%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEV430^1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n021.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 18:06:22 EDT 2022

% Result   : Theorem 2.22s 2.45s
% Output   : Proof 2.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   17 (  11 unt;   0 typ;   0 def)
%            Number of atoms       :   43 (  11 equ;   0 cnn)
%            Maximal formula atoms :    2 (   2 avg)
%            Number of connectives :   48 (  15   ~;   4   |;   0   &;  27   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   7 con; 0-2 aty)
%            Number of variables   :   16 (   0   ^  16   !;   0   ?;  16   :)

% Comments : 
%------------------------------------------------------------------------------
thf(invexists,conjecture,
    ~ ! [X1: $i > $i] :
        ~ ! [X2: $i] :
            ( ( f @ ( X1 @ X2 ) )
            = X2 ) ).

thf(h0,negated_conjecture,
    ! [X1: $i > $i] :
      ~ ! [X2: $i] :
          ( ( f @ ( X1 @ X2 ) )
          = X2 ),
    inference(assume_negation,[status(cth)],[invexists]) ).

thf(pax1,axiom,
    ( p1
   => ! [X3: $i > $i] :
        ~ ! [X2: $i] :
            ( ( ff @ ( X3 @ X2 ) )
            = X2 ) ),
    file('<stdin>',pax1) ).

thf(pax2,axiom,
    ( p2
   => ! [X1: $i] :
        ~ ! [X2: $i] :
            ( ( ff @ X2 )
           != X1 ) ),
    file('<stdin>',pax2) ).

thf(ax1284,axiom,
    p1,
    file('<stdin>',ax1284) ).

thf(ax1283,axiom,
    p2,
    file('<stdin>',ax1283) ).

thf(c_0_4,plain,
    ! [X766: $i > $i] :
      ( ~ p1
      | ( ( ff @ ( X766 @ ( esk382_1 @ X766 ) ) )
       != ( esk382_1 @ X766 ) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax1])])])]) ).

thf(c_0_5,plain,
    ! [X762: $i] :
      ( ~ p2
      | ( ( ff @ ( esk380_1 @ X762 ) )
        = X762 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax2])])])])]) ).

thf(c_0_6,plain,
    ! [X3: $i > $i] :
      ( ~ p1
      | ( ( ff @ ( X3 @ ( esk382_1 @ X3 ) ) )
       != ( esk382_1 @ X3 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

thf(c_0_7,plain,
    p1,
    inference(split_conjunct,[status(thm)],[ax1284]) ).

thf(c_0_8,plain,
    ! [X1: $i] :
      ( ( ( ff @ ( esk380_1 @ X1 ) )
        = X1 )
      | ~ p2 ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_9,plain,
    p2,
    inference(split_conjunct,[status(thm)],[ax1283]) ).

thf(c_0_10,plain,
    ! [X3: $i > $i] :
      ( ( ff @ ( X3 @ ( esk382_1 @ X3 ) ) )
     != ( esk382_1 @ X3 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_7])]) ).

thf(c_0_11,plain,
    ! [X1: $i] :
      ( ( ff @ ( esk380_1 @ X1 ) )
      = X1 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9])]) ).

thf(c_0_12,plain,
    $false,
    inference(spm,[status(thm)],[c_0_10,c_0_11]),
    [proof] ).

thf(1,plain,
    $false,
    inference(eprover,[status(thm),assumptions([h0])],]) ).

thf(0,theorem,
    ~ ! [X1: $i > $i] :
        ~ ! [X2: $i] :
            ( ( f @ ( X1 @ X2 ) )
            = X2 ),
    inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEV430^1 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n021.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 : Tue Jun 28 15:57:26 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 2.22/2.45  % SZS status Theorem
% 2.22/2.45  % Mode: mode506
% 2.22/2.45  % Inferences: 19037
% 2.22/2.45  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------