TSTP Solution File: SEV203^5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEV203^5 : 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 : n011.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 04:12:21 EDT 2024

% Result   : Theorem 0.21s 0.53s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   50
%            Number of leaves      :   17
% Syntax   : Number of formulae    :  137 (  23 unt;  10 typ;   0 def)
%            Number of atoms       : 1400 ( 548 equ;   0 cnn)
%            Maximal formula atoms :   12 (  11 avg)
%            Number of connectives : 3419 ( 141   ~; 287   |; 242   &;2414   @)
%                                         (   6 <=>;  77  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   6 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :  108 ( 108   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  14 usr;  13 con; 0-3 aty)
%                                         ( 120  !!; 132  ??;   0 @@+;   0 @@-)
%            Number of variables   :  861 ( 488   ^ 354   !;  18   ?; 861   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

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

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

thf(func_def_1,type,
    y: iS ).

thf(func_def_2,type,
    x: iS ).

thf(func_def_3,type,
    cP: iS > iS > iS ).

thf(func_def_4,type,
    c0: iS ).

thf(func_def_27,type,
    sK1: iS > iS > iS > $o ).

thf(func_def_28,type,
    sK2: ( iS > $o ) > iS ).

thf(func_def_29,type,
    sK3: ( iS > $o ) > iS ).

thf(func_def_30,type,
    ph4: 
      !>[X0: $tType] : X0 ).

thf(f496,plain,
    $false,
    inference(avatar_sat_refutation,[],[f198,f211,f304,f362,f414,f446,f493]) ).

thf(f493,plain,
    ( ~ spl0_3
    | spl0_4 ),
    inference(avatar_contradiction_clause,[],[f492]) ).

thf(f492,plain,
    ( $false
    | ~ spl0_3
    | spl0_4 ),
    inference(trivial_inequality_removal,[],[f482]) ).

thf(f482,plain,
    ( ( $true = $false )
    | ~ spl0_3
    | spl0_4 ),
    inference(superposition,[],[f447,f475]) ).

thf(f475,plain,
    ( ! [X0: iS] :
        ( $true
        = ( sK1 @ X0 @ X0 @ X0 ) )
    | ~ spl0_3
    | spl0_4 ),
    inference(subsumption_resolution,[],[f474,f296]) ).

thf(f296,plain,
    ( ( $false
     != ( sK1 @ c0 @ c0 @ c0 ) )
    | spl0_4 ),
    inference(avatar_component_clause,[],[f295]) ).

thf(f295,plain,
    ( spl0_4
  <=> ( $false
      = ( sK1 @ c0 @ c0 @ c0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

thf(f474,plain,
    ( ! [X0: iS] :
        ( ( $true
          = ( sK1 @ X0 @ X0 @ X0 ) )
        | ( $false
          = ( sK1 @ c0 @ c0 @ c0 ) ) )
    | ~ spl0_3 ),
    inference(trivial_inequality_removal,[],[f473]) ).

thf(f473,plain,
    ( ! [X0: iS] :
        ( ( ( sK3
            @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
         != ( sK3
            @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) ) )
        | ( $true
          = ( sK1 @ X0 @ X0 @ X0 ) )
        | ( $false
          = ( sK1 @ c0 @ c0 @ c0 ) ) )
    | ~ spl0_3 ),
    inference(beta_eta_normalization,[],[f472]) ).

thf(f472,plain,
    ( ! [X0: iS] :
        ( ( $false
          = ( sK1 @ c0
            @ ( ^ [Y0: iS] : Y0
              @ c0 )
            @ ( ^ [Y0: iS] : Y0
              @ c0 ) ) )
        | ( ( sK3
            @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
         != ( ^ [Y0: iS] : Y0
            @ ( sK3
              @ ^ [Y0: iS] :
                  ( sK1 @ Y0
                  @ ( ^ [Y1: iS] : Y1
                    @ Y0 )
                  @ ( ^ [Y1: iS] : Y1
                    @ Y0 ) ) ) ) )
        | ( $true
          = ( sK1 @ X0
            @ ( ^ [Y0: iS] : Y0
              @ X0 )
            @ ( ^ [Y0: iS] : Y0
              @ X0 ) ) ) )
    | ~ spl0_3 ),
    inference(trivial_inequality_removal,[],[f471]) ).

thf(f471,plain,
    ( ! [X0: iS] :
        ( ( $true
          = ( sK1 @ X0
            @ ( ^ [Y0: iS] : Y0
              @ X0 )
            @ ( ^ [Y0: iS] : Y0
              @ X0 ) ) )
        | ( ( sK3
            @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
         != ( ^ [Y0: iS] : Y0
            @ ( sK3
              @ ^ [Y0: iS] :
                  ( sK1 @ Y0
                  @ ( ^ [Y1: iS] : Y1
                    @ Y0 )
                  @ ( ^ [Y1: iS] : Y1
                    @ Y0 ) ) ) ) )
        | ( ( ^ [Y0: iS] : Y0 )
         != ( ^ [Y0: iS] : Y0 ) )
        | ( $false
          = ( sK1 @ c0
            @ ( ^ [Y0: iS] : Y0
              @ c0 )
            @ ( ^ [Y0: iS] : Y0
              @ c0 ) ) ) )
    | ~ spl0_3 ),
    inference(duplicate_literal_removal,[],[f468]) ).

thf(f468,plain,
    ( ! [X0: iS] :
        ( ( $true
          = ( sK1 @ X0
            @ ( ^ [Y0: iS] : Y0
              @ X0 )
            @ ( ^ [Y0: iS] : Y0
              @ X0 ) ) )
        | ( ( ^ [Y0: iS] : Y0 )
         != ( ^ [Y0: iS] : Y0 ) )
        | ( ( ^ [Y0: iS] : Y0 )
         != ( ^ [Y0: iS] : Y0 ) )
        | ( ( sK3
            @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
         != ( ^ [Y0: iS] : Y0
            @ ( sK3
              @ ^ [Y0: iS] :
                  ( sK1 @ Y0
                  @ ( ^ [Y1: iS] : Y1
                    @ Y0 )
                  @ ( ^ [Y1: iS] : Y1
                    @ Y0 ) ) ) ) )
        | ( $false
          = ( sK1 @ c0
            @ ( ^ [Y0: iS] : Y0
              @ c0 )
            @ ( ^ [Y0: iS] : Y0
              @ c0 ) ) ) )
    | ~ spl0_3 ),
    inference(equality_resolution,[],[f460]) ).

thf(f460,plain,
    ( ! [X2: iS,X0: iS > iS,X1: iS > iS] :
        ( ( ( sK3
            @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
         != ( X1
            @ ( sK3
              @ ^ [Y0: iS] : ( sK1 @ Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) )
        | ( ( ^ [Y0: iS] : Y0 )
         != X1 )
        | ( ( ^ [Y0: iS] : Y0 )
         != X0 )
        | ( ( sK3
            @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
         != ( X0
            @ ( sK3
              @ ^ [Y0: iS] : ( sK1 @ Y0 @ ( X0 @ Y0 ) @ ( X1 @ Y0 ) ) ) ) )
        | ( $false
          = ( sK1 @ c0 @ ( X0 @ c0 ) @ ( X1 @ c0 ) ) )
        | ( $true
          = ( sK1 @ X2 @ ( X0 @ X2 ) @ ( X1 @ X2 ) ) ) )
    | ~ spl0_3 ),
    inference(beta_eta_normalization,[],[f459]) ).

thf(f459,plain,
    ( ! [X2: iS,X0: iS > iS,X1: iS > iS] :
        ( ( $false
          = ( ^ [Y0: iS] :
                ( sK1
                @ ( ^ [Y1: iS] : Y1
                  @ Y0 )
                @ ( X0 @ Y0 )
                @ ( X1 @ Y0 ) )
            @ c0 ) )
        | ( ( sK3
            @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
         != ( X1
            @ ( sK3
              @ ^ [Y0: iS] :
                  ( sK1
                  @ ( ^ [Y1: iS] : Y1
                    @ Y0 )
                  @ ( X0 @ Y0 )
                  @ ( X1 @ Y0 ) ) ) ) )
        | ( ( sK3
            @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
         != ( X0
            @ ( sK3
              @ ^ [Y0: iS] :
                  ( sK1
                  @ ( ^ [Y1: iS] : Y1
                    @ Y0 )
                  @ ( X0 @ Y0 )
                  @ ( X1 @ Y0 ) ) ) ) )
        | ( $true
          = ( ^ [Y0: iS] :
                ( sK1
                @ ( ^ [Y1: iS] : Y1
                  @ Y0 )
                @ ( X0 @ Y0 )
                @ ( X1 @ Y0 ) )
            @ X2 ) )
        | ( ( ^ [Y0: iS] : Y0 )
         != ( ^ [Y0: iS] : ( X1 @ Y0 ) ) )
        | ( ( ^ [Y0: iS] : ( X0 @ Y0 ) )
         != ( ^ [Y0: iS] : Y0 ) ) )
    | ~ spl0_3 ),
    inference(trivial_inequality_removal,[],[f452]) ).

thf(f452,plain,
    ( ! [X2: iS,X0: iS > iS,X1: iS > iS] :
        ( ( $true = $false )
        | ( ( sK3
            @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
         != ( X0
            @ ( sK3
              @ ^ [Y0: iS] :
                  ( sK1
                  @ ( ^ [Y1: iS] : Y1
                    @ Y0 )
                  @ ( X0 @ Y0 )
                  @ ( X1 @ Y0 ) ) ) ) )
        | ( $false
          = ( ^ [Y0: iS] :
                ( sK1
                @ ( ^ [Y1: iS] : Y1
                  @ Y0 )
                @ ( X0 @ Y0 )
                @ ( X1 @ Y0 ) )
            @ c0 ) )
        | ( ( ^ [Y0: iS] : Y0 )
         != ( ^ [Y0: iS] : ( X1 @ Y0 ) ) )
        | ( $true
          = ( ^ [Y0: iS] :
                ( sK1
                @ ( ^ [Y1: iS] : Y1
                  @ Y0 )
                @ ( X0 @ Y0 )
                @ ( X1 @ Y0 ) )
            @ X2 ) )
        | ( ( ^ [Y0: iS] : ( X0 @ Y0 ) )
         != ( ^ [Y0: iS] : Y0 ) )
        | ( ( sK3
            @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
         != ( X1
            @ ( sK3
              @ ^ [Y0: iS] :
                  ( sK1
                  @ ( ^ [Y1: iS] : Y1
                    @ Y0 )
                  @ ( X0 @ Y0 )
                  @ ( X1 @ Y0 ) ) ) ) ) )
    | ~ spl0_3 ),
    inference(constrained_superposition,[],[f66,f447]) ).

thf(f66,plain,
    ! [X2: iS,X1: iS > $o] :
      ( ( $true
        = ( X1 @ ( sK3 @ X1 ) ) )
      | ( $false
        = ( X1 @ c0 ) )
      | ( $true
        = ( X1 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f64]) ).

thf(f64,plain,
    ! [X2: iS,X1: iS > $o] :
      ( ( $true
        = ( X1 @ X2 ) )
      | ( $false
        = ( X1 @ c0 ) )
      | ( $true
        = ( ( X1 @ ( sK3 @ X1 ) )
          & ( X1 @ ( sK2 @ X1 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f62]) ).

thf(f62,plain,
    ! [X2: iS,X1: iS > $o] :
      ( ( $false
        = ( X1 @ c0 ) )
      | ( $true
        = ( X1 @ X2 ) )
      | ( $false
        = ( ( ( X1 @ ( sK3 @ X1 ) )
            & ( X1 @ ( sK2 @ X1 ) ) )
         => ( X1 @ ( cP @ ( sK3 @ X1 ) @ ( sK2 @ X1 ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f61]) ).

thf(f61,plain,
    ! [X2: iS,X1: iS > $o] :
      ( ( $false
        = ( X1 @ c0 ) )
      | ( $false
        = ( ^ [Y0: iS] :
              ( ( ( X1 @ Y0 )
                & ( X1 @ ( sK2 @ X1 ) ) )
             => ( X1 @ ( cP @ Y0 @ ( sK2 @ X1 ) ) ) )
          @ ( sK3 @ X1 ) ) )
      | ( $true
        = ( X1 @ X2 ) ) ),
    inference(sigma_clausification,[],[f60]) ).

thf(f60,plain,
    ! [X2: iS,X1: iS > $o] :
      ( ( $false
        = ( X1 @ c0 ) )
      | ( ( !! @ iS
          @ ^ [Y0: iS] :
              ( ( ( X1 @ Y0 )
                & ( X1 @ ( sK2 @ X1 ) ) )
             => ( X1 @ ( cP @ Y0 @ ( sK2 @ X1 ) ) ) ) )
        = $false )
      | ( $true
        = ( X1 @ X2 ) ) ),
    inference(pi_clausification,[],[f59]) ).

thf(f59,plain,
    ! [X1: iS > $o] :
      ( ( $true
        = ( !! @ iS @ X1 ) )
      | ( $false
        = ( X1 @ c0 ) )
      | ( ( !! @ iS
          @ ^ [Y0: iS] :
              ( ( ( X1 @ Y0 )
                & ( X1 @ ( sK2 @ X1 ) ) )
             => ( X1 @ ( cP @ Y0 @ ( sK2 @ X1 ) ) ) ) )
        = $false ) ),
    inference(beta_eta_normalization,[],[f58]) ).

thf(f58,plain,
    ! [X1: iS > $o] :
      ( ( $true
        = ( !! @ iS @ X1 ) )
      | ( $false
        = ( X1 @ c0 ) )
      | ( $false
        = ( ^ [Y0: iS] :
              ( !! @ iS
              @ ^ [Y1: iS] :
                  ( ( ( X1 @ Y1 )
                    & ( X1 @ Y0 ) )
                 => ( X1 @ ( cP @ Y1 @ Y0 ) ) ) )
          @ ( sK2 @ X1 ) ) ) ),
    inference(sigma_clausification,[],[f57]) ).

thf(f57,plain,
    ! [X1: iS > $o] :
      ( ( $false
        = ( !! @ iS
          @ ^ [Y0: iS] :
              ( !! @ iS
              @ ^ [Y1: iS] :
                  ( ( ( X1 @ Y1 )
                    & ( X1 @ Y0 ) )
                 => ( X1 @ ( cP @ Y1 @ Y0 ) ) ) ) ) )
      | ( $false
        = ( X1 @ c0 ) )
      | ( $true
        = ( !! @ iS @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f56]) ).

thf(f56,plain,
    ! [X1: iS > $o] :
      ( ( $false
        = ( ( X1 @ c0 )
          & ( !! @ iS
            @ ^ [Y0: iS] :
                ( !! @ iS
                @ ^ [Y1: iS] :
                    ( ( ( X1 @ Y1 )
                      & ( X1 @ Y0 ) )
                   => ( X1 @ ( cP @ Y1 @ Y0 ) ) ) ) ) ) )
      | ( $true
        = ( !! @ iS @ X1 ) ) ),
    inference(binary_proxy_clausification,[],[f55]) ).

