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

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET622^5 : 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 : n017.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 03:12:30 EDT 2024

% Result   : Theorem 0.23s 0.39s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   98 (  12 unt;   7 typ;   0 def)
%            Number of atoms       :  840 ( 200 equ;   0 cnn)
%            Maximal formula atoms :    6 (   9 avg)
%            Number of connectives : 1074 ( 188   ~; 236   |; 172   &; 471   @)
%                                         (   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(f255,plain,
    $false,
    inference(avatar_sat_refutation,[],[f199,f212,f217,f228,f235,f241,f247,f254]) ).

thf(f254,plain,
    ( ~ spl3_1
    | ~ spl3_5 ),
    inference(avatar_contradiction_clause,[],[f253]) ).

thf(f253,plain,
    ( $false
    | ~ spl3_1
    | ~ spl3_5 ),
    inference(trivial_inequality_removal,[],[f250]) ).

thf(f250,plain,
    ( ( $true = $false )
    | ~ spl3_1
    | ~ spl3_5 ),
    inference(superposition,[],[f180,f197]) ).

thf(f197,plain,
    ( ( $true
      = ( sK0 @ sK5 ) )
    | ~ spl3_5 ),
    inference(avatar_component_clause,[],[f195]) ).

thf(f195,plain,
    ( spl3_5
  <=> ( $true
      = ( sK0 @ sK5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

thf(f180,plain,
    ( ( ( sK0 @ sK5 )
      = $false )
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f178]) ).

thf(f178,plain,
    ( spl3_1
  <=> ( ( sK0 @ sK5 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

thf(f247,plain,
    ( ~ spl3_3
    | ~ spl3_6 ),
    inference(avatar_contradiction_clause,[],[f246]) ).

thf(f246,plain,
    ( $false
    | ~ spl3_3
    | ~ spl3_6 ),
    inference(trivial_inequality_removal,[],[f243]) ).

thf(f243,plain,
    ( ( $true = $false )
    | ~ spl3_3
    | ~ spl3_6 ),
    inference(superposition,[],[f188,f227]) ).

thf(f227,plain,
    ( ( ( sK2 @ sK5 )
      = $false )
    | ~ spl3_6 ),
    inference(avatar_component_clause,[],[f225]) ).

thf(f225,plain,
    ( spl3_6
  <=> ( ( sK2 @ sK5 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).

thf(f188,plain,
    ( ( ( sK2 @ sK5 )
      = $true )
    | ~ spl3_3 ),
    inference(avatar_component_clause,[],[f186]) ).

thf(f186,plain,
    ( spl3_3
  <=> ( ( sK2 @ sK5 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

thf(f241,plain,
    ( ~ spl3_2
    | ~ spl3_4 ),
    inference(avatar_contradiction_clause,[],[f240]) ).

thf(f240,plain,
    ( $false
    | ~ spl3_2
    | ~ spl3_4 ),
    inference(trivial_inequality_removal,[],[f237]) ).

thf(f237,plain,
    ( ( $true = $false )
    | ~ spl3_2
    | ~ spl3_4 ),
    inference(superposition,[],[f184,f193]) ).

thf(f193,plain,
    ( ( ( sK1 @ sK5 )
      = $false )
    | ~ spl3_4 ),
    inference(avatar_component_clause,[],[f191]) ).

thf(f191,plain,
    ( spl3_4
  <=> ( ( sK1 @ sK5 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

thf(f184,plain,
    ( ( ( sK1 @ sK5 )
      = $true )
    | ~ spl3_2 ),
    inference(avatar_component_clause,[],[f182]) ).

thf(f182,plain,
    ( spl3_2
  <=> ( ( sK1 @ sK5 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

thf(f235,plain,
    ( spl3_6
    | spl3_1
    | spl3_4 ),
    inference(avatar_split_clause,[],[f28,f191,f178,f225]) ).

thf(f28,plain,
    ( ( ( sK2 @ sK5 )
      = $false )
    | ( ( sK1 @ sK5 )
      = $false )
    | ( ( sK0 @ sK5 )
      = $false ) ),
    inference(duplicate_literal_removal,[],[f27]) ).

