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Vampire-SAT---5.0.1.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---5.0.1
% Problem  : SET613^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT

% Computer : n013.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Sep 30 08:23:42 AM UTC 2026

% Result   : Theorem 0.08s 0.25s
% Output   : Refutation 0.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   71 (  14 unt;   0 typ;   4 def)
%            Number of atoms       :  491 ( 120 equ;   0 cnn)
%            Maximal formula atoms :    4 (   6 avg)
%            Number of connectives :  572 (  97   ~; 137   |;  79   &; 255   @)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  13 usr;   7 con; 0-4 aty)
%            Number of variables   :   30 (   0 sgn   8   !;   2   ?;  30   :)

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

thf(type_def_6,type,
    sTfun: ( $tType * $tType ) > $tType ).

thf(func_def_1,type,
    vAND: $o > $o > $o ).

thf(func_def_2,type,
    vOR: $o > $o > $o ).

thf(func_def_3,type,
    db0: 
      !>[X0: $tType] : X0 ).

thf(func_def_4,type,
    vNOT: $o > $o ).

thf(func_def_5,type,
    vLAM: 
      !>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).

thf(func_def_6,type,
    sK0: a > $o ).

thf(func_def_7,type,
    sK1: a > $o ).

thf(func_def_10,type,
    sK2: a ).

thf(f1,conjecture,
    ! [X0: a > $o,X1: a > $o] :
      ( ( ^ [X2: a] :
            ( ~ ( ( X1 @ X2 )
                & ( X0 @ X2 ) )
            & ( ( X1 @ X2 )
              | ( X0 @ X2 ) ) ) )
      = ( ^ [X3: a] :
            ( ( ~ ( X0 @ X3 )
              & ( X1 @ X3 ) )
            | ( ~ ( X1 @ X3 )
              & ( X0 @ X3 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_87_pme) ).

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

thf(f3,plain,
    ~ ! [X0: a > $o,X1: a > $o] :
        ( ( ^ [X2: a] :
              ( ~ ( ( X1 @ X2 )
                  & ( X0 @ X2 ) )
              & ( ( X1 @ X2 )
                | ( X0 @ X2 ) ) ) )
        = ( ^ [X3: a] :
              ( ( ~ ( X0 @ X3 )
                & ( X1 @ X3 ) )
              | ( ~ ( X1 @ X3 )
                & ( X0 @ X3 ) ) ) ) ),
    inference(rectify,[],[f2]) ).

thf(f4,plain,
    ~ ! [X0: a > $o,X1: a > $o] :
        ( ( ^ [Y0: a] :
              ( ( ( X0 @ Y0 )
                | ( X1 @ Y0 ) )
              & ~ ( ( X0 @ Y0 )
                  & ( X1 @ Y0 ) ) ) )
        = ( ^ [Y0: a] :
              ( ( ( X0 @ Y0 )
                & ~ ( X1 @ Y0 ) )
              | ( ( X1 @ Y0 )
                & ~ ( X0 @ Y0 ) ) ) ) ),
    inference(fool_elimination,[],[f3]) ).

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

thf(f6,plain,
    ( ( ^ [Y0: a] :
          ( ( ( sK0 @ Y0 )
            | ( sK1 @ Y0 ) )
          & ~ ( ( sK0 @ Y0 )
              & ( sK1 @ Y0 ) ) ) )
   != ( ^ [Y0: a] :
          ( ( ( sK0 @ Y0 )
            & ~ ( sK1 @ Y0 ) )
          | ( ( sK1 @ Y0 )
            & ~ ( sK0 @ Y0 ) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f5]) ).

thf(f7,plain,
    ( ( ^ [Y0: a] :
          ( ( ( sK0 @ Y0 )
            | ( sK1 @ Y0 ) )
          & ~ ( ( sK0 @ Y0 )
              & ( sK1 @ Y0 ) ) ) )
   != ( ^ [Y0: a] :
          ( ( ( sK0 @ Y0 )
            & ~ ( sK1 @ Y0 ) )
          | ( ( sK1 @ Y0 )
            & ~ ( sK0 @ Y0 ) ) ) ) ),
    inference(cnf_transformation,[],[f6]) ).

