TSTP Solution File: SEU676^2 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU676^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n025.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 03:29:03 EDT 2024

% Result   : Theorem 0.20s 0.49s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   30
% Syntax   : Number of formulae    :   60 (  24 unt;  22 typ;   0 def)
%            Number of atoms       :  172 (  31 equ;   0 cnn)
%            Maximal formula atoms :   22 (   4 avg)
%            Number of connectives :  710 (  36   ~;  35   |;  24   &; 589   @)
%                                         (   2 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   40 (  40   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   24 (  22 usr;   8 con; 0-4 aty)
%            Number of variables   :  161 (  57   ^  94   !;  10   ?; 161   :)

% 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_26,type,
    setunion: $i > $i ).

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

thf(decl_28,type,
    subset: $i > $i > $o ).

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

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

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

thf(decl_32,type,
    ex1: $i > ( $i > $o ) > $o ).

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

thf(decl_34,type,
    func: $i > $i > $i > $o ).

thf(decl_35,type,
    funcSet: $i > $i > $i ).

thf(decl_36,type,
    ap: $i > $i > $i > $i > $i ).

thf(decl_37,type,
    app: $o ).

thf(decl_38,type,
    infuncsetfunc: $o ).

thf(decl_39,type,
    esk1_3: $i > $i > $i > $i ).

thf(decl_40,type,
    esk2_4: $i > $i > $i > $i > $i ).

thf(decl_41,type,
    esk3_0: $i ).

thf(decl_42,type,
    esk4_0: $i ).

thf(decl_43,type,
    esk5_0: $i ).

thf(decl_44,type,
    esk6_0: $i ).

thf(ex1,axiom,
    ( ex1
    = ( ^ [X1: $i,X3: $i > $o] :
          ( singleton
          @ ( dsetconstr @ X1
            @ ^ [X2: $i] : ( X3 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1) ).

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

thf(func,axiom,
    ( func
    = ( ^ [X1: $i,X4: $i,X6: $i] :
          ( ( breln @ X1 @ X4 @ X6 )
          & ! [X2: $i] :
              ( ( in @ X2 @ X1 )
             => ( ex1 @ X4
                @ ^ [X7: $i] : ( in @ ( kpair @ X2 @ X7 ) @ X6 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',func) ).

thf(breln,axiom,
    ( breln
    = ( ^ [X1: $i,X4: $i,X5: $i] : ( subset @ X5 @ ( cartprod @ X1 @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln) ).

thf(infuncsetfunc,axiom,
    ( infuncsetfunc
  <=> ! [X1: $i,X4: $i,X8: $i] :
        ( ( in @ X8 @ ( funcSet @ X1 @ X4 ) )
       => ( func @ X1 @ X4 @ X8 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',infuncsetfunc) ).

thf(app,axiom,
    ( app
  <=> ! [X1: $i,X4: $i,X8: $i] :
        ( ( func @ X1 @ X4 @ X8 )
       => ! [X2: $i] :
            ( ( in @ X2 @ X1 )
           => ( in @ ( ap @ X1 @ X4 @ X8 @ X2 ) @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',app) ).

thf(ap2p,conjecture,
    ( app
   => ( infuncsetfunc
     => ! [X1: $i,X4: $i,X8: $i] :
          ( ( in @ X8 @ ( funcSet @ X1 @ X4 ) )
         => ! [X2: $i] :
              ( ( in @ X2 @ X1 )
             => ( in @ ( ap @ X1 @ X4 @ X8 @ X2 ) @ X4 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2p) ).

thf(ap,axiom,
    ( ap
    = ( ^ [X1: $i,X4: $i,X8: $i,X2: $i] :
          ( setunion
          @ ( dsetconstr @ X4
            @ ^ [X7: $i] : ( in @ ( kpair @ X2 @ X7 ) @ X8 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap) ).

thf(c_0_8,plain,
    ( ex1
    = ( ^ [Z0: $i,Z1: $i > $o] :
        ? [X20: $i] :
          ( ( in @ X20
            @ ( dsetconstr @ Z0
              @ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
          & ( ( dsetconstr @ Z0
              @ ^ [Z2: $i] : ( Z1 @ Z2 ) )
            = ( setadjoin @ X20 @ 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,
    ( func
    = ( ^ [Z0: $i,Z1: $i,Z2: $i] :
          ( ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) )
          & ! [X2: $i] :
              ( ( in @ X2 @ Z0 )
             => ? [X21: $i] :
                  ( ( in @ X21
                    @ ( dsetconstr @ Z1
                      @ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) ) )
                  & ( ( dsetconstr @ Z1
                      @ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) )
                    = ( setadjoin @ X21 @ emptyset ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[func]) ).

