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LEO-II---2.3.1.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : LEO-II---2.3.1
% Problem  : SET689+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n010.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Oct  7 10:40:52 AM UTC 2026

% Result   : Theorem 0.23s 0.27s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   64 (  37 unt;   0 typ;   0 def)
%            Number of atoms       :  369 (  89 equ;   0 cnn)
%            Maximal formula atoms :    4 (   5 avg)
%            Number of connectives :  648 ( 133   ~;  97   |;  15   &; 388   @)
%                                         (   6 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  16 usr;   6 con; 0-2 aty)
%            Number of variables   :  126 (   0   ^; 126   !;   0   ?; 126   :)

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

thf(tp_empty_set,type,
    empty_set: $i ).

thf(tp_equal_set,type,
    equal_set: $i > $i > $o ).

thf(tp_intersection,type,
    intersection: $i > $i > $i ).

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

thf(tp_power_set,type,
    power_set: $i > $i ).

thf(tp_product,type,
    product: $i > $i ).

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

thf(tp_sK2_SY8,type,
    sK2_SY8: $i ).

thf(tp_sK3_SY10,type,
    sK3_SY10: $i ).

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

thf(tp_singleton,type,
    singleton: $i > $i ).

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

thf(tp_sum,type,
    sum: $i > $i ).

thf(tp_union,type,
    union: $i > $i > $i ).

thf(tp_unordered_pair,type,
    unordered_pair: $i > $i > $i ).

thf(10,axiom,
    ! [A: $i,B: $i] :
      ( ( equal_set @ A @ B )
    <=> ( ( subset @ A @ B )
        & ( subset @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set) ).

thf(11,axiom,
    ! [A: $i,B: $i] :
      ( ( subset @ A @ B )
    <=> ! [X: $i] :
          ( ( member @ X @ A )
         => ( member @ X @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).

thf(12,conjecture,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( subset @ A @ B )
        & ( subset @ B @ C )
        & ( subset @ C @ A ) )
     => ( equal_set @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI05) ).

thf(13,negated_conjecture,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( ( subset @ A @ B )
            & ( subset @ B @ C )
            & ( subset @ C @ A ) )
         => ( equal_set @ A @ C ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[12]) ).

thf(14,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( ( subset @ A @ B )
            & ( subset @ B @ C )
            & ( subset @ C @ A ) )
         => ( equal_set @ A @ C ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(15,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( equal_set @ A @ B )
        <=> ( ( subset @ A @ B )
            & ( subset @ B @ A ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(16,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( subset @ A @ B )
        <=> ! [X: $i] :
              ( ( member @ X @ A )
             => ( member @ X @ B ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(17,plain,
    ( ( ! [SY8: $i,SY9: $i] :
          ( ( ( subset @ sK1_A @ SY8 )
            & ( subset @ SY8 @ SY9 )
            & ( subset @ SY9 @ sK1_A ) )
         => ( equal_set @ sK1_A @ SY9 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[14]) ).

thf(18,plain,
    ( ( ! [SY10: $i] :
          ( ( ( subset @ sK1_A @ sK2_SY8 )
            & ( subset @ sK2_SY8 @ SY10 )
            & ( subset @ SY10 @ sK1_A ) )
         => ( equal_set @ sK1_A @ SY10 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[17]) ).

thf(19,plain,
    ( ( ( ( subset @ sK1_A @ sK2_SY8 )
        & ( subset @ sK2_SY8 @ sK3_SY10 )
        & ( subset @ sK3_SY10 @ sK1_A ) )
     => ( equal_set @ sK1_A @ sK3_SY10 ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[18]) ).

thf(20,plain,
    ( ( subset @ sK1_A @ sK2_SY8 )
    = $true ),
    inference(standard_cnf,[status(thm)],[19]) ).

thf(21,plain,
    ( ( subset @ sK2_SY8 @ sK3_SY10 )
    = $true ),
    inference(standard_cnf,[status(thm)],[19]) ).

