TSTP Solution File: SEU711^2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEU711^2 : 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 : n016.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 12:14:07 EDT 2022

% Result   : Theorem 0.19s 0.53s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :   14
% Syntax   : Number of formulae    :  132 (  58 unt;  10 typ;   3 def)
%            Number of atoms       :  859 ( 240 equ;   0 cnn)
%            Maximal formula atoms :    6 (   7 avg)
%            Number of connectives : 1638 ( 267   ~; 354   |;  12   &; 959   @)
%                                         (   0 <=>;  46  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :  414 (   0   ^ 414   !;   0   ?; 414   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_binunion,type,
    binunion: $i > $i > $i ).

thf(tp_binunionEcases,type,
    binunionEcases: $o ).

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

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

thf(tp_powersetE,type,
    powersetE: $o ).

thf(tp_powersetI,type,
    powersetI: $o ).

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

thf(tp_sK2_SY16,type,
    sK2_SY16: $i ).

thf(tp_sK3_SY18,type,
    sK3_SY18: $i ).

thf(tp_sK4_Xx,type,
    sK4_Xx: $i > $i > $i ).

thf(binunionEcases,definition,
    ( binunionEcases
    = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
          ( ( in @ Xx @ ( binunion @ A @ B ) )
         => ( ( ( in @ Xx @ A )
             => Xphi )
           => ( ( ( in @ Xx @ B )
               => Xphi )
             => Xphi ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionEcases) ).

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

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

thf(1,conjecture,
    ( powersetI
   => ( powersetE
     => ( binunionEcases
       => ! [A: $i,X: $i] :
            ( ( in @ X @ ( powerset @ A ) )
           => ! [Y: $i] :
                ( ( in @ Y @ ( powerset @ A ) )
               => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionT_lem) ).

thf(2,negated_conjecture,
    ( ( powersetI
     => ( powersetE
       => ( binunionEcases
         => ! [A: $i,X: $i] :
              ( ( in @ X @ ( powerset @ A ) )
             => ! [Y: $i] :
                  ( ( in @ Y @ ( powerset @ A ) )
                 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [A: $i,B: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ B )
             => ( in @ Xx @ A ) )
         => ( in @ B @ ( powerset @ A ) ) )
     => ( ! [A: $i,B: $i,Xx: $i] :
            ( ( in @ B @ ( powerset @ A ) )
           => ( ( in @ Xx @ B )
             => ( in @ Xx @ A ) ) )
       => ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
              ( ( in @ Xx @ ( binunion @ A @ B ) )
             => ( ( ( in @ Xx @ A )
                 => Xphi )
               => ( ( ( in @ Xx @ B )
                   => Xphi )
                 => Xphi ) ) )
         => ! [A: $i,X: $i] :
              ( ( in @ X @ ( powerset @ A ) )
             => ! [Y: $i] :
                  ( ( in @ Y @ ( powerset @ A ) )
                 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2,binunionEcases,powersetE,powersetI]) ).

thf(4,plain,
    ( ( ! [A: $i,B: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ B )
             => ( in @ Xx @ A ) )
         => ( in @ B @ ( powerset @ A ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ( ( in @ Xx @ B )
           => ( in @ Xx @ A ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(6,plain,
    ( ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
          ( ( in @ Xx @ ( binunion @ A @ B ) )
         => ( ( ( in @ Xx @ A )
             => Xphi )
           => ( ( ( in @ Xx @ B )
               => Xphi )
             => Xphi ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(7,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[3]) ).

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

thf(9,plain,
    ( ( ( in @ sK2_SY16 @ ( powerset @ sK1_A ) )
      & ( in @ sK3_SY18 @ ( powerset @ sK1_A ) )
      & ~ ( in @ ( binunion @ sK2_SY16 @ sK3_SY18 ) @ ( powerset @ sK1_A ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(10,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( in @ ( sK4_Xx @ B @ A ) @ B )
            & ~ ( in @ ( sK4_Xx @ B @ A ) @ A ) )
          | ( in @ B @ ( powerset @ A ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[4]) ).

thf(11,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( in @ B @ ( powerset @ A ) )
          | ! [Xx: $i] :
              ( ~ ( in @ Xx @ B )
              | ( in @ Xx @ A ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5]) ).

thf(12,plain,
    ( ( ! [A: $i,B: $i] :
          ( ! [Xx: $i] :
              ( ~ ( in @ Xx @ ( binunion @ A @ B ) )
              | ( in @ Xx @ A )
              | ( in @ Xx @ B )
              | ! [Xphi: $o] : Xphi )
          & ! [Xx: $i] :
              ( ~ ( in @ Xx @ ( binunion @ A @ B ) )
              | ( in @ Xx @ A )
              | ! [Xphi: $o] :
                  ( ~ Xphi
                  | Xphi ) )
          & ! [Xx: $i] :
              ( ~ ( in @ Xx @ ( binunion @ A @ B ) )
              | ! [Xphi: $o] :
                  ( ~ Xphi
                  | ( in @ Xx @ B )
                  | Xphi ) )
          & ( ! [Xx: $i] :
                ~ ( in @ Xx @ ( binunion @ A @ B ) )
            | ! [Xphi: $o] :
                ( ~ Xphi
                | ~ Xphi
                | Xphi ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

