TSTP Solution File: SEU974^5 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEU974^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n024.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 : Thu Aug 31 17:38:03 EDT 2023

% Result   : Theorem 0.18s 0.41s
% Output   : Proof 0.18s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

thf(ty_cR,type,
    cR: a > a ).

thf(ty_eigen__1,type,
    eigen__1: a ).

thf(ty_cZ,type,
    cZ: a ).

thf(ty_eigen__0,type,
    eigen__0: a ).

thf(ty_cP,type,
    cP: a > a > a ).

thf(ty_eigen__2,type,
    eigen__2: a > $o ).

thf(ty_cL,type,
    cL: a > a ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: a,X2: a] :
        ( ( eigen__2 @ ( cP @ X1 @ X2 ) )
       => ~ ( ~ ( ( ( X2 = cZ )
                 => ( X1 = cZ ) )
               => ~ ( eigen__2 @ ( cP @ ( cL @ X1 ) @ ( cL @ X2 ) ) ) )
           => ~ ( eigen__2 @ ( cP @ ( cR @ X1 ) @ ( cR @ X2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( eigen__2 @ ( cP @ ( cR @ eigen__0 ) @ ( cR @ eigen__1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ~ ( ( ( eigen__1 = cZ )
           => ( eigen__0 = cZ ) )
         => ~ ( eigen__2 @ ( cP @ ( cL @ eigen__0 ) @ ( cL @ eigen__1 ) ) ) )
     => ~ sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: a] :
        ( ( eigen__2 @ ( cP @ eigen__0 @ X1 ) )
       => ~ ( ~ ( ( ( X1 = cZ )
                 => ( eigen__0 = cZ ) )
               => ~ ( eigen__2 @ ( cP @ ( cL @ eigen__0 ) @ ( cL @ X1 ) ) ) )
           => ~ ( eigen__2 @ ( cP @ ( cR @ eigen__0 ) @ ( cR @ X1 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( eigen__2 @ ( cP @ eigen__0 @ eigen__1 ) )
     => ~ sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( eigen__2 @ ( cP @ eigen__0 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: a > $o] :
        ( ( X1 @ ( cP @ ( cR @ eigen__0 ) @ ( cR @ eigen__1 ) ) )
       => ~ ! [X2: a,X3: a] :
              ( ( X1 @ ( cP @ X2 @ X3 ) )
             => ~ ( ~ ( ( ( X3 = cZ )
                       => ( X2 = cZ ) )
                     => ~ ( X1 @ ( cP @ ( cL @ X2 ) @ ( cL @ X3 ) ) ) )
                 => ~ ( X1 @ ( cP @ ( cR @ X2 ) @ ( cR @ X3 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( sP2
     => ~ sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(cPU_LEM2C_pme,conjecture,
    ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
                          = cZ )
                       => ( ( cR @ cZ )
                         != cZ ) )
                   => ~ ! [X1: a,X2: a] :
                          ( ( cL @ ( cP @ X1 @ X2 ) )
                          = X1 ) )
               => ~ ! [X1: a,X2: a] :
                      ( ( cR @ ( cP @ X1 @ X2 ) )
                      = X2 ) )
           => ~ ! [X1: a] :
                  ( ( X1 != cZ )
                  = ( X1
                    = ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) )
       => ~ ! [X1: a > $o] :
              ( ! [X2: a,X3: a] :
                  ( ( X1 @ ( cP @ X2 @ X3 ) )
                 => ~ ( ~ ( ( ( X2 = cZ )
                            = ( X3 = cZ ) )
