TSTP Solution File: SET009+3 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SET009+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n026.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 02:57:43 EDT 2022

% Result   : Theorem 0.22s 0.45s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   81 (  51 unt;   7 typ;   0 def)
%            Number of atoms       :  395 (  93 equ;   0 cnn)
%            Maximal formula atoms :    3 (   5 avg)
%            Number of connectives :  874 ( 149   ~; 113   |;  10   &; 590   @)
%                                         (   4 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :  207 (   0   ^ 207   !;   0   ?; 207   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_difference,type,
    difference: $i > $i > $i ).

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

thf(tp_sK1_B,type,
    sK1_B: $i ).

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

thf(tp_sK3_SY12,type,
    sK3_SY12: $i ).

thf(tp_sK4_D,type,
    sK4_D: $i > $i > $i ).

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

thf(1,axiom,
    ! [B: $i] : ( subset @ B @ B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).

thf(2,axiom,
    ! [B: $i,C: $i] :
      ( ( subset @ B @ C )
    <=> ! [D: $i] :
          ( ( member @ D @ B )
         => ( member @ D @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).

thf(3,axiom,
    ! [B: $i,C: $i,D: $i] :
      ( ( member @ D @ ( difference @ B @ C ) )
    <=> ( ( member @ D @ B )
        & ~ ( member @ D @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).

thf(4,conjecture,
    ! [B: $i,C: $i,D: $i] :
      ( ( subset @ B @ C )
     => ( subset @ ( difference @ D @ C ) @ ( difference @ D @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subset_difference) ).

thf(5,negated_conjecture,
    ( ( ! [B: $i,C: $i,D: $i] :
          ( ( subset @ B @ C )
         => ( subset @ ( difference @ D @ C ) @ ( difference @ D @ B ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[4]) ).

thf(6,plain,
    ( ( ! [B: $i,C: $i,D: $i] :
          ( ( subset @ B @ C )
         => ( subset @ ( difference @ D @ C ) @ ( difference @ D @ B ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ! [B: $i] : ( subset @ B @ B ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(8,plain,
    ( ( ! [B: $i,C: $i] :
          ( ( subset @ B @ C )
        <=> ! [D: $i] :
              ( ( member @ D @ B )
             => ( member @ D @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(9,plain,
    ( ( ! [B: $i,C: $i,D: $i] :
          ( ( member @ D @ ( difference @ B @ C ) )
        <=> ( ( member @ D @ B )
            & ~ ( member @ D @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(10,plain,
    ( ( ! [SY10: $i,SY11: $i] :
          ( ( subset @ sK1_B @ SY10 )
         => ( subset @ ( difference @ SY11 @ SY10 ) @ ( difference @ SY11 @ sK1_B ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[6]) ).

thf(11,plain,
    ( ( ! [SY12: $i] :
          ( ( subset @ sK1_B @ sK2_SY10 )
         => ( subset @ ( difference @ SY12 @ sK2_SY10 ) @ ( difference @ SY12 @ sK1_B ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[10]) ).

thf(12,plain,
    ( ( ( subset @ sK1_B @ sK2_SY10 )
     => ( subset @ ( difference @ sK3_SY12 @ sK2_SY10 ) @ ( difference @ sK3_SY12 @ sK1_B ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[11]) ).

thf(13,plain,
    ( ( subset @ sK1_B @ sK2_SY10 )
    = $true ),
    inference(standard_cnf,[status(thm)],[12]) ).

thf(14,plain,
    ( ( subset @ ( difference @ sK3_SY12 @ sK2_SY10 ) @ ( difference @ sK3_SY12 @ sK1_B ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[12]) ).

thf(15,plain,
    ( ( ~ ( subset @ ( difference @ sK3_SY12 @ sK2_SY10 ) @ ( difference @ sK3_SY12 @ sK1_B ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[14]) ).

