TSTP Solution File: SEU731^2 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU731^2 : TPTP v8.2.0. Released v3.7.0.
% 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 03:29:37 EDT 2024

% Result   : Theorem 0.19s 0.50s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   44 (   3 unt;  11 typ;   0 def)
%            Number of atoms       :  221 (  35 equ;   0 cnn)
%            Maximal formula atoms :   57 (   6 avg)
%            Number of connectives : 1119 ( 104   ~; 131   |;  13   &; 827   @)
%                                         (   4 <=>;  40  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   32 (  12 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  11 usr;   7 con; 0-3 aty)
%            Number of variables   :  107 (   0   ^ 107   !;   0   ?; 107   :)

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

thf(decl_23,type,
    powerset: $i > $i ).

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

thf(decl_25,type,
    complementT_lem: $o ).

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

thf(decl_27,type,
    doubleComplementI1: $o ).

thf(decl_28,type,
    doubleComplementE1: $o ).

thf(decl_29,type,
    esk1_3: $i > $i > $i > $i ).

thf(decl_30,type,
    esk2_3: $i > $i > $i > $i ).

thf(decl_31,type,
    esk3_0: $i ).

thf(decl_32,type,
    esk4_0: $i ).

thf(doubleComplementEq,conjecture,
    ( complementT_lem
   => ( setextT
     => ( doubleComplementI1
       => ( doubleComplementE1
         => ! [X1: $i,X2: $i] :
              ( ( in @ X2 @ ( powerset @ X1 ) )
             => ( X2
                = ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementEq) ).

thf(doubleComplementE1,axiom,
    ( doubleComplementE1
  <=> ! [X1: $i,X2: $i] :
        ( ( in @ X2 @ ( powerset @ X1 ) )
       => ! [X4: $i] :
            ( ( in @ X4 @ X1 )
           => ( ( in @ X4 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) )
             => ( in @ X4 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementE1) ).

thf(complementT_lem,axiom,
    ( complementT_lem
  <=> ! [X1: $i,X2: $i] :
        ( ( in @ X2 @ ( powerset @ X1 ) )
       => ( in @ ( setminus @ X1 @ X2 ) @ ( powerset @ X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementT_lem) ).

thf(setextT,axiom,
    ( setextT
  <=> ! [X1: $i,X2: $i] :
        ( ( in @ X2 @ ( powerset @ X1 ) )
       => ! [X3: $i] :
            ( ( in @ X3 @ ( powerset @ X1 ) )
           => ( ! [X4: $i] :
                  ( ( in @ X4 @ X1 )
                 => ( ( in @ X4 @ X2 )
                   => ( in @ X4 @ X3 ) ) )
             => ( ! [X4: $i] :
                    ( ( in @ X4 @ X1 )
                   => ( ( in @ X4 @ X3 )
                     => ( in @ X4 @ X2 ) ) )
               => ( X2 = X3 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextT) ).

thf(doubleComplementI1,axiom,
    ( doubleComplementI1
  <=> ! [X1: $i,X2: $i] :
        ( ( in @ X2 @ ( powerset @ X1 ) )
       => ! [X4: $i] :
            ( ( in @ X4 @ X1 )
           => ( ( in @ X4 @ X2 )
             => ( in @ X4 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementI1) ).

thf(c_0_5,negated_conjecture,
    ~ ( ! [X20: $i,X21: $i] :
          ( ( in @ X21 @ ( powerset @ X20 ) )
         => ( in @ ( setminus @ X20 @ X21 ) @ ( powerset @ X20 ) ) )
     => ( ! [X22: $i,X23: $i] :
            ( ( in @ X23 @ ( powerset @ X22 ) )
           => ! [X24: $i] :
                ( ( in @ X24 @ ( powerset @ X22 ) )
               => ( ! [X25: $i] :
                      ( ( in @ X25 @ X22 )
                     => ( ( in @ X25 @ X23 )
                       => ( in @ X25 @ X24 ) ) )
                 => ( ! [X26: $i] :
                        ( ( in @ X26 @ X22 )
                       => ( ( in @ X26 @ X24 )
                         => ( in @ X26 @ X23 ) ) )
                   => ( X23 = X24 ) ) ) ) )
       => ( ! [X27: $i,X28: $i] :
              ( ( in @ X28 @ ( powerset @ X27 ) )
             => ! [X29: $i] :
                  ( ( in @ X29 @ X27 )
                 => ( ( in @ X29 @ X28 )
                   => ( in @ X29 @ ( setminus @ X27 @ ( setminus @ X27 @ X28 ) ) ) ) ) )
         => ( ! [X30: $i,X31: $i] :
                ( ( in @ X31 @ ( powerset @ X30 ) )
               => ! [X32: $i] :
                    ( ( in @ X32 @ X30 )
                   => ( ( in @ X32 @ ( setminus @ X30 @ ( setminus @ X30 @ X31 ) ) )
                     => ( in @ X32 @ X31 ) ) ) )
           => ! [X1: $i,X2: $i] :
                ( ( in @ X2 @ ( powerset @ X1 ) )
               => ( X2
                  = ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ) ),
    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)],[doubleComplementEq]),doubleComplementE1]),complementT_lem]),setextT]),doubleComplementI1]) ).

