TSTP Solution File: ITP026^2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ITP026^2 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n008.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 22:48:25 EDT 2024

% Result   : Theorem 6.64s 1.32s
% Output   : Refutation 6.64s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :  183
% Syntax   : Number of formulae    :  258 (  31 unt; 167 typ;   0 def)
%            Number of atoms       :  650 ( 127 equ;   0 cnn)
%            Maximal formula atoms :    4 (   7 avg)
%            Number of connectives :  160 (  65   ~;  67   |;   1   &;   0   @)
%                                         (   3 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Number of types       :    9 (   8 usr)
%            Number of type conns  :  355 ( 344   >;  11   *;   0   +;   0  <<)
%            Number of symbols     :  157 ( 154 usr;  14 con; 0-9 aty)
%            Number of variables   :  204 (   0   ^  65   !;   0   ?; 204   :)
%                                         ( 139  !>;   0  ?*;   0  @-;   0  @+)

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

thf(type_def_6,type,
    set: $tType > $tType ).

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

thf(type_def_8,type,
    ring_ext: ( $tType * $tType ) > $tType ).

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

thf(type_def_10,type,
    module_ext: ( $tType * $tType * $tType ) > $tType ).

thf(type_def_11,type,
    product_unit: $tType ).

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

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

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

thf(type_def_15,type,
    c: $tType ).

thf(type_def_16,type,
    e: $tType ).

thf(type_def_17,type,
    f: $tType ).

thf(type_def_18,type,
    d: $tType ).

thf(func_def_0,type,
    carrier_ext: ( $tType * $tType ) > $tType ).

thf(func_def_1,type,
    module_ext: ( $tType * $tType * $tType ) > $tType ).

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

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

thf(func_def_4,type,
    product_unit: $tType ).

thf(func_def_5,type,
    set: $tType > $tType ).

thf(func_def_6,type,
    nat: $tType ).

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

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

thf(func_def_9,type,
    d: $tType ).

thf(func_def_10,type,
    c: $tType ).

thf(func_def_11,type,
    b: $tType ).

thf(func_def_12,type,
    a: $tType ).

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

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

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

thf(func_def_16,type,
    group_add: 
      !>[X0: $tType] : $o ).

thf(func_def_17,type,
    wellorder: 
      !>[X0: $tType] : $o ).

thf(func_def_18,type,
    comm_monoid_diff: 
      !>[X0: $tType] : $o ).

thf(func_def_19,type,
    ordered_ab_group_add: 
      !>[X0: $tType] : $o ).

thf(func_def_20,type,
    cancel1352612707id_add: 
      !>[X0: $tType] : $o ).

thf(func_def_21,type,
    canoni770627133id_add: 
      !>[X0: $tType] : $o ).

thf(func_def_22,type,
    carrier: 
      !>[X0: $tType,X1: $tType] : ( carrier_ext(X0,X1) > set(X0) ) ).

thf(func_def_23,type,
    ring: 
      !>[X0: $tType,X1: $tType] : ( carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X1))) > $o ) ).

thf(func_def_24,type,
    zero2: 
      !>[X0: $tType,X1: $tType] : ( carrier_ext(X0,aGroup_ext(X0,X1)) > X0 ) ).

thf(func_def_25,type,
    ideal: 
      !>[X0: $tType,X1: $tType] : ( carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X1))) > set(X0) > $o ) ).

thf(func_def_26,type,
    annihilator: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X1))) > carrier_ext(X2,aGroup_ext(X2,module_ext(X2,X0,X3))) > set(X0) ) ).

thf(func_def_27,type,
    hom: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X1))) > carrier_ext(X2,aGroup_ext(X2,module_ext(X2,X0,X3))) > carrier_ext(X4,aGroup_ext(X4,module_ext(X4,X0,X5))) > carrier_ext(sTfun(X2,X4),aGroup_ext(sTfun(X2,X4),module_ext(sTfun(X2,X4),X0,product_unit))) ) ).

thf(func_def_28,type,
    module: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( carrier_ext(X0,aGroup_ext(X0,module_ext(X0,X1,X2))) > carrier_ext(X1,aGroup_ext(X1,ring_ext(X1,X3))) > $o ) ).

