%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SYO885^1.033.003 : TPTP v8.1.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n014.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 19:35:09 EDT 2022

% Result   : Theorem 1.99s 2.21s
% Output   : Proof 1.99s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_a0,type,
    a0: $i ).

thf(ty_a1,type,
    a1: $i ).

thf(ty_a2,type,
    a2: $i ).

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

thf(sP1,plain,
    ( sP1
  <=> ( ~ ( ( ( f @ a0 @ a1 @ a2 )
            = ( f @ a0 @ a1 @ a2 ) )
         => ( ( f @ a0 @ a1 @ a2 )
           != ( f @ a0 @ a1 @ a2 ) ) )
     => ( ( f @ a0 @ a1 @ a2 )
       != ( f @ a0 @ a1 @ a2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( ( f @ a0 @ a1 @ a2 )
        = ( f @ a0 @ a1 @ a2 ) )
     => ( ( f @ a0 @ a1 @ a2 )
       != ( f @ a0 @ a1 @ a2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( f @ a0 @ a1 @ a2 )
      = ( f @ a0 @ a1 @ a2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: $i > $i > $i > $i] :
        ( ~ ( ( ( X1 @ a0 @ a1 @ a2 )
              = ( f @ a0 @ a1 @ a2 ) )
           => ( ( X1 @ a0 @ a2 @ a1 )
             != ( f @ a0 @ a1 @ a2 ) ) )
       => ( ( X1 @ a2 @ a1 @ a0 )
         != ( f @ a0 @ a1 @ a2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(goal,conjecture,
    ~ sP4 ).

thf(h0,negated_conjecture,
    sP4,
    inference(assume_negation,[status(cth)],[goal]) ).

thf(1,plain,
    sP3,
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP2
    | ~ sP3
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP1
    | sP2
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP4
    | sP1 ),
    inference(all_rule,[status(thm)],]) ).

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

thf(0,theorem,
    ~ sP4,
    inference(contra,[status(thm),contra(discharge,[h0])],[5,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYO885^1.033.003 : TPTP v8.1.0. Released v7.5.0.
% 0.07/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33  % Computer : n014.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 : Sat Jul  9 08:54:21 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 1.99/2.21  % SZS status Theorem
% 1.99/2.21  % Mode: mode506
% 1.99/2.21  % Inferences: 38895
% 1.99/2.21  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------