TSTP Solution File: SYO042^1 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SYO042^1 : 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 : n012.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 19:29:47 EDT 2022

% Result   : Unsatisfiable 0.19s 0.38s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   60
% Syntax   : Number of formulae    :   82 (  36 unt;   6 typ;   2 def)
%            Number of atoms       :  192 (  26 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  138 (  62   ~;  32   |;   0   &;  15   @)
%                                         (  18 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   27 (  25 usr;  24 con; 0-2 aty)
%            Number of variables   :    7 (   4   ^   3   !;   0   ?;   7   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_p,type,
    p: ( $o > $o ) > $o ).

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

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

thf(ty_y,type,
    y: $o ).

thf(ty_g,type,
    g: $o > $o ).

thf(ty_x,type,
    x: $o ).

thf(h0,assumption,
    ! [X1: $o > $o,X2: $o] :
      ( ( X1 @ X2 )
     => ( X1 @ ( eps__0 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(eigendef_eigen__1,definition,
    ( eigen__1
    = ( eps__0
      @ ^ [X1: $o] :
          ( ( g @ X1 )
         != ( ~ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__1])]) ).

thf(eigendef_eigen__0,definition,
    ( eigen__0
    = ( eps__0
      @ ^ [X1: $o] :
          ( ( g @ X1 )
         != ( ~ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__0])]) ).

thf(sP1,plain,
    ( sP1
  <=> ( p @ g ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

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

thf(sP3,plain,
    ( sP3
  <=> ( g
      = ( ^ [X1: $o] : ~ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

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

thf(sP5,plain,
    ( sP5
  <=> eigen__1 ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> y ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( sP5 = sP6 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

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

thf(sP9,plain,
    ( sP9
  <=> ( sP8
      = ( ~ sP2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( x = sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( g @ x ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> x ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( p
      @ ^ [X1: $o] : ~ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( g @ sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( sP6 = sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ! [X1: $o] :
        ( ( g @ X1 )
        = ( ~ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( sP2 = sP12 ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ( g @ sP6 ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(h1,assumption,
    ~ ( ~ ( ~ ( ( sP12 != sP6 )
             => ( sP11 != sP6 ) )
         => ( sP18 != sP12 ) )
     => ~ sP1 ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ sP13,
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ( ~ ( ( sP12 != sP6 )
         => ( sP11 != sP6 ) )
     => ( sP18 != sP12 ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ ( ( sP12 != sP6 )
     => ( sP11 != sP6 ) ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    sP18 = sP12,
    introduced(assumption,[]) ).

thf(h7,assumption,
    sP12 != sP6,
    introduced(assumption,[]) ).

thf(h8,assumption,
    sP11 = sP6,
    introduced(assumption,[]) ).

thf(h9,assumption,
    sP12,
    introduced(assumption,[]) ).

thf(h10,assumption,
    sP6,
    introduced(assumption,[]) ).

thf(h11,assumption,
    ~ sP12,
    introduced(assumption,[]) ).

thf(h12,assumption,
    ~ sP6,
    introduced(assumption,[]) ).

thf(h13,assumption,
    sP11,
    introduced(assumption,[]) ).

thf(h14,assumption,
    ~ sP11,
    introduced(assumption,[]) ).

thf(h15,assumption,
    sP18,
    introduced(assumption,[]) ).

thf(h16,assumption,
    ~ sP18,
    introduced(assumption,[]) ).

thf(1,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h15,h9,h13,h10,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[h10,h10]) ).

thf(2,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h16,h11,h13,h10,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[h10,h10]) ).

thf(3,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h13,h10,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h15,h9]),tab_bq(discharge,[h16,h11])],[h6,1,2,h15,h9,h16,h11]) ).

thf(4,plain,
    ( sP15
    | sP6
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP17
    | ~ sP2
    | ~ sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP18
    | sP8
    | ~ sP15 ),
    inference(mating_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP8
    | sP11
    | ~ sP17 ),
    inference(mating_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP9
    | ~ sP8
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( sP9
    | sP8
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( sP16
    | ~ sP9 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).

thf(11,plain,
    ( sP3
    | ~ sP16 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP1
    | sP13
    | ~ sP3 ),
    inference(mating_rule,[status(thm)],]) ).

thf(13,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h15,h9,h14,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[4,5,6,7,8,9,10,11,12,h14,h12,h15,h9,h4,h2]) ).

thf(14,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h16,h11,h14,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[h9,h11]) ).

thf(15,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h14,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h15,h9]),tab_bq(discharge,[h16,h11])],[h6,13,14,h15,h9,h16,h11]) ).

thf(16,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h13,h10]),tab_bq(discharge,[h14,h12])],[h8,3,15,h13,h10,h14,h12]) ).

thf(17,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h15,h9,h13,h10,h11,h12,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[h9,h11]) ).

thf(18,plain,
    ( sP10
    | sP12
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(19,plain,
    ( sP7
    | ~ sP5
    | ~ sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(20,plain,
    ( ~ sP11
    | sP14
    | ~ sP10 ),
    inference(mating_rule,[status(thm)],]) ).

thf(21,plain,
    ( ~ sP14
    | sP18
    | ~ sP7 ),
    inference(mating_rule,[status(thm)],]) ).

thf(22,plain,
    ( sP4
    | ~ sP14
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(23,plain,
    ( sP4
    | sP14
    | ~ sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(24,plain,
    ( sP16
    | ~ sP4 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).

thf(25,plain,
    ( sP3
    | ~ sP16 ),
    inference(prop_rule,[status(thm)],]) ).

thf(26,plain,
    ( ~ sP1
    | sP13
    | ~ sP3 ),
    inference(mating_rule,[status(thm)],]) ).

thf(27,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h16,h11,h13,h10,h11,h12,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[18,19,20,21,22,23,24,25,26,h13,h10,h16,h11,h4,h2]) ).

thf(28,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h13,h10,h11,h12,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h15,h9]),tab_bq(discharge,[h16,h11])],[h6,17,27,h15,h9,h16,h11]) ).

thf(29,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h15,h9,h14,h12,h11,h12,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[h12,h12]) ).

thf(30,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h16,h11,h14,h12,h11,h12,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[h12,h12]) ).

thf(31,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h14,h12,h11,h12,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h15,h9]),tab_bq(discharge,[h16,h11])],[h6,29,30,h15,h9,h16,h11]) ).

thf(32,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h11,h12,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_bq(discharge,[h13,h10]),tab_bq(discharge,[h14,h12])],[h8,28,31,h13,h10,h14,h12]) ).

thf(33,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_be(discharge,[h9,h10]),tab_be(discharge,[h11,h12])],[h7,16,32,h9,h10,h11,h12]) ).

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

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

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

thf('4_001',axiom,
    ~ ( ~ ( ~ ( ~ ( ( sP12 != sP6 )
                 => ( sP11 != sP6 ) )
             => ( sP18 != sP12 ) )
         => ~ sP1 )
     => sP13 ) ).

thf(37,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[4,36,h1,h2]) ).

thf(38,plain,
    $false,
    inference(eigenvar_choice,[status(thm),eigenvar_choice(discharge,[h0])],[37,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SYO042^1 : 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
% 0.12/0.34  % Computer : n012.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 : Sat Jul  9 04:38:29 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.38  % SZS status Unsatisfiable
% 0.19/0.38  % Mode: mode213
% 0.19/0.38  % Inferences: 52
% 0.19/0.38  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------