%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU919^5 : 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 14:10:50 EDT 2022

% Result   : Theorem 0.13s 0.35s
% Output   : Proof 0.13s
% 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
  <=> ( cP @ ( f @ ( g @ a ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: $i] :
        ( ( f @ ( g @ X1 ) )
        = ( g @ ( f @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

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

thf(sP4,plain,
    ( sP4
  <=> ( ( ^ [X1: $i] : ( f @ ( g @ X1 ) ) )
      = ( ^ [X1: $i] : ( g @ ( f @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

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

thf(cTHM127_pme,conjecture,
    ( sP4
   => ( sP1
     => sP5 ) ) ).

thf(h0,negated_conjecture,
    ~ ( sP4
     => ( sP1
       => sP5 ) ),
    inference(assume_negation,[status(cth)],[cTHM127_pme]) ).

thf(h1,assumption,
    sP4,
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ( sP1
     => sP5 ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ sP5,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP2
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP1
    | sP5
    | ~ sP3 ),
    inference(mating_rule,[status(thm)],]) ).

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

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

thf(5,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,4,h3,h4]) ).

thf(6,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,5,h1,h2]) ).

thf(0,theorem,
    ( sP4
   => ( sP1
     => sP5 ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU919^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33  % Computer : n009.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 : Sun Jun 19 21:46:52 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.35  % SZS status Theorem
% 0.13/0.35  % Mode: mode213
% 0.13/0.35  % Inferences: 7
% 0.13/0.35  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------