TSTP Solution File: SEU655^2 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU655^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n028.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 03:28:53 EDT 2024

% Result   : Theorem 0.20s 0.50s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   29
% Syntax   : Number of formulae    :   63 (  19 unt;  19 typ;   0 def)
%            Number of atoms       :  161 (  72 equ;   0 cnn)
%            Maximal formula atoms :   25 (   3 avg)
%            Number of connectives :  644 (  48   ~;  49   |;  25   &; 487   @)
%                                         (   5 <=>;  30  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   28 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   37 (  37   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   22 (  19 usr;   9 con; 0-3 aty)
%            Number of variables   :  117 (  26   ^  78   !;  13   ?; 117   :)

% 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,
    setunion: $i > $i ).

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

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

thf(decl_28,type,
    kpair: $i > $i > $i ).

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

thf(decl_30,type,
    ex1: $i > ( $i > $o ) > $o ).

thf(decl_31,type,
    ex1I: $o ).

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

thf(decl_33,type,
    kfstpairEq: $o ).

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

thf(decl_35,type,
    esk1_3: $i > ( $i > $o ) > $i > $i ).

thf(decl_36,type,
    esk2_3: $i > ( $i > $o ) > $i > $i ).

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

thf(decl_38,type,
    esk4_0: $i ).

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

thf(decl_40,type,
    epred1_0: $i > $o ).

thf(ex1,axiom,
    ( ex1
    = ( ^ [X1: $i,X4: $i > $o] :
          ( singleton
          @ ( dsetconstr @ X1
            @ ^ [X2: $i] : ( X4 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1) ).

thf(singleton,axiom,
    ( singleton
    = ( ^ [X1: $i] :
        ? [X2: $i] :
          ( ( in @ X2 @ X1 )
          & ( X1
            = ( setadjoin @ X2 @ emptyset ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).

thf(ex1I,axiom,
    ( ex1I
  <=> ! [X1: $i,X4: $i > $o,X2: $i] :
        ( ( in @ X2 @ X1 )
       => ( ( X4 @ X2 )
         => ( ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( ( X4 @ X3 )
                 => ( X3 = X2 ) ) )
           => ( ex1 @ X1
              @ ^ [X3: $i] : ( X4 @ X3 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1I) ).

thf(iskpair,axiom,
    ( iskpair
    = ( ^ [X1: $i] :
        ? [X2: $i] :
          ( ( in @ X2 @ ( setunion @ X1 ) )
          & ? [X3: $i] :
              ( ( in @ X3 @ ( setunion @ X1 ) )
              & ( X1
                = ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iskpair) ).

thf(ksndsingleton,conjecture,
    ( ex1I
   => ( kfstpairEq
     => ( setukpairinjR
       => ! [X6: $i] :
            ( ( iskpair @ X6 )
           => ( singleton
              @ ( dsetconstr @ ( setunion @ X6 )
                @ ^ [X2: $i] :
                    ( X6
                    = ( kpair @ ( kfst @ X6 ) @ X2 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ksndsingleton) ).

thf(setukpairinjR,axiom,
    ( setukpairinjR
  <=> ! [X2: $i,X3: $i,X5: $i,X6: $i] :
        ( ( ( kpair @ X2 @ X3 )
          = ( kpair @ X5 @ X6 ) )
       => ( X3 = X6 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR) ).

thf(kfstpairEq,axiom,
    ( kfstpairEq
  <=> ! [X2: $i,X3: $i] :
        ( ( kfst @ ( kpair @ X2 @ X3 ) )
        = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstpairEq) ).

thf(kpair,axiom,
    ( kpair
    = ( ^ [X2: $i,X3: $i] : ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpair) ).

thf(c_0_8,plain,
    ( ex1
    = ( ^ [Z0: $i,Z1: $i > $o] :
        ? [X18: $i] :
          ( ( in @ X18
            @ ( dsetconstr @ Z0
              @ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
          & ( ( dsetconstr @ Z0
              @ ^ [Z2: $i] : ( Z1 @ Z2 ) )
            = ( setadjoin @ X18 @ emptyset ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[ex1]) ).

thf(c_0_9,plain,
    ( singleton
    = ( ^ [Z0: $i] :
        ? [X2: $i] :
          ( ( in @ X2 @ Z0 )
          & ( Z0
            = ( setadjoin @ X2 @ emptyset ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[singleton]) ).

