TSTP Solution File: SEU633^2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEU633^2 : 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 : n024.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 12:13:31 EDT 2022

% Result   : Theorem 0.21s 0.40s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   73 (  22 unt;   6 typ;   1 def)
%            Number of atoms       :  513 ( 145 equ;   0 cnn)
%            Maximal formula atoms :    4 (   7 avg)
%            Number of connectives :  868 ( 179   ~; 141   |;  11   &; 517   @)
%                                         (   0 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   5 con; 0-3 aty)
%            Number of variables   :  149 (   0   ^ 144   !;   5   ?; 149   :)

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

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

thf(tp_sK2_SY10,type,
    sK2_SY10: $i ).

thf(tp_sK3_B,type,
    sK3_B: $o > $i > $i > $i ).

thf(tp_setunion,type,
    setunion: $i > $i ).

thf(tp_setunionE,type,
    setunionE: $o ).

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

thf(1,conjecture,
    ( setunionE
   => ! [A: $i,Xx: $i] :
        ( ( in @ Xx @ ( setunion @ A ) )
       => ? [X: $i] :
            ( ( in @ X @ A )
            & ( in @ Xx @ X ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE2) ).

thf(2,negated_conjecture,
    ( ( setunionE
     => ! [A: $i,Xx: $i] :
          ( ( in @ Xx @ ( setunion @ A ) )
         => ? [X: $i] :
              ( ( in @ X @ A )
              & ( in @ Xx @ X ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [A: $i,Xx: $i] :
          ( ( in @ Xx @ ( setunion @ A ) )
         => ! [Xphi: $o] :
              ( ! [B: $i] :
                  ( ( in @ Xx @ B )
                 => ( ( in @ B @ A )
                   => Xphi ) )
             => Xphi ) )
     => ! [A: $i,Xx: $i] :
          ( ( in @ Xx @ ( setunion @ A ) )
         => ? [X: $i] :
              ( ( in @ X @ A )
              & ( in @ Xx @ X ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2,setunionE]) ).

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

thf(5,plain,
    ( ( ! [A: $i,Xx: $i] :
          ( ( in @ Xx @ ( setunion @ A ) )
         => ? [X: $i] :
              ( ( in @ X @ A )
              & ( in @ Xx @ X ) ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(6,plain,
    ( ( ~ ! [A: $i,Xx: $i] :
            ( ( in @ Xx @ ( setunion @ A ) )
           => ? [X: $i] :
                ( ( in @ X @ A )
                & ( in @ Xx @ X ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ( in @ sK2_SY10 @ ( setunion @ sK1_A ) )
      & ! [SY12: $i] :
          ( ~ ( in @ SY12 @ sK1_A )
          | ~ ( in @ sK2_SY10 @ SY12 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

thf(8,plain,
    ( ( ! [A: $i,Xx: $i] :
          ( ~ ( in @ Xx @ ( setunion @ A ) )
          | ! [Xphi: $o] :
              ( ( ( in @ Xx @ ( sK3_B @ Xphi @ Xx @ A ) )
                & ( in @ ( sK3_B @ Xphi @ Xx @ A ) @ A )
                & ~ Xphi )
              | Xphi ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[4]) ).

thf(9,plain,
    ( ( ! [A: $i,Xx: $i] :
          ( ~ ( in @ Xx @ ( setunion @ A ) )
          | ! [Xphi: $o] :
              ( ( ( in @ Xx @ ( sK3_B @ Xphi @ Xx @ A ) )
                & ( in @ ( sK3_B @ Xphi @ Xx @ A ) @ A )
                & ~ Xphi )
              | Xphi ) ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(10,plain,
    ( ( ( in @ sK2_SY10 @ ( setunion @ sK1_A ) )
      & ! [SY12: $i] :
          ( ~ ( in @ SY12 @ sK1_A )
          | ~ ( in @ sK2_SY10 @ SY12 ) ) )
    = $true ),
    inference(copy,[status(thm)],[7]) ).

thf(11,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
          | ! [SX2: $o] :
              ( ~ ( ~ ( in @ SX1 @ ( sK3_B @ SX2 @ SX1 @ SX0 ) )
                  | ~ ~ ( ~ ( in @ ( sK3_B @ SX2 @ SX1 @ SX0 ) @ SX0 )
                        | ~ ~ SX2 ) )
              | SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9,setunionE]) ).

thf(12,plain,
    ( ( ~ ( ~ ( in @ sK2_SY10 @ ( setunion @ sK1_A ) )
          | ~ ! [SX0: $i] :
                ( ~ ( in @ SX0 @ sK1_A )
                | ~ ( in @ sK2_SY10 @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10,setunionE]) ).

