TSTP Solution File: SYO881^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SYO881^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n022.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  : 300s
% DateTime : Tue May 21 08:50:18 EDT 2024

% Result   : Theorem 122.13s 26.10s
% Output   : CNFRefutation 122.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   37
% Syntax   : Number of formulae    :  108 (  26 unt;  24 typ;   0 def)
%            Number of atoms       :  658 (  24 equ;   0 cnn)
%            Maximal formula atoms :  195 (   7 avg)
%            Number of connectives : 2178 ( 225   ~; 268   |;  79   &;1584   @)
%                                         (   6 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   35 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   84 (  84   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   27 (  24 usr;   8 con; 0-2 aty)
%            Number of variables   :  180 (   6   ^ 166   !;   8   ?; 180   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_23,type,
    c_False: $o ).

thf(decl_25,type,
    c_not: $o > $o ).

thf(decl_26,type,
    c_and: $o > $o > $o ).

thf(decl_28,type,
    c_iff: $o > $o > $o ).

thf(decl_29,type,
    c_In: $i > $i > $o ).

thf(decl_30,type,
    c_Subq: $i > $i > $o ).

thf(decl_31,type,
    c_Empty: $i ).

thf(decl_32,type,
    c_Union: $i > $i ).

thf(decl_33,type,
    c_Power: $i > $i ).

thf(decl_47,type,
    c_irreflexive_i: ( $i > $i > $o ) > $o ).

thf(decl_126,type,
    epred1_2: $i > $i > $o ).

thf(decl_268,type,
    esk1_0: $i ).

thf(decl_269,type,
    esk2_2: $i > $i > $i ).

thf(decl_270,type,
    esk3_2: $i > $i > $i ).

thf(decl_281,type,
    epred144_2: $o > $o > $o ).

thf(decl_283,type,
    esk13_2: $i > $i > $i ).

thf(decl_287,type,
    esk17_1: ( $i > $i > $o ) > $i ).

thf(decl_288,type,
    esk18_1: ( $i > $i > $o ) > $i ).

thf(decl_326,type,
    esk52_0: $i > $i > $i ).

thf(decl_327,type,
    esk53_0: $i > $i ).

thf(decl_328,type,
    esk54_0: $i ).

thf(decl_329,type,
    esk55_0: $i ).

thf(decl_330,type,
    esk56_0: $i ).

thf(decl_504,type,
    esk222_1: $i > $i > $i ).

thf(ax2,axiom,
    ! [X3: $o] :
      ( ( c_not @ ( c_not @ X3 ) )
     => X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).

thf(ax13,axiom,
    ( c_not
    = ( ^ [X17: $o] :
          ( X17
         => c_False ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax13) ).

thf(ax6,axiom,
    ! [X8: $i,X2: $i] :
      ( c_iff @ ( c_In @ X2 @ ( c_Union @ X8 ) )
      @ ? [X9: $i] : ( c_and @ ( c_In @ X2 @ X9 ) @ ( c_In @ X9 @ X8 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).

thf(ax14,axiom,
    ( c_and
    = ( ^ [X18: $o,X19: $o] :
        ! [X20: $o] :
          ( ( X18
           => ( X19
             => X20 ) )
         => X20 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax14) ).

thf(ax5,axiom,
    ( c_not
    @ ? [X7: $i] : ( c_In @ X7 @ c_Empty ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).

thf(ax3,axiom,
    ! [X4: $o,X5: $o] :
      ( ( c_iff @ X4 @ X5 )
     => ( X4
      <=> X5 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).

thf(ax17,axiom,
    ( c_Subq
    = ( ^ [X26: $i,X2: $i] :
        ! [X9: $i] :
          ( ( c_In @ X9 @ X26 )
         => ( c_In @ X9 @ X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).

thf(conj,conjecture,
    ( c_not
    @ ! [X201: $i > $i > $o,X202: $i > $i > $i,X203: $i > $o,X204: $i > $o,X205: $i > $i,X206: $i,X83: $i,X207: $i] :
        ( ( X205 @ ( X202 @ ( X202 @ ( X202 @ ( X202 @ ( X202 @ ( X202 @ X83 @ X206 ) @ ( X202 @ ( X202 @ ( X202 @ X83 @ X206 ) @ ( X202 @ X207 @ ( X202 @ ( X202 @ ( X202 @ X206 @ X206 ) @ ( X202 @ ( X202 @ ( X202 @ ( X202 @ X206 @ ( X202 @ ( X202 @ X83 @ ( X202 @ X206 @ ( X202 @ X206 @ X207 ) ) ) @ X206 ) ) @ X207 ) @ ( X202 @ ( X205 @ X83 ) @ X207 ) ) @ ( X202 @ ( X202 @ ( X202 @ ( X202 @ X206 @ ( X205 @ ( X202 @ X207 @ X206 ) ) ) @ ( X202 @ X83 @ X83 ) ) @ ( X202 @ X83 @ ( X202 @ X207 @ X206 ) ) ) @ X206 ) ) ) @ X207 ) ) ) @ X206 ) ) @ X83 ) @ ( X202 @ X83 @ ( X202 @ X206 @ ( X202 @ ( X202 @ ( X205 @ X206 ) @ ( X202 @ ( X202 @ X83 @ X83 ) @ X83 ) ) @ X206 ) ) ) ) @ ( X205 @ ( X205 @ X83 ) ) ) @ X206 ) )
        = ( X205 @ ( X205 @ X207 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).

thf(ax4,axiom,
    ! [X6: $i,X2: $i] :
      ( ( c_Subq @ X6 @ X2 )
     => ( ( c_Subq @ X2 @ X6 )
       => ( X6 = X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).

thf(ax30,axiom,
    ( c_irreflexive_i
    = ( ^ [X38: $i > $i > $o] :
        ! [X2: $i] : ( c_not @ ( X38 @ X2 @ X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax30) ).

thf(ax7,axiom,
    ! [X10: $i,X2: $i] : ( c_iff @ ( c_In @ X2 @ ( c_Power @ X10 ) ) @ ( c_Subq @ X2 @ X10 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).

thf(c_0_11,plain,
    ! [X2: $i,X8: $i] :
      ( ( epred1_2 @ X8 @ X2 )
    <=> ~ ? [X9: $i] :
            ( ( ~ ( c_In @ X2 @ X9 )
              | ( ( ~ ( c_In @ X9 @ X8 )
                  | ( c_and @ $true @ $true ) )
                & ( ( c_In @ X9 @ X8 )
                  | ( c_and @ $true @ $false ) ) ) )
            & ( ( c_In @ X2 @ X9 )
              | ( ( ~ ( c_In @ X9 @ X8 )
                  | ( c_and @ $false @ $true ) )
                & ( ( c_In @ X9 @ X8 )
                  | ( c_and @ $false @ $false ) ) ) ) ) ),
    introduced(definition) ).

thf(c_0_12,axiom,
    ! [X3: $o] :
      ( ( ( ~ ( c_not @ X3 )
          | ( c_not @ $true ) )
        & ( ( c_not @ X3 )
          | ( c_not @ $false ) ) )
     => X3 ),
    inference(fool_unroll,[status(thm)],[ax2]) ).

thf(c_0_13,plain,
    ! [X237: $o] :
      ( ( c_not @ X237 )
    <=> ( X237
       => c_False ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[ax13])]) ).