thf(func_def_29,type,
    free_generator: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X1))) > carrier_ext(X2,aGroup_ext(X2,module_ext(X2,X0,X3))) > set(X2) > $o ) ).

thf(func_def_30,type,
    generator: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X1))) > carrier_ext(X2,aGroup_ext(X2,module_ext(X2,X0,X3))) > set(X2) > $o ) ).

thf(func_def_31,type,
    l_comb: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X1))) > carrier_ext(X2,aGroup_ext(X2,module_ext(X2,X0,X3))) > nat > ( nat > X0 ) > ( nat > X2 ) > X2 ) ).

thf(func_def_32,type,
    linear_span: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X1))) > carrier_ext(X2,aGroup_ext(X2,module_ext(X2,X0,X3))) > set(X0) > set(X2) > set(X2) ) ).

thf(func_def_33,type,
    mdl: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( carrier_ext(X0,aGroup_ext(X0,module_ext(X0,X1,X2))) > set(X0) > carrier_ext(X0,aGroup_ext(X0,module_ext(X0,X1,product_unit))) ) ).

thf(func_def_34,type,
    misomorphic: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X1))) > carrier_ext(X2,aGroup_ext(X2,module_ext(X2,X0,X3))) > carrier_ext(X4,aGroup_ext(X4,module_ext(X4,X0,X5))) > $o ) ).

thf(func_def_35,type,
    quotie135653060odules: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X1))) > carrier_ext(X2,aGroup_ext(X2,module_ext(X2,X0,X3))) > set(X2) > set(X2) > set(X0) ) ).

thf(func_def_36,type,
    smodule_ideal_coeff: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X1))) > carrier_ext(X2,aGroup_ext(X2,module_ext(X2,X0,X3))) > set(X0) > set(X2) ) ).

thf(func_def_37,type,
    submodule: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X1))) > carrier_ext(X2,aGroup_ext(X2,module_ext(X2,X0,X3))) > set(X2) > $o ) ).

thf(func_def_38,type,
    algebr833503410le_fgs: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X1))) > carrier_ext(X2,aGroup_ext(X2,module_ext(X2,X0,X3))) > set(X2) > set(X2) ) ).

thf(func_def_39,type,
    pi: 
      !>[X0: $tType,X1: $tType] : ( set(X0) > ( X0 > set(X1) ) > set(sTfun(X0,X1)) ) ).

thf(func_def_40,type,
    minus_minus: 
      !>[X0: $tType] : ( X0 > X0 > X0 ) ).

thf(func_def_41,type,
    zero_zero: 
      !>[X0: $tType] : X0 ).

thf(func_def_42,type,
    suc: nat > nat ).

thf(func_def_43,type,
    bot_bot: 
      !>[X0: $tType] : X0 ).

thf(func_def_44,type,
    ord_less: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(func_def_45,type,
    ord_less_eq: 
      !>[X0: $tType] : ( X0 > X0 > $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,
    member: 
      !>[X0: $tType] : ( X0 > set(X0) > $o ) ).

thf(func_def_49,type,
    h: set(a) ).

thf(func_def_50,type,
    h1: set(a) ).

thf(func_def_51,type,
    m: carrier_ext(a,aGroup_ext(a,module_ext(a,b,c))) ).

thf(func_def_52,type,
    n: carrier_ext(e,aGroup_ext(e,module_ext(e,b,f))) ).

thf(func_def_53,type,
    r: carrier_ext(b,aGroup_ext(b,ring_ext(b,d))) ).

thf(func_def_54,type,
    g: nat > a ).

thf(func_def_55,type,
    h2: a ).

thf(func_def_56,type,
    m2: nat ).

thf(func_def_57,type,
    t: nat > b ).

thf(func_def_58,type,
    x: a ).

thf(func_def_59,type,
    xa: nat ).

thf(func_def_63,type,
    cCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).

thf(func_def_64,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_65,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_66,type,
    vAND: $o > $o > $o ).

