TSTP Solution File: SEU820^2 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU820^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n016.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 03:30:34 EDT 2024

% Result   : Theorem 0.21s 0.51s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   32
% Syntax   : Number of formulae    :   64 (  18 unt;  22 typ;   0 def)
%            Number of atoms       :  431 (  53 equ;   0 cnn)
%            Maximal formula atoms :   97 (  10 avg)
%            Number of connectives : 1098 ( 106   ~; 188   |;  90   &; 619   @)
%                                         (   4 <=>;  91  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   36 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   19 (  19   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   24 (  22 usr;  14 con; 0-2 aty)
%            Number of variables   :  107 (  12   ^  89   !;   6   ?; 107   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_22,type,
    in: $i > $i > $o ).

thf(decl_23,type,
    emptyset: $i ).

thf(decl_24,type,
    powerset: $i > $i ).

thf(decl_25,type,
    nonempty: $i > $o ).

thf(decl_26,type,
    vacuousDall: $o ).

thf(decl_27,type,
    subset: $i > $i > $o ).

thf(decl_28,type,
    subsetemptysetimpeq: $o ).

thf(decl_29,type,
    powersetE1: $o ).

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

thf(decl_31,type,
    stricttotalorderedByIn: $i > $o ).

thf(decl_32,type,
    wellorderedByIn: $i > $o ).

thf(decl_33,type,
    ordinal: $i > $o ).

thf(decl_34,type,
    epred1_0: $o ).

thf(decl_35,type,
    esk1_0: $i ).

thf(decl_36,type,
    esk2_0: $i ).

thf(decl_37,type,
    esk3_0: $i ).

thf(decl_38,type,
    esk4_1: $i > $i ).

thf(decl_39,type,
    esk5_0: $i ).

thf(decl_40,type,
    esk6_0: $i ).

thf(decl_41,type,
    esk7_0: $i ).

thf(decl_42,type,
    esk8_0: $i ).

thf(decl_43,type,
    esk9_0: $i ).

thf(wellorderedByIn,axiom,
    ( wellorderedByIn
    = ( ^ [X3: $i] :
          ( ( stricttotalorderedByIn @ X3 )
          & ! [X5: $i] :
              ( ( in @ X5 @ ( powerset @ X3 ) )
             => ( ( nonempty @ X5 )
               => ? [X1: $i] :
                    ( ( in @ X1 @ X5 )
                    & ! [X6: $i] :
                        ( ( in @ X6 @ X5 )
                       => ( ( X1 = X6 )
                          | ( in @ X1 @ X6 ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderedByIn) ).

thf(nonempty,axiom,
    ( nonempty
    = ( ^ [X1: $i] : ( X1 != emptyset ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).

thf(stricttotalorderedByIn,axiom,
    ( stricttotalorderedByIn
    = ( ^ [X3: $i] :
          ( ! [X1: $i] :
              ( ( in @ X1 @ X3 )
             => ! [X5: $i] :
                  ( ( in @ X5 @ X3 )
                 => ! [X6: $i] :
                      ( ( in @ X6 @ X3 )
                     => ( ( ( in @ X1 @ X5 )
                          & ( in @ X5 @ X6 ) )
                       => ( in @ X1 @ X6 ) ) ) ) )
          & ! [X5: $i] :
              ( ( in @ X5 @ X3 )
             => ! [X6: $i] :
                  ( ( in @ X6 @ X3 )
                 => ( ( X5 = X6 )
                    | ( in @ X5 @ X6 )
                    | ( in @ X6 @ X5 ) ) ) )
          & ! [X5: $i] :
              ( ( in @ X5 @ X3 )
             => ~ ( in @ X5 @ X5 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricttotalorderedByIn) ).

thf(ordinal,axiom,
    ( ordinal
    = ( ^ [X1: $i] :
          ( ( transitiveset @ X1 )
          & ( wellorderedByIn @ X1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal) ).

thf(transitiveset,axiom,
    ( transitiveset
    = ( ^ [X3: $i] :
        ! [X5: $i] :
          ( ( in @ X5 @ X3 )
         => ( subset @ X5 @ X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitiveset) ).

thf(emptysetOrdinal,conjecture,
    ( vacuousDall
   => ( subsetemptysetimpeq
     => ( powersetE1
       => ( ordinal @ emptyset ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetOrdinal) ).

thf(powersetE1,axiom,
    ( powersetE1
  <=> ! [X3: $i,X4: $i] :
        ( ( in @ X4 @ ( powerset @ X3 ) )
       => ( subset @ X4 @ X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).

