TSTP Solution File: SEV091^5 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEV091^5 : TPTP v7.5.0. 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
% DateTime : Tue Mar 30 22:04:56 EDT 2021

% Result   : Theorem 0.19s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : None (MakeTreeStats fails)
% Syntax   : Number of formulae    : 184

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
    eigen__2: $i ).

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

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

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

thf(ty_eigen__4,type,
    eigen__4: $i ).

thf(ty_eigen__3,type,
    eigen__3: $i ).

thf(ty_cQ,type,
    cQ: $i > $i > $o ).

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

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

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

thf(sP4,plain,
    ( sP4
  <=> ( ~ ( ( cP @ eigen__0 @ eigen__2 )
         => ~ ( cP @ eigen__2 @ eigen__1 ) )
     => sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( cP @ eigen__0 @ eigen__3 )
     => ~ ( cP @ eigen__3 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ( cQ @ eigen__4 @ eigen__0 )
     => ~ sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ~ ( ( cQ @ eigen__2 @ eigen__1 )
         => ~ ( cQ @ eigen__1 @ eigen__4 ) )
     => ( cQ @ eigen__2 @ eigen__4 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( cQ @ eigen__4 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: $i] :
        ( ~ ( ( cQ @ eigen__3 @ eigen__1 )
           => ~ ( cQ @ eigen__1 @ X1 ) )
       => ( cQ @ eigen__3 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ! [X1: $i,X2: $i] :
        ( ~ ( ( cQ @ eigen__3 @ X1 )
           => ~ ( cQ @ X1 @ X2 ) )
       => ( cQ @ eigen__3 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( sP8
     => ~ sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( ( cQ @ eigen__3 @ eigen__1 )
     => ~ ( cQ @ eigen__1 @ eigen__4 ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( cQ @ eigen__2 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ! [X1: $i,X2: $i,X3: $i] :
        ( ~ ( ( cQ @ X1 @ X2 )
           => ~ ( cQ @ X2 @ X3 ) )
       => ( cQ @ X1 @ X3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( ~ ( cP @ eigen__4 @ eigen__1 )
     => ( cQ @ eigen__4 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( cQ @ eigen__4 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( ~ ( sP8
         => ~ ( cQ @ eigen__0 @ eigen__3 ) )
     => ( cQ @ eigen__4 @ eigen__3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ( cQ @ eigen__1 @ eigen__4 ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ( ~ ( cP @ eigen__0 @ eigen__2 )
     => sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( cQ @ eigen__0 @ eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ( sP16
     => sP18 ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ( cQ @ eigen__0 @ eigen__4 ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ( cP @ eigen__0 @ eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ( cP @ eigen__0 @ eigen__4 ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ( ~ ( sP16
         => ~ ( cQ @ eigen__1 @ eigen__0 ) )
     => sP8 ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ( ~ sP24
     => sP22 ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ( ~ sP6
     => sP16 ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(sP28,plain,
    ( sP28
  <=> ( ( cQ @ eigen__3 @ eigen__4 )
     => ( cQ @ eigen__4 @ eigen__3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP28])]) ).

thf(sP29,plain,
    ( sP29
  <=> ( ~ ( cP @ eigen__2 @ eigen__1 )
     => sP13 ) ),
    introduced(definition,[new_symbols(definition,[sP29])]) ).

thf(sP30,plain,
    ( sP30
  <=> ! [X1: $i] :
        ( ~ ( sP8
           => ~ ( cQ @ eigen__0 @ X1 ) )
       => ( cQ @ eigen__4 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP30])]) ).

thf(sP31,plain,
    ( sP31
  <=> ! [X1: $i,X2: $i,X3: $i] :
        ( ~ ( ( cP @ X1 @ X2 )
           => ~ ( cP @ X2 @ X3 ) )
       => ( cP @ X1 @ X3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP31])]) ).