thf(c_0_14,axiom,
    ! [X8: $i,X2: $i] :
      ( ( ~ ( c_In @ X2 @ ( c_Union @ X8 ) )
        | ( ( ( epred1_2 @ X8 @ X2 )
            | ( c_iff @ $true @ $true ) )
          & ( ? [X9: $i] :
                ( ( ~ ( c_In @ X2 @ X9 )
                  | ( ( ~ ( c_In @ X9 @ X8 )
                      | ( c_and @ $true @ $true ) )
                    & ( ( c_In @ X9 @ X8 )
                      | ( c_and @ $true @ $false ) ) ) )
                & ( ( c_In @ X2 @ X9 )
                  | ( ( ~ ( c_In @ X9 @ X8 )
                      | ( c_and @ $false @ $true ) )
                    & ( ( c_In @ X9 @ X8 )
                      | ( c_and @ $false @ $false ) ) ) ) )
            | ( c_iff @ $true @ $false ) ) ) )
      & ( ( c_In @ X2 @ ( c_Union @ X8 ) )
        | ( ( ( epred1_2 @ X8 @ X2 )
            | ( c_iff @ $false @ $true ) )
          & ( ? [X9: $i] :
                ( ( ~ ( c_In @ X2 @ X9 )
                  | ( ( ~ ( c_In @ X9 @ X8 )
                      | ( c_and @ $true @ $true ) )
                    & ( ( c_In @ X9 @ X8 )
                      | ( c_and @ $true @ $false ) ) ) )
                & ( ( c_In @ X2 @ X9 )
                  | ( ( ~ ( c_In @ X9 @ X8 )
                      | ( c_and @ $false @ $true ) )
                    & ( ( c_In @ X9 @ X8 )
                      | ( c_and @ $false @ $false ) ) ) ) )
            | ( c_iff @ $false @ $false ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fool_unroll,[status(thm)],[ax6]),c_0_11]),c_0_11]) ).

thf(c_0_15,plain,
    ! [X238: $o,X239: $o] :
      ( ( c_and @ X238 @ X239 )
    <=> ! [X20: $o] :
          ( ( X238
           => ( X239
             => X20 ) )
         => X20 ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[ax14])]) ).

thf(c_0_16,axiom,
    ( ( ~ ? [X7: $i] : ( c_In @ X7 @ c_Empty )
      | ( c_not @ $true ) )
    & ( ? [X7: $i] : ( c_In @ X7 @ c_Empty )
      | ( c_not @ $false ) ) ),
    inference(fool_unroll,[status(thm)],[ax5]) ).

thf(c_0_17,plain,
    ! [X447: $o] :
      ( ( ~ ( c_not @ X447 )
        | ( c_not @ X447 )
        | X447 )
      & ( ~ ( c_not @ $false )
        | ( c_not @ X447 )
        | X447 )
      & ( ~ ( c_not @ X447 )
        | ~ ( c_not @ $true )
        | X447 )
      & ( ~ ( c_not @ $false )
        | ~ ( c_not @ $true )
        | X447 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).

thf(c_0_18,plain,
    ! [X485: $o] :
      ( ( ~ ( c_not @ X485 )
        | ~ X485
        | c_False )
      & ( X485
        | ( c_not @ X485 ) )
      & ( ~ c_False
        | ( c_not @ X485 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).

thf(c_0_19,plain,
    ! [X454: $i,X455: $i,X457: $i,X458: $i] :
      ( ( ( epred1_2 @ X454 @ X455 )
        | ( c_iff @ $true @ $true )
        | ~ ( c_In @ X455 @ ( c_Union @ X454 ) ) )
      & ( ~ ( c_In @ ( esk2_2 @ X454 @ X455 ) @ X454 )
        | ( c_and @ $true @ $true )
        | ~ ( c_In @ X455 @ ( esk2_2 @ X454 @ X455 ) )
        | ( c_iff @ $true @ $false )
        | ~ ( c_In @ X455 @ ( c_Union @ X454 ) ) )
      & ( ( c_In @ ( esk2_2 @ X454 @ X455 ) @ X454 )
        | ( c_and @ $true @ $false )
        | ~ ( c_In @ X455 @ ( esk2_2 @ X454 @ X455 ) )
        | ( c_iff @ $true @ $false )
        | ~ ( c_In @ X455 @ ( c_Union @ X454 ) ) )
      & ( ~ ( c_In @ ( esk2_2 @ X454 @ X455 ) @ X454 )
        | ( c_and @ $false @ $true )
        | ( c_In @ X455 @ ( esk2_2 @ X454 @ X455 ) )
        | ( c_iff @ $true @ $false )
        | ~ ( c_In @ X455 @ ( c_Union @ X454 ) ) )
      & ( ( c_In @ ( esk2_2 @ X454 @ X455 ) @ X454 )
        | ( c_and @ $false @ $false )
        | ( c_In @ X455 @ ( esk2_2 @ X454 @ X455 ) )
        | ( c_iff @ $true @ $false )
        | ~ ( c_In @ X455 @ ( c_Union @ X454 ) ) )
      & ( ( epred1_2 @ X457 @ X458 )
        | ( c_iff @ $false @ $true )
        | ( c_In @ X458 @ ( c_Union @ X457 ) ) )
      & ( ~ ( c_In @ ( esk3_2 @ X457 @ X458 ) @ X457 )
        | ( c_and @ $true @ $true )
        | ~ ( c_In @ X458 @ ( esk3_2 @ X457 @ X458 ) )
        | ( c_iff @ $false @ $false )
        | ( c_In @ X458 @ ( c_Union @ X457 ) ) )
      & ( ( c_In @ ( esk3_2 @ X457 @ X458 ) @ X457 )
        | ( c_and @ $true @ $false )
        | ~ ( c_In @ X458 @ ( esk3_2 @ X457 @ X458 ) )
        | ( c_iff @ $false @ $false )
        | ( c_In @ X458 @ ( c_Union @ X457 ) ) )
      & ( ~ ( c_In @ ( esk3_2 @ X457 @ X458 ) @ X457 )
        | ( c_and @ $false @ $true )
        | ( c_In @ X458 @ ( esk3_2 @ X457 @ X458 ) )
        | ( c_iff @ $false @ $false )
        | ( c_In @ X458 @ ( c_Union @ X457 ) ) )
      & ( ( c_In @ ( esk3_2 @ X457 @ X458 ) @ X457 )
        | ( c_and @ $false @ $false )
        | ( c_In @ X458 @ ( esk3_2 @ X457 @ X458 ) )
        | ( c_iff @ $false @ $false )
        | ( c_In @ X458 @ ( c_Union @ X457 ) ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_14])])])])])]) ).

thf(c_0_20,plain,
    ! [X448: $o,X449: $o] :
      ( ( ~ X448
        | X449
        | ~ ( c_iff @ X448 @ X449 ) )
      & ( ~ X449
        | X448
        | ~ ( c_iff @ X448 @ X449 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])])]) ).

thf(c_0_21,plain,
    ! [X486: $o,X487: $o,X488: $o,X489: $o,X490: $o] :
      ( ( X486
        | X488
        | ~ ( c_and @ X486 @ X487 ) )
      & ( X487
        | X488
        | ~ ( c_and @ X486 @ X487 ) )
      & ( ~ X488
        | X488
        | ~ ( c_and @ X486 @ X487 ) )
      & ( ~ X489
        | ~ X490
        | ( epred144_2 @ X489 @ X490 )
        | ( c_and @ X489 @ X490 ) )
      & ( ~ ( epred144_2 @ X489 @ X490 )
        | ( c_and @ X489 @ X490 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])])])])]) ).

