TSTP Solution File: SEV387^5 by Vampire---4.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.9
% Problem  : SEV387^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire %s %d THM

% Computer : n018.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon Jun 24 16:03:40 EDT 2024

% Result   : Theorem 0.21s 0.39s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   94 (  12 unt;   0 typ;   0 def)
%            Number of atoms       :  955 ( 222 equ;   0 cnn)
%            Maximal formula atoms :    5 (  10 avg)
%            Number of connectives : 1220 ( 172   ~; 206   |; 282   &; 553   @)
%                                         (   6 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   18 (  18   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  11 usr;   9 con; 0-2 aty)
%            Number of variables   :   38 (  20   ^  12   !;   6   ?;  38   :)

% 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(f332,plain,
    $false,
    inference(avatar_sat_refutation,[],[f273,f282,f300,f306,f312,f318,f325,f331]) ).

thf(f331,plain,
    ( ~ spl3_2
    | ~ spl3_3 ),
    inference(avatar_contradiction_clause,[],[f330]) ).

thf(f330,plain,
    ( $false
    | ~ spl3_2
    | ~ spl3_3 ),
    inference(trivial_inequality_removal,[],[f326]) ).

thf(f326,plain,
    ( ( $true = $false )
    | ~ spl3_2
    | ~ spl3_3 ),
    inference(superposition,[],[f243,f247]) ).

thf(f247,plain,
    ( ( ( sK1 @ sK5 )
      = $true )
    | ~ spl3_3 ),
    inference(avatar_component_clause,[],[f245]) ).

thf(f245,plain,
    ( spl3_3
  <=> ( ( sK1 @ sK5 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

thf(f243,plain,
    ( ( ( sK1 @ sK5 )
      = $false )
    | ~ spl3_2 ),
    inference(avatar_component_clause,[],[f241]) ).

thf(f241,plain,
    ( spl3_2
  <=> ( ( sK1 @ sK5 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

thf(f325,plain,
    ( ~ spl3_5
    | ~ spl3_6 ),
    inference(avatar_contradiction_clause,[],[f324]) ).

thf(f324,plain,
    ( $false
    | ~ spl3_5
    | ~ spl3_6 ),
    inference(trivial_inequality_removal,[],[f321]) ).

thf(f321,plain,
    ( ( $true = $false )
    | ~ spl3_5
    | ~ spl3_6 ),
    inference(superposition,[],[f257,f262]) ).

thf(f262,plain,
    ( ( ( sK0 @ sK5 )
      = $false )
    | ~ spl3_6 ),
    inference(avatar_component_clause,[],[f260]) ).

thf(f260,plain,
    ( spl3_6
  <=> ( ( sK0 @ sK5 )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).

thf(f257,plain,
    ( ( ( sK0 @ sK5 )
      = $true )
    | ~ spl3_5 ),
    inference(avatar_component_clause,[],[f255]) ).

thf(f255,plain,
    ( spl3_5
  <=> ( ( sK0 @ sK5 )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

thf(f318,plain,
    ( ~ spl3_1
    | ~ spl3_4 ),
    inference(avatar_contradiction_clause,[],[f317]) ).

thf(f317,plain,
    ( $false
    | ~ spl3_1
    | ~ spl3_4 ),
    inference(trivial_inequality_removal,[],[f314]) ).

thf(f314,plain,
    ( ( $true = $false )
    | ~ spl3_1
    | ~ spl3_4 ),
    inference(superposition,[],[f239,f252]) ).

thf(f252,plain,
    ( ( $false
      = ( sK2 @ sK5 ) )
    | ~ spl3_4 ),
    inference(avatar_component_clause,[],[f250]) ).

thf(f250,plain,
    ( spl3_4
  <=> ( $false
      = ( sK2 @ sK5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

thf(f239,plain,
    ( ( $true
      = ( sK2 @ sK5 ) )
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f237]) ).

thf(f237,plain,
    ( spl3_1
  <=> ( $true
      = ( sK2 @ sK5 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

thf(f312,plain,
    ( spl3_2
    | spl3_4
    | spl3_5 ),
    inference(avatar_split_clause,[],[f28,f255,f250,f241]) ).

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

thf(f27,plain,
    ( ( ( sK0 @ sK5 )
      = $true )
    | ( ( sK1 @ sK5 )
      = $false )
    | ( ( sK0 @ sK5 )
      = $true )
    | ( $false
      = ( sK2 @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f25]) ).

