TSTP Solution File: LCL962^16 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : LCL962^16 : TPTP v8.2.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n032.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 : Tue May 21 00:24:13 EDT 2024

% Result   : Theorem 0.15s 0.32s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :   32
% Syntax   : Number of formulae    :  118 (  46 unt;  20 typ;   0 def)
%            Number of atoms       :  604 ( 136 equ;   0 cnn)
%            Maximal formula atoms :    9 (   6 avg)
%            Number of connectives :  819 (  53   ~;  78   |;   0   &; 591   @)
%                                         (   3 <=>;  61  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   77 (  77   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   23 (  19 usr;  10 con; 0-3 aty)
%                                         (  33  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  156 ( 110   ^  45   !;   0   ?; 156   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

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

thf(type_def_6,type,
    mworld: $tType ).

thf(func_def_0,type,
    mworld: $tType ).

thf(func_def_1,type,
    mindex: $tType ).

thf(func_def_2,type,
    mrel: mindex > mworld > mworld > $o ).

thf(func_def_3,type,
    '#b': mindex ).

thf(func_def_4,type,
    '#a': mindex ).

thf(func_def_5,type,
    mactual: mworld ).

thf(func_def_6,type,
    mlocal: ( mworld > $o ) > $o ).

thf(func_def_8,type,
    mnot: ( mworld > $o ) > mworld > $o ).

thf(func_def_9,type,
    mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(func_def_10,type,
    mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(func_def_11,type,
    mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(func_def_12,type,
    mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(func_def_13,type,
    mbox: mindex > ( mworld > $o ) > mworld > $o ).

thf(func_def_14,type,
    mdia: mindex > ( mworld > $o ) > mworld > $o ).

thf(func_def_15,type,
    p: mworld > $o ).

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

thf(func_def_32,type,
    sK1: mworld > mworld ).

thf(func_def_33,type,
    sK2: mworld ).

thf(f188,plain,
    $false,
    inference(avatar_sat_refutation,[],[f111,f115,f160,f187]) ).

thf(f187,plain,
    ~ spl0_1,
    inference(avatar_contradiction_clause,[],[f186]) ).

thf(f186,plain,
    ( $false
    | ~ spl0_1 ),
    inference(trivial_inequality_removal,[],[f185]) ).

thf(f185,plain,
    ( ( $true = $false )
    | ~ spl0_1 ),
    inference(forward_demodulation,[],[f180,f84]) ).

thf(f84,plain,
    ( ( p @ mactual )
    = $false ),
    inference(not_proxy_clausification,[],[f83]) ).

thf(f83,plain,
    ( $true
    = ( ~ ( p @ mactual ) ) ),
    inference(beta_eta_normalization,[],[f74]) ).

thf(f74,plain,
    ( $true
    = ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
      @ ( ^ [Y0: mworld > $o,Y1: mworld] :
            ~ ( Y0 @ Y1 )
        @ p ) ) ),
    inference(definition_unfolding,[],[f66,f56,f65]) ).

thf(f65,plain,
    ( mnot
    = ( ^ [Y0: mworld > $o,Y1: mworld] :
          ~ ( Y0 @ Y1 ) ) ),
    inference(cnf_transformation,[],[f32]) ).

thf(f32,plain,
    ( mnot
    = ( ^ [Y0: mworld > $o,Y1: mworld] :
          ~ ( Y0 @ Y1 ) ) ),
    inference(fool_elimination,[],[f31]) ).

thf(f31,plain,
    ( ( ^ [X0: mworld > $o,X1: mworld] :
          ~ ( X0 @ X1 ) )
    = mnot ),
    inference(rectify,[],[f2]) ).

thf(f2,axiom,
    ( ( ^ [X1: mworld > $o,X2: mworld] :
          ~ ( X1 @ X2 ) )
    = mnot ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot_def) ).

thf(f56,plain,
    ( mlocal
    = ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
    inference(cnf_transformation,[],[f45]) ).

thf(f45,plain,
    ( mlocal
    = ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
    inference(fool_elimination,[],[f1]) ).

thf(f1,axiom,
    ( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
    = mlocal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def) ).