thf(13,plain,
    ! [SV1: $i] :
      ( ( ! [SY13: $i] :
            ( ~ ( in @ SY13 @ ( setunion @ SV1 ) )
            | ! [SY14: $o] :
                ( ~ ( ~ ( in @ SY13 @ ( sK3_B @ SY14 @ SY13 @ SV1 ) )
                    | ~ ~ ( ~ ( in @ ( sK3_B @ SY14 @ SY13 @ SV1 ) @ SV1 )
                          | ~ ~ SY14 ) )
                | SY14 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11]) ).

thf(14,plain,
    ( ( ~ ( in @ sK2_SY10 @ ( setunion @ sK1_A ) )
      | ~ ! [SX0: $i] :
            ( ~ ( in @ SX0 @ sK1_A )
            | ~ ( in @ sK2_SY10 @ SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[12]) ).

thf(15,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ~ ( in @ SV2 @ ( setunion @ SV1 ) )
        | ! [SY15: $o] :
            ( ~ ( ~ ( in @ SV2 @ ( sK3_B @ SY15 @ SV2 @ SV1 ) )
                | ~ ~ ( ~ ( in @ ( sK3_B @ SY15 @ SV2 @ SV1 ) @ SV1 )
                      | ~ ~ SY15 ) )
            | SY15 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[13]) ).

thf(16,plain,
    ( ( ~ ( in @ sK2_SY10 @ ( setunion @ sK1_A ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(17,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( in @ SX0 @ sK1_A )
            | ~ ( in @ sK2_SY10 @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(18,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( ~ ( in @ SV2 @ ( setunion @ SV1 ) ) )
        = $true )
      | ( ( ! [SY15: $o] :
              ( ~ ( ~ ( in @ SV2 @ ( sK3_B @ SY15 @ SV2 @ SV1 ) )
                  | ~ ~ ( ~ ( in @ ( sK3_B @ SY15 @ SV2 @ SV1 ) @ SV1 )
                        | ~ ~ SY15 ) )
              | SY15 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[15]) ).

thf(19,plain,
    ( ( in @ sK2_SY10 @ ( setunion @ sK1_A ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[16]) ).

thf(20,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( in @ SX0 @ sK1_A )
          | ~ ( in @ sK2_SY10 @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[17]) ).

thf(21,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false )
      | ( ( ! [SY15: $o] :
              ( ~ ( ~ ( in @ SV2 @ ( sK3_B @ SY15 @ SV2 @ SV1 ) )
                  | ~ ~ ( ~ ( in @ ( sK3_B @ SY15 @ SV2 @ SV1 ) @ SV1 )
                        | ~ ~ SY15 ) )
              | SY15 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[18]) ).

thf(22,plain,
    ! [SV3: $i] :
      ( ( ~ ( in @ SV3 @ sK1_A )
        | ~ ( in @ sK2_SY10 @ SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(23,plain,
    ! [SV1: $i,SV4: $o,SV2: $i] :
      ( ( ( ~ ( ~ ( in @ SV2 @ ( sK3_B @ SV4 @ SV2 @ SV1 ) )
              | ~ ~ ( ~ ( in @ ( sK3_B @ SV4 @ SV2 @ SV1 ) @ SV1 )
                    | ~ ~ SV4 ) )
          | SV4 )
        = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[21]) ).

thf(24,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( ~ ( ~ ( in @ SV2 @ ( sK3_B @ $true @ SV2 @ SV1 ) )
              | ~ ~ ( ~ ( in @ ( sK3_B @ $true @ SV2 @ SV1 ) @ SV1 )
                    | ~ ~ $true ) )
          | $true )
        = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[21]) ).

thf(25,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( ~ ( ~ ( in @ SV2 @ ( sK3_B @ $false @ SV2 @ SV1 ) )
              | ~ ~ ( ~ ( in @ ( sK3_B @ $false @ SV2 @ SV1 ) @ SV1 )
                    | ~ ~ $false ) )
          | $false )
        = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[21]) ).

thf(26,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( in @ SV3 @ sK1_A ) )
        = $true )
      | ( ( ~ ( in @ sK2_SY10 @ SV3 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[22]) ).

thf(27,plain,
    ! [SV1: $i,SV4: $o,SV2: $i] :
      ( ( ( ~ ( ~ ( in @ SV2 @ ( sK3_B @ SV4 @ SV2 @ SV1 ) )
              | ~ ~ ( ~ ( in @ ( sK3_B @ SV4 @ SV2 @ SV1 ) @ SV1 )
                    | ~ ~ SV4 ) ) )
        = $true )
      | ( SV4 = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[23]) ).

