TSTP Solution File: DAT183^1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : DAT183^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n018.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 05:06:10 EDT 2024

% Result   : Theorem 1.90s 0.67s
% Output   : Refutation 1.90s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :  177
% Syntax   : Number of formulae    :  216 (  20 unt; 169 typ;   0 def)
%            Number of atoms       :  319 (  64 equ;   0 cnn)
%            Maximal formula atoms :    3 (   6 avg)
%            Number of connectives :   78 (  43   ~;  20   |;   0   &;   0   @)
%                                         (   0 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :  358 ( 357   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :  171 ( 168 usr;   3 con; 0-6 aty)
%            Number of variables   :  248 (   0   ^  73   !;   4   ?; 248   :)
%                                         ( 171  !>;   0  ?*;   0  @-;   0  @+)

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

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

thf(type_def_7,type,
    coinductive_llist: $tType > $tType ).

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

thf(type_def_9,type,
    nat: $tType ).

thf(type_def_10,type,
    a: $tType ).

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

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

thf(func_def_2,type,
    nat: $tType ).

thf(func_def_3,type,
    itself: $tType > $tType ).

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

thf(func_def_5,type,
    bounded_lattice: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_6,type,
    type: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_7,type,
    ord: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_8,type,
    top: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

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

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

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

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

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

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

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

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

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

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

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

thf(func_def_20,type,
    condit1656338222tinuum: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_21,type,
    coindu328551480prefix: 
      !>[X0: $tType] : ( coinductive_llist(X0) > coinductive_llist(X0) > $o ) ).

thf(func_def_22,type,
    coinductive_lappend: 
      !>[X0: $tType] : ( coinductive_llist(X0) > coinductive_llist(X0) > coinductive_llist(X0) ) ).

thf(func_def_23,type,
    coinductive_lfinite: 
      !>[X0: $tType] : ( coinductive_llist(X0) > $o ) ).

thf(func_def_24,type,
    coinductive_llast: 
      !>[X0: $tType] : ( coinductive_llist(X0) > X0 ) ).

thf(func_def_25,type,
    coinductive_LCons: 
      !>[X0: $tType] : ( X0 > coinductive_llist(X0) > coinductive_llist(X0) ) ).

thf(func_def_26,type,
    coinductive_LNil: 
      !>[X0: $tType] : coinductive_llist(X0) ).

thf(func_def_27,type,
    coinductive_lnull: 
      !>[X0: $tType] : ( coinductive_llist(X0) > $o ) ).

thf(func_def_28,type,
    coinductive_lmember: 
      !>[X0: $tType] : ( X0 > coinductive_llist(X0) > $o ) ).

thf(func_def_29,type,
    coindu1478340336prefix: 
      !>[X0: $tType] : ( coinductive_llist(X0) > coinductive_llist(X0) > $o ) ).

thf(func_def_30,type,
    minus_minus: 
      !>[X0: $tType] : ( X0 > X0 > X0 ) ).

thf(func_def_31,type,
    undefined: 
      !>[X0: $tType] : X0 ).

thf(func_def_32,type,
    lList2435255213lllsts: 
      !>[X0: $tType] : ( set(X0) > set(coinductive_llist(X0)) ) ).

thf(func_def_33,type,
    lList21511617539llstsp: 
      !>[X0: $tType] : ( ( X0 > $o ) > coinductive_llist(X0) > $o ) ).

thf(func_def_34,type,
    lList2236698231inlsts: 
      !>[X0: $tType] : ( set(X0) > set(coinductive_llist(X0)) ) ).

thf(func_def_35,type,
    lList21916056377ts_rec: 
      !>[X0: $tType,X1: $tType] : ( X0 > ( X1 > coinductive_llist(X1) > X0 > X0 ) > coinductive_llist(X1) > X0 ) ).

thf(func_def_36,type,
    lList2860480441nlstsp: 
      !>[X0: $tType] : ( ( X0 > $o ) > coinductive_llist(X0) > $o ) ).

thf(func_def_37,type,
    lList22096119349pslsts: 
      !>[X0: $tType] : ( set(X0) > set(coinductive_llist(X0)) ) ).

thf(func_def_38,type,
    lList21612149805nflsts: 
      !>[X0: $tType] : ( set(X0) > set(coinductive_llist(X0)) ) ).

