TSTP Solution File: NUM705^1 by Vampire---4.8

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : NUM705^1 : TPTP v8.2.0. Released v3.7.0.
% 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 : n018.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 01:45:03 EDT 2024

% Result   : Theorem 0.24s 0.41s
% Output   : Refutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   81 (   5 unt;  11 typ;   0 def)
%            Number of atoms       :  560 ( 144 equ;   0 cnn)
%            Maximal formula atoms :   14 (   8 avg)
%            Number of connectives :  747 ( 174   ~;  86   |;  24   &; 342   @)
%                                         (   6 <=>;  97  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  15 usr;  13 con; 0-2 aty)
%                                         (  18  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  124 (  41   ^  74   !;   8   ?; 124   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

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

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

thf(func_def_1,type,
    p: nat > $o ).

thf(func_def_2,type,
    some: ( nat > $o ) > $o ).

thf(func_def_4,type,
    lessis: nat > nat > $o ).

thf(func_def_5,type,
    more: nat > nat > $o ).

thf(func_def_14,type,
    sK0: nat ).

thf(func_def_15,type,
    sK1: nat ).

thf(func_def_17,type,
    ph3: 
      !>[X0: $tType] : X0 ).

thf(func_def_18,type,
    sK4: nat ).

thf(func_def_19,type,
    sK5: nat ).

thf(f120,plain,
    $false,
    inference(avatar_sat_refutation,[],[f53,f58,f62,f67,f72,f103,f119]) ).

thf(f119,plain,
    ( ~ spl2_2
    | ~ spl2_3
    | ~ spl2_4
    | ~ spl2_5
    | spl2_6 ),
    inference(avatar_contradiction_clause,[],[f118]) ).

thf(f118,plain,
    ( $false
    | ~ spl2_2
    | ~ spl2_3
    | ~ spl2_4
    | ~ spl2_5
    | spl2_6 ),
    inference(subsumption_resolution,[],[f117,f113]) ).

thf(f113,plain,
    ( ( ( lessis @ sK1 @ sK0 )
     != $true )
    | ~ spl2_2
    | ~ spl2_3
    | spl2_6 ),
    inference(trivial_inequality_removal,[],[f112]) ).

thf(f112,plain,
    ( ( $true != $true )
    | ( ( lessis @ sK1 @ sK0 )
     != $true )
    | ~ spl2_2
    | ~ spl2_3
    | spl2_6 ),
    inference(superposition,[],[f42,f111]) ).

thf(f111,plain,
    ( ( ( more @ sK1 @ sK0 )
      = $true )
    | ~ spl2_2
    | ~ spl2_3
    | spl2_6 ),
    inference(subsumption_resolution,[],[f110,f71]) ).

thf(f71,plain,
    ( ( sK1 != sK0 )
    | spl2_6 ),
    inference(avatar_component_clause,[],[f69]) ).

thf(f69,plain,
    ( spl2_6
  <=> ( sK1 = sK0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).

thf(f110,plain,
    ( ( sK1 = sK0 )
    | ( ( more @ sK1 @ sK0 )
      = $true )
    | ~ spl2_2
    | ~ spl2_3 ),
    inference(trivial_inequality_removal,[],[f109]) ).

thf(f109,plain,
    ( ( $true != $true )
    | ( ( more @ sK1 @ sK0 )
      = $true )
    | ( sK1 = sK0 )
    | ~ spl2_2
    | ~ spl2_3 ),
    inference(superposition,[],[f44,f107]) ).

thf(f107,plain,
    ( ( $true
      = ( lessis @ sK0 @ sK1 ) )
    | ~ spl2_2
    | ~ spl2_3 ),
    inference(trivial_inequality_removal,[],[f104]) ).

thf(f104,plain,
    ( ( $true
      = ( lessis @ sK0 @ sK1 ) )
    | ( $true != $true )
    | ~ spl2_2
    | ~ spl2_3 ),
    inference(superposition,[],[f52,f57]) ).

thf(f57,plain,
    ( ( ( p @ sK1 )
      = $true )
    | ~ spl2_3 ),
    inference(avatar_component_clause,[],[f55]) ).

thf(f55,plain,
    ( spl2_3
  <=> ( ( p @ sK1 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).

