%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : NUM699^1 : 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 : n026.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 13:55:25 EDT 2022

% Result   : Theorem 0.20s 0.37s
% Output   : Proof 0.20s
% 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_less,type,
    less: nat > nat > $o ).

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

thf(ty_n_1,type,
    n_1: nat ).

thf(ty_x,type,
    x: nat ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: nat] :
        ( ( pl @ X1 @ n_1 )
        = ( suc @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: nat] :
        ( ( less @ X1 @ x )
       => ( lessis @ ( pl @ X1 @ n_1 ) @ x ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( lessis @ ( pl @ y @ n_1 ) @ x ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( less @ y @ x )
     => sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

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

thf(sP6,plain,
    ( sP6
  <=> ! [X1: nat,X2: nat] :
        ( ( less @ X2 @ X1 )
       => ( lessis @ ( pl @ X2 @ n_1 ) @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

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

thf(sP8,plain,
    ( sP8
  <=> ( ( pl @ y @ n_1 )
      = ( suc @ y ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

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

thf(satz25c,conjecture,
    sP7 ).

thf(h0,negated_conjecture,
    ~ sP7,
    inference(assume_negation,[status(cth)],[satz25c]) ).

thf(1,plain,
    sP5,
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP1
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP3
    | sP7
    | ~ sP8
    | ~ sP5 ),
    inference(mating_rule,[status(thm)],]) ).

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

thf(5,plain,
    ( ~ sP2
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP4
    | ~ sP9
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(l,axiom,
    sP9 ).

thf(satz25b,axiom,
    sP6 ).

thf(satz4a,axiom,
    sP1 ).

thf(7,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,l,satz25b,satz4a,h0]) ).

thf(0,theorem,
    sP7,
    inference(contra,[status(thm),contra(discharge,[h0])],[7,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM699^1 : TPTP v8.1.0. Released v3.7.0.
% 0.03/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n026.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Wed Jul  6 06:35:08 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.20/0.37  % SZS status Theorem
% 0.20/0.37  % Mode: mode213
% 0.20/0.37  % Inferences: 66
% 0.20/0.37  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------