thf(c_0_11,plain,
    ( breln
    = ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
    inference(fof_simplification,[status(thm)],[breln]) ).

thf(c_0_12,plain,
    ( ex1
    = ( ^ [Z0: $i,Z1: $i > $o] :
        ? [X20: $i] :
          ( ( in @ X20
            @ ( dsetconstr @ Z0
              @ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
          & ( ( dsetconstr @ Z0
              @ ^ [Z2: $i] : ( Z1 @ Z2 ) )
            = ( setadjoin @ X20 @ emptyset ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_8,c_0_9]) ).

thf(c_0_13,plain,
    ( func
    = ( ^ [Z0: $i,Z1: $i,Z2: $i] :
          ( ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) )
          & ! [X2: $i] :
              ( ( in @ X2 @ Z0 )
             => ? [X21: $i] :
                  ( ( in @ X21
                    @ ( dsetconstr @ Z1
                      @ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) ) )
                  & ( ( dsetconstr @ Z1
                      @ ^ [Z3: $i] : ( in @ ( kpair @ X2 @ Z3 ) @ Z2 ) )
                    = ( setadjoin @ X21 @ emptyset ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).

thf(c_0_14,axiom,
    ( infuncsetfunc
    = ( ! [X1: $i,X4: $i,X8: $i] :
          ( ( in @ X8 @ ( funcSet @ X1 @ X4 ) )
         => ( ( subset @ X8 @ ( cartprod @ X1 @ X4 ) )
            & ! [X24: $i] :
                ( ( in @ X24 @ X1 )
               => ? [X25: $i] :
                    ( ( in @ X25
                      @ ( dsetconstr @ X4
                        @ ^ [Z0: $i] : ( in @ ( kpair @ X24 @ Z0 ) @ X8 ) ) )
                    & ( ( dsetconstr @ X4
                        @ ^ [Z0: $i] : ( in @ ( kpair @ X24 @ Z0 ) @ X8 ) )
                      = ( setadjoin @ X25 @ emptyset ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[infuncsetfunc,c_0_13]) ).

thf(c_0_15,axiom,
    ( app
    = ( ! [X1: $i,X4: $i,X8: $i] :
          ( ( ( subset @ X8 @ ( cartprod @ X1 @ X4 ) )
            & ! [X22: $i] :
                ( ( in @ X22 @ X1 )
               => ? [X23: $i] :
                    ( ( in @ X23
                      @ ( dsetconstr @ X4
                        @ ^ [Z0: $i] : ( in @ ( kpair @ X22 @ Z0 ) @ X8 ) ) )
                    & ( ( dsetconstr @ X4
                        @ ^ [Z0: $i] : ( in @ ( kpair @ X22 @ Z0 ) @ X8 ) )
                      = ( setadjoin @ X23 @ emptyset ) ) ) ) )
         => ! [X2: $i] :
              ( ( in @ X2 @ X1 )
             => ( in @ ( ap @ X1 @ X4 @ X8 @ X2 ) @ X4 ) ) ) ) ),
    inference(apply_def,[status(thm)],[app,c_0_13]) ).

thf(c_0_16,negated_conjecture,
    ~ ( ! [X26: $i,X27: $i,X28: $i] :
          ( ( ( subset @ X28 @ ( cartprod @ X26 @ X27 ) )
            & ! [X29: $i] :
                ( ( in @ X29 @ X26 )
               => ? [X30: $i] :
                    ( ( in @ X30
                      @ ( dsetconstr @ X27
                        @ ^ [Z0: $i] : ( in @ ( kpair @ X29 @ Z0 ) @ X28 ) ) )
                    & ( ( dsetconstr @ X27
                        @ ^ [Z0: $i] : ( in @ ( kpair @ X29 @ Z0 ) @ X28 ) )
                      = ( setadjoin @ X30 @ emptyset ) ) ) ) )
         => ! [X31: $i] :
              ( ( in @ X31 @ X26 )
             => ( in @ ( ap @ X26 @ X27 @ X28 @ X31 ) @ X27 ) ) )
     => ( ! [X32: $i,X33: $i,X34: $i] :
            ( ( in @ X34 @ ( funcSet @ X32 @ X33 ) )
           => ( ( subset @ X34 @ ( cartprod @ X32 @ X33 ) )
              & ! [X35: $i] :
                  ( ( in @ X35 @ X32 )
                 => ? [X36: $i] :
                      ( ( in @ X36
                        @ ( dsetconstr @ X33
                          @ ^ [Z0: $i] : ( in @ ( kpair @ X35 @ Z0 ) @ X34 ) ) )
                      & ( ( dsetconstr @ X33
                          @ ^ [Z0: $i] : ( in @ ( kpair @ X35 @ Z0 ) @ X34 ) )
                        = ( setadjoin @ X36 @ emptyset ) ) ) ) ) )
       => ! [X1: $i,X4: $i,X8: $i] :
            ( ( in @ X8 @ ( funcSet @ X1 @ X4 ) )
           => ! [X2: $i] :
                ( ( in @ X2 @ X1 )
               => ( in @ ( ap @ X1 @ X4 @ X8 @ X2 ) @ X4 ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[ap2p]),c_0_14]),c_0_15]) ).