thf(c_0_6,negated_conjecture,
    ! [X33: $i,X34: $i,X35: $i,X36: $i,X37: $i,X40: $i,X41: $i,X42: $i,X43: $i,X44: $i,X45: $i] :
      ( ( ~ ( in @ X34 @ ( powerset @ X33 ) )
        | ( in @ ( setminus @ X33 @ X34 ) @ ( powerset @ X33 ) ) )
      & ( ( in @ ( esk2_3 @ X35 @ X36 @ X37 ) @ X35 )
        | ( X36 = X37 )
        | ( in @ ( esk1_3 @ X35 @ X36 @ X37 ) @ X35 )
        | ~ ( in @ X37 @ ( powerset @ X35 ) )
        | ~ ( in @ X36 @ ( powerset @ X35 ) ) )
      & ( ( in @ ( esk2_3 @ X35 @ X36 @ X37 ) @ X37 )
        | ( X36 = X37 )
        | ( in @ ( esk1_3 @ X35 @ X36 @ X37 ) @ X35 )
        | ~ ( in @ X37 @ ( powerset @ X35 ) )
        | ~ ( in @ X36 @ ( powerset @ X35 ) ) )
      & ( ~ ( in @ ( esk2_3 @ X35 @ X36 @ X37 ) @ X36 )
        | ( X36 = X37 )
        | ( in @ ( esk1_3 @ X35 @ X36 @ X37 ) @ X35 )
        | ~ ( in @ X37 @ ( powerset @ X35 ) )
        | ~ ( in @ X36 @ ( powerset @ X35 ) ) )
      & ( ( in @ ( esk2_3 @ X35 @ X36 @ X37 ) @ X35 )
        | ( X36 = X37 )
        | ( in @ ( esk1_3 @ X35 @ X36 @ X37 ) @ X36 )
        | ~ ( in @ X37 @ ( powerset @ X35 ) )
        | ~ ( in @ X36 @ ( powerset @ X35 ) ) )
      & ( ( in @ ( esk2_3 @ X35 @ X36 @ X37 ) @ X37 )
        | ( X36 = X37 )
        | ( in @ ( esk1_3 @ X35 @ X36 @ X37 ) @ X36 )
        | ~ ( in @ X37 @ ( powerset @ X35 ) )
        | ~ ( in @ X36 @ ( powerset @ X35 ) ) )
      & ( ~ ( in @ ( esk2_3 @ X35 @ X36 @ X37 ) @ X36 )
        | ( X36 = X37 )
        | ( in @ ( esk1_3 @ X35 @ X36 @ X37 ) @ X36 )
        | ~ ( in @ X37 @ ( powerset @ X35 ) )
        | ~ ( in @ X36 @ ( powerset @ X35 ) ) )
      & ( ( in @ ( esk2_3 @ X35 @ X36 @ X37 ) @ X35 )
        | ( X36 = X37 )
        | ~ ( in @ ( esk1_3 @ X35 @ X36 @ X37 ) @ X37 )
        | ~ ( in @ X37 @ ( powerset @ X35 ) )
        | ~ ( in @ X36 @ ( powerset @ X35 ) ) )
      & ( ( in @ ( esk2_3 @ X35 @ X36 @ X37 ) @ X37 )
        | ( X36 = X37 )
        | ~ ( in @ ( esk1_3 @ X35 @ X36 @ X37 ) @ X37 )
        | ~ ( in @ X37 @ ( powerset @ X35 ) )
        | ~ ( in @ X36 @ ( powerset @ X35 ) ) )
      & ( ~ ( in @ ( esk2_3 @ X35 @ X36 @ X37 ) @ X36 )
        | ( X36 = X37 )
        | ~ ( in @ ( esk1_3 @ X35 @ X36 @ X37 ) @ X37 )
        | ~ ( in @ X37 @ ( powerset @ X35 ) )
        | ~ ( in @ X36 @ ( powerset @ X35 ) ) )
      & ( ~ ( in @ X41 @ ( powerset @ X40 ) )
        | ~ ( in @ X42 @ X40 )
        | ~ ( in @ X42 @ X41 )
        | ( in @ X42 @ ( setminus @ X40 @ ( setminus @ X40 @ X41 ) ) ) )
      & ( ~ ( in @ X44 @ ( powerset @ X43 ) )
        | ~ ( in @ X45 @ X43 )
        | ~ ( in @ X45 @ ( setminus @ X43 @ ( setminus @ X43 @ X44 ) ) )
        | ( in @ X45 @ X44 ) )
      & ( in @ esk4_0 @ ( powerset @ esk3_0 ) )
      & ( esk4_0
       != ( setminus @ esk3_0 @ ( setminus @ esk3_0 @ esk4_0 ) ) ) ),
    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_5])])])])])]) ).