thf(f66,plain,
    ( ( mlocal @ ( mnot @ p ) )
    = $true ),
    inference(cnf_transformation,[],[f38]) ).

thf(f38,plain,
    ( ( mlocal @ ( mnot @ p ) )
    = $true ),
    inference(fool_elimination,[],[f37]) ).

thf(f37,plain,
    mlocal @ ( mnot @ p ),
    inference(rectify,[],[f15]) ).

thf(f15,axiom,
    mlocal @ ( mnot @ p ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_a_axiom_1) ).

thf(f180,plain,
    ( ( ( p @ mactual )
      = $true )
    | ~ spl0_1 ),
    inference(trivial_inequality_removal,[],[f178]) ).

thf(f178,plain,
    ( ( ( p @ mactual )
      = $true )
    | ( $true = $false )
    | ~ spl0_1 ),
    inference(superposition,[],[f60,f107]) ).

thf(f107,plain,
    ( ! [X2: mworld] :
        ( ( ( mrel @ '#b' @ mactual @ X2 )
          = $false )
        | ( ( p @ X2 )
          = $true ) )
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f106]) ).

thf(f106,plain,
    ( spl0_1
  <=> ! [X2: mworld] :
        ( ( ( mrel @ '#b' @ mactual @ X2 )
          = $false )
        | ( ( p @ X2 )
          = $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

thf(f60,plain,
    ! [X0: mworld] :
      ( ( mrel @ '#b' @ X0 @ X0 )
      = $true ),
    inference(cnf_transformation,[],[f47]) ).

thf(f47,plain,
    ! [X0: mworld] :
      ( ( mrel @ '#b' @ X0 @ X0 )
      = $true ),
    inference(fool_elimination,[],[f46]) ).

thf(f46,plain,
    ! [X0: mworld] : ( mrel @ '#b' @ X0 @ X0 ),
    inference(rectify,[],[f9]) ).

thf(f9,axiom,
    ! [X2: mworld] : ( mrel @ '#b' @ X2 @ X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','mrel_#b_reflexive') ).

thf(f160,plain,
    ( ~ spl0_2
    | ~ spl0_3 ),
    inference(avatar_contradiction_clause,[],[f159]) ).

thf(f159,plain,
    ( $false
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(trivial_inequality_removal,[],[f157]) ).

thf(f157,plain,
    ( ( $true = $false )
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(backward_demodulation,[],[f103,f154]) ).

thf(f154,plain,
    ( ( ( mrel @ '#a' @ mactual @ sK2 )
      = $false )
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(trivial_inequality_removal,[],[f153]) ).

thf(f153,plain,
    ( ( ( mrel @ '#a' @ mactual @ sK2 )
      = $false )
    | ( $true = $false )
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(forward_demodulation,[],[f152,f121]) ).

thf(f121,plain,
    ( ( ( p @ ( sK1 @ sK2 ) )
      = $false )
    | ~ spl0_2 ),
    inference(trivial_inequality_removal,[],[f117]) ).

thf(f117,plain,
    ( ( $true = $false )
    | ( ( p @ ( sK1 @ sK2 ) )
      = $false )
    | ~ spl0_2 ),
    inference(superposition,[],[f110,f103]) ).

thf(f110,plain,
    ( ! [X1: mworld] :
        ( ( ( mrel @ '#a' @ mactual @ X1 )
          = $false )
        | ( ( p @ ( sK1 @ X1 ) )
          = $false ) )
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f109]) ).

thf(f109,plain,
    ( spl0_2
  <=> ! [X1: mworld] :
        ( ( ( mrel @ '#a' @ mactual @ X1 )
          = $false )
        | ( ( p @ ( sK1 @ X1 ) )
          = $false ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

thf(f152,plain,
    ( ( ( mrel @ '#a' @ mactual @ sK2 )
      = $false )
    | ( ( p @ ( sK1 @ sK2 ) )
      = $true )
    | ~ spl0_3 ),
    inference(trivial_inequality_removal,[],[f148]) ).

