TSTP Solution File: ITP115^2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ITP115^2 : 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 : n010.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 22:52:22 EDT 2024

% Result   : Theorem 1.31s 0.56s
% Output   : Refutation 1.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :  147
% Syntax   : Number of formulae    :  191 (  11 unt; 135 typ;   0 def)
%            Number of atoms       :  593 ( 121 equ;   0 cnn)
%            Maximal formula atoms :   10 (  10 avg)
%            Number of connectives :  215 (  84   ~;  70   |;  48   &;   0   @)
%                                         (   6 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :  207 ( 206   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :  140 ( 137 usr;  14 con; 0-6 aty)
%            Number of variables   :  157 (   0   ^  14   !;  14   ?; 157   :)
%                                         ( 129  !>;   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,
    filter: $tType > $tType ).

thf(type_def_8,type,
    b: $tType ).

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

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

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

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

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

thf(func_def_3,type,
    b: $tType ).

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

thf(func_def_5,type,
    topolo2117631714pology: 
      !>[X0: $tType] : $o ).

thf(func_def_6,type,
    comple1035589618norder: 
      !>[X0: $tType] : $o ).

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

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

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

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

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

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

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

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

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

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

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

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

thf(func_def_22,type,
    ordered_ab_group_add: 
      !>[X0: $tType] : $o ).

thf(func_def_23,type,
    topological_t0_space: 
      !>[X0: $tType] : $o ).

thf(func_def_24,type,
    topological_t1_space: 
      !>[X0: $tType] : $o ).

thf(func_def_25,type,
    topological_t2_space: 
      !>[X0: $tType] : $o ).

thf(func_def_26,type,
    bounded_lattice_bot: 
      !>[X0: $tType] : $o ).

thf(func_def_27,type,
    cancel146912293up_add: 
      !>[X0: $tType] : $o ).

thf(func_def_28,type,
    topolo890362671_space: 
      !>[X0: $tType] : $o ).

thf(func_def_29,type,
    topolo47006728_space: 
      !>[X0: $tType] : $o ).

thf(func_def_30,type,
    topolo2133971006pology: 
      !>[X0: $tType] : $o ).

thf(func_def_31,type,
    topolo503727757_space: 
      !>[X0: $tType] : $o ).

thf(func_def_32,type,
    topolo2135403230pology: 
      !>[X0: $tType] : $o ).

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

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

thf(func_def_35,type,
    inf_inf: 
      !>[X0: $tType] : ( X0 > X0 > X0 ) ).

thf(func_def_36,type,
    lower_582600101lsc_at: 
      !>[X0: $tType,X1: $tType] : ( X0 > ( X0 > X1 ) > $o ) ).

thf(func_def_37,type,
    bot_bot: 
      !>[X0: $tType] : X0 ).

thf(func_def_38,type,
    ord_less_eq: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

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

thf(func_def_40,type,
    collect: 
      !>[X0: $tType] : ( ( X0 > $o ) > set(X0) ) ).

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

thf(func_def_42,type,
    is_empty: 
      !>[X0: $tType] : ( set(X0) > $o ) ).

thf(func_def_43,type,
    is_singleton: 
      !>[X0: $tType] : ( set(X0) > $o ) ).

thf(func_def_44,type,
    remove: 
      !>[X0: $tType] : ( X0 > set(X0) > set(X0) ) ).

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

thf(func_def_46,type,
    topolo1751647064n_open: 
      !>[X0: $tType] : ( set(X0) > $o ) ).

thf(func_def_47,type,
    topolo507301023within: 
      !>[X0: $tType] : ( X0 > set(X0) > filter(X0) ) ).

thf(func_def_48,type,
    topolo406746546ounded: 
      !>[X0: $tType] : ( set(X0) > $o ) ).

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

thf(func_def_50,type,
    a2: b ).

thf(func_def_51,type,
    f: a > b ).

thf(func_def_52,type,
    thesis: $o ).

thf(func_def_53,type,
    x0: a ).

thf(func_def_57,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(func_def_58,type,
    vAND: $o > $o > $o ).

thf(func_def_59,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_60,type,
    cCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).

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

thf(func_def_62,type,
    iCOMB: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_63,type,
    vSIGMA: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_64,type,
    vIMP: $o > $o > $o ).

thf(func_def_65,type,
    vPI: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

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

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

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

thf(func_def_69,type,
    sP0: $o ).