thf(c_0_7,negated_conjecture,
    ! [X3: $i,X2: $i,X1: $i] :
      ( ( X2 = X3 )
      | ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X2 )
      | ~ ( in @ ( esk2_3 @ X1 @ X2 @ X3 ) @ X2 )
      | ~ ( in @ X3 @ ( powerset @ X1 ) )
      | ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_8,negated_conjecture,
    ! [X3: $i,X2: $i,X1: $i] :
      ( ( in @ X3 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) )
      | ~ ( in @ X1 @ ( powerset @ X2 ) )
      | ~ ( in @ X3 @ X2 )
      | ~ ( in @ X3 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_9,negated_conjecture,
    ! [X3: $i,X2: $i,X1: $i] :
      ( ( X2 = X3 )
      | ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X1 )
      | ~ ( in @ ( esk2_3 @ X1 @ X2 @ X3 ) @ X2 )
      | ~ ( in @ X3 @ ( powerset @ X1 ) )
      | ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_10,negated_conjecture,
    ! [X3: $i,X2: $i,X1: $i] :
      ( ( X2 = X3 )
      | ~ ( in @ ( esk2_3 @ X1 @ X2 @ X3 ) @ X2 )
      | ~ ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X3 )
      | ~ ( in @ X3 @ ( powerset @ X1 ) )
      | ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_11,negated_conjecture,
    ! [X4: $i,X3: $i,X2: $i,X1: $i] :
      ( ( ( setminus @ X1 @ ( setminus @ X1 @ X2 ) )
        = X3 )
      | ( in @ ( esk1_3 @ X4 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) )
      | ~ ( in @ ( esk2_3 @ X4 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ X1 )
      | ~ ( in @ ( esk2_3 @ X4 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ X2 )
      | ~ ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ ( powerset @ X4 ) )
      | ~ ( in @ X3 @ ( powerset @ X4 ) )
      | ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

thf(c_0_12,negated_conjecture,
    ! [X3: $i,X2: $i,X1: $i] :
      ( ( in @ ( esk2_3 @ X1 @ X2 @ X3 ) @ X1 )
      | ( X2 = X3 )
      | ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X2 )
      | ~ ( in @ X3 @ ( powerset @ X1 ) )
      | ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_13,negated_conjecture,
    ! [X4: $i,X3: $i,X2: $i,X1: $i] :
      ( ( ( setminus @ X1 @ ( setminus @ X1 @ X2 ) )
        = X3 )
      | ( in @ ( esk1_3 @ X4 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ X4 )
      | ~ ( in @ ( esk2_3 @ X4 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ X1 )
      | ~ ( in @ ( esk2_3 @ X4 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ X2 )
      | ~ ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ ( powerset @ X4 ) )
      | ~ ( in @ X3 @ ( powerset @ X4 ) )
      | ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
    inference(spm,[status(thm)],[c_0_9,c_0_8]) ).

