TSTP Solution File: SYO102^5 by Lash---1.13

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%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SYO102^5 : 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 : n008.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 04:45:13 EDT 2023

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

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
    eigen__0: $i ).

thf(ty_eigen__1,type,
    eigen__1: $i ).

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

thf(ty_eigen__2,type,
    eigen__2: $i ).

thf(sP1,plain,
    ( sP1
  <=> ( cP @ eigen__1 @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

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

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

thf(sP4,plain,
    ( sP4
  <=> ( ~ ( ( cP @ eigen__2 @ eigen__2 )
         => ~ sP1 )
     => ( cP @ eigen__2 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

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

thf(sP6,plain,
    ( sP6
  <=> ( ( cP @ eigen__2 @ eigen__2 )
     => ~ sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: $i] :
        ( ~ ( ( cP @ eigen__2 @ eigen__1 )
           => ~ ( cP @ X1 @ eigen__1 ) )
       => ( cP @ eigen__2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ( cP @ eigen__2 @ eigen__1 )
     => ~ ( cP @ eigen__0 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: $i,X2: $i] :
        ( ~ ( ( cP @ eigen__2 @ X1 )
           => ~ ( cP @ X2 @ X1 ) )
       => ( cP @ eigen__2 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( sP3
     => ~ sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ! [X1: $i,X2: $i] :
        ( ~ ( ( cP @ eigen__0 @ X1 )
           => ~ ( cP @ X2 @ X1 ) )
       => ( cP @ eigen__0 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ! [X1: $i] :
        ( ~ ( sP3
           => ~ ( cP @ X1 @ eigen__0 ) )
       => ( cP @ eigen__0 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

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

thf(sP14,plain,
    ( sP14
  <=> ! [X1: $i] :
        ( ~ ( ( cP @ eigen__2 @ eigen__2 )
           => ~ ( cP @ X1 @ eigen__2 ) )
       => ( cP @ eigen__2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( cP @ eigen__0 @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( cP @ eigen__2 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( ~ sP10
     => sP15 ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

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

thf(sP19,plain,
    ( sP19
  <=> ( ~ sP8
     => sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( cP @ eigen__2 @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(cTHM101,conjecture,
    ( ~ ( sP5
       => ~ sP18 )
   => ! [X1: $i,X2: $i,X3: $i] :
        ( ~ ( ( cP @ X1 @ X2 )
           => ~ ( cP @ X2 @ X3 ) )
       => ( cP @ X1 @ X3 ) ) ) ).

thf(h0,negated_conjecture,
    ~ ( ~ ( sP5
         => ~ sP18 )
     => ! [X1: $i,X2: $i,X3: $i] :
          ( ~ ( ( cP @ X1 @ X2 )
             => ~ ( cP @ X2 @ X3 ) )
         => ( cP @ X1 @ X3 ) ) ),
    inference(assume_negation,[status(cth)],[cTHM101]) ).

thf(h1,assumption,
    ~ ( sP5
     => ~ sP18 ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ! [X1: $i,X2: $i,X3: $i] :
        ( ~ ( ( cP @ X1 @ X2 )
           => ~ ( cP @ X2 @ X3 ) )
       => ( cP @ X1 @ X3 ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP5,
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP18,
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ ! [X1: $i,X2: $i] :
        ( ~ ( ( cP @ eigen__0 @ X1 )
           => ~ ( cP @ X1 @ X2 ) )
       => ( cP @ eigen__0 @ X2 ) ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ ! [X1: $i] :
        ( ~ ( sP13
           => ~ ( cP @ eigen__1 @ X1 ) )
       => ( cP @ eigen__0 @ X1 ) ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    ~ ( ~ ( sP13
         => ~ sP1 )
     => sP15 ),
    introduced(assumption,[]) ).

thf(h8,assumption,
    ~ ( sP13
     => ~ sP1 ),
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ sP15,
    introduced(assumption,[]) ).

thf(h10,assumption,
    sP13,
    introduced(assumption,[]) ).

thf(h11,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP8
    | ~ sP16
    | ~ sP13 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP19
    | sP8
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP7
    | sP19 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP6
    | ~ sP20
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP4
    | sP6
    | sP16 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP9
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP14
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP9
    | sP14 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP10
    | ~ sP3
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP17
    | sP10
    | sP15 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP5
    | sP20 ),
    inference(all_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP18
    | sP9 ),
    inference(all_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP12
    | sP17 ),
    inference(all_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP11
    | sP12 ),
    inference(all_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP5
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP18
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(17,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h10,h11,h8,h9,h7,h6,h5,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,h3,h4,h10,h11,h9]) ).

thf(18,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h8,h9,h7,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h10,h11])],[h8,17,h10,h11]) ).

thf(19,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h7,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h8,h9])],[h7,18,h8,h9]) ).

thf(20,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,19,h7]) ).

thf(21,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h5,20,h6]) ).

thf(22,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h2,21,h5]) ).

thf(23,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,22,h3,h4]) ).

thf(24,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,23,h1,h2]) ).

thf(0,theorem,
    ( ~ ( sP5
       => ~ sP18 )
   => ! [X1: $i,X2: $i,X3: $i] :
        ( ~ ( ( cP @ X1 @ X2 )
           => ~ ( cP @ X2 @ X3 ) )
       => ( cP @ X1 @ X3 ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[24,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : SYO102^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35  % Computer : n008.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Sat Aug 26 04:29:47 EDT 2023
% 0.13/0.36  % CPUTime  : 
% 0.18/0.41  % SZS status Theorem
% 0.18/0.41  % Mode: cade22grackle2xfee4
% 0.18/0.41  % Steps: 73
% 0.18/0.41  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------