TSTP Solution File: SEV011^5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEV011^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n008.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 04:11:41 EDT 2024

% Result   : Theorem 0.18s 0.40s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :   18
% Syntax   : Number of formulae    :  116 (  37 unt;  11 typ;   0 def)
%            Number of atoms       :  721 ( 161 equ;   0 cnn)
%            Maximal formula atoms :    4 (   6 avg)
%            Number of connectives : 1474 (  91   ~;  84   |;  95   &; 899   @)
%                                         (  12 <=>; 119  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   84 (  84   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   20 (  15 usr;  15 con; 0-2 aty)
%                                         ( 165  !!;   9  ??;   0 @@+;   0 @@-)
%            Number of variables   :  262 ( 188   ^  70   !;   3   ?; 262   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

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

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

thf(func_def_19,type,
    ph1: 
      !>[X0: $tType] : X0 ).

thf(func_def_20,type,
    sK2: a > a > $o ).

thf(func_def_21,type,
    sK3: a ).

thf(func_def_22,type,
    sK4: a > $o ).

thf(func_def_23,type,
    sK5: a ).

thf(func_def_24,type,
    sK6: a > $o ).

thf(func_def_25,type,
    sK7: a ).

thf(func_def_26,type,
    sK8: a ).

thf(func_def_27,type,
    sK9: a ).

thf(f378,plain,
    $false,
    inference(avatar_sat_refutation,[],[f64,f215,f248,f255,f259,f357,f360,f377]) ).

thf(f377,plain,
    ( ~ spl0_1
    | ~ spl0_11
    | ~ spl0_14 ),
    inference(avatar_contradiction_clause,[],[f376]) ).

thf(f376,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_11
    | ~ spl0_14 ),
    inference(trivial_inequality_removal,[],[f375]) ).

thf(f375,plain,
    ( ( $true = $false )
    | ~ spl0_1
    | ~ spl0_11
    | ~ spl0_14 ),
    inference(forward_demodulation,[],[f370,f254]) ).

thf(f254,plain,
    ( ( $false
      = ( sK2 @ sK3 @ sK9 ) )
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f253]) ).

thf(f253,plain,
    ( spl0_14
  <=> ( $false
      = ( sK2 @ sK3 @ sK9 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

thf(f370,plain,
    ( ( $true
      = ( sK2 @ sK3 @ sK9 ) )
    | ~ spl0_1
    | ~ spl0_11 ),
    inference(boolean_simplification,[],[f363]) ).

thf(f363,plain,
    ( ( $true
      = ( $true
       => ( sK2 @ sK3 @ sK9 ) ) )
    | ~ spl0_1
    | ~ spl0_11 ),
    inference(superposition,[],[f235,f244]) ).

thf(f244,plain,
    ( ( $true
      = ( sK2 @ sK8 @ sK9 ) )
    | ~ spl0_11 ),
    inference(avatar_component_clause,[],[f243]) ).

thf(f243,plain,
    ( spl0_11
  <=> ( $true
      = ( sK2 @ sK8 @ sK9 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

thf(f235,plain,
    ( ! [X0: a] :
        ( $true
        = ( ( sK2 @ sK8 @ X0 )
         => ( sK2 @ sK3 @ X0 ) ) )
    | ~ spl0_1 ),
    inference(boolean_simplification,[],[f230]) ).

thf(f230,plain,
    ( ! [X0: a] :
        ( $true
        = ( ( $true
            & ( sK2 @ sK8 @ X0 ) )
         => ( sK2 @ sK3 @ X0 ) ) )
    | ~ spl0_1 ),
    inference(superposition,[],[f42,f224]) ).

thf(f224,plain,
    ( ( ( sK2 @ sK3 @ sK8 )
      = $true )
    | ~ spl0_1 ),
    inference(binary_proxy_clausification,[],[f222]) ).

thf(f222,plain,
    ( ( $false
      = ( ( sK2 @ sK3 @ sK8 )
       => ( !! @ a
          @ ^ [Y0: a] :
              ( ( sK2 @ sK8 @ Y0 )
              = ( sK2 @ sK3 @ Y0 ) ) ) ) )
    | ~ spl0_1 ),
    inference(beta_eta_normalization,[],[f218]) ).

thf(f218,plain,
    ( ( $false
      = ( ^ [Y0: a] :
            ( ( sK2 @ sK3 @ Y0 )
           => ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK2 @ Y0 @ Y1 )
                  = ( sK2 @ sK3 @ Y1 ) ) ) )
        @ sK8 ) )
    | ~ spl0_1 ),
    inference(sigma_clausification,[],[f60]) ).

thf(f60,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( ( sK2 @ sK3 @ Y0 )
           => ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK2 @ Y0 @ Y1 )
                  = ( sK2 @ sK3 @ Y1 ) ) ) ) )
      = $false )
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f59]) ).

thf(f59,plain,
    ( spl0_1
  <=> ( ( !! @ a
        @ ^ [Y0: a] :
            ( ( sK2 @ sK3 @ Y0 )
           => ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK2 @ Y0 @ Y1 )
                  = ( sK2 @ sK3 @ Y1 ) ) ) ) )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

thf(f42,plain,
    ! [X2: a,X3: a,X1: a] :
      ( $true
      = ( ( ( sK2 @ X3 @ X1 )
          & ( sK2 @ X1 @ X2 ) )
       => ( sK2 @ X3 @ X2 ) ) ),
    inference(beta_eta_normalization,[],[f41]) ).

thf(f41,plain,
    ! [X2: a,X3: a,X1: a] :
      ( $true
      = ( ^ [Y0: a] :
            ( ( ( sK2 @ Y0 @ X1 )
              & ( sK2 @ X1 @ X2 ) )
           => ( sK2 @ Y0 @ X2 ) )
        @ X3 ) ),
    inference(pi_clausification,[],[f38]) ).

thf(f38,plain,
    ! [X2: a,X1: a] :
      ( ( !! @ a
        @ ^ [Y0: a] :
            ( ( ( sK2 @ Y0 @ X1 )
              & ( sK2 @ X1 @ X2 ) )
           => ( sK2 @ Y0 @ X2 ) ) )
      = $true ),
    inference(beta_eta_normalization,[],[f37]) ).

thf(f37,plain,
    ! [X2: a,X1: a] :
      ( $true
      = ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( sK2 @ Y1 @ X1 )
                  & ( sK2 @ X1 @ Y0 ) )
               => ( sK2 @ Y1 @ Y0 ) ) )
        @ X2 ) ),
    inference(pi_clausification,[],[f34]) ).

thf(f34,plain,
    ! [X1: a] :
      ( $true
      = ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( sK2 @ Y1 @ X1 )
                  & ( sK2 @ X1 @ Y0 ) )
               => ( sK2 @ Y1 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f33]) ).

thf(f33,plain,
    ! [X1: a] :
      ( $true
      = ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( !! @ a
                @ ^ [Y2: a] :
                    ( ( ( sK2 @ Y2 @ Y0 )
                      & ( sK2 @ Y0 @ Y1 ) )
                   => ( sK2 @ Y2 @ Y1 ) ) ) )
        @ X1 ) ),
    inference(pi_clausification,[],[f32]) ).