thf(c_0_14,negated_conjecture,
    ! [X3: $i,X2: $i,X1: $i] :
      ( ( in @ ( esk2_3 @ X1 @ X2 @ X3 ) @ X1 )
      | ( X2 = X3 )
      | ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X1 )
      | ~ ( in @ X3 @ ( powerset @ X1 ) )
      | ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_15,negated_conjecture,
    ! [X4: $i,X3: $i,X2: $i,X1: $i] :
      ( ( ( setminus @ X1 @ ( setminus @ X1 @ X2 ) )
        = X3 )
      | ~ ( in @ ( esk1_3 @ X4 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ X3 )
      | ~ ( in @ ( esk2_3 @ X4 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ X1 )
      | ~ ( in @ ( esk2_3 @ X4 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ X2 )
      | ~ ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ ( powerset @ X4 ) )
      | ~ ( in @ X3 @ ( powerset @ X4 ) )
      | ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
    inference(spm,[status(thm)],[c_0_10,c_0_8]) ).

thf(c_0_16,negated_conjecture,
    ! [X3: $i,X2: $i,X1: $i] :
      ( ( in @ ( esk2_3 @ X1 @ X2 @ X3 ) @ X1 )
      | ( X2 = X3 )
      | ~ ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X3 )
      | ~ ( in @ X3 @ ( powerset @ X1 ) )
      | ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_17,negated_conjecture,
    ! [X3: $i,X2: $i,X1: $i] :
      ( ( ( setminus @ X1 @ ( setminus @ X1 @ X2 ) )
        = X3 )
      | ( in @ ( esk1_3 @ X1 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) )
      | ~ ( in @ ( esk2_3 @ X1 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ X2 )
      | ~ ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ ( powerset @ X1 ) )
      | ~ ( in @ X3 @ ( powerset @ X1 ) )
      | ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

thf(c_0_18,negated_conjecture,
    ! [X3: $i,X2: $i,X1: $i] :
      ( ( in @ ( esk2_3 @ X1 @ X2 @ X3 ) @ X3 )
      | ( X2 = X3 )
      | ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X2 )
      | ~ ( in @ X3 @ ( powerset @ X1 ) )
      | ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_19,negated_conjecture,
    ! [X3: $i,X2: $i,X1: $i] :
      ( ( ( setminus @ X1 @ ( setminus @ X1 @ X2 ) )
        = X3 )
      | ( in @ ( esk1_3 @ X1 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ X1 )
      | ~ ( in @ ( esk2_3 @ X1 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ X2 )
      | ~ ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ ( powerset @ X1 ) )
      | ~ ( in @ X3 @ ( powerset @ X1 ) )
      | ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

thf(c_0_20,negated_conjecture,
    ! [X3: $i,X2: $i,X1: $i] :
      ( ( in @ ( esk2_3 @ X1 @ X2 @ X3 ) @ X3 )
      | ( X2 = X3 )
      | ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X1 )
      | ~ ( in @ X3 @ ( powerset @ X1 ) )
      | ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_21,negated_conjecture,
    ! [X3: $i,X2: $i,X1: $i] :
      ( ( ( setminus @ X1 @ ( setminus @ X1 @ X2 ) )
        = X3 )
      | ~ ( in @ ( esk1_3 @ X1 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ X3 )
      | ~ ( in @ ( esk2_3 @ X1 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X3 ) @ X2 )
      | ~ ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ ( powerset @ X1 ) )
      | ~ ( in @ X3 @ ( powerset @ X1 ) )
      | ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

thf(c_0_22,negated_conjecture,
    ! [X3: $i,X2: $i,X1: $i] :
      ( ( in @ ( esk2_3 @ X1 @ X2 @ X3 ) @ X3 )
      | ( X2 = X3 )
      | ~ ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X3 )
      | ~ ( in @ X3 @ ( powerset @ X1 ) )
      | ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_23,negated_conjecture,
    ! [X3: $i,X2: $i,X1: $i] :
      ( ( in @ X3 @ X1 )
      | ~ ( in @ X1 @ ( powerset @ X2 ) )
      | ~ ( in @ X3 @ X2 )
      | ~ ( in @ X3 @ ( setminus @ X2 @ ( setminus @ X2 @ X1 ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_24,negated_conjecture,
    ! [X2: $i,X1: $i] :
      ( ( ( setminus @ X1 @ ( setminus @ X1 @ X2 ) )
        = X2 )
      | ( in @ ( esk1_3 @ X1 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X2 ) @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) )
      | ~ ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ ( powerset @ X1 ) )
      | ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

