TSTP Solution File: SET622^5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET622^5 : TPTP v8.1.2. Released v4.0.0.
% 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 : n002.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun May  5 09:07:39 EDT 2024

% Result   : Theorem 0.15s 0.39s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   96 (  12 unt;   7 typ;   0 def)
%            Number of atoms       :  857 ( 210 equ;   0 cnn)
%            Maximal formula atoms :    5 (   9 avg)
%            Number of connectives : 1045 ( 157   ~; 235   |; 173   &; 474   @)
%                                         (   5 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   21 (  21   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :   39 (  20   ^  12   !;   6   ?;  39   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

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

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

thf(func_def_9,type,
    sK0: a > $o ).

thf(func_def_10,type,
    sK1: a > $o ).

thf(func_def_11,type,
    sK2: a > $o ).

thf(func_def_13,type,
    ph4: 
      !>[X0: $tType] : X0 ).

thf(func_def_14,type,
    sK5: a ).

thf(f197,plain,
    $false,
    inference(avatar_sat_refutation,[],[f155,f163,f171,f175,f183,f189,f196]) ).

thf(f196,plain,
    ( ~ spl3_1
    | ~ spl3_2 ),
    inference(avatar_contradiction_clause,[],[f195]) ).

thf(f195,plain,
    ( $false
    | ~ spl3_1
    | ~ spl3_2 ),
    inference(trivial_inequality_removal,[],[f192]) ).

thf(f192,plain,
    ( ( $false = $true )
    | ~ spl3_1
    | ~ spl3_2 ),
    inference(superposition,[],[f145,f149]) ).

thf(f149,plain,
    ( ( ( sK1 @ sK5 )
      = $true )
    | ~ spl3_2 ),
    inference(avatar_component_clause,[],[f147]) ).

thf(f147,plain,
    ( spl3_2
  <=> ( ( sK1 @ sK5 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

thf(f145,plain,
    ( ( $false
      = ( sK1 @ sK5 ) )
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f143]) ).

thf(f143,plain,
    ( spl3_1
  <=> ( $false
      = ( sK1 @ sK5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

thf(f189,plain,
    ~ spl3_5,
    inference(avatar_contradiction_clause,[],[f188]) ).

thf(f188,plain,
    ( $false
    | ~ spl3_5 ),
    inference(trivial_inequality_removal,[],[f184]) ).

thf(f184,plain,
    ( ( $false = $true )
    | ~ spl3_5 ),
    inference(superposition,[],[f169,f141]) ).

thf(f141,plain,
    ( ( sK0 @ sK5 )
    = $true ),
    inference(duplicate_literal_removal,[],[f137]) ).

thf(f137,plain,
    ( ( ( sK0 @ sK5 )
      = $true )
    | ( ( sK0 @ sK5 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f136]) ).

thf(f136,plain,
    ( ( ( ( sK2 @ sK5 )
        & ( sK1 @ sK5 )
        & ( sK0 @ sK5 ) )
      = $true )
    | ( ( sK0 @ sK5 )
      = $true ) ),
    inference(duplicate_literal_removal,[],[f120]) ).

thf(f120,plain,
    ( ( ( sK0 @ sK5 )
      = $true )
    | ( ( ( sK2 @ sK5 )
        & ( sK1 @ sK5 )
        & ( sK0 @ sK5 ) )
      = $true )
    | ( ( sK0 @ sK5 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f119]) ).

thf(f119,plain,
    ( ( ( sK0 @ sK5 )
      = $true )
    | ( ( ~ ( ( sK2 @ sK5 )
            | ( sK1 @ sK5 ) )
        & ( sK0 @ sK5 ) )
      = $true )
    | ( ( ( sK2 @ sK5 )
        & ( sK1 @ sK5 )
        & ( sK0 @ sK5 ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f55]) ).

thf(f55,plain,
    ( ( ( ( ( sK2 @ sK5 )
          & ( sK1 @ sK5 )
          & ( sK0 @ sK5 ) )
        | ( ~ ( ( sK2 @ sK5 )
              | ( sK1 @ sK5 ) )
          & ( sK0 @ sK5 ) ) )
      = $true )
    | ( ( sK0 @ sK5 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f12]) ).

thf(f12,plain,
    ( ( ( ~ ( ( ( sK2 @ sK5 )
              & ~ ( sK1 @ sK5 ) )
            | ( ~ ( sK2 @ sK5 )
              & ( sK1 @ sK5 ) ) )
        & ( sK0 @ sK5 ) )
      = $true )
    | ( ( ( ( sK2 @ sK5 )
          & ( sK1 @ sK5 )
          & ( sK0 @ sK5 ) )
        | ( ~ ( ( sK2 @ sK5 )
              | ( sK1 @ sK5 ) )
          & ( sK0 @ sK5 ) ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f11]) ).