thf(f32,plain,
    ( $true
    = ( !! @ a
      @ ^ [Y0: a] :
          ( !! @ a
          @ ^ [Y1: a] :
              ( !! @ a
              @ ^ [Y2: a] :
                  ( ( ( sK2 @ Y2 @ Y0 )
                    & ( sK2 @ Y0 @ Y1 ) )
                 => ( sK2 @ Y2 @ Y1 ) ) ) ) ) ),
    inference(boolean_simplification,[],[f31]) ).

thf(f31,plain,
    ( ( $true
      & ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( !! @ a
                @ ^ [Y2: a] :
                    ( ( ( sK2 @ Y2 @ Y0 )
                      & ( sK2 @ Y0 @ Y1 ) )
                   => ( sK2 @ Y2 @ Y1 ) ) ) ) ) )
    = $true ),
    inference(backward_demodulation,[],[f17,f30]) ).

thf(f30,plain,
    ( $true
    = ( !! @ a
      @ ^ [Y0: a] :
          ( !! @ a
          @ ^ [Y1: a] :
              ( ( sK2 @ Y0 @ Y1 )
             => ( sK2 @ Y1 @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f17]) ).

thf(f17,plain,
    ( $true
    = ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK2 @ Y0 @ Y1 )
               => ( sK2 @ Y1 @ Y0 ) ) ) )
      & ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( !! @ a
                @ ^ [Y2: a] :
                    ( ( ( sK2 @ Y2 @ Y0 )
                      & ( sK2 @ Y0 @ Y1 ) )
                   => ( sK2 @ Y2 @ Y1 ) ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f13]) ).

thf(f13,plain,
    ( $true
    = ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK2 @ Y0 @ Y1 )
               => ( sK2 @ Y1 @ Y0 ) ) ) )
      & ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( !! @ a
                @ ^ [Y2: a] :
                    ( ( ( sK2 @ Y2 @ Y0 )
                      & ( sK2 @ Y0 @ Y1 ) )
                   => ( sK2 @ Y2 @ Y1 ) ) ) ) )
      & ( !! @ a
        @ ^ [Y0: a] : ( sK2 @ Y0 @ Y0 ) ) ) ),
    inference(binary_proxy_clausification,[],[f11]) ).

thf(f11,plain,
    ( $false
    = ( ( ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK2 @ Y0 @ Y1 )
                 => ( sK2 @ Y1 @ Y0 ) ) ) )
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( ( sK2 @ Y2 @ Y0 )
                        & ( sK2 @ Y0 @ Y1 ) )
                     => ( sK2 @ Y2 @ Y1 ) ) ) ) )
        & ( !! @ a
          @ ^ [Y0: a] : ( sK2 @ Y0 @ Y0 ) ) )
     => ( !! @ a
        @ ^ [Y0: a] :
            ( ?? @ ( a > $o )
            @ ^ [Y1: a > $o] :
                ( ( Y1 @ Y0 )
                & ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( Y1 @ Y2 )
                     => ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( sK2 @ Y2 @ Y3 )
                            = ( Y1 @ Y3 ) ) ) ) )
                & ( !! @ ( a > $o )
                  @ ^ [Y2: a > $o] :
                      ( ( ( !! @ a
                          @ ^ [Y3: a] :
                              ( ( Y2 @ Y3 )
                             => ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK2 @ Y3 @ Y4 )
                                    = ( Y2 @ Y4 ) ) ) ) )
                        & ( Y2 @ Y0 ) )
                     => ( Y1 = Y2 ) ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f10]) ).

thf(f10,plain,
    ( $false
    = ( ^ [Y0: a > a > $o] :
          ( ( ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( Y0 @ Y1 @ Y2 )
                     => ( Y0 @ Y2 @ Y1 ) ) ) )
            & ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( !! @ a
                      @ ^ [Y3: a] :
                          ( ( ( Y0 @ Y3 @ Y1 )
                            & ( Y0 @ Y1 @ Y2 ) )
                         => ( Y0 @ Y3 @ Y2 ) ) ) ) )
            & ( !! @ a
              @ ^ [Y1: a] : ( Y0 @ Y1 @ Y1 ) ) )
         => ( !! @ a
            @ ^ [Y1: a] :
                ( ?? @ ( a > $o )
                @ ^ [Y2: a > $o] :
                    ( ( Y2 @ Y1 )
                    & ( !! @ a
                      @ ^ [Y3: a] :
                          ( ( Y2 @ Y3 )
                         => ( !! @ a
                            @ ^ [Y4: a] :
                                ( ( Y0 @ Y3 @ Y4 )
                                = ( Y2 @ Y4 ) ) ) ) )
                    & ( !! @ ( a > $o )
                      @ ^ [Y3: a > $o] :
                          ( ( ( !! @ a
                              @ ^ [Y4: a] :
                                  ( ( Y3 @ Y4 )
                                 => ( !! @ a
                                    @ ^ [Y5: a] :
                                        ( ( Y0 @ Y4 @ Y5 )
                                        = ( Y3 @ Y5 ) ) ) ) )
                            & ( Y3 @ Y1 ) )
                         => ( Y2 = Y3 ) ) ) ) ) ) )
      @ sK2 ) ),
    inference(sigma_clausification,[],[f7]) ).

thf(f7,plain,
    ( $false
    = ( !! @ ( a > a > $o )
      @ ^ [Y0: a > a > $o] :
          ( ( ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( Y0 @ Y1 @ Y2 )
                     => ( Y0 @ Y2 @ Y1 ) ) ) )
            & ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( !! @ a
                      @ ^ [Y3: a] :
                          ( ( ( Y0 @ Y3 @ Y1 )
                            & ( Y0 @ Y1 @ Y2 ) )
                         => ( Y0 @ Y3 @ Y2 ) ) ) ) )
            & ( !! @ a
              @ ^ [Y1: a] : ( Y0 @ Y1 @ Y1 ) ) )
         => ( !! @ a
            @ ^ [Y1: a] :
                ( ?? @ ( a > $o )
                @ ^ [Y2: a > $o] :
                    ( ( Y2 @ Y1 )
                    & ( !! @ a
                      @ ^ [Y3: a] :
                          ( ( Y2 @ Y3 )
                         => ( !! @ a
                            @ ^ [Y4: a] :
                                ( ( Y0 @ Y3 @ Y4 )
                                = ( Y2 @ Y4 ) ) ) ) )
                    & ( !! @ ( a > $o )
                      @ ^ [Y3: a > $o] :
                          ( ( ( !! @ a
                              @ ^ [Y4: a] :
                                  ( ( Y3 @ Y4 )
                                 => ( !! @ a
                                    @ ^ [Y5: a] :
                                        ( ( Y0 @ Y4 @ Y5 )
                                        = ( Y3 @ Y5 ) ) ) ) )
                            & ( Y3 @ Y1 ) )
                         => ( Y2 = Y3 ) ) ) ) ) ) ) ) ),
    inference(not_proxy_clausification,[],[f6]) ).