thf(f17,plain,
    ( ( ^ [Y0: a] :
          ( ( ( sK0 @ Y0 )
            | ( sK1 @ Y0 ) )
          & ~ ( ( sK0 @ Y0 )
              & ( sK1 @ Y0 ) ) )
      @ sK2 )
   != ( ^ [Y0: a] :
          ( ( ( sK0 @ Y0 )
            & ~ ( sK1 @ Y0 ) )
          | ( ( sK1 @ Y0 )
            & ~ ( sK0 @ Y0 ) ) )
      @ sK2 ) ),
    inference(negative_extensionality,[],[f7]) ).

thf(f18,plain,
    ( ( $true
      = ( ^ [Y0: a] :
            ( ( ( sK0 @ Y0 )
              | ( sK1 @ Y0 ) )
            & ~ ( ( sK0 @ Y0 )
                & ( sK1 @ Y0 ) ) )
        @ sK2 ) )
    | ( $true
      = ( ^ [Y0: a] :
            ( ( ( sK0 @ Y0 )
              & ~ ( sK1 @ Y0 ) )
            | ( ( sK1 @ Y0 )
              & ~ ( sK0 @ Y0 ) ) )
        @ sK2 ) ) ),
    inference(xor_proxy_clausification,[],[f17]) ).

thf(f19,plain,
    ( ( $false
      = ( ^ [Y0: a] :
            ( ( ( sK0 @ Y0 )
              | ( sK1 @ Y0 ) )
            & ~ ( ( sK0 @ Y0 )
                & ( sK1 @ Y0 ) ) )
        @ sK2 ) )
    | ( $false
      = ( ^ [Y0: a] :
            ( ( ( sK0 @ Y0 )
              & ~ ( sK1 @ Y0 ) )
            | ( ( sK1 @ Y0 )
              & ~ ( sK0 @ Y0 ) ) )
        @ sK2 ) ) ),
    inference(xor_proxy_clausification,[],[f17]) ).

thf(f20,plain,
    ( ( $false
      = ( ( ( sK0 @ sK2 )
          | ( sK1 @ sK2 ) )
        & ~ ( ( sK0 @ sK2 )
            & ( sK1 @ sK2 ) ) ) )
    | ( $false
      = ( ( ( sK0 @ sK2 )
          & ~ ( sK1 @ sK2 ) )
        | ( ( sK1 @ sK2 )
          & ~ ( sK0 @ sK2 ) ) ) ) ),
    inference(beta-eta_normalization,[],[f19]) ).

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

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

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

thf(f24,plain,
    ( ( $true
      = ( sK0 @ sK2 ) )
    | ( $false
      = ( ( ( sK0 @ sK2 )
          & ~ ( sK1 @ sK2 ) )
        | ( ( sK1 @ sK2 )
          & ~ ( sK0 @ sK2 ) ) ) )
    | ( $false
      = ( ( sK0 @ sK2 )
        | ( sK1 @ sK2 ) ) ) ),
    inference(and_proxy_clausification,[],[f22]) ).

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

thf(f32,plain,
    ( ( $true
      = ( sK0 @ sK2 ) )
    | ( $false
      = ( ~ ( sK0 @ sK2 ) ) )
    | ( $false
      = ( ( sK0 @ sK2 )
        | ( sK1 @ sK2 ) ) )
    | ( $false
      = ( sK1 @ sK2 ) ) ),
    inference(and_proxy_clausification,[],[f25]) ).

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

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

thf(f37,plain,
    ( ( $true
      = ( sK0 @ sK2 ) )
    | ( $false
      = ( sK1 @ sK2 ) ) ),
    inference(duplicate_literal_removal,[],[f34]) ).

thf(f39,plain,
    ( ( $true
      = ( sK1 @ sK2 ) )
    | ( $false
      = ( ( sK0 @ sK2 )
        & ~ ( sK1 @ sK2 ) ) )
    | ( $false
      = ( ( sK0 @ sK2 )
        | ( sK1 @ sK2 ) ) ) ),
    inference(or_proxy_clausification,[],[f23]) ).

