TSTP Solution File: SEU997^5 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU997^5 : 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 : n025.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 14:11:11 EDT 2022

% Result   : Theorem 44.88s 44.70s
% Output   : Proof 44.88s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   67 (  45 unt;   0 typ;   0 def)
%            Number of atoms       :  471 ( 162 equ;   0 cnn)
%            Maximal formula atoms :   42 (   7 avg)
%            Number of connectives :  877 ( 151   ~;  38   |;  20   &; 587   @)
%                                         (   0 <=>;  80  =>;   1  <=;   0 <~>)
%            Maximal formula depth :   50 (   5 avg)
%            Number of types       :    0 (   0 usr)
%            Number of type conns  :   16 (  16   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (  10 usr;  11 con; 0-2 aty)
%            Number of variables   :  223 (   0   ^ 223   !;   0   ?; 223   :)

% Comments : 
%------------------------------------------------------------------------------
thf(cCD_LATTICE_THM_pme,conjecture,
    ! [X1: a > a > a,X2: a > a > a,X3: a,X4: a] :
      ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: a] :
                                                                  ( ( X1 @ X5 @ X5 )
                                                                  = X5 )
                                                             => ~ ! [X5: a] :
                                                                    ( ( X2 @ X5 @ X5 )
                                                                    = X5 ) )
                                                         => ~ ! [X5: a,X6: a,X7: a] :
                                                                ( ( X1 @ ( X1 @ X5 @ X6 ) @ X7 )
                                                                = ( X1 @ X5 @ ( X1 @ X6 @ X7 ) ) ) )
                                                     => ~ ! [X5: a,X6: a,X7: a] :
                                                            ( ( X2 @ ( X2 @ X5 @ X6 ) @ X7 )
                                                            = ( X2 @ X5 @ ( X2 @ X6 @ X7 ) ) ) )
                                                 => ~ ! [X5: a,X6: a] :
                                                        ( ( X1 @ X5 @ X6 )
                                                        = ( X1 @ X6 @ X5 ) ) )
                                             => ~ ! [X5: a,X6: a] :
                                                    ( ( X2 @ X5 @ X6 )
                                                    = ( X2 @ X6 @ X5 ) ) )
                                         => ~ ! [X5: a,X6: a] :
                                                ( ( X1 @ ( X2 @ X5 @ X6 ) @ X6 )
                                                = X6 ) )
                                     => ~ ! [X5: a,X6: a] :
                                            ( ( X2 @ ( X1 @ X5 @ X6 ) @ X6 )
                                            = X6 ) )
                                 => ~ ! [X5: a,X6: a,X7: a] :
                                        ( ( X2 @ X5 @ ( X1 @ X6 @ X7 ) )
                                        = ( X1 @ ( X2 @ X5 @ X6 ) @ ( X2 @ X5 @ X7 ) ) ) )
                             => ~ ! [X5: a,X6: a,X7: a] :
                                    ( ( X1 @ X5 @ ( X2 @ X6 @ X7 ) )
                                    = ( X2 @ ( X1 @ X5 @ X6 ) @ ( X1 @ X5 @ X7 ) ) ) )
                         => ~ ! [X5: a] :
                                ( ( X2 @ X3 @ X5 )
                                = X5 ) )
                     => ~ ! [X5: a] :
                            ( ( X1 @ X3 @ X5 )
                            = X3 ) )
                 => ~ ! [X5: a] :
                        ( ( X2 @ X4 @ X5 )
                        = X4 ) )
             => ~ ! [X5: a] :
                    ( ( X1 @ X4 @ X5 )
                    = X5 ) )
         => ~ ! [X5: a] :
                ~ ! [X6: a] :
                    ( ( ( X1 @ X5 @ X6 )
