TSTP Solution File: ALG248^3 by Vampire---4.8

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : ALG248^3 : TPTP v8.2.0. Bugfixed v5.2.0.
% 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 : n012.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 May 20 18:19:59 EDT 2024

% Result   : Theorem 0.18s 0.42s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   29
% Syntax   : Number of formulae    :   84 (  49 unt;  22 typ;   0 def)
%            Number of atoms       :  276 (  86 equ;   0 cnn)
%            Maximal formula atoms :    2 (   4 avg)
%            Number of connectives :  551 (  15   ~;   9   |;   0   &; 410   @)
%                                         (   4 <=>;  42  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :  103 ( 103   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   27 (  23 usr;  13 con; 0-4 aty)
%                                         (  71  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  132 ( 106   ^  26   !;   0   ?; 132   :)

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

thf(type_def_7,type,
    subst: $tType ).

thf(func_def_0,type,
    term: $tType ).

thf(func_def_1,type,
    subst: $tType ).

thf(func_def_2,type,
    one: term ).

thf(func_def_3,type,
    ap: term > term > term ).

thf(func_def_4,type,
    lam: term > term ).

thf(func_def_5,type,
    sub: term > subst > term ).

thf(func_def_6,type,
    id: subst ).

thf(func_def_7,type,
    sh: subst ).

thf(func_def_8,type,
    push: term > subst > subst ).

thf(func_def_9,type,
    comp: subst > subst > subst ).

thf(func_def_10,type,
    var: term > $o ).

thf(func_def_18,type,
    hoasap: subst > term > subst > term > term ).

thf(func_def_73,type,
    hoaslam: subst > ( subst > term > term ) > term ).

thf(func_def_86,type,
    hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).

thf(func_def_107,type,
    hoasvar: subst > term > subst > $o ).

thf(func_def_121,type,
    pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).

thf(func_def_144,type,
    sK1: term ).

thf(func_def_145,type,
    sK2: subst ).

thf(func_def_146,type,
    sK3: term > $o ).

thf(func_def_147,type,
    sK4: term > $o ).

thf(f574,plain,
    $false,
    inference(avatar_sat_refutation,[],[f561,f567,f573]) ).

thf(f573,plain,
    ~ spl0_1,
    inference(avatar_contradiction_clause,[],[f572]) ).

thf(f572,plain,
    ( $false
    | ~ spl0_1 ),
    inference(trivial_inequality_removal,[],[f568]) ).

thf(f568,plain,
    ( ( $true = $false )
    | ~ spl0_1 ),
    inference(superposition,[],[f556,f540]) ).

thf(f540,plain,
    ( ( sK3 @ one )
    = $false ),
    inference(binary_proxy_clausification,[],[f538]) ).

thf(f538,plain,
    ( ( ( !! @ term
        @ ^ [Y0: term] :
            ( ( sK4 @ ( sub @ Y0 @ ( push @ sK1 @ sK2 ) ) )
            = ( sK3 @ Y0 ) ) )
     => ( sK3 @ one ) )
    = $false ),
    inference(binary_proxy_clausification,[],[f537]) ).

thf(f537,plain,
    ( ( ( sK4 @ sK1 )
     => ( ( !! @ term
          @ ^ [Y0: term] :
              ( ( sK4 @ ( sub @ Y0 @ ( push @ sK1 @ sK2 ) ) )
              = ( sK3 @ Y0 ) ) )
       => ( sK3 @ one ) ) )
    = $false ),
    inference(beta_eta_normalization,[],[f536]) ).

thf(f536,plain,
    ( ( ^ [Y0: term > $o] :
          ( ( Y0 @ sK1 )
         => ( ( !! @ term
              @ ^ [Y1: term] :
                  ( ( Y0 @ ( sub @ Y1 @ ( push @ sK1 @ sK2 ) ) )
                  = ( sK3 @ Y1 ) ) )
           => ( sK3 @ one ) ) )
      @ sK4 )
    = $false ),
    inference(sigma_clausification,[],[f535]) ).

thf(f535,plain,
    ( ( !! @ ( term > $o )
      @ ^ [Y0: term > $o] :
          ( ( Y0 @ sK1 )
         => ( ( !! @ term
              @ ^ [Y1: term] :
                  ( ( Y0 @ ( sub @ Y1 @ ( push @ sK1 @ sK2 ) ) )
                  = ( sK3 @ Y1 ) ) )
           => ( sK3 @ one ) ) ) )
    = $false ),
    inference(beta_eta_normalization,[],[f534]) ).

