TSTP Solution File: SYO879^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SYO879^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n017.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 60.26s 16.83s
% Output   : CNFRefutation 60.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   44
% Syntax   : Number of formulae    :   99 (  19 unt;  30 typ;   0 def)
%            Number of atoms       : 1170 ( 139 equ;   0 cnn)
%            Maximal formula atoms :  223 (  16 avg)
%            Number of connectives : 4315 ( 367   ~; 583   |; 188   &;3128   @)
%                                         (  10 <=>;  39  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   66 (  13 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  292 ( 292   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   33 (  30 usr;  10 con; 0-10 aty)
%            Number of variables   :  399 (   5   ^ 337   !;  57   ?; 399   :)

% 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_33,type,
    c_Power: $i > $i ).

thf(decl_79,type,
    c_ordsucc: $i > $i ).

thf(decl_96,type,
    c_ap: $i > $i > $i ).

thf(decl_253,type,
    epred128_10: $i > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > $i > $i > $i > $o ).

thf(decl_269,type,
    epred144_8: $i > $i > $i > $i > ( $i > $o ) > ( $i > $i ) > ( $i > $i > $i ) > ( $i > $o ) > $o ).

thf(decl_270,type,
    epred145_7: $i > $i > $i > $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).

thf(decl_271,type,
    epred146_8: $i > $i > $i > $i > ( $i > $o ) > ( $i > $i ) > ( $i > $i > $i ) > ( $i > $o ) > $o ).

thf(decl_272,type,
    esk1_0: $i ).

thf(decl_285,type,
    epred148_2: $o > $o > $o ).

thf(decl_287,type,
    esk13_2: $i > $i > $i ).

thf(decl_330,type,
    esk52_0: $i > $i > $i ).

thf(decl_331,type,
    epred154_0: $i > $o ).

thf(decl_332,type,
    epred155_0: $i > $o ).

thf(decl_333,type,
    esk53_0: $i > $i ).

thf(decl_334,type,
    esk54_0: $i ).

thf(decl_335,type,
    esk55_0: $i ).

thf(decl_336,type,
    esk56_0: $i ).

thf(decl_337,type,
    esk57_0: $i ).

thf(decl_338,type,
    esk58_0: $i ).

thf(decl_496,type,
    esk214_8: ( $i > $i > $i ) > ( $i > $o ) > ( $i > $o ) > ( $i > $i ) > $i > $i > $i > $i > $i ).

thf(decl_497,type,
    esk215_8: ( $i > $i > $i ) > ( $i > $o ) > ( $i > $o ) > ( $i > $i ) > $i > $i > $i > $i > $i ).

thf(decl_505,type,
    esk219_0: $i > $i > $i ).

thf(decl_518,type,
    epred166_1: ( $i > $i > $o ) > $i > $o ).

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

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

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

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,X208: $i,X209: $i] :
        ( ( c_and
          @ ! [X210: $i] :
              ( ( ( X205 @ X209 )
                = X210 )
             => ( ( c_and @ ( X203 @ X210 )
                  @ ( ( X207 = X206 )
                   => ( c_and
                      @ ! [X211: $i] : ( X209 = X208 )
                      @ ? [X212: $i] : ( X204 @ X210 ) ) ) )
               => ? [X213: $i] : ( X207 = X207 ) ) )
          @ ( c_not @ ( X204 @ ( X205 @ ( X205 @ ( X202 @ X207 @ X206 ) ) ) ) ) )
       => ( X83 = X209 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).

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

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

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

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

thf(c_0_8,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_9,plain,
    ! [X243: $o] :
      ( ( c_not @ X243 )
    <=> ( X243
       => c_False ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[ax13])]) ).

thf(c_0_10,plain,
    ! [X202: $i > $i > $i,X203: $i > $o,X204: $i > $o,X205: $i > $i,X209: $i,X208: $i,X207: $i,X206: $i] :
      ( ( epred146_8 @ X206 @ X207 @ X208 @ X209 @ X204 @ X205 @ X202 @ X203 )
    <=> ( ! [X210: $i] :
            ( ( ( X205 @ X209 )
              = X210 )
           => ( ( ( ~ ( X203 @ X210 )
                  | ( ( ~ ( ( X207 = X206 )
                         => ( ( ~ ! [X211: $i] : ( X209 = X208 )
                              | ( ( ~ ? [X212: $i] : ( X204 @ X210 )
                                  | ( c_and @ $true @ $true ) )
                                & ( ? [X212: $i] : ( X204 @ X210 )
                                  | ( c_and @ $true @ $false ) ) ) )
                            & ( ! [X211: $i] : ( X209 = X208 )
                              | ( ( ~ ? [X212: $i] : ( X204 @ X210 )
                                  | ( c_and @ $false @ $true ) )
                                & ( ? [X212: $i] : ( X204 @ X210 )
                                  | ( c_and @ $false @ $false ) ) ) ) ) )
                      | ( c_and @ $true @ $true ) )
                    & ( ( ( X207 = X206 )
                       => ( ( ~ ! [X211: $i] : ( X209 = X208 )
                            | ( ( ~ ? [X212: $i] : ( X204 @ X210 )
                                | ( c_and @ $true @ $true ) )
                              & ( ? [X212: $i] : ( X204 @ X210 )
                                | ( c_and @ $true @ $false ) ) ) )
                          & ( ! [X211: $i] : ( X209 = X208 )
                            | ( ( ~ ? [X212: $i] : ( X204 @ X210 )
                                | ( c_and @ $false @ $true ) )
                              & ( ? [X212: $i] : ( X204 @ X210 )
                                | ( c_and @ $false @ $false ) ) ) ) ) )
                      | ( c_and @ $true @ $false ) ) ) )
                & ( ( X203 @ X210 )
                  | ( ( ~ ( ( X207 = X206 )
                         => ( ( ~ ! [X211: $i] : ( X209 = X208 )
                              | ( ( ~ ? [X212: $i] : ( X204 @ X210 )
                                  | ( c_and @ $true @ $true ) )
                                & ( ? [X212: $i] : ( X204 @ X210 )
                                  | ( c_and @ $true @ $false ) ) ) )
                            & ( ! [X211: $i] : ( X209 = X208 )
                              | ( ( ~ ? [X212: $i] : ( X204 @ X210 )
                                  | ( c_and @ $false @ $true ) )
                                & ( ? [X212: $i] : ( X204 @ X210 )
                                  | ( c_and @ $false @ $false ) ) ) ) ) )
                      | ( c_and @ $false @ $true ) )
                    & ( ( ( X207 = X206 )
                       => ( ( ~ ! [X211: $i] : ( X209 = X208 )
                            | ( ( ~ ? [X212: $i] : ( X204 @ X210 )
                                | ( c_and @ $true @ $true ) )
                              & ( ? [X212: $i] : ( X204 @ X210 )
                                | ( c_and @ $true @ $false ) ) ) )
                          & ( ! [X211: $i] : ( X209 = X208 )
                            | ( ( ~ ? [X212: $i] : ( X204 @ X210 )
                                | ( c_and @ $false @ $true ) )
                              & ( ? [X212: $i] : ( X204 @ X210 )
                                | ( c_and @ $false @ $false ) ) ) ) ) )
                      | ( c_and @ $false @ $false ) ) ) ) )
             => ? [X213: $i] : ( X207 = X207 ) ) )
        | ( ( ( ( ~ ( X204 @ ( X205 @ ( X205 @ ( X202 @ X207 @ X206 ) ) ) )
                | ~ ( c_not @ $true ) )
              & ( ( X204 @ ( X205 @ ( X205 @ ( X202 @ X207 @ X206 ) ) ) )
                | ~ ( c_not @ $false ) ) )
            | ( c_and @ $false @ $true ) )
          & ( ( ( ~ ( X204 @ ( X205 @ ( X205 @ ( X202 @ X207 @ X206 ) ) ) )
                | ( c_not @ $true ) )
              & ( ( X204 @ ( X205 @ ( X205 @ ( X202 @ X207 @ X206 ) ) ) )
                | ( c_not @ $false ) ) )
            | ( c_and @ $false @ $false ) ) ) ) ),
    introduced(definition) ).

thf(c_0_11,plain,
    ! [X203: $i > $o,X204: $i > $o,X206: $i,X207: $i,X208: $i,X209: $i,X210: $i] :
      ( ( epred145_7 @ X210 @ X207 @ X209 @ X208 @ X204 @ X206 @ X203 )
    <=> ( ( ~ ( X203 @ X210 )
          | ( ( ~ ( ( X207 = X206 )
                 => ( ( ~ ! [X211: $i] : ( X209 = X208 )
                      | ( ( ~ ? [X212: $i] : ( X204 @ X210 )
                          | ( c_and @ $true @ $true ) )
                        & ( ? [X212: $i] : ( X204 @ X210 )
                          | ( c_and @ $true @ $false ) ) ) )
                    & ( ! [X211: $i] : ( X209 = X208 )
                      | ( ( ~ ? [X212: $i] : ( X204 @ X210 )
                          | ( c_and @ $false @ $true ) )
                        & ( ? [X212: $i] : ( X204 @ X210 )
                          | ( c_and @ $false @ $false ) ) ) ) ) )
              | ( c_and @ $true @ $true ) )
            & ( ( ( X207 = X206 )
               => ( ( ~ ! [X211: $i] : ( X209 = X208 )
                    | ( ( ~ ? [X212: $i] : ( X204 @ X210 )
                        | ( c_and @ $true @ $true ) )
                      & ( ? [X212: $i] : ( X204 @ X210 )
                        | ( c_and @ $true @ $false ) ) ) )
                  & ( ! [X211: $i] : ( X209 = X208 )
                    | ( ( ~ ? [X212: $i] : ( X204 @ X210 )
                        | ( c_and @ $false @ $true ) )
                      & ( ? [X212: $i] : ( X204 @ X210 )
                        | ( c_and @ $false @ $false ) ) ) ) ) )
              | ( c_and @ $true @ $false ) ) ) )
        & ( ( X203 @ X210 )
          | ( ( ~ ( ( X207 = X206 )
                 => ( ( ~ ! [X211: $i] : ( X209 = X208 )
                      | ( ( ~ ? [X212: $i] : ( X204 @ X210 )
                          | ( c_and @ $true @ $true ) )
                        & ( ? [X212: $i] : ( X204 @ X210 )
                          | ( c_and @ $true @ $false ) ) ) )
                    & ( ! [X211: $i] : ( X209 = X208 )
                      | ( ( ~ ? [X212: $i] : ( X204 @ X210 )
                          | ( c_and @ $false @ $true ) )
                        & ( ? [X212: $i] : ( X204 @ X210 )
                          | ( c_and @ $false @ $false ) ) ) ) ) )
              | ( c_and @ $false @ $true ) )
            & ( ( ( X207 = X206 )
               => ( ( ~ ! [X211: $i] : ( X209 = X208 )
                    | ( ( ~ ? [X212: $i] : ( X204 @ X210 )
                        | ( c_and @ $true @ $true ) )
                      & ( ? [X212: $i] : ( X204 @ X210 )
                        | ( c_and @ $true @ $false ) ) ) )
                  & ( ! [X211: $i] : ( X209 = X208 )
                    | ( ( ~ ? [X212: $i] : ( X204 @ X210 )
                        | ( c_and @ $false @ $true ) )
                      & ( ? [X212: $i] : ( X204 @ X210 )
                        | ( c_and @ $false @ $false ) ) ) ) ) )
              | ( c_and @ $false @ $false ) ) ) ) ) ),
    introduced(definition) ).