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

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

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

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

thf(f23,plain,
    ( ( ( ~ ( sK0 @ sK5 ) )
      = $true )
    | ( $true
      = ( ~ ( sK1 @ sK5 ) ) )
    | ( ( ( sK2 @ sK5 )
        & ( sK0 @ sK5 ) )
      = $false )
    | ( ( sK2 @ sK5 )
      = $false )
    | ( ( sK1 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f22]) ).

thf(f22,plain,
    ( ( ( ( sK2 @ sK5 )
        & ( sK0 @ sK5 )
        & ( sK1 @ sK5 ) )
      = $false )
    | ( $true
      = ( ~ ( sK1 @ sK5 ) ) )
    | ( ( sK2 @ sK5 )
      = $false )
    | ( ( ~ ( sK0 @ sK5 ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f20]) ).

thf(f20,plain,
    ( ( ( ~ ( sK1 @ sK5 )
        & ( sK0 @ sK5 ) )
      = $true )
    | ( ( sK2 @ sK5 )
      = $false )
    | ( ( ( sK2 @ sK5 )
        & ( sK0 @ sK5 )
        & ( sK1 @ sK5 ) )
      = $false )
    | ( ( ~ ( sK0 @ sK5 ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f18]) ).

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

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

thf(f16,plain,
    ( ( ( ~ ( ( ~ ( sK0 @ sK5 )
              & ( sK1 @ sK5 ) )
            | ( ~ ( sK1 @ sK5 )
              & ( sK0 @ sK5 ) ) ) )
      = $false )
    | ( ( ( 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 ) )
            | ( ~ ( sK1 @ 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 )
              | ( sK0 @ sK5 ) )
          & ( sK2 @ sK5 ) ) )
      = $false )
    | ( $false
      = ( ( sK2 @ sK5 )
        & ~ ( ( ~ ( sK0 @ sK5 )
              & ( sK1 @ sK5 ) )
            | ( ~ ( sK1 @ sK5 )
              & ( sK0 @ sK5 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f11]) ).

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

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

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

thf(f8,plain,
    ( ( ^ [Y0: a] :
          ( ( sK2 @ Y0 )
          & ~ ( ( ~ ( sK0 @ Y0 )
                & ( sK1 @ Y0 ) )
              | ( ~ ( sK1 @ Y0 )
                & ( sK0 @ Y0 ) ) ) ) )
   != ( ^ [Y0: a] :
          ( ( ( sK2 @ Y0 )
            & ( sK0 @ Y0 )
            & ( sK1 @ Y0 ) )
          | ( ~ ( ( sK1 @ Y0 )
                | ( sK0 @ Y0 ) )
            & ( sK2 @ 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 )
                    | ( X0 @ Y0 ) )
                & ( X2 @ Y0 ) ) ) )
       != ( ^ [Y0: a] :
              ( ( X2 @ Y0 )
              & ~ ( ( ~ ( X0 @ Y0 )
                    & ( X1 @ Y0 ) )
                  | ( ~ ( X1 @ Y0 )
                    & ( X0 @ Y0 ) ) ) ) ) )
   => ( ( ^ [Y0: a] :
            ( ( sK2 @ Y0 )
            & ~ ( ( ~ ( sK0 @ Y0 )
                  & ( sK1 @ Y0 ) )
                | ( ~ ( sK1 @ Y0 )
                  & ( sK0 @ Y0 ) ) ) ) )
     != ( ^ [Y0: a] :
            ( ( ( sK2 @ Y0 )
              & ( sK0 @ Y0 )
              & ( sK1 @ Y0 ) )
            | ( ~ ( ( sK1 @ Y0 )
                  | ( sK0 @ Y0 ) )
              & ( sK2 @ 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 )
                  | ( X0 @ Y0 ) )
              & ( X2 @ Y0 ) ) ) )
     != ( ^ [Y0: a] :
            ( ( X2 @ Y0 )
            & ~ ( ( ~ ( X0 @ Y0 )
                  & ( X1 @ 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 )
                & ( X0 @ Y0 )
                & ( X1 @ Y0 ) )
              | ( ~ ( ( X1 @ Y0 )
                    | ( X0 @ Y0 ) )
                & ( X2 @ Y0 ) ) ) )
        = ( ^ [Y0: a] :
              ( ( X2 @ Y0 )
              & ~ ( ( ~ ( X0 @ Y0 )
                    & ( X1 @ Y0 ) )
                  | ( ~ ( X1 @ Y0 )
                    & ( X0 @ Y0 ) ) ) ) ) ),
    inference(fool_elimination,[],[f4]) ).

