TSTP Solution File: SYO868^1 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SYO868^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n031.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 : Fri Sep  1 04:48:16 EDT 2023

% Result   : Theorem 0.19s 0.45s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   58
% Syntax   : Number of formulae    :   71 (  19 unt;  22 typ;   2 def)
%            Number of atoms       :  299 (  16 equ;   0 cnn)
%            Maximal formula atoms :   22 (   6 avg)
%            Number of connectives :  633 (  36   ~;  12   |;   0   &; 439   @)
%                                         (  12 <=>; 134  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   28 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   30 (  30   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   38 (  36 usr;  20 con; 0-2 aty)
%            Number of variables   :   48 (   3   ^;  45   !;   0   ?;  48   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_c_exactly2,type,
    c_exactly2: $i > $o ).

thf(ty_c_exactly1of2,type,
    c_exactly1of2: $o > $o > $o ).

thf(ty_c_Empty,type,
    c_Empty: $i ).

thf(ty_c_SNoLt,type,
    c_SNoLt: $i > $i > $o ).

thf(ty_c_binrep,type,
    c_binrep: $i > $i > $i ).

thf(ty_c_and,type,
    c_and: $o > $o > $o ).

thf(ty_c_ordsucc,type,
    c_ordsucc: $i > $i ).

thf(ty_eigen__11,type,
    eigen__11: $i ).

thf(ty_c_nat_p,type,
    c_nat_p: $i > $o ).

thf(ty_eigen__5,type,
    eigen__5: $i > $o ).

thf(ty_eigen__2,type,
    eigen__2: $i ).

thf(ty_c_ordinal,type,
    c_ordinal: $i > $o ).

thf(ty_eigen__0,type,
    eigen__0: $i ).

thf(ty_c_atleast3,type,
    c_atleast3: $i > $o ).

thf(ty_c_exactly5,type,
    c_exactly5: $i > $o ).

thf(ty_c_In,type,
    c_In: $i > $i > $o ).

thf(ty_c_Power,type,
    c_Power: $i > $i ).

thf(ty_c_atleast2,type,
    c_atleast2: $i > $o ).

thf(ty_c_TransSet,type,
    c_TransSet: $i > $o ).

thf(ty_eigen__1,type,
    eigen__1: $i ).

thf(ty_c_not,type,
    c_not: $o > $o ).

thf(ty_c_atleast5,type,
    c_atleast5: $i > $o ).

thf(h0,assumption,
    ! [X1: $i > $o,X2: $i] :
      ( ( X1 @ X2 )
     => ( X1 @ ( eps__0 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(eigendef_eigen__11,definition,
    ( eigen__11
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ( ( ( c_ordinal @ c_Empty )
             => ( c_and @ ( c_exactly2 @ c_Empty ) @ ( c_not @ ( c_exactly5 @ X1 ) ) ) )
           => ( ( ( ( c_ordinal @ c_Empty )
                 => ( c_exactly2 @ c_Empty ) )
               => ( ( c_atleast2 @ c_Empty )
                 => ( ( ( ( c_not @ ( c_atleast2 @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) )
                       => ( c_Empty = X1 ) )
                     => ( c_atleast3 @ c_Empty ) )
                   => ( c_and @ ( c_atleast5 @ eigen__2 ) @ ( c_not @ ( c_exactly1of2 @ ( c_SNoLt @ eigen__2 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) @ c_Empty ) ) @ ( c_TransSet @ X1 ) ) ) ) ) ) )
             => ( c_nat_p @ c_Empty ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__11])]) ).