thf(c_0_12,plain,
    ! [X202: $i > $i > $i,X203: $i > $o,X204: $i > $o,X205: $i > $i,X209: $i,X208: $i,X207: $i,X206: $i] :
      ( ( epred144_8 @ X206 @ X207 @ X208 @ X209 @ X204 @ X205 @ X202 @ X203 )
    <=> ( ~ ! [X210: $i] :
              ( ( ( X205 @ X209 )
                = X210 )
             => ( ( ( ~ ( X203 @ X210 )
                    | ( ( ~ ( ( X207 = X206 )
                           => ( ( ~ ! [X211: $i] : ( X209 = X208 )
                                | ( ( ~ ? [X212: $i] : ( X204 @ X210 )
                                    | ( c_and @ $true @ $true ) )
                                  & ( ? [X212: $i] : ( X204 @ X210 )
                                    | ( c_and @ $true @ $false ) ) ) )
                              & ( ! [X211: $i] : ( X209 = X208 )
                                | ( ( ~ ? [X212: $i] : ( X204 @ X210 )
                                    | ( c_and @ $false @ $true ) )
                                  & ( ? [X212: $i] : ( X204 @ X210 )
                                    | ( c_and @ $false @ $false ) ) ) ) ) )
                        | ( c_and @ $true @ $true ) )
                      & ( ( ( X207 = X206 )
                         => ( ( ~ ! [X211: $i] : ( X209 = X208 )
                              | ( ( ~ ? [X212: $i] : ( X204 @ X210 )
                                  | ( c_and @ $true @ $true ) )
                                & ( ? [X212: $i] : ( X204 @ X210 )
                                  | ( c_and @ $true @ $false ) ) ) )
                            & ( ! [X211: $i] : ( X209 = X208 )
                              | ( ( ~ ? [X212: $i] : ( X204 @ X210 )
                                  | ( c_and @ $false @ $true ) )
                                & ( ? [X212: $i] : ( X204 @ X210 )
                                  | ( c_and @ $false @ $false ) ) ) ) ) )
                        | ( c_and @ $true @ $false ) ) ) )
                  & ( ( X203 @ X210 )
                    | ( ( ~ ( ( X207 = X206 )
                           => ( ( ~ ! [X211: $i] : ( X209 = X208 )
                                | ( ( ~ ? [X212: $i] : ( X204 @ X210 )
                                    | ( c_and @ $true @ $true ) )
                                  & ( ? [X212: $i] : ( X204 @ X210 )
                                    | ( c_and @ $true @ $false ) ) ) )
                              & ( ! [X211: $i] : ( X209 = X208 )
                                | ( ( ~ ? [X212: $i] : ( X204 @ X210 )
                                    | ( c_and @ $false @ $true ) )
                                  & ( ? [X212: $i] : ( X204 @ X210 )
                                    | ( c_and @ $false @ $false ) ) ) ) ) )
                        | ( c_and @ $false @ $true ) )
                      & ( ( ( X207 = X206 )
                         => ( ( ~ ! [X211: $i] : ( X209 = X208 )
                              | ( ( ~ ? [X212: $i] : ( X204 @ X210 )
                                  | ( c_and @ $true @ $true ) )
                                & ( ? [X212: $i] : ( X204 @ X210 )
                                  | ( c_and @ $true @ $false ) ) ) )
                            & ( ! [X211: $i] : ( X209 = X208 )
                              | ( ( ~ ? [X212: $i] : ( X204 @ X210 )
                                  | ( c_and @ $false @ $true ) )
                                & ( ? [X212: $i] : ( X204 @ X210 )
                                  | ( c_and @ $false @ $false ) ) ) ) ) )
                        | ( c_and @ $false @ $false ) ) ) ) )
               => ? [X213: $i] : ( X207 = X207 ) ) )
        | ( ( ( ( ~ ( X204 @ ( X205 @ ( X205 @ ( X202 @ X207 @ X206 ) ) ) )
                | ~ ( c_not @ $true ) )
              & ( ( X204 @ ( X205 @ ( X205 @ ( X202 @ X207 @ X206 ) ) ) )
                | ~ ( c_not @ $false ) ) )
            | ( c_and @ $true @ $true ) )
          & ( ( ( ~ ( X204 @ ( X205 @ ( X205 @ ( X202 @ X207 @ X206 ) ) ) )
                | ( c_not @ $true ) )
              & ( ( X204 @ ( X205 @ ( X205 @ ( X202 @ X207 @ X206 ) ) ) )
                | ( c_not @ $false ) ) )
            | ( c_and @ $true @ $false ) ) ) ) ),
    introduced(definition) ).

thf(c_0_13,plain,
    ! [X172: $i,X173: $i,X174: $i,X181: $i,X188: $i,X432: $i > $i > $i,X434: $i > $i > $i,X440: $i > $i > $i > $i,X437: $i > $i > $i > $i,X435: $i] :
      ( ( epred128_10 @ X435 @ X437 @ X440 @ X188 @ X434 @ X432 @ X181 @ X173 @ X174 @ X172 )
    <=> ( ( ( ( ( ( X437 @ X188 @ ( X432 @ ( X434 @ X435 @ X172 ) @ ( X440 @ X173 @ X174 @ X172 ) ) @ X181 )
               != X435 )
              | ~ ( c_not @ $true ) )
            & ( ( ( X437 @ X188 @ ( X432 @ ( X434 @ X435 @ X172 ) @ ( X440 @ X173 @ X174 @ X172 ) ) @ X181 )
                = X435 )
              | ~ ( c_not @ $false ) ) )
          | ( c_and @ $false @ $true ) )
        & ( ( ( ( ( X437 @ X188 @ ( X432 @ ( X434 @ X435 @ X172 ) @ ( X440 @ X173 @ X174 @ X172 ) ) @ X181 )
               != X435 )
              | ( c_not @ $true ) )
            & ( ( ( X437 @ X188 @ ( X432 @ ( X434 @ X435 @ X172 ) @ ( X440 @ X173 @ X174 @ X172 ) ) @ X181 )
                = X435 )
              | ( c_not @ $false ) ) )
          | ( c_and @ $false @ $false ) ) ) ),
    introduced(definition) ).

thf(c_0_14,plain,
    ! [X244: $o,X245: $o] :
      ( ( c_and @ X244 @ X245 )
    <=> ! [X20: $o] :
          ( ( X244
           => ( X245
             => X20 ) )
         => X20 ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[ax14])]) ).

thf(c_0_15,plain,
    ! [X453: $o] :
      ( ( ~ ( c_not @ X453 )
        | ( c_not @ X453 )
        | X453 )
      & ( ~ ( c_not @ $false )
        | ( c_not @ X453 )
        | X453 )
      & ( ~ ( c_not @ X453 )
        | ~ ( c_not @ $true )
        | X453 )
      & ( ~ ( c_not @ $false )
        | ~ ( c_not @ $true )
        | X453 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).

thf(c_0_16,plain,
    ! [X491: $o] :
      ( ( ~ ( c_not @ X491 )
        | ~ X491
        | c_False )
      & ( X491
        | ( c_not @ X491 ) )
      & ( ~ c_False
        | ( c_not @ X491 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).

thf(c_0_17,plain,
    ! [X202: $i > $i > $i,X203: $i > $o,X204: $i > $o,X205: $i > $i,X209: $i,X208: $i,X207: $i,X206: $i] :
      ( ( epred146_8 @ X206 @ X207 @ X208 @ X209 @ X204 @ X205 @ X202 @ X203 )
    <=> ( ! [X210: $i] :
            ( ( ( X205 @ X209 )
              = X210 )
           => ( ( epred145_7 @ X210 @ X207 @ X209 @ X208 @ X204 @ X206 @ X203 )
             => ? [X213: $i] : ( X207 = X207 ) ) )
        | ( ( ( ( ~ ( X204 @ ( X205 @ ( X205 @ ( X202 @ X207 @ X206 ) ) ) )
                | ~ ( c_not @ $true ) )
              & ( ( X204 @ ( X205 @ ( X205 @ ( X202 @ X207 @ X206 ) ) ) )
                | ~ ( c_not @ $false ) ) )
            | ( c_and @ $false @ $true ) )
          & ( ( ( ~ ( X204 @ ( X205 @ ( X205 @ ( X202 @ X207 @ X206 ) ) ) )
                | ( c_not @ $true ) )
              & ( ( X204 @ ( X205 @ ( X205 @ ( X202 @ X207 @ X206 ) ) ) )
                | ( c_not @ $false ) ) )
            | ( c_and @ $false @ $false ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_10,c_0_11]) ).

