%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : NUM640^1 : 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 : 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  : 600s
% DateTime : Mon Jul 18 13:54:28 EDT 2022

% Result   : Theorem 1.55s 1.96s
% Output   : Proof 1.55s
% 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_suc,type,
    suc: nat > nat ).

thf(ty_x,type,
    x: nat ).

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

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

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

thf(sP4,plain,
    ( sP4
  <=> ( ( pl @ x @ ( suc @ y ) )
      = ( suc @ ( pl @ x @ y ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

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

thf(sP6,plain,
    ( sP6
  <=> ( sP4
     => sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: nat,X2: nat] :
        ( ( X1 = X2 )
       => ( X2 = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(satz4f,conjecture,
    sP5 ).

thf(h0,negated_conjecture,
    ~ sP5,
    inference(assume_negation,[status(cth)],[satz4f]) ).

thf(1,plain,
    ( ~ sP3
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP1
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP6
    | ~ sP4
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP2
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP7
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    sP7,
    inference(eq_sym,[status(thm)],]) ).

thf(satz4b,axiom,
    sP1 ).

thf(7,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,satz4b,h0]) ).

thf(0,theorem,
    sP5,
    inference(contra,[status(thm),contra(discharge,[h0])],[7,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM640^1 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.32  % Computer : n023.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 600
% 0.12/0.32  % DateTime : Thu Jul  7 23:25:26 EDT 2022
% 0.12/0.32  % CPUTime  : 
% 1.55/1.96  % SZS status Theorem
% 1.55/1.96  % Mode: mode213
% 1.55/1.96  % Inferences: 3322
% 1.55/1.96  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------