thf(f6,plain,
    ( $true
    = ( ~ ( !! @ ( a > a > $o )
          @ ^ [Y0: a > a > $o] :
              ( ( ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( Y0 @ Y1 @ Y2 )
                         => ( Y0 @ Y2 @ Y1 ) ) ) )
                & ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( !! @ a
                          @ ^ [Y3: a] :
                              ( ( ( Y0 @ Y3 @ Y1 )
                                & ( Y0 @ Y1 @ Y2 ) )
                             => ( Y0 @ Y3 @ Y2 ) ) ) ) )
                & ( !! @ a
                  @ ^ [Y1: a] : ( Y0 @ Y1 @ Y1 ) ) )
             => ( !! @ a
                @ ^ [Y1: a] :
                    ( ?? @ ( a > $o )
                    @ ^ [Y2: a > $o] :
                        ( ( Y2 @ Y1 )
                        & ( !! @ a
                          @ ^ [Y3: a] :
                              ( ( Y2 @ Y3 )
                             => ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( Y0 @ Y3 @ Y4 )
                                    = ( Y2 @ Y4 ) ) ) ) )
                        & ( !! @ ( a > $o )
                          @ ^ [Y3: a > $o] :
                              ( ( ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( ( Y3 @ Y4 )
                                     => ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( Y0 @ Y4 @ Y5 )
                                            = ( Y3 @ Y5 ) ) ) ) )
                                & ( Y3 @ Y1 ) )
                             => ( Y2 = Y3 ) ) ) ) ) ) ) ) ) ),
    inference(cnf_transformation,[],[f5]) ).

thf(f5,plain,
    ( $true
    = ( ~ ( !! @ ( a > a > $o )
          @ ^ [Y0: a > a > $o] :
              ( ( ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( Y0 @ Y1 @ Y2 )
                         => ( Y0 @ Y2 @ Y1 ) ) ) )
                & ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( !! @ a
                          @ ^ [Y3: a] :
                              ( ( ( Y0 @ Y3 @ Y1 )
                                & ( Y0 @ Y1 @ Y2 ) )
                             => ( Y0 @ Y3 @ Y2 ) ) ) ) )
                & ( !! @ a
                  @ ^ [Y1: a] : ( Y0 @ Y1 @ Y1 ) ) )
             => ( !! @ a
                @ ^ [Y1: a] :
                    ( ?? @ ( a > $o )
                    @ ^ [Y2: a > $o] :
                        ( ( Y2 @ Y1 )
                        & ( !! @ a
                          @ ^ [Y3: a] :
                              ( ( Y2 @ Y3 )
                             => ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( Y0 @ Y3 @ Y4 )
                                    = ( Y2 @ Y4 ) ) ) ) )
                        & ( !! @ ( a > $o )
                          @ ^ [Y3: a > $o] :
                              ( ( ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( ( Y3 @ Y4 )
                                     => ( !! @ a
                                        @ ^ [Y5: a] :
                                            ( ( Y0 @ Y4 @ Y5 )
                                            = ( Y3 @ Y5 ) ) ) ) )
                                & ( Y3 @ Y1 ) )
                             => ( Y2 = Y3 ) ) ) ) ) ) ) ) ) ),
    inference(fool_elimination,[],[f4]) ).

thf(f4,plain,
    ~ ! [X0: a > a > $o] :
        ( ( ! [X1: a] : ( X0 @ X1 @ X1 )
          & ! [X2: a,X3: a,X4: a] :
              ( ( ( X0 @ X4 @ X3 )
                & ( X0 @ X2 @ X4 ) )
             => ( X0 @ X2 @ X3 ) )
          & ! [X5: a,X6: a] :
              ( ( X0 @ X6 @ X5 )
             => ( X0 @ X5 @ X6 ) ) )
       => ! [X7: a] :
          ? [X8: a > $o] :
            ( ! [X9: a > $o] :
                ( ( ( X9 @ X7 )
                  & ! [X10: a] :
                      ( ( X9 @ X10 )
                     => ! [X11: a] :
                          ( ( X0 @ X10 @ X11 )
                        <=> ( X9 @ X11 ) ) ) )
               => ( X8 = X9 ) )
            & ! [X12: a] :
                ( ( X8 @ X12 )
               => ! [X13: a] :
                    ( ( X0 @ X12 @ X13 )
                  <=> ( X8 @ X13 ) ) )
            & ( X8 @ X7 ) ) ),
    inference(rectify,[],[f2]) ).

thf(f2,negated_conjecture,
    ~ ! [X0: a > a > $o] :
        ( ( ! [X1: a] : ( X0 @ X1 @ X1 )
          & ! [X1: a,X3: a,X2: a] :
              ( ( ( X0 @ X2 @ X3 )
                & ( X0 @ X1 @ X2 ) )
             => ( X0 @ X1 @ X3 ) )
          & ! [X2: a,X1: a] :
              ( ( X0 @ X1 @ X2 )
             => ( X0 @ X2 @ X1 ) ) )
       => ! [X1: a] :
          ? [X4: a > $o] :
            ( ! [X6: a > $o] :
                ( ( ( X6 @ X1 )
                  & ! [X5: a] :
                      ( ( X6 @ X5 )
                     => ! [X2: a] :
                          ( ( X0 @ X5 @ X2 )
                        <=> ( X6 @ X2 ) ) ) )
               => ( X4 = X6 ) )
            & ! [X5: a] :
                ( ( X4 @ X5 )
               => ! [X2: a] :
                    ( ( X0 @ X5 @ X2 )
                  <=> ( X4 @ X2 ) ) )
            & ( X4 @ X1 ) ) ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ! [X0: a > a > $o] :
      ( ( ! [X1: a] : ( X0 @ X1 @ X1 )
        & ! [X1: a,X3: a,X2: a] :
            ( ( ( X0 @ X2 @ X3 )
              & ( X0 @ X1 @ X2 ) )
           => ( X0 @ X1 @ X3 ) )
        & ! [X2: a,X1: a] :
            ( ( X0 @ X1 @ X2 )
           => ( X0 @ X2 @ X1 ) ) )
     => ! [X1: a] :
        ? [X4: a > $o] :
          ( ! [X6: a > $o] :
              ( ( ( X6 @ X1 )
                & ! [X5: a] :
                    ( ( X6 @ X5 )
                   => ! [X2: a] :
                        ( ( X0 @ X5 @ X2 )
                      <=> ( X6 @ X2 ) ) ) )
             => ( X4 = X6 ) )
          & ! [X5: a] :
              ( ( X4 @ X5 )
             => ! [X2: a] :
                  ( ( X0 @ X5 @ X2 )
                <=> ( X4 @ X2 ) ) )
          & ( X4 @ X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM260_B_pme) ).

thf(f360,plain,
    ( ~ spl0_12
    | ~ spl0_14 ),
    inference(avatar_contradiction_clause,[],[f359]) ).