thf(c_0_18,plain,
    ! [X202: $i > $i > $i,X203: $i > $o,X204: $i > $o,X205: $i > $i,X209: $i,X208: $i,X207: $i,X206: $i] :
      ( ( epred144_8 @ X206 @ X207 @ X208 @ X209 @ X204 @ X205 @ X202 @ X203 )
    <=> ( ~ ! [X210: $i] :
              ( ( ( X205 @ X209 )
                = X210 )
             => ( ( epred145_7 @ X210 @ X207 @ X209 @ X208 @ X204 @ X206 @ X203 )
               => ? [X213: $i] : ( X207 = X207 ) ) )
        | ( ( ( ( ~ ( X204 @ ( X205 @ ( X205 @ ( X202 @ X207 @ X206 ) ) ) )
                | ~ ( c_not @ $true ) )
              & ( ( X204 @ ( X205 @ ( X205 @ ( X202 @ X207 @ X206 ) ) ) )
                | ~ ( c_not @ $false ) ) )
            | ( c_and @ $true @ $true ) )
          & ( ( ( ~ ( X204 @ ( X205 @ ( X205 @ ( X202 @ X207 @ X206 ) ) ) )
                | ( c_not @ $true ) )
              & ( ( X204 @ ( X205 @ ( X205 @ ( X202 @ X207 @ X206 ) ) ) )
                | ( c_not @ $false ) ) )
            | ( c_and @ $true @ $false ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_12,c_0_11]) ).

thf(c_0_19,plain,
    ! [X1751: $i,X1752: $i,X1753: $i,X1754: $i,X1755: $i,X1756: $i > $i > $i,X1757: $i > $i > $i,X1758: $i > $i > $i > $i,X1759: $i > $i > $i > $i,X1760: $i] :
      ( ( ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
         != X1760 )
        | ~ ( c_not @ $true )
        | ( c_and @ $false @ $true )
        | ~ ( epred128_10 @ X1760 @ X1759 @ X1758 @ X1755 @ X1757 @ X1756 @ X1754 @ X1752 @ X1753 @ X1751 ) )
      & ( ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
          = X1760 )
        | ~ ( c_not @ $false )
        | ( c_and @ $false @ $true )
        | ~ ( epred128_10 @ X1760 @ X1759 @ X1758 @ X1755 @ X1757 @ X1756 @ X1754 @ X1752 @ X1753 @ X1751 ) )
      & ( ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
         != X1760 )
        | ( c_not @ $true )
        | ( c_and @ $false @ $false )
        | ~ ( epred128_10 @ X1760 @ X1759 @ X1758 @ X1755 @ X1757 @ X1756 @ X1754 @ X1752 @ X1753 @ X1751 ) )
      & ( ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
          = X1760 )
        | ( c_not @ $false )
        | ( c_and @ $false @ $false )
        | ~ ( epred128_10 @ X1760 @ X1759 @ X1758 @ X1755 @ X1757 @ X1756 @ X1754 @ X1752 @ X1753 @ X1751 ) )
      & ( ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
         != X1760 )
        | ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
          = X1760 )
        | ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
         != X1760 )
        | ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
          = X1760 )
        | ( epred128_10 @ X1760 @ X1759 @ X1758 @ X1755 @ X1757 @ X1756 @ X1754 @ X1752 @ X1753 @ X1751 ) )
      & ( ~ ( c_not @ $false )
        | ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
          = X1760 )
        | ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
         != X1760 )
        | ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
          = X1760 )
        | ( epred128_10 @ X1760 @ X1759 @ X1758 @ X1755 @ X1757 @ X1756 @ X1754 @ X1752 @ X1753 @ X1751 ) )
      & ( ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
         != X1760 )
        | ~ ( c_not @ $true )
        | ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
         != X1760 )
        | ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
          = X1760 )
        | ( epred128_10 @ X1760 @ X1759 @ X1758 @ X1755 @ X1757 @ X1756 @ X1754 @ X1752 @ X1753 @ X1751 ) )
      & ( ~ ( c_not @ $false )
        | ~ ( c_not @ $true )
        | ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
         != X1760 )
        | ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
          = X1760 )
        | ( epred128_10 @ X1760 @ X1759 @ X1758 @ X1755 @ X1757 @ X1756 @ X1754 @ X1752 @ X1753 @ X1751 ) )
      & ( ~ ( c_and @ $false @ $false )
        | ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
         != X1760 )
        | ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
          = X1760 )
        | ( epred128_10 @ X1760 @ X1759 @ X1758 @ X1755 @ X1757 @ X1756 @ X1754 @ X1752 @ X1753 @ X1751 ) )
      & ( ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
         != X1760 )
        | ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
          = X1760 )
        | ( c_not @ $false )
        | ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
          = X1760 )
        | ( epred128_10 @ X1760 @ X1759 @ X1758 @ X1755 @ X1757 @ X1756 @ X1754 @ X1752 @ X1753 @ X1751 ) )
      & ( ~ ( c_not @ $false )
        | ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
          = X1760 )
        | ( c_not @ $false )
        | ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
          = X1760 )
        | ( epred128_10 @ X1760 @ X1759 @ X1758 @ X1755 @ X1757 @ X1756 @ X1754 @ X1752 @ X1753 @ X1751 ) )
      & ( ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
         != X1760 )
        | ~ ( c_not @ $true )
        | ( c_not @ $false )
        | ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
          = X1760 )
        | ( epred128_10 @ X1760 @ X1759 @ X1758 @ X1755 @ X1757 @ X1756 @ X1754 @ X1752 @ X1753 @ X1751 ) )
      & ( ~ ( c_not @ $false )
        | ~ ( c_not @ $true )
        | ( c_not @ $false )
        | ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
          = X1760 )
        | ( epred128_10 @ X1760 @ X1759 @ X1758 @ X1755 @ X1757 @ X1756 @ X1754 @ X1752 @ X1753 @ X1751 ) )
      & ( ~ ( c_and @ $false @ $false )
        | ( c_not @ $false )
        | ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
          = X1760 )
        | ( epred128_10 @ X1760 @ X1759 @ X1758 @ X1755 @ X1757 @ X1756 @ X1754 @ X1752 @ X1753 @ X1751 ) )
      & ( ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
         != X1760 )
        | ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
          = X1760 )
        | ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
         != X1760 )
        | ( c_not @ $true )
        | ( epred128_10 @ X1760 @ X1759 @ X1758 @ X1755 @ X1757 @ X1756 @ X1754 @ X1752 @ X1753 @ X1751 ) )
      & ( ~ ( c_not @ $false )
        | ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
          = X1760 )
        | ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
         != X1760 )
        | ( c_not @ $true )
        | ( epred128_10 @ X1760 @ X1759 @ X1758 @ X1755 @ X1757 @ X1756 @ X1754 @ X1752 @ X1753 @ X1751 ) )
      & ( ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
         != X1760 )
        | ~ ( c_not @ $true )
        | ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
         != X1760 )
        | ( c_not @ $true )
        | ( epred128_10 @ X1760 @ X1759 @ X1758 @ X1755 @ X1757 @ X1756 @ X1754 @ X1752 @ X1753 @ X1751 ) )
      & ( ~ ( c_not @ $false )
        | ~ ( c_not @ $true )
        | ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
         != X1760 )
        | ( c_not @ $true )
        | ( epred128_10 @ X1760 @ X1759 @ X1758 @ X1755 @ X1757 @ X1756 @ X1754 @ X1752 @ X1753 @ X1751 ) )
      & ( ~ ( c_and @ $false @ $false )
        | ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
         != X1760 )
        | ( c_not @ $true )
        | ( epred128_10 @ X1760 @ X1759 @ X1758 @ X1755 @ X1757 @ X1756 @ X1754 @ X1752 @ X1753 @ X1751 ) )
      & ( ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
         != X1760 )
        | ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
          = X1760 )
        | ( c_not @ $false )
        | ( c_not @ $true )
        | ( epred128_10 @ X1760 @ X1759 @ X1758 @ X1755 @ X1757 @ X1756 @ X1754 @ X1752 @ X1753 @ X1751 ) )
      & ( ~ ( c_not @ $false )
        | ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
          = X1760 )
        | ( c_not @ $false )
        | ( c_not @ $true )
        | ( epred128_10 @ X1760 @ X1759 @ X1758 @ X1755 @ X1757 @ X1756 @ X1754 @ X1752 @ X1753 @ X1751 ) )
      & ( ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
         != X1760 )
        | ~ ( c_not @ $true )
        | ( c_not @ $false )
        | ( c_not @ $true )
        | ( epred128_10 @ X1760 @ X1759 @ X1758 @ X1755 @ X1757 @ X1756 @ X1754 @ X1752 @ X1753 @ X1751 ) )
      & ( ~ ( c_not @ $false )
        | ~ ( c_not @ $true )
        | ( c_not @ $false )
        | ( c_not @ $true )
        | ( epred128_10 @ X1760 @ X1759 @ X1758 @ X1755 @ X1757 @ X1756 @ X1754 @ X1752 @ X1753 @ X1751 ) )
      & ( ~ ( c_and @ $false @ $false )
        | ( c_not @ $false )
        | ( c_not @ $true )
        | ( epred128_10 @ X1760 @ X1759 @ X1758 @ X1755 @ X1757 @ X1756 @ X1754 @ X1752 @ X1753 @ X1751 ) )
      & ( ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
         != X1760 )
        | ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
          = X1760 )
        | ~ ( c_and @ $false @ $true )
        | ( epred128_10 @ X1760 @ X1759 @ X1758 @ X1755 @ X1757 @ X1756 @ X1754 @ X1752 @ X1753 @ X1751 ) )
      & ( ~ ( c_not @ $false )
        | ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
          = X1760 )
        | ~ ( c_and @ $false @ $true )
        | ( epred128_10 @ X1760 @ X1759 @ X1758 @ X1755 @ X1757 @ X1756 @ X1754 @ X1752 @ X1753 @ X1751 ) )
      & ( ( ( X1759 @ X1755 @ ( X1756 @ ( X1757 @ X1760 @ X1751 ) @ ( X1758 @ X1752 @ X1753 @ X1751 ) ) @ X1754 )
         != X1760 )
        | ~ ( c_not @ $true )
        | ~ ( c_and @ $false @ $true )
        | ( epred128_10 @ X1760 @ X1759 @ X1758 @ X1755 @ X1757 @ X1756 @ X1754 @ X1752 @ X1753 @ X1751 ) )
      & ( ~ ( c_not @ $false )
        | ~ ( c_not @ $true )
        | ~ ( c_and @ $false @ $true )
        | ( epred128_10 @ X1760 @ X1759 @ X1758 @ X1755 @ X1757 @ X1756 @ X1754 @ X1752 @ X1753 @ X1751 ) )
      & ( ~ ( c_and @ $false @ $false )
        | ~ ( c_and @ $false @ $true )
        | ( epred128_10 @ X1760 @ X1759 @ X1758 @ X1755 @ X1757 @ X1756 @ X1754 @ X1752 @ X1753 @ X1751 ) ) ),
    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_20,plain,
    ! [X492: $o,X493: $o,X494: $o,X495: $o,X496: $o] :
      ( ( X492
        | X494
        | ~ ( c_and @ X492 @ X493 ) )
      & ( X493
        | X494
        | ~ ( c_and @ X492 @ X493 ) )
      & ( ~ X494
        | X494
        | ~ ( c_and @ X492 @ X493 ) )
      & ( ~ X495
        | ~ X496
        | ( epred148_2 @ X495 @ X496 )
        | ( c_and @ X495 @ X496 ) )
      & ( ~ ( epred148_2 @ X495 @ X496 )
        | ( c_and @ X495 @ X496 ) ) ),
    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_14])])])])])])]) ).