                      = X3 )
                   => ( ( X2 @ X5 @ X6 )
                     != X4 ) ) )
     => ! [X5: a,X6: a,X7: a] :
          ( ~ ( ~ ( ~ ( ( ( X1 @ X5 @ X6 )
                        = X3 )
                     => ( ( X2 @ X5 @ X6 )
                       != X4 ) )
                 => ( ( X1 @ X5 @ X7 )
                   != X3 ) )
             => ( ( X2 @ X5 @ X7 )
               != X4 ) )
         => ( X6 = X7 ) ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: a > a > a,X2: a > a > a,X3: a,X4: a] :
        ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: a] :
                                                                    ( ( X1 @ X5 @ X5 )
                                                                    = X5 )
                                                               => ~ ! [X5: a] :
                                                                      ( ( X2 @ X5 @ X5 )
                                                                      = X5 ) )
                                                           => ~ ! [X5: a,X6: a,X7: a] :
                                                                  ( ( X1 @ ( X1 @ X5 @ X6 ) @ X7 )
                                                                  = ( X1 @ X5 @ ( X1 @ X6 @ X7 ) ) ) )
                                                       => ~ ! [X5: a,X6: a,X7: a] :
                                                              ( ( X2 @ ( X2 @ X5 @ X6 ) @ X7 )
                                                              = ( X2 @ X5 @ ( X2 @ X6 @ X7 ) ) ) )
                                                   => ~ ! [X5: a,X6: a] :
                                                          ( ( X1 @ X5 @ X6 )
                                                          = ( X1 @ X6 @ X5 ) ) )
                                               => ~ ! [X5: a,X6: a] :
                                                      ( ( X2 @ X5 @ X6 )
                                                      = ( X2 @ X6 @ X5 ) ) )
                                           => ~ ! [X5: a,X6: a] :
                                                  ( ( X1 @ ( X2 @ X5 @ X6 ) @ X6 )
                                                  = X6 ) )
                                       => ~ ! [X5: a,X6: a] :
                                              ( ( X2 @ ( X1 @ X5 @ X6 ) @ X6 )
                                              = X6 ) )
                                   => ~ ! [X5: a,X6: a,X7: a] :
                                          ( ( X2 @ X5 @ ( X1 @ X6 @ X7 ) )
                                          = ( X1 @ ( X2 @ X5 @ X6 ) @ ( X2 @ X5 @ X7 ) ) ) )
                               => ~ ! [X5: a,X6: a,X7: a] :
                                      ( ( X1 @ X5 @ ( X2 @ X6 @ X7 ) )
                                      = ( X2 @ ( X1 @ X5 @ X6 ) @ ( X1 @ X5 @ X7 ) ) ) )
                           => ~ ! [X5: a] :
                                  ( ( X2 @ X3 @ X5 )
                                  = X5 ) )
                       => ~ ! [X5: a] :
                              ( ( X1 @ X3 @ X5 )
                              = X3 ) )
                   => ~ ! [X5: a] :
                          ( ( X2 @ X4 @ X5 )
                          = X4 ) )
               => ~ ! [X5: a] :
                      ( ( X1 @ X4 @ X5 )
                      = X5 ) )
           => ~ ! [X5: a] :
                  ~ ! [X6: a] :
                      ( ( ( X1 @ X5 @ X6 )
                        = X3 )
                     => ( ( X2 @ X5 @ X6 )
                       != X4 ) ) )
       => ! [X5: a,X6: a,X7: a] :
            ( ~ ( ~ ( ~ ( ( ( X1 @ X5 @ X6 )
                          = X3 )
                       => ( ( X2 @ X5 @ X6 )
                         != X4 ) )
                   => ( ( X1 @ X5 @ X7 )
                     != X3 ) )
               => ( ( X2 @ X5 @ X7 )
                 != X4 ) )
           => ( X6 = X7 ) ) ),
    inference(assume_negation,[status(cth)],[cCD_LATTICE_THM_pme]) ).

