TSTP Solution File: SEU332+1 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SEU332+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n024.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  : 300s
% DateTime : Fri May 19 11:58:20 EDT 2023

% Result   : Theorem 4.56s 2.37s
% Output   : Refutation 4.85s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   46
% Syntax   : Number of formulae    :   74 (   3 unt;  20 typ;   0 def)
%            Number of atoms       :  263 (  44 equ;   0 cnn)
%            Maximal formula atoms :   31 (   4 avg)
%            Number of connectives :  672 (  18   ~;   0   |; 109   &; 445   @)
%                                         (   3 <=>;  97  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   25 (  25   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   22 (  20 usr;   1 con; 0-2 aty)
%            Number of variables   :  151 (   0   ^; 115   !;  36   ?; 151   :)

% Comments : 
%------------------------------------------------------------------------------
thf(one_sorted_str_type,type,
    one_sorted_str: $i > $o ).

thf(element_type,type,
    element: $i > $i > $o ).

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

thf(the_carrier_type,type,
    the_carrier: $i > $i ).

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

thf(cartesian_product2_type,type,
    cartesian_product2: $i > $i > $i ).

thf(ordered_pair_type,type,
    ordered_pair: $i > $i > $i ).

thf(subset_complement_type,type,
    subset_complement: $i > $i > $i ).

thf(v2_membered_type,type,
    v2_membered: $i > $o ).

thf(v1_membered_type,type,
    v1_membered: $i > $o ).

thf(v4_membered_type,type,
    v4_membered: $i > $o ).

thf(v3_membered_type,type,
    v3_membered: $i > $o ).

thf(empty_type,type,
    empty: $i > $o ).

thf(v5_membered_type,type,
    v5_membered: $i > $o ).

thf(v1_xcmplx_0_type,type,
    v1_xcmplx_0: $i > $o ).

thf(relation_type,type,
    relation: $i > $o ).

thf(natural_type,type,
    natural: $i > $o ).

thf(v1_xreal_0_type,type,
    v1_xreal_0: $i > $o ).

thf(v1_int_1_type,type,
    v1_int_1: $i > $o ).

thf(v1_rat_1_type,type,
    v1_rat_1: $i > $o ).

thf(16,axiom,
    ! [A: $i] :
      ( ( v2_membered @ A )
     => ! [B: $i] :
          ( ( element @ B @ ( powerset @ A ) )
         => ( ( v1_membered @ B )
            & ( v2_membered @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc17_membered) ).

thf(88,plain,
    ! [A: $i] :
      ( ( v2_membered @ A )
     => ! [B: $i] :
          ( ( element @ B @ ( powerset @ A ) )
         => ( ( v1_membered @ B )
            & ( v2_membered @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(24,axiom,
    ! [A: $i] :
      ( ( v2_membered @ A )
     => ! [B: $i] :
          ( ( element @ B @ A )
         => ( ( v1_xcmplx_0 @ B )
            & ( v1_xreal_0 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc11_membered) ).

thf(116,plain,
    ! [A: $i] :
      ( ( v2_membered @ A )
     => ! [B: $i] :
          ( ( element @ B @ A )
         => ( ( v1_xcmplx_0 @ B )
            & ( v1_xreal_0 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(20,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( empty @ A )
        & ~ ( empty @ B ) )
     => ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).

thf(102,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( empty @ A )
        & ~ ( empty @ B ) )
     => ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(10,axiom,
    ! [A: $i] :
      ( ( v3_membered @ A )
     => ! [B: $i] :
          ( ( element @ B @ ( powerset @ A ) )
         => ( ( v1_membered @ B )
            & ( v2_membered @ B )
            & ( v3_membered @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc18_membered) ).

thf(73,plain,
    ! [A: $i] :
      ( ( v3_membered @ A )
     => ! [B: $i] :
          ( ( element @ B @ ( powerset @ A ) )
         => ( ( v1_membered @ B )
            & ( v2_membered @ B )
            & ( v3_membered @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(21,axiom,
    ! [A: $i,B: $i] :
      ( ( element @ B @ ( powerset @ A ) )
     => ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).

