TSTP Solution File: SEV028^5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEV028^5 : 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 : n004.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 04:11:45 EDT 2024

% Result   : Theorem 0.22s 0.45s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   36
%            Number of leaves      :   18
% Syntax   : Number of formulae    :  102 (  34 unt;  13 typ;   0 def)
%            Number of atoms       :  729 ( 140 equ;   0 cnn)
%            Maximal formula atoms :   10 (   8 avg)
%            Number of connectives : 1600 (  54   ~;  50   |; 139   &;1011   @)
%                                         (  13 <=>; 116  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   69 (  69   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   20 (  15 usr;  15 con; 0-2 aty)
%                                         ( 170  !!;  47  ??;   0 @@+;   0 @@-)
%            Number of variables   :  294 ( 199   ^  79   !;  15   ?; 294   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

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

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

thf(func_def_1,type,
    cQ: a > a > $o ).

thf(func_def_17,type,
    ph1: 
      !>[X0: $tType] : X0 ).

thf(func_def_18,type,
    sK2: a ).

thf(func_def_19,type,
    sK3: a ).

thf(func_def_20,type,
    sK4: a > a > $o ).

thf(func_def_21,type,
    sK5: a > a ).

thf(func_def_22,type,
    sK6: a ).

thf(func_def_23,type,
    sK7: a ).

thf(func_def_24,type,
    sK8: a ).

thf(func_def_25,type,
    sK9: a ).

thf(func_def_26,type,
    sK10: a ).

thf(f419,plain,
    $false,
    inference(avatar_sat_refutation,[],[f22,f207,f217,f242,f418]) ).

thf(f418,plain,
    ~ spl0_6,
    inference(avatar_contradiction_clause,[],[f417]) ).

thf(f417,plain,
    ( $false
    | ~ spl0_6 ),
    inference(trivial_inequality_removal,[],[f416]) ).

thf(f416,plain,
    ( ( $false = $true )
    | ~ spl0_6 ),
    inference(backward_demodulation,[],[f282,f414]) ).

thf(f414,plain,
    ( ( $false
      = ( cQ @ sK8 @ sK9 ) )
    | ~ spl0_6 ),
    inference(superposition,[],[f272,f331]) ).

thf(f331,plain,
    ( ! [X0: a] :
        ( ( cQ @ sK8 @ X0 )
        = ( cQ @ sK10 @ X0 ) )
    | ~ spl0_6 ),
    inference(superposition,[],[f327,f126]) ).

thf(f126,plain,
    ! [X0: a,X1: a] :
      ( ( cQ @ X0 @ X1 )
      = ( sK4 @ X0 @ X1 ) ),
    inference(binary_proxy_clausification,[],[f125]) ).

thf(f125,plain,
    ! [X0: a,X1: a] :
      ( ( ( sK4 @ X0 @ X1 )
        = ( cQ @ X0 @ X1 ) )
      = $true ),
    inference(beta_eta_normalization,[],[f123]) ).

thf(f123,plain,
    ! [X0: a,X1: a] :
      ( ( ^ [Y0: a] :
            ( ( sK4 @ X0 @ Y0 )
            = ( cQ @ X0 @ Y0 ) )
        @ X1 )
      = $true ),
    inference(pi_clausification,[],[f67]) ).

thf(f67,plain,
    ! [X0: a] :
      ( ( !! @ a
        @ ^ [Y0: a] :
            ( ( sK4 @ X0 @ Y0 )
            = ( cQ @ X0 @ Y0 ) ) )
      = $true ),
    inference(boolean_simplification,[],[f66]) ).

thf(f66,plain,
    ! [X0: a] :
      ( $true
      = ( $true
       => ( !! @ a
          @ ^ [Y0: a] :
              ( ( sK4 @ X0 @ Y0 )
              = ( cQ @ X0 @ Y0 ) ) ) ) ),
    inference(superposition,[],[f54,f63]) ).

thf(f63,plain,
    ! [X1: a] :
      ( ( sK4 @ X1 @ X1 )
      = $true ),
    inference(boolean_simplification,[],[f62]) ).

thf(f62,plain,
    ! [X1: a] :
      ( $true
      = ( ( sK4 @ X1 @ X1 )
        & $true ) ),
    inference(backward_demodulation,[],[f57,f60]) ).

thf(f60,plain,
    ! [X1: a] :
      ( ( ?? @ a @ ( sK4 @ X1 ) )
      = $true ),
    inference(binary_proxy_clausification,[],[f57]) ).

thf(f57,plain,
    ! [X1: a] :
      ( ( ( sK4 @ X1 @ X1 )
        & ( ?? @ a @ ( sK4 @ X1 ) ) )
      = $true ),
    inference(binary_proxy_clausification,[],[f47]) ).

thf(f47,plain,
    ! [X1: a] :
      ( ( ( sK4 @ X1 @ X1 )
        & ( ?? @ a @ ( sK4 @ X1 ) )
        & ( !! @ ( a > $o )
          @ ^ [Y0: a > $o] :
              ( ( ( ?? @ a @ Y0 )
                & ( Y0 @ X1 )
                & ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( Y0 @ Y1 )
                     => ( !! @ a
                        @ ^ [Y2: a] :
                            ( ( cQ @ Y1 @ Y2 )
                            = ( Y0 @ Y2 ) ) ) ) ) )
             => ( ( sK4 @ X1 )
                = Y0 ) ) ) )
      = $true ),
    inference(binary_proxy_clausification,[],[f45]) ).

thf(f45,plain,
    ! [X1: a] :
      ( $true
      = ( ( sK4 @ X1 @ X1 )
        & ( ?? @ a @ ( sK4 @ X1 ) )
        & ( !! @ ( a > $o )
          @ ^ [Y0: a > $o] :
              ( ( ( ?? @ a @ Y0 )
                & ( Y0 @ X1 )
                & ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( Y0 @ Y1 )
                     => ( !! @ a
                        @ ^ [Y2: a] :
                            ( ( cQ @ Y1 @ Y2 )
                            = ( Y0 @ Y2 ) ) ) ) ) )
             => ( ( sK4 @ X1 )
                = Y0 ) ) )
        & ( !! @ a
          @ ^ [Y0: a] :
              ( ( sK4 @ X1 @ Y0 )
             => ( !! @ a
                @ ^ [Y1: a] :
                    ( ( sK4 @ X1 @ Y1 )
                    = ( cQ @ Y0 @ Y1 ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f44]) ).

