TSTP Solution File: SEU413+1 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SEU413+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n032.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 11:58:51 EDT 2023

% Result   : Theorem 3.52s 1.88s
% Output   : Refutation 3.83s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   54
% Syntax   : Number of formulae    :   89 (  25 unt;  21 typ;   0 def)
%            Number of atoms       :  174 (  18 equ;   0 cnn)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :  576 (  14   ~;   2   |;  38   &; 456   @)
%                                         (   3 <=>;  63  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   35 (  35   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   23 (  21 usr;   2 con; 0-3 aty)
%            Number of variables   :  140 (   0   ^; 126   !;  14   ?; 140   :)

% Comments : 
%------------------------------------------------------------------------------
thf(l1_orders_2_type,type,
    l1_orders_2: $i > $o ).

thf(m1_subset_1_type,type,
    m1_subset_1: $i > $i > $o ).

thf(u1_struct_0_type,type,
    u1_struct_0: $i > $i ).

thf(k1_latsum_1_type,type,
    k1_latsum_1: $i > $i > $i ).

thf(v12_waybel_0_type,type,
    v12_waybel_0: $i > $i > $o ).

thf(k3_xboole_0_type,type,
    k3_xboole_0: $i > $i > $i ).

thf(k1_zfmisc_1_type,type,
    k1_zfmisc_1: $i > $i ).

thf(r1_orders_2_type,type,
    r1_orders_2: $i > $i > $i > $o ).

thf(r2_hidden_type,type,
    r2_hidden: $i > $i > $o ).

thf(m1_relset_1_type,type,
    m1_relset_1: $i > $i > $i > $o ).

thf(g1_orders_2_type,type,
    g1_orders_2: $i > $i > $i ).

thf(v1_xboole_0_type,type,
    v1_xboole_0: $i > $o ).

thf(k1_xboole_0_type,type,
    k1_xboole_0: $i ).

thf(m2_relset_1_type,type,
    m2_relset_1: $i > $i > $i > $o ).

thf(l1_struct_0_type,type,
    l1_struct_0: $i > $o ).

thf(r1_tarski_type,type,
    r1_tarski: $i > $i > $o ).

thf(k2_zfmisc_1_type,type,
    k2_zfmisc_1: $i > $i > $i ).

thf(v1_relat_1_type,type,
    v1_relat_1: $i > $o ).

thf(v1_orders_2_type,type,
    v1_orders_2: $i > $o ).

thf(k4_tarski_type,type,
    k4_tarski: $i > $i > $i ).

thf(u1_orders_2_type,type,
    u1_orders_2: $i > $i ).

thf(29,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( l1_struct_0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).

thf(115,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( l1_struct_0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(18,axiom,
    ! [A: $i] :
      ( ( k3_xboole_0 @ A @ k1_xboole_0 )
      = k1_xboole_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).

thf(84,plain,
    ! [A: $i] :
      ( ( k3_xboole_0 @ A @ k1_xboole_0 )
      = k1_xboole_0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(11,axiom,
    ! [A: $i,B: $i] : ( r1_tarski @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

thf(70,plain,
    ! [A: $i] : ( r1_tarski @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(34,axiom,
    ! [A: $i,B: $i] :
      ( ( ( l1_orders_2 @ A )
        & ( l1_orders_2 @ B ) )
     => ( ( v1_orders_2 @ ( k1_latsum_1 @ A @ B ) )
        & ( l1_orders_2 @ ( k1_latsum_1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_latsum_1) ).

thf(128,plain,
    ! [A: $i,B: $i] :
      ( ( ( l1_orders_2 @ A )
        & ( l1_orders_2 @ B ) )
     => ( ( v1_orders_2 @ ( k1_latsum_1 @ A @ B ) )
        & ( l1_orders_2 @ ( k1_latsum_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(3,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).

thf(45,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( m1_relset_1 @ C @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( A = k1_xboole_0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

thf(54,plain,
    ! [A: $i] :
      ( ( v1_xboole_0 @ A )
     => ( A = k1_xboole_0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(9,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).

thf(66,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( m2_relset_1 @ C @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(12,axiom,
    ? [A: $i] :
      ~ ( v1_xboole_0 @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).