thf(f148,plain,
    ( ( $true = $false )
    | ( ( mrel @ '#a' @ mactual @ sK2 )
      = $false )
    | ( ( p @ ( sK1 @ sK2 ) )
      = $true )
    | ~ spl0_3 ),
    inference(superposition,[],[f114,f133]) ).

thf(f133,plain,
    ! [X0: mworld] :
      ( ( ( mrel @ '#b' @ sK2 @ X0 )
        = $false )
      | ( $true
        = ( p @ X0 ) ) ),
    inference(trivial_inequality_removal,[],[f132]) ).

thf(f132,plain,
    ! [X0: mworld] :
      ( ( $true = $false )
      | ( ( mrel @ '#b' @ sK2 @ X0 )
        = $false )
      | ( $true
        = ( p @ X0 ) ) ),
    inference(forward_demodulation,[],[f129,f104]) ).

thf(f104,plain,
    ( $true
    = ( p @ sK2 ) ),
    inference(not_proxy_clausification,[],[f102]) ).

thf(f102,plain,
    ( ( ~ ( p @ sK2 ) )
    = $false ),
    inference(binary_proxy_clausification,[],[f101]) ).

thf(f101,plain,
    ( ( ( mrel @ '#a' @ mactual @ sK2 )
     => ~ ( p @ sK2 ) )
    = $false ),
    inference(beta_eta_normalization,[],[f100]) ).

thf(f100,plain,
    ( ( ^ [Y0: mworld] :
          ( ( mrel @ '#a' @ mactual @ Y0 )
         => ~ ( p @ Y0 ) )
      @ sK2 )
    = $false ),
    inference(sigma_clausification,[],[f99]) ).

thf(f99,plain,
    ( $true
   != ( !! @ mworld
      @ ^ [Y0: mworld] :
          ( ( mrel @ '#a' @ mactual @ Y0 )
         => ~ ( p @ Y0 ) ) ) ),
    inference(beta_eta_normalization,[],[f71]) ).

thf(f71,plain,
    ( $true
   != ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
      @ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
            ( !! @ mworld
            @ ^ [Y3: mworld] :
                ( ( mrel @ Y0 @ Y2 @ Y3 )
               => ( Y1 @ Y3 ) ) )
        @ '#a'
        @ ( ^ [Y0: mworld > $o,Y1: mworld] :
              ~ ( Y0 @ Y1 )
          @ p ) ) ) ),
    inference(definition_unfolding,[],[f59,f56,f67,f65]) ).

thf(f67,plain,
    ( mbox
    = ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
          ( !! @ mworld
          @ ^ [Y3: mworld] :
              ( ( mrel @ Y0 @ Y2 @ Y3 )
             => ( Y1 @ Y3 ) ) ) ) ),
    inference(cnf_transformation,[],[f44]) ).

thf(f44,plain,
    ( mbox
    = ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
          ( !! @ mworld
          @ ^ [Y3: mworld] :
              ( ( mrel @ Y0 @ Y2 @ Y3 )
             => ( Y1 @ Y3 ) ) ) ) ),
    inference(fool_elimination,[],[f43]) ).

thf(f43,plain,
    ( mbox
    = ( ^ [X0: mindex,X1: mworld > $o,X2: mworld] :
        ! [X3: mworld] :
          ( ( mrel @ X0 @ X2 @ X3 )
         => ( X1 @ X3 ) ) ) ),
    inference(rectify,[],[f7]) ).

thf(f7,axiom,
    ( mbox
    = ( ^ [X4: mindex,X0: mworld > $o,X2: mworld] :
        ! [X5: mworld] :
          ( ( mrel @ X4 @ X2 @ X5 )
         => ( X0 @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_def) ).

thf(f59,plain,
    ( ( mlocal @ ( mbox @ '#a' @ ( mnot @ p ) ) )
   != $true ),
    inference(cnf_transformation,[],[f50]) ).

thf(f50,plain,
    ( ( mlocal @ ( mbox @ '#a' @ ( mnot @ p ) ) )
   != $true ),
    inference(flattening,[],[f30]) ).

