TSTP Solution File: SET947+1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SET947+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 : 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 03:06:29 EDT 2022

% Result   : Theorem 0.21s 0.43s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   18
% Syntax   : Number of formulae    :  113 (  59 unt;  10 typ;   0 def)
%            Number of atoms       :  595 ( 185 equ;   0 cnn)
%            Maximal formula atoms :    3 (   5 avg)
%            Number of connectives : 1163 ( 215   ~; 182   |;  10   &; 744   @)
%                                         (   6 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   5 con; 0-2 aty)
%            Number of variables   :  239 (   0   ^ 235   !;   4   ?; 239   :)

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

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

thf(tp_powerset,type,
    powerset: $i > $i ).

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

thf(tp_sK2_A,type,
    sK2_A: $i ).

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

thf(tp_sK4_C,type,
    sK4_C: $i > $i > $i ).

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

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

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

thf(1,axiom,
    ! [A: $i,B: $i] : ( subset @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

thf(2,axiom,
    ? [A: $i] :
      ~ ( empty @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).

thf(3,axiom,
    ? [A: $i] : ( empty @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ( subset @ A @ ( union @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ( ( subset @ A @ B )
    <=> ! [C: $i] :
          ( ( in @ C @ A )
         => ( in @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

thf(6,axiom,
    ! [A: $i,B: $i] :
      ( ( B
        = ( powerset @ A ) )
    <=> ! [C: $i] :
          ( ( in @ C @ B )
        <=> ( subset @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).

thf(7,axiom,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ~ ( in @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(8,conjecture,
    ! [A: $i] : ( subset @ A @ ( powerset @ ( union @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_zfmisc_1) ).

thf(9,negated_conjecture,
    ( ( ! [A: $i] : ( subset @ A @ ( powerset @ ( union @ A ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[8]) ).

thf(10,plain,
    ( ( ! [A: $i] : ( subset @ A @ ( powerset @ ( union @ A ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(11,plain,
    ( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(12,plain,
    ( ( ? [A: $i] :
          ~ ( empty @ A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(13,plain,
    ( ( ? [A: $i] : ( empty @ A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(14,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( in @ A @ B )
         => ( subset @ A @ ( union @ B ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(15,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( subset @ A @ B )
        <=> ! [C: $i] :
              ( ( in @ C @ A )
             => ( in @ C @ B ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(16,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( B
            = ( powerset @ A ) )
        <=> ! [C: $i] :
              ( ( in @ C @ B )
            <=> ( subset @ C @ A ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(17,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( in @ A @ B )
         => ~ ( in @ B @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(18,plain,
    ( ( subset @ sK1_A @ ( powerset @ ( union @ sK1_A ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[10]) ).

thf(19,plain,
    ( ( ~ ( subset @ sK1_A @ ( powerset @ ( union @ sK1_A ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[18]) ).

thf(20,plain,
    ( ( ! [A: $i] : ( subset @ A @ A ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[11]) ).

thf(21,plain,
    ( ( ~ ( empty @ sK2_A ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[12]) ).

thf(22,plain,
    ( ( empty @ sK3_A )
    = $true ),
    inference(extcnf_combined,[status(esa)],[13]) ).

thf(23,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( in @ A @ B )
          | ( subset @ A @ ( union @ B ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[14]) ).

thf(24,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( in @ ( sK4_C @ B @ A ) @ A )
            & ~ ( in @ ( sK4_C @ B @ A ) @ B ) )
          | ( subset @ A @ B ) )
      & ! [A: $i,B: $i] :
          ( ~ ( subset @ A @ B )
          | ! [C: $i] :
              ( ~ ( in @ C @ A )
              | ( in @ C @ B ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[15]) ).

thf(25,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( ~ ( in @ ( sK5_C @ B @ A ) @ B )
              | ~ ( subset @ ( sK5_C @ B @ A ) @ A ) )
            & ( ( in @ ( sK5_C @ B @ A ) @ B )
              | ( subset @ ( sK5_C @ B @ A ) @ A ) ) )
          | ( B
            = ( powerset @ A ) ) )
      & ! [A: $i,B: $i] :
          ( ( B
           != ( powerset @ A ) )
          | ( ! [C: $i] :
                ( ~ ( in @ C @ B )
                | ( subset @ C @ A ) )
            & ! [C: $i] :
                ( ~ ( subset @ C @ A )
                | ( in @ C @ B ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[16]) ).