thf(f55,plain,
    ! [X1: iS > $o] :
      ( $true
      = ( ( ( X1 @ c0 )
          & ( !! @ iS
            @ ^ [Y0: iS] :
                ( !! @ iS
                @ ^ [Y1: iS] :
                    ( ( ( X1 @ Y1 )
                      & ( X1 @ Y0 ) )
                   => ( X1 @ ( cP @ Y1 @ Y0 ) ) ) ) ) )
       => ( !! @ iS @ X1 ) ) ),
    inference(beta_eta_normalization,[],[f54]) ).

thf(f54,plain,
    ! [X1: iS > $o] :
      ( $true
      = ( ^ [Y0: iS > $o] :
            ( ( ( Y0 @ c0 )
              & ( !! @ iS
                @ ^ [Y1: iS] :
                    ( !! @ iS
                    @ ^ [Y2: iS] :
                        ( ( ( Y0 @ Y2 )
                          & ( Y0 @ Y1 ) )
                       => ( Y0 @ ( cP @ Y2 @ Y1 ) ) ) ) ) )
           => ( !! @ iS @ Y0 ) )
        @ X1 ) ),
    inference(pi_clausification,[],[f52]) ).

thf(f52,plain,
    ( $true
    = ( !! @ ( iS > $o )
      @ ^ [Y0: iS > $o] :
          ( ( ( Y0 @ c0 )
            & ( !! @ iS
              @ ^ [Y1: iS] :
                  ( !! @ iS
                  @ ^ [Y2: iS] :
                      ( ( ( Y0 @ Y2 )
                        & ( Y0 @ Y1 ) )
                     => ( Y0 @ ( cP @ Y2 @ Y1 ) ) ) ) ) )
         => ( !! @ iS @ Y0 ) ) ) ),
    inference(binary_proxy_clausification,[],[f11]) ).

thf(f11,plain,
    ( $true
    = ( ( !! @ iS
        @ ^ [Y0: iS] :
            ( !! @ iS
            @ ^ [Y1: iS] :
                ( c0
               != ( cP @ Y1 @ Y0 ) ) ) )
      & ( !! @ iS
        @ ^ [Y0: iS] :
            ( !! @ iS
            @ ^ [Y1: iS] :
                ( !! @ iS
                @ ^ [Y2: iS] :
                    ( !! @ iS
                    @ ^ [Y3: iS] :
                        ( ( ( cP @ Y1 @ Y2 )
                          = ( cP @ Y0 @ Y3 ) )
                       => ( ( Y1 = Y0 )
                          & ( Y3 = Y2 ) ) ) ) ) ) )
      & ( !! @ ( iS > $o )
        @ ^ [Y0: iS > $o] :
            ( ( ( Y0 @ c0 )
              & ( !! @ iS
                @ ^ [Y1: iS] :
                    ( !! @ iS
                    @ ^ [Y2: iS] :
                        ( ( ( Y0 @ Y2 )
                          & ( Y0 @ Y1 ) )
                       => ( Y0 @ ( cP @ Y2 @ Y1 ) ) ) ) ) )
           => ( !! @ iS @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f9]) ).

thf(f9,plain,
    ( $false
    = ( ( ( !! @ iS
          @ ^ [Y0: iS] :
              ( !! @ iS
              @ ^ [Y1: iS] :
                  ( c0
                 != ( cP @ Y1 @ Y0 ) ) ) )
        & ( !! @ iS
          @ ^ [Y0: iS] :
              ( !! @ iS
              @ ^ [Y1: iS] :
                  ( !! @ iS
                  @ ^ [Y2: iS] :
                      ( !! @ iS
                      @ ^ [Y3: iS] :
                          ( ( ( cP @ Y1 @ Y2 )
                            = ( cP @ Y0 @ Y3 ) )
                         => ( ( Y1 = Y0 )
                            & ( Y3 = Y2 ) ) ) ) ) ) )
        & ( !! @ ( iS > $o )
          @ ^ [Y0: iS > $o] :
              ( ( ( Y0 @ c0 )
                & ( !! @ iS
                  @ ^ [Y1: iS] :
                      ( !! @ iS
                      @ ^ [Y2: iS] :
                          ( ( ( Y0 @ Y2 )
                            & ( Y0 @ Y1 ) )
                         => ( Y0 @ ( cP @ Y2 @ Y1 ) ) ) ) ) )
             => ( !! @ iS @ Y0 ) ) ) )
     => ( !! @ ( iS > iS > iS > $o )
        @ ^ [Y0: iS > iS > iS > $o] :
            ( ( !! @ iS
              @ ^ [Y1: iS] :
                  ( !! @ iS
                  @ ^ [Y2: iS] :
                      ( !! @ iS
                      @ ^ [Y3: iS] :
                          ( ( ( ( c0 = Y1 )
                              & ( Y3 = Y2 ) )
                            | ( ( Y2 = Y1 )
                              & ( c0 = Y3 ) )
                            | ( ?? @ iS
                              @ ^ [Y4: iS] :
                                  ( ?? @ iS
                                  @ ^ [Y5: iS] :
                                      ( ?? @ iS
                                      @ ^ [Y6: iS] :
                                          ( ?? @ iS
                                          @ ^ [Y7: iS] :
                                              ( ?? @ iS
                                              @ ^ [Y8: iS] :
                                                  ( ?? @ iS
                                                  @ ^ [Y9: iS] :
                                                      ( ( ( cP @ Y7 @ Y8 )
                                                        = Y3 )
                                                      & ( ( cP @ Y5 @ Y9 )
                                                        = Y1 )
                                                      & ( ( cP @ Y6 @ Y4 )
                                                        = Y2 )
                                                      & ( Y0 @ Y8 @ Y9 @ Y4 )
                                                      & ( Y0 @ Y7 @ Y5 @ Y6 ) ) ) ) ) ) ) ) )
                         => ( Y0 @ Y3 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ) ) ),
    inference(not_proxy_clausification,[],[f8]) ).

thf(f8,plain,
    ( $true
    = ( ~ ( ( ( !! @ iS
              @ ^ [Y0: iS] :
                  ( !! @ iS
                  @ ^ [Y1: iS] :
                      ( c0
                     != ( cP @ Y1 @ Y0 ) ) ) )
            & ( !! @ iS
              @ ^ [Y0: iS] :
                  ( !! @ iS
                  @ ^ [Y1: iS] :
                      ( !! @ iS
                      @ ^ [Y2: iS] :
                          ( !! @ iS
                          @ ^ [Y3: iS] :
                              ( ( ( cP @ Y1 @ Y2 )
                                = ( cP @ Y0 @ Y3 ) )
                             => ( ( Y1 = Y0 )
                                & ( Y3 = Y2 ) ) ) ) ) ) )
            & ( !! @ ( iS > $o )
              @ ^ [Y0: iS > $o] :
                  ( ( ( Y0 @ c0 )
                    & ( !! @ iS
                      @ ^ [Y1: iS] :
                          ( !! @ iS
                          @ ^ [Y2: iS] :
                              ( ( ( Y0 @ Y2 )
                                & ( Y0 @ Y1 ) )
                             => ( Y0 @ ( cP @ Y2 @ Y1 ) ) ) ) ) )
                 => ( !! @ iS @ Y0 ) ) ) )
         => ( !! @ ( iS > iS > iS > $o )
            @ ^ [Y0: iS > iS > iS > $o] :
                ( ( !! @ iS
                  @ ^ [Y1: iS] :
                      ( !! @ iS
                      @ ^ [Y2: iS] :
                          ( !! @ iS
                          @ ^ [Y3: iS] :
                              ( ( ( ( c0 = Y1 )
                                  & ( Y3 = Y2 ) )
                                | ( ( Y2 = Y1 )
                                  & ( c0 = Y3 ) )
                                | ( ?? @ iS
                                  @ ^ [Y4: iS] :
                                      ( ?? @ iS
                                      @ ^ [Y5: iS] :
                                          ( ?? @ iS
                                          @ ^ [Y6: iS] :
                                              ( ?? @ iS
                                              @ ^ [Y7: iS] :
                                                  ( ?? @ iS
                                                  @ ^ [Y8: iS] :
                                                      ( ?? @ iS
                                                      @ ^ [Y9: iS] :
                                                          ( ( ( cP @ Y7 @ Y8 )
                                                            = Y3 )
                                                          & ( ( cP @ Y5 @ Y9 )
                                                            = Y1 )
                                                          & ( ( cP @ Y6 @ Y4 )
                                                            = Y2 )
                                                          & ( Y0 @ Y8 @ Y9 @ Y4 )
                                                          & ( Y0 @ Y7 @ Y5 @ Y6 ) ) ) ) ) ) ) ) )
                             => ( Y0 @ Y3 @ Y1 @ Y2 ) ) ) ) )
               => ( Y0 @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ) ) ) ),
    inference(boolean_simplification,[],[f7]) ).

thf(f7,plain,
    ( $true
    = ( ~ ( ( ( !! @ iS
              @ ^ [Y0: iS] :
                  ( !! @ iS
                  @ ^ [Y1: iS] :
                      ( c0
                     != ( cP @ Y1 @ Y0 ) ) ) )
            & ( !! @ iS
              @ ^ [Y0: iS] :
                  ( !! @ iS
                  @ ^ [Y1: iS] :
                      ( !! @ iS
                      @ ^ [Y2: iS] :
                          ( !! @ iS
                          @ ^ [Y3: iS] :
                              ( ( ( cP @ Y1 @ Y2 )
                                = ( cP @ Y0 @ Y3 ) )
                             => ( ( Y1 = Y0 )
                                & ( Y3 = Y2 ) ) ) ) ) ) )
            & ( !! @ ( iS > $o )
              @ ^ [Y0: iS > $o] :
                  ( ( ( Y0 @ c0 )
                    & ( !! @ iS
                      @ ^ [Y1: iS] :
                          ( !! @ iS
                          @ ^ [Y2: iS] :
                              ( ( ( Y0 @ Y2 )
                                & ( Y0 @ Y1 ) )
                             => ( Y0 @ ( cP @ Y2 @ Y1 ) ) ) ) ) )
                 => ( !! @ iS @ Y0 ) ) ) )
         => ( !! @ ( iS > iS > iS > $o )
            @ ^ [Y0: iS > iS > iS > $o] :
                ( ( $true
                  & ( !! @ iS
                    @ ^ [Y1: iS] :
                        ( !! @ iS
                        @ ^ [Y2: iS] :
                            ( !! @ iS
                            @ ^ [Y3: iS] :
                                ( ( ( ( c0 = Y1 )
                                    & ( Y3 = Y2 ) )
                                  | ( ( Y2 = Y1 )
                                    & ( c0 = Y3 ) )
                                  | ( ?? @ iS
                                    @ ^ [Y4: iS] :
                                        ( ?? @ iS
                                        @ ^ [Y5: iS] :
                                            ( ?? @ iS
                                            @ ^ [Y6: iS] :
                                                ( ?? @ iS
                                                @ ^ [Y7: iS] :
                                                    ( ?? @ iS
                                                    @ ^ [Y8: iS] :
                                                        ( ?? @ iS
                                                        @ ^ [Y9: iS] :
                                                            ( ( ( cP @ Y7 @ Y8 )
                                                              = Y3 )
                                                            & ( ( cP @ Y5 @ Y9 )
                                                              = Y1 )
                                                            & ( ( cP @ Y6 @ Y4 )
                                                              = Y2 )
                                                            & ( Y0 @ Y8 @ Y9 @ Y4 )
                                                            & ( Y0 @ Y7 @ Y5 @ Y6 ) ) ) ) ) ) ) ) )
                               => ( Y0 @ Y3 @ Y1 @ Y2 ) ) ) ) ) )
               => ( Y0 @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f6]) ).

thf(f6,plain,
    ( $true
    = ( ~ ( ( ( !! @ iS
              @ ^ [Y0: iS] :
                  ( !! @ iS
                  @ ^ [Y1: iS] :
                      ( c0
                     != ( cP @ Y1 @ Y0 ) ) ) )
            & ( !! @ iS
              @ ^ [Y0: iS] :
                  ( !! @ iS
                  @ ^ [Y1: iS] :
                      ( !! @ iS
                      @ ^ [Y2: iS] :
                          ( !! @ iS
                          @ ^ [Y3: iS] :
                              ( ( ( cP @ Y1 @ Y2 )
                                = ( cP @ Y0 @ Y3 ) )
                             => ( ( Y1 = Y0 )
                                & ( Y3 = Y2 ) ) ) ) ) ) )
            & ( !! @ ( iS > $o )
              @ ^ [Y0: iS > $o] :
                  ( ( ( Y0 @ c0 )
                    & ( !! @ iS
                      @ ^ [Y1: iS] :
                          ( !! @ iS
                          @ ^ [Y2: iS] :
                              ( ( ( Y0 @ Y2 )
                                & ( Y0 @ Y1 ) )
                             => ( Y0 @ ( cP @ Y2 @ Y1 ) ) ) ) ) )
                 => ( !! @ iS
                    @ ^ [Y1: iS] : ( Y0 @ Y1 ) ) ) ) )
         => ( !! @ ( iS > iS > iS > $o )
            @ ^ [Y0: iS > iS > iS > $o] :
                ( ( $true
                  & ( !! @ iS
                    @ ^ [Y1: iS] :
                        ( !! @ iS
                        @ ^ [Y2: iS] :
                            ( !! @ iS
                            @ ^ [Y3: iS] :
                                ( ( ( ( c0 = Y1 )
                                    & ( Y3 = Y2 ) )
                                  | ( ( Y2 = Y1 )
                                    & ( c0 = Y3 ) )
                                  | ( ?? @ iS
                                    @ ^ [Y4: iS] :
                                        ( ?? @ iS
                                        @ ^ [Y5: iS] :
                                            ( ?? @ iS
                                            @ ^ [Y6: iS] :
                                                ( ?? @ iS
                                                @ ^ [Y7: iS] :
                                                    ( ?? @ iS
                                                    @ ^ [Y8: iS] :
                                                        ( ?? @ iS
                                                        @ ^ [Y9: iS] :
                                                            ( ( ( cP @ Y7 @ Y8 )
                                                              = Y3 )
                                                            & ( ( cP @ Y5 @ Y9 )
                                                              = Y1 )
                                                            & ( ( cP @ Y6 @ Y4 )
                                                              = Y2 )
                                                            & ( Y0 @ Y8 @ Y9 @ Y4 )
                                                            & ( Y0 @ Y7 @ Y5 @ Y6 ) ) ) ) ) ) ) ) )
                               => ( Y0 @ Y3 @ Y1 @ Y2 ) ) ) ) ) )
               => ( Y0 @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ) ) ) ),
    inference(cnf_transformation,[],[f5]) ).