thf(c_0_17,plain,
    ! [X39: $i,X40: $i,X41: $i,X42: $i] :
      ( ( ap @ X39 @ X40 @ X41 @ X42 )
      = ( setunion
        @ ( dsetconstr @ X40
          @ ^ [Z0: $i] : ( in @ ( kpair @ X42 @ Z0 ) @ X41 ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[ap])]) ).

thf(c_0_18,negated_conjecture,
    ! [X45: $i,X46: $i,X47: $i,X49: $i,X50: $i,X51: $i,X52: $i,X53: $i,X54: $i] :
      ( ( ( in @ ( esk1_3 @ X45 @ X46 @ X47 ) @ X45 )
        | ~ ( subset @ X47 @ ( cartprod @ X45 @ X46 ) )
        | ~ ( in @ X50 @ X45 )
        | ( in @ ( ap @ X45 @ X46 @ X47 @ X50 ) @ X46 ) )
      & ( ~ ( in @ X49
            @ ( dsetconstr @ X46
              @ ^ [Z0: $i] : ( in @ ( kpair @ ( esk1_3 @ X45 @ X46 @ X47 ) @ Z0 ) @ X47 ) ) )
        | ( ( dsetconstr @ X46
            @ ^ [Z0: $i] : ( in @ ( kpair @ ( esk1_3 @ X45 @ X46 @ X47 ) @ Z0 ) @ X47 ) )
         != ( setadjoin @ X49 @ emptyset ) )
        | ~ ( subset @ X47 @ ( cartprod @ X45 @ X46 ) )
        | ~ ( in @ X50 @ X45 )
        | ( in @ ( ap @ X45 @ X46 @ X47 @ X50 ) @ X46 ) )
      & ( ( subset @ X53 @ ( cartprod @ X51 @ X52 ) )
        | ~ ( in @ X53 @ ( funcSet @ X51 @ X52 ) ) )
      & ( ( in @ ( esk2_4 @ X51 @ X52 @ X53 @ X54 )
          @ ( dsetconstr @ X52
            @ ^ [Z0: $i] : ( in @ ( kpair @ X54 @ Z0 ) @ X53 ) ) )
        | ~ ( in @ X54 @ X51 )
        | ~ ( in @ X53 @ ( funcSet @ X51 @ X52 ) ) )
      & ( ( ( dsetconstr @ X52
            @ ^ [Z0: $i] : ( in @ ( kpair @ X54 @ Z0 ) @ X53 ) )
          = ( setadjoin @ ( esk2_4 @ X51 @ X52 @ X53 @ X54 ) @ emptyset ) )
        | ~ ( in @ X54 @ X51 )
        | ~ ( in @ X53 @ ( funcSet @ X51 @ X52 ) ) )
      & ( in @ esk5_0 @ ( funcSet @ esk3_0 @ esk4_0 ) )
      & ( in @ esk6_0 @ esk3_0 )
      & ~ ( in @ ( ap @ esk3_0 @ esk4_0 @ esk5_0 @ esk6_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_16])])])])])]) ).

thf(c_0_19,plain,
    ! [X60: $i,X61: $i,X62: $i,X63: $i] :
      ( ( ap @ X60 @ X61 @ X62 @ X63 )
      = ( setunion
        @ ( dsetconstr @ X61
          @ ^ [Z0: $i] : ( in @ ( kpair @ X63 @ Z0 ) @ X62 ) ) ) ),
    inference(variable_rename,[status(thm)],[c_0_17]) ).

