%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ALG260^2 : 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 : n013.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 16:33:45 EDT 2023

% Result   : Theorem 0.15s 0.38s
% Output   : Proof 0.15s
% 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(ty_comp,type,
    comp: subst > subst > subst ).

thf(ty_lam,type,
    lam: term > term ).

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

thf(ty_eigen__0,type,
    eigen__0: subst > term > term ).

thf(ty_var,type,
    var: term > $o ).

thf(ty_one,type,
    one: term ).

thf(ty_sh,type,
    sh: subst ).

thf(sP1,plain,
    ( sP1
  <=> ( var @ ( lam @ ( eigen__0 @ sh @ one ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: term] :
        ~ ( var @ ( lam @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( var @ ( sub @ ( lam @ ( eigen__0 @ sh @ one ) ) @ id ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: term] :
        ( ( sub @ X1 @ id )
        = X1 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( sub @ ( lam @ ( eigen__0 @ sh @ one ) ) @ id )
      = ( lam @ ( eigen__0 @ sh @ one ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(def_axvarid,definition,
    axvarid = sP4 ).

thf(def_lamnotvar,definition,
    ( lamnotvar
    = ( ! [X1: term] : ( (~) @ ( var @ ( lam @ X1 ) ) ) ) ) ).

thf(def_hoaslam,definition,
    ( hoaslam
    = ( ^ [X1: subst,X2: subst > term > term] : ( lam @ ( X2 @ sh @ one ) ) ) ) ).

thf(def_hoasvar,definition,
    ( hoasvar
    = ( ^ [X1: subst,X2: term,X3: subst] : ( var @ ( sub @ X2 @ X3 ) ) ) ) ).

thf(def_hoaslamnotvar,definition,
    ( hoaslamnotvar
    = ( ! [X1: subst > term > term] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ! [X2: subst,X3: term,X4: subst] :
              ( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
              = ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
          @ ( (~)
            @ ( hoasvar @ id
              @ ( hoaslam @ id
                @ ^ [X2: subst,X3: term] : ( X1 @ X2 @ X3 ) )
              @ id ) ) ) ) ) ).

thf(def_hoaslamnotvar_lthm,definition,
    ( hoaslamnotvar_lthm
    = ( ^ [X1: $o,X2: $o] :
          ( X1
         => X2 )
      @ axvarid
      @ ( ^ [X1: $o,X2: $o] :
            ( X1
           => X2 )
        @ lamnotvar
        @ hoaslamnotvar ) ) ) ).

thf(thm,conjecture,
    ( sP4
   => ( sP2
     => ! [X1: subst > term > term] :
          ( ! [X2: subst,X3: term,X4: subst] :
              ( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
              = ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
         => ~ ( var @ ( sub @ ( lam @ ( X1 @ sh @ one ) ) @ id ) ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ( sP4
     => ( sP2
       => ! [X1: subst > term > term] :
            ( ! [X2: subst,X3: term,X4: subst] :
                ( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
                = ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
           => ~ ( var @ ( sub @ ( lam @ ( X1 @ sh @ one ) ) @ id ) ) ) ) ),
    inference(assume_negation,[status(cth)],[thm]) ).

thf(h1,assumption,
    sP4,
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ( sP2
     => ! [X1: subst > term > term] :
          ( ! [X2: subst,X3: term,X4: subst] :
              ( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
              = ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
         => ~ ( var @ ( sub @ ( lam @ ( X1 @ sh @ one ) ) @ id ) ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP2,
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ! [X1: subst > term > term] :
        ( ! [X2: subst,X3: term,X4: subst] :
            ( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
            = ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
       => ~ ( var @ ( sub @ ( lam @ ( X1 @ sh @ one ) ) @ id ) ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ ( ! [X1: subst,X2: term,X3: subst] :
          ( ( sub @ ( eigen__0 @ X1 @ X2 ) @ X3 )
          = ( eigen__0 @ ( comp @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) ) )
     => ~ sP3 ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    ! [X1: subst,X2: term,X3: subst] :
      ( ( sub @ ( eigen__0 @ X1 @ X2 ) @ X3 )
      = ( eigen__0 @ ( comp @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) ) ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    sP3,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP4
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP3
    | sP1
    | ~ sP5 ),
    inference(mating_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP2
    | ~ sP1 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h6,h7,h5,h3,h4,h1,h2,h0])],[1,2,3,h1,h3,h7]) ).

thf(5,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h6,h7])],[h5,4,h6,h7]) ).

thf(6,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h4,5,h5]) ).

thf(7,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,6,h3,h4]) ).

thf(8,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,7,h1,h2]) ).

thf(0,theorem,
    ( sP4
   => ( sP2
     => ! [X1: subst > term > term] :
          ( ! [X2: subst,X3: term,X4: subst] :
              ( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
              = ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
         => ~ ( var @ ( sub @ ( lam @ ( X1 @ sh @ one ) ) @ id ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[8,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : ALG260^2 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.00/0.10  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.31  % Computer : n013.cluster.edu
% 0.13/0.31  % Model    : x86_64 x86_64
% 0.13/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31  % Memory   : 8042.1875MB
% 0.13/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31  % CPULimit : 300
% 0.13/0.31  % WCLimit  : 300
% 0.13/0.31  % DateTime : Mon Aug 28 02:55:32 EDT 2023
% 0.13/0.31  % CPUTime  : 
% 0.15/0.38  % SZS status Theorem
% 0.15/0.38  % Mode: cade22sinegrackle2x6978
% 0.15/0.38  % Steps: 64
% 0.15/0.38  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------