thf(f30,plain,
    ( ( mlocal @ ( mbox @ '#a' @ ( mnot @ p ) ) )
   != $true ),
    inference(fool_elimination,[],[f29]) ).

thf(f29,plain,
    ~ ( mlocal @ ( mbox @ '#a' @ ( mnot @ p ) ) ),
    inference(rectify,[],[f17]) ).

thf(f17,negated_conjecture,
    ~ ( mlocal @ ( mbox @ '#a' @ ( mnot @ p ) ) ),
    inference(negated_conjecture,[],[f16]) ).

thf(f16,conjecture,
    mlocal @ ( mbox @ '#a' @ ( mnot @ p ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).

thf(f129,plain,
    ! [X0: mworld] :
      ( ( ( p @ sK2 )
        = $false )
      | ( $true
        = ( p @ X0 ) )
      | ( ( mrel @ '#b' @ sK2 @ X0 )
        = $false ) ),
    inference(trivial_inequality_removal,[],[f125]) ).

thf(f125,plain,
    ! [X0: mworld] :
      ( ( ( mrel @ '#b' @ sK2 @ X0 )
        = $false )
      | ( $true
        = ( p @ X0 ) )
      | ( ( p @ sK2 )
        = $false )
      | ( $true = $false ) ),
    inference(superposition,[],[f82,f103]) ).

thf(f82,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ '#a' @ mactual @ X1 )
        = $false )
      | ( ( p @ X1 )
        = $false )
      | ( ( p @ X2 )
        = $true )
      | ( ( mrel @ '#b' @ X1 @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f81]) ).

thf(f81,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ '#a' @ mactual @ X1 )
        = $false )
      | ( ( p @ X1 )
        = $false )
      | ( $true
        = ( ( mrel @ '#b' @ X1 @ X2 )
         => ( p @ X2 ) ) ) ),
    inference(beta_eta_normalization,[],[f80]) ).

thf(f80,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ '#b' @ X1 @ Y0 )
             => ( p @ Y0 ) )
          @ X2 ) )
      | ( ( mrel @ '#a' @ mactual @ X1 )
        = $false )
      | ( ( p @ X1 )
        = $false ) ),
    inference(pi_clausification,[],[f79]) ).

thf(f79,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ '#b' @ X1 @ Y0 )
             => ( p @ Y0 ) ) ) )
      | ( ( mrel @ '#a' @ mactual @ X1 )
        = $false )
      | ( ( p @ X1 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f78]) ).

thf(f78,plain,
    ! [X1: mworld] :
      ( ( ( ( p @ X1 )
         => ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ '#b' @ X1 @ Y0 )
               => ( p @ Y0 ) ) ) )
        = $true )
      | ( ( mrel @ '#a' @ mactual @ X1 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f77]) ).

thf(f77,plain,
    ! [X1: mworld] :
      ( ( ( mrel @ '#a' @ mactual @ X1 )
       => ( ( p @ X1 )
         => ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ '#b' @ X1 @ Y0 )
               => ( p @ Y0 ) ) ) ) )
      = $true ),
    inference(beta_eta_normalization,[],[f76]) ).

thf(f76,plain,
    ! [X1: mworld] :
      ( $true
      = ( ^ [Y0: mworld] :
            ( ( mrel @ '#a' @ mactual @ Y0 )
           => ( ( p @ Y0 )
             => ( !! @ mworld
                @ ^ [Y1: mworld] :
                    ( ( mrel @ '#b' @ Y0 @ Y1 )
                   => ( p @ Y1 ) ) ) ) )
        @ X1 ) ),
    inference(pi_clausification,[],[f75]) ).

thf(f75,plain,
    ( $true
    = ( !! @ mworld
      @ ^ [Y0: mworld] :
          ( ( mrel @ '#a' @ mactual @ Y0 )
         => ( ( p @ Y0 )
           => ( !! @ mworld
              @ ^ [Y1: mworld] :
                  ( ( mrel @ '#b' @ Y0 @ Y1 )
                 => ( p @ Y1 ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f72]) ).