thf(subsetemptysetimpeq,axiom,
    ( subsetemptysetimpeq
  <=> ! [X3: $i] :
        ( ( subset @ X3 @ emptyset )
       => ( X3 = emptyset ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).

thf(vacuousDall,axiom,
    ( vacuousDall
  <=> ! [X2: $i > $o,X1: $i] :
        ( ( in @ X1 @ emptyset )
       => ( X2 @ X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).

thf(c_0_9,plain,
    ( wellorderedByIn
    = ( ^ [Z0: $i] :
          ( ! [X12: $i] :
              ( ( in @ X12 @ Z0 )
             => ! [X13: $i] :
                  ( ( in @ X13 @ Z0 )
                 => ! [X14: $i] :
                      ( ( in @ X14 @ Z0 )
                     => ( ( ( in @ X12 @ X13 )
                          & ( in @ X13 @ X14 ) )
                       => ( in @ X12 @ X14 ) ) ) ) )
          & ! [X15: $i] :
              ( ( in @ X15 @ Z0 )
             => ! [X16: $i] :
                  ( ( in @ X16 @ Z0 )
                 => ( ( X15 = X16 )
                    | ( in @ X15 @ X16 )
                    | ( in @ X16 @ X15 ) ) ) )
          & ! [X17: $i] :
              ( ( in @ X17 @ Z0 )
             => ~ ( in @ X17 @ X17 ) )
          & ! [X5: $i] :
              ( ( in @ X5 @ ( powerset @ Z0 ) )
             => ( ( X5 != emptyset )
               => ? [X1: $i] :
                    ( ( in @ X1 @ X5 )
                    & ! [X6: $i] :
                        ( ( in @ X6 @ X5 )
                       => ( ( X1 = X6 )
                          | ( in @ X1 @ X6 ) ) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[wellorderedByIn]) ).

thf(c_0_10,plain,
    ( nonempty
    = ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
    inference(fof_simplification,[status(thm)],[nonempty]) ).

thf(c_0_11,plain,
    ( stricttotalorderedByIn
    = ( ^ [Z0: $i] :
          ( ! [X1: $i] :
              ( ( in @ X1 @ Z0 )
             => ! [X5: $i] :
                  ( ( in @ X5 @ Z0 )
                 => ! [X6: $i] :
                      ( ( in @ X6 @ Z0 )
                     => ( ( ( in @ X1 @ X5 )
                          & ( in @ X5 @ X6 ) )
                       => ( in @ X1 @ X6 ) ) ) ) )
          & ! [X5: $i] :
              ( ( in @ X5 @ Z0 )
             => ! [X6: $i] :
                  ( ( in @ X6 @ Z0 )
                 => ( ( X5 = X6 )
                    | ( in @ X5 @ X6 )
                    | ( in @ X6 @ X5 ) ) ) )
          & ! [X5: $i] :
              ( ( in @ X5 @ Z0 )
             => ~ ( in @ X5 @ X5 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[stricttotalorderedByIn]) ).

thf(c_0_12,plain,
    ( ordinal
    = ( ^ [Z0: $i] :
          ( ! [X18: $i] :
              ( ( in @ X18 @ Z0 )
             => ( subset @ X18 @ Z0 ) )
          & ! [X19: $i] :
              ( ( in @ X19 @ Z0 )
             => ! [X20: $i] :
                  ( ( in @ X20 @ Z0 )
                 => ! [X21: $i] :
                      ( ( in @ X21 @ Z0 )
                     => ( ( ( in @ X19 @ X20 )
                          & ( in @ X20 @ X21 ) )
                       => ( in @ X19 @ X21 ) ) ) ) )
          & ! [X22: $i] :
              ( ( in @ X22 @ Z0 )
             => ! [X23: $i] :
                  ( ( in @ X23 @ Z0 )
                 => ( ( X22 = X23 )
                    | ( in @ X22 @ X23 )
                    | ( in @ X23 @ X22 ) ) ) )
          & ! [X24: $i] :
              ( ( in @ X24 @ Z0 )
             => ~ ( in @ X24 @ X24 ) )
          & ! [X25: $i] :
              ( ( in @ X25 @ ( powerset @ Z0 ) )
             => ( ( X25 != emptyset )
               => ? [X26: $i] :
                    ( ( in @ X26 @ X25 )
                    & ! [X27: $i] :
                        ( ( in @ X27 @ X25 )
                       => ( ( X26 = X27 )
                          | ( in @ X26 @ X27 ) ) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[ordinal]) ).