thf(26,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( in @ A @ B )
          | ~ ( in @ B @ A ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[17]) ).

thf(27,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( in @ A @ B )
          | ~ ( in @ B @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[26]) ).

thf(28,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( ~ ( in @ ( sK5_C @ B @ A ) @ B )
              | ~ ( subset @ ( sK5_C @ B @ A ) @ A ) )
            & ( ( in @ ( sK5_C @ B @ A ) @ B )
              | ( subset @ ( sK5_C @ B @ A ) @ A ) ) )
          | ( B
            = ( powerset @ A ) ) )
      & ! [A: $i,B: $i] :
          ( ( B
           != ( powerset @ A ) )
          | ( ! [C: $i] :
                ( ~ ( in @ C @ B )
                | ( subset @ C @ A ) )
            & ! [C: $i] :
                ( ~ ( subset @ C @ A )
                | ( in @ C @ B ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(29,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( in @ ( sK4_C @ B @ A ) @ A )
            & ~ ( in @ ( sK4_C @ B @ A ) @ B ) )
          | ( subset @ A @ B ) )
      & ! [A: $i,B: $i] :
          ( ~ ( subset @ A @ B )
          | ! [C: $i] :
              ( ~ ( in @ C @ A )
              | ( in @ C @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(30,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( in @ A @ B )
          | ( subset @ A @ ( union @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

thf(31,plain,
    ( ( empty @ sK3_A )
    = $true ),
    inference(copy,[status(thm)],[22]) ).

thf(32,plain,
    ( ( ~ ( empty @ sK2_A ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(33,plain,
    ( ( ! [A: $i] : ( subset @ A @ A ) )
    = $true ),
    inference(copy,[status(thm)],[20]) ).

thf(34,plain,
    ( ( ~ ( subset @ sK1_A @ ( powerset @ ( union @ sK1_A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[19]) ).

thf(35,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( ~ ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX0 )
                    | ~ ~ ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX1 ) )
                | ( subset @ SX0 @ SX1 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( subset @ SX0 @ SX1 )
                | ! [SX2: $i] :
                    ( ~ ( in @ SX2 @ SX0 )
                    | ( in @ SX2 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[29]) ).

thf(36,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( ~ ( ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 )
                        | ~ ( subset @ ( sK5_C @ SX1 @ SX0 ) @ SX0 ) )
                    | ~ ( ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 )
                        | ( subset @ ( sK5_C @ SX1 @ SX0 ) @ SX0 ) ) )
                | ( SX1
                  = ( powerset @ SX0 ) ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ( SX1
                 != ( powerset @ SX0 ) )
                | ~ ( ~ ! [SX2: $i] :
                          ( ~ ( in @ SX2 @ SX1 )
                          | ( subset @ SX2 @ SX0 ) )
                    | ~ ! [SX2: $i] :
                          ( ~ ( subset @ SX2 @ SX0 )
                          | ( in @ SX2 @ SX1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[28]) ).

thf(37,plain,
    ! [SV1: $i] :
      ( ( ! [SY15: $i] :
            ( ~ ( in @ SV1 @ SY15 )
            | ~ ( in @ SY15 @ SV1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[27]) ).

thf(38,plain,
    ! [SV2: $i] :
      ( ( ! [SY16: $i] :
            ( ~ ( in @ SV2 @ SY16 )
            | ( subset @ SV2 @ ( union @ SY16 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[30]) ).

thf(39,plain,
    ( ( empty @ sK2_A )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[32]) ).

thf(40,plain,
    ! [SV3: $i] :
      ( ( subset @ SV3 @ SV3 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[33]) ).

thf(41,plain,
    ( ( subset @ sK1_A @ ( powerset @ ( union @ sK1_A ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[34]) ).

thf(42,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( ~ ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX0 )
                | ~ ~ ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX1 ) )
            | ( subset @ SX0 @ SX1 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( subset @ SX0 @ SX1 )
            | ! [SX2: $i] :
                ( ~ ( in @ SX2 @ SX0 )
                | ( in @ SX2 @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[35]) ).