thf(13,plain,
    ( ( ! [A: $i,B: $i] :
          ( ! [Xx: $i] :
              ( ~ ( in @ Xx @ ( binunion @ A @ B ) )
              | ( in @ Xx @ A )
              | ( in @ Xx @ B )
              | ! [Xphi: $o] : Xphi )
          & ! [Xx: $i] :
              ( ~ ( in @ Xx @ ( binunion @ A @ B ) )
              | ( in @ Xx @ A )
              | ! [Xphi: $o] :
                  ( ~ Xphi
                  | Xphi ) )
          & ! [Xx: $i] :
              ( ~ ( in @ Xx @ ( binunion @ A @ B ) )
              | ! [Xphi: $o] :
                  ( ~ Xphi
                  | ( in @ Xx @ B )
                  | Xphi ) )
          & ( ! [Xx: $i] :
                ~ ( in @ Xx @ ( binunion @ A @ B ) )
            | ! [Xphi: $o] :
                ( ~ Xphi
                | ~ Xphi
                | Xphi ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(14,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( in @ B @ ( powerset @ A ) )
          | ! [Xx: $i] :
              ( ~ ( in @ Xx @ B )
              | ( in @ Xx @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(15,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( in @ ( sK4_Xx @ B @ A ) @ B )
            & ~ ( in @ ( sK4_Xx @ B @ A ) @ A ) )
          | ( in @ B @ ( powerset @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(16,plain,
    ( ( ( in @ sK2_SY16 @ ( powerset @ sK1_A ) )
      & ( in @ sK3_SY18 @ ( powerset @ sK1_A ) )
      & ~ ( in @ ( binunion @ sK2_SY16 @ sK3_SY18 ) @ ( powerset @ sK1_A ) ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(17,plain,
    ( ( ~ ( ~ ( in @ sK2_SY16 @ ( powerset @ sK1_A ) )
          | ~ ~ ( ~ ( in @ sK3_SY18 @ ( powerset @ sK1_A ) )
                | ~ ~ ( in @ ( binunion @ sK2_SY16 @ sK3_SY18 ) @ ( powerset @ sK1_A ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16,binunionEcases,powersetE,powersetI]) ).

thf(18,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ~ ( ~ ! [SX2: $i] :
                        ( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
                        | ( in @ SX2 @ SX0 )
                        | ( in @ SX2 @ SX1 )
                        | ! [SX3: $o] : SX3 )
                  | ~ ! [SX2: $i] :
                        ( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
                        | ( in @ SX2 @ SX0 )
                        | ! [SX3: $o] :
                            ( ~ SX3
                            | SX3 ) ) )
            | ~ ~ ( ~ ! [SX2: $i] :
                        ( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
                        | ! [SX3: $o] :
                            ( ~ SX3
                            | ( in @ SX2 @ SX1 )
                            | SX3 ) )
                  | ~ ( ! [SX2: $i] :
                          ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
                      | ! [SX2: $o] :
                          ( ~ SX2
                          | ~ SX2
                          | SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13,binunionEcases,powersetE,powersetI]) ).

thf(19,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( ~ ( in @ ( sK4_Xx @ SX1 @ SX0 ) @ SX1 )
              | ~ ~ ( in @ ( sK4_Xx @ SX1 @ SX0 ) @ SX0 ) )
          | ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15,binunionEcases,powersetE,powersetI]) ).

thf(20,plain,
    ! [SV1: $i] :
      ( ( ! [SY19: $i] :
            ( ~ ( in @ SY19 @ ( powerset @ SV1 ) )
            | ! [SY20: $i] :
                ( ~ ( in @ SY20 @ SY19 )
                | ( in @ SY20 @ SV1 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[14]) ).

thf(21,plain,
    ( ( ~ ( in @ sK2_SY16 @ ( powerset @ sK1_A ) )
      | ~ ~ ( ~ ( in @ sK3_SY18 @ ( powerset @ sK1_A ) )
            | ~ ~ ( in @ ( binunion @ sK2_SY16 @ sK3_SY18 ) @ ( powerset @ sK1_A ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[17]) ).

thf(22,plain,
    ! [SV2: $i] :
      ( ( ! [SY21: $i] :
            ~ ( ~ ~ ( ~ ! [SY22: $i] :
                          ( ~ ( in @ SY22 @ ( binunion @ SV2 @ SY21 ) )
                          | ( in @ SY22 @ SV2 )
                          | ( in @ SY22 @ SY21 )
                          | ! [SX3: $o] : SX3 )
                    | ~ ! [SY24: $i] :
                          ( ~ ( in @ SY24 @ ( binunion @ SV2 @ SY21 ) )
                          | ( in @ SY24 @ SV2 )
                          | ! [SX3: $o] :
                              ( ~ SX3
                              | SX3 ) ) )
              | ~ ~ ( ~ ! [SY26: $i] :
                          ( ~ ( in @ SY26 @ ( binunion @ SV2 @ SY21 ) )
                          | ! [SX3: $o] :
                              ( ~ SX3
                              | ( in @ SY26 @ SY21 )
                              | SX3 ) )
                    | ~ ( ! [SY28: $i] :
                            ~ ( in @ SY28 @ ( binunion @ SV2 @ SY21 ) )
                        | ! [SX2: $o] :
                            ( ~ SX2
                            | ~ SX2
                            | SX2 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[18]) ).

