TSTP Solution File: SET621^5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET621^5 : TPTP v8.2.0. 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 : n016.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 03:12:29 EDT 2024

% Result   : Theorem 0.12s 0.38s
% Output   : Refutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :   15
% Syntax   : Number of formulae    :  103 (  12 unt;   7 typ;   0 def)
%            Number of atoms       :  909 ( 220 equ;   0 cnn)
%            Maximal formula atoms :    5 (   9 avg)
%            Number of connectives : 1138 ( 199   ~; 294   |; 138   &; 500   @)
%                                         (   6 <=>;   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     :   14 (  11 usr;   9 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(f275,plain,
    $false,
    inference(avatar_sat_refutation,[],[f216,f233,f245,f261,f264,f267,f270,f274]) ).

thf(f274,plain,
    ( ~ spl3_2
    | ~ spl3_6 ),
    inference(avatar_contradiction_clause,[],[f273]) ).

thf(f273,plain,
    ( $false
    | ~ spl3_2
    | ~ spl3_6 ),
    inference(trivial_inequality_removal,[],[f272]) ).

thf(f272,plain,
    ( ( $true = $false )
    | ~ spl3_2
    | ~ spl3_6 ),
    inference(forward_demodulation,[],[f260,f199]) ).

thf(f199,plain,
    ( ( $false
      = ( sK1 @ sK5 ) )
    | ~ spl3_2 ),
    inference(avatar_component_clause,[],[f197]) ).

thf(f197,plain,
    ( spl3_2
  <=> ( $false
      = ( sK1 @ sK5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

thf(f260,plain,
    ( ( $true
      = ( sK1 @ sK5 ) )
    | ~ spl3_6 ),
    inference(avatar_component_clause,[],[f258]) ).

thf(f258,plain,
    ( spl3_6
  <=> ( $true
      = ( sK1 @ sK5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).

thf(f270,plain,
    ( ~ spl3_1
    | ~ spl3_3 ),
    inference(avatar_contradiction_clause,[],[f269]) ).

thf(f269,plain,
    ( $false
    | ~ spl3_1
    | ~ spl3_3 ),
    inference(trivial_inequality_removal,[],[f268]) ).

thf(f268,plain,
    ( ( $true = $false )
    | ~ spl3_1
    | ~ spl3_3 ),
    inference(forward_demodulation,[],[f195,f204]) ).

thf(f204,plain,
    ( ( ( sK0 @ sK5 )
      = $false )
    | ~ spl3_3 ),
    inference(avatar_component_clause,[],[f202]) ).

thf(f202,plain,
    ( spl3_3
  <=> ( ( sK0 @ sK5 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

thf(f195,plain,
    ( ( ( sK0 @ sK5 )
      = $true )
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f193]) ).

thf(f193,plain,
    ( spl3_1
  <=> ( ( sK0 @ sK5 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

thf(f267,plain,
    ( ~ spl3_4
    | ~ spl3_5 ),
    inference(avatar_contradiction_clause,[],[f266]) ).

thf(f266,plain,
    ( $false
    | ~ spl3_4
    | ~ spl3_5 ),
    inference(trivial_inequality_removal,[],[f265]) ).

thf(f265,plain,
    ( ( $true = $false )
    | ~ spl3_4
    | ~ spl3_5 ),
    inference(forward_demodulation,[],[f209,f214]) ).

thf(f214,plain,
    ( ( ( sK2 @ sK5 )
      = $false )
    | ~ spl3_5 ),
    inference(avatar_component_clause,[],[f212]) ).

thf(f212,plain,
    ( spl3_5
  <=> ( ( sK2 @ sK5 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

thf(f209,plain,
    ( ( ( sK2 @ sK5 )
      = $true )
    | ~ spl3_4 ),
    inference(avatar_component_clause,[],[f207]) ).

thf(f207,plain,
    ( spl3_4
  <=> ( ( sK2 @ sK5 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

thf(f264,plain,
    ( spl3_6
    | spl3_5
    | spl3_1 ),
    inference(avatar_split_clause,[],[f27,f193,f212,f258]) ).

thf(f27,plain,
    ( ( $true
      = ( sK1 @ sK5 ) )
    | ( ( sK0 @ sK5 )
      = $true )
    | ( ( sK2 @ sK5 )
      = $false ) ),
    inference(duplicate_literal_removal,[],[f26]) ).