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

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

thf(func_def_72,type,
    sP3: 
      !>[X0: $tType] : ( X0 > X0 > X0 > $o ) ).

thf(func_def_73,type,
    sP4: 
      !>[X0: $tType] : ( X0 > X0 > X0 > $o ) ).

thf(func_def_74,type,
    sP5: 
      !>[X0: $tType] : ( X0 > X0 > X0 > $o ) ).

thf(func_def_75,type,
    sK6: set(b) ).

thf(func_def_76,type,
    sK7: set(b) ).

thf(func_def_77,type,
    sK8: set(b) > set(a) ).

thf(func_def_78,type,
    sK9: set(b) > set(a) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(func_def_99,type,
    sK30: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).

thf(func_def_100,type,
    sK31: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).

thf(func_def_101,type,
    sK32: 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).

thf(func_def_102,type,
    sK33: 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).

thf(func_def_103,type,
    sK34: 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(func_def_117,type,
    sK48: 
      !>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > X1 ) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(f3019,plain,
    $false,
    inference(avatar_sat_refutation,[],[f2187,f2192,f2197,f2202,f2207,f2209,f3018]) ).

thf(f3018,plain,
    ( ~ spl50_2
    | ~ spl50_3
    | ~ spl50_4
    | ~ spl50_5
    | ~ spl50_6 ),
    inference(avatar_contradiction_clause,[],[f3017]) ).

thf(f3017,plain,
    ( $false
    | ~ spl50_2
    | ~ spl50_3
    | ~ spl50_4
    | ~ spl50_5
    | ~ spl50_6 ),
    inference(subsumption_resolution,[],[f3016,f2206]) ).

thf(f2206,plain,
    ( ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),sK6) )
    | ~ spl50_6 ),
    inference(avatar_component_clause,[],[f2204]) ).

thf(f2204,plain,
    ( spl50_6
  <=> ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),sK6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_6])]) ).

thf(f3016,plain,
    ( ( $true != vAPP(set(b),$o,topolo1751647064n_open(b),sK6) )
    | ~ spl50_2
    | ~ spl50_3
    | ~ spl50_4
    | ~ spl50_5 ),
    inference(subsumption_resolution,[],[f3015,f2201]) ).

thf(f2201,plain,
    ( ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),sK7) )
    | ~ spl50_5 ),
    inference(avatar_component_clause,[],[f2199]) ).

thf(f2199,plain,
    ( spl50_5
  <=> ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),sK7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_5])]) ).

thf(f3015,plain,
    ( ( $true != vAPP(set(b),$o,topolo1751647064n_open(b),sK7) )
    | ( $true != vAPP(set(b),$o,topolo1751647064n_open(b),sK6) )
    | ~ spl50_2
    | ~ spl50_3
    | ~ spl50_4 ),
    inference(subsumption_resolution,[],[f3014,f2196]) ).

thf(f2196,plain,
    ( ( $true = vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),vAPP(a,b,f,x0)),sK6) )
    | ~ spl50_4 ),
    inference(avatar_component_clause,[],[f2194]) ).

thf(f2194,plain,
    ( spl50_4
  <=> ( $true = vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),vAPP(a,b,f,x0)),sK6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_4])]) ).

thf(f3014,plain,
    ( ( $true != vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),vAPP(a,b,f,x0)),sK6) )
    | ( $true != vAPP(set(b),$o,topolo1751647064n_open(b),sK7) )
    | ( $true != vAPP(set(b),$o,topolo1751647064n_open(b),sK6) )
    | ~ spl50_2
    | ~ spl50_3 ),
    inference(subsumption_resolution,[],[f3013,f2191]) ).

thf(f2191,plain,
    ( ( $true = vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),a2),sK7) )
    | ~ spl50_3 ),
    inference(avatar_component_clause,[],[f2189]) ).

thf(f2189,plain,
    ( spl50_3
  <=> ( $true = vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),a2),sK7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_3])]) ).

thf(f3013,plain,
    ( ( $true != vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),a2),sK7) )
    | ( $true != vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),vAPP(a,b,f,x0)),sK6) )
    | ( $true != vAPP(set(b),$o,topolo1751647064n_open(b),sK7) )
    | ( $true != vAPP(set(b),$o,topolo1751647064n_open(b),sK6) )
    | ~ spl50_2 ),
    inference(trivial_inequality_removal,[],[f3012]) ).

thf(f3012,plain,
    ( ( bot_bot(set(b)) != bot_bot(set(b)) )
    | ( $true != vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),a2),sK7) )
    | ( $true != vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),vAPP(a,b,f,x0)),sK6) )
    | ( $true != vAPP(set(b),$o,topolo1751647064n_open(b),sK7) )
    | ( $true != vAPP(set(b),$o,topolo1751647064n_open(b),sK6) )
    | ~ spl50_2 ),
    inference(superposition,[],[f2178,f2186]) ).