thf(c_0_13,plain,
    ( wellorderedByIn
    = ( ^ [Z0: $i] :
          ( ! [X12: $i] :
              ( ( in @ X12 @ Z0 )
             => ! [X13: $i] :
                  ( ( in @ X13 @ Z0 )
                 => ! [X14: $i] :
                      ( ( in @ X14 @ Z0 )
                     => ( ( ( in @ X12 @ X13 )
                          & ( in @ X13 @ X14 ) )
                       => ( in @ X12 @ X14 ) ) ) ) )
          & ! [X15: $i] :
              ( ( in @ X15 @ Z0 )
             => ! [X16: $i] :
                  ( ( in @ X16 @ Z0 )
                 => ( ( X15 = X16 )
                    | ( in @ X15 @ X16 )
                    | ( in @ X16 @ X15 ) ) ) )
          & ! [X17: $i] :
              ( ( in @ X17 @ Z0 )
             => ~ ( in @ X17 @ X17 ) )
          & ! [X5: $i] :
              ( ( in @ X5 @ ( powerset @ Z0 ) )
             => ( ( X5 != emptyset )
               => ? [X1: $i] :
                    ( ( in @ X1 @ X5 )
                    & ! [X6: $i] :
                        ( ( in @ X6 @ X5 )
                       => ( ( X1 = X6 )
                          | ( in @ X1 @ X6 ) ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).

thf(c_0_14,plain,
    ( transitiveset
    = ( ^ [Z0: $i] :
        ! [X5: $i] :
          ( ( in @ X5 @ Z0 )
         => ( subset @ X5 @ Z0 ) ) ) ),
    inference(fof_simplification,[status(thm)],[transitiveset]) ).

thf(c_0_15,plain,
    ( ordinal
    = ( ^ [Z0: $i] :
          ( ! [X18: $i] :
              ( ( in @ X18 @ Z0 )
             => ( subset @ X18 @ Z0 ) )
          & ! [X19: $i] :
              ( ( in @ X19 @ Z0 )
             => ! [X20: $i] :
                  ( ( in @ X20 @ Z0 )
                 => ! [X21: $i] :
                      ( ( in @ X21 @ Z0 )
                     => ( ( ( in @ X19 @ X20 )
                          & ( in @ X20 @ X21 ) )
                       => ( in @ X19 @ X21 ) ) ) ) )
          & ! [X22: $i] :
              ( ( in @ X22 @ Z0 )
             => ! [X23: $i] :
                  ( ( in @ X23 @ Z0 )
                 => ( ( X22 = X23 )
                    | ( in @ X22 @ X23 )
                    | ( in @ X23 @ X22 ) ) ) )
          & ! [X24: $i] :
              ( ( in @ X24 @ Z0 )
             => ~ ( in @ X24 @ X24 ) )
          & ! [X25: $i] :
              ( ( in @ X25 @ ( powerset @ Z0 ) )
             => ( ( X25 != emptyset )
               => ? [X26: $i] :
                    ( ( in @ X26 @ X25 )
                    & ! [X27: $i] :
                        ( ( in @ X27 @ X25 )
                       => ( ( X26 = X27 )
                          | ( in @ X26 @ X27 ) ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).

thf(c_0_16,plain,
    ( epred1_0
  <=> ( ! [X34: $i] :
          ( ( in @ X34 @ emptyset )
         => ! [X35: $i] :
              ( ( in @ X35 @ emptyset )
             => ! [X36: $i] :
                  ( ( in @ X36 @ emptyset )
                 => ( ( ( in @ X34 @ X35 )
                      & ( in @ X35 @ X36 ) )
                   => ( in @ X34 @ X36 ) ) ) ) )
      & ! [X37: $i] :
          ( ( in @ X37 @ emptyset )
         => ! [X38: $i] :
              ( ( in @ X38 @ emptyset )
             => ( ( X37 = X38 )
                | ( in @ X37 @ X38 )
                | ( in @ X38 @ X37 ) ) ) ) ) ),
    introduced(definition) ).

thf(c_0_17,negated_conjecture,
    ~ ( ! [X28: $i > $o,X29: $i] :
          ( ( in @ X29 @ emptyset )
         => ( X28 @ X29 ) )
     => ( ! [X30: $i] :
            ( ( subset @ X30 @ emptyset )
           => ( X30 = emptyset ) )
       => ( ! [X31: $i,X32: $i] :
              ( ( in @ X32 @ ( powerset @ X31 ) )
             => ( subset @ X32 @ X31 ) )
         => ( ! [X33: $i] :
                ( ( in @ X33 @ emptyset )
               => ( subset @ X33 @ emptyset ) )
            & epred1_0
            & ! [X39: $i] :
                ( ( in @ X39 @ emptyset )
               => ~ ( in @ X39 @ X39 ) )
            & ! [X40: $i] :
                ( ( in @ X40 @ ( powerset @ emptyset ) )
               => ( ( X40 != emptyset )
                 => ? [X41: $i] :
                      ( ( in @ X41 @ X40 )
                      & ! [X42: $i] :
                          ( ( in @ X42 @ X40 )
                         => ( ( X41 = X42 )
                            | ( in @ X41 @ X42 ) ) ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[emptysetOrdinal]),c_0_15]),powersetE1]),subsetemptysetimpeq]),vacuousDall])]),c_0_16]) ).

