TSTP Solution File: SEU610^2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEU610^2 : 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 12:13:20 EDT 2022

% Result   : Theorem 0.19s 0.40s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   87 (  40 unt;  11 typ;   4 def)
%            Number of atoms       :  495 ( 195 equ;   0 cnn)
%            Maximal formula atoms :    6 (   6 avg)
%            Number of connectives :  731 ( 133   ~; 137   |;   6   &; 414   @)
%                                         (   3 <=>;  38  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  11 usr;   9 con; 0-2 aty)
%            Number of variables   :  220 (   0   ^ 220   !;   0   ?; 220   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_emptyset,type,
    emptyset: $i ).

thf(tp_emptysetE,type,
    emptysetE: $o ).

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

thf(tp_in__Cong,type,
    in__Cong: $o ).

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

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

thf(tp_sK3_Xx,type,
    sK3_Xx: $i > $i > $i ).

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

thf(tp_setminusI,type,
    setminusI: $o ).

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

thf(tp_subsetI2,type,
    subsetI2: $o ).

thf(emptysetE,definition,
    ( emptysetE
    = ( ! [Xx: $i] :
          ( ( in @ Xx @ emptyset )
         => ! [Xphi: $o] : Xphi ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).

thf(in__Cong,definition,
    ( in__Cong
    = ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ! [Xx: $i,Xy: $i] :
              ( ( Xx = Xy )
             => ( ( in @ Xx @ A )
              <=> ( in @ Xy @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).

thf(setminusI,definition,
    ( setminusI
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( ~ ( in @ Xx @ B )
           => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusI) ).

thf(subsetI2,definition,
    ( subsetI2
    = ( ! [A: $i,B: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ Xx @ B ) )
         => ( subset @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2) ).

thf(1,conjecture,
    ( emptysetE
   => ( in__Cong
     => ( subsetI2
       => ( setminusI
         => ! [A: $i,B: $i] :
              ( ( ( setminus @ A @ B )
                = emptyset )
             => ( subset @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset1) ).

thf(2,negated_conjecture,
    ( ( emptysetE
     => ( in__Cong
       => ( subsetI2
         => ( setminusI
           => ! [A: $i,B: $i] :
                ( ( ( setminus @ A @ B )
                  = emptyset )
               => ( subset @ A @ B ) ) ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [Xx: $i] :
          ( ( in @ Xx @ emptyset )
         => ! [Xphi: $o] : Xphi )
     => ( ! [A: $i,B: $i] :
            ( ( A = B )
           => ! [Xx: $i,Xy: $i] :
                ( ( Xx = Xy )
               => ( ( in @ Xx @ A )
                <=> ( in @ Xy @ B ) ) ) )
       => ( ! [A: $i,B: $i] :
              ( ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( in @ Xx @ B ) )
             => ( subset @ A @ B ) )
         => ( ! [A: $i,B: $i,Xx: $i] :
                ( ( in @ Xx @ A )
               => ( ~ ( in @ Xx @ B )
                 => ( in @ Xx @ ( setminus @ A @ B ) ) ) )
           => ! [A: $i,B: $i] :
                ( ( ( setminus @ A @ B )
                  = emptyset )
               => ( subset @ A @ B ) ) ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2,emptysetE,in__Cong,setminusI,subsetI2]) ).

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

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

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

thf(7,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( ~ ( in @ Xx @ B )
           => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(8,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( setminus @ A @ B )
            = emptyset )
         => ( subset @ A @ B ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(9,plain,
    ( ( ~ ! [A: $i,B: $i] :
            ( ( ( setminus @ A @ B )
              = emptyset )
           => ( subset @ A @ B ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[8]) ).

thf(10,plain,
    ( ( ( ( setminus @ sK1_A @ sK2_SY16 )
        = emptyset )
      & ~ ( subset @ sK1_A @ sK2_SY16 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[9]) ).