thf(c_0_22,plain,
    ! [X452: $i] :
      ( ( ~ ( c_In @ X452 @ c_Empty )
        | ( c_not @ $true ) )
      & ( ( c_In @ esk1_0 @ c_Empty )
        | ( c_not @ $false ) ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])])]) ).

thf(c_0_23,plain,
    ( ~ ( c_not @ ~ $true )
    | ~ ( c_not @ $true ) ),
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_17])])]) ).

thf(c_0_24,plain,
    c_not @ ~ $true,
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_18])])]) ).

thf(c_0_25,plain,
    ! [X244: $i,X245: $i] :
      ( ( c_Subq @ X244 @ X245 )
    <=> ! [X9: $i] :
          ( ( c_In @ X9 @ X244 )
         => ( c_In @ X9 @ X245 ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[ax17])]) ).

thf(c_0_26,plain,
    ! [X6: $i,X2: $i] :
      ( ( c_In @ ( esk2_2 @ X2 @ X6 ) @ X2 )
      | ( c_and @ ~ $true @ ~ $true )
      | ( c_In @ X6 @ ( esk2_2 @ X2 @ X6 ) )
      | ( c_iff @ $true @ ~ $true )
      | ~ ( c_In @ X6 @ ( c_Union @ X2 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

thf(c_0_27,plain,
    ~ ( c_iff @ $true @ ~ $true ),
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_20])])]) ).

thf(c_0_28,plain,
    ! [X5: $o] :
      ~ ( c_and @ X5 @ ~ $true ),
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_21])])]) ).

thf(c_0_29,negated_conjecture,
    ~ ( ( ~ ! [X201: $i > $i > $o,X202: $i > $i > $i,X203: $i > $o,X204: $i > $o,X205: $i > $i,X206: $i,X83: $i,X207: $i] :
              ( ( X205 @ ( X202 @ ( X202 @ ( X202 @ ( X202 @ ( X202 @ ( X202 @ X83 @ X206 ) @ ( X202 @ ( X202 @ ( X202 @ X83 @ X206 ) @ ( X202 @ X207 @ ( X202 @ ( X202 @ ( X202 @ X206 @ X206 ) @ ( X202 @ ( X202 @ ( X202 @ ( X202 @ X206 @ ( X202 @ ( X202 @ X83 @ ( X202 @ X206 @ ( X202 @ X206 @ X207 ) ) ) @ X206 ) ) @ X207 ) @ ( X202 @ ( X205 @ X83 ) @ X207 ) ) @ ( X202 @ ( X202 @ ( X202 @ ( X202 @ X206 @ ( X205 @ ( X202 @ X207 @ X206 ) ) ) @ ( X202 @ X83 @ X83 ) ) @ ( X202 @ X83 @ ( X202 @ X207 @ X206 ) ) ) @ X206 ) ) ) @ X207 ) ) ) @ X206 ) ) @ X83 ) @ ( X202 @ X83 @ ( X202 @ X206 @ ( X202 @ ( X202 @ ( X205 @ X206 ) @ ( X202 @ ( X202 @ X83 @ X83 ) @ X83 ) ) @ X206 ) ) ) ) @ ( X205 @ ( X205 @ X83 ) ) ) @ X206 ) )
              = ( X205 @ ( X205 @ X207 ) ) )
        | ( c_not @ $true ) )
      & ( ! [X201: $i > $i > $o,X202: $i > $i > $i,X203: $i > $o,X204: $i > $o,X205: $i > $i,X206: $i,X83: $i,X207: $i] :
            ( ( X205 @ ( X202 @ ( X202 @ ( X202 @ ( X202 @ ( X202 @ ( X202 @ X83 @ X206 ) @ ( X202 @ ( X202 @ ( X202 @ X83 @ X206 ) @ ( X202 @ X207 @ ( X202 @ ( X202 @ ( X202 @ X206 @ X206 ) @ ( X202 @ ( X202 @ ( X202 @ ( X202 @ X206 @ ( X202 @ ( X202 @ X83 @ ( X202 @ X206 @ ( X202 @ X206 @ X207 ) ) ) @ X206 ) ) @ X207 ) @ ( X202 @ ( X205 @ X83 ) @ X207 ) ) @ ( X202 @ ( X202 @ ( X202 @ ( X202 @ X206 @ ( X205 @ ( X202 @ X207 @ X206 ) ) ) @ ( X202 @ X83 @ X83 ) ) @ ( X202 @ X83 @ ( X202 @ X207 @ X206 ) ) ) @ X206 ) ) ) @ X207 ) ) ) @ X206 ) ) @ X83 ) @ ( X202 @ X83 @ ( X202 @ X206 @ ( X202 @ ( X202 @ ( X205 @ X206 ) @ ( X202 @ ( X202 @ X83 @ X83 ) @ X83 ) ) @ X206 ) ) ) ) @ ( X205 @ ( X205 @ X83 ) ) ) @ X206 ) )
            = ( X205 @ ( X205 @ X207 ) ) )
        | ( c_not @ $false ) ) ),
    inference(fool_unroll,[status(thm)],[inference(assume_negation,[status(cth)],[conj])]) ).

thf(c_0_30,plain,
    ! [X2: $i] :
      ( ( c_not @ $true )
      | ~ ( c_In @ X2 @ c_Empty ) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

thf(c_0_31,plain,
    ~ ( c_not @ $true ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]) ).

thf(c_0_32,plain,
    ! [X500: $i,X501: $i,X502: $i,X503: $i,X504: $i] :
      ( ( ~ ( c_Subq @ X500 @ X501 )
        | ~ ( c_In @ X502 @ X500 )
        | ( c_In @ X502 @ X501 ) )
      & ( ( c_In @ ( esk13_2 @ X503 @ X504 ) @ X503 )
        | ( c_Subq @ X503 @ X504 ) )
      & ( ~ ( c_In @ ( esk13_2 @ X503 @ X504 ) @ X504 )
        | ( c_Subq @ X503 @ X504 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])])])])])]) ).

thf(c_0_33,plain,
    ! [X6: $i,X2: $i] :
      ( ( c_In @ ( esk2_2 @ X2 @ X6 ) @ X2 )
      | ( c_and @ $true @ ~ $true )
      | ( c_iff @ $true @ ~ $true )
      | ~ ( c_In @ X6 @ ( esk2_2 @ X2 @ X6 ) )
      | ~ ( c_In @ X6 @ ( c_Union @ X2 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

thf(c_0_34,plain,
    ! [X6: $i,X2: $i] :
      ( ( c_In @ ( esk2_2 @ X2 @ X6 ) @ X2 )
      | ( c_In @ X6 @ ( esk2_2 @ X2 @ X6 ) )
      | ~ ( c_In @ X6 @ ( c_Union @ X2 ) ) ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).