thf(16,plain,
    ( ( ! [B: $i,C: $i] :
          ( ( ( member @ ( sK4_D @ C @ B ) @ B )
            & ~ ( member @ ( sK4_D @ C @ B ) @ C ) )
          | ( subset @ B @ C ) )
      & ! [B: $i,C: $i] :
          ( ~ ( subset @ B @ C )
          | ! [D: $i] :
              ( ~ ( member @ D @ B )
              | ( member @ D @ C ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(17,plain,
    ( ( ! [B: $i] :
          ( ! [C: $i,D: $i] :
              ( ~ ( member @ D @ B )
              | ( member @ D @ C )
              | ( member @ D @ ( difference @ B @ C ) ) )
          & ! [C: $i,D: $i] :
              ( ~ ( member @ D @ ( difference @ B @ C ) )
              | ( member @ D @ B ) )
          & ! [C: $i,D: $i] :
              ( ~ ( member @ D @ ( difference @ B @ C ) )
              | ~ ( member @ D @ C ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[9]) ).

thf(18,plain,
    ( ( ! [B: $i] :
          ( ! [C: $i,D: $i] :
              ( ~ ( member @ D @ B )
              | ( member @ D @ C )
              | ( member @ D @ ( difference @ B @ C ) ) )
          & ! [C: $i,D: $i] :
              ( ~ ( member @ D @ ( difference @ B @ C ) )
              | ( member @ D @ B ) )
          & ! [C: $i,D: $i] :
              ( ~ ( member @ D @ ( difference @ B @ C ) )
              | ~ ( member @ D @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[17]) ).

thf(19,plain,
    ( ( ! [B: $i,C: $i] :
          ( ( ( member @ ( sK4_D @ C @ B ) @ B )
            & ~ ( member @ ( sK4_D @ C @ B ) @ C ) )
          | ( subset @ B @ C ) )
      & ! [B: $i,C: $i] :
          ( ~ ( subset @ B @ C )
          | ! [D: $i] :
              ( ~ ( member @ D @ B )
              | ( member @ D @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(20,plain,
    ( ( ! [B: $i] : ( subset @ B @ B ) )
    = $true ),
    inference(copy,[status(thm)],[7]) ).

thf(21,plain,
    ( ( subset @ sK1_B @ sK2_SY10 )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(22,plain,
    ( ( ~ ( subset @ ( difference @ sK3_SY12 @ sK2_SY10 ) @ ( difference @ sK3_SY12 @ sK1_B ) ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(23,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
                    | ~ ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) )
                | ( subset @ SX0 @ SX1 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( subset @ SX0 @ SX1 )
                | ! [SX2: $i] :
                    ( ~ ( member @ SX2 @ SX0 )
                    | ( member @ SX2 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(24,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( member @ SX2 @ SX0 )
                  | ( member @ SX2 @ SX1 )
                  | ( member @ SX2 @ ( difference @ SX0 @ SX1 ) ) )
            | ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
                        ( ~ ( member @ SX2 @ ( difference @ SX0 @ SX1 ) )
                        | ( member @ SX2 @ SX0 ) )
                  | ~ ! [SX1: $i,SX2: $i] :
                        ( ~ ( member @ SX2 @ ( difference @ SX0 @ SX1 ) )
                        | ~ ( member @ SX2 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(25,plain,
    ! [SV1: $i] :
      ( ( subset @ SV1 @ SV1 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(26,plain,
    ( ( subset @ ( difference @ sK3_SY12 @ sK2_SY10 ) @ ( difference @ sK3_SY12 @ sK1_B ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[22]) ).

thf(27,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
                | ~ ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) )
            | ( subset @ SX0 @ SX1 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( subset @ SX0 @ SX1 )
            | ! [SX2: $i] :
                ( ~ ( member @ SX2 @ SX0 )
                | ( member @ SX2 @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[23]) ).