thf(43,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( ~ ( ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 )
                    | ~ ( subset @ ( sK5_C @ SX1 @ SX0 ) @ SX0 ) )
                | ~ ( ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 )
                    | ( subset @ ( sK5_C @ SX1 @ SX0 ) @ SX0 ) ) )
            | ( SX1
              = ( powerset @ SX0 ) ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ( SX1
             != ( powerset @ SX0 ) )
            | ~ ( ~ ! [SX2: $i] :
                      ( ~ ( in @ SX2 @ SX1 )
                      | ( subset @ SX2 @ SX0 ) )
                | ~ ! [SX2: $i] :
                      ( ~ ( subset @ SX2 @ SX0 )
                      | ( in @ SX2 @ SX1 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[36]) ).

thf(44,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ~ ( in @ SV1 @ SV4 )
        | ~ ( in @ SV4 @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[37]) ).

thf(45,plain,
    ! [SV5: $i,SV2: $i] :
      ( ( ~ ( in @ SV2 @ SV5 )
        | ( subset @ SV2 @ ( union @ SV5 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[38]) ).

thf(46,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( ~ ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX0 )
                | ~ ~ ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX1 ) )
            | ( subset @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[42]) ).

thf(47,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( subset @ SX0 @ SX1 )
            | ! [SX2: $i] :
                ( ~ ( in @ SX2 @ SX0 )
                | ( in @ SX2 @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[42]) ).

thf(48,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( ~ ( ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 )
                    | ~ ( subset @ ( sK5_C @ SX1 @ SX0 ) @ SX0 ) )
                | ~ ( ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 )
                    | ( subset @ ( sK5_C @ SX1 @ SX0 ) @ SX0 ) ) )
            | ( SX1
              = ( powerset @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[43]) ).

thf(49,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( SX1
             != ( powerset @ SX0 ) )
            | ~ ( ~ ! [SX2: $i] :
                      ( ~ ( in @ SX2 @ SX1 )
                      | ( subset @ SX2 @ SX0 ) )
                | ~ ! [SX2: $i] :
                      ( ~ ( subset @ SX2 @ SX0 )
                      | ( in @ SX2 @ SX1 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[43]) ).

thf(50,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ( ~ ( in @ SV1 @ SV4 ) )
        = $true )
      | ( ( ~ ( in @ SV4 @ SV1 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[44]) ).

thf(51,plain,
    ! [SV5: $i,SV2: $i] :
      ( ( ( ~ ( in @ SV2 @ SV5 ) )
        = $true )
      | ( ( subset @ SV2 @ ( union @ SV5 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[45]) ).

thf(52,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( ~ ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX0 )
              | ~ ~ ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX1 ) )
          | ( subset @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[46]) ).

thf(53,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( subset @ SX0 @ SX1 )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ SX0 )
              | ( in @ SX2 @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[47]) ).

thf(54,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( ~ ( ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 )
                  | ~ ( subset @ ( sK5_C @ SX1 @ SX0 ) @ SX0 ) )
              | ~ ( ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 )
                  | ( subset @ ( sK5_C @ SX1 @ SX0 ) @ SX0 ) ) )
          | ( SX1
            = ( powerset @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[48]) ).

thf(55,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX1
           != ( powerset @ SX0 ) )
          | ~ ( ~ ! [SX2: $i] :
                    ( ~ ( in @ SX2 @ SX1 )
                    | ( subset @ SX2 @ SX0 ) )
              | ~ ! [SX2: $i] :
                    ( ~ ( subset @ SX2 @ SX0 )
                    | ( in @ SX2 @ SX1 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[49]) ).

thf(56,plain,
    ! [SV4: $i,SV1: $i] :
      ( ( ( in @ SV1 @ SV4 )
        = $false )
      | ( ( ~ ( in @ SV4 @ SV1 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[50]) ).

thf(57,plain,
    ! [SV5: $i,SV2: $i] :
      ( ( ( in @ SV2 @ SV5 )
        = $false )
      | ( ( subset @ SV2 @ ( union @ SV5 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[51]) ).

thf(58,plain,
    ! [SV6: $i] :
      ( ( ! [SY17: $i] :
            ( ~ ( ~ ( in @ ( sK4_C @ SY17 @ SV6 ) @ SV6 )
                | ~ ~ ( in @ ( sK4_C @ SY17 @ SV6 ) @ SY17 ) )
            | ( subset @ SV6 @ SY17 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[52]) ).