thf(c_0_25,negated_conjecture,
    ! [X2: $i,X1: $i] :
      ( ( ( setminus @ X1 @ ( setminus @ X1 @ X2 ) )
        = X2 )
      | ( in @ ( esk1_3 @ X1 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X2 ) @ X1 )
      | ~ ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ ( powerset @ X1 ) )
      | ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

thf(c_0_26,negated_conjecture,
    ! [X2: $i,X1: $i] :
      ( ( ( setminus @ X1 @ ( setminus @ X1 @ X2 ) )
        = X2 )
      | ~ ( in @ ( esk1_3 @ X1 @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ X2 ) @ X2 )
      | ~ ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ ( powerset @ X1 ) )
      | ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

thf(c_0_27,negated_conjecture,
    ! [X2: $i,X1: $i] :
      ( ( ( setminus @ X1 @ ( setminus @ X1 @ X2 ) )
        = X2 )
      | ~ ( in @ ( setminus @ X1 @ ( setminus @ X1 @ X2 ) ) @ ( powerset @ X1 ) )
      | ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26]) ).

thf(c_0_28,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ( in @ ( setminus @ X2 @ X1 ) @ ( powerset @ X2 ) )
      | ~ ( in @ X1 @ ( powerset @ X2 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_29,negated_conjecture,
    ( esk4_0
   != ( setminus @ esk3_0 @ ( setminus @ esk3_0 @ esk4_0 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_30,negated_conjecture,
    ! [X2: $i,X1: $i] :
      ( ( ( setminus @ X1 @ ( setminus @ X1 @ X2 ) )
        = X2 )
      | ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_28]) ).