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

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

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

thf(func_def_70,type,
    vOR: $o > $o > $o ).

thf(func_def_71,type,
    vSIGMA: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_72,type,
    vPI: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_73,type,
    vIMP: $o > $o > $o ).

thf(func_def_74,type,
    sP0: nat > ( nat > $o ) > $o ).

thf(func_def_75,type,
    sP1: ( nat > nat > $o ) > $o ).

thf(func_def_76,type,
    sP2: 
      !>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > $o ) ).

thf(func_def_77,type,
    sK3: nat > nat ).

thf(func_def_78,type,
    sK4: nat > nat ).

thf(func_def_79,type,
    sK5: 
      !>[X0: $tType] : ( ( nat > X0 ) > nat ) ).

thf(func_def_80,type,
    sK6: 
      !>[X0: $tType] : ( ( nat > X0 ) > nat ) ).

thf(func_def_81,type,
    sK7: 
      !>[X0: $tType] : ( ( nat > X0 ) > nat ) ).

thf(func_def_82,type,
    sK8: 
      !>[X0: $tType] : ( ( nat > X0 ) > nat ) ).

thf(func_def_83,type,
    sK9: nat > nat ).

thf(func_def_84,type,
    sK10: a > set(a) > nat ).

thf(func_def_85,type,
    sK11: a > set(a) > nat > a ).

thf(func_def_86,type,
    sK12: a > set(a) > nat > b ).

thf(func_def_87,type,
    sK13: ( nat > $o ) > nat ).

thf(func_def_88,type,
    sK14: ( nat > $o ) > nat ).

thf(func_def_89,type,
    sK15: ( nat > $o ) > nat ).

thf(func_def_90,type,
    sK16: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > $o ) > ( X1 > X0 ) > X1 ) ).

thf(func_def_91,type,
    sK17: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > $o ) > ( X1 > X0 ) > X1 ) ).

thf(func_def_92,type,
    sK18: nat > ( nat > $o ) > nat ).

thf(func_def_93,type,
    sK19: nat > ( nat > $o ) > nat ).

thf(func_def_94,type,
    sK20: ( nat > $o ) > nat ).

thf(func_def_95,type,
    sK21: ( nat > $o ) > nat ).

thf(func_def_96,type,
    sK22: ( nat > $o ) > nat ).

thf(func_def_97,type,
    sK23: ( nat > $o ) > nat ).

thf(func_def_98,type,
    sK24: nat > nat > nat ).

thf(func_def_99,type,
    sK25: nat > nat > nat ).

thf(func_def_100,type,
    sK26: nat > nat ).

thf(func_def_101,type,
    sK27: a > set(b) > nat ).

thf(func_def_102,type,
    sK28: a > set(b) > nat > b ).

thf(func_def_103,type,
    sK29: a > set(b) > nat > a ).

thf(func_def_104,type,
    sK30: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).

thf(func_def_105,type,
    sK31: 
      !>[X0: $tType] : ( set(X0) > set(X0) > X0 ) ).

thf(func_def_106,type,
    sK32: ( nat > nat > $o ) > nat ).

thf(func_def_107,type,
    sK33: ( nat > nat > $o ) > nat ).

thf(func_def_108,type,
    sK34: ( nat > nat > $o ) > nat ).

thf(func_def_109,type,
    sK35: ( nat > nat > $o ) > nat ).

thf(func_def_110,type,
    sK36: ( nat > nat ) > nat ).

thf(func_def_111,type,
    sK37: ( nat > nat ) > nat ).

thf(func_def_112,type,
    sK38: ( nat > $o ) > nat ).

thf(func_def_113,type,
    sK39: nat > ( nat > $o ) > nat ).

thf(func_def_114,type,
    sK40: ( nat > $o ) > nat ).

thf(func_def_115,type,
    sK41: nat > ( nat > $o ) > nat ).

thf(func_def_116,type,
    sK42: ( nat > $o ) > nat > nat ).

thf(func_def_117,type,
    sK43: ( nat > nat > $o ) > nat ).

thf(func_def_118,type,
    sK44: ( nat > nat > $o ) > nat ).

thf(func_def_119,type,
    sK45: ( nat > nat > $o ) > nat ).

thf(func_def_120,type,
    sK46: ( nat > nat > $o ) > nat ).

thf(func_def_121,type,
    sK47: ( nat > nat > $o ) > nat ).

thf(func_def_122,type,
    sK48: ( nat > nat > $o ) > nat ).