thf(sP32,plain,
    ( sP32
  <=> ( sP22
     => sP8 ) ),
    introduced(definition,[new_symbols(definition,[sP32])]) ).

thf(sP33,plain,
    ( sP33
  <=> ( sP13
     => ~ sP18 ) ),
    introduced(definition,[new_symbols(definition,[sP33])]) ).

thf(sP34,plain,
    ( sP34
  <=> ! [X1: $i] :
        ( ~ ( sP23
           => ~ ( cP @ eigen__3 @ X1 ) )
       => ( cP @ eigen__0 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP34])]) ).

thf(sP35,plain,
    ( sP35
  <=> ( ~ ( sP24
         => ~ ( cP @ eigen__4 @ eigen__1 ) )
     => sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP35])]) ).

thf(sP36,plain,
    ( sP36
  <=> ( sP16
     => ~ ( cQ @ eigen__1 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP36])]) ).

thf(sP37,plain,
    ( sP37
  <=> ! [X1: $i,X2: $i] :
        ( ~ ( ( cQ @ eigen__4 @ X1 )
           => ~ ( cQ @ X1 @ X2 ) )
       => ( cQ @ eigen__4 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP37])]) ).

thf(sP38,plain,
    ( sP38
  <=> ( cQ @ eigen__4 @ eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP38])]) ).

thf(sP39,plain,
    ( sP39
  <=> ( ~ sP5
     => sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP39])]) ).

thf(sP40,plain,
    ( sP40
  <=> ( sP3
     => ( cQ @ eigen__1 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP40])]) ).

thf(sP41,plain,
    ( sP41
  <=> ( sP8
     => ~ sP20 ) ),
    introduced(definition,[new_symbols(definition,[sP41])]) ).

thf(sP42,plain,
    ( sP42
  <=> ! [X1: $i] :
        ( ~ ( sP24
           => ~ ( cP @ eigen__4 @ X1 ) )
       => ( cP @ eigen__0 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP42])]) ).

thf(sP43,plain,
    ( sP43
  <=> ! [X1: $i] :
        ( ~ ( ( cP @ eigen__0 @ eigen__2 )
           => ~ ( cP @ eigen__2 @ X1 ) )
       => ( cP @ eigen__0 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP43])]) ).

thf(sP44,plain,
    ( sP44
  <=> ( sP24
     => ~ ( cP @ eigen__4 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP44])]) ).

thf(sP45,plain,
    ( sP45
  <=> ( ~ sP11
     => ( cQ @ eigen__4 @ eigen__2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP45])]) ).

thf(sP46,plain,
    ( sP46
  <=> ! [X1: $i] :
        ( ~ ( sP13
           => ~ ( cQ @ eigen__1 @ X1 ) )
       => ( cQ @ eigen__2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP46])]) ).

thf(sP47,plain,
    ( sP47
  <=> ! [X1: $i] :
        ( ~ ( cP @ eigen__0 @ X1 )
       => ( cQ @ eigen__0 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP47])]) ).

thf(sP48,plain,
    ( sP48
  <=> ( cP @ eigen__2 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP48])]) ).

thf(sP49,plain,
    ( sP49
  <=> ( ~ sP23
     => sP20 ) ),
    introduced(definition,[new_symbols(definition,[sP49])]) ).

thf(sP50,plain,
    ( sP50
  <=> ! [X1: $i] :
        ( ~ ( cP @ eigen__4 @ X1 )
       => ( cQ @ eigen__4 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP50])]) ).

thf(sP51,plain,
    ( sP51
  <=> ! [X1: $i,X2: $i] :
        ( ~ ( ( cP @ eigen__0 @ X1 )
           => ~ ( cP @ X1 @ X2 ) )
       => ( cP @ eigen__0 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP51])]) ).

thf(sP52,plain,
    ( sP52
  <=> ( ~ sP12
     => ( cQ @ eigen__3 @ eigen__4 ) ) ),
    introduced(definition,[new_symbols(definition,[sP52])]) ).