thf(104,plain,
    ! [A: $i,B: $i] :
      ( ( element @ B @ ( powerset @ A ) )
     => ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(25,axiom,
    ! [A: $i,B: $i] :
      ( ( ( one_sorted_str @ A )
        & ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
     => ! [C: $i] :
          ( ! [D: $i,E: $i,F: $i] :
              ( ( ( D = E )
                & ? [G: $i,H: $i] :
                    ( ( ( ordered_pair @ G @ H )
                      = E )
                    & ( in @ G @ B )
                    & ! [I: $i] :
                        ( ( element @ I @ ( powerset @ ( the_carrier @ A ) ) )
                       => ( ( I = G )
                         => ( H
                            = ( subset_complement @ ( the_carrier @ A ) @ I ) ) ) ) )
                & ( D = F )
                & ? [G: $i,H: $i] :
                    ( ( ( ordered_pair @ G @ H )
                      = F )
                    & ( in @ G @ B )
                    & ! [I: $i] :
                        ( ( element @ I @ ( powerset @ ( the_carrier @ A ) ) )
                       => ( ( I = G )
                         => ( H
                            = ( subset_complement @ ( the_carrier @ A ) @ I ) ) ) ) ) )
             => ( E = F ) )
         => ? [D: $i] :
            ! [E: $i] :
              ( ( in @ E @ D )
            <=> ? [F: $i] :
                  ( ( in @ F @ ( cartesian_product2 @ B @ C ) )
                  & ( F = E )
                  & ? [G: $i,H: $i] :
                      ( ( ( ordered_pair @ G @ H )
                        = E )
                      & ( in @ G @ B )
                      & ! [I: $i] :
                          ( ( element @ I @ ( powerset @ ( the_carrier @ A ) ) )
                         => ( ( I = G )
                           => ( H
                              = ( subset_complement @ ( the_carrier @ A ) @ I ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e4_7_2__tops_2__2) ).

thf(119,plain,
    ! [A: $i,B: $i] :
      ( ( ( one_sorted_str @ A )
        & ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
     => ! [C: $i] :
          ( ! [D: $i,E: $i,F: $i] :
              ( ( ( D = E )
                & ? [G: $i,H: $i] :
                    ( ( ( ordered_pair @ G @ H )
                      = E )
                    & ( in @ G @ B )
                    & ! [I: $i] :
                        ( ( element @ I @ ( powerset @ ( the_carrier @ A ) ) )
                       => ( ( I = G )
                         => ( H
                            = ( subset_complement @ ( the_carrier @ A ) @ I ) ) ) ) )
                & ( D = F )
                & ? [G: $i,H: $i] :
                    ( ( ( ordered_pair @ G @ H )
                      = F )
                    & ( in @ G @ B )
                    & ! [I: $i] :
                        ( ( element @ I @ ( powerset @ ( the_carrier @ A ) ) )
                       => ( ( I = G )
                         => ( H
                            = ( subset_complement @ ( the_carrier @ A ) @ I ) ) ) ) ) )
             => ( E = F ) )
         => ? [D: $i] :
            ! [E: $i] :
              ( ( ( in @ E @ D )
               => ? [F: $i] :
                    ( ( in @ F @ ( cartesian_product2 @ B @ C ) )
                    & ( F = E )
                    & ? [G: $i,H: $i] :
                        ( ( ( ordered_pair @ G @ H )
                          = E )
                        & ( in @ G @ B )
                        & ! [I: $i] :
                            ( ( element @ I @ ( powerset @ ( the_carrier @ A ) ) )
                           => ( ( I = G )
                             => ( H
                                = ( subset_complement @ ( the_carrier @ A ) @ I ) ) ) ) ) ) )
              & ( ? [F: $i] :
                    ( ( in @ F @ ( cartesian_product2 @ B @ C ) )
                    & ( F = E )
                    & ? [G: $i,H: $i] :
                        ( ( ( ordered_pair @ G @ H )
                          = E )
                        & ( in @ G @ B )
                        & ! [I: $i] :
                            ( ( element @ I @ ( powerset @ ( the_carrier @ A ) ) )
                           => ( ( I = G )
                             => ( H
                                = ( subset_complement @ ( the_carrier @ A ) @ I ) ) ) ) ) )
               => ( in @ E @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(5,axiom,
    ! [A: $i] :
      ( ( empty @ A )
     => ( ( v1_membered @ A )
        & ( v2_membered @ A )
        & ( v3_membered @ A )
        & ( v4_membered @ A )
        & ( v5_membered @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc15_membered) ).

