TSTP Solution File: ALG273^5 by Satallax---3.5

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%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : ALG273^5 : TPTP v8.1.0. Bugfixed v5.3.0.
% 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 : Thu Jul 14 17:57:53 EDT 2022

% Result   : Theorem 152.21s 151.82s
% Output   : Proof 152.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   48
%            Number of leaves      :   59
% Syntax   : Number of formulae    :  282 (  49 unt;   0 typ;   7 def)
%            Number of atoms       : 1364 ( 217 equ;   0 cnn)
%            Maximal formula atoms :    6 (   4 avg)
%            Number of connectives : 1348 ( 264   ~; 255   |;   6   &; 775   @)
%                                         (   0 <=>;  35  =>;  13  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Number of types       :    0 (   0 usr)
%            Number of type conns  :   20 (  20   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   66 (  64 usr;  65 con; 0-2 aty)
%            Number of variables   :  232 (  13   ^ 219   !;   0   ?; 232   :)

% Comments : 
%------------------------------------------------------------------------------
thf(def_cGRP_ASSOC,definition,
    ( cGRP_ASSOC
    = ( ^ [X1: g > g > g] :
        ! [X2: g,X3: g,X4: g] :
          ( ( X1 @ ( X1 @ X2 @ X3 ) @ X4 )
          = ( X1 @ X2 @ ( X1 @ X3 @ X4 ) ) ) ) ) ).

thf(def_cGRP_LEFT_INVERSE,definition,
    ( cGRP_LEFT_INVERSE
    = ( ^ [X1: g > g > g,X2: g] :
        ! [X3: g] :
          ~ ! [X4: g] :
              ( ( X1 @ X4 @ X3 )
             != X2 ) ) ) ).

thf(def_cGRP_LEFT_UNIT,definition,
    ( cGRP_LEFT_UNIT
    = ( ^ [X1: g > g > g,X2: g] :
        ! [X3: g] :
          ( ( X1 @ X2 @ X3 )
          = X3 ) ) ) ).

thf(def_cGRP_RIGHT_INVERSE,definition,
    ( cGRP_RIGHT_INVERSE
    = ( ^ [X1: g > g > g,X2: g] :
        ! [X3: g] :
          ~ ! [X4: g] :
              ( ( X1 @ X3 @ X4 )
             != X2 ) ) ) ).

thf(def_cGRP_RIGHT_UNIT,definition,
    ( cGRP_RIGHT_UNIT
    = ( ^ [X1: g > g > g,X2: g] :
        ! [X3: g] :
          ( ( X1 @ X3 @ X2 )
          = X3 ) ) ) ).

thf(def_cGROUP2,definition,
    ( cGROUP2
    = ( ^ [X1: g > g > g,X2: g] :
          ~ ( ~ ( ( cGRP_ASSOC @ X1 )
               => ~ ( cGRP_LEFT_UNIT @ X1 @ X2 ) )
           => ~ ( cGRP_LEFT_INVERSE @ X1 @ X2 ) ) ) ) ).

thf(def_cGROUP3,definition,
    ( cGROUP3
    = ( ^ [X1: g > g > g,X2: g] :
          ~ ( ~ ( ( cGRP_ASSOC @ X1 )
               => ~ ( cGRP_RIGHT_UNIT @ X1 @ X2 ) )
           => ~ ( cGRP_RIGHT_INVERSE @ X1 @ X2 ) ) ) ) ).

thf(cEQUIV_02_03,conjecture,
    ! [X1: g > g > g,X2: g] :
      ( ( ~ ( ~ ( ! [X3: g,X4: g,X5: g] :
                    ( ( X1 @ ( X1 @ X3 @ X4 ) @ X5 )
                    = ( X1 @ X3 @ ( X1 @ X4 @ X5 ) ) )
               => ~ ! [X3: g] :
                      ( ( X1 @ X2 @ X3 )
                      = X3 ) )
           => ~ ! [X3: g] :
                  ~ ! [X4: g] :
                      ( ( X1 @ X4 @ X3 )
                     != X2 ) ) )
      = ( ~ ( ~ ( ! [X3: g,X4: g,X5: g] :
                    ( ( X1 @ ( X1 @ X3 @ X4 ) @ X5 )
                    = ( X1 @ X3 @ ( X1 @ X4 @ X5 ) ) )
               => ~ ! [X3: g] :
                      ( ( X1 @ X3 @ X2 )
                      = X3 ) )
           => ~ ! [X3: g] :
                  ~ ! [X4: g] :
                      ( ( X1 @ X3 @ X4 )
                     != X2 ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: g > g > g,X2: g] :
        ( ( ~ ( ~ ( ! [X3: g,X4: g,X5: g] :
                      ( ( X1 @ ( X1 @ X3 @ X4 ) @ X5 )
                      = ( X1 @ X3 @ ( X1 @ X4 @ X5 ) ) )
                 => ~ ! [X3: g] :
                        ( ( X1 @ X2 @ X3 )
                        = X3 ) )
             => ~ ! [X3: g] :
                    ~ ! [X4: g] :
                        ( ( X1 @ X4 @ X3 )
                       != X2 ) ) )
        = ( ~ ( ~ ( ! [X3: g,X4: g,X5: g] :
                      ( ( X1 @ ( X1 @ X3 @ X4 ) @ X5 )
                      = ( X1 @ X3 @ ( X1 @ X4 @ X5 ) ) )
                 => ~ ! [X3: g] :
                        ( ( X1 @ X3 @ X2 )
                        = X3 ) )
             => ~ ! [X3: g] :
                    ~ ! [X4: g] :
                        ( ( X1 @ X3 @ X4 )
                       != X2 ) ) ) ),
    inference(assume_negation,[status(cth)],[cEQUIV_02_03]) ).

thf(ax1480,axiom,
    ( p1
    | ~ p2 ),
    file('<stdin>',ax1480) ).

thf(ax1481,axiom,
    ~ p1,
    file('<stdin>',ax1481) ).

thf(ax1479,axiom,
    ( p2
    | ~ p3 ),
    file('<stdin>',ax1479) ).

thf(ax1471,axiom,
    ( p3
    | ~ p10
    | ~ p11 ),
    file('<stdin>',ax1471) ).

thf(nax11,axiom,
    ( p11
   <= ( ~ ( ! [X1: g,X2: g,X3: g] :
              ( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
              = ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) )
         => ~ ! [X1: g] :
                ( ( f__0 @ X1 @ f__1 )
                = X1 ) )
     => ~ ! [X1: g] :
            ~ ! [X2: g] :
                ( ( f__0 @ X1 @ X2 )
               != f__1 ) ) ),
    file('<stdin>',nax11) ).

thf(nax10,axiom,
    ( p10
   <= ( ~ ( ! [X1: g,X2: g,X3: g] :
              ( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
              = ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) )
         => ~ ! [X1: g] :
                ( ( f__0 @ f__1 @ X1 )
                = X1 ) )
     => ~ ! [X1: g] :
            ~ ! [X2: g] :
                ( ( f__0 @ X2 @ X1 )
               != f__1 ) ) ),
    file('<stdin>',nax10) ).

thf(pax32,axiom,
    ( p32
   => ! [X1: g] :
        ( ( f__0 @ X1 @ f__3 )
       != f__1 ) ),
    file('<stdin>',pax32) ).

thf(ax979,axiom,
    ( p32
    | p341 ),
    file('<stdin>',ax979) ).

thf(ax1445,axiom,
    ( ~ p13
    | ~ p32 ),
    file('<stdin>',ax1445) ).

thf(ax1458,axiom,
    ( p10
    | p13 ),
    file('<stdin>',ax1458) ).