thf(f359,plain,
    ( $false
    | ~ spl0_12
    | ~ spl0_14 ),
    inference(trivial_inequality_removal,[],[f358]) ).

thf(f358,plain,
    ( ( $true = $false )
    | ~ spl0_12
    | ~ spl0_14 ),
    inference(backward_demodulation,[],[f247,f254]) ).

thf(f247,plain,
    ( ( $true
      = ( sK2 @ sK3 @ sK9 ) )
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f246]) ).

thf(f246,plain,
    ( spl0_12
  <=> ( $true
      = ( sK2 @ sK3 @ sK9 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

thf(f357,plain,
    ( ~ spl0_1
    | ~ spl0_12
    | ~ spl0_13 ),
    inference(avatar_contradiction_clause,[],[f356]) ).

thf(f356,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_12
    | ~ spl0_13 ),
    inference(trivial_inequality_removal,[],[f355]) ).

thf(f355,plain,
    ( ( $true = $false )
    | ~ spl0_1
    | ~ spl0_12
    | ~ spl0_13 ),
    inference(forward_demodulation,[],[f347,f308]) ).

thf(f308,plain,
    ( ( $false
      = ( sK2 @ sK9 @ sK8 ) )
    | ~ spl0_13 ),
    inference(not_proxy_clausification,[],[f280]) ).

thf(f280,plain,
    ( ( $true
      = ( ~ ( sK2 @ sK9 @ sK8 ) ) )
    | ~ spl0_13 ),
    inference(boolean_simplification,[],[f276]) ).

thf(f276,plain,
    ( ( $true
      = ( ( sK2 @ sK9 @ sK8 )
       => $false ) )
    | ~ spl0_13 ),
    inference(superposition,[],[f40,f251]) ).

thf(f251,plain,
    ( ( $false
      = ( sK2 @ sK8 @ sK9 ) )
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f250]) ).

thf(f250,plain,
    ( spl0_13
  <=> ( $false
      = ( sK2 @ sK8 @ sK9 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

thf(f40,plain,
    ! [X2: a,X1: a] :
      ( $true
      = ( ( sK2 @ X1 @ X2 )
       => ( sK2 @ X2 @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f39]) ).

thf(f39,plain,
    ! [X2: a,X1: a] :
      ( $true
      = ( ^ [Y0: a] :
            ( ( sK2 @ X1 @ Y0 )
           => ( sK2 @ Y0 @ X1 ) )
        @ X2 ) ),
    inference(pi_clausification,[],[f36]) ).

thf(f36,plain,
    ! [X1: a] :
      ( $true
      = ( !! @ a
        @ ^ [Y0: a] :
            ( ( sK2 @ X1 @ Y0 )
           => ( sK2 @ Y0 @ X1 ) ) ) ),
    inference(beta_eta_normalization,[],[f35]) ).

thf(f35,plain,
    ! [X1: a] :
      ( $true
      = ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( sK2 @ Y0 @ Y1 )
               => ( sK2 @ Y1 @ Y0 ) ) )
        @ X1 ) ),
    inference(pi_clausification,[],[f30]) ).

thf(f347,plain,
    ( ( $true
      = ( sK2 @ sK9 @ sK8 ) )
    | ~ spl0_1
    | ~ spl0_12 ),
    inference(boolean_simplification,[],[f343]) ).

thf(f343,plain,
    ( ( $true
      = ( $true
       => ( sK2 @ sK9 @ sK8 ) ) )
    | ~ spl0_1
    | ~ spl0_12 ),
    inference(superposition,[],[f237,f269]) ).

thf(f269,plain,
    ( ( $true
      = ( sK2 @ sK9 @ sK3 ) )
    | ~ spl0_12 ),
    inference(boolean_simplification,[],[f265]) ).

thf(f265,plain,
    ( ( $true
      = ( $true
       => ( sK2 @ sK9 @ sK3 ) ) )
    | ~ spl0_12 ),
    inference(superposition,[],[f40,f247]) ).

thf(f237,plain,
    ( ! [X0: a] :
        ( $true
        = ( ( sK2 @ X0 @ sK3 )
         => ( sK2 @ X0 @ sK8 ) ) )
    | ~ spl0_1 ),
    inference(boolean_simplification,[],[f231]) ).

thf(f231,plain,
    ( ! [X0: a] :
        ( $true
        = ( ( ( sK2 @ X0 @ sK3 )
            & $true )
         => ( sK2 @ X0 @ sK8 ) ) )
    | ~ spl0_1 ),
    inference(superposition,[],[f42,f224]) ).

thf(f259,plain,
    ( ~ spl0_11
    | ~ spl0_13 ),
    inference(avatar_contradiction_clause,[],[f258]) ).

thf(f258,plain,
    ( $false
    | ~ spl0_11
    | ~ spl0_13 ),
    inference(trivial_inequality_removal,[],[f257]) ).

thf(f257,plain,
    ( ( $true = $false )
    | ~ spl0_11
    | ~ spl0_13 ),
    inference(backward_demodulation,[],[f244,f251]) ).

thf(f255,plain,
    ( spl0_13
    | spl0_14
    | ~ spl0_1 ),
    inference(avatar_split_clause,[],[f241,f59,f253,f250]) ).

thf(f241,plain,
    ( ( $false
      = ( sK2 @ sK3 @ sK9 ) )
    | ( $false
      = ( sK2 @ sK8 @ sK9 ) )
    | ~ spl0_1 ),
    inference(binary_proxy_clausification,[],[f229]) ).

thf(f229,plain,
    ( ( ( sK2 @ sK8 @ sK9 )
     != ( sK2 @ sK3 @ sK9 ) )
    | ~ spl0_1 ),
    inference(binary_proxy_clausification,[],[f228]) ).

thf(f228,plain,
    ( ( $false
      = ( ( sK2 @ sK8 @ sK9 )
        = ( sK2 @ sK3 @ sK9 ) ) )
    | ~ spl0_1 ),
    inference(beta_eta_normalization,[],[f227]) ).

thf(f227,plain,
    ( ( ( ^ [Y0: a] :
            ( ( sK2 @ sK8 @ Y0 )
            = ( sK2 @ sK3 @ Y0 ) )
        @ sK9 )
      = $false )
    | ~ spl0_1 ),
    inference(sigma_clausification,[],[f226]) ).

thf(f226,plain,
    ( ( $false
      = ( !! @ a
        @ ^ [Y0: a] :
            ( ( sK2 @ sK8 @ Y0 )
            = ( sK2 @ sK3 @ Y0 ) ) ) )
    | ~ spl0_1 ),
    inference(boolean_simplification,[],[f225]) ).

thf(f225,plain,
    ( ( ( $true
       => ( !! @ a
          @ ^ [Y0: a] :
              ( ( sK2 @ sK8 @ Y0 )
              = ( sK2 @ sK3 @ Y0 ) ) ) )
      = $false )
    | ~ spl0_1 ),
    inference(backward_demodulation,[],[f222,f224]) ).