thf(23,plain,
    ! [SV3: $i] :
      ( ( ! [SY30: $i] :
            ( ~ ( ~ ( in @ ( sK4_Xx @ SY30 @ SV3 ) @ SY30 )
                | ~ ~ ( in @ ( sK4_Xx @ SY30 @ SV3 ) @ SV3 ) )
            | ( in @ SY30 @ ( powerset @ SV3 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[19]) ).

thf(24,plain,
    ! [SV1: $i,SV4: $i] :
      ( ( ~ ( in @ SV4 @ ( powerset @ SV1 ) )
        | ! [SY31: $i] :
            ( ~ ( in @ SY31 @ SV4 )
            | ( in @ SY31 @ SV1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(25,plain,
    ( ( ~ ( in @ sK2_SY16 @ ( powerset @ sK1_A ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[21]) ).

thf(26,plain,
    ( ( ~ ~ ( ~ ( in @ sK3_SY18 @ ( powerset @ sK1_A ) )
            | ~ ~ ( in @ ( binunion @ sK2_SY16 @ sK3_SY18 ) @ ( powerset @ sK1_A ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[21]) ).

thf(27,plain,
    ! [SV5: $i,SV2: $i] :
      ( ( ~ ( ~ ~ ( ~ ! [SY32: $i] :
                        ( ~ ( in @ SY32 @ ( binunion @ SV2 @ SV5 ) )
                        | ( in @ SY32 @ SV2 )
                        | ( in @ SY32 @ SV5 )
                        | ! [SX3: $o] : SX3 )
                  | ~ ! [SY34: $i] :
                        ( ~ ( in @ SY34 @ ( binunion @ SV2 @ SV5 ) )
                        | ( in @ SY34 @ SV2 )
                        | ! [SX3: $o] :
                            ( ~ SX3
                            | SX3 ) ) )
            | ~ ~ ( ~ ! [SY36: $i] :
                        ( ~ ( in @ SY36 @ ( binunion @ SV2 @ SV5 ) )
                        | ! [SY37: $o] :
                            ( ~ SY37
                            | ( in @ SY36 @ SV5 )
                            | SY37 ) )
                  | ~ ( ! [SY38: $i] :
                          ~ ( in @ SY38 @ ( binunion @ SV2 @ SV5 ) )
                      | ! [SX2: $o] :
                          ( ~ SX2
                          | ~ SX2
                          | SX2 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[22]) ).

thf(28,plain,
    ! [SV3: $i,SV6: $i] :
      ( ( ~ ( ~ ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV6 )
            | ~ ~ ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV3 ) )
        | ( in @ SV6 @ ( powerset @ SV3 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[23]) ).

thf(29,plain,
    ! [SV1: $i,SV4: $i] :
      ( ( ( ~ ( in @ SV4 @ ( powerset @ SV1 ) ) )
        = $true )
      | ( ( ! [SY31: $i] :
              ( ~ ( in @ SY31 @ SV4 )
              | ( in @ SY31 @ SV1 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[24]) ).

thf(30,plain,
    ( ( in @ sK2_SY16 @ ( powerset @ sK1_A ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[25]) ).

thf(31,plain,
    ( ( ~ ( ~ ( in @ sK3_SY18 @ ( powerset @ sK1_A ) )
          | ~ ~ ( in @ ( binunion @ sK2_SY16 @ sK3_SY18 ) @ ( powerset @ sK1_A ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[26]) ).

thf(32,plain,
    ! [SV5: $i,SV2: $i] :
      ( ( ~ ~ ( ~ ! [SY32: $i] :
                    ( ~ ( in @ SY32 @ ( binunion @ SV2 @ SV5 ) )
                    | ( in @ SY32 @ SV2 )
                    | ( in @ SY32 @ SV5 )
                    | ! [SX3: $o] : SX3 )
              | ~ ! [SY34: $i] :
                    ( ~ ( in @ SY34 @ ( binunion @ SV2 @ SV5 ) )
                    | ( in @ SY34 @ SV2 )
                    | ! [SX3: $o] :
                        ( ~ SX3
                        | SX3 ) ) )
        | ~ ~ ( ~ ! [SY36: $i] :
                    ( ~ ( in @ SY36 @ ( binunion @ SV2 @ SV5 ) )
                    | ! [SY37: $o] :
                        ( ~ SY37
                        | ( in @ SY36 @ SV5 )
                        | SY37 ) )
              | ~ ( ! [SY38: $i] :
                      ~ ( in @ SY38 @ ( binunion @ SV2 @ SV5 ) )
                  | ! [SX2: $o] :
                      ( ~ SX2
                      | ~ SX2
                      | SX2 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[27]) ).

thf(33,plain,
    ! [SV3: $i,SV6: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV6 )
              | ~ ~ ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV3 ) ) )
        = $true )
      | ( ( in @ SV6 @ ( powerset @ SV3 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[28]) ).

thf(34,plain,
    ! [SV1: $i,SV4: $i] :
      ( ( ( in @ SV4 @ ( powerset @ SV1 ) )
        = $false )
      | ( ( ! [SY31: $i] :
              ( ~ ( in @ SY31 @ SV4 )
              | ( in @ SY31 @ SV1 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[29]) ).