thf(c_0_21,plain,
    ( ~ ( c_not @ ~ $true )
    | ~ ( c_not @ $true ) ),
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_15])])]) ).

thf(c_0_22,plain,
    c_not @ ~ $true,
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_16])])]) ).

thf(c_0_23,plain,
    ! [X2036: $i] :
      ( ( esk219_0 @ X2036 )
      = c_ordsucc ),
    inference(variable_rename,[status(thm)],]) ).

thf(c_0_24,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,X208: $i,X209: $i] :
              ( ( ( epred144_8 @ X206 @ X207 @ X208 @ X209 @ X204 @ X205 @ X202 @ X203 )
                & ( epred146_8 @ X206 @ X207 @ X208 @ X209 @ X204 @ X205 @ X202 @ X203 ) )
             => ( X83 = X209 ) )
        | ( 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,X208: $i,X209: $i] :
            ( ( ( epred144_8 @ X206 @ X207 @ X208 @ X209 @ X204 @ X205 @ X202 @ X203 )
              & ( epred146_8 @ X206 @ X207 @ X208 @ X209 @ X204 @ X205 @ X202 @ X203 ) )
           => ( X83 = X209 ) )
        | ( c_not @ $false ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(assume_negation,[status(cth)],[conj])]),c_0_12]),c_0_10]),c_0_12]),c_0_10]) ).

thf(c_0_25,plain,
    ! [X1940: $i > $i > $i,X1941: $i > $o,X1942: $i > $o,X1943: $i > $i,X1944: $i,X1945: $i,X1946: $i,X1947: $i,X1948: $i,X1949: $i > $i > $i,X1950: $i > $o,X1951: $i > $o,X1952: $i > $i,X1953: $i,X1954: $i,X1955: $i,X1956: $i] :
      ( ( ~ ( X1942 @ ( X1943 @ ( X1943 @ ( X1940 @ X1946 @ X1947 ) ) ) )
        | ~ ( c_not @ $true )
        | ( c_and @ $false @ $true )
        | ( ( X1943 @ X1944 )
         != X1948 )
        | ~ ( epred145_7 @ X1948 @ X1946 @ X1944 @ X1945 @ X1942 @ X1947 @ X1941 )
        | ( X1946 = X1946 )
        | ~ ( epred146_8 @ X1947 @ X1946 @ X1945 @ X1944 @ X1942 @ X1943 @ X1940 @ X1941 ) )
      & ( ( X1942 @ ( X1943 @ ( X1943 @ ( X1940 @ X1946 @ X1947 ) ) ) )
        | ~ ( c_not @ $false )
        | ( c_and @ $false @ $true )
        | ( ( X1943 @ X1944 )
         != X1948 )
        | ~ ( epred145_7 @ X1948 @ X1946 @ X1944 @ X1945 @ X1942 @ X1947 @ X1941 )
        | ( X1946 = X1946 )
        | ~ ( epred146_8 @ X1947 @ X1946 @ X1945 @ X1944 @ X1942 @ X1943 @ X1940 @ X1941 ) )
      & ( ~ ( X1942 @ ( X1943 @ ( X1943 @ ( X1940 @ X1946 @ X1947 ) ) ) )
        | ( c_not @ $true )
        | ( c_and @ $false @ $false )
        | ( ( X1943 @ X1944 )
         != X1948 )
        | ~ ( epred145_7 @ X1948 @ X1946 @ X1944 @ X1945 @ X1942 @ X1947 @ X1941 )
        | ( X1946 = X1946 )
        | ~ ( epred146_8 @ X1947 @ X1946 @ X1945 @ X1944 @ X1942 @ X1943 @ X1940 @ X1941 ) )
      & ( ( X1942 @ ( X1943 @ ( X1943 @ ( X1940 @ X1946 @ X1947 ) ) ) )
        | ( c_not @ $false )
        | ( c_and @ $false @ $false )
        | ( ( X1943 @ X1944 )
         != X1948 )
        | ~ ( epred145_7 @ X1948 @ X1946 @ X1944 @ X1945 @ X1942 @ X1947 @ X1941 )
        | ( X1946 = X1946 )
        | ~ ( epred146_8 @ X1947 @ X1946 @ X1945 @ X1944 @ X1942 @ X1943 @ X1940 @ X1941 ) )
      & ( ( ( X1952 @ X1953 )
          = ( esk215_8 @ X1949 @ X1950 @ X1951 @ X1952 @ X1953 @ X1954 @ X1955 @ X1956 ) )
        | ( epred146_8 @ X1956 @ X1955 @ X1954 @ X1953 @ X1951 @ X1952 @ X1949 @ X1950 ) )
      & ( ( epred145_7 @ ( esk215_8 @ X1949 @ X1950 @ X1951 @ X1952 @ X1953 @ X1954 @ X1955 @ X1956 ) @ X1955 @ X1953 @ X1954 @ X1951 @ X1956 @ X1950 )
        | ( epred146_8 @ X1956 @ X1955 @ X1954 @ X1953 @ X1951 @ X1952 @ X1949 @ X1950 ) )
      & ( ( X1955 != X1955 )
        | ( epred146_8 @ X1956 @ X1955 @ X1954 @ X1953 @ X1951 @ X1952 @ X1949 @ X1950 ) )
      & ( ~ ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ~ ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ( epred146_8 @ X1956 @ X1955 @ X1954 @ X1953 @ X1951 @ X1952 @ X1949 @ X1950 ) )
      & ( ~ ( c_not @ $false )
        | ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ~ ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ( epred146_8 @ X1956 @ X1955 @ X1954 @ X1953 @ X1951 @ X1952 @ X1949 @ X1950 ) )
      & ( ~ ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ~ ( c_not @ $true )
        | ~ ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ( epred146_8 @ X1956 @ X1955 @ X1954 @ X1953 @ X1951 @ X1952 @ X1949 @ X1950 ) )
      & ( ~ ( c_not @ $false )
        | ~ ( c_not @ $true )
        | ~ ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ( epred146_8 @ X1956 @ X1955 @ X1954 @ X1953 @ X1951 @ X1952 @ X1949 @ X1950 ) )
      & ( ~ ( c_and @ $false @ $false )
        | ~ ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ( epred146_8 @ X1956 @ X1955 @ X1954 @ X1953 @ X1951 @ X1952 @ X1949 @ X1950 ) )
      & ( ~ ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ( c_not @ $false )
        | ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ( epred146_8 @ X1956 @ X1955 @ X1954 @ X1953 @ X1951 @ X1952 @ X1949 @ X1950 ) )
      & ( ~ ( c_not @ $false )
        | ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ( c_not @ $false )
        | ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ( epred146_8 @ X1956 @ X1955 @ X1954 @ X1953 @ X1951 @ X1952 @ X1949 @ X1950 ) )
      & ( ~ ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ~ ( c_not @ $true )
        | ( c_not @ $false )
        | ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ( epred146_8 @ X1956 @ X1955 @ X1954 @ X1953 @ X1951 @ X1952 @ X1949 @ X1950 ) )
      & ( ~ ( c_not @ $false )
        | ~ ( c_not @ $true )
        | ( c_not @ $false )
        | ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ( epred146_8 @ X1956 @ X1955 @ X1954 @ X1953 @ X1951 @ X1952 @ X1949 @ X1950 ) )
      & ( ~ ( c_and @ $false @ $false )
        | ( c_not @ $false )
        | ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ( epred146_8 @ X1956 @ X1955 @ X1954 @ X1953 @ X1951 @ X1952 @ X1949 @ X1950 ) )
      & ( ~ ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ~ ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ( c_not @ $true )
        | ( epred146_8 @ X1956 @ X1955 @ X1954 @ X1953 @ X1951 @ X1952 @ X1949 @ X1950 ) )
      & ( ~ ( c_not @ $false )
        | ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ~ ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ( c_not @ $true )
        | ( epred146_8 @ X1956 @ X1955 @ X1954 @ X1953 @ X1951 @ X1952 @ X1949 @ X1950 ) )
      & ( ~ ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ~ ( c_not @ $true )
        | ~ ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ( c_not @ $true )
        | ( epred146_8 @ X1956 @ X1955 @ X1954 @ X1953 @ X1951 @ X1952 @ X1949 @ X1950 ) )
      & ( ~ ( c_not @ $false )
        | ~ ( c_not @ $true )
        | ~ ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ( c_not @ $true )
        | ( epred146_8 @ X1956 @ X1955 @ X1954 @ X1953 @ X1951 @ X1952 @ X1949 @ X1950 ) )
      & ( ~ ( c_and @ $false @ $false )
        | ~ ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ( c_not @ $true )
        | ( epred146_8 @ X1956 @ X1955 @ X1954 @ X1953 @ X1951 @ X1952 @ X1949 @ X1950 ) )
      & ( ~ ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ( c_not @ $false )
        | ( c_not @ $true )
        | ( epred146_8 @ X1956 @ X1955 @ X1954 @ X1953 @ X1951 @ X1952 @ X1949 @ X1950 ) )
      & ( ~ ( c_not @ $false )
        | ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ( c_not @ $false )
        | ( c_not @ $true )
        | ( epred146_8 @ X1956 @ X1955 @ X1954 @ X1953 @ X1951 @ X1952 @ X1949 @ X1950 ) )
      & ( ~ ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ~ ( c_not @ $true )
        | ( c_not @ $false )
        | ( c_not @ $true )
        | ( epred146_8 @ X1956 @ X1955 @ X1954 @ X1953 @ X1951 @ X1952 @ X1949 @ X1950 ) )
      & ( ~ ( c_not @ $false )
        | ~ ( c_not @ $true )
        | ( c_not @ $false )
        | ( c_not @ $true )
        | ( epred146_8 @ X1956 @ X1955 @ X1954 @ X1953 @ X1951 @ X1952 @ X1949 @ X1950 ) )
      & ( ~ ( c_and @ $false @ $false )
        | ( c_not @ $false )
        | ( c_not @ $true )
        | ( epred146_8 @ X1956 @ X1955 @ X1954 @ X1953 @ X1951 @ X1952 @ X1949 @ X1950 ) )
      & ( ~ ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ~ ( c_and @ $false @ $true )
        | ( epred146_8 @ X1956 @ X1955 @ X1954 @ X1953 @ X1951 @ X1952 @ X1949 @ X1950 ) )
      & ( ~ ( c_not @ $false )
        | ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ~ ( c_and @ $false @ $true )
        | ( epred146_8 @ X1956 @ X1955 @ X1954 @ X1953 @ X1951 @ X1952 @ X1949 @ X1950 ) )
      & ( ~ ( X1951 @ ( X1952 @ ( X1952 @ ( X1949 @ X1955 @ X1956 ) ) ) )
        | ~ ( c_not @ $true )
        | ~ ( c_and @ $false @ $true )
        | ( epred146_8 @ X1956 @ X1955 @ X1954 @ X1953 @ X1951 @ X1952 @ X1949 @ X1950 ) )
      & ( ~ ( c_not @ $false )
        | ~ ( c_not @ $true )
        | ~ ( c_and @ $false @ $true )
        | ( epred146_8 @ X1956 @ X1955 @ X1954 @ X1953 @ X1951 @ X1952 @ X1949 @ X1950 ) )
      & ( ~ ( c_and @ $false @ $false )
        | ~ ( c_and @ $false @ $true )
        | ( epred146_8 @ X1956 @ X1955 @ X1954 @ X1953 @ X1951 @ X1952 @ X1949 @ X1950 ) ) ),
    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)],[inference(fof_simplification,[status(thm)],[c_0_17])])])])])])])]) ).