thf(c_0_10,plain,
    ( ex1I
  <=> ! [X1: $i,X4: $i > $o,X2: $i] :
        ( ( in @ X2 @ X1 )
       => ( ( X4 @ X2 )
         => ( ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( ( X4 @ X3 )
                 => ( X3 = X2 ) ) )
           => ( ex1 @ X1
              @ ^ [Z0: $i] : ( X4 @ Z0 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[ex1I]) ).

thf(c_0_11,plain,
    ( ex1
    = ( ^ [Z0: $i,Z1: $i > $o] :
        ? [X18: $i] :
          ( ( in @ X18
            @ ( dsetconstr @ Z0
              @ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
          & ( ( dsetconstr @ Z0
              @ ^ [Z2: $i] : ( Z1 @ Z2 ) )
            = ( setadjoin @ X18 @ emptyset ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_8,c_0_9]) ).

thf(c_0_12,plain,
    ( ex1I
    = ( ! [X1: $i,X4: $i > $o,X2: $i] :
          ( ( in @ X2 @ X1 )
         => ( ( X4 @ X2 )
           => ( ! [X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ( ( X4 @ X3 )
                   => ( X3 = X2 ) ) )
             => ? [X19: $i] :
                  ( ( in @ X19
                    @ ( dsetconstr @ X1
                      @ ^ [Z0: $i] : ( X4 @ Z0 ) ) )
                  & ( ( dsetconstr @ X1
                      @ ^ [Z0: $i] : ( X4 @ Z0 ) )
                    = ( setadjoin @ X19 @ emptyset ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_10,c_0_11]) ).

thf(c_0_13,plain,
    ( iskpair
    = ( ^ [Z0: $i] :
        ? [X2: $i] :
          ( ( in @ X2 @ ( setunion @ Z0 ) )
          & ? [X3: $i] :
              ( ( in @ X3 @ ( setunion @ Z0 ) )
              & ( Z0
                = ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[iskpair]) ).

thf(c_0_14,negated_conjecture,
    ~ ( ! [X20: $i,X21: $i > $o,X22: $i] :
          ( ( in @ X22 @ X20 )
         => ( ( X21 @ X22 )
           => ( ! [X23: $i] :
                  ( ( in @ X23 @ X20 )
                 => ( ( X21 @ X23 )
                   => ( X23 = X22 ) ) )
             => ? [X24: $i] :
                  ( ( in @ X24 @ ( dsetconstr @ X20 @ X21 ) )
                  & ( ( dsetconstr @ X20 @ X21 )
                    = ( setadjoin @ X24 @ emptyset ) ) ) ) ) )
     => ( ! [X25: $i,X26: $i] :
            ( ( kfst @ ( kpair @ X25 @ X26 ) )
            = X25 )
       => ( ! [X27: $i,X28: $i,X29: $i,X30: $i] :
              ( ( ( kpair @ X27 @ X28 )
                = ( kpair @ X29 @ X30 ) )
             => ( X28 = X30 ) )
         => ! [X6: $i] :
              ( ? [X31: $i] :
                  ( ( in @ X31 @ ( setunion @ X6 ) )
                  & ? [X32: $i] :
                      ( ( in @ X32 @ ( setunion @ X6 ) )
                      & ( X6
                        = ( setadjoin @ ( setadjoin @ X31 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X31 @ ( setadjoin @ X32 @ emptyset ) ) @ emptyset ) ) ) ) )
             => ? [X33: $i] :
                  ( ( in @ X33
                    @ ( dsetconstr @ ( setunion @ X6 )
                      @ ^ [Z0: $i] :
                          ( X6
                          = ( kpair @ ( kfst @ X6 ) @ Z0 ) ) ) )
                  & ( ( dsetconstr @ ( setunion @ X6 )
                      @ ^ [Z0: $i] :
                          ( X6
                          = ( kpair @ ( kfst @ X6 ) @ Z0 ) ) )
                    = ( setadjoin @ X33 @ emptyset ) ) ) ) ) ) ),
    inference(fool_unroll,[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)],[ksndsingleton])]),c_0_9]),c_0_12]),c_0_13]),setukpairinjR]),kfstpairEq])]) ).

thf(c_0_15,plain,
    ! [X34: $i,X35: $i] :
      ( ( kpair @ X34 @ X35 )
      = ( setadjoin @ ( setadjoin @ X34 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X34 @ ( setadjoin @ X35 @ emptyset ) ) @ emptyset ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[kpair])]) ).