thf(c_0_35,negated_conjecture,
    ! [X816: $i > $i > $i,X817: $i > $i,X818: $i,X819: $i,X820: $i] :
      ( ( ( ( esk53_0 @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ esk55_0 @ esk54_0 ) @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ esk55_0 @ esk54_0 ) @ ( esk52_0 @ esk56_0 @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ esk54_0 @ esk54_0 ) @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ esk54_0 @ ( esk52_0 @ ( esk52_0 @ esk55_0 @ ( esk52_0 @ esk54_0 @ ( esk52_0 @ esk54_0 @ esk56_0 ) ) ) @ esk54_0 ) ) @ esk56_0 ) @ ( esk52_0 @ ( esk53_0 @ esk55_0 ) @ esk56_0 ) ) @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ esk54_0 @ ( esk53_0 @ ( esk52_0 @ esk56_0 @ esk54_0 ) ) ) @ ( esk52_0 @ esk55_0 @ esk55_0 ) ) @ ( esk52_0 @ esk55_0 @ ( esk52_0 @ esk56_0 @ esk54_0 ) ) ) @ esk54_0 ) ) ) @ esk56_0 ) ) ) @ esk54_0 ) ) @ esk55_0 ) @ ( esk52_0 @ esk55_0 @ ( esk52_0 @ esk54_0 @ ( esk52_0 @ ( esk52_0 @ ( esk53_0 @ esk54_0 ) @ ( esk52_0 @ ( esk52_0 @ esk55_0 @ esk55_0 ) @ esk55_0 ) ) @ esk54_0 ) ) ) ) @ ( esk53_0 @ ( esk53_0 @ esk55_0 ) ) ) @ esk54_0 ) )
         != ( esk53_0 @ ( esk53_0 @ esk56_0 ) ) )
        | ( ( X817 @ ( X816 @ ( X816 @ ( X816 @ ( X816 @ ( X816 @ ( X816 @ X819 @ X818 ) @ ( X816 @ ( X816 @ ( X816 @ X819 @ X818 ) @ ( X816 @ X820 @ ( X816 @ ( X816 @ ( X816 @ X818 @ X818 ) @ ( X816 @ ( X816 @ ( X816 @ ( X816 @ X818 @ ( X816 @ ( X816 @ X819 @ ( X816 @ X818 @ ( X816 @ X818 @ X820 ) ) ) @ X818 ) ) @ X820 ) @ ( X816 @ ( X817 @ X819 ) @ X820 ) ) @ ( X816 @ ( X816 @ ( X816 @ ( X816 @ X818 @ ( X817 @ ( X816 @ X820 @ X818 ) ) ) @ ( X816 @ X819 @ X819 ) ) @ ( X816 @ X819 @ ( X816 @ X820 @ X818 ) ) ) @ X818 ) ) ) @ X820 ) ) ) @ X818 ) ) @ X819 ) @ ( X816 @ X819 @ ( X816 @ X818 @ ( X816 @ ( X816 @ ( X817 @ X818 ) @ ( X816 @ ( X816 @ X819 @ X819 ) @ X819 ) ) @ X818 ) ) ) ) @ ( X817 @ ( X817 @ X819 ) ) ) @ X818 ) )
          = ( X817 @ ( X817 @ X820 ) ) ) )
      & ( ~ ( c_not @ $false )
        | ( ( X817 @ ( X816 @ ( X816 @ ( X816 @ ( X816 @ ( X816 @ ( X816 @ X819 @ X818 ) @ ( X816 @ ( X816 @ ( X816 @ X819 @ X818 ) @ ( X816 @ X820 @ ( X816 @ ( X816 @ ( X816 @ X818 @ X818 ) @ ( X816 @ ( X816 @ ( X816 @ ( X816 @ X818 @ ( X816 @ ( X816 @ X819 @ ( X816 @ X818 @ ( X816 @ X818 @ X820 ) ) ) @ X818 ) ) @ X820 ) @ ( X816 @ ( X817 @ X819 ) @ X820 ) ) @ ( X816 @ ( X816 @ ( X816 @ ( X816 @ X818 @ ( X817 @ ( X816 @ X820 @ X818 ) ) ) @ ( X816 @ X819 @ X819 ) ) @ ( X816 @ X819 @ ( X816 @ X820 @ X818 ) ) ) @ X818 ) ) ) @ X820 ) ) ) @ X818 ) ) @ X819 ) @ ( X816 @ X819 @ ( X816 @ X818 @ ( X816 @ ( X816 @ ( X817 @ X818 ) @ ( X816 @ ( X816 @ X819 @ X819 ) @ X819 ) ) @ X818 ) ) ) ) @ ( X817 @ ( X817 @ X819 ) ) ) @ X818 ) )
          = ( X817 @ ( X817 @ X820 ) ) ) )
      & ( ( ( esk53_0 @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ esk55_0 @ esk54_0 ) @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ esk55_0 @ esk54_0 ) @ ( esk52_0 @ esk56_0 @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ esk54_0 @ esk54_0 ) @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ esk54_0 @ ( esk52_0 @ ( esk52_0 @ esk55_0 @ ( esk52_0 @ esk54_0 @ ( esk52_0 @ esk54_0 @ esk56_0 ) ) ) @ esk54_0 ) ) @ esk56_0 ) @ ( esk52_0 @ ( esk53_0 @ esk55_0 ) @ esk56_0 ) ) @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ ( esk52_0 @ esk54_0 @ ( esk53_0 @ ( esk52_0 @ esk56_0 @ esk54_0 ) ) ) @ ( esk52_0 @ esk55_0 @ esk55_0 ) ) @ ( esk52_0 @ esk55_0 @ ( esk52_0 @ esk56_0 @ esk54_0 ) ) ) @ esk54_0 ) ) ) @ esk56_0 ) ) ) @ esk54_0 ) ) @ esk55_0 ) @ ( esk52_0 @ esk55_0 @ ( esk52_0 @ esk54_0 @ ( esk52_0 @ ( esk52_0 @ ( esk53_0 @ esk54_0 ) @ ( esk52_0 @ ( esk52_0 @ esk55_0 @ esk55_0 ) @ esk55_0 ) ) @ esk54_0 ) ) ) ) @ ( esk53_0 @ ( esk53_0 @ esk55_0 ) ) ) @ esk54_0 ) )
         != ( esk53_0 @ ( esk53_0 @ esk56_0 ) ) )
        | ~ ( c_not @ $true ) )
      & ( ~ ( c_not @ $false )
        | ~ ( c_not @ $true ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[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)],[c_0_29])])])])])])]) ).

thf(c_0_36,plain,
    ! [X450: $i,X451: $i] :
      ( ~ ( c_Subq @ X450 @ X451 )
      | ~ ( c_Subq @ X451 @ X450 )
      | ( X450 = X451 ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])]) ).

thf(c_0_37,plain,
    ! [X2: $i] :
      ~ ( c_In @ X2 @ c_Empty ),
    inference(sr,[status(thm)],[c_0_30,c_0_31]) ).

thf(c_0_38,plain,
    ! [X2: $i,X6: $i] :
      ( ( c_In @ ( esk13_2 @ X2 @ X6 ) @ X2 )
      | ( c_Subq @ X2 @ X6 ) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

thf(c_0_39,plain,
    ! [X6: $i,X2: $i] :
      ( ( c_In @ ( esk2_2 @ X2 @ X6 ) @ X2 )
      | ~ ( c_In @ X6 @ ( c_Union @ X2 ) ) ),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_33,c_0_28]),c_0_27]),c_0_34]) ).