thf(f534,plain,
    ( ( ^ [Y0: term > $o] :
          ( !! @ ( term > $o )
          @ ^ [Y1: term > $o] :
              ( ( Y1 @ sK1 )
             => ( ( !! @ term
                  @ ^ [Y2: term] :
                      ( ( Y1 @ ( sub @ Y2 @ ( push @ sK1 @ sK2 ) ) )
                      = ( Y0 @ Y2 ) ) )
               => ( Y0 @ one ) ) ) )
      @ sK3 )
    = $false ),
    inference(sigma_clausification,[],[f533]) ).

thf(f533,plain,
    ( ( !! @ ( term > $o )
      @ ^ [Y0: term > $o] :
          ( !! @ ( term > $o )
          @ ^ [Y1: term > $o] :
              ( ( Y1 @ sK1 )
             => ( ( !! @ term
                  @ ^ [Y2: term] :
                      ( ( Y1 @ ( sub @ Y2 @ ( push @ sK1 @ sK2 ) ) )
                      = ( Y0 @ Y2 ) ) )
               => ( Y0 @ one ) ) ) ) )
    = $false ),
    inference(beta_eta_normalization,[],[f532]) ).

thf(f532,plain,
    ( ( ^ [Y0: subst] :
          ( !! @ ( term > $o )
          @ ^ [Y1: term > $o] :
              ( !! @ ( term > $o )
              @ ^ [Y2: term > $o] :
                  ( ( Y2 @ sK1 )
                 => ( ( !! @ term
                      @ ^ [Y3: term] :
                          ( ( Y2 @ ( sub @ Y3 @ ( push @ sK1 @ Y0 ) ) )
                          = ( Y1 @ Y3 ) ) )
                   => ( Y1 @ one ) ) ) ) )
      @ sK2 )
    = $false ),
    inference(sigma_clausification,[],[f531]) ).

thf(f531,plain,
    ( ( !! @ subst
      @ ^ [Y0: subst] :
          ( !! @ ( term > $o )
          @ ^ [Y1: term > $o] :
              ( !! @ ( term > $o )
              @ ^ [Y2: term > $o] :
                  ( ( Y2 @ sK1 )
                 => ( ( !! @ term
                      @ ^ [Y3: term] :
                          ( ( Y2 @ ( sub @ Y3 @ ( push @ sK1 @ Y0 ) ) )
                          = ( Y1 @ Y3 ) ) )
                   => ( Y1 @ one ) ) ) ) ) )
    = $false ),
    inference(beta_eta_normalization,[],[f530]) ).

thf(f530,plain,
    ( ( ^ [Y0: term] :
          ( !! @ subst
          @ ^ [Y1: subst] :
              ( !! @ ( term > $o )
              @ ^ [Y2: term > $o] :
                  ( !! @ ( term > $o )
                  @ ^ [Y3: term > $o] :
                      ( ( Y3 @ Y0 )
                     => ( ( !! @ term
                          @ ^ [Y4: term] :
                              ( ( Y3 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
                              = ( Y2 @ Y4 ) ) )
                       => ( Y2 @ one ) ) ) ) ) )
      @ sK1 )
    = $false ),
    inference(sigma_clausification,[],[f523]) ).

thf(f523,plain,
    ( $false
    = ( !! @ term
      @ ^ [Y0: term] :
          ( !! @ subst
          @ ^ [Y1: subst] :
              ( !! @ ( term > $o )
              @ ^ [Y2: term > $o] :
                  ( !! @ ( term > $o )
                  @ ^ [Y3: term > $o] :
                      ( ( Y3 @ Y0 )
                     => ( ( !! @ term
                          @ ^ [Y4: term] :
                              ( ( Y3 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
                              = ( Y2 @ Y4 ) ) )
                       => ( Y2 @ one ) ) ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f522]) ).