thf(f52,plain,
    ( ! [X2: nat] :
        ( ( ( p @ X2 )
         != $true )
        | ( $true
          = ( lessis @ sK0 @ X2 ) ) )
    | ~ spl2_2 ),
    inference(avatar_component_clause,[],[f51]) ).

thf(f51,plain,
    ( spl2_2
  <=> ! [X2: nat] :
        ( ( ( p @ X2 )
         != $true )
        | ( $true
          = ( lessis @ sK0 @ X2 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

thf(f44,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( lessis @ X0 @ X1 )
       != $true )
      | ( ( more @ X1 @ X0 )
        = $true )
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f28]) ).

thf(f28,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( lessis @ X0 @ X1 )
       != $true )
      | ( X0 = X1 )
      | ( ( more @ X1 @ X0 )
        = $true ) ),
    inference(flattening,[],[f27]) ).

thf(f27,plain,
    ! [X0: nat,X1: nat] :
      ( ( X0 = X1 )
      | ( ( more @ X1 @ X0 )
        = $true )
      | ( ( lessis @ X0 @ X1 )
       != $true ) ),
    inference(ennf_transformation,[],[f23]) ).

thf(f23,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( lessis @ X0 @ X1 )
        = $true )
     => ( ( ( more @ X1 @ X0 )
         != $true )
       => ( X0 = X1 ) ) ),
    inference(flattening,[],[f14]) ).

thf(f14,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( lessis @ X0 @ X1 )
        = $true )
     => ( ( ( more @ X1 @ X0 )
         != $true )
       => ( X0 = X1 ) ) ),
    inference(fool_elimination,[],[f13]) ).

thf(f13,plain,
    ! [X0: nat,X1: nat] :
      ( ( lessis @ X0 @ X1 )
     => ( ~ ( more @ X1 @ X0 )
       => ( X0 = X1 ) ) ),
    inference(rectify,[],[f2]) ).

thf(f2,axiom,
    ! [X0: nat,X1: nat] :
      ( ( lessis @ X0 @ X1 )
     => ( ~ ( more @ X1 @ X0 )
       => ( X0 = X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz14) ).

thf(f42,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( more @ X0 @ X1 )
       != $true )
      | ( ( lessis @ X0 @ X1 )
       != $true ) ),
    inference(cnf_transformation,[],[f31]) ).

thf(f31,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( lessis @ X0 @ X1 )
       != $true )
      | ( ( more @ X0 @ X1 )
       != $true ) ),
    inference(ennf_transformation,[],[f24]) ).

thf(f24,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( lessis @ X0 @ X1 )
        = $true )
     => ( ( more @ X0 @ X1 )
       != $true ) ),
    inference(flattening,[],[f18]) ).

thf(f18,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( lessis @ X0 @ X1 )
        = $true )
     => ( ( more @ X0 @ X1 )
       != $true ) ),
    inference(fool_elimination,[],[f17]) ).

thf(f17,plain,
    ! [X0: nat,X1: nat] :
      ( ( lessis @ X0 @ X1 )
     => ~ ( more @ X0 @ X1 ) ),
    inference(rectify,[],[f4]) ).

thf(f4,axiom,
    ! [X0: nat,X1: nat] :
      ( ( lessis @ X0 @ X1 )
     => ~ ( more @ X0 @ X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10d) ).

thf(f117,plain,
    ( ( ( lessis @ sK1 @ sK0 )
      = $true )
    | ~ spl2_4
    | ~ spl2_5 ),
    inference(trivial_inequality_removal,[],[f115]) ).

thf(f115,plain,
    ( ( $true != $true )
    | ( ( lessis @ sK1 @ sK0 )
      = $true )
    | ~ spl2_4
    | ~ spl2_5 ),
    inference(superposition,[],[f61,f66]) ).

thf(f66,plain,
    ( ( ( p @ sK0 )
      = $true )
    | ~ spl2_5 ),
    inference(avatar_component_clause,[],[f64]) ).

thf(f64,plain,
    ( spl2_5
  <=> ( ( p @ sK0 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).

thf(f61,plain,
    ( ! [X3: nat] :
        ( ( $true
         != ( p @ X3 ) )
        | ( $true
          = ( lessis @ sK1 @ X3 ) ) )
    | ~ spl2_4 ),
    inference(avatar_component_clause,[],[f60]) ).