thf(f26,plain,
    ( ( $true
      = ( sK1 @ sK5 ) )
    | ( ( sK0 @ sK5 )
      = $true )
    | ( ( sK0 @ sK5 )
      = $true )
    | ( ( sK2 @ sK5 )
      = $false ) ),
    inference(not_proxy_clausification,[],[f25]) ).

thf(f25,plain,
    ( ( ( sK0 @ sK5 )
      = $true )
    | ( $true
      = ( sK1 @ sK5 ) )
    | ( ( sK2 @ sK5 )
      = $false )
    | ( ( ~ ( sK0 @ sK5 ) )
      = $false ) ),
    inference(duplicate_literal_removal,[],[f24]) ).

thf(f24,plain,
    ( ( $true
      = ( sK1 @ sK5 ) )
    | ( ( ~ ( sK0 @ sK5 ) )
      = $false )
    | ( ( sK0 @ sK5 )
      = $true )
    | ( ( sK2 @ sK5 )
      = $false )
    | ( ( sK2 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f23]) ).

thf(f23,plain,
    ( ( $true
      = ( sK1 @ sK5 ) )
    | ( ( sK2 @ sK5 )
      = $false )
    | ( $false
      = ( ( sK2 @ sK5 )
        & ~ ( sK0 @ sK5 ) ) )
    | ( ( sK0 @ sK5 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f21]) ).

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

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

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

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

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

thf(f16,plain,
    ( ( ( ~ ( ( sK0 @ sK5 )
            | ( sK1 @ sK5 ) ) )
      = $false )
    | ( ( ( ( ( sK2 @ sK5 )
            & ~ ( sK0 @ sK5 ) )
          | ( ~ ( sK2 @ sK5 )
            & ( sK0 @ sK5 ) ) )
        & ~ ( sK1 @ sK5 ) )
      = $false )
    | ( ( sK2 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f15]) ).

thf(f15,plain,
    ( ( $false
      = ( ( sK2 @ sK5 )
        & ~ ( ( sK0 @ sK5 )
            | ( sK1 @ sK5 ) ) ) )
    | ( ( ( ( ( sK2 @ sK5 )
            & ~ ( sK0 @ sK5 ) )
          | ( ~ ( sK2 @ sK5 )
            & ( sK0 @ sK5 ) ) )
        & ~ ( sK1 @ sK5 ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f13]) ).

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

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

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

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

thf(f8,plain,
    ( ( ^ [Y0: a] :
          ( ( ( sK2 @ Y0 )
            & ~ ( ( sK0 @ Y0 )
                | ( sK1 @ Y0 ) ) )
          | ( ~ ( ( sK1 @ Y0 )
                | ( sK2 @ Y0 ) )
            & ( sK0 @ Y0 ) ) ) )
   != ( ^ [Y0: a] :
          ( ( ( ( sK2 @ Y0 )
              & ~ ( sK0 @ Y0 ) )
            | ( ~ ( sK2 @ Y0 )
              & ( sK0 @ Y0 ) ) )
          & ~ ( sK1 @ 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 )
                & ~ ( ( X0 @ Y0 )
                    | ( X1 @ Y0 ) ) )
              | ( ~ ( ( X1 @ Y0 )
                    | ( X2 @ Y0 ) )
                & ( X0 @ Y0 ) ) ) )
       != ( ^ [Y0: a] :
              ( ( ( ( X2 @ Y0 )
                  & ~ ( X0 @ Y0 ) )
                | ( ~ ( X2 @ Y0 )
                  & ( X0 @ Y0 ) ) )
              & ~ ( X1 @ Y0 ) ) ) )
   => ( ( ^ [Y0: a] :
            ( ( ( sK2 @ Y0 )
              & ~ ( ( sK0 @ Y0 )
                  | ( sK1 @ Y0 ) ) )
            | ( ~ ( ( sK1 @ Y0 )
                  | ( sK2 @ Y0 ) )
              & ( sK0 @ Y0 ) ) ) )
     != ( ^ [Y0: a] :
            ( ( ( ( sK2 @ Y0 )
                & ~ ( sK0 @ Y0 ) )
              | ( ~ ( sK2 @ Y0 )
                & ( sK0 @ Y0 ) ) )
            & ~ ( sK1 @ Y0 ) ) ) ) ),
    introduced(choice_axiom,[]) ).

