TSTP Solution File: SYO901^11 by Vampire---4.8

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SYO901^11 : 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/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n014.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 09:09:38 EDT 2024

% Result   : Theorem 0.21s 0.40s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   29
% Syntax   : Number of formulae    :  113 (  51 unt;  19 typ;   0 def)
%            Number of atoms       :  535 ( 122 equ;   0 cnn)
%            Maximal formula atoms :   12 (   5 avg)
%            Number of connectives :  670 (  36   ~;  48   |;  11   &; 469   @)
%                                         (   5 <=>;  61  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   69 (  69   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   24 (  20 usr;  11 con; 0-3 aty)
%                                         (  40  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  148 ( 103   ^  44   !;   0   ?; 148   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

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

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

thf(func_def_1,type,
    mrel: mworld > mworld > $o ).

thf(func_def_2,type,
    mactual: mworld ).

thf(func_def_3,type,
    mlocal: ( mworld > $o ) > $o ).

thf(func_def_5,type,
    mnot: ( mworld > $o ) > mworld > $o ).

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

thf(func_def_7,type,
    mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

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

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

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

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

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

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

thf(func_def_28,type,
    ph1: 
      !>[X0: $tType] : X0 ).

thf(func_def_29,type,
    sK2: mworld ).

thf(func_def_30,type,
    sK3: mworld ).

thf(func_def_31,type,
    sK4: mworld ).

thf(func_def_32,type,
    sK5: mworld ).

thf(f416,plain,
    $false,
    inference(avatar_sat_refutation,[],[f308,f321,f385,f412,f415]) ).

thf(f415,plain,
    ( ~ spl0_13
    | ~ spl0_14
    | spl0_15 ),
    inference(avatar_contradiction_clause,[],[f414]) ).

thf(f414,plain,
    ( $false
    | ~ spl0_13
    | ~ spl0_14
    | spl0_15 ),
    inference(subsumption_resolution,[],[f413,f306]) ).

thf(f306,plain,
    ( ( $false
     != ( q @ sK5 ) )
    | spl0_15 ),
    inference(avatar_component_clause,[],[f305]) ).

thf(f305,plain,
    ( spl0_15
  <=> ( $false
      = ( q @ sK5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

thf(f413,plain,
    ( ( $false
      = ( q @ sK5 ) )
    | ~ spl0_13
    | ~ spl0_14 ),
    inference(forward_demodulation,[],[f381,f298]) ).

thf(f298,plain,
    ( ( $false
      = ( p @ sK5 ) )
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f296]) ).

thf(f296,plain,
    ( spl0_13
  <=> ( $false
      = ( p @ sK5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

thf(f381,plain,
    ( ( ( p @ sK5 )
      = ( q @ sK5 ) )
    | ~ spl0_14 ),
    inference(trivial_inequality_removal,[],[f368]) ).

thf(f368,plain,
    ( ( ( p @ sK5 )
      = ( q @ sK5 ) )
    | ( $false = $true )
    | ~ spl0_14 ),
    inference(superposition,[],[f341,f302]) ).

thf(f302,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK5 ) )
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f300]) ).

thf(f300,plain,
    ( spl0_14
  <=> ( $true
      = ( mrel @ sK2 @ sK5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

thf(f341,plain,
    ! [X0: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X0 ) )
      | ( ( p @ X0 )
        = ( q @ X0 ) ) ),
    inference(trivial_inequality_removal,[],[f326]) ).

thf(f326,plain,
    ! [X0: mworld] :
      ( ( $false = $true )
      | ( $false
        = ( mrel @ sK2 @ X0 ) )
      | ( ( p @ X0 )
        = ( q @ X0 ) ) ),
    inference(superposition,[],[f217,f76]) ).

thf(f76,plain,
    ! [X1: mworld] :
      ( ( $false
        = ( mrel @ mactual @ X1 ) )
      | ( ( p @ X1 )
        = ( q @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f75]) ).

thf(f75,plain,
    ! [X1: mworld] :
      ( ( $false
        = ( mrel @ mactual @ X1 ) )
      | ( ( ( p @ X1 )
          = ( q @ X1 ) )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f74]) ).