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

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

thf(f1,conjecture,
    ! [X1: a > $o,X2: a > $o,X0: a > $o] :
      ( ( ^ [X4: a] :
            ( ( ( X0 @ X4 )
              & ~ ( ( X1 @ X4 )
                  | ( X2 @ X4 ) ) )
            | ( ( X2 @ X4 )
              & ( X1 @ X4 )
              & ( X0 @ X4 ) ) ) )
      = ( ^ [X3: a] :
            ( ~ ( ( ( X1 @ X3 )
                  & ~ ( X2 @ X3 ) )
                | ( ( X2 @ X3 )
                  & ~ ( X1 @ X3 ) ) )
            & ( X0 @ X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_98_pme) ).

thf(f228,plain,
    ( spl3_5
    | spl3_2
    | spl3_6 ),
    inference(avatar_split_clause,[],[f62,f225,f182,f195]) ).

thf(f62,plain,
    ( ( ( sK1 @ sK5 )
      = $true )
    | ( ( sK2 @ sK5 )
      = $false )
    | ( $true
      = ( sK0 @ sK5 ) ) ),
    inference(duplicate_literal_removal,[],[f61]) ).

thf(f61,plain,
    ( ( $true
      = ( sK0 @ sK5 ) )
    | ( $true
      = ( sK0 @ sK5 ) )
    | ( ( sK1 @ sK5 )
      = $true )
    | ( ( sK1 @ sK5 )
      = $true )
    | ( ( sK2 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f56]) ).

thf(f56,plain,
    ( ( ( sK1 @ sK5 )
      = $true )
    | ( ( sK2 @ sK5 )
      = $false )
    | ( $true
      = ( sK0 @ sK5 ) )
    | ( ( ( sK1 @ sK5 )
        | ( sK0 @ sK5 ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f46]) ).

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

thf(f45,plain,
    ( ( ( ~ ( sK1 @ sK5 )
        & ( sK0 @ sK5 ) )
      = $true )
    | ( ( ( sK1 @ sK5 )
        | ( sK0 @ sK5 ) )
      = $true )
    | ( $true
      = ( ~ ( sK0 @ sK5 )
        & ( sK1 @ sK5 ) ) )
    | ( ( sK2 @ sK5 )
      = $false ) ),
    inference(not_proxy_clausification,[],[f44]) ).

thf(f44,plain,
    ( ( $false
      = ( ~ ( ( sK1 @ sK5 )
            | ( sK0 @ sK5 ) ) ) )
    | ( ( ~ ( sK1 @ sK5 )
        & ( sK0 @ sK5 ) )
      = $true )
    | ( $true
      = ( ~ ( sK0 @ sK5 )
        & ( sK1 @ sK5 ) ) )
    | ( ( sK2 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f43]) ).

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

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

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

thf(f40,plain,
    ( ( ( sK2 @ sK5 )
      = $false )
    | ( ( ~ ( ( sK1 @ sK5 )
            | ( sK0 @ sK5 ) )
        & ( sK2 @ sK5 ) )
      = $false )
    | ( ( ~ ( ( ~ ( sK0 @ sK5 )
              & ( sK1 @ sK5 ) )
            | ( ~ ( sK1 @ sK5 )
              & ( sK0 @ sK5 ) ) ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f14]) ).

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

thf(f217,plain,
    spl3_3,
    inference(avatar_split_clause,[],[f98,f186]) ).

thf(f98,plain,
    ( ( sK2 @ sK5 )
    = $true ),
    inference(duplicate_literal_removal,[],[f97]) ).

thf(f97,plain,
    ( ( ( sK2 @ sK5 )
      = $true )
    | ( ( sK2 @ sK5 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f95]) ).

thf(f95,plain,
    ( ( $true
      = ( ( sK2 @ sK5 )
        & ~ ( ( ~ ( sK0 @ sK5 )
              & ( sK1 @ sK5 ) )
            | ( ~ ( sK1 @ sK5 )
              & ( sK0 @ sK5 ) ) ) ) )
    | ( ( sK2 @ sK5 )
      = $true ) ),
    inference(duplicate_literal_removal,[],[f68]) ).

thf(f68,plain,
    ( ( $true
      = ( ( sK2 @ sK5 )
        & ~ ( ( ~ ( sK0 @ sK5 )
              & ( sK1 @ sK5 ) )
            | ( ~ ( sK1 @ sK5 )
              & ( sK0 @ sK5 ) ) ) ) )
    | ( ( sK2 @ sK5 )
      = $true )
    | ( ( sK2 @ sK5 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f67]) ).