thf(f44,plain,
    ! [X1: a] :
      ( ( ^ [Y0: a > $o] :
            ( ( Y0 @ X1 )
            & ( ?? @ a @ Y0 )
            & ( !! @ ( a > $o )
              @ ^ [Y1: a > $o] :
                  ( ( ( ?? @ a @ Y1 )
                    & ( Y1 @ X1 )
                    & ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( Y1 @ Y2 )
                         => ( !! @ a
                            @ ^ [Y3: a] :
                                ( ( cQ @ Y2 @ Y3 )
                                = ( Y1 @ Y3 ) ) ) ) ) )
                 => ( Y0 = Y1 ) ) )
            & ( !! @ a
              @ ^ [Y1: a] :
                  ( ( Y0 @ Y1 )
                 => ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( Y0 @ Y2 )
                        = ( cQ @ Y1 @ Y2 ) ) ) ) ) )
        @ ( sK4 @ X1 ) )
      = $true ),
    inference(sigma_clausification,[],[f42]) ).

thf(f42,plain,
    ! [X1: a] :
      ( $true
      = ( ?? @ ( a > $o )
        @ ^ [Y0: a > $o] :
            ( ( Y0 @ X1 )
            & ( ?? @ a @ Y0 )
            & ( !! @ ( a > $o )
              @ ^ [Y1: a > $o] :
                  ( ( ( ?? @ a @ Y1 )
                    & ( Y1 @ X1 )
                    & ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( Y1 @ Y2 )
                         => ( !! @ a
                            @ ^ [Y3: a] :
                                ( ( cQ @ Y2 @ Y3 )
                                = ( Y1 @ Y3 ) ) ) ) ) )
                 => ( Y0 = Y1 ) ) )
            & ( !! @ a
              @ ^ [Y1: a] :
                  ( ( Y0 @ Y1 )
                 => ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( Y0 @ Y2 )
                        = ( cQ @ Y1 @ Y2 ) ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f41]) ).

thf(f41,plain,
    ! [X1: a] :
      ( ( ^ [Y0: a] :
            ( ?? @ ( a > $o )
            @ ^ [Y1: a > $o] :
                ( ( Y1 @ Y0 )
                & ( ?? @ a @ Y1 )
                & ( !! @ ( a > $o )
                  @ ^ [Y2: a > $o] :
                      ( ( ( ?? @ a @ Y2 )
                        & ( Y2 @ Y0 )
                        & ( !! @ a
                          @ ^ [Y3: a] :
                              ( ( Y2 @ Y3 )
                             => ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( cQ @ Y3 @ Y4 )
                                    = ( Y2 @ Y4 ) ) ) ) ) )
                     => ( Y1 = Y2 ) ) )
                & ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( Y1 @ Y2 )
                     => ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( Y1 @ Y3 )
                            = ( cQ @ Y2 @ Y3 ) ) ) ) ) ) )
        @ X1 )
      = $true ),
    inference(pi_clausification,[],[f38]) ).

thf(f38,plain,
    ( ( !! @ a
      @ ^ [Y0: a] :
          ( ?? @ ( a > $o )
          @ ^ [Y1: a > $o] :
              ( ( Y1 @ Y0 )
              & ( ?? @ a @ Y1 )
              & ( !! @ ( a > $o )
                @ ^ [Y2: a > $o] :
                    ( ( ( ?? @ a @ Y2 )
                      & ( Y2 @ Y0 )
                      & ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( Y2 @ Y3 )
                           => ( !! @ a
                              @ ^ [Y4: a] :
                                  ( ( cQ @ Y3 @ Y4 )
                                  = ( Y2 @ Y4 ) ) ) ) ) )
                   => ( Y1 = Y2 ) ) )
              & ( !! @ a
                @ ^ [Y2: a] :
                    ( ( Y1 @ Y2 )
                   => ( !! @ a
                      @ ^ [Y3: a] :
                          ( ( Y1 @ Y3 )
                          = ( cQ @ Y2 @ Y3 ) ) ) ) ) ) ) )
    = $true ),
    inference(boolean_simplification,[],[f37]) ).

thf(f37,plain,
    ( $true
    = ( ( !! @ a
        @ ^ [Y0: a] :
            ( ?? @ ( a > $o )
            @ ^ [Y1: a > $o] :
                ( ( Y1 @ Y0 )
                & ( ?? @ a @ Y1 )
                & ( !! @ ( a > $o )
                  @ ^ [Y2: a > $o] :
                      ( ( ( ?? @ a @ Y2 )
                        & ( Y2 @ Y0 )
                        & ( !! @ a
                          @ ^ [Y3: a] :
                              ( ( Y2 @ Y3 )
                             => ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( cQ @ Y3 @ Y4 )
                                    = ( Y2 @ Y4 ) ) ) ) ) )
                     => ( Y1 = Y2 ) ) )
                & ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( Y1 @ Y2 )
                     => ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( Y1 @ Y3 )
                            = ( cQ @ Y2 @ Y3 ) ) ) ) ) ) ) )
      & $true ) ),
    inference(backward_demodulation,[],[f12,f35]) ).

thf(f35,plain,
    ( ( !! @ ( a > $o )
      @ ^ [Y0: a > $o] :
          ( ( ( ?? @ a @ Y0 )
            & ( !! @ a
              @ ^ [Y1: a] :
                  ( ( Y0 @ Y1 )
                 => ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( Y0 @ Y2 )
                        = ( cQ @ Y1 @ Y2 ) ) ) ) ) )
         => ( ?? @ a @ Y0 ) ) )
    = $true ),
    inference(binary_proxy_clausification,[],[f12]) ).

thf(f12,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( ?? @ ( a > $o )
            @ ^ [Y1: a > $o] :
                ( ( Y1 @ Y0 )
                & ( ?? @ a @ Y1 )
                & ( !! @ ( a > $o )
                  @ ^ [Y2: a > $o] :
                      ( ( ( ?? @ a @ Y2 )
                        & ( Y2 @ Y0 )
                        & ( !! @ a
                          @ ^ [Y3: a] :
                              ( ( Y2 @ Y3 )
                             => ( !! @ a
                                @ ^ [Y4: a] :
                                    ( ( cQ @ Y3 @ Y4 )
                                    = ( Y2 @ Y4 ) ) ) ) ) )
                     => ( Y1 = Y2 ) ) )
                & ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( Y1 @ Y2 )
                     => ( !! @ a
                        @ ^ [Y3: a] :
                            ( ( Y1 @ Y3 )
                            = ( cQ @ Y2 @ Y3 ) ) ) ) ) ) ) )
      & ( !! @ ( a > $o )
        @ ^ [Y0: a > $o] :
            ( ( ( ?? @ a @ Y0 )
              & ( !! @ a
                @ ^ [Y1: a] :
                    ( ( Y0 @ Y1 )
                   => ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( Y0 @ Y2 )
                          = ( cQ @ Y1 @ Y2 ) ) ) ) ) )
           => ( ?? @ a @ Y0 ) ) ) )
    = $true ),
    inference(binary_proxy_clausification,[],[f8]) ).