thf(f74,plain,
    ! [X1: mworld] :
      ( ( ( mrel @ mactual @ X1 )
       => ( ( p @ X1 )
          = ( q @ X1 ) ) )
      = $true ),
    inference(beta_eta_normalization,[],[f73]) ).

thf(f73,plain,
    ! [X1: mworld] :
      ( $true
      = ( ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( ( p @ Y0 )
              = ( q @ Y0 ) ) )
        @ X1 ) ),
    inference(pi_clausification,[],[f67]) ).

thf(f67,plain,
    ( $true
    = ( !! @ mworld
      @ ^ [Y0: mworld] :
          ( ( mrel @ mactual @ Y0 )
         => ( ( p @ Y0 )
            = ( q @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f65]) ).

thf(f65,plain,
    ( $false
    = ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( ( p @ Y0 )
              = ( q @ Y0 ) ) ) )
     => ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ mactual @ Y0 )
           => ( ( !! @ mworld
                @ ^ [Y1: mworld] :
                    ( ( mrel @ Y0 @ Y1 )
                   => ( p @ Y1 ) ) )
              = ( !! @ mworld
                @ ^ [Y1: mworld] :
                    ( ( mrel @ Y0 @ Y1 )
                   => ( q @ Y1 ) ) ) ) ) ) ) ),
    inference(not_proxy_clausification,[],[f47]) ).

thf(f47,plain,
    ( $true
    = ( ~ ( ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ mactual @ Y0 )
               => ( ( p @ Y0 )
                  = ( q @ Y0 ) ) ) )
         => ( !! @ mworld
            @ ^ [Y0: mworld] :
                ( ( mrel @ mactual @ Y0 )
               => ( ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( p @ Y1 ) ) )
                  = ( !! @ mworld
                    @ ^ [Y1: mworld] :
                        ( ( mrel @ Y0 @ Y1 )
                       => ( q @ Y1 ) ) ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f46]) ).

thf(f46,plain,
    ( ( ~ ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
          @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                ( ( Y0 @ Y2 )
               => ( Y1 @ Y2 ) )
            @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                  ( !! @ mworld
                  @ ^ [Y2: mworld] :
                      ( ( mrel @ Y1 @ Y2 )
                     => ( Y0 @ Y2 ) ) )
              @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                    ( ( Y0 @ Y2 )
                    = ( Y1 @ Y2 ) )
                @ p
                @ q ) )
            @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                  ( !! @ mworld
                  @ ^ [Y2: mworld] :
                      ( ( mrel @ Y1 @ Y2 )
                     => ( Y0 @ Y2 ) ) )
              @ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
                    ( ( Y0 @ Y2 )
                    = ( Y1 @ Y2 ) )
                @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                      ( !! @ mworld
                      @ ^ [Y2: mworld] :
                          ( ( mrel @ Y1 @ Y2 )
                         => ( Y0 @ Y2 ) ) )
                  @ p )
                @ ( ^ [Y0: mworld > $o,Y1: mworld] :
                      ( !! @ mworld
                      @ ^ [Y2: mworld] :
                          ( ( mrel @ Y1 @ Y2 )
                         => ( Y0 @ Y2 ) ) )
                  @ q ) ) ) ) ) )
    = $true ),
    inference(definition_unfolding,[],[f45,f36,f44,f37,f40,f37,f40,f37,f37]) ).

thf(f40,plain,
    ( mequiv
    = ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
          ( ( Y0 @ Y2 )
          = ( Y1 @ Y2 ) ) ) ),
    inference(cnf_transformation,[],[f27]) ).

thf(f27,plain,
    ( mequiv
    = ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
          ( ( Y0 @ Y2 )
          = ( Y1 @ Y2 ) ) ) ),
    inference(fool_elimination,[],[f26]) ).

thf(f26,plain,
    ( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
          ( ( X0 @ X2 )
        <=> ( X1 @ X2 ) ) )
    = mequiv ),
    inference(rectify,[],[f6]) ).

thf(f6,axiom,
    ( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
          ( ( X1 @ X2 )
        <=> ( X3 @ X2 ) ) )
    = mequiv ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv_def) ).

thf(f37,plain,
    ( mbox
    = ( ^ [Y0: mworld > $o,Y1: mworld] :
          ( !! @ mworld
          @ ^ [Y2: mworld] :
              ( ( mrel @ Y1 @ Y2 )
             => ( Y0 @ Y2 ) ) ) ) ),
    inference(cnf_transformation,[],[f34]) ).