thf(72,plain,
    ? [A: $i] :
      ~ ( v1_xboole_0 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(26,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ! [B: $i] :
          ( ( l1_orders_2 @ B )
         => ! [C: $i,D: $i] :
              ( ( ( v12_waybel_0 @ ( k3_xboole_0 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ B )
                & ( m1_subset_1 @ ( k3_xboole_0 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
                & ( r2_hidden @ ( k4_tarski @ C @ D ) @ ( u1_orders_2 @ ( k1_latsum_1 @ A @ B ) ) )
                & ( r2_hidden @ D @ ( u1_struct_0 @ A ) ) )
             => ( r2_hidden @ C @ ( u1_struct_0 @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_latsum_1) ).

thf(107,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ! [B: $i] :
          ( ( l1_orders_2 @ B )
         => ! [C: $i,D: $i] :
              ( ( ( v12_waybel_0 @ ( k3_xboole_0 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ B )
                & ( m1_subset_1 @ ( k3_xboole_0 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
                & ( r2_hidden @ ( k4_tarski @ C @ D ) @ ( u1_orders_2 @ ( k1_latsum_1 @ A @ B ) ) )
                & ( r2_hidden @ D @ ( u1_struct_0 @ A ) ) )
             => ( r2_hidden @ C @ ( u1_struct_0 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(5,axiom,
    ? [A: $i] : ( v1_xboole_0 @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

thf(52,plain,
    ? [A: $i] : ( v1_xboole_0 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(27,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( v1_xboole_0 @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

thf(110,plain,
    ! [A: $i,B: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( v1_xboole_0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(33,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( v1_orders_2 @ A )
       => ( A
          = ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).

thf(125,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( ( v1_orders_2 @ A )
       => ( A
          = ( g1_orders_2 @ ( u1_struct_0 @ A ) @ ( u1_orders_2 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(21,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
    <=> ( r1_tarski @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).

thf(93,plain,
    ! [A: $i,B: $i] :
      ( ( ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) )
       => ( r1_tarski @ A @ B ) )
      & ( ( r1_tarski @ A @ B )
       => ( m1_subset_1 @ A @ ( k1_zfmisc_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(7,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
    <=> ( m1_relset_1 @ C @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).

thf(57,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( m2_relset_1 @ C @ A @ B )
       => ( m1_relset_1 @ C @ A @ B ) )
      & ( ( m1_relset_1 @ C @ A @ B )
       => ( m2_relset_1 @ C @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(15,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).

thf(78,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m2_relset_1 @ C @ A @ B )
     => ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(30,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ A @ B )
     => ( ( v1_xboole_0 @ B )
        | ( r2_hidden @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).

thf(117,plain,
    ! [A: $i,B: $i] :
      ( ( m1_subset_1 @ A @ B )
     => ( ( v1_xboole_0 @ B )
        | ( r2_hidden @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(24,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( m2_relset_1 @ ( u1_orders_2 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_orders_2) ).

thf(102,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ( m2_relset_1 @ ( u1_orders_2 @ A ) @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(28,axiom,
    ! [A: $i] :
    ? [B: $i] : ( m1_subset_1 @ B @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).

thf(113,plain,
    ! [A: $i] :
    ? [B: $i] : ( m1_subset_1 @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(14,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
     => ( v1_relat_1 @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).

thf(76,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) )
     => ( v1_relat_1 @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(22,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( m1_subset_1 @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).

thf(98,plain,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ( m1_subset_1 @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(16,axiom,
    ? [A: $i] : ( l1_orders_2 @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_orders_2) ).

