TSTP Solution File: SET880+1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SET880+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n029.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 03:05:56 EDT 2022

% Result   : Theorem 0.19s 0.39s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   99 (  55 unt;  10 typ;   0 def)
%            Number of atoms       :  495 ( 260 equ;   0 cnn)
%            Maximal formula atoms :    3 (   5 avg)
%            Number of connectives :  801 ( 170   ~; 147   |;   8   &; 463   @)
%                                         (   6 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   7 con; 0-2 aty)
%            Number of variables   :  189 (   0   ^ 185   !;   4   ?; 189   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_empty,type,
    empty: $i > $o ).

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

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

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

thf(tp_sK2_SY11,type,
    sK2_SY11: $i ).

thf(tp_sK3_A,type,
    sK3_A: $i ).

thf(tp_sK4_A,type,
    sK4_A: $i ).

thf(tp_sK5_C,type,
    sK5_C: $i > $i > $i ).

thf(tp_set_difference,type,
    set_difference: $i > $i > $i ).

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

thf(1,axiom,
    ? [A: $i] :
      ~ ( empty @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).

thf(2,axiom,
    ? [A: $i] : ( empty @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).

thf(3,axiom,
    ! [A: $i,B: $i] :
      ( ( ( set_difference @ ( singleton @ A ) @ B )
        = empty_set )
    <=> ( in @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l36_zfmisc_1) ).

thf(4,axiom,
    empty @ empty_set,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ( ( B
        = ( singleton @ A ) )
    <=> ! [C: $i] :
          ( ( in @ C @ B )
        <=> ( C = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

thf(6,axiom,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ~ ( in @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(7,conjecture,
    ! [A: $i,B: $i] :
      ( ( ( set_difference @ ( singleton @ A ) @ ( singleton @ B ) )
        = empty_set )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_zfmisc_1) ).

thf(8,negated_conjecture,
    ( ( ! [A: $i,B: $i] :
          ( ( ( set_difference @ ( singleton @ A ) @ ( singleton @ B ) )
            = empty_set )
         => ( A = B ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[7]) ).

thf(9,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( set_difference @ ( singleton @ A ) @ ( singleton @ B ) )
            = empty_set )
         => ( A = B ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(10,plain,
    ( ( ? [A: $i] :
          ~ ( empty @ A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(11,plain,
    ( ( ? [A: $i] : ( empty @ A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(12,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( set_difference @ ( singleton @ A ) @ B )
            = empty_set )
        <=> ( in @ A @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(13,plain,
    ( ( empty @ empty_set )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(14,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( B
            = ( singleton @ A ) )
        <=> ! [C: $i] :
              ( ( in @ C @ B )
            <=> ( C = A ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(15,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( in @ A @ B )
         => ~ ( in @ B @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(16,plain,
    ( ( ! [SY11: $i] :
          ( ( ( set_difference @ ( singleton @ sK1_A ) @ ( singleton @ SY11 ) )
            = empty_set )
         => ( sK1_A = SY11 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[9]) ).

thf(17,plain,
    ( ( ( ( set_difference @ ( singleton @ sK1_A ) @ ( singleton @ sK2_SY11 ) )
        = empty_set )
     => ( sK1_A = sK2_SY11 ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[16]) ).

thf(18,plain,
    ( ( ( set_difference @ ( singleton @ sK1_A ) @ ( singleton @ sK2_SY11 ) )
      = empty_set )
    = $true ),
    inference(standard_cnf,[status(thm)],[17]) ).

thf(19,plain,
    ( ( sK1_A = sK2_SY11 )
    = $false ),
    inference(standard_cnf,[status(thm)],[17]) ).

thf(20,plain,
    ( ( ( sK1_A != sK2_SY11 ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[19]) ).

thf(21,plain,
    ( ( ~ ( empty @ sK3_A ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[10]) ).

thf(22,plain,
    ( ( empty @ sK4_A )
    = $true ),
    inference(extcnf_combined,[status(esa)],[11]) ).

thf(23,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( set_difference @ ( singleton @ A ) @ B )
           != empty_set )
          | ( in @ A @ B ) )
      & ! [A: $i,B: $i] :
          ( ~ ( in @ A @ B )
          | ( ( set_difference @ ( singleton @ A ) @ B )
            = empty_set ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[12]) ).