thf(c_0_16,negated_conjecture,
    ! [X36: $i,X37: $i > $o,X38: $i,X41: $i,X42: $i,X43: $i,X44: $i,X45: $i,X46: $i,X50: $i] :
      ( ( ( in @ ( esk2_3 @ X36 @ X37 @ X38 ) @ ( dsetconstr @ X36 @ X37 ) )
        | ( in @ ( esk1_3 @ X36 @ X37 @ X38 ) @ X36 )
        | ~ ( X37 @ X38 )
        | ~ ( in @ X38 @ X36 ) )
      & ( ( ( dsetconstr @ X36 @ X37 )
          = ( setadjoin @ ( esk2_3 @ X36 @ X37 @ X38 ) @ emptyset ) )
        | ( in @ ( esk1_3 @ X36 @ X37 @ X38 ) @ X36 )
        | ~ ( X37 @ X38 )
        | ~ ( in @ X38 @ X36 ) )
      & ( ( in @ ( esk2_3 @ X36 @ X37 @ X38 ) @ ( dsetconstr @ X36 @ X37 ) )
        | ( X37 @ ( esk1_3 @ X36 @ X37 @ X38 ) )
        | ~ ( X37 @ X38 )
        | ~ ( in @ X38 @ X36 ) )
      & ( ( ( dsetconstr @ X36 @ X37 )
          = ( setadjoin @ ( esk2_3 @ X36 @ X37 @ X38 ) @ emptyset ) )
        | ( X37 @ ( esk1_3 @ X36 @ X37 @ X38 ) )
        | ~ ( X37 @ X38 )
        | ~ ( in @ X38 @ X36 ) )
      & ( ( in @ ( esk2_3 @ X36 @ X37 @ X38 ) @ ( dsetconstr @ X36 @ X37 ) )
        | ( ( esk1_3 @ X36 @ X37 @ X38 )
         != X38 )
        | ~ ( X37 @ X38 )
        | ~ ( in @ X38 @ X36 ) )
      & ( ( ( dsetconstr @ X36 @ X37 )
          = ( setadjoin @ ( esk2_3 @ X36 @ X37 @ X38 ) @ emptyset ) )
        | ( ( esk1_3 @ X36 @ X37 @ X38 )
         != X38 )
        | ~ ( X37 @ X38 )
        | ~ ( in @ X38 @ X36 ) )
      & ( ( kfst @ ( kpair @ X41 @ X42 ) )
        = X41 )
      & ( ( ( kpair @ X43 @ X44 )
         != ( kpair @ X45 @ X46 ) )
        | ( X44 = X46 ) )
      & ( in @ esk4_0 @ ( setunion @ esk3_0 ) )
      & ( in @ esk5_0 @ ( setunion @ esk3_0 ) )
      & ( esk3_0
        = ( setadjoin @ ( setadjoin @ esk4_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk4_0 @ ( setadjoin @ esk5_0 @ emptyset ) ) @ emptyset ) ) )
      & ( ~ ( in @ X50
            @ ( dsetconstr @ ( setunion @ esk3_0 )
              @ ^ [Z0: $i] :
                  ( esk3_0
                  = ( kpair @ ( kfst @ esk3_0 ) @ Z0 ) ) ) )
        | ( ( dsetconstr @ ( setunion @ esk3_0 )
            @ ^ [Z0: $i] :
                ( esk3_0
                = ( kpair @ ( kfst @ esk3_0 ) @ Z0 ) ) )
         != ( setadjoin @ X50 @ 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_14])])])])])]) ).

thf(c_0_17,plain,
    ! [X51: $i,X52: $i] :
      ( ( kpair @ X51 @ X52 )
      = ( setadjoin @ ( setadjoin @ X51 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X51 @ ( setadjoin @ X52 @ emptyset ) ) @ emptyset ) ) ),
    inference(variable_rename,[status(thm)],[c_0_15]) ).

thf(c_0_18,negated_conjecture,
    ( esk3_0
    = ( setadjoin @ ( setadjoin @ esk4_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk4_0 @ ( setadjoin @ esk5_0 @ emptyset ) ) @ emptyset ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

thf(c_0_19,plain,
    ! [X1: $i,X2: $i] :
      ( ( kpair @ X1 @ X2 )
      = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

thf(c_0_20,plain,
    ! [X55: $i] :
      ( ( ~ ( epred1_0 @ X55 )
        | ( esk3_0
          = ( kpair @ ( kfst @ esk3_0 ) @ X55 ) ) )
      & ( ( esk3_0
         != ( kpair @ ( kfst @ esk3_0 ) @ X55 ) )
        | ( epred1_0 @ X55 ) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])]) ).