thf(func_def_39,type,
    lList2370560421utlast: 
      !>[X0: $tType] : ( coinductive_llist(X0) > coinductive_llist(X0) ) ).

thf(func_def_40,type,
    lList2508575361_ldrop: 
      !>[X0: $tType] : ( coinductive_llist(X0) > nat > coinductive_llist(X0) ) ).

thf(func_def_41,type,
    lList2170638824_llast: 
      !>[X0: $tType] : ( coinductive_llist(X0) > X0 ) ).

thf(func_def_42,type,
    lList21232602520length: 
      !>[X0: $tType] : ( coinductive_llist(X0) > nat ) ).

thf(func_def_43,type,
    lList2281150353e_lrev: 
      !>[X0: $tType] : ( coinductive_llist(X0) > coinductive_llist(X0) ) ).

thf(func_def_44,type,
    lList22119844313_ltake: 
      !>[X0: $tType] : ( coinductive_llist(X0) > nat > coinductive_llist(X0) ) ).

thf(func_def_45,type,
    lList21148268032oslsts: 
      !>[X0: $tType] : ( set(X0) > set(coinductive_llist(X0)) ) ).

thf(func_def_46,type,
    sup_sup: 
      !>[X0: $tType] : ( X0 > X0 > X0 ) ).

thf(func_def_47,type,
    suc: nat > nat ).

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

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

thf(func_def_50,type,
    type2: 
      !>[X0: $tType] : itself(X0) ).

thf(func_def_51,type,
    collect: 
      !>[X0: $tType] : ( ( X0 > $o ) > set(X0) ) ).

thf(func_def_52,type,
    member: 
      !>[X0: $tType] : ( X0 > set(X0) > $o ) ).

thf(func_def_53,type,
    r: coinductive_llist(a) ).

thf(func_def_57,type,
    vOR: $o > $o > $o ).

thf(func_def_58,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(func_def_59,type,
    vAND: $o > $o > $o ).

thf(func_def_60,type,
    vSIGMA: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_61,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_62,type,
    cCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).

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

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

thf(func_def_65,type,
    vNOT: $o > $o ).

thf(func_def_66,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_67,type,
    vIMP: $o > $o > $o ).

thf(func_def_68,type,
    vPI: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_69,type,
    sP0: 
      !>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > $o ) ).

thf(func_def_70,type,
    sP1: 
      !>[X0: $tType] : ( set(X0) > ( coinductive_llist(X0) > $o ) > $o ) ).

thf(func_def_71,type,
    sP2: 
      !>[X0: $tType] : ( set(X0) > ( coinductive_llist(X0) > $o ) > $o ) ).

thf(func_def_72,type,
    sK3: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_73,type,
    sK4: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_74,type,
    sK5: 
      !>[X0: $tType] : ( X0 > X0 > X0 ) ).

thf(func_def_75,type,
    sK6: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_76,type,
    sK7: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_77,type,
    sK8: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_78,type,
    sK9: 
      !>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).

thf(func_def_79,type,
    sK10: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_80,type,
    sK11: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_81,type,
    sK12: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_82,type,
    sK13: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_83,type,
    sK14: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_84,type,
    sK15: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_85,type,
    sK16: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_86,type,
    sK17: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_87,type,
    sK18: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).

thf(func_def_88,type,
    sK19: 
      !>[X0: $tType] : ( X0 > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).

thf(func_def_89,type,
    sK20: 
      !>[X0: $tType] : ( X0 > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).

thf(func_def_90,type,
    sK21: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).

thf(func_def_91,type,
    sK22: 
      !>[X0: $tType] : ( X0 > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).

thf(func_def_92,type,
    sK23: 
      !>[X0: $tType] : ( X0 > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).

thf(func_def_93,type,
    sK24: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).

thf(func_def_94,type,
    sK25: 
      !>[X0: $tType] : ( X0 > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).

thf(func_def_95,type,
    sK26: 
      !>[X0: $tType] : ( X0 > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).

thf(func_def_96,type,
    sK27: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).

thf(func_def_97,type,
    sK28: 
      !>[X0: $tType] : ( X0 > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).

thf(func_def_98,type,
    sK29: 
      !>[X0: $tType] : ( X0 > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).

thf(func_def_99,type,
    sK30: 
      !>[X0: $tType] : ( ( nat > X0 ) > nat ) ).

thf(func_def_100,type,
    sK31: 
      !>[X0: $tType] : ( ( nat > X0 ) > nat ) ).