thf(11,plain,
    ( ( ! [Xx: $i] :
          ~ ( in @ Xx @ emptyset )
      | ! [Xphi: $o] : Xphi )
    = $true ),
    inference(extcnf_combined,[status(esa)],[4]) ).

thf(12,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A != B )
          | ( ! [Xx: $i,Xy: $i] :
                ( ( Xx != Xy )
                | ~ ( in @ Xx @ A )
                | ( in @ Xy @ B ) )
            & ! [Xx: $i,Xy: $i] :
                ( ( Xx != Xy )
                | ~ ( in @ Xy @ B )
                | ( in @ Xx @ A ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5]) ).

thf(13,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( in @ ( sK3_Xx @ B @ A ) @ A )
            & ~ ( in @ ( sK3_Xx @ B @ A ) @ B ) )
          | ( subset @ A @ B ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

thf(14,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
          | ( in @ Xx @ B )
          | ( in @ Xx @ ( setminus @ A @ B ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[7]) ).

thf(15,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
          | ( in @ Xx @ B )
          | ( in @ Xx @ ( setminus @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(16,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( in @ ( sK3_Xx @ B @ A ) @ A )
            & ~ ( in @ ( sK3_Xx @ B @ A ) @ B ) )
          | ( subset @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(17,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A != B )
          | ( ! [Xx: $i,Xy: $i] :
                ( ( Xx != Xy )
                | ~ ( in @ Xx @ A )
                | ( in @ Xy @ B ) )
            & ! [Xx: $i,Xy: $i] :
                ( ( Xx != Xy )
                | ~ ( in @ Xy @ B )
                | ( in @ Xx @ A ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(18,plain,
    ( ( ! [Xx: $i] :
          ~ ( in @ Xx @ emptyset )
      | ! [Xphi: $o] : Xphi )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(19,plain,
    ( ( ( ( setminus @ sK1_A @ sK2_SY16 )
        = emptyset )
      & ~ ( subset @ sK1_A @ sK2_SY16 ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(20,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( ~ ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX0 )
              | ~ ~ ( in @ ( sK3_Xx @ SX1 @ SX0 ) @ SX1 ) )
          | ( subset @ SX0 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16,emptysetE,in__Cong,setminusI,subsetI2]) ).

thf(21,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ~ ( ~ ! [SX2: $i,SX3: $i] :
                    ( ( SX2 != SX3 )
                    | ~ ( in @ SX2 @ SX0 )
                    | ( in @ SX3 @ SX1 ) )
              | ~ ! [SX2: $i,SX3: $i] :
                    ( ( SX2 != SX3 )
                    | ~ ( in @ SX3 @ SX1 )
                    | ( in @ SX2 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17,emptysetE,in__Cong,setminusI,subsetI2]) ).

thf(22,plain,
    ( ( ~ ( ( ( setminus @ sK1_A @ sK2_SY16 )
           != emptyset )
          | ~ ~ ( subset @ sK1_A @ sK2_SY16 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[19,emptysetE,in__Cong,setminusI,subsetI2]) ).

thf(23,plain,
    ! [SV1: $i] :
      ( ( ! [SY17: $i,SY18: $i] :
            ( ~ ( in @ SY18 @ SV1 )
            | ( in @ SY18 @ SY17 )
            | ( in @ SY18 @ ( setminus @ SV1 @ SY17 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[15]) ).

thf(24,plain,
    ( ( ( ! [Xx: $i] :
            ~ ( in @ Xx @ emptyset ) )
      = $true )
    | ( ( ! [Xphi: $o] : Xphi )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[18]) ).