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

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

thf(f43,plain,
    ( ( $true
      = ( sK1 @ sK2 ) )
    | ( $true
      = ( sK1 @ sK2 ) )
    | ( $false
      = ( sK0 @ sK2 ) )
    | ( $false
      = ( sK0 @ sK2 ) ) ),
    inference(or_proxy_clausification,[],[f41]) ).

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

thf(f51,plain,
    ( ( $true
      = ( ( ( sK0 @ sK2 )
          | ( sK1 @ sK2 ) )
        & ~ ( ( sK0 @ sK2 )
            & ( sK1 @ sK2 ) ) ) )
    | ( $true
      = ( ( ( sK0 @ sK2 )
          & ~ ( sK1 @ sK2 ) )
        | ( ( sK1 @ sK2 )
          & ~ ( sK0 @ sK2 ) ) ) ) ),
    inference(beta-eta_normalization,[],[f18]) ).

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

thf(f53,plain,
    ( ( $true
      = ( ( sK0 @ sK2 )
        | ( sK1 @ sK2 ) ) )
    | ( $true
      = ( ( ( sK0 @ sK2 )
          & ~ ( sK1 @ sK2 ) )
        | ( ( sK1 @ sK2 )
          & ~ ( sK0 @ sK2 ) ) ) ) ),
    inference(and_proxy_clausification,[],[f51]) ).

thf(f54,plain,
    ( ( $true
      = ( sK1 @ sK2 ) )
    | ( $true
      = ( ( ( sK0 @ sK2 )
          & ~ ( sK1 @ sK2 ) )
        | ( ( sK1 @ sK2 )
          & ~ ( sK0 @ sK2 ) ) ) )
    | ( $true
      = ( sK0 @ sK2 ) ) ),
    inference(or_proxy_clausification,[],[f53]) ).

thf(f55,plain,
    ( ( $true
      = ( sK1 @ sK2 ) )
    | ( $true
      = ( ( sK1 @ sK2 )
        & ~ ( sK0 @ sK2 ) ) )
    | ( $true
      = ( sK0 @ sK2 ) )
    | ( $true
      = ( ( sK0 @ sK2 )
        & ~ ( sK1 @ sK2 ) ) ) ),
    inference(or_proxy_clausification,[],[f54]) ).

thf(f57,plain,
    ( ( $true
      = ( sK1 @ sK2 ) )
    | ( $true
      = ( sK1 @ sK2 ) )
    | ( $true
      = ( sK0 @ sK2 ) )
    | ( $true
      = ( ( sK0 @ sK2 )
        & ~ ( sK1 @ sK2 ) ) ) ),
    inference(and_proxy_clausification,[],[f55]) ).

thf(f59,plain,
    ( ( $true
      = ( sK1 @ sK2 ) )
    | ( $true
      = ( sK1 @ sK2 ) )
    | ( $true
      = ( sK0 @ sK2 ) )
    | ( $true
      = ( sK0 @ sK2 ) ) ),
    inference(and_proxy_clausification,[],[f57]) ).

thf(f60,plain,
    ( ( $true
      = ( sK1 @ sK2 ) )
    | ( $true
      = ( sK0 @ sK2 ) ) ),
    inference(duplicate_literal_removal,[],[f59]) ).

thf(f68,plain,
    ( ( $false
      = ( ( sK0 @ sK2 )
        & ( sK1 @ sK2 ) ) )
    | ( $true
      = ( ( ( sK0 @ sK2 )
          & ~ ( sK1 @ sK2 ) )
        | ( ( sK1 @ sK2 )
          & ~ ( sK0 @ sK2 ) ) ) ) ),
    inference(not_proxy_clausification,[],[f52]) ).

thf(f69,plain,
    ( ( $false
      = ( sK1 @ sK2 ) )
    | ( $true
      = ( ( ( sK0 @ sK2 )
          & ~ ( sK1 @ sK2 ) )
        | ( ( sK1 @ sK2 )
          & ~ ( sK0 @ sK2 ) ) ) )
    | ( $false
      = ( sK0 @ sK2 ) ) ),
    inference(and_proxy_clausification,[],[f68]) ).