thf(c_0_40,negated_conjecture,
    ! [X2: $i,X6: $i,X12: $i > $i,X89: $i > $i > $i,X7: $i] :
      ( ( ( X12 @ ( X89 @ ( X89 @ ( X89 @ ( X89 @ ( X89 @ ( X89 @ X2 @ X6 ) @ ( X89 @ ( X89 @ ( X89 @ X2 @ X6 ) @ ( X89 @ X7 @ ( X89 @ ( X89 @ ( X89 @ X6 @ X6 ) @ ( X89 @ ( X89 @ ( X89 @ ( X89 @ X6 @ ( X89 @ ( X89 @ X2 @ ( X89 @ X6 @ ( X89 @ X6 @ X7 ) ) ) @ X6 ) ) @ X7 ) @ ( X89 @ ( X12 @ X2 ) @ X7 ) ) @ ( X89 @ ( X89 @ ( X89 @ ( X89 @ X6 @ ( X12 @ ( X89 @ X7 @ X6 ) ) ) @ ( X89 @ X2 @ X2 ) ) @ ( X89 @ X2 @ ( X89 @ X7 @ X6 ) ) ) @ X6 ) ) ) @ X7 ) ) ) @ X6 ) ) @ X2 ) @ ( X89 @ X2 @ ( X89 @ X6 @ ( X89 @ ( X89 @ ( X12 @ X6 ) @ ( X89 @ ( X89 @ X2 @ X2 ) @ X2 ) ) @ X6 ) ) ) ) @ ( X12 @ ( X12 @ X2 ) ) ) @ X6 ) )
        = ( X12 @ ( X12 @ X7 ) ) )
      | ~ ( c_not @ ~ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

thf(c_0_41,plain,
    ! [X1967: $i,X1968: $i] :
      ( ( esk222_1 @ X1968 @ X1967 )
      = X1968 ),
    inference(variable_rename,[status(thm)],]) ).

thf(c_0_42,plain,
    ! [X6: $i,X2: $i] :
      ( ( X2 = X6 )
      | ~ ( c_Subq @ X2 @ X6 )
      | ~ ( c_Subq @ X6 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

thf(c_0_43,plain,
    ! [X2: $i] : ( c_Subq @ c_Empty @ X2 ),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

thf(c_0_44,plain,
    ! [X2: $i] :
      ~ ( c_In @ X2 @ ( c_Union @ c_Empty ) ),
    inference(spm,[status(thm)],[c_0_37,c_0_39]) ).

thf(c_0_45,plain,
    ! [X2: $i,X8: $i] :
      ( ( epred1_2 @ X8 @ X2 )
     => ~ ? [X9: $i] :
            ( ( ~ ( c_In @ X2 @ X9 )
              | ( ( ~ ( c_In @ X9 @ X8 )
                  | ( c_and @ $true @ $true ) )
                & ( ( c_In @ X9 @ X8 )
                  | ( c_and @ $true @ $false ) ) ) )
            & ( ( c_In @ X2 @ X9 )
              | ( ( ~ ( c_In @ X9 @ X8 )
                  | ( c_and @ $false @ $true ) )
                & ( ( c_In @ X9 @ X8 )
                  | ( c_and @ $false @ $false ) ) ) ) ) ),
    inference(split_equiv,[status(thm)],[c_0_11]) ).

thf(c_0_46,negated_conjecture,
    ! [X2: $i,X6: $i,X12: $i > $i,X89: $i > $i > $i,X7: $i] :
      ( ( X12 @ ( X89 @ ( X89 @ ( X89 @ ( X89 @ ( X89 @ ( X89 @ X2 @ X6 ) @ ( X89 @ ( X89 @ ( X89 @ X2 @ X6 ) @ ( X89 @ X7 @ ( X89 @ ( X89 @ ( X89 @ X6 @ X6 ) @ ( X89 @ ( X89 @ ( X89 @ ( X89 @ X6 @ ( X89 @ ( X89 @ X2 @ ( X89 @ X6 @ ( X89 @ X6 @ X7 ) ) ) @ X6 ) ) @ X7 ) @ ( X89 @ ( X12 @ X2 ) @ X7 ) ) @ ( X89 @ ( X89 @ ( X89 @ ( X89 @ X6 @ ( X12 @ ( X89 @ X7 @ X6 ) ) ) @ ( X89 @ X2 @ X2 ) ) @ ( X89 @ X2 @ ( X89 @ X7 @ X6 ) ) ) @ X6 ) ) ) @ X7 ) ) ) @ X6 ) ) @ X2 ) @ ( X89 @ X2 @ ( X89 @ X6 @ ( X89 @ ( X89 @ ( X12 @ X6 ) @ ( X89 @ ( X89 @ X2 @ X2 ) @ X2 ) ) @ X6 ) ) ) ) @ ( X12 @ ( X12 @ X2 ) ) ) @ X6 ) )
      = ( X12 @ ( X12 @ X7 ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_24])]) ).

thf(c_0_47,plain,
    ! [X6: $i,X2: $i] :
      ( ( esk222_1 @ X2 @ X6 )
      = X2 ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

thf(c_0_48,plain,
    ! [X2: $i] :
      ( ( X2 = c_Empty )
      | ~ ( c_Subq @ X2 @ c_Empty ) ),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

thf(c_0_49,plain,
    ! [X2: $i] : ( c_Subq @ ( c_Union @ c_Empty ) @ X2 ),
    inference(spm,[status(thm)],[c_0_44,c_0_38]) ).