thf(28,plain,
    ! [SV2: $i] :
      ( ( ~ ( ~ ! [SY13: $i,SY14: $i] :
                  ( ~ ( member @ SY14 @ SV2 )
                  | ( member @ SY14 @ SY13 )
                  | ( member @ SY14 @ ( difference @ SV2 @ SY13 ) ) )
            | ~ ~ ( ~ ! [SY15: $i,SY16: $i] :
                        ( ~ ( member @ SY16 @ ( difference @ SV2 @ SY15 ) )
                        | ( member @ SY16 @ SV2 ) )
                  | ~ ! [SY17: $i,SY18: $i] :
                        ( ~ ( member @ SY18 @ ( difference @ SV2 @ SY17 ) )
                        | ~ ( member @ SY18 @ SY17 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[24]) ).

thf(29,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
                | ~ ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) )
            | ( subset @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[27]) ).

thf(30,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( subset @ SX0 @ SX1 )
            | ! [SX2: $i] :
                ( ~ ( member @ SX2 @ SX0 )
                | ( member @ SX2 @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[27]) ).

thf(31,plain,
    ! [SV2: $i] :
      ( ( ~ ! [SY13: $i,SY14: $i] :
              ( ~ ( member @ SY14 @ SV2 )
              | ( member @ SY14 @ SY13 )
              | ( member @ SY14 @ ( difference @ SV2 @ SY13 ) ) )
        | ~ ~ ( ~ ! [SY15: $i,SY16: $i] :
                    ( ~ ( member @ SY16 @ ( difference @ SV2 @ SY15 ) )
                    | ( member @ SY16 @ SV2 ) )
              | ~ ! [SY17: $i,SY18: $i] :
                    ( ~ ( member @ SY18 @ ( difference @ SV2 @ SY17 ) )
                    | ~ ( member @ SY18 @ SY17 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[28]) ).

thf(32,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX0 )
              | ~ ~ ( member @ ( sK4_D @ SX1 @ SX0 ) @ SX1 ) )
          | ( subset @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[29]) ).

thf(33,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( subset @ SX0 @ SX1 )
          | ! [SX2: $i] :
              ( ~ ( member @ SX2 @ SX0 )
              | ( member @ SX2 @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[30]) ).

thf(34,plain,
    ! [SV2: $i] :
      ( ( ~ ! [SY13: $i,SY14: $i] :
              ( ~ ( member @ SY14 @ SV2 )
              | ( member @ SY14 @ SY13 )
              | ( member @ SY14 @ ( difference @ SV2 @ SY13 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[31]) ).

thf(35,plain,
    ! [SV2: $i] :
      ( ( ~ ~ ( ~ ! [SY15: $i,SY16: $i] :
                    ( ~ ( member @ SY16 @ ( difference @ SV2 @ SY15 ) )
                    | ( member @ SY16 @ SV2 ) )
              | ~ ! [SY17: $i,SY18: $i] :
                    ( ~ ( member @ SY18 @ ( difference @ SV2 @ SY17 ) )
                    | ~ ( member @ SY18 @ SY17 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[31]) ).

thf(36,plain,
    ! [SV3: $i] :
      ( ( ! [SY19: $i] :
            ( ~ ( ~ ( member @ ( sK4_D @ SY19 @ SV3 ) @ SV3 )
                | ~ ~ ( member @ ( sK4_D @ SY19 @ SV3 ) @ SY19 ) )
            | ( subset @ SV3 @ SY19 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[32]) ).

thf(37,plain,
    ! [SV4: $i] :
      ( ( ! [SY20: $i] :
            ( ~ ( subset @ SV4 @ SY20 )
            | ! [SY21: $i] :
                ( ~ ( member @ SY21 @ SV4 )
                | ( member @ SY21 @ SY20 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[33]) ).

thf(38,plain,
    ! [SV2: $i] :
      ( ( ! [SY13: $i,SY14: $i] :
            ( ~ ( member @ SY14 @ SV2 )
            | ( member @ SY14 @ SY13 )
            | ( member @ SY14 @ ( difference @ SV2 @ SY13 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[34]) ).