thf(func_def_101,type,
    sK32: 
      !>[X0: $tType] : X0 ).

thf(func_def_102,type,
    sK33: 
      !>[X0: $tType] : ( coinductive_llist(X0) > X0 ) ).

thf(func_def_103,type,
    sK34: 
      !>[X0: $tType] : ( coinductive_llist(X0) > coinductive_llist(X0) ) ).

thf(func_def_104,type,
    sK35: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).

thf(func_def_105,type,
    sK36: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).

thf(func_def_106,type,
    sK37: 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).

thf(func_def_107,type,
    sK38: 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).

thf(func_def_108,type,
    sK39: 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).

thf(func_def_109,type,
    sK40: 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).

thf(func_def_110,type,
    sK41: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).

thf(func_def_111,type,
    sK42: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).

thf(func_def_112,type,
    sK43: 
      !>[X0: $tType] : ( set(X0) > X0 ) ).

thf(func_def_113,type,
    sK44: 
      !>[X0: $tType] : ( coinductive_llist(X0) > coinductive_llist(X0) ) ).

thf(func_def_114,type,
    sK45: 
      !>[X0: $tType] : ( coinductive_llist(X0) > X0 ) ).

thf(func_def_115,type,
    sK46: 
      !>[X0: $tType,X1: $tType] : ( X1 > X0 ) ).

thf(func_def_116,type,
    sK47: 
      !>[X0: $tType,X1: $tType] : ( X1 > X0 ) ).

thf(func_def_117,type,
    sK48: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).

thf(func_def_118,type,
    sK49: 
      !>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > coinductive_llist(X0) ) ).

thf(func_def_119,type,
    sK50: 
      !>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > X0 ) ).

thf(func_def_120,type,
    sK51: 
      !>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > coinductive_llist(X0) ) ).

thf(func_def_121,type,
    sK52: 
      !>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > coinductive_llist(X0) ) ).

thf(func_def_122,type,
    sK53: 
      !>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > X0 ) ).

thf(func_def_123,type,
    sK54: 
      !>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > X0 ) ).

thf(func_def_124,type,
    sK55: 
      !>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > coinductive_llist(X0) ) ).

thf(func_def_125,type,
    sK56: 
      !>[X0: $tType] : ( set(X0) > set(X0) > X0 ) ).

thf(func_def_126,type,
    sK57: 
      !>[X0: $tType] : ( coinductive_llist(X0) > ( X0 > $o ) > coinductive_llist(X0) ) ).

thf(func_def_127,type,
    sK58: 
      !>[X0: $tType] : ( coinductive_llist(X0) > ( X0 > $o ) > X0 ) ).

thf(func_def_128,type,
    sK59: 
      !>[X0: $tType] : ( coinductive_llist(X0) > ( X0 > $o ) > coinductive_llist(X0) ) ).

thf(func_def_129,type,
    sK60: 
      !>[X0: $tType] : ( coinductive_llist(X0) > ( X0 > $o ) > X0 ) ).

thf(func_def_130,type,
    sK61: 
      !>[X0: $tType] : ( set(X0) > coinductive_llist(X0) > X0 ) ).

thf(func_def_131,type,
    sK62: 
      !>[X0: $tType] : ( set(X0) > coinductive_llist(X0) > coinductive_llist(X0) ) ).

thf(func_def_132,type,
    sK63: 
      !>[X0: $tType] : ( set(X0) > coinductive_llist(X0) > coinductive_llist(X0) ) ).

thf(func_def_133,type,
    sK64: 
      !>[X0: $tType] : ( set(X0) > coinductive_llist(X0) > X0 ) ).

thf(func_def_134,type,
    sK65: 
      !>[X0: $tType] : ( set(X0) > coinductive_llist(X0) > X0 ) ).

thf(func_def_135,type,
    sK66: 
      !>[X0: $tType] : ( set(X0) > coinductive_llist(X0) > coinductive_llist(X0) ) ).

thf(func_def_136,type,
    sK67: 
      !>[X0: $tType] : ( set(X0) > coinductive_llist(X0) > coinductive_llist(X0) ) ).

thf(func_def_137,type,
    sK68: 
      !>[X0: $tType] : ( set(X0) > coinductive_llist(X0) > X0 ) ).

thf(func_def_138,type,
    sK69: 
      !>[X0: $tType] : ( set(X0) > coinductive_llist(X0) > X0 ) ).

