TSTP Solution File: SEU731^2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEU731^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n032.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  : 600s
% DateTime : Tue Jul 19 12:14:16 EDT 2022

% Result   : Theorem 0.13s 0.36s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   18
% Syntax   : Number of formulae    :  109 (  38 unt;  13 typ;   4 def)
%            Number of atoms       :  974 ( 320 equ;   0 cnn)
%            Maximal formula atoms :    6 (  10 avg)
%            Number of connectives : 1757 ( 184   ~; 321   |;   2   &;1223   @)
%                                         (   0 <=>;  27  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (  17   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  13 usr;   8 con; 0-3 aty)
%            Number of variables   :  256 (   0   ^ 256   !;   0   ?; 256   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_complementT_lem,type,
    complementT_lem: $o ).

thf(tp_doubleComplementE1,type,
    doubleComplementE1: $o ).

thf(tp_doubleComplementI1,type,
    doubleComplementI1: $o ).

thf(tp_in,type,
    in: $i > $i > $o ).

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

thf(tp_sK1_A,type,
    sK1_A: $i ).

thf(tp_sK2_SY0,type,
    sK2_SY0: $i ).

thf(tp_sK3_SY15,type,
    sK3_SY15: $i > $i > $i > $i ).

thf(tp_sK4_SY16,type,
    sK4_SY16: $i > $i > $i > $i ).

thf(tp_sK5_SY16,type,
    sK5_SY16: $i > $i > $i > $i ).

thf(tp_sK6_SY16,type,
    sK6_SY16: $i > $i > $i > $i ).

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

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

thf(complementT_lem,definition,
    ( complementT_lem
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementT_lem) ).

thf(doubleComplementE1,definition,
    ( doubleComplementE1
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
               => ( in @ Xx @ X ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementE1) ).

thf(doubleComplementI1,definition,
    ( doubleComplementI1
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ( in @ Xx @ X )
               => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementI1) ).

thf(setextT,definition,
    ( setextT
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ A )
                   => ( ( in @ Xx @ X )
                     => ( in @ Xx @ Y ) ) )
               => ( ! [Xx: $i] :
                      ( ( in @ Xx @ A )
                     => ( ( in @ Xx @ Y )
                       => ( in @ Xx @ X ) ) )
                 => ( X = Y ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextT) ).

thf(1,conjecture,
    ( complementT_lem
   => ( setextT
     => ( doubleComplementI1
       => ( doubleComplementE1
         => ! [A: $i,X: $i] :
              ( ( in @ X @ ( powerset @ A ) )
             => ( X
                = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementEq) ).

thf(2,negated_conjecture,
    ( ( complementT_lem
     => ( setextT
       => ( doubleComplementI1
         => ( doubleComplementE1
           => ! [A: $i,X: $i] :
                ( ( in @ X @ ( powerset @ A ) )
               => ( X
                  = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    complementT_lem = $true,
    inference(standard_cnf,[status(thm)],[2]) ).

thf(4,plain,
    setextT = $true,
    inference(standard_cnf,[status(thm)],[2]) ).

thf(5,plain,
    doubleComplementI1 = $true,
    inference(standard_cnf,[status(thm)],[2]) ).

thf(6,plain,
    doubleComplementE1 = $true,
    inference(standard_cnf,[status(thm)],[2]) ).

thf(7,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ( X
            = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[2]) ).

thf(8,plain,
    ( ( ~ ! [A: $i,X: $i] :
            ( ( in @ X @ ( powerset @ A ) )
           => ( X
              = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[7]) ).

thf(9,plain,
    ( ( ( in @ sK2_SY0 @ ( powerset @ sK1_A ) )
      & ( sK2_SY0
       != ( setminus @ sK1_A @ ( setminus @ sK1_A @ sK2_SY0 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(10,plain,
    doubleComplementE1 = $true,
    inference(copy,[status(thm)],[6]) ).

thf(11,plain,
    doubleComplementI1 = $true,
    inference(copy,[status(thm)],[5]) ).

thf(12,plain,
    setextT = $true,
    inference(copy,[status(thm)],[4]) ).

thf(13,plain,
    complementT_lem = $true,
    inference(copy,[status(thm)],[3]) ).

thf(14,plain,
    ( ( ( in @ sK2_SY0 @ ( powerset @ sK1_A ) )
      & ( sK2_SY0
       != ( setminus @ sK1_A @ ( setminus @ sK1_A @ sK2_SY0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(15,plain,
    ( ( ~ ( ~ ( in @ sK2_SY0 @ ( powerset @ sK1_A ) )
          | ~ ( ( sK2_SY0
               != ( setminus @ sK1_A @ ( setminus @ sK1_A @ sK2_SY0 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14,complementT_lem,doubleComplementE1,doubleComplementI1,setextT]) ).