thf(35,plain,
    ( ( ~ ( in @ sK3_SY18 @ ( powerset @ sK1_A ) )
      | ~ ~ ( in @ ( binunion @ sK2_SY16 @ sK3_SY18 ) @ ( powerset @ sK1_A ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[31]) ).

thf(36,plain,
    ! [SV5: $i,SV2: $i] :
      ( ( ~ ~ ( ~ ! [SY32: $i] :
                    ( ~ ( in @ SY32 @ ( binunion @ SV2 @ SV5 ) )
                    | ( in @ SY32 @ SV2 )
                    | ( in @ SY32 @ SV5 )
                    | ! [SX3: $o] : SX3 )
              | ~ ! [SY34: $i] :
                    ( ~ ( in @ SY34 @ ( binunion @ SV2 @ SV5 ) )
                    | ( in @ SY34 @ SV2 )
                    | ! [SX3: $o] :
                        ( ~ SX3
                        | SX3 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[32]) ).

thf(37,plain,
    ! [SV5: $i,SV2: $i] :
      ( ( ~ ~ ( ~ ! [SY36: $i] :
                    ( ~ ( in @ SY36 @ ( binunion @ SV2 @ SV5 ) )
                    | ! [SY37: $o] :
                        ( ~ SY37
                        | ( in @ SY36 @ SV5 )
                        | SY37 ) )
              | ~ ( ! [SY38: $i] :
                      ~ ( in @ SY38 @ ( binunion @ SV2 @ SV5 ) )
                  | ! [SX2: $o] :
                      ( ~ SX2
                      | ~ SX2
                      | SX2 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[32]) ).

thf(38,plain,
    ! [SV3: $i,SV6: $i] :
      ( ( ( ~ ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV6 )
          | ~ ~ ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV3 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV3 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[33]) ).

thf(39,plain,
    ! [SV1: $i,SV4: $i,SV7: $i] :
      ( ( ( ~ ( in @ SV7 @ SV4 )
          | ( in @ SV7 @ SV1 ) )
        = $true )
      | ( ( in @ SV4 @ ( powerset @ SV1 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[34]) ).

thf(40,plain,
    ( ( ~ ( in @ sK3_SY18 @ ( powerset @ sK1_A ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[35]) ).

thf(41,plain,
    ( ( ~ ~ ( in @ ( binunion @ sK2_SY16 @ sK3_SY18 ) @ ( powerset @ sK1_A ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[35]) ).

thf(42,plain,
    ! [SV5: $i,SV2: $i] :
      ( ( ~ ( ~ ! [SY32: $i] :
                  ( ~ ( in @ SY32 @ ( binunion @ SV2 @ SV5 ) )
                  | ( in @ SY32 @ SV2 )
                  | ( in @ SY32 @ SV5 )
                  | ! [SX3: $o] : SX3 )
            | ~ ! [SY34: $i] :
                  ( ~ ( in @ SY34 @ ( binunion @ SV2 @ SV5 ) )
                  | ( in @ SY34 @ SV2 )
                  | ! [SX3: $o] :
                      ( ~ SX3
                      | SX3 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[36]) ).

thf(43,plain,
    ! [SV5: $i,SV2: $i] :
      ( ( ~ ( ~ ! [SY36: $i] :
                  ( ~ ( in @ SY36 @ ( binunion @ SV2 @ SV5 ) )
                  | ! [SY37: $o] :
                      ( ~ SY37
                      | ( in @ SY36 @ SV5 )
                      | SY37 ) )
            | ~ ( ! [SY38: $i] :
                    ~ ( in @ SY38 @ ( binunion @ SV2 @ SV5 ) )
                | ! [SX2: $o] :
                    ( ~ SX2
                    | ~ SX2
                    | SX2 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[37]) ).

thf(44,plain,
    ! [SV3: $i,SV6: $i] :
      ( ( ( ~ ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV6 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV3 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[38]) ).

thf(45,plain,
    ! [SV3: $i,SV6: $i] :
      ( ( ( ~ ~ ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV3 ) )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV3 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[38]) ).

thf(46,plain,
    ! [SV1: $i,SV4: $i,SV7: $i] :
      ( ( ( ~ ( in @ SV7 @ SV4 ) )
        = $true )
      | ( ( in @ SV7 @ SV1 )
        = $true )
      | ( ( in @ SV4 @ ( powerset @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[39]) ).

thf(47,plain,
    ( ( in @ sK3_SY18 @ ( powerset @ sK1_A ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[40]) ).

thf(48,plain,
    ( ( ~ ( in @ ( binunion @ sK2_SY16 @ sK3_SY18 ) @ ( powerset @ sK1_A ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[41]) ).

thf(49,plain,
    ! [SV5: $i,SV2: $i] :
      ( ( ~ ! [SY32: $i] :
              ( ~ ( in @ SY32 @ ( binunion @ SV2 @ SV5 ) )
              | ( in @ SY32 @ SV2 )
              | ( in @ SY32 @ SV5 )
              | ! [SX3: $o] : SX3 )
        | ~ ! [SY34: $i] :
              ( ~ ( in @ SY34 @ ( binunion @ SV2 @ SV5 ) )
              | ( in @ SY34 @ SV2 )
              | ! [SX3: $o] :
                  ( ~ SX3
                  | SX3 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[42]) ).

