TSTP Solution File: SYO170^5 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SYO170^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n009.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  : 600s
% DateTime : Thu Jul 21 19:30:38 EDT 2022

% Result   : Theorem 28.19s 28.36s
% Output   : Proof 28.19s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

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

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

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

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

thf(sP1,plain,
    ( sP1
  <=> ( ~ ( ~ ( ! [X1: $i] : ( cP @ e @ X1 @ X1 )
             => ~ ! [X1: $i] : ( cP @ X1 @ e @ X1 ) )
         => ~ ! [X1: $i] : ( cP @ X1 @ X1 @ e ) )
     => ~ ! [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,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( cP @ a @ e @ a ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

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

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

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

thf(sP6,plain,
    ( sP6
  <=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
        ( ~ ( ( cP @ a @ a @ X2 )
           => ~ ( cP @ a @ X1 @ X3 ) )
       => ( ( cP @ X2 @ X1 @ X4 )
          = ( cP @ a @ X3 @ X4 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [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,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ( cP @ b @ b @ e )
     => ~ sP5 ) ),
    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 @ e @ b @ b )
      = ( cP @ a @ ab @ b ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
        ( ~ ( ( cP @ b @ b @ X2 )
           => ~ ( cP @ b @ X1 @ X3 ) )
       => ( ( cP @ X2 @ X1 @ X4 )
          = ( cP @ b @ X3 @ X4 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ! [X1: $i,X2: $i,X3: $i] :
        ( ~ ( ( cP @ b @ b @ X1 )
           => ~ ( cP @ b @ ab @ X2 ) )
       => ( ( cP @ X1 @ ab @ X3 )
          = ( cP @ b @ X2 @ X3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
        ( ~ ( ( cP @ b @ X1 @ X3 )
           => ~ ( cP @ X1 @ X2 @ X4 ) )
       => ( ( cP @ X3 @ X2 @ X5 )
          = ( cP @ b @ X4 @ X5 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

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

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

thf(sP16,plain,
    ( sP16
  <=> ( ~ ( ( cP @ a @ ab @ b )
         => ~ ( cP @ ab @ ab @ e ) )
     => ( sP5 = sP2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( cP @ a @ b @ ab ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ( ~ sP8
     => ( ( cP @ e @ ab @ ab )
        = sP3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ( ( cP @ a @ ab @ b )
     => ~ ( cP @ ab @ ab @ e ) ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ! [X1: $i,X2: $i,X3: $i] :
        ( ~ ( ( cP @ a @ a @ X1 )
           => ~ ( cP @ a @ b @ X2 ) )
       => ( ( cP @ X1 @ b @ X3 )
          = ( cP @ a @ X2 @ X3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ! [X1: $i] :
        ( ~ sP8
       => ( ( cP @ e @ ab @ X1 )
          = ( cP @ b @ a @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ( sP5 = sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

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

thf(sP24,plain,
    ( sP24
  <=> ( cP @ ab @ ab @ e ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ! [X1: $i] : ( cP @ X1 @ X1 @ e ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ( cP @ e @ ab @ ab ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ! [X1: $i] : ( cP @ X1 @ e @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(sP28,plain,
    ( sP28
  <=> ( cP @ b @ b @ e ) ),
    introduced(definition,[new_symbols(definition,[sP28])]) ).

thf(sP29,plain,
    ( sP29
  <=> ( sP9
     => ~ sP17 ) ),
    introduced(definition,[new_symbols(definition,[sP29])]) ).

thf(sP30,plain,
    ( sP30
  <=> ! [X1: $i] :
        ( ~ sP29
       => ( ( cP @ e @ b @ X1 )
          = ( cP @ a @ ab @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP30])]) ).

thf(sP31,plain,
    ( sP31
  <=> ( sP17
     => sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP31])]) ).

thf(sP32,plain,
    ( sP32
  <=> ( cP @ a @ ab @ b ) ),
    introduced(definition,[new_symbols(definition,[sP32])]) ).

thf(sP33,plain,
    ( sP33
  <=> ! [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,[sP33])]) ).

thf(sP34,plain,
    ( sP34
  <=> ( ~ sP1
     => sP31 ) ),
    introduced(definition,[new_symbols(definition,[sP34])]) ).

thf(sP35,plain,
    ( sP35
  <=> ! [X1: $i,X2: $i] :
        ( ~ ( sP28
           => ~ ( cP @ b @ ab @ X1 ) )
       => ( ( cP @ e @ ab @ X2 )
          = ( cP @ b @ X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP35])]) ).

thf(sP36,plain,
    ( sP36
  <=> ( sP4
     => ~ sP27 ) ),
    introduced(definition,[new_symbols(definition,[sP36])]) ).

thf(sP37,plain,
    ( sP37
  <=> ( sP26 = sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP37])]) ).