thf(24,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( ( ( sK5_C @ B @ A )
               != A )
              | ~ ( in @ ( sK5_C @ B @ A ) @ B ) )
            & ( ( ( sK5_C @ B @ A )
                = A )
              | ( in @ ( sK5_C @ B @ A ) @ B ) ) )
          | ( B
            = ( singleton @ A ) ) )
      & ! [A: $i,B: $i] :
          ( ( B
           != ( singleton @ A ) )
          | ( ! [C: $i] :
                ( ( C != A )
                | ( in @ C @ B ) )
            & ! [C: $i] :
                ( ~ ( in @ C @ B )
                | ( C = A ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[14]) ).

thf(25,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( in @ A @ B )
          | ~ ( in @ B @ A ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[15]) ).

thf(26,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( in @ A @ B )
          | ~ ( in @ B @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(27,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( ( ( sK5_C @ B @ A )
               != A )
              | ~ ( in @ ( sK5_C @ B @ A ) @ B ) )
            & ( ( ( sK5_C @ B @ A )
                = A )
              | ( in @ ( sK5_C @ B @ A ) @ B ) ) )
          | ( B
            = ( singleton @ A ) ) )
      & ! [A: $i,B: $i] :
          ( ( B
           != ( singleton @ A ) )
          | ( ! [C: $i] :
                ( ( C != A )
                | ( in @ C @ B ) )
            & ! [C: $i] :
                ( ~ ( in @ C @ B )
                | ( C = A ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(28,plain,
    ( ( empty @ empty_set )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(29,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( set_difference @ ( singleton @ A ) @ B )
           != empty_set )
          | ( in @ A @ B ) )
      & ! [A: $i,B: $i] :
          ( ~ ( in @ A @ B )
          | ( ( set_difference @ ( singleton @ A ) @ B )
            = empty_set ) ) )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

thf(30,plain,
    ( ( empty @ sK4_A )
    = $true ),
    inference(copy,[status(thm)],[22]) ).

thf(31,plain,
    ( ( ~ ( empty @ sK3_A ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(32,plain,
    ( ( ( set_difference @ ( singleton @ sK1_A ) @ ( singleton @ sK2_SY11 ) )
      = empty_set )
    = $true ),
    inference(copy,[status(thm)],[18]) ).

thf(33,plain,
    ( ( ( sK1_A != sK2_SY11 ) )
    = $true ),
    inference(copy,[status(thm)],[20]) ).

thf(34,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ( ( set_difference @ ( singleton @ SX0 ) @ SX1 )
                 != empty_set )
                | ( in @ SX0 @ SX1 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( in @ SX0 @ SX1 )
                | ( ( set_difference @ ( singleton @ SX0 ) @ SX1 )
                  = empty_set ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[29]) ).

thf(35,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( ~ ( ( ( sK5_C @ SX1 @ SX0 )
                         != SX0 )
                        | ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) )
                    | ~ ( ( ( sK5_C @ SX1 @ SX0 )
                          = SX0 )
                        | ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) ) )
                | ( SX1
                  = ( singleton @ SX0 ) ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ( SX1
                 != ( singleton @ SX0 ) )
                | ~ ( ~ ! [SX2: $i] :
                          ( ( SX2 != SX0 )
                          | ( in @ SX2 @ SX1 ) )
                    | ~ ! [SX2: $i] :
                          ( ~ ( in @ SX2 @ SX1 )
                          | ( SX2 = SX0 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[27]) ).

thf(36,plain,
    ! [SV1: $i] :
      ( ( ! [SY12: $i] :
            ( ~ ( in @ SV1 @ SY12 )
            | ~ ( in @ SY12 @ SV1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[26]) ).

thf(37,plain,
    ( ( empty @ sK3_A )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[31]) ).

thf(38,plain,
    ( ( sK1_A = sK2_SY11 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[33]) ).

thf(39,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( set_difference @ ( singleton @ SX0 ) @ SX1 )
             != empty_set )
            | ( in @ SX0 @ SX1 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( in @ SX0 @ SX1 )
            | ( ( set_difference @ ( singleton @ SX0 ) @ SX1 )
              = empty_set ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[34]) ).