                         => ~ ( X1 @ ( cP @ ( cL @ X2 ) @ ( cL @ X3 ) ) ) )
                     => ~ ( X1 @ ( cP @ ( cR @ X2 ) @ ( cR @ X3 ) ) ) ) )
             => ! [X2: a,X3: a] :
                  ( ( X1 @ ( cP @ X2 @ X3 ) )
                 => ( X2 = X3 ) ) ) )
   => ! [X1: a,X2: a] :
        ( ~ ! [X3: a > $o] :
              ( ( X3 @ ( cP @ X1 @ X2 ) )
             => ~ ! [X4: a,X5: a] :
                    ( ( X3 @ ( cP @ X4 @ X5 ) )
                   => ~ ( ~ ( ( ( X5 = cZ )
                             => ( X4 = cZ ) )
                           => ~ ( X3 @ ( cP @ ( cL @ X4 ) @ ( cL @ X5 ) ) ) )
                       => ~ ( X3 @ ( cP @ ( cR @ X4 ) @ ( cR @ X5 ) ) ) ) ) )
       => ~ ! [X3: a > $o] :
              ( ( X3 @ ( cP @ ( cR @ X1 ) @ ( cR @ X2 ) ) )
             => ~ ! [X4: a,X5: a] :
                    ( ( X3 @ ( cP @ X4 @ X5 ) )
                   => ~ ( ~ ( ( ( X5 = cZ )
                             => ( X4 = cZ ) )
                           => ~ ( X3 @ ( cP @ ( cL @ X4 ) @ ( cL @ X5 ) ) ) )
                       => ~ ( X3 @ ( cP @ ( cR @ X4 ) @ ( cR @ X5 ) ) ) ) ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
                            = cZ )
                         => ( ( cR @ cZ )
                           != cZ ) )
                     => ~ ! [X1: a,X2: a] :
                            ( ( cL @ ( cP @ X1 @ X2 ) )
                            = X1 ) )
                 => ~ ! [X1: a,X2: a] :
                        ( ( cR @ ( cP @ X1 @ X2 ) )
                        = X2 ) )
             => ~ ! [X1: a] :
                    ( ( X1 != cZ )
                    = ( X1
                      = ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) )
         => ~ ! [X1: a > $o] :
                ( ! [X2: a,X3: a] :
                    ( ( X1 @ ( cP @ X2 @ X3 ) )
                   => ~ ( ~ ( ( ( X2 = cZ )
                              = ( X3 = cZ ) )
                           => ~ ( X1 @ ( cP @ ( cL @ X2 ) @ ( cL @ X3 ) ) ) )
                       => ~ ( X1 @ ( cP @ ( cR @ X2 ) @ ( cR @ X3 ) ) ) ) )
               => ! [X2: a,X3: a] :
                    ( ( X1 @ ( cP @ X2 @ X3 ) )
                   => ( X2 = X3 ) ) ) )
     => ! [X1: a,X2: a] :
          ( ~ ! [X3: a > $o] :
                ( ( X3 @ ( cP @ X1 @ X2 ) )
               => ~ ! [X4: a,X5: a] :
                      ( ( X3 @ ( cP @ X4 @ X5 ) )
                     => ~ ( ~ ( ( ( X5 = cZ )
                               => ( X4 = cZ ) )
                             => ~ ( X3 @ ( cP @ ( cL @ X4 ) @ ( cL @ X5 ) ) ) )
                         => ~ ( X3 @ ( cP @ ( cR @ X4 ) @ ( cR @ X5 ) ) ) ) ) )
         => ~ ! [X3: a > $o] :
                ( ( X3 @ ( cP @ ( cR @ X1 ) @ ( cR @ X2 ) ) )
               => ~ ! [X4: a,X5: a] :
                      ( ( X3 @ ( cP @ X4 @ X5 ) )
                     => ~ ( ~ ( ( ( X5 = cZ )
                               => ( X4 = cZ ) )
                             => ~ ( X3 @ ( cP @ ( cL @ X4 ) @ ( cL @ X5 ) ) ) )
                         => ~ ( X3 @ ( cP @ ( cR @ X4 ) @ ( cR @ X5 ) ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[cPU_LEM2C_pme]) ).