thf(c_0_20,negated_conjecture,
    ! [X2: $i,X5: $i,X4: $i,X1: $i] :
      ( ( in @ ( esk1_3 @ X1 @ X2 @ X4 ) @ X1 )
      | ( in @ ( ap @ X1 @ X2 @ X4 @ X5 ) @ X2 )
      | ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
      | ~ ( in @ X5 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

thf(c_0_21,negated_conjecture,
    ! [X1: $i,X2: $i,X4: $i] :
      ( ( subset @ X1 @ ( cartprod @ X2 @ X4 ) )
      | ~ ( in @ X1 @ ( funcSet @ X2 @ X4 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

thf(c_0_22,plain,
    ! [X1: $i,X2: $i,X5: $i,X4: $i] :
      ( ( ap @ X1 @ X2 @ X4 @ X5 )
      = ( setunion
        @ ( dsetconstr @ X2
          @ ^ [Z0: $i] : ( in @ ( kpair @ X5 @ Z0 ) @ X4 ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

thf(c_0_23,negated_conjecture,
    ! [X2: $i,X5: $i,X4: $i,X1: $i] :
      ( ( in @ ( ap @ X1 @ X2 @ X4 @ X5 ) @ X2 )
      | ( in @ ( esk1_3 @ X1 @ X2 @ X4 ) @ X1 )
      | ~ ( in @ X4 @ ( funcSet @ X1 @ X2 ) )
      | ~ ( in @ X5 @ X1 ) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

thf(c_0_24,negated_conjecture,
    in @ esk5_0 @ ( funcSet @ esk3_0 @ esk4_0 ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

thf(c_0_25,negated_conjecture,
    ~ ( in @ ( ap @ esk3_0 @ esk4_0 @ esk5_0 @ esk6_0 ) @ esk4_0 ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

thf(c_0_26,plain,
    ! [X1: $i,X2: $i,X4: $i,X6: $i,X5: $i] :
      ( ( ap @ X1 @ X2 @ X4 @ X5 )
      = ( ap @ X6 @ X2 @ X4 @ X5 ) ),
    inference(spm,[status(thm)],[c_0_22,c_0_22]) ).

thf(c_0_27,negated_conjecture,
    ! [X1: $i,X2: $i,X5: $i,X6: $i,X4: $i] :
      ( ( in @ ( ap @ X4 @ X2 @ X5 @ X6 ) @ X2 )
      | ~ ( in @ X1
          @ ( dsetconstr @ X2
            @ ^ [Z0: $i] : ( in @ ( kpair @ ( esk1_3 @ X4 @ X2 @ X5 ) @ Z0 ) @ X5 ) ) )
      | ( ( dsetconstr @ X2
          @ ^ [Z0: $i] : ( in @ ( kpair @ ( esk1_3 @ X4 @ X2 @ X5 ) @ Z0 ) @ X5 ) )
       != ( setadjoin @ X1 @ emptyset ) )
      | ~ ( subset @ X5 @ ( cartprod @ X4 @ X2 ) )
      | ~ ( in @ X6 @ X4 ) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

thf(c_0_28,negated_conjecture,
    ! [X1: $i,X5: $i,X4: $i,X2: $i] :
      ( ( in @ ( esk2_4 @ X1 @ X2 @ X4 @ X5 )
        @ ( dsetconstr @ X2
          @ ^ [Z0: $i] : ( in @ ( kpair @ X5 @ Z0 ) @ X4 ) ) )
      | ~ ( in @ X5 @ X1 )
      | ~ ( in @ X4 @ ( funcSet @ X1 @ X2 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

thf(c_0_29,negated_conjecture,
    ! [X2: $i,X5: $i,X4: $i,X1: $i] :
      ( ( ( dsetconstr @ X1
          @ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X4 ) )
        = ( setadjoin @ ( esk2_4 @ X5 @ X1 @ X4 @ X2 ) @ emptyset ) )
      | ~ ( in @ X2 @ X5 )
      | ~ ( in @ X4 @ ( funcSet @ X5 @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

thf(c_0_30,negated_conjecture,
    ! [X1: $i] :
      ( ( in @ ( ap @ esk3_0 @ esk4_0 @ esk5_0 @ X1 ) @ esk4_0 )
      | ( in @ ( esk1_3 @ esk3_0 @ esk4_0 @ esk5_0 ) @ esk3_0 )
      | ~ ( in @ X1 @ esk3_0 ) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

