TSTP Solution File: SEU375+1 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SEU375+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n019.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 11:58:36 EDT 2023

% Result   : Theorem 4.11s 2.35s
% Output   : Refutation 4.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   55
% Syntax   : Number of formulae    :   93 (   7 unt;  19 typ;   0 def)
%            Number of atoms       :  248 (  14 equ;   0 cnn)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  580 (  28   ~;   2   |;  81   &; 378   @)
%                                         (   1 <=>;  90  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   29 (  29   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   21 (  19 usr;   2 con; 0-3 aty)
%            Number of variables   :  129 (   0   ^;  99   !;  30   ?; 129   :)

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

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

thf(net_str_type,type,
    net_str: $i > $i > $o ).

thf(full_subnetstr_type,type,
    full_subnetstr: $i > $i > $i > $o ).

thf(subnetstr_type,type,
    subnetstr: $i > $i > $i > $o ).

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

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

thf(related_type,type,
    related: $i > $i > $i > $o ).

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

thf(relation_empty_yielding_type,type,
    relation_empty_yielding: $i > $o ).

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

thf(function_type,type,
    function: $i > $o ).

thf(one_to_one_type,type,
    one_to_one: $i > $o ).

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

thf(rel_str_type,type,
    rel_str: $i > $o ).

thf(subrelstr_type,type,
    subrelstr: $i > $i > $o ).

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

thf(full_subrelstr_type,type,
    full_subrelstr: $i > $i > $o ).

thf(v1_yellow_3_type,type,
    v1_yellow_3: $i > $o ).

thf(12,axiom,
    ! [A: $i] :
      ( ( empty @ A )
     => ( relation @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).

thf(88,plain,
    ! [A: $i] :
      ( ( empty @ A )
     => ( relation @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(9,axiom,
    ( ( empty @ empty_set )
    & ( relation @ empty_set )
    & ( relation_empty_yielding @ empty_set ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).

thf(78,plain,
    ( ( empty @ empty_set )
    & ( relation @ empty_set )
    & ( relation_empty_yielding @ empty_set ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(15,axiom,
    ! [A: $i] :
      ( ( rel_str @ A )
     => ? [B: $i] : ( subrelstr @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_yellow_0) ).

thf(97,plain,
    ! [A: $i] :
      ( ( rel_str @ A )
     => ? [B: $i] : ( subrelstr @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(33,axiom,
    ! [A: $i] :
      ( ( rel_str @ A )
     => ( one_sorted_str @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).

thf(141,plain,
    ! [A: $i] :
      ( ( rel_str @ A )
     => ( one_sorted_str @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(37,axiom,
    ! [A: $i] :
      ( ( one_sorted_str @ A )
     => ! [B: $i] :
          ( ( net_str @ B @ A )
         => ( rel_str @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_waybel_0) ).

thf(149,plain,
    ! [A: $i] :
      ( ( one_sorted_str @ A )
     => ! [B: $i] :
          ( ( net_str @ B @ A )
         => ( rel_str @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(24,axiom,
    ! [A: $i] :
      ( ( rel_str @ A )
     => ! [B: $i] :
          ( ( ( full_subrelstr @ B @ A )
            & ( subrelstr @ B @ A ) )
         => ! [C: $i] :
              ( ( element @ C @ ( the_carrier @ A ) )
             => ! [D: $i] :
                  ( ( element @ D @ ( the_carrier @ A ) )
                 => ! [E: $i] :
                      ( ( element @ E @ ( the_carrier @ B ) )
                     => ! [F: $i] :
                          ( ( element @ F @ ( the_carrier @ B ) )
                         => ( ( ( E = C )
                              & ( F = D )
                              & ( related @ A @ C @ D )
                              & ( in @ E @ ( the_carrier @ B ) )
                              & ( in @ F @ ( the_carrier @ B ) ) )
                           => ( related @ B @ E @ F ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_yellow_0) ).

thf(118,plain,
    ! [A: $i] :
      ( ( rel_str @ A )
     => ! [B: $i] :
          ( ( ( full_subrelstr @ B @ A )
            & ( subrelstr @ B @ A ) )
         => ! [C: $i] :
              ( ( element @ C @ ( the_carrier @ A ) )
             => ! [D: $i] :
                  ( ( element @ D @ ( the_carrier @ A ) )
                 => ! [E: $i] :
                      ( ( element @ E @ ( the_carrier @ B ) )
                     => ! [F: $i] :
                          ( ( element @ F @ ( the_carrier @ B ) )
                         => ( ( ( E = C )
                              & ( F = D )
                              & ( related @ A @ C @ D )
                              & ( in @ E @ ( the_carrier @ B ) )
                              & ( in @ F @ ( the_carrier @ B ) ) )
                           => ( related @ B @ E @ F ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(6,axiom,
    ? [A: $i] :
      ( ( relation @ A )
      & ( relation_empty_yielding @ A )
      & ( function @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_pboole) ).