thf(40,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( ~ ( ( ( sK5_C @ SX1 @ SX0 )
                     != SX0 )
                    | ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) )
                | ~ ( ( ( sK5_C @ SX1 @ SX0 )
                      = SX0 )
                    | ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) ) )
            | ( SX1
              = ( singleton @ SX0 ) ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ( SX1
             != ( singleton @ SX0 ) )
            | ~ ( ~ ! [SX2: $i] :
                      ( ( SX2 != SX0 )
                      | ( in @ SX2 @ SX1 ) )
                | ~ ! [SX2: $i] :
                      ( ~ ( in @ SX2 @ SX1 )
                      | ( SX2 = SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[35]) ).

thf(41,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ~ ( in @ SV1 @ SV2 )
        | ~ ( in @ SV2 @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[36]) ).

thf(42,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( set_difference @ ( singleton @ SX0 ) @ SX1 )
             != empty_set )
            | ( in @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[39]) ).

thf(43,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( in @ SX0 @ SX1 )
            | ( ( set_difference @ ( singleton @ SX0 ) @ SX1 )
              = empty_set ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[39]) ).

thf(44,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( ~ ( ( ( sK5_C @ SX1 @ SX0 )
                     != SX0 )
                    | ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) )
                | ~ ( ( ( sK5_C @ SX1 @ SX0 )
                      = SX0 )
                    | ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) ) )
            | ( SX1
              = ( singleton @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[40]) ).

thf(45,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( SX1
             != ( singleton @ SX0 ) )
            | ~ ( ~ ! [SX2: $i] :
                      ( ( SX2 != SX0 )
                      | ( in @ SX2 @ SX1 ) )
                | ~ ! [SX2: $i] :
                      ( ~ ( in @ SX2 @ SX1 )
                      | ( SX2 = SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[40]) ).

thf(46,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ( ~ ( in @ SV1 @ SV2 ) )
        = $true )
      | ( ( ~ ( in @ SV2 @ SV1 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[41]) ).

thf(47,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ( set_difference @ ( singleton @ SX0 ) @ SX1 )
           != empty_set )
          | ( in @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[42]) ).

thf(48,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX0 @ SX1 )
          | ( ( set_difference @ ( singleton @ SX0 ) @ SX1 )
            = empty_set ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[43]) ).

thf(49,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( ~ ( ( ( sK5_C @ SX1 @ SX0 )
                   != SX0 )
                  | ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) )
              | ~ ( ( ( sK5_C @ SX1 @ SX0 )
                    = SX0 )
                  | ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) ) )
          | ( SX1
            = ( singleton @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[44]) ).

thf(50,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX1
           != ( singleton @ SX0 ) )
          | ~ ( ~ ! [SX2: $i] :
                    ( ( SX2 != SX0 )
                    | ( in @ SX2 @ SX1 ) )
              | ~ ! [SX2: $i] :
                    ( ~ ( in @ SX2 @ SX1 )
                    | ( SX2 = SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[45]) ).

thf(51,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ( in @ SV1 @ SV2 )
        = $false )
      | ( ( ~ ( in @ SV2 @ SV1 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[46]) ).

thf(52,plain,
    ! [SV3: $i] :
      ( ( ! [SY13: $i] :
            ( ( ( set_difference @ ( singleton @ SV3 ) @ SY13 )
             != empty_set )
            | ( in @ SV3 @ SY13 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[47]) ).

thf(53,plain,
    ! [SV4: $i] :
      ( ( ! [SY14: $i] :
            ( ~ ( in @ SV4 @ SY14 )
            | ( ( set_difference @ ( singleton @ SV4 ) @ SY14 )
              = empty_set ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[48]) ).

thf(54,plain,
    ! [SV5: $i] :
      ( ( ! [SY15: $i] :
            ( ~ ( ~ ( ( ( sK5_C @ SY15 @ SV5 )
                     != SV5 )
                    | ~ ( in @ ( sK5_C @ SY15 @ SV5 ) @ SY15 ) )
                | ~ ( ( ( sK5_C @ SY15 @ SV5 )
                      = SV5 )
                    | ( in @ ( sK5_C @ SY15 @ SV5 ) @ SY15 ) ) )
            | ( SY15
              = ( singleton @ SV5 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[49]) ).