thf(c_0_18,plain,
    ( ( ! [X34: $i] :
          ( ( in @ X34 @ emptyset )
         => ! [X35: $i] :
              ( ( in @ X35 @ emptyset )
             => ! [X36: $i] :
                  ( ( in @ X36 @ emptyset )
                 => ( ( ( in @ X34 @ X35 )
                      & ( in @ X35 @ X36 ) )
                   => ( in @ X34 @ X36 ) ) ) ) )
      & ! [X37: $i] :
          ( ( in @ X37 @ emptyset )
         => ! [X38: $i] :
              ( ( in @ X38 @ emptyset )
             => ( ( X37 = X38 )
                | ( in @ X37 @ X38 )
                | ( in @ X38 @ X37 ) ) ) ) )
   => epred1_0 ),
    inference(split_equiv,[status(thm)],[c_0_16]) ).

thf(c_0_19,negated_conjecture,
    ! [X43: $i > $o,X44: $i,X45: $i,X46: $i,X47: $i,X51: $i] :
      ( ( ~ ( in @ X44 @ emptyset )
        | ( X43 @ X44 ) )
      & ( ~ ( subset @ X45 @ emptyset )
        | ( X45 = emptyset ) )
      & ( ~ ( in @ X47 @ ( powerset @ X46 ) )
        | ( subset @ X47 @ X46 ) )
      & ( ( in @ esk3_0 @ ( powerset @ emptyset ) )
        | ( in @ esk2_0 @ emptyset )
        | ~ epred1_0
        | ( in @ esk1_0 @ emptyset ) )
      & ( ( esk3_0 != emptyset )
        | ( in @ esk2_0 @ emptyset )
        | ~ epred1_0
        | ( in @ esk1_0 @ emptyset ) )
      & ( ( in @ ( esk4_1 @ X51 ) @ esk3_0 )
        | ~ ( in @ X51 @ esk3_0 )
        | ( in @ esk2_0 @ emptyset )
        | ~ epred1_0
        | ( in @ esk1_0 @ emptyset ) )
      & ( ( X51
         != ( esk4_1 @ X51 ) )
        | ~ ( in @ X51 @ esk3_0 )
        | ( in @ esk2_0 @ emptyset )
        | ~ epred1_0
        | ( in @ esk1_0 @ emptyset ) )
      & ( ~ ( in @ X51 @ ( esk4_1 @ X51 ) )
        | ~ ( in @ X51 @ esk3_0 )
        | ( in @ esk2_0 @ emptyset )
        | ~ epred1_0
        | ( in @ esk1_0 @ emptyset ) )
      & ( ( in @ esk3_0 @ ( powerset @ emptyset ) )
        | ( in @ esk2_0 @ esk2_0 )
        | ~ epred1_0
        | ( in @ esk1_0 @ emptyset ) )
      & ( ( esk3_0 != emptyset )
        | ( in @ esk2_0 @ esk2_0 )
        | ~ epred1_0
        | ( in @ esk1_0 @ emptyset ) )
      & ( ( in @ ( esk4_1 @ X51 ) @ esk3_0 )
        | ~ ( in @ X51 @ esk3_0 )
        | ( in @ esk2_0 @ esk2_0 )
        | ~ epred1_0
        | ( in @ esk1_0 @ emptyset ) )
      & ( ( X51
         != ( esk4_1 @ X51 ) )
        | ~ ( in @ X51 @ esk3_0 )
        | ( in @ esk2_0 @ esk2_0 )
        | ~ epred1_0
        | ( in @ esk1_0 @ emptyset ) )
      & ( ~ ( in @ X51 @ ( esk4_1 @ X51 ) )
        | ~ ( in @ X51 @ esk3_0 )
        | ( in @ esk2_0 @ esk2_0 )
        | ~ epred1_0
        | ( in @ esk1_0 @ emptyset ) )
      & ( ( in @ esk3_0 @ ( powerset @ emptyset ) )
        | ( in @ esk2_0 @ emptyset )
        | ~ epred1_0
        | ~ ( subset @ esk1_0 @ emptyset ) )
      & ( ( esk3_0 != emptyset )
        | ( in @ esk2_0 @ emptyset )
        | ~ epred1_0
        | ~ ( subset @ esk1_0 @ emptyset ) )
      & ( ( in @ ( esk4_1 @ X51 ) @ esk3_0 )
        | ~ ( in @ X51 @ esk3_0 )
        | ( in @ esk2_0 @ emptyset )
        | ~ epred1_0
        | ~ ( subset @ esk1_0 @ emptyset ) )
      & ( ( X51
         != ( esk4_1 @ X51 ) )
        | ~ ( in @ X51 @ esk3_0 )
        | ( in @ esk2_0 @ emptyset )
        | ~ epred1_0
        | ~ ( subset @ esk1_0 @ emptyset ) )
      & ( ~ ( in @ X51 @ ( esk4_1 @ X51 ) )
        | ~ ( in @ X51 @ esk3_0 )
        | ( in @ esk2_0 @ emptyset )
        | ~ epred1_0
        | ~ ( subset @ esk1_0 @ emptyset ) )
      & ( ( in @ esk3_0 @ ( powerset @ emptyset ) )
        | ( in @ esk2_0 @ esk2_0 )
        | ~ epred1_0
        | ~ ( subset @ esk1_0 @ emptyset ) )
      & ( ( esk3_0 != emptyset )
        | ( in @ esk2_0 @ esk2_0 )
        | ~ epred1_0
        | ~ ( subset @ esk1_0 @ emptyset ) )
      & ( ( in @ ( esk4_1 @ X51 ) @ esk3_0 )
        | ~ ( in @ X51 @ esk3_0 )
        | ( in @ esk2_0 @ esk2_0 )
        | ~ epred1_0
        | ~ ( subset @ esk1_0 @ emptyset ) )
      & ( ( X51
         != ( esk4_1 @ X51 ) )
        | ~ ( in @ X51 @ esk3_0 )
        | ( in @ esk2_0 @ esk2_0 )
        | ~ epred1_0
        | ~ ( subset @ esk1_0 @ emptyset ) )
      & ( ~ ( in @ X51 @ ( esk4_1 @ X51 ) )
        | ~ ( in @ X51 @ esk3_0 )
        | ( in @ esk2_0 @ esk2_0 )
        | ~ epred1_0
        | ~ ( subset @ esk1_0 @ emptyset ) ) ),
    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)],[c_0_17])])])])])]) ).