thf(f5,plain,
    ( $true
    = ( ~ ( ( ( !! @ iS
              @ ^ [Y0: iS] :
                  ( !! @ iS
                  @ ^ [Y1: iS] :
                      ( c0
                     != ( cP @ Y1 @ Y0 ) ) ) )
            & ( !! @ iS
              @ ^ [Y0: iS] :
                  ( !! @ iS
                  @ ^ [Y1: iS] :
                      ( !! @ iS
                      @ ^ [Y2: iS] :
                          ( !! @ iS
                          @ ^ [Y3: iS] :
                              ( ( ( cP @ Y1 @ Y2 )
                                = ( cP @ Y0 @ Y3 ) )
                             => ( ( Y1 = Y0 )
                                & ( Y3 = Y2 ) ) ) ) ) ) )
            & ( !! @ ( iS > $o )
              @ ^ [Y0: iS > $o] :
                  ( ( ( Y0 @ c0 )
                    & ( !! @ iS
                      @ ^ [Y1: iS] :
                          ( !! @ iS
                          @ ^ [Y2: iS] :
                              ( ( ( Y0 @ Y2 )
                                & ( Y0 @ Y1 ) )
                             => ( Y0 @ ( cP @ Y2 @ Y1 ) ) ) ) ) )
                 => ( !! @ iS
                    @ ^ [Y1: iS] : ( Y0 @ Y1 ) ) ) ) )
         => ( !! @ ( iS > iS > iS > $o )
            @ ^ [Y0: iS > iS > iS > $o] :
                ( ( $true
                  & ( !! @ iS
                    @ ^ [Y1: iS] :
                        ( !! @ iS
                        @ ^ [Y2: iS] :
                            ( !! @ iS
                            @ ^ [Y3: iS] :
                                ( ( ( ( c0 = Y1 )
                                    & ( Y3 = Y2 ) )
                                  | ( ( Y2 = Y1 )
                                    & ( c0 = Y3 ) )
                                  | ( ?? @ iS
                                    @ ^ [Y4: iS] :
                                        ( ?? @ iS
                                        @ ^ [Y5: iS] :
                                            ( ?? @ iS
                                            @ ^ [Y6: iS] :
                                                ( ?? @ iS
                                                @ ^ [Y7: iS] :
                                                    ( ?? @ iS
                                                    @ ^ [Y8: iS] :
                                                        ( ?? @ iS
                                                        @ ^ [Y9: iS] :
                                                            ( ( ( cP @ Y7 @ Y8 )
                                                              = Y3 )
                                                            & ( ( cP @ Y5 @ Y9 )
                                                              = Y1 )
                                                            & ( ( cP @ Y6 @ Y4 )
                                                              = Y2 )
                                                            & ( Y0 @ Y8 @ Y9 @ Y4 )
                                                            & ( Y0 @ Y7 @ Y5 @ Y6 ) ) ) ) ) ) ) ) )
                               => ( Y0 @ Y3 @ Y1 @ Y2 ) ) ) ) ) )
               => ( Y0 @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ) ) ) ),
    inference(fool_elimination,[],[f4]) ).

thf(f4,plain,
    ~ ( ( ! [X0: iS > $o] :
            ( ( ! [X1: iS,X2: iS] :
                  ( ( ( X0 @ X2 )
                    & ( X0 @ X1 ) )
                 => ( X0 @ ( cP @ X1 @ X2 ) ) )
              & ( X0 @ c0 ) )
           => ! [X3: iS] : ( X0 @ X3 ) )
        & ! [X4: iS,X5: iS,X6: iS,X7: iS] :
            ( ( ( cP @ X6 @ X5 )
              = ( cP @ X7 @ X4 ) )
           => ( ( X4 = X5 )
              & ( X6 = X7 ) ) )
        & ! [X8: iS,X9: iS] :
            ( c0
           != ( cP @ X8 @ X9 ) ) )
     => ! [X10: iS > iS > iS > $o] :
          ( ( ! [X11: iS,X12: iS,X13: iS] :
                ( ( ? [X14: iS,X15: iS,X16: iS,X17: iS,X18: iS,X19: iS] :
                      ( ( X10 @ X16 @ X18 @ X17 )
                      & ( X10 @ X15 @ X14 @ X19 )
                      & ( ( cP @ X17 @ X19 )
                        = X12 )
                      & ( ( cP @ X18 @ X14 )
                        = X13 )
                      & ( ( cP @ X16 @ X15 )
                        = X11 ) )
                  | ( ( c0 = X11 )
                    & ( X12 = X13 ) )
                  | ( ( X11 = X12 )
                    & ( c0 = X13 ) ) )
               => ( X10 @ X11 @ X13 @ X12 ) )
            & $true )
         => ( X10 @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ),
    inference(rectify,[],[f2]) ).

thf(f2,negated_conjecture,
    ~ ( ( ! [X4: iS > $o] :
            ( ( ! [X0: iS,X1: iS] :
                  ( ( ( X4 @ X1 )
                    & ( X4 @ X0 ) )
                 => ( X4 @ ( cP @ X0 @ X1 ) ) )
              & ( X4 @ c0 ) )
           => ! [X0: iS] : ( X4 @ X0 ) )
        & ! [X3: iS,X2: iS,X0: iS,X1: iS] :
            ( ( ( cP @ X0 @ X2 )
              = ( cP @ X1 @ X3 ) )
           => ( ( X2 = X3 )
              & ( X0 = X1 ) ) )
        & ! [X0: iS,X1: iS] :
            ( ( cP @ X0 @ X1 )
           != c0 ) )
     => ! [X5: iS > iS > iS > $o] :
          ( ( ! [X6: iS,X8: iS,X7: iS] :
                ( ( ? [X12: iS,X10: iS,X9: iS,X13: iS,X11: iS,X14: iS] :
                      ( ( X5 @ X9 @ X11 @ X13 )
                      & ( X5 @ X10 @ X12 @ X14 )
                      & ( ( cP @ X13 @ X14 )
                        = X8 )
                      & ( ( cP @ X11 @ X12 )
                        = X7 )
                      & ( ( cP @ X9 @ X10 )
                        = X6 ) )
                  | ( ( c0 = X6 )
                    & ( X7 = X8 ) )
                  | ( ( X6 = X8 )
                    & ( c0 = X7 ) ) )
               => ( X5 @ X6 @ X7 @ X8 ) )
            & $true )
         => ( X5 @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ),
    inference(negated_conjecture,[],[f1]) ).

thf(f1,conjecture,
    ( ( ! [X4: iS > $o] :
          ( ( ! [X0: iS,X1: iS] :
                ( ( ( X4 @ X1 )
                  & ( X4 @ X0 ) )
               => ( X4 @ ( cP @ X0 @ X1 ) ) )
            & ( X4 @ c0 ) )
         => ! [X0: iS] : ( X4 @ X0 ) )
      & ! [X3: iS,X2: iS,X0: iS,X1: iS] :
          ( ( ( cP @ X0 @ X2 )
            = ( cP @ X1 @ X3 ) )
         => ( ( X2 = X3 )
            & ( X0 = X1 ) ) )
      & ! [X0: iS,X1: iS] :
          ( ( cP @ X0 @ X1 )
         != c0 ) )
   => ! [X5: iS > iS > iS > $o] :
        ( ( ! [X6: iS,X8: iS,X7: iS] :
              ( ( ? [X12: iS,X10: iS,X9: iS,X13: iS,X11: iS,X14: iS] :
                    ( ( X5 @ X9 @ X11 @ X13 )
                    & ( X5 @ X10 @ X12 @ X14 )
                    & ( ( cP @ X13 @ X14 )
                      = X8 )
                    & ( ( cP @ X11 @ X12 )
                      = X7 )
                    & ( ( cP @ X9 @ X10 )
                      = X6 ) )
                | ( ( c0 = X6 )
                  & ( X7 = X8 ) )
                | ( ( X6 = X8 )
                  & ( c0 = X7 ) ) )
             => ( X5 @ X6 @ X7 @ X8 ) )
          & $true )
       => ( X5 @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cS_INCL_LEM5_pme) ).

thf(f447,plain,
    ( ( $false
      = ( sK1
        @ ( sK3
          @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
        @ ( sK3
          @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
        @ ( sK3
          @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) ) ) )
    | ~ spl0_3 ),
    inference(equality_resolution,[],[f293]) ).

thf(f293,plain,
    ( ! [X0: iS] :
        ( ( ( sK3
            @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
         != X0 )
        | ( $false
          = ( sK1
            @ ( sK3
              @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
            @ ( sK3
              @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
            @ X0 ) ) )
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f292]) ).

thf(f292,plain,
    ( spl0_3
  <=> ! [X0: iS] :
        ( ( ( sK3
            @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
         != X0 )
        | ( $false
          = ( sK1
            @ ( sK3
              @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
            @ ( sK3
              @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
            @ X0 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

thf(f446,plain,
    ( spl0_5
    | spl0_4
    | ~ spl0_6 ),
    inference(avatar_split_clause,[],[f445,f302,f295,f299]) ).

thf(f299,plain,
    ( spl0_5
  <=> ! [X1: iS] :
        ( $true
        = ( sK1 @ X1 @ X1 @ X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

thf(f302,plain,
    ( spl0_6
  <=> ! [X2: iS] :
        ( ( $false
          = ( sK1
            @ ( sK2
              @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
            @ ( sK2
              @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
            @ X2 ) )
        | ( ( sK2
            @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
         != X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

thf(f445,plain,
    ( ! [X0: iS] :
        ( $true
        = ( sK1 @ X0 @ X0 @ X0 ) )
    | spl0_4
    | ~ spl0_6 ),
    inference(subsumption_resolution,[],[f443,f296]) ).

thf(f443,plain,
    ( ! [X0: iS] :
        ( ( $true
          = ( sK1 @ X0 @ X0 @ X0 ) )
        | ( $false
          = ( sK1 @ c0 @ c0 @ c0 ) ) )
    | ~ spl0_6 ),
    inference(trivial_inequality_removal,[],[f442]) ).

thf(f442,plain,
    ( ! [X0: iS] :
        ( ( $false
          = ( sK1 @ c0 @ c0 @ c0 ) )
        | ( $true
          = ( sK1 @ X0 @ X0 @ X0 ) )
        | ( ( sK2
            @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
         != ( sK2
            @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) ) ) )
    | ~ spl0_6 ),
    inference(beta_eta_normalization,[],[f441]) ).

thf(f441,plain,
    ( ! [X0: iS] :
        ( ( $true
          = ( sK1
            @ ( ^ [Y0: iS] : Y0
              @ X0 )
            @ ( ^ [Y0: iS] : Y0
              @ X0 )
            @ X0 ) )
        | ( ( sK2
            @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
         != ( ^ [Y0: iS] : Y0
            @ ( sK2
              @ ^ [Y0: iS] :
                  ( sK1
                  @ ( ^ [Y1: iS] : Y1
                    @ Y0 )
                  @ ( ^ [Y1: iS] : Y1
                    @ Y0 )
                  @ Y0 ) ) ) )
        | ( $false
          = ( sK1
            @ ( ^ [Y0: iS] : Y0
              @ c0 )
            @ ( ^ [Y0: iS] : Y0
              @ c0 )
            @ c0 ) ) )
    | ~ spl0_6 ),
    inference(trivial_inequality_removal,[],[f440]) ).

thf(f440,plain,
    ( ! [X0: iS] :
        ( ( ( ^ [Y0: iS] : Y0 )
         != ( ^ [Y0: iS] : Y0 ) )
        | ( ( sK2
            @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
         != ( ^ [Y0: iS] : Y0
            @ ( sK2
              @ ^ [Y0: iS] :
                  ( sK1
                  @ ( ^ [Y1: iS] : Y1
                    @ Y0 )
                  @ ( ^ [Y1: iS] : Y1
                    @ Y0 )
                  @ Y0 ) ) ) )
        | ( $false
          = ( sK1
            @ ( ^ [Y0: iS] : Y0
              @ c0 )
            @ ( ^ [Y0: iS] : Y0
              @ c0 )
            @ c0 ) )
        | ( $true
          = ( sK1
            @ ( ^ [Y0: iS] : Y0
              @ X0 )
            @ ( ^ [Y0: iS] : Y0
              @ X0 )
            @ X0 ) ) )
    | ~ spl0_6 ),
    inference(duplicate_literal_removal,[],[f438]) ).

thf(f438,plain,
    ( ! [X0: iS] :
        ( ( ( ^ [Y0: iS] : Y0 )
         != ( ^ [Y0: iS] : Y0 ) )
        | ( $false
          = ( sK1
            @ ( ^ [Y0: iS] : Y0
              @ c0 )
            @ ( ^ [Y0: iS] : Y0
              @ c0 )
            @ c0 ) )
        | ( $true
          = ( sK1
            @ ( ^ [Y0: iS] : Y0
              @ X0 )
            @ ( ^ [Y0: iS] : Y0
              @ X0 )
            @ X0 ) )
        | ( ( sK2
            @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
         != ( ^ [Y0: iS] : Y0
            @ ( sK2
              @ ^ [Y0: iS] :
                  ( sK1
                  @ ( ^ [Y1: iS] : Y1
                    @ Y0 )
                  @ ( ^ [Y1: iS] : Y1
                    @ Y0 )
                  @ Y0 ) ) ) )
        | ( ( ^ [Y0: iS] : Y0 )
         != ( ^ [Y0: iS] : Y0 ) ) )
    | ~ spl0_6 ),
    inference(equality_resolution,[],[f429]) ).

thf(f429,plain,
    ( ! [X2: iS,X0: iS > iS,X1: iS > iS] :
        ( ( ( sK2
            @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
         != ( X1
            @ ( sK2
              @ ^ [Y0: iS] : ( sK1 @ ( X1 @ Y0 ) @ ( X0 @ Y0 ) @ Y0 ) ) ) )
        | ( $true
          = ( sK1 @ ( X1 @ X2 ) @ ( X0 @ X2 ) @ X2 ) )
        | ( $false
          = ( sK1 @ ( X1 @ c0 ) @ ( X0 @ c0 ) @ c0 ) )
        | ( ( ^ [Y0: iS] : Y0 )
         != X1 )
        | ( ( ^ [Y0: iS] : Y0 )
         != X0 )
        | ( ( sK2
            @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
         != ( X0
            @ ( sK2
              @ ^ [Y0: iS] : ( sK1 @ ( X1 @ Y0 ) @ ( X0 @ Y0 ) @ Y0 ) ) ) ) )
    | ~ spl0_6 ),
    inference(beta_eta_normalization,[],[f428]) ).

