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%------------------------------------------------------------------------------
% File     : Vampire---5.0.1
% Problem  : SEV121^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM

% Computer : n002.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 08:37:50 AM UTC 2026

% Result   : Theorem 0.21s 0.29s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   67 (  15 unt;   0 typ;   6 def)
%            Number of atoms       :  375 ( 101 equ;  13 cnn)
%            Maximal formula atoms :    4 (   5 avg)
%            Number of connectives :  456 (  54   ~;  85   |;   0   &; 247   @)
%                                         (   6 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   92 (  92   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   24 (  19 usr;  12 con; 0-4 aty)
%                                         (  40  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  109 (   0 sgn  17   !;   0   ?; 109   :)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    sTfun: ( $tType * $tType ) > $tType ).

thf(func_def_1,type,
    vPI: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

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

thf(func_def_3,type,
    db1: 
      !>[X0: $tType] : X0 ).

thf(func_def_4,type,
    db0: 
      !>[X0: $tType] : X0 ).

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

thf(func_def_6,type,
    db2: 
      !>[X0: $tType] : X0 ).

thf(func_def_7,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(func_def_10,type,
    vNOT: $o > $o ).

thf(func_def_14,type,
    sK3: $i > $i > $o ).

thf(func_def_15,type,
    sK4: ( $i > $i > $o ) > $i ).

thf(f1,conjecture,
    ( ( ^ [X2: $i,X3: $i] :
        ! [X4: $i > $i > $o] :
          ( ! [X5: $i] : ( X4 @ X5 @ X5 )
         => ( X4 @ X2 @ X3 ) ) )
    = ( ^ [X0: $i,X1: $i] : ( X0 = X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM47C_pme) ).

thf(f2,negated_conjecture,
    ( ( ^ [X2: $i,X3: $i] :
        ! [X4: $i > $i > $o] :
          ( ! [X5: $i] : ( X4 @ X5 @ X5 )
         => ( X4 @ X2 @ X3 ) ) )
   != ( ^ [X0: $i,X1: $i] : ( X0 = X1 ) ) ),
    inference(negated_conjecture,[status(cth)],[f1]) ).

thf(f3,plain,
    ( ( ^ [X0: $i,X1: $i] :
        ! [X2: $i > $i > $o] :
          ( ! [X3: $i] : ( X2 @ X3 @ X3 )
         => ( X2 @ X0 @ X1 ) ) )
   != ( ^ [X4: $i,X5: $i] : ( X4 = X5 ) ) ),
    inference(rectify,[],[f2]) ).

thf(f4,plain,
    ( ( ^ [Y0: $i,Y1: $i] :
          ( !! @ ( $i > $i > $o )
          @ ^ [Y2: $i > $i > $o] :
              ( ( !! @ $i
                @ ^ [Y3: $i] : ( Y2 @ Y3 @ Y3 ) )
             => ( Y2 @ Y0 @ Y1 ) ) ) )
   != ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 ) ) ),
    inference(fool_elimination,[],[f3]) ).

thf(f5,plain,
    ( ( ^ [Y0: $i,Y1: $i] :
          ( !! @ ( $i > $i > $o )
          @ ^ [Y2: $i > $i > $o] :
              ( ( !! @ $i
                @ ^ [Y3: $i] : ( Y2 @ Y3 @ Y3 ) )
             => ( Y2 @ Y0 @ Y1 ) ) ) )
   != ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 ) ) ),
    inference(flattening,[],[f4]) ).

thf(f6,plain,
    ( ( ^ [Y0: $i,Y1: $i] :
          ( !! @ ( $i > $i > $o )
          @ ^ [Y2: $i > $i > $o] :
              ( ( !! @ $i
                @ ^ [Y3: $i] : ( Y2 @ Y3 @ Y3 ) )
             => ( Y2 @ Y0 @ Y1 ) ) ) )
   != ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 ) ) ),
    inference(cnf_transformation,[],[f5]) ).

thf(f8,plain,
    ( (=)
   != ( ^ [Y0: $i,Y1: $i] :
          ( !! @ ( $i > $i > $o )
          @ ^ [Y2: $i > $i > $o] :
              ( ( !! @ $i
                @ ^ [Y3: $i] : ( Y2 @ Y3 @ Y3 ) )
             => ( Y2 @ Y0 @ Y1 ) ) ) ) ),
    inference(beta-eta_normalization,[],[f6]) ).