thf(func_def_139,type,
    sK70: 
      !>[X0: $tType] : ( set(X0) > coinductive_llist(X0) > coinductive_llist(X0) ) ).

thf(func_def_140,type,
    sK71: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > X1 ) ).

thf(func_def_141,type,
    sK72: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( coinductive_llist(X0) > $o ) > coinductive_llist(X0) ) ).

thf(func_def_142,type,
    sK73: 
      !>[X0: $tType] : ( set(X0) > ( coinductive_llist(X0) > $o ) > coinductive_llist(X0) ) ).

thf(func_def_143,type,
    sK74: 
      !>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > ( X0 > $o ) > coinductive_llist(X0) ) ).

thf(func_def_144,type,
    sK75: 
      !>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > ( X0 > $o ) > X0 ) ).

thf(func_def_145,type,
    sK76: 
      !>[X0: $tType] : ( set(X0) > ( coinductive_llist(X0) > $o ) > X0 ) ).

thf(func_def_146,type,
    sK77: 
      !>[X0: $tType] : ( set(X0) > ( coinductive_llist(X0) > $o ) > coinductive_llist(X0) ) ).

thf(func_def_147,type,
    sK78: 
      !>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > set(X0) > X0 ) ).

thf(func_def_148,type,
    sK79: 
      !>[X0: $tType] : ( set(X0) > ( coinductive_llist(X0) > $o ) > X0 ) ).

thf(func_def_149,type,
    sK80: 
      !>[X0: $tType] : ( set(X0) > ( coinductive_llist(X0) > $o ) > coinductive_llist(X0) ) ).

thf(func_def_150,type,
    sK81: 
      !>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > coinductive_llist(X0) ) ).

thf(func_def_151,type,
    sK82: 
      !>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > set(X0) > coinductive_llist(X0) ) ).

thf(func_def_152,type,
    sK83: 
      !>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > set(X0) > X0 ) ).

thf(func_def_153,type,
    sK84: 
      !>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > set(X0) > X0 ) ).

thf(func_def_154,type,
    sK85: 
      !>[X0: $tType] : ( ( coinductive_llist(X0) > $o ) > set(X0) > coinductive_llist(X0) ) ).

thf(func_def_155,type,
    sK86: 
      !>[X0: $tType] : ( coinductive_llist(X0) > coinductive_llist(X0) > X0 > coinductive_llist(X0) ) ).

thf(func_def_156,type,
    sK87: 
      !>[X0: $tType] : ( ( X0 > $o ) > set(X0) > X0 ) ).

thf(func_def_157,type,
    sK88: 
      !>[X0: $tType] : ( ( X0 > $o ) > set(X0) > X0 ) ).

thf(func_def_158,type,
    sK89: 
      !>[X0: $tType] : ( ( X0 > $o ) > set(X0) > set(X0) > X0 ) ).

thf(func_def_159,type,
    sK90: 
      !>[X0: $tType] : ( ( X0 > $o ) > set(X0) > set(X0) > X0 ) ).

thf(func_def_160,type,
    sK91: 
      !>[X0: $tType] : ( ( X0 > $o ) > set(X0) > X0 ) ).

thf(func_def_161,type,
    sK92: 
      !>[X0: $tType] : ( ( X0 > $o ) > set(X0) > X0 ) ).

thf(func_def_162,type,
    sK93: 
      !>[X0: $tType] : ( coinductive_llist(X0) > set(X0) > X0 ) ).

thf(func_def_163,type,
    sK94: 
      !>[X0: $tType] : ( coinductive_llist(X0) > set(X0) > X0 ) ).

thf(func_def_164,type,
    sK95: 
      !>[X0: $tType] : ( coinductive_llist(X0) > coinductive_llist(X0) ) ).

thf(func_def_165,type,
    sK96: 
      !>[X0: $tType] : ( coinductive_llist(X0) > coinductive_llist(X0) ) ).

thf(f9125,plain,
    $false,
    inference(trivial_inequality_removal,[],[f9124]) ).

thf(f9124,plain,
    $true = $false,
    inference(forward_demodulation,[],[f9122,f2357]) ).

thf(f2357,plain,
    ! [X0: $tType,X1: coinductive_llist(X0)] : ( $false = vAPP(coinductive_llist(X0),$o,vAPP(coinductive_llist(X0),sTfun(coinductive_llist(X0),$o),ord_less(coinductive_llist(X0)),X1),X1) ),
    inference(trivial_inequality_removal,[],[f2350]) ).

