%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : NUM654^1 : 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 : n031.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 11:40:11 EDT 2023

% Result   : Theorem 0.21s 0.41s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

thf(ty_x,type,
    x: nat ).

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

thf(ty_y,type,
    y: nat ).

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

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

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

thf(sP3,plain,
    ( sP3
  <=> ! [X1: nat] :
        ( ( x != X1 )
       => ( ~ ( more @ x @ X1 )
         => ( less @ x @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

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

thf(sP5,plain,
    ( sP5
  <=> ( x = y ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

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

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

thf(satz10e,conjecture,
    ( ~ sP7
   => sP5 ) ).

thf(h0,negated_conjecture,
    ~ ( ~ sP7
     => sP5 ),
    inference(assume_negation,[status(cth)],[satz10e]) ).

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

thf(h2,assumption,
    ~ sP5,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP4
    | sP6
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP2
    | sP5
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP3
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP1
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(satz10a,axiom,
    sP1 ).

thf(n,axiom,
    ~ sP6 ).

thf(5,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h1,h2,h0])],[1,2,3,4,h1,h2,satz10a,n]) ).

thf(6,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,5,h1,h2]) ).

thf(0,theorem,
    ( ~ sP7
   => sP5 ),
    inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14  % Problem  : NUM654^1 : TPTP v8.1.2. Released v3.7.0.
% 0.12/0.15  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36  % Computer : n031.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Fri Aug 25 16:10:22 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.21/0.41  % SZS status Theorem
% 0.21/0.41  % Mode: cade22grackle2xfee4
% 0.21/0.41  % Steps: 13
% 0.21/0.41  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------