thf(39,plain,
    ! [SV2: $i] :
      ( ( ~ ( ~ ! [SY15: $i,SY16: $i] :
                  ( ~ ( member @ SY16 @ ( difference @ SV2 @ SY15 ) )
                  | ( member @ SY16 @ SV2 ) )
            | ~ ! [SY17: $i,SY18: $i] :
                  ( ~ ( member @ SY18 @ ( difference @ SV2 @ SY17 ) )
                  | ~ ( member @ SY18 @ SY17 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[35]) ).

thf(40,plain,
    ! [SV3: $i,SV5: $i] :
      ( ( ~ ( ~ ( member @ ( sK4_D @ SV5 @ SV3 ) @ SV3 )
            | ~ ~ ( member @ ( sK4_D @ SV5 @ SV3 ) @ SV5 ) )
        | ( subset @ SV3 @ SV5 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[36]) ).

thf(41,plain,
    ! [SV6: $i,SV4: $i] :
      ( ( ~ ( subset @ SV4 @ SV6 )
        | ! [SY22: $i] :
            ( ~ ( member @ SY22 @ SV4 )
            | ( member @ SY22 @ SV6 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[37]) ).

thf(42,plain,
    ! [SV7: $i,SV2: $i] :
      ( ( ! [SY23: $i] :
            ( ~ ( member @ SY23 @ SV2 )
            | ( member @ SY23 @ SV7 )
            | ( member @ SY23 @ ( difference @ SV2 @ SV7 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[38]) ).

thf(43,plain,
    ! [SV2: $i] :
      ( ( ~ ! [SY15: $i,SY16: $i] :
              ( ~ ( member @ SY16 @ ( difference @ SV2 @ SY15 ) )
              | ( member @ SY16 @ SV2 ) )
        | ~ ! [SY17: $i,SY18: $i] :
              ( ~ ( member @ SY18 @ ( difference @ SV2 @ SY17 ) )
              | ~ ( member @ SY18 @ SY17 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[39]) ).

thf(44,plain,
    ! [SV3: $i,SV5: $i] :
      ( ( ( ~ ( ~ ( member @ ( sK4_D @ SV5 @ SV3 ) @ SV3 )
              | ~ ~ ( member @ ( sK4_D @ SV5 @ SV3 ) @ SV5 ) ) )
        = $true )
      | ( ( subset @ SV3 @ SV5 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[40]) ).

thf(45,plain,
    ! [SV6: $i,SV4: $i] :
      ( ( ( ~ ( subset @ SV4 @ SV6 ) )
        = $true )
      | ( ( ! [SY22: $i] :
              ( ~ ( member @ SY22 @ SV4 )
              | ( member @ SY22 @ SV6 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[41]) ).

thf(46,plain,
    ! [SV7: $i,SV2: $i,SV8: $i] :
      ( ( ~ ( member @ SV8 @ SV2 )
        | ( member @ SV8 @ SV7 )
        | ( member @ SV8 @ ( difference @ SV2 @ SV7 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[42]) ).

thf(47,plain,
    ! [SV2: $i] :
      ( ( ~ ! [SY15: $i,SY16: $i] :
              ( ~ ( member @ SY16 @ ( difference @ SV2 @ SY15 ) )
              | ( member @ SY16 @ SV2 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[43]) ).

thf(48,plain,
    ! [SV2: $i] :
      ( ( ~ ! [SY17: $i,SY18: $i] :
              ( ~ ( member @ SY18 @ ( difference @ SV2 @ SY17 ) )
              | ~ ( member @ SY18 @ SY17 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[43]) ).

thf(49,plain,
    ! [SV3: $i,SV5: $i] :
      ( ( ( ~ ( member @ ( sK4_D @ SV5 @ SV3 ) @ SV3 )
          | ~ ~ ( member @ ( sK4_D @ SV5 @ SV3 ) @ SV5 ) )
        = $false )
      | ( ( subset @ SV3 @ SV5 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[44]) ).