thf(f522,plain,
    ( ( ( !! @ subst
        @ ^ [Y0: subst] :
            ( !! @ term
            @ ^ [Y1: term] :
                ( ( sub @ one @ ( push @ Y1 @ Y0 ) )
                = Y1 ) ) )
     => ( !! @ term
        @ ^ [Y0: term] :
            ( !! @ subst
            @ ^ [Y1: subst] :
                ( !! @ ( term > $o )
                @ ^ [Y2: term > $o] :
                    ( !! @ ( term > $o )
                    @ ^ [Y3: term > $o] :
                        ( ( Y3 @ Y0 )
                       => ( ( !! @ term
                            @ ^ [Y4: term] :
                                ( ( Y3 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
                                = ( Y2 @ Y4 ) ) )
                         => ( Y2 @ one ) ) ) ) ) ) ) )
   != $true ),
    inference(beta_eta_normalization,[],[f521]) ).

thf(f521,plain,
    ( ( ( !! @ subst
        @ ^ [Y0: subst] :
            ( !! @ term
            @ ^ [Y1: term] :
                ( ( sub @ one @ ( push @ Y1 @ Y0 ) )
                = Y1 ) ) )
     => ( !! @ term
        @ ^ [Y0: term] :
            ( !! @ subst
            @ ^ [Y1: subst] :
                ( !! @ ( term > $o )
                @ ^ [Y2: term > $o] :
                    ( !! @ ( term > $o )
                    @ ^ [Y3: term > $o] :
                        ( ( Y3 @ Y0 )
                       => ( ( ^ [Y4: term,Y5: subst,Y6: term > $o,Y7: term > $o] :
                                ( !! @ term
                                @ ^ [Y8: term] :
                                    ( ( Y6 @ ( sub @ Y8 @ ( push @ Y4 @ Y5 ) ) )
                                    = ( Y7 @ Y8 ) ) )
                            @ Y0
                            @ Y1
                            @ Y3
                            @ Y2 )
                         => ( Y2 @ one ) ) ) ) ) ) ) )
   != $true ),
    inference(definition_unfolding,[],[f365,f477]) ).

thf(f477,plain,
    ( pushprop_lem1v2_lthm
    = ( ( !! @ subst
        @ ^ [Y0: subst] :
            ( !! @ term
            @ ^ [Y1: term] :
                ( ( sub @ one @ ( push @ Y1 @ Y0 ) )
                = Y1 ) ) )
     => ( !! @ term
        @ ^ [Y0: term] :
            ( !! @ subst
            @ ^ [Y1: subst] :
                ( !! @ ( term > $o )
                @ ^ [Y2: term > $o] :
                    ( !! @ ( term > $o )
                    @ ^ [Y3: term > $o] :
                        ( ( Y3 @ Y0 )
                       => ( ( ^ [Y4: term,Y5: subst,Y6: term > $o,Y7: term > $o] :
                                ( !! @ term
                                @ ^ [Y8: term] :
                                    ( ( Y6 @ ( sub @ Y8 @ ( push @ Y4 @ Y5 ) ) )
                                    = ( Y7 @ Y8 ) ) )
                            @ Y0
                            @ Y1
                            @ Y3
                            @ Y2 )
                         => ( Y2 @ one ) ) ) ) ) ) ) ) ),
    inference(definition_unfolding,[],[f410,f440,f444]) ).

thf(f444,plain,
    ( pushprop_lem1v2
    = ( !! @ term
      @ ^ [Y0: term] :
          ( !! @ subst
          @ ^ [Y1: subst] :
              ( !! @ ( term > $o )
              @ ^ [Y2: term > $o] :
                  ( !! @ ( term > $o )
                  @ ^ [Y3: term > $o] :
                      ( ( Y3 @ Y0 )
                     => ( ( ^ [Y4: term,Y5: subst,Y6: term > $o,Y7: term > $o] :
                              ( !! @ term
                              @ ^ [Y8: term] :
                                  ( ( Y6 @ ( sub @ Y8 @ ( push @ Y4 @ Y5 ) ) )
                                  = ( Y7 @ Y8 ) ) )
                          @ Y0
                          @ Y1
                          @ Y3
                          @ Y2 )
                       => ( Y2 @ one ) ) ) ) ) ) ) ),
    inference(definition_unfolding,[],[f427,f348]) ).

thf(f348,plain,
    ( pushprop_p_and_p_prime
    = ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
          ( !! @ term
          @ ^ [Y4: term] :
              ( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
              = ( Y3 @ Y4 ) ) ) ) ),
    inference(cnf_transformation,[],[f243]) ).

thf(f243,plain,
    ( pushprop_p_and_p_prime
    = ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
          ( !! @ term
          @ ^ [Y4: term] :
              ( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
              = ( Y3 @ Y4 ) ) ) ) ),
    inference(fool_elimination,[],[f242]) ).