thf(f60,plain,
    ( spl2_4
  <=> ! [X3: nat] :
        ( ( $true
          = ( lessis @ sK1 @ X3 ) )
        | ( $true
         != ( p @ X3 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).

thf(f103,plain,
    spl2_1,
    inference(avatar_contradiction_clause,[],[f102]) ).

thf(f102,plain,
    ( $false
    | spl2_1 ),
    inference(subsumption_resolution,[],[f101,f49]) ).

thf(f49,plain,
    ( ( ( some
        @ ^ [Y0: nat] :
            ~ ( ( !! @ nat
                @ ^ [Y1: nat] :
                    ( ( p @ Y1 )
                   => ( lessis @ Y0 @ Y1 ) ) )
             => ~ ( p @ Y0 ) ) )
     != $true )
    | spl2_1 ),
    inference(avatar_component_clause,[],[f47]) ).

thf(f47,plain,
    ( spl2_1
  <=> ( ( some
        @ ^ [Y0: nat] :
            ~ ( ( !! @ nat
                @ ^ [Y1: nat] :
                    ( ( p @ Y1 )
                   => ( lessis @ Y0 @ Y1 ) ) )
             => ~ ( p @ Y0 ) ) )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).

thf(f101,plain,
    ( ( some
      @ ^ [Y0: nat] :
          ~ ( ( !! @ nat
              @ ^ [Y1: nat] :
                  ( ( p @ Y1 )
                 => ( lessis @ Y0 @ Y1 ) ) )
           => ~ ( p @ Y0 ) ) )
    = $true ),
    inference(trivial_inequality_removal,[],[f100]) ).

thf(f100,plain,
    ( ( ( some
        @ ^ [Y0: nat] :
            ~ ( ( !! @ nat
                @ ^ [Y1: nat] :
                    ( ( p @ Y1 )
                   => ( lessis @ Y0 @ Y1 ) ) )
             => ~ ( p @ Y0 ) ) )
      = $true )
    | ( $true != $true ) ),
    inference(superposition,[],[f41,f43]) ).

thf(f43,plain,
    ( ( some @ p )
    = $true ),
    inference(cnf_transformation,[],[f16]) ).

thf(f16,plain,
    ( ( some @ p )
    = $true ),
    inference(fool_elimination,[],[f15]) ).

thf(f15,plain,
    some @ p,
    inference(rectify,[],[f1]) ).

thf(f1,axiom,
    some @ p,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s) ).

thf(f41,plain,
    ! [X0: nat > $o] :
      ( ( ( some @ X0 )
       != $true )
      | ( $true
        = ( some
          @ ^ [Y0: nat] :
              ~ ( ( !! @ nat
                  @ ^ [Y1: nat] :
                      ( ( X0 @ Y1 )
                     => ( lessis @ Y0 @ Y1 ) ) )
               => ~ ( X0 @ Y0 ) ) ) ) ),
    inference(cnf_transformation,[],[f30]) ).

thf(f30,plain,
    ! [X0: nat > $o] :
      ( ( $true
        = ( some
          @ ^ [Y0: nat] :
              ~ ( ( !! @ nat
                  @ ^ [Y1: nat] :
                      ( ( X0 @ Y1 )
                     => ( lessis @ Y0 @ Y1 ) ) )
               => ~ ( X0 @ Y0 ) ) ) )
      | ( ( some @ X0 )
       != $true ) ),
    inference(ennf_transformation,[],[f20]) ).

thf(f20,plain,
    ! [X0: nat > $o] :
      ( ( ( some @ X0 )
        = $true )
     => ( $true
        = ( some
          @ ^ [Y0: nat] :
              ~ ( ( !! @ nat
                  @ ^ [Y1: nat] :
                      ( ( X0 @ Y1 )
                     => ( lessis @ Y0 @ Y1 ) ) )
               => ~ ( X0 @ Y0 ) ) ) ) ),
    inference(fool_elimination,[],[f19]) ).

