TSTP Solution File: SEU321+1 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SEU321+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n009.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 11:58:15 EDT 2023

% Result   : Theorem 4.15s 2.00s
% Output   : Refutation 4.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   57
% Syntax   : Number of formulae    :   96 (   7 unt;  20 typ;   0 def)
%            Number of atoms       :  267 (   8 equ;   0 cnn)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  650 (  37   ~;   2   |;  95   &; 422   @)
%                                         (   3 <=>;  91  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   23 (  23   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   22 (  20 usr;   2 con; 0-2 aty)
%            Number of variables   :  136 (   0   ^; 126   !;  10   ?; 136   :)

% Comments : 
%------------------------------------------------------------------------------
thf(empty_carrier_type,type,
    empty_carrier: $i > $o ).

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

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

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

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

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

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

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

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

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

thf(v1_xcmplx_0_type,type,
    v1_xcmplx_0: $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(33,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(142,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)],[33]) ).

thf(25,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( in @ A @ B )
        & ( element @ B @ ( powerset @ C ) ) )
     => ( element @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).

thf(121,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( in @ A @ B )
        & ( element @ B @ ( powerset @ C ) ) )
     => ( element @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(27,axiom,
    ! [A: $i] :
    ? [B: $i] : ( element @ B @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).

thf(129,plain,
    ! [A: $i] :
    ? [B: $i] : ( element @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(3,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( empty @ A )
        & ( A != B )
        & ( empty @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).

thf(48,plain,
    ! [A: $i,B: $i] :
      ~ ( ( empty @ A )
        & ( A != B )
        & ( empty @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(36,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(154,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)],[36]) ).

thf(5,axiom,
    ! [A: $i] :
      ( ( v2_membered @ A )
     => ( v1_membered @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_membered) ).

thf(58,plain,
    ! [A: $i] :
      ( ( v2_membered @ A )
     => ( v1_membered @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(10,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(69,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)],[10]) ).

thf(31,axiom,
    ! [A: $i,B: $i] :
      ( ( element @ A @ B )
     => ( ( empty @ B )
        | ( in @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).

thf(138,plain,
    ! [A: $i,B: $i] :
      ( ( element @ A @ B )
     => ( ( empty @ B )
        | ( in @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(4,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(52,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)],[4]) ).

thf(22,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(110,plain,
    ! [A: $i,B: $i] :
      ( ( element @ B @ ( powerset @ A ) )
     => ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(37,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(157,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)],[37]) ).

thf(13,axiom,
    ! [A: $i,B: $i] :
      ( ( element @ A @ ( powerset @ B ) )
    <=> ( subset @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).

thf(85,plain,
    ! [A: $i,B: $i] :
      ( ( ( element @ A @ ( powerset @ B ) )
       => ( subset @ A @ B ) )
      & ( ( subset @ A @ B )
       => ( element @ A @ ( powerset @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ( v4_membered @ A )
     => ( v3_membered @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_membered) ).

thf(60,plain,
    ! [A: $i] :
      ( ( v4_membered @ A )
     => ( v3_membered @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(24,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(117,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)],[24]) ).

thf(15,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( element @ C @ ( powerset @ A ) )
     => ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
          & ( in @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).

thf(92,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( element @ C @ ( powerset @ A ) )
     => ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
          & ( in @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(17,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( in @ A @ B )
        & ( element @ B @ ( powerset @ C ) )
        & ( empty @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).

thf(97,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( in @ A @ B )
        & ( element @ B @ ( powerset @ C ) )
        & ( empty @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(29,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(134,plain,
    ! [A: $i] :
      ( ( v1_membered @ A )
     => ! [B: $i] :
          ( ( element @ B @ A )
         => ( v1_xcmplx_0 @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(20,axiom,
    ! [A: $i] :
      ( ( ~ ( empty_carrier @ A )
        & ( one_sorted_str @ A ) )
     => ? [B: $i] :
          ( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
          & ~ ( empty @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_struct_0) ).

thf(105,plain,
    ! [A: $i] :
      ( ( ~ ( empty_carrier @ A )
        & ( one_sorted_str @ A ) )
     => ? [B: $i] :
          ( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
          & ~ ( empty @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(35,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(148,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)],[35]) ).

thf(38,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(161,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)],[38]) ).

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

thf(64,plain,
    ! [A: $i] :
      ( ( v5_membered @ A )
     => ( v4_membered @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(11,axiom,
    ( ( empty @ empty_set )
    & ( v1_membered @ empty_set )
    & ( v2_membered @ empty_set )
    & ( v3_membered @ empty_set )
    & ( v4_membered @ empty_set )
    & ( v5_membered @ empty_set ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_membered) ).

thf(76,plain,
    ( ( empty @ empty_set )
    & ( v1_membered @ empty_set )
    & ( v2_membered @ empty_set )
    & ( v3_membered @ empty_set )
    & ( v4_membered @ empty_set )
    & ( v5_membered @ empty_set ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(1,conjecture,
    ! [A: $i] :
      ( ( ~ ( empty_carrier @ A )
        & ( one_sorted_str @ A ) )
     => ! [B: $i] :
          ( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
         => ! [C: $i] :
              ( ( element @ C @ ( the_carrier @ A ) )
             => ( ( in @ C @ ( subset_complement @ ( the_carrier @ A ) @ B ) )
              <=> ~ ( in @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l40_tops_1) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ( ( ~ ( empty_carrier @ A )
          & ( one_sorted_str @ A ) )
       => ! [B: $i] :
            ( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
           => ! [C: $i] :
                ( ( element @ C @ ( the_carrier @ A ) )
               => ( ( in @ C @ ( subset_complement @ ( the_carrier @ A ) @ B ) )
                <=> ~ ( in @ C @ B ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(39,plain,
    ~ ! [A: $i] :
        ( ( ~ ( empty_carrier @ A )
          & ( one_sorted_str @ A ) )
       => ! [B: $i] :
            ( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
           => ! [C: $i] :
                ( ( element @ C @ ( the_carrier @ A ) )
               => ( ( ( in @ C @ ( subset_complement @ ( the_carrier @ A ) @ B ) )
                   => ~ ( in @ C @ B ) )
                  & ( ~ ( in @ C @ B )
                   => ( in @ C @ ( subset_complement @ ( the_carrier @ A ) @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(19,axiom,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ( element @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).