thf(51,plain,
    ! [A: $i] :
      ( ( empty @ A )
     => ( ( v1_membered @ A )
        & ( v2_membered @ A )
        & ( v3_membered @ A )
        & ( v4_membered @ A )
        & ( v5_membered @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(14,axiom,
    ! [A: $i] :
      ( ~ ( empty @ A )
     => ? [B: $i] :
          ( ( element @ B @ ( powerset @ A ) )
          & ~ ( empty @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).

thf(83,plain,
    ! [A: $i] :
      ( ~ ( empty @ A )
     => ? [B: $i] :
          ( ( element @ B @ ( powerset @ A ) )
          & ~ ( empty @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(18,axiom,
    ! [A: $i] :
      ~ ( empty @ ( powerset @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).

thf(93,plain,
    ! [A: $i] :
      ~ ( empty @ ( powerset @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(6,axiom,
    ? [A: $i] :
      ( ~ ( empty @ A )
      & ( v1_membered @ A )
      & ( v2_membered @ A )
      & ( v3_membered @ A )
      & ( v4_membered @ A )
      & ( v5_membered @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_membered) ).

thf(57,plain,
    ? [A: $i] :
      ( ~ ( empty @ A )
      & ( v1_membered @ A )
      & ( v2_membered @ A )
      & ( v3_membered @ A )
      & ( v4_membered @ A )
      & ( v5_membered @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(1,conjecture,
    ! [A: $i,B: $i] :
      ( ( ( one_sorted_str @ A )
        & ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
     => ! [C: $i] :
        ? [D: $i] :
        ! [E: $i] :
          ( ( in @ E @ D )
        <=> ( ( in @ E @ ( cartesian_product2 @ B @ C ) )
            & ? [F: $i,G: $i] :
                ( ( ( ordered_pair @ F @ G )
                  = E )
                & ( in @ F @ B )
                & ! [H: $i] :
                    ( ( element @ H @ ( powerset @ ( the_carrier @ A ) ) )
                   => ( ( H = F )
                     => ( G
                        = ( subset_complement @ ( the_carrier @ A ) @ H ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e4_7_2__tops_2__1) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i] :
        ( ( ( one_sorted_str @ A )
          & ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
       => ! [C: $i] :
          ? [D: $i] :
          ! [E: $i] :
            ( ( in @ E @ D )
          <=> ( ( in @ E @ ( cartesian_product2 @ B @ C ) )
              & ? [F: $i,G: $i] :
                  ( ( ( ordered_pair @ F @ G )
                    = E )
                  & ( in @ F @ B )
                  & ! [H: $i] :
                      ( ( element @ H @ ( powerset @ ( the_carrier @ A ) ) )
                     => ( ( H = F )
                       => ( G
                          = ( subset_complement @ ( the_carrier @ A ) @ H ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(28,plain,
    ~ ! [A: $i,B: $i] :
        ( ( ( one_sorted_str @ A )
          & ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
       => ! [C: $i] :
          ? [D: $i] :
          ! [E: $i] :
            ( ( ( in @ E @ D )
             => ( ( in @ E @ ( cartesian_product2 @ B @ C ) )
                & ? [F: $i,G: $i] :
                    ( ( ( ordered_pair @ F @ G )
                      = E )
                    & ( in @ F @ B )
                    & ! [H: $i] :
                        ( ( element @ H @ ( powerset @ ( the_carrier @ A ) ) )
                       => ( ( H = F )
                         => ( G
                            = ( subset_complement @ ( the_carrier @ A ) @ H ) ) ) ) ) ) )
            & ( ( ( in @ E @ ( cartesian_product2 @ B @ C ) )
                & ? [F: $i,G: $i] :
                    ( ( ( ordered_pair @ F @ G )
                      = E )
                    & ( in @ F @ B )
                    & ! [H: $i] :
                        ( ( element @ H @ ( powerset @ ( the_carrier @ A ) ) )
                       => ( ( H = F )
                         => ( G
                            = ( subset_complement @ ( the_carrier @ A ) @ H ) ) ) ) ) )
             => ( in @ E @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(27,axiom,
    ! [A: $i] :
      ( ( v4_membered @ A )
     => ! [B: $i] :
          ( ( element @ B @ A )
         => ( ( v1_xcmplx_0 @ B )
            & ( v1_xreal_0 @ B )
            & ( v1_int_1 @ B )
            & ( v1_rat_1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc13_membered) ).