thf(f248,plain,
    ( spl0_11
    | spl0_12
    | ~ spl0_1 ),
    inference(avatar_split_clause,[],[f240,f59,f246,f243]) ).

thf(f240,plain,
    ( ( $true
      = ( sK2 @ sK3 @ sK9 ) )
    | ( $true
      = ( sK2 @ sK8 @ sK9 ) )
    | ~ spl0_1 ),
    inference(binary_proxy_clausification,[],[f229]) ).

thf(f215,plain,
    ~ spl0_2,
    inference(avatar_contradiction_clause,[],[f214]) ).

thf(f214,plain,
    ( $false
    | ~ spl0_2 ),
    inference(subsumption_resolution,[],[f78,f183]) ).

thf(f183,plain,
    ( ! [X1: a] :
        ( ( sK2 @ sK3 @ X1 )
        = ( sK4 @ X1 ) )
    | ~ spl0_2 ),
    inference(binary_proxy_clausification,[],[f182]) ).

thf(f182,plain,
    ( ! [X1: a] :
        ( $true
        = ( ( sK2 @ sK3 @ X1 )
          = ( sK4 @ X1 ) ) )
    | ~ spl0_2 ),
    inference(beta_eta_normalization,[],[f179]) ).

thf(f179,plain,
    ( ! [X1: a] :
        ( $true
        = ( ^ [Y0: a] :
              ( ( sK2 @ sK3 @ Y0 )
              = ( sK4 @ Y0 ) )
          @ X1 ) )
    | ~ spl0_2 ),
    inference(pi_clausification,[],[f124]) ).

thf(f124,plain,
    ( ( $true
      = ( !! @ a
        @ ^ [Y0: a] :
            ( ( sK2 @ sK3 @ Y0 )
            = ( sK4 @ Y0 ) ) ) )
    | ~ spl0_2 ),
    inference(boolean_simplification,[],[f122]) ).

thf(f122,plain,
    ( ( $true
      = ( $true
       => ( !! @ a
          @ ^ [Y0: a] :
              ( ( sK2 @ sK3 @ Y0 )
              = ( sK4 @ Y0 ) ) ) ) )
    | ~ spl0_2 ),
    inference(superposition,[],[f108,f82]) ).

thf(f82,plain,
    ( ( $true
      = ( sK4 @ sK3 ) )
    | ~ spl0_2 ),
    inference(boolean_simplification,[],[f81]) ).

thf(f81,plain,
    ( ( $true
      = ( $true
        & ( sK4 @ sK3 ) ) )
    | ~ spl0_2 ),
    inference(backward_demodulation,[],[f72,f80]) ).

thf(f80,plain,
    ( ( $true
      = ( !! @ a
        @ ^ [Y0: a] :
            ( ( sK4 @ Y0 )
           => ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK2 @ Y0 @ Y1 )
                  = ( sK4 @ Y1 ) ) ) ) ) )
    | ~ spl0_2 ),
    inference(binary_proxy_clausification,[],[f72]) ).

thf(f72,plain,
    ( ( $true
      = ( ( !! @ a
          @ ^ [Y0: a] :
              ( ( sK4 @ Y0 )
             => ( !! @ a
                @ ^ [Y1: a] :
                    ( ( sK2 @ Y0 @ Y1 )
                    = ( sK4 @ Y1 ) ) ) ) )
        & ( sK4 @ sK3 ) ) )
    | ~ spl0_2 ),
    inference(binary_proxy_clausification,[],[f69]) ).

thf(f69,plain,
    ( ( ( ( ( !! @ a
            @ ^ [Y0: a] :
                ( ( sK4 @ Y0 )
               => ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( sK2 @ Y0 @ Y1 )
                      = ( sK4 @ Y1 ) ) ) ) )
          & ( sK4 @ sK3 ) )
       => ( ( sK2 @ sK3 )
          = sK4 ) )
      = $false )
    | ~ spl0_2 ),
    inference(beta_eta_normalization,[],[f67]) ).

thf(f67,plain,
    ( ( ( ^ [Y0: a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( ( Y0 @ Y1 )
                   => ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( sK2 @ Y1 @ Y2 )
                          = ( Y0 @ Y2 ) ) ) ) )
              & ( Y0 @ sK3 ) )
           => ( ( sK2 @ sK3 )
              = Y0 ) )
        @ sK4 )
      = $false )
    | ~ spl0_2 ),
    inference(sigma_clausification,[],[f63]) ).

thf(f63,plain,
    ( ( $false
      = ( !! @ ( a > $o )
        @ ^ [Y0: a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( ( Y0 @ Y1 )
                   => ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( sK2 @ Y1 @ Y2 )
                          = ( Y0 @ Y2 ) ) ) ) )
              & ( Y0 @ sK3 ) )
           => ( ( sK2 @ sK3 )
              = Y0 ) ) ) )
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f62]) ).

thf(f62,plain,
    ( spl0_2
  <=> ( $false
      = ( !! @ ( a > $o )
        @ ^ [Y0: a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( ( Y0 @ Y1 )
                   => ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( sK2 @ Y1 @ Y2 )
                          = ( Y0 @ Y2 ) ) ) ) )
              & ( Y0 @ sK3 ) )
           => ( ( sK2 @ sK3 )
              = Y0 ) ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

thf(f108,plain,
    ( ! [X1: a] :
        ( $true
        = ( ( sK4 @ X1 )
         => ( !! @ a
            @ ^ [Y0: a] :
                ( ( sK2 @ X1 @ Y0 )
                = ( sK4 @ Y0 ) ) ) ) )
    | ~ spl0_2 ),
    inference(beta_eta_normalization,[],[f105]) ).

thf(f105,plain,
    ( ! [X1: a] :
        ( ( ^ [Y0: a] :
              ( ( sK4 @ Y0 )
             => ( !! @ a
                @ ^ [Y1: a] :
                    ( ( sK2 @ Y0 @ Y1 )
                    = ( sK4 @ Y1 ) ) ) )
          @ X1 )
        = $true )
    | ~ spl0_2 ),
    inference(pi_clausification,[],[f80]) ).

thf(f78,plain,
    ( ( ( sK4 @ sK5 )
     != ( sK2 @ sK3 @ sK5 ) )
    | ~ spl0_2 ),
    inference(negative_extensionality,[],[f77]) ).

thf(f77,plain,
    ( ( sK4
     != ( sK2 @ sK3 ) )
    | ~ spl0_2 ),
    inference(equality_proxy_clausification,[],[f71]) ).

thf(f71,plain,
    ( ( $false
      = ( ( sK2 @ sK3 )
        = sK4 ) )
    | ~ spl0_2 ),
    inference(binary_proxy_clausification,[],[f69]) ).

thf(f64,plain,
    ( spl0_1
    | spl0_2 ),
    inference(avatar_split_clause,[],[f57,f62,f59]) ).

