%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : ALG267^2 : TPTP v8.1.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n018.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 14 17:57:51 EDT 2022

% Result   : Theorem 0.59s 0.82s
% Output   : Proof 0.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   22 (  10 unt;   7 typ;   3 def)
%            Number of atoms       :   26 (   7 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   45 (   9   ~;   2   |;   0   &;  30   @)
%                                         (   3 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  11 usr;  10 con; 0-2 aty)
%            Number of variables   :    7 (   1   ^   6   !;   0   ?;   7   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_subst,type,
    subst: $tType ).

thf(ty_term,type,
    term: $tType ).

thf(ty_push,type,
    push: term > subst > subst ).

thf(ty_eigen__0,type,
    eigen__0: term ).

thf(ty_one,type,
    one: term ).

thf(ty_sub,type,
    sub: term > subst > term ).

thf(ty_sh,type,
    sh: subst ).

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

thf(eigendef_eigen__0,definition,
    ( eigen__0
    = ( eps__0
      @ ^ [X1: term] :
          ~ ~ ! [X2: subst > term > term] :
                ( ( sub @ X1 @ ( push @ one @ sh ) )
               != ( X2 @ sh @ one ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__0])]) ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: subst > term > term] :
        ( ( sub @ eigen__0 @ ( push @ one @ sh ) )
       != ( X1 @ sh @ one ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( sub @ eigen__0 @ ( push @ one @ sh ) )
      = ( sub @ eigen__0 @ ( push @ one @ sh ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: term] :
        ~ ! [X2: subst > term > term] :
            ( ( sub @ X1 @ ( push @ one @ sh ) )
           != ( X2 @ sh @ one ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(def_hoasinduction_lem3b,definition,
    hoasinduction_lem3b = sP3 ).

thf(def_hoasinduction_lem3b_lthm,definition,
    hoasinduction_lem3b_lthm = hoasinduction_lem3b ).

thf(thm,conjecture,
    sP3 ).

thf(h1,negated_conjecture,
    ~ sP3,
    inference(assume_negation,[status(cth)],[thm]) ).

thf(1,plain,
    sP2,
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP1
    | ~ sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP3
    | sP1 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).

thf(4,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,h1]) ).

thf(5,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[4,h0]) ).

thf(0,theorem,
    sP3,
    inference(contra,[status(thm),contra(discharge,[h1])],[4,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : ALG267^2 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.03/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n018.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 : Wed Jun  8 20:01:52 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.59/0.82  % SZS status Theorem
% 0.59/0.82  % Mode: mode485:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=4.:SINE_DEPTH=0
% 0.59/0.82  % Inferences: 3
% 0.59/0.82  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------