TSTP Solution File: SYO506^1 by Satallax---3.5

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%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SYO506^1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n013.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 19:33:06 EDT 2022

% Result   : Theorem 64.01s 64.61s
% Output   : Proof 64.01s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
    eigen__1: $i ).

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

thf(ty_c,type,
    c: $o > $i > $i > $i ).

thf(sP1,plain,
    ( sP1
  <=> ( ( c @ $false @ eigen__1 @ eigen__1 )
      = ( c @ ( eigen__0 = eigen__1 ) @ eigen__0 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: $i,X2: $i] :
        ( ( c @ ~ $false @ X1 @ X2 )
        = X1 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( eigen__1 = eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: $i] :
        ( ( c @ sP3 @ eigen__0 @ X1 )
        = X1 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ( c @ ~ sP3 @ eigen__0 @ eigen__0 )
      = ( c @ ( eigen__0 = eigen__1 ) @ eigen__0 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: $i] :
        ( ( ( c @ ~ sP3 @ eigen__0 @ eigen__0 )
          = X1 )
       => ( X1
          = ( c @ ~ sP3 @ eigen__0 @ eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: $i,X2: $i] :
        ( ( X1 = X2 )
       => ( X2 = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( eigen__0 = eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( ( c @ ~ sP3 @ eigen__0 @ eigen__0 )
      = eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( sP10
     => ( eigen__0
        = ( c @ ~ sP3 @ eigen__0 @ eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( sP3
      = ( eigen__0 = eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( ( c @ ( eigen__0 = eigen__1 ) @ eigen__0 @ eigen__1 )
      = ( c @ sP3 @ eigen__1 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( ( c @ sP3 @ eigen__0 @ eigen__1 )
      = ( c @ ( eigen__0 = eigen__1 ) @ eigen__0 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ! [X1: $i] :
        ( ( ( c @ ( eigen__0 = eigen__1 ) @ eigen__0 @ eigen__1 )
          = X1 )
       => ( X1
          = ( c @ ( eigen__0 = eigen__1 ) @ eigen__0 @ eigen__1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( eigen__0
      = ( c @ sP3 @ eigen__1 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ! [X1: $i] :
        ( ( c @ sP3 @ eigen__1 @ X1 )
        = X1 ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ( eigen__0
      = ( c @ ~ sP3 @ eigen__0 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ! [X1: $i] :
        ( ( c @ ~ sP3 @ eigen__0 @ X1 )
        = eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( eigen__1 = eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ( ( ~ sP3 )
      = ( eigen__0 = eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ( sP13
     => sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ( ( c @ ( eigen__0 = eigen__1 ) @ eigen__0 @ eigen__1 )
      = eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ( ( c @ sP3 @ eigen__0 @ eigen__1 )
      = eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ! [X1: $i,X2: $i] :
        ( ( c @ sP3 @ X1 @ X2 )
        = X2 ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ( ( c @ sP3 @ eigen__1 @ eigen__1 )
      = ( c @ sP3 @ eigen__1 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ( ( c @ ~ sP3 @ eigen__0 @ eigen__0 )
      = ( c @ sP3 @ eigen__1 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(sP28,plain,
    ( sP28
  <=> ( ( c @ sP3 @ eigen__1 @ eigen__1 )
      = eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP28])]) ).

thf(sP29,plain,
    ( sP29
  <=> ( eigen__0 = eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP29])]) ).

thf(sP30,plain,
    ( sP30
  <=> ( ( c @ sP3 @ eigen__0 @ ( c @ ~ sP3 @ eigen__0 @ eigen__0 ) )
      = ( c @ ~ sP3 @ eigen__0 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP30])]) ).

thf(sP31,plain,
    ( sP31
  <=> ( ( c @ ~ sP3 @ eigen__0 @ eigen__1 )
      = eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP31])]) ).

thf(claim,conjecture,
    ( ~ ( ~ ! [X1: $i,X2: $i] :
              ( ( c @ ( X1 = X2 ) @ X1 @ X2 )
              = X2 )
       => ~ sP2 )
   => ~ sP25 ) ).