thf(pax341,axiom,
    ( p341
   => ( ( f__0 @ f__8 @ f__3 )
      = f__1 ) ),
    file('<stdin>',pax341) ).

thf(ax1442,axiom,
    ( ~ p18
    | ~ p35 ),
    file('<stdin>',ax1442) ).

thf(ax1247,axiom,
    ( p35
    | p165 ),
    file('<stdin>',ax1247) ).

thf(nax35,axiom,
    ( p35
   <= ! [X1: g] :
        ( ( f__0 @ f__3 @ X1 )
       != f__1 ) ),
    file('<stdin>',nax35) ).

thf(ax1465,axiom,
    ( p11
    | p18 ),
    file('<stdin>',ax1465) ).

thf(ax1438,axiom,
    ( ~ p15
    | p20 ),
    file('<stdin>',ax1438) ).

thf(ax1459,axiom,
    ( p10
    | ~ p12 ),
    file('<stdin>',ax1459) ).

thf(ax1440,axiom,
    ( p12
    | p15 ),
    file('<stdin>',ax1440) ).

thf(nax15,axiom,
    ( p15
   <= ! [X1: g] :
        ( ( f__0 @ f__1 @ X1 )
        = X1 ) ),
    file('<stdin>',nax15) ).

thf(pax15,axiom,
    ( p15
   => ! [X1: g] :
        ( ( f__0 @ f__1 @ X1 )
        = X1 ) ),
    file('<stdin>',pax15) ).

thf(ax1462,axiom,
    ( p15
    | ~ p20 ),
    file('<stdin>',ax1462) ).

thf(nax28,axiom,
    ( p28
   <= ! [X1: g] :
        ( ( f__0 @ X1 @ ( f__0 @ f__1 @ f__3 ) )
       != f__1 ) ),
    file('<stdin>',nax28) ).

thf(pax165,axiom,
    ( p165
   => ( ( f__0 @ f__3 @ f__7 )
      = f__1 ) ),
    file('<stdin>',pax165) ).

thf(pax10,axiom,
    ( p10
   => ( ~ ( ! [X1: g,X2: g,X3: g] :
              ( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
              = ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) )
         => ~ ! [X1: g] :
                ( ( f__0 @ f__1 @ X1 )
                = X1 ) )
     => ~ ! [X1: g] :
            ~ ! [X2: g] :
                ( ( f__0 @ X2 @ X1 )
               != f__1 ) ) ),
    file('<stdin>',pax10) ).

thf(ax1468,axiom,
    ( ~ p12
    | ~ p14
    | ~ p15 ),
    file('<stdin>',ax1468) ).

thf(nax14,axiom,
    ( p14
   <= ! [X1: g,X2: g,X3: g] :
        ( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
        = ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) ) ),
    file('<stdin>',nax14) ).

thf(nax12,axiom,
    ( p12
   <= ( ! [X1: g,X2: g,X3: g] :
          ( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
          = ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) )
     => ~ ! [X1: g] :
            ( ( f__0 @ f__1 @ X1 )
            = X1 ) ) ),
    file('<stdin>',nax12) ).

thf(ax1470,axiom,
    ( p3
    | p10
    | p11 ),
    file('<stdin>',ax1470) ).

thf(ax1449,axiom,
    ( ~ p13
    | ~ p28 ),
    file('<stdin>',ax1449) ).

thf(nax13,axiom,
    ( p13
   <= ! [X1: g] :
        ~ ! [X2: g] :
            ( ( f__0 @ X2 @ X1 )
           != f__1 ) ),
    file('<stdin>',nax13) ).

thf(nax17,axiom,
    ( p17
   <= ( ! [X1: g,X2: g,X3: g] :
          ( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
          = ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) )
     => ~ ! [X1: g] :
            ( ( f__0 @ X1 @ f__1 )
            = X1 ) ) ),
    file('<stdin>',nax17) ).

thf(ax1466,axiom,
    ( p11
    | ~ p17 ),
    file('<stdin>',ax1466) ).

thf(nax32,axiom,
    ( p32
   <= ! [X1: g] :
        ( ( f__0 @ X1 @ f__3 )
       != f__1 ) ),
    file('<stdin>',nax32) ).

thf(ax1404,axiom,
    ( ~ p43
    | p63 ),
    file('<stdin>',ax1404) ).

thf(ax1443,axiom,
    ( ~ p19
    | p34 ),
    file('<stdin>',ax1443) ).

thf(ax1204,axiom,
    ( ~ p63
    | p201 ),
    file('<stdin>',ax1204) ).

thf(ax1431,axiom,
    p43,
    file('<stdin>',ax1431) ).

thf(ax1463,axiom,
    ( p17
    | p19 ),
    file('<stdin>',ax1463) ).

thf(ax1205,axiom,
    ( ~ p201
    | p200 ),
    file('<stdin>',ax1205) ).

thf(ax1206,axiom,
    ( ~ p200
    | ~ p186
    | p194 ),
    file('<stdin>',ax1206) ).

thf(ax1213,axiom,
    ( ~ p194
    | ~ p34
    | p20 ),
    file('<stdin>',ax1213) ).

thf(nax186,axiom,
    ( p186
   <= ( ( f__0 @ f__1 @ f__3 )
      = ( f__0 @ f__3 @ f__1 ) ) ),
    file('<stdin>',nax186) ).

thf(pax18,axiom,
    ( p18
   => ! [X1: g] :
        ~ ! [X2: g] :
            ( ( f__0 @ X1 @ X2 )
           != f__1 ) ),
    file('<stdin>',pax18) ).

thf(pax11,axiom,
    ( p11
   => ( ~ ( ! [X1: g,X2: g,X3: g] :
              ( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
              = ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) )
         => ~ ! [X1: g] :
                ( ( f__0 @ X1 @ f__1 )
                = X1 ) )
     => ~ ! [X1: g] :
            ~ ! [X2: g] :
                ( ( f__0 @ X1 @ X2 )
               != f__1 ) ) ),
    file('<stdin>',pax11) ).

thf(pax13,axiom,
    ( p13
   => ! [X1: g] :
        ~ ! [X2: g] :
            ( ( f__0 @ X2 @ X1 )
           != f__1 ) ),
    file('<stdin>',pax13) ).

thf(nax37,axiom,
    ( p37
   <= ! [X1: g] :
        ( ( f__0 @ f__5 @ X1 )
       != f__1 ) ),
    file('<stdin>',nax37) ).

thf(ax1437,axiom,
    ( p18
    | p37 ),
    file('<stdin>',ax1437) ).

thf(ax1460,axiom,
    ( ~ p17
    | ~ p14
    | ~ p19 ),
    file('<stdin>',ax1460) ).

thf(pax37,axiom,
    ( p37
   => ! [X1: g] :
        ( ( f__0 @ f__5 @ X1 )
       != f__1 ) ),
    file('<stdin>',pax37) ).

thf(nax19,axiom,
    ( p19
   <= ! [X1: g] :
        ( ( f__0 @ X1 @ f__1 )
        = X1 ) ),
    file('<stdin>',nax19) ).

thf(c_0_50,plain,
    ( p1
    | ~ p2 ),
    inference(fof_simplification,[status(thm)],[ax1480]) ).

thf(c_0_51,plain,
    ~ p1,
    inference(fof_simplification,[status(thm)],[ax1481]) ).

thf(c_0_52,plain,
    ( p2
    | ~ p3 ),
    inference(fof_simplification,[status(thm)],[ax1479]) ).

thf(c_0_53,plain,
    ( p1
    | ~ p2 ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

thf(c_0_54,plain,
    ~ p1,
    inference(split_conjunct,[status(thm)],[c_0_51]) ).

thf(c_0_55,plain,
    ( p3
    | ~ p10
    | ~ p11 ),
    inference(fof_simplification,[status(thm)],[ax1471]) ).