thf(50,plain,
    ! [SV6: $i,SV4: $i] :
      ( ( ( subset @ SV4 @ SV6 )
        = $false )
      | ( ( ! [SY22: $i] :
              ( ~ ( member @ SY22 @ SV4 )
              | ( member @ SY22 @ SV6 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[45]) ).

thf(51,plain,
    ! [SV7: $i,SV2: $i,SV8: $i] :
      ( ( ( ~ ( member @ SV8 @ SV2 )
          | ( member @ SV8 @ SV7 ) )
        = $true )
      | ( ( member @ SV8 @ ( difference @ SV2 @ SV7 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[46]) ).

thf(52,plain,
    ! [SV2: $i] :
      ( ( ! [SY15: $i,SY16: $i] :
            ( ~ ( member @ SY16 @ ( difference @ SV2 @ SY15 ) )
            | ( member @ SY16 @ SV2 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[47]) ).

thf(53,plain,
    ! [SV2: $i] :
      ( ( ! [SY17: $i,SY18: $i] :
            ( ~ ( member @ SY18 @ ( difference @ SV2 @ SY17 ) )
            | ~ ( member @ SY18 @ SY17 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[48]) ).

thf(54,plain,
    ! [SV3: $i,SV5: $i] :
      ( ( ( ~ ( member @ ( sK4_D @ SV5 @ SV3 ) @ SV3 ) )
        = $false )
      | ( ( subset @ SV3 @ SV5 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[49]) ).

thf(55,plain,
    ! [SV3: $i,SV5: $i] :
      ( ( ( ~ ~ ( member @ ( sK4_D @ SV5 @ SV3 ) @ SV5 ) )
        = $false )
      | ( ( subset @ SV3 @ SV5 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[49]) ).

thf(56,plain,
    ! [SV6: $i,SV4: $i,SV9: $i] :
      ( ( ( ~ ( member @ SV9 @ SV4 )
          | ( member @ SV9 @ SV6 ) )
        = $true )
      | ( ( subset @ SV4 @ SV6 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[50]) ).

thf(57,plain,
    ! [SV7: $i,SV2: $i,SV8: $i] :
      ( ( ( ~ ( member @ SV8 @ SV2 ) )
        = $true )
      | ( ( member @ SV8 @ SV7 )
        = $true )
      | ( ( member @ SV8 @ ( difference @ SV2 @ SV7 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[51]) ).

thf(58,plain,
    ! [SV10: $i,SV2: $i] :
      ( ( ! [SY24: $i] :
            ( ~ ( member @ SY24 @ ( difference @ SV2 @ SV10 ) )
            | ( member @ SY24 @ SV2 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[52]) ).

thf(59,plain,
    ! [SV11: $i,SV2: $i] :
      ( ( ! [SY25: $i] :
            ( ~ ( member @ SY25 @ ( difference @ SV2 @ SV11 ) )
            | ~ ( member @ SY25 @ SV11 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(60,plain,
    ! [SV3: $i,SV5: $i] :
      ( ( ( member @ ( sK4_D @ SV5 @ SV3 ) @ SV3 )
        = $true )
      | ( ( subset @ SV3 @ SV5 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[54]) ).

thf(61,plain,
    ! [SV3: $i,SV5: $i] :
      ( ( ( ~ ( member @ ( sK4_D @ SV5 @ SV3 ) @ SV5 ) )
        = $true )
      | ( ( subset @ SV3 @ SV5 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[55]) ).

thf(62,plain,
    ! [SV6: $i,SV4: $i,SV9: $i] :
      ( ( ( ~ ( member @ SV9 @ SV4 ) )
        = $true )
      | ( ( member @ SV9 @ SV6 )
        = $true )
      | ( ( subset @ SV4 @ SV6 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[56]) ).

thf(63,plain,
    ! [SV7: $i,SV2: $i,SV8: $i] :
      ( ( ( member @ SV8 @ SV2 )
        = $false )
      | ( ( member @ SV8 @ SV7 )
        = $true )
      | ( ( member @ SV8 @ ( difference @ SV2 @ SV7 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[57]) ).