thf(f428,plain,
    ( ! [X2: iS,X0: iS > iS,X1: iS > iS] :
        ( ( ( sK2
            @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
         != ( X0
            @ ( sK2
              @ ^ [Y0: iS] :
                  ( sK1 @ ( X1 @ Y0 ) @ ( X0 @ Y0 )
                  @ ( ^ [Y1: iS] : Y1
                    @ Y0 ) ) ) ) )
        | ( ( ^ [Y0: iS] : ( X0 @ Y0 ) )
         != ( ^ [Y0: iS] : Y0 ) )
        | ( ( ^ [Y0: iS] :
                ( sK1 @ ( X1 @ Y0 ) @ ( X0 @ Y0 )
                @ ( ^ [Y1: iS] : Y1
                  @ Y0 ) )
            @ c0 )
          = $false )
        | ( ( sK2
            @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
         != ( X1
            @ ( sK2
              @ ^ [Y0: iS] :
                  ( sK1 @ ( X1 @ Y0 ) @ ( X0 @ Y0 )
                  @ ( ^ [Y1: iS] : Y1
                    @ Y0 ) ) ) ) )
        | ( $true
          = ( ^ [Y0: iS] :
                ( sK1 @ ( X1 @ Y0 ) @ ( X0 @ Y0 )
                @ ( ^ [Y1: iS] : Y1
                  @ Y0 ) )
            @ X2 ) )
        | ( ( ^ [Y0: iS] : Y0 )
         != ( ^ [Y0: iS] : ( X1 @ Y0 ) ) ) )
    | ~ spl0_6 ),
    inference(trivial_inequality_removal,[],[f423]) ).

thf(f423,plain,
    ( ! [X2: iS,X0: iS > iS,X1: iS > iS] :
        ( ( ( ^ [Y0: iS] : ( X0 @ Y0 ) )
         != ( ^ [Y0: iS] : Y0 ) )
        | ( ( sK2
            @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
         != ( X1
            @ ( sK2
              @ ^ [Y0: iS] :
                  ( sK1 @ ( X1 @ Y0 ) @ ( X0 @ Y0 )
                  @ ( ^ [Y1: iS] : Y1
                    @ Y0 ) ) ) ) )
        | ( ( ^ [Y0: iS] :
                ( sK1 @ ( X1 @ Y0 ) @ ( X0 @ Y0 )
                @ ( ^ [Y1: iS] : Y1
                  @ Y0 ) )
            @ c0 )
          = $false )
        | ( ( ^ [Y0: iS] : Y0 )
         != ( ^ [Y0: iS] : ( X1 @ Y0 ) ) )
        | ( ( sK2
            @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
         != ( X0
            @ ( sK2
              @ ^ [Y0: iS] :
                  ( sK1 @ ( X1 @ Y0 ) @ ( X0 @ Y0 )
                  @ ( ^ [Y1: iS] : Y1
                    @ Y0 ) ) ) ) )
        | ( $true = $false )
        | ( $true
          = ( ^ [Y0: iS] :
                ( sK1 @ ( X1 @ Y0 ) @ ( X0 @ Y0 )
                @ ( ^ [Y1: iS] : Y1
                  @ Y0 ) )
            @ X2 ) ) )
    | ~ spl0_6 ),
    inference(constrained_superposition,[],[f65,f415]) ).

thf(f415,plain,
    ( ( ( sK1
        @ ( sK2
          @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
        @ ( sK2
          @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
        @ ( sK2
          @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) ) )
      = $false )
    | ~ spl0_6 ),
    inference(equality_resolution,[],[f303]) ).

thf(f303,plain,
    ( ! [X2: iS] :
        ( ( ( sK2
            @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
         != X2 )
        | ( $false
          = ( sK1
            @ ( sK2
              @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
            @ ( sK2
              @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
            @ X2 ) ) )
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f302]) ).

thf(f65,plain,
    ! [X2: iS,X1: iS > $o] :
      ( ( $true
        = ( X1 @ ( sK2 @ X1 ) ) )
      | ( $false
        = ( X1 @ c0 ) )
      | ( $true
        = ( X1 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f64]) ).

thf(f414,plain,
    ( ~ spl0_1
    | ~ spl0_5 ),
    inference(avatar_contradiction_clause,[],[f413]) ).

thf(f413,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_5 ),
    inference(trivial_inequality_removal,[],[f402]) ).

thf(f402,plain,
    ( ( $true = $false )
    | ~ spl0_1
    | ~ spl0_5 ),
    inference(superposition,[],[f300,f192]) ).

thf(f192,plain,
    ( ( $false
      = ( sK1 @ y @ y @ y ) )
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f190]) ).

thf(f190,plain,
    ( spl0_1
  <=> ( $false
      = ( sK1 @ y @ y @ y ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

thf(f300,plain,
    ( ! [X1: iS] :
        ( $true
        = ( sK1 @ X1 @ X1 @ X1 ) )
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f299]) ).

thf(f362,plain,
    ~ spl0_4,
    inference(avatar_contradiction_clause,[],[f361]) ).

thf(f361,plain,
    ( $false
    | ~ spl0_4 ),
    inference(trivial_inequality_removal,[],[f325]) ).

thf(f325,plain,
    ( ( $true = $false )
    | ( c0 != c0 )
    | ~ spl0_4 ),
    inference(superposition,[],[f113,f297]) ).

thf(f297,plain,
    ( ( $false
      = ( sK1 @ c0 @ c0 @ c0 ) )
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f295]) ).

thf(f113,plain,
    ! [X0: iS,X1: iS] :
      ( ( $true
        = ( sK1 @ X0 @ c0 @ X1 ) )
      | ( X0 != X1 ) ),
    inference(equality_resolution,[],[f51]) ).

thf(f51,plain,
    ! [X2: iS,X3: iS,X1: iS] :
      ( ( c0 != X1 )
      | ( $true
        = ( sK1 @ X3 @ X1 @ X2 ) )
      | ( X2 != X3 ) ),
    inference(equality_proxy_clausification,[],[f50]) ).

thf(f50,plain,
    ! [X2: iS,X3: iS,X1: iS] :
      ( ( $false
        = ( c0 = X1 ) )
      | ( X2 != X3 )
      | ( $true
        = ( sK1 @ X3 @ X1 @ X2 ) ) ),
    inference(equality_proxy_clausification,[],[f49]) ).

thf(f49,plain,
    ! [X2: iS,X3: iS,X1: iS] :
      ( ( $false
        = ( X3 = X2 ) )
      | ( $true
        = ( sK1 @ X3 @ X1 @ X2 ) )
      | ( $false
        = ( c0 = X1 ) ) ),
    inference(binary_proxy_clausification,[],[f45]) ).

thf(f45,plain,
    ! [X2: iS,X3: iS,X1: iS] :
      ( ( $false
        = ( ( c0 = X1 )
          & ( X3 = X2 ) ) )
      | ( $true
        = ( sK1 @ X3 @ X1 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f24]) ).

thf(f24,plain,
    ! [X2: iS,X3: iS,X1: iS] :
      ( ( $true
        = ( sK1 @ X3 @ X1 @ X2 ) )
      | ( $false
        = ( ( ( c0 = X1 )
            & ( X3 = X2 ) )
          | ( ( X2 = X1 )
            & ( c0 = X3 ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f22]) ).

thf(f22,plain,
    ! [X2: iS,X3: iS,X1: iS] :
      ( ( ( ( ( c0 = X1 )
            & ( X3 = X2 ) )
          | ( ( X2 = X1 )
            & ( c0 = X3 ) )
          | ( ?? @ iS
            @ ^ [Y0: iS] :
                ( ?? @ iS
                @ ^ [Y1: iS] :
                    ( ?? @ iS
                    @ ^ [Y2: iS] :
                        ( ?? @ iS
                        @ ^ [Y3: iS] :
                            ( ?? @ iS
                            @ ^ [Y4: iS] :
                                ( ?? @ iS
                                @ ^ [Y5: iS] :
                                    ( ( ( cP @ Y3 @ Y4 )
                                      = X3 )
                                    & ( ( cP @ Y1 @ Y5 )
                                      = X1 )
                                    & ( ( cP @ Y2 @ Y0 )
                                      = X2 )
                                    & ( sK1 @ Y4 @ Y5 @ Y0 )
                                    & ( sK1 @ Y3 @ Y1 @ Y2 ) ) ) ) ) ) ) ) )
        = $false )
      | ( $true
        = ( sK1 @ X3 @ X1 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f21]) ).

thf(f21,plain,
    ! [X2: iS,X3: iS,X1: iS] :
      ( $true
      = ( ( ( ( c0 = X1 )
            & ( X3 = X2 ) )
          | ( ( X2 = X1 )
            & ( c0 = X3 ) )
          | ( ?? @ iS
            @ ^ [Y0: iS] :
                ( ?? @ iS
                @ ^ [Y1: iS] :
                    ( ?? @ iS
                    @ ^ [Y2: iS] :
                        ( ?? @ iS
                        @ ^ [Y3: iS] :
                            ( ?? @ iS
                            @ ^ [Y4: iS] :
                                ( ?? @ iS
                                @ ^ [Y5: iS] :
                                    ( ( ( cP @ Y3 @ Y4 )
                                      = X3 )
                                    & ( ( cP @ Y1 @ Y5 )
                                      = X1 )
                                    & ( ( cP @ Y2 @ Y0 )
                                      = X2 )
                                    & ( sK1 @ Y4 @ Y5 @ Y0 )
                                    & ( sK1 @ Y3 @ Y1 @ Y2 ) ) ) ) ) ) ) ) )
       => ( sK1 @ X3 @ X1 @ X2 ) ) ),
    inference(beta_eta_normalization,[],[f20]) ).

thf(f20,plain,
    ! [X2: iS,X3: iS,X1: iS] :
      ( $true
      = ( ^ [Y0: iS] :
            ( ( ( ( c0 = X1 )
                & ( Y0 = X2 ) )
              | ( ( X2 = X1 )
                & ( c0 = Y0 ) )
              | ( ?? @ iS
                @ ^ [Y1: iS] :
                    ( ?? @ iS
                    @ ^ [Y2: iS] :
                        ( ?? @ iS
                        @ ^ [Y3: iS] :
                            ( ?? @ iS
                            @ ^ [Y4: iS] :
                                ( ?? @ iS
                                @ ^ [Y5: iS] :
                                    ( ?? @ iS
                                    @ ^ [Y6: iS] :
                                        ( ( ( cP @ Y4 @ Y5 )
                                          = Y0 )
                                        & ( ( cP @ Y2 @ Y6 )
                                          = X1 )
                                        & ( ( cP @ Y3 @ Y1 )
                                          = X2 )
                                        & ( sK1 @ Y5 @ Y6 @ Y1 )
                                        & ( sK1 @ Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
           => ( sK1 @ Y0 @ X1 @ X2 ) )
        @ X3 ) ),
    inference(pi_clausification,[],[f19]) ).

thf(f19,plain,
    ! [X2: iS,X1: iS] :
      ( $true
      = ( !! @ iS
        @ ^ [Y0: iS] :
            ( ( ( ( c0 = X1 )
                & ( Y0 = X2 ) )
              | ( ( X2 = X1 )
                & ( c0 = Y0 ) )
              | ( ?? @ iS
                @ ^ [Y1: iS] :
                    ( ?? @ iS
                    @ ^ [Y2: iS] :
                        ( ?? @ iS
                        @ ^ [Y3: iS] :
                            ( ?? @ iS
                            @ ^ [Y4: iS] :
                                ( ?? @ iS
                                @ ^ [Y5: iS] :
                                    ( ?? @ iS
                                    @ ^ [Y6: iS] :
                                        ( ( ( cP @ Y4 @ Y5 )
                                          = Y0 )
                                        & ( ( cP @ Y2 @ Y6 )
                                          = X1 )
                                        & ( ( cP @ Y3 @ Y1 )
                                          = X2 )
                                        & ( sK1 @ Y5 @ Y6 @ Y1 )
                                        & ( sK1 @ Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
           => ( sK1 @ Y0 @ X1 @ X2 ) ) ) ),
    inference(beta_eta_normalization,[],[f18]) ).

thf(f18,plain,
    ! [X2: iS,X1: iS] :
      ( $true
      = ( ^ [Y0: iS] :
            ( !! @ iS
            @ ^ [Y1: iS] :
                ( ( ( ( c0 = X1 )
                    & ( Y1 = Y0 ) )
                  | ( ( Y0 = X1 )
                    & ( c0 = Y1 ) )
                  | ( ?? @ iS
                    @ ^ [Y2: iS] :
                        ( ?? @ iS
                        @ ^ [Y3: iS] :
                            ( ?? @ iS
                            @ ^ [Y4: iS] :
                                ( ?? @ iS
                                @ ^ [Y5: iS] :
                                    ( ?? @ iS
                                    @ ^ [Y6: iS] :
                                        ( ?? @ iS
                                        @ ^ [Y7: iS] :
                                            ( ( ( cP @ Y5 @ Y6 )
                                              = Y1 )
                                            & ( ( cP @ Y3 @ Y7 )
                                              = X1 )
                                            & ( ( cP @ Y4 @ Y2 )
                                              = Y0 )
                                            & ( sK1 @ Y6 @ Y7 @ Y2 )
                                            & ( sK1 @ Y5 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
               => ( sK1 @ Y1 @ X1 @ Y0 ) ) )
        @ X2 ) ),
    inference(pi_clausification,[],[f17]) ).

thf(f17,plain,
    ! [X1: iS] :
      ( $true
      = ( !! @ iS
        @ ^ [Y0: iS] :
            ( !! @ iS
            @ ^ [Y1: iS] :
                ( ( ( ( c0 = X1 )
                    & ( Y1 = Y0 ) )
                  | ( ( Y0 = X1 )
                    & ( c0 = Y1 ) )
                  | ( ?? @ iS
                    @ ^ [Y2: iS] :
                        ( ?? @ iS
                        @ ^ [Y3: iS] :
                            ( ?? @ iS
                            @ ^ [Y4: iS] :
                                ( ?? @ iS
                                @ ^ [Y5: iS] :
                                    ( ?? @ iS
                                    @ ^ [Y6: iS] :
                                        ( ?? @ iS
                                        @ ^ [Y7: iS] :
                                            ( ( ( cP @ Y5 @ Y6 )
                                              = Y1 )
                                            & ( ( cP @ Y3 @ Y7 )
                                              = X1 )
                                            & ( ( cP @ Y4 @ Y2 )
                                              = Y0 )
                                            & ( sK1 @ Y6 @ Y7 @ Y2 )
                                            & ( sK1 @ Y5 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
               => ( sK1 @ Y1 @ X1 @ Y0 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f16]) ).