thf(h1,assumption,
    ! [X1: ( $i > $o ) > $o,X2: $i > $o] :
      ( ( X1 @ X2 )
     => ( X1 @ ( eps__1 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(eigendef_eigen__5,definition,
    ( eigen__5
    = ( eps__1
      @ ^ [X1: $i > $o] :
          ~ ( ( X1 @ c_Empty )
           => ( ! [X2: $i] :
                  ( ( X1 @ X2 )
                 => ( X1 @ ( c_ordsucc @ X2 ) ) )
             => ( X1 @ c_Empty ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__5])]) ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: $i] :
        ( ( c_nat_p @ X1 )
        = ( ! [X2: $i > $o] :
              ( ( X2 @ c_Empty )
             => ( ! [X3: $i] :
                    ( ( X2 @ X3 )
                   => ( X2 @ ( c_ordsucc @ X3 ) ) )
               => ( X2 @ X1 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( ( ( c_ordinal @ c_Empty )
         => ( c_exactly2 @ c_Empty ) )
       => ( ( c_atleast2 @ c_Empty )
         => ( ( ( ( c_not @ ( c_atleast2 @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) )
               => ( c_Empty = eigen__11 ) )
             => ( c_atleast3 @ c_Empty ) )
           => ( c_and @ ( c_atleast5 @ eigen__2 ) @ ( c_not @ ( c_exactly1of2 @ ( c_SNoLt @ eigen__2 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) @ c_Empty ) ) @ ( c_TransSet @ eigen__11 ) ) ) ) ) ) )
     => ( c_nat_p @ c_Empty ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: $i] :
        ~ ! [X2: $i] :
            ( ( ( c_ordinal @ X1 )
             => ( c_and @ ( c_exactly2 @ X1 ) @ ( c_not @ ( c_exactly5 @ X2 ) ) ) )
           => ( ( ( ( c_ordinal @ X1 )
                 => ( c_exactly2 @ X1 ) )
               => ( ( c_atleast2 @ X1 )
                 => ( ( ( ( c_not @ ( c_atleast2 @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) )
                       => ( X1 = X2 ) )
                     => ( c_atleast3 @ X1 ) )
                   => ( c_and @ ( c_atleast5 @ eigen__2 ) @ ( c_not @ ( c_exactly1of2 @ ( c_SNoLt @ eigen__2 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) @ c_Empty ) ) @ ( c_TransSet @ X2 ) ) ) ) ) ) )
             => ( c_nat_p @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( eigen__5 @ c_Empty ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ! [X1: $i] :
          ( ( eigen__5 @ X1 )
         => ( eigen__5 @ ( c_ordsucc @ X1 ) ) )
     => sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( sP4
     => sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: $i > $o] :
        ( ( X1 @ c_Empty )
       => ( ! [X2: $i] :
              ( ( X1 @ X2 )
             => ( X1 @ ( c_ordsucc @ X2 ) ) )
         => ( X1 @ c_Empty ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: $i] :
        ( ( ( c_ordinal @ c_Empty )
         => ( c_and @ ( c_exactly2 @ c_Empty ) @ ( c_not @ ( c_exactly5 @ X1 ) ) ) )
       => ( ( ( ( c_ordinal @ c_Empty )
             => ( c_exactly2 @ c_Empty ) )
           => ( ( c_atleast2 @ c_Empty )
             => ( ( ( ( c_not @ ( c_atleast2 @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) )
                   => ( c_Empty = X1 ) )
                 => ( c_atleast3 @ c_Empty ) )
               => ( c_and @ ( c_atleast5 @ eigen__2 ) @ ( c_not @ ( c_exactly1of2 @ ( c_SNoLt @ eigen__2 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) @ c_Empty ) ) @ ( c_TransSet @ X1 ) ) ) ) ) ) )
         => ( c_nat_p @ c_Empty ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( c_nat_p @ c_Empty ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( sP9 = sP7 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( c_nat_p
      = ( ^ [X1: $i] :
          ! [X2: $i > $o] :
            ( ( X2 @ c_Empty )
           => ( ! [X3: $i] :
                  ( ( X2 @ X3 )
                 => ( X2 @ ( c_ordsucc @ X3 ) ) )
             => ( X2 @ X1 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( ( ( c_ordinal @ c_Empty )
       => ( c_and @ ( c_exactly2 @ c_Empty ) @ ( c_not @ ( c_exactly5 @ eigen__11 ) ) ) )
     => sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(conj,conjecture,
    ! [X1: $i] :
      ( ( c_In @ X1 @ c_Empty )
     => ! [X2: $i] :
          ( ( c_In @ X2 @ X1 )
         => ! [X3: $i] :
              ( ( c_In @ X3 @ X2 )
             => ~ ! [X4: $i] :
                    ~ ! [X5: $i] :
                        ( ( ( c_ordinal @ X4 )
                         => ( c_and @ ( c_exactly2 @ X4 ) @ ( c_not @ ( c_exactly5 @ X5 ) ) ) )
                       => ( ( ( ( c_ordinal @ X4 )
                             => ( c_exactly2 @ X4 ) )
                           => ( ( c_atleast2 @ X4 )
                             => ( ( ( ( c_not @ ( c_atleast2 @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) )
                                   => ( X4 = X5 ) )
                                 => ( c_atleast3 @ X4 ) )
                               => ( c_and @ ( c_atleast5 @ X3 ) @ ( c_not @ ( c_exactly1of2 @ ( c_SNoLt @ X3 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) @ c_Empty ) ) @ ( c_TransSet @ X5 ) ) ) ) ) ) )
                         => ( c_nat_p @ X4 ) ) ) ) ) ) ).