thf(f11,plain,
    ( ( ~ ( ( ( sK2 @ sK5 )
            & ~ ( sK1 @ sK5 ) )
          | ( ~ ( sK2 @ sK5 )
            & ( sK1 @ sK5 ) ) )
      & ( sK0 @ sK5 ) )
   != ( ( ( sK2 @ sK5 )
        & ( sK1 @ sK5 )
        & ( sK0 @ sK5 ) )
      | ( ~ ( ( sK2 @ sK5 )
            | ( sK1 @ sK5 ) )
        & ( sK0 @ sK5 ) ) ) ),
    inference(beta_eta_normalization,[],[f10]) ).

thf(f10,plain,
    ( ( ^ [Y0: a] :
          ( ~ ( ( ( sK2 @ Y0 )
                & ~ ( sK1 @ Y0 ) )
              | ( ~ ( sK2 @ Y0 )
                & ( sK1 @ Y0 ) ) )
          & ( sK0 @ Y0 ) )
      @ sK5 )
   != ( ^ [Y0: a] :
          ( ( ( sK2 @ Y0 )
            & ( sK1 @ Y0 )
            & ( sK0 @ Y0 ) )
          | ( ~ ( ( sK2 @ Y0 )
                | ( sK1 @ Y0 ) )
            & ( sK0 @ Y0 ) ) )
      @ sK5 ) ),
    inference(negative_extensionality,[],[f9]) ).

thf(f9,plain,
    ( ( ^ [Y0: a] :
          ( ( ( sK2 @ Y0 )
            & ( sK1 @ Y0 )
            & ( sK0 @ Y0 ) )
          | ( ~ ( ( sK2 @ Y0 )
                | ( sK1 @ Y0 ) )
            & ( sK0 @ Y0 ) ) ) )
   != ( ^ [Y0: a] :
          ( ~ ( ( ( sK2 @ Y0 )
                & ~ ( sK1 @ Y0 ) )
              | ( ~ ( sK2 @ Y0 )
                & ( sK1 @ Y0 ) ) )
          & ( sK0 @ Y0 ) ) ) ),
    inference(cnf_transformation,[],[f8]) ).

thf(f8,plain,
    ( ( ^ [Y0: a] :
          ( ( ( sK2 @ Y0 )
            & ( sK1 @ Y0 )
            & ( sK0 @ Y0 ) )
          | ( ~ ( ( sK2 @ Y0 )
                | ( sK1 @ Y0 ) )
            & ( sK0 @ Y0 ) ) ) )
   != ( ^ [Y0: a] :
          ( ~ ( ( ( sK2 @ Y0 )
                & ~ ( sK1 @ Y0 ) )
              | ( ~ ( sK2 @ Y0 )
                & ( sK1 @ Y0 ) ) )
          & ( sK0 @ Y0 ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f7]) ).

thf(f7,plain,
    ( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
        ( ( ^ [Y0: a] :
              ( ~ ( ( ( X2 @ Y0 )
                    & ~ ( X1 @ Y0 ) )
                  | ( ~ ( X2 @ Y0 )
                    & ( X1 @ Y0 ) ) )
              & ( X0 @ Y0 ) ) )
       != ( ^ [Y0: a] :
              ( ( ( X2 @ Y0 )
                & ( X1 @ Y0 )
                & ( X0 @ Y0 ) )
              | ( ~ ( ( X2 @ Y0 )
                    | ( X1 @ Y0 ) )
                & ( X0 @ Y0 ) ) ) ) )
   => ( ( ^ [Y0: a] :
            ( ( ( sK2 @ Y0 )
              & ( sK1 @ Y0 )
              & ( sK0 @ Y0 ) )
            | ( ~ ( ( sK2 @ Y0 )
                  | ( sK1 @ Y0 ) )
              & ( sK0 @ Y0 ) ) ) )
     != ( ^ [Y0: a] :
            ( ~ ( ( ( sK2 @ Y0 )
                  & ~ ( sK1 @ Y0 ) )
                | ( ~ ( sK2 @ Y0 )
                  & ( sK1 @ Y0 ) ) )
            & ( sK0 @ Y0 ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f6,plain,
    ? [X0: a > $o,X1: a > $o,X2: a > $o] :
      ( ( ^ [Y0: a] :
            ( ~ ( ( ( X2 @ Y0 )
                  & ~ ( X1 @ Y0 ) )
                | ( ~ ( X2 @ Y0 )
                  & ( X1 @ Y0 ) ) )
            & ( X0 @ Y0 ) ) )
     != ( ^ [Y0: a] :
            ( ( ( X2 @ Y0 )
              & ( X1 @ Y0 )
              & ( X0 @ Y0 ) )
            | ( ~ ( ( X2 @ Y0 )
                  | ( X1 @ Y0 ) )
              & ( X0 @ Y0 ) ) ) ) ),
    inference(ennf_transformation,[],[f5]) ).