thf(f8,plain,
    ( $false
    = ( ( ( !! @ a
          @ ^ [Y0: a] :
              ( ?? @ ( a > $o )
              @ ^ [Y1: a > $o] :
                  ( ( Y1 @ Y0 )
                  & ( ?? @ a @ Y1 )
                  & ( !! @ ( a > $o )
                    @ ^ [Y2: a > $o] :
                        ( ( ( ?? @ a @ Y2 )
                          & ( Y2 @ Y0 )
                          & ( !! @ a
                            @ ^ [Y3: a] :
                                ( ( Y2 @ Y3 )
                               => ( !! @ a
                                  @ ^ [Y4: a] :
                                      ( ( cQ @ Y3 @ Y4 )
                                      = ( Y2 @ Y4 ) ) ) ) ) )
                       => ( Y1 = Y2 ) ) )
                  & ( !! @ a
                    @ ^ [Y2: a] :
                        ( ( Y1 @ Y2 )
                       => ( !! @ a
                          @ ^ [Y3: a] :
                              ( ( Y1 @ Y3 )
                              = ( cQ @ Y2 @ Y3 ) ) ) ) ) ) ) )
        & ( !! @ ( a > $o )
          @ ^ [Y0: a > $o] :
              ( ( ( ?? @ a @ Y0 )
                & ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( Y0 @ Y1 )
                     => ( !! @ a
                        @ ^ [Y2: a] :
                            ( ( Y0 @ Y2 )
                            = ( cQ @ Y1 @ Y2 ) ) ) ) ) )
             => ( ?? @ a @ Y0 ) ) ) )
     => ( ( !! @ a
          @ ^ [Y0: a] : ( cQ @ Y0 @ Y0 ) )
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( ( cQ @ Y2 @ Y0 )
                        & ( cQ @ Y0 @ Y1 ) )
                     => ( cQ @ Y2 @ Y1 ) ) ) ) )
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( cQ @ Y0 @ Y1 )
                 => ( cQ @ Y1 @ Y0 ) ) ) ) ) ) ),
    inference(not_proxy_clausification,[],[f7]) ).

thf(f7,plain,
    ( $true
    = ( ~ ( ( ( !! @ a
              @ ^ [Y0: a] :
                  ( ?? @ ( a > $o )
                  @ ^ [Y1: a > $o] :
                      ( ( Y1 @ Y0 )
                      & ( ?? @ a @ Y1 )
                      & ( !! @ ( a > $o )
                        @ ^ [Y2: a > $o] :
                            ( ( ( ?? @ a @ Y2 )
                              & ( Y2 @ Y0 )
                              & ( !! @ a
                                @ ^ [Y3: a] :
                                    ( ( Y2 @ Y3 )
                                   => ( !! @ a
                                      @ ^ [Y4: a] :
                                          ( ( cQ @ Y3 @ Y4 )
                                          = ( Y2 @ Y4 ) ) ) ) ) )
                           => ( Y1 = Y2 ) ) )
                      & ( !! @ a
                        @ ^ [Y2: a] :
                            ( ( Y1 @ Y2 )
                           => ( !! @ a
                              @ ^ [Y3: a] :
                                  ( ( Y1 @ Y3 )
                                  = ( cQ @ Y2 @ Y3 ) ) ) ) ) ) ) )
            & ( !! @ ( a > $o )
              @ ^ [Y0: a > $o] :
                  ( ( ( ?? @ a @ Y0 )
                    & ( !! @ a
                      @ ^ [Y1: a] :
                          ( ( Y0 @ Y1 )
                         => ( !! @ a
                            @ ^ [Y2: a] :
                                ( ( Y0 @ Y2 )
                                = ( cQ @ Y1 @ Y2 ) ) ) ) ) )
                 => ( ?? @ a @ Y0 ) ) ) )
         => ( ( !! @ a
              @ ^ [Y0: a] : ( cQ @ Y0 @ Y0 ) )
            & ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( !! @ a
                      @ ^ [Y2: a] :
                          ( ( ( cQ @ Y2 @ Y0 )
                            & ( cQ @ Y0 @ Y1 ) )
                         => ( cQ @ Y2 @ Y1 ) ) ) ) )
            & ( !! @ a
              @ ^ [Y0: a] :
                  ( !! @ a
                  @ ^ [Y1: a] :
                      ( ( cQ @ Y0 @ Y1 )
                     => ( cQ @ Y1 @ Y0 ) ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f6]) ).

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

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

thf(f4,plain,
    ~ ( ( ! [X0: a > $o] :
            ( ( ! [X1: a] :
                  ( ( X0 @ X1 )
                 => ! [X2: a] :
                      ( ( X0 @ X2 )
                    <=> ( cQ @ X1 @ X2 ) ) )
              & ? [X3: a] : ( X0 @ X3 ) )
           => ? [X4: a] : ( X0 @ X4 ) )
        & ! [X5: a] :
          ? [X6: a > $o] :
            ( ! [X7: a] :
                ( ( X6 @ X7 )
               => ! [X8: a] :
                    ( ( X6 @ X8 )
                  <=> ( cQ @ X7 @ X8 ) ) )
            & ! [X9: a > $o] :
                ( ( ! [X10: a] :
                      ( ( X9 @ X10 )
                     => ! [X11: a] :
                          ( ( cQ @ X10 @ X11 )
                        <=> ( X9 @ X11 ) ) )
                  & ( X9 @ X5 )
                  & ? [X12: a] : ( X9 @ X12 ) )
               => ( X6 = X9 ) )
            & ? [X13: a] : ( X6 @ X13 )
            & ( X6 @ X5 ) ) )
     => ( ! [X14: a,X15: a] :
            ( ( cQ @ X15 @ X14 )
           => ( cQ @ X14 @ X15 ) )
        & ! [X16: a,X17: a,X18: a] :
            ( ( ( cQ @ X18 @ X17 )
              & ( cQ @ X16 @ X18 ) )
           => ( cQ @ X16 @ X17 ) )
        & ! [X19: a] : ( cQ @ X19 @ X19 ) ) ),
    inference(rectify,[],[f2]) ).