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

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

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

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

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

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

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

thf(f18,plain,
    ( ( ( ~ ( sK0 @ sK5 )
        & ( sK1 @ sK5 ) )
      = $false )
    | ( $false
      = ( ( sK2 @ sK5 )
        & ~ ( ( sK0 @ sK5 )
            & ( sK2 @ sK5 ) )
        & ( sK1 @ sK5 ) ) )
    | ( $false
      = ( sK2 @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f16]) ).

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

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

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

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

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

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

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

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

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

thf(f1,conjecture,
    ! [X1: a > $o,X2: a > $o,X0: a > $o] :
      ( ( ^ [X3: a] :
            ( ( ( ~ ( X2 @ X3 )
                & ( X1 @ X3 ) )
              | ( ( X2 @ X3 )
                & ~ ( X1 @ X3 ) ) )
            & ( X0 @ X3 ) ) )
      = ( ^ [X4: a] :
            ( ( ( X0 @ X4 )
              & ~ ( ( X0 @ X4 )
                  & ( X2 @ X4 ) )
              & ( X1 @ X4 ) )
            | ( ( X2 @ X4 )
              & ~ ( ( X0 @ X4 )
                  & ( X1 @ X4 ) )
              & ( X0 @ X4 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGAZING_THM44_pme) ).

thf(f306,plain,
    ( spl3_6
    | spl3_3
    | spl3_4 ),
    inference(avatar_split_clause,[],[f56,f250,f245,f260]) ).

thf(f56,plain,
    ( ( $false
      = ( sK2 @ sK5 ) )
    | ( ( sK1 @ sK5 )
      = $true )
    | ( ( sK0 @ sK5 )
      = $false ) ),
    inference(duplicate_literal_removal,[],[f55]) ).

thf(f55,plain,
    ( ( ( sK1 @ sK5 )
      = $true )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( ( sK1 @ sK5 )
      = $true )
    | ( $false
      = ( sK2 @ sK5 ) ) ),
    inference(not_proxy_clausification,[],[f54]) ).

thf(f54,plain,
    ( ( $false
      = ( ~ ( sK1 @ sK5 ) ) )
    | ( $false
      = ( sK2 @ sK5 ) )
    | ( ( sK1 @ sK5 )
      = $true )
    | ( ( sK0 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f52]) ).

thf(f52,plain,
    ( ( $true
      = ( ( sK1 @ sK5 )
        & ( sK2 @ sK5 ) ) )
    | ( $false
      = ( sK2 @ sK5 ) )
    | ( $false
      = ( ~ ( sK1 @ sK5 ) ) )
    | ( ( sK0 @ sK5 )
      = $false ) ),
    inference(not_proxy_clausification,[],[f51]) ).

thf(f51,plain,
    ( ( ( ~ ( ( sK1 @ sK5 )
            & ( sK2 @ sK5 ) ) )
      = $false )
    | ( $false
      = ( sK2 @ sK5 ) )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( $false
      = ( ~ ( sK1 @ sK5 ) ) ) ),
    inference(duplicate_literal_removal,[],[f50]) ).

thf(f50,plain,
    ( ( $false
      = ( sK2 @ sK5 ) )
    | ( $false
      = ( ~ ( sK1 @ sK5 ) ) )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( ( ~ ( ( sK1 @ sK5 )
            & ( sK2 @ sK5 ) ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f49]) ).

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

thf(f48,plain,
    ( ( ( ( sK0 @ sK5 )
        & ~ ( ( sK1 @ sK5 )
            & ( sK2 @ sK5 ) ) )
      = $false )
    | ( $false
      = ( sK2 @ sK5 ) )
    | ( $false
      = ( ( sK0 @ sK5 )
        & ~ ( sK1 @ sK5 ) ) ) ),
    inference(duplicate_literal_removal,[],[f47]) ).

thf(f47,plain,
    ( ( ( ( sK0 @ sK5 )
        & ~ ( ( sK1 @ sK5 )
            & ( sK2 @ sK5 ) ) )
      = $false )
    | ( $false
      = ( ( sK0 @ sK5 )
        & ~ ( sK1 @ sK5 ) ) )
    | ( $false
      = ( sK2 @ sK5 ) )
    | ( $false
      = ( sK2 @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f37]) ).

thf(f37,plain,
    ( ( $false
      = ( sK2 @ sK5 ) )
    | ( $false
      = ( ( sK0 @ sK5 )
        & ~ ( ( sK1 @ sK5 )
            & ( sK2 @ sK5 ) )
        & ( sK2 @ sK5 ) ) )
    | ( $false
      = ( ( sK0 @ sK5 )
        & ~ ( sK1 @ sK5 ) ) ) ),
    inference(binary_proxy_clausification,[],[f15]) ).