thf(f19,plain,
    ! [X0: nat > $o] :
      ( ( some @ X0 )
     => ( some
        @ ^ [X1: nat] :
            ~ ( ! [X2: nat] :
                  ( ( X0 @ X2 )
                 => ( lessis @ X1 @ X2 ) )
             => ~ ( X0 @ X1 ) ) ) ),
    inference(rectify,[],[f5]) ).

thf(f5,axiom,
    ! [X3: nat > $o] :
      ( ( some @ X3 )
     => ( some
        @ ^ [X0: nat] :
            ~ ( ! [X4: nat] :
                  ( ( X3 @ X4 )
                 => ( lessis @ X0 @ X4 ) )
             => ~ ( X3 @ X0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz27) ).

thf(f72,plain,
    ( ~ spl2_6
    | ~ spl2_1 ),
    inference(avatar_split_clause,[],[f38,f47,f69]) ).

thf(f38,plain,
    ( ( ( some
        @ ^ [Y0: nat] :
            ~ ( ( !! @ nat
                @ ^ [Y1: nat] :
                    ( ( p @ Y1 )
                   => ( lessis @ Y0 @ Y1 ) ) )
             => ~ ( p @ Y0 ) ) )
     != $true )
    | ( sK1 != sK0 ) ),
    inference(cnf_transformation,[],[f34]) ).

thf(f34,plain,
    ( ( ! [X2: nat] :
          ( ( ( p @ X2 )
           != $true )
          | ( $true
            = ( lessis @ sK0 @ X2 ) ) )
      & ( ( p @ sK0 )
        = $true )
      & ( sK1 != sK0 )
      & ! [X3: nat] :
          ( ( $true
            = ( lessis @ sK1 @ X3 ) )
          | ( $true
           != ( p @ X3 ) ) )
      & ( ( p @ sK1 )
        = $true ) )
    | ( ( some
        @ ^ [Y0: nat] :
            ~ ( ( !! @ nat
                @ ^ [Y1: nat] :
                    ( ( p @ Y1 )
                   => ( lessis @ Y0 @ Y1 ) ) )
             => ~ ( p @ Y0 ) ) )
     != $true ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f32,f33]) ).

thf(f33,plain,
    ( ? [X0: nat,X1: nat] :
        ( ! [X2: nat] :
            ( ( ( p @ X2 )
             != $true )
            | ( ( lessis @ X0 @ X2 )
              = $true ) )
        & ( ( p @ X0 )
          = $true )
        & ( X0 != X1 )
        & ! [X3: nat] :
            ( ( ( lessis @ X1 @ X3 )
              = $true )
            | ( $true
             != ( p @ X3 ) ) )
        & ( ( p @ X1 )
          = $true ) )
   => ( ! [X2: nat] :
          ( ( ( p @ X2 )
           != $true )
          | ( $true
            = ( lessis @ sK0 @ X2 ) ) )
      & ( ( p @ sK0 )
        = $true )
      & ( sK1 != sK0 )
      & ! [X3: nat] :
          ( ( $true
            = ( lessis @ sK1 @ X3 ) )
          | ( $true
           != ( p @ X3 ) ) )
      & ( ( p @ sK1 )
        = $true ) ) ),
    introduced(choice_axiom,[]) ).

thf(f32,plain,
    ( ? [X0: nat,X1: nat] :
        ( ! [X2: nat] :
            ( ( ( p @ X2 )
             != $true )
            | ( ( lessis @ X0 @ X2 )
              = $true ) )
        & ( ( p @ X0 )
          = $true )
        & ( X0 != X1 )
        & ! [X3: nat] :
            ( ( ( lessis @ X1 @ X3 )
              = $true )
            | ( $true
             != ( p @ X3 ) ) )
        & ( ( p @ X1 )
          = $true ) )
    | ( ( some
        @ ^ [Y0: nat] :
            ~ ( ( !! @ nat
                @ ^ [Y1: nat] :
                    ( ( p @ Y1 )
                   => ( lessis @ Y0 @ Y1 ) ) )
             => ~ ( p @ Y0 ) ) )
     != $true ) ),
    inference(rectify,[],[f26]) ).

