%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : NUM729^1 : 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 : n008.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 13:55:47 EDT 2022

% Result   : Theorem 0.12s 0.36s
% Output   : Proof 0.12s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

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

thf(ty_n,type,
    n: nat ).

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

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

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

thf(ty_x2,type,
    x2: nat ).

thf(ty_x1,type,
    x1: nat ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: nat,X2: nat,X3: nat] : ( eq @ ( fr @ X1 @ X2 ) @ ( fr @ ( ts @ X1 @ X3 ) @ ( ts @ X2 @ X3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: nat,X2: nat] : ( eq @ ( fr @ x1 @ X1 ) @ ( fr @ ( ts @ x1 @ X2 ) @ ( ts @ X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( eq @ ( fr @ x1 @ x2 ) @ ( fr @ ( ts @ x1 @ n ) @ ( ts @ x2 @ n ) ) )
     => ( eq @ ( fr @ ( ts @ x1 @ n ) @ ( ts @ x2 @ n ) ) @ ( fr @ x1 @ x2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: frac] :
        ( ( eq @ ( fr @ x1 @ x2 ) @ X1 )
       => ( eq @ X1 @ ( fr @ x1 @ x2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: nat] : ( eq @ ( fr @ x1 @ x2 ) @ ( fr @ ( ts @ x1 @ X1 ) @ ( ts @ x2 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: frac,X2: frac] :
        ( ( eq @ X1 @ X2 )
       => ( eq @ X2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( eq @ ( fr @ ( ts @ x1 @ n ) @ ( ts @ x2 @ n ) ) @ ( fr @ x1 @ x2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( eq @ ( fr @ x1 @ x2 ) @ ( fr @ ( ts @ x1 @ n ) @ ( ts @ x2 @ n ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(satz40c,conjecture,
    sP7 ).

thf(h0,negated_conjecture,
    ~ sP7,
    inference(assume_negation,[status(cth)],[satz40c]) ).

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

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

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

thf(4,plain,
    ( ~ sP6
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP4
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP3
    | ~ sP8
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(satz38,axiom,
    sP6 ).

thf(satz40b,axiom,
    sP1 ).

thf(7,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,satz38,satz40b,h0]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : NUM729^1 : TPTP v8.1.0. Released v3.7.0.
% 0.11/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n008.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Wed Jul  6 01:22:08 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.36  % SZS status Theorem
% 0.12/0.36  % Mode: mode213
% 0.12/0.36  % Inferences: 6
% 0.12/0.36  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------