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

thf(f300,plain,
    spl3_1,
    inference(avatar_split_clause,[],[f82,f237]) ).

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

thf(f81,plain,
    ( ( $true
      = ( sK2 @ sK5 ) )
    | ( $true
      = ( sK2 @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f79]) ).

thf(f79,plain,
    ( ( ( ( sK2 @ sK5 )
        & ~ ( ( sK0 @ sK5 )
            & ( sK2 @ sK5 ) ) )
      = $true )
    | ( $true
      = ( sK2 @ sK5 ) ) ),
    inference(duplicate_literal_removal,[],[f63]) ).

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

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

thf(f60,plain,
    ( ( $true
      = ( sK2 @ sK5 ) )
    | ( $true
      = ( ( sK2 @ sK5 )
        & ~ ( ( sK0 @ sK5 )
            & ( sK2 @ sK5 ) )
        & ( sK1 @ sK5 ) ) )
    | ( $true
      = ( ( sK0 @ sK5 )
        & ~ ( ( sK1 @ sK5 )
            & ( sK2 @ sK5 ) )
        & ( sK2 @ sK5 ) ) ) ),
    inference(binary_proxy_clausification,[],[f59]) ).

thf(f59,plain,
    ( ( $true
      = ( sK2 @ sK5 ) )
    | ( $true
      = ( ( ( sK2 @ sK5 )
          & ~ ( ( sK0 @ sK5 )
              & ( sK2 @ sK5 ) )
          & ( sK1 @ sK5 ) )
        | ( ( sK0 @ sK5 )
          & ~ ( ( sK1 @ sK5 )
              & ( sK2 @ sK5 ) )
          & ( sK2 @ sK5 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f12]) ).

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

thf(f282,plain,
    ( spl3_5
    | spl3_3 ),
    inference(avatar_split_clause,[],[f155,f245,f255]) ).

thf(f155,plain,
    ( ( ( sK0 @ sK5 )
      = $true )
    | ( ( sK1 @ sK5 )
      = $true ) ),
    inference(duplicate_literal_removal,[],[f152]) ).

thf(f152,plain,
    ( ( ( sK1 @ sK5 )
      = $true )
    | ( ( sK1 @ sK5 )
      = $true )
    | ( ( sK0 @ sK5 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f151]) ).

thf(f151,plain,
    ( ( ( ~ ( sK0 @ sK5 )
        & ( sK1 @ sK5 ) )
      = $true )
    | ( ( sK0 @ sK5 )
      = $true )
    | ( ( sK1 @ sK5 )
      = $true ) ),
    inference(duplicate_literal_removal,[],[f150]) ).

thf(f150,plain,
    ( ( ( sK0 @ sK5 )
      = $true )
    | ( ( ~ ( sK0 @ sK5 )
        & ( sK1 @ sK5 ) )
      = $true )
    | ( ( sK1 @ sK5 )
      = $true )
    | ( ( sK0 @ sK5 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f148]) ).

thf(f148,plain,
    ( ( ( ( sK0 @ sK5 )
        & ~ ( ( sK1 @ sK5 )
            & ( sK2 @ sK5 ) ) )
      = $true )
    | ( ( sK1 @ sK5 )
      = $true )
    | ( ( sK0 @ sK5 )
      = $true )
    | ( ( ~ ( sK0 @ sK5 )
        & ( sK1 @ sK5 ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f96]) ).

thf(f96,plain,
    ( ( $true
      = ( ( sK0 @ sK5 )
        & ~ ( ( sK1 @ sK5 )
            & ( sK2 @ sK5 ) )
        & ( sK2 @ sK5 ) ) )
    | ( ( sK0 @ sK5 )
      = $true )
    | ( ( ~ ( sK0 @ sK5 )
        & ( sK1 @ sK5 ) )
      = $true )
    | ( ( sK1 @ sK5 )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f95]) ).