thf(c_0_56,plain,
    ( p2
    | ~ p3 ),
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

thf(c_0_57,plain,
    ~ p2,
    inference(sr,[status(thm)],[c_0_53,c_0_54]) ).

thf(c_0_58,plain,
    ( p3
    | ~ p10
    | ~ p11 ),
    inference(split_conjunct,[status(thm)],[c_0_55]) ).

thf(c_0_59,plain,
    ~ p3,
    inference(sr,[status(thm)],[c_0_56,c_0_57]) ).

thf(c_0_60,plain,
    ! [X460: g,X461: g,X462: g,X463: g,X464: g] :
      ( ( ( ( f__0 @ ( f__0 @ X460 @ X461 ) @ X462 )
          = ( f__0 @ X460 @ ( f__0 @ X461 @ X462 ) ) )
        | p11 )
      & ( ( ( f__0 @ X463 @ f__1 )
          = X463 )
        | p11 )
      & ( ( ( f__0 @ X464 @ ( esk231_1 @ X464 ) )
          = f__1 )
        | p11 ) ),
    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)],[nax11])])])])])]) ).

thf(c_0_61,plain,
    ! [X472: g,X473: g,X474: g,X475: g,X476: g] :
      ( ( ( ( f__0 @ ( f__0 @ X472 @ X473 ) @ X474 )
          = ( f__0 @ X472 @ ( f__0 @ X473 @ X474 ) ) )
        | p10 )
      & ( ( ( f__0 @ f__1 @ X475 )
          = X475 )
        | p10 )
      & ( ( ( f__0 @ ( esk237_1 @ X476 ) @ X476 )
          = f__1 )
        | p10 ) ),
    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)],[nax10])])])])])]) ).

thf(c_0_62,plain,
    ! [X396: g] :
      ( ~ p32
      | ( ( f__0 @ X396 @ f__3 )
       != f__1 ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax32])])])]) ).

thf(c_0_63,plain,
    ( ~ p10
    | ~ p11 ),
    inference(sr,[status(thm)],[c_0_58,c_0_59]) ).

thf(c_0_64,plain,
    ! [X1: g,X2: g,X3: g] :
      ( ( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
        = ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) )
      | p11 ),
    inference(split_conjunct,[status(thm)],[c_0_60]) ).

thf(c_0_65,plain,
    ! [X1: g,X2: g,X3: g] :
      ( ( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
        = ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) )
      | p10 ),
    inference(split_conjunct,[status(thm)],[c_0_61]) ).

thf(c_0_66,plain,
    ! [X1: g] :
      ( ~ p32
      | ( ( f__0 @ X1 @ f__3 )
       != f__1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

thf(c_0_67,plain,
    ( p32
    | p341 ),
    inference(split_conjunct,[status(thm)],[ax979]) ).

thf(c_0_68,plain,
    ! [X1: g] :
      ( ( ( f__0 @ X1 @ ( esk231_1 @ X1 ) )
        = f__1 )
      | p11 ),
    inference(split_conjunct,[status(thm)],[c_0_60]) ).

thf(c_0_69,plain,
    ! [X1: g,X2: g,X3: g] :
      ( ( f__0 @ ( f__0 @ X1 @ X2 ) @ X3 )
      = ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]) ).

thf(c_0_70,plain,
    ! [X1: g] :
      ( p341
      | ( ( f__0 @ X1 @ f__3 )
       != f__1 ) ),
    inference(spm,[status(thm)],[c_0_66,c_0_67]) ).

thf(c_0_71,plain,
    ! [X1: g,X2: g] :
      ( ( ( f__0 @ X1 @ ( f__0 @ X2 @ ( esk231_1 @ ( f__0 @ X1 @ X2 ) ) ) )
        = f__1 )
      | p11 ),
    inference(spm,[status(thm)],[c_0_68,c_0_69]) ).

thf(c_0_72,plain,
    ! [X1: g] :
      ( ( ( f__0 @ X1 @ f__1 )
        = X1 )
      | p11 ),
    inference(split_conjunct,[status(thm)],[c_0_60]) ).

thf(c_0_73,plain,
    ! [X1: g,X2: g] :
      ( ( ( f__0 @ X1 @ ( f__0 @ ( esk231_1 @ X1 ) @ X2 ) )
        = ( f__0 @ f__1 @ X2 ) )
      | p11 ),
    inference(spm,[status(thm)],[c_0_69,c_0_68]) ).

thf(c_0_74,plain,
    ! [X1: g,X2: g] :
      ( p341
      | ( ( f__0 @ X1 @ ( f__0 @ X2 @ f__3 ) )
       != f__1 ) ),
    inference(spm,[status(thm)],[c_0_70,c_0_69]) ).

thf(c_0_75,plain,
    ! [X1: g] :
      ( ( ( f__0 @ X1 @ ( f__0 @ f__1 @ ( esk231_1 @ X1 ) ) )
        = f__1 )
      | p11 ),
    inference(spm,[status(thm)],[c_0_71,c_0_72]) ).

thf(c_0_76,plain,
    ! [X1: g] :
      ( ( ( f__0 @ f__1 @ ( esk231_1 @ ( esk231_1 @ X1 ) ) )
        = ( f__0 @ X1 @ f__1 ) )
      | p11 ),
    inference(spm,[status(thm)],[c_0_73,c_0_68]) ).

thf(c_0_77,plain,
    ( ~ p13
    | ~ p32 ),
    inference(fof_simplification,[status(thm)],[ax1445]) ).

thf(c_0_78,plain,
    ! [X1: g,X2: g,X3: g] :
      ( p341
      | ( ( f__0 @ X1 @ ( f__0 @ X2 @ ( f__0 @ X3 @ f__3 ) ) )
       != f__1 ) ),
    inference(spm,[status(thm)],[c_0_74,c_0_69]) ).

thf(c_0_79,plain,
    ! [X1: g,X2: g] :
      ( ( ( f__0 @ X1 @ ( f__0 @ X2 @ f__1 ) )
        = ( f__0 @ X1 @ X2 ) )
      | p11 ),
    inference(spm,[status(thm)],[c_0_72,c_0_69]) ).

thf(c_0_80,plain,
    ! [X1: g] :
      ( ( ( f__0 @ ( esk231_1 @ X1 ) @ ( f__0 @ X1 @ f__1 ) )
        = f__1 )
      | p11 ),
    inference(spm,[status(thm)],[c_0_75,c_0_76]) ).

thf(c_0_81,plain,
    ( ~ p13
    | ~ p32 ),
    inference(split_conjunct,[status(thm)],[c_0_77]) ).

thf(c_0_82,plain,
    ! [X1: g,X2: g,X3: g,X4: g] :
      ( p341
      | ( ( f__0 @ X1 @ ( f__0 @ X2 @ ( f__0 @ X3 @ ( f__0 @ X4 @ f__3 ) ) ) )
       != f__1 ) ),
    inference(spm,[status(thm)],[c_0_78,c_0_69]) ).

thf(c_0_83,plain,
    ! [X1: g] :
      ( ( ( f__0 @ ( esk231_1 @ X1 ) @ X1 )
        = f__1 )
      | p11 ),
    inference(spm,[status(thm)],[c_0_79,c_0_80]) ).

thf(c_0_84,plain,
    ( p341
    | ~ p13 ),
    inference(spm,[status(thm)],[c_0_81,c_0_67]) ).

thf(c_0_85,plain,
    ( p10
    | p13 ),
    inference(split_conjunct,[status(thm)],[ax1458]) ).

thf(c_0_86,plain,
    ( ~ p341
    | ( ( f__0 @ f__8 @ f__3 )
      = f__1 ) ),
    inference(fof_nnf,[status(thm)],[pax341]) ).

