%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : NUM665^1 : 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 : n015.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 11:40:17 EDT 2023

% Result   : Theorem 0.12s 0.35s
% Output   : Proof 0.12s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

thf(ty_x,type,
    x: nat ).

thf(ty_diffprop,type,
    diffprop: nat > nat > nat > $o ).

thf(ty_moreis,type,
    moreis: nat > nat > $o ).

thf(ty_some,type,
    some: ( nat > $o ) > $o ).

thf(ty_y,type,
    y: nat ).

thf(ty_lessis,type,
    lessis: nat > nat > $o ).

thf(ty_z,type,
    z: nat ).

thf(sP1,plain,
    ( sP1
  <=> ( some @ ( diffprop @ y @ z ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: nat] :
        ( sP1
       => ( ( lessis @ y @ X1 )
         => ( some @ ( diffprop @ X1 @ z ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

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

thf(sP4,plain,
    ( sP4
  <=> ( some @ ( diffprop @ x @ z ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: nat,X2: nat] :
        ( ( some @ ( diffprop @ X1 @ z ) )
       => ( ( lessis @ X1 @ X2 )
         => ( some @ ( diffprop @ X2 @ z ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( sP1
     => ( ( lessis @ y @ x )
       => sP4 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

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

thf(sP8,plain,
    ( sP8
  <=> ! [X1: nat,X2: nat,X3: nat] :
        ( ( some @ ( diffprop @ X2 @ X1 ) )
       => ( ( lessis @ X2 @ X3 )
         => ( some @ ( diffprop @ X3 @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( moreis @ x @ y ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( sP7
     => sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ! [X1: nat] :
        ( ( moreis @ x @ X1 )
       => ( lessis @ X1 @ x ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ! [X1: nat,X2: nat] :
        ( ( moreis @ X1 @ X2 )
       => ( lessis @ X2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(satz16c,conjecture,
    sP4 ).

thf(h0,negated_conjecture,
    ~ sP4,
    inference(assume_negation,[status(cth)],[satz16c]) ).

thf(1,plain,
    ( ~ sP10
    | ~ sP7
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP6
    | ~ sP1
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP2
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

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

thf(5,plain,
    ( ~ sP8
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP3
    | ~ sP9
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP11
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP12
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(satz13,axiom,
    sP12 ).

thf(satz16b,axiom,
    sP8 ).

thf(n,axiom,
    sP1 ).

thf(m,axiom,
    sP9 ).

thf(9,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,h0,satz13,satz16b,n,m]) ).

thf(0,theorem,
    sP4,
    inference(contra,[status(thm),contra(discharge,[h0])],[9,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem  : NUM665^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.08  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.06/0.28  % Computer : n015.cluster.edu
% 0.06/0.28  % Model    : x86_64 x86_64
% 0.06/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.28  % Memory   : 8042.1875MB
% 0.06/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.06/0.28  % CPULimit : 300
% 0.06/0.28  % WCLimit  : 300
% 0.06/0.28  % DateTime : Fri Aug 25 07:57:06 EDT 2023
% 0.06/0.28  % CPUTime  : 
% 0.12/0.35  % SZS status Theorem
% 0.12/0.35  % Mode: cade22grackle2xfee4
% 0.12/0.35  % Steps: 361
% 0.12/0.35  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------