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

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

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

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

thf(f1,conjecture,
    ! [X0: a > $o,X2: a > $o,X1: a > $o] :
      ( ( ^ [X3: a] :
            ( ~ ( X2 @ X3 )
            & ( ( ( X0 @ X3 )
                & ~ ( X1 @ X3 ) )
              | ( ~ ( X0 @ X3 )
                & ( X1 @ X3 ) ) ) ) )
      = ( ^ [X4: a] :
            ( ( ( X0 @ X4 )
              & ~ ( ( X1 @ X4 )
                  | ( X2 @ X4 ) ) )
            | ( ~ ( ( X2 @ X4 )
                  | ( X0 @ X4 ) )
              & ( X1 @ X4 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_97_pme) ).

thf(f261,plain,
    ( spl3_4
    | spl3_6
    | spl3_3 ),
    inference(avatar_split_clause,[],[f43,f202,f258,f207]) ).

thf(f43,plain,
    ( ( $true
      = ( sK1 @ sK5 ) )
    | ( ( sK2 @ sK5 )
      = $true )
    | ( ( sK0 @ sK5 )
      = $false ) ),
    inference(duplicate_literal_removal,[],[f42]) ).

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

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

thf(f40,plain,
    ( ( ( ~ ( sK2 @ sK5 ) )
      = $false )
    | ( $true
      = ( sK1 @ sK5 ) )
    | ( ( sK2 @ sK5 )
      = $true )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( ( sK0 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f36]) ).

thf(f36,plain,
    ( ( ( sK0 @ sK5 )
      = $false )
    | ( ( ~ ( sK2 @ sK5 )
        & ( sK0 @ sK5 ) )
      = $false )
    | ( ( sK2 @ sK5 )
      = $true )
    | ( $true
      = ( sK1 @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f35]) ).

thf(f35,plain,
    ( ( ( sK0 @ sK5 )
      = $false )
    | ( $true
      = ( sK1 @ sK5 ) )
    | ( ( sK2 @ sK5 )
      = $true )
    | ( ( ( ( sK2 @ sK5 )
          & ~ ( sK0 @ sK5 ) )
        | ( ~ ( sK2 @ sK5 )
          & ( sK0 @ sK5 ) ) )
      = $false ) ),
    inference(duplicate_literal_removal,[],[f34]) ).

thf(f34,plain,
    ( ( $true
      = ( sK1 @ sK5 ) )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( ( sK2 @ sK5 )
      = $true )
    | ( ( ( ( sK2 @ sK5 )
          & ~ ( sK0 @ sK5 ) )
        | ( ~ ( sK2 @ sK5 )
          & ( sK0 @ sK5 ) ) )
      = $false )
    | ( $true
      = ( sK1 @ sK5 ) ) ),
    inference(not_proxy_clausification,[],[f33]) ).

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

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

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

thf(f30,plain,
    ( ( ( sK0 @ sK5 )
      = $false )
    | ( ( ( ( ( sK2 @ sK5 )
            & ~ ( sK0 @ sK5 ) )
          | ( ~ ( sK2 @ sK5 )
            & ( sK0 @ sK5 ) ) )
        & ~ ( sK1 @ sK5 ) )
      = $false )
    | ( ( ~ ( ( sK1 @ sK5 )
            | ( sK2 @ sK5 ) ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f14]) ).

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

thf(f245,plain,
    ( spl3_1
    | spl3_4 ),
    inference(avatar_split_clause,[],[f87,f207,f193]) ).

thf(f87,plain,
    ( ( ( sK0 @ sK5 )
      = $true )
    | ( ( sK2 @ sK5 )
      = $true ) ),
    inference(duplicate_literal_removal,[],[f82]) ).

thf(f82,plain,
    ( ( ( sK0 @ sK5 )
      = $true )
    | ( ( sK0 @ sK5 )
      = $true )
    | ( ( sK2 @ sK5 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f81]) ).