thf(80,plain,
    ? [A: $i] : ( l1_orders_2 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(1,conjecture,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ! [B: $i] :
          ( ( l1_orders_2 @ B )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k1_latsum_1 @ A @ B ) ) )
             => ! [D: $i] :
                  ( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k1_latsum_1 @ A @ B ) ) )
                 => ( ( ( v12_waybel_0 @ ( k3_xboole_0 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ B )
                      & ( m1_subset_1 @ ( k3_xboole_0 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
                      & ( r1_orders_2 @ ( k1_latsum_1 @ A @ B ) @ C @ D )
                      & ( r2_hidden @ D @ ( u1_struct_0 @ A ) ) )
                   => ( r2_hidden @ C @ ( u1_struct_0 @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_latsum_1) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ( ( l1_orders_2 @ A )
       => ! [B: $i] :
            ( ( l1_orders_2 @ B )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k1_latsum_1 @ A @ B ) ) )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k1_latsum_1 @ A @ B ) ) )
                   => ( ( ( v12_waybel_0 @ ( k3_xboole_0 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ B )
                        & ( m1_subset_1 @ ( k3_xboole_0 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
                        & ( r1_orders_2 @ ( k1_latsum_1 @ A @ B ) @ C @ D )
                        & ( r2_hidden @ D @ ( u1_struct_0 @ A ) ) )
                     => ( r2_hidden @ C @ ( u1_struct_0 @ A ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(35,plain,
    ~ ! [A: $i] :
        ( ( l1_orders_2 @ A )
       => ! [B: $i] :
            ( ( l1_orders_2 @ B )
           => ! [C: $i] :
                ( ( m1_subset_1 @ C @ ( u1_struct_0 @ ( k1_latsum_1 @ A @ B ) ) )
               => ! [D: $i] :
                    ( ( m1_subset_1 @ D @ ( u1_struct_0 @ ( k1_latsum_1 @ A @ B ) ) )
                   => ( ( ( v12_waybel_0 @ ( k3_xboole_0 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ B )
                        & ( m1_subset_1 @ ( k3_xboole_0 @ ( u1_struct_0 @ A ) @ ( u1_struct_0 @ B ) ) @ ( k1_zfmisc_1 @ ( u1_struct_0 @ B ) ) )
                        & ( r1_orders_2 @ ( k1_latsum_1 @ A @ B ) @ C @ D )
                        & ( r2_hidden @ D @ ( u1_struct_0 @ A ) ) )
                     => ( r2_hidden @ C @ ( u1_struct_0 @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(19,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_relset_1 @ B @ A @ A )
     => ( ( v1_orders_2 @ ( g1_orders_2 @ A @ B ) )
        & ( l1_orders_2 @ ( g1_orders_2 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g1_orders_2) ).

thf(87,plain,
    ! [A: $i,B: $i] :
      ( ( m1_relset_1 @ B @ A @ A )
     => ( ( v1_orders_2 @ ( g1_orders_2 @ A @ B ) )
        & ( l1_orders_2 @ ( g1_orders_2 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(25,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) )
        & ( v1_xboole_0 @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).

thf(104,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( r2_hidden @ A @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) )
        & ( v1_xboole_0 @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(13,axiom,
    v1_xboole_0 @ k1_xboole_0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).

thf(75,plain,
    v1_xboole_0 @ k1_xboole_0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(31,axiom,
    ! [A: $i,B: $i] :
      ( ( k3_xboole_0 @ A @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).

thf(119,plain,
    ! [A: $i] :
      ( ( k3_xboole_0 @ A @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(17,axiom,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ~ ( r2_hidden @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(82,plain,
    ! [A: $i,B: $i] :
      ( ( r2_hidden @ A @ B )
     => ~ ( r2_hidden @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ( m1_relset_1 @ B @ A @ A )
     => ! [C: $i,D: $i] :
          ( ( ( g1_orders_2 @ A @ B )
            = ( g1_orders_2 @ C @ D ) )
         => ( ( A = C )
            & ( B = D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_orders_2) ).

thf(47,plain,
    ! [A: $i,B: $i] :
      ( ( m1_relset_1 @ B @ A @ A )
     => ! [C: $i,D: $i] :
          ( ( ( g1_orders_2 @ A @ B )
            = ( g1_orders_2 @ C @ D ) )
         => ( ( A = C )
            & ( B = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(10,axiom,
    ? [A: $i] : ( l1_struct_0 @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).

thf(68,plain,
    ? [A: $i] : ( l1_struct_0 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(8,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( v1_xboole_0 @ A )
        & ( A != B )
        & ( v1_xboole_0 @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).

thf(62,plain,
    ! [A: $i,B: $i] :
      ~ ( ( v1_xboole_0 @ A )
        & ( A != B )
        & ( v1_xboole_0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(20,axiom,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
             => ( ( r1_orders_2 @ A @ B @ C )
              <=> ( r2_hidden @ ( k4_tarski @ B @ C ) @ ( u1_orders_2 @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_orders_2) ).

