TSTP Solution File: SET013^7 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SET013^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n021.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 : Sat May  4 09:17:19 EDT 2024

% Result   : Theorem 4.05s 1.07s
% Output   : CNFRefutation 4.05s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   31
% Syntax   : Number of formulae    :  101 (  32 unt;  18 typ;   0 def)
%            Number of atoms       :  287 (  17 equ;   0 cnn)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives : 1446 ( 163   ~; 134   |;  10   &;1124   @)
%                                         (   0 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   8 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   76 (  76   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  17 usr;   4 con; 0-3 aty)
%            Number of variables   :  130 (  52   ^  78   !;   0   ?; 130   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_sort1,type,
    mu: $tType ).

thf(decl_24,type,
    mnot: ( $i > $o ) > $i > $o ).

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

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

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

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

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

thf(decl_37,type,
    mforall_ind: ( mu > $i > $o ) > $i > $o ).

thf(decl_50,type,
    mvalid: ( $i > $o ) > $o ).

thf(decl_57,type,
    subset: mu > mu > $i > $o ).

thf(decl_58,type,
    member: mu > mu > $i > $o ).

thf(decl_59,type,
    equal_set: mu > mu > $i > $o ).

thf(decl_60,type,
    power_set: mu > mu ).

thf(decl_68,type,
    intersection: mu > mu > mu ).

thf(decl_70,type,
    esk2_3: $i > mu > mu > mu ).

thf(decl_73,type,
    esk5_0: $i ).

thf(decl_74,type,
    esk6_0: mu ).

thf(decl_75,type,
    esk7_0: mu ).

thf(mand,axiom,
    ( mand
    = ( ^ [X4: $i > $o,X5: $i > $o] : ( mnot @ ( mor @ ( mnot @ X4 ) @ ( mnot @ X5 ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.uwQJOMpTIm/E---3.1_8419.p',mand) ).

thf(mnot,axiom,
    ( mnot
    = ( ^ [X4: $i > $o,X3: $i] :
          ~ ( X4 @ X3 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.uwQJOMpTIm/E---3.1_8419.p',mnot) ).

thf(mor,axiom,
    ( mor
    = ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
          ( ( X4 @ X3 )
          | ( X5 @ X3 ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.uwQJOMpTIm/E---3.1_8419.p',mor) ).

thf(mimplies,axiom,
    ( mimplies
    = ( ^ [X4: $i > $o,X5: $i > $o] : ( mor @ ( mnot @ X4 ) @ X5 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.uwQJOMpTIm/E---3.1_8419.p',mimplies) ).

thf(mequiv,axiom,
    ( mequiv
    = ( ^ [X4: $i > $o,X5: $i > $o] : ( mand @ ( mimplies @ X4 @ X5 ) @ ( mimplies @ X5 @ X4 ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.uwQJOMpTIm/E---3.1_8419.p',mequiv) ).

thf(mforall_ind,axiom,
    ( mforall_ind
    = ( ^ [X11: mu > $i > $o,X3: $i] :
        ! [X12: mu] :
          ( ( exists_in_world @ X12 @ X3 )
         => ( X11 @ X12 @ X3 ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.uwQJOMpTIm/E---3.1_8419.p',mforall_ind) ).

thf(mvalid,axiom,
    ( mvalid
    = ( ^ [X4: $i > $o] :
        ! [X3: $i] : ( X4 @ X3 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.uwQJOMpTIm/E---3.1_8419.p',mvalid) ).

thf(thI06,conjecture,
    ( mvalid
    @ ( mforall_ind
      @ ^ [X28: mu] :
          ( mforall_ind
          @ ^ [X29: mu] : ( equal_set @ ( intersection @ X28 @ X29 ) @ ( intersection @ X29 @ X28 ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.uwQJOMpTIm/E---3.1_8419.p',thI06) ).

thf(equal_set,axiom,
    ( mvalid
    @ ( mforall_ind
      @ ^ [X28: mu] :
          ( mforall_ind
          @ ^ [X29: mu] : ( mequiv @ ( equal_set @ X28 @ X29 ) @ ( mand @ ( subset @ X28 @ X29 ) @ ( subset @ X29 @ X28 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.uwQJOMpTIm/E---3.1_8419.p',equal_set) ).

thf(existence_of_intersection_ax,axiom,
    ! [X7: $i,X21: mu,X20: mu] : ( exists_in_world @ ( intersection @ X21 @ X20 ) @ X7 ),
    file('/export/starexec/sandbox2/tmp/tmp.uwQJOMpTIm/E---3.1_8419.p',existence_of_intersection_ax) ).