thf(nax1,axiom,
    ( p1
   <= ! [X6: a > a > a,X8: a > a > a,X3: a,X4: a] :
        ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: a] :
                                                                    ( ( X6 @ X5 @ X5 )
                                                                    = X5 )
                                                               => ~ ! [X5: a] :
                                                                      ( ( X8 @ X5 @ X5 )
                                                                      = X5 ) )
                                                           => ~ ! [X5: a,X7: a,X9: a] :
                                                                  ( ( X6 @ ( X6 @ X5 @ X7 ) @ X9 )
                                                                  = ( X6 @ X5 @ ( X6 @ X7 @ X9 ) ) ) )
                                                       => ~ ! [X5: a,X7: a,X9: a] :
                                                              ( ( X8 @ ( X8 @ X5 @ X7 ) @ X9 )
                                                              = ( X8 @ X5 @ ( X8 @ X7 @ X9 ) ) ) )
                                                   => ~ ! [X5: a,X7: a] :
                                                          ( ( X6 @ X5 @ X7 )
                                                          = ( X6 @ X7 @ X5 ) ) )
                                               => ~ ! [X5: a,X7: a] :
                                                      ( ( X8 @ X5 @ X7 )
                                                      = ( X8 @ X7 @ X5 ) ) )
                                           => ~ ! [X5: a,X7: a] :
                                                  ( ( X6 @ ( X8 @ X5 @ X7 ) @ X7 )
                                                  = X7 ) )
                                       => ~ ! [X5: a,X7: a] :
                                              ( ( X8 @ ( X6 @ X5 @ X7 ) @ X7 )
                                              = X7 ) )
                                   => ~ ! [X5: a,X7: a,X9: a] :
                                          ( ( X8 @ X5 @ ( X6 @ X7 @ X9 ) )
                                          = ( X6 @ ( X8 @ X5 @ X7 ) @ ( X8 @ X5 @ X9 ) ) ) )
                               => ~ ! [X5: a,X7: a,X9: a] :
                                      ( ( X6 @ X5 @ ( X8 @ X7 @ X9 ) )
                                      = ( X8 @ ( X6 @ X5 @ X7 ) @ ( X6 @ X5 @ X9 ) ) ) )
                           => ~ ! [X5: a] :
                                  ( ( X8 @ X3 @ X5 )
                                  = X5 ) )
                       => ~ ! [X5: a] :
                              ( ( X6 @ X3 @ X5 )
                              = X3 ) )
                   => ~ ! [X5: a] :
                          ( ( X8 @ X4 @ X5 )
                          = X4 ) )
               => ~ ! [X5: a] :
                      ( ( X6 @ X4 @ X5 )
                      = X5 ) )
           => ~ ! [X5: a] :
                  ~ ! [X7: a] :
                      ( ( ( X6 @ X5 @ X7 )
                        = X3 )
                     => ( ( X8 @ X5 @ X7 )
                       != X4 ) ) )
       => ! [X5: a,X7: a,X9: a] :
            ( ~ ( ~ ( ~ ( ( ( X6 @ X5 @ X7 )
                          = X3 )
                       => ( ( X8 @ X5 @ X7 )
                         != X4 ) )
                   => ( ( X6 @ X5 @ X9 )
                     != X3 ) )
               => ( ( X8 @ X5 @ X9 )
                 != X4 ) )
           => ( X7 = X9 ) ) ) ),
    file('<stdin>',nax1) ).

thf(ax101,axiom,
    ~ p1,
    file('<stdin>',ax101) ).