thf(f2350,plain,
    ! [X0: $tType,X1: coinductive_llist(X0)] :
      ( ( $true != $true )
      | ( $false = vAPP(coinductive_llist(X0),$o,vAPP(coinductive_llist(X0),sTfun(coinductive_llist(X0),$o),ord_less(coinductive_llist(X0)),X1),X1) ) ),
    inference(superposition,[],[f2342,f1308]) ).

thf(f1308,plain,
    ! [X0: $tType] : ( $true = vAPP(itself(coinductive_llist(X0)),$o,preorder(coinductive_llist(X0)),type2(coinductive_llist(X0))) ),
    inference(cnf_transformation,[],[f433]) ).

thf(f433,plain,
    ! [X0: $tType] : ( $true = vAPP(itself(coinductive_llist(X0)),$o,preorder(coinductive_llist(X0)),type2(coinductive_llist(X0))) ),
    inference(fool_elimination,[],[f432]) ).

thf(f432,plain,
    ! [X0: $tType] : vAPP(itself(coinductive_llist(X0)),$o,preorder(coinductive_llist(X0)),type2(coinductive_llist(X0))),
    inference(rectify,[],[f283]) ).

thf(f283,axiom,
    ! [X66: $tType] : vAPP(itself(coinductive_llist(X66)),$o,preorder(coinductive_llist(X66)),type2(coinductive_llist(X66))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Coinductive__List_Ollist___Orderings_Opreorder_19) ).

thf(f2342,plain,
    ! [X0: $tType,X1: X0] :
      ( ( vAPP(itself(X0),$o,preorder(X0),type2(X0)) != $true )
      | ( $false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1) ) ),
    inference(trivial_inequality_removal,[],[f2341]) ).

thf(f2341,plain,
    ! [X0: $tType,X1: X0] :
      ( ( $true != $true )
      | ( vAPP(itself(X0),$o,preorder(X0),type2(X0)) != $true )
      | ( $false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1) ) ),
    inference(superposition,[],[f1245,f289]) ).

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

thf(f1245,plain,
    ! [X0: $tType,X1: X0] :
      ( ( $true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1) )
      | ( vAPP(itself(X0),$o,preorder(X0),type2(X0)) != $true ) ),
    inference(cnf_transformation,[],[f870]) ).

thf(f870,plain,
    ! [X0: $tType] :
      ( ! [X1: X0] : ( $true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1) )
      | ( vAPP(itself(X0),$o,preorder(X0),type2(X0)) != $true ) ),
    inference(ennf_transformation,[],[f784]) ).

thf(f784,plain,
    ! [X0: $tType] :
      ( ( vAPP(itself(X0),$o,preorder(X0),type2(X0)) = $true )
     => ! [X1: X0] : ( $true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1) ) ),
    inference(flattening,[],[f331]) ).

thf(f331,plain,
    ! [X0: $tType] :
      ( ( vAPP(itself(X0),$o,preorder(X0),type2(X0)) = $true )
     => ! [X1: X0] : ( $true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1) ) ),
    inference(fool_elimination,[],[f330]) ).

thf(f330,plain,
    ! [X0: $tType] :
      ( vAPP(itself(X0),$o,preorder(X0),type2(X0))
     => ! [X1: X0] : ~ vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1) ),
    inference(rectify,[],[f129]) ).

thf(f129,axiom,
    ! [X0: $tType] :
      ( vAPP(itself(X0),$o,preorder(X0),type2(X0))
     => ! [X31: X0] : ~ vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X31),X31) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_less__irrefl) ).

thf(f9122,plain,
    $true = vAPP(coinductive_llist(a),$o,vAPP(coinductive_llist(a),sTfun(coinductive_llist(a),$o),ord_less(coinductive_llist(a)),r),r),
    inference(backward_demodulation,[],[f1217,f9120]) ).

thf(f9120,plain,
    r = coinductive_LNil(a),
    inference(trivial_inequality_removal,[],[f9116]) ).

thf(f9116,plain,
    ( ( $true != $true )
    | ( r = coinductive_LNil(a) ) ),
    inference(superposition,[],[f9108,f7870]) ).

