%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : NUM771^1 : 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 : n015.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 11:41:03 EDT 2023

% Result   : Theorem 0.14s 0.42s
% Output   : Proof 0.14s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

thf(ty_frac,type,
    frac: $tType ).

thf(ty_x,type,
    x: frac ).

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

thf(ty_fr,type,
    fr: nat > nat > frac ).

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

thf(ty_y,type,
    y: frac ).

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

thf(ty_eq,type,
    eq: frac > frac > $o ).

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

thf(sP2,plain,
    ( sP2
  <=> ( ( ts @ ( den @ x ) @ ( den @ y ) )
      = ( ts @ ( den @ y ) @ ( den @ x ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

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

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

thf(sP5,plain,
    ( sP5
  <=> ! [X1: nat] :
        ( ( ts @ ( den @ x ) @ X1 )
        = ( ts @ X1 @ ( den @ x ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( fr @ ( ts @ ( num @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) )
      = ( fr @ ( ts @ ( num @ y ) @ ( num @ x ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( eq @ ( fr @ ( ts @ ( num @ x ) @ ( num @ y ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) @ ( fr @ ( ts @ ( num @ y ) @ ( num @ x ) ) @ ( ts @ ( den @ y ) @ ( den @ x ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: frac] : ( eq @ X1 @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( ( ts @ ( num @ x ) @ ( num @ y ) )
      = ( ts @ ( num @ y ) @ ( num @ x ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(satz69,conjecture,
    sP8 ).

thf(h0,negated_conjecture,
    ~ sP8,
    inference(assume_negation,[status(cth)],[satz69]) ).

thf(1,plain,
    ( sP7
    | ~ sP2
    | ~ sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ~ sP6,
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP4
    | sP8
    | ~ sP7
    | sP6 ),
    inference(mating_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP9
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP5
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP1
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP3
    | sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP1
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(satz29,axiom,
    sP1 ).

thf(satz37,axiom,
    sP9 ).

thf(9,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,h0,satz29,satz37]) ).

thf(0,theorem,
    sP8,
    inference(contra,[status(thm),contra(discharge,[h0])],[9,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14  % Problem  : NUM771^1 : TPTP v8.1.2. Released v3.7.0.
% 0.09/0.15  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35  % Computer : n015.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Fri Aug 25 15:25:37 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.14/0.42  % SZS status Theorem
% 0.14/0.42  % Mode: cade22grackle2xfee4
% 0.14/0.42  % Steps: 165
% 0.14/0.42  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------