thf(func_def_123,type,
    sK49: ( nat > nat > $o ) > nat ).

thf(func_def_124,type,
    sK50: ( nat > nat > $o ) > nat ).

thf(func_def_125,type,
    sK51: ( nat > nat > $o ) > nat ).

thf(func_def_126,type,
    sK52: ( nat > $o ) > nat > nat ).

thf(func_def_127,type,
    sK53: ( nat > $o ) > nat > nat > nat ).

thf(func_def_128,type,
    sK54: ( nat > $o ) > nat > nat > nat ).

thf(func_def_129,type,
    sK55: 
      !>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > X0 ) ).

thf(func_def_130,type,
    sK56: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > nat ) > X0 ) ).

thf(func_def_131,type,
    sK57: 
      !>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > X0 ) ).

thf(func_def_132,type,
    sK58: ( nat > a ) > ( nat > a ) > nat > nat ).

thf(func_def_133,type,
    sK59: ( nat > a ) > ( nat > a ) > nat > nat ).

thf(func_def_134,type,
    sK60: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( X3 > set(X3) > carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X2))) > carrier_ext(X3,aGroup_ext(X3,module_ext(X3,X0,X1))) > nat ) ).

thf(func_def_135,type,
    sK61: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( X3 > set(X3) > carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X2))) > carrier_ext(X3,aGroup_ext(X3,module_ext(X3,X0,X1))) > nat > X3 ) ).

thf(func_def_136,type,
    sK62: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( X3 > set(X3) > carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X2))) > carrier_ext(X3,aGroup_ext(X3,module_ext(X3,X0,X1))) > nat > X0 ) ).

thf(func_def_137,type,
    sK63: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( X3 > set(X0) > carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X2))) > carrier_ext(X3,aGroup_ext(X3,module_ext(X3,X0,X1))) > nat ) ).

thf(func_def_138,type,
    sK64: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( X3 > set(X0) > carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X2))) > carrier_ext(X3,aGroup_ext(X3,module_ext(X3,X0,X1))) > nat > X0 ) ).

thf(func_def_139,type,
    sK65: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( X3 > set(X0) > carrier_ext(X0,aGroup_ext(X0,ring_ext(X0,X2))) > carrier_ext(X3,aGroup_ext(X3,module_ext(X3,X0,X1))) > nat > X3 ) ).

thf(func_def_140,type,
    sK66: 
      !>[X0: $tType] : ( ( nat > X0 ) > ( nat > X0 ) > nat > nat ) ).

thf(func_def_141,type,
    sK67: 
      !>[X0: $tType] : ( ( nat > X0 ) > ( nat > X0 ) > nat > nat ) ).

thf(func_def_143,type,
    sK69: nat > nat > nat ).

thf(func_def_144,type,
    sK70: nat > nat > nat ).

thf(func_def_145,type,
    sK71: ( nat > $o ) > nat > nat ).

thf(func_def_146,type,
    sK72: ( nat > $o ) > nat > nat ).

thf(func_def_147,type,
    sK73: ( nat > $o ) > nat > nat ).

thf(func_def_148,type,
    sK74: ( nat > $o ) > nat > nat ).

thf(func_def_149,type,
    sK75: 
      !>[X0: $tType] : ( set(X0) > X0 ) ).

thf(func_def_150,type,
    sK76: ( nat > $o ) > nat > nat ).

thf(func_def_151,type,
    sK77: ( nat > $o ) > nat > nat ).

thf(func_def_152,type,
    sK78: ( nat > $o ) > nat > nat ).

thf(func_def_153,type,
    sK79: ( nat > $o ) > nat > nat ).

thf(func_def_154,type,
    sK80: 
      !>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).

thf(func_def_155,type,
    sK81: 
      !>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).

thf(func_def_156,type,
    sK82: nat > nat ).

thf(f12221,plain,
    $false,
    inference(avatar_sat_refutation,[],[f10182,f11320,f12126,f12216]) ).

thf(f12216,plain,
    spl68_98,
    inference(avatar_contradiction_clause,[],[f12215]) ).

thf(f12215,plain,
    ( $false
    | spl68_98 ),
    inference(trivial_inequality_removal,[],[f12214]) ).