thf(f16,plain,
    ! [X1: iS] :
      ( ( ^ [Y0: iS] :
            ( !! @ iS
            @ ^ [Y1: iS] :
                ( !! @ iS
                @ ^ [Y2: iS] :
                    ( ( ( ( c0 = Y0 )
                        & ( Y2 = Y1 ) )
                      | ( ( Y1 = Y0 )
                        & ( c0 = Y2 ) )
                      | ( ?? @ iS
                        @ ^ [Y3: iS] :
                            ( ?? @ iS
                            @ ^ [Y4: iS] :
                                ( ?? @ iS
                                @ ^ [Y5: iS] :
                                    ( ?? @ iS
                                    @ ^ [Y6: iS] :
                                        ( ?? @ iS
                                        @ ^ [Y7: iS] :
                                            ( ?? @ iS
                                            @ ^ [Y8: iS] :
                                                ( ( ( cP @ Y6 @ Y7 )
                                                  = Y2 )
                                                & ( ( cP @ Y4 @ Y8 )
                                                  = Y0 )
                                                & ( ( cP @ Y5 @ Y3 )
                                                  = Y1 )
                                                & ( sK1 @ Y7 @ Y8 @ Y3 )
                                                & ( sK1 @ Y6 @ Y4 @ Y5 ) ) ) ) ) ) ) ) )
                   => ( sK1 @ Y2 @ Y0 @ Y1 ) ) ) )
        @ X1 )
      = $true ),
    inference(pi_clausification,[],[f15]) ).

thf(f15,plain,
    ( $true
    = ( !! @ iS
      @ ^ [Y0: iS] :
          ( !! @ iS
          @ ^ [Y1: iS] :
              ( !! @ iS
              @ ^ [Y2: iS] :
                  ( ( ( ( c0 = Y0 )
                      & ( Y2 = Y1 ) )
                    | ( ( Y1 = Y0 )
                      & ( c0 = Y2 ) )
                    | ( ?? @ iS
                      @ ^ [Y3: iS] :
                          ( ?? @ iS
                          @ ^ [Y4: iS] :
                              ( ?? @ iS
                              @ ^ [Y5: iS] :
                                  ( ?? @ iS
                                  @ ^ [Y6: iS] :
                                      ( ?? @ iS
                                      @ ^ [Y7: iS] :
                                          ( ?? @ iS
                                          @ ^ [Y8: iS] :
                                              ( ( ( cP @ Y6 @ Y7 )
                                                = Y2 )
                                              & ( ( cP @ Y4 @ Y8 )
                                                = Y0 )
                                              & ( ( cP @ Y5 @ Y3 )
                                                = Y1 )
                                              & ( sK1 @ Y7 @ Y8 @ Y3 )
                                              & ( sK1 @ Y6 @ Y4 @ Y5 ) ) ) ) ) ) ) ) )
                 => ( sK1 @ Y2 @ Y0 @ Y1 ) ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f13]) ).

thf(f13,plain,
    ( $false
    = ( ( !! @ iS
        @ ^ [Y0: iS] :
            ( !! @ iS
            @ ^ [Y1: iS] :
                ( !! @ iS
                @ ^ [Y2: iS] :
                    ( ( ( ( c0 = Y0 )
                        & ( Y2 = Y1 ) )
                      | ( ( Y1 = Y0 )
                        & ( c0 = Y2 ) )
                      | ( ?? @ iS
                        @ ^ [Y3: iS] :
                            ( ?? @ iS
                            @ ^ [Y4: iS] :
                                ( ?? @ iS
                                @ ^ [Y5: iS] :
                                    ( ?? @ iS
                                    @ ^ [Y6: iS] :
                                        ( ?? @ iS
                                        @ ^ [Y7: iS] :
                                            ( ?? @ iS
                                            @ ^ [Y8: iS] :
                                                ( ( ( cP @ Y6 @ Y7 )
                                                  = Y2 )
                                                & ( ( cP @ Y4 @ Y8 )
                                                  = Y0 )
                                                & ( ( cP @ Y5 @ Y3 )
                                                  = Y1 )
                                                & ( sK1 @ Y7 @ Y8 @ Y3 )
                                                & ( sK1 @ Y6 @ Y4 @ Y5 ) ) ) ) ) ) ) ) )
                   => ( sK1 @ Y2 @ Y0 @ Y1 ) ) ) ) )
     => ( sK1 @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ),
    inference(beta_eta_normalization,[],[f12]) ).

thf(f12,plain,
    ( $false
    = ( ^ [Y0: iS > iS > iS > $o] :
          ( ( !! @ iS
            @ ^ [Y1: iS] :
                ( !! @ iS
                @ ^ [Y2: iS] :
                    ( !! @ iS
                    @ ^ [Y3: iS] :
                        ( ( ( ( c0 = Y1 )
                            & ( Y3 = Y2 ) )
                          | ( ( Y2 = Y1 )
                            & ( c0 = Y3 ) )
                          | ( ?? @ iS
                            @ ^ [Y4: iS] :
                                ( ?? @ iS
                                @ ^ [Y5: iS] :
                                    ( ?? @ iS
                                    @ ^ [Y6: iS] :
                                        ( ?? @ iS
                                        @ ^ [Y7: iS] :
                                            ( ?? @ iS
                                            @ ^ [Y8: iS] :
                                                ( ?? @ iS
                                                @ ^ [Y9: iS] :
                                                    ( ( ( cP @ Y7 @ Y8 )
                                                      = Y3 )
                                                    & ( ( cP @ Y5 @ Y9 )
                                                      = Y1 )
                                                    & ( ( cP @ Y6 @ Y4 )
                                                      = Y2 )
                                                    & ( Y0 @ Y8 @ Y9 @ Y4 )
                                                    & ( Y0 @ Y7 @ Y5 @ Y6 ) ) ) ) ) ) ) ) )
                       => ( Y0 @ Y3 @ Y1 @ Y2 ) ) ) ) )
         => ( Y0 @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) )
      @ sK1 ) ),
    inference(sigma_clausification,[],[f10]) ).

thf(f10,plain,
    ( $false
    = ( !! @ ( iS > iS > iS > $o )
      @ ^ [Y0: iS > iS > iS > $o] :
          ( ( !! @ iS
            @ ^ [Y1: iS] :
                ( !! @ iS
                @ ^ [Y2: iS] :
                    ( !! @ iS
                    @ ^ [Y3: iS] :
                        ( ( ( ( c0 = Y1 )
                            & ( Y3 = Y2 ) )
                          | ( ( Y2 = Y1 )
                            & ( c0 = Y3 ) )
                          | ( ?? @ iS
                            @ ^ [Y4: iS] :
                                ( ?? @ iS
                                @ ^ [Y5: iS] :
                                    ( ?? @ iS
                                    @ ^ [Y6: iS] :
                                        ( ?? @ iS
                                        @ ^ [Y7: iS] :
                                            ( ?? @ iS
                                            @ ^ [Y8: iS] :
                                                ( ?? @ iS
                                                @ ^ [Y9: iS] :
                                                    ( ( ( cP @ Y7 @ Y8 )
                                                      = Y3 )
                                                    & ( ( cP @ Y5 @ Y9 )
                                                      = Y1 )
                                                    & ( ( cP @ Y6 @ Y4 )
                                                      = Y2 )
                                                    & ( Y0 @ Y8 @ Y9 @ Y4 )
                                                    & ( Y0 @ Y7 @ Y5 @ Y6 ) ) ) ) ) ) ) ) )
                       => ( Y0 @ Y3 @ Y1 @ Y2 ) ) ) ) )
         => ( Y0 @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ) ),
    inference(binary_proxy_clausification,[],[f9]) ).

thf(f304,plain,
    ( spl0_3
    | spl0_4
    | spl0_5
    | spl0_6 ),
    inference(avatar_split_clause,[],[f289,f302,f299,f295,f292]) ).

thf(f289,plain,
    ! [X2: iS,X0: iS,X1: iS] :
      ( ( $false
        = ( sK1 @ c0 @ c0 @ c0 ) )
      | ( ( sK3
          @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
       != X0 )
      | ( $false
        = ( sK1
          @ ( sK2
            @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
          @ ( sK2
            @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
          @ X2 ) )
      | ( $true
        = ( sK1 @ X1 @ X1 @ X1 ) )
      | ( $false
        = ( sK1
          @ ( sK3
            @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
          @ ( sK3
            @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
          @ X0 ) )
      | ( ( sK2
          @ ^ [Y0: iS] : ( sK1 @ Y0 @ Y0 @ Y0 ) )
       != X2 ) ),
    inference(beta_eta_normalization,[],[f287]) ).

thf(f287,plain,
    ! [X2: iS,X0: iS,X1: iS] :
      ( ( ( sK1
          @ ( sK3
            @ ^ [Y0: iS] :
                ( sK1
                @ ( ^ [Y1: iS] : Y1
                  @ Y0 )
                @ Y0
                @ Y0 ) )
          @ ( sK3
            @ ^ [Y0: iS] :
                ( sK1
                @ ( ^ [Y1: iS] : Y1
                  @ Y0 )
                @ Y0
                @ Y0 ) )
          @ X0 )
        = $false )
      | ( $false
        = ( sK1
          @ ( sK2
            @ ^ [Y0: iS] :
                ( sK1
                @ ( ^ [Y1: iS] : Y1
                  @ Y0 )
                @ Y0
                @ Y0 ) )
          @ ( sK2
            @ ^ [Y0: iS] :
                ( sK1
                @ ( ^ [Y1: iS] : Y1
                  @ Y0 )
                @ Y0
                @ Y0 ) )
          @ X2 ) )
      | ( $true
        = ( sK1
          @ ( ^ [Y0: iS] : Y0
            @ X1 )
          @ X1
          @ X1 ) )
      | ( $false
        = ( sK1
          @ ( ^ [Y0: iS] : Y0
            @ c0 )
          @ c0
          @ c0 ) )
      | ( ( sK2
          @ ^ [Y0: iS] :
              ( sK1
              @ ( ^ [Y1: iS] : Y1
                @ Y0 )
              @ Y0
              @ Y0 ) )
       != X2 )
      | ( ( sK3
          @ ^ [Y0: iS] :
              ( sK1
              @ ( ^ [Y1: iS] : Y1
                @ Y0 )
              @ Y0
              @ Y0 ) )
       != X0 ) ),
    inference(equality_resolution,[],[f286]) ).

thf(f286,plain,
    ! [X2: iS,X3: iS,X0: iS,X1: iS > iS,X4: iS,X5: iS] :
      ( ( ( cP @ X0 @ X4 )
       != ( X1
          @ ( cP
            @ ( sK3
              @ ^ [Y0: iS] : ( sK1 @ ( X1 @ Y0 ) @ Y0 @ Y0 ) )
            @ ( sK2
              @ ^ [Y0: iS] : ( sK1 @ ( X1 @ Y0 ) @ Y0 @ Y0 ) ) ) ) )
      | ( ( sK1 @ ( X1 @ c0 ) @ c0 @ c0 )
        = $false )
      | ( $false
        = ( sK1 @ X0
          @ ( sK3
            @ ^ [Y0: iS] : ( sK1 @ ( X1 @ Y0 ) @ Y0 @ Y0 ) )
          @ X2 ) )
      | ( $true
        = ( sK1 @ ( X1 @ X3 ) @ X3 @ X3 ) )
      | ( ( sK3
          @ ^ [Y0: iS] : ( sK1 @ ( X1 @ Y0 ) @ Y0 @ Y0 ) )
       != X2 )
      | ( ( sK1 @ X4
          @ ( sK2
            @ ^ [Y0: iS] : ( sK1 @ ( X1 @ Y0 ) @ Y0 @ Y0 ) )
          @ X5 )
        = $false )
      | ( ( sK2
          @ ^ [Y0: iS] : ( sK1 @ ( X1 @ Y0 ) @ Y0 @ Y0 ) )
       != X5 ) ),
    inference(beta_eta_normalization,[],[f283]) ).

thf(f283,plain,
    ! [X2: iS,X3: iS,X0: iS,X1: iS > iS,X4: iS,X5: iS] :
      ( ( $false
        = ( sK1 @ X0
          @ ( sK3
            @ ^ [Y0: iS] :
                ( sK1 @ ( X1 @ Y0 )
                @ ( ^ [Y1: iS] : Y1
                  @ Y0 )
                @ Y0 ) )
          @ X2 ) )
      | ( ( cP @ X0 @ X4 )
       != ( X1
          @ ( cP
            @ ( sK3
              @ ^ [Y0: iS] :
                  ( sK1 @ ( X1 @ Y0 )
                  @ ( ^ [Y1: iS] : Y1
                    @ Y0 )
                  @ Y0 ) )
            @ ( sK2
              @ ^ [Y0: iS] :
                  ( sK1 @ ( X1 @ Y0 )
                  @ ( ^ [Y1: iS] : Y1
                    @ Y0 )
                  @ Y0 ) ) ) ) )
      | ( $false
        = ( sK1 @ X4
          @ ( sK2
            @ ^ [Y0: iS] :
                ( sK1 @ ( X1 @ Y0 )
                @ ( ^ [Y1: iS] : Y1
                  @ Y0 )
                @ Y0 ) )
          @ X5 ) )
      | ( $false
        = ( sK1 @ ( X1 @ c0 )
          @ ( ^ [Y0: iS] : Y0
            @ c0 )
          @ c0 ) )
      | ( ( sK2
          @ ^ [Y0: iS] :
              ( sK1 @ ( X1 @ Y0 )
              @ ( ^ [Y1: iS] : Y1
                @ Y0 )
              @ Y0 ) )
       != X5 )
      | ( $true
        = ( sK1 @ ( X1 @ X3 )
          @ ( ^ [Y0: iS] : Y0
            @ X3 )
          @ X3 ) )
      | ( ( sK3
          @ ^ [Y0: iS] :
              ( sK1 @ ( X1 @ Y0 )
              @ ( ^ [Y1: iS] : Y1
                @ Y0 )
              @ Y0 ) )
       != X2 ) ),
    inference(equality_resolution,[],[f180]) ).

thf(f180,plain,
    ! [X2: iS > iS,X3: iS > iS,X0: iS,X1: iS,X8: iS,X6: iS,X7: iS,X4: iS,X5: iS] :
      ( ( ( cP @ X0 @ X1 )
       != ( X2
          @ ( cP
            @ ( sK3
              @ ^ [Y0: iS] : ( sK1 @ ( X3 @ Y0 ) @ ( X2 @ Y0 ) @ Y0 ) )
            @ ( sK2
              @ ^ [Y0: iS] : ( sK1 @ ( X3 @ Y0 ) @ ( X2 @ Y0 ) @ Y0 ) ) ) ) )
      | ( ( sK1 @ X4 @ X0 @ X7 )
        = $false )
      | ( ( sK3
          @ ^ [Y0: iS] : ( sK1 @ ( X3 @ Y0 ) @ ( X2 @ Y0 ) @ Y0 ) )
       != X7 )
      | ( $true
        = ( sK1 @ ( X3 @ X8 ) @ ( X2 @ X8 ) @ X8 ) )
      | ( ( X3
          @ ( cP
            @ ( sK3
              @ ^ [Y0: iS] : ( sK1 @ ( X3 @ Y0 ) @ ( X2 @ Y0 ) @ Y0 ) )
            @ ( sK2
              @ ^ [Y0: iS] : ( sK1 @ ( X3 @ Y0 ) @ ( X2 @ Y0 ) @ Y0 ) ) ) )
       != ( cP @ X4 @ X5 ) )
      | ( ( sK1 @ X5 @ X1 @ X6 )
        = $false )
      | ( ( sK2
          @ ^ [Y0: iS] : ( sK1 @ ( X3 @ Y0 ) @ ( X2 @ Y0 ) @ Y0 ) )
       != X6 )
      | ( ( sK1 @ ( X3 @ c0 ) @ ( X2 @ c0 ) @ c0 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f179]) ).

