%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SYO502^1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n027.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 : Thu Jul 21 19:33:04 EDT 2022

% Result   : Theorem 0.19s 0.36s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_a,type,
    a: $i ).

thf(ty_b,type,
    b: $i ).

thf(ty_g,type,
    g: $i > $i ).

thf(ty_f,type,
    f: $i > $i ).

thf(sP1,plain,
    ( sP1
  <=> ( ( f @ a )
      = ( g @ b ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( f @ a )
      = ( f @ b ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: $i,X2: $i] :
        ( ( X1 = X2 )
       => ( X2 = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( a = b )
     => ( b = a ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: $i] :
        ( ( a = X1 )
       => ( X1 = a ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( a = b ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( g @ b )
      = ( g @ a ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ( f @ b )
      = ( g @ a ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( b = a ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(claim,conjecture,
    ( ~ ( sP6
       => ~ sP1 )
   => sP8 ) ).

thf(h0,negated_conjecture,
    ~ ( ~ ( sP6
         => ~ sP1 )
     => sP8 ),
    inference(assume_negation,[status(cth)],[claim]) ).

thf(h1,assumption,
    ~ ( sP6
     => ~ sP1 ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ sP8,
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP6,
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(1,plain,
    ( sP7
    | ~ sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( sP2
    | ~ sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP1
    | sP8
    | ~ sP2
    | ~ sP7 ),
    inference(confrontation_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP4
    | ~ sP6
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP5
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP3
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    sP3,
    inference(eq_sym,[status(thm)],]) ).

thf(8,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,h3,h4,h2]) ).

thf(9,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,8,h3,h4]) ).

thf(10,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,9,h1,h2]) ).

thf(0,theorem,
    ( ~ ( sP6
       => ~ sP1 )
   => sP8 ),
    inference(contra,[status(thm),contra(discharge,[h0])],[10,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SYO502^1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n027.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 : Sat Jul  9 08:57:01 EDT 2022
% 0.19/0.33  % CPUTime  : 
% 0.19/0.36  % SZS status Theorem
% 0.19/0.36  % Mode: mode213
% 0.19/0.36  % Inferences: 9
% 0.19/0.36  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------