thf(c_0_2,plain,
    ! [X3219: a,X3220: a,X3221: a,X3222: a,X3223: a,X3224: a,X3225: a,X3226: a,X3227: a,X3228: a,X3229: a,X3230: a,X3231: a,X3232: a,X3233: a,X3234: a,X3235: a,X3236: a,X3237: a,X3238: a,X3239: a,X3240: a,X3241: a,X3242: a,X3243: a,X3244: a,X3245: a] :
      ( ( ( ( esk1613_0 @ X3219 @ X3219 )
          = X3219 )
        | p1 )
      & ( ( ( esk1614_0 @ X3220 @ X3220 )
          = X3220 )
        | p1 )
      & ( ( ( esk1613_0 @ ( esk1613_0 @ X3221 @ X3222 ) @ X3223 )
          = ( esk1613_0 @ X3221 @ ( esk1613_0 @ X3222 @ X3223 ) ) )
        | p1 )
      & ( ( ( esk1614_0 @ ( esk1614_0 @ X3224 @ X3225 ) @ X3226 )
          = ( esk1614_0 @ X3224 @ ( esk1614_0 @ X3225 @ X3226 ) ) )
        | p1 )
      & ( ( ( esk1613_0 @ X3227 @ X3228 )
          = ( esk1613_0 @ X3228 @ X3227 ) )
        | p1 )
      & ( ( ( esk1614_0 @ X3229 @ X3230 )
          = ( esk1614_0 @ X3230 @ X3229 ) )
        | p1 )
      & ( ( ( esk1613_0 @ ( esk1614_0 @ X3231 @ X3232 ) @ X3232 )
          = X3232 )
        | p1 )
      & ( ( ( esk1614_0 @ ( esk1613_0 @ X3233 @ X3234 ) @ X3234 )
          = X3234 )
        | p1 )
      & ( ( ( esk1614_0 @ X3235 @ ( esk1613_0 @ X3236 @ X3237 ) )
          = ( esk1613_0 @ ( esk1614_0 @ X3235 @ X3236 ) @ ( esk1614_0 @ X3235 @ X3237 ) ) )
        | p1 )
      & ( ( ( esk1613_0 @ X3238 @ ( esk1614_0 @ X3239 @ X3240 ) )
          = ( esk1614_0 @ ( esk1613_0 @ X3238 @ X3239 ) @ ( esk1613_0 @ X3238 @ X3240 ) ) )
        | p1 )
      & ( ( ( esk1614_0 @ esk1615_0 @ X3241 )
          = X3241 )
        | p1 )
      & ( ( ( esk1613_0 @ esk1615_0 @ X3242 )
          = esk1615_0 )
        | p1 )
      & ( ( ( esk1614_0 @ esk1616_0 @ X3243 )
          = esk1616_0 )
        | p1 )
      & ( ( ( esk1613_0 @ esk1616_0 @ X3244 )
          = X3244 )
        | p1 )
      & ( ( ( esk1613_0 @ X3245 @ ( esk1617_1 @ X3245 ) )
          = esk1615_0 )
        | p1 )
      & ( ( ( esk1614_0 @ X3245 @ ( esk1617_1 @ X3245 ) )
          = esk1616_0 )
        | p1 )
      & ( ( ( esk1613_0 @ esk1618_0 @ esk1619_0 )
          = esk1615_0 )
        | p1 )
      & ( ( ( esk1614_0 @ esk1618_0 @ esk1619_0 )
          = esk1616_0 )
        | p1 )
      & ( ( ( esk1613_0 @ esk1618_0 @ esk1620_0 )
          = esk1615_0 )
        | p1 )
      & ( ( ( esk1614_0 @ esk1618_0 @ esk1620_0 )
          = esk1616_0 )
        | p1 )
      & ( ( esk1619_0 != esk1620_0 )
        | p1 ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])])])])])]) ).

thf(c_0_3,plain,
    ~ p1,
    inference(fof_simplification,[status(thm)],[ax101]) ).

thf(c_0_4,plain,
    ! [X1: a,X2: a] :
      ( ( ( esk1613_0 @ ( esk1614_0 @ X1 @ X2 ) @ X2 )
        = X2 )
      | p1 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_5,plain,
    ~ p1,
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

thf(c_0_6,plain,
    ! [X2: a,X1: a] :
      ( ( ( esk1613_0 @ X1 @ X2 )
        = ( esk1613_0 @ X2 @ X1 ) )
      | p1 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_7,plain,
    ! [X1: a,X2: a,X3: a] :
      ( ( ( esk1613_0 @ X1 @ ( esk1614_0 @ X2 @ X3 ) )
        = ( esk1614_0 @ ( esk1613_0 @ X1 @ X2 ) @ ( esk1613_0 @ X1 @ X3 ) ) )
      | p1 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_8,plain,
    ( ( ( esk1613_0 @ esk1618_0 @ esk1620_0 )
      = esk1615_0 )
    | p1 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_9,plain,
    ! [X1: a] :
      ( ( ( esk1614_0 @ esk1615_0 @ X1 )
        = X1 )
      | p1 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_10,plain,
    ! [X1: a,X2: a] :
      ( ( esk1613_0 @ ( esk1614_0 @ X1 @ X2 ) @ X2 )
      = X2 ),
    inference(sr,[status(thm)],[c_0_4,c_0_5]) ).

