TSTP Solution File: SEU704^2 by E---3.2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.2.0
% Problem  : SEU704^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n029.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 : Mon Jun 24 15:10:15 EDT 2024

% Result   : Theorem 0.20s 0.50s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   37 (  11 unt;   0 typ;   0 def)
%            Number of atoms       :  231 ( 108 equ;   0 cnn)
%            Maximal formula atoms :   24 (   6 avg)
%            Number of connectives :  609 (  91   ~;  81   |;  67   &; 313   @)
%                                         (   8 <=>;  48  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   32 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  14 usr;  11 con; 0-2 aty)
%            Number of variables   :  146 (  41   ^ 102   !;   3   ?; 146   :)

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

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

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

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

thf(decl_26,type,
    singleton: $i > $o ).

thf(decl_27,type,
    iffalseProp1: $o ).

thf(decl_28,type,
    iffalseProp2: $o ).

thf(decl_29,type,
    iftrueProp1: $o ).

thf(decl_30,type,
    iftrueProp2: $o ).

thf(decl_31,type,
    esk1_0: $i ).

thf(decl_32,type,
    epred1_0: $o ).

thf(decl_33,type,
    esk2_0: $i ).

thf(decl_34,type,
    esk3_0: $i ).

thf(decl_39,type,
    esk8_1: $i > $i ).

thf(singleton,axiom,
    ( singleton
    = ( ^ [X1: $i] :
        ? [X2: $i] :
          ( ( in @ X2 @ X1 )
          & ( X1
            = ( setadjoin @ X2 @ emptyset ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.RyF4DKnMdq/E---3.1_9701.p',singleton) ).

thf(iftrueProp2,axiom,
    ( iftrueProp2
  <=> ! [X1: $i,X3: $o,X2: $i] :
        ( ( in @ X2 @ X1 )
       => ! [X4: $i] :
            ( ( in @ X4 @ X1 )
           => ( X3
             => ( ( dsetconstr @ X1
                  @ ^ [X5: $i] :
                      ( ( X3
                        & ( X5 = X2 ) )
                      | ( ~ X3
                        & ( X5 = X4 ) ) ) )
                = ( setadjoin @ X2 @ emptyset ) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.RyF4DKnMdq/E---3.1_9701.p',iftrueProp2) ).

thf(iftrueProp1,axiom,
    ( iftrueProp1
  <=> ! [X1: $i,X3: $o,X2: $i] :
        ( ( in @ X2 @ X1 )
       => ! [X4: $i] :
            ( ( in @ X4 @ X1 )
           => ( X3
             => ( in @ X2
                @ ( dsetconstr @ X1
                  @ ^ [X5: $i] :
                      ( ( X3
                        & ( X5 = X2 ) )
                      | ( ~ X3
                        & ( X5 = X4 ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.RyF4DKnMdq/E---3.1_9701.p',iftrueProp1) ).

thf(iffalseProp2,axiom,
    ( iffalseProp2
  <=> ! [X1: $i,X3: $o,X2: $i] :
        ( ( in @ X2 @ X1 )
       => ! [X4: $i] :
            ( ( in @ X4 @ X1 )
           => ( ~ X3
             => ( ( dsetconstr @ X1
                  @ ^ [X5: $i] :
                      ( ( X3
                        & ( X5 = X2 ) )
                      | ( ~ X3
                        & ( X5 = X4 ) ) ) )
                = ( setadjoin @ X4 @ emptyset ) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.RyF4DKnMdq/E---3.1_9701.p',iffalseProp2) ).

thf(iffalseProp1,axiom,
    ( iffalseProp1
  <=> ! [X1: $i,X3: $o,X2: $i] :
        ( ( in @ X2 @ X1 )
       => ! [X4: $i] :
            ( ( in @ X4 @ X1 )
           => ( ~ X3
             => ( in @ X4
                @ ( dsetconstr @ X1
                  @ ^ [X5: $i] :
                      ( ( X3
                        & ( X5 = X2 ) )
                      | ( ~ X3
                        & ( X5 = X4 ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.RyF4DKnMdq/E---3.1_9701.p',iffalseProp1) ).

