%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SYO379^5 : TPTP v8.1.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n019.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 19:31:44 EDT 2022

% Result   : Theorem 5.50s 5.68s
% Output   : Proof 5.50s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_c,type,
    c: $i ).

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

thf(sP2,plain,
    ( sP2
  <=> ( c = c ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

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

thf(sP4,plain,
    ( sP4
  <=> ! [X1: $i > $o] :
        ( ( X1
          = ( ^ [X2: $i] : ( X2 = c ) ) )
       => ! [X2: $i] :
            ~ ( X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

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

thf(def_cQDP0,definition,
    ( cQDP0
    = ( ^ [X1: $i] : ( X1 = c ) ) ) ).

thf(def_cQDP1,definition,
    ( cQDP1
    = ( ^ [X1: $i > $o] :
          ~ ( ( X1 = cQDP0 )
           => ! [X2: $i] :
                ~ ( X1 @ X2 ) ) ) ) ).

thf(cQDTHM1,conjecture,
    ~ ! [X1: $i > $o] :
        ~ ~ ( ( X1
              = ( ^ [X2: $i] : ( X2 = c ) ) )
           => ! [X2: $i] :
                ~ ( X1 @ X2 ) ) ).

thf(h0,negated_conjecture,
    sP4,
    inference(assume_negation,[status(cth)],[cQDTHM1]) ).

thf(1,plain,
    sP2,
    inference(prop_rule,[status(thm)],]) ).

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

thf(3,plain,
    ( ~ sP5
    | ~ sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP1
    | ~ sP3
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP4
    | sP1 ),
    inference(all_rule,[status(thm)],]) ).

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

thf(0,theorem,
    ~ ! [X1: $i > $o] :
        ~ ~ ( ( X1
              = ( ^ [X2: $i] : ( X2 = c ) ) )
           => ! [X2: $i] :
                ~ ( X1 @ X2 ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SYO379^5 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.04/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n019.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 Jul  9 15:28:23 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 5.50/5.68  % SZS status Theorem
% 5.50/5.68  % Mode: mode506
% 5.50/5.68  % Inferences: 98440
% 5.50/5.68  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------