thf(f70,plain,
    ( ( $false
      = ( sK1 @ sK2 ) )
    | ( $true
      = ( ( sK1 @ sK2 )
        & ~ ( sK0 @ sK2 ) ) )
    | ( $false
      = ( sK0 @ sK2 ) )
    | ( $true
      = ( ( sK0 @ sK2 )
        & ~ ( sK1 @ sK2 ) ) ) ),
    inference(or_proxy_clausification,[],[f69]) ).

thf(f71,plain,
    ( ( $false
      = ( sK1 @ sK2 ) )
    | ( $true
      = ( ~ ( sK0 @ sK2 ) ) )
    | ( $false
      = ( sK0 @ sK2 ) )
    | ( $true
      = ( ( sK0 @ sK2 )
        & ~ ( sK1 @ sK2 ) ) ) ),
    inference(and_proxy_clausification,[],[f70]) ).

thf(f77,plain,
    ( ( $false
      = ( sK1 @ sK2 ) )
    | ( $false
      = ( sK0 @ sK2 ) )
    | ( $false
      = ( sK0 @ sK2 ) )
    | ( $true
      = ( ( sK0 @ sK2 )
        & ~ ( sK1 @ sK2 ) ) ) ),
    inference(not_proxy_clausification,[],[f71]) ).

thf(f78,plain,
    ( ( $false
      = ( sK1 @ sK2 ) )
    | ( $false
      = ( sK0 @ sK2 ) )
    | ( $false
      = ( sK0 @ sK2 ) )
    | ( $true
      = ( ~ ( sK1 @ sK2 ) ) ) ),
    inference(and_proxy_clausification,[],[f77]) ).

thf(f81,plain,
    ( ( $false
      = ( sK1 @ sK2 ) )
    | ( $false
      = ( sK0 @ sK2 ) )
    | ( $false
      = ( sK0 @ sK2 ) )
    | ( $false
      = ( sK1 @ sK2 ) ) ),
    inference(not_proxy_clausification,[],[f78]) ).

thf(f82,plain,
    ( ( $false
      = ( sK1 @ sK2 ) )
    | ( $false
      = ( sK0 @ sK2 ) ) ),
    inference(duplicate_literal_removal,[],[f81]) ).

thf(f84,definition,
    ( spl3_1
  <=> ( $false
      = ( sK1 @ sK2 ) ) ),
    introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).

thf(f86,plain,
    ( ( $false
      = ( sK1 @ sK2 ) )
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f84]) ).

thf(f88,definition,
    ( spl3_2
  <=> ( $true
      = ( sK0 @ sK2 ) ) ),
    introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).

thf(f90,plain,
    ( ( $true
      = ( sK0 @ sK2 ) )
    | ~ spl3_2 ),
    inference(avatar_component_clause,[],[f88]) ).

thf(f91,plain,
    ( spl3_1
    | spl3_2 ),
    inference(avatar_split_clause,[],[f37,f88,f84]) ).

thf(f93,definition,
    ( spl3_3
  <=> ( $false
      = ( sK0 @ sK2 ) ) ),
    introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).

thf(f95,plain,
    ( ( $false
      = ( sK0 @ sK2 ) )
    | ~ spl3_3 ),
    inference(avatar_component_clause,[],[f93]) ).

thf(f97,definition,
    ( spl3_4
  <=> ( $true
      = ( sK1 @ sK2 ) ) ),
    introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).

thf(f99,plain,
    ( ( $true
      = ( sK1 @ sK2 ) )
    | ~ spl3_4 ),
    inference(avatar_component_clause,[],[f97]) ).

thf(f100,plain,
    ( spl3_3
    | spl3_4 ),
    inference(avatar_split_clause,[],[f44,f97,f93]) ).

thf(f101,plain,
    ( spl3_2
    | spl3_4 ),
    inference(avatar_split_clause,[],[f60,f97,f88]) ).

thf(f102,plain,
    ( spl3_3
    | spl3_1 ),
    inference(avatar_split_clause,[],[f82,f84,f93]) ).