thf(c_0_31,negated_conjecture,
    in @ esk6_0 @ esk3_0,
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

thf(c_0_32,negated_conjecture,
    ! [X1: $i] :
      ~ ( in @ ( ap @ X1 @ esk4_0 @ esk5_0 @ esk6_0 ) @ esk4_0 ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

thf(c_0_33,negated_conjecture,
    ! [X4: $i,X6: $i,X5: $i,X2: $i,X1: $i] :
      ( ( in @ ( ap @ X1 @ X2 @ X4 @ X5 ) @ X2 )
      | ~ ( in @ ( esk1_3 @ X1 @ X2 @ X4 ) @ X6 )
      | ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
      | ~ ( in @ X4 @ ( funcSet @ X6 @ X2 ) )
      | ~ ( in @ X5 @ X1 ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).

thf(c_0_34,negated_conjecture,
    in @ ( esk1_3 @ esk3_0 @ esk4_0 @ esk5_0 ) @ esk3_0,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).

thf(c_0_35,negated_conjecture,
    ! [X1: $i] :
      ( ( in @ ( ap @ esk3_0 @ esk4_0 @ esk5_0 @ X1 ) @ esk4_0 )
      | ~ ( subset @ esk5_0 @ ( cartprod @ esk3_0 @ esk4_0 ) )
      | ~ ( in @ X1 @ esk3_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_24])]) ).

thf(c_0_36,negated_conjecture,
    ~ ( subset @ esk5_0 @ ( cartprod @ esk3_0 @ esk4_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_35]),c_0_31])]) ).