thf(ifSingleton,conjecture,
    ( iffalseProp1
   => ( iffalseProp2
     => ( iftrueProp1
       => ( iftrueProp2
         => ! [X1: $i,X3: $o,X2: $i] :
              ( ( in @ X2 @ X1 )
             => ! [X4: $i] :
                  ( ( in @ X4 @ X1 )
                 => ( singleton
                    @ ( dsetconstr @ X1
                      @ ^ [X5: $i] :
                          ( ( X3
                            & ( X5 = X2 ) )
                          | ( ~ X3
                            & ( X5 = X4 ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.RyF4DKnMdq/E---3.1_9701.p',ifSingleton) ).

thf(c_0_6,plain,
    ( singleton
    = ( ^ [Z0: $i] :
        ? [X2: $i] :
          ( ( in @ X2 @ Z0 )
          & ( Z0
            = ( setadjoin @ X2 @ emptyset ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[singleton]) ).

thf(c_0_7,plain,
    ( iftrueProp2
  <=> ! [X1: $i,X3: $o,X2: $i] :
        ( ( in @ X2 @ X1 )
       => ! [X4: $i] :
            ( ( in @ X4 @ X1 )
           => ( X3
             => ( ( dsetconstr @ X1
                  @ ^ [Z0: $i] :
                      ( ( X3
                        & ( Z0 = X2 ) )
                      | ( ~ X3
                        & ( Z0 = X4 ) ) ) )
                = ( setadjoin @ X2 @ emptyset ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[iftrueProp2]) ).

thf(c_0_8,plain,
    ( iftrueProp1
  <=> ! [X1: $i,X3: $o,X2: $i] :
        ( ( in @ X2 @ X1 )
       => ! [X4: $i] :
            ( ( in @ X4 @ X1 )
           => ( X3
             => ( in @ X2
                @ ( dsetconstr @ X1
                  @ ^ [Z0: $i] :
                      ( ( X3
                        & ( Z0 = X2 ) )
                      | ( ~ X3
                        & ( Z0 = X4 ) ) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[iftrueProp1]) ).

thf(c_0_9,plain,
    ( iffalseProp2
  <=> ! [X1: $i,X3: $o,X2: $i] :
        ( ( in @ X2 @ X1 )
       => ! [X4: $i] :
            ( ( in @ X4 @ X1 )
           => ( ~ X3
             => ( ( dsetconstr @ X1
                  @ ^ [Z0: $i] :
                      ( ( X3
                        & ( Z0 = X2 ) )
                      | ( ~ X3
                        & ( Z0 = X4 ) ) ) )
                = ( setadjoin @ X4 @ emptyset ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[iffalseProp2]) ).

thf(c_0_10,plain,
    ( iffalseProp1
  <=> ! [X1: $i,X3: $o,X2: $i] :
        ( ( in @ X2 @ X1 )
       => ! [X4: $i] :
            ( ( in @ X4 @ X1 )
           => ( ~ X3
             => ( in @ X4
                @ ( dsetconstr @ X1
                  @ ^ [Z0: $i] :
                      ( ( X3
                        & ( Z0 = X2 ) )
                      | ( ~ X3
                        & ( Z0 = X4 ) ) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[iffalseProp1]) ).