thf(16,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ( in @ ( setminus @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13,complementT_lem,doubleComplementE1,doubleComplementI1,setextT]) ).

thf(17,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
              | ~ ! [SX3: $i] :
                    ( ~ ( in @ SX3 @ SX0 )
                    | ~ ( in @ SX3 @ SX1 )
                    | ( in @ SX3 @ SX2 ) )
              | ~ ! [SX3: $i] :
                    ( ~ ( in @ SX3 @ SX0 )
                    | ~ ( in @ SX3 @ SX2 )
                    | ( in @ SX3 @ SX1 ) )
              | ( SX1 = SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12,complementT_lem,doubleComplementE1,doubleComplementI1,setextT]) ).

thf(18,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ SX0 )
              | ~ ( in @ SX2 @ SX1 )
              | ( in @ SX2 @ ( setminus @ SX0 @ ( setminus @ SX0 @ SX1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11,complementT_lem,doubleComplementE1,doubleComplementI1,setextT]) ).

thf(19,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ SX0 )
              | ~ ( in @ SX2 @ ( setminus @ SX0 @ ( setminus @ SX0 @ SX1 ) ) )
              | ( in @ SX2 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10,complementT_lem,doubleComplementE1,doubleComplementI1,setextT]) ).

thf(20,plain,
    ( ( ~ ( in @ sK2_SY0 @ ( powerset @ sK1_A ) )
      | ~ ( ( sK2_SY0
           != ( setminus @ sK1_A @ ( setminus @ sK1_A @ sK2_SY0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[15]) ).

thf(21,plain,
    ! [SV1: $i] :
      ( ( ! [SY1: $i] :
            ( ~ ( in @ SY1 @ ( powerset @ SV1 ) )
            | ( in @ ( setminus @ SV1 @ SY1 ) @ ( powerset @ SV1 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[16]) ).

thf(22,plain,
    ! [SV2: $i] :
      ( ( ! [SY2: $i] :
            ( ~ ( in @ SY2 @ ( powerset @ SV2 ) )
            | ! [SY3: $i] :
                ( ~ ( in @ SY3 @ ( powerset @ SV2 ) )
                | ~ ! [SY4: $i] :
                      ( ~ ( in @ SY4 @ SV2 )
                      | ~ ( in @ SY4 @ SY2 )
                      | ( in @ SY4 @ SY3 ) )
                | ~ ! [SY5: $i] :
                      ( ~ ( in @ SY5 @ SV2 )
                      | ~ ( in @ SY5 @ SY3 )
                      | ( in @ SY5 @ SY2 ) )
                | ( SY2 = SY3 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[17]) ).

thf(23,plain,
    ! [SV3: $i] :
      ( ( ! [SY6: $i] :
            ( ~ ( in @ SY6 @ ( powerset @ SV3 ) )
            | ! [SY7: $i] :
                ( ~ ( in @ SY7 @ SV3 )
                | ~ ( in @ SY7 @ SY6 )
                | ( in @ SY7 @ ( setminus @ SV3 @ ( setminus @ SV3 @ SY6 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[18]) ).

thf(24,plain,
    ! [SV4: $i] :
      ( ( ! [SY8: $i] :
            ( ~ ( in @ SY8 @ ( powerset @ SV4 ) )
            | ! [SY9: $i] :
                ( ~ ( in @ SY9 @ SV4 )
                | ~ ( in @ SY9 @ ( setminus @ SV4 @ ( setminus @ SV4 @ SY8 ) ) )
                | ( in @ SY9 @ SY8 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[19]) ).

thf(25,plain,
    ( ( ~ ( in @ sK2_SY0 @ ( powerset @ sK1_A ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[20]) ).

thf(26,plain,
    ( ( ~ ( ( sK2_SY0
           != ( setminus @ sK1_A @ ( setminus @ sK1_A @ sK2_SY0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[20]) ).

thf(27,plain,
    ! [SV1: $i,SV5: $i] :
      ( ( ~ ( in @ SV5 @ ( powerset @ SV1 ) )
        | ( in @ ( setminus @ SV1 @ SV5 ) @ ( powerset @ SV1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[21]) ).

thf(28,plain,
    ! [SV2: $i,SV6: $i] :
      ( ( ~ ( in @ SV6 @ ( powerset @ SV2 ) )
        | ! [SY10: $i] :
            ( ~ ( in @ SY10 @ ( powerset @ SV2 ) )
            | ~ ! [SY11: $i] :
                  ( ~ ( in @ SY11 @ SV2 )
                  | ~ ( in @ SY11 @ SV6 )
                  | ( in @ SY11 @ SY10 ) )
            | ~ ! [SY12: $i] :
                  ( ~ ( in @ SY12 @ SV2 )
                  | ~ ( in @ SY12 @ SY10 )
                  | ( in @ SY12 @ SV6 ) )
            | ( SV6 = SY10 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[22]) ).