thf(28,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( ~ ( ~ ( in @ SV2 @ ( sK3_B @ $true @ SV2 @ SV1 ) )
              | ~ ~ ( ~ ( in @ ( sK3_B @ $true @ SV2 @ SV1 ) @ SV1 )
                    | ~ ~ $true ) ) )
        = $true )
      | ( $true = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[24]) ).

thf(29,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( ~ ( ~ ( in @ SV2 @ ( sK3_B @ $false @ SV2 @ SV1 ) )
              | ~ ~ ( ~ ( in @ ( sK3_B @ $false @ SV2 @ SV1 ) @ SV1 )
                    | ~ ~ $false ) ) )
        = $true )
      | ( $false = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[25]) ).

thf(30,plain,
    ! [SV3: $i] :
      ( ( ( in @ SV3 @ sK1_A )
        = $false )
      | ( ( ~ ( in @ sK2_SY10 @ SV3 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[26]) ).

thf(31,plain,
    ! [SV1: $i,SV4: $o,SV2: $i] :
      ( ( ( ~ ( in @ SV2 @ ( sK3_B @ SV4 @ SV2 @ SV1 ) )
          | ~ ~ ( ~ ( in @ ( sK3_B @ SV4 @ SV2 @ SV1 ) @ SV1 )
                | ~ ~ SV4 ) )
        = $false )
      | ( SV4 = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[27]) ).

thf(32,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( ~ ( in @ SV2 @ ( sK3_B @ $true @ SV2 @ SV1 ) )
          | ~ ~ ( ~ ( in @ ( sK3_B @ $true @ SV2 @ SV1 ) @ SV1 )
                | ~ ~ $true ) )
        = $false )
      | ( $true = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[28]) ).

thf(33,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( ~ ( in @ SV2 @ ( sK3_B @ $false @ SV2 @ SV1 ) )
          | ~ ~ ( ~ ( in @ ( sK3_B @ $false @ SV2 @ SV1 ) @ SV1 )
                | ~ ~ $false ) )
        = $false )
      | ( $false = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[29]) ).

thf(34,plain,
    ! [SV3: $i] :
      ( ( ( in @ sK2_SY10 @ SV3 )
        = $false )
      | ( ( in @ SV3 @ sK1_A )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[30]) ).

thf(35,plain,
    ! [SV1: $i,SV4: $o,SV2: $i] :
      ( ( ( ~ ( in @ SV2 @ ( sK3_B @ SV4 @ SV2 @ SV1 ) ) )
        = $false )
      | ( SV4 = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[31]) ).

thf(36,plain,
    ! [SV1: $i,SV2: $i,SV4: $o] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK3_B @ SV4 @ SV2 @ SV1 ) @ SV1 )
                | ~ ~ SV4 ) )
        = $false )
      | ( SV4 = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[31]) ).

thf(37,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( ~ ( in @ SV2 @ ( sK3_B @ $true @ SV2 @ SV1 ) ) )
        = $false )
      | ( $true = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[32]) ).

thf(38,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK3_B @ $true @ SV2 @ SV1 ) @ SV1 )
                | ~ ~ $true ) )
        = $false )
      | ( $true = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[32]) ).

thf(39,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( ~ ( in @ SV2 @ ( sK3_B @ $false @ SV2 @ SV1 ) ) )
        = $false )
      | ( $false = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[33]) ).

thf(40,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK3_B @ $false @ SV2 @ SV1 ) @ SV1 )
                | ~ ~ $false ) )
        = $false )
      | ( $false = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[33]) ).

thf(41,plain,
    ! [SV1: $i,SV4: $o,SV2: $i] :
      ( ( ( in @ SV2 @ ( sK3_B @ SV4 @ SV2 @ SV1 ) )
        = $true )
      | ( SV4 = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[35]) ).

thf(42,plain,
    ! [SV1: $i,SV2: $i,SV4: $o] :
      ( ( ( ~ ( ~ ( in @ ( sK3_B @ SV4 @ SV2 @ SV1 ) @ SV1 )
              | ~ ~ SV4 ) )
        = $true )
      | ( SV4 = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[36]) ).

thf(43,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( in @ SV2 @ ( sK3_B @ $true @ SV2 @ SV1 ) )
        = $true )
      | ( $true = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[37]) ).

thf(44,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK3_B @ $true @ SV2 @ SV1 ) @ SV1 )
              | ~ ~ $true ) )
        = $true )
      | ( $true = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[38]) ).