thf(c_0_11,negated_conjecture,
    ~ ( ! [X26: $i,X27: $o,X28: $i] :
          ( ( in @ X28 @ X26 )
         => ! [X29: $i] :
              ( ( in @ X29 @ X26 )
             => ( ~ X27
               => ( in @ X29
                  @ ( dsetconstr @ X26
                    @ ^ [Z0: $i] :
                        ( ( X27
                          & ( Z0 = X28 ) )
                        | ( ~ X27
                          & ( Z0 = X29 ) ) ) ) ) ) ) )
     => ( ! [X30: $i,X31: $o,X32: $i] :
            ( ( in @ X32 @ X30 )
           => ! [X33: $i] :
                ( ( in @ X33 @ X30 )
               => ( ~ X31
                 => ( ( dsetconstr @ X30
                      @ ^ [Z0: $i] :
                          ( ( X31
                            & ( Z0 = X32 ) )
                          | ( ~ X31
                            & ( Z0 = X33 ) ) ) )
                    = ( setadjoin @ X33 @ emptyset ) ) ) ) )
       => ( ! [X34: $i,X35: $o,X36: $i] :
              ( ( in @ X36 @ X34 )
             => ! [X37: $i] :
                  ( ( in @ X37 @ X34 )
                 => ( X35
                   => ( in @ X36
                      @ ( dsetconstr @ X34
                        @ ^ [Z0: $i] :
                            ( ( X35
                              & ( Z0 = X36 ) )
                            | ( ~ X35
                              & ( Z0 = X37 ) ) ) ) ) ) ) )
         => ( ! [X38: $i,X39: $o,X40: $i] :
                ( ( in @ X40 @ X38 )
               => ! [X41: $i] :
                    ( ( in @ X41 @ X38 )
                   => ( X39
                     => ( ( dsetconstr @ X38
                          @ ^ [Z0: $i] :
                              ( ( X39
                                & ( Z0 = X40 ) )
                              | ( ~ X39
                                & ( Z0 = X41 ) ) ) )
                        = ( setadjoin @ X40 @ emptyset ) ) ) ) )
           => ! [X1: $i,X3: $o,X2: $i] :
                ( ( in @ X2 @ X1 )
               => ! [X4: $i] :
                    ( ( in @ X4 @ X1 )
                   => ? [X42: $i] :
                        ( ( in @ X42
                          @ ( dsetconstr @ X1
                            @ ^ [Z0: $i] :
                                ( ( X3
                                  & ( Z0 = X2 ) )
                                | ( ~ X3
                                  & ( Z0 = X4 ) ) ) ) )
                        & ( ( dsetconstr @ X1
                            @ ^ [Z0: $i] :
                                ( ( X3
                                  & ( Z0 = X2 ) )
                                | ( ~ X3
                                  & ( Z0 = X4 ) ) ) )
                          = ( setadjoin @ X42 @ emptyset ) ) ) ) ) ) ) ) ),
    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(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[ifSingleton])]),c_0_6]),c_0_7]),c_0_8]),c_0_9]),c_0_10])]) ).

thf(c_0_12,negated_conjecture,
    ! [X43: $i,X44: $o,X45: $i,X46: $i,X47: $i,X48: $o,X49: $i,X50: $i,X51: $i,X52: $o,X53: $i,X54: $i,X55: $i,X56: $o,X57: $i,X58: $i,X63: $i] :
      ( ( ~ ( in @ X45 @ X43 )
        | ~ ( in @ X46 @ X43 )
        | X44
        | ( in @ X46
          @ ( dsetconstr @ X43
            @ ^ [Z0: $i] :
                ( ( X44
                  & ( Z0 = X45 ) )
                | ( ~ X44
                  & ( Z0 = X46 ) ) ) ) ) )
      & ( ~ ( in @ X49 @ X47 )
        | ~ ( in @ X50 @ X47 )
        | X48
        | ( ( dsetconstr @ X47
            @ ^ [Z0: $i] :
                ( ( X48
                  & ( Z0 = X49 ) )
                | ( ~ X48
                  & ( Z0 = X50 ) ) ) )
          = ( setadjoin @ X50 @ emptyset ) ) )
      & ( ~ ( in @ X53 @ X51 )
        | ~ ( in @ X54 @ X51 )
        | ~ X52
        | ( in @ X53
          @ ( dsetconstr @ X51
            @ ^ [Z0: $i] :
                ( ( X52
                  & ( Z0 = X53 ) )
                | ( ~ X52
                  & ( Z0 = X54 ) ) ) ) ) )
      & ( ~ ( in @ X57 @ X55 )
        | ~ ( in @ X58 @ X55 )
        | ~ X56
        | ( ( dsetconstr @ X55
            @ ^ [Z0: $i] :
                ( ( X56
                  & ( Z0 = X57 ) )
                | ( ~ X56
                  & ( Z0 = X58 ) ) ) )
          = ( setadjoin @ X57 @ emptyset ) ) )
      & ( in @ esk2_0 @ esk1_0 )
      & ( in @ esk3_0 @ esk1_0 )
      & ( ~ ( in @ X63
            @ ( dsetconstr @ esk1_0
              @ ^ [Z0: $i] :
                  ( ( epred1_0
                    & ( Z0 = esk2_0 ) )
                  | ( ~ epred1_0
                    & ( Z0 = esk3_0 ) ) ) ) )
        | ( ( dsetconstr @ esk1_0
            @ ^ [Z0: $i] :
                ( ( epred1_0
                  & ( Z0 = esk2_0 ) )
                | ( ~ epred1_0
                  & ( Z0 = esk3_0 ) ) ) )
         != ( setadjoin @ X63 @ emptyset ) ) ) ),
    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_11])])])])]) ).