thf(25,plain,
    ! [SV2: $i] :
      ( ( ! [SY19: $i] :
            ( ~ ( ~ ( in @ ( sK3_Xx @ SY19 @ SV2 ) @ SV2 )
                | ~ ~ ( in @ ( sK3_Xx @ SY19 @ SV2 ) @ SY19 ) )
            | ( subset @ SV2 @ SY19 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(26,plain,
    ! [SV3: $i] :
      ( ( ! [SY20: $i] :
            ( ( SV3 != SY20 )
            | ~ ( ~ ! [SY21: $i,SY22: $i] :
                      ( ( SY21 != SY22 )
                      | ~ ( in @ SY21 @ SV3 )
                      | ( in @ SY22 @ SY20 ) )
                | ~ ! [SY23: $i,SY24: $i] :
                      ( ( SY23 != SY24 )
                      | ~ ( in @ SY24 @ SY20 )
                      | ( in @ SY23 @ SV3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[21]) ).

thf(27,plain,
    ( ( ( ( setminus @ sK1_A @ sK2_SY16 )
       != emptyset )
      | ~ ~ ( subset @ sK1_A @ sK2_SY16 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[22]) ).

thf(28,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ! [SY25: $i] :
            ( ~ ( in @ SY25 @ SV1 )
            | ( in @ SY25 @ SV4 )
            | ( in @ SY25 @ ( setminus @ SV1 @ SV4 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[23]) ).

thf(29,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( in @ SV5 @ emptyset ) )
        = $true )
      | ( ( ! [Xphi: $o] : Xphi )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[24]) ).

thf(30,plain,
    ! [SV2: $i,SV6: $i] :
      ( ( ~ ( ~ ( in @ ( sK3_Xx @ SV6 @ SV2 ) @ SV2 )
            | ~ ~ ( in @ ( sK3_Xx @ SV6 @ SV2 ) @ SV6 ) )
        | ( subset @ SV2 @ SV6 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[25]) ).

thf(31,plain,
    ! [SV7: $i,SV3: $i] :
      ( ( ( SV3 != SV7 )
        | ~ ( ~ ! [SY26: $i,SY27: $i] :
                  ( ( SY26 != SY27 )
                  | ~ ( in @ SY26 @ SV3 )
                  | ( in @ SY27 @ SV7 ) )
            | ~ ! [SY28: $i,SY29: $i] :
                  ( ( SY28 != SY29 )
                  | ~ ( in @ SY29 @ SV7 )
                  | ( in @ SY28 @ SV3 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[26]) ).

thf(32,plain,
    ( ( ( ( setminus @ sK1_A @ sK2_SY16 )
       != emptyset ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[27]) ).

thf(33,plain,
    ( ( ~ ~ ( subset @ sK1_A @ sK2_SY16 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[27]) ).

thf(34,plain,
    ! [SV4: $i,SV1: $i,SV8: $i] :
      ( ( ~ ( in @ SV8 @ SV1 )
        | ( in @ SV8 @ SV4 )
        | ( in @ SV8 @ ( setminus @ SV1 @ SV4 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(35,plain,
    ! [SV5: $i] :
      ( ( ( in @ SV5 @ emptyset )
        = $false )
      | ( ( ! [Xphi: $o] : Xphi )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[29]) ).

thf(36,plain,
    ! [SV2: $i,SV6: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK3_Xx @ SV6 @ SV2 ) @ SV2 )
              | ~ ~ ( in @ ( sK3_Xx @ SV6 @ SV2 ) @ SV6 ) ) )
        = $true )
      | ( ( subset @ SV2 @ SV6 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[30]) ).

thf(37,plain,
    ! [SV7: $i,SV3: $i] :
      ( ( ( ( SV3 != SV7 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY26: $i,SY27: $i] :
                    ( ( SY26 != SY27 )
                    | ~ ( in @ SY26 @ SV3 )
                    | ( in @ SY27 @ SV7 ) )
              | ~ ! [SY28: $i,SY29: $i] :
                    ( ( SY28 != SY29 )
                    | ~ ( in @ SY29 @ SV7 )
                    | ( in @ SY28 @ SV3 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[31]) ).

thf(38,plain,
    ( ( ( setminus @ sK1_A @ sK2_SY16 )
      = emptyset )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[32]) ).