thf(50,plain,
    ! [SV5: $i,SV2: $i] :
      ( ( ~ ! [SY36: $i] :
              ( ~ ( in @ SY36 @ ( binunion @ SV2 @ SV5 ) )
              | ! [SY37: $o] :
                  ( ~ SY37
                  | ( in @ SY36 @ SV5 )
                  | SY37 ) )
        | ~ ( ! [SY38: $i] :
                ~ ( in @ SY38 @ ( binunion @ SV2 @ SV5 ) )
            | ! [SX2: $o] :
                ( ~ SX2
                | ~ SX2
                | SX2 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[43]) ).

thf(51,plain,
    ! [SV3: $i,SV6: $i] :
      ( ( ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV6 )
        = $true )
      | ( ( in @ SV6 @ ( powerset @ SV3 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[44]) ).

thf(52,plain,
    ! [SV3: $i,SV6: $i] :
      ( ( ( ~ ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV3 ) )
        = $true )
      | ( ( in @ SV6 @ ( powerset @ SV3 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[45]) ).

thf(53,plain,
    ! [SV1: $i,SV4: $i,SV7: $i] :
      ( ( ( in @ SV7 @ SV4 )
        = $false )
      | ( ( in @ SV7 @ SV1 )
        = $true )
      | ( ( in @ SV4 @ ( powerset @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[46]) ).

thf(54,plain,
    ( ( in @ ( binunion @ sK2_SY16 @ sK3_SY18 ) @ ( powerset @ sK1_A ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[48]) ).

thf(55,plain,
    ! [SV5: $i,SV2: $i] :
      ( ( ~ ! [SY32: $i] :
              ( ~ ( in @ SY32 @ ( binunion @ SV2 @ SV5 ) )
              | ( in @ SY32 @ SV2 )
              | ( in @ SY32 @ SV5 )
              | ! [SX3: $o] : SX3 ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[49]) ).

thf(56,plain,
    ! [SV5: $i,SV2: $i] :
      ( ( ~ ! [SY34: $i] :
              ( ~ ( in @ SY34 @ ( binunion @ SV2 @ SV5 ) )
              | ( in @ SY34 @ SV2 )
              | ! [SX3: $o] :
                  ( ~ SX3
                  | SX3 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[49]) ).

thf(57,plain,
    ! [SV5: $i,SV2: $i] :
      ( ( ~ ! [SY36: $i] :
              ( ~ ( in @ SY36 @ ( binunion @ SV2 @ SV5 ) )
              | ! [SY37: $o] :
                  ( ~ SY37
                  | ( in @ SY36 @ SV5 )
                  | SY37 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[50]) ).

thf(58,plain,
    ! [SV5: $i,SV2: $i] :
      ( ( ~ ( ! [SY38: $i] :
                ~ ( in @ SY38 @ ( binunion @ SV2 @ SV5 ) )
            | ! [SX2: $o] :
                ( ~ SX2
                | ~ SX2
                | SX2 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[50]) ).

thf(59,plain,
    ! [SV3: $i,SV6: $i] :
      ( ( ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV3 )
        = $false )
      | ( ( in @ SV6 @ ( powerset @ SV3 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[52]) ).

thf(60,plain,
    ! [SV5: $i,SV2: $i] :
      ( ( ! [SY32: $i] :
            ( ~ ( in @ SY32 @ ( binunion @ SV2 @ SV5 ) )
            | ( in @ SY32 @ SV2 )
            | ( in @ SY32 @ SV5 )
            | ! [SX3: $o] : SX3 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[55]) ).

thf(61,plain,
    ! [SV5: $i,SV2: $i] :
      ( ( ! [SY34: $i] :
            ( ~ ( in @ SY34 @ ( binunion @ SV2 @ SV5 ) )
            | ( in @ SY34 @ SV2 )
            | ! [SX3: $o] :
                ( ~ SX3
                | SX3 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[56]) ).

thf(62,plain,
    ! [SV5: $i,SV2: $i] :
      ( ( ! [SY36: $i] :
            ( ~ ( in @ SY36 @ ( binunion @ SV2 @ SV5 ) )
            | ! [SY37: $o] :
                ( ~ SY37
                | ( in @ SY36 @ SV5 )
                | SY37 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[57]) ).

thf(63,plain,
    ! [SV5: $i,SV2: $i] :
      ( ( ! [SY38: $i] :
            ~ ( in @ SY38 @ ( binunion @ SV2 @ SV5 ) )
        | ! [SX2: $o] :
            ( ~ SX2
            | ~ SX2
            | SX2 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[58]) ).

thf(64,plain,
    ! [SV5: $i,SV2: $i,SV8: $i] :
      ( ( ~ ( in @ SV8 @ ( binunion @ SV2 @ SV5 ) )
        | ( in @ SV8 @ SV2 )
        | ( in @ SV8 @ SV5 )
        | ! [SX3: $o] : SX3 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[60]) ).

thf(65,plain,
    ! [SV5: $i,SV2: $i,SV9: $i] :
      ( ( ~ ( in @ SV9 @ ( binunion @ SV2 @ SV5 ) )
        | ( in @ SV9 @ SV2 )
        | ! [SX3: $o] :
            ( ~ SX3
            | SX3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[61]) ).