thf(29,plain,
    ! [SV3: $i,SV7: $i] :
      ( ( ~ ( in @ SV7 @ ( powerset @ SV3 ) )
        | ! [SY13: $i] :
            ( ~ ( in @ SY13 @ SV3 )
            | ~ ( in @ SY13 @ SV7 )
            | ( in @ SY13 @ ( setminus @ SV3 @ ( setminus @ SV3 @ SV7 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[23]) ).

thf(30,plain,
    ! [SV4: $i,SV8: $i] :
      ( ( ~ ( in @ SV8 @ ( powerset @ SV4 ) )
        | ! [SY14: $i] :
            ( ~ ( in @ SY14 @ SV4 )
            | ~ ( in @ SY14 @ ( setminus @ SV4 @ ( setminus @ SV4 @ SV8 ) ) )
            | ( in @ SY14 @ SV8 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[24]) ).

thf(31,plain,
    ( ( in @ sK2_SY0 @ ( powerset @ sK1_A ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[25]) ).

thf(32,plain,
    ( ( ( sK2_SY0
       != ( setminus @ sK1_A @ ( setminus @ sK1_A @ sK2_SY0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[26]) ).

thf(33,plain,
    ! [SV1: $i,SV5: $i] :
      ( ( ( ~ ( in @ SV5 @ ( powerset @ SV1 ) ) )
        = $true )
      | ( ( in @ ( setminus @ SV1 @ SV5 ) @ ( powerset @ SV1 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[27]) ).

thf(34,plain,
    ! [SV2: $i,SV6: $i] :
      ( ( ( ~ ( in @ SV6 @ ( powerset @ SV2 ) ) )
        = $true )
      | ( ( ! [SY10: $i] :
              ( ~ ( in @ SY10 @ ( powerset @ SV2 ) )
              | ~ ! [SY11: $i] :
                    ( ~ ( in @ SY11 @ SV2 )
                    | ~ ( in @ SY11 @ SV6 )
                    | ( in @ SY11 @ SY10 ) )
              | ~ ! [SY12: $i] :
                    ( ~ ( in @ SY12 @ SV2 )
                    | ~ ( in @ SY12 @ SY10 )
                    | ( in @ SY12 @ SV6 ) )
              | ( SV6 = SY10 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[28]) ).

thf(35,plain,
    ! [SV3: $i,SV7: $i] :
      ( ( ( ~ ( in @ SV7 @ ( powerset @ SV3 ) ) )
        = $true )
      | ( ( ! [SY13: $i] :
              ( ~ ( in @ SY13 @ SV3 )
              | ~ ( in @ SY13 @ SV7 )
              | ( in @ SY13 @ ( setminus @ SV3 @ ( setminus @ SV3 @ SV7 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[29]) ).

thf(36,plain,
    ! [SV4: $i,SV8: $i] :
      ( ( ( ~ ( in @ SV8 @ ( powerset @ SV4 ) ) )
        = $true )
      | ( ( ! [SY14: $i] :
              ( ~ ( in @ SY14 @ SV4 )
              | ~ ( in @ SY14 @ ( setminus @ SV4 @ ( setminus @ SV4 @ SV8 ) ) )
              | ( in @ SY14 @ SV8 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[30]) ).

thf(37,plain,
    ( ( sK2_SY0
      = ( setminus @ sK1_A @ ( setminus @ sK1_A @ sK2_SY0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[32]) ).

thf(38,plain,
    ! [SV1: $i,SV5: $i] :
      ( ( ( in @ SV5 @ ( powerset @ SV1 ) )
        = $false )
      | ( ( in @ ( setminus @ SV1 @ SV5 ) @ ( powerset @ SV1 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[33]) ).

thf(39,plain,
    ! [SV2: $i,SV6: $i] :
      ( ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( ! [SY10: $i] :
              ( ~ ( in @ SY10 @ ( powerset @ SV2 ) )
              | ~ ! [SY11: $i] :
                    ( ~ ( in @ SY11 @ SV2 )
                    | ~ ( in @ SY11 @ SV6 )
                    | ( in @ SY11 @ SY10 ) )
              | ~ ! [SY12: $i] :
                    ( ~ ( in @ SY12 @ SV2 )
                    | ~ ( in @ SY12 @ SY10 )
                    | ( in @ SY12 @ SV6 ) )
              | ( SV6 = SY10 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[34]) ).

thf(40,plain,
    ! [SV3: $i,SV7: $i] :
      ( ( ( in @ SV7 @ ( powerset @ SV3 ) )
        = $false )
      | ( ( ! [SY13: $i] :
              ( ~ ( in @ SY13 @ SV3 )
              | ~ ( in @ SY13 @ SV7 )
              | ( in @ SY13 @ ( setminus @ SV3 @ ( setminus @ SV3 @ SV7 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[35]) ).