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

thf(f1,conjecture,
    ( ( ! [X0: a > $o] :
          ( ( ! [X2: a] :
                ( ( X0 @ X2 )
               => ! [X3: a] :
                    ( ( X0 @ X3 )
                  <=> ( cQ @ X2 @ X3 ) ) )
            & ? [X1: a] : ( X0 @ X1 ) )
         => ? [X1: a] : ( X0 @ X1 ) )
      & ! [X2: a] :
        ? [X0: a > $o] :
          ( ! [X4: a] :
              ( ( X0 @ X4 )
             => ! [X3: a] :
                  ( ( X0 @ X3 )
                <=> ( cQ @ X4 @ X3 ) ) )
          & ! [X5: a > $o] :
              ( ( ! [X4: a] :
                    ( ( X5 @ X4 )
                   => ! [X3: a] :
                        ( ( cQ @ X4 @ X3 )
                      <=> ( X5 @ X3 ) ) )
                & ( X5 @ X2 )
                & ? [X1: a] : ( X5 @ X1 ) )
             => ( X0 = X5 ) )
          & ? [X1: a] : ( X0 @ X1 )
          & ( X0 @ X2 ) ) )
   => ( ! [X3: a,X2: a] :
          ( ( cQ @ X2 @ X3 )
         => ( cQ @ X3 @ X2 ) )
      & ! [X2: a,X1: a,X3: a] :
          ( ( ( cQ @ X3 @ X1 )
            & ( cQ @ X2 @ X3 ) )
         => ( cQ @ X2 @ X1 ) )
      & ! [X2: a] : ( cQ @ X2 @ X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM558_pme) ).

thf(f54,plain,
    ! [X2: a,X1: a] :
      ( ( ( sK4 @ X1 @ X2 )
       => ( !! @ a
          @ ^ [Y0: a] :
              ( ( sK4 @ X1 @ Y0 )
              = ( cQ @ X2 @ Y0 ) ) ) )
      = $true ),
    inference(beta_eta_normalization,[],[f50]) ).

thf(f50,plain,
    ! [X2: a,X1: a] :
      ( $true
      = ( ^ [Y0: a] :
            ( ( sK4 @ X1 @ Y0 )
           => ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK4 @ X1 @ Y1 )
                  = ( cQ @ Y0 @ Y1 ) ) ) )
        @ X2 ) ),
    inference(pi_clausification,[],[f49]) ).

thf(f49,plain,
    ! [X1: a] :
      ( $true
      = ( !! @ a
        @ ^ [Y0: a] :
            ( ( sK4 @ X1 @ Y0 )
           => ( !! @ a
              @ ^ [Y1: a] :
                  ( ( sK4 @ X1 @ Y1 )
                  = ( cQ @ Y0 @ Y1 ) ) ) ) ) ),
    inference(boolean_simplification,[],[f48]) ).

thf(f48,plain,
    ! [X1: a] :
      ( $true
      = ( $true
        & ( !! @ a
          @ ^ [Y0: a] :
              ( ( sK4 @ X1 @ Y0 )
             => ( !! @ a
                @ ^ [Y1: a] :
                    ( ( sK4 @ X1 @ Y1 )
                    = ( cQ @ Y0 @ Y1 ) ) ) ) ) ) ),
    inference(backward_demodulation,[],[f45,f47]) ).

thf(f327,plain,
    ( ! [X1: a] :
        ( ( cQ @ sK8 @ X1 )
        = ( sK4 @ sK10 @ X1 ) )
    | ~ spl0_6 ),
    inference(binary_proxy_clausification,[],[f326]) ).

thf(f326,plain,
    ( ! [X1: a] :
        ( $true
        = ( ( sK4 @ sK10 @ X1 )
          = ( cQ @ sK8 @ X1 ) ) )
    | ~ spl0_6 ),
    inference(beta_eta_normalization,[],[f323]) ).

thf(f323,plain,
    ( ! [X1: a] :
        ( $true
        = ( ^ [Y0: a] :
              ( ( sK4 @ sK10 @ Y0 )
              = ( cQ @ sK8 @ Y0 ) )
          @ X1 ) )
    | ~ spl0_6 ),
    inference(pi_clausification,[],[f290]) ).

thf(f290,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( ( sK4 @ sK10 @ Y0 )
            = ( cQ @ sK8 @ Y0 ) ) )
      = $true )
    | ~ spl0_6 ),
    inference(boolean_simplification,[],[f287]) ).

thf(f287,plain,
    ( ( $true
      = ( $true
       => ( !! @ a
          @ ^ [Y0: a] :
              ( ( sK4 @ sK10 @ Y0 )
              = ( cQ @ sK8 @ Y0 ) ) ) ) )
    | ~ spl0_6 ),
    inference(superposition,[],[f130,f280]) ).

thf(f280,plain,
    ( ( ( cQ @ sK10 @ sK8 )
      = $true )
    | ~ spl0_6 ),
    inference(binary_proxy_clausification,[],[f270]) ).

thf(f270,plain,
    ( ( ( ( cQ @ sK10 @ sK8 )
        & ( cQ @ sK8 @ sK9 ) )
      = $true )
    | ~ spl0_6 ),
    inference(binary_proxy_clausification,[],[f262]) ).

thf(f262,plain,
    ( ( $false
      = ( ( ( cQ @ sK10 @ sK8 )
          & ( cQ @ sK8 @ sK9 ) )
       => ( cQ @ sK10 @ sK9 ) ) )
    | ~ spl0_6 ),
    inference(beta_eta_normalization,[],[f261]) ).

thf(f261,plain,
    ( ( ( ^ [Y0: a] :
            ( ( ( cQ @ Y0 @ sK8 )
              & ( cQ @ sK8 @ sK9 ) )
           => ( cQ @ Y0 @ sK9 ) )
        @ sK10 )
      = $false )
    | ~ spl0_6 ),
    inference(sigma_clausification,[],[f252]) ).