thf(f179,plain,
    ! [X2: iS > iS,X3: iS > iS,X0: iS,X1: iS,X8: iS,X6: iS,X7: iS,X4: iS,X5: iS] :
      ( ( ( cP @ X0 @ X1 )
       != ( X2
          @ ( cP
            @ ( sK3
              @ ^ [Y0: iS] :
                  ( sK1 @ ( X3 @ Y0 ) @ ( X2 @ Y0 )
                  @ ( ^ [Y1: iS] : Y1
                    @ Y0 ) ) )
            @ ( sK2
              @ ^ [Y0: iS] :
                  ( sK1 @ ( X3 @ Y0 ) @ ( X2 @ Y0 )
                  @ ( ^ [Y1: iS] : Y1
                    @ Y0 ) ) ) ) ) )
      | ( ( sK1 @ X4 @ X0 @ X7 )
        = $false )
      | ( ( X3
          @ ( cP
            @ ( sK3
              @ ^ [Y0: iS] :
                  ( sK1 @ ( X3 @ Y0 ) @ ( X2 @ Y0 )
                  @ ( ^ [Y1: iS] : Y1
                    @ Y0 ) ) )
            @ ( sK2
              @ ^ [Y0: iS] :
                  ( sK1 @ ( X3 @ Y0 ) @ ( X2 @ Y0 )
                  @ ( ^ [Y1: iS] : Y1
                    @ Y0 ) ) ) ) )
       != ( cP @ X4 @ X5 ) )
      | ( ( sK1 @ X5 @ X1 @ X6 )
        = $false )
      | ( ( sK3
          @ ^ [Y0: iS] :
              ( sK1 @ ( X3 @ Y0 ) @ ( X2 @ Y0 )
              @ ( ^ [Y1: iS] : Y1
                @ Y0 ) ) )
       != X7 )
      | ( $false
        = ( ^ [Y0: iS] :
              ( sK1 @ ( X3 @ Y0 ) @ ( X2 @ Y0 )
              @ ( ^ [Y1: iS] : Y1
                @ Y0 ) )
          @ c0 ) )
      | ( $true
        = ( ^ [Y0: iS] :
              ( sK1 @ ( X3 @ Y0 ) @ ( X2 @ Y0 )
              @ ( ^ [Y1: iS] : Y1
                @ Y0 ) )
          @ X8 ) )
      | ( ( sK2
          @ ^ [Y0: iS] :
              ( sK1 @ ( X3 @ Y0 ) @ ( X2 @ Y0 )
              @ ( ^ [Y1: iS] : Y1
                @ Y0 ) ) )
       != X6 ) ),
    inference(trivial_inequality_removal,[],[f174]) ).

thf(f174,plain,
    ! [X2: iS > iS,X3: iS > iS,X0: iS,X1: iS,X8: iS,X6: iS,X7: iS,X4: iS,X5: iS] :
      ( ( ( sK2
          @ ^ [Y0: iS] :
              ( sK1 @ ( X3 @ Y0 ) @ ( X2 @ Y0 )
              @ ( ^ [Y1: iS] : Y1
                @ Y0 ) ) )
       != X6 )
      | ( ( sK1 @ X5 @ X1 @ X6 )
        = $false )
      | ( ( cP @ X0 @ X1 )
       != ( X2
          @ ( cP
            @ ( sK3
              @ ^ [Y0: iS] :
                  ( sK1 @ ( X3 @ Y0 ) @ ( X2 @ Y0 )
                  @ ( ^ [Y1: iS] : Y1
                    @ Y0 ) ) )
            @ ( sK2
              @ ^ [Y0: iS] :
                  ( sK1 @ ( X3 @ Y0 ) @ ( X2 @ Y0 )
                  @ ( ^ [Y1: iS] : Y1
                    @ Y0 ) ) ) ) ) )
      | ( $true
        = ( ^ [Y0: iS] :
              ( sK1 @ ( X3 @ Y0 ) @ ( X2 @ Y0 )
              @ ( ^ [Y1: iS] : Y1
                @ Y0 ) )
          @ X8 ) )
      | ( $true = $false )
      | ( ( sK3
          @ ^ [Y0: iS] :
              ( sK1 @ ( X3 @ Y0 ) @ ( X2 @ Y0 )
              @ ( ^ [Y1: iS] : Y1
                @ Y0 ) ) )
       != X7 )
      | ( ( X3
          @ ( cP
            @ ( sK3
              @ ^ [Y0: iS] :
                  ( sK1 @ ( X3 @ Y0 ) @ ( X2 @ Y0 )
                  @ ( ^ [Y1: iS] : Y1
                    @ Y0 ) ) )
            @ ( sK2
              @ ^ [Y0: iS] :
                  ( sK1 @ ( X3 @ Y0 ) @ ( X2 @ Y0 )
                  @ ( ^ [Y1: iS] : Y1
                    @ Y0 ) ) ) ) )
       != ( cP @ X4 @ X5 ) )
      | ( $false
        = ( ^ [Y0: iS] :
              ( sK1 @ ( X3 @ Y0 ) @ ( X2 @ Y0 )
              @ ( ^ [Y1: iS] : Y1
                @ Y0 ) )
          @ c0 ) )
      | ( ( sK1 @ X4 @ X0 @ X7 )
        = $false ) ),
    inference(constrained_superposition,[],[f171,f63]) ).

thf(f63,plain,
    ! [X2: iS,X1: iS > $o] :
      ( ( ( X1 @ ( cP @ ( sK3 @ X1 ) @ ( sK2 @ X1 ) ) )
        = $false )
      | ( $false
        = ( X1 @ c0 ) )
      | ( $true
        = ( X1 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f62]) ).

thf(f171,plain,
    ! [X2: iS,X3: iS,X0: iS,X1: iS,X4: iS,X5: iS] :
      ( ( $true
        = ( sK1 @ ( cP @ X0 @ X3 ) @ ( cP @ X1 @ X4 ) @ ( cP @ X2 @ X5 ) ) )
      | ( $false
        = ( sK1 @ X3 @ X4 @ X5 ) )
      | ( $false
        = ( sK1 @ X0 @ X1 @ X2 ) ) ),
    inference(equality_resolution,[],[f170]) ).

thf(f170,plain,
    ! [X2: iS,X3: iS,X0: iS,X1: iS,X6: iS,X4: iS,X5: iS] :
      ( ( ( cP @ X0 @ X1 )
       != X2 )
      | ( $false
        = ( sK1 @ X5 @ X0 @ X6 ) )
      | ( $true
        = ( sK1 @ ( cP @ X5 @ X3 ) @ X2 @ ( cP @ X6 @ X4 ) ) )
      | ( $false
        = ( sK1 @ X3 @ X1 @ X4 ) ) ),
    inference(equality_resolution,[],[f169]) ).

thf(f169,plain,
    ! [X2: iS,X3: iS,X0: iS,X1: iS,X6: iS,X7: iS,X4: iS,X5: iS] :
      ( ( ( cP @ X2 @ X6 )
       != X5 )
      | ( ( cP @ X1 @ X7 )
       != X4 )
      | ( $false
        = ( sK1 @ X3 @ X7 @ X6 ) )
      | ( $false
        = ( sK1 @ X0 @ X1 @ X2 ) )
      | ( ( sK1 @ ( cP @ X0 @ X3 ) @ X4 @ X5 )
        = $true ) ),
    inference(equality_resolution,[],[f43]) ).

thf(f43,plain,
    ! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X9: iS,X7: iS,X4: iS,X5: iS] :
      ( ( ( cP @ X7 @ X8 )
       != X3 )
      | ( $false
        = ( sK1 @ X7 @ X5 @ X6 ) )
      | ( $true
        = ( sK1 @ X3 @ X1 @ X2 ) )
      | ( ( cP @ X6 @ X4 )
       != X2 )
      | ( $false
        = ( sK1 @ X8 @ X9 @ X4 ) )
      | ( ( cP @ X5 @ X9 )
       != X1 ) ),
    inference(equality_proxy_clausification,[],[f42]) ).

thf(f42,plain,
    ! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X9: iS,X7: iS,X4: iS,X5: iS] :
      ( ( $true
        = ( sK1 @ X3 @ X1 @ X2 ) )
      | ( ( cP @ X6 @ X4 )
       != X2 )
      | ( $false
        = ( sK1 @ X7 @ X5 @ X6 ) )
      | ( $false
        = ( sK1 @ X8 @ X9 @ X4 ) )
      | ( ( cP @ X7 @ X8 )
       != X3 )
      | ( $false
        = ( ( cP @ X5 @ X9 )
          = X1 ) ) ),
    inference(equality_proxy_clausification,[],[f41]) ).

thf(f41,plain,
    ! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X9: iS,X7: iS,X4: iS,X5: iS] :
      ( ( $false
        = ( ( cP @ X7 @ X8 )
          = X3 ) )
      | ( ( cP @ X6 @ X4 )
       != X2 )
      | ( $false
        = ( sK1 @ X7 @ X5 @ X6 ) )
      | ( $false
        = ( sK1 @ X8 @ X9 @ X4 ) )
      | ( $true
        = ( sK1 @ X3 @ X1 @ X2 ) )
      | ( $false
        = ( ( cP @ X5 @ X9 )
          = X1 ) ) ),
    inference(equality_proxy_clausification,[],[f40]) ).

thf(f40,plain,
    ! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X9: iS,X7: iS,X4: iS,X5: iS] :
      ( ( $false
        = ( sK1 @ X7 @ X5 @ X6 ) )
      | ( $true
        = ( sK1 @ X3 @ X1 @ X2 ) )
      | ( $false
        = ( ( cP @ X6 @ X4 )
          = X2 ) )
      | ( $false
        = ( ( cP @ X7 @ X8 )
          = X3 ) )
      | ( $false
        = ( ( cP @ X5 @ X9 )
          = X1 ) )
      | ( $false
        = ( sK1 @ X8 @ X9 @ X4 ) ) ),
    inference(binary_proxy_clausification,[],[f39]) ).

thf(f39,plain,
    ! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X9: iS,X7: iS,X4: iS,X5: iS] :
      ( ( $true
        = ( sK1 @ X3 @ X1 @ X2 ) )
      | ( $false
        = ( ( ( cP @ X7 @ X8 )
            = X3 )
          & ( ( cP @ X5 @ X9 )
            = X1 ) ) )
      | ( $false
        = ( sK1 @ X8 @ X9 @ X4 ) )
      | ( $false
        = ( ( cP @ X6 @ X4 )
          = X2 ) )
      | ( $false
        = ( sK1 @ X7 @ X5 @ X6 ) ) ),
    inference(binary_proxy_clausification,[],[f38]) ).

thf(f38,plain,
    ! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X9: iS,X7: iS,X4: iS,X5: iS] :
      ( ( $true
        = ( sK1 @ X3 @ X1 @ X2 ) )
      | ( ( ( ( cP @ X7 @ X8 )
            = X3 )
          & ( ( cP @ X5 @ X9 )
            = X1 )
          & ( ( cP @ X6 @ X4 )
            = X2 ) )
        = $false )
      | ( $false
        = ( sK1 @ X8 @ X9 @ X4 ) )
      | ( $false
        = ( sK1 @ X7 @ X5 @ X6 ) ) ),
    inference(binary_proxy_clausification,[],[f37]) ).

thf(f37,plain,
    ! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X9: iS,X7: iS,X4: iS,X5: iS] :
      ( ( $false
        = ( sK1 @ X7 @ X5 @ X6 ) )
      | ( $true
        = ( sK1 @ X3 @ X1 @ X2 ) )
      | ( $false
        = ( ( ( cP @ X7 @ X8 )
            = X3 )
          & ( ( cP @ X5 @ X9 )
            = X1 )
          & ( ( cP @ X6 @ X4 )
            = X2 )
          & ( sK1 @ X8 @ X9 @ X4 ) ) ) ),
    inference(binary_proxy_clausification,[],[f36]) ).

thf(f36,plain,
    ! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X9: iS,X7: iS,X4: iS,X5: iS] :
      ( ( $true
        = ( sK1 @ X3 @ X1 @ X2 ) )
      | ( ( ( ( cP @ X7 @ X8 )
            = X3 )
          & ( ( cP @ X5 @ X9 )
            = X1 )
          & ( ( cP @ X6 @ X4 )
            = X2 )
          & ( sK1 @ X8 @ X9 @ X4 )
          & ( sK1 @ X7 @ X5 @ X6 ) )
        = $false ) ),
    inference(beta_eta_normalization,[],[f35]) ).

thf(f35,plain,
    ! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X9: iS,X7: iS,X4: iS,X5: iS] :
      ( ( $true
        = ( sK1 @ X3 @ X1 @ X2 ) )
      | ( $false
        = ( ^ [Y0: iS] :
              ( ( ( cP @ X7 @ X8 )
                = X3 )
              & ( ( cP @ X5 @ Y0 )
                = X1 )
              & ( ( cP @ X6 @ X4 )
                = X2 )
              & ( sK1 @ X8 @ Y0 @ X4 )
              & ( sK1 @ X7 @ X5 @ X6 ) )
          @ X9 ) ) ),
    inference(pi_clausification,[],[f34]) ).

thf(f34,plain,
    ! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X7: iS,X4: iS,X5: iS] :
      ( ( $true
        = ( sK1 @ X3 @ X1 @ X2 ) )
      | ( $false
        = ( ?? @ iS
          @ ^ [Y0: iS] :
              ( ( ( cP @ X7 @ X8 )
                = X3 )
              & ( ( cP @ X5 @ Y0 )
                = X1 )
              & ( ( cP @ X6 @ X4 )
                = X2 )
              & ( sK1 @ X8 @ Y0 @ X4 )
              & ( sK1 @ X7 @ X5 @ X6 ) ) ) ) ),
    inference(beta_eta_normalization,[],[f33]) ).

thf(f33,plain,
    ! [X2: iS,X3: iS,X1: iS,X8: iS,X6: iS,X7: iS,X4: iS,X5: iS] :
      ( ( $true
        = ( sK1 @ X3 @ X1 @ X2 ) )
      | ( $false
        = ( ^ [Y0: iS] :
              ( ?? @ iS
              @ ^ [Y1: iS] :
                  ( ( ( cP @ X7 @ Y0 )
                    = X3 )
                  & ( ( cP @ X5 @ Y1 )
                    = X1 )
                  & ( ( cP @ X6 @ X4 )
                    = X2 )
                  & ( sK1 @ Y0 @ Y1 @ X4 )
                  & ( sK1 @ X7 @ X5 @ X6 ) ) )
          @ X8 ) ) ),
    inference(pi_clausification,[],[f32]) ).