thf(c_0_87,plain,
    ( p11
    | p341 ),
    inference(spm,[status(thm)],[c_0_82,c_0_83]) ).

thf(c_0_88,plain,
    ( p10
    | p341 ),
    inference(spm,[status(thm)],[c_0_84,c_0_85]) ).

thf(c_0_89,plain,
    ( ~ p18
    | ~ p35 ),
    inference(fof_simplification,[status(thm)],[ax1442]) ).

thf(c_0_90,plain,
    ! [X1: g] :
      ( ( ( f__0 @ X1 @ f__1 )
        = X1 )
      | ~ p10 ),
    inference(spm,[status(thm)],[c_0_63,c_0_72]) ).

thf(c_0_91,plain,
    ! [X1: g] :
      ( ( ( f__0 @ f__1 @ X1 )
        = X1 )
      | p10 ),
    inference(split_conjunct,[status(thm)],[c_0_61]) ).

thf(c_0_92,plain,
    ( ( ( f__0 @ f__8 @ f__3 )
      = f__1 )
    | ~ p341 ),
    inference(split_conjunct,[status(thm)],[c_0_86]) ).

thf(c_0_93,plain,
    p341,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_87]),c_0_88]) ).

thf(c_0_94,plain,
    ( ~ p18
    | ~ p35 ),
    inference(split_conjunct,[status(thm)],[c_0_89]) ).

thf(c_0_95,plain,
    ( p35
    | p165 ),
    inference(split_conjunct,[status(thm)],[ax1247]) ).

thf(c_0_96,plain,
    ! [X1: g,X2: g] :
      ( ( ( f__0 @ f__1 @ X1 )
        = X1 )
      | ( ( f__0 @ X2 @ f__1 )
        = X2 ) ),
    inference(spm,[status(thm)],[c_0_90,c_0_91]) ).

thf(c_0_97,plain,
    ( ( f__0 @ f__8 @ f__3 )
    = f__1 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_93])]) ).

thf(c_0_98,plain,
    ( ( ( f__0 @ f__3 @ esk194_0 )
      = f__1 )
    | p35 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax35])])])]) ).

thf(c_0_99,plain,
    ( p165
    | ~ p18 ),
    inference(spm,[status(thm)],[c_0_94,c_0_95]) ).

thf(c_0_100,plain,
    ( p11
    | p18 ),
    inference(split_conjunct,[status(thm)],[ax1465]) ).

thf(c_0_101,plain,
    ( ~ p15
    | p20 ),
    inference(fof_simplification,[status(thm)],[ax1438]) ).

thf(c_0_102,plain,
    ( ( f__0 @ f__1 @ f__1 )
    = f__1 ),
    inference(ef,[status(thm)],[c_0_96]) ).

thf(c_0_103,plain,
    ! [X1: g] :
      ( ( f__0 @ f__8 @ ( f__0 @ f__3 @ X1 ) )
      = ( f__0 @ f__1 @ X1 ) ),
    inference(spm,[status(thm)],[c_0_69,c_0_97]) ).

thf(c_0_104,plain,
    ( ( ( f__0 @ f__3 @ esk194_0 )
      = f__1 )
    | p35 ),
    inference(split_conjunct,[status(thm)],[c_0_98]) ).

thf(c_0_105,plain,
    ( p11
    | p165 ),
    inference(spm,[status(thm)],[c_0_99,c_0_100]) ).

thf(c_0_106,plain,
    ( p10
    | ~ p12 ),
    inference(fof_simplification,[status(thm)],[ax1459]) ).

thf(c_0_107,plain,
    ( p20
    | ~ p15 ),
    inference(split_conjunct,[status(thm)],[c_0_101]) ).

thf(c_0_108,plain,
    ( p12
    | p15 ),
    inference(split_conjunct,[status(thm)],[ax1440]) ).

thf(c_0_109,plain,
    ! [X1: g] :
      ( ( f__0 @ f__1 @ ( f__0 @ f__1 @ X1 ) )
      = ( f__0 @ f__1 @ X1 ) ),
    inference(spm,[status(thm)],[c_0_69,c_0_102]) ).

thf(c_0_110,plain,
    ( ( ( f__0 @ f__1 @ esk194_0 )
      = ( f__0 @ f__8 @ f__1 ) )
    | p35 ),
    inference(spm,[status(thm)],[c_0_103,c_0_104]) ).

thf(c_0_111,plain,
    ( ( ( f__0 @ f__1 @ esk216_0 )
     != esk216_0 )
    | p15 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax15])])])]) ).

thf(c_0_112,plain,
    ( p165
    | ~ p10 ),
    inference(spm,[status(thm)],[c_0_63,c_0_105]) ).

thf(c_0_113,plain,
    ( p10
    | ~ p12 ),
    inference(split_conjunct,[status(thm)],[c_0_106]) ).

thf(c_0_114,plain,
    ( p12
    | p20 ),
    inference(spm,[status(thm)],[c_0_107,c_0_108]) ).

thf(c_0_115,plain,
    ( ( ( f__0 @ f__1 @ ( esk231_1 @ f__3 ) )
      = ( f__0 @ f__8 @ f__1 ) )
    | p11 ),
    inference(spm,[status(thm)],[c_0_103,c_0_68]) ).

thf(c_0_116,plain,
    ( ( ( f__0 @ f__1 @ ( f__0 @ f__8 @ f__1 ) )
      = ( f__0 @ f__8 @ f__1 ) )
    | p35 ),
    inference(spm,[status(thm)],[c_0_109,c_0_110]) ).

thf(c_0_117,plain,
    ( p15
    | ( ( f__0 @ f__1 @ esk216_0 )
     != esk216_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_111]) ).

thf(c_0_118,plain,
    ! [X1: g] :
      ( ( ( f__0 @ f__1 @ X1 )
        = X1 )
      | p165 ),
    inference(spm,[status(thm)],[c_0_112,c_0_91]) ).

thf(c_0_119,plain,
    ( p20
    | p10 ),
    inference(spm,[status(thm)],[c_0_113,c_0_114]) ).

thf(c_0_120,plain,
    ( ( ( f__0 @ f__3 @ ( f__0 @ f__8 @ f__1 ) )
      = f__1 )
    | p11 ),
    inference(spm,[status(thm)],[c_0_75,c_0_115]) ).

thf(c_0_121,plain,
    ( ( ( f__0 @ f__1 @ ( f__0 @ f__8 @ f__1 ) )
      = ( f__0 @ f__8 @ f__1 ) )
    | ~ p18 ),
    inference(spm,[status(thm)],[c_0_94,c_0_116]) ).

thf(c_0_122,plain,
    ! [X434: g] :
      ( ~ p15
      | ( ( f__0 @ f__1 @ X434 )
        = X434 ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax15])])]) ).

thf(c_0_123,plain,
    ( p15
    | ~ p20 ),
    inference(fof_simplification,[status(thm)],[ax1462]) ).

thf(c_0_124,plain,
    ( ( ( f__0 @ esk201_0 @ ( f__0 @ f__1 @ f__3 ) )
      = f__1 )
    | p28 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax28])])])]) ).

thf(c_0_125,plain,
    ( ~ p165
    | ( ( f__0 @ f__3 @ f__7 )
      = f__1 ) ),
    inference(fof_nnf,[status(thm)],[pax165]) ).

thf(c_0_126,plain,
    ( p165
    | p15 ),
    inference(spm,[status(thm)],[c_0_117,c_0_118]) ).

thf(c_0_127,plain,
    ! [X1: g] :
      ( ( ( f__0 @ X1 @ f__1 )
        = X1 )
      | p20 ),
    inference(spm,[status(thm)],[c_0_90,c_0_119]) ).

