%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU922^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n009.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 : Tue Jul 19 14:10:51 EDT 2022

% Result   : Theorem 1.97s 2.17s
% Output   : Proof 1.97s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

thf(ty_cP,type,
    cP: $i > $o ).

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

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

thf(sP1,plain,
    ( sP1
  <=> ( ( ^ [X1: $i] : ( f @ ( g @ X1 ) ) )
      = ( ^ [X1: $i] : ( g @ ( f @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

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

thf(sP3,plain,
    ( sP3
  <=> ( cP @ ( g @ ( f @ ( f @ a ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( ( f @ ( g @ a ) )
        = ( g @ ( f @ a ) ) )
     => ~ sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( f @ ( f @ ( g @ a ) ) )
      = ( g @ ( f @ ( f @ a ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: $i] :
        ( ( f @ ( g @ X1 ) )
        = ( g @ ( f @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: $i,X2: $i > $o] :
        ( ( X2 @ X1 )
       => ! [X3: $i] :
            ( ( X1 = X3 )
           => ( X2 @ X3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

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

thf(sP9,plain,
    ( sP9
  <=> ( ~ sP5
     => ! [X1: $i] :
          ( ( ( f @ ( g @ a ) )
            = X1 )
         => ( ( f @ X1 )
           != ( g @ ( f @ ( f @ a ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( ( cP @ ( f @ ( f @ ( g @ a ) ) ) )
     => sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ! [X1: $i] :
        ( ( ( f @ ( g @ a ) )
          = X1 )
       => ( ( f @ X1 )
         != ( g @ ( f @ ( f @ a ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( sP1
     => sP10 ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( cP @ ( f @ ( f @ ( g @ a ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ! [X1: $i > $o] :
        ( ( X1 @ ( f @ ( g @ a ) ) )
       => ! [X2: $i] :
            ( ( ( f @ ( g @ a ) )
              = X2 )
           => ( X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(cTHM128_pme,conjecture,
    sP12 ).

thf(h0,negated_conjecture,
    ~ sP12,
    inference(assume_negation,[status(cth)],[cTHM128_pme]) ).

thf(1,plain,
    ( ~ sP6
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP6
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP4
    | ~ sP8
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP11
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP9
    | sP5
    | sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP14
    | sP9 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP7
    | sP14 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    sP7,
    inference(eq_ind,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP1
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP13
    | sP3
    | ~ sP5 ),
    inference(mating_rule,[status(thm)],]) ).

thf(11,plain,
    ( sP10
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    ( sP10
    | sP13 ),
    inference(prop_rule,[status(thm)],]) ).

thf(13,plain,
    ( sP12
    | ~ sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(14,plain,
    ( sP12
    | sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(15,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,h0]) ).

thf(0,theorem,
    sP12,
    inference(contra,[status(thm),contra(discharge,[h0])],[15,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SEU922^5 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n009.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 : Sat Jun 18 23:01:08 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 1.97/2.17  % SZS status Theorem
% 1.97/2.17  % Mode: mode506
% 1.97/2.17  % Inferences: 8
% 1.97/2.17  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------