thf(f5,plain,
    ~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
        ( ( ^ [Y0: a] :
              ( ~ ( ( ( X2 @ Y0 )
                    & ~ ( X1 @ Y0 ) )
                  | ( ~ ( X2 @ Y0 )
                    & ( X1 @ Y0 ) ) )
              & ( X0 @ Y0 ) ) )
        = ( ^ [Y0: a] :
              ( ( ( X2 @ Y0 )
                & ( X1 @ Y0 )
                & ( X0 @ Y0 ) )
              | ( ~ ( ( X2 @ Y0 )
                    | ( X1 @ Y0 ) )
                & ( X0 @ Y0 ) ) ) ) ),
    inference(fool_elimination,[],[f4]) ).

thf(f4,plain,
    ~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
        ( ( ^ [X3: a] :
              ( ( ( X0 @ X3 )
                & ~ ( ( X1 @ X3 )
                    | ( X2 @ X3 ) ) )
              | ( ( X0 @ X3 )
                & ( X1 @ X3 )
                & ( X2 @ X3 ) ) ) )
        = ( ^ [X4: a] :
              ( ( X0 @ X4 )
              & ~ ( ( ( X1 @ X4 )
                    & ~ ( X2 @ X4 ) )
                  | ( ~ ( X1 @ X4 )
                    & ( X2 @ X4 ) ) ) ) ) ),
    inference(rectify,[],[f2]) ).

thf(f2,negated_conjecture,
    ~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
        ( ( ^ [X4: a] :
              ( ( ( X0 @ X4 )
                & ~ ( ( X1 @ X4 )
                    | ( X2 @ X4 ) ) )
              | ( ( X0 @ X4 )
                & ( X1 @ X4 )
                & ( X2 @ X4 ) ) ) )
        = ( ^ [X3: a] :
              ( ( X0 @ X3 )
              & ~ ( ( ( X1 @ X3 )
                    & ~ ( X2 @ X3 ) )
                  | ( ~ ( X1 @ X3 )
                    & ( X2 @ X3 ) ) ) ) ) ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ! [X0: a > $o,X1: a > $o,X2: a > $o] :
      ( ( ^ [X4: a] :
            ( ( ( X0 @ X4 )
              & ~ ( ( X1 @ X4 )
                  | ( X2 @ X4 ) ) )
            | ( ( X0 @ X4 )
              & ( X1 @ X4 )
              & ( X2 @ X4 ) ) ) )
      = ( ^ [X3: a] :
            ( ( X0 @ X3 )
            & ~ ( ( ( X1 @ X3 )
                  & ~ ( X2 @ X3 ) )
                | ( ~ ( X1 @ X3 )
                  & ( X2 @ X3 ) ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.wM3fBz4V8T/Vampire---4.8_26587',cBOOL_PROP_98_pme) ).

thf(f169,plain,
    ( ( ( sK0 @ sK5 )
      = $false )
    | ~ spl3_5 ),
    inference(avatar_component_clause,[],[f167]) ).

thf(f167,plain,
    ( spl3_5
  <=> ( ( sK0 @ sK5 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

thf(f183,plain,
    ( ~ spl3_3
    | ~ spl3_4 ),
    inference(avatar_contradiction_clause,[],[f182]) ).

thf(f182,plain,
    ( $false
    | ~ spl3_3
    | ~ spl3_4 ),
    inference(trivial_inequality_removal,[],[f178]) ).

thf(f178,plain,
    ( ( $false = $true )
    | ~ spl3_3
    | ~ spl3_4 ),
    inference(superposition,[],[f159,f153]) ).

thf(f153,plain,
    ( ( ( sK2 @ sK5 )
      = $true )
    | ~ spl3_3 ),
    inference(avatar_component_clause,[],[f151]) ).

thf(f151,plain,
    ( spl3_3
  <=> ( ( sK2 @ sK5 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

thf(f159,plain,
    ( ( ( sK2 @ sK5 )
      = $false )
    | ~ spl3_4 ),
    inference(avatar_component_clause,[],[f157]) ).

thf(f157,plain,
    ( spl3_4
  <=> ( ( sK2 @ sK5 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

thf(f175,plain,
    ( spl3_4
    | spl3_1
    | spl3_5 ),
    inference(avatar_split_clause,[],[f33,f167,f143,f157]) ).

thf(f33,plain,
    ( ( ( sK2 @ sK5 )
      = $false )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( $false
      = ( sK1 @ sK5 ) ) ),
    inference(duplicate_literal_removal,[],[f32]) ).

thf(f32,plain,
    ( ( ( sK2 @ sK5 )
      = $false )
    | ( ( sK2 @ sK5 )
      = $false )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( $false
      = ( sK1 @ sK5 ) ) ),
    inference(not_proxy_clausification,[],[f31]) ).