thf(power_set,axiom,
    ( mvalid
    @ ( mforall_ind
      @ ^ [X32: mu] :
          ( mforall_ind
          @ ^ [X28: mu] : ( mequiv @ ( member @ X32 @ ( power_set @ X28 ) ) @ ( subset @ X32 @ X28 ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.uwQJOMpTIm/E---3.1_8419.p',power_set) ).

thf(subset,axiom,
    ( mvalid
    @ ( mforall_ind
      @ ^ [X28: mu] :
          ( mforall_ind
          @ ^ [X29: mu] :
              ( mequiv @ ( subset @ X28 @ X29 )
              @ ( mforall_ind
                @ ^ [X31: mu] : ( mimplies @ ( member @ X31 @ X28 ) @ ( member @ X31 @ X29 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.uwQJOMpTIm/E---3.1_8419.p',subset) ).

thf(intersection,axiom,
    ( mvalid
    @ ( mforall_ind
      @ ^ [X33: mu] :
          ( mforall_ind
          @ ^ [X28: mu] :
              ( mforall_ind
              @ ^ [X29: mu] : ( mequiv @ ( member @ X33 @ ( intersection @ X28 @ X29 ) ) @ ( mand @ ( member @ X33 @ X28 ) @ ( member @ X33 @ X29 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.uwQJOMpTIm/E---3.1_8419.p',intersection) ).

thf(c_0_13,plain,
    ( mand
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ~ ( ~ ( Z0 @ Z2 )
            | ~ ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mand]) ).

thf(c_0_14,plain,
    ( mnot
    = ( ^ [Z0: $i > $o,Z1: $i] :
          ~ ( Z0 @ Z1 ) ) ),
    inference(fof_simplification,[status(thm)],[mnot]) ).

thf(c_0_15,plain,
    ( mor
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ( Z0 @ Z2 )
          | ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mor]) ).

thf(c_0_16,plain,
    ( mimplies
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ~ ( Z0 @ Z2 )
          | ( Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mimplies]) ).

thf(c_0_17,plain,
    ( mequiv
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ~ ( ~ ( ~ ( Z0 @ Z2 )
                | ( Z1 @ Z2 ) )
            | ~ ( ~ ( Z1 @ Z2 )
                | ( Z0 @ Z2 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[mequiv]) ).

thf(c_0_18,plain,
    ( mand
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ~ ( ~ ( Z0 @ Z2 )
            | ~ ( Z1 @ Z2 ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).

thf(c_0_19,plain,
    ( mimplies
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ( ~ ( Z0 @ Z2 )
          | ( Z1 @ Z2 ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_16,c_0_14]),c_0_15]) ).

thf(c_0_20,plain,
    ( mforall_ind
    = ( ^ [Z0: mu > $i > $o,Z1: $i] :
        ! [X12: mu] :
          ( ( exists_in_world @ X12 @ Z1 )
         => ( Z0 @ X12 @ Z1 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mforall_ind]) ).

thf(c_0_21,plain,
    ( mvalid
    = ( ^ [Z0: $i > $o] :
        ! [X3: $i] : ( Z0 @ X3 ) ) ),
    inference(fof_simplification,[status(thm)],[mvalid]) ).

thf(c_0_22,plain,
    ( mequiv
    = ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
          ~ ( ~ ( ~ ( Z0 @ Z2 )
                | ( Z1 @ Z2 ) )
            | ~ ( ~ ( Z1 @ Z2 )
                | ( Z0 @ Z2 ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).

thf(c_0_23,negated_conjecture,
    ~ ! [X195: $i,X194: mu] :
        ( ( exists_in_world @ X194 @ X195 )
       => ! [X193: mu] :
            ( ( exists_in_world @ X193 @ X195 )
           => ( equal_set @ ( intersection @ X194 @ X193 ) @ ( intersection @ X193 @ X194 ) @ X195 ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[thI06])]),c_0_20]),c_0_21]) ).

thf(c_0_24,plain,
    ! [X160: $i,X159: mu] :
      ( ( exists_in_world @ X159 @ X160 )
     => ! [X158: mu] :
          ( ( exists_in_world @ X158 @ X160 )
         => ~ ( ~ ( ~ ( equal_set @ X159 @ X158 @ X160 )
                  | ~ ( ~ ( subset @ X159 @ X158 @ X160 )
                      | ~ ( subset @ X158 @ X159 @ X160 ) ) )
              | ~ ( ~ ~ ( ~ ( subset @ X159 @ X158 @ X160 )
                        | ~ ( subset @ X158 @ X159 @ X160 ) )
                  | ( equal_set @ X159 @ X158 @ X160 ) ) ) ) ),
    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(fof_simplification,[status(thm)],[equal_set]),c_0_18]),c_0_22]),c_0_20]),c_0_21])]) ).