thf(f252,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( ( ( cQ @ Y0 @ sK8 )
              & ( cQ @ sK8 @ sK9 ) )
           => ( cQ @ Y0 @ sK9 ) ) )
      = $false )
    | ~ spl0_6 ),
    inference(beta_eta_normalization,[],[f251]) ).

thf(f251,plain,
    ( ( $false
      = ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( cQ @ Y1 @ sK8 )
                  & ( cQ @ sK8 @ Y0 ) )
               => ( cQ @ Y1 @ Y0 ) ) )
        @ sK9 ) )
    | ~ spl0_6 ),
    inference(sigma_clausification,[],[f246]) ).

thf(f246,plain,
    ( ( $false
      = ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( ( cQ @ Y1 @ sK8 )
                  & ( cQ @ sK8 @ Y0 ) )
               => ( cQ @ Y1 @ Y0 ) ) ) ) )
    | ~ spl0_6 ),
    inference(beta_eta_normalization,[],[f245]) ).

thf(f245,plain,
    ( ( $false
      = ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( !! @ a
                @ ^ [Y2: a] :
                    ( ( ( cQ @ Y2 @ Y0 )
                      & ( cQ @ Y0 @ Y1 ) )
                   => ( cQ @ Y2 @ Y1 ) ) ) )
        @ sK8 ) )
    | ~ spl0_6 ),
    inference(sigma_clausification,[],[f216]) ).

thf(f216,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( !! @ a
                @ ^ [Y2: a] :
                    ( ( ( cQ @ Y2 @ Y0 )
                      & ( cQ @ Y0 @ Y1 ) )
                   => ( cQ @ Y2 @ Y1 ) ) ) ) )
      = $false )
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f215]) ).

thf(f215,plain,
    ( spl0_6
  <=> ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( !! @ a
                @ ^ [Y2: a] :
                    ( ( ( cQ @ Y2 @ Y0 )
                      & ( cQ @ Y0 @ Y1 ) )
                   => ( cQ @ Y2 @ Y1 ) ) ) ) )
      = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

thf(f130,plain,
    ! [X2: a,X1: a] :
      ( ( ( cQ @ X1 @ X2 )
       => ( !! @ a
          @ ^ [Y0: a] :
              ( ( sK4 @ X1 @ Y0 )
              = ( cQ @ X2 @ Y0 ) ) ) )
      = $true ),
    inference(backward_demodulation,[],[f54,f126]) ).

thf(f272,plain,
    ( ( ( cQ @ sK10 @ sK9 )
      = $false )
    | ~ spl0_6 ),
    inference(boolean_simplification,[],[f271]) ).

thf(f271,plain,
    ( ( $false
      = ( $true
       => ( cQ @ sK10 @ sK9 ) ) )
    | ~ spl0_6 ),
    inference(backward_demodulation,[],[f262,f270]) ).

thf(f282,plain,
    ( ( $true
      = ( cQ @ sK8 @ sK9 ) )
    | ~ spl0_6 ),
    inference(boolean_simplification,[],[f281]) ).

thf(f281,plain,
    ( ( ( $true
        & ( cQ @ sK8 @ sK9 ) )
      = $true )
    | ~ spl0_6 ),
    inference(backward_demodulation,[],[f270,f280]) ).

thf(f242,plain,
    ~ spl0_5,
    inference(avatar_contradiction_clause,[],[f241]) ).

thf(f241,plain,
    ( $false
    | ~ spl0_5 ),
    inference(trivial_inequality_removal,[],[f231]) ).

thf(f231,plain,
    ( ( $false = $true )
    | ~ spl0_5 ),
    inference(superposition,[],[f230,f174]) ).

thf(f174,plain,
    ! [X0: a] :
      ( $true
      = ( cQ @ X0 @ X0 ) ),
    inference(superposition,[],[f63,f126]) ).

thf(f230,plain,
    ( ( ( cQ @ sK7 @ sK7 )
      = $false )
    | ~ spl0_5 ),
    inference(beta_eta_normalization,[],[f229]) ).

thf(f229,plain,
    ( ( ( ^ [Y0: a] : ( cQ @ Y0 @ Y0 )
        @ sK7 )
      = $false )
    | ~ spl0_5 ),
    inference(sigma_clausification,[],[f213]) ).

thf(f213,plain,
    ( ( $false
      = ( !! @ a
        @ ^ [Y0: a] : ( cQ @ Y0 @ Y0 ) ) )
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f212]) ).

thf(f212,plain,
    ( spl0_5
  <=> ( $false
      = ( !! @ a
        @ ^ [Y0: a] : ( cQ @ Y0 @ Y0 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

thf(f217,plain,
    ( spl0_5
    | spl0_6
    | ~ spl0_1 ),
    inference(avatar_split_clause,[],[f210,f17,f215,f212]) ).

thf(f17,plain,
    ( spl0_1
  <=> ( $false
      = ( ( !! @ a
          @ ^ [Y0: a] : ( cQ @ Y0 @ Y0 ) )
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( ( cQ @ Y2 @ Y0 )
                        & ( cQ @ Y0 @ Y1 ) )
                     => ( cQ @ Y2 @ Y1 ) ) ) ) ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

thf(f210,plain,
    ( ( $false
      = ( !! @ a
        @ ^ [Y0: a] : ( cQ @ Y0 @ Y0 ) ) )
    | ( ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( !! @ a
                @ ^ [Y2: a] :
                    ( ( ( cQ @ Y2 @ Y0 )
                      & ( cQ @ Y0 @ Y1 ) )
                   => ( cQ @ Y2 @ Y1 ) ) ) ) )
      = $false )
    | ~ spl0_1 ),
    inference(binary_proxy_clausification,[],[f18]) ).

thf(f18,plain,
    ( ( $false
      = ( ( !! @ a
          @ ^ [Y0: a] : ( cQ @ Y0 @ Y0 ) )
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( ( cQ @ Y2 @ Y0 )
                        & ( cQ @ Y0 @ Y1 ) )
                     => ( cQ @ Y2 @ Y1 ) ) ) ) ) ) )
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f17]) ).

thf(f207,plain,
    ~ spl0_2,
    inference(avatar_contradiction_clause,[],[f206]) ).

thf(f206,plain,
    ( $false
    | ~ spl0_2 ),
    inference(trivial_inequality_removal,[],[f195]) ).

thf(f195,plain,
    ( ( $false = $true )
    | ~ spl0_2 ),
    inference(superposition,[],[f174,f160]) ).