thf(c_0_13,negated_conjecture,
    ! [X1: $i,X4: $i,X2: $i] :
      ( ( ( dsetconstr @ X2
          @ ^ [Z0: $i] :
              ( ( $true
                & ( Z0 = X1 ) )
              | ( ~ $true
                & ( Z0 = X4 ) ) ) )
        = ( setadjoin @ X1 @ emptyset ) )
      | ~ ( in @ X1 @ X2 )
      | ~ ( in @ X4 @ X2 ) ),
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_12])])]) ).

thf(c_0_14,negated_conjecture,
    ! [X4: $i,X2: $i,X1: $i] :
      ( ( ( dsetconstr @ X1
          @ ^ [Z0: $i] : ( Z0 = X2 ) )
        = ( setadjoin @ X2 @ emptyset ) )
      | ~ ( in @ X4 @ X1 )
      | ~ ( in @ X2 @ X1 ) ),
    inference(cn,[status(thm)],[c_0_13]) ).

thf(c_0_15,negated_conjecture,
    ! [X1: $i] :
      ( ~ ( in @ X1
          @ ( dsetconstr @ esk1_0
            @ ^ [Z0: $i] :
                ( ( epred1_0
                  & ( Z0 = esk2_0 ) )
                | ( ~ epred1_0
                  & ( Z0 = esk3_0 ) ) ) ) )
      | ( ( dsetconstr @ esk1_0
          @ ^ [Z0: $i] :
              ( ( epred1_0
                & ( Z0 = esk2_0 ) )
              | ( ~ epred1_0
                & ( Z0 = esk3_0 ) ) ) )
       != ( setadjoin @ X1 @ emptyset ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

thf(c_0_16,negated_conjecture,
    ! [X2: $i,X1: $i] :
      ( ( ( dsetconstr @ X1
          @ ^ [Z0: $i] : ( Z0 = X2 ) )
        = ( setadjoin @ X2 @ emptyset ) )
      | ~ ( in @ X2 @ X1 ) ),
    inference(condense,[status(thm)],[c_0_14]) ).

thf(c_0_17,negated_conjecture,
    ! [X1: $i,X4: $i,X2: $i] :
      ( ( in @ X4
        @ ( dsetconstr @ X2
          @ ^ [Z0: $i] :
              ( ( ~ $true
                & ( Z0 = X1 ) )
              | ( ~ ~ $true
                & ( Z0 = X4 ) ) ) ) )
      | ~ ( in @ X1 @ X2 )
      | ~ ( in @ X4 @ X2 ) ),
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_12])])]) ).

thf(c_0_18,plain,
    ! [X1: $i,X2: $i] :
      ( ( ( dsetconstr @ esk1_0
          @ ^ [Z0: $i] :
              ( ( epred1_0
                & ( Z0 = esk2_0 ) )
              | ( ~ epred1_0
                & ( Z0 = esk3_0 ) ) ) )
       != ( setadjoin @ X1 @ emptyset ) )
      | ( ( ^ [Z0: $i] :
              ( ( epred1_0
                & ( Z0 = esk2_0 ) )
              | ( ~ epred1_0
                & ( Z0 = esk3_0 ) ) ) )
       != ( ^ [Z0: $i] : ( Z0 = X2 ) ) )
      | ~ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
      | ~ ( in @ X2 @ esk1_0 ) ),
    inference(er,[status(thm)],[inference(ext_sup,[status(thm)],[c_0_15,c_0_16])]) ).

thf(c_0_19,negated_conjecture,
    ! [X1: $i,X4: $i,X2: $i] :
      ( ( in @ X1
        @ ( dsetconstr @ X2
          @ ^ [Z0: $i] : ( Z0 = X1 ) ) )
      | ~ ( in @ X1 @ X2 )
      | ~ ( in @ X4 @ X2 ) ),
    inference(cn,[status(thm)],[c_0_17]) ).