thf(f31,plain,
    ( ( $true
      = ( ~ ( sK2 @ sK5 ) ) )
    | ( $false
      = ( sK1 @ sK5 ) )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( ( sK2 @ sK5 )
      = $false ) ),
    inference(duplicate_literal_removal,[],[f30]) ).

thf(f30,plain,
    ( ( $false
      = ( sK1 @ sK5 ) )
    | ( $false
      = ( sK1 @ sK5 ) )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( ( sK2 @ sK5 )
      = $false )
    | ( $true
      = ( ~ ( sK2 @ sK5 ) ) ) ),
    inference(not_proxy_clausification,[],[f29]) ).

thf(f29,plain,
    ( ( ( sK2 @ sK5 )
      = $false )
    | ( $true
      = ( ~ ( sK1 @ sK5 ) ) )
    | ( $false
      = ( sK1 @ sK5 ) )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( $true
      = ( ~ ( sK2 @ sK5 ) ) ) ),
    inference(binary_proxy_clausification,[],[f22]) ).

thf(f22,plain,
    ( ( ( ~ ( sK2 @ sK5 )
        & ( sK1 @ sK5 ) )
      = $true )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( $true
      = ( ~ ( sK1 @ sK5 ) ) )
    | ( $false
      = ( sK1 @ sK5 ) )
    | ( ( sK2 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f21]) ).

thf(f21,plain,
    ( ( ( ( sK2 @ sK5 )
        & ~ ( sK1 @ sK5 ) )
      = $true )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( ( sK2 @ sK5 )
      = $false )
    | ( ( ~ ( sK2 @ sK5 )
        & ( sK1 @ sK5 ) )
      = $true )
    | ( $false
      = ( sK1 @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f20]) ).

thf(f20,plain,
    ( ( $false
      = ( ( sK2 @ sK5 )
        & ( sK1 @ sK5 ) ) )
    | ( ( ~ ( sK2 @ sK5 )
        & ( sK1 @ sK5 ) )
      = $true )
    | ( ( ( sK2 @ sK5 )
        & ~ ( sK1 @ sK5 ) )
      = $true )
    | ( ( sK0 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f19]) ).

thf(f19,plain,
    ( ( $true
      = ( ( ( sK2 @ sK5 )
          & ~ ( sK1 @ sK5 ) )
        | ( ~ ( sK2 @ sK5 )
          & ( sK1 @ sK5 ) ) ) )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( $false
      = ( ( sK2 @ sK5 )
        & ( sK1 @ sK5 ) ) ) ),
    inference(duplicate_literal_removal,[],[f18]) ).

thf(f18,plain,
    ( ( ( sK0 @ sK5 )
      = $false )
    | ( $true
      = ( ( ( sK2 @ sK5 )
          & ~ ( sK1 @ sK5 ) )
        | ( ~ ( sK2 @ sK5 )
          & ( sK1 @ sK5 ) ) ) )
    | ( $false
      = ( ( sK2 @ sK5 )
        & ( sK1 @ sK5 ) ) )
    | ( ( sK0 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f17]) ).

thf(f17,plain,
    ( ( ( sK0 @ sK5 )
      = $false )
    | ( $false
      = ( ( sK2 @ sK5 )
        & ( sK1 @ sK5 )
        & ( sK0 @ sK5 ) ) )
    | ( $true
      = ( ( ( sK2 @ sK5 )
          & ~ ( sK1 @ sK5 ) )
        | ( ~ ( sK2 @ sK5 )
          & ( sK1 @ sK5 ) ) ) ) ),
    inference(not_proxy_clausification,[],[f16]) ).

thf(f16,plain,
    ( ( $false
      = ( ~ ( ( ( sK2 @ sK5 )
              & ~ ( sK1 @ sK5 ) )
            | ( ~ ( sK2 @ sK5 )
              & ( sK1 @ sK5 ) ) ) ) )
    | ( $false
      = ( ( sK2 @ sK5 )
        & ( sK1 @ sK5 )
        & ( sK0 @ sK5 ) ) )
    | ( ( sK0 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f14]) ).

thf(f14,plain,
    ( ( $false
      = ( ( ( sK2 @ sK5 )
          & ( sK1 @ sK5 )
          & ( sK0 @ sK5 ) )
        | ( ~ ( ( sK2 @ sK5 )
              | ( sK1 @ sK5 ) )
          & ( sK0 @ sK5 ) ) ) )
    | ( $false
      = ( ~ ( ( ( sK2 @ sK5 )
              & ~ ( sK1 @ sK5 ) )
            | ( ~ ( sK2 @ sK5 )
              & ( sK1 @ sK5 ) ) ) ) )
    | ( ( sK0 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f13]) ).