thf(f57,plain,
    ( ( $false
      = ( !! @ ( a > $o )
        @ ^ [Y0: a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( ( Y0 @ Y1 )
                   => ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( sK2 @ Y1 @ Y2 )
                          = ( Y0 @ Y2 ) ) ) ) )
              & ( Y0 @ sK3 ) )
           => ( ( sK2 @ sK3 )
              = Y0 ) ) ) )
    | ( ( !! @ a
        @ ^ [Y0: a] :
            ( ( sK2 @ sK3 @ Y0 )
           => ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK2 @ Y0 @ Y1 )
                  = ( sK2 @ sK3 @ Y1 ) ) ) ) )
      = $false ) ),
    inference(binary_proxy_clausification,[],[f28]) ).

thf(f28,plain,
    ( $false
    = ( ( !! @ a
        @ ^ [Y0: a] :
            ( ( sK2 @ sK3 @ Y0 )
           => ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK2 @ Y0 @ Y1 )
                  = ( sK2 @ sK3 @ Y1 ) ) ) ) )
      & ( !! @ ( a > $o )
        @ ^ [Y0: a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( ( Y0 @ Y1 )
                   => ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( sK2 @ Y1 @ Y2 )
                          = ( Y0 @ Y2 ) ) ) ) )
              & ( Y0 @ sK3 ) )
           => ( ( sK2 @ sK3 )
              = Y0 ) ) ) ) ),
    inference(boolean_simplification,[],[f27]) ).

thf(f27,plain,
    ( ( $true
      & ( !! @ a
        @ ^ [Y0: a] :
            ( ( sK2 @ sK3 @ Y0 )
           => ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK2 @ Y0 @ Y1 )
                  = ( sK2 @ sK3 @ Y1 ) ) ) ) )
      & ( !! @ ( a > $o )
        @ ^ [Y0: a > $o] :
            ( ( ( !! @ a
                @ ^ [Y1: a] :
                    ( ( Y0 @ Y1 )
                   => ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( sK2 @ Y1 @ Y2 )
                          = ( Y0 @ Y2 ) ) ) ) )
              & ( Y0 @ sK3 ) )
           => ( ( sK2 @ sK3 )
              = Y0 ) ) ) )
    = $false ),
    inference(superposition,[],[f25,f23]) ).

thf(f23,plain,
    ! [X1: a] :
      ( $true
      = ( sK2 @ X1 @ X1 ) ),
    inference(beta_eta_normalization,[],[f22]) ).

thf(f22,plain,
    ! [X1: a] :
      ( ( ^ [Y0: a] : ( sK2 @ Y0 @ Y0 )
        @ X1 )
      = $true ),
    inference(pi_clausification,[],[f19]) ).

thf(f19,plain,
    ( $true
    = ( !! @ a
      @ ^ [Y0: a] : ( sK2 @ Y0 @ Y0 ) ) ),
    inference(boolean_simplification,[],[f18]) ).

thf(f18,plain,
    ( $true
    = ( $true
      & ( !! @ a
        @ ^ [Y0: a] : ( sK2 @ Y0 @ Y0 ) ) ) ),
    inference(backward_demodulation,[],[f13,f17]) ).

thf(f25,plain,
    ! [X1: a > $o] :
      ( $false
      = ( ( X1 @ sK3 )
        & ( !! @ a
          @ ^ [Y0: a] :
              ( ( X1 @ Y0 )
             => ( !! @ a
                @ ^ [Y1: a] :
                    ( ( sK2 @ Y0 @ Y1 )
                    = ( X1 @ Y1 ) ) ) ) )
        & ( !! @ ( a > $o )
          @ ^ [Y0: a > $o] :
              ( ( ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( Y0 @ Y1 )
                     => ( !! @ a
                        @ ^ [Y2: a] :
                            ( ( sK2 @ Y1 @ Y2 )
                            = ( Y0 @ Y2 ) ) ) ) )
                & ( Y0 @ sK3 ) )
             => ( X1 = Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f24]) ).

thf(f24,plain,
    ! [X1: a > $o] :
      ( $false
      = ( ^ [Y0: a > $o] :
            ( ( Y0 @ sK3 )
            & ( !! @ a
              @ ^ [Y1: a] :
                  ( ( Y0 @ Y1 )
                 => ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( sK2 @ Y1 @ Y2 )
                        = ( Y0 @ Y2 ) ) ) ) )
            & ( !! @ ( a > $o )
              @ ^ [Y1: a > $o] :
                  ( ( ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( Y1 @ Y2 )
                         => ( !! @ a
                            @ ^ [Y3: a] :
                                ( ( sK2 @ Y2 @ Y3 )
                                = ( Y1 @ Y3 ) ) ) ) )
                    & ( Y1 @ sK3 ) )
                 => ( Y0 = Y1 ) ) ) )
        @ X1 ) ),
    inference(pi_clausification,[],[f21]) ).

thf(f21,plain,
    ( $false
    = ( ?? @ ( a > $o )
      @ ^ [Y0: a > $o] :
          ( ( Y0 @ sK3 )
          & ( !! @ a
            @ ^ [Y1: a] :
                ( ( Y0 @ Y1 )
               => ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( sK2 @ Y1 @ Y2 )
                      = ( Y0 @ Y2 ) ) ) ) )
          & ( !! @ ( a > $o )
            @ ^ [Y1: a > $o] :
                ( ( ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( Y1 @ Y2 )
                       => ( !! @ a
                          @ ^ [Y3: a] :
                              ( ( sK2 @ Y2 @ Y3 )
                              = ( Y1 @ Y3 ) ) ) ) )
                  & ( Y1 @ sK3 ) )
               => ( Y0 = Y1 ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f20]) ).

thf(f20,plain,
    ( ( ^ [Y0: a] :
          ( ?? @ ( a > $o )
          @ ^ [Y1: a > $o] :
              ( ( Y1 @ Y0 )
              & ( !! @ a
                @ ^ [Y2: a] :
                    ( ( Y1 @ Y2 )
                   => ( !! @ a
                      @ ^ [Y3: a] :
                          ( ( sK2 @ Y2 @ Y3 )
                          = ( Y1 @ Y3 ) ) ) ) )
              & ( !! @ ( a > $o )
                @ ^ [Y2: a > $o] :
                    ( ( ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( Y2 @ Y3 )
                           => ( !! @ a
                              @ ^ [Y4: a] :
                                  ( ( sK2 @ Y3 @ Y4 )
                                  = ( Y2 @ Y4 ) ) ) ) )
                      & ( Y2 @ Y0 ) )
                   => ( Y1 = Y2 ) ) ) ) )
      @ sK3 )
    = $false ),
    inference(sigma_clausification,[],[f15]) ).