thf(64,plain,
    ! [SV10: $i,SV2: $i,SV12: $i] :
      ( ( ~ ( member @ SV12 @ ( difference @ SV2 @ SV10 ) )
        | ( member @ SV12 @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[58]) ).

thf(65,plain,
    ! [SV11: $i,SV2: $i,SV13: $i] :
      ( ( ~ ( member @ SV13 @ ( difference @ SV2 @ SV11 ) )
        | ~ ( member @ SV13 @ SV11 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[59]) ).

thf(66,plain,
    ! [SV3: $i,SV5: $i] :
      ( ( ( member @ ( sK4_D @ SV5 @ SV3 ) @ SV5 )
        = $false )
      | ( ( subset @ SV3 @ SV5 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[61]) ).

thf(67,plain,
    ! [SV6: $i,SV4: $i,SV9: $i] :
      ( ( ( member @ SV9 @ SV4 )
        = $false )
      | ( ( member @ SV9 @ SV6 )
        = $true )
      | ( ( subset @ SV4 @ SV6 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[62]) ).

thf(68,plain,
    ! [SV10: $i,SV2: $i,SV12: $i] :
      ( ( ( ~ ( member @ SV12 @ ( difference @ SV2 @ SV10 ) ) )
        = $true )
      | ( ( member @ SV12 @ SV2 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[64]) ).

thf(69,plain,
    ! [SV11: $i,SV2: $i,SV13: $i] :
      ( ( ( ~ ( member @ SV13 @ ( difference @ SV2 @ SV11 ) ) )
        = $true )
      | ( ( ~ ( member @ SV13 @ SV11 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[65]) ).

thf(70,plain,
    ! [SV10: $i,SV2: $i,SV12: $i] :
      ( ( ( member @ SV12 @ ( difference @ SV2 @ SV10 ) )
        = $false )
      | ( ( member @ SV12 @ SV2 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[68]) ).

thf(71,plain,
    ! [SV11: $i,SV2: $i,SV13: $i] :
      ( ( ( member @ SV13 @ ( difference @ SV2 @ SV11 ) )
        = $false )
      | ( ( ~ ( member @ SV13 @ SV11 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[69]) ).

thf(72,plain,
    ! [SV2: $i,SV11: $i,SV13: $i] :
      ( ( ( member @ SV13 @ SV11 )
        = $false )
      | ( ( member @ SV13 @ ( difference @ SV2 @ SV11 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[71]) ).

thf(73,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[21,72,70,67,66,63,60,26,25]) ).

thf(74,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[73]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SET009+3 : TPTP v8.1.0. Released v2.2.0.
% 0.08/0.14  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.15/0.36  % Computer : n026.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 600
% 0.15/0.36  % DateTime : Mon Jul 11 10:08:27 EDT 2022
% 0.15/0.36  % CPUTime  : 
% 0.15/0.37  
% 0.15/0.37   No.of.Axioms: 3
% 0.15/0.37  
% 0.15/0.37   Length.of.Defs: 0
% 0.15/0.37  
% 0.15/0.37   Contains.Choice.Funs: false
% 0.15/0.37  (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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:5,loop_count:0,foatp_calls:0,translation:fof_full)....
% 0.22/0.45  
% 0.22/0.45  ********************************
% 0.22/0.45  *   All subproblems solved!    *
% 0.22/0.45  ********************************
% 0.22/0.45  % 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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:73,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.22/0.45  
% 0.22/0.45  %**** Beginning of derivation protocol ****
% 0.22/0.45  % SZS output start CNFRefutation
% See solution above
% 0.22/0.45  
% 0.22/0.45  %**** End of derivation protocol ****
% 0.22/0.45  %**** no. of clauses in derivation: 74 ****
% 0.22/0.45  %**** clause counter: 73 ****
% 0.22/0.45  
% 0.22/0.45  % 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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:73,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------