thf(c_0_11,plain,
    ! [X2: a,X1: a] :
      ( ( esk1613_0 @ X1 @ X2 )
      = ( esk1613_0 @ X2 @ X1 ) ),
    inference(sr,[status(thm)],[c_0_6,c_0_5]) ).

thf(c_0_12,plain,
    ! [X1: a] :
      ( ( ( esk1614_0 @ esk1616_0 @ X1 )
        = esk1616_0 )
      | p1 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_13,plain,
    ( ( ( esk1613_0 @ esk1618_0 @ esk1619_0 )
      = esk1615_0 )
    | p1 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_14,plain,
    ! [X1: a,X2: a] :
      ( ( ( esk1614_0 @ ( esk1613_0 @ X1 @ X2 ) @ X2 )
        = X2 )
      | p1 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_15,plain,
    ! [X2: a,X1: a] :
      ( ( ( esk1614_0 @ X1 @ X2 )
        = ( esk1614_0 @ X2 @ X1 ) )
      | p1 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_16,plain,
    ! [X1: a,X2: a,X3: a] :
      ( ( esk1614_0 @ ( esk1613_0 @ X1 @ X2 ) @ ( esk1613_0 @ X1 @ X3 ) )
      = ( esk1613_0 @ X1 @ ( esk1614_0 @ X2 @ X3 ) ) ),
    inference(sr,[status(thm)],[c_0_7,c_0_5]) ).

thf(c_0_17,plain,
    ( ( esk1613_0 @ esk1618_0 @ esk1620_0 )
    = esk1615_0 ),
    inference(sr,[status(thm)],[c_0_8,c_0_5]) ).

thf(c_0_18,plain,
    ! [X1: a] :
      ( ( esk1614_0 @ esk1615_0 @ X1 )
      = X1 ),
    inference(sr,[status(thm)],[c_0_9,c_0_5]) ).

thf(c_0_19,plain,
    ! [X1: a] :
      ( ( ( esk1614_0 @ X1 @ ( esk1617_1 @ X1 ) )
        = esk1616_0 )
      | p1 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_20,plain,
    ! [X2: a,X1: a] :
      ( ( esk1613_0 @ X1 @ ( esk1614_0 @ X2 @ X1 ) )
      = X1 ),
    inference(rw,[status(thm)],[c_0_10,c_0_11]) ).

thf(c_0_21,plain,
    ! [X1: a] :
      ( ( esk1614_0 @ esk1616_0 @ X1 )
      = esk1616_0 ),
    inference(sr,[status(thm)],[c_0_12,c_0_5]) ).

thf(c_0_22,plain,
    ( ( esk1613_0 @ esk1618_0 @ esk1619_0 )
    = esk1615_0 ),
    inference(sr,[status(thm)],[c_0_13,c_0_5]) ).

thf(c_0_23,plain,
    ! [X1: a] :
      ( ( ( esk1613_0 @ X1 @ ( esk1617_1 @ X1 ) )
        = esk1615_0 )
      | p1 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_24,plain,
    ! [X1: a,X2: a,X3: a] :
      ( ( ( esk1614_0 @ X1 @ ( esk1613_0 @ X2 @ X3 ) )
        = ( esk1613_0 @ ( esk1614_0 @ X1 @ X2 ) @ ( esk1614_0 @ X1 @ X3 ) ) )
      | p1 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_25,plain,
    ( ( ( esk1614_0 @ esk1618_0 @ esk1620_0 )
      = esk1616_0 )
    | p1 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_26,plain,
    ! [X1: a] :
      ( ( ( esk1613_0 @ esk1616_0 @ X1 )
        = X1 )
      | p1 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_27,plain,
    ! [X1: a,X2: a] :
      ( ( esk1614_0 @ ( esk1613_0 @ X1 @ X2 ) @ X2 )
      = X2 ),
    inference(sr,[status(thm)],[c_0_14,c_0_5]) ).