thf(f81,plain,
    ( ( ( ~ ( ( sK1 @ sK5 )
            | ( sK2 @ sK5 ) )
        & ( sK0 @ sK5 ) )
      = $true )
    | ( ( sK0 @ sK5 )
      = $true )
    | ( ( sK2 @ sK5 )
      = $true ) ),
    inference(duplicate_literal_removal,[],[f80]) ).

thf(f80,plain,
    ( ( ( ~ ( ( sK1 @ sK5 )
            | ( sK2 @ sK5 ) )
        & ( sK0 @ sK5 ) )
      = $true )
    | ( ( sK2 @ sK5 )
      = $true )
    | ( ( sK2 @ sK5 )
      = $true )
    | ( ( sK0 @ sK5 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f78]) ).

thf(f78,plain,
    ( ( ( sK0 @ sK5 )
      = $true )
    | ( $true
      = ( ( sK2 @ sK5 )
        & ~ ( ( sK0 @ sK5 )
            | ( sK1 @ sK5 ) ) ) )
    | ( ( sK2 @ sK5 )
      = $true )
    | ( ( ~ ( ( sK1 @ sK5 )
            | ( sK2 @ sK5 ) )
        & ( sK0 @ sK5 ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f49]) ).

thf(f49,plain,
    ( ( ( sK2 @ sK5 )
      = $true )
    | ( $true
      = ( ( ( sK2 @ sK5 )
          & ~ ( ( sK0 @ sK5 )
              | ( sK1 @ sK5 ) ) )
        | ( ~ ( ( sK1 @ sK5 )
              | ( sK2 @ sK5 ) )
          & ( sK0 @ sK5 ) ) ) )
    | ( ( sK0 @ sK5 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f48]) ).

thf(f48,plain,
    ( ( ( ~ ( sK2 @ sK5 )
        & ( sK0 @ sK5 ) )
      = $true )
    | ( $true
      = ( ( ( sK2 @ sK5 )
          & ~ ( ( sK0 @ sK5 )
              | ( sK1 @ sK5 ) ) )
        | ( ~ ( ( sK1 @ sK5 )
              | ( sK2 @ sK5 ) )
          & ( sK0 @ sK5 ) ) ) )
    | ( ( sK2 @ sK5 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f46]) ).

thf(f46,plain,
    ( ( $true
      = ( ( sK2 @ sK5 )
        & ~ ( sK0 @ sK5 ) ) )
    | ( ( ~ ( sK2 @ sK5 )
        & ( sK0 @ sK5 ) )
      = $true )
    | ( $true
      = ( ( ( sK2 @ sK5 )
          & ~ ( ( sK0 @ sK5 )
              | ( sK1 @ sK5 ) ) )
        | ( ~ ( ( sK1 @ sK5 )
              | ( sK2 @ sK5 ) )
          & ( sK0 @ sK5 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f45]) ).

thf(f45,plain,
    ( ( $true
      = ( ( ( sK2 @ sK5 )
          & ~ ( sK0 @ sK5 ) )
        | ( ~ ( sK2 @ sK5 )
          & ( sK0 @ sK5 ) ) ) )
    | ( $true
      = ( ( ( sK2 @ sK5 )
          & ~ ( ( sK0 @ sK5 )
              | ( sK1 @ sK5 ) ) )
        | ( ~ ( ( sK1 @ sK5 )
              | ( sK2 @ sK5 ) )
          & ( sK0 @ sK5 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f12]) ).

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

thf(f233,plain,
    ( spl3_5
    | spl3_3 ),
    inference(avatar_split_clause,[],[f132,f202,f212]) ).

thf(f132,plain,
    ( ( ( sK2 @ sK5 )
      = $false )
    | ( ( sK0 @ sK5 )
      = $false ) ),
    inference(duplicate_literal_removal,[],[f131]) ).

thf(f131,plain,
    ( ( ( sK0 @ sK5 )
      = $false )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( ( sK2 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f129]) ).

thf(f129,plain,
    ( ( ( sK2 @ sK5 )
      = $false )
    | ( $false
      = ( ( sK0 @ sK5 )
        | ( sK1 @ sK5 ) ) )
    | ( ( sK0 @ sK5 )
      = $false ) ),
    inference(duplicate_literal_removal,[],[f123]) ).