thf(f26,plain,
    ( ? [X0: nat,X1: nat] :
        ( ! [X3: nat] :
            ( ( $true
             != ( p @ X3 ) )
            | ( ( lessis @ X0 @ X3 )
              = $true ) )
        & ( ( p @ X0 )
          = $true )
        & ( X0 != X1 )
        & ! [X2: nat] :
            ( ( ( lessis @ X1 @ X2 )
              = $true )
            | ( ( p @ X2 )
             != $true ) )
        & ( ( p @ X1 )
          = $true ) )
    | ( ( some
        @ ^ [Y0: nat] :
            ~ ( ( !! @ nat
                @ ^ [Y1: nat] :
                    ( ( p @ Y1 )
                   => ( lessis @ Y0 @ Y1 ) ) )
             => ~ ( p @ Y0 ) ) )
     != $true ) ),
    inference(flattening,[],[f25]) ).

thf(f25,plain,
    ( ( ( some
        @ ^ [Y0: nat] :
            ~ ( ( !! @ nat
                @ ^ [Y1: nat] :
                    ( ( p @ Y1 )
                   => ( lessis @ Y0 @ Y1 ) ) )
             => ~ ( p @ Y0 ) ) )
     != $true )
    | ? [X0: nat,X1: nat] :
        ( ( X0 != X1 )
        & ( ( p @ X0 )
          = $true )
        & ! [X3: nat] :
            ( ( $true
             != ( p @ X3 ) )
            | ( ( lessis @ X0 @ X3 )
              = $true ) )
        & ( ( p @ X1 )
          = $true )
        & ! [X2: nat] :
            ( ( ( lessis @ X1 @ X2 )
              = $true )
            | ( ( p @ X2 )
             != $true ) ) ) ),
    inference(ennf_transformation,[],[f21]) ).

thf(f21,plain,
    ( ! [X0: nat,X1: nat] :
        ( ~ ( ! [X2: nat] :
                ( ( ( p @ X2 )
                  = $true )
               => ( ( lessis @ X1 @ X2 )
                  = $true ) )
           => ( ( p @ X1 )
             != $true ) )
       => ( ~ ( ! [X3: nat] :
                  ( ( $true
                    = ( p @ X3 ) )
                 => ( ( lessis @ X0 @ X3 )
                    = $true ) )
             => ( ( p @ X0 )
               != $true ) )
         => ( X0 = X1 ) ) )
   => ( ( some
        @ ^ [Y0: nat] :
            ~ ( ( !! @ nat
                @ ^ [Y1: nat] :
                    ( ( p @ Y1 )
                   => ( lessis @ Y0 @ Y1 ) ) )
             => ~ ( p @ Y0 ) ) )
     != $true ) ),
    inference(flattening,[],[f10]) ).

thf(f10,plain,
    ~ ~ ( ! [X0: nat,X1: nat] :
            ( ~ ( ! [X2: nat] :
                    ( ( ( p @ X2 )
                      = $true )
                   => ( ( lessis @ X1 @ X2 )
                      = $true ) )
               => ( ( p @ X1 )
                 != $true ) )
           => ( ~ ( ! [X3: nat] :
                      ( ( $true
                        = ( p @ X3 ) )
                     => ( ( lessis @ X0 @ X3 )
                        = $true ) )
                 => ( ( p @ X0 )
                   != $true ) )
             => ( X0 = X1 ) ) )
       => ( ( some
            @ ^ [Y0: nat] :
                ~ ( ( !! @ nat
                    @ ^ [Y1: nat] :
                        ( ( p @ Y1 )
                       => ( lessis @ Y0 @ Y1 ) ) )
                 => ~ ( p @ Y0 ) ) )
         != $true ) ),
    inference(fool_elimination,[],[f9]) ).

thf(f9,plain,
    ~ ~ ( ! [X0: nat,X1: nat] :
            ( ~ ( ! [X2: nat] :
                    ( ( p @ X2 )
                   => ( lessis @ X1 @ X2 ) )
               => ~ ( p @ X1 ) )
           => ( ~ ( ! [X3: nat] :
                      ( ( p @ X3 )
                     => ( lessis @ X0 @ X3 ) )
                 => ~ ( p @ X0 ) )
             => ( X0 = X1 ) ) )
       => ~ ( some
            @ ^ [X4: nat] :
                ~ ( ! [X5: nat] :
                      ( ( p @ X5 )
                     => ( lessis @ X4 @ X5 ) )
                 => ~ ( p @ X4 ) ) ) ),
    inference(rectify,[],[f7]) ).