thf(h2,negated_conjecture,
    ~ ! [X1: $i] :
        ( ( c_In @ X1 @ c_Empty )
       => ! [X2: $i] :
            ( ( c_In @ X2 @ X1 )
           => ! [X3: $i] :
                ( ( c_In @ X3 @ X2 )
               => ~ ! [X4: $i] :
                      ~ ! [X5: $i] :
                          ( ( ( c_ordinal @ X4 )
                           => ( c_and @ ( c_exactly2 @ X4 ) @ ( c_not @ ( c_exactly5 @ X5 ) ) ) )
                         => ( ( ( ( c_ordinal @ X4 )
                               => ( c_exactly2 @ X4 ) )
                             => ( ( c_atleast2 @ X4 )
                               => ( ( ( ( c_not @ ( c_atleast2 @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) )
                                     => ( X4 = X5 ) )
                                   => ( c_atleast3 @ X4 ) )
                                 => ( c_and @ ( c_atleast5 @ X3 ) @ ( c_not @ ( c_exactly1of2 @ ( c_SNoLt @ X3 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) @ c_Empty ) ) @ ( c_TransSet @ X5 ) ) ) ) ) ) )
                           => ( c_nat_p @ X4 ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[conj]) ).

thf(h3,assumption,
    ~ ( ( c_In @ eigen__0 @ c_Empty )
     => ! [X1: $i] :
          ( ( c_In @ X1 @ eigen__0 )
         => ! [X2: $i] :
              ( ( c_In @ X2 @ X1 )
             => ~ ! [X3: $i] :
                    ~ ! [X4: $i] :
                        ( ( ( c_ordinal @ X3 )
                         => ( c_and @ ( c_exactly2 @ X3 ) @ ( c_not @ ( c_exactly5 @ X4 ) ) ) )
                       => ( ( ( ( c_ordinal @ X3 )
                             => ( c_exactly2 @ X3 ) )
                           => ( ( c_atleast2 @ X3 )
                             => ( ( ( ( c_not @ ( c_atleast2 @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) )
                                   => ( X3 = X4 ) )
                                 => ( c_atleast3 @ X3 ) )
                               => ( c_and @ ( c_atleast5 @ X2 ) @ ( c_not @ ( c_exactly1of2 @ ( c_SNoLt @ X2 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) @ c_Empty ) ) @ ( c_TransSet @ X4 ) ) ) ) ) ) )
                         => ( c_nat_p @ X3 ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    c_In @ eigen__0 @ c_Empty,
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ ! [X1: $i] :
        ( ( c_In @ X1 @ eigen__0 )
       => ! [X2: $i] :
            ( ( c_In @ X2 @ X1 )
           => ~ ! [X3: $i] :
                  ~ ! [X4: $i] :
                      ( ( ( c_ordinal @ X3 )
                       => ( c_and @ ( c_exactly2 @ X3 ) @ ( c_not @ ( c_exactly5 @ X4 ) ) ) )
                     => ( ( ( ( c_ordinal @ X3 )
                           => ( c_exactly2 @ X3 ) )
                         => ( ( c_atleast2 @ X3 )
                           => ( ( ( ( c_not @ ( c_atleast2 @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) )
                                 => ( X3 = X4 ) )
                               => ( c_atleast3 @ X3 ) )
                             => ( c_and @ ( c_atleast5 @ X2 ) @ ( c_not @ ( c_exactly1of2 @ ( c_SNoLt @ X2 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) @ c_Empty ) ) @ ( c_TransSet @ X4 ) ) ) ) ) ) )
                       => ( c_nat_p @ X3 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ ( ( c_In @ eigen__1 @ eigen__0 )
     => ! [X1: $i] :
          ( ( c_In @ X1 @ eigen__1 )
         => ~ ! [X2: $i] :
                ~ ! [X3: $i] :
                    ( ( ( c_ordinal @ X2 )
                     => ( c_and @ ( c_exactly2 @ X2 ) @ ( c_not @ ( c_exactly5 @ X3 ) ) ) )
                   => ( ( ( ( c_ordinal @ X2 )
                         => ( c_exactly2 @ X2 ) )
                       => ( ( c_atleast2 @ X2 )
                         => ( ( ( ( c_not @ ( c_atleast2 @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) )
                               => ( X2 = X3 ) )
                             => ( c_atleast3 @ X2 ) )
                           => ( c_and @ ( c_atleast5 @ X1 ) @ ( c_not @ ( c_exactly1of2 @ ( c_SNoLt @ X1 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) @ c_Empty ) ) @ ( c_TransSet @ X3 ) ) ) ) ) ) )
                     => ( c_nat_p @ X2 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    c_In @ eigen__1 @ eigen__0,
    introduced(assumption,[]) ).