thf(f123,plain,
    ( ( ( sK2 @ sK5 )
      = $false )
    | ( ( sK2 @ sK5 )
      = $false )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( $false
      = ( ( sK0 @ sK5 )
        | ( sK1 @ sK5 ) ) ) ),
    inference(binary_proxy_clausification,[],[f122]) ).

thf(f122,plain,
    ( ( ( ( sK1 @ sK5 )
        | ( sK2 @ sK5 ) )
      = $false )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( $false
      = ( ( sK0 @ sK5 )
        | ( sK1 @ sK5 ) ) )
    | ( ( sK2 @ sK5 )
      = $false ) ),
    inference(not_proxy_clausification,[],[f121]) ).

thf(f121,plain,
    ( ( ( sK2 @ sK5 )
      = $false )
    | ( $true
      = ( ~ ( ( sK0 @ sK5 )
            | ( sK1 @ sK5 ) ) ) )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( ( ( sK1 @ sK5 )
        | ( sK2 @ sK5 ) )
      = $false ) ),
    inference(not_proxy_clausification,[],[f120]) ).

thf(f120,plain,
    ( ( ( sK0 @ sK5 )
      = $false )
    | ( ( sK2 @ sK5 )
      = $false )
    | ( ( ~ ( ( sK1 @ sK5 )
            | ( sK2 @ sK5 ) ) )
      = $true )
    | ( $true
      = ( ~ ( ( sK0 @ sK5 )
            | ( sK1 @ sK5 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f118]) ).

thf(f118,plain,
    ( ( ( sK2 @ sK5 )
      = $false )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( ( ~ ( ( sK1 @ sK5 )
            | ( sK2 @ sK5 ) )
        & ( sK0 @ sK5 ) )
      = $true )
    | ( $true
      = ( ~ ( ( sK0 @ sK5 )
            | ( sK1 @ sK5 ) ) ) ) ),
    inference(not_proxy_clausification,[],[f108]) ).

thf(f108,plain,
    ( ( ( sK0 @ sK5 )
      = $false )
    | ( $true
      = ( ~ ( sK2 @ sK5 ) ) )
    | ( ( ~ ( ( sK1 @ sK5 )
            | ( sK2 @ sK5 ) )
        & ( sK0 @ sK5 ) )
      = $true )
    | ( $true
      = ( ~ ( ( sK0 @ sK5 )
            | ( sK1 @ sK5 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f107]) ).

thf(f107,plain,
    ( ( $true
      = ( ( sK2 @ sK5 )
        & ~ ( ( sK0 @ sK5 )
            | ( sK1 @ sK5 ) ) ) )
    | ( ( ~ ( ( sK1 @ sK5 )
            | ( sK2 @ sK5 ) )
        & ( sK0 @ sK5 ) )
      = $true )
    | ( $true
      = ( ~ ( sK2 @ sK5 ) ) )
    | ( ( sK0 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f106]) ).

thf(f106,plain,
    ( ( $true
      = ( ( ( sK2 @ sK5 )
          & ~ ( ( sK0 @ sK5 )
              | ( sK1 @ sK5 ) ) )
        | ( ~ ( ( sK1 @ sK5 )
              | ( sK2 @ sK5 ) )
          & ( sK0 @ sK5 ) ) ) )
    | ( $true
      = ( ~ ( sK2 @ sK5 ) ) )
    | ( ( sK0 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f104]) ).

thf(f104,plain,
    ( ( ( sK0 @ sK5 )
      = $false )
    | ( ( ~ ( sK2 @ sK5 )
        & ( sK0 @ sK5 ) )
      = $true )
    | ( $true
      = ( ( ( sK2 @ sK5 )
          & ~ ( ( sK0 @ sK5 )
              | ( sK1 @ sK5 ) ) )
        | ( ~ ( ( sK1 @ sK5 )
              | ( sK2 @ sK5 ) )
          & ( sK0 @ sK5 ) ) ) ) ),
    inference(not_proxy_clausification,[],[f47]) ).

thf(f47,plain,
    ( ( $true
      = ( ~ ( sK0 @ sK5 ) ) )
    | ( ( ~ ( sK2 @ sK5 )
        & ( sK0 @ sK5 ) )
      = $true )
    | ( $true
      = ( ( ( sK2 @ sK5 )
          & ~ ( ( sK0 @ sK5 )
              | ( sK1 @ sK5 ) ) )
        | ( ~ ( ( sK1 @ sK5 )
              | ( sK2 @ sK5 ) )
          & ( sK0 @ sK5 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f46]) ).