thf(f10,definition,
    ( spl0_1
  <=> ( (=)
      = ( ^ [Y0: $i,Y1: $i] :
            ( !! @ ( $i > $i > $o )
            @ ^ [Y2: $i > $i > $o] :
                ( ( !! @ $i
                  @ ^ [Y3: $i] : ( Y2 @ Y3 @ Y3 ) )
               => ( Y2 @ Y0 @ Y1 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).

thf(f12,plain,
    ( ( (=)
     != ( ^ [Y0: $i,Y1: $i] :
            ( !! @ ( $i > $i > $o )
            @ ^ [Y2: $i > $i > $o] :
                ( ( !! @ $i
                  @ ^ [Y3: $i] : ( Y2 @ Y3 @ Y3 ) )
               => ( Y2 @ Y0 @ Y1 ) ) ) ) )
    | spl0_1 ),
    inference(avatar_component_clause,[],[f10]) ).

thf(f13,plain,
    ~ spl0_1,
    inference(avatar_split_clause,[],[f8,f10]) ).

thf(f14,plain,
    ( ( ( (=) @ sK1 )
     != ( ^ [Y0: $i,Y1: $i] :
            ( !! @ ( $i > $i > $o )
            @ ^ [Y2: $i > $i > $o] :
                ( ( !! @ $i
                  @ ^ [Y3: $i] : ( Y2 @ Y3 @ Y3 ) )
               => ( Y2 @ Y0 @ Y1 ) ) )
        @ sK1 ) )
    | spl0_1 ),
    inference(negative_extensionality,[],[f12]) ).

thf(f15,plain,
    ( ( ( (=) @ sK1 )
     != ( ^ [Y0: $i] :
            ( !! @ ( $i > $i > $o )
            @ ^ [Y1: $i > $i > $o] :
                ( ( !! @ $i
                  @ ^ [Y2: $i] : ( Y1 @ Y2 @ Y2 ) )
               => ( Y1 @ sK1 @ Y0 ) ) ) ) )
    | spl0_1 ),
    inference(beta-eta_normalization,[],[f14]) ).

thf(f17,definition,
    ( spl0_2
  <=> ( ( (=) @ sK1 )
      = ( ^ [Y0: $i] :
            ( !! @ ( $i > $i > $o )
            @ ^ [Y1: $i > $i > $o] :
                ( ( !! @ $i
                  @ ^ [Y2: $i] : ( Y1 @ Y2 @ Y2 ) )
               => ( Y1 @ sK1 @ Y0 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).

thf(f19,plain,
    ( ( ( (=) @ sK1 )
     != ( ^ [Y0: $i] :
            ( !! @ ( $i > $i > $o )
            @ ^ [Y1: $i > $i > $o] :
                ( ( !! @ $i
                  @ ^ [Y2: $i] : ( Y1 @ Y2 @ Y2 ) )
               => ( Y1 @ sK1 @ Y0 ) ) ) ) )
    | spl0_2 ),
    inference(avatar_component_clause,[],[f17]) ).

thf(f20,plain,
    ( ~ spl0_2
    | spl0_1 ),
    inference(avatar_split_clause,[],[f15,f10,f17]) ).

thf(f21,plain,
    ( ( ( sK1 = sK2 )
     != ( ^ [Y0: $i] :
            ( !! @ ( $i > $i > $o )
            @ ^ [Y1: $i > $i > $o] :
                ( ( !! @ $i
                  @ ^ [Y2: $i] : ( Y1 @ Y2 @ Y2 ) )
               => ( Y1 @ sK1 @ Y0 ) ) )
        @ sK2 ) )
    | spl0_2 ),
    inference(negative_extensionality,[],[f19]) ).

thf(f22,plain,
    ( ( ( sK1 = sK2 )
      = $true )
    | ( $true
      = ( ^ [Y0: $i] :
            ( !! @ ( $i > $i > $o )
            @ ^ [Y1: $i > $i > $o] :
                ( ( !! @ $i
                  @ ^ [Y2: $i] : ( Y1 @ Y2 @ Y2 ) )
               => ( Y1 @ sK1 @ Y0 ) ) )
        @ sK2 ) )
    | spl0_2 ),
    inference(xor_proxy_clausification,[],[f21]) ).

thf(f23,plain,
    ( ( ( sK1 = sK2 )
      = $false )
    | ( $false
      = ( ^ [Y0: $i] :
            ( !! @ ( $i > $i > $o )
            @ ^ [Y1: $i > $i > $o] :
                ( ( !! @ $i
                  @ ^ [Y2: $i] : ( Y1 @ Y2 @ Y2 ) )
               => ( Y1 @ sK1 @ Y0 ) ) )
        @ sK2 ) )
    | spl0_2 ),
    inference(xor_proxy_clausification,[],[f21]) ).