thf(c_0_26,plain,
    ! [X1915: $i > $i > $i,X1916: $i > $o,X1917: $i > $o,X1918: $i > $i,X1919: $i,X1920: $i,X1921: $i,X1922: $i,X1924: $i > $i > $i,X1925: $i > $o,X1926: $i > $o,X1927: $i > $i,X1928: $i,X1929: $i,X1930: $i,X1931: $i,X1932: $i] :
      ( ( ~ ( X1917 @ ( X1918 @ ( X1918 @ ( X1915 @ X1921 @ X1922 ) ) ) )
        | ~ ( c_not @ $true )
        | ( c_and @ $true @ $true )
        | ( ( X1918 @ X1919 )
          = ( esk214_8 @ X1915 @ X1916 @ X1917 @ X1918 @ X1919 @ X1920 @ X1921 @ X1922 ) )
        | ~ ( epred144_8 @ X1922 @ X1921 @ X1920 @ X1919 @ X1917 @ X1918 @ X1915 @ X1916 ) )
      & ( ( X1917 @ ( X1918 @ ( X1918 @ ( X1915 @ X1921 @ X1922 ) ) ) )
        | ~ ( c_not @ $false )
        | ( c_and @ $true @ $true )
        | ( ( X1918 @ X1919 )
          = ( esk214_8 @ X1915 @ X1916 @ X1917 @ X1918 @ X1919 @ X1920 @ X1921 @ X1922 ) )
        | ~ ( epred144_8 @ X1922 @ X1921 @ X1920 @ X1919 @ X1917 @ X1918 @ X1915 @ X1916 ) )
      & ( ~ ( X1917 @ ( X1918 @ ( X1918 @ ( X1915 @ X1921 @ X1922 ) ) ) )
        | ( c_not @ $true )
        | ( c_and @ $true @ $false )
        | ( ( X1918 @ X1919 )
          = ( esk214_8 @ X1915 @ X1916 @ X1917 @ X1918 @ X1919 @ X1920 @ X1921 @ X1922 ) )
        | ~ ( epred144_8 @ X1922 @ X1921 @ X1920 @ X1919 @ X1917 @ X1918 @ X1915 @ X1916 ) )
      & ( ( X1917 @ ( X1918 @ ( X1918 @ ( X1915 @ X1921 @ X1922 ) ) ) )
        | ( c_not @ $false )
        | ( c_and @ $true @ $false )
        | ( ( X1918 @ X1919 )
          = ( esk214_8 @ X1915 @ X1916 @ X1917 @ X1918 @ X1919 @ X1920 @ X1921 @ X1922 ) )
        | ~ ( epred144_8 @ X1922 @ X1921 @ X1920 @ X1919 @ X1917 @ X1918 @ X1915 @ X1916 ) )
      & ( ~ ( X1917 @ ( X1918 @ ( X1918 @ ( X1915 @ X1921 @ X1922 ) ) ) )
        | ~ ( c_not @ $true )
        | ( c_and @ $true @ $true )
        | ( epred145_7 @ ( esk214_8 @ X1915 @ X1916 @ X1917 @ X1918 @ X1919 @ X1920 @ X1921 @ X1922 ) @ X1921 @ X1919 @ X1920 @ X1917 @ X1922 @ X1916 )
        | ~ ( epred144_8 @ X1922 @ X1921 @ X1920 @ X1919 @ X1917 @ X1918 @ X1915 @ X1916 ) )
      & ( ( X1917 @ ( X1918 @ ( X1918 @ ( X1915 @ X1921 @ X1922 ) ) ) )
        | ~ ( c_not @ $false )
        | ( c_and @ $true @ $true )
        | ( epred145_7 @ ( esk214_8 @ X1915 @ X1916 @ X1917 @ X1918 @ X1919 @ X1920 @ X1921 @ X1922 ) @ X1921 @ X1919 @ X1920 @ X1917 @ X1922 @ X1916 )
        | ~ ( epred144_8 @ X1922 @ X1921 @ X1920 @ X1919 @ X1917 @ X1918 @ X1915 @ X1916 ) )
      & ( ~ ( X1917 @ ( X1918 @ ( X1918 @ ( X1915 @ X1921 @ X1922 ) ) ) )
        | ( c_not @ $true )
        | ( c_and @ $true @ $false )
        | ( epred145_7 @ ( esk214_8 @ X1915 @ X1916 @ X1917 @ X1918 @ X1919 @ X1920 @ X1921 @ X1922 ) @ X1921 @ X1919 @ X1920 @ X1917 @ X1922 @ X1916 )
        | ~ ( epred144_8 @ X1922 @ X1921 @ X1920 @ X1919 @ X1917 @ X1918 @ X1915 @ X1916 ) )
      & ( ( X1917 @ ( X1918 @ ( X1918 @ ( X1915 @ X1921 @ X1922 ) ) ) )
        | ( c_not @ $false )
        | ( c_and @ $true @ $false )
        | ( epred145_7 @ ( esk214_8 @ X1915 @ X1916 @ X1917 @ X1918 @ X1919 @ X1920 @ X1921 @ X1922 ) @ X1921 @ X1919 @ X1920 @ X1917 @ X1922 @ X1916 )
        | ~ ( epred144_8 @ X1922 @ X1921 @ X1920 @ X1919 @ X1917 @ X1918 @ X1915 @ X1916 ) )
      & ( ~ ( X1917 @ ( X1918 @ ( X1918 @ ( X1915 @ X1921 @ X1922 ) ) ) )
        | ~ ( c_not @ $true )
        | ( c_and @ $true @ $true )
        | ( X1921 != X1921 )
        | ~ ( epred144_8 @ X1922 @ X1921 @ X1920 @ X1919 @ X1917 @ X1918 @ X1915 @ X1916 ) )
      & ( ( X1917 @ ( X1918 @ ( X1918 @ ( X1915 @ X1921 @ X1922 ) ) ) )
        | ~ ( c_not @ $false )
        | ( c_and @ $true @ $true )
        | ( X1921 != X1921 )
        | ~ ( epred144_8 @ X1922 @ X1921 @ X1920 @ X1919 @ X1917 @ X1918 @ X1915 @ X1916 ) )
      & ( ~ ( X1917 @ ( X1918 @ ( X1918 @ ( X1915 @ X1921 @ X1922 ) ) ) )
        | ( c_not @ $true )
        | ( c_and @ $true @ $false )
        | ( X1921 != X1921 )
        | ~ ( epred144_8 @ X1922 @ X1921 @ X1920 @ X1919 @ X1917 @ X1918 @ X1915 @ X1916 ) )
      & ( ( X1917 @ ( X1918 @ ( X1918 @ ( X1915 @ X1921 @ X1922 ) ) ) )
        | ( c_not @ $false )
        | ( c_and @ $true @ $false )
        | ( X1921 != X1921 )
        | ~ ( epred144_8 @ X1922 @ X1921 @ X1920 @ X1919 @ X1917 @ X1918 @ X1915 @ X1916 ) )
      & ( ( ( X1927 @ X1928 )
         != X1932 )
        | ~ ( epred145_7 @ X1932 @ X1930 @ X1928 @ X1929 @ X1926 @ X1931 @ X1925 )
        | ( X1930 = X1930 )
        | ( epred144_8 @ X1931 @ X1930 @ X1929 @ X1928 @ X1926 @ X1927 @ X1924 @ X1925 ) )
      & ( ~ ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ~ ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ( epred144_8 @ X1931 @ X1930 @ X1929 @ X1928 @ X1926 @ X1927 @ X1924 @ X1925 ) )
      & ( ~ ( c_not @ $false )
        | ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ~ ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ( epred144_8 @ X1931 @ X1930 @ X1929 @ X1928 @ X1926 @ X1927 @ X1924 @ X1925 ) )
      & ( ~ ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ~ ( c_not @ $true )
        | ~ ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ( epred144_8 @ X1931 @ X1930 @ X1929 @ X1928 @ X1926 @ X1927 @ X1924 @ X1925 ) )
      & ( ~ ( c_not @ $false )
        | ~ ( c_not @ $true )
        | ~ ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ( epred144_8 @ X1931 @ X1930 @ X1929 @ X1928 @ X1926 @ X1927 @ X1924 @ X1925 ) )
      & ( ~ ( c_and @ $true @ $false )
        | ~ ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ( epred144_8 @ X1931 @ X1930 @ X1929 @ X1928 @ X1926 @ X1927 @ X1924 @ X1925 ) )
      & ( ~ ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ( c_not @ $false )
        | ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ( epred144_8 @ X1931 @ X1930 @ X1929 @ X1928 @ X1926 @ X1927 @ X1924 @ X1925 ) )
      & ( ~ ( c_not @ $false )
        | ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ( c_not @ $false )
        | ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ( epred144_8 @ X1931 @ X1930 @ X1929 @ X1928 @ X1926 @ X1927 @ X1924 @ X1925 ) )
      & ( ~ ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ~ ( c_not @ $true )
        | ( c_not @ $false )
        | ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ( epred144_8 @ X1931 @ X1930 @ X1929 @ X1928 @ X1926 @ X1927 @ X1924 @ X1925 ) )
      & ( ~ ( c_not @ $false )
        | ~ ( c_not @ $true )
        | ( c_not @ $false )
        | ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ( epred144_8 @ X1931 @ X1930 @ X1929 @ X1928 @ X1926 @ X1927 @ X1924 @ X1925 ) )
      & ( ~ ( c_and @ $true @ $false )
        | ( c_not @ $false )
        | ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ( epred144_8 @ X1931 @ X1930 @ X1929 @ X1928 @ X1926 @ X1927 @ X1924 @ X1925 ) )
      & ( ~ ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ~ ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ( c_not @ $true )
        | ( epred144_8 @ X1931 @ X1930 @ X1929 @ X1928 @ X1926 @ X1927 @ X1924 @ X1925 ) )
      & ( ~ ( c_not @ $false )
        | ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ~ ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ( c_not @ $true )
        | ( epred144_8 @ X1931 @ X1930 @ X1929 @ X1928 @ X1926 @ X1927 @ X1924 @ X1925 ) )
      & ( ~ ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ~ ( c_not @ $true )
        | ~ ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ( c_not @ $true )
        | ( epred144_8 @ X1931 @ X1930 @ X1929 @ X1928 @ X1926 @ X1927 @ X1924 @ X1925 ) )
      & ( ~ ( c_not @ $false )
        | ~ ( c_not @ $true )
        | ~ ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ( c_not @ $true )
        | ( epred144_8 @ X1931 @ X1930 @ X1929 @ X1928 @ X1926 @ X1927 @ X1924 @ X1925 ) )
      & ( ~ ( c_and @ $true @ $false )
        | ~ ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ( c_not @ $true )
        | ( epred144_8 @ X1931 @ X1930 @ X1929 @ X1928 @ X1926 @ X1927 @ X1924 @ X1925 ) )
      & ( ~ ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ( c_not @ $false )
        | ( c_not @ $true )
        | ( epred144_8 @ X1931 @ X1930 @ X1929 @ X1928 @ X1926 @ X1927 @ X1924 @ X1925 ) )
      & ( ~ ( c_not @ $false )
        | ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ( c_not @ $false )
        | ( c_not @ $true )
        | ( epred144_8 @ X1931 @ X1930 @ X1929 @ X1928 @ X1926 @ X1927 @ X1924 @ X1925 ) )
      & ( ~ ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ~ ( c_not @ $true )
        | ( c_not @ $false )
        | ( c_not @ $true )
        | ( epred144_8 @ X1931 @ X1930 @ X1929 @ X1928 @ X1926 @ X1927 @ X1924 @ X1925 ) )
      & ( ~ ( c_not @ $false )
        | ~ ( c_not @ $true )
        | ( c_not @ $false )
        | ( c_not @ $true )
        | ( epred144_8 @ X1931 @ X1930 @ X1929 @ X1928 @ X1926 @ X1927 @ X1924 @ X1925 ) )
      & ( ~ ( c_and @ $true @ $false )
        | ( c_not @ $false )
        | ( c_not @ $true )
        | ( epred144_8 @ X1931 @ X1930 @ X1929 @ X1928 @ X1926 @ X1927 @ X1924 @ X1925 ) )
      & ( ~ ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ~ ( c_and @ $true @ $true )
        | ( epred144_8 @ X1931 @ X1930 @ X1929 @ X1928 @ X1926 @ X1927 @ X1924 @ X1925 ) )
      & ( ~ ( c_not @ $false )
        | ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ~ ( c_and @ $true @ $true )
        | ( epred144_8 @ X1931 @ X1930 @ X1929 @ X1928 @ X1926 @ X1927 @ X1924 @ X1925 ) )
      & ( ~ ( X1926 @ ( X1927 @ ( X1927 @ ( X1924 @ X1930 @ X1931 ) ) ) )
        | ~ ( c_not @ $true )
        | ~ ( c_and @ $true @ $true )
        | ( epred144_8 @ X1931 @ X1930 @ X1929 @ X1928 @ X1926 @ X1927 @ X1924 @ X1925 ) )
      & ( ~ ( c_not @ $false )
        | ~ ( c_not @ $true )
        | ~ ( c_and @ $true @ $true )
        | ( epred144_8 @ X1931 @ X1930 @ X1929 @ X1928 @ X1926 @ X1927 @ X1924 @ X1925 ) )
      & ( ~ ( c_and @ $true @ $false )
        | ~ ( c_and @ $true @ $true )
        | ( epred144_8 @ X1931 @ X1930 @ X1929 @ X1928 @ X1926 @ X1927 @ X1924 @ X1925 ) ) ),
    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)],[inference(fof_simplification,[status(thm)],[c_0_18])])])])])])])]) ).