thf(f15,plain,
    ( $false
    = ( !! @ a
      @ ^ [Y0: a] :
          ( ?? @ ( a > $o )
          @ ^ [Y1: a > $o] :
              ( ( Y1 @ Y0 )
              & ( !! @ a
                @ ^ [Y2: a] :
                    ( ( Y1 @ Y2 )
                   => ( !! @ a
                      @ ^ [Y3: a] :
                          ( ( sK2 @ Y2 @ Y3 )
                          = ( Y1 @ Y3 ) ) ) ) )
              & ( !! @ ( a > $o )
                @ ^ [Y2: a > $o] :
                    ( ( ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( Y2 @ Y3 )
                           => ( !! @ a
                              @ ^ [Y4: a] :
                                  ( ( sK2 @ Y3 @ Y4 )
                                  = ( Y2 @ Y4 ) ) ) ) )
                      & ( Y2 @ Y0 ) )
                   => ( Y1 = Y2 ) ) ) ) ) ) ),
    inference(boolean_simplification,[],[f14]) ).

thf(f14,plain,
    ( ( $true
     => ( !! @ a
        @ ^ [Y0: a] :
            ( ?? @ ( a > $o )
            @ ^ [Y1: a > $o] :
                ( ( Y1 @ Y0 )
                & ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( Y1 @ Y2 )
                     => ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( sK2 @ Y2 @ Y3 )
                            = ( Y1 @ Y3 ) ) ) ) )
                & ( !! @ ( a > $o )
                  @ ^ [Y2: a > $o] :
                      ( ( ( !! @ a
                          @ ^ [Y3: a] :
                              ( ( Y2 @ Y3 )
                             => ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( sK2 @ Y3 @ Y4 )
                                    = ( Y2 @ Y4 ) ) ) ) )
                        & ( Y2 @ Y0 ) )
                     => ( Y1 = Y2 ) ) ) ) ) ) )
    = $false ),
    inference(backward_demodulation,[],[f11,f13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11  % Problem    : SEV011^5 : TPTP v8.2.0. Released v4.0.0.
% 0.04/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.12/0.33  % Computer : n008.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   : Sun May 19 19:11:37 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.12/0.33  This is a TH0_THM_EQU_NAR problem
% 0.12/0.33  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/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34  % (6548)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.12/0.35  % (6552)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.12/0.35  % (6552)Instruction limit reached!
% 0.12/0.35  % (6552)------------------------------
% 0.12/0.35  % (6552)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.35  % (6552)Termination reason: Unknown
% 0.12/0.35  % (6552)Termination phase: Saturation
% 0.12/0.35  
% 0.12/0.35  % (6552)Memory used [KB]: 5500
% 0.12/0.35  % (6552)Time elapsed: 0.003 s
% 0.12/0.35  % (6552)Instructions burned: 4 (million)
% 0.12/0.35  % (6552)------------------------------
% 0.12/0.35  % (6552)------------------------------
% 0.12/0.35  % (6549)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (3000ds/4Mi)
% 0.12/0.35  % (6549)Instruction limit reached!
% 0.12/0.35  % (6549)------------------------------
% 0.12/0.35  % (6549)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.35  % (6549)Termination reason: Unknown
% 0.12/0.35  % (6549)Termination phase: Saturation
% 0.12/0.35  
% 0.12/0.35  % (6549)Memory used [KB]: 5500
% 0.12/0.35  % (6549)Time elapsed: 0.003 s
% 0.12/0.35  % (6549)Instructions burned: 4 (million)
% 0.12/0.35  % (6549)------------------------------
% 0.12/0.35  % (6549)------------------------------
% 0.12/0.35  % (6553)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (3000ds/275Mi)
% 0.12/0.35  % (6554)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.12/0.35  % (6555)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (3000ds/3Mi)
% 0.12/0.35  % (6555)Instruction limit reached!
% 0.12/0.35  % (6555)------------------------------
% 0.12/0.35  % (6555)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.35  % (6555)Termination reason: Unknown
% 0.12/0.35  % (6555)Termination phase: Saturation
% 0.12/0.35  
% 0.12/0.35  % (6555)Memory used [KB]: 5500
% 0.12/0.35  % (6555)Time elapsed: 0.003 s
% 0.12/0.35  % (6555)Instructions burned: 3 (million)
% 0.12/0.35  % (6555)------------------------------
% 0.12/0.35  % (6555)------------------------------
% 0.12/0.36  % (6551)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.12/0.36  % (6556)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)
% 0.12/0.36  % (6551)Instruction limit reached!
% 0.12/0.36  % (6551)------------------------------
% 0.12/0.36  % (6551)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.36  % (6551)Termination reason: Unknown
% 0.12/0.36  % (6551)Termination phase: shuffling
% 0.12/0.36  
% 0.12/0.36  % (6551)Memory used [KB]: 1023
% 0.12/0.36  % (6551)Time elapsed: 0.002 s
% 0.12/0.36  % (6551)Instructions burned: 2 (million)
% 0.12/0.36  % (6551)------------------------------
% 0.12/0.36  % (6551)------------------------------
% 0.12/0.36  % (6550)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (3000ds/27Mi)
% 0.12/0.36  % (6554)Instruction limit reached!
% 0.12/0.36  % (6554)------------------------------
% 0.12/0.36  % (6554)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.36  % (6554)Termination reason: Unknown
% 0.12/0.36  % (6554)Termination phase: Saturation
% 0.12/0.36  
% 0.12/0.36  % (6554)Memory used [KB]: 5628
% 0.12/0.36  % (6554)Time elapsed: 0.012 s
% 0.12/0.36  % (6554)Instructions burned: 19 (million)
% 0.12/0.36  % (6554)------------------------------
% 0.12/0.36  % (6554)------------------------------
% 0.18/0.36  % (6557)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)
% 0.18/0.37  % (6558)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)
% 0.18/0.37  % (6558)Instruction limit reached!
% 0.18/0.37  % (6558)------------------------------
% 0.18/0.37  % (6558)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.37  % (6558)Termination reason: Unknown
% 0.18/0.37  % (6558)Termination phase: Saturation
% 0.18/0.37  
% 0.18/0.37  % (6558)Memory used [KB]: 5500
% 0.18/0.37  % (6558)Time elapsed: 0.003 s
% 0.18/0.37  % (6558)Instructions burned: 3 (million)
% 0.18/0.37  % (6558)------------------------------
% 0.18/0.37  % (6558)------------------------------
% 0.18/0.37  % (6556)Instruction limit reached!
% 0.18/0.37  % (6556)------------------------------
% 0.18/0.37  % (6556)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.37  % (6556)Termination reason: Unknown
% 0.18/0.37  % (6556)Termination phase: Saturation
% 0.18/0.37  
% 0.18/0.37  % (6556)Memory used [KB]: 5884
% 0.18/0.37  % (6556)Time elapsed: 0.014 s
% 0.18/0.37  % (6556)Instructions burned: 37 (million)
% 0.18/0.37  % (6556)------------------------------
% 0.18/0.37  % (6556)------------------------------
% 0.18/0.37  % (6550)Instruction limit reached!
