%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : NUM736^1 : 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 : n020.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 13:55:51 EDT 2022

% Result   : Theorem 0.13s 0.36s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_frac,type,
    frac: $tType ).

thf(ty_nat,type,
    nat: $tType ).

thf(ty_num,type,
    num: frac > nat ).

thf(ty_y,type,
    y: frac ).

thf(ty_less,type,
    less: nat > nat > $o ).

thf(ty_ts,type,
    ts: nat > nat > nat ).

thf(ty_den,type,
    den: frac > nat ).

thf(ty_more,type,
    more: nat > nat > $o ).

thf(ty_x,type,
    x: frac ).

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

thf(sP2,plain,
    ( sP2
  <=> ! [X1: nat] :
        ( ( more @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ X1 )
       => ( less @ X1 @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( more @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

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

thf(sP5,plain,
    ( sP5
  <=> ( sP3
     => sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(satz42,conjecture,
    sP4 ).

thf(h0,negated_conjecture,
    ~ sP4,
    inference(assume_negation,[status(cth)],[satz42]) ).

thf(1,plain,
    ( ~ sP1
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP2
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP5
    | ~ sP3
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(m,axiom,
    sP3 ).

thf(satz11,axiom,
    sP1 ).

thf(4,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,m,satz11,h0]) ).

thf(0,theorem,
    sP4,
    inference(contra,[status(thm),contra(discharge,[h0])],[4,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM736^1 : TPTP v8.1.0. Released v3.7.0.
% 0.03/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33  % Computer : n020.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Wed Jul  6 12:10:44 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.36  % SZS status Theorem
% 0.13/0.36  % Mode: mode213
% 0.13/0.36  % Inferences: 2
% 0.13/0.36  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------