TSTP Solution File: SEV194^5 by Lash---1.13

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%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEV194^5 : 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 : n002.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 19:32:57 EDT 2023

% Result   : Theorem 0.16s 0.43s
% Output   : Proof 0.16s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

thf(ty_x,type,
    x: a ).

thf(ty_eigen__0,type,
    eigen__0: a > a > a > $o ).

thf(ty_c0,type,
    c0: a ).

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

thf(sP1,plain,
    ( sP1
  <=> ! [X1: a,X2: a,X3: a] :
        ( ( ~ ( ( ( X1 = c0 )
               => ( X2 != X3 ) )
             => ~ ( ( X2 = c0 )
                 => ( X1 != X3 ) ) )
         => ~ ! [X4: a,X5: a,X6: a,X7: a,X8: a,X9: a] :
                ( ~ ( ~ ( ~ ( ( X1
                              = ( cP @ X4 @ X5 ) )
                           => ( X2
                             != ( cP @ X6 @ X7 ) ) )
                       => ( X3
                         != ( cP @ X8 @ X9 ) ) )
                   => ~ ( eigen__0 @ X4 @ X6 @ X8 ) )
               => ~ ( eigen__0 @ X5 @ X7 @ X9 ) ) )
       => ( eigen__0 @ X1 @ X2 @ X3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: a] :
        ( ( ~ ( ( x != X1 )
             => ~ ( ( x = c0 )
                 => ( c0 != X1 ) ) )
         => ~ ! [X2: a,X3: a,X4: a,X5: a,X6: a,X7: a] :
                ( ~ ( ~ ( ~ ( ( c0
                              = ( cP @ X2 @ X3 ) )
                           => ( x
                             != ( cP @ X4 @ X5 ) ) )
                       => ( X1
                         != ( cP @ X6 @ X7 ) ) )
                   => ~ ( eigen__0 @ X2 @ X4 @ X6 ) )
               => ~ ( eigen__0 @ X3 @ X5 @ X7 ) ) )
       => ( eigen__0 @ c0 @ x @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: a,X2: a] :
        ( ( ~ ( ( X1 != X2 )
             => ~ ( ( X1 = c0 )
                 => ( c0 != X2 ) ) )
         => ~ ! [X3: a,X4: a,X5: a,X6: a,X7: a,X8: a] :
                ( ~ ( ~ ( ~ ( ( c0
                              = ( cP @ X3 @ X4 ) )
                           => ( X1
                             != ( cP @ X5 @ X6 ) ) )
                       => ( X2
                         != ( cP @ X7 @ X8 ) ) )
                   => ~ ( eigen__0 @ X3 @ X5 @ X7 ) )
               => ~ ( eigen__0 @ X4 @ X6 @ X8 ) ) )
       => ( eigen__0 @ c0 @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( eigen__0 @ c0 @ x @ x ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(cS_INCL_LEM2_pme,conjecture,
    ! [X1: a > a > a > $o] :
      ( ! [X2: a,X3: a,X4: a] :
          ( ( ~ ( ( ( X2 = c0 )
                 => ( X3 != X4 ) )
               => ~ ( ( X3 = c0 )
                   => ( X2 != X4 ) ) )
           => ~ ! [X5: a,X6: a,X7: a,X8: a,X9: a,X10: a] :
                  ( ~ ( ~ ( ~ ( ( X2
                                = ( cP @ X5 @ X6 ) )
                             => ( X3
                               != ( cP @ X7 @ X8 ) ) )
                         => ( X4
                           != ( cP @ X9 @ X10 ) ) )
                     => ~ ( X1 @ X5 @ X7 @ X9 ) )
                 => ~ ( X1 @ X6 @ X8 @ X10 ) ) )
         => ( X1 @ X2 @ X3 @ X4 ) )
     => ( X1 @ c0 @ x @ x ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: a > a > a > $o] :
        ( ! [X2: a,X3: a,X4: a] :
            ( ( ~ ( ( ( X2 = c0 )
                   => ( X3 != X4 ) )
                 => ~ ( ( X3 = c0 )
                     => ( X2 != X4 ) ) )
             => ~ ! [X5: a,X6: a,X7: a,X8: a,X9: a,X10: a] :
                    ( ~ ( ~ ( ~ ( ( X2
                                  = ( cP @ X5 @ X6 ) )
                               => ( X3
                                 != ( cP @ X7 @ X8 ) ) )
                           => ( X4
                             != ( cP @ X9 @ X10 ) ) )
                       => ~ ( X1 @ X5 @ X7 @ X9 ) )
                   => ~ ( X1 @ X6 @ X8 @ X10 ) ) )
           => ( X1 @ X2 @ X3 @ X4 ) )
       => ( X1 @ c0 @ x @ x ) ),
    inference(assume_negation,[status(cth)],[cS_INCL_LEM2_pme]) ).

thf(h1,assumption,
    ~ ( sP1
     => sP4 ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ sP4,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP2
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP3
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP1
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h2,h3,h1,h0])],[1,2,3,h2,h3]) ).

thf(5,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,4,h2,h3]) ).

thf(6,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,5,h1]) ).

thf(0,theorem,
    ! [X1: a > a > a > $o] :
      ( ! [X2: a,X3: a,X4: a] :
          ( ( ~ ( ( ( X2 = c0 )
                 => ( X3 != X4 ) )
               => ~ ( ( X3 = c0 )
                   => ( X2 != X4 ) ) )
           => ~ ! [X5: a,X6: a,X7: a,X8: a,X9: a,X10: a] :
                  ( ~ ( ~ ( ~ ( ( X2
                                = ( cP @ X5 @ X6 ) )
                             => ( X3
                               != ( cP @ X7 @ X8 ) ) )
                         => ( X4
                           != ( cP @ X9 @ X10 ) ) )
                     => ~ ( X1 @ X5 @ X7 @ X9 ) )
                 => ~ ( X1 @ X6 @ X8 @ X10 ) ) )
         => ( X1 @ X2 @ X3 @ X4 ) )
     => ( X1 @ c0 @ x @ x ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : SEV194^5 : TPTP v8.1.2. Released v4.0.0.
% 0.15/0.15  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.16/0.37  % Computer : n002.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Thu Aug 24 04:03:01 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 0.16/0.43  % SZS status Theorem
% 0.16/0.43  % Mode: cade22grackle2xfee4
% 0.16/0.43  % Steps: 11
% 0.16/0.43  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------