thf(f160,plain,
    ( ( ( cQ @ sK2 @ sK2 )
      = $false )
    | ~ spl0_2 ),
    inference(superposition,[],[f29,f155]) ).

thf(f155,plain,
    ( ! [X1: a] :
        ( ( cQ @ sK2 @ X1 )
        = ( cQ @ sK3 @ X1 ) )
    | ~ spl0_2 ),
    inference(forward_demodulation,[],[f153,f126]) ).

thf(f153,plain,
    ( ! [X1: a] :
        ( ( cQ @ sK3 @ X1 )
        = ( sK4 @ sK2 @ X1 ) )
    | ~ spl0_2 ),
    inference(binary_proxy_clausification,[],[f152]) ).

thf(f152,plain,
    ( ! [X1: a] :
        ( $true
        = ( ( sK4 @ sK2 @ X1 )
          = ( cQ @ sK3 @ X1 ) ) )
    | ~ spl0_2 ),
    inference(beta_eta_normalization,[],[f150]) ).

thf(f150,plain,
    ( ! [X1: a] :
        ( $true
        = ( ^ [Y0: a] :
              ( ( sK4 @ sK2 @ Y0 )
              = ( cQ @ sK3 @ Y0 ) )
          @ X1 ) )
    | ~ spl0_2 ),
    inference(pi_clausification,[],[f142]) ).

thf(f142,plain,
    ( ( ( !! @ a
        @ ^ [Y0: a] :
            ( ( sK4 @ sK2 @ Y0 )
            = ( cQ @ sK3 @ Y0 ) ) )
      = $true )
    | ~ spl0_2 ),
    inference(boolean_simplification,[],[f138]) ).

thf(f138,plain,
    ( ( ( $true
       => ( !! @ a
          @ ^ [Y0: a] :
              ( ( sK4 @ sK2 @ Y0 )
              = ( cQ @ sK3 @ Y0 ) ) ) )
      = $true )
    | ~ spl0_2 ),
    inference(superposition,[],[f130,f30]) ).

thf(f30,plain,
    ( ( ( cQ @ sK2 @ sK3 )
      = $true )
    | ~ spl0_2 ),
    inference(binary_proxy_clausification,[],[f28]) ).

thf(f28,plain,
    ( ( ( ( cQ @ sK2 @ sK3 )
       => ( cQ @ sK3 @ sK2 ) )
      = $false )
    | ~ spl0_2 ),
    inference(beta_eta_normalization,[],[f27]) ).

thf(f27,plain,
    ( ( $false
      = ( ^ [Y0: a] :
            ( ( cQ @ sK2 @ Y0 )
           => ( cQ @ Y0 @ sK2 ) )
        @ sK3 ) )
    | ~ spl0_2 ),
    inference(sigma_clausification,[],[f26]) ).

thf(f26,plain,
    ( ( $false
      = ( !! @ a
        @ ^ [Y0: a] :
            ( ( cQ @ sK2 @ Y0 )
           => ( cQ @ Y0 @ sK2 ) ) ) )
    | ~ spl0_2 ),
    inference(beta_eta_normalization,[],[f25]) ).

thf(f25,plain,
    ( ( $false
      = ( ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( cQ @ Y0 @ Y1 )
               => ( cQ @ Y1 @ Y0 ) ) )
        @ sK2 ) )
    | ~ spl0_2 ),
    inference(sigma_clausification,[],[f21]) ).

thf(f21,plain,
    ( ( $false
      = ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( cQ @ Y0 @ Y1 )
               => ( cQ @ Y1 @ Y0 ) ) ) ) )
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f20]) ).

thf(f20,plain,
    ( spl0_2
  <=> ( $false
      = ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( cQ @ Y0 @ Y1 )
               => ( cQ @ Y1 @ Y0 ) ) ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

thf(f29,plain,
    ( ( $false
      = ( cQ @ sK3 @ sK2 ) )
    | ~ spl0_2 ),
    inference(binary_proxy_clausification,[],[f28]) ).

thf(f22,plain,
    ( spl0_1
    | spl0_2 ),
    inference(avatar_split_clause,[],[f15,f20,f17]) ).

thf(f15,plain,
    ( ( $false
      = ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( cQ @ Y0 @ Y1 )
               => ( cQ @ Y1 @ Y0 ) ) ) ) )
    | ( $false
      = ( ( !! @ a
          @ ^ [Y0: a] : ( cQ @ Y0 @ Y0 ) )
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( ( cQ @ Y2 @ Y0 )
                        & ( cQ @ Y0 @ Y1 ) )
                     => ( cQ @ Y2 @ Y1 ) ) ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f14]) ).

thf(f14,plain,
    ( $false
    = ( ( !! @ a
        @ ^ [Y0: a] : ( cQ @ Y0 @ Y0 ) )
      & ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( !! @ a
                @ ^ [Y2: a] :
                    ( ( ( cQ @ Y2 @ Y0 )
                      & ( cQ @ Y0 @ Y1 ) )
                   => ( cQ @ Y2 @ Y1 ) ) ) ) )
      & ( !! @ a
        @ ^ [Y0: a] :
            ( !! @ a
            @ ^ [Y1: a] :
                ( ( cQ @ Y0 @ Y1 )
               => ( cQ @ Y1 @ Y0 ) ) ) ) ) ),
    inference(boolean_simplification,[],[f13]) ).