thf(f13,plain,
    ( ( ( ~ ( ( ( sK2 @ sK5 )
              & ~ ( sK1 @ sK5 ) )
            | ( ~ ( sK2 @ sK5 )
              & ( sK1 @ sK5 ) ) )
        & ( sK0 @ sK5 ) )
      = $false )
    | ( $false
      = ( ( ( sK2 @ sK5 )
          & ( sK1 @ sK5 )
          & ( sK0 @ sK5 ) )
        | ( ~ ( ( sK2 @ sK5 )
              | ( sK1 @ sK5 ) )
          & ( sK0 @ sK5 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f11]) ).

thf(f171,plain,
    ( spl3_3
    | spl3_5
    | spl3_2 ),
    inference(avatar_split_clause,[],[f53,f147,f167,f151]) ).

thf(f53,plain,
    ( ( ( sK1 @ sK5 )
      = $true )
    | ( ( sK2 @ sK5 )
      = $true )
    | ( ( sK0 @ sK5 )
      = $false ) ),
    inference(duplicate_literal_removal,[],[f52]) ).

thf(f52,plain,
    ( ( ( sK2 @ sK5 )
      = $true )
    | ( ( sK2 @ sK5 )
      = $true )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( ( sK1 @ sK5 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f50]) ).

thf(f50,plain,
    ( ( ( ( sK2 @ sK5 )
        & ~ ( sK1 @ sK5 ) )
      = $true )
    | ( ( sK2 @ sK5 )
      = $true )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( ( sK1 @ sK5 )
      = $true ) ),
    inference(duplicate_literal_removal,[],[f42]) ).

thf(f42,plain,
    ( ( ( sK2 @ sK5 )
      = $true )
    | ( ( sK1 @ sK5 )
      = $true )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( ( sK1 @ sK5 )
      = $true )
    | ( ( ( sK2 @ sK5 )
        & ~ ( sK1 @ sK5 ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f41]) ).

thf(f41,plain,
    ( ( ( sK1 @ sK5 )
      = $true )
    | ( ( sK2 @ sK5 )
      = $true )
    | ( ( ~ ( sK2 @ sK5 )
        & ( sK1 @ sK5 ) )
      = $true )
    | ( ( ( sK2 @ sK5 )
        & ~ ( sK1 @ sK5 ) )
      = $true )
    | ( ( sK0 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f40]) ).

thf(f40,plain,
    ( ( ( sK0 @ sK5 )
      = $false )
    | ( ( sK2 @ sK5 )
      = $true )
    | ( ( sK1 @ sK5 )
      = $true )
    | ( $true
      = ( ( ( sK2 @ sK5 )
          & ~ ( sK1 @ sK5 ) )
        | ( ~ ( sK2 @ sK5 )
          & ( sK1 @ sK5 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f39]) ).

thf(f39,plain,
    ( ( $true
      = ( ( sK2 @ sK5 )
        | ( sK1 @ sK5 ) ) )
    | ( $true
      = ( ( ( sK2 @ sK5 )
          & ~ ( sK1 @ sK5 ) )
        | ( ~ ( sK2 @ sK5 )
          & ( sK1 @ sK5 ) ) ) )
    | ( ( sK0 @ sK5 )
      = $false ) ),
    inference(not_proxy_clausification,[],[f38]) ).

thf(f38,plain,
    ( ( $false
      = ( ~ ( ( ( sK2 @ sK5 )
              & ~ ( sK1 @ sK5 ) )
            | ( ~ ( sK2 @ sK5 )
              & ( sK1 @ sK5 ) ) ) ) )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( $true
      = ( ( sK2 @ sK5 )
        | ( sK1 @ sK5 ) ) ) ),
    inference(not_proxy_clausification,[],[f37]) ).

thf(f37,plain,
    ( ( $false
      = ( ~ ( ( sK2 @ sK5 )
            | ( sK1 @ sK5 ) ) ) )
    | ( $false
      = ( ~ ( ( ( sK2 @ sK5 )
              & ~ ( sK1 @ sK5 ) )
            | ( ~ ( sK2 @ sK5 )
              & ( sK1 @ sK5 ) ) ) ) )
    | ( ( sK0 @ sK5 )
      = $false ) ),
    inference(duplicate_literal_removal,[],[f36]) ).

thf(f36,plain,
    ( ( ( sK0 @ sK5 )
      = $false )
    | ( $false
      = ( ~ ( ( ( sK2 @ sK5 )
              & ~ ( sK1 @ sK5 ) )
            | ( ~ ( sK2 @ sK5 )
              & ( sK1 @ sK5 ) ) ) ) )
    | ( $false
      = ( ~ ( ( sK2 @ sK5 )
            | ( sK1 @ sK5 ) ) ) )
    | ( ( sK0 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f15]) ).