thf(59,plain,
    ! [SV7: $i] :
      ( ( ! [SY18: $i] :
            ( ~ ( subset @ SV7 @ SY18 )
            | ! [SY19: $i] :
                ( ~ ( in @ SY19 @ SV7 )
                | ( in @ SY19 @ SY18 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(60,plain,
    ! [SV8: $i] :
      ( ( ! [SY20: $i] :
            ( ~ ( ~ ( ~ ( in @ ( sK5_C @ SY20 @ SV8 ) @ SY20 )
                    | ~ ( subset @ ( sK5_C @ SY20 @ SV8 ) @ SV8 ) )
                | ~ ( ( in @ ( sK5_C @ SY20 @ SV8 ) @ SY20 )
                    | ( subset @ ( sK5_C @ SY20 @ SV8 ) @ SV8 ) ) )
            | ( SY20
              = ( powerset @ SV8 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[54]) ).

thf(61,plain,
    ! [SV9: $i] :
      ( ( ! [SY21: $i] :
            ( ( SY21
             != ( powerset @ SV9 ) )
            | ~ ( ~ ! [SY22: $i] :
                      ( ~ ( in @ SY22 @ SY21 )
                      | ( subset @ SY22 @ SV9 ) )
                | ~ ! [SY23: $i] :
                      ( ~ ( subset @ SY23 @ SV9 )
                      | ( in @ SY23 @ SY21 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[55]) ).

thf(62,plain,
    ! [SV1: $i,SV4: $i] :
      ( ( ( in @ SV4 @ SV1 )
        = $false )
      | ( ( in @ SV1 @ SV4 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[56]) ).

thf(63,plain,
    ! [SV6: $i,SV10: $i] :
      ( ( ~ ( ~ ( in @ ( sK4_C @ SV10 @ SV6 ) @ SV6 )
            | ~ ~ ( in @ ( sK4_C @ SV10 @ SV6 ) @ SV10 ) )
        | ( subset @ SV6 @ SV10 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[58]) ).

thf(64,plain,
    ! [SV11: $i,SV7: $i] :
      ( ( ~ ( subset @ SV7 @ SV11 )
        | ! [SY24: $i] :
            ( ~ ( in @ SY24 @ SV7 )
            | ( in @ SY24 @ SV11 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[59]) ).

thf(65,plain,
    ! [SV8: $i,SV12: $i] :
      ( ( ~ ( ~ ( ~ ( in @ ( sK5_C @ SV12 @ SV8 ) @ SV12 )
                | ~ ( subset @ ( sK5_C @ SV12 @ SV8 ) @ SV8 ) )
            | ~ ( ( in @ ( sK5_C @ SV12 @ SV8 ) @ SV12 )
                | ( subset @ ( sK5_C @ SV12 @ SV8 ) @ SV8 ) ) )
        | ( SV12
          = ( powerset @ SV8 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[60]) ).

thf(66,plain,
    ! [SV9: $i,SV13: $i] :
      ( ( ( SV13
         != ( powerset @ SV9 ) )
        | ~ ( ~ ! [SY25: $i] :
                  ( ~ ( in @ SY25 @ SV13 )
                  | ( subset @ SY25 @ SV9 ) )
            | ~ ! [SY26: $i] :
                  ( ~ ( subset @ SY26 @ SV9 )
                  | ( in @ SY26 @ SV13 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[61]) ).

thf(67,plain,
    ! [SV6: $i,SV10: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK4_C @ SV10 @ SV6 ) @ SV6 )
              | ~ ~ ( in @ ( sK4_C @ SV10 @ SV6 ) @ SV10 ) ) )
        = $true )
      | ( ( subset @ SV6 @ SV10 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[63]) ).

thf(68,plain,
    ! [SV11: $i,SV7: $i] :
      ( ( ( ~ ( subset @ SV7 @ SV11 ) )
        = $true )
      | ( ( ! [SY24: $i] :
              ( ~ ( in @ SY24 @ SV7 )
              | ( in @ SY24 @ SV11 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[64]) ).