thf(f72,plain,
    ( $true
    = ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
      @ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
            ( !! @ mworld
            @ ^ [Y3: mworld] :
                ( ( mrel @ Y0 @ Y2 @ Y3 )
               => ( Y1 @ Y3 ) ) )
        @ '#a'
        @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
              ( ( Y0 @ Y2 )
             => ( Y1 @ Y2 ) )
          @ p
          @ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
                ( !! @ mworld
                @ ^ [Y3: mworld] :
                    ( ( mrel @ Y0 @ Y2 @ Y3 )
                   => ( Y1 @ Y3 ) ) )
            @ '#b'
            @ p ) ) ) ) ),
    inference(definition_unfolding,[],[f62,f56,f67,f70,f67]) ).

thf(f70,plain,
    ( mimplies
    = ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
          ( ( Y0 @ Y2 )
         => ( Y1 @ Y2 ) ) ) ),
    inference(cnf_transformation,[],[f40]) ).

thf(f40,plain,
    ( mimplies
    = ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
          ( ( Y0 @ Y2 )
         => ( Y1 @ Y2 ) ) ) ),
    inference(fool_elimination,[],[f39]) ).

thf(f39,plain,
    ( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
          ( ( X0 @ X2 )
         => ( X1 @ X2 ) ) )
    = mimplies ),
    inference(rectify,[],[f5]) ).

thf(f5,axiom,
    ( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
          ( ( X1 @ X2 )
         => ( X3 @ X2 ) ) )
    = mimplies ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies_def) ).

thf(f62,plain,
    ( ( mlocal @ ( mbox @ '#a' @ ( mimplies @ p @ ( mbox @ '#b' @ p ) ) ) )
    = $true ),
    inference(cnf_transformation,[],[f20]) ).

thf(f20,plain,
    ( ( mlocal @ ( mbox @ '#a' @ ( mimplies @ p @ ( mbox @ '#b' @ p ) ) ) )
    = $true ),
    inference(fool_elimination,[],[f19]) ).

thf(f19,plain,
    mlocal @ ( mbox @ '#a' @ ( mimplies @ p @ ( mbox @ '#b' @ p ) ) ),
    inference(rectify,[],[f13]) ).

thf(f13,axiom,
    mlocal @ ( mbox @ '#a' @ ( mimplies @ p @ ( mbox @ '#b' @ p ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_axiom_1) ).

thf(f114,plain,
    ( ! [X1: mworld] :
        ( ( $true
          = ( mrel @ '#b' @ X1 @ ( sK1 @ X1 ) ) )
        | ( ( mrel @ '#a' @ mactual @ X1 )
          = $false ) )
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f113]) ).

thf(f113,plain,
    ( spl0_3
  <=> ! [X1: mworld] :
        ( ( ( mrel @ '#a' @ mactual @ X1 )
          = $false )
        | ( $true
          = ( mrel @ '#b' @ X1 @ ( sK1 @ X1 ) ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

thf(f103,plain,
    ( $true
    = ( mrel @ '#a' @ mactual @ sK2 ) ),
    inference(binary_proxy_clausification,[],[f101]) ).

thf(f115,plain,
    ( spl0_1
    | spl0_3 ),
    inference(avatar_split_clause,[],[f98,f113,f106]) ).

thf(f98,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ '#a' @ mactual @ X1 )
        = $false )
      | ( ( p @ X2 )
        = $true )
      | ( $true
        = ( mrel @ '#b' @ X1 @ ( sK1 @ X1 ) ) )
      | ( ( mrel @ '#b' @ mactual @ X2 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f96]) ).

thf(f96,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ '#b' @ mactual @ X2 )
        = $false )
      | ( ( p @ X2 )
        = $true )
      | ( ( ( mrel @ '#b' @ X1 @ ( sK1 @ X1 ) )
         => ( p @ ( sK1 @ X1 ) ) )
        = $false )
      | ( ( mrel @ '#a' @ mactual @ X1 )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f95]) ).

thf(f95,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ( mrel @ '#b' @ mactual @ X2 )
         => ( p @ X2 ) )
        = $true )
      | ( ( mrel @ '#a' @ mactual @ X1 )
        = $false )
      | ( ( ( mrel @ '#b' @ X1 @ ( sK1 @ X1 ) )
         => ( p @ ( sK1 @ X1 ) ) )
        = $false ) ),
    inference(beta_eta_normalization,[],[f94]) ).