thf(f95,plain,
    ( ( $true
      = ( ( sK2 @ sK5 )
        & ~ ( ( sK0 @ sK5 )
            & ( sK2 @ sK5 ) )
        & ( sK1 @ sK5 ) ) )
    | ( ( sK0 @ sK5 )
      = $true )
    | ( $true
      = ( ( sK0 @ sK5 )
        & ~ ( ( sK1 @ sK5 )
            & ( sK2 @ sK5 ) )
        & ( sK2 @ sK5 ) ) )
    | ( ( ~ ( sK0 @ sK5 )
        & ( sK1 @ sK5 ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f94]) ).

thf(f94,plain,
    ( ( ( sK0 @ sK5 )
      = $true )
    | ( $true
      = ( ( ( sK2 @ sK5 )
          & ~ ( ( sK0 @ sK5 )
              & ( sK2 @ sK5 ) )
          & ( sK1 @ sK5 ) )
        | ( ( sK0 @ sK5 )
          & ~ ( ( sK1 @ sK5 )
              & ( sK2 @ sK5 ) )
          & ( sK2 @ sK5 ) ) ) )
    | ( ( ~ ( sK0 @ sK5 )
        & ( sK1 @ sK5 ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f92]) ).

thf(f92,plain,
    ( ( $true
      = ( ( sK0 @ sK5 )
        & ~ ( sK1 @ sK5 ) ) )
    | ( ( ~ ( sK0 @ sK5 )
        & ( sK1 @ sK5 ) )
      = $true )
    | ( $true
      = ( ( ( sK2 @ sK5 )
          & ~ ( ( sK0 @ sK5 )
              & ( sK2 @ sK5 ) )
          & ( sK1 @ sK5 ) )
        | ( ( sK0 @ sK5 )
          & ~ ( ( sK1 @ sK5 )
              & ( sK2 @ sK5 ) )
          & ( sK2 @ sK5 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f58]) ).

thf(f58,plain,
    ( ( ( ( ~ ( sK0 @ sK5 )
          & ( sK1 @ sK5 ) )
        | ( ( sK0 @ sK5 )
          & ~ ( sK1 @ sK5 ) ) )
      = $true )
    | ( $true
      = ( ( ( sK2 @ sK5 )
          & ~ ( ( sK0 @ sK5 )
              & ( sK2 @ sK5 ) )
          & ( sK1 @ sK5 ) )
        | ( ( sK0 @ sK5 )
          & ~ ( ( sK1 @ sK5 )
              & ( sK2 @ sK5 ) )
          & ( sK2 @ sK5 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f12]) ).

thf(f273,plain,
    ( spl3_6
    | spl3_4
    | spl3_2 ),
    inference(avatar_split_clause,[],[f194,f241,f250,f260]) ).

thf(f194,plain,
    ( ( ( sK0 @ sK5 )
      = $false )
    | ( ( sK1 @ sK5 )
      = $false )
    | ( $false
      = ( sK2 @ sK5 ) ) ),
    inference(duplicate_literal_removal,[],[f193]) ).

thf(f193,plain,
    ( ( ( sK0 @ sK5 )
      = $false )
    | ( $false
      = ( sK2 @ sK5 ) )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( ( sK1 @ sK5 )
      = $false )
    | ( $false
      = ( sK2 @ sK5 ) ) ),
    inference(binary_proxy_clausification,[],[f192]) ).

thf(f192,plain,
    ( ( $false
      = ( sK2 @ sK5 ) )
    | ( ( sK1 @ sK5 )
      = $false )
    | ( ( ( sK0 @ sK5 )
        & ( sK2 @ sK5 ) )
      = $false )
    | ( ( sK0 @ sK5 )
      = $false ) ),
    inference(not_proxy_clausification,[],[f191]) ).

thf(f191,plain,
    ( ( $false
      = ( sK2 @ sK5 ) )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( $true
      = ( ~ ( ( sK0 @ sK5 )
            & ( sK2 @ sK5 ) ) ) )
    | ( ( sK1 @ sK5 )
      = $false ) ),
    inference(duplicate_literal_removal,[],[f190]) ).