thf(c_0_25,negated_conjecture,
    ( ( exists_in_world @ esk6_0 @ esk5_0 )
    & ( exists_in_world @ esk7_0 @ esk5_0 )
    & ~ ( equal_set @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 ) ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])]) ).

thf(c_0_26,plain,
    ! [X308: $i,X309: mu,X310: mu] :
      ( ( ( subset @ X309 @ X310 @ X308 )
        | ~ ( equal_set @ X309 @ X310 @ X308 )
        | ~ ( exists_in_world @ X310 @ X308 )
        | ~ ( exists_in_world @ X309 @ X308 ) )
      & ( ( subset @ X310 @ X309 @ X308 )
        | ~ ( equal_set @ X309 @ X310 @ X308 )
        | ~ ( exists_in_world @ X310 @ X308 )
        | ~ ( exists_in_world @ X309 @ X308 ) )
      & ( ~ ( subset @ X309 @ X310 @ X308 )
        | ~ ( subset @ X310 @ X309 @ X308 )
        | ( equal_set @ X309 @ X310 @ X308 )
        | ~ ( exists_in_world @ X310 @ X308 )
        | ~ ( exists_in_world @ X309 @ X308 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])])]) ).

thf(c_0_27,plain,
    ! [X223: $i,X224: mu,X225: mu] : ( exists_in_world @ ( intersection @ X224 @ X225 ) @ X223 ),
    inference(variable_rename,[status(thm)],[existence_of_intersection_ax]) ).

thf(c_0_28,plain,
    ! [X163: $i,X162: mu] :
      ( ( exists_in_world @ X162 @ X163 )
     => ! [X161: mu] :
          ( ( exists_in_world @ X161 @ X163 )
         => ~ ( ~ ( ~ ( member @ X162 @ ( power_set @ X161 ) @ X163 )
                  | ( subset @ X162 @ X161 @ X163 ) )
              | ~ ( ~ ( subset @ X162 @ X161 @ X163 )
                  | ( member @ X162 @ ( power_set @ X161 ) @ X163 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[power_set]),c_0_22]),c_0_20]),c_0_21])]) ).

thf(c_0_29,negated_conjecture,
    ~ ( equal_set @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

thf(c_0_30,plain,
    ! [X12: mu,X10: mu,X3: $i] :
      ( ( equal_set @ X10 @ X12 @ X3 )
      | ~ ( subset @ X10 @ X12 @ X3 )
      | ~ ( subset @ X12 @ X10 @ X3 )
      | ~ ( exists_in_world @ X12 @ X3 )
      | ~ ( exists_in_world @ X10 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

thf(c_0_31,plain,
    ! [X12: mu,X10: mu,X3: $i] : ( exists_in_world @ ( intersection @ X10 @ X12 ) @ X3 ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

thf(c_0_32,plain,
    ! [X311: $i,X312: mu,X313: mu] :
      ( ( ~ ( member @ X312 @ ( power_set @ X313 ) @ X311 )
        | ( subset @ X312 @ X313 @ X311 )
        | ~ ( exists_in_world @ X313 @ X311 )
        | ~ ( exists_in_world @ X312 @ X311 ) )
      & ( ~ ( subset @ X312 @ X313 @ X311 )
        | ( member @ X312 @ ( power_set @ X313 ) @ X311 )
        | ~ ( exists_in_world @ X313 @ X311 )
        | ~ ( exists_in_world @ X312 @ X311 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])])])]) ).

thf(c_0_33,plain,
    ! [X157: $i,X156: mu] :
      ( ( exists_in_world @ X156 @ X157 )
     => ! [X155: mu] :
          ( ( exists_in_world @ X155 @ X157 )
         => ~ ( ~ ( ~ ( subset @ X156 @ X155 @ X157 )
                  | ! [X154: mu] :
                      ( ( exists_in_world @ X154 @ X157 )
                     => ( ~ ( member @ X154 @ X156 @ X157 )
                        | ( member @ X154 @ X155 @ X157 ) ) ) )
              | ~ ( ~ ! [X154: mu] :
                        ( ( exists_in_world @ X154 @ X157 )
                       => ( ~ ( member @ X154 @ X156 @ X157 )
                          | ( member @ X154 @ X155 @ X157 ) ) )
                  | ( subset @ X156 @ X155 @ X157 ) ) ) ) ),
    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(fof_simplification,[status(thm)],[subset]),c_0_19]),c_0_22]),c_0_20]),c_0_21])]) ).