thf(f94,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ( mrel @ '#b' @ mactual @ X2 )
         => ( p @ X2 ) )
        = $true )
      | ( ( mrel @ '#a' @ mactual @ X1 )
        = $false )
      | ( ( ^ [Y0: mworld] :
              ( ( mrel @ '#b' @ X1 @ Y0 )
             => ( p @ Y0 ) )
          @ ( sK1 @ X1 ) )
        = $false ) ),
    inference(sigma_clausification,[],[f93]) ).

thf(f93,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ '#b' @ X1 @ Y0 )
             => ( p @ Y0 ) ) )
        = $false )
      | ( ( ( mrel @ '#b' @ mactual @ X2 )
         => ( p @ X2 ) )
        = $true )
      | ( ( mrel @ '#a' @ mactual @ X1 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f92]) ).

thf(f92,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( ^ [Y0: mworld] :
              ( ( mrel @ '#b' @ mactual @ Y0 )
             => ( p @ Y0 ) )
          @ X2 )
        = $true )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ '#b' @ X1 @ Y0 )
             => ( p @ Y0 ) ) )
        = $false )
      | ( ( mrel @ '#a' @ mactual @ X1 )
        = $false ) ),
    inference(pi_clausification,[],[f91]) ).

thf(f91,plain,
    ! [X1: mworld] :
      ( ( $true
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ '#b' @ mactual @ Y0 )
             => ( p @ Y0 ) ) ) )
      | ( ( mrel @ '#a' @ mactual @ X1 )
        = $false )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ '#b' @ X1 @ Y0 )
             => ( p @ Y0 ) ) )
        = $false ) ),
    inference(not_proxy_clausification,[],[f90]) ).

thf(f90,plain,
    ! [X1: mworld] :
      ( ( ( mrel @ '#a' @ mactual @ X1 )
        = $false )
      | ( ( ~ ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ '#b' @ mactual @ Y0 )
                 => ( p @ Y0 ) ) ) )
        = $false )
      | ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ '#b' @ X1 @ Y0 )
             => ( p @ Y0 ) ) )
        = $false ) ),
    inference(not_proxy_clausification,[],[f89]) ).

thf(f89,plain,
    ! [X1: mworld] :
      ( ( ( ~ ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ '#b' @ X1 @ Y0 )
                 => ( p @ Y0 ) ) ) )
        = $true )
      | ( ( mrel @ '#a' @ mactual @ X1 )
        = $false )
      | ( ( ~ ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ '#b' @ mactual @ Y0 )
                 => ( p @ Y0 ) ) ) )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f88]) ).

thf(f88,plain,
    ! [X1: mworld] :
      ( ( ( ( mrel @ '#a' @ mactual @ X1 )
         => ~ ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ '#b' @ X1 @ Y0 )
                 => ( p @ Y0 ) ) ) )
        = $true )
      | ( ( ~ ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ '#b' @ mactual @ Y0 )
                 => ( p @ Y0 ) ) ) )
        = $false ) ),
    inference(beta_eta_normalization,[],[f87]) ).

thf(f87,plain,
    ! [X1: mworld] :
      ( ( ( ~ ( !! @ mworld
              @ ^ [Y0: mworld] :
                  ( ( mrel @ '#b' @ mactual @ Y0 )
                 => ( p @ Y0 ) ) ) )
        = $false )
      | ( $true
        = ( ^ [Y0: mworld] :
              ( ( mrel @ '#a' @ mactual @ Y0 )
             => ~ ( !! @ mworld
                  @ ^ [Y1: mworld] :
                      ( ( mrel @ '#b' @ Y0 @ Y1 )
                     => ( p @ Y1 ) ) ) )
          @ X1 ) ) ),
    inference(pi_clausification,[],[f86]) ).