thf(f34,plain,
    ( mbox
    = ( ^ [Y0: mworld > $o,Y1: mworld] :
          ( !! @ mworld
          @ ^ [Y2: mworld] :
              ( ( mrel @ Y1 @ Y2 )
             => ( Y0 @ Y2 ) ) ) ) ),
    inference(fool_elimination,[],[f33]) ).

thf(f33,plain,
    ( ( ^ [X0: mworld > $o,X1: mworld] :
        ! [X2: mworld] :
          ( ( mrel @ X1 @ X2 )
         => ( X0 @ X2 ) ) )
    = mbox ),
    inference(rectify,[],[f7]) ).

thf(f7,axiom,
    ( ( ^ [X0: mworld > $o,X2: mworld] :
        ! [X4: mworld] :
          ( ( mrel @ X2 @ X4 )
         => ( X0 @ X4 ) ) )
    = mbox ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).

thf(f44,plain,
    ( mimplies
    = ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
          ( ( Y0 @ Y2 )
         => ( Y1 @ Y2 ) ) ) ),
    inference(cnf_transformation,[],[f29]) ).

thf(f29,plain,
    ( mimplies
    = ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
          ( ( Y0 @ Y2 )
         => ( Y1 @ Y2 ) ) ) ),
    inference(fool_elimination,[],[f28]) ).

thf(f28,plain,
    ( mimplies
    = ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
          ( ( X0 @ X2 )
         => ( X1 @ X2 ) ) ) ),
    inference(rectify,[],[f5]) ).

thf(f5,axiom,
    ( mimplies
    = ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
          ( ( X1 @ X2 )
         => ( X3 @ X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def) ).

thf(f36,plain,
    ( mlocal
    = ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
    inference(cnf_transformation,[],[f30]) ).

thf(f30,plain,
    ( mlocal
    = ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
    inference(fool_elimination,[],[f1]) ).

thf(f1,axiom,
    ( mlocal
    = ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).

thf(f45,plain,
    ( ( ~ ( mlocal @ ( mimplies @ ( mbox @ ( mequiv @ p @ q ) ) @ ( mbox @ ( mequiv @ ( mbox @ p ) @ ( mbox @ q ) ) ) ) ) )
    = $true ),
    inference(cnf_transformation,[],[f23]) ).

thf(f23,plain,
    ( ( ~ ( mlocal @ ( mimplies @ ( mbox @ ( mequiv @ p @ q ) ) @ ( mbox @ ( mequiv @ ( mbox @ p ) @ ( mbox @ q ) ) ) ) ) )
    = $true ),
    inference(fool_elimination,[],[f22]) ).

thf(f22,plain,
    ~ ( mlocal @ ( mimplies @ ( mbox @ ( mequiv @ p @ q ) ) @ ( mbox @ ( mequiv @ ( mbox @ p ) @ ( mbox @ q ) ) ) ) ),
    inference(rectify,[],[f12]) ).

thf(f12,negated_conjecture,
    ~ ( mlocal @ ( mimplies @ ( mbox @ ( mequiv @ p @ q ) ) @ ( mbox @ ( mequiv @ ( mbox @ p ) @ ( mbox @ q ) ) ) ) ),
    inference(negated_conjecture,[],[f11]) ).

thf(f11,conjecture,
    mlocal @ ( mimplies @ ( mbox @ ( mequiv @ p @ q ) ) @ ( mbox @ ( mequiv @ ( mbox @ p ) @ ( mbox @ q ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).

thf(f217,plain,
    ! [X0: mworld] :
      ( ( $true
        = ( mrel @ mactual @ X0 ) )
      | ( $false
        = ( mrel @ sK2 @ X0 ) ) ),
    inference(trivial_inequality_removal,[],[f212]) ).

thf(f212,plain,
    ! [X0: mworld] :
      ( ( $false
        = ( mrel @ sK2 @ X0 ) )
      | ( $true
        = ( mrel @ mactual @ X0 ) )
      | ( $false = $true ) ),
    inference(superposition,[],[f55,f206]) ).

thf(f206,plain,
    ( $true
    = ( mrel @ sK2 @ mactual ) ),
    inference(trivial_inequality_removal,[],[f200]) ).