thf(c_0_20,negated_conjecture,
    in @ esk2_0 @ esk1_0,
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

thf(c_0_21,plain,
    ! [X1: $i,X2: $i] :
      ( ( ( dsetconstr @ esk1_0
          @ ^ [Z0: $i] :
              ( ( epred1_0
                & ( Z0 = esk2_0 ) )
              | ( ~ epred1_0
                & ( Z0 = esk3_0 ) ) ) )
       != ( setadjoin @ X1 @ emptyset ) )
      | ( ( ( epred1_0
            & ( ( esk8_1 @ X2 )
              = esk2_0 ) )
          | ( ~ epred1_0
            & ( ( esk8_1 @ X2 )
              = esk3_0 ) ) )
      <~> ( ( esk8_1 @ X2 )
          = X2 ) )
      | ~ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
      | ~ ( in @ X2 @ esk1_0 ) ),
    inference(neg_ext,[status(thm)],[c_0_18]) ).

thf(c_0_22,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ( in @ X1
        @ ( dsetconstr @ X2
          @ ^ [Z0: $i] : ( Z0 = X1 ) ) )
      | ~ ( in @ X1 @ X2 ) ),
    inference(condense,[status(thm)],[c_0_19]) ).

thf(c_0_23,negated_conjecture,
    ( ( dsetconstr @ esk1_0
      @ ^ [Z0: $i] : ( Z0 = esk2_0 ) )
    = ( setadjoin @ esk2_0 @ emptyset ) ),
    inference(spm,[status(thm)],[c_0_16,c_0_20]) ).

thf(c_0_24,negated_conjecture,
    in @ esk3_0 @ esk1_0,
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

thf(c_0_25,plain,
    ! [X1: $i,X2: $i] :
      ( ( ( dsetconstr @ esk1_0
          @ ^ [Z0: $i] : ( Z0 = esk2_0 ) )
       != ( setadjoin @ X1 @ emptyset ) )
      | ( ( esk8_1 @ X2 )
       != esk2_0 )
      | ( ( esk8_1 @ X2 )
       != X2 )
      | ~ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
      | ~ ( in @ X2 @ esk1_0 )
      | ~ epred1_0 ),
    inference(cn,[status(thm)],[inference(local_rw,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_21])])]) ).

thf(c_0_26,negated_conjecture,
    in @ esk2_0 @ ( setadjoin @ esk2_0 @ emptyset ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_20])]) ).

thf(c_0_27,negated_conjecture,
    ( ( dsetconstr @ esk1_0
      @ ^ [Z0: $i] : ( Z0 = esk3_0 ) )
    = ( setadjoin @ esk3_0 @ emptyset ) ),
    inference(spm,[status(thm)],[c_0_16,c_0_24]) ).

thf(c_0_28,plain,
    ! [X2: $i,X1: $i] :
      ( ( ( esk8_1 @ X1 )
        = esk2_0 )
      | ( ( esk8_1 @ X1 )
        = X1 )
      | ( ( dsetconstr @ esk1_0
          @ ^ [Z0: $i] : ( Z0 = esk2_0 ) )
       != ( setadjoin @ X2 @ emptyset ) )
      | ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) )
      | ~ ( in @ X1 @ esk1_0 )
      | ~ epred1_0 ),
    inference(cn,[status(thm)],[inference(local_rw,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_21])])]) ).

thf(c_0_29,negated_conjecture,
    ( ( ( esk8_1 @ esk2_0 )
     != esk2_0 )
    | ~ epred1_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_23]),c_0_20])]) ).

thf(c_0_30,plain,
    ! [X1: $i,X2: $i] :
      ( epred1_0
      | ( ( dsetconstr @ esk1_0
          @ ^ [Z0: $i] : ( Z0 = esk3_0 ) )
       != ( setadjoin @ X1 @ emptyset ) )
      | ( ( esk8_1 @ X2 )
       != esk3_0 )
      | ( ( esk8_1 @ X2 )
       != X2 )
      | ~ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
      | ~ ( in @ X2 @ esk1_0 ) ),
    inference(cn,[status(thm)],[inference(local_rw,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_21])])]) ).

thf(c_0_31,negated_conjecture,
    in @ esk3_0 @ ( setadjoin @ esk3_0 @ emptyset ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_27]),c_0_24])]) ).

