%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ALG247^2 : 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 : n016.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 16:33:40 EDT 2023

% Result   : Theorem 201.57s 201.98s
% Output   : Proof 201.57s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

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

thf(ty_eigen__1,type,
    eigen__1: term ).

thf(ty_eigen__2,type,
    eigen__2: subst ).

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

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

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

thf(sP1,plain,
    ( sP1
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: term > $o] :
        ( ( X1
          @ @+[X2: term] :
              ( ( X1 @ X2 )
             != ( eigen__0 @ ( sub @ X2 @ ( push @ eigen__1 @ eigen__2 ) ) ) ) )
       != ( eigen__0
          @ ( sub
            @ @+[X2: term] :
                ( ( X1 @ X2 )
               != ( eigen__0 @ ( sub @ X2 @ ( push @ eigen__1 @ eigen__2 ) ) ) )
            @ ( push @ eigen__1 @ eigen__2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(def_pushprop_p_and_p_prime,definition,
    ( pushprop_p_and_p_prime
    = ( ^ [X1: term,X2: subst,X3: term > $o,X4: term > $o] :
        ! [X5: term] :
          ( ( X4 @ X5 )
        <=> ( X3 @ ( sub @ X5 @ ( push @ X1 @ X2 ) ) ) ) ) ) ).

thf(def_pushprop_lem0,definition,
    ( pushprop_lem0
    = ( ! [X1: term > $o,X2: term,X3: subst] :
        ? [X4: term > $o] : ( pushprop_p_and_p_prime @ X2 @ X3 @ X1 @ X4 ) ) ) ).

thf(def_pushprop_lem0_lthm,definition,
    pushprop_lem0_lthm = pushprop_lem0 ).

thf(thm,conjecture,
    ! [X1: term > $o,X2: term,X3: subst] :
      ~ ! [X4: term > $o] :
          ~ ! [X5: term] :
              ( ( X4 @ X5 )
              = ( X1 @ ( sub @ X5 @ ( push @ X2 @ X3 ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: term > $o,X2: term,X3: subst] :
        ~ ! [X4: term > $o] :
            ~ ! [X5: term] :
                ( ( X4 @ X5 )
                = ( X1 @ ( sub @ X5 @ ( push @ X2 @ X3 ) ) ) ),
    inference(assume_negation,[status(cth)],[thm]) ).

thf(h1,assumption,
    ~ ! [X1: term,X2: subst] :
        ~ ! [X3: term > $o] :
            ~ ! [X4: term] :
                ( ( X3 @ X4 )
                = ( eigen__0 @ ( sub @ X4 @ ( push @ X1 @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ! [X1: subst] :
        ~ ! [X2: term > $o] :
            ~ ! [X3: term] :
                ( ( X2 @ X3 )
                = ( eigen__0 @ ( sub @ X3 @ ( push @ eigen__1 @ X1 ) ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ! [X1: term > $o] :
      ~ ! [X2: term] :
          ( ( X1 @ X2 )
          = ( eigen__0 @ ( sub @ X2 @ ( push @ eigen__1 @ eigen__2 ) ) ) ),
    introduced(assumption,[]) ).

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

thf(2,plain,
    ~ sP1,
    inference(prop_rule,[status(thm)],]) ).

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

thf(4,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,3,h3]) ).

thf(5,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,4,h2]) ).

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

thf(0,theorem,
    ! [X1: term > $o,X2: term,X3: subst] :
      ~ ! [X4: term > $o] :
          ~ ! [X5: term] :
              ( ( X4 @ X5 )
              = ( X1 @ ( sub @ X5 @ ( push @ X2 @ X3 ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : ALG247^2 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.00/0.14  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.15/0.36  % Computer : n016.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Mon Aug 28 03:54:44 EDT 2023
% 0.22/0.36  % CPUTime  : 
% 201.57/201.98  % SZS status Theorem
% 201.57/201.98  % Mode: cade22sinegrackle2xb79a
% 201.57/201.98  % Steps: 55640
% 201.57/201.98  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------