thf(69,plain,
    ! [SV8: $i,SV12: $i] :
      ( ( ( ~ ( ~ ( ~ ( in @ ( sK5_C @ SV12 @ SV8 ) @ SV12 )
                  | ~ ( subset @ ( sK5_C @ SV12 @ SV8 ) @ SV8 ) )
              | ~ ( ( in @ ( sK5_C @ SV12 @ SV8 ) @ SV12 )
                  | ( subset @ ( sK5_C @ SV12 @ SV8 ) @ SV8 ) ) ) )
        = $true )
      | ( ( SV12
          = ( powerset @ SV8 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[65]) ).

thf(70,plain,
    ! [SV9: $i,SV13: $i] :
      ( ( ( ( SV13
           != ( powerset @ SV9 ) ) )
        = $true )
      | ( ( ~ ( ~ ! [SY25: $i] :
                    ( ~ ( in @ SY25 @ SV13 )
                    | ( subset @ SY25 @ SV9 ) )
              | ~ ! [SY26: $i] :
                    ( ~ ( subset @ SY26 @ SV9 )
                    | ( in @ SY26 @ SV13 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[66]) ).

thf(71,plain,
    ! [SV6: $i,SV10: $i] :
      ( ( ( ~ ( in @ ( sK4_C @ SV10 @ SV6 ) @ SV6 )
          | ~ ~ ( in @ ( sK4_C @ SV10 @ SV6 ) @ SV10 ) )
        = $false )
      | ( ( subset @ SV6 @ SV10 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[67]) ).

thf(72,plain,
    ! [SV11: $i,SV7: $i] :
      ( ( ( subset @ SV7 @ SV11 )
        = $false )
      | ( ( ! [SY24: $i] :
              ( ~ ( in @ SY24 @ SV7 )
              | ( in @ SY24 @ SV11 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[68]) ).

thf(73,plain,
    ! [SV8: $i,SV12: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK5_C @ SV12 @ SV8 ) @ SV12 )
              | ~ ( subset @ ( sK5_C @ SV12 @ SV8 ) @ SV8 ) )
          | ~ ( ( in @ ( sK5_C @ SV12 @ SV8 ) @ SV12 )
              | ( subset @ ( sK5_C @ SV12 @ SV8 ) @ SV8 ) ) )
        = $false )
      | ( ( SV12
          = ( powerset @ SV8 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[69]) ).

thf(74,plain,
    ! [SV9: $i,SV13: $i] :
      ( ( ( SV13
          = ( powerset @ SV9 ) )
        = $false )
      | ( ( ~ ( ~ ! [SY25: $i] :
                    ( ~ ( in @ SY25 @ SV13 )
                    | ( subset @ SY25 @ SV9 ) )
              | ~ ! [SY26: $i] :
                    ( ~ ( subset @ SY26 @ SV9 )
                    | ( in @ SY26 @ SV13 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[70]) ).

thf(75,plain,
    ! [SV6: $i,SV10: $i] :
      ( ( ( ~ ( in @ ( sK4_C @ SV10 @ SV6 ) @ SV6 ) )
        = $false )
      | ( ( subset @ SV6 @ SV10 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[71]) ).

thf(76,plain,
    ! [SV6: $i,SV10: $i] :
      ( ( ( ~ ~ ( in @ ( sK4_C @ SV10 @ SV6 ) @ SV10 ) )
        = $false )
      | ( ( subset @ SV6 @ SV10 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[71]) ).

thf(77,plain,
    ! [SV11: $i,SV7: $i,SV14: $i] :
      ( ( ( ~ ( in @ SV14 @ SV7 )
          | ( in @ SV14 @ SV11 ) )
        = $true )
      | ( ( subset @ SV7 @ SV11 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[72]) ).

thf(78,plain,
    ! [SV8: $i,SV12: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK5_C @ SV12 @ SV8 ) @ SV12 )
              | ~ ( subset @ ( sK5_C @ SV12 @ SV8 ) @ SV8 ) ) )
        = $false )
      | ( ( SV12
          = ( powerset @ SV8 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[73]) ).

thf(79,plain,
    ! [SV8: $i,SV12: $i] :
      ( ( ( ~ ( ( in @ ( sK5_C @ SV12 @ SV8 ) @ SV12 )
              | ( subset @ ( sK5_C @ SV12 @ SV8 ) @ SV8 ) ) )
        = $false )
      | ( ( SV12
          = ( powerset @ SV8 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[73]) ).