thf(c_0_50,plain,
    ! [X826: $i,X827: $i,X828: $i] :
      ( ( ~ ( c_In @ X826 @ X828 )
        | ( c_In @ X826 @ X828 )
        | ~ ( epred1_2 @ X827 @ X826 ) )
      & ( ~ ( c_In @ X828 @ X827 )
        | ( c_In @ X828 @ X827 )
        | ( c_In @ X826 @ X828 )
        | ~ ( epred1_2 @ X827 @ X826 ) )
      & ( ~ ( c_and @ $false @ $false )
        | ( c_In @ X828 @ X827 )
        | ( c_In @ X826 @ X828 )
        | ~ ( epred1_2 @ X827 @ X826 ) )
      & ( ~ ( c_In @ X828 @ X827 )
        | ~ ( c_and @ $false @ $true )
        | ( c_In @ X826 @ X828 )
        | ~ ( epred1_2 @ X827 @ X826 ) )
      & ( ~ ( c_and @ $false @ $false )
        | ~ ( c_and @ $false @ $true )
        | ( c_In @ X826 @ X828 )
        | ~ ( epred1_2 @ X827 @ X826 ) )
      & ( ~ ( c_In @ X826 @ X828 )
        | ~ ( c_In @ X828 @ X827 )
        | ( c_In @ X828 @ X827 )
        | ~ ( epred1_2 @ X827 @ X826 ) )
      & ( ~ ( c_In @ X828 @ X827 )
        | ( c_In @ X828 @ X827 )
        | ~ ( c_In @ X828 @ X827 )
        | ( c_In @ X828 @ X827 )
        | ~ ( epred1_2 @ X827 @ X826 ) )
      & ( ~ ( c_and @ $false @ $false )
        | ( c_In @ X828 @ X827 )
        | ~ ( c_In @ X828 @ X827 )
        | ( c_In @ X828 @ X827 )
        | ~ ( epred1_2 @ X827 @ X826 ) )
      & ( ~ ( c_In @ X828 @ X827 )
        | ~ ( c_and @ $false @ $true )
        | ~ ( c_In @ X828 @ X827 )
        | ( c_In @ X828 @ X827 )
        | ~ ( epred1_2 @ X827 @ X826 ) )
      & ( ~ ( c_and @ $false @ $false )
        | ~ ( c_and @ $false @ $true )
        | ~ ( c_In @ X828 @ X827 )
        | ( c_In @ X828 @ X827 )
        | ~ ( epred1_2 @ X827 @ X826 ) )
      & ( ~ ( c_In @ X826 @ X828 )
        | ~ ( c_and @ $true @ $false )
        | ( c_In @ X828 @ X827 )
        | ~ ( epred1_2 @ X827 @ X826 ) )
      & ( ~ ( c_In @ X828 @ X827 )
        | ( c_In @ X828 @ X827 )
        | ~ ( c_and @ $true @ $false )
        | ( c_In @ X828 @ X827 )
        | ~ ( epred1_2 @ X827 @ X826 ) )
      & ( ~ ( c_and @ $false @ $false )
        | ( c_In @ X828 @ X827 )
        | ~ ( c_and @ $true @ $false )
        | ( c_In @ X828 @ X827 )
        | ~ ( epred1_2 @ X827 @ X826 ) )
      & ( ~ ( c_In @ X828 @ X827 )
        | ~ ( c_and @ $false @ $true )
        | ~ ( c_and @ $true @ $false )
        | ( c_In @ X828 @ X827 )
        | ~ ( epred1_2 @ X827 @ X826 ) )
      & ( ~ ( c_and @ $false @ $false )
        | ~ ( c_and @ $false @ $true )
        | ~ ( c_and @ $true @ $false )
        | ( c_In @ X828 @ X827 )
        | ~ ( epred1_2 @ X827 @ X826 ) )
      & ( ~ ( c_In @ X826 @ X828 )
        | ~ ( c_In @ X828 @ X827 )
        | ~ ( c_and @ $true @ $true )
        | ~ ( epred1_2 @ X827 @ X826 ) )
      & ( ~ ( c_In @ X828 @ X827 )
        | ( c_In @ X828 @ X827 )
        | ~ ( c_In @ X828 @ X827 )
        | ~ ( c_and @ $true @ $true )
        | ~ ( epred1_2 @ X827 @ X826 ) )
      & ( ~ ( c_and @ $false @ $false )
        | ( c_In @ X828 @ X827 )
        | ~ ( c_In @ X828 @ X827 )
        | ~ ( c_and @ $true @ $true )
        | ~ ( epred1_2 @ X827 @ X826 ) )
      & ( ~ ( c_In @ X828 @ X827 )
        | ~ ( c_and @ $false @ $true )
        | ~ ( c_In @ X828 @ X827 )
        | ~ ( c_and @ $true @ $true )
        | ~ ( epred1_2 @ X827 @ X826 ) )
      & ( ~ ( c_and @ $false @ $false )
        | ~ ( c_and @ $false @ $true )
        | ~ ( c_In @ X828 @ X827 )
        | ~ ( c_and @ $true @ $true )
        | ~ ( epred1_2 @ X827 @ X826 ) )
      & ( ~ ( c_In @ X826 @ X828 )
        | ~ ( c_and @ $true @ $false )
        | ~ ( c_and @ $true @ $true )
        | ~ ( epred1_2 @ X827 @ X826 ) )
      & ( ~ ( c_In @ X828 @ X827 )
        | ( c_In @ X828 @ X827 )
        | ~ ( c_and @ $true @ $false )
        | ~ ( c_and @ $true @ $true )
        | ~ ( epred1_2 @ X827 @ X826 ) )
      & ( ~ ( c_and @ $false @ $false )
        | ( c_In @ X828 @ X827 )
        | ~ ( c_and @ $true @ $false )
        | ~ ( c_and @ $true @ $true )
        | ~ ( epred1_2 @ X827 @ X826 ) )
      & ( ~ ( c_In @ X828 @ X827 )
        | ~ ( c_and @ $false @ $true )
        | ~ ( c_and @ $true @ $false )
        | ~ ( c_and @ $true @ $true )
        | ~ ( epred1_2 @ X827 @ X826 ) )
      & ( ~ ( c_and @ $false @ $false )
        | ~ ( c_and @ $false @ $true )
        | ~ ( c_and @ $true @ $false )
        | ~ ( c_and @ $true @ $true )
        | ~ ( epred1_2 @ X827 @ X826 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])])])]) ).

thf(c_0_51,plain,
    ! [X3: $o,X4: $o] :
      ( ( c_and @ X3 @ X4 )
      | ~ ( epred144_2 @ X3 @ X4 ) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

thf(c_0_52,plain,
    ( ( epred144_2 @ $true @ $true )
    | ( c_and @ $true @ $true ) ),
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_21])])]) ).

thf(c_0_53,plain,
    ! [X6: $i,X2: $i] :
      ( ( epred1_2 @ X2 @ X6 )
      | ( c_iff @ ~ $true @ $true )
      | ( c_In @ X6 @ ( c_Union @ X2 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

thf(c_0_54,plain,
    ~ ( c_iff @ ~ $true @ $true ),
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_20])])]) ).

thf(c_0_55,plain,
    ! [X2: $i,X12: $i > $i,X6: $i] :
      ( ( X12 @ X2 )
      = ( X12 @ ( X12 @ X6 ) ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]) ).

thf(c_0_56,plain,
    ( ( c_Union @ c_Empty )
    = c_Empty ),
    inference(spm,[status(thm)],[c_0_48,c_0_49]) ).

thf(c_0_57,plain,
    ! [X258: $i > $i > $o] :
      ( ( c_irreflexive_i @ X258 )
    <=> ! [X2: $i] :
          ( ( ~ ( X258 @ X2 @ X2 )
            | ( c_not @ $true ) )
          & ( ( X258 @ X2 @ X2 )
            | ( c_not @ $false ) ) ) ),
    inference(fool_unroll,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[ax30])])]) ).

thf(c_0_58,plain,
    ! [X7: $i,X6: $i,X2: $i] :
      ( ~ ( c_In @ X2 @ X6 )
      | ~ ( c_In @ X6 @ X7 )
      | ~ ( c_and @ $true @ $true )
      | ~ ( epred1_2 @ X7 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

thf(c_0_59,plain,
    c_and @ $true @ $true,
    inference(spm,[status(thm)],[c_0_51,c_0_52]) ).

thf(c_0_60,plain,
    ! [X6: $i,X2: $i] :
      ( ( c_In @ X2 @ ( c_Union @ X6 ) )
      | ( epred1_2 @ X6 @ X2 ) ),
    inference(sr,[status(thm)],[c_0_53,c_0_54]) ).

thf(c_0_61,plain,
    ! [X2: $i] :
      ( ( c_Union @ X2 )
      = c_Empty ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_56]) ).

thf(c_0_62,plain,
    ! [X527: $i > $i > $o,X528: $i,X529: $i,X530: $i > $i > $o] :
      ( ( ~ ( X527 @ X528 @ X528 )
        | ( c_not @ $true )
        | ~ ( c_irreflexive_i @ X527 ) )
      & ( ( X527 @ X529 @ X529 )
        | ( c_not @ $false )
        | ~ ( c_irreflexive_i @ X527 ) )
      & ( ~ ( X530 @ ( esk18_1 @ X530 ) @ ( esk18_1 @ X530 ) )
        | ( X530 @ ( esk17_1 @ X530 ) @ ( esk17_1 @ X530 ) )
        | ( c_irreflexive_i @ X530 ) )
      & ( ~ ( c_not @ $false )
        | ( X530 @ ( esk17_1 @ X530 ) @ ( esk17_1 @ X530 ) )
        | ( c_irreflexive_i @ X530 ) )
      & ( ~ ( X530 @ ( esk18_1 @ X530 ) @ ( esk18_1 @ X530 ) )
        | ~ ( c_not @ $true )
        | ( c_irreflexive_i @ X530 ) )
      & ( ~ ( c_not @ $false )
        | ~ ( c_not @ $true )
        | ( c_irreflexive_i @ X530 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])])])])])]) ).