thf(f242,plain,
    ( ( ^ [X0: term,X1: subst,X2: term > $o,X3: term > $o] :
        ! [X4: term] :
          ( ( X2 @ ( sub @ X4 @ ( push @ X0 @ X1 ) ) )
        <=> ( X3 @ X4 ) ) )
    = pushprop_p_and_p_prime ),
    inference(rectify,[],[f24]) ).

thf(f24,axiom,
    ( ( ^ [X0: term,X2: subst,X5: term > $o,X8: term > $o] :
        ! [X9: term] :
          ( ( X5 @ ( sub @ X9 @ ( push @ X0 @ X2 ) ) )
        <=> ( X8 @ X9 ) ) )
    = pushprop_p_and_p_prime ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_p_and_p_prime) ).

thf(f427,plain,
    ( pushprop_lem1v2
    = ( !! @ term
      @ ^ [Y0: term] :
          ( !! @ subst
          @ ^ [Y1: subst] :
              ( !! @ ( term > $o )
              @ ^ [Y2: term > $o] :
                  ( !! @ ( term > $o )
                  @ ^ [Y3: term > $o] :
                      ( ( Y3 @ Y0 )
                     => ( ( pushprop_p_and_p_prime @ Y0 @ Y1 @ Y3 @ Y2 )
                       => ( Y2 @ one ) ) ) ) ) ) ) ),
    inference(cnf_transformation,[],[f135]) ).

thf(f135,plain,
    ( pushprop_lem1v2
    = ( !! @ term
      @ ^ [Y0: term] :
          ( !! @ subst
          @ ^ [Y1: subst] :
              ( !! @ ( term > $o )
              @ ^ [Y2: term > $o] :
                  ( !! @ ( term > $o )
                  @ ^ [Y3: term > $o] :
                      ( ( Y3 @ Y0 )
                     => ( ( pushprop_p_and_p_prime @ Y0 @ Y1 @ Y3 @ Y2 )
                       => ( Y2 @ one ) ) ) ) ) ) ) ),
    inference(fool_elimination,[],[f134]) ).

thf(f134,plain,
    ! [X0: term > $o,X1: term > $o,X2: subst,X3: term] :
      ( ( ( X0 @ X3 )
       => ( ( pushprop_p_and_p_prime @ X3 @ X2 @ X0 @ X1 )
         => ( X1 @ one ) ) )
      = pushprop_lem1v2 ),
    inference(rectify,[],[f31]) ).

thf(f31,axiom,
    ! [X5: term > $o,X8: term > $o,X2: subst,X0: term] :
      ( ( ( X5 @ X0 )
       => ( ( pushprop_p_and_p_prime @ X0 @ X2 @ X5 @ X8 )
         => ( X8 @ one ) ) )
      = pushprop_lem1v2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem1v2) ).

thf(f440,plain,
    ( axvarcons
    = ( !! @ subst
      @ ^ [Y0: subst] :
          ( !! @ term
          @ ^ [Y1: term] :
              ( ( sub @ one @ ( push @ Y1 @ Y0 ) )
              = Y1 ) ) ) ),
    inference(cnf_transformation,[],[f130]) ).

thf(f130,plain,
    ( axvarcons
    = ( !! @ subst
      @ ^ [Y0: subst] :
          ( !! @ term
          @ ^ [Y1: term] :
              ( ( sub @ one @ ( push @ Y1 @ Y0 ) )
              = Y1 ) ) ) ),
    inference(fool_elimination,[],[f129]) ).

thf(f129,plain,
    ( axvarcons
    = ( ! [X0: term,X1: subst] :
          ( ( sub @ one @ ( push @ X0 @ X1 ) )
          = X0 ) ) ),
    inference(rectify,[],[f2]) ).

thf(f2,axiom,
    ( axvarcons
    = ( ! [X0: term,X2: subst] :
          ( ( sub @ one @ ( push @ X0 @ X2 ) )
          = X0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axvarcons) ).

thf(f410,plain,
    ( pushprop_lem1v2_lthm
    = ( axvarcons
     => pushprop_lem1v2 ) ),
    inference(cnf_transformation,[],[f322]) ).

thf(f322,plain,
    ( pushprop_lem1v2_lthm
    = ( axvarcons
     => pushprop_lem1v2 ) ),
    inference(fool_elimination,[],[f321]) ).