thf(c_0_27,plain,
    ! [X2: $i,X6: $i,X166: $i > $i > $i > $i,X164: $i > $i > $i > $i,X123: $i > $i > $i,X89: $i > $i > $i,X10: $i,X9: $i,X8: $i,X7: $i] :
      ( ( c_not @ $true )
      | ( c_and @ ~ $true @ ~ $true )
      | ( ( X164 @ X2 @ ( X89 @ ( X123 @ X6 @ X7 ) @ ( X166 @ X8 @ X9 @ X7 ) ) @ X10 )
       != X6 )
      | ~ ( epred128_10 @ X6 @ X164 @ X166 @ X2 @ X123 @ X89 @ X10 @ X8 @ X9 @ X7 ) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

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_20])])]) ).

thf(c_0_29,plain,
    ~ ( c_not @ $true ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]) ).

thf(c_0_30,plain,
    ! [X2074: $i,X2075: $i > $i > $o] :
      ( ( ~ ( epred166_1 @ X2075 @ X2074 )
        | ( X2075 @ ( c_ap @ X2074 @ c_Empty ) @ ( c_ap @ X2074 @ ( c_ordsucc @ c_Empty ) ) ) )
      & ( ~ ( X2075 @ ( c_ap @ X2074 @ c_Empty ) @ ( c_ap @ X2074 @ ( c_ordsucc @ c_Empty ) ) )
        | ( epred166_1 @ X2075 @ X2074 ) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])]) ).

thf(c_0_31,plain,
    ! [X2: $i] :
      ( ( esk219_0 @ X2 )
      = c_ordsucc ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

thf(c_0_32,negated_conjecture,
    ! [X822: $i > $i > $i,X823: $i > $o,X824: $i > $o,X825: $i > $i,X826: $i,X827: $i,X828: $i,X829: $i,X830: $i] :
      ( ( ( epred144_8 @ esk54_0 @ esk56_0 @ esk57_0 @ esk58_0 @ epred155_0 @ esk53_0 @ esk52_0 @ epred154_0 )
        | ~ ( epred144_8 @ X826 @ X828 @ X829 @ X830 @ X824 @ X825 @ X822 @ X823 )
        | ~ ( epred146_8 @ X826 @ X828 @ X829 @ X830 @ X824 @ X825 @ X822 @ X823 )
        | ( X827 = X830 ) )
      & ( ( epred146_8 @ esk54_0 @ esk56_0 @ esk57_0 @ esk58_0 @ epred155_0 @ esk53_0 @ esk52_0 @ epred154_0 )
        | ~ ( epred144_8 @ X826 @ X828 @ X829 @ X830 @ X824 @ X825 @ X822 @ X823 )
        | ~ ( epred146_8 @ X826 @ X828 @ X829 @ X830 @ X824 @ X825 @ X822 @ X823 )
        | ( X827 = X830 ) )
      & ( ( esk55_0 != esk58_0 )
        | ~ ( epred144_8 @ X826 @ X828 @ X829 @ X830 @ X824 @ X825 @ X822 @ X823 )
        | ~ ( epred146_8 @ X826 @ X828 @ X829 @ X830 @ X824 @ X825 @ X822 @ X823 )
        | ( X827 = X830 ) )
      & ( ~ ( c_not @ $false )
        | ~ ( epred144_8 @ X826 @ X828 @ X829 @ X830 @ X824 @ X825 @ X822 @ X823 )
        | ~ ( epred146_8 @ X826 @ X828 @ X829 @ X830 @ X824 @ X825 @ X822 @ X823 )
        | ( X827 = X830 ) )
      & ( ( epred144_8 @ esk54_0 @ esk56_0 @ esk57_0 @ esk58_0 @ epred155_0 @ esk53_0 @ esk52_0 @ epred154_0 )
        | ~ ( c_not @ $true ) )
      & ( ( epred146_8 @ esk54_0 @ esk56_0 @ esk57_0 @ esk58_0 @ epred155_0 @ esk53_0 @ esk52_0 @ epred154_0 )
        | ~ ( c_not @ $true ) )
      & ( ( esk55_0 != esk58_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_24])])])])])])]) ).