thf(c_0_63,plain,
    ! [X2: $i,X6: $i,X7: $i] :
      ( ~ ( c_In @ X2 @ X6 )
      | ~ ( c_In @ X7 @ X2 )
      | ~ ( epred1_2 @ X6 @ X7 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59])]) ).

thf(c_0_64,plain,
    ! [X2: $i,X6: $i] : ( epred1_2 @ X2 @ X6 ),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_61]),c_0_37]) ).

thf(c_0_65,plain,
    ! [X37: $i > $i > $o] :
      ( ( X37 @ ( esk17_1 @ X37 ) @ ( esk17_1 @ X37 ) )
      | ( c_irreflexive_i @ X37 )
      | ~ ( c_not @ ~ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

thf(c_0_66,plain,
    ! [X7: $i,X6: $i,X2: $i] :
      ( ~ ( c_In @ X2 @ X6 )
      | ~ ( c_In @ X7 @ X2 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64])]) ).

thf(c_0_67,plain,
    ! [X37: $i > $i > $o] :
      ( ( X37 @ ( esk17_1 @ X37 ) @ ( esk17_1 @ X37 ) )
      | ( c_irreflexive_i @ X37 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_24])]) ).

thf(c_0_68,axiom,
    ! [X10: $i,X2: $i] :
      ( ( ~ ( c_In @ X2 @ ( c_Power @ X10 ) )
        | ( ( ~ ( c_Subq @ X2 @ X10 )
            | ( c_iff @ $true @ $true ) )
          & ( ( c_Subq @ X2 @ X10 )
            | ( c_iff @ $true @ $false ) ) ) )
      & ( ( c_In @ X2 @ ( c_Power @ X10 ) )
        | ( ( ~ ( c_Subq @ X2 @ X10 )
            | ( c_iff @ $false @ $true ) )
          & ( ( c_Subq @ X2 @ X10 )
            | ( c_iff @ $false @ $false ) ) ) ) ),
    inference(fool_unroll,[status(thm)],[ax7]) ).

thf(c_0_69,plain,
    ! [X2: $i,X37: $i > $i > $o] :
      ( ( c_not @ $true )
      | ~ ( X37 @ X2 @ X2 )
      | ~ ( c_irreflexive_i @ X37 ) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

thf(c_0_70,plain,
    ! [X2: $i] :
      ( ( c_irreflexive_i @ c_In )
      | ~ ( c_In @ X2 @ ( esk17_1 @ c_In ) ) ),
    inference(spm,[status(thm)],[c_0_66,c_0_67]) ).

thf(c_0_71,plain,
    ! [X460: $i,X461: $i] :
      ( ( ~ ( c_Subq @ X461 @ X460 )
        | ( c_iff @ $true @ $true )
        | ~ ( c_In @ X461 @ ( c_Power @ X460 ) ) )
      & ( ( c_Subq @ X461 @ X460 )
        | ( c_iff @ $true @ $false )
        | ~ ( c_In @ X461 @ ( c_Power @ X460 ) ) )
      & ( ~ ( c_Subq @ X461 @ X460 )
        | ( c_iff @ $false @ $true )
        | ( c_In @ X461 @ ( c_Power @ X460 ) ) )
      & ( ( c_Subq @ X461 @ X460 )
        | ( c_iff @ $false @ $false )
        | ( c_In @ X461 @ ( c_Power @ X460 ) ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_68])])]) ).

thf(c_0_72,plain,
    ! [X37: $i > $i > $o,X2: $i] :
      ( ~ ( c_irreflexive_i @ X37 )
      | ~ ( X37 @ X2 @ X2 ) ),
    inference(sr,[status(thm)],[c_0_69,c_0_31]) ).

thf(c_0_73,plain,
    c_irreflexive_i @ c_In,
    inference(spm,[status(thm)],[c_0_70,c_0_67]) ).

thf(c_0_74,plain,
    ! [X2: $i,X6: $i] :
      ( ( c_iff @ ~ $true @ $true )
      | ( c_In @ X2 @ ( c_Power @ X6 ) )
      | ~ ( c_Subq @ X2 @ X6 ) ),
    inference(split_conjunct,[status(thm)],[c_0_71]) ).

thf(c_0_75,plain,
    ! [X2: $i] :
      ~ ( c_In @ X2 @ X2 ),
    inference(spm,[status(thm)],[c_0_72,c_0_73]) ).

thf(c_0_76,plain,
    ! [X2: $i,X6: $i] :
      ( ( c_In @ X2 @ ( c_Power @ X6 ) )
      | ~ ( c_Subq @ X2 @ X6 ) ),
    inference(sr,[status(thm)],[c_0_74,c_0_54]) ).

thf(c_0_77,plain,
    ! [X2: $i,X12: $i > $i] :
      ( ( X12 @ X2 )
      = ( X12 @ c_Empty ) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_55]),c_0_55]) ).

thf(c_0_78,plain,
    ! [X2: $i] :
      ~ ( c_Subq @ ( c_Power @ X2 ) @ X2 ),
    inference(spm,[status(thm)],[c_0_75,c_0_76]) ).

thf(c_0_79,plain,
    ! [X2: $i,X12: $i > $i,X6: $i] :
      ( ( X12 @ X2 )
      = ( X12 @ X6 ) ),
    inference(spm,[status(thm)],[c_0_77,c_0_77]) ).

thf(c_0_80,plain,
    ! [X2: $i,X6: $i] :
      ( ( c_Subq @ X2 @ X6 )
      | ~ ( c_In @ ( esk13_2 @ X2 @ X6 ) @ X6 ) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

thf(c_0_81,plain,
    ! [X2: $i,X6: $i] :
      ~ ( c_Subq @ ( c_Power @ X2 ) @ X6 ),
    inference(spm,[status(thm)],[c_0_78,c_0_79]) ).

thf(c_0_82,plain,
    ! [X2: $i] : ( c_Subq @ X2 @ X2 ),
    inference(spm,[status(thm)],[c_0_80,c_0_38]) ).