thf(c_0_128,plain,
    ( ( ( f__0 @ f__3 @ ( f__0 @ f__8 @ f__1 ) )
      = f__1 )
    | ~ p10 ),
    inference(spm,[status(thm)],[c_0_63,c_0_120]) ).

thf(c_0_129,plain,
    ( ( ( f__0 @ f__1 @ ( f__0 @ f__8 @ f__1 ) )
      = ( f__0 @ f__8 @ f__1 ) )
    | p11 ),
    inference(spm,[status(thm)],[c_0_121,c_0_100]) ).

thf(c_0_130,plain,
    ! [X1: g] :
      ( ( ( f__0 @ f__1 @ X1 )
        = X1 )
      | ~ p15 ),
    inference(split_conjunct,[status(thm)],[c_0_122]) ).

thf(c_0_131,plain,
    ( p15
    | ~ p20 ),
    inference(split_conjunct,[status(thm)],[c_0_123]) ).

thf(c_0_132,plain,
    ! [X471: g] :
      ( ~ p10
      | ( ( f__0 @ ( f__0 @ esk232_0 @ esk233_0 ) @ esk234_0 )
       != ( f__0 @ esk232_0 @ ( f__0 @ esk233_0 @ esk234_0 ) ) )
      | ( ( f__0 @ f__1 @ esk235_0 )
       != esk235_0 )
      | ( ( f__0 @ X471 @ esk236_0 )
       != f__1 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax10])])])])]) ).

thf(c_0_133,plain,
    ( ( ( f__0 @ esk201_0 @ ( f__0 @ f__1 @ f__3 ) )
      = f__1 )
    | p28 ),
    inference(split_conjunct,[status(thm)],[c_0_124]) ).

thf(c_0_134,plain,
    ( ( ( f__0 @ f__3 @ f__7 )
      = f__1 )
    | ~ p165 ),
    inference(split_conjunct,[status(thm)],[c_0_125]) ).

thf(c_0_135,plain,
    ( p165
    | p20 ),
    inference(spm,[status(thm)],[c_0_107,c_0_126]) ).

thf(c_0_136,plain,
    ! [X1: g,X2: g] :
      ( ( ( f__0 @ X1 @ ( f__0 @ X2 @ f__1 ) )
        = ( f__0 @ X1 @ X2 ) )
      | p20 ),
    inference(spm,[status(thm)],[c_0_127,c_0_69]) ).

thf(c_0_137,plain,
    ( ( ( f__0 @ f__3 @ ( f__0 @ f__8 @ f__1 ) )
      = f__1 )
    | p20 ),
    inference(spm,[status(thm)],[c_0_128,c_0_119]) ).

thf(c_0_138,plain,
    ( ( f__0 @ f__1 @ ( f__0 @ f__8 @ f__1 ) )
    = ( f__0 @ f__8 @ f__1 ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_129]),c_0_91]) ).

thf(c_0_139,plain,
    ! [X1: g] :
      ( ( ( f__0 @ f__1 @ X1 )
        = X1 )
      | ~ p20 ),
    inference(spm,[status(thm)],[c_0_130,c_0_131]) ).

thf(c_0_140,plain,
    ( ~ p12
    | ~ p14
    | ~ p15 ),
    inference(fof_simplification,[status(thm)],[ax1468]) ).

thf(c_0_141,plain,
    ( ( ( f__0 @ ( f__0 @ esk217_0 @ esk218_0 ) @ esk219_0 )
     != ( f__0 @ esk217_0 @ ( f__0 @ esk218_0 @ esk219_0 ) ) )
    | p14 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax14])])])]) ).

thf(c_0_142,plain,
    ! [X1: g] :
      ( ~ p10
      | ( ( f__0 @ ( f__0 @ esk232_0 @ esk233_0 ) @ esk234_0 )
       != ( f__0 @ esk232_0 @ ( f__0 @ esk233_0 @ esk234_0 ) ) )
      | ( ( f__0 @ f__1 @ esk235_0 )
       != esk235_0 )
      | ( ( f__0 @ X1 @ esk236_0 )
       != f__1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_132]) ).

thf(c_0_143,plain,
    ! [X450: g,X451: g,X452: g,X453: g] :
      ( ( ( ( f__0 @ ( f__0 @ X450 @ X451 ) @ X452 )
          = ( f__0 @ X450 @ ( f__0 @ X451 @ X452 ) ) )
        | p12 )
      & ( ( ( f__0 @ f__1 @ X453 )
          = X453 )
        | p12 ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax12])])])])]) ).

thf(c_0_144,plain,
    ! [X1: g] :
      ( ( ( f__0 @ esk201_0 @ ( f__0 @ f__1 @ ( f__0 @ f__3 @ X1 ) ) )
        = ( f__0 @ f__1 @ X1 ) )
      | p28 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_133]),c_0_69]) ).

thf(c_0_145,plain,
    ( ( ( f__0 @ f__3 @ f__7 )
      = f__1 )
    | p20 ),
    inference(spm,[status(thm)],[c_0_134,c_0_135]) ).

thf(c_0_146,plain,
    ( ( ( f__0 @ f__3 @ f__8 )
      = f__1 )
    | p20 ),
    inference(spm,[status(thm)],[c_0_136,c_0_137]) ).

thf(c_0_147,plain,
    ( ( f__0 @ f__1 @ f__8 )
    = f__8 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_127]),c_0_139]) ).

thf(c_0_148,plain,
    ( ~ p12
    | ~ p14
    | ~ p15 ),
    inference(split_conjunct,[status(thm)],[c_0_140]) ).

thf(c_0_149,plain,
    ( p14
    | ( ( f__0 @ ( f__0 @ esk217_0 @ esk218_0 ) @ esk219_0 )
     != ( f__0 @ esk217_0 @ ( f__0 @ esk218_0 @ esk219_0 ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_141]) ).

thf(c_0_150,plain,
    ! [X1: g] :
      ( ( ( f__0 @ f__1 @ esk235_0 )
       != esk235_0 )
      | ( ( f__0 @ X1 @ esk236_0 )
       != f__1 )
      | ~ p10 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_142,c_0_69])]) ).

thf(c_0_151,plain,
    ! [X1: g] :
      ( ( ( f__0 @ f__1 @ X1 )
        = X1 )
      | p12 ),
    inference(split_conjunct,[status(thm)],[c_0_143]) ).

thf(c_0_152,plain,
    ( p3
    | p10
    | p11 ),
    inference(split_conjunct,[status(thm)],[ax1470]) ).

thf(c_0_153,plain,
    ( ~ p13
    | ~ p28 ),
    inference(fof_simplification,[status(thm)],[ax1449]) ).

thf(c_0_154,plain,
    ( ( ( f__0 @ esk201_0 @ f__1 )
      = ( f__0 @ f__1 @ f__7 ) )
    | p20
    | p28 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_102]) ).

thf(c_0_155,plain,
    ( ( ( f__0 @ esk201_0 @ f__1 )
      = f__8 )
    | p20
    | p28 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_146]),c_0_102]),c_0_147]) ).

thf(c_0_156,plain,
    ! [X445: g] :
      ( ( ( f__0 @ X445 @ esk221_0 )
       != f__1 )
      | p13 ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax13])])])])]) ).

thf(c_0_157,plain,
    ( ~ p12
    | ~ p14
    | ~ p20 ),
    inference(spm,[status(thm)],[c_0_148,c_0_131]) ).

thf(c_0_158,plain,
    p14,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_149,c_0_69])]) ).

thf(c_0_159,plain,
    ! [X1: g] :
      ( p12
      | ( ( f__0 @ X1 @ esk236_0 )
       != f__1 )
      | ~ p10 ),
    inference(spm,[status(thm)],[c_0_150,c_0_151]) ).