thf(f15,plain,
    ( ( ( ~ ( ( sK2 @ sK5 )
            | ( sK1 @ sK5 ) )
        & ( sK0 @ sK5 ) )
      = $false )
    | ( $false
      = ( ~ ( ( ( sK2 @ sK5 )
              & ~ ( sK1 @ sK5 ) )
            | ( ~ ( sK2 @ sK5 )
              & ( sK1 @ sK5 ) ) ) ) )
    | ( ( sK0 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f14]) ).

thf(f163,plain,
    ( spl3_2
    | spl3_4 ),
    inference(avatar_split_clause,[],[f76,f157,f147]) ).

thf(f76,plain,
    ( ( ( sK2 @ sK5 )
      = $false )
    | ( ( sK1 @ sK5 )
      = $true ) ),
    inference(duplicate_literal_removal,[],[f75]) ).

thf(f75,plain,
    ( ( ( sK2 @ sK5 )
      = $false )
    | ( ( sK1 @ sK5 )
      = $true )
    | ( ( sK2 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f73]) ).

thf(f73,plain,
    ( ( $false
      = ( ( sK2 @ sK5 )
        | ( sK1 @ sK5 ) ) )
    | ( ( sK1 @ sK5 )
      = $true )
    | ( ( sK2 @ sK5 )
      = $false ) ),
    inference(duplicate_literal_removal,[],[f68]) ).

thf(f68,plain,
    ( ( ( sK1 @ sK5 )
      = $true )
    | ( ( sK2 @ sK5 )
      = $false )
    | ( ( sK1 @ sK5 )
      = $true )
    | ( $false
      = ( ( sK2 @ sK5 )
        | ( sK1 @ sK5 ) ) ) ),
    inference(binary_proxy_clausification,[],[f67]) ).

thf(f67,plain,
    ( ( ( sK2 @ sK5 )
      = $false )
    | ( ( sK1 @ sK5 )
      = $true )
    | ( ( ( sK2 @ sK5 )
        & ( sK1 @ sK5 ) )
      = $true )
    | ( $false
      = ( ( sK2 @ sK5 )
        | ( sK1 @ sK5 ) ) ) ),
    inference(not_proxy_clausification,[],[f66]) ).

thf(f66,plain,
    ( ( ( sK1 @ sK5 )
      = $true )
    | ( ( ~ ( ( sK2 @ sK5 )
            | ( sK1 @ sK5 ) ) )
      = $true )
    | ( ( sK2 @ sK5 )
      = $false )
    | ( ( ( sK2 @ sK5 )
        & ( sK1 @ sK5 ) )
      = $true ) ),
    inference(not_proxy_clausification,[],[f65]) ).

thf(f65,plain,
    ( ( $false
      = ( ~ ( sK1 @ sK5 ) ) )
    | ( ( ( sK2 @ sK5 )
        & ( sK1 @ sK5 ) )
      = $true )
    | ( ( sK2 @ sK5 )
      = $false )
    | ( ( ~ ( ( sK2 @ sK5 )
            | ( sK1 @ sK5 ) ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f63]) ).

thf(f63,plain,
    ( ( ( sK2 @ sK5 )
      = $false )
    | ( ( ~ ( ( sK2 @ sK5 )
            | ( sK1 @ sK5 ) )
        & ( sK0 @ sK5 ) )
      = $true )
    | ( $false
      = ( ~ ( sK1 @ sK5 ) ) )
    | ( ( ( sK2 @ sK5 )
        & ( sK1 @ sK5 ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f62]) ).

thf(f62,plain,
    ( ( $false
      = ( ( sK2 @ sK5 )
        & ~ ( sK1 @ sK5 ) ) )
    | ( ( ( sK2 @ sK5 )
        & ( sK1 @ sK5 ) )
      = $true )
    | ( ( ~ ( ( sK2 @ sK5 )
            | ( sK1 @ sK5 ) )
        & ( sK0 @ sK5 ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f60]) ).

thf(f60,plain,
    ( ( ( ( sK2 @ sK5 )
        & ( sK1 @ sK5 )
        & ( sK0 @ sK5 ) )
      = $true )
    | ( $false
      = ( ( sK2 @ sK5 )
        & ~ ( sK1 @ sK5 ) ) )
    | ( ( ~ ( ( sK2 @ sK5 )
            | ( sK1 @ sK5 ) )
        & ( sK0 @ sK5 ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f58]) ).

thf(f58,plain,
    ( ( $false
      = ( ( ( sK2 @ sK5 )
          & ~ ( sK1 @ sK5 ) )
        | ( ~ ( sK2 @ sK5 )
          & ( sK1 @ sK5 ) ) ) )
    | ( ( ( sK2 @ sK5 )
        & ( sK1 @ sK5 )
        & ( sK0 @ sK5 ) )
      = $true )
    | ( ( ~ ( ( sK2 @ sK5 )
            | ( sK1 @ sK5 ) )
        & ( sK0 @ sK5 ) )
      = $true ) ),
    inference(not_proxy_clausification,[],[f57]) ).