thf(f67,plain,
    ( ( ( sK2 @ sK5 )
      = $true )
    | ( ( ~ ( ( sK1 @ sK5 )
            | ( sK0 @ sK5 ) )
        & ( sK2 @ sK5 ) )
      = $true )
    | ( $true
      = ( ( sK2 @ sK5 )
        & ~ ( ( ~ ( sK0 @ sK5 )
              & ( sK1 @ sK5 ) )
            | ( ~ ( sK1 @ sK5 )
              & ( sK0 @ sK5 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f65]) ).

thf(f65,plain,
    ( ( ( ( sK2 @ sK5 )
        & ( sK0 @ sK5 ) )
      = $true )
    | ( ( ~ ( ( sK1 @ sK5 )
            | ( sK0 @ sK5 ) )
        & ( sK2 @ sK5 ) )
      = $true )
    | ( $true
      = ( ( sK2 @ sK5 )
        & ~ ( ( ~ ( sK0 @ sK5 )
              & ( sK1 @ sK5 ) )
            | ( ~ ( sK1 @ sK5 )
              & ( sK0 @ sK5 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f63]) ).

thf(f63,plain,
    ( ( ( ( sK2 @ sK5 )
        & ( sK0 @ sK5 )
        & ( sK1 @ sK5 ) )
      = $true )
    | ( $true
      = ( ( sK2 @ sK5 )
        & ~ ( ( ~ ( sK0 @ sK5 )
              & ( sK1 @ sK5 ) )
            | ( ~ ( sK1 @ sK5 )
              & ( sK0 @ sK5 ) ) ) ) )
    | ( ( ~ ( ( sK1 @ sK5 )
            | ( sK0 @ sK5 ) )
        & ( sK2 @ sK5 ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f12]) ).

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

thf(f212,plain,
    ( spl3_5
    | spl3_4 ),
    inference(avatar_split_clause,[],[f122,f191,f195]) ).

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

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

thf(f120,plain,
    ( ( ( ~ ( sK0 @ sK5 ) )
      = $false )
    | ( ( sK1 @ sK5 )
      = $false )
    | ( $true
      = ( sK0 @ sK5 ) ) ),
    inference(duplicate_literal_removal,[],[f119]) ).

thf(f119,plain,
    ( ( ( sK1 @ sK5 )
      = $false )
    | ( ( sK1 @ sK5 )
      = $false )
    | ( $true
      = ( sK0 @ sK5 ) )
    | ( ( ~ ( sK0 @ sK5 ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f118]) ).

thf(f118,plain,
    ( ( ( sK1 @ sK5 )
      = $false )
    | ( $false
      = ( ~ ( sK0 @ sK5 )
        & ( sK1 @ sK5 ) ) )
    | ( $true
      = ( sK0 @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f116]) ).

thf(f116,plain,
    ( ( $false
      = ( ( ~ ( sK0 @ sK5 )
          & ( sK1 @ sK5 ) )
        | ( ~ ( sK1 @ sK5 )
          & ( sK0 @ sK5 ) ) ) )
    | ( ( sK1 @ sK5 )
      = $false )
    | ( $true
      = ( sK0 @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f114]) ).

thf(f114,plain,
    ( ( ( ( sK1 @ sK5 )
        | ( sK0 @ sK5 ) )
      = $false )
    | ( $false
      = ( ( ~ ( sK0 @ sK5 )
          & ( sK1 @ sK5 ) )
        | ( ~ ( sK1 @ sK5 )
          & ( sK0 @ sK5 ) ) ) )
    | ( $true
      = ( sK0 @ sK5 ) ) ),
    inference(not_proxy_clausification,[],[f113]) ).

thf(f113,plain,
    ( ( $true
      = ( sK0 @ sK5 ) )
    | ( $true
      = ( ~ ( ( sK1 @ sK5 )
            | ( sK0 @ sK5 ) ) ) )
    | ( $false
      = ( ( ~ ( sK0 @ sK5 )
          & ( sK1 @ sK5 ) )
        | ( ~ ( sK1 @ sK5 )
          & ( sK0 @ sK5 ) ) ) ) ),
    inference(not_proxy_clausification,[],[f108]) ).