thf(c_0_20,plain,
    ( ( ( in @ esk8_0 @ emptyset )
      | ( in @ esk5_0 @ emptyset )
      | epred1_0 )
    & ( ( in @ esk9_0 @ emptyset )
      | ( in @ esk5_0 @ emptyset )
      | epred1_0 )
    & ( ( esk8_0 != esk9_0 )
      | ( in @ esk5_0 @ emptyset )
      | epred1_0 )
    & ( ~ ( in @ esk8_0 @ esk9_0 )
      | ( in @ esk5_0 @ emptyset )
      | epred1_0 )
    & ( ~ ( in @ esk9_0 @ esk8_0 )
      | ( in @ esk5_0 @ emptyset )
      | epred1_0 )
    & ( ( in @ esk8_0 @ emptyset )
      | ( in @ esk6_0 @ emptyset )
      | epred1_0 )
    & ( ( in @ esk9_0 @ emptyset )
      | ( in @ esk6_0 @ emptyset )
      | epred1_0 )
    & ( ( esk8_0 != esk9_0 )
      | ( in @ esk6_0 @ emptyset )
      | epred1_0 )
    & ( ~ ( in @ esk8_0 @ esk9_0 )
      | ( in @ esk6_0 @ emptyset )
      | epred1_0 )
    & ( ~ ( in @ esk9_0 @ esk8_0 )
      | ( in @ esk6_0 @ emptyset )
      | epred1_0 )
    & ( ( in @ esk8_0 @ emptyset )
      | ( in @ esk7_0 @ emptyset )
      | epred1_0 )
    & ( ( in @ esk9_0 @ emptyset )
      | ( in @ esk7_0 @ emptyset )
      | epred1_0 )
    & ( ( esk8_0 != esk9_0 )
      | ( in @ esk7_0 @ emptyset )
      | epred1_0 )
    & ( ~ ( in @ esk8_0 @ esk9_0 )
      | ( in @ esk7_0 @ emptyset )
      | epred1_0 )
    & ( ~ ( in @ esk9_0 @ esk8_0 )
      | ( in @ esk7_0 @ emptyset )
      | epred1_0 )
    & ( ( in @ esk8_0 @ emptyset )
      | ( in @ esk5_0 @ esk6_0 )
      | epred1_0 )
    & ( ( in @ esk9_0 @ emptyset )
      | ( in @ esk5_0 @ esk6_0 )
      | epred1_0 )
    & ( ( esk8_0 != esk9_0 )
      | ( in @ esk5_0 @ esk6_0 )
      | epred1_0 )
    & ( ~ ( in @ esk8_0 @ esk9_0 )
      | ( in @ esk5_0 @ esk6_0 )
      | epred1_0 )
    & ( ~ ( in @ esk9_0 @ esk8_0 )
      | ( in @ esk5_0 @ esk6_0 )
      | epred1_0 )
    & ( ( in @ esk8_0 @ emptyset )
      | ( in @ esk6_0 @ esk7_0 )
      | epred1_0 )
    & ( ( in @ esk9_0 @ emptyset )
      | ( in @ esk6_0 @ esk7_0 )
      | epred1_0 )
    & ( ( esk8_0 != esk9_0 )
      | ( in @ esk6_0 @ esk7_0 )
      | epred1_0 )
    & ( ~ ( in @ esk8_0 @ esk9_0 )
      | ( in @ esk6_0 @ esk7_0 )
      | epred1_0 )
    & ( ~ ( in @ esk9_0 @ esk8_0 )
      | ( in @ esk6_0 @ esk7_0 )
      | epred1_0 )
    & ( ( in @ esk8_0 @ emptyset )
      | ~ ( in @ esk5_0 @ esk7_0 )
      | epred1_0 )
    & ( ( in @ esk9_0 @ emptyset )
      | ~ ( in @ esk5_0 @ esk7_0 )
      | epred1_0 )
    & ( ( esk8_0 != esk9_0 )
      | ~ ( in @ esk5_0 @ esk7_0 )
      | epred1_0 )
    & ( ~ ( in @ esk8_0 @ esk9_0 )
      | ~ ( in @ esk5_0 @ esk7_0 )
      | epred1_0 )
    & ( ~ ( in @ esk9_0 @ esk8_0 )
      | ~ ( in @ esk5_0 @ esk7_0 )
      | epred1_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])])]) ).