% 0.18/0.37  % (6550)------------------------------
% 0.18/0.37  % (6550)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.37  % (6550)Termination reason: Unknown
% 0.18/0.37  % (6550)Termination phase: Saturation
% 0.18/0.37  
% 0.18/0.37  % (6550)Memory used [KB]: 5756
% 0.18/0.37  % (6550)Time elapsed: 0.013 s
% 0.18/0.37  % (6550)Instructions burned: 28 (million)
% 0.18/0.37  % (6550)------------------------------
% 0.18/0.37  % (6550)------------------------------
% 0.18/0.37  % (6557)Instruction limit reached!
% 0.18/0.37  % (6557)------------------------------
% 0.18/0.37  % (6557)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.37  % (6557)Termination reason: Unknown
% 0.18/0.37  % (6557)Termination phase: Saturation
% 0.18/0.37  
% 0.18/0.37  % (6557)Memory used [KB]: 5628
% 0.18/0.37  % (6557)Time elapsed: 0.009 s
% 0.18/0.37  % (6557)Instructions burned: 15 (million)
% 0.18/0.37  % (6557)------------------------------
% 0.18/0.37  % (6557)------------------------------
% 0.18/0.37  % (6560)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.18/0.38  % (6559)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)
% 0.18/0.38  % (6561)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.18/0.38  % (6562)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)
% 0.18/0.38  % (6563)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)
% 0.18/0.38  % (6560)Instruction limit reached!
% 0.18/0.38  % (6560)------------------------------
% 0.18/0.38  % (6560)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.38  % (6560)Termination reason: Unknown
% 0.18/0.38  % (6560)Termination phase: Saturation
% 0.18/0.38  
% 0.18/0.38  % (6560)Memory used [KB]: 1023
% 0.18/0.38  % (6560)Time elapsed: 0.005 s
% 0.18/0.38  % (6560)Instructions burned: 7 (million)
% 0.18/0.38  % (6560)------------------------------
% 0.18/0.38  % (6560)------------------------------
% 0.18/0.38  % (6562)Instruction limit reached!
% 0.18/0.38  % (6562)------------------------------
% 0.18/0.38  % (6562)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.38  % (6562)Termination reason: Unknown
% 0.18/0.38  % (6562)Termination phase: Property scanning
% 0.18/0.38  
% 0.18/0.38  % (6562)Memory used [KB]: 1023
% 0.18/0.38  % (6562)Time elapsed: 0.002 s
% 0.18/0.38  % (6562)Instructions burned: 4 (million)
% 0.18/0.38  % (6562)------------------------------
% 0.18/0.38  % (6562)------------------------------
% 0.18/0.38  % (6563)Instruction limit reached!
% 0.18/0.38  % (6563)------------------------------
% 0.18/0.38  % (6563)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.38  % (6563)Termination reason: Unknown
% 0.18/0.38  % (6563)Termination phase: Saturation
% 0.18/0.38  
% 0.18/0.38  % (6563)Memory used [KB]: 1023
% 0.18/0.38  % (6563)Time elapsed: 0.004 s
% 0.18/0.38  % (6563)Instructions burned: 4 (million)
% 0.18/0.38  % (6563)------------------------------
% 0.18/0.38  % (6563)------------------------------
% 0.18/0.38  % (6561)Instruction limit reached!
% 0.18/0.38  % (6561)------------------------------
% 0.18/0.38  % (6561)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.38  % (6561)Termination reason: Unknown
% 0.18/0.38  % (6561)Termination phase: Saturation
% 0.18/0.38  
% 0.18/0.38  % (6561)Memory used [KB]: 5628
% 0.18/0.38  % (6561)Time elapsed: 0.007 s
% 0.18/0.38  % (6561)Instructions burned: 16 (million)
% 0.18/0.38  % (6561)------------------------------
% 0.18/0.38  % (6561)------------------------------
% 0.18/0.39  % (6565)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)
% 0.18/0.39  % (6565)Instruction limit reached!
% 0.18/0.39  % (6565)------------------------------
% 0.18/0.39  % (6565)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.39  % (6565)Termination reason: Unknown
% 0.18/0.39  % (6565)Termination phase: Property scanning
% 0.18/0.39  
% 0.18/0.39  % (6565)Memory used [KB]: 895
% 0.18/0.39  % (6565)Time elapsed: 0.002 s
% 0.18/0.39  % (6565)Instructions burned: 3 (million)
% 0.18/0.39  % (6565)------------------------------
% 0.18/0.39  % (6565)------------------------------
% 0.18/0.39  % (6564)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)
% 0.18/0.39  % (6567)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)
% 0.18/0.39  % (6564)Instruction limit reached!
% 0.18/0.39  % (6564)------------------------------
% 0.18/0.39  % (6564)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.39  % (6564)Termination reason: Unknown
% 0.18/0.39  % (6564)Termination phase: Saturation
% 0.18/0.39  
% 0.18/0.39  % (6564)Memory used [KB]: 5500
% 0.18/0.39  % (6564)Time elapsed: 0.005 s
% 0.18/0.39  % (6564)Instructions burned: 7 (million)
% 0.18/0.39  % (6564)------------------------------
% 0.18/0.39  % (6564)------------------------------
% 0.18/0.39  % (6566)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.18/0.39  % (6568)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.18/0.39  % (6566)Instruction limit reached!
% 0.18/0.39  % (6566)------------------------------
% 0.18/0.39  % (6566)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.39  % (6566)Termination reason: Unknown
% 0.18/0.39  % (6566)Termination phase: Saturation
% 0.18/0.39  
% 0.18/0.39  % (6566)Memory used [KB]: 5500
% 0.18/0.39  % (6566)Time elapsed: 0.004 s
% 0.18/0.39  % (6566)Instructions burned: 5 (million)
% 0.18/0.39  % (6566)------------------------------
% 0.18/0.39  % (6566)------------------------------
% 0.18/0.40  % (6567)Instruction limit reached!
% 0.18/0.40  % (6567)------------------------------
% 0.18/0.40  % (6567)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.40  % (6567)Termination reason: Unknown
% 0.18/0.40  % (6567)Termination phase: Saturation
% 0.18/0.40  
% 0.18/0.40  % (6567)Memory used [KB]: 5500
% 0.18/0.40  % (6567)Time elapsed: 0.011 s
% 0.18/0.40  % (6567)Instructions burned: 18 (million)
% 0.18/0.40  % (6567)------------------------------
% 0.18/0.40  % (6567)------------------------------
% 0.18/0.40  % (6559)First to succeed.
% 0.18/0.40  % (6569)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.18/0.40  % (6559)Refutation found. Thanks to Tanya!
% 0.18/0.40  % SZS status Theorem for theBenchmark
% 0.18/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.40  % (6559)------------------------------
% 0.18/0.40  % (6559)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.40  % (6559)Termination reason: Refutation
% 0.18/0.40  
% 0.18/0.40  % (6559)Memory used [KB]: 5884
% 0.18/0.40  % (6559)Time elapsed: 0.029 s
% 0.18/0.40  % (6559)Instructions burned: 53 (million)
% 0.18/0.40  % (6559)------------------------------
% 0.18/0.40  % (6559)------------------------------
% 0.18/0.40  % (6547)Success in time 0.052 s
% 0.18/0.40  % Vampire---4.8 exiting
%------------------------------------------------------------------------------