%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : NUM668^1 : 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 : n023.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 11:40:19 EDT 2023

% Result   : Theorem 0.13s 0.35s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

thf(ty_x,type,
    x: nat ).

thf(ty_y,type,
    y: nat ).

thf(ty_pl,type,
    pl: nat > nat > nat ).

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

thf(sP2,plain,
    ( sP2
  <=> ! [X1: nat] :
        ( ( pl @ x @ y )
       != ( pl @ x @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(satz18,conjecture,
    ~ sP2 ).

thf(h0,negated_conjecture,
    sP2,
    inference(assume_negation,[status(cth)],[satz18]) ).

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([h0])],[1,2,h0]) ).

thf(0,theorem,
    ~ sP2,
    inference(contra,[status(thm),contra(discharge,[h0])],[3,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : NUM668^1 : TPTP v8.1.2. Released v3.7.0.
% 0.07/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.32  % Computer : n023.cluster.edu
% 0.13/0.32  % Model    : x86_64 x86_64
% 0.13/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32  % Memory   : 8042.1875MB
% 0.13/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32  % CPULimit : 300
% 0.13/0.32  % WCLimit  : 300
% 0.13/0.32  % DateTime : Fri Aug 25 12:25:12 EDT 2023
% 0.13/0.32  % CPUTime  : 
% 0.13/0.35  % SZS status Theorem
% 0.13/0.35  % Mode: cade22grackle2xfee4
% 0.13/0.35  % Steps: 6
% 0.13/0.35  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------