thf(c_0_21,negated_conjecture,
    ! [X2: $i,X1: $i] :
      ( ( kfst @ ( kpair @ X1 @ X2 ) )
      = X1 ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

thf(c_0_22,negated_conjecture,
    ( ( kpair @ esk4_0 @ esk5_0 )
    = esk3_0 ),
    inference(rw,[status(thm)],[c_0_18,c_0_19]) ).

thf(c_0_23,plain,
    ! [X53: $i] :
      ( ( epred1_0 @ X53 )
    <=> ( esk3_0
        = ( kpair @ ( kfst @ esk3_0 ) @ X53 ) ) ),
    introduced(definition) ).

thf(c_0_24,negated_conjecture,
    ! [X1: $i,X2: $i,X3: $i,X5: $i] :
      ( ( X2 = X5 )
      | ( ( kpair @ X1 @ X2 )
       != ( kpair @ X3 @ X5 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

thf(c_0_25,plain,
    ! [X1: $i] :
      ( ( esk3_0
        = ( kpair @ ( kfst @ esk3_0 ) @ X1 ) )
      | ~ ( epred1_0 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

thf(c_0_26,negated_conjecture,
    ( ( kfst @ esk3_0 )
    = esk4_0 ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

thf(c_0_27,negated_conjecture,
    ! [X1: $i] :
      ( ( ( in @ X1 @ ( dsetconstr @ ( setunion @ esk3_0 ) @ epred1_0 ) )
       != $true )
      | ( ( dsetconstr @ ( setunion @ esk3_0 ) @ epred1_0 )
       != ( setadjoin @ X1 @ emptyset ) ) ),
    inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_16]),c_0_23]),c_0_23]) ).

thf(c_0_28,negated_conjecture,
    ! [X2: $i,X1: $i] :
      ( ( X1 = esk5_0 )
      | ( ( kpair @ X2 @ X1 )
       != esk3_0 ) ),
    inference(spm,[status(thm)],[c_0_24,c_0_22]) ).

thf(c_0_29,plain,
    ! [X1: $i] :
      ( ( ( kpair @ esk4_0 @ X1 )
        = esk3_0 )
      | ~ ( epred1_0 @ X1 ) ),
    inference(rw,[status(thm)],[c_0_25,c_0_26]) ).

thf(c_0_30,negated_conjecture,
    ! [X1: $i] :
      ( ( ( dsetconstr @ ( setunion @ esk3_0 ) @ epred1_0 )
       != ( setadjoin @ X1 @ emptyset ) )
      | ~ ( in @ X1 @ ( dsetconstr @ ( setunion @ esk3_0 ) @ epred1_0 ) ) ),
    inference(cn,[status(thm)],[c_0_27]) ).

thf(c_0_31,negated_conjecture,
    ! [X4: $i > $o,X2: $i,X1: $i] :
      ( ( in @ ( esk2_3 @ X1 @ X4 @ X2 ) @ ( dsetconstr @ X1 @ X4 ) )
      | ( X4 @ ( esk1_3 @ X1 @ X4 @ X2 ) )
      | ~ ( X4 @ X2 )
      | ~ ( in @ X2 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

thf(c_0_32,negated_conjecture,
    ! [X4: $i > $o,X2: $i,X1: $i] :
      ( ( ( dsetconstr @ X1 @ X4 )
        = ( setadjoin @ ( esk2_3 @ X1 @ X4 @ X2 ) @ emptyset ) )
      | ( X4 @ ( esk1_3 @ X1 @ X4 @ X2 ) )
      | ~ ( X4 @ X2 )
      | ~ ( in @ X2 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

thf(c_0_33,plain,
    ! [X1: $i] :
      ( ( epred1_0 @ X1 )
      | ( esk3_0
       != ( kpair @ ( kfst @ esk3_0 ) @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

thf(c_0_34,negated_conjecture,
    ! [X4: $i > $o,X2: $i,X1: $i] :
      ( ( in @ ( esk2_3 @ X1 @ X4 @ X2 ) @ ( dsetconstr @ X1 @ X4 ) )
      | ( ( esk1_3 @ X1 @ X4 @ X2 )
       != X2 )
      | ~ ( X4 @ X2 )
      | ~ ( in @ X2 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