thf(f190,plain,
    ( ( $true
      = ( ~ ( ( sK0 @ sK5 )
            & ( sK2 @ sK5 ) ) ) )
    | ( ( sK1 @ sK5 )
      = $false )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( $false
      = ( sK2 @ sK5 ) )
    | ( ( sK1 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f189]) ).

thf(f189,plain,
    ( ( ( ( sK1 @ sK5 )
        & ( sK2 @ sK5 ) )
      = $false )
    | ( ( sK1 @ sK5 )
      = $false )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( $true
      = ( ~ ( ( sK0 @ sK5 )
            & ( sK2 @ sK5 ) ) ) ) ),
    inference(not_proxy_clausification,[],[f184]) ).

thf(f184,plain,
    ( ( ( ~ ( ( sK1 @ sK5 )
            & ( sK2 @ sK5 ) ) )
      = $true )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( $true
      = ( ~ ( ( sK0 @ sK5 )
            & ( sK2 @ sK5 ) ) ) )
    | ( ( sK1 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f183]) ).

thf(f183,plain,
    ( ( ( sK1 @ sK5 )
      = $false )
    | ( ( ( sK2 @ sK5 )
        & ~ ( ( sK0 @ sK5 )
            & ( sK2 @ sK5 ) ) )
      = $true )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( ( ~ ( ( sK1 @ sK5 )
            & ( sK2 @ sK5 ) ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f173]) ).

thf(f173,plain,
    ( ( $true
      = ( ( sK2 @ sK5 )
        & ~ ( ( sK0 @ sK5 )
            & ( sK2 @ sK5 ) )
        & ( sK1 @ sK5 ) ) )
    | ( ( sK1 @ sK5 )
      = $false )
    | ( ( ~ ( ( sK1 @ sK5 )
            & ( sK2 @ sK5 ) ) )
      = $true )
    | ( ( sK0 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f172]) ).

thf(f172,plain,
    ( ( ( ( sK0 @ sK5 )
        & ~ ( ( sK1 @ sK5 )
            & ( sK2 @ sK5 ) ) )
      = $true )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( $true
      = ( ( sK2 @ sK5 )
        & ~ ( ( sK0 @ sK5 )
            & ( sK2 @ sK5 ) )
        & ( sK1 @ sK5 ) ) )
    | ( ( sK1 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f170]) ).

thf(f170,plain,
    ( ( ( sK0 @ sK5 )
      = $false )
    | ( $true
      = ( ( sK0 @ sK5 )
        & ~ ( ( sK1 @ sK5 )
            & ( sK2 @ sK5 ) )
        & ( sK2 @ sK5 ) ) )
    | ( ( sK1 @ sK5 )
      = $false )
    | ( $true
      = ( ( sK2 @ sK5 )
        & ~ ( ( sK0 @ sK5 )
            & ( sK2 @ sK5 ) )
        & ( sK1 @ sK5 ) ) ) ),
    inference(binary_proxy_clausification,[],[f169]) ).

thf(f169,plain,
    ( ( $true
      = ( ( ( sK2 @ sK5 )
          & ~ ( ( sK0 @ sK5 )
              & ( sK2 @ sK5 ) )
          & ( sK1 @ sK5 ) )
        | ( ( sK0 @ sK5 )
          & ~ ( ( sK1 @ sK5 )
              & ( sK2 @ sK5 ) )
          & ( sK2 @ sK5 ) ) ) )
    | ( ( sK0 @ sK5 )
      = $false )
    | ( ( sK1 @ sK5 )
      = $false ) ),
    inference(not_proxy_clausification,[],[f168]) ).

thf(f168,plain,
    ( ( ( ~ ( sK0 @ sK5 ) )
      = $true )
    | ( $true
      = ( ( ( sK2 @ sK5 )
          & ~ ( ( sK0 @ sK5 )
              & ( sK2 @ sK5 ) )
          & ( sK1 @ sK5 ) )
        | ( ( sK0 @ sK5 )
          & ~ ( ( sK1 @ sK5 )
              & ( sK2 @ sK5 ) )
          & ( sK2 @ sK5 ) ) ) )
    | ( ( sK1 @ sK5 )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f166]) ).