thf(66,plain,
    ? [A: $i] :
      ( ( relation @ A )
      & ( relation_empty_yielding @ A )
      & ( function @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

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

thf(35,axiom,
    ! [A: $i] :
      ( ( one_sorted_str @ A )
     => ? [B: $i] : ( net_str @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_waybel_0) ).

thf(145,plain,
    ! [A: $i] :
      ( ( one_sorted_str @ A )
     => ? [B: $i] : ( net_str @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(34,axiom,
    ! [A: $i] :
      ( ( rel_str @ A )
     => ( ~ ( v1_yellow_3 @ A )
       => ~ ( empty_carrier @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_yellow_3) ).

thf(143,plain,
    ! [A: $i] :
      ( ( rel_str @ A )
     => ( ~ ( v1_yellow_3 @ A )
       => ~ ( empty_carrier @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(16,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( in @ A @ B )
        & ( empty @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).

thf(99,plain,
    ! [A: $i,B: $i] :
      ~ ( ( in @ A @ B )
        & ( empty @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(36,axiom,
    ! [A: $i,B: $i] :
      ( ( ( one_sorted_str @ A )
        & ( net_str @ B @ A ) )
     => ! [C: $i] :
          ( ( subnetstr @ C @ A @ B )
         => ( net_str @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_yellow_6) ).

thf(147,plain,
    ! [A: $i,B: $i] :
      ( ( ( one_sorted_str @ A )
        & ( net_str @ B @ A ) )
     => ! [C: $i] :
          ( ( subnetstr @ C @ A @ B )
         => ( net_str @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(30,axiom,
    ! [A: $i] :
      ( ( rel_str @ A )
     => ( ( empty_carrier @ A )
       => ( v1_yellow_3 @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_yellow_3) ).

thf(133,plain,
    ! [A: $i] :
      ( ( rel_str @ A )
     => ( ( empty_carrier @ A )
       => ( v1_yellow_3 @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(23,axiom,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ( element @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).

thf(116,plain,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ( element @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(8,axiom,
    ? [A: $i] :
      ( ( relation @ A )
      & ( empty @ A )
      & ( function @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).

thf(74,plain,
    ? [A: $i] :
      ( ( relation @ A )
      & ( empty @ A )
      & ( function @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(11,axiom,
    ? [A: $i] :
      ( ~ ( empty @ A )
      & ( relation @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).

thf(85,plain,
    ? [A: $i] :
      ( ~ ( empty @ A )
      & ( relation @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(17,axiom,
    ? [A: $i] :
      ( ( empty @ A )
      & ( relation @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).