thf(c_0_21,negated_conjecture,
    ! [X2: $i > $o,X1: $i] :
      ( ( X2 @ X1 )
      | ~ ( in @ X1 @ emptyset ) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

thf(c_0_22,plain,
    ( ( in @ esk8_0 @ emptyset )
    | ( in @ esk7_0 @ emptyset )
    | epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

thf(c_0_23,plain,
    ( ( in @ esk8_0 @ emptyset )
    | epred1_0
    | ~ ( in @ esk5_0 @ esk7_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

thf(c_0_24,negated_conjecture,
    ! [X2: $i > $o] :
      ( ( in @ esk8_0 @ emptyset )
      | ( X2 @ esk7_0 )
      | epred1_0 ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

thf(c_0_25,plain,
    ( ( in @ esk8_0 @ emptyset )
    | epred1_0 ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

thf(c_0_26,plain,
    ( ( in @ esk7_0 @ emptyset )
    | epred1_0
    | ~ ( in @ esk9_0 @ esk8_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

thf(c_0_27,negated_conjecture,
    ! [X2: $i > $o] :
      ( ( X2 @ esk8_0 )
      | epred1_0 ),
    inference(spm,[status(thm)],[c_0_21,c_0_25]) ).

thf(c_0_28,plain,
    ( ( in @ esk7_0 @ emptyset )
    | epred1_0 ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

thf(c_0_29,plain,
    ( epred1_0
    | ~ ( in @ esk9_0 @ esk8_0 )
    | ~ ( in @ esk5_0 @ esk7_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

thf(c_0_30,negated_conjecture,
    ! [X2: $i > $o] :
      ( ( X2 @ esk7_0 )
      | epred1_0 ),
    inference(spm,[status(thm)],[c_0_21,c_0_28]) ).

thf(c_0_31,negated_conjecture,
    ( ( in @ esk3_0 @ ( powerset @ emptyset ) )
    | ( in @ esk2_0 @ emptyset )
    | ( in @ esk1_0 @ emptyset )
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

thf(c_0_32,plain,
    epred1_0,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_27]) ).

