%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : NUM670^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n006.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 : Thu Aug 31 11:40:20 EDT 2023

% Result   : Theorem 120.14s 120.29s
% Output   : Proof 120.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   44
% Syntax   : Number of formulae    :   49 (  11 unt;   6 typ;   1 def)
%            Number of atoms       :   83 (  19 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  167 (  24   ~;  20   |;   0   &; 104   @)
%                                         (  18 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   26 (  24 usr;  24 con; 0-2 aty)
%            Number of variables   :   15 (   1   ^;  14   !;   0   ?;  15   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_nat,type,
    nat: $tType ).

thf(ty_x,type,
    x: nat ).

thf(ty_pl,type,
    pl: nat > nat > nat ).

thf(ty_eigen__0,type,
    eigen__0: nat ).

thf(ty_y,type,
    y: nat ).

thf(ty_z,type,
    z: nat ).

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

thf(eigendef_eigen__0,definition,
    ( eigen__0
    = ( eps__0
      @ ^ [X1: nat] :
          ( x
         != ( pl @ y @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__0])]) ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: nat] :
        ( x
       != ( pl @ y @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

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

thf(sP3,plain,
    ( sP3
  <=> ! [X1: nat,X2: nat,X3: nat] :
        ( ( pl @ ( pl @ X1 @ X2 ) @ X3 )
        = ( pl @ X1 @ ( pl @ X2 @ X3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( pl @ ( pl @ y @ eigen__0 ) @ z )
      = ( pl @ y @ ( pl @ eigen__0 @ z ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( pl @ ( pl @ y @ z ) @ eigen__0 )
      = ( pl @ y @ ( pl @ z @ eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: nat] :
        ( ( pl @ ( pl @ y @ z ) @ X1 )
        = ( pl @ y @ ( pl @ z @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( pl @ y @ ( pl @ eigen__0 @ z ) )
      = ( pl @ y @ ( pl @ z @ eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ( pl @ ( pl @ y @ eigen__0 ) @ z )
      = ( pl @ x @ z ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

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

thf(sP10,plain,
    ( sP10
  <=> ! [X1: nat] :
        ( ( pl @ ( pl @ y @ eigen__0 ) @ X1 )
        = ( pl @ y @ ( pl @ eigen__0 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( ( pl @ eigen__0 @ z )
      = ( pl @ z @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

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

thf(sP13,plain,
    ( sP13
  <=> ! [X1: nat] :
        ( ( pl @ x @ z )
       != ( pl @ ( pl @ y @ z ) @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( ( pl @ x @ z )
      = ( pl @ ( pl @ y @ z ) @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ! [X1: nat] :
        ( ( pl @ eigen__0 @ X1 )
        = ( pl @ X1 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ! [X1: nat,X2: nat] :
        ( ( pl @ X1 @ X2 )
        = ( pl @ X2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( ( pl @ y @ ( pl @ z @ eigen__0 ) )
      = ( pl @ x @ z ) ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ! [X1: nat,X2: nat] :
        ( ( pl @ ( pl @ y @ X1 ) @ X2 )
        = ( pl @ y @ ( pl @ X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(satz19a,conjecture,
    ~ sP13 ).

thf(h1,negated_conjecture,
    sP13,
    inference(assume_negation,[status(cth)],[satz19a]) ).

thf(1,plain,
    ( ~ sP4
    | sP17
    | ~ sP7
    | ~ sP8 ),
    inference(confrontation_rule,[status(thm)],]) ).

thf(2,plain,
    ( sP7
    | ~ sP11
    | sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP8
    | sP12
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP5
    | sP14
    | ~ sP17
    | sP12 ),
    inference(confrontation_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP10
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP15
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP13
    | ~ sP14 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP16
    | sP15 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP18
    | sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP6
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP18
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP3
    | sP18 ),
    inference(all_rule,[status(thm)],]) ).

thf(13,plain,
    ~ sP12,
    inference(prop_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP9
    | sP2 ),
    inference(symeq,[status(thm)],]) ).

thf(15,plain,
    ( sP1
    | sP9 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).

thf(satz5,axiom,
    sP3 ).

thf(satz6,axiom,
    sP16 ).

thf(m,axiom,
    ~ sP1 ).

thf(16,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,satz5,satz6,m,h1]) ).

thf(17,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[16,h0]) ).

thf(0,theorem,
    ~ sP13,
    inference(contra,[status(thm),contra(discharge,[h1])],[16,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM670^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n006.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  : 300
% 0.13/0.34  % DateTime : Fri Aug 25 13:41:38 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 120.14/120.29  % SZS status Theorem
% 120.14/120.29  % Mode: cade22grackle2x052f
% 120.14/120.29  % Steps: 321486
% 120.14/120.29  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------