thf(f2186,plain,
    ( ( bot_bot(set(b)) = vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),sK6),sK7) )
    | ~ spl50_2 ),
    inference(avatar_component_clause,[],[f2184]) ).

thf(f2184,plain,
    ( spl50_2
  <=> ( bot_bot(set(b)) = vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),sK6),sK7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_2])]) ).

thf(f2178,plain,
    ! [X0: set(b),X1: set(b)] :
      ( ( bot_bot(set(b)) != vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),X0),X1) )
      | ( $true != vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),a2),X1) )
      | ( $true != vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),vAPP(a,b,f,x0)),X0) )
      | ( $true != vAPP(set(b),$o,topolo1751647064n_open(b),X1) )
      | ( $true != vAPP(set(b),$o,topolo1751647064n_open(b),X0) ) ),
    inference(subsumption_resolution,[],[f1421,f1420]) ).

thf(f1420,plain,
    thesis != $true,
    inference(cnf_transformation,[],[f1014]) ).

thf(f1014,plain,
    thesis != $true,
    inference(flattening,[],[f363]) ).

thf(f363,plain,
    thesis != $true,
    inference(fool_elimination,[],[f362]) ).

thf(f362,plain,
    ~ thesis,
    inference(rectify,[],[f359]) ).

thf(f359,negated_conjecture,
    ~ thesis,
    inference(negated_conjecture,[],[f358]) ).

thf(f358,conjecture,
    thesis,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).

thf(f1421,plain,
    ! [X0: set(b),X1: set(b)] :
      ( ( thesis = $true )
      | ( bot_bot(set(b)) != vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),X0),X1) )
      | ( $true != vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),a2),X1) )
      | ( $true != vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),vAPP(a,b,f,x0)),X0) )
      | ( $true != vAPP(set(b),$o,topolo1751647064n_open(b),X1) )
      | ( $true != vAPP(set(b),$o,topolo1751647064n_open(b),X0) ) ),
    inference(cnf_transformation,[],[f1075]) ).

thf(f1075,plain,
    ! [X0: set(b),X1: set(b)] :
      ( ( thesis = $true )
      | ( bot_bot(set(b)) != vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),X0),X1) )
      | ( $true != vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),a2),X1) )
      | ( $true != vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),vAPP(a,b,f,x0)),X0) )
      | ( $true != vAPP(set(b),$o,topolo1751647064n_open(b),X1) )
      | ( $true != vAPP(set(b),$o,topolo1751647064n_open(b),X0) ) ),
    inference(flattening,[],[f1074]) ).

thf(f1074,plain,
    ! [X0: set(b),X1: set(b)] :
      ( ( thesis = $true )
      | ( bot_bot(set(b)) != vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),X0),X1) )
      | ( $true != vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),a2),X1) )
      | ( $true != vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),vAPP(a,b,f,x0)),X0) )
      | ( $true != vAPP(set(b),$o,topolo1751647064n_open(b),X1) )
      | ( $true != vAPP(set(b),$o,topolo1751647064n_open(b),X0) ) ),
    inference(ennf_transformation,[],[f365]) ).

thf(f365,plain,
    ! [X0: set(b),X1: set(b)] :
      ( ( ( bot_bot(set(b)) = vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),X0),X1) )
        & ( $true = vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),a2),X1) )
        & ( $true = vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),vAPP(a,b,f,x0)),X0) )
        & ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),X1) )
        & ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),X0) ) )
     => ( thesis = $true ) ),
    inference(fool_elimination,[],[f364]) ).

thf(f364,plain,
    ! [X0: set(b),X1: set(b)] :
      ( ( ( bot_bot(set(b)) = vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),X0),X1) )
        & vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),a2),X1)
        & vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),vAPP(a,b,f,x0)),X0)
        & vAPP(set(b),$o,topolo1751647064n_open(b),X1)
        & vAPP(set(b),$o,topolo1751647064n_open(b),X0) )
     => thesis ),
    inference(rectify,[],[f357]) ).

thf(f357,axiom,
    ! [X19: set(b),X59: set(b)] :
      ( ( ( bot_bot(set(b)) = vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),X19),X59) )
        & vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),a2),X59)
        & vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),vAPP(a,b,f,x0)),X19)
        & vAPP(set(b),$o,topolo1751647064n_open(b),X59)
        & vAPP(set(b),$o,topolo1751647064n_open(b),X19) )
     => thesis ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(f2209,plain,
    spl50_1,
    inference(avatar_split_clause,[],[f2208,f2180]) ).