thf(41,plain,
    ! [SV4: $i,SV8: $i] :
      ( ( ( in @ SV8 @ ( powerset @ SV4 ) )
        = $false )
      | ( ( ! [SY14: $i] :
              ( ~ ( in @ SY14 @ SV4 )
              | ~ ( in @ SY14 @ ( setminus @ SV4 @ ( setminus @ SV4 @ SV8 ) ) )
              | ( in @ SY14 @ SV8 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[36]) ).

thf(42,plain,
    ! [SV6: $i,SV2: $i,SV9: $i] :
      ( ( ( ~ ( in @ SV9 @ ( powerset @ SV2 ) )
          | ~ ! [SY15: $i] :
                ( ~ ( in @ SY15 @ SV2 )
                | ~ ( in @ SY15 @ SV6 )
                | ( in @ SY15 @ SV9 ) )
          | ~ ! [SY16: $i] :
                ( ~ ( in @ SY16 @ SV2 )
                | ~ ( in @ SY16 @ SV9 )
                | ( in @ SY16 @ SV6 ) )
          | ( SV6 = SV9 ) )
        = $true )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[39]) ).

thf(43,plain,
    ! [SV7: $i,SV3: $i,SV10: $i] :
      ( ( ( ~ ( in @ SV10 @ SV3 )
          | ~ ( in @ SV10 @ SV7 )
          | ( in @ SV10 @ ( setminus @ SV3 @ ( setminus @ SV3 @ SV7 ) ) ) )
        = $true )
      | ( ( in @ SV7 @ ( powerset @ SV3 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[40]) ).

thf(44,plain,
    ! [SV8: $i,SV4: $i,SV11: $i] :
      ( ( ( ~ ( in @ SV11 @ SV4 )
          | ~ ( in @ SV11 @ ( setminus @ SV4 @ ( setminus @ SV4 @ SV8 ) ) )
          | ( in @ SV11 @ SV8 ) )
        = $true )
      | ( ( in @ SV8 @ ( powerset @ SV4 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[41]) ).

thf(45,plain,
    ! [SV6: $i,SV2: $i,SV9: $i] :
      ( ( ( ~ ( in @ SV9 @ ( powerset @ SV2 ) ) )
        = $true )
      | ( ( ~ ! [SY15: $i] :
                ( ~ ( in @ SY15 @ SV2 )
                | ~ ( in @ SY15 @ SV6 )
                | ( in @ SY15 @ SV9 ) )
          | ~ ! [SY16: $i] :
                ( ~ ( in @ SY16 @ SV2 )
                | ~ ( in @ SY16 @ SV9 )
                | ( in @ SY16 @ SV6 ) )
          | ( SV6 = SV9 ) )
        = $true )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[42]) ).

thf(46,plain,
    ! [SV7: $i,SV3: $i,SV10: $i] :
      ( ( ( ~ ( in @ SV10 @ SV3 ) )
        = $true )
      | ( ( ~ ( in @ SV10 @ SV7 )
          | ( in @ SV10 @ ( setminus @ SV3 @ ( setminus @ SV3 @ SV7 ) ) ) )
        = $true )
      | ( ( in @ SV7 @ ( powerset @ SV3 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[43]) ).

thf(47,plain,
    ! [SV8: $i,SV4: $i,SV11: $i] :
      ( ( ( ~ ( in @ SV11 @ SV4 ) )
        = $true )
      | ( ( ~ ( in @ SV11 @ ( setminus @ SV4 @ ( setminus @ SV4 @ SV8 ) ) )
          | ( in @ SV11 @ SV8 ) )
        = $true )
      | ( ( in @ SV8 @ ( powerset @ SV4 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[44]) ).

thf(48,plain,
    ! [SV6: $i,SV2: $i,SV9: $i] :
      ( ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( ~ ! [SY15: $i] :
                ( ~ ( in @ SY15 @ SV2 )
                | ~ ( in @ SY15 @ SV6 )
                | ( in @ SY15 @ SV9 ) )
          | ~ ! [SY16: $i] :
                ( ~ ( in @ SY16 @ SV2 )
                | ~ ( in @ SY16 @ SV9 )
                | ( in @ SY16 @ SV6 ) )
          | ( SV6 = SV9 ) )
        = $true )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[45]) ).

thf(49,plain,
    ! [SV7: $i,SV3: $i,SV10: $i] :
      ( ( ( in @ SV10 @ SV3 )
        = $false )
      | ( ( ~ ( in @ SV10 @ SV7 )
          | ( in @ SV10 @ ( setminus @ SV3 @ ( setminus @ SV3 @ SV7 ) ) ) )
        = $true )
      | ( ( in @ SV7 @ ( powerset @ SV3 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[46]) ).

