%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ALG262^2 : TPTP v8.1.2. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n001.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 : Wed Aug 30 16:33:46 EDT 2023

% Result   : Theorem 83.51s 83.87s
% Output   : Proof 83.51s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

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

thf(ty_id,type,
    id: subst ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: term > $o] :
        ( ( X1
          @ @+[X2: term] :
              ( ( X1 @ X2 )
             != ( @+[X3: subst > term > subst > $o] :
                  ! [X4: term > $o] :
                    ~ ! [X5: term] :
                        ( ( X4 @ X5 )
                        = ( X3 @ id @ X5 @ id ) )
                @ id
                @ X2
                @ id ) ) )
       != ( @+[X2: subst > term > subst > $o] :
            ! [X3: term > $o] :
              ~ ! [X4: term] :
                  ( ( X3 @ X4 )
                  = ( X2 @ id @ X4 @ id ) )
          @ id
          @ @+[X2: term] :
              ( ( X1 @ X2 )
             != ( @+[X3: subst > term > subst > $o] :
                  ! [X4: term > $o] :
                    ~ ! [X5: term] :
                        ( ( X4 @ X5 )
                        = ( X3 @ id @ X5 @ id ) )
                @ id
                @ X2
                @ id ) )
          @ id ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

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

thf(def_hoasinduction_p_and_p_prime,definition,
    ( hoasinduction_p_and_p_prime
    = ( ^ [X1: subst > term > subst > $o,X2: term > $o] :
        ! [X3: term] :
          ( ( X2 @ X3 )
        <=> ( X1 @ id @ X3 @ id ) ) ) ) ).

thf(def_hoasinduction_lem0,definition,
    ( hoasinduction_lem0
    = ( ! [X1: subst > term > subst > $o] :
        ? [X2: term > $o] : ( hoasinduction_p_and_p_prime @ X1 @ X2 ) ) ) ).

thf(def_hoasinduction_lem0_lthm,definition,
    hoasinduction_lem0_lthm = hoasinduction_lem0 ).

thf(thm,conjecture,
    ! [X1: subst > term > subst > $o] :
      ~ ! [X2: term > $o] :
          ~ ! [X3: term] :
              ( ( X2 @ X3 )
              = ( X1 @ id @ X3 @ id ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: subst > term > subst > $o] :
        ~ ! [X2: term > $o] :
            ~ ! [X3: term] :
                ( ( X2 @ X3 )
                = ( X1 @ id @ X3 @ id ) ),
    inference(assume_negation,[status(cth)],[thm]) ).

thf(1,plain,
    ( ~ sP1
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

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

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

thf(0,theorem,
    ! [X1: subst > term > subst > $o] :
      ~ ! [X2: term > $o] :
          ~ ! [X3: term] :
              ( ( X2 @ X3 )
              = ( X1 @ id @ X3 @ id ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[3,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : ALG262^2 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35  % Computer : n001.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 : Mon Aug 28 06:39:34 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 83.51/83.87  % SZS status Theorem
% 83.51/83.87  % Mode: cade22sinegrackle2x1406
% 83.51/83.87  % Steps: 77
% 83.51/83.87  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------