thf(c_0_160,plain,
    ( p11
    | p10 ),
    inference(sr,[status(thm)],[c_0_152,c_0_59]) ).

thf(c_0_161,plain,
    ( ~ p13
    | ~ p28 ),
    inference(split_conjunct,[status(thm)],[c_0_153]) ).

thf(c_0_162,plain,
    ( ( ( f__0 @ f__1 @ f__7 )
      = f__8 )
    | p28
    | p20 ),
    inference(spm,[status(thm)],[c_0_154,c_0_155]) ).

thf(c_0_163,plain,
    ! [X1: g] :
      ( p13
      | ( ( f__0 @ X1 @ esk221_0 )
       != f__1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_156]) ).

thf(c_0_164,plain,
    ( ~ p12
    | ~ p20 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_157,c_0_158])]) ).

thf(c_0_165,plain,
    ( p11
    | p12 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_83]),c_0_160]) ).

thf(c_0_166,plain,
    ( ( ( f__0 @ f__1 @ f__7 )
      = f__8 )
    | p20
    | ~ p13 ),
    inference(spm,[status(thm)],[c_0_161,c_0_162]) ).

thf(c_0_167,plain,
    ( p11
    | p13 ),
    inference(spm,[status(thm)],[c_0_163,c_0_83]) ).

thf(c_0_168,plain,
    ( p11
    | ~ p20 ),
    inference(spm,[status(thm)],[c_0_164,c_0_165]) ).

thf(c_0_169,plain,
    ( ( ( f__0 @ f__1 @ f__7 )
      = f__8 )
    | p11 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_167]),c_0_168]) ).

thf(c_0_170,plain,
    ! [X426: g,X427: g,X428: g,X429: g] :
      ( ( ( ( f__0 @ ( f__0 @ X426 @ X427 ) @ X428 )
          = ( f__0 @ X426 @ ( f__0 @ X427 @ X428 ) ) )
        | p17 )
      & ( ( ( f__0 @ X429 @ f__1 )
          = X429 )
        | p17 ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax17])])])])]) ).

thf(c_0_171,plain,
    ( ( ( f__0 @ f__1 @ f__7 )
      = f__8 )
    | ~ p10 ),
    inference(spm,[status(thm)],[c_0_63,c_0_169]) ).

thf(c_0_172,plain,
    ! [X1: g] :
      ( ( ( f__0 @ X1 @ f__1 )
        = X1 )
      | p17 ),
    inference(split_conjunct,[status(thm)],[c_0_170]) ).

thf(c_0_173,plain,
    ( p11
    | ~ p17 ),
    inference(fof_simplification,[status(thm)],[ax1466]) ).

thf(c_0_174,plain,
    ! [X1: g,X2: g] :
      ( ( ( f__0 @ X1 @ ( f__0 @ f__1 @ X2 ) )
        = ( f__0 @ X1 @ X2 ) )
      | p20 ),
    inference(spm,[status(thm)],[c_0_69,c_0_127]) ).

thf(c_0_175,plain,
    ( ( ( f__0 @ f__1 @ f__7 )
      = f__8 )
    | p20 ),
    inference(spm,[status(thm)],[c_0_171,c_0_119]) ).

thf(c_0_176,plain,
    ! [X1: g,X2: g] :
      ( ( ( f__0 @ X1 @ ( f__0 @ X2 @ f__1 ) )
        = ( f__0 @ X1 @ X2 ) )
      | p17 ),
    inference(spm,[status(thm)],[c_0_172,c_0_69]) ).

thf(c_0_177,plain,
    ( p11
    | ~ p17 ),
    inference(split_conjunct,[status(thm)],[c_0_173]) ).

thf(c_0_178,plain,
    ! [X1: g] :
      ( ( ( f__0 @ X1 @ f__7 )
        = ( f__0 @ X1 @ f__8 ) )
      | p20 ),
    inference(spm,[status(thm)],[c_0_174,c_0_175]) ).

thf(c_0_179,plain,
    ! [X1: g,X2: g] :
      ( ( ( f__0 @ X1 @ ( f__0 @ ( esk231_1 @ X1 ) @ X2 ) )
        = ( f__0 @ f__1 @ ( f__0 @ X2 @ f__1 ) ) )
      | p11 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_176]),c_0_177]) ).

thf(c_0_180,plain,
    ( ( ( f__0 @ ( esk231_1 @ f__7 ) @ f__8 )
      = f__1 )
    | p11 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_178]),c_0_168]) ).

thf(c_0_181,plain,
    ! [X1: g] :
      ( ( f__0 @ f__1 @ ( f__0 @ f__8 @ X1 ) )
      = ( f__0 @ f__8 @ X1 ) ),
    inference(spm,[status(thm)],[c_0_69,c_0_147]) ).

thf(c_0_182,plain,
    ( ( ( f__0 @ esk197_0 @ f__3 )
      = f__1 )
    | p32 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax32])])])]) ).

thf(c_0_183,plain,
    ( ( ( f__0 @ f__7 @ f__1 )
      = ( f__0 @ f__8 @ f__1 ) )
    | p11 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_180]),c_0_181]) ).

thf(c_0_184,plain,
    ( ( ( f__0 @ esk197_0 @ f__3 )
      = f__1 )
    | p32 ),
    inference(split_conjunct,[status(thm)],[c_0_182]) ).

thf(c_0_185,plain,
    ( ( ( f__0 @ f__7 @ f__1 )
      = ( f__0 @ f__8 @ f__1 ) )
    | ~ p10 ),
    inference(spm,[status(thm)],[c_0_63,c_0_183]) ).

thf(c_0_186,plain,
    ! [X1: g] :
      ( ( ( f__0 @ esk197_0 @ ( f__0 @ f__3 @ X1 ) )
        = ( f__0 @ f__1 @ X1 ) )
      | p32 ),
    inference(spm,[status(thm)],[c_0_69,c_0_184]) ).

thf(c_0_187,plain,
    ( ( ( f__0 @ f__7 @ f__1 )
      = ( f__0 @ f__8 @ f__1 ) )
    | p20 ),
    inference(spm,[status(thm)],[c_0_185,c_0_119]) ).

thf(c_0_188,plain,
    ( ( ( f__0 @ esk197_0 @ f__1 )
      = ( f__0 @ f__1 @ f__7 ) )
    | p20
    | p32 ),
    inference(spm,[status(thm)],[c_0_186,c_0_145]) ).

thf(c_0_189,plain,
    ( ( ( f__0 @ f__8 @ f__1 )
      = f__7 )
    | p20 ),
    inference(spm,[status(thm)],[c_0_127,c_0_187]) ).

thf(c_0_190,plain,
    ( ~ p43
    | p63 ),
    inference(fof_simplification,[status(thm)],[ax1404]) ).

thf(c_0_191,plain,
    ( ~ p19
    | p34 ),
    inference(fof_simplification,[status(thm)],[ax1443]) ).

thf(c_0_192,plain,
    ( ( esk197_0
      = ( f__0 @ f__1 @ f__7 ) )
    | p32
    | p20 ),
    inference(spm,[status(thm)],[c_0_127,c_0_188]) ).

thf(c_0_193,plain,
    ( ( f__0 @ f__1 @ f__7 )
    = f__7 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_189]),c_0_139]) ).

thf(c_0_194,plain,
    ( ~ p63
    | p201 ),
    inference(fof_simplification,[status(thm)],[ax1204]) ).

thf(c_0_195,plain,
    ( p63
    | ~ p43 ),
    inference(split_conjunct,[status(thm)],[c_0_190]) ).

thf(c_0_196,plain,
    p43,
    inference(split_conjunct,[status(thm)],[ax1431]) ).

