%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : NUM668^1 : TPTP v8.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n003.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  : 600s
% DateTime : Mon Jul 18 13:54:56 EDT 2022

% Result   : Theorem 1.95s 2.17s
% Output   : Proof 1.95s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

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

thf(ty_y,type,
    y: nat ).

thf(ty_x,type,
    x: nat ).

thf(sP1,plain,
    ( sP1
  <=> ( ( pl @ x @ y )
      = ( pl @ x @ y ) ) ),
    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,
    sP1,
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP2
    | ~ sP1 ),
    inference(all_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
% 0.00/0.12  % Problem  : NUM668^1 : TPTP v8.1.0. Released v3.7.0.
% 0.12/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34  % Computer : n003.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Wed Jul  6 09:26:41 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 1.95/2.17  % SZS status Theorem
% 1.95/2.17  % Mode: mode506
% 1.95/2.17  % Inferences: 3
% 1.95/2.17  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------