thf(f24,plain,
    ( ( sK1 != sK2 )
    | ( $false
      = ( ^ [Y0: $i] :
            ( !! @ ( $i > $i > $o )
            @ ^ [Y1: $i > $i > $o] :
                ( ( !! @ $i
                  @ ^ [Y2: $i] : ( Y1 @ Y2 @ Y2 ) )
               => ( Y1 @ sK1 @ Y0 ) ) )
        @ sK2 ) )
    | spl0_2 ),
    inference(equality_proxy_clausification,[],[f23]) ).

thf(f25,plain,
    ( ( sK1 != sK2 )
    | ( ( !! @ ( $i > $i > $o )
        @ ^ [Y0: $i > $i > $o] :
            ( ( !! @ $i
              @ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
           => ( Y0 @ sK1 @ sK2 ) ) )
      = $false )
    | spl0_2 ),
    inference(beta-eta_normalization,[],[f24]) ).

thf(f26,plain,
    ( ( $false
      = ( ^ [Y0: $i > $i > $o] :
            ( ( !! @ $i
              @ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
           => ( Y0 @ sK1 @ sK2 ) )
        @ sK3 ) )
    | ( sK1 != sK2 )
    | spl0_2 ),
    inference(sigma_proxy_clausification,[],[f25]) ).

thf(f27,plain,
    ( ( ( ( !! @ $i
          @ ^ [Y0: $i] : ( sK3 @ Y0 @ Y0 ) )
       => ( sK3 @ sK1 @ sK2 ) )
      = $false )
    | ( sK1 != sK2 )
    | spl0_2 ),
    inference(beta-eta_normalization,[],[f26]) ).

thf(f28,plain,
    ( ( sK1 != sK2 )
    | ( ( sK3 @ sK1 @ sK2 )
      = $false )
    | spl0_2 ),
    inference(imp_proxy_clausification,[],[f27]) ).

thf(f29,plain,
    ( ( $true
      = ( !! @ $i
        @ ^ [Y0: $i] : ( sK3 @ Y0 @ Y0 ) ) )
    | ( sK1 != sK2 )
    | spl0_2 ),
    inference(imp_proxy_clausification,[],[f27]) ).

thf(f30,plain,
    ( ! [X1: $i] :
        ( ( sK1 != sK2 )
        | ( $true
          = ( ^ [Y0: $i] : ( sK3 @ Y0 @ Y0 )
            @ X1 ) ) )
    | spl0_2 ),
    inference(pi_proxy_clausification,[],[f29]) ).

thf(f31,plain,
    ( ! [X1: $i] :
        ( ( sK1 != sK2 )
        | ( $true
          = ( sK3 @ X1 @ X1 ) ) )
    | spl0_2 ),
    inference(beta-eta_normalization,[],[f30]) ).

thf(f32,plain,
    ( ( sK1 = sK2 )
    | ( $true
      = ( ^ [Y0: $i] :
            ( !! @ ( $i > $i > $o )
            @ ^ [Y1: $i > $i > $o] :
                ( ( !! @ $i
                  @ ^ [Y2: $i] : ( Y1 @ Y2 @ Y2 ) )
               => ( Y1 @ sK1 @ Y0 ) ) )
        @ sK2 ) )
    | spl0_2 ),
    inference(equality_proxy_clausification,[],[f22]) ).

thf(f33,plain,
    ( ( $true
      = ( !! @ ( $i > $i > $o )
        @ ^ [Y0: $i > $i > $o] :
            ( ( !! @ $i
              @ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
           => ( Y0 @ sK1 @ sK2 ) ) ) )
    | ( sK1 = sK2 )
    | spl0_2 ),
    inference(beta-eta_normalization,[],[f32]) ).

thf(f34,plain,
    ( ! [X1: $i > $i > $o] :
        ( ( sK1 = sK2 )
        | ( $true
          = ( ^ [Y0: $i > $i > $o] :
                ( ( !! @ $i
                  @ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
               => ( Y0 @ sK1 @ sK2 ) )
            @ X1 ) ) )
    | spl0_2 ),
    inference(pi_proxy_clausification,[],[f33]) ).