thf(f216,plain,
    spl3_2,
    inference(avatar_split_clause,[],[f185,f197]) ).

thf(f185,plain,
    ( $false
    = ( sK1 @ sK5 ) ),
    inference(duplicate_literal_removal,[],[f184]) ).

thf(f184,plain,
    ( ( $false
      = ( sK1 @ sK5 ) )
    | ( $false
      = ( sK1 @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f182]) ).

thf(f182,plain,
    ( ( ( ( sK1 @ sK5 )
        | ( sK2 @ sK5 ) )
      = $false )
    | ( $false
      = ( sK1 @ sK5 ) ) ),
    inference(not_proxy_clausification,[],[f181]) ).

thf(f181,plain,
    ( ( $false
      = ( sK1 @ sK5 ) )
    | ( ( ~ ( ( sK1 @ sK5 )
            | ( sK2 @ sK5 ) ) )
      = $true ) ),
    inference(duplicate_literal_removal,[],[f175]) ).

thf(f175,plain,
    ( ( ( ~ ( ( sK1 @ sK5 )
            | ( sK2 @ sK5 ) ) )
      = $true )
    | ( $false
      = ( sK1 @ sK5 ) )
    | ( $false
      = ( sK1 @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f174]) ).

thf(f174,plain,
    ( ( $false
      = ( sK1 @ sK5 ) )
    | ( $false
      = ( ( sK0 @ sK5 )
        | ( sK1 @ sK5 ) ) )
    | ( ( ~ ( ( sK1 @ sK5 )
            | ( sK2 @ sK5 ) ) )
      = $true ) ),
    inference(not_proxy_clausification,[],[f168]) ).

thf(f168,plain,
    ( ( $false
      = ( sK1 @ sK5 ) )
    | ( $true
      = ( ~ ( ( sK0 @ sK5 )
            | ( sK1 @ sK5 ) ) ) )
    | ( ( ~ ( ( sK1 @ sK5 )
            | ( sK2 @ sK5 ) ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f167]) ).

thf(f167,plain,
    ( ( $true
      = ( ( sK2 @ sK5 )
        & ~ ( ( sK0 @ sK5 )
            | ( sK1 @ sK5 ) ) ) )
    | ( ( ~ ( ( sK1 @ sK5 )
            | ( sK2 @ sK5 ) ) )
      = $true )
    | ( $false
      = ( sK1 @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f165]) ).

thf(f165,plain,
    ( ( ( ~ ( ( sK1 @ sK5 )
            | ( sK2 @ sK5 ) )
        & ( sK0 @ sK5 ) )
      = $true )
    | ( $false
      = ( sK1 @ sK5 ) )
    | ( $true
      = ( ( sK2 @ sK5 )
        & ~ ( ( sK0 @ sK5 )
            | ( sK1 @ sK5 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f164]) ).

thf(f164,plain,
    ( ( $false
      = ( sK1 @ sK5 ) )
    | ( $true
      = ( ( ( sK2 @ sK5 )
          & ~ ( ( sK0 @ sK5 )
              | ( sK1 @ sK5 ) ) )
        | ( ~ ( ( sK1 @ sK5 )
              | ( sK2 @ sK5 ) )
          & ( sK0 @ sK5 ) ) ) ) ),
    inference(not_proxy_clausification,[],[f44]) ).