thf(102,plain,
    ? [A: $i] :
      ( ( empty @ A )
      & ( relation @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(1,conjecture,
    ! [A: $i] :
      ( ( one_sorted_str @ A )
     => ! [B: $i] :
          ( ( ~ ( empty_carrier @ B )
            & ( net_str @ B @ A ) )
         => ! [C: $i] :
              ( ( ~ ( empty_carrier @ C )
                & ( full_subnetstr @ C @ A @ B )
                & ( subnetstr @ C @ A @ B ) )
             => ! [D: $i] :
                  ( ( element @ D @ ( the_carrier @ B ) )
                 => ! [E: $i] :
                      ( ( element @ E @ ( the_carrier @ B ) )
                     => ! [F: $i] :
                          ( ( element @ F @ ( the_carrier @ C ) )
                         => ! [G: $i] :
                              ( ( element @ G @ ( the_carrier @ C ) )
                             => ( ( ( D = F )
                                  & ( E = G )
                                  & ( related @ B @ D @ E ) )
                               => ( related @ C @ F @ G ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_yellow_6) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ( ( one_sorted_str @ A )
       => ! [B: $i] :
            ( ( ~ ( empty_carrier @ B )
              & ( net_str @ B @ A ) )
           => ! [C: $i] :
                ( ( ~ ( empty_carrier @ C )
                  & ( full_subnetstr @ C @ A @ B )
                  & ( subnetstr @ C @ A @ B ) )
               => ! [D: $i] :
                    ( ( element @ D @ ( the_carrier @ B ) )
                   => ! [E: $i] :
                        ( ( element @ E @ ( the_carrier @ B ) )
                       => ! [F: $i] :
                            ( ( element @ F @ ( the_carrier @ C ) )
                           => ! [G: $i] :
                                ( ( element @ G @ ( the_carrier @ C ) )
                               => ( ( ( D = F )
                                    & ( E = G )
                                    & ( related @ B @ D @ E ) )
                                 => ( related @ C @ F @ G ) ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(38,plain,
    ~ ! [A: $i] :
        ( ( one_sorted_str @ A )
       => ! [B: $i] :
            ( ( ~ ( empty_carrier @ B )
              & ( net_str @ B @ A ) )
           => ! [C: $i] :
                ( ( ~ ( empty_carrier @ C )
                  & ( full_subnetstr @ C @ A @ B )
                  & ( subnetstr @ C @ A @ B ) )
               => ! [D: $i] :
                    ( ( element @ D @ ( the_carrier @ B ) )
                   => ! [E: $i] :
                        ( ( element @ E @ ( the_carrier @ B ) )
                       => ! [F: $i] :
                            ( ( element @ F @ ( the_carrier @ C ) )
                           => ! [G: $i] :
                                ( ( element @ G @ ( the_carrier @ C ) )
                               => ( ( ( D = F )
                                    & ( E = G )
                                    & ( related @ B @ D @ E ) )
                                 => ( related @ C @ F @ G ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(7,axiom,
    ? [A: $i] :
      ( ( relation @ A )
      & ( relation_empty_yielding @ A )
      & ( function @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_funct_1) ).

thf(70,plain,
    ? [A: $i] :
      ( ( relation @ A )
      & ( relation_empty_yielding @ A )
      & ( function @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(32,axiom,
    ! [A: $i] :
      ( ( one_sorted_str @ A )
     => ! [B: $i] :
          ( ( net_str @ B @ A )
         => ! [C: $i] :
              ( ( subnetstr @ C @ A @ B )
             => ( ( full_subnetstr @ C @ A @ B )
              <=> ( ( full_subrelstr @ C @ B )
                  & ( subrelstr @ C @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_yellow_6) ).

thf(137,plain,
    ! [A: $i] :
      ( ( one_sorted_str @ A )
     => ! [B: $i] :
          ( ( net_str @ B @ A )
         => ! [C: $i] :
              ( ( subnetstr @ C @ A @ B )
             => ( ( ( full_subnetstr @ C @ A @ B )
                 => ( ( full_subrelstr @ C @ B )
                    & ( subrelstr @ C @ B ) ) )
                & ( ( ( full_subrelstr @ C @ B )
                    & ( subrelstr @ C @ B ) )
                 => ( full_subnetstr @ C @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(20,axiom,
    ! [A: $i] :
      ( ( rel_str @ A )
     => ! [B: $i] :
          ( ( subrelstr @ B @ A )
         => ( rel_str @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_yellow_0) ).

thf(109,plain,
    ! [A: $i] :
      ( ( rel_str @ A )
     => ! [B: $i] :
          ( ( subrelstr @ B @ A )
         => ( rel_str @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(26,axiom,
    ! [A: $i,B: $i] :
      ( ( ( one_sorted_str @ A )
        & ( net_str @ B @ A ) )
     => ? [C: $i] : ( subnetstr @ C @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_yellow_6) ).

thf(124,plain,
    ! [A: $i,B: $i] :
      ( ( ( one_sorted_str @ A )
        & ( net_str @ B @ A ) )
     => ? [C: $i] : ( subnetstr @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

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

thf(128,plain,
    ? [A: $i] :
      ( ( one_sorted_str @ A )
      & ~ ( empty_carrier @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(18,axiom,
    ? [A: $i] : ( rel_str @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_orders_2) ).

thf(105,plain,
    ? [A: $i] : ( rel_str @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(3,axiom,
    ? [A: $i] :
      ( ( relation @ A )
      & ( relation_empty_yielding @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).

thf(55,plain,
    ? [A: $i] :
      ( ( relation @ A )
      & ( relation_empty_yielding @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(22,axiom,
    ! [A: $i] :
      ( ( empty @ A )
     => ( function @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).

thf(114,plain,
    ! [A: $i] :
      ( ( empty @ A )
     => ( function @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(4,axiom,
    ! [A: $i] :
      ( ( ( relation @ A )
        & ( empty @ A )
        & ( function @ A ) )
     => ( ( relation @ A )
        & ( function @ A )
        & ( one_to_one @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).