thf(c_0_33,plain,
    ! [X1: $i > $o,X6: $i,X7: $i,X89: $i > $i > $i,X8: $i,X65: $i > $o,X12: $i > $i,X2: $i] :
      ( ( epred146_8 @ X6 @ X2 @ X7 @ X8 @ X1 @ X12 @ X89 @ X65 )
      | ( X2 != X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

thf(c_0_34,plain,
    ! [X6: $i,X2: $i,X1: $i > $o,X8: $i,X7: $i,X89: $i > $i > $i,X12: $i > $i,X65: $i > $o] :
      ( ( X1 @ ( X12 @ ( X12 @ ( X89 @ X2 @ X6 ) ) ) )
      | ( epred144_8 @ X6 @ X2 @ X7 @ X8 @ X1 @ X12 @ X89 @ X65 )
      | ~ ( c_not @ ~ $true )
      | ~ ( c_and @ $true @ $true ) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

thf(c_0_35,plain,
    ! [X3: $o,X4: $o] :
      ( ( c_and @ X3 @ X4 )
      | ~ ( epred148_2 @ X3 @ X4 ) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

thf(c_0_36,plain,
    ( ( epred148_2 @ $true @ $true )
    | ( c_and @ $true @ $true ) ),
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_20])])]) ).

thf(c_0_37,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_38,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_39,plain,
    ! [X2: $i,X6: $i,X166: $i > $i > $i > $i,X164: $i > $i > $i > $i,X123: $i > $i > $i,X89: $i > $i > $i,X10: $i,X9: $i,X8: $i,X7: $i] :
      ( ( ( X164 @ X2 @ ( X89 @ ( X123 @ X6 @ X7 ) @ ( X166 @ X8 @ X9 @ X7 ) ) @ X10 )
        = X6 )
      | ( c_and @ ~ $true @ $true )
      | ~ ( c_not @ ~ $true )
      | ~ ( epred128_10 @ X6 @ X164 @ X166 @ X2 @ X123 @ X89 @ X10 @ X8 @ X9 @ X7 ) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

thf(c_0_40,plain,
    ! [X5: $o] :
      ~ ( c_and @ ~ $true @ X5 ),
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_20])])]) ).

thf(c_0_41,plain,
    ! [X2: $i,X6: $i,X166: $i > $i > $i > $i,X164: $i > $i > $i > $i,X123: $i > $i > $i,X89: $i > $i > $i,X10: $i,X9: $i,X8: $i,X7: $i] :
      ( ( ( X164 @ X2 @ ( X89 @ ( X123 @ X6 @ X7 ) @ ( X166 @ X8 @ X9 @ X7 ) ) @ X10 )
       != X6 )
      | ~ ( epred128_10 @ X6 @ X164 @ X166 @ X2 @ X123 @ X89 @ X10 @ X8 @ X9 @ X7 ) ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).

thf(c_0_42,plain,
    ! [X37: $i > $i > $o,X2: $i] :
      ( ( X37 @ ( c_ap @ X2 @ c_Empty ) @ ( c_ap @ X2 @ ( c_ordsucc @ c_Empty ) ) )
      | ~ ( epred166_1 @ X37 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

thf(c_0_43,plain,
    ! [X2: $i,X6: $i] :
      ( ( esk219_0 @ X2 @ X6 )
      = ( c_ordsucc @ X6 ) ),
    inference(arg_cong,[status(thm)],[c_0_31]) ).

thf(c_0_44,negated_conjecture,
    ! [X6: $i,X2: $i,X1: $i > $o,X8: $i,X7: $i,X9: $i,X89: $i > $i > $i,X12: $i > $i,X65: $i > $o] :
      ( ( X9 = X8 )
      | ~ ( c_not @ ~ $true )
      | ~ ( epred144_8 @ X2 @ X6 @ X7 @ X8 @ X1 @ X12 @ X89 @ X65 )
      | ~ ( epred146_8 @ X2 @ X6 @ X7 @ X8 @ X1 @ X12 @ X89 @ X65 ) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

thf(c_0_45,plain,
    ! [X1: $i > $o,X6: $i,X7: $i,X2: $i,X8: $i,X89: $i > $i > $i,X12: $i > $i,X65: $i > $o] : ( epred146_8 @ X6 @ X2 @ X7 @ X8 @ X1 @ X12 @ X89 @ X65 ),
    inference(cn,[status(thm)],[c_0_33]) ).

thf(c_0_46,plain,
    ! [X1: $i > $o,X7: $i,X65: $i > $o,X12: $i > $i,X89: $i > $i > $i,X8: $i,X6: $i,X2: $i] :
      ( ( epred144_8 @ X2 @ X6 @ X7 @ X8 @ X1 @ X12 @ X89 @ X65 )
      | ( X1 @ ( X12 @ ( X12 @ ( X89 @ X6 @ X2 ) ) ) )
      | ~ ( c_and @ $true @ $true ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_22])]) ).

thf(c_0_47,plain,
    c_and @ $true @ $true,
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

thf(c_0_48,plain,
    ! [X458: $i] :
      ( ( ~ ( c_In @ X458 @ 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_37])])])])]) ).

thf(c_0_49,plain,
    ! [X250: $i,X251: $i] :
      ( ( c_Subq @ X250 @ X251 )
    <=> ! [X9: $i] :
          ( ( c_In @ X9 @ X250 )
         => ( c_In @ X9 @ X251 ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[ax17])]) ).

thf(c_0_50,plain,
    ! [X466: $i,X467: $i] :
      ( ( ~ ( c_Subq @ X467 @ X466 )
        | ( c_iff @ $true @ $true )
        | ~ ( c_In @ X467 @ ( c_Power @ X466 ) ) )
      & ( ( c_Subq @ X467 @ X466 )
        | ( c_iff @ $true @ $false )
        | ~ ( c_In @ X467 @ ( c_Power @ X466 ) ) )
      & ( ~ ( c_Subq @ X467 @ X466 )
        | ( c_iff @ $false @ $true )
        | ( c_In @ X467 @ ( c_Power @ X466 ) ) )
      & ( ( c_Subq @ X467 @ X466 )
        | ( c_iff @ $false @ $false )
        | ( c_In @ X467 @ ( c_Power @ X466 ) ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_38])])]) ).

thf(c_0_51,plain,
    ! [X454: $o,X455: $o] :
      ( ( ~ X454
        | X455
        | ~ ( c_iff @ X454 @ X455 ) )
      & ( ~ X455
        | X454
        | ~ ( c_iff @ X454 @ X455 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])])]) ).

thf(c_0_52,plain,
    ! [X2: $i,X6: $i,X7: $i,X8: $i,X9: $i,X166: $i > $i > $i > $i,X164: $i > $i > $i > $i,X123: $i > $i > $i,X89: $i > $i > $i,X10: $i] :
      ~ ( epred128_10 @ X2 @ X164 @ X166 @ X6 @ X89 @ X123 @ X7 @ X8 @ X9 @ X10 ),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_22])]),c_0_40]),c_0_41]) ).

thf(c_0_53,plain,
    ! [X37: $i > $i > $o,X2: $i] :
      ( ( X37 @ ( c_ap @ X2 @ c_Empty ) @ ( c_ap @ X2 @ ( esk219_0 @ c_Empty @ c_Empty ) ) )
      | ~ ( epred166_1 @ X37 @ X2 ) ),
    inference(rw,[status(thm)],[c_0_42,c_0_43]) ).

thf(c_0_54,negated_conjecture,
    ! [X1: $i > $o,X7: $i,X6: $i,X8: $i,X2: $i,X9: $i,X89: $i > $i > $i,X12: $i > $i,X65: $i > $o] :
      ( ( X2 = X6 )
      | ~ ( epred144_8 @ X7 @ X8 @ X9 @ X2 @ X1 @ X12 @ X89 @ X65 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_22]),c_0_45])]) ).

thf(c_0_55,plain,
    ! [X1: $i > $o,X7: $i,X65: $i > $o,X12: $i > $i,X89: $i > $i > $i,X8: $i,X6: $i,X2: $i] :
      ( ( epred144_8 @ X2 @ X6 @ X7 @ X8 @ X1 @ X12 @ X89 @ X65 )
      | ( X1 @ ( X12 @ ( X12 @ ( X89 @ X6 @ X2 ) ) ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]) ).

thf(c_0_56,plain,
    ! [X2: $i] :
      ( ( c_not @ $true )
      | ~ ( c_In @ X2 @ c_Empty ) ),
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

thf(c_0_57,plain,
    ! [X506: $i,X507: $i,X508: $i,X509: $i,X510: $i] :
      ( ( ~ ( c_Subq @ X506 @ X507 )
        | ~ ( c_In @ X508 @ X506 )
        | ( c_In @ X508 @ X507 ) )
      & ( ( c_In @ ( esk13_2 @ X509 @ X510 ) @ X509 )
        | ( c_Subq @ X509 @ X510 ) )
      & ( ~ ( c_In @ ( esk13_2 @ X509 @ X510 ) @ X510 )
        | ( c_Subq @ X509 @ X510 ) ) ),
    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_49])])])])])])]) ).