thf(55,plain,
    ! [SV6: $i] :
      ( ( ! [SY16: $i] :
            ( ( SY16
             != ( singleton @ SV6 ) )
            | ~ ( ~ ! [SY17: $i] :
                      ( ( SY17 != SV6 )
                      | ( in @ SY17 @ SY16 ) )
                | ~ ! [SY18: $i] :
                      ( ~ ( in @ SY18 @ SY16 )
                      | ( SY18 = SV6 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[50]) ).

thf(56,plain,
    ! [SV1: $i,SV2: $i] :
      ( ( ( in @ SV2 @ SV1 )
        = $false )
      | ( ( in @ SV1 @ SV2 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[51]) ).

thf(57,plain,
    ! [SV7: $i,SV3: $i] :
      ( ( ( ( set_difference @ ( singleton @ SV3 ) @ SV7 )
         != empty_set )
        | ( in @ SV3 @ SV7 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[52]) ).

thf(58,plain,
    ! [SV8: $i,SV4: $i] :
      ( ( ~ ( in @ SV4 @ SV8 )
        | ( ( set_difference @ ( singleton @ SV4 ) @ SV8 )
          = empty_set ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(59,plain,
    ! [SV5: $i,SV9: $i] :
      ( ( ~ ( ~ ( ( ( sK5_C @ SV9 @ SV5 )
                 != SV5 )
                | ~ ( in @ ( sK5_C @ SV9 @ SV5 ) @ SV9 ) )
            | ~ ( ( ( sK5_C @ SV9 @ SV5 )
                  = SV5 )
                | ( in @ ( sK5_C @ SV9 @ SV5 ) @ SV9 ) ) )
        | ( SV9
          = ( singleton @ SV5 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[54]) ).

thf(60,plain,
    ! [SV6: $i,SV10: $i] :
      ( ( ( SV10
         != ( singleton @ SV6 ) )
        | ~ ( ~ ! [SY19: $i] :
                  ( ( SY19 != SV6 )
                  | ( in @ SY19 @ SV10 ) )
            | ~ ! [SY20: $i] :
                  ( ~ ( in @ SY20 @ SV10 )
                  | ( SY20 = SV6 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[55]) ).

thf(61,plain,
    ! [SV7: $i,SV3: $i] :
      ( ( ( ( ( set_difference @ ( singleton @ SV3 ) @ SV7 )
           != empty_set ) )
        = $true )
      | ( ( in @ SV3 @ SV7 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[57]) ).

thf(62,plain,
    ! [SV8: $i,SV4: $i] :
      ( ( ( ~ ( in @ SV4 @ SV8 ) )
        = $true )
      | ( ( ( set_difference @ ( singleton @ SV4 ) @ SV8 )
          = empty_set )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[58]) ).

thf(63,plain,
    ! [SV5: $i,SV9: $i] :
      ( ( ( ~ ( ~ ( ( ( sK5_C @ SV9 @ SV5 )
                   != SV5 )
                  | ~ ( in @ ( sK5_C @ SV9 @ SV5 ) @ SV9 ) )
              | ~ ( ( ( sK5_C @ SV9 @ SV5 )
                    = SV5 )
                  | ( in @ ( sK5_C @ SV9 @ SV5 ) @ SV9 ) ) ) )
        = $true )
      | ( ( SV9
          = ( singleton @ SV5 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[59]) ).

thf(64,plain,
    ! [SV6: $i,SV10: $i] :
      ( ( ( ( SV10
           != ( singleton @ SV6 ) ) )
        = $true )
      | ( ( ~ ( ~ ! [SY19: $i] :
                    ( ( SY19 != SV6 )
                    | ( in @ SY19 @ SV10 ) )
              | ~ ! [SY20: $i] :
                    ( ~ ( in @ SY20 @ SV10 )
                    | ( SY20 = SV6 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[60]) ).

thf(65,plain,
    ! [SV7: $i,SV3: $i] :
      ( ( ( ( set_difference @ ( singleton @ SV3 ) @ SV7 )
          = empty_set )
        = $false )
      | ( ( in @ SV3 @ SV7 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[61]) ).

thf(66,plain,
    ! [SV8: $i,SV4: $i] :
      ( ( ( in @ SV4 @ SV8 )
        = $false )
      | ( ( ( set_difference @ ( singleton @ SV4 ) @ SV8 )
          = empty_set )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[62]) ).