thf(50,plain,
    ! [SV8: $i,SV4: $i,SV11: $i] :
      ( ( ( in @ SV11 @ SV4 )
        = $false )
      | ( ( ~ ( in @ SV11 @ ( setminus @ SV4 @ ( setminus @ SV4 @ SV8 ) ) )
          | ( in @ SV11 @ SV8 ) )
        = $true )
      | ( ( in @ SV8 @ ( powerset @ SV4 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[47]) ).

thf(51,plain,
    ! [SV9: $i,SV6: $i,SV2: $i] :
      ( ( ( ~ ! [SY15: $i] :
                ( ~ ( in @ SY15 @ SV2 )
                | ~ ( in @ SY15 @ SV6 )
                | ( in @ SY15 @ SV9 ) ) )
        = $true )
      | ( ( ~ ! [SY16: $i] :
                ( ~ ( in @ SY16 @ SV2 )
                | ~ ( in @ SY16 @ SV9 )
                | ( in @ SY16 @ SV6 ) )
          | ( SV6 = SV9 ) )
        = $true )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[48]) ).

thf(52,plain,
    ! [SV3: $i,SV7: $i,SV10: $i] :
      ( ( ( ~ ( in @ SV10 @ SV7 ) )
        = $true )
      | ( ( in @ SV10 @ ( setminus @ SV3 @ ( setminus @ SV3 @ SV7 ) ) )
        = $true )
      | ( ( in @ SV10 @ SV3 )
        = $false )
      | ( ( in @ SV7 @ ( powerset @ SV3 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[49]) ).

thf(53,plain,
    ! [SV8: $i,SV4: $i,SV11: $i] :
      ( ( ( ~ ( in @ SV11 @ ( setminus @ SV4 @ ( setminus @ SV4 @ SV8 ) ) ) )
        = $true )
      | ( ( in @ SV11 @ SV8 )
        = $true )
      | ( ( in @ SV11 @ SV4 )
        = $false )
      | ( ( in @ SV8 @ ( powerset @ SV4 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[50]) ).

thf(54,plain,
    ! [SV9: $i,SV6: $i,SV2: $i] :
      ( ( ( ! [SY15: $i] :
              ( ~ ( in @ SY15 @ SV2 )
              | ~ ( in @ SY15 @ SV6 )
              | ( in @ SY15 @ SV9 ) ) )
        = $false )
      | ( ( ~ ! [SY16: $i] :
                ( ~ ( in @ SY16 @ SV2 )
                | ~ ( in @ SY16 @ SV9 )
                | ( in @ SY16 @ SV6 ) )
          | ( SV6 = SV9 ) )
        = $true )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[51]) ).

thf(55,plain,
    ! [SV3: $i,SV7: $i,SV10: $i] :
      ( ( ( in @ SV10 @ SV7 )
        = $false )
      | ( ( in @ SV10 @ ( setminus @ SV3 @ ( setminus @ SV3 @ SV7 ) ) )
        = $true )
      | ( ( in @ SV10 @ SV3 )
        = $false )
      | ( ( in @ SV7 @ ( powerset @ SV3 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[52]) ).

thf(56,plain,
    ! [SV8: $i,SV4: $i,SV11: $i] :
      ( ( ( in @ SV11 @ ( setminus @ SV4 @ ( setminus @ SV4 @ SV8 ) ) )
        = $false )
      | ( ( in @ SV11 @ SV8 )
        = $true )
      | ( ( in @ SV11 @ SV4 )
        = $false )
      | ( ( in @ SV8 @ ( powerset @ SV4 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[53]) ).

thf(57,plain,
    ! [SV2: $i,SV6: $i,SV9: $i] :
      ( ( ( ~ ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV2 )
          | ~ ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV6 )
          | ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV9 ) )
        = $false )
      | ( ( ~ ! [SY16: $i] :
                ( ~ ( in @ SY16 @ SV2 )
                | ~ ( in @ SY16 @ SV9 )
                | ( in @ SY16 @ SV6 ) )
          | ( SV6 = SV9 ) )
        = $true )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[54]) ).

thf(58,plain,
    ! [SV2: $i,SV6: $i,SV9: $i] :
      ( ( ( ~ ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV2 ) )
        = $false )
      | ( ( ~ ! [SY16: $i] :
                ( ~ ( in @ SY16 @ SV2 )
                | ~ ( in @ SY16 @ SV9 )
                | ( in @ SY16 @ SV6 ) )
          | ( SV6 = SV9 ) )
        = $true )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[57]) ).

thf(59,plain,
    ! [SV2: $i,SV6: $i,SV9: $i] :
      ( ( ( ~ ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV6 )
          | ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV9 ) )
        = $false )
      | ( ( ~ ! [SY16: $i] :
                ( ~ ( in @ SY16 @ SV2 )
                | ~ ( in @ SY16 @ SV9 )
                | ( in @ SY16 @ SV6 ) )
          | ( SV6 = SV9 ) )
        = $true )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[57]) ).