thf(103,plain,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ( element @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(32,axiom,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ~ ( in @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(140,plain,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ~ ( in @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ( empty @ A )
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

thf(66,plain,
    ! [A: $i] :
      ( ( empty @ A )
     => ( A = empty_set ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(21,axiom,
    ? [A: $i] : ( one_sorted_str @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).

thf(108,plain,
    ? [A: $i] : ( one_sorted_str @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(23,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(112,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)],[23]) ).

thf(26,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(123,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)],[26]) ).

thf(34,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(145,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)],[34]) ).

thf(30,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(136,plain,
    ! [A: $i] :
      ( ( v1_membered @ A )
     => ! [B: $i] :
          ( ( element @ B @ ( powerset @ A ) )
         => ( v1_membered @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(16,axiom,
    ! [A: $i] :
      ( ( A != empty_set )
     => ! [B: $i] :
          ( ( element @ B @ ( powerset @ A ) )
         => ! [C: $i] :
              ( ( element @ C @ A )
             => ( ~ ( in @ C @ B )
               => ( in @ C @ ( subset_complement @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).

thf(94,plain,
    ! [A: $i] :
      ( ( A != empty_set )
     => ! [B: $i] :
          ( ( element @ B @ ( powerset @ A ) )
         => ! [C: $i] :
              ( ( element @ C @ A )
             => ( ~ ( in @ C @ B )
               => ( in @ C @ ( subset_complement @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(28,axiom,
    ? [A: $i] :
      ( ( one_sorted_str @ A )
      & ~ ( empty_carrier @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).

thf(131,plain,
    ? [A: $i] :
      ( ( one_sorted_str @ A )
      & ~ ( empty_carrier @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(7,axiom,
    ! [A: $i,B: $i] : ( subset @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

thf(62,plain,
    ! [A: $i] : ( subset @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(14,axiom,
    ! [A: $i] :
      ( ( ~ ( empty_carrier @ A )
        & ( one_sorted_str @ A ) )
     => ~ ( empty @ ( the_carrier @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).

thf(90,plain,
    ! [A: $i] :
      ( ( ~ ( empty_carrier @ A )
        & ( one_sorted_str @ A ) )
     => ~ ( empty @ ( the_carrier @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(12,axiom,
    ! [A: $i] :
      ( ( v3_membered @ A )
     => ( v2_membered @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_membered) ).

thf(83,plain,
    ! [A: $i] :
      ( ( v3_membered @ A )
     => ( v2_membered @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(18,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( in @ A @ B )
        & ( empty @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).

thf(100,plain,
    ! [A: $i,B: $i] :
      ~ ( ( in @ A @ B )
        & ( empty @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(166,plain,
    $false,
    inference(cvc4,[status(thm)],[142,121,129,48,154,58,69,138,52,110,157,85,60,117,92,97,134,105,148,161,64,76,39,103,140,66,108,112,123,145,136,94,131,62,90,83,100]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU321+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n009.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu May 18 13:28:34 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.95/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.24/1.04  % [INFO] 	 Parsing done (145ms). 
% 1.24/1.04  % [INFO] 	 Running in sequential loop mode. 
% 1.80/1.25  % [INFO] 	 eprover registered as external prover. 
% 1.80/1.25  % [INFO] 	 cvc4 registered as external prover. 
% 1.80/1.25  % [INFO] 	 Scanning for conjecture ... 
% 1.90/1.32  % [INFO] 	 Found a conjecture and 41 axioms. Running axiom selection ... 
% 2.19/1.37  % [INFO] 	 Axiom selection finished. Selected 36 axioms (removed 5 axioms). 
% 2.19/1.41  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.19/1.42  % [INFO] 	 Type checking passed. 
% 2.19/1.42  % [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 ... 
% 4.15/1.99  % External prover 'cvc4' found a proof!
% 4.15/1.99  % [INFO] 	 Killing All external provers ... 
% 4.15/1.99  % Time passed: 1477ms (effective reasoning time: 946ms)
% 4.15/1.99  % 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)>
% 4.15/2.00  % Axioms used in derivation (36): cc12_membered, rc1_membered, involutiveness_k3_subset_1, t6_boole, t5_subset, cc19_membered, fc6_membered, cc4_membered, cc18_membered, cc15_membered, cc17_membered, existence_l1_struct_0, cc16_membered, cc10_membered, t1_subset, cc11_membered, t4_subset, cc20_membered, t7_boole, rc3_struct_0, t3_subset, cc13_membered, existence_m1_subset_1, fc1_struct_0, reflexivity_r1_tarski, t54_subset_1, t8_boole, rc5_struct_0, t2_subset, cc1_membered, cc2_membered, cc14_membered, cc3_membered, t50_subset_1, dt_k3_subset_1, antisymmetry_r2_hidden
% 4.15/2.00  % No. of inferences in proof: 76
% 4.15/2.00  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1477 ms resp. 946 ms w/o parsing
% 4.38/2.06  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.38/2.06  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------