thf(67,plain,
    ! [SV5: $i,SV9: $i] :
      ( ( ( ~ ( ( ( sK5_C @ SV9 @ SV5 )
               != SV5 )
              | ~ ( in @ ( sK5_C @ SV9 @ SV5 ) @ SV9 ) )
          | ~ ( ( ( sK5_C @ SV9 @ SV5 )
                = SV5 )
              | ( in @ ( sK5_C @ SV9 @ SV5 ) @ SV9 ) ) )
        = $false )
      | ( ( SV9
          = ( singleton @ SV5 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[63]) ).

thf(68,plain,
    ! [SV6: $i,SV10: $i] :
      ( ( ( SV10
          = ( singleton @ SV6 ) )
        = $false )
      | ( ( ~ ( ~ ! [SY19: $i] :
                    ( ( SY19 != SV6 )
                    | ( in @ SY19 @ SV10 ) )
              | ~ ! [SY20: $i] :
                    ( ~ ( in @ SY20 @ SV10 )
                    | ( SY20 = SV6 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[64]) ).

thf(69,plain,
    ! [SV5: $i,SV9: $i] :
      ( ( ( ~ ( ( ( sK5_C @ SV9 @ SV5 )
               != SV5 )
              | ~ ( in @ ( sK5_C @ SV9 @ SV5 ) @ SV9 ) ) )
        = $false )
      | ( ( SV9
          = ( singleton @ SV5 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[67]) ).

thf(70,plain,
    ! [SV5: $i,SV9: $i] :
      ( ( ( ~ ( ( ( sK5_C @ SV9 @ SV5 )
                = SV5 )
              | ( in @ ( sK5_C @ SV9 @ SV5 ) @ SV9 ) ) )
        = $false )
      | ( ( SV9
          = ( singleton @ SV5 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[67]) ).

thf(71,plain,
    ! [SV10: $i,SV6: $i] :
      ( ( ( ~ ! [SY19: $i] :
                ( ( SY19 != SV6 )
                | ( in @ SY19 @ SV10 ) )
          | ~ ! [SY20: $i] :
                ( ~ ( in @ SY20 @ SV10 )
                | ( SY20 = SV6 ) ) )
        = $false )
      | ( ( SV10
          = ( singleton @ SV6 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[68]) ).

thf(72,plain,
    ! [SV5: $i,SV9: $i] :
      ( ( ( ( ( sK5_C @ SV9 @ SV5 )
           != SV5 )
          | ~ ( in @ ( sK5_C @ SV9 @ SV5 ) @ SV9 ) )
        = $true )
      | ( ( SV9
          = ( singleton @ SV5 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[69]) ).

thf(73,plain,
    ! [SV5: $i,SV9: $i] :
      ( ( ( ( ( sK5_C @ SV9 @ SV5 )
            = SV5 )
          | ( in @ ( sK5_C @ SV9 @ SV5 ) @ SV9 ) )
        = $true )
      | ( ( SV9
          = ( singleton @ SV5 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[70]) ).

thf(74,plain,
    ! [SV10: $i,SV6: $i] :
      ( ( ( ~ ! [SY19: $i] :
                ( ( SY19 != SV6 )
                | ( in @ SY19 @ SV10 ) ) )
        = $false )
      | ( ( SV10
          = ( singleton @ SV6 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[71]) ).

thf(75,plain,
    ! [SV6: $i,SV10: $i] :
      ( ( ( ~ ! [SY20: $i] :
                ( ~ ( in @ SY20 @ SV10 )
                | ( SY20 = SV6 ) ) )
        = $false )
      | ( ( SV10
          = ( singleton @ SV6 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[71]) ).

thf(76,plain,
    ! [SV5: $i,SV9: $i] :
      ( ( ( ( ( sK5_C @ SV9 @ SV5 )
           != SV5 ) )
        = $true )
      | ( ( ~ ( in @ ( sK5_C @ SV9 @ SV5 ) @ SV9 ) )
        = $true )
      | ( ( SV9
          = ( singleton @ SV5 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[72]) ).

thf(77,plain,
    ! [SV5: $i,SV9: $i] :
      ( ( ( ( sK5_C @ SV9 @ SV5 )
          = SV5 )
        = $true )
      | ( ( in @ ( sK5_C @ SV9 @ SV5 ) @ SV9 )
        = $true )
      | ( ( SV9
          = ( singleton @ SV5 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[73]) ).