thf(f7870,plain,
    ! [X0: $tType,X1: coinductive_llist(X0)] :
      ( ( $true = vAPP(coinductive_llist(X0),$o,vAPP(coinductive_llist(X0),sTfun(coinductive_llist(X0),$o),ord_less(coinductive_llist(X0)),coinductive_LNil(X0)),X1) )
      | ( coinductive_LNil(X0) = X1 ) ),
    inference(superposition,[],[f1462,f1327]) ).

thf(f1327,plain,
    ! [X0: $tType,X1: coinductive_llist(X0)] :
      ( ( vAPP(coinductive_llist(X0),coinductive_llist(X0),vAPP(X0,sTfun(coinductive_llist(X0),coinductive_llist(X0)),coinductive_LCons(X0),vAPP(coinductive_llist(X0),X0,sK33(X0),X1)),vAPP(coinductive_llist(X0),coinductive_llist(X0),sK34(X0),X1)) = X1 )
      | ( coinductive_LNil(X0) = X1 ) ),
    inference(cnf_transformation,[],[f1146]) ).

thf(f1146,plain,
    ! [X0: $tType,X1: coinductive_llist(X0)] :
      ( ( vAPP(coinductive_llist(X0),coinductive_llist(X0),vAPP(X0,sTfun(coinductive_llist(X0),coinductive_llist(X0)),coinductive_LCons(X0),vAPP(coinductive_llist(X0),X0,sK33(X0),X1)),vAPP(coinductive_llist(X0),coinductive_llist(X0),sK34(X0),X1)) = X1 )
      | ( coinductive_LNil(X0) = X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK33,sK34])],[f922,f1145]) ).

thf(f1145,plain,
    ! [X0: $tType,X1: coinductive_llist(X0)] :
      ( ? [X2: X0,X3: coinductive_llist(X0)] : ( vAPP(coinductive_llist(X0),coinductive_llist(X0),vAPP(X0,sTfun(coinductive_llist(X0),coinductive_llist(X0)),coinductive_LCons(X0),X2),X3) = X1 )
     => ( vAPP(coinductive_llist(X0),coinductive_llist(X0),vAPP(X0,sTfun(coinductive_llist(X0),coinductive_llist(X0)),coinductive_LCons(X0),vAPP(coinductive_llist(X0),X0,sK33(X0),X1)),vAPP(coinductive_llist(X0),coinductive_llist(X0),sK34(X0),X1)) = X1 ) ),
    introduced(choice_axiom,[]) ).

thf(f922,plain,
    ! [X0: $tType,X1: coinductive_llist(X0)] :
      ( ? [X2: X0,X3: coinductive_llist(X0)] : ( vAPP(coinductive_llist(X0),coinductive_llist(X0),vAPP(X0,sTfun(coinductive_llist(X0),coinductive_llist(X0)),coinductive_LCons(X0),X2),X3) = X1 )
      | ( coinductive_LNil(X0) = X1 ) ),
    inference(ennf_transformation,[],[f807]) ).

thf(f807,plain,
    ! [X0: $tType,X1: coinductive_llist(X0)] :
      ( ( coinductive_LNil(X0) != X1 )
     => ~ ! [X2: X0,X3: coinductive_llist(X0)] : ( vAPP(coinductive_llist(X0),coinductive_llist(X0),vAPP(X0,sTfun(coinductive_llist(X0),coinductive_llist(X0)),coinductive_LCons(X0),X2),X3) != X1 ) ),
    inference(rectify,[],[f13]) ).

thf(f13,axiom,
    ! [X0: $tType,X15: coinductive_llist(X0)] :
      ( ( coinductive_LNil(X0) != X15 )
     => ~ ! [X16: X0,X17: coinductive_llist(X0)] : ( vAPP(coinductive_llist(X0),coinductive_llist(X0),vAPP(X0,sTfun(coinductive_llist(X0),coinductive_llist(X0)),coinductive_LCons(X0),X16),X17) != X15 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_llistE) ).

thf(f1462,plain,
    ! [X0: $tType,X2: coinductive_llist(X0),X1: X0] : ( $true = vAPP(coinductive_llist(X0),$o,vAPP(coinductive_llist(X0),sTfun(coinductive_llist(X0),$o),ord_less(coinductive_llist(X0)),coinductive_LNil(X0)),vAPP(coinductive_llist(X0),coinductive_llist(X0),vAPP(X0,sTfun(coinductive_llist(X0),coinductive_llist(X0)),coinductive_LCons(X0),X1),X2)) ),
    inference(cnf_transformation,[],[f625]) ).