thf(f13,plain,
    ( ( $true
     => ( ( !! @ a
          @ ^ [Y0: a] : ( cQ @ Y0 @ Y0 ) )
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( !! @ a
                  @ ^ [Y2: a] :
                      ( ( ( cQ @ Y2 @ Y0 )
                        & ( cQ @ Y0 @ Y1 ) )
                     => ( cQ @ Y2 @ Y1 ) ) ) ) )
        & ( !! @ a
          @ ^ [Y0: a] :
              ( !! @ a
              @ ^ [Y1: a] :
                  ( ( cQ @ Y0 @ Y1 )
                 => ( cQ @ Y1 @ Y0 ) ) ) ) ) )
    = $false ),
    inference(backward_demodulation,[],[f8,f12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SEV028^5 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.14  % 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
% 0.13/0.35  % Computer : n004.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sun May 19 18:41:08 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  This is a TH0_THM_EQU_NAR problem
% 0.13/0.35  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
% 0.22/0.37  % (21390)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)
% 0.22/0.37  % (21385)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)
% 0.22/0.37  % (21384)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)
% 0.22/0.37  % (21386)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.22/0.37  % (21387)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)
% 0.22/0.37  % (21388)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)
% 0.22/0.37  % (21386)Instruction limit reached!
% 0.22/0.37  % (21386)------------------------------
% 0.22/0.37  % (21386)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.37  % (21386)Termination reason: Unknown
% 0.22/0.37  % (21387)Instruction limit reached!
% 0.22/0.37  % (21387)------------------------------
% 0.22/0.37  % (21387)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.37  % (21386)Termination phase: Preprocessing 3
% 0.22/0.37  
% 0.22/0.37  % (21386)Memory used [KB]: 1023
% 0.22/0.37  % (21386)Time elapsed: 0.003 s
% 0.22/0.37  % (21386)Instructions burned: 2 (million)
% 0.22/0.37  % (21386)------------------------------
% 0.22/0.37  % (21386)------------------------------
% 0.22/0.37  % (21387)Termination reason: Unknown
% 0.22/0.37  % (21387)Termination phase: Property scanning
% 0.22/0.37  
% 0.22/0.37  % (21387)Memory used [KB]: 1023
% 0.22/0.37  % (21387)Time elapsed: 0.003 s
% 0.22/0.37  % (21387)Instructions burned: 3 (million)
% 0.22/0.37  % (21387)------------------------------
% 0.22/0.37  % (21387)------------------------------
% 0.22/0.37  % (21390)Instruction limit reached!
% 0.22/0.37  % (21390)------------------------------
% 0.22/0.37  % (21390)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.37  % (21390)Termination reason: Unknown
% 0.22/0.37  % (21390)Termination phase: Saturation
% 0.22/0.37  
% 0.22/0.37  % (21390)Memory used [KB]: 5500
% 0.22/0.37  % (21390)Time elapsed: 0.004 s
% 0.22/0.37  % (21390)Instructions burned: 4 (million)
% 0.22/0.37  % (21390)------------------------------
% 0.22/0.37  % (21390)------------------------------
% 0.22/0.37  % (21384)Instruction limit reached!
% 0.22/0.37  % (21384)------------------------------
% 0.22/0.37  % (21384)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.37  % (21384)Termination reason: Unknown
% 0.22/0.37  % (21384)Termination phase: Saturation
% 0.22/0.37  
% 0.22/0.37  % (21384)Memory used [KB]: 5500
% 0.22/0.37  % (21384)Time elapsed: 0.005 s
% 0.22/0.37  % (21384)Instructions burned: 5 (million)
% 0.22/0.37  % (21384)------------------------------
% 0.22/0.37  % (21384)------------------------------
% 0.22/0.37  % (21389)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.22/0.38  % (21389)Instruction limit reached!
% 0.22/0.38  % (21389)------------------------------
% 0.22/0.38  % (21389)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.38  % (21389)Termination reason: Unknown
% 0.22/0.38  % (21389)Termination phase: Saturation
% 0.22/0.38  
% 0.22/0.38  % (21389)Memory used [KB]: 5628
% 0.22/0.38  % (21389)Time elapsed: 0.012 s
% 0.22/0.38  % (21389)Instructions burned: 18 (million)
% 0.22/0.38  % (21389)------------------------------
% 0.22/0.38  % (21389)------------------------------
% 0.22/0.38  % (21383)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.22/0.38  % (21391)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)
% 0.22/0.38  % (21392)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)
% 0.22/0.39  % (21395)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)
% 0.22/0.39  % (21385)Instruction limit reached!
% 0.22/0.39  % (21385)------------------------------
% 0.22/0.39  % (21385)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.39  % (21385)Termination reason: Unknown
% 0.22/0.39  % (21385)Termination phase: Saturation
% 0.22/0.39  
% 0.22/0.39  % (21385)Memory used [KB]: 5756
% 0.22/0.39  % (21385)Time elapsed: 0.021 s
% 0.22/0.39  % (21385)Instructions burned: 28 (million)
% 0.22/0.39  % (21385)------------------------------
% 0.22/0.39  % (21385)------------------------------
% 0.22/0.39  % (21393)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)
% 0.22/0.39  % (21393)Instruction limit reached!
% 0.22/0.39  % (21393)------------------------------
% 0.22/0.39  % (21393)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.39  % (21393)Termination reason: Unknown
% 0.22/0.39  % (21393)Termination phase: Saturation
% 0.22/0.39  
% 0.22/0.39  % (21393)Memory used [KB]: 5500
% 0.22/0.39  % (21393)Time elapsed: 0.003 s
% 0.22/0.39  % (21393)Instructions burned: 3 (million)
% 0.22/0.39  % (21393)------------------------------
% 0.22/0.39  % (21393)------------------------------
% 0.22/0.40  % (21392)Instruction limit reached!
% 0.22/0.40  % (21392)------------------------------
% 0.22/0.40  % (21392)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40  % (21392)Termination reason: Unknown
% 0.22/0.40  % (21392)Termination phase: Saturation
% 0.22/0.40  
% 0.22/0.40  % (21392)Memory used [KB]: 5628
% 0.22/0.40  % (21392)Time elapsed: 0.013 s
% 0.22/0.40  % (21392)Instructions burned: 16 (million)
% 0.22/0.40  % (21392)------------------------------
% 0.22/0.40  % (21392)------------------------------
% 0.22/0.40  % (21396)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.22/0.40  % (21396)Instruction limit reached!
% 0.22/0.40  % (21396)------------------------------
% 0.22/0.40  % (21396)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40  % (21396)Termination reason: Unknown
% 0.22/0.40  % (21396)Termination phase: Saturation
% 0.22/0.40  
% 0.22/0.40  % (21396)Memory used [KB]: 1023
% 0.22/0.40  % (21396)Time elapsed: 0.006 s