thf(78,plain,
    ! [SV10: $i,SV6: $i] :
      ( ( ( ! [SY19: $i] :
              ( ( SY19 != SV6 )
              | ( in @ SY19 @ SV10 ) ) )
        = $true )
      | ( ( SV10
          = ( singleton @ SV6 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[74]) ).

thf(79,plain,
    ! [SV6: $i,SV10: $i] :
      ( ( ( ! [SY20: $i] :
              ( ~ ( in @ SY20 @ SV10 )
              | ( SY20 = SV6 ) ) )
        = $true )
      | ( ( SV10
          = ( singleton @ SV6 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[75]) ).

thf(80,plain,
    ! [SV5: $i,SV9: $i] :
      ( ( ( ( sK5_C @ SV9 @ SV5 )
          = SV5 )
        = $false )
      | ( ( ~ ( in @ ( sK5_C @ SV9 @ SV5 ) @ SV9 ) )
        = $true )
      | ( ( SV9
          = ( singleton @ SV5 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[76]) ).

thf(81,plain,
    ! [SV10: $i,SV6: $i,SV11: $i] :
      ( ( ( ( SV11 != SV6 )
          | ( in @ SV11 @ SV10 ) )
        = $true )
      | ( ( SV10
          = ( singleton @ SV6 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[78]) ).

thf(82,plain,
    ! [SV6: $i,SV10: $i,SV12: $i] :
      ( ( ( ~ ( in @ SV12 @ SV10 )
          | ( SV12 = SV6 ) )
        = $true )
      | ( ( SV10
          = ( singleton @ SV6 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[79]) ).

thf(83,plain,
    ! [SV5: $i,SV9: $i] :
      ( ( ( in @ ( sK5_C @ SV9 @ SV5 ) @ SV9 )
        = $false )
      | ( ( ( sK5_C @ SV9 @ SV5 )
          = SV5 )
        = $false )
      | ( ( SV9
          = ( singleton @ SV5 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[80]) ).

thf(84,plain,
    ! [SV10: $i,SV6: $i,SV11: $i] :
      ( ( ( ( SV11 != SV6 ) )
        = $true )
      | ( ( in @ SV11 @ SV10 )
        = $true )
      | ( ( SV10
          = ( singleton @ SV6 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[81]) ).

thf(85,plain,
    ! [SV6: $i,SV10: $i,SV12: $i] :
      ( ( ( ~ ( in @ SV12 @ SV10 ) )
        = $true )
      | ( ( SV12 = SV6 )
        = $true )
      | ( ( SV10
          = ( singleton @ SV6 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[82]) ).

thf(86,plain,
    ! [SV10: $i,SV6: $i,SV11: $i] :
      ( ( ( SV11 = SV6 )
        = $false )
      | ( ( in @ SV11 @ SV10 )
        = $true )
      | ( ( SV10
          = ( singleton @ SV6 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[84]) ).

thf(87,plain,
    ! [SV6: $i,SV10: $i,SV12: $i] :
      ( ( ( in @ SV12 @ SV10 )
        = $false )
      | ( ( SV12 = SV6 )
        = $true )
      | ( ( SV10
          = ( singleton @ SV6 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[85]) ).

thf(88,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[28,87,86,83,77,66,65,56,38,37,32,30]) ).

thf(89,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[88]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET880+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n029.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sun Jul 10 04:07:01 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  
% 0.12/0.34   No.of.Axioms: 6
% 0.12/0.34  
% 0.12/0.34   Length.of.Defs: 0
% 0.12/0.34  
% 0.12/0.34   Contains.Choice.Funs: false
% 0.12/0.34  (rf:0,axioms:6,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:8,loop_count:0,foatp_calls:0,translation:fof_full).....
% 0.19/0.39  
% 0.19/0.39  ********************************
% 0.19/0.39  *   All subproblems solved!    *
% 0.19/0.39  ********************************
% 0.19/0.39  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:7,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:88,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: 89 ****
% 0.19/0.40  %**** clause counter: 88 ****
% 0.19/0.40  
% 0.19/0.40  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:7,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:88,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------