thf(80,plain,
    ! [SV9: $i,SV13: $i] :
      ( ( ( ~ ! [SY25: $i] :
                ( ~ ( in @ SY25 @ SV13 )
                | ( subset @ SY25 @ SV9 ) )
          | ~ ! [SY26: $i] :
                ( ~ ( subset @ SY26 @ SV9 )
                | ( in @ SY26 @ SV13 ) ) )
        = $false )
      | ( ( SV13
          = ( powerset @ SV9 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[74]) ).

thf(81,plain,
    ! [SV6: $i,SV10: $i] :
      ( ( ( in @ ( sK4_C @ SV10 @ SV6 ) @ SV6 )
        = $true )
      | ( ( subset @ SV6 @ SV10 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[75]) ).

thf(82,plain,
    ! [SV6: $i,SV10: $i] :
      ( ( ( ~ ( in @ ( sK4_C @ SV10 @ SV6 ) @ SV10 ) )
        = $true )
      | ( ( subset @ SV6 @ SV10 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[76]) ).

thf(83,plain,
    ! [SV11: $i,SV7: $i,SV14: $i] :
      ( ( ( ~ ( in @ SV14 @ SV7 ) )
        = $true )
      | ( ( in @ SV14 @ SV11 )
        = $true )
      | ( ( subset @ SV7 @ SV11 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[77]) ).

thf(84,plain,
    ! [SV8: $i,SV12: $i] :
      ( ( ( ~ ( in @ ( sK5_C @ SV12 @ SV8 ) @ SV12 )
          | ~ ( subset @ ( sK5_C @ SV12 @ SV8 ) @ SV8 ) )
        = $true )
      | ( ( SV12
          = ( powerset @ SV8 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[78]) ).

thf(85,plain,
    ! [SV8: $i,SV12: $i] :
      ( ( ( ( in @ ( sK5_C @ SV12 @ SV8 ) @ SV12 )
          | ( subset @ ( sK5_C @ SV12 @ SV8 ) @ SV8 ) )
        = $true )
      | ( ( SV12
          = ( powerset @ SV8 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[79]) ).

thf(86,plain,
    ! [SV9: $i,SV13: $i] :
      ( ( ( ~ ! [SY25: $i] :
                ( ~ ( in @ SY25 @ SV13 )
                | ( subset @ SY25 @ SV9 ) ) )
        = $false )
      | ( ( SV13
          = ( powerset @ SV9 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[80]) ).

thf(87,plain,
    ! [SV13: $i,SV9: $i] :
      ( ( ( ~ ! [SY26: $i] :
                ( ~ ( subset @ SY26 @ SV9 )
                | ( in @ SY26 @ SV13 ) ) )
        = $false )
      | ( ( SV13
          = ( powerset @ SV9 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[80]) ).

thf(88,plain,
    ! [SV6: $i,SV10: $i] :
      ( ( ( in @ ( sK4_C @ SV10 @ SV6 ) @ SV10 )
        = $false )
      | ( ( subset @ SV6 @ SV10 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[82]) ).

thf(89,plain,
    ! [SV11: $i,SV7: $i,SV14: $i] :
      ( ( ( in @ SV14 @ SV7 )
        = $false )
      | ( ( in @ SV14 @ SV11 )
        = $true )
      | ( ( subset @ SV7 @ SV11 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[83]) ).

thf(90,plain,
    ! [SV8: $i,SV12: $i] :
      ( ( ( ~ ( in @ ( sK5_C @ SV12 @ SV8 ) @ SV12 ) )
        = $true )
      | ( ( ~ ( subset @ ( sK5_C @ SV12 @ SV8 ) @ SV8 ) )
        = $true )
      | ( ( SV12
          = ( powerset @ SV8 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[84]) ).

thf(91,plain,
    ! [SV8: $i,SV12: $i] :
      ( ( ( in @ ( sK5_C @ SV12 @ SV8 ) @ SV12 )
        = $true )
      | ( ( subset @ ( sK5_C @ SV12 @ SV8 ) @ SV8 )
        = $true )
      | ( ( SV12
          = ( powerset @ SV8 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[85]) ).

thf(92,plain,
    ! [SV9: $i,SV13: $i] :
      ( ( ( ! [SY25: $i] :
              ( ~ ( in @ SY25 @ SV13 )
              | ( subset @ SY25 @ SV9 ) ) )
        = $true )
      | ( ( SV13
          = ( powerset @ SV9 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[86]) ).