thf(66,plain,
    ! [SV5: $i,SV2: $i,SV10: $i] :
      ( ( ~ ( in @ SV10 @ ( binunion @ SV2 @ SV5 ) )
        | ! [SY42: $o] :
            ( ~ SY42
            | ( in @ SV10 @ SV5 )
            | SY42 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[62]) ).

thf(67,plain,
    ! [SV5: $i,SV2: $i] :
      ( ( ( ! [SY38: $i] :
              ~ ( in @ SY38 @ ( binunion @ SV2 @ SV5 ) ) )
        = $true )
      | ( ( ! [SX2: $o] :
              ( ~ SX2
              | ~ SX2
              | SX2 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[63]) ).

thf(68,plain,
    ! [SV5: $i,SV2: $i,SV8: $i] :
      ( ( ( ~ ( in @ SV8 @ ( binunion @ SV2 @ SV5 ) ) )
        = $true )
      | ( ( ( in @ SV8 @ SV2 )
          | ( in @ SV8 @ SV5 )
          | ! [SX3: $o] : SX3 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[64]) ).

thf(69,plain,
    ! [SV5: $i,SV2: $i,SV9: $i] :
      ( ( ( ~ ( in @ SV9 @ ( binunion @ SV2 @ SV5 ) ) )
        = $true )
      | ( ( ( in @ SV9 @ SV2 )
          | ! [SX3: $o] :
              ( ~ SX3
              | SX3 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[65]) ).

thf(70,plain,
    ! [SV5: $i,SV2: $i,SV10: $i] :
      ( ( ( ~ ( in @ SV10 @ ( binunion @ SV2 @ SV5 ) ) )
        = $true )
      | ( ( ! [SY42: $o] :
              ( ~ SY42
              | ( in @ SV10 @ SV5 )
              | SY42 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[66]) ).

thf(71,plain,
    ! [SV5: $i,SV2: $i,SV11: $i] :
      ( ( ( ~ ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) ) )
        = $true )
      | ( ( ! [SX2: $o] :
              ( ~ SX2
              | ~ SX2
              | SX2 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[67]) ).

thf(72,plain,
    ! [SV5: $i,SV2: $i,SV8: $i] :
      ( ( ( in @ SV8 @ ( binunion @ SV2 @ SV5 ) )
        = $false )
      | ( ( ( in @ SV8 @ SV2 )
          | ( in @ SV8 @ SV5 )
          | ! [SX3: $o] : SX3 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[68]) ).

thf(73,plain,
    ! [SV5: $i,SV2: $i,SV9: $i] :
      ( ( ( in @ SV9 @ ( binunion @ SV2 @ SV5 ) )
        = $false )
      | ( ( ( in @ SV9 @ SV2 )
          | ! [SX3: $o] :
              ( ~ SX3
              | SX3 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[69]) ).

thf(74,plain,
    ! [SV5: $i,SV2: $i,SV10: $i] :
      ( ( ( in @ SV10 @ ( binunion @ SV2 @ SV5 ) )
        = $false )
      | ( ( ! [SY42: $o] :
              ( ~ SY42
              | ( in @ SV10 @ SV5 )
              | SY42 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[70]) ).

thf(75,plain,
    ! [SV5: $i,SV2: $i,SV11: $i] :
      ( ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
        = $false )
      | ( ( ! [SX2: $o] :
              ( ~ SX2
              | ~ SX2
              | SX2 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[71]) ).

thf(76,plain,
    ! [SV5: $i,SV2: $i,SV8: $i] :
      ( ( ( in @ SV8 @ SV2 )
        = $true )
      | ( ( ( in @ SV8 @ SV5 )
          | ! [SX3: $o] : SX3 )
        = $true )
      | ( ( in @ SV8 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[72]) ).

thf(77,plain,
    ! [SV5: $i,SV2: $i,SV9: $i] :
      ( ( ( in @ SV9 @ SV2 )
        = $true )
      | ( ( ! [SX3: $o] :
              ( ~ SX3
              | SX3 ) )
        = $true )
      | ( ( in @ SV9 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[73]) ).

thf(78,plain,
    ! [SV2: $i,SV5: $i,SV10: $i,SV12: $o] :
      ( ( ( ~ SV12
          | ( in @ SV10 @ SV5 )
          | SV12 )
        = $true )
      | ( ( in @ SV10 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[74]) ).

thf(79,plain,
    ! [SV2: $i,SV5: $i,SV10: $i] :
      ( ( ( ~ $true
          | ( in @ SV10 @ SV5 )
          | $true )
        = $true )
      | ( ( in @ SV10 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[74]) ).

thf(80,plain,
    ! [SV2: $i,SV5: $i,SV10: $i] :
      ( ( ( ~ $false
          | ( in @ SV10 @ SV5 )
          | $false )
        = $true )
      | ( ( in @ SV10 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[74]) ).

thf(81,plain,
    ! [SV5: $i,SV2: $i,SV11: $i,SV13: $o] :
      ( ( ( ~ SV13
          | ~ SV13
          | SV13 )
        = $true )
      | ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[75]) ).