thf(sP38,plain,
    ( sP38
  <=> ! [X1: $i,X2: $i] :
        ( ~ ( sP9
           => ~ ( cP @ a @ b @ X1 ) )
       => ( ( cP @ e @ b @ X2 )
          = ( cP @ a @ X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP38])]) ).

thf(sP39,plain,
    ( sP39
  <=> ( ~ sP36
     => ~ sP25 ) ),
    introduced(definition,[new_symbols(definition,[sP39])]) ).

thf(sP40,plain,
    ( sP40
  <=> ( ~ sP29
     => sP10 ) ),
    introduced(definition,[new_symbols(definition,[sP40])]) ).

thf(sP41,plain,
    ( sP41
  <=> ( cP @ e @ b @ b ) ),
    introduced(definition,[new_symbols(definition,[sP41])]) ).

thf(sP42,plain,
    ( sP42
  <=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
        ( ~ ( ( cP @ a @ ab @ X2 )
           => ~ ( cP @ ab @ X1 @ X3 ) )
       => ( ( cP @ X2 @ X1 @ X4 )
          = ( cP @ a @ X3 @ X4 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP42])]) ).

thf(cTHM105,conjecture,
    sP34 ).

thf(h0,negated_conjecture,
    ~ sP34,
    inference(assume_negation,[status(cth)],[cTHM105]) ).

thf(1,plain,
    ( ~ sP29
    | ~ sP9
    | ~ sP17 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP8
    | ~ sP28
    | ~ sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP37
    | ~ sP26
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP10
    | ~ sP41
    | sP32 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP19
    | ~ sP32
    | ~ sP24 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP40
    | sP29
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP22
    | sP5
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP18
    | sP8
    | sP37 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP16
    | sP19
    | sP22 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP30
    | sP40 ),
    inference(all_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP21
    | sP18 ),
    inference(all_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP14
    | sP16 ),
    inference(all_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP38
    | sP30 ),
    inference(all_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP35
    | sP21 ),
    inference(all_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP23
    | sP14 ),
    inference(all_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP20
    | sP38 ),
    inference(all_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP12
    | sP35 ),
    inference(all_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP15
    | sP23 ),
    inference(all_rule,[status(thm)],]) ).

thf(19,plain,
    ( ~ sP42
    | sP15 ),
    inference(all_rule,[status(thm)],]) ).

thf(20,plain,
    ( ~ sP25
    | sP24 ),
    inference(all_rule,[status(thm)],]) ).

thf(21,plain,
    ( ~ sP4
    | sP26 ),
    inference(all_rule,[status(thm)],]) ).

thf(22,plain,
    ( ~ sP33
    | sP42 ),
    inference(all_rule,[status(thm)],]) ).

thf(23,plain,
    ( ~ sP11
    | sP12 ),
    inference(all_rule,[status(thm)],]) ).

thf(24,plain,
    ( ~ sP6
    | sP20 ),
    inference(all_rule,[status(thm)],]) ).

thf(25,plain,
    ( ~ sP13
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(26,plain,
    ( ~ sP33
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(27,plain,
    ( ~ sP7
    | sP13 ),
    inference(all_rule,[status(thm)],]) ).

thf(28,plain,
    ( ~ sP25
    | sP28 ),
    inference(all_rule,[status(thm)],]) ).

thf(29,plain,
    ( ~ sP4
    | sP41 ),
    inference(all_rule,[status(thm)],]) ).

thf(30,plain,
    ( ~ sP7
    | sP33 ),
    inference(all_rule,[status(thm)],]) ).

thf(31,plain,
    ( ~ sP25
    | sP9 ),
    inference(all_rule,[status(thm)],]) ).

thf(32,plain,
    ( ~ sP27
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(33,plain,
    ( sP36
    | sP27 ),
    inference(prop_rule,[status(thm)],]) ).

thf(34,plain,
    ( sP36
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(35,plain,
    ( sP39
    | sP25 ),
    inference(prop_rule,[status(thm)],]) ).

thf(36,plain,
    ( sP39
    | ~ sP36 ),
    inference(prop_rule,[status(thm)],]) ).

thf(37,plain,
    ( sP31
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(38,plain,
    ( sP31
    | sP17 ),
    inference(prop_rule,[status(thm)],]) ).

thf(39,plain,
    ( sP1
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(40,plain,
    ( sP1
    | ~ sP39 ),
    inference(prop_rule,[status(thm)],]) ).

thf(41,plain,
    ( sP34
    | ~ sP31 ),
    inference(prop_rule,[status(thm)],]) ).

thf(42,plain,
    ( sP34
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(43,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,h0]) ).

thf(0,theorem,
    sP34,
    inference(contra,[status(thm),contra(discharge,[h0])],[43,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SYO170^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n009.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  : 600
% 0.13/0.34  % DateTime : Sat Jul  9 04:58:07 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 28.19/28.36  % SZS status Theorem
% 28.19/28.36  % Mode: mode454
% 28.19/28.36  % Inferences: 11205
% 28.19/28.36  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------