thf(f86,plain,
    ( ( $true
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ '#a' @ mactual @ Y0 )
           => ~ ( !! @ mworld
                @ ^ [Y1: mworld] :
                    ( ( mrel @ '#b' @ Y0 @ Y1 )
                   => ( p @ Y1 ) ) ) ) ) )
    | ( ( ~ ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ '#b' @ mactual @ Y0 )
               => ( p @ Y0 ) ) ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f85]) ).

thf(f85,plain,
    ( $true
    = ( ~ ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ '#b' @ mactual @ Y0 )
             => ( p @ Y0 ) ) )
     => ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ '#a' @ mactual @ Y0 )
           => ~ ( !! @ mworld
                @ ^ [Y1: mworld] :
                    ( ( mrel @ '#b' @ Y0 @ Y1 )
                   => ( p @ Y1 ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f73]) ).

thf(f73,plain,
    ( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
      @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
            ( ( Y0 @ Y2 )
           => ( Y1 @ Y2 ) )
        @ ( ^ [Y0: mworld > $o,Y1: mworld] :
              ~ ( Y0 @ Y1 )
          @ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
                ( !! @ mworld
                @ ^ [Y3: mworld] :
                    ( ( mrel @ Y0 @ Y2 @ Y3 )
                   => ( Y1 @ Y3 ) ) )
            @ '#b'
            @ p ) )
        @ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
              ( !! @ mworld
              @ ^ [Y3: mworld] :
                  ( ( mrel @ Y0 @ Y2 @ Y3 )
                 => ( Y1 @ Y3 ) ) )
          @ '#a'
          @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                ~ ( Y0 @ Y1 )
            @ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
                  ( !! @ mworld
                  @ ^ [Y3: mworld] :
                      ( ( mrel @ Y0 @ Y2 @ Y3 )
                     => ( Y1 @ Y3 ) ) )
              @ '#b'
              @ p ) ) ) ) )
    = $true ),
    inference(definition_unfolding,[],[f63,f56,f70,f65,f67,f67,f65,f67]) ).

thf(f63,plain,
    ( ( mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#b' @ p ) ) @ ( mbox @ '#a' @ ( mnot @ ( mbox @ '#b' @ p ) ) ) ) )
    = $true ),
    inference(cnf_transformation,[],[f34]) ).

thf(f34,plain,
    ( ( mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#b' @ p ) ) @ ( mbox @ '#a' @ ( mnot @ ( mbox @ '#b' @ p ) ) ) ) )
    = $true ),
    inference(fool_elimination,[],[f33]) ).

thf(f33,plain,
    mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#b' @ p ) ) @ ( mbox @ '#a' @ ( mnot @ ( mbox @ '#b' @ p ) ) ) ),
    inference(rectify,[],[f14]) ).

thf(f14,axiom,
    mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#b' @ p ) ) @ ( mbox @ '#a' @ ( mnot @ ( mbox @ '#b' @ p ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_axiom_2) ).

thf(f111,plain,
    ( spl0_1
    | spl0_2 ),
    inference(avatar_split_clause,[],[f97,f109,f106]) ).