thf(c_0_34,plain,
    ! [X167: $i,X166: mu] :
      ( ( exists_in_world @ X166 @ X167 )
     => ! [X165: mu] :
          ( ( exists_in_world @ X165 @ X167 )
         => ! [X164: mu] :
              ( ( exists_in_world @ X164 @ X167 )
             => ~ ( ~ ( ~ ( member @ X166 @ ( intersection @ X165 @ X164 ) @ X167 )
                      | ~ ( ~ ( member @ X166 @ X165 @ X167 )
                          | ~ ( member @ X166 @ X164 @ X167 ) ) )
                  | ~ ( ~ ~ ( ~ ( member @ X166 @ X165 @ X167 )
                            | ~ ( member @ X166 @ X164 @ X167 ) )
                      | ( member @ X166 @ ( intersection @ X165 @ X164 ) @ X167 ) ) ) ) ) ),
    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(fof_simplification,[status(thm)],[intersection]),c_0_18]),c_0_22]),c_0_20]),c_0_21])]) ).

thf(c_0_35,negated_conjecture,
    ( ~ ( subset @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) @ esk5_0 )
    | ~ ( subset @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_31])]) ).

thf(c_0_36,plain,
    ! [X12: mu,X10: mu,X3: $i] :
      ( ( subset @ X10 @ X12 @ X3 )
      | ~ ( member @ X10 @ ( power_set @ X12 ) @ X3 )
      | ~ ( exists_in_world @ X12 @ X3 )
      | ~ ( exists_in_world @ X10 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

thf(c_0_37,plain,
    ! [X303: $i,X304: mu,X305: mu,X306: mu] :
      ( ( ~ ( subset @ X304 @ X305 @ X303 )
        | ~ ( exists_in_world @ X306 @ X303 )
        | ~ ( member @ X306 @ X304 @ X303 )
        | ( member @ X306 @ X305 @ X303 )
        | ~ ( exists_in_world @ X305 @ X303 )
        | ~ ( exists_in_world @ X304 @ X303 ) )
      & ( ( exists_in_world @ ( esk2_3 @ X303 @ X304 @ X305 ) @ X303 )
        | ( subset @ X304 @ X305 @ X303 )
        | ~ ( exists_in_world @ X305 @ X303 )
        | ~ ( exists_in_world @ X304 @ X303 ) )
      & ( ( member @ ( esk2_3 @ X303 @ X304 @ X305 ) @ X304 @ X303 )
        | ( subset @ X304 @ X305 @ X303 )
        | ~ ( exists_in_world @ X305 @ X303 )
        | ~ ( exists_in_world @ X304 @ X303 ) )
      & ( ~ ( member @ ( esk2_3 @ X303 @ X304 @ X305 ) @ X305 @ X303 )
        | ( subset @ X304 @ X305 @ X303 )
        | ~ ( exists_in_world @ X305 @ X303 )
        | ~ ( exists_in_world @ X304 @ X303 ) ) ),
    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_33])])])])])]) ).

thf(c_0_38,plain,
    ! [X314: $i,X315: mu,X316: mu,X317: mu] :
      ( ( ( member @ X315 @ X316 @ X314 )
        | ~ ( member @ X315 @ ( intersection @ X316 @ X317 ) @ X314 )
        | ~ ( exists_in_world @ X317 @ X314 )
        | ~ ( exists_in_world @ X316 @ X314 )
        | ~ ( exists_in_world @ X315 @ X314 ) )
      & ( ( member @ X315 @ X317 @ X314 )
        | ~ ( member @ X315 @ ( intersection @ X316 @ X317 ) @ X314 )
        | ~ ( exists_in_world @ X317 @ X314 )
        | ~ ( exists_in_world @ X316 @ X314 )
        | ~ ( exists_in_world @ X315 @ X314 ) )
      & ( ~ ( member @ X315 @ X316 @ X314 )
        | ~ ( member @ X315 @ X317 @ X314 )
        | ( member @ X315 @ ( intersection @ X316 @ X317 ) @ X314 )
        | ~ ( exists_in_world @ X317 @ X314 )
        | ~ ( exists_in_world @ X316 @ X314 )
        | ~ ( exists_in_world @ X315 @ X314 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])])])]) ).

thf(c_0_39,negated_conjecture,
    ( ~ ( member @ ( intersection @ esk7_0 @ esk6_0 ) @ ( power_set @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk5_0 )
    | ~ ( subset @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_31]),c_0_31])]) ).