thf(h8,assumption,
    ~ ! [X1: $i] :
        ( ( c_In @ X1 @ eigen__1 )
       => ~ ! [X2: $i] :
              ~ ! [X3: $i] :
                  ( ( ( c_ordinal @ X2 )
                   => ( c_and @ ( c_exactly2 @ X2 ) @ ( c_not @ ( c_exactly5 @ X3 ) ) ) )
                 => ( ( ( ( c_ordinal @ X2 )
                       => ( c_exactly2 @ X2 ) )
                     => ( ( c_atleast2 @ X2 )
                       => ( ( ( ( c_not @ ( c_atleast2 @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) )
                             => ( X2 = X3 ) )
                           => ( c_atleast3 @ X2 ) )
                         => ( c_and @ ( c_atleast5 @ X1 ) @ ( c_not @ ( c_exactly1of2 @ ( c_SNoLt @ X1 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) @ c_Empty ) ) @ ( c_TransSet @ X3 ) ) ) ) ) ) )
                   => ( c_nat_p @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ ( ( c_In @ eigen__2 @ eigen__1 )
     => ~ sP3 ),
    introduced(assumption,[]) ).

thf(h10,assumption,
    c_In @ eigen__2 @ eigen__1,
    introduced(assumption,[]) ).

thf(h11,assumption,
    sP3,
    introduced(assumption,[]) ).

thf(1,plain,
    ( sP2
    | ~ sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( sP12
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP8
    | ~ sP12 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).

thf(4,plain,
    ( sP5
    | ~ sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP6
    | ~ sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( sP6
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( sP7
    | ~ sP6 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__5]) ).

thf(8,plain,
    ( ~ sP10
    | sP9
    | ~ sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP1
    | sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP3
    | ~ sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP11
    | sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(ax63,axiom,
    sP11 ).

thf(12,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h10,h11,h9,h7,h8,h6,h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,h11,ax63]) ).

thf(13,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h9,h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,12,h10,h11]) ).

thf(14,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[h8,13,h9]) ).

thf(15,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,14,h7,h8]) ).

thf(16,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h5,15,h6]) ).

thf(17,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,16,h4,h5]) ).

thf(18,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,17,h3]) ).

thf(19,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[18,h1]) ).

thf(20,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[19,h0]) ).

thf(0,theorem,
    ! [X1: $i] :
      ( ( c_In @ X1 @ c_Empty )
     => ! [X2: $i] :
          ( ( c_In @ X2 @ X1 )
         => ! [X3: $i] :
              ( ( c_In @ X3 @ X2 )
             => ~ ! [X4: $i] :
                    ~ ! [X5: $i] :
                        ( ( ( c_ordinal @ X4 )
                         => ( c_and @ ( c_exactly2 @ X4 ) @ ( c_not @ ( c_exactly5 @ X5 ) ) ) )
                       => ( ( ( ( c_ordinal @ X4 )
                             => ( c_exactly2 @ X4 ) )
                           => ( ( c_atleast2 @ X4 )
                             => ( ( ( ( c_not @ ( c_atleast2 @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) )
                                   => ( X4 = X5 ) )
                                 => ( c_atleast3 @ X4 ) )
                               => ( c_and @ ( c_atleast5 @ X3 ) @ ( c_not @ ( c_exactly1of2 @ ( c_SNoLt @ X3 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) @ c_Empty ) ) @ ( c_TransSet @ X5 ) ) ) ) ) ) )
                         => ( c_nat_p @ X4 ) ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h2])],[18,h2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SYO868^1 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34  % Computer : n031.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Sat Aug 26 06:51:52 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.45  % SZS status Theorem
% 0.19/0.45  % Mode: cade22sinegrackle2x6978
% 0.19/0.45  % Steps: 220
% 0.19/0.45  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------