% 0.22/0.40  % (21396)Instructions burned: 8 (million)
% 0.22/0.40  % (21396)------------------------------
% 0.22/0.40  % (21396)------------------------------
% 0.22/0.40  % (21397)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.22/0.40  % (21398)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)
% 0.22/0.40  % (21398)Instruction limit reached!
% 0.22/0.40  % (21398)------------------------------
% 0.22/0.40  % (21398)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40  % (21398)Termination reason: Unknown
% 0.22/0.40  % (21398)Termination phase: Twee Goal Transformation
% 0.22/0.40  
% 0.22/0.40  % (21398)Memory used [KB]: 1023
% 0.22/0.40  % (21398)Time elapsed: 0.003 s
% 0.22/0.40  % (21398)Instructions burned: 3 (million)
% 0.22/0.40  % (21398)------------------------------
% 0.22/0.40  % (21398)------------------------------
% 0.22/0.41  % (21391)Instruction limit reached!
% 0.22/0.41  % (21391)------------------------------
% 0.22/0.41  % (21391)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41  % (21391)Termination reason: Unknown
% 0.22/0.41  % (21391)Termination phase: Saturation
% 0.22/0.41  
% 0.22/0.41  % (21391)Memory used [KB]: 5884
% 0.22/0.41  % (21391)Time elapsed: 0.023 s
% 0.22/0.41  % (21391)Instructions burned: 37 (million)
% 0.22/0.41  % (21391)------------------------------
% 0.22/0.41  % (21391)------------------------------
% 0.22/0.41  % (21399)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)
% 0.22/0.41  % (21399)Instruction limit reached!
% 0.22/0.41  % (21399)------------------------------
% 0.22/0.41  % (21399)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41  % (21399)Termination reason: Unknown
% 0.22/0.41  % (21399)Termination phase: Saturation
% 0.22/0.41  
% 0.22/0.41  % (21399)Memory used [KB]: 1023
% 0.22/0.41  % (21399)Time elapsed: 0.004 s
% 0.22/0.41  % (21399)Instructions burned: 4 (million)
% 0.22/0.41  % (21397)Instruction limit reached!
% 0.22/0.41  % (21397)------------------------------
% 0.22/0.41  % (21397)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41  % (21397)Termination reason: Unknown
% 0.22/0.41  % (21397)Termination phase: Saturation
% 0.22/0.41  
% 0.22/0.41  % (21397)Memory used [KB]: 5628
% 0.22/0.41  % (21397)Time elapsed: 0.012 s
% 0.22/0.41  % (21397)Instructions burned: 16 (million)
% 0.22/0.41  % (21397)------------------------------
% 0.22/0.41  % (21397)------------------------------
% 0.22/0.41  % (21399)------------------------------
% 0.22/0.41  % (21399)------------------------------
% 0.22/0.42  % (21400)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)
% 0.22/0.42  % (21401)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)
% 0.22/0.42  % (21401)Instruction limit reached!
% 0.22/0.42  % (21401)------------------------------
% 0.22/0.42  % (21401)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42  % (21401)Termination reason: Unknown
% 0.22/0.42  % (21401)Termination phase: Property scanning
% 0.22/0.42  
% 0.22/0.42  % (21401)Memory used [KB]: 1023
% 0.22/0.42  % (21401)Time elapsed: 0.003 s
% 0.22/0.42  % (21401)Instructions burned: 3 (million)
% 0.22/0.42  % (21401)------------------------------
% 0.22/0.42  % (21401)------------------------------
% 0.22/0.42  % (21402)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.22/0.42  % (21400)Instruction limit reached!
% 0.22/0.42  % (21400)------------------------------
% 0.22/0.42  % (21400)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42  % (21400)Termination reason: Unknown
% 0.22/0.42  % (21400)Termination phase: Saturation
% 0.22/0.42  
% 0.22/0.42  % (21400)Memory used [KB]: 5500
% 0.22/0.42  % (21400)Time elapsed: 0.006 s
% 0.22/0.42  % (21400)Instructions burned: 8 (million)
% 0.22/0.42  % (21400)------------------------------
% 0.22/0.42  % (21400)------------------------------
% 0.22/0.42  % (21402)Instruction limit reached!
% 0.22/0.42  % (21402)------------------------------
% 0.22/0.42  % (21402)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42  % (21402)Termination reason: Unknown
% 0.22/0.42  % (21402)Termination phase: Saturation
% 0.22/0.42  
% 0.22/0.42  % (21402)Memory used [KB]: 5500
% 0.22/0.42  % (21402)Time elapsed: 0.004 s
% 0.22/0.42  % (21402)Instructions burned: 4 (million)
% 0.22/0.42  % (21402)------------------------------
% 0.22/0.42  % (21402)------------------------------
% 0.22/0.43  % (21403)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)
% 0.22/0.43  % (21404)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.22/0.43  % (21406)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on theBenchmark for (2999ds/902Mi)
% 0.22/0.44  % (21407)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.22/0.44  % (21403)Instruction limit reached!
% 0.22/0.44  % (21403)------------------------------
% 0.22/0.44  % (21403)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44  % (21403)Termination reason: Unknown
% 0.22/0.44  % (21403)Termination phase: Saturation
% 0.22/0.44  
% 0.22/0.44  % (21403)Memory used [KB]: 5628
% 0.22/0.44  % (21403)Time elapsed: 0.014 s
% 0.22/0.44  % (21403)Instructions burned: 18 (million)
% 0.22/0.44  % (21403)------------------------------
% 0.22/0.44  % (21403)------------------------------
% 0.22/0.45  % (21395)First to succeed.
% 0.22/0.45  % (21407)Instruction limit reached!
% 0.22/0.45  % (21407)------------------------------
% 0.22/0.45  % (21407)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45  % (21407)Termination reason: Unknown
% 0.22/0.45  % (21407)Termination phase: Saturation
% 0.22/0.45  
% 0.22/0.45  % (21407)Memory used [KB]: 5756
% 0.22/0.45  % (21407)Time elapsed: 0.014 s
% 0.22/0.45  % (21407)Instructions burned: 21 (million)
% 0.22/0.45  % (21407)------------------------------
% 0.22/0.45  % (21407)------------------------------
% 0.22/0.45  % (21405)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.22/0.45  % (21395)Refutation found. Thanks to Tanya!
% 0.22/0.45  % SZS status Theorem for theBenchmark
% 0.22/0.45  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.45  % (21395)------------------------------
% 0.22/0.45  % (21395)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45  % (21395)Termination reason: Refutation
% 0.22/0.45  
% 0.22/0.45  % (21395)Memory used [KB]: 6140
% 0.22/0.45  % (21395)Time elapsed: 0.067 s
% 0.22/0.45  % (21395)Instructions burned: 95 (million)
% 0.22/0.45  % (21395)------------------------------
% 0.22/0.45  % (21395)------------------------------
% 0.22/0.45  % (21382)Success in time 0.082 s
% 0.22/0.45  % Vampire---4.8 exiting
%------------------------------------------------------------------------------