thf(c_0_197,plain,
    ( p34
    | ~ p19 ),
    inference(split_conjunct,[status(thm)],[c_0_191]) ).

thf(c_0_198,plain,
    ( p17
    | p19 ),
    inference(split_conjunct,[status(thm)],[ax1463]) ).

thf(c_0_199,plain,
    ( ( esk197_0 = f__7 )
    | p20
    | p32 ),
    inference(rw,[status(thm)],[c_0_192,c_0_193]) ).

thf(c_0_200,plain,
    ( ~ p201
    | p200 ),
    inference(fof_simplification,[status(thm)],[ax1205]) ).

thf(c_0_201,plain,
    ( p201
    | ~ p63 ),
    inference(split_conjunct,[status(thm)],[c_0_194]) ).

thf(c_0_202,plain,
    p63,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_195,c_0_196])]) ).

thf(c_0_203,plain,
    ( p17
    | p34 ),
    inference(spm,[status(thm)],[c_0_197,c_0_198]) ).

thf(c_0_204,plain,
    ( ( ( f__0 @ f__7 @ f__3 )
      = f__1 )
    | p20
    | p32 ),
    inference(spm,[status(thm)],[c_0_184,c_0_199]) ).

thf(c_0_205,plain,
    ( ~ p200
    | ~ p186
    | p194 ),
    inference(fof_simplification,[status(thm)],[ax1206]) ).

thf(c_0_206,plain,
    ( p200
    | ~ p201 ),
    inference(split_conjunct,[status(thm)],[c_0_200]) ).

thf(c_0_207,plain,
    p201,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_201,c_0_202])]) ).

thf(c_0_208,plain,
    ( p34
    | p11 ),
    inference(spm,[status(thm)],[c_0_177,c_0_203]) ).

thf(c_0_209,plain,
    ( ( ( f__0 @ f__7 @ f__3 )
      = f__1 )
    | p20
    | ~ p13 ),
    inference(spm,[status(thm)],[c_0_81,c_0_204]) ).

thf(c_0_210,plain,
    ( ~ p194
    | ~ p34
    | p20 ),
    inference(fof_simplification,[status(thm)],[ax1213]) ).

thf(c_0_211,plain,
    ( p194
    | ~ p200
    | ~ p186 ),
    inference(split_conjunct,[status(thm)],[c_0_205]) ).

thf(c_0_212,plain,
    p200,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_206,c_0_207])]) ).

thf(c_0_213,plain,
    ( p34
    | ~ p10 ),
    inference(spm,[status(thm)],[c_0_63,c_0_208]) ).

thf(c_0_214,plain,
    ( ( ( f__0 @ f__7 @ f__3 )
      = f__1 )
    | p11 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_167]),c_0_168]) ).

thf(c_0_215,plain,
    ( p20
    | ~ p194
    | ~ p34 ),
    inference(split_conjunct,[status(thm)],[c_0_210]) ).

thf(c_0_216,plain,
    ( p194
    | ~ p186 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_211,c_0_212])]) ).

thf(c_0_217,plain,
    ( p20
    | p34 ),
    inference(spm,[status(thm)],[c_0_213,c_0_119]) ).

thf(c_0_218,plain,
    ( ( ( f__0 @ f__1 @ f__3 )
     != ( f__0 @ f__3 @ f__1 ) )
    | p186 ),
    inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax186])]) ).

thf(c_0_219,plain,
    ( ( ( f__0 @ f__7 @ f__3 )
      = f__1 )
    | ~ p10 ),
    inference(spm,[status(thm)],[c_0_63,c_0_214]) ).

thf(c_0_220,plain,
    ( p20
    | ~ p186 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_216]),c_0_217]) ).

thf(c_0_221,plain,
    ( p186
    | ( ( f__0 @ f__1 @ f__3 )
     != ( f__0 @ f__3 @ f__1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_218]) ).

thf(c_0_222,plain,
    ! [X1: g] :
      ( ( ( f__0 @ f__3 @ ( f__0 @ f__7 @ X1 ) )
        = ( f__0 @ f__1 @ X1 ) )
      | p20 ),
    inference(spm,[status(thm)],[c_0_69,c_0_145]) ).

thf(c_0_223,plain,
    ( ( ( f__0 @ f__7 @ f__3 )
      = f__1 )
    | p20 ),
    inference(spm,[status(thm)],[c_0_219,c_0_119]) ).

thf(c_0_224,plain,
    ( p20
    | ( ( f__0 @ f__3 @ f__1 )
     != ( f__0 @ f__1 @ f__3 ) ) ),
    inference(spm,[status(thm)],[c_0_220,c_0_221]) ).

thf(c_0_225,plain,
    ! [X418: g] :
      ( ~ p18
      | ( ( f__0 @ X418 @ ( esk208_1 @ X418 ) )
        = f__1 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax18])])])])]) ).

thf(c_0_226,plain,
    ! [X1: g] :
      ( ( ( f__0 @ ( esk237_1 @ X1 ) @ X1 )
        = f__1 )
      | p10 ),
    inference(split_conjunct,[status(thm)],[c_0_61]) ).

thf(c_0_227,plain,
    ( ~ p10
    | ~ p20 ),
    inference(spm,[status(thm)],[c_0_63,c_0_168]) ).

thf(c_0_228,plain,
    p20,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_222,c_0_223]),c_0_224]) ).

thf(c_0_229,plain,
    ! [X459: g] :
      ( ~ p11
      | ( ( f__0 @ ( f__0 @ esk226_0 @ esk227_0 ) @ esk228_0 )
       != ( f__0 @ esk226_0 @ ( f__0 @ esk227_0 @ esk228_0 ) ) )
      | ( ( f__0 @ esk229_0 @ f__1 )
       != esk229_0 )
      | ( ( f__0 @ esk230_0 @ X459 )
       != f__1 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax11])])])])]) ).

thf(c_0_230,plain,
    ! [X1: g] :
      ( ( ( f__0 @ X1 @ ( esk208_1 @ X1 ) )
        = f__1 )
      | ~ p18 ),
    inference(split_conjunct,[status(thm)],[c_0_225]) ).

thf(c_0_231,plain,
    ! [X442: g] :
      ( ~ p13
      | ( ( f__0 @ ( esk220_1 @ X442 ) @ X442 )
        = f__1 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax13])])])])]) ).

thf(c_0_232,plain,
    ! [X1: g,X2: g] :
      ( ( ( f__0 @ ( esk237_1 @ X1 ) @ ( f__0 @ X1 @ X2 ) )
        = ( f__0 @ f__1 @ X2 ) )
      | p10 ),
    inference(spm,[status(thm)],[c_0_69,c_0_226]) ).

thf(c_0_233,plain,
    ~ p10,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_227,c_0_228])]) ).

thf(c_0_234,plain,
    ! [X1: g] :
      ( ( f__0 @ f__1 @ X1 )
      = X1 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_139,c_0_228])]) ).

thf(c_0_235,plain,
    ! [X1: g] :
      ( ~ p11
      | ( ( f__0 @ ( f__0 @ esk226_0 @ esk227_0 ) @ esk228_0 )
       != ( f__0 @ esk226_0 @ ( f__0 @ esk227_0 @ esk228_0 ) ) )
      | ( ( f__0 @ esk229_0 @ f__1 )
       != esk229_0 )
      | ( ( f__0 @ esk230_0 @ X1 )
       != f__1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_229]) ).

thf(c_0_236,plain,
    ! [X1: g,X2: g] :
      ( ( ( f__0 @ X1 @ ( f__0 @ X2 @ ( esk208_1 @ ( f__0 @ X1 @ X2 ) ) ) )
        = f__1 )
      | ~ p18 ),
    inference(spm,[status(thm)],[c_0_230,c_0_69]) ).