thf(f35,plain,
    ( ! [X1: $i > $i > $o] :
        ( ( sK1 = sK2 )
        | ( ( ( !! @ $i
              @ ^ [Y0: $i] : ( X1 @ Y0 @ Y0 ) )
           => ( X1 @ sK1 @ sK2 ) )
          = $true ) )
    | spl0_2 ),
    inference(beta-eta_normalization,[],[f34]) ).

thf(f36,plain,
    ( ! [X1: $i > $i > $o] :
        ( ( $true
          = ( X1 @ sK1 @ sK2 ) )
        | ( sK1 = sK2 )
        | ( ( !! @ $i
            @ ^ [Y0: $i] : ( X1 @ Y0 @ Y0 ) )
          = $false ) )
    | spl0_2 ),
    inference(imp_proxy_clausification,[],[f35]) ).

thf(f37,plain,
    ( ! [X1: $i > $i > $o] :
        ( ( sK1 = sK2 )
        | ( $true
          = ( X1 @ sK1 @ sK2 ) )
        | ( $false
          = ( ^ [Y0: $i] : ( X1 @ Y0 @ Y0 )
            @ ( sK4 @ X1 ) ) ) )
    | spl0_2 ),
    inference(sigma_proxy_clausification,[],[f36]) ).

thf(f38,plain,
    ( ! [X1: $i > $i > $o] :
        ( ( sK1 = sK2 )
        | ( $true
          = ( X1 @ sK1 @ sK2 ) )
        | ( ( X1 @ ( sK4 @ X1 ) @ ( sK4 @ X1 ) )
          = $false ) )
    | spl0_2 ),
    inference(beta-eta_normalization,[],[f37]) ).

thf(f40,definition,
    ( spl0_3
  <=> ! [X1: $i] :
        ( $true
        = ( sK3 @ X1 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).

thf(f41,plain,
    ( ! [X1: $i] :
        ( $true
        = ( sK3 @ X1 @ X1 ) )
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f40]) ).

thf(f43,definition,
    ( spl0_4
  <=> ( sK1 = sK2 ) ),
    introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).

thf(f44,plain,
    ( ( sK1 = sK2 )
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f43]) ).

thf(f46,plain,
    ( spl0_3
    | ~ spl0_4
    | spl0_2 ),
    inference(avatar_split_clause,[],[f31,f17,f43,f40]) ).

thf(f48,definition,
    ( spl0_5
  <=> ( ( sK3 @ sK1 @ sK2 )
      = $false ) ),
    introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).

thf(f50,plain,
    ( ( ( sK3 @ sK1 @ sK2 )
      = $false )
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f48]) ).

thf(f51,plain,
    ( ~ spl0_4
    | spl0_5
    | spl0_2 ),
    inference(avatar_split_clause,[],[f28,f17,f48,f43]) ).

thf(f53,definition,
    ( spl0_6
  <=> ! [X1: $i > $i > $o] :
        ( ( $true
          = ( X1 @ sK1 @ sK2 ) )
        | ( ( X1 @ ( sK4 @ X1 ) @ ( sK4 @ X1 ) )
          = $false ) ) ),
    introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).

thf(f54,plain,
    ( ! [X1: $i > $i > $o] :
        ( ( ( X1 @ ( sK4 @ X1 ) @ ( sK4 @ X1 ) )
          = $false )
        | ( $true
          = ( X1 @ sK1 @ sK2 ) ) )
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f53]) ).

thf(f55,plain,
    ( spl0_6
    | spl0_4
    | spl0_2 ),
    inference(avatar_split_clause,[],[f38,f17,f43,f53]) ).

thf(f56,plain,
    ( ( ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 )
        @ ( sK4
          @ ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 ) )
        @ ( sK4
          @ ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 ) ) )
      = $false )
    | ( ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 )
        @ sK1
        @ sK2 )
      = $true )
    | ~ spl0_6 ),
    inference(primitive_instantiation,[],[f54]) ).

thf(f71,plain,
    ( ( ( sK1 = sK2 )
      = $true )
    | ( $false
      = ( ( sK4 @ (=) )
        = ( sK4 @ (=) ) ) )
    | ~ spl0_6 ),
    inference(beta-eta_normalization,[],[f56]) ).

thf(f72,plain,
    ( ( sK1 = sK2 )
    | ( $false
      = ( ( sK4 @ (=) )
        = ( sK4 @ (=) ) ) )
    | ~ spl0_6 ),
    inference(equality_proxy_clausification,[],[f71]) ).