thf(f44,plain,
    ( ( $true
      = ( ~ ( sK1 @ sK5 ) ) )
    | ( $true
      = ( ( ( sK2 @ sK5 )
          & ~ ( ( sK0 @ sK5 )
              | ( sK1 @ sK5 ) ) )
        | ( ~ ( ( sK1 @ sK5 )
              | ( sK2 @ sK5 ) )
          & ( sK0 @ sK5 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : SET621^5 : TPTP v8.2.0. Released v4.0.0.
% 0.10/0.14  % 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
% 0.12/0.35  % Computer : n016.cluster.edu
% 0.12/0.35  % Model    : x86_64 x86_64
% 0.12/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35  % Memory   : 8042.1875MB
% 0.12/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35  % CPULimit   : 300
% 0.12/0.35  % WCLimit    : 300
% 0.12/0.35  % DateTime   : Mon May 20 13:19:37 EDT 2024
% 0.12/0.35  % CPUTime    : 
% 0.12/0.35  This is a TH0_THM_EQU_NAR problem
% 0.12/0.35  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/sandbox/benchmark/theBenchmark.p
% 0.12/0.37  % (6740)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)
% 0.12/0.37  % (6746)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)
% 0.12/0.37  % (6744)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)
% 0.12/0.37  % (6741)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)
% 0.12/0.37  % (6739)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.12/0.37  % (6743)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)
% 0.12/0.37  % (6742)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.12/0.37  % (6742)Instruction limit reached!
% 0.12/0.37  % (6742)------------------------------
% 0.12/0.37  % (6742)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.37  % (6742)Termination reason: Unknown
% 0.12/0.37  % (6742)Termination phase: Saturation
% 0.12/0.37  % (6743)Instruction limit reached!
% 0.12/0.37  % (6743)------------------------------
% 0.12/0.37  % (6743)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.37  
% 0.12/0.37  % (6742)Memory used [KB]: 895
% 0.12/0.37  % (6742)Time elapsed: 0.003 s
% 0.12/0.37  % (6742)Instructions burned: 2 (million)
% 0.12/0.37  % (6742)------------------------------
% 0.12/0.37  % (6742)------------------------------
% 0.12/0.37  % (6743)Termination reason: Unknown
% 0.12/0.37  % (6743)Termination phase: Saturation
% 0.12/0.37  
% 0.12/0.37  % (6743)Memory used [KB]: 895
% 0.12/0.37  % (6743)Time elapsed: 0.003 s
% 0.12/0.37  % (6743)Instructions burned: 2 (million)
% 0.12/0.37  % (6743)------------------------------
% 0.12/0.37  % (6743)------------------------------
% 0.12/0.37  % (6746)Refutation not found, incomplete strategy
% 0.12/0.37  % (6746)------------------------------
% 0.12/0.37  % (6746)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.37  % (6746)Termination reason: Refutation not found, incomplete strategy
% 0.12/0.37  
% 0.12/0.37  
% 0.12/0.37  % (6746)Memory used [KB]: 5500
% 0.12/0.37  % (6746)Time elapsed: 0.003 s
% 0.12/0.37  % (6746)Instructions burned: 2 (million)
% 0.12/0.37  % (6746)------------------------------
% 0.12/0.37  % (6746)------------------------------
% 0.12/0.37  % (6740)Instruction limit reached!
% 0.12/0.37  % (6740)------------------------------
% 0.12/0.37  % (6740)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.37  % (6740)Termination reason: Unknown
% 0.12/0.37  % (6740)Termination phase: Saturation
% 0.12/0.37  
% 0.12/0.37  % (6740)Memory used [KB]: 5500
% 0.12/0.37  % (6740)Time elapsed: 0.005 s
% 0.12/0.37  % (6740)Instructions burned: 4 (million)
% 0.12/0.37  % (6740)------------------------------
% 0.12/0.37  % (6740)------------------------------
% 0.12/0.37  % (6745)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.12/0.37  % (6744)First to succeed.
% 0.12/0.38  % (6739)Also succeeded, but the first one will report.
% 0.12/0.38  % (6741)Also succeeded, but the first one will report.
% 0.12/0.38  % (6744)Refutation found. Thanks to Tanya!
% 0.12/0.38  % SZS status Theorem for theBenchmark
% 0.12/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.38  % (6744)------------------------------
% 0.12/0.38  % (6744)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.38  % (6744)Termination reason: Refutation
% 0.12/0.38  
% 0.12/0.38  % (6744)Memory used [KB]: 5500
% 0.12/0.38  % (6744)Time elapsed: 0.010 s
% 0.12/0.38  % (6744)Instructions burned: 8 (million)
% 0.12/0.38  % (6744)------------------------------
% 0.12/0.38  % (6744)------------------------------
% 0.12/0.38  % (6738)Success in time 0.022 s
% 0.12/0.38  % Vampire---4.8 exiting
%------------------------------------------------------------------------------