thf(f12214,plain,
    ( ( $true = $false )
    | spl68_98 ),
    inference(forward_demodulation,[],[f12213,f12146]) ).

thf(f12146,plain,
    ( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),xa),m2) )
    | spl68_98 ),
    inference(trivial_inequality_removal,[],[f12145]) ).

thf(f12145,plain,
    ( ( $true != $true )
    | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),xa),m2) )
    | spl68_98 ),
    inference(superposition,[],[f10177,f289]) ).

thf(f289,plain,
    ! [X0: $o] :
      ( ( $true = X0 )
      | ( $false = X0 ) ),
    introduced(fool_axiom,[]) ).

thf(f10177,plain,
    ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),xa),m2) )
    | spl68_98 ),
    inference(avatar_component_clause,[],[f10175]) ).

thf(f10175,plain,
    ( spl68_98
  <=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),xa),m2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl68_98])]) ).

thf(f12213,plain,
    $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),xa),m2),
    inference(forward_demodulation,[],[f11281,f12203]) ).

thf(f12203,plain,
    m2 = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),m2),vAPP(nat,nat,suc,zero_zero(nat)))),
    inference(trivial_inequality_removal,[],[f12180]) ).

thf(f12180,plain,
    ( ( $true != $true )
    | ( m2 = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),m2),vAPP(nat,nat,suc,zero_zero(nat)))) ) ),
    inference(superposition,[],[f1287,f1234]) ).

thf(f1234,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),m2) = $true,
    inference(cnf_transformation,[],[f299]) ).

thf(f299,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),m2) = $true,
    inference(fool_elimination,[],[f298]) ).

thf(f298,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),m2),
    inference(rectify,[],[f281]) ).

thf(f281,axiom,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),m2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_16) ).

thf(f1287,plain,
    ! [X0: nat] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) )
      | ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,suc,zero_zero(nat)))) = X0 ) ),
    inference(cnf_transformation,[],[f871]) ).

thf(f871,plain,
    ! [X0: nat] :
      ( ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,suc,zero_zero(nat)))) = X0 )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) ) ),
    inference(ennf_transformation,[],[f379]) ).

thf(f379,plain,
    ! [X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) )
     => ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,suc,zero_zero(nat)))) = X0 ) ),
    inference(fool_elimination,[],[f378]) ).

thf(f378,plain,
    ! [X0: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0)
     => ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,suc,zero_zero(nat)))) = X0 ) ),
    inference(rectify,[],[f27]) ).

thf(f27,axiom,
    ! [X19: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X19)
     => ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X19),vAPP(nat,nat,suc,zero_zero(nat)))) = X19 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_Suc__pred) ).

thf(f11281,plain,
    $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),xa),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),m2),vAPP(nat,nat,suc,zero_zero(nat))))),
    inference(trivial_inequality_removal,[],[f11278]) ).

thf(f11278,plain,
    ( ( $true != $true )
    | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),xa),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),m2),vAPP(nat,nat,suc,zero_zero(nat))))) ) ),
    inference(superposition,[],[f1401,f1237]) ).

thf(f1237,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),xa),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),m2),vAPP(nat,nat,suc,zero_zero(nat)))) = $true,
    inference(cnf_transformation,[],[f305]) ).

thf(f305,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),xa),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),m2),vAPP(nat,nat,suc,zero_zero(nat)))) = $true,
    inference(fool_elimination,[],[f304]) ).

thf(f304,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),xa),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),m2),vAPP(nat,nat,suc,zero_zero(nat)))),
    inference(rectify,[],[f284]) ).

thf(f284,axiom,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),xa),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),m2),vAPP(nat,nat,suc,zero_zero(nat)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_19) ).

thf(f1401,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,suc,X1)) ) ),
    inference(cnf_transformation,[],[f938]) ).

thf(f938,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,suc,X1)) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) ) ),
    inference(ennf_transformation,[],[f547]) ).

thf(f547,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,suc,X1)) ) ),
    inference(fool_elimination,[],[f546]) ).

thf(f546,plain,
    ! [X0: nat,X1: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,suc,X1)) ),
    inference(rectify,[],[f93]) ).