thf(c_0_28,plain,
    ! [X2: a,X1: a] :
      ( ( esk1614_0 @ X1 @ X2 )
      = ( esk1614_0 @ X2 @ X1 ) ),
    inference(sr,[status(thm)],[c_0_15,c_0_5]) ).

thf(c_0_29,plain,
    ! [X1: a] :
      ( ( ( esk1613_0 @ esk1615_0 @ X1 )
        = esk1615_0 )
      | p1 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_30,plain,
    ! [X1: a] :
      ( ( esk1613_0 @ esk1618_0 @ ( esk1614_0 @ esk1620_0 @ X1 ) )
      = ( esk1613_0 @ esk1618_0 @ X1 ) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).

thf(c_0_31,plain,
    ! [X1: a] :
      ( ( esk1614_0 @ X1 @ ( esk1617_1 @ X1 ) )
      = esk1616_0 ),
    inference(sr,[status(thm)],[c_0_19,c_0_5]) ).

thf(c_0_32,plain,
    ! [X1: a] :
      ( ( esk1613_0 @ X1 @ esk1616_0 )
      = X1 ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

thf(c_0_33,plain,
    ( ( ( esk1614_0 @ esk1618_0 @ esk1619_0 )
      = esk1616_0 )
    | p1 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_34,plain,
    ! [X1: a] :
      ( ( esk1613_0 @ esk1618_0 @ ( esk1614_0 @ esk1619_0 @ X1 ) )
      = ( esk1613_0 @ esk1618_0 @ X1 ) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_22]),c_0_18]) ).

thf(c_0_35,plain,
    ! [X1: a] :
      ( ( esk1613_0 @ X1 @ ( esk1617_1 @ X1 ) )
      = esk1615_0 ),
    inference(sr,[status(thm)],[c_0_23,c_0_5]) ).

thf(c_0_36,plain,
    ! [X1: a,X2: a,X3: a] :
      ( ( esk1613_0 @ ( esk1614_0 @ X1 @ X2 ) @ ( esk1614_0 @ X1 @ X3 ) )
      = ( esk1614_0 @ X1 @ ( esk1613_0 @ X2 @ X3 ) ) ),
    inference(sr,[status(thm)],[c_0_24,c_0_5]) ).

thf(c_0_37,plain,
    ( ( esk1614_0 @ esk1618_0 @ esk1620_0 )
    = esk1616_0 ),
    inference(sr,[status(thm)],[c_0_25,c_0_5]) ).

thf(c_0_38,plain,
    ! [X1: a] :
      ( ( esk1613_0 @ esk1616_0 @ X1 )
      = X1 ),
    inference(sr,[status(thm)],[c_0_26,c_0_5]) ).

thf(c_0_39,plain,
    ! [X2: a,X1: a] :
      ( ( esk1614_0 @ X1 @ ( esk1613_0 @ X2 @ X1 ) )
      = X1 ),
    inference(rw,[status(thm)],[c_0_27,c_0_28]) ).

thf(c_0_40,plain,
    ! [X1: a] :
      ( ( esk1613_0 @ esk1615_0 @ X1 )
      = esk1615_0 ),
    inference(sr,[status(thm)],[c_0_29,c_0_5]) ).

thf(c_0_41,plain,
    ( ( esk1613_0 @ esk1618_0 @ ( esk1617_1 @ esk1620_0 ) )
    = esk1618_0 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).