thf(c_0_40,plain,
    ! [X12: mu,X10: mu,X3: $i] :
      ( ( member @ ( esk2_3 @ X3 @ X10 @ X12 ) @ X10 @ X3 )
      | ( subset @ X10 @ X12 @ X3 )
      | ~ ( exists_in_world @ X12 @ X3 )
      | ~ ( exists_in_world @ X10 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

thf(c_0_41,plain,
    ! [X12: mu,X10: mu,X3: $i] :
      ( ( exists_in_world @ ( esk2_3 @ X3 @ X10 @ X12 ) @ X3 )
      | ( subset @ X10 @ X12 @ X3 )
      | ~ ( exists_in_world @ X12 @ X3 )
      | ~ ( exists_in_world @ X10 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

thf(c_0_42,plain,
    ! [X12: mu,X10: mu,X3: $i] :
      ( ( subset @ X10 @ X12 @ X3 )
      | ~ ( member @ ( esk2_3 @ X3 @ X10 @ X12 ) @ X12 @ X3 )
      | ~ ( exists_in_world @ X12 @ X3 )
      | ~ ( exists_in_world @ X10 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

thf(c_0_43,plain,
    ! [X12: mu,X14: mu,X10: mu,X3: $i] :
      ( ( member @ X10 @ X12 @ X3 )
      | ~ ( member @ X10 @ ( intersection @ X14 @ X12 ) @ X3 )
      | ~ ( exists_in_world @ X12 @ X3 )
      | ~ ( exists_in_world @ X14 @ X3 )
      | ~ ( exists_in_world @ X10 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

thf(c_0_44,negated_conjecture,
    ( ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ ( intersection @ esk6_0 @ esk7_0 ) @ esk5_0 )
    | ~ ( member @ ( intersection @ esk7_0 @ esk6_0 ) @ ( power_set @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk5_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_31]),c_0_31])]) ).

thf(c_0_45,negated_conjecture,
    exists_in_world @ esk6_0 @ esk5_0,
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

thf(c_0_46,negated_conjecture,
    exists_in_world @ esk7_0 @ esk5_0,
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

thf(c_0_47,negated_conjecture,
    ( ( exists_in_world @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ esk5_0 )
    | ~ ( member @ ( intersection @ esk7_0 @ esk6_0 ) @ ( power_set @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk5_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_41]),c_0_31]),c_0_31])]) ).

thf(c_0_48,plain,
    ! [X14: mu,X12: mu,X10: mu,X3: $i] :
      ( ( member @ X10 @ X12 @ X3 )
      | ~ ( member @ X10 @ ( intersection @ X12 @ X14 ) @ X3 )
      | ~ ( exists_in_world @ X14 @ X3 )
      | ~ ( exists_in_world @ X12 @ X3 )
      | ~ ( exists_in_world @ X10 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

thf(c_0_49,negated_conjecture,
    ( ~ ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 )
    | ~ ( member @ ( intersection @ esk7_0 @ esk6_0 ) @ ( power_set @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk5_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_42]),c_0_31]),c_0_31])]) ).

thf(c_0_50,plain,
    ! [X14: mu,X12: mu,X10: mu,X3: $i] :
      ( ( member @ X10 @ ( intersection @ X12 @ X14 ) @ X3 )
      | ~ ( member @ X10 @ X12 @ X3 )
      | ~ ( member @ X10 @ X14 @ X3 )
      | ~ ( exists_in_world @ X14 @ X3 )
      | ~ ( exists_in_world @ X12 @ X3 )
      | ~ ( exists_in_world @ X10 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

thf(c_0_51,negated_conjecture,
    ( ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ esk7_0 @ esk5_0 )
    | ~ ( member @ ( intersection @ esk7_0 @ esk6_0 ) @ ( power_set @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk5_0 ) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_46])]),c_0_47]) ).

thf(c_0_52,negated_conjecture,
    ( ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ esk6_0 @ esk5_0 )
    | ~ ( member @ ( intersection @ esk7_0 @ esk6_0 ) @ ( power_set @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk5_0 ) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_44]),c_0_46]),c_0_45])]),c_0_47]) ).

thf(c_0_53,plain,
    ! [X12: mu,X10: mu,X3: $i] :
      ( ( member @ X10 @ ( power_set @ X12 ) @ X3 )
      | ~ ( subset @ X10 @ X12 @ X3 )
      | ~ ( exists_in_world @ X12 @ X3 )
      | ~ ( exists_in_world @ X10 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

thf(c_0_54,negated_conjecture,
    ( ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 )
    | ~ ( subset @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_40]),c_0_31]),c_0_31])]) ).

thf(c_0_55,negated_conjecture,
    ( ( exists_in_world @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk5_0 )
    | ~ ( subset @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_41]),c_0_31]),c_0_31])]) ).

thf(c_0_56,negated_conjecture,
    ( ~ ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ ( intersection @ esk6_0 @ esk7_0 ) @ esk5_0 )
    | ~ ( subset @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_42]),c_0_31]),c_0_31])]) ).

thf(c_0_57,negated_conjecture,
    ~ ( member @ ( intersection @ esk7_0 @ esk6_0 ) @ ( power_set @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk5_0 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_45]),c_0_46])]),c_0_47]),c_0_51]),c_0_52]) ).