thf(c_0_35,negated_conjecture,
    ! [X4: $i > $o,X2: $i,X1: $i] :
      ( ( ( dsetconstr @ X1 @ X4 )
        = ( setadjoin @ ( esk2_3 @ X1 @ X4 @ X2 ) @ emptyset ) )
      | ( ( esk1_3 @ X1 @ X4 @ X2 )
       != X2 )
      | ~ ( X4 @ X2 )
      | ~ ( in @ X2 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

thf(c_0_36,plain,
    ! [X1: $i] :
      ( ( X1 = esk5_0 )
      | ~ ( epred1_0 @ X1 ) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

thf(c_0_37,negated_conjecture,
    ! [X1: $i] :
      ( ( epred1_0 @ ( esk1_3 @ ( setunion @ esk3_0 ) @ epred1_0 @ X1 ) )
      | ~ ( in @ X1 @ ( setunion @ esk3_0 ) )
      | ~ ( epred1_0 @ X1 ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).

thf(c_0_38,plain,
    ! [X1: $i] :
      ( ( epred1_0 @ X1 )
      | ( ( kpair @ esk4_0 @ X1 )
       != esk3_0 ) ),
    inference(rw,[status(thm)],[c_0_33,c_0_26]) ).

thf(c_0_39,negated_conjecture,
    ! [X1: $i] :
      ( ( ( esk1_3 @ ( setunion @ esk3_0 ) @ epred1_0 @ X1 )
       != X1 )
      | ~ ( in @ X1 @ ( setunion @ esk3_0 ) )
      | ~ ( epred1_0 @ X1 ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_34]),c_0_35]) ).

thf(c_0_40,plain,
    ! [X1: $i] :
      ( ( ( esk1_3 @ ( setunion @ esk3_0 ) @ epred1_0 @ X1 )
        = esk5_0 )
      | ~ ( in @ X1 @ ( setunion @ esk3_0 ) )
      | ~ ( epred1_0 @ X1 ) ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

thf(c_0_41,negated_conjecture,
    in @ esk5_0 @ ( setunion @ esk3_0 ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

thf(c_0_42,negated_conjecture,
    epred1_0 @ esk5_0,
    inference(spm,[status(thm)],[c_0_38,c_0_22]) ).