thf(165,plain,
    ! [A: $i] :
      ( ( v4_membered @ A )
     => ! [B: $i] :
          ( ( element @ B @ A )
         => ( ( v1_xcmplx_0 @ B )
            & ( v1_xreal_0 @ B )
            & ( v1_int_1 @ B )
            & ( v1_rat_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(11,axiom,
    ! [A: $i] :
      ( ( v1_membered @ A )
     => ! [B: $i] :
          ( ( element @ B @ A )
         => ( v1_xcmplx_0 @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc10_membered) ).

thf(77,plain,
    ! [A: $i] :
      ( ( v1_membered @ A )
     => ! [B: $i] :
          ( ( element @ B @ A )
         => ( v1_xcmplx_0 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(19,axiom,
    ! [A: $i] :
      ( ( v5_membered @ A )
     => ! [B: $i] :
          ( ( element @ B @ ( powerset @ A ) )
         => ( ( v1_membered @ B )
            & ( v2_membered @ B )
            & ( v3_membered @ B )
            & ( v4_membered @ B )
            & ( v5_membered @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc20_membered) ).

thf(96,plain,
    ! [A: $i] :
      ( ( v5_membered @ A )
     => ! [B: $i] :
          ( ( element @ B @ ( powerset @ A ) )
         => ( ( v1_membered @ B )
            & ( v2_membered @ B )
            & ( v3_membered @ B )
            & ( v4_membered @ B )
            & ( v5_membered @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(26,axiom,
    ! [A: $i] :
      ( ( v3_membered @ A )
     => ! [B: $i] :
          ( ( element @ B @ A )
         => ( ( v1_xcmplx_0 @ B )
            & ( v1_xreal_0 @ B )
            & ( v1_rat_1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc12_membered) ).

thf(161,plain,
    ! [A: $i] :
      ( ( v3_membered @ A )
     => ! [B: $i] :
          ( ( element @ B @ A )
         => ( ( v1_xcmplx_0 @ B )
            & ( v1_xreal_0 @ B )
            & ( v1_rat_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(7,axiom,
    ! [A: $i] :
      ( ( v3_membered @ A )
     => ( v2_membered @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_membered) ).

thf(64,plain,
    ! [A: $i] :
      ( ( v3_membered @ A )
     => ( v2_membered @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(4,axiom,
    ! [A: $i] :
      ( ( v4_membered @ A )
     => ( v3_membered @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_membered) ).

thf(49,plain,
    ! [A: $i] :
      ( ( v4_membered @ A )
     => ( v3_membered @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(15,axiom,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ~ ( in @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(86,plain,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ~ ( in @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(23,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ( element @ B @ ( powerset @ A ) )
      & ( empty @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).

thf(113,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ( element @ B @ ( powerset @ A ) )
      & ( empty @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(13,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
     => ( relation @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).

thf(81,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
     => ( relation @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(17,axiom,
    ! [A: $i,B: $i] :
      ( ( element @ B @ ( powerset @ A ) )
     => ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).

thf(91,plain,
    ! [A: $i,B: $i] :
      ( ( element @ B @ ( powerset @ A ) )
     => ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(8,axiom,
    ! [A: $i] :
      ( ( v5_membered @ A )
     => ( v4_membered @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_membered) ).