thf(f200,plain,
    ( ( $true
      = ( mrel @ sK2 @ mactual ) )
    | ( $false = $true ) ),
    inference(superposition,[],[f80,f57]) ).

thf(f57,plain,
    ! [X1: mworld] :
      ( $true
      = ( mrel @ X1 @ X1 ) ),
    inference(beta_eta_normalization,[],[f56]) ).

thf(f56,plain,
    ! [X1: mworld] :
      ( $true
      = ( ^ [Y0: mworld] : ( mrel @ Y0 @ Y0 )
        @ X1 ) ),
    inference(pi_clausification,[],[f43]) ).

thf(f43,plain,
    ( $true
    = ( !! @ mworld
      @ ^ [Y0: mworld] : ( mrel @ Y0 @ Y0 ) ) ),
    inference(cnf_transformation,[],[f25]) ).

thf(f25,plain,
    ( $true
    = ( !! @ mworld
      @ ^ [Y0: mworld] : ( mrel @ Y0 @ Y0 ) ) ),
    inference(fool_elimination,[],[f24]) ).

thf(f24,plain,
    ! [X0: mworld] : ( mrel @ X0 @ X0 ),
    inference(rectify,[],[f9]) ).

thf(f9,axiom,
    ! [X2: mworld] : ( mrel @ X2 @ X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).

thf(f80,plain,
    ! [X0: mworld] :
      ( ( $false
        = ( mrel @ mactual @ X0 ) )
      | ( ( mrel @ sK2 @ X0 )
        = $true ) ),
    inference(trivial_inequality_removal,[],[f77]) ).

thf(f77,plain,
    ! [X0: mworld] :
      ( ( $false
        = ( mrel @ mactual @ X0 ) )
      | ( ( mrel @ sK2 @ X0 )
        = $true )
      | ( $false = $true ) ),
    inference(superposition,[],[f71,f55]) ).

thf(f71,plain,
    ( $true
    = ( mrel @ mactual @ sK2 ) ),
    inference(binary_proxy_clausification,[],[f69]) ).

thf(f69,plain,
    ( $false
    = ( ( mrel @ mactual @ sK2 )
     => ( ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( p @ Y0 ) ) )
        = ( !! @ mworld
          @ ^ [Y0: mworld] :
              ( ( mrel @ sK2 @ Y0 )
             => ( q @ Y0 ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f68]) ).

thf(f68,plain,
    ( $false
    = ( ^ [Y0: mworld] :
          ( ( mrel @ mactual @ Y0 )
         => ( ( !! @ mworld
              @ ^ [Y1: mworld] :
                  ( ( mrel @ Y0 @ Y1 )
                 => ( p @ Y1 ) ) )
            = ( !! @ mworld
              @ ^ [Y1: mworld] :
                  ( ( mrel @ Y0 @ Y1 )
                 => ( q @ Y1 ) ) ) ) )
      @ sK2 ) ),
    inference(sigma_clausification,[],[f66]) ).

thf(f66,plain,
    ( $false
    = ( !! @ mworld
      @ ^ [Y0: mworld] :
          ( ( mrel @ mactual @ Y0 )
         => ( ( !! @ mworld
              @ ^ [Y1: mworld] :
                  ( ( mrel @ Y0 @ Y1 )
                 => ( p @ Y1 ) ) )
            = ( !! @ mworld
              @ ^ [Y1: mworld] :
                  ( ( mrel @ Y0 @ Y1 )
                 => ( q @ Y1 ) ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f65]) ).

thf(f55,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ X2 @ X3 ) )
      | ( ( mrel @ X3 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ X2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f54]) ).

thf(f54,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( $false
        = ( ( mrel @ X2 @ X1 )
          & ( mrel @ X2 @ X3 ) ) )
      | ( ( mrel @ X3 @ X1 )
        = $true ) ),
    inference(binary_proxy_clausification,[],[f53]) ).

thf(f53,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( $true
      = ( ( ( mrel @ X2 @ X1 )
          & ( mrel @ X2 @ X3 ) )
       => ( mrel @ X3 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f52]) ).

