TSTP Solution File: SYO170^5 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SYO170^5 : 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 : n021.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 04:45:43 EDT 2023

% Result   : Theorem 0.21s 0.63s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

thf(ty_e,type,
    e: $i ).

thf(ty_b,type,
    b: $i ).

thf(ty_ab,type,
    ab: $i ).

thf(ty_cP,type,
    cP: $i > $i > $i > $o ).

thf(sP1,plain,
    ( sP1
  <=> ( cP @ a @ b @ ab ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
        ( ~ ( ( cP @ ab @ ab @ X2 )
           => ~ ( cP @ ab @ X1 @ X3 ) )
       => ( ( cP @ X2 @ X1 @ X4 )
          = ( cP @ ab @ X3 @ X4 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( cP @ b @ b @ e ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
        ( ~ ( ( cP @ ab @ X1 @ X3 )
           => ~ ( cP @ X1 @ X2 @ X4 ) )
       => ( ( cP @ X3 @ X2 @ X5 )
          = ( cP @ ab @ X4 @ X5 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( cP @ ab @ b @ a )
      = ( cP @ a @ e @ a ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: $i] : ( cP @ X1 @ e @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( cP @ e @ b @ b )
      = ( cP @ ab @ a @ b ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( cP @ ab @ e @ ab ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( cP @ a @ a @ e ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( cP @ ab @ b @ a ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( ( cP @ ab @ ab @ e )
     => ~ sP10 ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( ( cP @ b @ a @ ab )
      = sP8 ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ! [X1: $i] : ( cP @ e @ X1 @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ! [X1: $i,X2: $i] :
        ( ~ ( ( cP @ ab @ ab @ e )
           => ~ ( cP @ ab @ b @ X1 ) )
       => ( ( cP @ e @ b @ X2 )
          = ( cP @ ab @ X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
        ( ~ ( ( cP @ a @ X1 @ X3 )
           => ~ ( cP @ X1 @ X2 @ X4 ) )
       => ( ( cP @ X3 @ X2 @ X5 )
          = ( cP @ a @ X4 @ X5 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
        ( ~ ( ( cP @ a @ b @ X2 )
           => ~ ( cP @ b @ X1 @ X3 ) )
       => ( ( cP @ X2 @ X1 @ X4 )
          = ( cP @ a @ X3 @ X4 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( sP1
     => ~ sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ! [X1: $i,X2: $i,X3: $i] :
        ( ~ ( ( cP @ ab @ a @ X1 )
           => ~ ( cP @ a @ a @ X2 ) )
       => ( ( cP @ X1 @ a @ X3 )
          = ( cP @ ab @ X2 @ X3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ! [X1: $i] :
        ( ~ sP11
       => ( ( cP @ e @ b @ X1 )
          = ( cP @ ab @ a @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( ~ sP17
     => sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ! [X1: $i,X2: $i,X3: $i] :
        ( ~ ( ( cP @ ab @ ab @ X1 )
           => ~ ( cP @ ab @ b @ X2 ) )
       => ( ( cP @ X1 @ b @ X3 )
          = ( cP @ ab @ X2 @ X3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ( cP @ a @ e @ a ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ( cP @ ab @ a @ b ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
        ( ~ ( ( cP @ X1 @ X2 @ X4 )
           => ~ ( cP @ X2 @ X3 @ X5 ) )
       => ( ( cP @ X4 @ X3 @ X6 )
          = ( cP @ X1 @ X5 @ X6 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ( cP @ b @ a @ ab ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ( sP23
     => ~ sP9 ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ! [X1: $i,X2: $i,X3: $i] :
        ( ~ ( ( cP @ a @ b @ X1 )
           => ~ ( cP @ b @ b @ X2 ) )
       => ( ( cP @ X1 @ b @ X3 )
          = ( cP @ a @ X2 @ X3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(sP28,plain,
    ( sP28
  <=> ( ~ sP11
     => sP7 ) ),
    introduced(definition,[new_symbols(definition,[sP28])]) ).

thf(sP29,plain,
    ( sP29
  <=> ( cP @ ab @ ab @ e ) ),
    introduced(definition,[new_symbols(definition,[sP29])]) ).

thf(sP30,plain,
    ( sP30
  <=> ! [X1: $i,X2: $i] :
        ( ~ ( sP1
           => ~ ( cP @ b @ b @ X1 ) )
       => ( ( cP @ ab @ b @ X2 )
          = ( cP @ a @ X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP30])]) ).

thf(sP31,plain,
    ( sP31
  <=> ( cP @ e @ b @ b ) ),
    introduced(definition,[new_symbols(definition,[sP31])]) ).

thf(sP32,plain,
    ( sP32
  <=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
        ( ~ ( ( cP @ ab @ a @ X2 )
           => ~ ( cP @ a @ X1 @ X3 ) )
       => ( ( cP @ X2 @ X1 @ X4 )
          = ( cP @ ab @ X3 @ X4 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP32])]) ).

thf(sP33,plain,
    ( sP33
  <=> ! [X1: $i] :
        ( ~ sP17
       => ( ( cP @ ab @ b @ X1 )
          = ( cP @ a @ e @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP33])]) ).