thf(45,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( in @ SV2 @ ( sK3_B @ $false @ SV2 @ SV1 ) )
        = $true )
      | ( $false = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[39]) ).

thf(46,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK3_B @ $false @ SV2 @ SV1 ) @ SV1 )
              | ~ ~ $false ) )
        = $true )
      | ( $false = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[40]) ).

thf(47,plain,
    ! [SV1: $i,SV2: $i,SV4: $o] :
      ( ( ( ~ ( in @ ( sK3_B @ SV4 @ SV2 @ SV1 ) @ SV1 )
          | ~ ~ SV4 )
        = $false )
      | ( SV4 = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[42]) ).

thf(48,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( ~ ( in @ ( sK3_B @ $true @ SV2 @ SV1 ) @ SV1 )
          | ~ ~ $true )
        = $false )
      | ( $true = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[44]) ).

thf(49,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( ~ ( in @ ( sK3_B @ $false @ SV2 @ SV1 ) @ SV1 )
          | ~ ~ $false )
        = $false )
      | ( $false = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[46]) ).

thf(50,plain,
    ! [SV1: $i,SV2: $i,SV4: $o] :
      ( ( ( ~ ( in @ ( sK3_B @ SV4 @ SV2 @ SV1 ) @ SV1 ) )
        = $false )
      | ( SV4 = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[47]) ).

thf(51,plain,
    ! [SV1: $i,SV2: $i,SV4: $o] :
      ( ( ( ~ ~ SV4 )
        = $false )
      | ( SV4 = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[47]) ).

thf(52,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( ~ ( in @ ( sK3_B @ $true @ SV2 @ SV1 ) @ SV1 ) )
        = $false )
      | ( $true = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[48]) ).

thf(53,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( ~ ~ $true )
        = $false )
      | ( $true = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[48]) ).

thf(54,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( ~ ( in @ ( sK3_B @ $false @ SV2 @ SV1 ) @ SV1 ) )
        = $false )
      | ( $false = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[49]) ).

thf(55,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( ~ ~ $false )
        = $false )
      | ( $false = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[49]) ).

thf(56,plain,
    ! [SV1: $i,SV2: $i,SV4: $o] :
      ( ( ( in @ ( sK3_B @ SV4 @ SV2 @ SV1 ) @ SV1 )
        = $true )
      | ( SV4 = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[50]) ).

thf(57,plain,
    ! [SV1: $i,SV2: $i,SV4: $o] :
      ( ( ( ~ SV4 )
        = $true )
      | ( SV4 = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[51]) ).

thf(58,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( in @ ( sK3_B @ $true @ SV2 @ SV1 ) @ SV1 )
        = $true )
      | ( $true = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[52]) ).

thf(59,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( ~ $true )
        = $true )
      | ( $true = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[53]) ).

thf(60,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( in @ ( sK3_B @ $false @ SV2 @ SV1 ) @ SV1 )
        = $true )
      | ( $false = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[54]) ).

thf(61,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( ~ $false )
        = $true )
      | ( $false = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[55]) ).

thf(62,plain,
    ! [SV1: $i,SV2: $i,SV4: $o] :
      ( ( SV4 = $false )
      | ( SV4 = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[57]) ).

thf(63,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( $true = $false )
      | ( $true = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[59]) ).

thf(64,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( $false = $false )
      | ( $false = $true )
      | ( ( in @ SV2 @ ( setunion @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[61]) ).

thf(65,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[19,64,63,62,60,58,56,45,43,41,34]) ).

thf(66,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[65]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SEU633^2 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35  % Computer : n024.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Sun Jun 19 16:57:32 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  
% 0.13/0.36   No.of.Axioms: 0
% 0.13/0.36  
% 0.13/0.36   Length.of.Defs: 229
% 0.13/0.36  
% 0.13/0.36   Contains.Choice.Funs: false
% 0.13/0.36  (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)..
% 0.21/0.40  
% 0.21/0.40  ********************************
% 0.21/0.40  *   All subproblems solved!    *
% 0.21/0.40  ********************************
% 0.21/0.40  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,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:65,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.21/0.40  
% 0.21/0.40  %**** Beginning of derivation protocol ****
% 0.21/0.40  % SZS output start CNFRefutation
% See solution above
% 0.21/0.40  
% 0.21/0.40  %**** End of derivation protocol ****
% 0.21/0.40  %**** no. of clauses in derivation: 66 ****
% 0.21/0.40  %**** clause counter: 65 ****
% 0.21/0.40  
% 0.21/0.40  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,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:65,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------