thf(f52,plain,
    ! [X2: mworld,X3: mworld,X1: mworld] :
      ( ( ^ [Y0: mworld] :
            ( ( ( mrel @ X2 @ X1 )
              & ( mrel @ X2 @ Y0 ) )
           => ( mrel @ Y0 @ X1 ) )
        @ X3 )
      = $true ),
    inference(pi_clausification,[],[f51]) ).

thf(f51,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( ( mrel @ X2 @ X1 )
              & ( mrel @ X2 @ Y0 ) )
           => ( mrel @ Y0 @ X1 ) ) )
      = $true ),
    inference(beta_eta_normalization,[],[f50]) ).

thf(f50,plain,
    ! [X2: mworld,X1: mworld] :
      ( ( ^ [Y0: mworld] :
            ( !! @ mworld
            @ ^ [Y1: mworld] :
                ( ( ( mrel @ Y0 @ X1 )
                  & ( mrel @ Y0 @ Y1 ) )
               => ( mrel @ Y1 @ X1 ) ) )
        @ X2 )
      = $true ),
    inference(pi_clausification,[],[f49]) ).

thf(f49,plain,
    ! [X1: mworld] :
      ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( !! @ mworld
            @ ^ [Y1: mworld] :
                ( ( ( mrel @ Y0 @ X1 )
                  & ( mrel @ Y0 @ Y1 ) )
               => ( mrel @ Y1 @ X1 ) ) ) )
      = $true ),
    inference(beta_eta_normalization,[],[f48]) ).

thf(f48,plain,
    ! [X1: mworld] :
      ( ( ^ [Y0: mworld] :
            ( !! @ mworld
            @ ^ [Y1: mworld] :
                ( !! @ mworld
                @ ^ [Y2: mworld] :
                    ( ( ( mrel @ Y1 @ Y0 )
                      & ( mrel @ Y1 @ Y2 ) )
                   => ( mrel @ Y2 @ Y0 ) ) ) )
        @ X1 )
      = $true ),
    inference(pi_clausification,[],[f41]) ).

thf(f41,plain,
    ( ( !! @ mworld
      @ ^ [Y0: mworld] :
          ( !! @ mworld
          @ ^ [Y1: mworld] :
              ( !! @ mworld
              @ ^ [Y2: mworld] :
                  ( ( ( mrel @ Y1 @ Y0 )
                    & ( mrel @ Y1 @ Y2 ) )
                 => ( mrel @ Y2 @ Y0 ) ) ) ) )
    = $true ),
    inference(cnf_transformation,[],[f19]) ).

thf(f19,plain,
    ( ( !! @ mworld
      @ ^ [Y0: mworld] :
          ( !! @ mworld
          @ ^ [Y1: mworld] :
              ( !! @ mworld
              @ ^ [Y2: mworld] :
                  ( ( ( mrel @ Y1 @ Y0 )
                    & ( mrel @ Y1 @ Y2 ) )
                 => ( mrel @ Y2 @ Y0 ) ) ) ) )
    = $true ),
    inference(fool_elimination,[],[f18]) ).

thf(f18,plain,
    ! [X0: mworld,X1: mworld,X2: mworld] :
      ( ( ( mrel @ X1 @ X0 )
        & ( mrel @ X1 @ X2 ) )
     => ( mrel @ X0 @ X2 ) ),
    inference(rectify,[],[f10]) ).

thf(f10,axiom,
    ! [X5: mworld,X2: mworld,X4: mworld] :
      ( ( ( mrel @ X2 @ X5 )
        & ( mrel @ X2 @ X4 ) )
     => ( mrel @ X5 @ X4 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_euclidean) ).

thf(f412,plain,
    ( ~ spl0_15
    | ~ spl0_13 ),
    inference(avatar_split_clause,[],[f411,f296,f305]) ).

thf(f411,plain,
    ( ( $false
     != ( q @ sK5 ) )
    | ~ spl0_13 ),
    inference(forward_demodulation,[],[f278,f298]) ).

thf(f278,plain,
    ( ( p @ sK5 )
   != ( q @ sK5 ) ),
    inference(equality_resolution,[],[f272]) ).

thf(f272,plain,
    ( ( ( mrel @ sK2 @ sK5 )
     => ( q @ sK5 ) )
   != ( ( mrel @ sK2 @ sK5 )
     => ( p @ sK5 ) ) ),
    inference(beta_eta_normalization,[],[f271]) ).