thf(f321,plain,
    ( ( pushprop_lem1v2_lthm = axvarcons )
   => pushprop_lem1v2 ),
    inference(rectify,[],[f33]) ).

thf(f33,axiom,
    ( ( pushprop_lem1v2_lthm = axvarcons )
   => pushprop_lem1v2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem1v2_lthm) ).

thf(f365,plain,
    pushprop_lem1v2_lthm != $true,
    inference(cnf_transformation,[],[f329]) ).

thf(f329,plain,
    pushprop_lem1v2_lthm != $true,
    inference(flattening,[],[f205]) ).

thf(f205,plain,
    pushprop_lem1v2_lthm != $true,
    inference(fool_elimination,[],[f204]) ).

thf(f204,plain,
    ~ pushprop_lem1v2_lthm,
    inference(rectify,[],[f115]) ).

thf(f115,negated_conjecture,
    ~ pushprop_lem1v2_lthm,
    inference(negated_conjecture,[],[f114]) ).

thf(f114,conjecture,
    pushprop_lem1v2_lthm,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).

thf(f556,plain,
    ( ( ( sK3 @ one )
      = $true )
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f554]) ).

thf(f554,plain,
    ( spl0_1
  <=> ( ( sK3 @ one )
      = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

thf(f567,plain,
    ~ spl0_2,
    inference(avatar_contradiction_clause,[],[f566]) ).

thf(f566,plain,
    ( $false
    | ~ spl0_2 ),
    inference(trivial_inequality_removal,[],[f562]) ).

thf(f562,plain,
    ( ( $true = $false )
    | ~ spl0_2 ),
    inference(superposition,[],[f560,f539]) ).

thf(f539,plain,
    ( $true
    = ( sK4 @ sK1 ) ),
    inference(binary_proxy_clausification,[],[f537]) ).

thf(f560,plain,
    ( ( $false
      = ( sK4 @ sK1 ) )
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f558]) ).

thf(f558,plain,
    ( spl0_2
  <=> ( $false
      = ( sK4 @ sK1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

thf(f561,plain,
    ( spl0_1
    | spl0_2 ),
    inference(avatar_split_clause,[],[f548,f558,f554]) ).

thf(f548,plain,
    ( ( ( sK3 @ one )
      = $true )
    | ( $false
      = ( sK4 @ sK1 ) ) ),
    inference(superposition,[],[f546,f529]) ).

thf(f529,plain,
    ! [X2: term,X1: subst] :
      ( ( sub @ one @ ( push @ X2 @ X1 ) )
      = X2 ),
    inference(equality_proxy_clausification,[],[f528]) ).

thf(f528,plain,
    ! [X2: term,X1: subst] :
      ( ( ( sub @ one @ ( push @ X2 @ X1 ) )
        = X2 )
      = $true ),
    inference(beta_eta_normalization,[],[f527]) ).

thf(f527,plain,
    ! [X2: term,X1: subst] :
      ( ( ^ [Y0: term] :
            ( ( sub @ one @ ( push @ Y0 @ X1 ) )
            = Y0 )
        @ X2 )
      = $true ),
    inference(pi_clausification,[],[f526]) ).

thf(f526,plain,
    ! [X1: subst] :
      ( $true
      = ( !! @ term
        @ ^ [Y0: term] :
            ( ( sub @ one @ ( push @ Y0 @ X1 ) )
            = Y0 ) ) ),
    inference(beta_eta_normalization,[],[f525]) ).

thf(f525,plain,
    ! [X1: subst] :
      ( $true
      = ( ^ [Y0: subst] :
            ( !! @ term
            @ ^ [Y1: term] :
                ( ( sub @ one @ ( push @ Y1 @ Y0 ) )
                = Y1 ) )
        @ X1 ) ),
    inference(pi_clausification,[],[f524]) ).

thf(f524,plain,
    ( ( !! @ subst
      @ ^ [Y0: subst] :
          ( !! @ term
          @ ^ [Y1: term] :
              ( ( sub @ one @ ( push @ Y1 @ Y0 ) )
              = Y1 ) ) )
    = $true ),
    inference(binary_proxy_clausification,[],[f522]) ).

thf(f546,plain,
    ! [X1: term] :
      ( ( $false
        = ( sK4 @ ( sub @ X1 @ ( push @ sK1 @ sK2 ) ) ) )
      | ( $true
        = ( sK3 @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f544]) ).