thf(39,plain,
    ( ( ~ ( subset @ sK1_A @ sK2_SY16 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[33]) ).

thf(40,plain,
    ! [SV4: $i,SV1: $i,SV8: $i] :
      ( ( ( ~ ( in @ SV8 @ SV1 ) )
        = $true )
      | ( ( ( in @ SV8 @ SV4 )
          | ( in @ SV8 @ ( setminus @ SV1 @ SV4 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[34]) ).

thf(41,plain,
    ! [SV5: $i,SV9: $o] :
      ( ( SV9 = $true )
      | ( ( in @ SV5 @ emptyset )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[35]) ).

thf(42,plain,
    ! [SV5: $i] :
      ( ( $true = $true )
      | ( ( in @ SV5 @ emptyset )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[35]) ).

thf(43,plain,
    ! [SV5: $i] :
      ( ( $false = $true )
      | ( ( in @ SV5 @ emptyset )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[35]) ).

thf(44,plain,
    ! [SV2: $i,SV6: $i] :
      ( ( ( ~ ( in @ ( sK3_Xx @ SV6 @ SV2 ) @ SV2 )
          | ~ ~ ( in @ ( sK3_Xx @ SV6 @ SV2 ) @ SV6 ) )
        = $false )
      | ( ( subset @ SV2 @ SV6 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[36]) ).

thf(45,plain,
    ! [SV7: $i,SV3: $i] :
      ( ( ( SV3 = SV7 )
        = $false )
      | ( ( ~ ( ~ ! [SY26: $i,SY27: $i] :
                    ( ( SY26 != SY27 )
                    | ~ ( in @ SY26 @ SV3 )
                    | ( in @ SY27 @ SV7 ) )
              | ~ ! [SY28: $i,SY29: $i] :
                    ( ( SY28 != SY29 )
                    | ~ ( in @ SY29 @ SV7 )
                    | ( in @ SY28 @ SV3 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[37]) ).

thf(46,plain,
    ( ( subset @ sK1_A @ sK2_SY16 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[39]) ).

thf(47,plain,
    ! [SV4: $i,SV1: $i,SV8: $i] :
      ( ( ( in @ SV8 @ SV1 )
        = $false )
      | ( ( ( in @ SV8 @ SV4 )
          | ( in @ SV8 @ ( setminus @ SV1 @ SV4 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[40]) ).

thf(48,plain,
    ! [SV2: $i,SV6: $i] :
      ( ( ( ~ ( in @ ( sK3_Xx @ SV6 @ SV2 ) @ SV2 ) )
        = $false )
      | ( ( subset @ SV2 @ SV6 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[44]) ).

thf(49,plain,
    ! [SV2: $i,SV6: $i] :
      ( ( ( ~ ~ ( in @ ( sK3_Xx @ SV6 @ SV2 ) @ SV6 ) )
        = $false )
      | ( ( subset @ SV2 @ SV6 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[44]) ).

thf(50,plain,
    ! [SV7: $i,SV3: $i] :
      ( ( ( ~ ! [SY26: $i,SY27: $i] :
                ( ( SY26 != SY27 )
                | ~ ( in @ SY26 @ SV3 )
                | ( in @ SY27 @ SV7 ) )
          | ~ ! [SY28: $i,SY29: $i] :
                ( ( SY28 != SY29 )
                | ~ ( in @ SY29 @ SV7 )
                | ( in @ SY28 @ SV3 ) ) )
        = $false )
      | ( ( SV3 = SV7 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[45]) ).

thf(51,plain,
    ! [SV1: $i,SV4: $i,SV8: $i] :
      ( ( ( in @ SV8 @ SV4 )
        = $true )
      | ( ( in @ SV8 @ ( setminus @ SV1 @ SV4 ) )
        = $true )
      | ( ( in @ SV8 @ SV1 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[47]) ).