thf(f271,plain,
    ( ( ^ [Y0: mworld] :
          ( ( mrel @ sK2 @ Y0 )
         => ( p @ Y0 ) )
      @ sK5 )
   != ( ^ [Y0: mworld] :
          ( ( mrel @ sK2 @ Y0 )
         => ( q @ Y0 ) )
      @ sK5 ) ),
    inference(negative_extensionality,[],[f149]) ).

thf(f149,plain,
    ( ( ^ [Y0: mworld] :
          ( ( mrel @ sK2 @ Y0 )
         => ( p @ Y0 ) ) )
   != ( ^ [Y0: mworld] :
          ( ( mrel @ sK2 @ Y0 )
         => ( q @ Y0 ) ) ) ),
    inference(equality_resolution,[],[f72]) ).

thf(f72,plain,
    ( ( !! @ mworld
      @ ^ [Y0: mworld] :
          ( ( mrel @ sK2 @ Y0 )
         => ( q @ Y0 ) ) )
   != ( !! @ mworld
      @ ^ [Y0: mworld] :
          ( ( mrel @ sK2 @ Y0 )
         => ( p @ Y0 ) ) ) ),
    inference(binary_proxy_clausification,[],[f70]) ).

thf(f70,plain,
    ( $false
    = ( ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( p @ Y0 ) ) )
      = ( !! @ mworld
        @ ^ [Y0: mworld] :
            ( ( mrel @ sK2 @ Y0 )
           => ( q @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f69]) ).

thf(f385,plain,
    ( spl0_13
    | ~ spl0_14
    | ~ spl0_15 ),
    inference(avatar_split_clause,[],[f384,f305,f300,f296]) ).

thf(f384,plain,
    ( ( $false
      = ( p @ sK5 ) )
    | ~ spl0_14
    | ~ spl0_15 ),
    inference(forward_demodulation,[],[f380,f307]) ).

thf(f307,plain,
    ( ( $false
      = ( q @ sK5 ) )
    | ~ spl0_15 ),
    inference(avatar_component_clause,[],[f305]) ).

thf(f380,plain,
    ( ( ( p @ sK5 )
      = ( q @ sK5 ) )
    | ~ spl0_14 ),
    inference(trivial_inequality_removal,[],[f372]) ).

thf(f372,plain,
    ( ( ( p @ sK5 )
      = ( q @ sK5 ) )
    | ( $false = $true )
    | ~ spl0_14 ),
    inference(superposition,[],[f302,f341]) ).

thf(f321,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f281,f300]) ).

thf(f281,plain,
    ( $true
    = ( mrel @ sK2 @ sK5 ) ),
    inference(trivial_inequality_removal,[],[f280]) ).

thf(f280,plain,
    ( ( $true != $true )
    | ( $true
      = ( mrel @ sK2 @ sK5 ) ) ),
    inference(boolean_simplification,[],[f279]) ).

thf(f279,plain,
    ( ( $true
     != ( $false
       => ( q @ sK5 ) ) )
    | ( $true
      = ( mrel @ sK2 @ sK5 ) ) ),
    inference(boolean_simplification,[],[f276]) ).

thf(f276,plain,
    ( ( $true
      = ( mrel @ sK2 @ sK5 ) )
    | ( ( $false
       => ( q @ sK5 ) )
     != ( $false
       => ( p @ sK5 ) ) ) ),
    inference(superposition,[],[f272,f64]) ).

thf(f64,plain,
    ! [X0: mworld,X1: mworld] :
      ( ( $false
        = ( mrel @ X0 @ X1 ) )
      | ( ( mrel @ X0 @ X1 )
        = $true ) ),
    inference(trivial_inequality_removal,[],[f59]) ).

thf(f59,plain,
    ! [X0: mworld,X1: mworld] :
      ( ( ( mrel @ X0 @ X1 )
        = $true )
      | ( $false
        = ( mrel @ X0 @ X1 ) )
      | ( $false = $true ) ),
    inference(superposition,[],[f57,f55]) ).

thf(f308,plain,
    ( spl0_13
    | spl0_15 ),
    inference(avatar_split_clause,[],[f293,f305,f296]) ).

thf(f293,plain,
    ( ( $false
      = ( p @ sK5 ) )
    | ( $false
      = ( q @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f291]) ).