thf(c_0_37,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_21]),c_0_24])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SEU676^2 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n025.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sun May 19 16:15:52 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.20/0.47  Running higher-order theorem proving
% 0.20/0.47  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
% 0.20/0.49  # Version: 3.1.0-ho
% 0.20/0.49  # partial match(1): HSSSSLSSSLMNHFN
% 0.20/0.49  # Preprocessing class: HSSSSLSSMLMNHFN.
% 0.20/0.49  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.49  # Starting ho_unfolding_6 with 1500s (5) cores
% 0.20/0.49  # Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.20/0.49  # Starting pre_casc_5 with 300s (1) cores
% 0.20/0.49  # Starting ehoh_best_sine with 300s (1) cores
% 0.20/0.49  # ehoh_best_sine with pid 20046 completed with status 0
% 0.20/0.49  # Result found by ehoh_best_sine
% 0.20/0.49  # partial match(1): HSSSSLSSSLMNHFN
% 0.20/0.49  # Preprocessing class: HSSSSLSSMLMNHFN.
% 0.20/0.49  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.49  # Starting ho_unfolding_6 with 1500s (5) cores
% 0.20/0.49  # Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.20/0.49  # Starting pre_casc_5 with 300s (1) cores
% 0.20/0.49  # Starting ehoh_best_sine with 300s (1) cores
% 0.20/0.49  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.20/0.49  # Search class: HGUSS-FFSF32-DHFSMFNN
% 0.20/0.49  # partial match(3): HGUSF-FFSF32-MHFFMFNN
% 0.20/0.49  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.49  # Starting new_ho_10 with 163s (1) cores
% 0.20/0.49  # new_ho_10 with pid 20054 completed with status 0
% 0.20/0.49  # Result found by new_ho_10
% 0.20/0.49  # partial match(1): HSSSSLSSSLMNHFN
% 0.20/0.49  # Preprocessing class: HSSSSLSSMLMNHFN.
% 0.20/0.49  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.49  # Starting ho_unfolding_6 with 1500s (5) cores
% 0.20/0.49  # Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.20/0.49  # Starting pre_casc_5 with 300s (1) cores
% 0.20/0.49  # Starting ehoh_best_sine with 300s (1) cores
% 0.20/0.49  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.20/0.49  # Search class: HGUSS-FFSF32-DHFSMFNN
% 0.20/0.49  # partial match(3): HGUSF-FFSF32-MHFFMFNN
% 0.20/0.49  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.49  # Starting new_ho_10 with 163s (1) cores
% 0.20/0.49  # Preprocessing time       : 0.001 s
% 0.20/0.49  # Presaturation interreduction done
% 0.20/0.49  
% 0.20/0.49  # Proof found!
% 0.20/0.49  # SZS status Theorem
% 0.20/0.49  # SZS output start CNFRefutation
% See solution above
% 0.20/0.49  # Parsed axioms                        : 26
% 0.20/0.49  # Removed by relevancy pruning/SinE    : 17
% 0.20/0.49  # Initial clauses                      : 10
% 0.20/0.49  # Removed in clause preprocessing      : 0
% 0.20/0.49  # Initial clauses in saturation        : 10
% 0.20/0.49  # Processed clauses                    : 60
% 0.20/0.49  # ...of these trivial                  : 0
% 0.20/0.49  # ...subsumed                          : 29
% 0.20/0.49  # ...remaining for further processing  : 31
% 0.20/0.49  # Other redundant clauses eliminated   : 0
% 0.20/0.49  # Clauses deleted for lack of memory   : 0
% 0.20/0.49  # Backward-subsumed                    : 2
% 0.20/0.49  # Backward-rewritten                   : 1
% 0.20/0.49  # Generated clauses                    : 45
% 0.20/0.49  # ...of the previous two non-redundant : 44
% 0.20/0.49  # ...aggressively subsumed             : 0
% 0.20/0.49  # Contextual simplify-reflections      : 1
% 0.20/0.49  # Paramodulations                      : 33
% 0.20/0.49  # Factorizations                       : 0
% 0.20/0.49  # NegExts                              : 0
% 0.20/0.49  # Equation resolutions                 : 0
% 0.20/0.49  # Disequality decompositions           : 0
% 0.20/0.49  # Total rewrite steps                  : 6
% 0.20/0.49  # ...of those cached                   : 1
% 0.20/0.49  # Propositional unsat checks           : 0
% 0.20/0.49  #    Propositional check models        : 0
% 0.20/0.49  #    Propositional check unsatisfiable : 0
% 0.20/0.49  #    Propositional clauses             : 0
% 0.20/0.49  #    Propositional clauses after purity: 0
% 0.20/0.49  #    Propositional unsat core size     : 0
% 0.20/0.49  #    Propositional preprocessing time  : 0.000
% 0.20/0.49  #    Propositional encoding time       : 0.000
% 0.20/0.49  #    Propositional solver time         : 0.000
% 0.20/0.49  #    Success case prop preproc time    : 0.000
% 0.20/0.49  #    Success case prop encoding time   : 0.000
% 0.20/0.49  #    Success case prop solver time     : 0.000
% 0.20/0.49  # Current number of processed clauses  : 18
% 0.20/0.49  #    Positive orientable unit clauses  : 4
% 0.20/0.49  #    Positive unorientable unit clauses: 5
% 0.20/0.49  #    Negative unit clauses             : 2
% 0.20/0.49  #    Non-unit-clauses                  : 7
% 0.20/0.49  # Current number of unprocessed clauses: 3
% 0.20/0.49  # ...number of literals in the above   : 7
% 0.20/0.49  # Current number of archived formulas  : 0
% 0.20/0.49  # Current number of archived clauses   : 13
% 0.20/0.49  # Clause-clause subsumption calls (NU) : 14
% 0.20/0.49  # Rec. Clause-clause subsumption calls : 3
% 0.20/0.49  # Non-unit clause-clause subsumptions  : 1
% 0.20/0.49  # Unit Clause-clause subsumption calls : 17
% 0.20/0.49  # Rewrite failures with RHS unbound    : 0
% 0.20/0.49  # BW rewrite match attempts            : 31
% 0.20/0.49  # BW rewrite match successes           : 7
% 0.20/0.49  # Condensation attempts                : 60
% 0.20/0.49  # Condensation successes               : 0
% 0.20/0.49  # Termbank termtop insertions          : 2714
% 0.20/0.49  # Search garbage collected termcells   : 618
% 0.20/0.49  
% 0.20/0.49  # -------------------------------------------------
% 0.20/0.49  # User time                : 0.008 s
% 0.20/0.49  # System time              : 0.002 s
% 0.20/0.49  # Total time               : 0.010 s
% 0.20/0.49  # Maximum resident set size: 1888 pages
% 0.20/0.49  
% 0.20/0.49  # -------------------------------------------------
% 0.20/0.49  # User time                : 0.008 s
% 0.20/0.49  # System time              : 0.005 s
% 0.20/0.49  # Total time               : 0.014 s
% 0.20/0.49  # Maximum resident set size: 1732 pages
% 0.20/0.49  % E---3.1 exiting
% 0.20/0.49  % E exiting
%------------------------------------------------------------------------------