thf(h1,assumption,
    ~ ( ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
                        = cZ )
                     => ( ( cR @ cZ )
                       != cZ ) )
                 => ~ ! [X1: a,X2: a] :
                        ( ( cL @ ( cP @ X1 @ X2 ) )
                        = X1 ) )
             => ~ ! [X1: a,X2: a] :
                    ( ( cR @ ( cP @ X1 @ X2 ) )
                    = X2 ) )
         => ~ ! [X1: a] :
                ( ( X1 != cZ )
                = ( X1
                  = ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) )
     => ~ ! [X1: a > $o] :
            ( ! [X2: a,X3: a] :
                ( ( X1 @ ( cP @ X2 @ X3 ) )
               => ~ ( ~ ( ( ( X2 = cZ )
                          = ( X3 = cZ ) )
                       => ~ ( X1 @ ( cP @ ( cL @ X2 ) @ ( cL @ X3 ) ) ) )
                   => ~ ( X1 @ ( cP @ ( cR @ X2 ) @ ( cR @ X3 ) ) ) ) )
           => ! [X2: a,X3: a] :
                ( ( X1 @ ( cP @ X2 @ X3 ) )
               => ( X2 = X3 ) ) ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ! [X1: a,X2: a] :
        ( ~ ! [X3: a > $o] :
              ( ( X3 @ ( cP @ X1 @ X2 ) )
             => ~ ! [X4: a,X5: a] :
                    ( ( X3 @ ( cP @ X4 @ X5 ) )
                   => ~ ( ~ ( ( ( X5 = cZ )
                             => ( X4 = cZ ) )
                           => ~ ( X3 @ ( cP @ ( cL @ X4 ) @ ( cL @ X5 ) ) ) )
                       => ~ ( X3 @ ( cP @ ( cR @ X4 ) @ ( cR @ X5 ) ) ) ) ) )
       => ~ ! [X3: a > $o] :
              ( ( X3 @ ( cP @ ( cR @ X1 ) @ ( cR @ X2 ) ) )
             => ~ ! [X4: a,X5: a] :
                    ( ( X3 @ ( cP @ X4 @ X5 ) )
                   => ~ ( ~ ( ( ( X5 = cZ )
                             => ( X4 = cZ ) )
                           => ~ ( X3 @ ( cP @ ( cL @ X4 ) @ ( cL @ X5 ) ) ) )
                       => ~ ( X3 @ ( cP @ ( cR @ X4 ) @ ( cR @ X5 ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
                    = cZ )
                 => ( ( cR @ cZ )
                   != cZ ) )
             => ~ ! [X1: a,X2: a] :
                    ( ( cL @ ( cP @ X1 @ X2 ) )
                    = X1 ) )
         => ~ ! [X1: a,X2: a] :
                ( ( cR @ ( cP @ X1 @ X2 ) )
                = X2 ) )
     => ~ ! [X1: a] :
            ( ( X1 != cZ )
            = ( X1
              = ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ! [X1: a > $o] :
      ( ! [X2: a,X3: a] :
          ( ( X1 @ ( cP @ X2 @ X3 ) )
         => ~ ( ~ ( ( ( X2 = cZ )
                    = ( X3 = cZ ) )
                 => ~ ( X1 @ ( cP @ ( cL @ X2 ) @ ( cL @ X3 ) ) ) )
             => ~ ( X1 @ ( cP @ ( cR @ X2 ) @ ( cR @ X3 ) ) ) ) )
     => ! [X2: a,X3: a] :
          ( ( X1 @ ( cP @ X2 @ X3 ) )
         => ( X2 = X3 ) ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ ( ~ ( ~ ( ( ( cL @ cZ )
                = cZ )
             => ( ( cR @ cZ )
               != cZ ) )
         => ~ ! [X1: a,X2: a] :
                ( ( cL @ ( cP @ X1 @ X2 ) )
                = X1 ) )
     => ~ ! [X1: a,X2: a] :
            ( ( cR @ ( cP @ X1 @ X2 ) )
            = X2 ) ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    ! [X1: a] :
      ( ( X1 != cZ )
      = ( X1
        = ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    ~ ( ~ ( ( ( cL @ cZ )
            = cZ )
         => ( ( cR @ cZ )
           != cZ ) )
     => ~ ! [X1: a,X2: a] :
            ( ( cL @ ( cP @ X1 @ X2 ) )
            = X1 ) ),
    introduced(assumption,[]) ).