thf(93,plain,
    ! [SV13: $i,SV9: $i] :
      ( ( ( ! [SY26: $i] :
              ( ~ ( subset @ SY26 @ SV9 )
              | ( in @ SY26 @ SV13 ) ) )
        = $true )
      | ( ( SV13
          = ( powerset @ SV9 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[87]) ).

thf(94,plain,
    ! [SV8: $i,SV12: $i] :
      ( ( ( in @ ( sK5_C @ SV12 @ SV8 ) @ SV12 )
        = $false )
      | ( ( ~ ( subset @ ( sK5_C @ SV12 @ SV8 ) @ SV8 ) )
        = $true )
      | ( ( SV12
          = ( powerset @ SV8 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[90]) ).

thf(95,plain,
    ! [SV9: $i,SV13: $i,SV15: $i] :
      ( ( ( ~ ( in @ SV15 @ SV13 )
          | ( subset @ SV15 @ SV9 ) )
        = $true )
      | ( ( SV13
          = ( powerset @ SV9 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[92]) ).

thf(96,plain,
    ! [SV13: $i,SV9: $i,SV16: $i] :
      ( ( ( ~ ( subset @ SV16 @ SV9 )
          | ( in @ SV16 @ SV13 ) )
        = $true )
      | ( ( SV13
          = ( powerset @ SV9 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[93]) ).

thf(97,plain,
    ! [SV8: $i,SV12: $i] :
      ( ( ( subset @ ( sK5_C @ SV12 @ SV8 ) @ SV8 )
        = $false )
      | ( ( in @ ( sK5_C @ SV12 @ SV8 ) @ SV12 )
        = $false )
      | ( ( SV12
          = ( powerset @ SV8 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[94]) ).

thf(98,plain,
    ! [SV9: $i,SV13: $i,SV15: $i] :
      ( ( ( ~ ( in @ SV15 @ SV13 ) )
        = $true )
      | ( ( subset @ SV15 @ SV9 )
        = $true )
      | ( ( SV13
          = ( powerset @ SV9 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[95]) ).

thf(99,plain,
    ! [SV13: $i,SV9: $i,SV16: $i] :
      ( ( ( ~ ( subset @ SV16 @ SV9 ) )
        = $true )
      | ( ( in @ SV16 @ SV13 )
        = $true )
      | ( ( SV13
          = ( powerset @ SV9 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[96]) ).

thf(100,plain,
    ! [SV9: $i,SV13: $i,SV15: $i] :
      ( ( ( in @ SV15 @ SV13 )
        = $false )
      | ( ( subset @ SV15 @ SV9 )
        = $true )
      | ( ( SV13
          = ( powerset @ SV9 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[98]) ).

thf(101,plain,
    ! [SV13: $i,SV9: $i,SV16: $i] :
      ( ( ( subset @ SV16 @ SV9 )
        = $false )
      | ( ( in @ SV16 @ SV13 )
        = $true )
      | ( ( SV13
          = ( powerset @ SV9 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[99]) ).

thf(102,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[31,101,100,97,91,89,88,81,62,57,41,40,39]) ).

thf(103,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[102]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET947+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34  % Computer : n026.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Mon Jul 11 01:29:11 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.35  
% 0.14/0.35   No.of.Axioms: 7
% 0.14/0.35  
% 0.14/0.35   Length.of.Defs: 0
% 0.14/0.35  
% 0.14/0.35   Contains.Choice.Funs: false
% 0.14/0.35  (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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:9,loop_count:0,foatp_calls:0,translation:fof_full)......
% 0.21/0.43  
% 0.21/0.43  ********************************
% 0.21/0.43  *   All subproblems solved!    *
% 0.21/0.43  ********************************
% 0.21/0.43  % 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:102,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.21/0.43  
% 0.21/0.43  %**** Beginning of derivation protocol ****
% 0.21/0.43  % SZS output start CNFRefutation
% See solution above
% 0.21/0.43  
% 0.21/0.43  %**** End of derivation protocol ****
% 0.21/0.43  %**** no. of clauses in derivation: 103 ****
% 0.21/0.43  %**** clause counter: 102 ****
% 0.21/0.43  
% 0.21/0.43  % 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:102,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------