thf(60,plain,
    ! [SV2: $i,SV6: $i,SV9: $i] :
      ( ( ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV2 )
        = $true )
      | ( ( ~ ! [SY16: $i] :
                ( ~ ( in @ SY16 @ SV2 )
                | ~ ( in @ SY16 @ SV9 )
                | ( in @ SY16 @ SV6 ) )
          | ( SV6 = SV9 ) )
        = $true )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[58]) ).

thf(61,plain,
    ! [SV2: $i,SV6: $i,SV9: $i] :
      ( ( ( ~ ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV6 ) )
        = $false )
      | ( ( ~ ! [SY16: $i] :
                ( ~ ( in @ SY16 @ SV2 )
                | ~ ( in @ SY16 @ SV9 )
                | ( in @ SY16 @ SV6 ) )
          | ( SV6 = SV9 ) )
        = $true )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[59]) ).

thf(62,plain,
    ! [SV2: $i,SV6: $i,SV9: $i] :
      ( ( ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV9 )
        = $false )
      | ( ( ~ ! [SY16: $i] :
                ( ~ ( in @ SY16 @ SV2 )
                | ~ ( in @ SY16 @ SV9 )
                | ( in @ SY16 @ SV6 ) )
          | ( SV6 = SV9 ) )
        = $true )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[59]) ).

thf(63,plain,
    ! [SV6: $i,SV9: $i,SV2: $i] :
      ( ( ( ~ ! [SY16: $i] :
                ( ~ ( in @ SY16 @ SV2 )
                | ~ ( in @ SY16 @ SV9 )
                | ( in @ SY16 @ SV6 ) ) )
        = $true )
      | ( ( SV6 = SV9 )
        = $true )
      | ( ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV2 )
        = $true )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[60]) ).

thf(64,plain,
    ! [SV2: $i,SV6: $i,SV9: $i] :
      ( ( ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV6 )
        = $true )
      | ( ( ~ ! [SY16: $i] :
                ( ~ ( in @ SY16 @ SV2 )
                | ~ ( in @ SY16 @ SV9 )
                | ( in @ SY16 @ SV6 ) )
          | ( SV6 = SV9 ) )
        = $true )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[61]) ).

thf(65,plain,
    ! [SV6: $i,SV9: $i,SV2: $i] :
      ( ( ( ~ ! [SY16: $i] :
                ( ~ ( in @ SY16 @ SV2 )
                | ~ ( in @ SY16 @ SV9 )
                | ( in @ SY16 @ SV6 ) ) )
        = $true )
      | ( ( SV6 = SV9 )
        = $true )
      | ( ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV9 )
        = $false )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[62]) ).

thf(66,plain,
    ! [SV6: $i,SV9: $i,SV2: $i] :
      ( ( ( ! [SY16: $i] :
              ( ~ ( in @ SY16 @ SV2 )
              | ~ ( in @ SY16 @ SV9 )
              | ( in @ SY16 @ SV6 ) ) )
        = $false )
      | ( ( SV6 = SV9 )
        = $true )
      | ( ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV2 )
        = $true )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[63]) ).

thf(67,plain,
    ! [SV6: $i,SV9: $i,SV2: $i] :
      ( ( ( ~ ! [SY16: $i] :
                ( ~ ( in @ SY16 @ SV2 )
                | ~ ( in @ SY16 @ SV9 )
                | ( in @ SY16 @ SV6 ) ) )
        = $true )
      | ( ( SV6 = SV9 )
        = $true )
      | ( ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV6 )
        = $true )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[64]) ).

thf(68,plain,
    ! [SV6: $i,SV9: $i,SV2: $i] :
      ( ( ( ! [SY16: $i] :
              ( ~ ( in @ SY16 @ SV2 )
              | ~ ( in @ SY16 @ SV9 )
              | ( in @ SY16 @ SV6 ) ) )
        = $false )
      | ( ( SV6 = SV9 )
        = $true )
      | ( ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV9 )
        = $false )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[65]) ).

thf(69,plain,
    ! [SV2: $i,SV9: $i,SV6: $i] :
      ( ( ( ~ ( in @ ( sK4_SY16 @ SV6 @ SV9 @ SV2 ) @ SV2 )
          | ~ ( in @ ( sK4_SY16 @ SV6 @ SV9 @ SV2 ) @ SV9 )
          | ( in @ ( sK4_SY16 @ SV6 @ SV9 @ SV2 ) @ SV6 ) )
        = $false )
      | ( ( SV6 = SV9 )
        = $true )
      | ( ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV2 )
        = $true )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[66]) ).

thf(70,plain,
    ! [SV6: $i,SV9: $i,SV2: $i] :
      ( ( ( ! [SY16: $i] :
              ( ~ ( in @ SY16 @ SV2 )
              | ~ ( in @ SY16 @ SV9 )
              | ( in @ SY16 @ SV6 ) ) )
        = $false )
      | ( ( SV6 = SV9 )
        = $true )
      | ( ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV6 )
        = $true )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[67]) ).