thf(sP53,plain,
    ( sP53
  <=> ( cQ @ eigen__2 @ eigen__4 ) ),
    introduced(definition,[new_symbols(definition,[sP53])]) ).

thf(sP54,plain,
    ( sP54
  <=> ( cP @ eigen__4 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP54])]) ).

thf(sP55,plain,
    ( sP55
  <=> ( cQ @ eigen__1 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP55])]) ).

thf(sP56,plain,
    ( sP56
  <=> ! [X1: $i,X2: $i] :
        ( ~ ( cP @ X1 @ X2 )
       => ( cQ @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP56])]) ).

thf(sP57,plain,
    ( sP57
  <=> ( sP53
     => ~ sP38 ) ),
    introduced(definition,[new_symbols(definition,[sP57])]) ).

thf(sP58,plain,
    ( sP58
  <=> ! [X1: $i] :
        ( ~ ( cP @ eigen__3 @ X1 )
       => ( cQ @ eigen__3 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP58])]) ).

thf(sP59,plain,
    ( sP59
  <=> ( cQ @ eigen__2 @ eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP59])]) ).

thf(sP60,plain,
    ( sP60
  <=> ( cQ @ eigen__3 @ eigen__4 ) ),
    introduced(definition,[new_symbols(definition,[sP60])]) ).

thf(sP61,plain,
    ( sP61
  <=> ( ~ ( cP @ eigen__3 @ eigen__1 )
     => ( cQ @ eigen__3 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP61])]) ).

thf(sP62,plain,
    ( sP62
  <=> ( ~ sP57
     => sP59 ) ),
    introduced(definition,[new_symbols(definition,[sP62])]) ).

thf(sP63,plain,
    ( sP63
  <=> ( ( cQ @ eigen__4 @ eigen__2 )
     => sP53 ) ),
    introduced(definition,[new_symbols(definition,[sP63])]) ).

thf(sP64,plain,
    ( sP64
  <=> ( ~ sP1
     => sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP64])]) ).

thf(sP65,plain,
    ( sP65
  <=> ! [X1: $i] :
        ( ~ ( sP16
           => ~ ( cQ @ eigen__1 @ X1 ) )
       => ( cQ @ eigen__4 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP65])]) ).

thf(sP66,plain,
    ( sP66
  <=> ( cQ @ eigen__4 @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP66])]) ).

thf(sP67,plain,
    ( sP67
  <=> ! [X1: $i] :
        ( ~ ( cP @ eigen__2 @ X1 )
       => ( cQ @ eigen__2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP67])]) ).

thf(sP68,plain,
    ( sP68
  <=> ! [X1: $i] :
        ( ~ ( sP53
           => ~ ( cQ @ eigen__4 @ X1 ) )
       => ( cQ @ eigen__2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP68])]) ).

thf(sP69,plain,
    ( sP69
  <=> ! [X1: $i] :
        ( ( cQ @ eigen__4 @ X1 )
       => ( cQ @ X1 @ eigen__4 ) ) ),
    introduced(definition,[new_symbols(definition,[sP69])]) ).

thf(sP70,plain,
    ( sP70
  <=> ! [X1: $i] :
        ( ( cQ @ eigen__3 @ X1 )
       => ( cQ @ X1 @ eigen__3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP70])]) ).

thf(sP71,plain,
    ( sP71
  <=> ( cP @ eigen__0 @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP71])]) ).

thf(sP72,plain,
    ( sP72
  <=> ! [X1: $i,X2: $i] :
        ( ( cQ @ X1 @ X2 )
       => ( cQ @ X2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP72])]) ).

thf(sP73,plain,
    ( sP73
  <=> ( cP @ eigen__3 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP73])]) ).