thf(f32,plain,
    ! [X2: iS,X3: iS,X1: iS,X6: iS,X7: iS,X4: iS,X5: iS] :
      ( ( $true
        = ( sK1 @ X3 @ X1 @ X2 ) )
      | ( $false
        = ( ?? @ iS
          @ ^ [Y0: iS] :
              ( ?? @ iS
              @ ^ [Y1: iS] :
                  ( ( ( cP @ X7 @ Y0 )
                    = X3 )
                  & ( ( cP @ X5 @ Y1 )
                    = X1 )
                  & ( ( cP @ X6 @ X4 )
                    = X2 )
                  & ( sK1 @ Y0 @ Y1 @ X4 )
                  & ( sK1 @ X7 @ X5 @ X6 ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f31]) ).

thf(f31,plain,
    ! [X2: iS,X3: iS,X1: iS,X6: iS,X7: iS,X4: iS,X5: iS] :
      ( ( $true
        = ( sK1 @ X3 @ X1 @ X2 ) )
      | ( $false
        = ( ^ [Y0: iS] :
              ( ?? @ iS
              @ ^ [Y1: iS] :
                  ( ?? @ iS
                  @ ^ [Y2: iS] :
                      ( ( ( cP @ Y0 @ Y1 )
                        = X3 )
                      & ( ( cP @ X5 @ Y2 )
                        = X1 )
                      & ( ( cP @ X6 @ X4 )
                        = X2 )
                      & ( sK1 @ Y1 @ Y2 @ X4 )
                      & ( sK1 @ Y0 @ X5 @ X6 ) ) ) )
          @ X7 ) ) ),
    inference(pi_clausification,[],[f30]) ).

thf(f30,plain,
    ! [X2: iS,X3: iS,X1: iS,X6: iS,X4: iS,X5: iS] :
      ( ( $true
        = ( sK1 @ X3 @ X1 @ X2 ) )
      | ( $false
        = ( ?? @ iS
          @ ^ [Y0: iS] :
              ( ?? @ iS
              @ ^ [Y1: iS] :
                  ( ?? @ iS
                  @ ^ [Y2: iS] :
                      ( ( ( cP @ Y0 @ Y1 )
                        = X3 )
                      & ( ( cP @ X5 @ Y2 )
                        = X1 )
                      & ( ( cP @ X6 @ X4 )
                        = X2 )
                      & ( sK1 @ Y1 @ Y2 @ X4 )
                      & ( sK1 @ Y0 @ X5 @ X6 ) ) ) ) ) ) ),
    inference(beta_eta_normalization,[],[f29]) ).

thf(f29,plain,
    ! [X2: iS,X3: iS,X1: iS,X6: iS,X4: iS,X5: iS] :
      ( ( ( ^ [Y0: iS] :
              ( ?? @ iS
              @ ^ [Y1: iS] :
                  ( ?? @ iS
                  @ ^ [Y2: iS] :
                      ( ?? @ iS
                      @ ^ [Y3: iS] :
                          ( ( ( cP @ Y1 @ Y2 )
                            = X3 )
                          & ( ( cP @ X5 @ Y3 )
                            = X1 )
                          & ( ( cP @ Y0 @ X4 )
                            = X2 )
                          & ( sK1 @ Y2 @ Y3 @ X4 )
                          & ( sK1 @ Y1 @ X5 @ Y0 ) ) ) ) )
          @ X6 )
        = $false )
      | ( $true
        = ( sK1 @ X3 @ X1 @ X2 ) ) ),
    inference(pi_clausification,[],[f28]) ).

thf(f28,plain,
    ! [X2: iS,X3: iS,X1: iS,X4: iS,X5: iS] :
      ( ( $false
        = ( ?? @ iS
          @ ^ [Y0: iS] :
              ( ?? @ iS
              @ ^ [Y1: iS] :
                  ( ?? @ iS
                  @ ^ [Y2: iS] :
                      ( ?? @ iS
                      @ ^ [Y3: iS] :
                          ( ( ( cP @ Y1 @ Y2 )
                            = X3 )
                          & ( ( cP @ X5 @ Y3 )
                            = X1 )
                          & ( ( cP @ Y0 @ X4 )
                            = X2 )
                          & ( sK1 @ Y2 @ Y3 @ X4 )
                          & ( sK1 @ Y1 @ X5 @ Y0 ) ) ) ) ) ) )
      | ( $true
        = ( sK1 @ X3 @ X1 @ X2 ) ) ),
    inference(beta_eta_normalization,[],[f27]) ).

thf(f27,plain,
    ! [X2: iS,X3: iS,X1: iS,X4: iS,X5: iS] :
      ( ( $true
        = ( sK1 @ X3 @ X1 @ X2 ) )
      | ( $false
        = ( ^ [Y0: iS] :
              ( ?? @ iS
              @ ^ [Y1: iS] :
                  ( ?? @ iS
                  @ ^ [Y2: iS] :
                      ( ?? @ iS
                      @ ^ [Y3: iS] :
                          ( ?? @ iS
                          @ ^ [Y4: iS] :
                              ( ( ( cP @ Y2 @ Y3 )
                                = X3 )
                              & ( ( cP @ Y0 @ Y4 )
                                = X1 )
                              & ( ( cP @ Y1 @ X4 )
                                = X2 )
                              & ( sK1 @ Y3 @ Y4 @ X4 )
                              & ( sK1 @ Y2 @ Y0 @ Y1 ) ) ) ) ) )
          @ X5 ) ) ),
    inference(pi_clausification,[],[f26]) ).

thf(f26,plain,
    ! [X2: iS,X3: iS,X1: iS,X4: iS] :
      ( ( $false
        = ( ?? @ iS
          @ ^ [Y0: iS] :
              ( ?? @ iS
              @ ^ [Y1: iS] :
                  ( ?? @ iS
                  @ ^ [Y2: iS] :
                      ( ?? @ iS
                      @ ^ [Y3: iS] :
                          ( ?? @ iS
                          @ ^ [Y4: iS] :
                              ( ( ( cP @ Y2 @ Y3 )
                                = X3 )
                              & ( ( cP @ Y0 @ Y4 )
                                = X1 )
                              & ( ( cP @ Y1 @ X4 )
                                = X2 )
                              & ( sK1 @ Y3 @ Y4 @ X4 )
                              & ( sK1 @ Y2 @ Y0 @ Y1 ) ) ) ) ) ) ) )
      | ( $true
        = ( sK1 @ X3 @ X1 @ X2 ) ) ),
    inference(beta_eta_normalization,[],[f25]) ).

thf(f25,plain,
    ! [X2: iS,X3: iS,X1: iS,X4: iS] :
      ( ( $true
        = ( sK1 @ X3 @ X1 @ X2 ) )
      | ( $false
        = ( ^ [Y0: iS] :
              ( ?? @ iS
              @ ^ [Y1: iS] :
                  ( ?? @ iS
                  @ ^ [Y2: iS] :
                      ( ?? @ iS
                      @ ^ [Y3: iS] :
                          ( ?? @ iS
                          @ ^ [Y4: iS] :
                              ( ?? @ iS
                              @ ^ [Y5: iS] :
                                  ( ( ( cP @ Y3 @ Y4 )
                                    = X3 )
                                  & ( ( cP @ Y1 @ Y5 )
                                    = X1 )
                                  & ( ( cP @ Y2 @ Y0 )
                                    = X2 )
                                  & ( sK1 @ Y4 @ Y5 @ Y0 )
                                  & ( sK1 @ Y3 @ Y1 @ Y2 ) ) ) ) ) ) )
          @ X4 ) ) ),
    inference(pi_clausification,[],[f23]) ).

thf(f23,plain,
    ! [X2: iS,X3: iS,X1: iS] :
      ( ( $false
        = ( ?? @ iS
          @ ^ [Y0: iS] :
              ( ?? @ iS
              @ ^ [Y1: iS] :
                  ( ?? @ iS
                  @ ^ [Y2: iS] :
                      ( ?? @ iS
                      @ ^ [Y3: iS] :
                          ( ?? @ iS
                          @ ^ [Y4: iS] :
                              ( ?? @ iS
                              @ ^ [Y5: iS] :
                                  ( ( ( cP @ Y3 @ Y4 )
                                    = X3 )
                                  & ( ( cP @ Y1 @ Y5 )
                                    = X1 )
                                  & ( ( cP @ Y2 @ Y0 )
                                    = X2 )
                                  & ( sK1 @ Y4 @ Y5 @ Y0 )
                                  & ( sK1 @ Y3 @ Y1 @ Y2 ) ) ) ) ) ) ) ) )
      | ( $true
        = ( sK1 @ X3 @ X1 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f22]) ).

thf(f211,plain,
    ~ spl0_2,
    inference(avatar_contradiction_clause,[],[f210]) ).

thf(f210,plain,
    ( $false
    | ~ spl0_2 ),
    inference(trivial_inequality_removal,[],[f203]) ).

thf(f203,plain,
    ( ( $true = $false )
    | ( x != x )
    | ~ spl0_2 ),
    inference(superposition,[],[f94,f196]) ).

thf(f196,plain,
    ( ( $false
      = ( sK1 @ c0 @ x @ x ) )
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f194]) ).

thf(f194,plain,
    ( spl0_2
  <=> ( $false
      = ( sK1 @ c0 @ x @ x ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

thf(f94,plain,
    ! [X0: iS,X1: iS] :
      ( ( $true
        = ( sK1 @ c0 @ X0 @ X1 ) )
      | ( X0 != X1 ) ),
    inference(equality_resolution,[],[f48]) ).

thf(f48,plain,
    ! [X2: iS,X3: iS,X1: iS] :
      ( ( c0 != X3 )
      | ( $true
        = ( sK1 @ X3 @ X1 @ X2 ) )
      | ( X1 != X2 ) ),
    inference(equality_proxy_clausification,[],[f47]) ).

thf(f47,plain,
    ! [X2: iS,X3: iS,X1: iS] :
      ( ( $true
        = ( sK1 @ X3 @ X1 @ X2 ) )
      | ( $false
        = ( c0 = X3 ) )
      | ( X1 != X2 ) ),
    inference(equality_proxy_clausification,[],[f46]) ).

thf(f46,plain,
    ! [X2: iS,X3: iS,X1: iS] :
      ( ( $false
        = ( X2 = X1 ) )
      | ( $false
        = ( c0 = X3 ) )
      | ( $true
        = ( sK1 @ X3 @ X1 @ X2 ) ) ),
    inference(binary_proxy_clausification,[],[f44]) ).

thf(f44,plain,
    ! [X2: iS,X3: iS,X1: iS] :
      ( ( $true
        = ( sK1 @ X3 @ X1 @ X2 ) )
      | ( ( ( X2 = X1 )
          & ( c0 = X3 ) )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f24]) ).

thf(f198,plain,
    ( spl0_1
    | spl0_2 ),
    inference(avatar_split_clause,[],[f181,f194,f190]) ).

thf(f181,plain,
    ( ( $false
      = ( sK1 @ c0 @ x @ x ) )
    | ( $false
      = ( sK1 @ y @ y @ y ) ) ),
    inference(trivial_inequality_removal,[],[f173]) ).

thf(f173,plain,
    ( ( $true = $false )
    | ( $false
      = ( sK1 @ y @ y @ y ) )
    | ( $false
      = ( sK1 @ c0 @ x @ x ) ) ),
    inference(superposition,[],[f171,f14]) ).