thf(22,plain,
    ( ( subset @ sK3_SY10 @ sK1_A )
    = $true ),
    inference(standard_cnf,[status(thm)],[19]) ).

thf(23,plain,
    ( ( equal_set @ sK1_A @ sK3_SY10 )
    = $false ),
    inference(standard_cnf,[status(thm)],[19]) ).

thf(24,plain,
    ( ( ~ ( equal_set @ sK1_A @ sK3_SY10 ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[23]) ).

thf(25,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( subset @ A @ B )
        <=> ! [X: $i] :
              ( ( member @ X @ A )
             => ( member @ X @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(26,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( equal_set @ A @ B )
        <=> ( ( subset @ A @ B )
            & ( subset @ B @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(27,plain,
    ( ( subset @ sK3_SY10 @ sK1_A )
    = $true ),
    inference(copy,[status(thm)],[22]) ).

thf(28,plain,
    ( ( subset @ sK2_SY8 @ sK3_SY10 )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(29,plain,
    ( ( subset @ sK1_A @ sK2_SY8 )
    = $true ),
    inference(copy,[status(thm)],[20]) ).

thf(30,plain,
    ( ( ~ ( equal_set @ sK1_A @ sK3_SY10 ) )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(31,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ( ~ ( equal_set @ SX0 @ SX1 )
                | ~ ( ~ ( subset @ SX0 @ SX1 )
                    | ~ ( subset @ SX1 @ SX0 ) ) )
            | ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
                      | ~ ( subset @ SX1 @ SX0 ) )
                | ( equal_set @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[26]) ).

thf(32,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
                | ! [SX2: $i] :
                    ( ~ ( member @ SX2 @ SX0 )
                    | ( member @ SX2 @ SX1 ) ) )
            | ~ ( ~ ! [SX2: $i] :
                      ( ~ ( member @ SX2 @ SX0 )
                      | ( member @ SX2 @ SX1 ) )
                | ( subset @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[25]) ).

thf(33,plain,
    ( ( equal_set @ sK1_A @ sK3_SY10 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[30]) ).

thf(34,plain,
    ! [SV1: $i] :
      ( ( ! [SY11: $i] :
            ~ ( ~ ( ~ ( equal_set @ SV1 @ SY11 )
                  | ~ ( ~ ( subset @ SV1 @ SY11 )
                      | ~ ( subset @ SY11 @ SV1 ) ) )
              | ~ ( ~ ~ ( ~ ( subset @ SV1 @ SY11 )
                        | ~ ( subset @ SY11 @ SV1 ) )
                  | ( equal_set @ SV1 @ SY11 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[31]) ).

thf(35,plain,
    ! [SV2: $i] :
      ( ( ! [SY12: $i] :
            ~ ( ~ ( ~ ( subset @ SV2 @ SY12 )
                  | ! [SY13: $i] :
                      ( ~ ( member @ SY13 @ SV2 )
                      | ( member @ SY13 @ SY12 ) ) )
              | ~ ( ~ ! [SY14: $i] :
                        ( ~ ( member @ SY14 @ SV2 )
                        | ( member @ SY14 @ SY12 ) )
                  | ( subset @ SV2 @ SY12 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[32]) ).

thf(36,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ~ ( ~ ( ~ ( equal_set @ SV1 @ SV3 )
                | ~ ( ~ ( subset @ SV1 @ SV3 )
                    | ~ ( subset @ SV3 @ SV1 ) ) )
            | ~ ( ~ ~ ( ~ ( subset @ SV1 @ SV3 )
                      | ~ ( subset @ SV3 @ SV1 ) )
                | ( equal_set @ SV1 @ SV3 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[34]) ).