thf(f2180,plain,
    ( spl50_1
  <=> ( $true = sP0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl50_1])]) ).

thf(f2208,plain,
    $true = sP0,
    inference(subsumption_resolution,[],[f1431,f1425]) ).

thf(f1425,plain,
    a2 != vAPP(a,b,f,x0),
    inference(cnf_transformation,[],[f1]) ).

thf(f1,axiom,
    a2 != vAPP(a,b,f,x0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062A_A_092_060noteq_062_Af_Ax0_092_060close_062) ).

thf(f1431,plain,
    ( ( $true = sP0 )
    | ( a2 = vAPP(a,b,f,x0) ) ),
    inference(cnf_transformation,[],[f1341]) ).

thf(f1341,plain,
    ( ( $true = sP0 )
    | ( a2 = vAPP(a,b,f,x0) ) ),
    inference(definition_folding,[],[f1076,f1340]) ).

thf(f1340,plain,
    ( ? [X0: set(b),X1: set(b)] :
        ( ( bot_bot(set(b)) = vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),X0),X1) )
        & ( $true = vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),a2),X1) )
        & ( $true = vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),vAPP(a,b,f,x0)),X0) )
        & ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),X1) )
        & ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),X0) ) )
    | ( $true != sP0 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).

thf(f1076,plain,
    ( ? [X0: set(b),X1: set(b)] :
        ( ( bot_bot(set(b)) = vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),X0),X1) )
        & ( $true = vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),a2),X1) )
        & ( $true = vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),vAPP(a,b,f,x0)),X0) )
        & ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),X1) )
        & ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),X0) ) )
    | ( a2 = vAPP(a,b,f,x0) ) ),
    inference(ennf_transformation,[],[f373]) ).

thf(f373,plain,
    ( ( a2 != vAPP(a,b,f,x0) )
   => ? [X0: set(b),X1: set(b)] :
        ( ( bot_bot(set(b)) = vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),X0),X1) )
        & ( $true = vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),a2),X1) )
        & ( $true = vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),vAPP(a,b,f,x0)),X0) )
        & ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),X1) )
        & ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),X0) ) ) ),
    inference(fool_elimination,[],[f372]) ).

thf(f372,plain,
    ( ( a2 != vAPP(a,b,f,x0) )
   => ? [X0: set(b),X1: set(b)] :
        ( ( bot_bot(set(b)) = vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),X0),X1) )
        & vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),a2),X1)
        & vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),vAPP(a,b,f,x0)),X0)
        & vAPP(set(b),$o,topolo1751647064n_open(b),X1)
        & vAPP(set(b),$o,topolo1751647064n_open(b),X0) ) ),
    inference(rectify,[],[f2]) ).

thf(f2,axiom,
    ( ( a2 != vAPP(a,b,f,x0) )
   => ? [X2: set(b),X3: set(b)] :
        ( ( vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),X2),X3) = bot_bot(set(b)) )
        & vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),a2),X3)
        & vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),vAPP(a,b,f,x0)),X2)
        & vAPP(set(b),$o,topolo1751647064n_open(b),X3)
        & vAPP(set(b),$o,topolo1751647064n_open(b),X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062f_Ax0_A_092_060noteq_062_AA_A_092_060Longrightarrow_062_A_092_060exists_062U_AV_O_Aopen_AU_A_092_060and_062_Aopen_AV_A_092_060and_062_Af_Ax0_A_092_060in_062_AU_A_092_060and_062_AA_A_092_060in_062_AV_A_092_060and_062_AU_A_092_060inter_062_AV_A_061_A_123_125_092_060close_062) ).

thf(f2207,plain,
    ( ~ spl50_1
    | spl50_6 ),
    inference(avatar_split_clause,[],[f1426,f2204,f2180]) ).

thf(f1426,plain,
    ( ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),sK6) )
    | ( $true != sP0 ) ),
    inference(cnf_transformation,[],[f1351]) ).

thf(f1351,plain,
    ( ( ( bot_bot(set(b)) = vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),sK6),sK7) )
      & ( $true = vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),a2),sK7) )
      & ( $true = vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),vAPP(a,b,f,x0)),sK6) )
      & ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),sK7) )
      & ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),sK6) ) )
    | ( $true != sP0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f1349,f1350]) ).