thf(f97,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ( mrel @ '#b' @ mactual @ X2 )
        = $false )
      | ( ( p @ X2 )
        = $true )
      | ( ( mrel @ '#a' @ mactual @ X1 )
        = $false )
      | ( ( p @ ( sK1 @ X1 ) )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f96]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09  % Problem    : LCL962^16 : TPTP v8.2.0. Released v8.1.0.
% 0.08/0.10  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.11/0.30  % Computer : n032.cluster.edu
% 0.11/0.30  % Model    : x86_64 x86_64
% 0.11/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30  % Memory   : 8042.1875MB
% 0.11/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30  % CPULimit   : 300
% 0.11/0.30  % WCLimit    : 300
% 0.11/0.30  % DateTime   : Mon May 20 02:25:37 EDT 2024
% 0.11/0.30  % CPUTime    : 
% 0.11/0.30  This is a TH0_THM_EQU_NAR problem
% 0.11/0.30  Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.31  % (1231)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (3000ds/27Mi)
% 0.11/0.31  % (1232)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.11/0.31  % (1233)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.11/0.31  % (1230)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (3000ds/4Mi)
% 0.11/0.31  % (1234)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (3000ds/275Mi)
% 0.11/0.31  % (1235)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.11/0.31  % (1232)Instruction limit reached!
% 0.11/0.31  % (1232)------------------------------
% 0.11/0.31  % (1232)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.31  % (1232)Termination reason: Unknown
% 0.11/0.31  % (1232)Termination phase: Preprocessing 1
% 0.11/0.31  
% 0.11/0.31  % (1232)Memory used [KB]: 1023
% 0.11/0.31  % (1233)Instruction limit reached!
% 0.11/0.31  % (1233)------------------------------
% 0.11/0.31  % (1233)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.31  % (1233)Termination reason: Unknown
% 0.11/0.31  % (1233)Termination phase: Property scanning
% 0.11/0.31  
% 0.11/0.31  % (1233)Memory used [KB]: 1023
% 0.11/0.31  % (1233)Time elapsed: 0.002 s
% 0.11/0.31  % (1233)Instructions burned: 3 (million)
% 0.11/0.31  % (1233)------------------------------
% 0.11/0.31  % (1233)------------------------------
% 0.11/0.31  % (1232)Time elapsed: 0.002 s
% 0.11/0.31  % (1232)Instructions burned: 3 (million)
% 0.11/0.31  % (1232)------------------------------
% 0.11/0.31  % (1232)------------------------------
% 0.11/0.31  % (1236)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (3000ds/3Mi)
% 0.11/0.31  % (1234)Refutation not found, incomplete strategy
% 0.11/0.31  % (1234)------------------------------
% 0.11/0.31  % (1234)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.31  % (1234)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.31  
% 0.11/0.31  
% 0.11/0.31  % (1234)Memory used [KB]: 5500
% 0.11/0.31  % (1234)Time elapsed: 0.002 s
% 0.11/0.31  % (1234)Instructions burned: 3 (million)
% 0.11/0.31  % (1234)------------------------------
% 0.11/0.31  % (1234)------------------------------
% 0.11/0.31  % (1230)Instruction limit reached!
% 0.11/0.31  % (1230)------------------------------
% 0.11/0.31  % (1230)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.31  % (1230)Termination reason: Unknown
% 0.11/0.31  % (1230)Termination phase: Saturation
% 0.11/0.31  
% 0.11/0.31  % (1230)Memory used [KB]: 5500
% 0.11/0.31  % (1230)Time elapsed: 0.003 s
% 0.11/0.31  % (1230)Instructions burned: 5 (million)
% 0.11/0.31  % (1230)------------------------------
% 0.11/0.31  % (1230)------------------------------
% 0.11/0.31  % (1236)Instruction limit reached!
% 0.11/0.31  % (1236)------------------------------
% 0.11/0.31  % (1236)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.31  % (1236)Termination reason: Unknown
% 0.11/0.31  % (1236)Termination phase: Property scanning
% 0.11/0.31  
% 0.11/0.31  % (1236)Memory used [KB]: 1023
% 0.11/0.31  % (1236)Time elapsed: 0.002 s
% 0.11/0.31  % (1236)Instructions burned: 3 (million)
% 0.11/0.31  % (1236)------------------------------
% 0.11/0.31  % (1236)------------------------------
% 0.15/0.32  % (1231)First to succeed.
% 0.15/0.32  % (1231)Refutation found. Thanks to Tanya!
% 0.15/0.32  % SZS status Theorem for theBenchmark
% 0.15/0.32  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.32  % (1231)------------------------------
% 0.15/0.32  % (1231)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.32  % (1231)Termination reason: Refutation
% 0.15/0.32  
% 0.15/0.32  % (1231)Memory used [KB]: 5628
% 0.15/0.32  % (1231)Time elapsed: 0.009 s
% 0.15/0.32  % (1231)Instructions burned: 14 (million)
% 0.15/0.32  % (1231)------------------------------
% 0.15/0.32  % (1231)------------------------------
% 0.15/0.32  % (1228)Success in time 0.007 s
% 0.15/0.32  % Vampire---4.8 exiting
%------------------------------------------------------------------------------