thf(f57,plain,
    ( ( ( ~ ( ( ( sK2 @ sK5 )
              & ~ ( sK1 @ sK5 ) )
            | ( ~ ( sK2 @ sK5 )
              & ( sK1 @ sK5 ) ) ) )
      = $true )
    | ( ( ~ ( ( sK2 @ sK5 )
            | ( sK1 @ sK5 ) )
        & ( sK0 @ sK5 ) )
      = $true )
    | ( ( ( sK2 @ sK5 )
        & ( sK1 @ sK5 )
        & ( sK0 @ sK5 ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f56]) ).

thf(f56,plain,
    ( ( ( ( ( sK2 @ sK5 )
          & ( sK1 @ sK5 )
          & ( sK0 @ sK5 ) )
        | ( ~ ( ( sK2 @ sK5 )
              | ( sK1 @ sK5 ) )
          & ( sK0 @ sK5 ) ) )
      = $true )
    | ( ( ~ ( ( ( sK2 @ sK5 )
              & ~ ( sK1 @ sK5 ) )
            | ( ~ ( sK2 @ sK5 )
              & ( sK1 @ sK5 ) ) ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f12]) ).

thf(f155,plain,
    ( spl3_1
    | spl3_3 ),
    inference(avatar_split_clause,[],[f108,f151,f143]) ).

thf(f108,plain,
    ( ( ( sK2 @ sK5 )
      = $true )
    | ( $false
      = ( sK1 @ sK5 ) ) ),
    inference(duplicate_literal_removal,[],[f107]) ).

thf(f107,plain,
    ( ( $false
      = ( sK1 @ sK5 ) )
    | ( ( sK2 @ sK5 )
      = $true )
    | ( ( sK2 @ sK5 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f105]) ).

thf(f105,plain,
    ( ( ( sK2 @ sK5 )
      = $true )
    | ( $false
      = ( sK1 @ sK5 ) )
    | ( ( ( sK2 @ sK5 )
        & ( sK1 @ sK5 ) )
      = $true ) ),
    inference(duplicate_literal_removal,[],[f100]) ).

thf(f100,plain,
    ( ( $false
      = ( sK1 @ sK5 ) )
    | ( ( ( sK2 @ sK5 )
        & ( sK1 @ sK5 ) )
      = $true )
    | ( ( sK2 @ sK5 )
      = $true )
    | ( $false
      = ( sK1 @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f99]) ).

thf(f99,plain,
    ( ( $false
      = ( ( sK2 @ sK5 )
        | ( sK1 @ sK5 ) ) )
    | ( ( sK2 @ sK5 )
      = $true )
    | ( ( ( sK2 @ sK5 )
        & ( sK1 @ sK5 ) )
      = $true )
    | ( $false
      = ( sK1 @ sK5 ) ) ),
    inference(not_proxy_clausification,[],[f98]) ).

thf(f98,plain,
    ( ( ( ~ ( ( sK2 @ sK5 )
            | ( sK1 @ sK5 ) ) )
      = $true )
    | ( $false
      = ( sK1 @ sK5 ) )
    | ( ( ( sK2 @ sK5 )
        & ( sK1 @ sK5 ) )
      = $true )
    | ( ( sK2 @ sK5 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f96]) ).

thf(f96,plain,
    ( ( ( ~ ( ( sK2 @ sK5 )
            | ( sK1 @ sK5 ) )
        & ( sK0 @ sK5 ) )
      = $true )
    | ( $false
      = ( sK1 @ sK5 ) )
    | ( ( sK2 @ sK5 )
      = $true )
    | ( ( ( sK2 @ sK5 )
        & ( sK1 @ sK5 ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f94]) ).

thf(f94,plain,
    ( ( $false
      = ( sK1 @ sK5 ) )
    | ( ( sK2 @ sK5 )
      = $true )
    | ( ( ( sK2 @ sK5 )
        & ( sK1 @ sK5 )
        & ( sK0 @ sK5 ) )
      = $true )
    | ( ( ~ ( ( sK2 @ sK5 )
            | ( sK1 @ sK5 ) )
        & ( sK0 @ sK5 ) )
      = $true ) ),
    inference(not_proxy_clausification,[],[f93]) ).

thf(f93,plain,
    ( ( $false
      = ( ~ ( sK2 @ sK5 ) ) )
    | ( ( ~ ( ( sK2 @ sK5 )
            | ( sK1 @ sK5 ) )
        & ( sK0 @ sK5 ) )
      = $true )
    | ( ( ( sK2 @ sK5 )
        & ( sK1 @ sK5 )
        & ( sK0 @ sK5 ) )
      = $true )
    | ( $false
      = ( sK1 @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f59]) ).

