%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : NUM653^1 : 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 : 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  : 300s
% DateTime : Thu Aug 31 11:40:10 EDT 2023

% Result   : Theorem 0.18s 0.39s
% Output   : Proof 0.18s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_nat,type,
    nat: $tType ).

thf(ty_x,type,
    x: nat ).

thf(ty_more,type,
    more: nat > nat > $o ).

thf(ty_y,type,
    y: nat ).

thf(ty_less,type,
    less: nat > nat > $o ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: nat,X2: nat] :
        ~ ( ( ( X1 = X2 )
           => ~ ( more @ X1 @ X2 ) )
         => ( ( ( more @ X1 @ X2 )
             => ~ ( less @ X1 @ X2 ) )
           => ~ ( ( less @ X1 @ X2 )
               => ( X1 != X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( more @ x @ y )
     => ~ ( less @ x @ y ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( x = y ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: nat] :
        ~ ( ( ( x = X1 )
           => ~ ( more @ x @ X1 ) )
         => ( ( ( more @ x @ X1 )
             => ~ ( less @ x @ X1 ) )
           => ~ ( ( less @ x @ X1 )
               => ( x != X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( sP2
     => ~ ( ( less @ x @ y )
         => ~ sP3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( sP3
     => ~ ( more @ x @ y ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( more @ x @ y ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ~ ( less @ x @ y )
     => sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( sP6
     => sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( less @ x @ y ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(satz10d,conjecture,
    ~ sP7 ).

thf(h0,negated_conjecture,
    sP7,
    inference(assume_negation,[status(cth)],[satz10d]) ).

thf(1,plain,
    ( ~ sP2
    | ~ sP7
    | ~ sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( sP5
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP6
    | ~ sP3
    | ~ sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP9
    | ~ sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP9
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP4
    | ~ sP9 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP1
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP8
    | sP10
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(satz10b,axiom,
    sP1 ).

thf(l,axiom,
    sP8 ).

thf(9,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,h0,satz10b,l]) ).

thf(0,theorem,
    ~ sP7,
    inference(contra,[status(thm),contra(discharge,[h0])],[9,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM653^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.11/0.33  % Computer : n018.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Fri Aug 25 10:24:28 EDT 2023
% 0.11/0.33  % CPUTime  : 
% 0.18/0.39  % SZS status Theorem
% 0.18/0.39  % Mode: cade22grackle2xfee4
% 0.18/0.39  % Steps: 25
% 0.18/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------