thf(c_0_31,negated_conjecture,
    in @ esk4_0 @ ( powerset @ esk3_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_32,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SEU731^2 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.13  % Command    : run_E %s %d THM
% 0.13/0.33  % Computer : n017.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Sun May 19 17:42:53 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.19/0.47  Running higher-order theorem proving
% 0.19/0.47  Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.50  # Version: 3.1.0-ho
% 0.19/0.50  # Preprocessing class: HSSSSLSSSLSNFFN.
% 0.19/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.50  # Starting lpo6_lambda_fix with 1500s (5) cores
% 0.19/0.50  # Starting post_as_ho8 with 300s (1) cores
% 0.19/0.50  # Starting post_as_ho3 with 300s (1) cores
% 0.19/0.50  # Starting post_as_ho2 with 300s (1) cores
% 0.19/0.50  # post_as_ho8 with pid 7334 completed with status 0
% 0.19/0.50  # Result found by post_as_ho8
% 0.19/0.50  # Preprocessing class: HSSSSLSSSLSNFFN.
% 0.19/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.50  # Starting lpo6_lambda_fix with 1500s (5) cores
% 0.19/0.50  # Starting post_as_ho8 with 300s (1) cores
% 0.19/0.50  # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.19/0.50  # Search class: HGUSF-FFMF32-SFFFMFNN
% 0.19/0.50  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.50  # Starting full_lambda_5 with 163s (1) cores
% 0.19/0.50  # full_lambda_5 with pid 7339 completed with status 0
% 0.19/0.50  # Result found by full_lambda_5
% 0.19/0.50  # Preprocessing class: HSSSSLSSSLSNFFN.
% 0.19/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.50  # Starting lpo6_lambda_fix with 1500s (5) cores
% 0.19/0.50  # Starting post_as_ho8 with 300s (1) cores
% 0.19/0.50  # SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.19/0.50  # Search class: HGUSF-FFMF32-SFFFMFNN
% 0.19/0.50  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.50  # Starting full_lambda_5 with 163s (1) cores
% 0.19/0.50  # Preprocessing time       : 0.001 s
% 0.19/0.50  # Presaturation interreduction done
% 0.19/0.50  
% 0.19/0.50  # Proof found!
% 0.19/0.50  # SZS status Theorem
% 0.19/0.50  # SZS output start CNFRefutation
% See solution above
% 0.19/0.50  # Parsed axioms                        : 12
% 0.19/0.50  # Removed by relevancy pruning/SinE    : 7
% 0.19/0.50  # Initial clauses                      : 14
% 0.19/0.50  # Removed in clause preprocessing      : 0
% 0.19/0.50  # Initial clauses in saturation        : 14
% 0.19/0.50  # Processed clauses                    : 126
% 0.19/0.50  # ...of these trivial                  : 0
% 0.19/0.50  # ...subsumed                          : 64
% 0.19/0.50  # ...remaining for further processing  : 62
% 0.19/0.50  # Other redundant clauses eliminated   : 0
% 0.19/0.50  # Clauses deleted for lack of memory   : 0
% 0.19/0.50  # Backward-subsumed                    : 7
% 0.19/0.50  # Backward-rewritten                   : 0
% 0.19/0.50  # Generated clauses                    : 257
% 0.19/0.50  # ...of the previous two non-redundant : 193
% 0.19/0.50  # ...aggressively subsumed             : 0
% 0.19/0.50  # Contextual simplify-reflections      : 4
% 0.19/0.50  # Paramodulations                      : 257
% 0.19/0.50  # Factorizations                       : 0
% 0.19/0.50  # NegExts                              : 0
% 0.19/0.50  # Equation resolutions                 : 0
% 0.19/0.50  # Disequality decompositions           : 0
% 0.19/0.50  # Total rewrite steps                  : 1
% 0.19/0.50  # ...of those cached                   : 0
% 0.19/0.50  # Propositional unsat checks           : 0
% 0.19/0.50  #    Propositional check models        : 0
% 0.19/0.50  #    Propositional check unsatisfiable : 0
% 0.19/0.50  #    Propositional clauses             : 0
% 0.19/0.50  #    Propositional clauses after purity: 0
% 0.19/0.50  #    Propositional unsat core size     : 0
% 0.19/0.50  #    Propositional preprocessing time  : 0.000
% 0.19/0.50  #    Propositional encoding time       : 0.000
% 0.19/0.50  #    Propositional solver time         : 0.000
% 0.19/0.50  #    Success case prop preproc time    : 0.000
% 0.19/0.50  #    Success case prop encoding time   : 0.000
% 0.19/0.50  #    Success case prop solver time     : 0.000
% 0.19/0.50  # Current number of processed clauses  : 41
% 0.19/0.50  #    Positive orientable unit clauses  : 1
% 0.19/0.50  #    Positive unorientable unit clauses: 0
% 0.19/0.50  #    Negative unit clauses             : 1
% 0.19/0.50  #    Non-unit-clauses                  : 39
% 0.19/0.50  # Current number of unprocessed clauses: 95
% 0.19/0.50  # ...number of literals in the above   : 666
% 0.19/0.50  # Current number of archived formulas  : 0
% 0.19/0.50  # Current number of archived clauses   : 21
% 0.19/0.50  # Clause-clause subsumption calls (NU) : 1645
% 0.19/0.50  # Rec. Clause-clause subsumption calls : 138
% 0.19/0.50  # Non-unit clause-clause subsumptions  : 75
% 0.19/0.50  # Unit Clause-clause subsumption calls : 0
% 0.19/0.50  # Rewrite failures with RHS unbound    : 0
% 0.19/0.50  # BW rewrite match attempts            : 0
% 0.19/0.50  # BW rewrite match successes           : 0
% 0.19/0.50  # Condensation attempts                : 0
% 0.19/0.50  # Condensation successes               : 0
% 0.19/0.50  # Termbank termtop insertions          : 12099
% 0.19/0.50  # Search garbage collected termcells   : 585
% 0.19/0.50  
% 0.19/0.50  # -------------------------------------------------
% 0.19/0.50  # User time                : 0.014 s
% 0.19/0.50  # System time              : 0.001 s
% 0.19/0.50  # Total time               : 0.015 s
% 0.19/0.50  # Maximum resident set size: 1968 pages
% 0.19/0.50  
% 0.19/0.50  # -------------------------------------------------
% 0.19/0.50  # User time                : 0.018 s
% 0.19/0.50  # System time              : 0.001 s
% 0.19/0.50  # Total time               : 0.019 s
% 0.19/0.50  # Maximum resident set size: 1700 pages
% 0.19/0.50  % E---3.1 exiting
% 0.19/0.50  % E exiting
%------------------------------------------------------------------------------