thf(sP74,plain,
    ( sP74
  <=> ! [X1: $i,X2: $i] :
        ( ~ ( ( cQ @ eigen__2 @ X1 )
           => ~ ( cQ @ X1 @ X2 ) )
       => ( cQ @ eigen__2 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP74])]) ).

thf(sP75,plain,
    ( sP75
  <=> ( cQ @ eigen__3 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP75])]) ).

thf(sP76,plain,
    ( sP76
  <=> ! [X1: $i] :
        ( ( cQ @ eigen__0 @ X1 )
       => ( cQ @ X1 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP76])]) ).

thf(sP77,plain,
    ( sP77
  <=> ( sP71
     => ~ sP48 ) ),
    introduced(definition,[new_symbols(definition,[sP77])]) ).

thf(cCADE13_pme,conjecture,
    ( ~ ( ~ ( ~ ( sP31
               => ~ sP14 )
           => ~ sP72 )
       => ~ sP56 )
   => ( ~ ! [X1: $i] : ( !! @ ( cP @ X1 ) )
     => ! [X1: $i] : ( !! @ ( cQ @ X1 ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ( ~ ( ~ ( ~ ( sP31
                 => ~ sP14 )
             => ~ sP72 )
         => ~ sP56 )
     => ( ~ ! [X1: $i] : ( !! @ ( cP @ X1 ) )
       => ! [X1: $i] : ( !! @ ( cQ @ X1 ) ) ) ),
    inference(assume_negation,[status(cth)],[cCADE13_pme]) ).

thf(h1,assumption,
    ~ ( ~ ( ~ ( sP31
             => ~ sP14 )
         => ~ sP72 )
     => ~ sP56 ),
    introduced(assumption,[]) ).

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

thf(h3,assumption,
    ~ ( ~ ( sP31
         => ~ sP14 )
     => ~ sP72 ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP56,
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ ( sP31
     => ~ sP14 ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    sP72,
    introduced(assumption,[]) ).

thf(h7,assumption,
    sP31,
    introduced(assumption,[]) ).

thf(h8,assumption,
    sP14,
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ ! [X1: $i] : ( !! @ ( cP @ X1 ) ),
    introduced(assumption,[]) ).

thf(h10,assumption,
    ~ ! [X1: $i] : ( !! @ ( cQ @ X1 ) ),
    introduced(assumption,[]) ).

thf(h11,assumption,
    ~ ( !! @ ( cP @ eigen__0 ) ),
    introduced(assumption,[]) ).

thf(h12,assumption,
    ~ sP1,
    introduced(assumption,[]) ).

thf(h13,assumption,
    ~ ( !! @ ( cQ @ eigen__2 ) ),
    introduced(assumption,[]) ).

thf(h14,assumption,
    ~ sP59,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP43
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP4
    | sP77
    | sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP77
    | ~ sP71
    | ~ sP48 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP51
    | sP43 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP34
    | sP39 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP39
    | sP5
    | sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP5
    | ~ sP23
    | ~ sP73 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP51
    | sP34 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP47
    | sP26 ),
    inference(all_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP26
    | sP24
    | sP22 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP31
    | sP51 ),
    inference(all_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP51
    | sP42 ),
    inference(all_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP42
    | sP35 ),
    inference(all_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP35
    | sP44
    | sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP44
    | ~ sP24
    | ~ sP54 ),
    inference(prop_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP58
    | sP61 ),
    inference(all_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP61
    | sP73
    | sP75 ),
    inference(prop_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP67
    | sP29 ),
    inference(all_rule,[status(thm)],]) ).

thf(19,plain,
    ( ~ sP29
    | sP48
    | sP13 ),
    inference(prop_rule,[status(thm)],]) ).

thf(20,plain,
    ( ~ sP47
    | sP19 ),
    inference(all_rule,[status(thm)],]) ).

thf(21,plain,
    ( ~ sP19
    | sP71
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(22,plain,
    ( ~ sP47
    | sP49 ),
    inference(all_rule,[status(thm)],]) ).