thf(f93,axiom,
    ! [X26: nat,X19: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X26),X19)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X26),vAPP(nat,nat,suc,X19)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_le__SucI) ).

thf(f12126,plain,
    ~ spl68_102,
    inference(avatar_contradiction_clause,[],[f12125]) ).

thf(f12125,plain,
    ( $false
    | ~ spl68_102 ),
    inference(subsumption_resolution,[],[f12124,f1253]) ).

thf(f1253,plain,
    ! [X0: nat] : ( vAPP(nat,nat,suc,X0) != X0 ),
    inference(cnf_transformation,[],[f796]) ).

thf(f796,plain,
    ! [X0: nat] : ( vAPP(nat,nat,suc,X0) != X0 ),
    inference(rectify,[],[f72]) ).

thf(f72,axiom,
    ! [X19: nat] : ( vAPP(nat,nat,suc,X19) != X19 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_n__not__Suc__n) ).

thf(f12124,plain,
    ( ( xa = vAPP(nat,nat,suc,xa) )
    | ~ spl68_102 ),
    inference(forward_demodulation,[],[f12123,f11515]) ).

thf(f11515,plain,
    ( ( xa = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),xa),vAPP(nat,nat,suc,zero_zero(nat))) )
    | ~ spl68_102 ),
    inference(forward_demodulation,[],[f11514,f10251]) ).

thf(f10251,plain,
    ( ( m2 = xa )
    | ~ spl68_102 ),
    inference(avatar_component_clause,[],[f10249]) ).

thf(f10249,plain,
    ( spl68_102
  <=> ( m2 = xa ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl68_102])]) ).

thf(f11514,plain,
    ( ( xa = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),m2),vAPP(nat,nat,suc,zero_zero(nat))) )
    | ~ spl68_102 ),
    inference(subsumption_resolution,[],[f11513,f1430]) ).

thf(f1430,plain,
    ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),X0) ),
    inference(cnf_transformation,[],[f599]) ).

thf(f599,plain,
    ! [X0: nat,X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),X0) ),
    inference(fool_elimination,[],[f598]) ).

thf(f598,plain,
    ! [X0: nat,X1: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),X0),
    inference(rectify,[],[f146]) ).

thf(f146,axiom,
    ! [X26: nat,X19: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X26),X19)),X26),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_diff__le__self) ).

thf(f11513,plain,
    ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),xa),vAPP(nat,nat,suc,zero_zero(nat)))),xa) )
    | ( xa = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),m2),vAPP(nat,nat,suc,zero_zero(nat))) )
    | ~ spl68_102 ),
    inference(forward_demodulation,[],[f11283,f10251]) ).

thf(f11283,plain,
    ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),m2),vAPP(nat,nat,suc,zero_zero(nat)))),xa) )
    | ( xa = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),m2),vAPP(nat,nat,suc,zero_zero(nat))) ) ),
    inference(trivial_inequality_removal,[],[f11276]) ).

thf(f11276,plain,
    ( ( $true != $true )
    | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),m2),vAPP(nat,nat,suc,zero_zero(nat)))),xa) )
    | ( xa = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),m2),vAPP(nat,nat,suc,zero_zero(nat))) ) ),
    inference(superposition,[],[f1399,f1237]) ).

thf(f1399,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0) )
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f936]) ).

thf(f936,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) ) ),
    inference(flattening,[],[f935]) ).

thf(f935,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) ) ),
    inference(ennf_transformation,[],[f543]) ).

thf(f543,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) )
     => ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0) )
       => ( X0 = X1 ) ) ),
    inference(fool_elimination,[],[f542]) ).

thf(f542,plain,
    ! [X0: nat,X1: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)
       => ( X0 = X1 ) ) ),
    inference(rectify,[],[f70]) ).

thf(f70,axiom,
    ! [X26: nat,X19: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X26),X19)
     => ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X19),X26)
       => ( X19 = X26 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_le__antisym) ).

thf(f12123,plain,
    ( ( xa = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),xa),vAPP(nat,nat,suc,zero_zero(nat)))) )
    | ~ spl68_102 ),
    inference(trivial_inequality_removal,[],[f12105]) ).