thf(c_0_237,plain,
    ( ( ( f__0 @ f__5 @ esk193_0 )
      = f__1 )
    | p37 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax37])])])]) ).

thf(c_0_238,plain,
    ! [X1: g] :
      ( ( ( f__0 @ ( esk220_1 @ X1 ) @ X1 )
        = f__1 )
      | ~ p13 ),
    inference(split_conjunct,[status(thm)],[c_0_231]) ).

thf(c_0_239,plain,
    ! [X1: g,X2: g] :
      ( ( f__0 @ ( esk237_1 @ X1 ) @ ( f__0 @ X1 @ X2 ) )
      = X2 ),
    inference(rw,[status(thm)],[inference(sr,[status(thm)],[c_0_232,c_0_233]),c_0_234]) ).

thf(c_0_240,plain,
    ! [X1: g] :
      ( ( f__0 @ ( esk237_1 @ X1 ) @ X1 )
      = f__1 ),
    inference(sr,[status(thm)],[c_0_226,c_0_233]) ).

thf(c_0_241,plain,
    ! [X1: g] :
      ( ( ( f__0 @ esk229_0 @ f__1 )
       != esk229_0 )
      | ( ( f__0 @ esk230_0 @ X1 )
       != f__1 )
      | ~ p11 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_235,c_0_69])]) ).

thf(c_0_242,plain,
    p11,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_168,c_0_228])]) ).

thf(c_0_243,plain,
    ! [X1: g,X2: g,X3: g] :
      ( ( ( f__0 @ X1 @ ( f__0 @ X2 @ ( f__0 @ X3 @ ( esk208_1 @ ( f__0 @ X1 @ ( f__0 @ X2 @ X3 ) ) ) ) ) )
        = f__1 )
      | ~ p18 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_236]),c_0_69]) ).

thf(c_0_244,plain,
    ( ( ( f__0 @ f__5 @ esk193_0 )
      = f__1 )
    | p37 ),
    inference(split_conjunct,[status(thm)],[c_0_237]) ).

thf(c_0_245,plain,
    ( p18
    | p37 ),
    inference(split_conjunct,[status(thm)],[ax1437]) ).

thf(c_0_246,plain,
    ! [X1: g,X2: g] :
      ( ( ( f__0 @ ( esk220_1 @ X1 ) @ ( f__0 @ X1 @ X2 ) )
        = ( f__0 @ f__1 @ X2 ) )
      | ~ p13 ),
    inference(spm,[status(thm)],[c_0_69,c_0_238]) ).

thf(c_0_247,plain,
    p13,
    inference(sr,[status(thm)],[c_0_85,c_0_233]) ).

thf(c_0_248,plain,
    ! [X1: g] :
      ( ( f__0 @ ( esk237_1 @ ( esk237_1 @ X1 ) ) @ f__1 )
      = X1 ),
    inference(spm,[status(thm)],[c_0_239,c_0_240]) ).

thf(c_0_249,plain,
    ! [X1: g] :
      ( ( ( f__0 @ esk229_0 @ f__1 )
       != esk229_0 )
      | ( ( f__0 @ esk230_0 @ X1 )
       != f__1 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_241,c_0_242])]) ).

thf(c_0_250,plain,
    ! [X1: g] :
      ( ( ( f__0 @ X1 @ ( f__0 @ f__5 @ ( f__0 @ esk193_0 @ ( esk208_1 @ ( f__0 @ X1 @ f__1 ) ) ) ) )
        = f__1 )
      | p37 ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_243,c_0_244]),c_0_245]) ).

thf(c_0_251,plain,
    ! [X1: g,X2: g] :
      ( ( f__0 @ ( esk220_1 @ X1 ) @ ( f__0 @ X1 @ X2 ) )
      = X2 ),
    inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_246,c_0_247])]),c_0_234]) ).

thf(c_0_252,plain,
    ! [X1: g] :
      ( ( f__0 @ ( esk220_1 @ X1 ) @ X1 )
      = f__1 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_238,c_0_247])]) ).

thf(c_0_253,plain,
    ( ~ p17
    | ~ p14
    | ~ p19 ),
    inference(fof_simplification,[status(thm)],[ax1460]) ).

thf(c_0_254,plain,
    ! [X388: g] :
      ( ~ p37
      | ( ( f__0 @ f__5 @ X388 )
       != f__1 ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax37])])])]) ).

thf(c_0_255,plain,
    ! [X1: g] :
      ( ( ( esk237_1 @ ( esk237_1 @ X1 ) )
        = X1 )
      | p17 ),
    inference(spm,[status(thm)],[c_0_172,c_0_248]) ).

thf(c_0_256,plain,
    ( p37
    | ( ( f__0 @ esk229_0 @ f__1 )
     != esk229_0 ) ),
    inference(spm,[status(thm)],[c_0_249,c_0_250]) ).

thf(c_0_257,plain,
    ! [X1: g] :
      ( ( f__0 @ ( esk220_1 @ ( esk237_1 @ ( esk237_1 @ X1 ) ) ) @ X1 )
      = f__1 ),
    inference(spm,[status(thm)],[c_0_251,c_0_248]) ).

thf(c_0_258,plain,
    ! [X1: g] :
      ( ( f__0 @ ( esk220_1 @ ( esk220_1 @ X1 ) ) @ f__1 )
      = X1 ),
    inference(spm,[status(thm)],[c_0_251,c_0_252]) ).

thf(c_0_259,plain,
    ( ~ p17
    | ~ p14
    | ~ p19 ),
    inference(split_conjunct,[status(thm)],[c_0_253]) ).

thf(c_0_260,plain,
    ! [X1: g] :
      ( ~ p37
      | ( ( f__0 @ f__5 @ X1 )
       != f__1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_254]) ).

thf(c_0_261,plain,
    ! [X1: g] :
      ( ( ( f__0 @ X1 @ ( esk237_1 @ X1 ) )
        = f__1 )
      | p17 ),
    inference(spm,[status(thm)],[c_0_240,c_0_255]) ).

thf(c_0_262,plain,
    ( p17
    | p37 ),
    inference(spm,[status(thm)],[c_0_256,c_0_172]) ).

thf(c_0_263,plain,
    ( ( ( f__0 @ esk207_0 @ f__1 )
     != esk207_0 )
    | p19 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax19])])])]) ).

thf(c_0_264,plain,
    ! [X1: g] :
      ( ( esk237_1 @ ( esk237_1 @ X1 ) )
      = X1 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_251,c_0_257]),c_0_258]) ).

thf(c_0_265,plain,
    ( ~ p17
    | ~ p19 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_259,c_0_158])]) ).

thf(c_0_266,plain,
    p17,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_260,c_0_261]),c_0_262]) ).

thf(c_0_267,plain,
    ( p19
    | ( ( f__0 @ esk207_0 @ f__1 )
     != esk207_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_263]) ).

thf(c_0_268,plain,
    ! [X1: g] :
      ( ( f__0 @ X1 @ f__1 )
      = X1 ),
    inference(rw,[status(thm)],[c_0_248,c_0_264]) ).

thf(c_0_269,plain,
    ~ p19,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_265,c_0_266])]) ).

thf(c_0_270,plain,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_267,c_0_268])]),c_0_269]),
    [proof] ).

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

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : ALG273^5 : TPTP v8.1.0. Bugfixed v5.3.0.
% 0.07/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.33  % Computer : n025.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 600
% 0.11/0.33  % DateTime : Wed Jun  8 02:58:04 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 152.21/151.82  % SZS status Theorem
% 152.21/151.82  % Mode: mode446
% 152.21/151.82  % Inferences: 15598
% 152.21/151.82  % SZS output start Proof
% See solution above
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