thf(f544,plain,
    ! [X1: term] :
      ( ( sK4 @ ( sub @ X1 @ ( push @ sK1 @ sK2 ) ) )
      = ( sK3 @ X1 ) ),
    inference(binary_proxy_clausification,[],[f543]) ).

thf(f543,plain,
    ! [X1: term] :
      ( $true
      = ( ( sK4 @ ( sub @ X1 @ ( push @ sK1 @ sK2 ) ) )
        = ( sK3 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f542]) ).

thf(f542,plain,
    ! [X1: term] :
      ( ( ^ [Y0: term] :
            ( ( sK4 @ ( sub @ Y0 @ ( push @ sK1 @ sK2 ) ) )
            = ( sK3 @ Y0 ) )
        @ X1 )
      = $true ),
    inference(pi_clausification,[],[f541]) ).

thf(f541,plain,
    ( $true
    = ( !! @ term
      @ ^ [Y0: term] :
          ( ( sK4 @ ( sub @ Y0 @ ( push @ sK1 @ sK2 ) ) )
          = ( sK3 @ Y0 ) ) ) ),
    inference(binary_proxy_clausification,[],[f538]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : ALG248^3 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.06/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.12/0.34  % Computer : n012.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Sat May 18 22:49:38 EDT 2024
% 0.12/0.34  % CPUTime    : 
% 0.12/0.34  This is a TH0_THM_EQU_NAR problem
% 0.12/0.34  Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37  % (440)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)
% 0.12/0.37  % (437)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)
% 0.12/0.37  % (441)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.12/0.37  % (439)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)
% 0.12/0.37  % (442)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.12/0.37  % (438)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.12/0.37  % (436)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)
% 0.12/0.37  % (435)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.12/0.37  % (438)Instruction limit reached!
% 0.12/0.37  % (438)------------------------------
% 0.12/0.37  % (438)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.37  % (438)Termination reason: Unknown
% 0.12/0.37  % (438)Termination phase: shuffling
% 0.12/0.37  % (439)Instruction limit reached!
% 0.12/0.37  % (439)------------------------------
% 0.12/0.37  % (439)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.37  % (439)Termination reason: Unknown
% 0.12/0.37  % (439)Termination phase: shuffling
% 0.12/0.37  
% 0.12/0.37  % (439)Memory used [KB]: 1279
% 0.12/0.37  % (439)Time elapsed: 0.003 s
% 0.12/0.37  % (439)Instructions burned: 2 (million)
% 0.12/0.37  % (439)------------------------------
% 0.12/0.37  % (439)------------------------------
% 0.12/0.37  
% 0.12/0.37  % (438)Memory used [KB]: 1151
% 0.12/0.37  % (438)Time elapsed: 0.002 s
% 0.12/0.37  % (438)Instructions burned: 2 (million)
% 0.12/0.37  % (438)------------------------------
% 0.12/0.37  % (438)------------------------------
% 0.12/0.37  % (442)Instruction limit reached!
% 0.12/0.37  % (442)------------------------------
% 0.12/0.37  % (442)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.37  % (442)Termination reason: Unknown
% 0.12/0.37  % (442)Termination phase: shuffling
% 0.12/0.37  
% 0.12/0.37  % (442)Memory used [KB]: 1279
% 0.12/0.37  % (442)Time elapsed: 0.004 s
% 0.12/0.37  % (442)Instructions burned: 5 (million)
% 0.12/0.37  % (442)------------------------------
% 0.12/0.37  % (442)------------------------------
% 0.12/0.37  % (436)Instruction limit reached!
% 0.12/0.37  % (436)------------------------------
% 0.12/0.37  % (436)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.37  % (436)Termination reason: Unknown
% 0.12/0.37  % (436)Termination phase: shuffling
% 0.12/0.37  
% 0.12/0.37  % (436)Memory used [KB]: 1279
% 0.12/0.37  % (436)Time elapsed: 0.004 s
% 0.12/0.37  % (436)Instructions burned: 5 (million)
% 0.12/0.37  % (436)------------------------------
% 0.12/0.37  % (436)------------------------------
% 0.12/0.38  % (441)Instruction limit reached!
% 0.12/0.38  % (441)------------------------------
% 0.12/0.38  % (441)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.38  % (441)Termination reason: Unknown