thf(f59,plain,
    ( ( $false
      = ( ~ ( sK2 @ sK5 )
        & ( sK1 @ sK5 ) ) )
    | ( ( ( sK2 @ sK5 )
        & ( sK1 @ sK5 )
        & ( sK0 @ sK5 ) )
      = $true )
    | ( ( ~ ( ( sK2 @ sK5 )
            | ( sK1 @ sK5 ) )
        & ( sK0 @ sK5 ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f58]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SET622^5 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14  % 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
% 0.15/0.35  % Computer : n002.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Fri May  3 16:26:08 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  This is a TH0_THM_EQU_NAR problem
% 0.15/0.36  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/tmp/tmp.wM3fBz4V8T/Vampire---4.8_26587
% 0.15/0.38  % (26698)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 Vampire---4 for (3000ds/27Mi)
% 0.15/0.38  % (26696)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (3000ds/183Mi)
% 0.15/0.38  % (26697)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 Vampire---4 for (3000ds/4Mi)
% 0.15/0.38  % (26699)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (3000ds/2Mi)
% 0.15/0.38  % (26700)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (3000ds/2Mi)
% 0.15/0.38  % (26702)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (3000ds/18Mi)
% 0.15/0.38  % (26703)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (3000ds/3Mi)
% 0.15/0.38  % (26701)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (3000ds/275Mi)
% 0.15/0.38  % (26700)Instruction limit reached!
% 0.15/0.38  % (26700)------------------------------
% 0.15/0.38  % (26700)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38  % (26700)Termination reason: Unknown
% 0.15/0.38  % (26700)Termination phase: Property scanning
% 0.15/0.38  
% 0.15/0.38  % (26700)Memory used [KB]: 895
% 0.15/0.38  % (26700)Time elapsed: 0.003 s
% 0.15/0.38  % (26700)Instructions burned: 2 (million)
% 0.15/0.38  % (26700)------------------------------
% 0.15/0.38  % (26700)------------------------------
% 0.15/0.38  % (26699)Instruction limit reached!
% 0.15/0.38  % (26699)------------------------------
% 0.15/0.38  % (26699)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38  % (26699)Termination reason: Unknown
% 0.15/0.38  % (26699)Termination phase: Saturation
% 0.15/0.38  
% 0.15/0.38  % (26699)Memory used [KB]: 5500
% 0.15/0.38  % (26699)Time elapsed: 0.004 s
% 0.15/0.38  % (26699)Instructions burned: 2 (million)
% 0.15/0.38  % (26699)------------------------------
% 0.15/0.38  % (26699)------------------------------
% 0.15/0.38  % (26703)Refutation not found, incomplete strategy
% 0.15/0.38  % (26703)------------------------------
% 0.15/0.38  % (26703)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38  % (26703)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.38  
% 0.15/0.38  
% 0.15/0.38  % (26703)Memory used [KB]: 5500
% 0.15/0.38  % (26703)Time elapsed: 0.004 s
% 0.15/0.38  % (26703)Instructions burned: 2 (million)
% 0.15/0.38  % (26703)------------------------------
% 0.15/0.38  % (26703)------------------------------
% 0.15/0.38  % (26697)Instruction limit reached!
% 0.15/0.38  % (26697)------------------------------
% 0.15/0.38  % (26697)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38  % (26697)Termination reason: Unknown
% 0.15/0.38  % (26697)Termination phase: Saturation
% 0.15/0.38  
% 0.15/0.38  % (26697)Memory used [KB]: 5500
% 0.15/0.38  % (26697)Time elapsed: 0.006 s
% 0.15/0.38  % (26697)Instructions burned: 5 (million)
% 0.15/0.38  % (26697)------------------------------
% 0.15/0.38  % (26697)------------------------------
% 0.15/0.38  % (26696)First to succeed.
% 0.15/0.39  % (26698)Also succeeded, but the first one will report.
% 0.15/0.39  % (26696)Refutation found. Thanks to Tanya!
% 0.15/0.39  % SZS status Theorem for Vampire---4
% 0.15/0.39  % SZS output start Proof for Vampire---4
% See solution above
% 0.15/0.39  % (26696)------------------------------
% 0.15/0.39  % (26696)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39  % (26696)Termination reason: Refutation
% 0.15/0.39  
% 0.15/0.39  % (26696)Memory used [KB]: 5500
% 0.15/0.39  % (26696)Time elapsed: 0.011 s
% 0.15/0.39  % (26696)Instructions burned: 6 (million)
% 0.15/0.39  % (26696)------------------------------
% 0.15/0.39  % (26696)------------------------------
% 0.15/0.39  % (26695)Success in time 0.01 s
% 0.15/0.39  % Vampire---4.8 exiting
%------------------------------------------------------------------------------