thf(f625,plain,
    ! [X0: $tType,X1: X0,X2: coinductive_llist(X0)] : ( $true = vAPP(coinductive_llist(X0),$o,vAPP(coinductive_llist(X0),sTfun(coinductive_llist(X0),$o),ord_less(coinductive_llist(X0)),coinductive_LNil(X0)),vAPP(coinductive_llist(X0),coinductive_llist(X0),vAPP(X0,sTfun(coinductive_llist(X0),coinductive_llist(X0)),coinductive_LCons(X0),X1),X2)) ),
    inference(fool_elimination,[],[f624]) ).

thf(f624,plain,
    ! [X0: $tType,X1: X0,X2: coinductive_llist(X0)] : vAPP(coinductive_llist(X0),$o,vAPP(coinductive_llist(X0),sTfun(coinductive_llist(X0),$o),ord_less(coinductive_llist(X0)),coinductive_LNil(X0)),vAPP(coinductive_llist(X0),coinductive_llist(X0),vAPP(X0,sTfun(coinductive_llist(X0),coinductive_llist(X0)),coinductive_LCons(X0),X1),X2)),
    inference(rectify,[],[f2]) ).

thf(f2,axiom,
    ! [X0: $tType,X2: X0,X3: coinductive_llist(X0)] : vAPP(coinductive_llist(X0),$o,vAPP(coinductive_llist(X0),sTfun(coinductive_llist(X0),$o),ord_less(coinductive_llist(X0)),coinductive_LNil(X0)),vAPP(coinductive_llist(X0),coinductive_llist(X0),vAPP(X0,sTfun(coinductive_llist(X0),coinductive_llist(X0)),coinductive_LCons(X0),X2),X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_LNil__less__LCons) ).

thf(f9108,plain,
    $true != vAPP(coinductive_llist(a),$o,vAPP(coinductive_llist(a),sTfun(coinductive_llist(a),$o),ord_less(coinductive_llist(a)),coinductive_LNil(a)),r),
    inference(trivial_inequality_removal,[],[f9107]) ).

thf(f9107,plain,
    ( ( $true != $true )
    | ( $true != vAPP(coinductive_llist(a),$o,vAPP(coinductive_llist(a),sTfun(coinductive_llist(a),$o),ord_less(coinductive_llist(a)),coinductive_LNil(a)),r) ) ),
    inference(forward_demodulation,[],[f9075,f1308]) ).

thf(f9075,plain,
    ( ( $true != vAPP(coinductive_llist(a),$o,vAPP(coinductive_llist(a),sTfun(coinductive_llist(a),$o),ord_less(coinductive_llist(a)),coinductive_LNil(a)),r) )
    | ( $true != vAPP(itself(coinductive_llist(a)),$o,preorder(coinductive_llist(a)),type2(coinductive_llist(a))) ) ),
    inference(trivial_inequality_removal,[],[f9058]) ).

thf(f9058,plain,
    ( ( $true != $true )
    | ( $true != vAPP(coinductive_llist(a),$o,vAPP(coinductive_llist(a),sTfun(coinductive_llist(a),$o),ord_less(coinductive_llist(a)),coinductive_LNil(a)),r) )
    | ( $true != vAPP(itself(coinductive_llist(a)),$o,preorder(coinductive_llist(a)),type2(coinductive_llist(a))) ) ),
    inference(superposition,[],[f1246,f1217]) ).

thf(f1246,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ( $true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1) )
      | ( $true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) )
      | ( vAPP(itself(X0),$o,preorder(X0),type2(X0)) != $true ) ),
    inference(cnf_transformation,[],[f871]) ).

thf(f871,plain,
    ! [X0: $tType] :
      ( ! [X1: X0,X2: X0] :
          ( ( $true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1) )
          | ( $true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) ) )
      | ( vAPP(itself(X0),$o,preorder(X0),type2(X0)) != $true ) ),
    inference(ennf_transformation,[],[f785]) ).

thf(f785,plain,
    ! [X0: $tType] :
      ( ( vAPP(itself(X0),$o,preorder(X0),type2(X0)) = $true )
     => ! [X1: X0,X2: X0] :
          ( ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) )
         => ( $true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1) ) ) ),
    inference(flattening,[],[f333]) ).