thf(52,plain,
    ! [SV2: $i,SV6: $i] :
      ( ( ( in @ ( sK3_Xx @ SV6 @ SV2 ) @ SV2 )
        = $true )
      | ( ( subset @ SV2 @ SV6 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[48]) ).

thf(53,plain,
    ! [SV2: $i,SV6: $i] :
      ( ( ( ~ ( in @ ( sK3_Xx @ SV6 @ SV2 ) @ SV6 ) )
        = $true )
      | ( ( subset @ SV2 @ SV6 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[49]) ).

thf(54,plain,
    ! [SV7: $i,SV3: $i] :
      ( ( ( ~ ! [SY26: $i,SY27: $i] :
                ( ( SY26 != SY27 )
                | ~ ( in @ SY26 @ SV3 )
                | ( in @ SY27 @ SV7 ) ) )
        = $false )
      | ( ( SV3 = SV7 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[50]) ).

thf(55,plain,
    ! [SV3: $i,SV7: $i] :
      ( ( ( ~ ! [SY28: $i,SY29: $i] :
                ( ( SY28 != SY29 )
                | ~ ( in @ SY29 @ SV7 )
                | ( in @ SY28 @ SV3 ) ) )
        = $false )
      | ( ( SV3 = SV7 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[50]) ).

thf(56,plain,
    ! [SV2: $i,SV6: $i] :
      ( ( ( in @ ( sK3_Xx @ SV6 @ SV2 ) @ SV6 )
        = $false )
      | ( ( subset @ SV2 @ SV6 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[53]) ).

thf(57,plain,
    ! [SV7: $i,SV3: $i] :
      ( ( ( ! [SY26: $i,SY27: $i] :
              ( ( SY26 != SY27 )
              | ~ ( in @ SY26 @ SV3 )
              | ( in @ SY27 @ SV7 ) ) )
        = $true )
      | ( ( SV3 = SV7 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[54]) ).

thf(58,plain,
    ! [SV3: $i,SV7: $i] :
      ( ( ( ! [SY28: $i,SY29: $i] :
              ( ( SY28 != SY29 )
              | ~ ( in @ SY29 @ SV7 )
              | ( in @ SY28 @ SV3 ) ) )
        = $true )
      | ( ( SV3 = SV7 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[55]) ).

thf(59,plain,
    ! [SV7: $i,SV3: $i,SV10: $i] :
      ( ( ( ! [SY30: $i] :
              ( ( SV10 != SY30 )
              | ~ ( in @ SV10 @ SV3 )
              | ( in @ SY30 @ SV7 ) ) )
        = $true )
      | ( ( SV3 = SV7 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[57]) ).

thf(60,plain,
    ! [SV3: $i,SV7: $i,SV11: $i] :
      ( ( ( ! [SY31: $i] :
              ( ( SV11 != SY31 )
              | ~ ( in @ SY31 @ SV7 )
              | ( in @ SV11 @ SV3 ) ) )
        = $true )
      | ( ( SV3 = SV7 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[58]) ).

thf(61,plain,
    ! [SV7: $i,SV3: $i,SV12: $i,SV10: $i] :
      ( ( ( ( SV10 != SV12 )
          | ~ ( in @ SV10 @ SV3 )
          | ( in @ SV12 @ SV7 ) )
        = $true )
      | ( ( SV3 = SV7 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[59]) ).

thf(62,plain,
    ! [SV3: $i,SV7: $i,SV13: $i,SV11: $i] :
      ( ( ( ( SV11 != SV13 )
          | ~ ( in @ SV13 @ SV7 )
          | ( in @ SV11 @ SV3 ) )
        = $true )
      | ( ( SV3 = SV7 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[60]) ).

thf(63,plain,
    ! [SV7: $i,SV3: $i,SV12: $i,SV10: $i] :
      ( ( ( ( SV10 != SV12 ) )
        = $true )
      | ( ( ~ ( in @ SV10 @ SV3 )
          | ( in @ SV12 @ SV7 ) )
        = $true )
      | ( ( SV3 = SV7 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[61]) ).