thf(82,plain,
    ! [SV5: $i,SV2: $i,SV11: $i] :
      ( ( ( ~ $true
          | ~ $true
          | $true )
        = $true )
      | ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[75]) ).

thf(83,plain,
    ! [SV5: $i,SV2: $i,SV11: $i] :
      ( ( ( ~ $false
          | ~ $false
          | $false )
        = $true )
      | ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[75]) ).

thf(84,plain,
    ! [SV2: $i,SV5: $i,SV8: $i] :
      ( ( ( in @ SV8 @ SV5 )
        = $true )
      | ( ( ! [SX3: $o] : SX3 )
        = $true )
      | ( ( in @ SV8 @ SV2 )
        = $true )
      | ( ( in @ SV8 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[76]) ).

thf(85,plain,
    ! [SV5: $i,SV2: $i,SV9: $i,SV14: $o] :
      ( ( ( ~ SV14
          | SV14 )
        = $true )
      | ( ( in @ SV9 @ SV2 )
        = $true )
      | ( ( in @ SV9 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[77]) ).

thf(86,plain,
    ! [SV5: $i,SV2: $i,SV9: $i] :
      ( ( ( ~ $true
          | $true )
        = $true )
      | ( ( in @ SV9 @ SV2 )
        = $true )
      | ( ( in @ SV9 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[77]) ).

thf(87,plain,
    ! [SV5: $i,SV2: $i,SV9: $i] :
      ( ( ( ~ $false
          | $false )
        = $true )
      | ( ( in @ SV9 @ SV2 )
        = $true )
      | ( ( in @ SV9 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[77]) ).

thf(88,plain,
    ! [SV2: $i,SV5: $i,SV10: $i,SV12: $o] :
      ( ( ( ~ SV12 )
        = $true )
      | ( ( ( in @ SV10 @ SV5 )
          | SV12 )
        = $true )
      | ( ( in @ SV10 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[78]) ).

thf(89,plain,
    ! [SV2: $i,SV5: $i,SV10: $i] :
      ( ( ( ~ $true )
        = $true )
      | ( ( ( in @ SV10 @ SV5 )
          | $true )
        = $true )
      | ( ( in @ SV10 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[79]) ).

thf(90,plain,
    ! [SV2: $i,SV5: $i,SV10: $i] :
      ( ( ( ~ $false )
        = $true )
      | ( ( ( in @ SV10 @ SV5 )
          | $false )
        = $true )
      | ( ( in @ SV10 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[80]) ).

thf(91,plain,
    ! [SV5: $i,SV2: $i,SV11: $i,SV13: $o] :
      ( ( ( ~ SV13 )
        = $true )
      | ( ( ~ SV13
          | SV13 )
        = $true )
      | ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[81]) ).

thf(92,plain,
    ! [SV5: $i,SV2: $i,SV11: $i] :
      ( ( ( ~ $true )
        = $true )
      | ( ( ~ $true
          | $true )
        = $true )
      | ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[82]) ).

thf(93,plain,
    ! [SV5: $i,SV2: $i,SV11: $i] :
      ( ( ( ~ $false )
        = $true )
      | ( ( ~ $false
          | $false )
        = $true )
      | ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[83]) ).

thf(94,plain,
    ! [SV2: $i,SV5: $i,SV8: $i,SV15: $o] :
      ( ( SV15 = $true )
      | ( ( in @ SV8 @ SV5 )
        = $true )
      | ( ( in @ SV8 @ SV2 )
        = $true )
      | ( ( in @ SV8 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[84]) ).

thf(95,plain,
    ! [SV2: $i,SV5: $i,SV8: $i] :
      ( ( $true = $true )
      | ( ( in @ SV8 @ SV5 )
        = $true )
      | ( ( in @ SV8 @ SV2 )
        = $true )
      | ( ( in @ SV8 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[84]) ).

thf(96,plain,
    ! [SV2: $i,SV5: $i,SV8: $i] :
      ( ( $false = $true )
      | ( ( in @ SV8 @ SV5 )
        = $true )
      | ( ( in @ SV8 @ SV2 )
        = $true )
      | ( ( in @ SV8 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[84]) ).

thf(97,plain,
    ! [SV5: $i,SV2: $i,SV9: $i,SV14: $o] :
      ( ( ( ~ SV14 )
        = $true )
      | ( SV14 = $true )
      | ( ( in @ SV9 @ SV2 )
        = $true )
      | ( ( in @ SV9 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[85]) ).

thf(98,plain,
    ! [SV5: $i,SV2: $i,SV9: $i] :
      ( ( ( ~ $true )
        = $true )
      | ( $true = $true )
      | ( ( in @ SV9 @ SV2 )
        = $true )
      | ( ( in @ SV9 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[86]) ).

thf(99,plain,
    ! [SV5: $i,SV2: $i,SV9: $i] :
      ( ( ( ~ $false )
        = $true )
      | ( $false = $true )
      | ( ( in @ SV9 @ SV2 )
        = $true )
      | ( ( in @ SV9 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[87]) ).

thf(100,plain,
    ! [SV2: $i,SV5: $i,SV10: $i,SV12: $o] :
      ( ( SV12 = $false )
      | ( ( ( in @ SV10 @ SV5 )
          | SV12 )
        = $true )
      | ( ( in @ SV10 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[88]) ).