thf(c_0_58,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_50]) ).

thf(c_0_59,plain,
    ~ ( c_iff @ ~ $true @ $true ),
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_51])])]) ).

thf(c_0_60,plain,
    ! [X2: $i,X6: $i,X7: $i,X8: $i,X166: $i > $i > $i > $i,X164: $i > $i > $i > $i,X123: $i > $i > $i,X89: $i > $i > $i,X9: $i] :
      ~ ( epred166_1 @ ( epred128_10 @ X2 @ X164 @ X166 @ X6 @ X89 @ X123 @ X7 @ X8 ) @ X9 ),
    inference(spm,[status(thm)],[c_0_52,c_0_53]) ).

thf(c_0_61,negated_conjecture,
    ! [X1: $i > $o,X2: $i,X6: $i,X7: $i,X12: $i > $i,X89: $i > $i > $i,X8: $i] :
      ( ( X2 = X6 )
      | ( X1 @ ( X12 @ ( X12 @ ( X89 @ X7 @ X8 ) ) ) ) ),
    inference(spm,[status(thm)],[c_0_54,c_0_55]) ).

thf(c_0_62,plain,
    ! [X2: $i] :
      ~ ( c_In @ X2 @ c_Empty ),
    inference(sr,[status(thm)],[c_0_56,c_0_29]) ).

thf(c_0_63,plain,
    ! [X2: $i,X6: $i] :
      ( ( c_In @ ( esk13_2 @ X2 @ X6 ) @ X2 )
      | ( c_Subq @ X2 @ X6 ) ),
    inference(split_conjunct,[status(thm)],[c_0_57]) ).

thf(c_0_64,plain,
    ! [X2: $i,X6: $i] :
      ( ( c_In @ X2 @ ( c_Power @ X6 ) )
      | ~ ( c_Subq @ X2 @ X6 ) ),
    inference(sr,[status(thm)],[c_0_58,c_0_59]) ).

thf(c_0_65,plain,
    ! [X2: $i,X6: $i] : ( X2 = X6 ),
    inference(spm,[status(thm)],[c_0_60,c_0_61]) ).

thf(c_0_66,plain,
    ! [X2: $i] : ( c_Subq @ c_Empty @ X2 ),
    inference(spm,[status(thm)],[c_0_62,c_0_63]) ).

thf(c_0_67,plain,
    ! [X2: $i,X6: $i] :
      ~ ( c_Subq @ X2 @ X6 ),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65]),c_0_62]) ).

thf(c_0_68,plain,
    $false,
    inference(sr,[status(thm)],[c_0_66,c_0_67]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SYO879^1 : TPTP v8.2.0. Released v7.5.0.
% 0.12/0.13  % Command    : run_E %s %d THM
% 0.13/0.35  % Computer : n017.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Mon May 20 08:39:52 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.20/0.48  Running higher-order theorem proving
% 0.20/0.48  Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 60.26/16.83  # Version: 3.1.0-ho
% 60.26/16.83  # partial match(1): HSLMSMSSSSLCHSA
% 60.26/16.83  # Preprocessing class: HSLMSLSSSSLCHSA.
% 60.26/16.83  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 60.26/16.83  # Starting pre_casc_6 with 1500s (5) cores
% 60.26/16.83  # Starting ehoh_best7 with 300s (1) cores
% 60.26/16.83  # Starting new_bool_8 with 300s (1) cores
% 60.26/16.83  # Starting new_ho_11 with 300s (1) cores
% 60.26/16.83  # new_bool_8 with pid 8761 completed with status 8
% 60.26/16.83  # ehoh_best7 with pid 8760 completed with status 0
% 60.26/16.83  # Result found by ehoh_best7
% 60.26/16.83  # partial match(1): HSLMSMSSSSLCHSA
% 60.26/16.83  # Preprocessing class: HSLMSLSSSSLCHSA.
% 60.26/16.83  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 60.26/16.83  # Starting pre_casc_6 with 1500s (5) cores
% 60.26/16.83  # Starting ehoh_best7 with 300s (1) cores
% 60.26/16.83  # No SInE strategy applied
% 60.26/16.83  # Search class: HGHSM-SMLM33-DHSFFSBC
% 60.26/16.83  # partial match(1): HGHSM-SMLM32-DHSFFSBC
% 60.26/16.83  # Scheduled 6 strats onto 1 cores with 288 seconds (288 total)
% 60.26/16.83  # Starting new_ho_10 with 87s (1) cores
% 60.26/16.83  # new_ho_10 with pid 8795 completed with status 0
% 60.26/16.83  # Result found by new_ho_10
% 60.26/16.83  # partial match(1): HSLMSMSSSSLCHSA
% 60.26/16.83  # Preprocessing class: HSLMSLSSSSLCHSA.
% 60.26/16.83  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 60.26/16.83  # Starting pre_casc_6 with 1500s (5) cores
% 60.26/16.83  # Starting ehoh_best7 with 300s (1) cores
% 60.26/16.83  # No SInE strategy applied
% 60.26/16.83  # Search class: HGHSM-SMLM33-DHSFFSBC
% 60.26/16.83  # partial match(1): HGHSM-SMLM32-DHSFFSBC
% 60.26/16.83  # Scheduled 6 strats onto 1 cores with 288 seconds (288 total)
% 60.26/16.83  # Starting new_ho_10 with 87s (1) cores
% 60.26/16.83  # Preprocessing time       : 0.140 s
% 60.26/16.83  # Presaturation interreduction done
% 60.26/16.83  
% 60.26/16.83  # Proof found!
% 60.26/16.83  # SZS status Theorem
% 60.26/16.83  # SZS output start CNFRefutation
% See solution above
% 60.26/16.83  # Parsed axioms                        : 213
% 60.26/16.83  # Removed by relevancy pruning/SinE    : 0
% 60.26/16.83  # Initial clauses                      : 468845
% 60.26/16.83  # Removed in clause preprocessing      : 463944
% 60.26/16.83  # Initial clauses in saturation        : 4901
% 60.26/16.83  # Processed clauses                    : 8404
% 60.26/16.83  # ...of these trivial                  : 375
% 60.26/16.83  # ...subsumed                          : 4121
% 60.26/16.83  # ...remaining for further processing  : 3908
% 60.26/16.83  # Other redundant clauses eliminated   : 149
% 60.26/16.83  # Clauses deleted for lack of memory   : 0
% 60.26/16.83  # Backward-subsumed                    : 236
% 60.26/16.83  # Backward-rewritten                   : 1779
% 60.26/16.83  # Generated clauses                    : 53244
% 60.26/16.83  # ...of the previous two non-redundant : 53112
% 60.26/16.83  # ...aggressively subsumed             : 0
% 60.26/16.83  # Contextual simplify-reflections      : 314
% 60.26/16.83  # Paramodulations                      : 53077
% 60.26/16.83  # Factorizations                       : 0
% 60.26/16.83  # NegExts                              : 0
% 60.26/16.83  # Equation resolutions                 : 149
% 60.26/16.83  # Disequality decompositions           : 0
% 60.26/16.83  # Total rewrite steps                  : 11084
% 60.26/16.83  # ...of those cached                   : 7533
% 60.26/16.83  # Propositional unsat checks           : 0
% 60.26/16.83  #    Propositional check models        : 0
% 60.26/16.83  #    Propositional check unsatisfiable : 0
% 60.26/16.83  #    Propositional clauses             : 0
% 60.26/16.83  #    Propositional clauses after purity: 0
% 60.26/16.83  #    Propositional unsat core size     : 0
% 60.26/16.83  #    Propositional preprocessing time  : 0.000
% 60.26/16.83  #    Propositional encoding time       : 0.000
% 60.26/16.83  #    Propositional solver time         : 0.000
% 60.26/16.83  #    Success case prop preproc time    : 0.000
% 60.26/16.83  #    Success case prop encoding time   : 0.000
% 60.26/16.83  #    Success case prop solver time     : 0.000
% 60.26/16.83  # Current number of processed clauses  : 605
% 60.26/16.83  #    Positive orientable unit clauses  : 102
% 60.26/16.83  #    Positive unorientable unit clauses: 2
% 60.26/16.83  #    Negative unit clauses             : 83
% 60.26/16.83  #    Non-unit-clauses                  : 418
% 60.26/16.83  # Current number of unprocessed clauses: 50733
% 60.26/16.83  # ...number of literals in the above   : 218671
% 60.26/16.83  # Current number of archived formulas  : 0
% 60.26/16.83  # Current number of archived clauses   : 3241
% 60.26/16.83  # Clause-clause subsumption calls (NU) : 1974202
% 60.26/16.83  # Rec. Clause-clause subsumption calls : 646512
% 60.26/16.83  # Non-unit clause-clause subsumptions  : 2000
% 60.26/16.83  # Unit Clause-clause subsumption calls : 101894
% 60.26/16.83  # Rewrite failures with RHS unbound    : 0
% 60.26/16.83  # BW rewrite match attempts            : 7832
% 60.26/16.83  # BW rewrite match successes           : 2565
% 60.26/16.83  # Condensation attempts                : 8614
% 60.26/16.83  # Condensation successes               : 249
% 60.26/16.83  # Termbank termtop insertions          : 21216229
% 60.26/16.83  # Search garbage collected termcells   : 2012573
% 60.26/16.83  
% 60.26/16.83  # -------------------------------------------------
% 60.26/16.83  # User time                : 14.621 s
% 60.26/16.83  # System time              : 1.143 s
% 60.26/16.83  # Total time               : 15.764 s
% 60.26/16.83  # Maximum resident set size: 1255384 pages
% 60.26/16.83  
% 60.26/16.83  # -------------------------------------------------
% 60.26/16.83  # User time                : 14.712 s
% 60.26/16.83  # System time              : 1.274 s
% 60.26/16.83  # Total time               : 15.987 s
% 60.26/16.83  # Maximum resident set size: 2112 pages
% 60.26/16.83  % E---3.1 exiting
% 60.26/16.83  % E exiting
%------------------------------------------------------------------------------