thf(c_0_43,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40])]),c_0_41]),c_0_42])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SEU655^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.14  % Command    : run_E %s %d THM
% 0.15/0.35  % Computer : n028.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Sun May 19 17:44:08 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.20/0.48  Running higher-order theorem proving
% 0.20/0.48  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
% 0.20/0.50  # Version: 3.1.0-ho
% 0.20/0.50  # Preprocessing class: HSSSSLSSSLMNHSA.
% 0.20/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.50  # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.50  # Starting new_ho_7 with 300s (1) cores
% 0.20/0.50  # Starting lpo8_lambda_fix with 300s (1) cores
% 0.20/0.50  # Starting lpo9_lambda_fix with 300s (1) cores
% 0.20/0.50  # lpo8_lambda_fix with pid 27537 completed with status 0
% 0.20/0.50  # Result found by lpo8_lambda_fix
% 0.20/0.50  # Preprocessing class: HSSSSLSSSLMNHSA.
% 0.20/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.50  # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.50  # Starting new_ho_7 with 300s (1) cores
% 0.20/0.50  # Starting lpo8_lambda_fix with 300s (1) cores
% 0.20/0.50  # SinE strategy is GSinE(CountFormulas,,5.0,,4,20000,1.0)
% 0.20/0.50  # Search class: HGHSS-FFMS32-MHSFMSBN
% 0.20/0.50  # partial match(3): HGHSS-FFMS31-SHSSMSBN
% 0.20/0.50  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.50  # Starting new_ho_10 with 163s (1) cores
% 0.20/0.50  # new_ho_10 with pid 27540 completed with status 0
% 0.20/0.50  # Result found by new_ho_10
% 0.20/0.50  # Preprocessing class: HSSSSLSSSLMNHSA.
% 0.20/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.50  # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.50  # Starting new_ho_7 with 300s (1) cores
% 0.20/0.50  # Starting lpo8_lambda_fix with 300s (1) cores
% 0.20/0.50  # SinE strategy is GSinE(CountFormulas,,5.0,,4,20000,1.0)
% 0.20/0.50  # Search class: HGHSS-FFMS32-MHSFMSBN
% 0.20/0.50  # partial match(3): HGHSS-FFMS31-SHSSMSBN
% 0.20/0.50  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.50  # Starting new_ho_10 with 163s (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
% 0.20/0.51  # Parsed axioms                        : 21
% 0.20/0.51  # Removed by relevancy pruning/SinE    : 13
% 0.20/0.51  # Initial clauses                      : 15
% 0.20/0.51  # Removed in clause preprocessing      : 0
% 0.20/0.51  # Initial clauses in saturation        : 15
% 0.20/0.51  # Processed clauses                    : 58
% 0.20/0.51  # ...of these trivial                  : 0
% 0.20/0.51  # ...subsumed                          : 4
% 0.20/0.51  # ...remaining for further processing  : 54
% 0.20/0.51  # Other redundant clauses eliminated   : 2
% 0.20/0.51  # Clauses deleted for lack of memory   : 0
% 0.20/0.51  # Backward-subsumed                    : 0
% 0.20/0.51  # Backward-rewritten                   : 2
% 0.20/0.51  # Generated clauses                    : 85
% 0.20/0.51  # ...of the previous two non-redundant : 76
% 0.20/0.51  # ...aggressively subsumed             : 0
% 0.20/0.51  # Contextual simplify-reflections      : 3
% 0.20/0.51  # Paramodulations                      : 82
% 0.20/0.51  # Factorizations                       : 0
% 0.20/0.51  # NegExts                              : 0
% 0.20/0.51  # Equation resolutions                 : 3
% 0.20/0.51  # Disequality decompositions           : 0
% 0.20/0.51  # Total rewrite steps                  : 18
% 0.20/0.51  # ...of those cached                   : 10
% 0.20/0.51  # Propositional unsat checks           : 0
% 0.20/0.51  #    Propositional check models        : 0
% 0.20/0.51  #    Propositional check unsatisfiable : 0
% 0.20/0.51  #    Propositional clauses             : 0
% 0.20/0.51  #    Propositional clauses after purity: 0
% 0.20/0.51  #    Propositional unsat core size     : 0
% 0.20/0.51  #    Propositional preprocessing time  : 0.000
% 0.20/0.51  #    Propositional encoding time       : 0.000
% 0.20/0.51  #    Propositional solver time         : 0.000
% 0.20/0.51  #    Success case prop preproc time    : 0.000
% 0.20/0.51  #    Success case prop encoding time   : 0.000
% 0.20/0.51  #    Success case prop solver time     : 0.000
% 0.20/0.51  # Current number of processed clauses  : 37
% 0.20/0.51  #    Positive orientable unit clauses  : 8
% 0.20/0.51  #    Positive unorientable unit clauses: 0
% 0.20/0.51  #    Negative unit clauses             : 0
% 0.20/0.51  #    Non-unit-clauses                  : 29
% 0.20/0.51  # Current number of unprocessed clauses: 47
% 0.20/0.51  # ...number of literals in the above   : 260
% 0.20/0.51  # Current number of archived formulas  : 0
% 0.20/0.51  # Current number of archived clauses   : 17
% 0.20/0.51  # Clause-clause subsumption calls (NU) : 119
% 0.20/0.51  # Rec. Clause-clause subsumption calls : 59
% 0.20/0.51  # Non-unit clause-clause subsumptions  : 7
% 0.20/0.51  # Unit Clause-clause subsumption calls : 3
% 0.20/0.51  # Rewrite failures with RHS unbound    : 0
% 0.20/0.51  # BW rewrite match attempts            : 2
% 0.20/0.51  # BW rewrite match successes           : 2
% 0.20/0.51  # Condensation attempts                : 58
% 0.20/0.51  # Condensation successes               : 0
% 0.20/0.51  # Termbank termtop insertions          : 4841
% 0.20/0.51  # Search garbage collected termcells   : 567
% 0.20/0.51  
% 0.20/0.51  # -------------------------------------------------
% 0.20/0.51  # User time                : 0.010 s
% 0.20/0.51  # System time              : 0.004 s
% 0.20/0.51  # Total time               : 0.014 s
% 0.20/0.51  # Maximum resident set size: 1896 pages
% 0.20/0.51  
% 0.20/0.51  # -------------------------------------------------
% 0.20/0.51  # User time                : 0.011 s
% 0.20/0.51  # System time              : 0.006 s
% 0.20/0.51  # Total time               : 0.017 s
% 0.20/0.51  # Maximum resident set size: 1724 pages
% 0.20/0.51  % E---3.1 exiting
% 0.20/0.51  % E exiting
%------------------------------------------------------------------------------