thf(c_0_32,plain,
    ! [X2: $i,X1: $i] :
      ( ( ( esk8_1 @ X1 )
        = esk3_0 )
      | ( ( esk8_1 @ X1 )
        = X1 )
      | epred1_0
      | ( ( dsetconstr @ esk1_0
          @ ^ [Z0: $i] : ( Z0 = esk3_0 ) )
       != ( setadjoin @ X2 @ emptyset ) )
      | ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) )
      | ~ ( in @ X1 @ esk1_0 ) ),
    inference(cn,[status(thm)],[inference(local_rw,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_21])])]) ).

thf(c_0_33,negated_conjecture,
    ~ epred1_0,
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_26]),c_0_23]),c_0_20])]),c_0_29]) ).

thf(c_0_34,negated_conjecture,
    ( epred1_0
    | ( ( esk8_1 @ esk3_0 )
     != esk3_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_27]),c_0_24])]) ).

thf(c_0_35,negated_conjecture,
    ( ( esk8_1 @ esk3_0 )
    = esk3_0 ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_31]),c_0_27]),c_0_24])]),c_0_33]) ).

thf(c_0_36,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]),c_0_33]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SEU704^2 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.12  % Command    : run_E %s %d THM
% 0.12/0.32  % Computer : n029.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Fri Jun 21 13:21:24 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.20/0.47  Running higher-order theorem proving
% 0.20/0.47  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/tmp/tmp.RyF4DKnMdq/E---3.1_9701.p
% 0.20/0.50  # Version: 3.2.0-ho
% 0.20/0.50  # Preprocessing class: HSSSSLSSSLMNSSN.
% 0.20/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.50  # Starting full_lambda_10 with 1500s (5) cores
% 0.20/0.50  # Starting lpo4_fix with 300s (1) cores
% 0.20/0.50  # Starting new_bool_6 with 300s (1) cores
% 0.20/0.50  # Starting lpo8_s with 300s (1) cores
% 0.20/0.50  # full_lambda_10 with pid 9781 completed with status 0
% 0.20/0.50  # Result found by full_lambda_10
% 0.20/0.50  # Preprocessing class: HSSSSLSSSLMNSSN.
% 0.20/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.50  # Starting full_lambda_10 with 1500s (5) cores
% 0.20/0.50  # SinE strategy is GSinE(CountFormulas,hypos,5,,5,20000,3.0,true)
% 0.20/0.50  # Search class: HHHSF-FFSF22-MSSFMFNN
% 0.20/0.50  # partial match(3): HHUSF-FFSF22-SSSFFFNN
% 0.20/0.50  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.50  # Starting new_ho_10 with 811s (1) cores
% 0.20/0.50  # Starting full_lambda_10 with 151s (1) cores
% 0.20/0.50  # Starting new_bool_1 with 136s (1) cores
% 0.20/0.50  # Starting new_bool_2 with 136s (1) cores
% 0.20/0.50  # Starting new_bool_9 with 136s (1) cores
% 0.20/0.50  # new_ho_10 with pid 9785 completed with status 9
% 0.20/0.50  # Starting sh5l with 130s (1) cores
% 0.20/0.50  # full_lambda_10 with pid 9786 completed with status 0
% 0.20/0.50  # Result found by full_lambda_10
% 0.20/0.50  # Preprocessing class: HSSSSLSSSLMNSSN.
% 0.20/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.50  # Starting full_lambda_10 with 1500s (5) cores
% 0.20/0.50  # SinE strategy is GSinE(CountFormulas,hypos,5,,5,20000,3.0,true)
% 0.20/0.50  # Search class: HHHSF-FFSF22-MSSFMFNN
% 0.20/0.50  # partial match(3): HHUSF-FFSF22-SSSFFFNN
% 0.20/0.50  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.50  # Starting new_ho_10 with 811s (1) cores
% 0.20/0.50  # Starting full_lambda_10 with 151s (1) cores
% 0.20/0.50  # Preprocessing time       : 0.001 s
% 0.20/0.50  # Presaturation interreduction done
% 0.20/0.50  
% 0.20/0.50  # Proof found!
% 0.20/0.50  # SZS status Theorem
% 0.20/0.50  # SZS output start CNFRefutation
% See solution above
% 0.20/0.50  # Parsed axioms                        : 15
% 0.20/0.50  # Removed by relevancy pruning/SinE    : 9