thf(f12105,plain,
    ( ( $true != $true )
    | ( xa = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),xa),vAPP(nat,nat,suc,zero_zero(nat)))) )
    | ~ spl68_102 ),
    inference(superposition,[],[f1287,f11324]) ).

thf(f11324,plain,
    ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),xa) )
    | ~ spl68_102 ),
    inference(backward_demodulation,[],[f1234,f10251]) ).

thf(f11320,plain,
    ( spl68_102
    | ~ spl68_99 ),
    inference(avatar_split_clause,[],[f11319,f10179,f10249]) ).

thf(f10179,plain,
    ( spl68_99
  <=> ! [X0: nat] :
        ( ( h2 != vAPP(nat,a,g,X0) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),m2) )
        | ( xa = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl68_99])]) ).

thf(f11319,plain,
    ( ( m2 = xa )
    | ~ spl68_99 ),
    inference(subsumption_resolution,[],[f11318,f1575]) ).

thf(f1575,plain,
    ! [X1: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X1) ),
    inference(equality_resolution,[],[f1354]) ).

thf(f1354,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) )
      | ( X0 != X1 ) ),
    inference(cnf_transformation,[],[f895]) ).

thf(f895,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) )
      | ( ( X0 != X1 )
        & ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) ) ),
    inference(ennf_transformation,[],[f483]) ).

thf(f483,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( X0 = X1 )
        | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) ) ),
    inference(fool_elimination,[],[f482]) ).

thf(f482,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( X0 = X1 )
        | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) )
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) ),
    inference(rectify,[],[f115]) ).

thf(f115,axiom,
    ! [X26: nat,X19: nat] :
      ( ( ( X19 = X26 )
        | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X26),X19) )
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X26),X19) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_less__or__eq__imp__le) ).

thf(f11318,plain,
    ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),m2),m2) )
    | ( m2 = xa )
    | ~ spl68_99 ),
    inference(trivial_inequality_removal,[],[f11317]) ).

thf(f11317,plain,
    ( ( h2 != h2 )
    | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),m2),m2) )
    | ( m2 = xa )
    | ~ spl68_99 ),
    inference(superposition,[],[f10180,f1229]) ).

thf(f1229,plain,
    h2 = vAPP(nat,a,g,m2),
    inference(cnf_transformation,[],[f268]) ).

thf(f268,axiom,
    h2 = vAPP(nat,a,g,m2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).

thf(f10180,plain,
    ( ! [X0: nat] :
        ( ( h2 != vAPP(nat,a,g,X0) )
        | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),m2) )
        | ( xa = X0 ) )
    | ~ spl68_99 ),
    inference(avatar_component_clause,[],[f10179]) ).

thf(f10182,plain,
    ( ~ spl68_98
    | spl68_99 ),
    inference(avatar_split_clause,[],[f10160,f10179,f10175]) ).

thf(f10160,plain,
    ! [X0: nat] :
      ( ( h2 != vAPP(nat,a,g,X0) )
      | ( xa = X0 )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),m2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),xa),m2) ) ),
    inference(superposition,[],[f1233,f1816]) ).

thf(f1816,plain,
    h2 = vAPP(nat,a,g,xa),
    inference(subsumption_resolution,[],[f1231,f1228]) ).

thf(f1228,plain,
    vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(nat,a,g,xa)),h1) != $true,
    inference(cnf_transformation,[],[f794]) ).

thf(f794,plain,
    vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(nat,a,g,xa)),h1) != $true,
    inference(flattening,[],[f291]) ).

thf(f291,plain,
    vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(nat,a,g,xa)),h1) != $true,
    inference(fool_elimination,[],[f290]) ).

thf(f290,plain,
    ~ vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(nat,a,g,xa)),h1),
    inference(rectify,[],[f287]) ).

thf(f287,negated_conjecture,
    ~ vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(nat,a,g,xa)),h1),
    inference(negated_conjecture,[],[f286]) ).

thf(f286,conjecture,
    vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(nat,a,g,xa)),h1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_21) ).

thf(f1231,plain,
    ( ( vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(nat,a,g,xa)),h1) = $true )
    | ( h2 = vAPP(nat,a,g,xa) ) ),
    inference(cnf_transformation,[],[f293]) ).