thf(58,plain,
    ! [A: $i] :
      ( ( ( relation @ A )
        & ( empty @ A )
        & ( function @ A ) )
     => ( ( relation @ A )
        & ( function @ A )
        & ( one_to_one @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(10,axiom,
    ? [A: $i] :
      ( ( relation @ A )
      & ( function @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).

thf(82,plain,
    ? [A: $i] :
      ( ( relation @ A )
      & ( function @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(19,axiom,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ~ ( in @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(107,plain,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ~ ( in @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

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

thf(126,plain,
    ! [A: $i] :
    ? [B: $i] : ( element @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(14,axiom,
    ( ( empty @ empty_set )
    & ( relation @ empty_set ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).

thf(94,plain,
    ( ( empty @ empty_set )
    & ( relation @ empty_set ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(29,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(131,plain,
    ! [A: $i] :
      ( ( ~ ( empty_carrier @ A )
        & ( one_sorted_str @ A ) )
     => ~ ( empty @ ( the_carrier @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(5,axiom,
    ? [A: $i] :
      ( ( relation @ A )
      & ( function @ A )
      & ( one_to_one @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).

thf(62,plain,
    ? [A: $i] :
      ( ( relation @ A )
      & ( function @ A )
      & ( one_to_one @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(25,axiom,
    ? [A: $i] : ( one_sorted_str @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).

thf(122,plain,
    ? [A: $i] : ( one_sorted_str @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(13,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( empty @ A )
        & ( A != B )
        & ( empty @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).

thf(90,plain,
    ! [A: $i,B: $i] :
      ~ ( ( empty @ A )
        & ( A != B )
        & ( empty @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(21,axiom,
    ! [A: $i] :
      ( ( empty @ A )
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

thf(111,plain,
    ! [A: $i] :
      ( ( empty @ A )
     => ( A = empty_set ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(151,plain,
    $false,
    inference(e,[status(thm)],[88,78,97,141,149,118,66,135,145,143,99,147,133,116,74,85,102,38,70,137,109,124,128,105,55,114,58,82,107,126,94,131,62,122,90,111]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU375+1 : TPTP v8.1.2. Released v3.3.0.
% 0.14/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n019.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Thu May 18 13:41:58 EDT 2023
% 0.16/0.36  % CPUTime  : 
% 0.96/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.27/0.98  % [INFO] 	 Parsing done (129ms). 
% 1.27/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.72/1.20  % [INFO] 	 eprover registered as external prover. 
% 1.72/1.20  % [INFO] 	 cvc4 registered as external prover. 
% 1.83/1.20  % [INFO] 	 Scanning for conjecture ... 
% 1.91/1.27  % [INFO] 	 Found a conjecture and 39 axioms. Running axiom selection ... 
% 1.91/1.32  % [INFO] 	 Axiom selection finished. Selected 35 axioms (removed 4 axioms). 
% 2.23/1.36  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.23/1.36  % [INFO] 	 Type checking passed. 
% 2.23/1.37  % [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 ... 
% 4.11/2.35  % External prover 'e' found a proof!
% 4.11/2.35  % [INFO] 	 Killing All external provers ... 
% 4.11/2.35  % Time passed: 1821ms (effective reasoning time: 1357ms)
% 4.11/2.35  % 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)>
% 4.11/2.35  % Axioms used in derivation (35): t61_yellow_0, rc3_funct_1, cc1_relat_1, rc1_funct_1, rc2_funct_1, rc2_relat_1, dt_l1_orders_2, t8_boole, cc2_yellow_3, antisymmetry_r2_hidden, fc4_relat_1, t1_subset, rc3_relat_1, t6_boole, rc4_funct_1, dt_l1_waybel_0, existence_l1_waybel_0, t7_boole, existence_l1_orders_2, cc1_funct_1, rc3_struct_0, cc2_funct_1, existence_m1_subset_1, fc1_struct_0, rc1_relat_1, cc1_yellow_3, rc1_pboole, existence_m1_yellow_0, dt_m1_yellow_0, t2_subset, dt_m1_yellow_6, d9_yellow_6, fc12_relat_1, existence_l1_struct_0, existence_m1_yellow_6
% 4.11/2.35  % No. of inferences in proof: 74
% 4.11/2.35  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1821 ms resp. 1357 ms w/o parsing
% 4.50/2.42  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.50/2.42  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------