% 0.20/0.50  # Initial clauses                      : 7
% 0.20/0.50  # Removed in clause preprocessing      : 0
% 0.20/0.50  # Initial clauses in saturation        : 7
% 0.20/0.50  # Processed clauses                    : 59
% 0.20/0.50  # ...of these trivial                  : 5
% 0.20/0.50  # ...subsumed                          : 1
% 0.20/0.50  # ...remaining for further processing  : 53
% 0.20/0.50  # Other redundant clauses eliminated   : 6
% 0.20/0.50  # Clauses deleted for lack of memory   : 0
% 0.20/0.50  # Backward-subsumed                    : 9
% 0.20/0.50  # Backward-rewritten                   : 2
% 0.20/0.50  # Generated clauses                    : 116
% 0.20/0.50  # ...of the previous two non-redundant : 101
% 0.20/0.50  # ...aggressively subsumed             : 0
% 0.20/0.50  # Contextual simplify-reflections      : 3
% 0.20/0.50  # Paramodulations                      : 77
% 0.20/0.50  # Factorizations                       : 0
% 0.20/0.50  # NegExts                              : 5
% 0.20/0.50  # Equation resolutions                 : 7
% 0.20/0.50  # Disequality decompositions           : 0
% 0.20/0.50  # Total rewrite steps                  : 52
% 0.20/0.50  # ...of those cached                   : 43
% 0.20/0.50  # Propositional unsat checks           : 0
% 0.20/0.50  #    Propositional check models        : 0
% 0.20/0.50  #    Propositional check unsatisfiable : 0
% 0.20/0.50  #    Propositional clauses             : 0
% 0.20/0.50  #    Propositional clauses after purity: 0
% 0.20/0.50  #    Propositional unsat core size     : 0
% 0.20/0.50  #    Propositional preprocessing time  : 0.000
% 0.20/0.50  #    Propositional encoding time       : 0.000
% 0.20/0.50  #    Propositional solver time         : 0.000
% 0.20/0.50  #    Success case prop preproc time    : 0.000
% 0.20/0.50  #    Success case prop encoding time   : 0.000
% 0.20/0.50  #    Success case prop solver time     : 0.000
% 0.20/0.50  # Current number of processed clauses  : 32
% 0.20/0.50  #    Positive orientable unit clauses  : 9
% 0.20/0.50  #    Positive unorientable unit clauses: 0
% 0.20/0.50  #    Negative unit clauses             : 1
% 0.20/0.50  #    Non-unit-clauses                  : 22
% 0.20/0.50  # Current number of unprocessed clauses: 52
% 0.20/0.50  # ...number of literals in the above   : 247
% 0.20/0.50  # Current number of archived formulas  : 0
% 0.20/0.50  # Current number of archived clauses   : 21
% 0.20/0.50  # Clause-clause subsumption calls (NU) : 138
% 0.20/0.50  # Rec. Clause-clause subsumption calls : 20
% 0.20/0.50  # Non-unit clause-clause subsumptions  : 7
% 0.20/0.50  # Unit Clause-clause subsumption calls : 40
% 0.20/0.50  # Rewrite failures with RHS unbound    : 0
% 0.20/0.50  # BW rewrite match attempts            : 1
% 0.20/0.50  # BW rewrite match successes           : 1
% 0.20/0.50  # Condensation attempts                : 59
% 0.20/0.50  # Condensation successes               : 2
% 0.20/0.50  # Termbank termtop insertions          : 11676
% 0.20/0.50  # Search garbage collected termcells   : 596
% 0.20/0.50  
% 0.20/0.50  # -------------------------------------------------
% 0.20/0.50  # User time                : 0.014 s
% 0.20/0.50  # System time              : 0.004 s
% 0.20/0.50  # Total time               : 0.018 s
% 0.20/0.50  # Maximum resident set size: 1984 pages
% 0.20/0.50  
% 0.20/0.50  # -------------------------------------------------
% 0.20/0.50  # User time                : 0.056 s
% 0.20/0.50  # System time              : 0.009 s
% 0.20/0.50  # Total time               : 0.065 s
% 0.20/0.50  # Maximum resident set size: 1716 pages
% 0.20/0.50  % E---3.1 exiting
% 0.20/0.50  % E exiting
%------------------------------------------------------------------------------