thf(101,plain,
    ! [SV2: $i,SV5: $i,SV10: $i] :
      ( ( $true = $false )
      | ( ( ( in @ SV10 @ SV5 )
          | $true )
        = $true )
      | ( ( in @ SV10 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[89]) ).

thf(102,plain,
    ! [SV2: $i,SV5: $i,SV10: $i] :
      ( ( $false = $false )
      | ( ( ( in @ SV10 @ SV5 )
          | $false )
        = $true )
      | ( ( in @ SV10 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[90]) ).

thf(103,plain,
    ! [SV5: $i,SV2: $i,SV11: $i,SV13: $o] :
      ( ( SV13 = $false )
      | ( ( ~ SV13
          | SV13 )
        = $true )
      | ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[91]) ).

thf(104,plain,
    ! [SV5: $i,SV2: $i,SV11: $i] :
      ( ( $true = $false )
      | ( ( ~ $true
          | $true )
        = $true )
      | ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[92]) ).

thf(105,plain,
    ! [SV5: $i,SV2: $i,SV11: $i] :
      ( ( $false = $false )
      | ( ( ~ $false
          | $false )
        = $true )
      | ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[93]) ).

thf(106,plain,
    ! [SV5: $i,SV2: $i,SV9: $i,SV14: $o] :
      ( ( SV14 = $false )
      | ( SV14 = $true )
      | ( ( in @ SV9 @ SV2 )
        = $true )
      | ( ( in @ SV9 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[97]) ).

thf(107,plain,
    ! [SV5: $i,SV2: $i,SV9: $i] :
      ( ( $true = $false )
      | ( $true = $true )
      | ( ( in @ SV9 @ SV2 )
        = $true )
      | ( ( in @ SV9 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[98]) ).

thf(108,plain,
    ! [SV5: $i,SV2: $i,SV9: $i] :
      ( ( $false = $false )
      | ( $false = $true )
      | ( ( in @ SV9 @ SV2 )
        = $true )
      | ( ( in @ SV9 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[99]) ).

thf(109,plain,
    ! [SV2: $i,SV12: $o,SV5: $i,SV10: $i] :
      ( ( ( in @ SV10 @ SV5 )
        = $true )
      | ( SV12 = $true )
      | ( SV12 = $false )
      | ( ( in @ SV10 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[100]) ).

thf(110,plain,
    ! [SV2: $i,SV5: $i,SV10: $i] :
      ( ( ( in @ SV10 @ SV5 )
        = $true )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV10 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[101]) ).

thf(111,plain,
    ! [SV2: $i,SV5: $i,SV10: $i] :
      ( ( ( in @ SV10 @ SV5 )
        = $true )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV10 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[102]) ).

thf(112,plain,
    ! [SV5: $i,SV2: $i,SV11: $i,SV13: $o] :
      ( ( ( ~ SV13 )
        = $true )
      | ( SV13 = $true )
      | ( SV13 = $false )
      | ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[103]) ).

thf(113,plain,
    ! [SV5: $i,SV2: $i,SV11: $i] :
      ( ( ( ~ $true )
        = $true )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[104]) ).

thf(114,plain,
    ! [SV5: $i,SV2: $i,SV11: $i] :
      ( ( ( ~ $false )
        = $true )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[105]) ).

thf(115,plain,
    ! [SV5: $i,SV2: $i,SV11: $i,SV13: $o] :
      ( ( SV13 = $false )
      | ( SV13 = $true )
      | ( SV13 = $false )
      | ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[112]) ).

thf(116,plain,
    ! [SV5: $i,SV2: $i,SV11: $i] :
      ( ( $true = $false )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[113]) ).

thf(117,plain,
    ! [SV5: $i,SV2: $i,SV11: $i] :
      ( ( $false = $false )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV11 @ ( binunion @ SV2 @ SV5 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[114]) ).

thf(118,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[30,117,116,115,111,110,109,108,107,106,96,95,94,59,54,53,51,47]) ).

thf(119,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[118]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU711^2 : TPTP v8.1.0. Released v3.7.0.
% 0.03/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n016.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  : 600
% 0.13/0.34  % DateTime : Sat Jun 18 20:59:22 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  
% 0.13/0.35   No.of.Axioms: 0
% 0.13/0.35  
% 0.13/0.35   Length.of.Defs: 631
% 0.13/0.35  
% 0.13/0.35   Contains.Choice.Funs: false
% 0.13/0.35  (rf:0,axioms:0,ps:3,u:6,ude:true,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)........
% 0.19/0.53  
% 0.19/0.53  ********************************
% 0.19/0.53  *   All subproblems solved!    *
% 0.19/0.53  ********************************
% 0.19/0.53  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,ps:3,u:6,ude:true,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:118,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.54  
% 0.19/0.54  %**** Beginning of derivation protocol ****
% 0.19/0.54  % SZS output start CNFRefutation
% See solution above
% 0.19/0.54  
% 0.19/0.54  %**** End of derivation protocol ****
% 0.19/0.54  %**** no. of clauses in derivation: 119 ****
% 0.19/0.54  %**** clause counter: 118 ****
% 0.19/0.54  
% 0.19/0.54  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,ps:3,u:6,ude:true,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:118,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------