thf(90,plain,
    ! [A: $i] :
      ( ( l1_orders_2 @ A )
     => ! [B: $i] :
          ( ( m1_subset_1 @ B @ ( u1_struct_0 @ A ) )
         => ! [C: $i] :
              ( ( m1_subset_1 @ C @ ( u1_struct_0 @ A ) )
             => ( ( ( r1_orders_2 @ A @ B @ C )
                 => ( r2_hidden @ ( k4_tarski @ B @ C ) @ ( u1_orders_2 @ A ) ) )
                & ( ( r2_hidden @ ( k4_tarski @ B @ C ) @ ( u1_orders_2 @ A ) )
                 => ( r1_orders_2 @ A @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(32,axiom,
    ! [A: $i,B: $i] :
      ( ( k3_xboole_0 @ A @ B )
      = ( k3_xboole_0 @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

thf(122,plain,
    ! [A: $i,B: $i] :
      ( ( k3_xboole_0 @ A @ B )
      = ( k3_xboole_0 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(23,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r2_hidden @ A @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) )
     => ( m1_subset_1 @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).

thf(100,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( r2_hidden @ A @ B )
        & ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ C ) ) )
     => ( m1_subset_1 @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(131,plain,
    $false,
    inference(e,[status(thm)],[115,84,70,128,45,54,66,72,107,52,110,125,93,57,78,117,102,113,76,98,80,35,87,104,75,119,82,47,68,62,90,122,100]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem  : SEU413+1 : TPTP v8.1.2. Released v3.4.0.
% 0.09/0.10  % Command  : run_Leo-III %s %d
% 0.10/0.29  % Computer : n032.cluster.edu
% 0.10/0.29  % Model    : x86_64 x86_64
% 0.10/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29  % Memory   : 8042.1875MB
% 0.10/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29  % CPULimit : 300
% 0.10/0.29  % WCLimit  : 300
% 0.10/0.29  % DateTime : Thu May 18 13:18:05 EDT 2023
% 0.10/0.29  % CPUTime  : 
% 0.74/0.74  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.14/0.88  % [INFO] 	 Parsing done (135ms). 
% 1.14/0.89  % [INFO] 	 Running in sequential loop mode. 
% 1.52/1.11  % [INFO] 	 eprover registered as external prover. 
% 1.52/1.12  % [INFO] 	 cvc4 registered as external prover. 
% 1.52/1.12  % [INFO] 	 Scanning for conjecture ... 
% 1.76/1.19  % [INFO] 	 Found a conjecture and 41 axioms. Running axiom selection ... 
% 1.90/1.25  % [INFO] 	 Axiom selection finished. Selected 32 axioms (removed 9 axioms). 
% 1.90/1.28  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.90/1.29  % [INFO] 	 Type checking passed. 
% 1.90/1.29  % [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 ... 
% 3.52/1.87  % External prover 'e' found a proof!
% 3.52/1.87  % [INFO] 	 Killing All external provers ... 
% 3.52/1.87  % Time passed: 1456ms (effective reasoning time: 981ms)
% 3.52/1.87  % 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)>
% 3.52/1.88  % Axioms used in derivation (32): redefinition_m2_relset_1, idempotence_k3_xboole_0, t2_boole, dt_k1_latsum_1, dt_u1_orders_2, d9_orders_2, t6_boole, t5_subset, existence_m1_relset_1, t21_latsum_1, t4_subset, dt_g1_orders_2, abstractness_v1_orders_2, existence_m2_relset_1, dt_l1_orders_2, t2_subset, existence_l1_struct_0, rc2_xboole_0, antisymmetry_r2_hidden, fc1_xboole_0, t1_subset, dt_m2_relset_1, commutativity_k3_xboole_0, t7_boole, existence_l1_orders_2, t3_subset, cc1_relset_1, existence_m1_subset_1, free_g1_orders_2, reflexivity_r1_tarski, t8_boole, rc1_xboole_0
% 3.52/1.88  % No. of inferences in proof: 68
% 3.52/1.88  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1456 ms resp. 981 ms w/o parsing
% 3.83/1.93  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.83/1.93  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------