thf(f333,plain,
    ! [X0: $tType] :
      ( ( vAPP(itself(X0),$o,preorder(X0),type2(X0)) = $true )
     => ! [X1: X0,X2: X0] :
          ( ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) )
         => ( $true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1) ) ) ),
    inference(fool_elimination,[],[f332]) ).

thf(f332,plain,
    ! [X0: $tType] :
      ( vAPP(itself(X0),$o,preorder(X0),type2(X0))
     => ! [X1: X0,X2: X0] :
          ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)
         => ~ vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1) ) ),
    inference(rectify,[],[f134]) ).

thf(f134,axiom,
    ! [X0: $tType] :
      ( vAPP(itself(X0),$o,preorder(X0),type2(X0))
     => ! [X31: X0,X15: X0] :
          ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X31),X15)
         => ~ vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X15),X31) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_less__not__sym) ).

thf(f1217,plain,
    vAPP(coinductive_llist(a),$o,vAPP(coinductive_llist(a),sTfun(coinductive_llist(a),$o),ord_less(coinductive_llist(a)),r),coinductive_LNil(a)) = $true,
    inference(cnf_transformation,[],[f780]) ).

thf(f780,plain,
    vAPP(coinductive_llist(a),$o,vAPP(coinductive_llist(a),sTfun(coinductive_llist(a),$o),ord_less(coinductive_llist(a)),r),coinductive_LNil(a)) = $true,
    inference(flattening,[],[f291]) ).

thf(f291,plain,
    vAPP(coinductive_llist(a),$o,vAPP(coinductive_llist(a),sTfun(coinductive_llist(a),$o),ord_less(coinductive_llist(a)),r),coinductive_LNil(a)) != $true,
    inference(fool_elimination,[],[f290]) ).

thf(f290,plain,
    ~ ~ vAPP(coinductive_llist(a),$o,vAPP(coinductive_llist(a),sTfun(coinductive_llist(a),$o),ord_less(coinductive_llist(a)),r),coinductive_LNil(a)),
    inference(rectify,[],[f287]) ).

thf(f287,negated_conjecture,
    ~ ~ vAPP(coinductive_llist(a),$o,vAPP(coinductive_llist(a),sTfun(coinductive_llist(a),$o),ord_less(coinductive_llist(a)),r),coinductive_LNil(a)),
    inference(negated_conjecture,[],[f286]) ).

thf(f286,conjecture,
    ~ vAPP(coinductive_llist(a),$o,vAPP(coinductive_llist(a),sTfun(coinductive_llist(a),$o),ord_less(coinductive_llist(a)),r),coinductive_LNil(a)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : DAT183^1 : TPTP v8.1.2. Released v7.0.0.
% 0.03/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n018.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Fri May  3 13:06:01 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (26375)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.39  % (26380)WARNING: value z3 for option sas not known
% 0.21/0.40  % (26378)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.40  % (26379)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.40  % (26381)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.40  % (26380)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)
% 0.21/0.40  % (26382)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)
% 0.21/0.40  % (26383)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)
% 0.21/0.40  % (26384)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)
% 0.21/0.43  % (26384)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.44  % Exception at run slice level
% 0.21/0.44  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.44  % Exception at run slice level
% 0.21/0.44  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.44  % Exception at run slice level
% 0.21/0.44  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.45  % (26385)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.45  % (26386)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)
% 0.21/0.46  % (26387)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)
% 0.21/0.48  % (26385)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.48  % (26386)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.49  % Exception at run slice level
% 0.21/0.49  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.50  % (26388)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)
% 1.90/0.67  % (26383)First to succeed.
% 1.90/0.67  % (26383)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-26375"
% 1.90/0.67  % (26383)Refutation found. Thanks to Tanya!
% 1.90/0.67  % SZS status Theorem for theBenchmark
% 1.90/0.67  % SZS output start Proof for theBenchmark
% See solution above
% 1.90/0.67  % (26383)------------------------------
% 1.90/0.67  % (26383)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.90/0.67  % (26383)Termination reason: Refutation
% 1.90/0.67  
% 1.90/0.67  % (26383)Memory used [KB]: 3961
% 1.90/0.67  % (26383)Time elapsed: 0.273 s
% 1.90/0.67  % (26383)Instructions burned: 877 (million)
% 1.90/0.67  % (26375)Success in time 0.295 s
%------------------------------------------------------------------------------