thf(c_0_83,plain,
    $false,
    inference(spm,[status(thm)],[c_0_81,c_0_82]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08  % Problem    : SYO881^1 : TPTP v8.2.0. Released v7.5.0.
% 0.04/0.09  % Command    : run_E %s %d THM
% 0.09/0.28  % Computer : n022.cluster.edu
% 0.09/0.28  % Model    : x86_64 x86_64
% 0.09/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28  % Memory   : 8042.1875MB
% 0.09/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28  % CPULimit   : 300
% 0.09/0.28  % WCLimit    : 300
% 0.09/0.28  % DateTime   : Mon May 20 11:02:22 EDT 2024
% 0.09/0.28  % CPUTime    : 
% 0.14/0.38  Running higher-order theorem proving
% 0.14/0.38  Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 122.13/26.10  # Version: 3.1.0-ho
% 122.13/26.10  # partial match(1): HSLMSMSSSSLCHSA
% 122.13/26.10  # Preprocessing class: HSLMSLSSSSLCHSA.
% 122.13/26.10  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 122.13/26.10  # Starting pre_casc_6 with 1500s (5) cores
% 122.13/26.10  # Starting ehoh_best7 with 300s (1) cores
% 122.13/26.10  # Starting new_bool_8 with 300s (1) cores
% 122.13/26.10  # Starting new_ho_11 with 300s (1) cores
% 122.13/26.10  # new_ho_11 with pid 14694 completed with status 0
% 122.13/26.10  # Result found by new_ho_11
% 122.13/26.10  # partial match(1): HSLMSMSSSSLCHSA
% 122.13/26.10  # Preprocessing class: HSLMSLSSSSLCHSA.
% 122.13/26.10  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 122.13/26.10  # Starting pre_casc_6 with 1500s (5) cores
% 122.13/26.10  # Starting ehoh_best7 with 300s (1) cores
% 122.13/26.10  # Starting new_bool_8 with 300s (1) cores
% 122.13/26.10  # Starting new_ho_11 with 300s (1) cores
% 122.13/26.10  # No SInE strategy applied
% 122.13/26.10  # Search class: HGHSM-SMLM33-DHSFFSBC
% 122.13/26.10  # partial match(1): HGHSM-SMLM32-DHSFFSBC
% 122.13/26.10  # Scheduled 6 strats onto 1 cores with 280 seconds (280 total)
% 122.13/26.10  # Starting new_ho_10 with 84s (1) cores
% 122.13/26.10  # new_ho_10 with pid 15781 completed with status 0
% 122.13/26.10  # Result found by new_ho_10
% 122.13/26.10  # partial match(1): HSLMSMSSSSLCHSA
% 122.13/26.10  # Preprocessing class: HSLMSLSSSSLCHSA.
% 122.13/26.10  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 122.13/26.10  # Starting pre_casc_6 with 1500s (5) cores
% 122.13/26.10  # Starting ehoh_best7 with 300s (1) cores
% 122.13/26.10  # Starting new_bool_8 with 300s (1) cores
% 122.13/26.10  # Starting new_ho_11 with 300s (1) cores
% 122.13/26.10  # No SInE strategy applied
% 122.13/26.10  # Search class: HGHSM-SMLM33-DHSFFSBC
% 122.13/26.10  # partial match(1): HGHSM-SMLM32-DHSFFSBC
% 122.13/26.10  # Scheduled 6 strats onto 1 cores with 280 seconds (280 total)
% 122.13/26.10  # Starting new_ho_10 with 84s (1) cores
% 122.13/26.10  # Preprocessing time       : 0.130 s
% 122.13/26.10  # Presaturation interreduction done
% 122.13/26.10  
% 122.13/26.10  # Proof found!
% 122.13/26.10  # SZS status Theorem
% 122.13/26.10  # SZS output start CNFRefutation
% See solution above
% 122.13/26.10  # Parsed axioms                        : 213
% 122.13/26.10  # Removed by relevancy pruning/SinE    : 0
% 122.13/26.10  # Initial clauses                      : 468687
% 122.13/26.10  # Removed in clause preprocessing      : 463862
% 122.13/26.10  # Initial clauses in saturation        : 4825
% 122.13/26.10  # Processed clauses                    : 7679
% 122.13/26.10  # ...of these trivial                  : 330
% 122.13/26.10  # ...subsumed                          : 3956
% 122.13/26.10  # ...remaining for further processing  : 3393
% 122.13/26.10  # Other redundant clauses eliminated   : 130
% 122.13/26.10  # Clauses deleted for lack of memory   : 0
% 122.13/26.10  # Backward-subsumed                    : 202
% 122.13/26.10  # Backward-rewritten                   : 509
% 122.13/26.10  # Generated clauses                    : 42532
% 122.13/26.10  # ...of the previous two non-redundant : 41057
% 122.13/26.10  # ...aggressively subsumed             : 0
% 122.13/26.10  # Contextual simplify-reflections      : 281
% 122.13/26.10  # Paramodulations                      : 42376
% 122.13/26.10  # Factorizations                       : 0
% 122.13/26.10  # NegExts                              : 0
% 122.13/26.10  # Equation resolutions                 : 130
% 122.13/26.10  # Disequality decompositions           : 0
% 122.13/26.10  # Total rewrite steps                  : 16329
% 122.13/26.10  # ...of those cached                   : 14684
% 122.13/26.10  # Propositional unsat checks           : 0
% 122.13/26.10  #    Propositional check models        : 0
% 122.13/26.10  #    Propositional check unsatisfiable : 0
% 122.13/26.10  #    Propositional clauses             : 0
% 122.13/26.10  #    Propositional clauses after purity: 0
% 122.13/26.10  #    Propositional unsat core size     : 0
% 122.13/26.10  #    Propositional preprocessing time  : 0.000
% 122.13/26.10  #    Propositional encoding time       : 0.000
% 122.13/26.10  #    Propositional solver time         : 0.000
% 122.13/26.10  #    Success case prop preproc time    : 0.000
% 122.13/26.10  #    Success case prop encoding time   : 0.000
% 122.13/26.10  #    Success case prop solver time     : 0.000
% 122.13/26.10  # Current number of processed clauses  : 1402
% 122.13/26.10  #    Positive orientable unit clauses  : 154
% 122.13/26.10  #    Positive unorientable unit clauses: 5
% 122.13/26.10  #    Negative unit clauses             : 86
% 122.13/26.10  #    Non-unit-clauses                  : 1157
% 122.13/26.10  # Current number of unprocessed clauses: 39285
% 122.13/26.10  # ...number of literals in the above   : 193099
% 122.13/26.10  # Current number of archived formulas  : 0
% 122.13/26.10  # Current number of archived clauses   : 1933
% 122.13/26.10  # Clause-clause subsumption calls (NU) : 1774000
% 122.13/26.10  # Rec. Clause-clause subsumption calls : 395059
% 122.13/26.10  # Non-unit clause-clause subsumptions  : 1777
% 122.13/26.10  # Unit Clause-clause subsumption calls : 103342
% 122.13/26.10  # Rewrite failures with RHS unbound    : 0
% 122.13/26.10  # BW rewrite match attempts            : 14865
% 122.13/26.10  # BW rewrite match successes           : 1230
% 122.13/26.10  # Condensation attempts                : 7888
% 122.13/26.10  # Condensation successes               : 221
% 122.13/26.10  # Termbank termtop insertions          : 21204624
% 122.13/26.10  # Search garbage collected termcells   : 2011264
% 122.13/26.10  
% 122.13/26.10  # -------------------------------------------------
% 122.13/26.10  # User time                : 23.238 s
% 122.13/26.10  # System time              : 1.521 s
% 122.13/26.10  # Total time               : 24.759 s
% 122.13/26.10  # Maximum resident set size: 1254296 pages
% 122.13/26.10  
% 122.13/26.10  # -------------------------------------------------
% 122.13/26.10  # User time                : 23.246 s
% 122.13/26.10  # System time              : 1.678 s
% 122.13/26.10  # Total time               : 24.924 s
% 122.13/26.10  # Maximum resident set size: 2188 pages
% 122.13/26.10  % E---3.1 exiting
% 122.13/26.10  % E exiting
%------------------------------------------------------------------------------