thf(c_0_33,negated_conjecture,
    ! [X1: $i,X3: $i] :
      ( ( subset @ X1 @ X3 )
      | ~ ( in @ X1 @ ( powerset @ X3 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

thf(c_0_34,negated_conjecture,
    ( ( in @ esk3_0 @ ( powerset @ emptyset ) )
    | ( in @ esk2_0 @ emptyset )
    | ( in @ esk1_0 @ emptyset ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]) ).

thf(c_0_35,negated_conjecture,
    ( ( in @ esk2_0 @ emptyset )
    | ( in @ esk1_0 @ emptyset )
    | ( esk3_0 != emptyset )
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

thf(c_0_36,negated_conjecture,
    ! [X1: $i] :
      ( ( X1 = emptyset )
      | ~ ( subset @ X1 @ emptyset ) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

thf(c_0_37,negated_conjecture,
    ( ( in @ esk1_0 @ emptyset )
    | ( in @ esk2_0 @ emptyset )
    | ( subset @ esk3_0 @ emptyset ) ),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

thf(c_0_38,negated_conjecture,
    ( ( in @ esk2_0 @ emptyset )
    | ( in @ esk1_0 @ emptyset )
    | ( esk3_0 != emptyset ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_32])]) ).

thf(c_0_39,negated_conjecture,
    ( ( in @ esk2_0 @ emptyset )
    | ( in @ esk1_0 @ emptyset ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).

thf(c_0_40,negated_conjecture,
    ! [X2: $i > $o] :
      ( ( in @ esk2_0 @ emptyset )
      | ( X2 @ esk1_0 ) ),
    inference(spm,[status(thm)],[c_0_21,c_0_39]) ).