thf(71,plain,
    ! [SV2: $i,SV9: $i,SV6: $i] :
      ( ( ( ~ ( in @ ( sK5_SY16 @ SV6 @ SV9 @ SV2 ) @ SV2 )
          | ~ ( in @ ( sK5_SY16 @ SV6 @ SV9 @ SV2 ) @ SV9 )
          | ( in @ ( sK5_SY16 @ SV6 @ SV9 @ SV2 ) @ SV6 ) )
        = $false )
      | ( ( SV6 = SV9 )
        = $true )
      | ( ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV9 )
        = $false )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[68]) ).

thf(72,plain,
    ! [SV2: $i,SV9: $i,SV6: $i] :
      ( ( ( ~ ( in @ ( sK4_SY16 @ SV6 @ SV9 @ SV2 ) @ SV2 ) )
        = $false )
      | ( ( SV6 = SV9 )
        = $true )
      | ( ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV2 )
        = $true )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[69]) ).

thf(73,plain,
    ! [SV2: $i,SV9: $i,SV6: $i] :
      ( ( ( ~ ( in @ ( sK4_SY16 @ SV6 @ SV9 @ SV2 ) @ SV9 )
          | ( in @ ( sK4_SY16 @ SV6 @ SV9 @ SV2 ) @ SV6 ) )
        = $false )
      | ( ( SV6 = SV9 )
        = $true )
      | ( ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV2 )
        = $true )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[69]) ).

thf(74,plain,
    ! [SV2: $i,SV9: $i,SV6: $i] :
      ( ( ( ~ ( in @ ( sK6_SY16 @ SV6 @ SV9 @ SV2 ) @ SV2 )
          | ~ ( in @ ( sK6_SY16 @ SV6 @ SV9 @ SV2 ) @ SV9 )
          | ( in @ ( sK6_SY16 @ SV6 @ SV9 @ SV2 ) @ SV6 ) )
        = $false )
      | ( ( SV6 = SV9 )
        = $true )
      | ( ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV6 )
        = $true )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[70]) ).

thf(75,plain,
    ! [SV2: $i,SV9: $i,SV6: $i] :
      ( ( ( ~ ( in @ ( sK5_SY16 @ SV6 @ SV9 @ SV2 ) @ SV2 ) )
        = $false )
      | ( ( SV6 = SV9 )
        = $true )
      | ( ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV9 )
        = $false )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[71]) ).

thf(76,plain,
    ! [SV2: $i,SV9: $i,SV6: $i] :
      ( ( ( ~ ( in @ ( sK5_SY16 @ SV6 @ SV9 @ SV2 ) @ SV9 )
          | ( in @ ( sK5_SY16 @ SV6 @ SV9 @ SV2 ) @ SV6 ) )
        = $false )
      | ( ( SV6 = SV9 )
        = $true )
      | ( ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV9 )
        = $false )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[71]) ).

thf(77,plain,
    ! [SV2: $i,SV9: $i,SV6: $i] :
      ( ( ( in @ ( sK4_SY16 @ SV6 @ SV9 @ SV2 ) @ SV2 )
        = $true )
      | ( ( SV6 = SV9 )
        = $true )
      | ( ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV2 )
        = $true )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[72]) ).

thf(78,plain,
    ! [SV2: $i,SV9: $i,SV6: $i] :
      ( ( ( ~ ( in @ ( sK4_SY16 @ SV6 @ SV9 @ SV2 ) @ SV9 ) )
        = $false )
      | ( ( SV6 = SV9 )
        = $true )
      | ( ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV2 )
        = $true )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[73]) ).

thf(79,plain,
    ! [SV2: $i,SV9: $i,SV6: $i] :
      ( ( ( in @ ( sK4_SY16 @ SV6 @ SV9 @ SV2 ) @ SV6 )
        = $false )
      | ( ( SV6 = SV9 )
        = $true )
      | ( ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV2 )
        = $true )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[73]) ).

thf(80,plain,
    ! [SV2: $i,SV9: $i,SV6: $i] :
      ( ( ( ~ ( in @ ( sK6_SY16 @ SV6 @ SV9 @ SV2 ) @ SV2 ) )
        = $false )
      | ( ( SV6 = SV9 )
        = $true )
      | ( ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV6 )
        = $true )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[74]) ).

thf(81,plain,
    ! [SV2: $i,SV9: $i,SV6: $i] :
      ( ( ( ~ ( in @ ( sK6_SY16 @ SV6 @ SV9 @ SV2 ) @ SV9 )
          | ( in @ ( sK6_SY16 @ SV6 @ SV9 @ SV2 ) @ SV6 ) )
        = $false )
      | ( ( SV6 = SV9 )
        = $true )
      | ( ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV6 )
        = $true )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[74]) ).