thf(f166,plain,
    ( ( ( sK1 @ sK5 )
      = $false )
    | ( ( ~ ( sK0 @ sK5 )
        & ( sK1 @ sK5 ) )
      = $true )
    | ( $true
      = ( ( ( sK2 @ sK5 )
          & ~ ( ( sK0 @ sK5 )
              & ( sK2 @ sK5 ) )
          & ( sK1 @ sK5 ) )
        | ( ( sK0 @ sK5 )
          & ~ ( ( sK1 @ sK5 )
              & ( sK2 @ sK5 ) )
          & ( sK2 @ sK5 ) ) ) ) ),
    inference(not_proxy_clausification,[],[f93]) ).

thf(f93,plain,
    ( ( $true
      = ( ~ ( sK1 @ sK5 ) ) )
    | ( $true
      = ( ( ( sK2 @ sK5 )
          & ~ ( ( sK0 @ sK5 )
              & ( sK2 @ sK5 ) )
          & ( sK1 @ sK5 ) )
        | ( ( sK0 @ sK5 )
          & ~ ( ( sK1 @ sK5 )
              & ( sK2 @ sK5 ) )
          & ( sK2 @ sK5 ) ) ) )
    | ( ( ~ ( sK0 @ sK5 )
        & ( sK1 @ sK5 ) )
      = $true ) ),
    inference(binary_proxy_clausification,[],[f92]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SEV387^5 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.12  % Command    : run_vampire %s %d THM
% 0.12/0.33  % Computer : n018.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Fri Jun 21 18:52:09 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.12/0.35  This is a TH0_THM_EQU_NAR problem
% 0.12/0.36  Running higher-order theorem proving
% 0.12/0.36  Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/benchmark/theBenchmark.p -m 16384 -t 300
% 0.21/0.38  % (674)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.21/0.38  % (673)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.21/0.38  % (676)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.38  % (677)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.38  % (679)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.38  % (675)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.21/0.38  % (678)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.21/0.38  % (674)Instruction limit reached!
% 0.21/0.38  % (674)------------------------------
% 0.21/0.38  % (674)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.38  % (674)Termination reason: Unknown
% 0.21/0.38  % (674)Termination phase: Saturation
% 0.21/0.38  
% 0.21/0.38  % (674)Memory used [KB]: 5500
% 0.21/0.38  % (674)Time elapsed: 0.005 s
% 0.21/0.38  % (674)Instructions burned: 5 (million)
% 0.21/0.38  % (674)------------------------------
% 0.21/0.38  % (674)------------------------------
% 0.21/0.38  % (676)Instruction limit reached!
% 0.21/0.38  % (676)------------------------------
% 0.21/0.38  % (676)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.38  % (676)Termination reason: Unknown
% 0.21/0.38  % (676)Termination phase: Saturation
% 0.21/0.38  
% 0.21/0.38  % (676)Memory used [KB]: 5500
% 0.21/0.38  % (676)Time elapsed: 0.004 s
% 0.21/0.38  % (676)Instructions burned: 2 (million)
% 0.21/0.38  % (676)------------------------------
% 0.21/0.38  % (676)------------------------------
% 0.21/0.38  % (677)Instruction limit reached!
% 0.21/0.38  % (677)------------------------------
% 0.21/0.38  % (677)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.38  % (677)Termination reason: Unknown
% 0.21/0.38  % (677)Termination phase: Saturation
% 0.21/0.38  
% 0.21/0.38  % (677)Memory used [KB]: 5500
% 0.21/0.38  % (677)Time elapsed: 0.004 s
% 0.21/0.38  % (677)Instructions burned: 2 (million)
% 0.21/0.38  % (677)------------------------------
% 0.21/0.38  % (677)------------------------------
% 0.21/0.38  % (673)First to succeed.
% 0.21/0.39  % (675)Also succeeded, but the first one will report.
% 0.21/0.39  % (673)Refutation found. Thanks to Tanya!
% 0.21/0.39  % SZS status Theorem for theBenchmark
% 0.21/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.39  % (673)------------------------------
% 0.21/0.39  % (673)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.39  % (673)Termination reason: Refutation
% 0.21/0.39  
% 0.21/0.39  % (673)Memory used [KB]: 5628
% 0.21/0.39  % (673)Time elapsed: 0.011 s
% 0.21/0.39  % (673)Instructions burned: 10 (million)
% 0.21/0.39  % (673)------------------------------
% 0.21/0.39  % (673)------------------------------
% 0.21/0.39  % (672)Success in time 0.027 s
%------------------------------------------------------------------------------