thf(h0,negated_conjecture,
    ~ ( ~ ( ~ ! [X1: $i,X2: $i] :
                ( ( c @ ( X1 = X2 ) @ X1 @ X2 )
                = X2 )
         => ~ sP2 )
     => ~ sP25 ),
    inference(assume_negation,[status(cth)],[claim]) ).

thf(h1,assumption,
    ~ ( ~ ! [X1: $i,X2: $i] :
            ( ( c @ ( X1 = X2 ) @ X1 @ X2 )
            = X2 )
     => ~ sP2 ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    sP25,
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ! [X1: $i,X2: $i] :
        ( ( c @ ( X1 = X2 ) @ X1 @ X2 )
        = X2 ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP2,
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ ! [X1: $i] :
        ( ( c @ ( eigen__0 = X1 ) @ eigen__0 @ X1 )
        = X1 ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ sP23,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP28
    | sP16
    | ~ sP4
    | ~ sP26 ),
    inference(confrontation_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP31
    | sP27
    | ~ sP18
    | ~ sP16 ),
    inference(confrontation_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP30
    | sP13
    | ~ sP6
    | ~ sP27 ),
    inference(confrontation_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP6
    | ~ sP21
    | ~ sP9
    | ~ sP29 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP21
    | sP3
    | ~ sP29 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP5
    | sP30 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( sP14
    | ~ sP12
    | ~ sP9
    | ~ sP20 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP24
    | sP23
    | ~ sP14
    | ~ sP20 ),
    inference(confrontation_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP5
    | sP24 ),
    inference(all_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP11
    | ~ sP10
    | sP18 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP7
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP8
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP19
    | sP31 ),
    inference(all_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP19
    | sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(15,plain,
    sP26,
    inference(prop_rule,[status(thm)],]) ).

thf(16,plain,
    ~ sP3,
    inference(prop_rule,[status(thm)],]) ).

thf(17,plain,
    sP9,
    inference(prop_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP29
    | sP4
    | ~ sP20
    | ~ sP9 ),
    inference(confrontation_rule,[status(thm)],]) ).

thf(19,plain,
    ( sP12
    | sP3
    | sP29 ),
    inference(prop_rule,[status(thm)],]) ).

thf(20,plain,
    ( ~ sP2
    | sP19 ),
    inference(all_rule,[status(thm)],]) ).

thf(21,plain,
    ( ~ sP25
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(22,plain,
    ( ~ sP22
    | ~ sP13
    | sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(23,plain,
    ( ~ sP15
    | sP22 ),
    inference(all_rule,[status(thm)],]) ).

thf(24,plain,
    sP20,
    inference(prop_rule,[status(thm)],]) ).

thf(25,plain,
    ( ~ sP28
    | sP23
    | ~ sP1
    | ~ sP28 ),
    inference(confrontation_rule,[status(thm)],]) ).

thf(26,plain,
    ( ~ sP17
    | sP28 ),
    inference(all_rule,[status(thm)],]) ).

thf(27,plain,
    ( ~ sP25
    | sP17 ),
    inference(all_rule,[status(thm)],]) ).

thf(28,plain,
    ( ~ sP8
    | sP15 ),
    inference(all_rule,[status(thm)],]) ).

thf(29,plain,
    sP8,
    inference(eq_sym,[status(thm)],]) ).

thf(30,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h6,h5,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,h6,h4,h2]) ).

thf(31,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h5,30,h6]) ).

thf(32,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h3,31,h5]) ).

thf(33,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,32,h3,h4]) ).

thf(34,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,33,h1,h2]) ).

thf(0,theorem,
    ( ~ ( ~ ! [X1: $i,X2: $i] :
              ( ( c @ ( X1 = X2 ) @ X1 @ X2 )
              = X2 )
       => ~ sP2 )
   => ~ sP25 ),
    inference(contra,[status(thm),contra(discharge,[h0])],[34,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SYO506^1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n013.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  : 600
% 0.12/0.33  % DateTime : Fri Jul  8 21:34:30 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 64.01/64.61  % SZS status Theorem
% 64.01/64.61  % Mode: mode453
% 64.01/64.61  % Inferences: 4284
% 64.01/64.61  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------