thf(23,plain,
    ( ~ sP49
    | sP23
    | sP20 ),
    inference(prop_rule,[status(thm)],]) ).

thf(24,plain,
    ( ~ sP10
    | sP9 ),
    inference(all_rule,[status(thm)],]) ).

thf(25,plain,
    ( ~ sP9
    | sP52 ),
    inference(all_rule,[status(thm)],]) ).

thf(26,plain,
    ( ~ sP52
    | sP12
    | sP60 ),
    inference(prop_rule,[status(thm)],]) ).

thf(27,plain,
    ( ~ sP12
    | ~ sP75
    | ~ sP18 ),
    inference(prop_rule,[status(thm)],]) ).

thf(28,plain,
    ( ~ sP74
    | sP46 ),
    inference(all_rule,[status(thm)],]) ).

thf(29,plain,
    ( ~ sP46
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(30,plain,
    ( ~ sP7
    | sP33
    | sP53 ),
    inference(prop_rule,[status(thm)],]) ).

thf(31,plain,
    ( ~ sP33
    | ~ sP13
    | ~ sP18 ),
    inference(prop_rule,[status(thm)],]) ).

thf(32,plain,
    ( ~ sP76
    | sP32 ),
    inference(all_rule,[status(thm)],]) ).

thf(33,plain,
    ( ~ sP32
    | ~ sP22
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(34,plain,
    ( ~ sP50
    | sP15 ),
    inference(all_rule,[status(thm)],]) ).

thf(35,plain,
    ( ~ sP15
    | sP54
    | sP16 ),
    inference(prop_rule,[status(thm)],]) ).

thf(36,plain,
    ( ~ sP30
    | sP45 ),
    inference(all_rule,[status(thm)],]) ).

thf(37,plain,
    ( ~ sP45
    | sP11
    | sP66 ),
    inference(prop_rule,[status(thm)],]) ).

thf(38,plain,
    ( ~ sP11
    | ~ sP8
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(39,plain,
    ( ~ sP30
    | sP17 ),
    inference(all_rule,[status(thm)],]) ).

thf(40,plain,
    ( ~ sP17
    | sP41
    | sP38 ),
    inference(prop_rule,[status(thm)],]) ).

thf(41,plain,
    ( ~ sP41
    | ~ sP8
    | ~ sP20 ),
    inference(prop_rule,[status(thm)],]) ).

thf(42,plain,
    ( ~ sP69
    | sP21 ),
    inference(all_rule,[status(thm)],]) ).

thf(43,plain,
    ( ~ sP21
    | ~ sP16
    | sP18 ),
    inference(prop_rule,[status(thm)],]) ).

thf(44,plain,
    ( ~ sP37
    | sP30 ),
    inference(all_rule,[status(thm)],]) ).

thf(45,plain,
    ( ~ sP30
    | sP27 ),
    inference(all_rule,[status(thm)],]) ).

thf(46,plain,
    ( ~ sP27
    | sP6
    | sP16 ),
    inference(prop_rule,[status(thm)],]) ).

thf(47,plain,
    ( ~ sP6
    | ~ sP8
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(48,plain,
    ( ~ sP37
    | sP65 ),
    inference(all_rule,[status(thm)],]) ).

thf(49,plain,
    ( ~ sP65
    | sP25 ),
    inference(all_rule,[status(thm)],]) ).

thf(50,plain,
    ( ~ sP25
    | sP36
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(51,plain,
    ( ~ sP36
    | ~ sP16
    | ~ sP55 ),
    inference(prop_rule,[status(thm)],]) ).

thf(52,plain,
    ( ~ sP70
    | sP28 ),
    inference(all_rule,[status(thm)],]) ).

thf(53,plain,
    ( ~ sP28
    | ~ sP60
    | sP38 ),
    inference(prop_rule,[status(thm)],]) ).