% 0.12/0.38  % (441)Termination phase: Property scanning
% 0.12/0.38  
% 0.12/0.38  % (441)Memory used [KB]: 1663
% 0.12/0.38  % (441)Time elapsed: 0.011 s
% 0.12/0.38  % (441)Instructions burned: 18 (million)
% 0.12/0.38  % (441)------------------------------
% 0.12/0.38  % (441)------------------------------
% 0.12/0.38  % (437)Instruction limit reached!
% 0.12/0.38  % (437)------------------------------
% 0.12/0.38  % (437)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.38  % (437)Termination reason: Unknown
% 0.12/0.38  % (437)Termination phase: shuffling
% 0.12/0.38  
% 0.12/0.38  % (437)Memory used [KB]: 1791
% 0.12/0.38  % (437)Time elapsed: 0.016 s
% 0.12/0.38  % (437)Instructions burned: 27 (million)
% 0.12/0.38  % (437)------------------------------
% 0.12/0.38  % (437)------------------------------
% 0.12/0.39  % (440)Refutation not found, incomplete strategy
% 0.12/0.39  % (440)------------------------------
% 0.12/0.39  % (440)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.39  % (440)Termination reason: Refutation not found, incomplete strategy
% 0.12/0.39  
% 0.12/0.39  
% 0.12/0.39  % (440)Memory used [KB]: 6140
% 0.12/0.39  % (440)Time elapsed: 0.017 s
% 0.12/0.39  % (440)Instructions burned: 26 (million)
% 0.12/0.39  % (440)------------------------------
% 0.12/0.39  % (440)------------------------------
% 0.12/0.39  % (444)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.12/0.39  % (445)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.12/0.39  % (443)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.12/0.39  % (445)Instruction limit reached!
% 0.12/0.39  % (445)------------------------------
% 0.12/0.39  % (445)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.39  % (445)Termination reason: Unknown
% 0.12/0.39  % (445)Termination phase: shuffling
% 0.12/0.39  
% 0.12/0.39  % (445)Memory used [KB]: 1279
% 0.12/0.39  % (445)Time elapsed: 0.003 s
% 0.12/0.39  % (445)Instructions burned: 4 (million)
% 0.12/0.39  % (445)------------------------------
% 0.12/0.39  % (445)------------------------------
% 0.12/0.39  % (446)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.12/0.39  % (444)Instruction limit reached!
% 0.12/0.39  % (444)------------------------------
% 0.12/0.39  % (444)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.39  % (444)Termination reason: Unknown
% 0.12/0.39  % (444)Termination phase: Property scanning
% 0.12/0.39  
% 0.12/0.39  % (444)Memory used [KB]: 1663
% 0.12/0.39  % (444)Time elapsed: 0.010 s
% 0.12/0.39  % (444)Instructions burned: 15 (million)
% 0.12/0.39  % (444)------------------------------
% 0.12/0.39  % (444)------------------------------
% 0.12/0.40  % (447)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.18/0.40  % (448)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.18/0.40  % (447)Instruction limit reached!
% 0.18/0.40  % (447)------------------------------
% 0.18/0.40  % (447)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.40  % (447)Termination reason: Unknown
% 0.18/0.40  % (447)Termination phase: shuffling
% 0.18/0.40  
% 0.18/0.40  % (447)Memory used [KB]: 1407
% 0.18/0.40  % (447)Time elapsed: 0.006 s
% 0.18/0.40  % (447)Instructions burned: 8 (million)
% 0.18/0.40  % (447)------------------------------
% 0.18/0.40  % (447)------------------------------
% 0.18/0.40  % (449)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.18/0.40  % (450)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.18/0.40  % (450)Instruction limit reached!
% 0.18/0.40  % (450)------------------------------
% 0.18/0.40  % (450)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.40  % (450)Termination reason: Unknown
% 0.18/0.40  % (449)Instruction limit reached!
% 0.18/0.40  % (449)------------------------------
% 0.18/0.40  % (449)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.40  % (450)Termination phase: shuffling
% 0.18/0.40  
% 0.18/0.40  % (450)Memory used [KB]: 1279
% 0.18/0.40  % (450)Time elapsed: 0.003 s
% 0.18/0.40  % (450)Instructions burned: 3 (million)
% 0.18/0.40  % (450)------------------------------