thf(c_0_58,plain,
    ! [X12: mu,X10: mu,X3: $i] :
      ( ( exists_in_world @ ( esk2_3 @ X3 @ X10 @ X12 ) @ X3 )
      | ( member @ X10 @ ( power_set @ X12 ) @ X3 )
      | ~ ( exists_in_world @ X12 @ X3 )
      | ~ ( exists_in_world @ X10 @ X3 ) ),
    inference(spm,[status(thm)],[c_0_53,c_0_41]) ).

thf(c_0_59,negated_conjecture,
    ( ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 )
    | ~ ( member @ ( intersection @ esk6_0 @ esk7_0 ) @ ( power_set @ ( intersection @ esk7_0 @ esk6_0 ) ) @ esk5_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_36]),c_0_31]),c_0_31])]) ).

thf(c_0_60,negated_conjecture,
    ( ( exists_in_world @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk5_0 )
    | ~ ( member @ ( intersection @ esk6_0 @ esk7_0 ) @ ( power_set @ ( intersection @ esk7_0 @ esk6_0 ) ) @ esk5_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_36]),c_0_31]),c_0_31])]) ).

thf(c_0_61,negated_conjecture,
    ( ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 )
    | ~ ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_42]),c_0_31]),c_0_31])]) ).

thf(c_0_62,negated_conjecture,
    ( ( exists_in_world @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk5_0 )
    | ~ ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_42]),c_0_31]),c_0_31])]) ).

thf(c_0_63,negated_conjecture,
    ( ~ ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ ( intersection @ esk6_0 @ esk7_0 ) @ esk5_0 )
    | ~ ( member @ ( intersection @ esk6_0 @ esk7_0 ) @ ( power_set @ ( intersection @ esk7_0 @ esk6_0 ) ) @ esk5_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_36]),c_0_31]),c_0_31])]) ).

thf(c_0_64,negated_conjecture,
    exists_in_world @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk5_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_31]),c_0_31])]) ).

thf(c_0_65,negated_conjecture,
    ( ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk6_0 @ esk5_0 )
    | ~ ( member @ ( intersection @ esk6_0 @ esk7_0 ) @ ( power_set @ ( intersection @ esk7_0 @ esk6_0 ) ) @ esk5_0 ) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_59]),c_0_46]),c_0_45])]),c_0_60]) ).

thf(c_0_66,negated_conjecture,
    ( ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk7_0 @ esk5_0 )
    | ~ ( member @ ( intersection @ esk6_0 @ esk7_0 ) @ ( power_set @ ( intersection @ esk7_0 @ esk6_0 ) ) @ esk5_0 ) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_59]),c_0_45]),c_0_46])]),c_0_60]) ).

thf(c_0_67,negated_conjecture,
    ( ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ ( intersection @ esk6_0 @ esk7_0 ) @ esk5_0 )
    | ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_40]),c_0_31]),c_0_31])]) ).

thf(c_0_68,negated_conjecture,
    ( ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ ( intersection @ esk6_0 @ esk7_0 ) @ esk5_0 )
    | ( exists_in_world @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk5_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_40]),c_0_31]),c_0_31])]) ).

thf(c_0_69,negated_conjecture,
    ( ~ ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ ( intersection @ esk6_0 @ esk7_0 ) @ esk5_0 )
    | ~ ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_42]),c_0_31]),c_0_31])]) ).

thf(c_0_70,negated_conjecture,
    ( ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk6_0 @ esk5_0 )
    | ~ ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 ) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_61]),c_0_46]),c_0_45])]),c_0_62]) ).

thf(c_0_71,negated_conjecture,
    ( ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk7_0 @ esk5_0 )
    | ~ ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 ) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_61]),c_0_45]),c_0_46])]),c_0_62]) ).

thf(c_0_72,negated_conjecture,
    ~ ( member @ ( intersection @ esk6_0 @ esk7_0 ) @ ( power_set @ ( intersection @ esk7_0 @ esk6_0 ) ) @ esk5_0 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_50]),c_0_46]),c_0_45])]),c_0_64])]),c_0_65]),c_0_66]) ).

thf(c_0_73,negated_conjecture,
    ( ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ ( intersection @ esk6_0 @ esk7_0 ) @ esk5_0 )
    | ~ ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ ( intersection @ esk6_0 @ esk7_0 ) @ esk5_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_40]),c_0_31]),c_0_31])]) ).

thf(c_0_74,negated_conjecture,
    ( ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ ( intersection @ esk6_0 @ esk7_0 ) @ esk5_0 )
    | ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk6_0 @ esk5_0 ) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_67]),c_0_46]),c_0_45])]),c_0_68]) ).