thf(f105,plain,
    ( ( $true = $false )
    | ~ spl3_2
    | ~ spl3_3 ),
    inference(constrained_superposition,[],[f90,f95]) ).

thf(f106,plain,
    ( $false
    | ~ spl3_2
    | ~ spl3_3 ),
    inference(trivial_inequality_removal,[],[f105]) ).

thf(f107,plain,
    ( ~ spl3_2
    | ~ spl3_3 ),
    inference(avatar_contradiction_clause,[],[f106]) ).

thf(f112,plain,
    ( ( $true = $false )
    | ~ spl3_1
    | ~ spl3_4 ),
    inference(forward_demodulation,[],[f99,f86]) ).

thf(f113,plain,
    ( $false
    | ~ spl3_1
    | ~ spl3_4 ),
    inference(trivial_inequality_removal,[],[f112]) ).

thf(f114,plain,
    ( ~ spl3_1
    | ~ spl3_4 ),
    inference(avatar_contradiction_clause,[],[f113]) ).

cnf(s1,plain,
    ( spl3_1
    | spl3_2 ),
    inference(sat_conversion,[],[f91]) ).

cnf(s2,plain,
    ( spl3_3
    | spl3_4 ),
    inference(sat_conversion,[],[f100]) ).

cnf(s3,plain,
    ( spl3_2
    | spl3_4 ),
    inference(sat_conversion,[],[f101]) ).

cnf(s4,plain,
    ( spl3_1
    | spl3_3 ),
    inference(sat_conversion,[],[f102]) ).

cnf(s5,plain,
    ( ~ spl3_2
    | ~ spl3_3 ),
    inference(sat_conversion,[],[f107]) ).

cnf(s7,plain,
    ( ~ spl3_1
    | ~ spl3_4 ),
    inference(sat_conversion,[],[f114]) ).

cnf(s8,plain,
    spl3_1,
    inference(rat,[],[s5,s1,s4]) ).

cnf(s9,plain,
    ~ spl3_4,
    inference(rat,[],[s7,s8]) ).

cnf(s10,plain,
    spl3_2,
    inference(rat,[],[s3,s9]) ).

cnf(s11,plain,
    spl3_3,
    inference(rat,[],[s2,s9]) ).

cnf(s12,plain,
    $false,
    inference(rat,[],[s5,s11,s10]) ).

thf(f115,plain,
    $false,
    inference(avatar_sat_refutation,[],[s12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SET613^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05  % Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18  % Computer : n013.cluster.edu
% 0.08/0.18  % Model    : x86_64 x86_64
% 0.08/0.18  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18  % Memory   : 8046.5625MB
% 0.08/0.18  % OS       : Linux 6.8.0-71-generic
% 0.08/0.18  % CPULimit : 300
% 0.08/0.18  % WCLimit  : 300
% 0.08/0.18  % DateTime : Tue Sep 29 13:38:37 UTC 2026
% 0.08/0.18  % CPUTime  : 
% 0.08/0.18  Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21  Running first-order model finding
% 0.08/0.21  Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.25  % (2122164)Will run a generic schedule for satisfiability detection.
% 0.08/0.25  % (2122173)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3904492788:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.25  % (2122173)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.25  % (2122173) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2122164-2122173"...
% 0.08/0.25  % (2122173)...printing done.
% 0.08/0.25  % (2122170)% WARNING: option uhcvi not known.
% 0.08/0.25  % (2122173)Refutation found. Thanks to Tanya!
% 0.08/0.25  % SZS status Theorem for theBenchmark
% 0.08/0.25  % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.25  % (2122173)------------------------------
% 0.08/0.25  % (2122173)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.25  % (2122173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.25  % (2122173)CaDiCaL version: 2.1.3
% 0.08/0.25  % (2122173)Termination reason: Refutation
% 0.08/0.25  % (2122173)Time elapsed: 0.002 s
% 0.08/0.25  % (2122173)Peak memory usage: 12 MB
% 0.08/0.25  % (2122173)Instructions burned: 6 (million)
% 0.08/0.25  % (2122164)Success in time 0.028 s
% 0.08/0.25  % Vampire exiting
%------------------------------------------------------------------------------