%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SWV447^1 : 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 : n026.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 22:49:15 EDT 2023

% Result   : Theorem 0.20s 0.57s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_cons,type,
    cons: $i > $i > $i ).

thf(ty_map,type,
    map: ( $i > $i ) > $i > $i ).

thf(ty_nil,type,
    nil: $i ).

thf(ty_eigen__0,type,
    eigen__0: $i ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: $i > $i,X2: $i,X3: $i] :
        ( ( map @ X1 @ ( cons @ X2 @ X3 ) )
        = ( cons @ ( X1 @ X2 ) @ ( map @ X1 @ X3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( map
        @ ^ [X1: $i] : X1
        @ ( cons @ eigen__0 @ nil ) )
      = ( cons @ eigen__0
        @ ( map
          @ ^ [X1: $i] : X1
          @ nil ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( map
        @ ^ [X1: $i] : X1
        @ nil )
      = nil ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( cons @ eigen__0
        @ ( map
          @ ^ [X1: $i] : X1
          @ nil ) )
      = ( cons @ eigen__0 @ nil ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: $i] :
        ( ( map
          @ ^ [X2: $i] : X2
          @ ( cons @ eigen__0 @ X1 ) )
        = ( cons @ eigen__0
          @ ( map
            @ ^ [X2: $i] : X2
            @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( map
        @ ^ [X1: $i] : X1
        @ ( cons @ eigen__0 @ nil ) )
      = ( cons @ eigen__0 @ nil ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: $i > $i] :
        ( ( map @ X1 @ nil )
        = nil ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: $i,X2: $i] :
        ( ( map
          @ ^ [X3: $i] : X3
          @ ( cons @ X1 @ X2 ) )
        = ( cons @ X1
          @ ( map
            @ ^ [X3: $i] : X3
            @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(test,conjecture,
    ! [X1: $i] :
      ( ( map
        @ ^ [X2: $i] : X2
        @ ( cons @ X1 @ nil ) )
      = ( cons @ X1 @ nil ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: $i] :
        ( ( map
          @ ^ [X2: $i] : X2
          @ ( cons @ X1 @ nil ) )
        = ( cons @ X1 @ nil ) ),
    inference(assume_negation,[status(cth)],[test]) ).

thf(h1,assumption,
    ~ sP7,
    introduced(assumption,[]) ).

thf(1,plain,
    ( sP4
    | ~ sP3
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP2
    | sP7
    | sP6
    | ~ sP4 ),
    inference(confrontation_rule,[status(thm)],]) ).

thf(3,plain,
    ~ sP6,
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP5
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP9
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP8
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP1
    | sP9 ),
    inference(all_rule,[status(thm)],]) ).

thf(ax2,axiom,
    sP1 ).

thf(ax1,axiom,
    sP8 ).

thf(8,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,h1,ax2,ax1]) ).

thf(9,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,8,h1]) ).

thf(0,theorem,
    ! [X1: $i] :
      ( ( map
        @ ^ [X2: $i] : X2
        @ ( cons @ X1 @ nil ) )
      = ( cons @ X1 @ nil ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[9,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWV447^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35  % Computer : n026.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 : Tue Aug 29 03:51:50 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.57  % SZS status Theorem
% 0.20/0.57  % Mode: cade22grackle2xfee4
% 0.20/0.57  % Steps: 4376
% 0.20/0.57  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------