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

thf(f107,plain,
    ( ( $true
      = ( ( sK2 @ sK5 )
        & ~ ( ( ~ ( sK0 @ sK5 )
              & ( sK1 @ sK5 ) )
            | ( ~ ( sK1 @ sK5 )
              & ( sK0 @ sK5 ) ) ) ) )
    | ( $true
      = ( sK0 @ sK5 ) )
    | ( $true
      = ( ~ ( ( sK1 @ sK5 )
            | ( sK0 @ sK5 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f66]) ).

thf(f66,plain,
    ( ( $true
      = ( sK0 @ sK5 ) )
    | ( ( ~ ( ( sK1 @ sK5 )
            | ( sK0 @ sK5 ) )
        & ( sK2 @ sK5 ) )
      = $true )
    | ( $true
      = ( ( sK2 @ sK5 )
        & ~ ( ( ~ ( sK0 @ sK5 )
              & ( sK1 @ sK5 ) )
            | ( ~ ( sK1 @ sK5 )
              & ( sK0 @ sK5 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f65]) ).

thf(f199,plain,
    ( spl3_2
    | spl3_1 ),
    inference(avatar_split_clause,[],[f169,f178,f182]) ).

thf(f169,plain,
    ( ( ( sK1 @ sK5 )
      = $true )
    | ( ( sK0 @ sK5 )
      = $false ) ),
    inference(duplicate_literal_removal,[],[f167]) ).

thf(f167,plain,
    ( ( ( sK0 @ sK5 )
      = $false )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( ( sK1 @ sK5 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f166]) ).

thf(f166,plain,
    ( ( ( ( sK1 @ sK5 )
        | ( sK0 @ sK5 ) )
      = $false )
    | ( ( sK1 @ sK5 )
      = $true )
    | ( ( sK0 @ sK5 )
      = $false ) ),
    inference(duplicate_literal_removal,[],[f165]) ).

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

thf(f164,plain,
    ( ( ( sK1 @ sK5 )
      = $true )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( ( ~ ( sK1 @ sK5 ) )
      = $false )
    | ( ( ( sK1 @ sK5 )
        | ( sK0 @ sK5 ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f156]) ).

thf(f156,plain,
    ( ( ( ~ ( sK1 @ sK5 )
        & ( sK0 @ sK5 ) )
      = $false )
    | ( ( sK1 @ sK5 )
      = $true )
    | ( ( ( sK1 @ sK5 )
        | ( sK0 @ sK5 ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f155]) ).

thf(f155,plain,
    ( ( $false
      = ( ( ~ ( sK0 @ sK5 )
          & ( sK1 @ sK5 ) )
        | ( ~ ( sK1 @ sK5 )
          & ( sK0 @ sK5 ) ) ) )
    | ( ( sK1 @ sK5 )
      = $true )
    | ( ( ( sK1 @ sK5 )
        | ( sK0 @ sK5 ) )
      = $false ) ),
    inference(not_proxy_clausification,[],[f154]) ).

thf(f154,plain,
    ( ( ( sK1 @ sK5 )
      = $true )
    | ( $true
      = ( ~ ( ( sK1 @ sK5 )
            | ( sK0 @ sK5 ) ) ) )
    | ( $false
      = ( ( ~ ( sK0 @ sK5 )
          & ( sK1 @ sK5 ) )
        | ( ~ ( sK1 @ sK5 )
          & ( sK0 @ sK5 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f152]) ).

thf(f152,plain,
    ( ( ( sK1 @ sK5 )
      = $true )
    | ( ( ~ ( ( sK1 @ sK5 )
            | ( sK0 @ sK5 ) )
        & ( sK2 @ sK5 ) )
      = $true )
    | ( $false
      = ( ( ~ ( sK0 @ sK5 )
          & ( sK1 @ sK5 ) )
        | ( ~ ( sK1 @ sK5 )
          & ( sK0 @ sK5 ) ) ) ) ),
    inference(not_proxy_clausification,[],[f144]) ).

thf(f144,plain,
    ( ( ( sK1 @ sK5 )
      = $true )
    | ( ( ~ ( ( ~ ( sK0 @ sK5 )
              & ( sK1 @ sK5 ) )
            | ( ~ ( sK1 @ sK5 )
              & ( sK0 @ sK5 ) ) ) )
      = $true )
    | ( ( ~ ( ( sK1 @ sK5 )
            | ( sK0 @ sK5 ) )
        & ( sK2 @ sK5 ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f64]) ).