thf(54,plain,
    ( ~ sP69
    | sP63 ),
    inference(all_rule,[status(thm)],]) ).

thf(55,plain,
    ( ~ sP63
    | ~ sP66
    | sP53 ),
    inference(prop_rule,[status(thm)],]) ).

thf(56,plain,
    ( ~ sP14
    | sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(57,plain,
    ( ~ sP14
    | sP74 ),
    inference(all_rule,[status(thm)],]) ).

thf(58,plain,
    ( ~ sP74
    | sP68 ),
    inference(all_rule,[status(thm)],]) ).

thf(59,plain,
    ( ~ sP68
    | sP62 ),
    inference(all_rule,[status(thm)],]) ).

thf(60,plain,
    ( ~ sP62
    | sP57
    | sP59 ),
    inference(prop_rule,[status(thm)],]) ).

thf(61,plain,
    ( ~ sP57
    | ~ sP53
    | ~ sP38 ),
    inference(prop_rule,[status(thm)],]) ).

thf(62,plain,
    ( ~ sP56
    | sP50 ),
    inference(all_rule,[status(thm)],]) ).

thf(63,plain,
    ( ~ sP72
    | sP69 ),
    inference(all_rule,[status(thm)],]) ).

thf(64,plain,
    ( ~ sP14
    | sP37 ),
    inference(all_rule,[status(thm)],]) ).

thf(65,plain,
    ( ~ sP56
    | sP58 ),
    inference(all_rule,[status(thm)],]) ).

thf(66,plain,
    ( ~ sP72
    | sP76 ),
    inference(all_rule,[status(thm)],]) ).

thf(67,plain,
    ( ~ sP76
    | sP40 ),
    inference(all_rule,[status(thm)],]) ).

thf(68,plain,
    ( ~ sP40
    | ~ sP3
    | sP55 ),
    inference(prop_rule,[status(thm)],]) ).

thf(69,plain,
    ( ~ sP72
    | sP70 ),
    inference(all_rule,[status(thm)],]) ).

thf(70,plain,
    ( ~ sP56
    | sP67 ),
    inference(all_rule,[status(thm)],]) ).

thf(71,plain,
    ( ~ sP56
    | sP47 ),
    inference(all_rule,[status(thm)],]) ).

thf(72,plain,
    ( ~ sP47
    | sP64 ),
    inference(all_rule,[status(thm)],]) ).

thf(73,plain,
    ( ~ sP64
    | sP1
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(74,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h14,h13,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,h7,h8,h6,h4,h12,h14]) ).

thf(75,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h13,h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__3)],[h13,74,h14]) ).

thf(76,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__2)],[h10,75,h13]) ).

thf(77,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__1)],[h11,76,h12]) ).

thf(78,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__0)],[h9,77,h11]) ).

thf(79,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h2,78,h9,h10]) ).

thf(80,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h5,79,h7,h8]) ).

thf(81,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,80,h5,h6]) ).

thf(82,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,81,h3,h4]) ).

thf(83,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,82,h1,h2]) ).

thf(0,theorem,
    ( ~ ( ~ ( ~ ( sP31
               => ~ sP14 )
           => ~ sP72 )
       => ~ sP56 )
   => ( ~ ! [X1: $i] : ( !! @ ( cP @ X1 ) )
     => ! [X1: $i] : ( !! @ ( cQ @ X1 ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[83,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEV091^5 : TPTP v7.5.0. Released v4.0.0.
% 0.03/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34  % Computer : n009.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Fri Mar 26 14:17:38 EDT 2021
% 0.12/0.34  % CPUTime  : 
% 0.19/0.45  % SZS status Theorem
% 0.19/0.45  % Mode: mode213
% 0.19/0.45  % Inferences: 595
% 0.19/0.45  % SZS output start Proof
% See solution above
% 0.19/0.45  % SZS output end Proof
%------------------------------------------------------------------------------