thf(f73,plain,
    ( ( sK1 = sK2 )
    | ( ( sK4 @ (=) )
     != ( sK4 @ (=) ) )
    | ~ spl0_6 ),
    inference(equality_proxy_clausification,[],[f72]) ).

thf(f74,plain,
    ( ( sK1 = sK2 )
    | ~ spl0_6 ),
    inference(trivial_inequality_removal,[],[f73]) ).

thf(f75,plain,
    ( spl0_4
    | ~ spl0_6 ),
    inference(avatar_split_clause,[],[f74,f53,f43]) ).

thf(f76,plain,
    ( ( $false
      = ( sK3 @ sK1 @ sK1 ) )
    | ~ spl0_4
    | ~ spl0_5 ),
    inference(forward_demodulation,[],[f50,f44]) ).

thf(f77,plain,
    ( ( $true = $false )
    | ~ spl0_3
    | ~ spl0_4
    | ~ spl0_5 ),
    inference(forward_demodulation,[],[f76,f41]) ).

thf(f78,plain,
    ( $false
    | ~ spl0_3
    | ~ spl0_4
    | ~ spl0_5 ),
    inference(trivial_inequality_removal,[],[f77]) ).

thf(f79,plain,
    ( ~ spl0_3
    | ~ spl0_4
    | ~ spl0_5 ),
    inference(avatar_contradiction_clause,[],[f78]) ).

cnf(s1,plain,
    ~ spl0_1,
    inference(sat_conversion,[],[f13]) ).

cnf(s2,plain,
    ( spl0_1
    | ~ spl0_2 ),
    inference(sat_conversion,[],[f20]) ).

cnf(s3,plain,
    ( spl0_2
    | spl0_3
    | ~ spl0_4 ),
    inference(sat_conversion,[],[f46]) ).

cnf(s4,plain,
    ( spl0_2
    | ~ spl0_4
    | spl0_5 ),
    inference(sat_conversion,[],[f51]) ).

cnf(s5,plain,
    ( spl0_2
    | spl0_4
    | spl0_6 ),
    inference(sat_conversion,[],[f55]) ).

cnf(s6,plain,
    ( spl0_4
    | ~ spl0_6 ),
    inference(sat_conversion,[],[f75]) ).

cnf(s7,plain,
    ( ~ spl0_3
    | ~ spl0_4
    | ~ spl0_5 ),
    inference(sat_conversion,[],[f79]) ).

cnf(s8,plain,
    ~ spl0_2,
    inference(rat,[],[s2,s1]) ).

cnf(s9,plain,
    spl0_4,
    inference(rat,[],[s5,s6,s8]) ).

cnf(s10,plain,
    spl0_5,
    inference(rat,[],[s4,s8,s9]) ).

cnf(s11,plain,
    spl0_3,
    inference(rat,[],[s3,s8,s9]) ).

cnf(s12,plain,
    $false,
    inference(rat,[],[s7,s9,s11,s10]) ).

thf(f80,plain,
    $false,
    inference(avatar_sat_refutation,[],[s12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SEV121^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05  % Command  : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19  % Computer : n002.cluster.edu
% 0.09/0.19  % Model    : x86_64 x86_64
% 0.09/0.19  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19  % Memory   : 8046.5625MB
% 0.09/0.19  % OS       : Linux 6.8.0-71-generic
% 0.09/0.19  % CPULimit : 300
% 0.09/0.19  % WCLimit  : 300
% 0.09/0.19  % DateTime : Tue Sep 29 15:14:38 UTC 2026
% 0.09/0.19  % CPUTime  : 
% 0.09/0.20  Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23  Running higher-order theorem proving
% 0.09/0.24  Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.29  % (1415609)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29  % (1415617)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2366425942:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.29  % (1415617) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1415609-1415617"...
% 0.21/0.29  % (1415617)...printing done.
% 0.21/0.29  % (1415617)Refutation found. Thanks to Tanya!
% 0.21/0.29  % SZS status Theorem for theBenchmark
% 0.21/0.29  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29  % (1415617)------------------------------
% 0.21/0.29  % (1415617)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29  % (1415617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29  % (1415617)CaDiCaL version: 2.1.3
% 0.21/0.29  % (1415617)Termination reason: Refutation
% 0.21/0.29  % (1415617)Time elapsed: 0.003 s
% 0.21/0.29  % (1415617)Peak memory usage: 13 MB
% 0.21/0.29  % (1415617)Instructions burned: 6 (million)
% 0.21/0.29  % (1415609)Success in time 0.034 s
% 0.21/0.29  % Vampire exiting
%------------------------------------------------------------------------------