thf(f1350,plain,
    ( ? [X0: set(b),X1: set(b)] :
        ( ( bot_bot(set(b)) = vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),X0),X1) )
        & ( $true = vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),a2),X1) )
        & ( $true = vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),vAPP(a,b,f,x0)),X0) )
        & ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),X1) )
        & ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),X0) ) )
   => ( ( bot_bot(set(b)) = vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),sK6),sK7) )
      & ( $true = vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),a2),sK7) )
      & ( $true = vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),vAPP(a,b,f,x0)),sK6) )
      & ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),sK7) )
      & ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),sK6) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f1349,plain,
    ( ? [X0: set(b),X1: set(b)] :
        ( ( bot_bot(set(b)) = vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),X0),X1) )
        & ( $true = vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),a2),X1) )
        & ( $true = vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),vAPP(a,b,f,x0)),X0) )
        & ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),X1) )
        & ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),X0) ) )
    | ( $true != sP0 ) ),
    inference(nnf_transformation,[],[f1340]) ).

thf(f2202,plain,
    ( ~ spl50_1
    | spl50_5 ),
    inference(avatar_split_clause,[],[f1427,f2199,f2180]) ).

thf(f1427,plain,
    ( ( $true = vAPP(set(b),$o,topolo1751647064n_open(b),sK7) )
    | ( $true != sP0 ) ),
    inference(cnf_transformation,[],[f1351]) ).

thf(f2197,plain,
    ( ~ spl50_1
    | spl50_4 ),
    inference(avatar_split_clause,[],[f1428,f2194,f2180]) ).

thf(f1428,plain,
    ( ( $true = vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),vAPP(a,b,f,x0)),sK6) )
    | ( $true != sP0 ) ),
    inference(cnf_transformation,[],[f1351]) ).

thf(f2192,plain,
    ( ~ spl50_1
    | spl50_3 ),
    inference(avatar_split_clause,[],[f1429,f2189,f2180]) ).

thf(f1429,plain,
    ( ( $true = vAPP(set(b),$o,vAPP(b,sTfun(set(b),$o),member(b),a2),sK7) )
    | ( $true != sP0 ) ),
    inference(cnf_transformation,[],[f1351]) ).

thf(f2187,plain,
    ( ~ spl50_1
    | spl50_2 ),
    inference(avatar_split_clause,[],[f1430,f2184,f2180]) ).

thf(f1430,plain,
    ( ( bot_bot(set(b)) = vAPP(set(b),set(b),vAPP(set(b),sTfun(set(b),set(b)),inf_inf(set(b)),sK6),sK7) )
    | ( $true != sP0 ) ),
    inference(cnf_transformation,[],[f1351]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem    : ITP115^2 : TPTP v8.2.0. Released v7.5.0.
% 0.05/0.11  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31  % Computer : n010.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit   : 300
% 0.10/0.32  % WCLimit    : 300
% 0.10/0.32  % DateTime   : Sat May 18 17:00:22 EDT 2024
% 0.10/0.32  % CPUTime    : 
% 0.10/0.32  % (9762)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.35  % (9767)WARNING: value z3 for option sas not known
% 0.10/0.35  % (9771)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)
% 0.10/0.35  % (9765)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.10/0.35  % (9770)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)
% 0.10/0.35  % (9769)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)
% 0.10/0.35  % (9766)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.10/0.35  % (9768)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.10/0.35  % (9767)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)
% 0.10/0.38  % (9771)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.16/0.39  % Exception at run slice level
% 0.16/0.39  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.39  % Exception at run slice level
% 0.16/0.39  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.39  % Exception at run slice level
% 0.16/0.39  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.40  % (9774)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.16/0.44  % (9775)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)
% 0.16/0.44  % (9776)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)
% 0.16/0.45  % (9774)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.16/0.45  % Exception at run slice level
% 0.16/0.45  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.16/0.47  % (9777)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)
% 0.16/0.49  % (9775)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.31/0.55  % (9776)First to succeed.
% 1.31/0.56  % (9776)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-9762"
% 1.31/0.56  % (9776)Refutation found. Thanks to Tanya!
% 1.31/0.56  % SZS status Theorem for theBenchmark
% 1.31/0.56  % SZS output start Proof for theBenchmark
% See solution above
% 1.31/0.56  % (9776)------------------------------
% 1.31/0.56  % (9776)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.31/0.56  % (9776)Termination reason: Refutation
% 1.31/0.56  
% 1.31/0.56  % (9776)Memory used [KB]: 2578
% 1.31/0.56  % (9776)Time elapsed: 0.156 s
% 1.31/0.56  % (9776)Instructions burned: 258 (million)
% 1.31/0.56  % (9762)Success in time 0.235 s
%------------------------------------------------------------------------------