thf(c_0_41,negated_conjecture,
    $false,
    inference(flex_resolve,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_40])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : SEU820^2 : TPTP v8.2.0. Released v3.7.0.
% 0.04/0.14  % Command    : run_E %s %d THM
% 0.14/0.35  % Computer : n016.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sun May 19 17:12:38 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.21/0.48  Running higher-order theorem proving
% 0.21/0.48  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
% 0.21/0.51  # Version: 3.1.0-ho
% 0.21/0.51  # partial match(1): HSSSSLSSSLSNSFA
% 0.21/0.51  # Preprocessing class: HSSSSLSSMLSNSFA.
% 0.21/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51  # Starting post_as_ho5 with 1500s (5) cores
% 0.21/0.51  # Starting post_as_ho10 with 300s (1) cores
% 0.21/0.51  # Starting post_as_ho4 with 300s (1) cores
% 0.21/0.51  # Starting sh5l with 300s (1) cores
% 0.21/0.51  # post_as_ho5 with pid 21841 completed with status 8
% 0.21/0.51  # sh5l with pid 21844 completed with status 0
% 0.21/0.51  # Result found by sh5l
% 0.21/0.51  # partial match(1): HSSSSLSSSLSNSFA
% 0.21/0.51  # Preprocessing class: HSSSSLSSMLSNSFA.
% 0.21/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51  # Starting post_as_ho5 with 1500s (5) cores
% 0.21/0.51  # Starting post_as_ho10 with 300s (1) cores
% 0.21/0.51  # Starting post_as_ho4 with 300s (1) cores
% 0.21/0.51  # Starting sh5l with 300s (1) cores
% 0.21/0.51  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.21/0.51  # Search class: HGUSF-FFMM11-SSFSMFBN
% 0.21/0.51  # partial match(4): HGHSF-FFMM11-SSSFFFBN
% 0.21/0.51  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.51  # Starting ho_unfolding_3 with 181s (1) cores
% 0.21/0.51  # ho_unfolding_3 with pid 21850 completed with status 0
% 0.21/0.51  # Result found by ho_unfolding_3
% 0.21/0.51  # partial match(1): HSSSSLSSSLSNSFA
% 0.21/0.51  # Preprocessing class: HSSSSLSSMLSNSFA.
% 0.21/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51  # Starting post_as_ho5 with 1500s (5) cores
% 0.21/0.51  # Starting post_as_ho10 with 300s (1) cores
% 0.21/0.51  # Starting post_as_ho4 with 300s (1) cores
% 0.21/0.51  # Starting sh5l with 300s (1) cores
% 0.21/0.51  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.21/0.51  # Search class: HGUSF-FFMM11-SSFSMFBN
% 0.21/0.51  # partial match(4): HGHSF-FFMM11-SSSFFFBN
% 0.21/0.51  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.51  # Starting ho_unfolding_3 with 181s (1) cores
% 0.21/0.51  # Preprocessing time       : 0.002 s
% 0.21/0.51  # Presaturation interreduction done
% 0.21/0.51  
% 0.21/0.51  # Proof found!
% 0.21/0.51  # SZS status Theorem
% 0.21/0.51  # SZS output start CNFRefutation
% See solution above
% 0.21/0.51  # Parsed axioms                        : 21
% 0.21/0.51  # Removed by relevancy pruning/SinE    : 12
% 0.21/0.51  # Initial clauses                      : 53
% 0.21/0.51  # Removed in clause preprocessing      : 0
% 0.21/0.51  # Initial clauses in saturation        : 53
% 0.21/0.51  # Processed clauses                    : 140
% 0.21/0.51  # ...of these trivial                  : 0
% 0.21/0.51  # ...subsumed                          : 1
% 0.21/0.51  # ...remaining for further processing  : 138
% 0.21/0.51  # Other redundant clauses eliminated   : 0
% 0.21/0.51  # Clauses deleted for lack of memory   : 0
% 0.21/0.51  # Backward-subsumed                    : 33
% 0.21/0.51  # Backward-rewritten                   : 36
% 0.21/0.51  # Generated clauses                    : 113
% 0.21/0.51  # ...of the previous two non-redundant : 133
% 0.21/0.51  # ...aggressively subsumed             : 0
% 0.21/0.51  # Contextual simplify-reflections      : 3
% 0.21/0.51  # Paramodulations                      : 113
% 0.21/0.51  # Factorizations                       : 0
% 0.21/0.51  # NegExts                              : 0
% 0.21/0.51  # Equation resolutions                 : 0
% 0.21/0.51  # Disequality decompositions           : 0
% 0.21/0.51  # Total rewrite steps                  : 36
% 0.21/0.51  # ...of those cached                   : 35
% 0.21/0.51  # Propositional unsat checks           : 0
% 0.21/0.51  #    Propositional check models        : 0
% 0.21/0.51  #    Propositional check unsatisfiable : 0
% 0.21/0.51  #    Propositional clauses             : 0
% 0.21/0.51  #    Propositional clauses after purity: 0
% 0.21/0.51  #    Propositional unsat core size     : 0
% 0.21/0.51  #    Propositional preprocessing time  : 0.000
% 0.21/0.51  #    Propositional encoding time       : 0.000
% 0.21/0.51  #    Propositional solver time         : 0.000
% 0.21/0.51  #    Success case prop preproc time    : 0.000
% 0.21/0.51  #    Success case prop encoding time   : 0.000
% 0.21/0.51  #    Success case prop solver time     : 0.000
% 0.21/0.51  # Current number of processed clauses  : 16
% 0.21/0.51  #    Positive orientable unit clauses  : 1
% 0.21/0.51  #    Positive unorientable unit clauses: 0
% 0.21/0.51  #    Negative unit clauses             : 0
% 0.21/0.51  #    Non-unit-clauses                  : 15
% 0.21/0.51  # Current number of unprocessed clauses: 71
% 0.21/0.51  # ...number of literals in the above   : 364
% 0.21/0.51  # Current number of archived formulas  : 0
% 0.21/0.51  # Current number of archived clauses   : 122
% 0.21/0.51  # Clause-clause subsumption calls (NU) : 1011
% 0.21/0.51  # Rec. Clause-clause subsumption calls : 589
% 0.21/0.51  # Non-unit clause-clause subsumptions  : 34
% 0.21/0.51  # Unit Clause-clause subsumption calls : 3
% 0.21/0.51  # Rewrite failures with RHS unbound    : 0
% 0.21/0.51  # BW rewrite match attempts            : 1
% 0.21/0.51  # BW rewrite match successes           : 1
% 0.21/0.51  # Condensation attempts                : 140
% 0.21/0.51  # Condensation successes               : 0
% 0.21/0.51  # Termbank termtop insertions          : 6183
% 0.21/0.51  # Search garbage collected termcells   : 782
% 0.21/0.51  
% 0.21/0.51  # -------------------------------------------------
% 0.21/0.51  # User time                : 0.015 s
% 0.21/0.51  # System time              : 0.003 s
% 0.21/0.51  # Total time               : 0.018 s
% 0.21/0.51  # Maximum resident set size: 1912 pages
% 0.21/0.51  
% 0.21/0.51  # -------------------------------------------------
% 0.21/0.51  # User time                : 0.050 s
% 0.21/0.51  # System time              : 0.022 s
% 0.21/0.51  # Total time               : 0.072 s
% 0.21/0.51  # Maximum resident set size: 1728 pages
% 0.21/0.51  % E---3.1 exiting
% 0.21/0.51  % E exiting
%------------------------------------------------------------------------------