thf(h8,assumption,
    ! [X1: a,X2: a] :
      ( ( cR @ ( cP @ X1 @ X2 ) )
      = X2 ),
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ ( ( ( cL @ cZ )
        = cZ )
     => ( ( cR @ cZ )
       != cZ ) ),
    introduced(assumption,[]) ).

thf(h10,assumption,
    ! [X1: a,X2: a] :
      ( ( cL @ ( cP @ X1 @ X2 ) )
      = X1 ),
    introduced(assumption,[]) ).

thf(h11,assumption,
    ( ( cL @ cZ )
    = cZ ),
    introduced(assumption,[]) ).

thf(h12,assumption,
    ( ( cR @ cZ )
    = cZ ),
    introduced(assumption,[]) ).

thf(h13,assumption,
    ~ ! [X1: a] :
        ( ~ ! [X2: a > $o] :
              ( ( X2 @ ( cP @ eigen__0 @ X1 ) )
             => ~ ! [X3: a,X4: a] :
                    ( ( X2 @ ( cP @ X3 @ X4 ) )
                   => ~ ( ~ ( ( ( X4 = cZ )
                             => ( X3 = cZ ) )
                           => ~ ( X2 @ ( cP @ ( cL @ X3 ) @ ( cL @ X4 ) ) ) )
                       => ~ ( X2 @ ( cP @ ( cR @ X3 ) @ ( cR @ X4 ) ) ) ) ) )
       => ~ ! [X2: a > $o] :
              ( ( X2 @ ( cP @ ( cR @ eigen__0 ) @ ( cR @ X1 ) ) )
             => ~ ! [X3: a,X4: a] :
                    ( ( X2 @ ( cP @ X3 @ X4 ) )
                   => ~ ( ~ ( ( ( X4 = cZ )
                             => ( X3 = cZ ) )
                           => ~ ( X2 @ ( cP @ ( cL @ X3 ) @ ( cL @ X4 ) ) ) )
                       => ~ ( X2 @ ( cP @ ( cR @ X3 ) @ ( cR @ X4 ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h14,assumption,
    ~ ( ~ ! [X1: a > $o] :
            ( ( X1 @ ( cP @ eigen__0 @ eigen__1 ) )
           => ~ ! [X2: a,X3: a] :
                  ( ( X1 @ ( cP @ X2 @ X3 ) )
                 => ~ ( ~ ( ( ( X3 = cZ )
                           => ( X2 = cZ ) )
                         => ~ ( X1 @ ( cP @ ( cL @ X2 ) @ ( cL @ X3 ) ) ) )
                     => ~ ( X1 @ ( cP @ ( cR @ X2 ) @ ( cR @ X3 ) ) ) ) ) )
     => ~ sP7 ),
    introduced(assumption,[]) ).

thf(h15,assumption,
    ~ ! [X1: a > $o] :
        ( ( X1 @ ( cP @ eigen__0 @ eigen__1 ) )
       => ~ ! [X2: a,X3: a] :
              ( ( X1 @ ( cP @ X2 @ X3 ) )
             => ~ ( ~ ( ( ( X3 = cZ )
                       => ( X2 = cZ ) )
                     => ~ ( X1 @ ( cP @ ( cL @ X2 ) @ ( cL @ X3 ) ) ) )
                 => ~ ( X1 @ ( cP @ ( cR @ X2 ) @ ( cR @ X3 ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h16,assumption,
    sP7,
    introduced(assumption,[]) ).