thf(f293,plain,
    ( ( vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(nat,a,g,xa)),h1) = $true )
    | ( h2 = vAPP(nat,a,g,xa) ) ),
    inference(fool_elimination,[],[f292]) ).

thf(f292,plain,
    ( vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(nat,a,g,xa)),h1)
    | ( h2 = vAPP(nat,a,g,xa) ) ),
    inference(rectify,[],[f285]) ).

thf(f285,axiom,
    ( vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(nat,a,g,xa)),h1)
    | ( h2 = vAPP(nat,a,g,xa) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_20) ).

thf(f1233,plain,
    ! [X0: nat,X1: nat] :
      ( ( vAPP(nat,a,g,X0) != vAPP(nat,a,g,X1) )
      | ( X0 = X1 )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),m2) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),m2) ) ),
    inference(cnf_transformation,[],[f850]) ).

thf(f850,plain,
    ! [X0: nat] :
      ( ! [X1: nat] :
          ( ( X0 = X1 )
          | ( vAPP(nat,a,g,X0) != vAPP(nat,a,g,X1) )
          | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),m2) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),m2) ) ),
    inference(flattening,[],[f849]) ).

thf(f849,plain,
    ! [X0: nat] :
      ( ! [X1: nat] :
          ( ( X0 = X1 )
          | ( vAPP(nat,a,g,X0) != vAPP(nat,a,g,X1) )
          | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),m2) ) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),m2) ) ),
    inference(ennf_transformation,[],[f297]) ).

thf(f297,plain,
    ! [X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),m2) )
     => ! [X1: nat] :
          ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),m2) )
         => ( ( vAPP(nat,a,g,X0) = vAPP(nat,a,g,X1) )
           => ( X0 = X1 ) ) ) ),
    inference(fool_elimination,[],[f296]) ).

thf(f296,plain,
    ! [X0: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),m2)
     => ! [X1: nat] :
          ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),m2)
         => ( ( vAPP(nat,a,g,X0) = vAPP(nat,a,g,X1) )
           => ( X0 = X1 ) ) ) ),
    inference(rectify,[],[f266]) ).

thf(f266,axiom,
    ! [X79: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X79),m2)
     => ! [X48: nat] :
          ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X48),m2)
         => ( ( vAPP(nat,a,g,X79) = vAPP(nat,a,g,X48) )
           => ( X48 = X79 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12  % Problem    : ITP026^2 : TPTP v8.2.0. Released v7.5.0.
% 0.02/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.34  % Computer : n008.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Sat May 18 18:34:52 EDT 2024
% 0.12/0.34  % CPUTime    : 
% 0.12/0.34  % (764)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.39  % (767)WARNING: value z3 for option sas not known
% 0.18/0.39  % (769)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)
% 0.18/0.39  % (771)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)
% 0.18/0.39  % (774)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)
% 0.18/0.39  % (767)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)
% 0.18/0.39  % (765)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.18/0.39  % (768)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.18/0.39  % (766)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.18/0.44  % (774)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.18/0.44  % Exception at run slice level
% 0.18/0.44  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.45  % Exception at run slice level
% 0.18/0.45  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.45  % Exception at run slice level
% 0.18/0.45  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.46  % (775)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.18/0.46  % (776)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)
% 0.18/0.46  % (777)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)
% 0.18/0.51  % (776)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.18/0.51  % (775)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.18/0.52  % Exception at run slice level
% 0.18/0.52  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.54  % (778)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)
% 6.64/1.31  % (777)First to succeed.
% 6.64/1.31  % (777)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-764"
% 6.64/1.32  % (777)Refutation found. Thanks to Tanya!
% 6.64/1.32  % SZS status Theorem for theBenchmark
% 6.64/1.32  % SZS output start Proof for theBenchmark
% See solution above
% 6.64/1.32  % (777)------------------------------
% 6.64/1.32  % (777)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 6.64/1.32  % (777)Termination reason: Refutation
% 6.64/1.32  
% 6.64/1.32  % (777)Memory used [KB]: 4385
% 6.64/1.32  % (777)Time elapsed: 0.849 s
% 6.64/1.32  % (777)Instructions burned: 1518 (million)
% 6.64/1.32  % (764)Success in time 0.956 s
%------------------------------------------------------------------------------