thf(82,plain,
    ! [SV2: $i,SV9: $i,SV6: $i] :
      ( ( ( in @ ( sK5_SY16 @ SV6 @ SV9 @ SV2 ) @ SV2 )
        = $true )
      | ( ( SV6 = SV9 )
        = $true )
      | ( ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV9 )
        = $false )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[75]) ).

thf(83,plain,
    ! [SV2: $i,SV9: $i,SV6: $i] :
      ( ( ( ~ ( in @ ( sK5_SY16 @ SV6 @ SV9 @ SV2 ) @ SV9 ) )
        = $false )
      | ( ( SV6 = SV9 )
        = $true )
      | ( ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV9 )
        = $false )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[76]) ).

thf(84,plain,
    ! [SV2: $i,SV9: $i,SV6: $i] :
      ( ( ( in @ ( sK5_SY16 @ SV6 @ SV9 @ SV2 ) @ SV6 )
        = $false )
      | ( ( SV6 = SV9 )
        = $true )
      | ( ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV9 )
        = $false )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[76]) ).

thf(85,plain,
    ! [SV2: $i,SV9: $i,SV6: $i] :
      ( ( ( in @ ( sK4_SY16 @ SV6 @ SV9 @ SV2 ) @ SV9 )
        = $true )
      | ( ( SV6 = SV9 )
        = $true )
      | ( ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV2 )
        = $true )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[78]) ).

thf(86,plain,
    ! [SV2: $i,SV9: $i,SV6: $i] :
      ( ( ( in @ ( sK6_SY16 @ SV6 @ SV9 @ SV2 ) @ SV2 )
        = $true )
      | ( ( SV6 = SV9 )
        = $true )
      | ( ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV6 )
        = $true )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[80]) ).

thf(87,plain,
    ! [SV2: $i,SV9: $i,SV6: $i] :
      ( ( ( ~ ( in @ ( sK6_SY16 @ SV6 @ SV9 @ SV2 ) @ SV9 ) )
        = $false )
      | ( ( SV6 = SV9 )
        = $true )
      | ( ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV6 )
        = $true )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[81]) ).

thf(88,plain,
    ! [SV2: $i,SV9: $i,SV6: $i] :
      ( ( ( in @ ( sK6_SY16 @ SV6 @ SV9 @ SV2 ) @ SV6 )
        = $false )
      | ( ( SV6 = SV9 )
        = $true )
      | ( ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV6 )
        = $true )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[81]) ).

thf(89,plain,
    ! [SV2: $i,SV9: $i,SV6: $i] :
      ( ( ( in @ ( sK5_SY16 @ SV6 @ SV9 @ SV2 ) @ SV9 )
        = $true )
      | ( ( SV6 = SV9 )
        = $true )
      | ( ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV9 )
        = $false )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[83]) ).

thf(90,plain,
    ! [SV2: $i,SV9: $i,SV6: $i] :
      ( ( ( in @ ( sK6_SY16 @ SV6 @ SV9 @ SV2 ) @ SV9 )
        = $true )
      | ( ( SV6 = SV9 )
        = $true )
      | ( ( in @ ( sK3_SY15 @ SV9 @ SV6 @ SV2 ) @ SV6 )
        = $true )
      | ( ( in @ SV9 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[87]) ).

thf(91,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[31,90,89,88,86,85,84,82,79,77,56,55,38,37]) ).

thf(92,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[91]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : SEU731^2 : TPTP v8.1.0. Released v3.7.0.
% 0.00/0.10  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.09/0.28  % Computer : n032.cluster.edu
% 0.09/0.28  % Model    : x86_64 x86_64
% 0.09/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28  % Memory   : 8042.1875MB
% 0.09/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28  % CPULimit : 300
% 0.09/0.28  % WCLimit  : 600
% 0.09/0.28  % DateTime : Mon Jun 20 04:54:33 EDT 2022
% 0.09/0.28  % CPUTime  : 
% 0.09/0.29  
% 0.09/0.29   No.of.Axioms: 0
% 0.09/0.29  
% 0.09/0.29   Length.of.Defs: 1067
% 0.09/0.29  
% 0.09/0.29   Contains.Choice.Funs: false
% 0.09/0.29  (rf:0,axioms:0,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)....
% 0.13/0.36  
% 0.13/0.36  ********************************
% 0.13/0.36  *   All subproblems solved!    *
% 0.13/0.36  ********************************
% 0.13/0.36  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:91,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.37  
% 0.13/0.37  %**** Beginning of derivation protocol ****
% 0.13/0.37  % SZS output start CNFRefutation
% See solution above
% 0.13/0.37  
% 0.13/0.37  %**** End of derivation protocol ****
% 0.13/0.37  %**** no. of clauses in derivation: 92 ****
% 0.13/0.37  %**** clause counter: 91 ****
% 0.13/0.37  
% 0.13/0.37  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:91,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------