thf(66,plain,
    ! [A: $i] :
      ( ( v5_membered @ A )
     => ( v4_membered @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(22,axiom,
    ! [A: $i] :
      ( ( v5_membered @ A )
     => ! [B: $i] :
          ( ( element @ B @ A )
         => ( ( v1_xcmplx_0 @ B )
            & ( natural @ B )
            & ( v1_xreal_0 @ B )
            & ( v1_int_1 @ B )
            & ( v1_rat_1 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc14_membered) ).

thf(107,plain,
    ! [A: $i] :
      ( ( v5_membered @ A )
     => ! [B: $i] :
          ( ( element @ B @ A )
         => ( ( v1_xcmplx_0 @ B )
            & ( natural @ B )
            & ( v1_xreal_0 @ B )
            & ( v1_int_1 @ B )
            & ( v1_rat_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(12,axiom,
    ! [A: $i] :
      ( ( v1_membered @ A )
     => ! [B: $i] :
          ( ( element @ B @ ( powerset @ A ) )
         => ( v1_membered @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc16_membered) ).

thf(79,plain,
    ! [A: $i] :
      ( ( v1_membered @ A )
     => ! [B: $i] :
          ( ( element @ B @ ( powerset @ A ) )
         => ( v1_membered @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(3,axiom,
    ! [A: $i] :
      ( ( v2_membered @ A )
     => ( v1_membered @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_membered) ).

thf(47,plain,
    ! [A: $i] :
      ( ( v2_membered @ A )
     => ( v1_membered @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ( v4_membered @ A )
     => ! [B: $i] :
          ( ( element @ B @ ( powerset @ A ) )
         => ( ( v1_membered @ B )
            & ( v2_membered @ B )
            & ( v3_membered @ B )
            & ( v4_membered @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc19_membered) ).

thf(68,plain,
    ! [A: $i] :
      ( ( v4_membered @ A )
     => ! [B: $i] :
          ( ( element @ B @ ( powerset @ A ) )
         => ( ( v1_membered @ B )
            & ( v2_membered @ B )
            & ( v3_membered @ B )
            & ( v4_membered @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(170,plain,
    $false,
    inference(cvc4,[status(thm)],[88,116,102,73,104,119,51,83,93,57,28,165,77,96,161,64,49,86,113,81,91,66,107,79,47,68]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SEU332+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n024.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Thu May 18 12:46:52 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 0.98/0.95  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.25/1.10  % [INFO] 	 Parsing done (147ms). 
% 1.25/1.11  % [INFO] 	 Running in sequential loop mode. 
% 1.79/1.34  % [INFO] 	 eprover registered as external prover. 
% 1.79/1.35  % [INFO] 	 cvc4 registered as external prover. 
% 1.79/1.35  % [INFO] 	 Scanning for conjecture ... 
% 1.91/1.44  % [INFO] 	 Found a conjecture and 31 axioms. Running axiom selection ... 
% 2.05/1.50  % [INFO] 	 Axiom selection finished. Selected 25 axioms (removed 6 axioms). 
% 2.29/1.54  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.29/1.55  % [INFO] 	 Type checking passed. 
% 2.29/1.55  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 4.56/2.36  % External prover 'cvc4' found a proof!
% 4.56/2.36  % [INFO] 	 Killing All external provers ... 
% 4.56/2.36  % Time passed: 1818ms (effective reasoning time: 1250ms)
% 4.56/2.36  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 4.56/2.36  % Axioms used in derivation (25): cc12_membered, cc10_membered, involutiveness_k3_subset_1, rc2_subset_1, cc19_membered, s1_tarski__e4_7_2__tops_2__2, cc11_membered, cc18_membered, cc15_membered, cc17_membered, cc1_membered, cc16_membered, fc4_subset_1, rc1_membered, cc20_membered, fc1_subset_1, rc1_subset_1, cc4_membered, cc1_relset_1, cc13_membered, cc2_membered, cc3_membered, cc14_membered, dt_k3_subset_1, antisymmetry_r2_hidden
% 4.56/2.36  % No. of inferences in proof: 54
% 4.56/2.37  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1818 ms resp. 1250 ms w/o parsing
% 4.85/2.43  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.85/2.43  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------