thf(f291,plain,
    ( ( $false
      = ( p @ sK5 ) )
    | ( $false
      = ( ( mrel @ sK2 @ sK5 )
       => ( q @ sK5 ) ) ) ),
    inference(binary_proxy_clausification,[],[f274]) ).

thf(f274,plain,
    ( ( $false
      = ( ( mrel @ sK2 @ sK5 )
       => ( p @ sK5 ) ) )
    | ( $false
      = ( ( mrel @ sK2 @ sK5 )
       => ( q @ sK5 ) ) ) ),
    inference(binary_proxy_clausification,[],[f272]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SYO901^11 : TPTP v8.2.0. Released v8.1.0.
% 0.06/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.13/0.34  % Computer : n014.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Mon May 20 10:04:08 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  This is a TH0_THM_EQU_NAR problem
% 0.13/0.35  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/sandbox2/benchmark/theBenchmark.p
% 0.13/0.37  % (22167)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 (2999ds/4Mi)
% 0.13/0.37  % (22167)Instruction limit reached!
% 0.13/0.37  % (22167)------------------------------
% 0.13/0.37  % (22167)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37  % (22167)Termination reason: Unknown
% 0.13/0.37  % (22167)Termination phase: Saturation
% 0.13/0.37  
% 0.13/0.37  % (22167)Memory used [KB]: 5500
% 0.13/0.37  % (22167)Time elapsed: 0.004 s
% 0.13/0.37  % (22167)Instructions burned: 4 (million)
% 0.13/0.37  % (22167)------------------------------
% 0.13/0.37  % (22167)------------------------------
% 0.13/0.37  % (22168)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 (2999ds/27Mi)
% 0.13/0.37  % (22166)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.37  % (22169)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.37  % (22172)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.13/0.37  % (22171)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 (2999ds/275Mi)
% 0.13/0.37  % (22173)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.13/0.37  % (22169)Instruction limit reached!
% 0.13/0.37  % (22169)------------------------------
% 0.13/0.37  % (22169)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37  % (22169)Termination reason: Unknown
% 0.13/0.37  % (22169)Termination phase: shuffling
% 0.13/0.37  
% 0.13/0.37  % (22169)Memory used [KB]: 895
% 0.13/0.37  % (22169)Time elapsed: 0.003 s
% 0.13/0.37  % (22169)Instructions burned: 2 (million)
% 0.13/0.37  % (22169)------------------------------
% 0.13/0.37  % (22169)------------------------------
% 0.13/0.37  % (22173)Instruction limit reached!
% 0.13/0.37  % (22173)------------------------------
% 0.13/0.37  % (22173)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37  % (22173)Termination reason: Unknown
% 0.13/0.37  % (22173)Termination phase: Saturation
% 0.13/0.37  
% 0.13/0.37  % (22173)Memory used [KB]: 1023
% 0.13/0.37  % (22173)Time elapsed: 0.004 s
% 0.13/0.37  % (22173)Instructions burned: 3 (million)
% 0.13/0.37  % (22173)------------------------------
% 0.13/0.37  % (22173)------------------------------
% 0.13/0.37  % (22171)Refutation not found, incomplete strategy
% 0.13/0.37  % (22171)------------------------------
% 0.13/0.37  % (22171)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37  % (22171)Termination reason: Refutation not found, incomplete strategy
% 0.13/0.37  
% 0.13/0.37  
% 0.13/0.37  % (22171)Memory used [KB]: 5500
% 0.13/0.37  % (22171)Time elapsed: 0.003 s
% 0.13/0.37  % (22171)Instructions burned: 3 (million)
% 0.13/0.37  % (22171)------------------------------
% 0.13/0.37  % (22171)------------------------------
% 0.13/0.37  % (22170)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 (2999ds/2Mi)
% 0.13/0.37  % (22170)Instruction limit reached!
% 0.13/0.37  % (22170)------------------------------
% 0.13/0.37  % (22170)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37  % (22170)Termination reason: Unknown
% 0.13/0.37  % (22170)Termination phase: Property scanning
% 0.13/0.37  
% 0.13/0.37  % (22170)Memory used [KB]: 895
% 0.13/0.37  % (22170)Time elapsed: 0.003 s
% 0.13/0.37  % (22170)Instructions burned: 2 (million)