thf(64,plain,
    ! [SV3: $i,SV7: $i,SV13: $i,SV11: $i] :
      ( ( ( ( SV11 != SV13 ) )
        = $true )
      | ( ( ~ ( in @ SV13 @ SV7 )
          | ( in @ SV11 @ SV3 ) )
        = $true )
      | ( ( SV3 = SV7 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[62]) ).

thf(65,plain,
    ! [SV7: $i,SV3: $i,SV12: $i,SV10: $i] :
      ( ( ( SV10 = SV12 )
        = $false )
      | ( ( ~ ( in @ SV10 @ SV3 )
          | ( in @ SV12 @ SV7 ) )
        = $true )
      | ( ( SV3 = SV7 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[63]) ).

thf(66,plain,
    ! [SV3: $i,SV7: $i,SV13: $i,SV11: $i] :
      ( ( ( SV11 = SV13 )
        = $false )
      | ( ( ~ ( in @ SV13 @ SV7 )
          | ( in @ SV11 @ SV3 ) )
        = $true )
      | ( ( SV3 = SV7 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[64]) ).

thf(67,plain,
    ! [SV7: $i,SV12: $i,SV3: $i,SV10: $i] :
      ( ( ( ~ ( in @ SV10 @ SV3 ) )
        = $true )
      | ( ( in @ SV12 @ SV7 )
        = $true )
      | ( ( SV10 = SV12 )
        = $false )
      | ( ( SV3 = SV7 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[65]) ).

thf(68,plain,
    ! [SV3: $i,SV11: $i,SV7: $i,SV13: $i] :
      ( ( ( ~ ( in @ SV13 @ SV7 ) )
        = $true )
      | ( ( in @ SV11 @ SV3 )
        = $true )
      | ( ( SV11 = SV13 )
        = $false )
      | ( ( SV3 = SV7 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[66]) ).

thf(69,plain,
    ! [SV7: $i,SV12: $i,SV3: $i,SV10: $i] :
      ( ( ( in @ SV10 @ SV3 )
        = $false )
      | ( ( in @ SV12 @ SV7 )
        = $true )
      | ( ( SV10 = SV12 )
        = $false )
      | ( ( SV3 = SV7 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[67]) ).

thf(70,plain,
    ! [SV3: $i,SV11: $i,SV7: $i,SV13: $i] :
      ( ( ( in @ SV13 @ SV7 )
        = $false )
      | ( ( in @ SV11 @ SV3 )
        = $true )
      | ( ( SV11 = SV13 )
        = $false )
      | ( ( SV3 = SV7 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[68]) ).

thf(71,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[38,70,69,56,52,51,46,43,42,41]) ).

thf(72,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[71]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : SEU610^2 : TPTP v8.1.0. Released v3.7.0.
% 0.08/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34  % Computer : n016.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Mon Jun 20 07:48:40 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  
% 0.12/0.35   No.of.Axioms: 0
% 0.12/0.35  
% 0.12/0.35   Length.of.Defs: 745
% 0.12/0.35  
% 0.12/0.35   Contains.Choice.Funs: false
% 0.12/0.35  (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)....
% 0.19/0.40  
% 0.19/0.40  ********************************
% 0.19/0.40  *   All subproblems solved!    *
% 0.19/0.40  ********************************
% 0.19/0.40  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,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:71,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.40  
% 0.19/0.40  %**** Beginning of derivation protocol ****
% 0.19/0.40  % SZS output start CNFRefutation
% See solution above
% 0.19/0.40  
% 0.19/0.40  %**** End of derivation protocol ****
% 0.19/0.40  %**** no. of clauses in derivation: 72 ****
% 0.19/0.40  %**** clause counter: 71 ****
% 0.19/0.40  
% 0.19/0.40  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,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:71,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------