thf(37,plain,
    ! [SV4: $i,SV2: $i] :
      ( ( ~ ( ~ ( ~ ( subset @ SV2 @ SV4 )
                | ! [SY15: $i] :
                    ( ~ ( member @ SY15 @ SV2 )
                    | ( member @ SY15 @ SV4 ) ) )
            | ~ ( ~ ! [SY16: $i] :
                      ( ~ ( member @ SY16 @ SV2 )
                      | ( member @ SY16 @ SV4 ) )
                | ( subset @ SV2 @ SV4 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[35]) ).

thf(38,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ~ ( ~ ( equal_set @ SV1 @ SV3 )
            | ~ ( ~ ( subset @ SV1 @ SV3 )
                | ~ ( subset @ SV3 @ SV1 ) ) )
        | ~ ( ~ ~ ( ~ ( subset @ SV1 @ SV3 )
                  | ~ ( subset @ SV3 @ SV1 ) )
            | ( equal_set @ SV1 @ SV3 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[36]) ).

thf(39,plain,
    ! [SV4: $i,SV2: $i] :
      ( ( ~ ( ~ ( subset @ SV2 @ SV4 )
            | ! [SY15: $i] :
                ( ~ ( member @ SY15 @ SV2 )
                | ( member @ SY15 @ SV4 ) ) )
        | ~ ( ~ ! [SY16: $i] :
                  ( ~ ( member @ SY16 @ SV2 )
                  | ( member @ SY16 @ SV4 ) )
            | ( subset @ SV2 @ SV4 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[37]) ).

thf(40,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ~ ( ~ ( equal_set @ SV1 @ SV3 )
            | ~ ( ~ ( subset @ SV1 @ SV3 )
                | ~ ( subset @ SV3 @ SV1 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[38]) ).

thf(41,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ~ ( ~ ~ ( ~ ( subset @ SV1 @ SV3 )
                  | ~ ( subset @ SV3 @ SV1 ) )
            | ( equal_set @ SV1 @ SV3 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[38]) ).

thf(42,plain,
    ! [SV4: $i,SV2: $i] :
      ( ( ~ ( ~ ( subset @ SV2 @ SV4 )
            | ! [SY15: $i] :
                ( ~ ( member @ SY15 @ SV2 )
                | ( member @ SY15 @ SV4 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[39]) ).

thf(43,plain,
    ! [SV4: $i,SV2: $i] :
      ( ( ~ ( ~ ! [SY16: $i] :
                  ( ~ ( member @ SY16 @ SV2 )
                  | ( member @ SY16 @ SV4 ) )
            | ( subset @ SV2 @ SV4 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[39]) ).

thf(44,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ~ ( equal_set @ SV1 @ SV3 )
        | ~ ( ~ ( subset @ SV1 @ SV3 )
            | ~ ( subset @ SV3 @ SV1 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[40]) ).

thf(45,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ~ ~ ( ~ ( subset @ SV1 @ SV3 )
              | ~ ( subset @ SV3 @ SV1 ) )
        | ( equal_set @ SV1 @ SV3 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[41]) ).

thf(46,plain,
    ! [SV4: $i,SV2: $i] :
      ( ( ~ ( subset @ SV2 @ SV4 )
        | ! [SY15: $i] :
            ( ~ ( member @ SY15 @ SV2 )
            | ( member @ SY15 @ SV4 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[42]) ).

thf(47,plain,
    ! [SV4: $i,SV2: $i] :
      ( ( ~ ! [SY16: $i] :
              ( ~ ( member @ SY16 @ SV2 )
              | ( member @ SY16 @ SV4 ) )
        | ( subset @ SV2 @ SV4 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[43]) ).

thf(48,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ( ~ ( equal_set @ SV1 @ SV3 ) )
        = $true )
      | ( ( ~ ( ~ ( subset @ SV1 @ SV3 )
              | ~ ( subset @ SV3 @ SV1 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[44]) ).