thf(c_0_42,plain,
    ( ( esk1614_0 @ esk1618_0 @ esk1619_0 )
    = esk1616_0 ),
    inference(sr,[status(thm)],[c_0_33,c_0_5]) ).

thf(c_0_43,plain,
    ( ( esk1613_0 @ esk1618_0 @ ( esk1617_1 @ esk1619_0 ) )
    = esk1618_0 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_31]),c_0_32]) ).

thf(c_0_44,plain,
    ! [X1: a,X2: a] :
      ( ( esk1613_0 @ X1 @ ( esk1614_0 @ ( esk1617_1 @ X1 ) @ X2 ) )
      = ( esk1613_0 @ X1 @ X2 ) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_35]),c_0_18]) ).

thf(c_0_45,plain,
    ! [X1: a] :
      ( ( esk1614_0 @ esk1618_0 @ ( esk1613_0 @ esk1620_0 @ X1 ) )
      = ( esk1614_0 @ esk1618_0 @ X1 ) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).

thf(c_0_46,plain,
    ! [X1: a] :
      ( ( esk1614_0 @ X1 @ esk1615_0 )
      = X1 ),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

thf(c_0_47,plain,
    ( ( esk1614_0 @ esk1618_0 @ ( esk1617_1 @ esk1620_0 ) )
    = ( esk1617_1 @ esk1620_0 ) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_41]),c_0_28]) ).

thf(c_0_48,plain,
    ! [X1: a] :
      ( ( esk1614_0 @ esk1618_0 @ ( esk1613_0 @ esk1619_0 @ X1 ) )
      = ( esk1614_0 @ esk1618_0 @ X1 ) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_42]),c_0_38]) ).

thf(c_0_49,plain,
    ( ( esk1614_0 @ esk1618_0 @ ( esk1617_1 @ esk1619_0 ) )
    = ( esk1617_1 @ esk1619_0 ) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_43]),c_0_28]) ).

thf(c_0_50,plain,
    ! [X1: a] :
      ( ( esk1613_0 @ X1 @ ( esk1617_1 @ ( esk1617_1 @ X1 ) ) )
      = X1 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_31]),c_0_32]) ).

thf(c_0_51,plain,
    ( ( esk1617_1 @ esk1620_0 )
    = esk1618_0 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_35]),c_0_46]),c_0_47]) ).

thf(c_0_52,plain,
    ( ( esk1617_1 @ esk1619_0 )
    = esk1618_0 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_35]),c_0_46]),c_0_49]) ).

thf(c_0_53,plain,
    ! [X1: a,X2: a] :
      ( ( esk1614_0 @ X1 @ ( esk1613_0 @ ( esk1617_1 @ X1 ) @ X2 ) )
      = ( esk1614_0 @ X1 @ X2 ) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_31]),c_0_38]) ).

thf(c_0_54,plain,
    ( ( esk1613_0 @ esk1620_0 @ ( esk1617_1 @ esk1618_0 ) )
    = esk1620_0 ),
    inference(spm,[status(thm)],[c_0_50,c_0_51]) ).

thf(c_0_55,plain,
    ( ( esk1613_0 @ esk1619_0 @ ( esk1617_1 @ esk1618_0 ) )
    = esk1619_0 ),
    inference(spm,[status(thm)],[c_0_50,c_0_52]) ).

thf(c_0_56,plain,
    ! [X1: a] :
      ( ( esk1614_0 @ X1 @ ( esk1617_1 @ ( esk1617_1 @ X1 ) ) )
      = X1 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_35]),c_0_46]) ).

thf(c_0_57,plain,
    ( ( esk1614_0 @ esk1620_0 @ ( esk1617_1 @ esk1618_0 ) )
    = ( esk1617_1 @ esk1618_0 ) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_54]),c_0_28]) ).

thf(c_0_58,plain,
    ( p1
    | ( esk1619_0 != esk1620_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_59,plain,
    ( ( esk1614_0 @ esk1619_0 @ ( esk1617_1 @ esk1618_0 ) )
    = ( esk1617_1 @ esk1618_0 ) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_55]),c_0_28]) ).

thf(c_0_60,plain,
    ( ( esk1617_1 @ esk1618_0 )
    = esk1620_0 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_51]),c_0_57]) ).

thf(c_0_61,plain,
    esk1620_0 != esk1619_0,
    inference(sr,[status(thm)],[c_0_58,c_0_5]) ).

thf(c_0_62,plain,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_52]),c_0_59]),c_0_60]),c_0_61]),
    [proof] ).