thf(h17,assumption,
    ~ ( sP6
     => ~ sP1 ),
    introduced(assumption,[]) ).

thf(h18,assumption,
    sP6,
    introduced(assumption,[]) ).

thf(h19,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP8
    | ~ sP2
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP7
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP3
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP5
    | ~ sP6
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP4
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP1
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h18,h19,h17,h15,h16,h14,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,h18,h19,h16]) ).

thf(8,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h17,h15,h16,h14,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h18,h19])],[h17,7,h18,h19]) ).

thf(9,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h15,h16,h14,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__2)],[h15,8,h17]) ).

thf(10,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h14,h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h15,h16])],[h14,9,h15,h16]) ).

thf(11,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h13,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__1)],[h13,10,h14]) ).

thf(12,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__0)],[h2,11,h13]) ).

thf(13,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h9,12,h11,h12]) ).

thf(14,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h7,13,h9,h10]) ).

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

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

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

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

thf(0,theorem,
    ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ( cL @ cZ )
                          = cZ )
                       => ( ( cR @ cZ )
                         != cZ ) )
                   => ~ ! [X1: a,X2: a] :
                          ( ( cL @ ( cP @ X1 @ X2 ) )
                          = X1 ) )
               => ~ ! [X1: a,X2: a] :
                      ( ( cR @ ( cP @ X1 @ X2 ) )
                      = X2 ) )
           => ~ ! [X1: a] :
                  ( ( X1 != cZ )
                  = ( X1
                    = ( cP @ ( cL @ X1 ) @ ( cR @ X1 ) ) ) ) )
       => ~ ! [X1: a > $o] :
              ( ! [X2: a,X3: a] :
                  ( ( X1 @ ( cP @ X2 @ X3 ) )
                 => ~ ( ~ ( ( ( X2 = cZ )
                            = ( X3 = cZ ) )
                         => ~ ( X1 @ ( cP @ ( cL @ X2 ) @ ( cL @ X3 ) ) ) )
                     => ~ ( X1 @ ( cP @ ( cR @ X2 ) @ ( cR @ X3 ) ) ) ) )
             => ! [X2: a,X3: a] :
                  ( ( X1 @ ( cP @ X2 @ X3 ) )
                 => ( X2 = X3 ) ) ) )
   => ! [X1: a,X2: a] :
        ( ~ ! [X3: a > $o] :
              ( ( X3 @ ( cP @ X1 @ X2 ) )
             => ~ ! [X4: a,X5: a] :
                    ( ( X3 @ ( cP @ X4 @ X5 ) )
                   => ~ ( ~ ( ( ( X5 = cZ )
                             => ( X4 = cZ ) )
                           => ~ ( X3 @ ( cP @ ( cL @ X4 ) @ ( cL @ X5 ) ) ) )
                       => ~ ( X3 @ ( cP @ ( cR @ X4 ) @ ( cR @ X5 ) ) ) ) ) )
       => ~ ! [X3: a > $o] :
              ( ( X3 @ ( cP @ ( cR @ X1 ) @ ( cR @ X2 ) ) )
             => ~ ! [X4: a,X5: a] :
                    ( ( X3 @ ( cP @ X4 @ X5 ) )
                   => ~ ( ~ ( ( ( X5 = cZ )
                             => ( X4 = cZ ) )
                           => ~ ( X3 @ ( cP @ ( cL @ X4 ) @ ( cL @ X5 ) ) ) )
                       => ~ ( X3 @ ( cP @ ( cR @ X4 ) @ ( cR @ X5 ) ) ) ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[18,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SEU974^5 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n024.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Wed Aug 23 14:02:54 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.18/0.41  % SZS status Theorem
% 0.18/0.41  % Mode: cade22grackle2xfee4
% 0.18/0.41  % Steps: 242
% 0.18/0.41  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------