thf(f7,negated_conjecture,
    ~ ~ ( ! [X1: nat,X0: nat] :
            ( ~ ( ! [X4: nat] :
                    ( ( p @ X4 )
                   => ( lessis @ X0 @ X4 ) )
               => ~ ( p @ X0 ) )
           => ( ~ ( ! [X4: nat] :
                      ( ( p @ X4 )
                     => ( lessis @ X1 @ X4 ) )
                 => ~ ( p @ X1 ) )
             => ( X0 = X1 ) ) )
       => ~ ( some
            @ ^ [X0: nat] :
                ~ ( ! [X4: nat] :
                      ( ( p @ X4 )
                     => ( lessis @ X0 @ X4 ) )
                 => ~ ( p @ X0 ) ) ) ),
    inference(negated_conjecture,[],[f6]) ).

thf(f6,conjecture,
    ~ ( ! [X1: nat,X0: nat] :
          ( ~ ( ! [X4: nat] :
                  ( ( p @ X4 )
                 => ( lessis @ X0 @ X4 ) )
             => ~ ( p @ X0 ) )
         => ( ~ ( ! [X4: nat] :
                    ( ( p @ X4 )
                   => ( lessis @ X1 @ X4 ) )
               => ~ ( p @ X1 ) )
           => ( X0 = X1 ) ) )
     => ~ ( some
          @ ^ [X0: nat] :
              ~ ( ! [X4: nat] :
                    ( ( p @ X4 )
                   => ( lessis @ X0 @ X4 ) )
               => ~ ( p @ X0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz27a) ).

thf(f67,plain,
    ( ~ spl2_1
    | spl2_5 ),
    inference(avatar_split_clause,[],[f39,f64,f47]) ).

thf(f39,plain,
    ( ( ( some
        @ ^ [Y0: nat] :
            ~ ( ( !! @ nat
                @ ^ [Y1: nat] :
                    ( ( p @ Y1 )
                   => ( lessis @ Y0 @ Y1 ) ) )
             => ~ ( p @ Y0 ) ) )
     != $true )
    | ( ( p @ sK0 )
      = $true ) ),
    inference(cnf_transformation,[],[f34]) ).

thf(f62,plain,
    ( spl2_4
    | ~ spl2_1 ),
    inference(avatar_split_clause,[],[f37,f47,f60]) ).

thf(f37,plain,
    ! [X3: nat] :
      ( ( $true
        = ( lessis @ sK1 @ X3 ) )
      | ( ( some
          @ ^ [Y0: nat] :
              ~ ( ( !! @ nat
                  @ ^ [Y1: nat] :
                      ( ( p @ Y1 )
                     => ( lessis @ Y0 @ Y1 ) ) )
               => ~ ( p @ Y0 ) ) )
       != $true )
      | ( $true
       != ( p @ X3 ) ) ),
    inference(cnf_transformation,[],[f34]) ).

thf(f58,plain,
    ( ~ spl2_1
    | spl2_3 ),
    inference(avatar_split_clause,[],[f36,f55,f47]) ).

thf(f36,plain,
    ( ( ( some
        @ ^ [Y0: nat] :
            ~ ( ( !! @ nat
                @ ^ [Y1: nat] :
                    ( ( p @ Y1 )
                   => ( lessis @ Y0 @ Y1 ) ) )
             => ~ ( p @ Y0 ) ) )
     != $true )
    | ( ( p @ sK1 )
      = $true ) ),
    inference(cnf_transformation,[],[f34]) ).

thf(f53,plain,
    ( ~ spl2_1
    | spl2_2 ),
    inference(avatar_split_clause,[],[f40,f51,f47]) ).