thf(49,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ( ~ ~ ( ~ ( subset @ SV1 @ SV3 )
                | ~ ( subset @ SV3 @ SV1 ) ) )
        = $true )
      | ( ( equal_set @ SV1 @ SV3 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[45]) ).

thf(50,plain,
    ! [SV4: $i,SV2: $i] :
      ( ( ( ~ ( subset @ SV2 @ SV4 ) )
        = $true )
      | ( ( ! [SY15: $i] :
              ( ~ ( member @ SY15 @ SV2 )
              | ( member @ SY15 @ SV4 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[46]) ).

thf(51,plain,
    ! [SV4: $i,SV2: $i] :
      ( ( ( ~ ! [SY16: $i] :
                ( ~ ( member @ SY16 @ SV2 )
                | ( member @ SY16 @ SV4 ) ) )
        = $true )
      | ( ( subset @ SV2 @ SV4 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[47]) ).

thf(52,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ( equal_set @ SV1 @ SV3 )
        = $false )
      | ( ( ~ ( ~ ( subset @ SV1 @ SV3 )
              | ~ ( subset @ SV3 @ SV1 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[48]) ).

thf(53,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ( ~ ( ~ ( subset @ SV1 @ SV3 )
              | ~ ( subset @ SV3 @ SV1 ) ) )
        = $false )
      | ( ( equal_set @ SV1 @ SV3 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[49]) ).

thf(54,plain,
    ! [SV4: $i,SV2: $i] :
      ( ( ( subset @ SV2 @ SV4 )
        = $false )
      | ( ( ! [SY15: $i] :
              ( ~ ( member @ SY15 @ SV2 )
              | ( member @ SY15 @ SV4 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[50]) ).

thf(55,plain,
    ! [SV4: $i,SV2: $i] :
      ( ( ( ! [SY16: $i] :
              ( ~ ( member @ SY16 @ SV2 )
              | ( member @ SY16 @ SV4 ) ) )
        = $false )
      | ( ( subset @ SV2 @ SV4 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[51]) ).

thf(56,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ( ~ ( subset @ SV1 @ SV3 )
          | ~ ( subset @ SV3 @ SV1 ) )
        = $false )
      | ( ( equal_set @ SV1 @ SV3 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[52]) ).

thf(57,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ( ~ ( subset @ SV1 @ SV3 )
          | ~ ( subset @ SV3 @ SV1 ) )
        = $true )
      | ( ( equal_set @ SV1 @ SV3 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[53]) ).

thf(58,plain,
    ! [SV4: $i,SV2: $i,SV5: $i] :
      ( ( ( ~ ( member @ SV5 @ SV2 )
          | ( member @ SV5 @ SV4 ) )
        = $true )
      | ( ( subset @ SV2 @ SV4 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[54]) ).

thf(59,plain,
    ! [SV2: $i,SV4: $i] :
      ( ( ( ~ ( member @ ( sK4_SY16 @ SV4 @ SV2 ) @ SV2 )
          | ( member @ ( sK4_SY16 @ SV4 @ SV2 ) @ SV4 ) )
        = $false )
      | ( ( subset @ SV2 @ SV4 )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[55]) ).

thf(60,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ( ~ ( subset @ SV1 @ SV3 ) )
        = $false )
      | ( ( equal_set @ SV1 @ SV3 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[56]) ).

thf(61,plain,
    ! [SV1: $i,SV3: $i] :
      ( ( ( ~ ( subset @ SV3 @ SV1 ) )
        = $false )
      | ( ( equal_set @ SV1 @ SV3 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[56]) ).

thf(62,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ( ~ ( subset @ SV1 @ SV3 ) )
        = $true )
      | ( ( ~ ( subset @ SV3 @ SV1 ) )
        = $true )
      | ( ( equal_set @ SV1 @ SV3 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[57]) ).