thf(f64,plain,
    ( ( ( sK1 @ sK5 )
      = $true )
    | ( $true
      = ( ( sK2 @ sK5 )
        & ~ ( ( ~ ( sK0 @ sK5 )
              & ( sK1 @ sK5 ) )
            | ( ~ ( sK1 @ sK5 )
              & ( sK0 @ sK5 ) ) ) ) )
    | ( ( ~ ( ( sK1 @ sK5 )
            | ( sK0 @ sK5 ) )
        & ( sK2 @ sK5 ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f63]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SET622^5 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.15  % 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
% 0.16/0.36  % Computer : n017.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit   : 300
% 0.16/0.36  % WCLimit    : 300
% 0.16/0.36  % DateTime   : Mon May 20 11:33:08 EDT 2024
% 0.16/0.36  % CPUTime    : 
% 0.16/0.36  This is a TH0_THM_EQU_NAR problem
% 0.16/0.36  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/benchmark/theBenchmark.p
% 0.23/0.38  % (26785)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)
% 0.23/0.38  % (26778)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.23/0.38  % (26781)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.23/0.38  % (26782)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)
% 0.23/0.38  % (26779)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)
% 0.23/0.38  % (26783)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)
% 0.23/0.38  % (26780)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)
% 0.23/0.38  % (26784)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.23/0.38  % (26785)Refutation not found, incomplete strategy
% 0.23/0.38  % (26785)------------------------------
% 0.23/0.38  % (26785)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.38  % (26785)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.38  
% 0.23/0.38  
% 0.23/0.38  % (26785)Memory used [KB]: 5500
% 0.23/0.38  % (26785)Time elapsed: 0.003 s
% 0.23/0.38  % (26785)Instructions burned: 2 (million)
% 0.23/0.38  % (26785)------------------------------
% 0.23/0.38  % (26785)------------------------------
% 0.23/0.38  % (26781)Instruction limit reached!
% 0.23/0.38  % (26781)------------------------------
% 0.23/0.38  % (26781)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.38  % (26781)Termination reason: Unknown
% 0.23/0.38  % (26781)Termination phase: Property scanning
% 0.23/0.38  
% 0.23/0.38  % (26782)Instruction limit reached!
% 0.23/0.38  % (26782)------------------------------
% 0.23/0.38  % (26782)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.38  % (26781)Memory used [KB]: 895
% 0.23/0.38  % (26781)Time elapsed: 0.003 s
% 0.23/0.38  % (26781)Instructions burned: 2 (million)
% 0.23/0.38  % (26781)------------------------------
% 0.23/0.38  % (26781)------------------------------
% 0.23/0.38  % (26782)Termination reason: Unknown
% 0.23/0.38  % (26782)Termination phase: Saturation
% 0.23/0.38  
% 0.23/0.38  % (26782)Memory used [KB]: 895
% 0.23/0.38  % (26782)Time elapsed: 0.003 s
% 0.23/0.38  % (26782)Instructions burned: 2 (million)
% 0.23/0.38  % (26782)------------------------------
% 0.23/0.38  % (26782)------------------------------
% 0.23/0.39  % (26779)Instruction limit reached!
% 0.23/0.39  % (26779)------------------------------
% 0.23/0.39  % (26779)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.39  % (26779)Termination reason: Unknown
% 0.23/0.39  % (26779)Termination phase: Saturation
% 0.23/0.39  
% 0.23/0.39  % (26779)Memory used [KB]: 5500
% 0.23/0.39  % (26779)Time elapsed: 0.005 s
% 0.23/0.39  % (26779)Instructions burned: 4 (million)
% 0.23/0.39  % (26779)------------------------------
% 0.23/0.39  % (26779)------------------------------
% 0.23/0.39  % (26778)First to succeed.
% 0.23/0.39  % (26780)Also succeeded, but the first one will report.
% 0.23/0.39  % (26778)Refutation found. Thanks to Tanya!
% 0.23/0.39  % SZS status Theorem for theBenchmark
% 0.23/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.39  % (26778)------------------------------
% 0.23/0.39  % (26778)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.39  % (26778)Termination reason: Refutation
% 0.23/0.39  
% 0.23/0.39  % (26778)Memory used [KB]: 5500
% 0.23/0.39  % (26778)Time elapsed: 0.011 s
% 0.23/0.39  % (26778)Instructions burned: 7 (million)
% 0.23/0.39  % (26778)------------------------------
% 0.23/0.39  % (26778)------------------------------
% 0.23/0.39  % (26777)Success in time 0.011 s
% 0.23/0.39  % Vampire---4.8 exiting
%------------------------------------------------------------------------------