% 0.18/0.40  % (450)------------------------------
% 0.18/0.40  % (449)Termination reason: Unknown
% 0.18/0.40  % (449)Termination phase: shuffling
% 0.18/0.40  
% 0.18/0.40  % (449)Memory used [KB]: 1279
% 0.18/0.40  % (449)Time elapsed: 0.004 s
% 0.18/0.40  % (449)Instructions burned: 3 (million)
% 0.18/0.40  % (449)------------------------------
% 0.18/0.40  % (449)------------------------------
% 0.18/0.40  % (443)Instruction limit reached!
% 0.18/0.40  % (443)------------------------------
% 0.18/0.40  % (443)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.40  % (443)Termination reason: Unknown
% 0.18/0.40  % (443)Termination phase: Property scanning
% 0.18/0.40  
% 0.18/0.40  % (443)Memory used [KB]: 1791
% 0.18/0.40  % (443)Time elapsed: 0.020 s
% 0.18/0.40  % (443)Instructions burned: 37 (million)
% 0.18/0.41  % (443)------------------------------
% 0.18/0.41  % (443)------------------------------
% 0.18/0.41  % (448)Instruction limit reached!
% 0.18/0.41  % (448)------------------------------
% 0.18/0.41  % (448)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.41  % (448)Termination reason: Unknown
% 0.18/0.41  % (448)Termination phase: shuffling
% 0.18/0.41  
% 0.18/0.41  % (448)Memory used [KB]: 1535
% 0.18/0.41  % (448)Time elapsed: 0.010 s
% 0.18/0.41  % (448)Instructions burned: 17 (million)
% 0.18/0.41  % (448)------------------------------
% 0.18/0.41  % (448)------------------------------
% 0.18/0.41  % (451)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.18/0.41  % (451)Instruction limit reached!
% 0.18/0.41  % (451)------------------------------
% 0.18/0.41  % (451)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.41  % (451)Termination reason: Unknown
% 0.18/0.41  % (451)Termination phase: shuffling
% 0.18/0.41  
% 0.18/0.41  % (451)Memory used [KB]: 1407
% 0.18/0.41  % (451)Time elapsed: 0.005 s
% 0.18/0.41  % (451)Instructions burned: 7 (million)
% 0.18/0.41  % (451)------------------------------
% 0.18/0.41  % (451)------------------------------
% 0.18/0.41  % (435)First to succeed.
% 0.18/0.42  % (452)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.18/0.42  % (453)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.18/0.42  % (454)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.18/0.42  % (452)Instruction limit reached!
% 0.18/0.42  % (452)------------------------------
% 0.18/0.42  % (452)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.42  % (452)Termination reason: Unknown
% 0.18/0.42  % (452)Termination phase: shuffling
% 0.18/0.42  
% 0.18/0.42  % (452)Memory used [KB]: 1279
% 0.18/0.42  % (452)Time elapsed: 0.003 s
% 0.18/0.42  % (452)Instructions burned: 3 (million)
% 0.18/0.42  % (452)------------------------------
% 0.18/0.42  % (452)------------------------------
% 0.18/0.42  % (453)Instruction limit reached!
% 0.18/0.42  % (453)------------------------------
% 0.18/0.42  % (453)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.42  % (453)Termination reason: Unknown
% 0.18/0.42  % (453)Termination phase: shuffling
% 0.18/0.42  
% 0.18/0.42  % (453)Memory used [KB]: 1279
% 0.18/0.42  % (453)Time elapsed: 0.004 s
% 0.18/0.42  % (453)Instructions burned: 5 (million)
% 0.18/0.42  % (453)------------------------------
% 0.18/0.42  % (453)------------------------------
% 0.18/0.42  % (435)Refutation found. Thanks to Tanya!
% 0.18/0.42  % SZS status Theorem for theBenchmark
% 0.18/0.42  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.42  % (435)------------------------------
% 0.18/0.42  % (435)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.42  % (435)Termination reason: Refutation
% 0.18/0.42  
% 0.18/0.42  % (435)Memory used [KB]: 6652
% 0.18/0.42  % (435)Time elapsed: 0.047 s
% 0.18/0.42  % (435)Instructions burned: 89 (million)
% 0.18/0.42  % (435)------------------------------
% 0.18/0.42  % (435)------------------------------
% 0.18/0.42  % (434)Success in time 0.057 s
% 0.18/0.42  % Vampire---4.8 exiting
%------------------------------------------------------------------------------