% 0.13/0.37  % (22170)------------------------------
% 0.13/0.37  % (22170)------------------------------
% 0.13/0.38  % (22174)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.13/0.38  % (22172)Instruction limit reached!
% 0.13/0.38  % (22172)------------------------------
% 0.13/0.38  % (22172)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38  % (22172)Termination reason: Unknown
% 0.13/0.38  % (22172)Termination phase: Saturation
% 0.13/0.38  
% 0.13/0.38  % (22172)Memory used [KB]: 5628
% 0.13/0.38  % (22172)Time elapsed: 0.015 s
% 0.13/0.38  % (22172)Instructions burned: 18 (million)
% 0.13/0.38  % (22172)------------------------------
% 0.13/0.38  % (22172)------------------------------
% 0.13/0.38  % (22175)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.13/0.38  % (22176)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.13/0.39  % (22177)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.13/0.39  % (22176)Instruction limit reached!
% 0.13/0.39  % (22176)------------------------------
% 0.13/0.39  % (22176)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39  % (22176)Termination reason: Unknown
% 0.13/0.39  % (22176)Termination phase: Saturation
% 0.13/0.39  
% 0.13/0.39  % (22176)Memory used [KB]: 5500
% 0.13/0.39  % (22176)Time elapsed: 0.004 s
% 0.13/0.39  % (22176)Instructions burned: 4 (million)
% 0.13/0.39  % (22176)------------------------------
% 0.13/0.39  % (22176)------------------------------
% 0.13/0.39  % (22168)Instruction limit reached!
% 0.13/0.39  % (22168)------------------------------
% 0.13/0.39  % (22168)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39  % (22168)Termination reason: Unknown
% 0.13/0.39  % (22168)Termination phase: Saturation
% 0.13/0.39  % (22178)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.13/0.39  
% 0.13/0.39  % (22168)Memory used [KB]: 5628
% 0.13/0.39  % (22168)Time elapsed: 0.022 s
% 0.13/0.39  % (22168)Instructions burned: 28 (million)
% 0.13/0.39  % (22168)------------------------------
% 0.13/0.39  % (22168)------------------------------
% 0.13/0.39  % (22178)Instruction limit reached!
% 0.13/0.39  % (22178)------------------------------
% 0.13/0.39  % (22178)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39  % (22178)Termination reason: Unknown
% 0.13/0.39  % (22178)Termination phase: Saturation
% 0.13/0.39  
% 0.13/0.39  % (22178)Memory used [KB]: 1023
% 0.13/0.39  % (22178)Time elapsed: 0.007 s
% 0.13/0.39  % (22178)Instructions burned: 7 (million)
% 0.13/0.39  % (22178)------------------------------
% 0.13/0.39  % (22178)------------------------------
% 0.13/0.39  % (22175)Instruction limit reached!
% 0.13/0.39  % (22175)------------------------------
% 0.13/0.39  % (22175)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39  % (22175)Termination reason: Unknown
% 0.13/0.39  % (22175)Termination phase: Saturation
% 0.13/0.39  
% 0.13/0.39  % (22175)Memory used [KB]: 5628
% 0.13/0.39  % (22175)Time elapsed: 0.013 s
% 0.13/0.39  % (22175)Instructions burned: 16 (million)
% 0.13/0.39  % (22175)------------------------------
% 0.13/0.39  % (22175)------------------------------
% 0.21/0.40  % (22179)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.21/0.40  % (22174)First to succeed.
% 0.21/0.40  % (22174)Refutation found. Thanks to Tanya!
% 0.21/0.40  % SZS status Theorem for theBenchmark
% 0.21/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.40  % (22174)------------------------------
% 0.21/0.40  % (22174)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40  % (22174)Termination reason: Refutation
% 0.21/0.40  
% 0.21/0.40  % (22174)Memory used [KB]: 5756
% 0.21/0.40  % (22174)Time elapsed: 0.020 s
% 0.21/0.40  % (22174)Instructions burned: 30 (million)
% 0.21/0.40  % (22174)------------------------------
% 0.21/0.40  % (22174)------------------------------
% 0.21/0.40  % (22165)Success in time 0.049 s
% 0.21/0.40  % Vampire---4.8 exiting
%------------------------------------------------------------------------------