thf(63,plain,
    ! [SV4: $i,SV2: $i,SV5: $i] :
      ( ( ( ~ ( member @ SV5 @ SV2 ) )
        = $true )
      | ( ( member @ SV5 @ SV4 )
        = $true )
      | ( ( subset @ SV2 @ SV4 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[58]) ).

thf(64,plain,
    ! [SV2: $i,SV4: $i] :
      ( ( ( ~ ( member @ ( sK4_SY16 @ SV4 @ SV2 ) @ SV2 ) )
        = $false )
      | ( ( subset @ SV2 @ SV4 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[59]) ).

thf(65,plain,
    ! [SV2: $i,SV4: $i] :
      ( ( ( member @ ( sK4_SY16 @ SV4 @ SV2 ) @ SV4 )
        = $false )
      | ( ( subset @ SV2 @ SV4 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[59]) ).

thf(66,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ( subset @ SV1 @ SV3 )
        = $true )
      | ( ( equal_set @ SV1 @ SV3 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[60]) ).

thf(67,plain,
    ! [SV1: $i,SV3: $i] :
      ( ( ( subset @ SV3 @ SV1 )
        = $true )
      | ( ( equal_set @ SV1 @ SV3 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[61]) ).

thf(68,plain,
    ! [SV3: $i,SV1: $i] :
      ( ( ( subset @ SV1 @ SV3 )
        = $false )
      | ( ( ~ ( subset @ SV3 @ SV1 ) )
        = $true )
      | ( ( equal_set @ SV1 @ SV3 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[62]) ).

thf(69,plain,
    ! [SV4: $i,SV2: $i,SV5: $i] :
      ( ( ( member @ SV5 @ SV2 )
        = $false )
      | ( ( member @ SV5 @ SV4 )
        = $true )
      | ( ( subset @ SV2 @ SV4 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[63]) ).

thf(70,plain,
    ! [SV2: $i,SV4: $i] :
      ( ( ( member @ ( sK4_SY16 @ SV4 @ SV2 ) @ SV2 )
        = $true )
      | ( ( subset @ SV2 @ SV4 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[64]) ).

thf(71,plain,
    ! [SV1: $i,SV3: $i] :
      ( ( ( subset @ SV3 @ SV1 )
        = $false )
      | ( ( subset @ SV1 @ SV3 )
        = $false )
      | ( ( equal_set @ SV1 @ SV3 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[68]) ).

thf(72,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[27,71,70,69,67,66,65,33,29,28]) ).

thf(73,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[72]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SET689+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04  % Command  : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.19  % Computer : n010.cluster.edu
% 0.07/0.19  % Model    : x86_64 x86_64
% 0.07/0.19  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19  % Memory   : 8046.5625MB
% 0.07/0.19  % OS       : Linux 6.8.0-71-generic
% 0.07/0.19  % CPULimit : 300
% 0.07/0.19  % WCLimit  : 300
% 0.07/0.19  % DateTime : Tue Oct  6 14:49:25 UTC 2026
% 0.07/0.20  % CPUTime  : 
% 0.07/0.20  Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.27  
% 0.23/0.27   No.of.Axioms: 2
% 0.23/0.27  
% 0.23/0.27   Length.of.Defs: 0
% 0.23/0.27  
% 0.23/0.27   Contains.Choice.Funs: false
% 0.23/0.27  .
% 0.23/0.27  
% 0.23/0.27  ********************************
% 0.23/0.27  *   All subproblems solved!    *
% 0.23/0.27  ********************************
% 0.23/0.27  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:5,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:72,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.23/0.27  
% 0.23/0.27  %**** Beginning of derivation protocol ****
% 0.23/0.27  % SZS output start CNFRefutation
% See solution above
% 0.23/0.27  
% 0.23/0.27  %**** End of derivation protocol ****
% 0.23/0.27  %**** no. of clauses in derivation: 64 ****
% 0.23/0.27  %**** clause counter: 72 ****
% 0.23/0.27  
% 0.23/0.27  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:5,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:72,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------