thf(c_0_75,negated_conjecture,
    ( ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ ( intersection @ esk6_0 @ esk7_0 ) @ esk5_0 )
    | ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk7_0 @ esk6_0 ) @ ( intersection @ esk6_0 @ esk7_0 ) ) @ esk7_0 @ esk5_0 ) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_67]),c_0_45]),c_0_46])]),c_0_68]) ).

thf(c_0_76,negated_conjecture,
    ~ ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ ( intersection @ esk7_0 @ esk6_0 ) @ esk5_0 ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_50]),c_0_46]),c_0_45])]),c_0_64])]),c_0_70]),c_0_71]) ).

thf(c_0_77,negated_conjecture,
    exists_in_world @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ esk5_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_58]),c_0_31]),c_0_31])]) ).

thf(c_0_78,negated_conjecture,
    member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ ( intersection @ esk6_0 @ esk7_0 ) @ esk5_0,
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_50]),c_0_46]),c_0_45])]),c_0_64])]),c_0_74]),c_0_75]) ).

thf(c_0_79,negated_conjecture,
    ( ~ ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ esk6_0 @ esk5_0 )
    | ~ ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ esk7_0 @ esk5_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_50]),c_0_45]),c_0_46]),c_0_77])]) ).

thf(c_0_80,negated_conjecture,
    member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ esk6_0 @ esk5_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_78]),c_0_46]),c_0_45]),c_0_77])]) ).

thf(c_0_81,negated_conjecture,
    ~ ( member @ ( esk2_3 @ esk5_0 @ ( intersection @ esk6_0 @ esk7_0 ) @ ( intersection @ esk7_0 @ esk6_0 ) ) @ esk7_0 @ esk5_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80])]) ).