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

thf(0,theorem,
    ! [X1: a > a > a,X2: a > a > a,X3: a,X4: a] :
      ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: a] :
                                                                  ( ( X1 @ X5 @ X5 )
                                                                  = X5 )
                                                             => ~ ! [X5: a] :
                                                                    ( ( X2 @ X5 @ X5 )
                                                                    = X5 ) )
                                                         => ~ ! [X5: a,X6: a,X7: a] :
                                                                ( ( X1 @ ( X1 @ X5 @ X6 ) @ X7 )
                                                                = ( X1 @ X5 @ ( X1 @ X6 @ X7 ) ) ) )
                                                     => ~ ! [X5: a,X6: a,X7: a] :
                                                            ( ( X2 @ ( X2 @ X5 @ X6 ) @ X7 )
                                                            = ( X2 @ X5 @ ( X2 @ X6 @ X7 ) ) ) )
                                                 => ~ ! [X5: a,X6: a] :
                                                        ( ( X1 @ X5 @ X6 )
                                                        = ( X1 @ X6 @ X5 ) ) )
                                             => ~ ! [X5: a,X6: a] :
                                                    ( ( X2 @ X5 @ X6 )
                                                    = ( X2 @ X6 @ X5 ) ) )
                                         => ~ ! [X5: a,X6: a] :
                                                ( ( X1 @ ( X2 @ X5 @ X6 ) @ X6 )
                                                = X6 ) )
                                     => ~ ! [X5: a,X6: a] :
                                            ( ( X2 @ ( X1 @ X5 @ X6 ) @ X6 )
                                            = X6 ) )
                                 => ~ ! [X5: a,X6: a,X7: a] :
                                        ( ( X2 @ X5 @ ( X1 @ X6 @ X7 ) )
                                        = ( X1 @ ( X2 @ X5 @ X6 ) @ ( X2 @ X5 @ X7 ) ) ) )
                             => ~ ! [X5: a,X6: a,X7: a] :
                                    ( ( X1 @ X5 @ ( X2 @ X6 @ X7 ) )
                                    = ( X2 @ ( X1 @ X5 @ X6 ) @ ( X1 @ X5 @ X7 ) ) ) )
                         => ~ ! [X5: a] :
                                ( ( X2 @ X3 @ X5 )
                                = X5 ) )
                     => ~ ! [X5: a] :
                            ( ( X1 @ X3 @ X5 )
                            = X3 ) )
                 => ~ ! [X5: a] :
                        ( ( X2 @ X4 @ X5 )
                        = X4 ) )
             => ~ ! [X5: a] :
                    ( ( X1 @ X4 @ X5 )
                    = X5 ) )
         => ~ ! [X5: a] :
                ~ ! [X6: a] :
                    ( ( ( X1 @ X5 @ X6 )
                      = X3 )
                   => ( ( X2 @ X5 @ X6 )
                     != X4 ) ) )
     => ! [X5: a,X6: a,X7: a] :
          ( ~ ( ~ ( ~ ( ( ( X1 @ X5 @ X6 )
                        = X3 )
                     => ( ( X2 @ X5 @ X6 )
                       != X4 ) )
                 => ( ( X1 @ X5 @ X7 )
                   != X3 ) )
             => ( ( X2 @ X5 @ X7 )
               != X4 ) )
         => ( X6 = X7 ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU997^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33  % Computer : n025.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 : Mon Jun 20 12:25:29 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 44.88/44.70  % SZS status Theorem
% 44.88/44.70  % Mode: mode459
% 44.88/44.70  % Inferences: 12
% 44.88/44.70  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------