thf(f40,plain,
    ! [X2: nat] :
      ( ( ( p @ X2 )
       != $true )
      | ( $true
        = ( lessis @ sK0 @ X2 ) )
      | ( ( some
          @ ^ [Y0: nat] :
              ~ ( ( !! @ nat
                  @ ^ [Y1: nat] :
                      ( ( p @ Y1 )
                     => ( lessis @ Y0 @ Y1 ) ) )
               => ~ ( p @ Y0 ) ) )
       != $true ) ),
    inference(cnf_transformation,[],[f34]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14  % Problem    : NUM705^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.16  % 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
% 0.16/0.38  % Computer : n018.cluster.edu
% 0.16/0.38  % Model    : x86_64 x86_64
% 0.16/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38  % Memory   : 8042.1875MB
% 0.16/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38  % CPULimit   : 300
% 0.16/0.38  % WCLimit    : 300
% 0.16/0.38  % DateTime   : Mon May 20 05:21:53 EDT 2024
% 0.16/0.38  % CPUTime    : 
% 0.16/0.38  This is a TH0_THM_EQU_NAR problem
% 0.16/0.38  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
% 0.24/0.40  % (5775)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)
% 0.24/0.40  % (5777)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.24/0.40  % (5776)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)
% 0.24/0.40  % (5778)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)
% 0.24/0.40  % (5771)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.24/0.40  % (5772)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)
% 0.24/0.40  % (5775)Instruction limit reached!
% 0.24/0.40  % (5775)------------------------------
% 0.24/0.40  % (5775)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.40  % (5775)Termination reason: Unknown
% 0.24/0.40  % (5775)Termination phase: Property scanning
% 0.24/0.40  
% 0.24/0.40  % (5775)Memory used [KB]: 895
% 0.24/0.40  % (5775)Time elapsed: 0.003 s
% 0.24/0.40  % (5775)Instructions burned: 2 (million)
% 0.24/0.40  % (5775)------------------------------
% 0.24/0.40  % (5775)------------------------------
% 0.24/0.40  % (5778)Instruction limit reached!
% 0.24/0.40  % (5778)------------------------------
% 0.24/0.40  % (5778)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.40  % (5778)Termination reason: Unknown
% 0.24/0.40  % (5778)Termination phase: Property scanning
% 0.24/0.40  
% 0.24/0.40  % (5778)Memory used [KB]: 1023
% 0.24/0.40  % (5778)Time elapsed: 0.003 s
% 0.24/0.40  % (5778)Instructions burned: 3 (million)
% 0.24/0.40  % (5778)------------------------------
% 0.24/0.40  % (5778)------------------------------
% 0.24/0.40  % (5772)Instruction limit reached!
% 0.24/0.40  % (5772)------------------------------
% 0.24/0.40  % (5772)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.40  % (5772)Termination reason: Unknown
% 0.24/0.40  % (5772)Termination phase: Saturation
% 0.24/0.40  
% 0.24/0.40  % (5772)Memory used [KB]: 5500
% 0.24/0.40  % (5772)Time elapsed: 0.004 s
% 0.24/0.40  % (5772)Instructions burned: 4 (million)
% 0.24/0.40  % (5772)------------------------------
% 0.24/0.40  % (5772)------------------------------
% 0.24/0.40  % (5776)Refutation not found, incomplete strategy
% 0.24/0.40  % (5776)------------------------------
% 0.24/0.40  % (5776)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.40  % (5776)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.40  
% 0.24/0.40  
% 0.24/0.40  % (5776)Memory used [KB]: 5500
% 0.24/0.40  % (5776)Time elapsed: 0.005 s
% 0.24/0.40  % (5776)Instructions burned: 5 (million)
% 0.24/0.40  % (5776)------------------------------
% 0.24/0.40  % (5776)------------------------------
% 0.24/0.41  % (5777)First to succeed.
% 0.24/0.41  % (5777)Refutation found. Thanks to Tanya!
% 0.24/0.41  % SZS status Theorem for theBenchmark
% 0.24/0.41  % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.41  % (5777)------------------------------
% 0.24/0.41  % (5777)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.41  % (5777)Termination reason: Refutation
% 0.24/0.41  
% 0.24/0.41  % (5777)Memory used [KB]: 5628
% 0.24/0.41  % (5777)Time elapsed: 0.010 s
% 0.24/0.41  % (5777)Instructions burned: 9 (million)
% 0.24/0.41  % (5777)------------------------------
% 0.24/0.41  % (5777)------------------------------
% 0.24/0.41  % (5770)Success in time 0.024 s
% 0.24/0.41  % Vampire---4.8 exiting
%------------------------------------------------------------------------------