thf(c_0_82,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_78]),c_0_45]),c_0_46]),c_0_77])]),c_0_81]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem    : SET013^7 : TPTP v8.1.2. Released v5.5.0.
% 0.04/0.15  % Command    : run_E %s %d THM
% 0.16/0.36  % Computer : n021.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit   : 300
% 0.16/0.36  % WCLimit    : 300
% 0.16/0.36  % DateTime   : Fri May  3 10:22:13 EDT 2024
% 0.16/0.37  % CPUTime    : 
% 0.23/0.52  Running higher-order theorem proving
% 0.23/0.52  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.uwQJOMpTIm/E---3.1_8419.p
% 4.05/1.07  # Version: 3.1.0-ho
% 4.05/1.07  # Preprocessing class: HSLSSMSSMLLNHSN.
% 4.05/1.07  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.05/1.07  # Starting almost_fo_3 with 1500s (5) cores
% 4.05/1.07  # Starting sh10 with 300s (1) cores
% 4.05/1.07  # Starting new_ho_16 with 300s (1) cores
% 4.05/1.07  # Starting post_as_ho11 with 300s (1) cores
% 4.05/1.07  # new_ho_16 with pid 8564 completed with status 8
% 4.05/1.07  # almost_fo_3 with pid 8562 completed with status 0
% 4.05/1.07  # Result found by almost_fo_3
% 4.05/1.07  # Preprocessing class: HSLSSMSSMLLNHSN.
% 4.05/1.07  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.05/1.07  # Starting almost_fo_3 with 1500s (5) cores
% 4.05/1.07  # No SInE strategy applied
% 4.05/1.07  # Search class: HGHNM-FFMF31-SHSSMFNN
% 4.05/1.07  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 4.05/1.07  # Starting new_ho_10 with 811s (1) cores
% 4.05/1.07  # Starting almost_fo_3 with 151s (1) cores
% 4.05/1.07  # Starting full_lambda_9 with 136s (1) cores
% 4.05/1.07  # Starting new_ho_14 with 136s (1) cores
% 4.05/1.07  # Starting pre_casc_4 with 136s (1) cores
% 4.05/1.07  # new_ho_14 with pid 8584 completed with status 0
% 4.05/1.07  # Result found by new_ho_14
% 4.05/1.07  # Preprocessing class: HSLSSMSSMLLNHSN.
% 4.05/1.07  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.05/1.07  # Starting almost_fo_3 with 1500s (5) cores
% 4.05/1.07  # No SInE strategy applied
% 4.05/1.07  # Search class: HGHNM-FFMF31-SHSSMFNN
% 4.05/1.07  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 4.05/1.07  # Starting new_ho_10 with 811s (1) cores
% 4.05/1.07  # Starting almost_fo_3 with 151s (1) cores
% 4.05/1.07  # Starting full_lambda_9 with 136s (1) cores
% 4.05/1.07  # Starting new_ho_14 with 136s (1) cores
% 4.05/1.07  # Preprocessing time       : 0.006 s
% 4.05/1.07  # Presaturation interreduction done
% 4.05/1.07  
% 4.05/1.07  # Proof found!
% 4.05/1.07  # SZS status Theorem
% 4.05/1.07  # SZS output start CNFRefutation
% See solution above
% 4.05/1.07  # Parsed axioms                        : 126
% 4.05/1.07  # Removed by relevancy pruning/SinE    : 0
% 4.05/1.07  # Initial clauses                      : 117
% 4.05/1.07  # Removed in clause preprocessing      : 48
% 4.05/1.07  # Initial clauses in saturation        : 69
% 4.05/1.07  # Processed clauses                    : 1756
% 4.05/1.07  # ...of these trivial                  : 0
% 4.05/1.07  # ...subsumed                          : 622
% 4.05/1.07  # ...remaining for further processing  : 1133
% 4.05/1.07  # Other redundant clauses eliminated   : 0
% 4.05/1.07  # Clauses deleted for lack of memory   : 0
% 4.05/1.07  # Backward-subsumed                    : 46
% 4.05/1.07  # Backward-rewritten                   : 52
% 4.05/1.07  # Generated clauses                    : 37171
% 4.05/1.07  # ...of the previous two non-redundant : 35054
% 4.05/1.07  # ...aggressively subsumed             : 0
% 4.05/1.07  # Contextual simplify-reflections      : 28
% 4.05/1.07  # Paramodulations                      : 37169
% 4.05/1.07  # Factorizations                       : 0
% 4.05/1.07  # NegExts                              : 0
% 4.05/1.07  # Equation resolutions                 : 0
% 4.05/1.07  # Disequality decompositions           : 0
% 4.05/1.07  # Total rewrite steps                  : 52176
% 4.05/1.07  # ...of those cached                   : 51477
% 4.05/1.07  # Propositional unsat checks           : 0
% 4.05/1.07  #    Propositional check models        : 0
% 4.05/1.07  #    Propositional check unsatisfiable : 0
% 4.05/1.07  #    Propositional clauses             : 0
% 4.05/1.07  #    Propositional clauses after purity: 0
% 4.05/1.07  #    Propositional unsat core size     : 0
% 4.05/1.07  #    Propositional preprocessing time  : 0.000
% 4.05/1.07  #    Propositional encoding time       : 0.000
% 4.05/1.07  #    Propositional solver time         : 0.000
% 4.05/1.07  #    Success case prop preproc time    : 0.000
% 4.05/1.07  #    Success case prop encoding time   : 0.000
% 4.05/1.07  #    Success case prop solver time     : 0.000
% 4.05/1.07  # Current number of processed clauses  : 964
% 4.05/1.07  #    Positive orientable unit clauses  : 18
% 4.05/1.07  #    Positive unorientable unit clauses: 0
% 4.05/1.07  #    Negative unit clauses             : 7
% 4.05/1.07  #    Non-unit-clauses                  : 939
% 4.05/1.07  # Current number of unprocessed clauses: 33373
% 4.05/1.07  # ...number of literals in the above   : 129255
% 4.05/1.07  # Current number of archived formulas  : 0
% 4.05/1.07  # Current number of archived clauses   : 169
% 4.05/1.07  # Clause-clause subsumption calls (NU) : 133218
% 4.05/1.07  # Rec. Clause-clause subsumption calls : 26959
% 4.05/1.07  # Non-unit clause-clause subsumptions  : 573
% 4.05/1.07  # Unit Clause-clause subsumption calls : 753
% 4.05/1.07  # Rewrite failures with RHS unbound    : 0
% 4.05/1.07  # BW rewrite match attempts            : 15
% 4.05/1.07  # BW rewrite match successes           : 5
% 4.05/1.07  # Condensation attempts                : 0
% 4.05/1.07  # Condensation successes               : 0
% 4.05/1.07  # Termbank termtop insertions          : 1036018
% 4.05/1.07  # Search garbage collected termcells   : 8249
% 4.05/1.07  
% 4.05/1.07  # -------------------------------------------------
% 4.05/1.07  # User time                : 0.496 s
% 4.05/1.07  # System time              : 0.034 s
% 4.05/1.07  # Total time               : 0.530 s
% 4.05/1.07  # Maximum resident set size: 3264 pages
% 4.05/1.07  
% 4.05/1.07  # -------------------------------------------------
% 4.05/1.07  # User time                : 2.502 s
% 4.05/1.07  # System time              : 0.154 s
% 4.05/1.07  # Total time               : 2.656 s
% 4.05/1.07  # Maximum resident set size: 1868 pages
% 4.05/1.07  % E---3.1 exiting
% 4.05/1.08  % E exiting
%------------------------------------------------------------------------------