43  % (24392)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.17/0.44  % (24393)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.17/0.47  % (24391)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.17/0.47  % (24392)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.17/0.48  % Exception at run slice level
% 0.17/0.48  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.50  % (24394)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 175.36/25.46  % (24392)First to succeed.
% 175.36/25.46  % (24392)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-24382"
% 175.36/25.47  % (24392)Refutation found. Thanks to Tanya!
% 175.36/25.47  % SZS status Theorem for theBenchmark
% 175.36/25.47  % SZS output start Proof for theBenchmark
% See solution above
% 175.36/25.47  % (24392)------------------------------
% 175.36/25.47  % (24392)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 175.36/25.47  % (24392)Termination reason: Refutation
% 175.36/25.47  
% 175.36/25.47  % (24392)Memory used [KB]: 31752
% 175.36/25.47  % (24392)Time elapsed: 25.038 s
% 175.36/25.47  % (24392)Instructions burned: 66067 (million)
% 175.36/25.47  % (24382)Success in time 24.958 s
%------------------------------------------------------------------------------