thf(sP34,plain,
    ( sP34
  <=> ! [X1: $i,X2: $i] :
        ( ~ ( sP23
           => ~ ( cP @ a @ a @ X1 ) )
       => ( ( cP @ b @ a @ X2 )
          = ( cP @ ab @ X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP34])]) ).

thf(sP35,plain,
    ( sP35
  <=> ! [X1: $i] : ( cP @ X1 @ X1 @ e ) ),
    introduced(definition,[new_symbols(definition,[sP35])]) ).

thf(sP36,plain,
    ( sP36
  <=> ( ~ sP26
     => sP12 ) ),
    introduced(definition,[new_symbols(definition,[sP36])]) ).

thf(sP37,plain,
    ( sP37
  <=> ! [X1: $i] :
        ( ~ sP26
       => ( ( cP @ b @ a @ X1 )
          = ( cP @ ab @ e @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP37])]) ).

thf(cTHM105,conjecture,
    ( ~ ( ~ ( ~ ( sP13
               => ~ sP6 )
           => ~ sP35 )
       => ~ sP24 )
   => ( sP1
     => sP25 ) ) ).

thf(h0,negated_conjecture,
    ~ ( ~ ( ~ ( ~ ( sP13
                 => ~ sP6 )
             => ~ sP35 )
         => ~ sP24 )
     => ( sP1
       => sP25 ) ),
    inference(assume_negation,[status(cth)],[cTHM105]) ).

thf(h1,assumption,
    ~ ( ~ ( ~ ( sP13
             => ~ sP6 )
         => ~ sP35 )
     => ~ sP24 ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ( sP1
     => sP25 ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ( ~ ( sP13
         => ~ sP6 )
     => ~ sP35 ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP24,
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ ( sP13
     => ~ sP6 ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    sP35,
    introduced(assumption,[]) ).

thf(h7,assumption,
    sP13,
    introduced(assumption,[]) ).

thf(h8,assumption,
    sP6,
    introduced(assumption,[]) ).

thf(h9,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h10,assumption,
    ~ sP25,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP28
    | sP11
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP11
    | ~ sP29
    | ~ sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP7
    | ~ sP31
    | sP23 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP20
    | sP17
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP17
    | ~ sP1
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP5
    | sP10
    | ~ sP22 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP19
    | sP28 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP36
    | sP26
    | sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP26
    | ~ sP23
    | ~ sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP12
    | sP25
    | ~ sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP33
    | sP20 ),
    inference(all_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP14
    | sP19 ),
    inference(all_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP37
    | sP36 ),
    inference(all_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP30
    | sP33 ),
    inference(all_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP21
    | sP14 ),
    inference(all_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP34
    | sP37 ),
    inference(all_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP18
    | sP34 ),
    inference(all_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP32
    | sP18 ),
    inference(all_rule,[status(thm)],]) ).

thf(19,plain,
    ( ~ sP2
    | sP21 ),
    inference(all_rule,[status(thm)],]) ).

thf(20,plain,
    ( ~ sP4
    | sP32 ),
    inference(all_rule,[status(thm)],]) ).

thf(21,plain,
    ( ~ sP4
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(22,plain,
    ( ~ sP35
    | sP29 ),
    inference(all_rule,[status(thm)],]) ).

thf(23,plain,
    ( ~ sP6
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(24,plain,
    ( ~ sP24
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(25,plain,
    ( ~ sP27
    | sP30 ),
    inference(all_rule,[status(thm)],]) ).

thf(26,plain,
    ( ~ sP16
    | sP27 ),
    inference(all_rule,[status(thm)],]) ).

thf(27,plain,
    ( ~ sP15
    | sP16 ),
    inference(all_rule,[status(thm)],]) ).

thf(28,plain,
    ( ~ sP35
    | sP9 ),
    inference(all_rule,[status(thm)],]) ).

thf(29,plain,
    ( ~ sP6
    | sP22 ),
    inference(all_rule,[status(thm)],]) ).

thf(30,plain,
    ( ~ sP24
    | sP15 ),
    inference(all_rule,[status(thm)],]) ).

thf(31,plain,
    ( ~ sP35
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(32,plain,
    ( ~ sP13
    | sP31 ),
    inference(all_rule,[status(thm)],]) ).

thf(33,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,h7,h8,h6,h4,h9,h10]) ).

thf(34,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h2,33,h9,h10]) ).

thf(35,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h5,34,h7,h8]) ).

thf(36,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,35,h5,h6]) ).

thf(37,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,36,h3,h4]) ).

thf(38,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,37,h1,h2]) ).

thf(0,theorem,
    ( ~ ( ~ ( ~ ( sP13
               => ~ sP6 )
           => ~ sP35 )
       => ~ sP24 )
   => ( sP1
     => sP25 ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[38,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SYO170^5 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n021.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sat Aug 26 05:30:57 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.21/0.63  % SZS status Theorem
% 0.21/0.63  % Mode: cade22grackle2xfee4
% 0.21/0.63  % Steps: 2882
% 0.21/0.63  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------