thf(f14,plain,
    ( $false
    = ( sK1 @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ),
    inference(binary_proxy_clausification,[],[f13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SEV203^5 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.14  % 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
% 0.14/0.35  % Computer : n011.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sun May 19 18:54:23 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  This is a TH0_THM_EQU_NAR problem
% 0.14/0.36  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
% 0.14/0.38  % (31237)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.38  % (31238)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)
% 0.14/0.38  % (31240)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.38  % (31241)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)
% 0.14/0.38  % (31242)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)
% 0.14/0.38  % (31239)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)
% 0.14/0.38  % (31243)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.38  % (31244)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)
% 0.14/0.38  % (31240)Instruction limit reached!
% 0.14/0.38  % (31240)------------------------------
% 0.14/0.38  % (31240)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38  % (31241)Instruction limit reached!
% 0.14/0.38  % (31241)------------------------------
% 0.14/0.38  % (31241)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38  % (31241)Termination reason: Unknown
% 0.14/0.38  % (31241)Termination phase: Property scanning
% 0.14/0.38  
% 0.14/0.38  % (31241)Memory used [KB]: 1023
% 0.14/0.38  % (31241)Time elapsed: 0.004 s
% 0.14/0.38  % (31241)Instructions burned: 3 (million)
% 0.14/0.38  % (31241)------------------------------
% 0.14/0.38  % (31241)------------------------------
% 0.14/0.38  % (31240)Termination reason: Unknown
% 0.14/0.38  % (31240)Termination phase: Saturation
% 0.14/0.38  
% 0.14/0.38  % (31240)Memory used [KB]: 1023
% 0.14/0.38  % (31240)Time elapsed: 0.004 s
% 0.14/0.38  % (31240)Instructions burned: 3 (million)
% 0.14/0.38  % (31240)------------------------------
% 0.14/0.38  % (31240)------------------------------
% 0.14/0.38  % (31244)Instruction limit reached!
% 0.14/0.38  % (31244)------------------------------
% 0.14/0.38  % (31244)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38  % (31244)Termination reason: Unknown
% 0.14/0.38  % (31244)Termination phase: Saturation
% 0.14/0.38  
% 0.14/0.38  % (31244)Memory used [KB]: 1023
% 0.14/0.38  % (31244)Time elapsed: 0.004 s
% 0.14/0.38  % (31244)Instructions burned: 3 (million)
% 0.14/0.38  % (31244)------------------------------
% 0.14/0.38  % (31244)------------------------------
% 0.14/0.38  % (31238)Instruction limit reached!
% 0.14/0.38  % (31238)------------------------------
% 0.14/0.38  % (31238)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38  % (31238)Termination reason: Unknown
% 0.14/0.38  % (31238)Termination phase: Saturation
% 0.14/0.38  
% 0.14/0.38  % (31238)Memory used [KB]: 5500
% 0.14/0.38  % (31238)Time elapsed: 0.005 s
% 0.14/0.38  % (31238)Instructions burned: 4 (million)
% 0.14/0.38  % (31238)------------------------------
% 0.14/0.38  % (31238)------------------------------
% 0.14/0.39  % (31243)Instruction limit reached!
% 0.14/0.39  % (31243)------------------------------
% 0.14/0.39  % (31243)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39  % (31243)Termination reason: Unknown
% 0.14/0.39  % (31243)Termination phase: Saturation
% 0.14/0.39  
% 0.14/0.39  % (31243)Memory used [KB]: 5628
% 0.14/0.39  % (31243)Time elapsed: 0.014 s
% 0.14/0.39  % (31243)Instructions burned: 18 (million)
% 0.14/0.39  % (31243)------------------------------
% 0.14/0.39  % (31243)------------------------------
% 0.14/0.39  % (31251)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)
% 0.14/0.39  % (31252)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)
% 0.14/0.39  % (31253)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)
% 0.14/0.39  % (31254)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)
% 0.14/0.39  % (31239)Instruction limit reached!
% 0.14/0.39  % (31239)------------------------------
% 0.14/0.39  % (31239)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39  % (31239)Termination reason: Unknown
% 0.14/0.39  % (31239)Termination phase: Saturation
% 0.14/0.39  
% 0.14/0.39  % (31239)Memory used [KB]: 5628
% 0.14/0.39  % (31239)Time elapsed: 0.020 s
% 0.14/0.39  % (31239)Instructions burned: 28 (million)
% 0.14/0.39  % (31239)------------------------------
% 0.14/0.39  % (31239)------------------------------
% 0.14/0.39  % (31253)Instruction limit reached!
% 0.14/0.39  % (31253)------------------------------
% 0.14/0.39  % (31253)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39  % (31253)Termination reason: Unknown
% 0.14/0.39  % (31253)Termination phase: Saturation
% 0.14/0.39  
% 0.14/0.39  % (31253)Memory used [KB]: 5500
% 0.14/0.39  % (31253)Time elapsed: 0.004 s
% 0.14/0.39  % (31253)Instructions burned: 3 (million)
% 0.14/0.39  % (31253)------------------------------
% 0.14/0.39  % (31253)------------------------------
% 0.14/0.40  % (31252)Instruction limit reached!
% 0.14/0.40  % (31252)------------------------------
% 0.14/0.40  % (31252)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40  % (31252)Termination reason: Unknown
% 0.14/0.40  % (31252)Termination phase: Saturation
% 0.14/0.40  
% 0.14/0.40  % (31252)Memory used [KB]: 5628
% 0.14/0.40  % (31252)Time elapsed: 0.034 s
% 0.14/0.40  % (31252)Instructions burned: 15 (million)
% 0.14/0.40  % (31252)------------------------------
% 0.14/0.40  % (31252)------------------------------
% 0.14/0.40  % (31259)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.14/0.41  % (31259)Instruction limit reached!
% 0.14/0.41  % (31259)------------------------------
% 0.14/0.41  % (31259)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.41  % (31259)Termination reason: Unknown
% 0.14/0.41  % (31259)Termination phase: Saturation
% 0.14/0.41  
% 0.14/0.41  % (31259)Memory used [KB]: 1023
% 0.14/0.41  % (31259)Time elapsed: 0.007 s
% 0.14/0.41  % (31259)Instructions burned: 7 (million)
% 0.14/0.41  % (31259)------------------------------
% 0.14/0.41  % (31259)------------------------------
% 0.14/0.41  % (31263)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)
% 0.14/0.41  % (31262)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.14/0.41  % (31263)Instruction limit reached!
% 0.14/0.41  % (31263)------------------------------
% 0.14/0.41  % (31263)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.41  % (31263)Termination reason: Unknown
% 0.14/0.41  % (31263)Termination phase: Twee Goal Transformation
% 0.14/0.41  
% 0.14/0.41  % (31263)Memory used [KB]: 1023
% 0.14/0.41  % (31263)Time elapsed: 0.004 s
% 0.14/0.41  % (31263)Instructions burned: 3 (million)
% 0.14/0.41  % (31263)------------------------------
% 0.14/0.41  % (31263)------------------------------
% 0.14/0.41  % (31251)Instruction limit reached!
% 0.14/0.41  % (31251)------------------------------
% 0.14/0.41  % (31251)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.41  % (31251)Termination reason: Unknown
% 0.14/0.41  % (31251)Termination phase: Saturation
% 0.14/0.41  
% 0.14/0.41  % (31251)Memory used [KB]: 5756
% 0.14/0.41  % (31251)Time elapsed: 0.023 s
% 0.14/0.41  % (31251)Instructions burned: 37 (million)
% 0.14/0.41  % (31251)------------------------------
% 0.14/0.41  % (31251)------------------------------
% 0.21/0.42  % (31266)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)
% 0.21/0.42  % (31266)Instruction limit reached!
% 0.21/0.42  % (31266)------------------------------
% 0.21/0.42  % (31266)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42  % (31266)Termination reason: Unknown
% 0.21/0.42  % (31266)Termination phase: Property scanning
% 0.21/0.42  
% 0.21/0.42  % (31266)Memory used [KB]: 1023
% 0.21/0.42  % (31266)Time elapsed: 0.004 s
% 0.21/0.42  % (31266)Instructions burned: 4 (million)
% 0.21/0.42  % (31266)------------------------------
% 0.21/0.42  % (31266)------------------------------
% 0.21/0.42  % (31262)Instruction limit reached!
% 0.21/0.42  % (31262)------------------------------
% 0.21/0.42  % (31262)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42  % (31262)Termination reason: Unknown
% 0.21/0.42  % (31262)Termination phase: Saturation
% 0.21/0.42  
% 0.21/0.42  % (31262)Memory used [KB]: 5756
% 0.21/0.42  % (31262)Time elapsed: 0.038 s
% 0.21/0.42  % (31262)Instructions burned: 16 (million)
% 0.21/0.42  % (31262)------------------------------
% 0.21/0.42  % (31262)------------------------------
% 0.21/0.42  % (31269)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)
% 0.21/0.43  % (31271)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)
% 0.21/0.43  % (31269)Instruction limit reached!
% 0.21/0.43  % (31269)------------------------------
% 0.21/0.43  % (31269)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43  % (31269)Termination reason: Unknown
% 0.21/0.43  % (31269)Termination phase: Saturation
% 0.21/0.43  
% 0.21/0.43  % (31269)Memory used [KB]: 5500
% 0.21/0.43  % (31269)Time elapsed: 0.007 s
% 0.21/0.43  % (31269)Instructions burned: 7 (million)
% 0.21/0.43  % (31269)------------------------------
% 0.21/0.43  % (31269)------------------------------
% 0.21/0.43  % (31271)Instruction limit reached!
% 0.21/0.43  % (31271)------------------------------
% 0.21/0.43  % (31271)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43  % (31271)Termination reason: Unknown
% 0.21/0.43  % (31271)Termination phase: Saturation
% 0.21/0.43  
% 0.21/0.43  % (31271)Memory used [KB]: 5500
% 0.21/0.43  % (31271)Time elapsed: 0.004 s
% 0.21/0.43  % (31271)Instructions burned: 4 (million)
% 0.21/0.43  % (31271)------------------------------
% 0.21/0.43  % (31271)------------------------------
% 0.21/0.43  % (31273)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.21/0.43  % (31276)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)
% 0.21/0.43  % (31273)Instruction limit reached!
% 0.21/0.43  % (31273)------------------------------
% 0.21/0.43  % (31273)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43  % (31273)Termination reason: Unknown
% 0.21/0.43  % (31273)Termination phase: Saturation
% 0.21/0.43  
% 0.21/0.43  % (31273)Memory used [KB]: 5500
% 0.21/0.43  % (31273)Time elapsed: 0.005 s
% 0.21/0.43  % (31273)Instructions burned: 4 (million)
% 0.21/0.43  % (31273)------------------------------
% 0.21/0.43  % (31273)------------------------------
% 0.21/0.43  % (31276)Refutation not found, incomplete strategy
% 0.21/0.43  % (31276)------------------------------
% 0.21/0.43  % (31276)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43  % (31276)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.43  
% 0.21/0.43  
% 0.21/0.43  % (31276)Memory used [KB]: 5500
% 0.21/0.43  % (31276)Time elapsed: 0.005 s
% 0.21/0.43  % (31276)Instructions burned: 8 (million)
% 0.21/0.43  % (31276)------------------------------
% 0.21/0.43  % (31276)------------------------------
% 0.21/0.44  % (31279)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.21/0.44  % (31280)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.21/0.44  % (31281)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)
% 0.21/0.44  % (31283)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.21/0.45  % (31283)Instruction limit reached!
% 0.21/0.45  % (31283)------------------------------
% 0.21/0.45  % (31283)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45  % (31283)Termination reason: Unknown
% 0.21/0.45  % (31283)Termination phase: Saturation
% 0.21/0.45  
% 0.21/0.45  % (31283)Memory used [KB]: 5500
% 0.21/0.45  % (31283)Time elapsed: 0.003 s
% 0.21/0.45  % (31283)Instructions burned: 6 (million)
% 0.21/0.45  % (31283)------------------------------
% 0.21/0.45  % (31283)------------------------------
% 0.21/0.45  % (31280)Instruction limit reached!
% 0.21/0.45  % (31280)------------------------------
% 0.21/0.45  % (31280)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45  % (31280)Termination reason: Unknown
% 0.21/0.45  % (31280)Termination phase: Saturation
% 0.21/0.45  
% 0.21/0.45  % (31280)Memory used [KB]: 5500
% 0.21/0.45  % (31280)Time elapsed: 0.006 s
% 0.21/0.45  % (31280)Instructions burned: 6 (million)
% 0.21/0.45  % (31280)------------------------------
% 0.21/0.45  % (31280)------------------------------
% 0.21/0.45  % (31282)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)
% 0.21/0.45  % (31284)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.21/0.46  % (31284)Instruction limit reached!
% 0.21/0.46  % (31284)------------------------------
% 0.21/0.46  % (31284)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.46  % (31284)Termination reason: Unknown
% 0.21/0.46  % (31284)Termination phase: Saturation
% 0.21/0.46  
% 0.21/0.46  % (31284)Memory used [KB]: 5500
% 0.21/0.46  % (31284)Time elapsed: 0.003 s
% 0.21/0.46  % (31284)Instructions burned: 6 (million)
% 0.21/0.46  % (31284)------------------------------
% 0.21/0.46  % (31284)------------------------------
% 0.21/0.46  % (31282)Instruction limit reached!
% 0.21/0.46  % (31282)------------------------------
% 0.21/0.46  % (31282)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.46  % (31282)Termination reason: Unknown
% 0.21/0.46  % (31282)Termination phase: Saturation
% 0.21/0.46  
% 0.21/0.46  % (31282)Memory used [KB]: 5628
% 0.21/0.46  % (31282)Time elapsed: 0.015 s
% 0.21/0.46  % (31282)Instructions burned: 21 (million)
% 0.21/0.46  % (31282)------------------------------
% 0.21/0.46  % (31282)------------------------------
% 0.21/0.46  % (31285)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.21/0.46  % (31286)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on theBenchmark for (2999ds/779Mi)
% 0.21/0.47  % (31287)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on theBenchmark for (2999ds/19Mi)
% 0.21/0.48  % (31237)Instruction limit reached!
% 0.21/0.48  % (31237)------------------------------
% 0.21/0.48  % (31237)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.48  % (31237)Termination reason: Unknown
% 0.21/0.48  % (31237)Termination phase: Saturation
% 0.21/0.48  
% 0.21/0.48  % (31237)Memory used [KB]: 6396
% 0.21/0.48  % (31237)Time elapsed: 0.103 s
% 0.21/0.48  % (31237)Instructions burned: 185 (million)
% 0.21/0.48  % (31237)------------------------------
% 0.21/0.48  % (31237)------------------------------
% 0.21/0.48  % (31287)Instruction limit reached!
% 0.21/0.48  % (31287)------------------------------
% 0.21/0.48  % (31287)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.48  % (31287)Termination reason: Unknown
% 0.21/0.48  % (31287)Termination phase: Saturation
% 0.21/0.48  
% 0.21/0.48  % (31287)Memory used [KB]: 5628
% 0.21/0.48  % (31287)Time elapsed: 0.011 s
% 0.21/0.48  % (31287)Instructions burned: 20 (million)
% 0.21/0.48  % (31287)------------------------------
% 0.21/0.48  % (31287)------------------------------
% 0.21/0.49  % (31295)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2998ds/879Mi)
% 0.21/0.49  % (31298)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2998ds/17Mi)
% 0.21/0.50  % (31298)Instruction limit reached!
% 0.21/0.50  % (31298)------------------------------
% 0.21/0.50  % (31298)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.50  % (31298)Termination reason: Unknown
% 0.21/0.50  % (31298)Termination phase: Saturation
% 0.21/0.50  
% 0.21/0.50  % (31298)Memory used [KB]: 5628
% 0.21/0.50  % (31298)Time elapsed: 0.009 s
% 0.21/0.50  % (31298)Instructions burned: 19 (million)
% 0.21/0.50  % (31298)------------------------------
% 0.21/0.50  % (31298)------------------------------
% 0.21/0.51  % (31304)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.21/0.51  % (31242)Instruction limit reached!
% 0.21/0.51  % (31242)------------------------------
% 0.21/0.51  % (31242)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.51  % (31242)Termination reason: Unknown
% 0.21/0.51  % (31242)Termination phase: Saturation
% 0.21/0.51  
% 0.21/0.51  % (31242)Memory used [KB]: 6140
% 0.21/0.51  % (31242)Time elapsed: 0.135 s
% 0.21/0.51  % (31242)Instructions burned: 277 (million)
% 0.21/0.51  % (31242)------------------------------
% 0.21/0.51  % (31242)------------------------------
% 0.21/0.51  % (31304)Instruction limit reached!
% 0.21/0.51  % (31304)------------------------------
% 0.21/0.51  % (31304)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.51  % (31304)Termination reason: Unknown
% 0.21/0.51  % (31304)Termination phase: Equality resolution with deletion
% 0.21/0.51  
% 0.21/0.51  % (31304)Memory used [KB]: 1023
% 0.21/0.51  % (31304)Time elapsed: 0.002 s
% 0.21/0.51  % (31304)Instructions burned: 3 (million)
% 0.21/0.51  % (31304)------------------------------
% 0.21/0.51  % (31304)------------------------------
% 0.21/0.52  % (31307)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 0.21/0.52  % (31308)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on theBenchmark for (2998ds/127Mi)
% 0.21/0.52  % (31286)First to succeed.
% 0.21/0.53  % (31286)Refutation found. Thanks to Tanya!
% 0.21/0.53  % SZS status Theorem for theBenchmark
% 0.21/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.53  % (31286)------------------------------
% 0.21/0.53  % (31286)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.53  % (31286)Termination reason: Refutation
% 0.21/0.53  
% 0.21/0.53  % (31286)Memory used [KB]: 6396
% 0.21/0.53  % (31286)Time elapsed: 0.062 s
% 0.21/0.53  % (31286)Instructions burned: 167 (million)
% 0.21/0.53  % (31286)------------------------------
% 0.21/0.53  % (31286)------------------------------
% 0.21/0.53  % (31233)Success in time 0.162 s
% 0.21/0.53  % Vampire---4.8 exiting
%------------------------------------------------------------------------------