TSTP Solution File: SEU291+1 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SEU291+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n021.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 11:58:02 EDT 2023

% Result   : Theorem 4.07s 2.00s
% Output   : Refutation 4.45s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   62
% Syntax   : Number of formulae    :  110 (  17 unt;  16 typ;   0 def)
%            Number of atoms       :  258 (  28 equ;   0 cnn)
%            Maximal formula atoms :   13 (   2 avg)
%            Number of connectives :  631 (  35   ~;   7   |;  93   &; 432   @)
%                                         (   4 <=>;  60  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   27 (  27   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  16 usr;   2 con; 0-3 aty)
%            Number of variables   :  171 (   0   ^; 137   !;  34   ?; 171   :)

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

thf(quasi_total_type,type,
    quasi_total: $i > $i > $i > $o ).

thf(relation_of2_as_subset_type,type,
    relation_of2_as_subset: $i > $i > $i > $o ).

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

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

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

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

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

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

thf(relation_of2_type,type,
    relation_of2: $i > $i > $i > $o ).

thf(relation_dom_as_subset_type,type,
    relation_dom_as_subset: $i > $i > $i > $i ).

thf(relation_dom_type,type,
    relation_dom: $i > $i ).

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

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

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

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

thf(26,axiom,
    ! [A: $i] :
    ? [B: $i] : ( element @ B @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).

thf(115,plain,
    ! [A: $i] :
    ? [B: $i] : ( element @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(3,axiom,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ~ ( in @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(56,plain,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ~ ( in @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(39,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( relation_of2_as_subset @ D @ C @ A )
     => ( ( subset @ A @ B )
       => ( relation_of2_as_subset @ D @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_1) ).

thf(174,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( relation_of2_as_subset @ D @ C @ A )
     => ( ( subset @ A @ B )
       => ( relation_of2_as_subset @ D @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(24,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ( element @ B @ ( powerset @ A ) )
      & ( empty @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).

thf(110,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ( element @ B @ ( powerset @ A ) )
      & ( empty @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(11,axiom,
    ? [A: $i] :
      ( ( empty @ A )
      & ( relation @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).

thf(78,plain,
    ? [A: $i] :
      ( ( empty @ A )
      & ( relation @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(27,axiom,
    ! [A: $i] :
      ( ( ( relation @ A )
        & ( empty @ A )
        & ( function @ A ) )
     => ( ( relation @ A )
        & ( function @ A )
        & ( one_to_one @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).

thf(117,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)],[27]) ).

thf(38,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] :
      ( ( relation_of2 @ C @ A @ B )
      & ( relation @ C )
      & ( function @ C )
      & ( quasi_total @ C @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_2) ).

thf(169,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] :
      ( ( relation_of2 @ C @ A @ B )
      & ( relation @ C )
      & ( function @ C )
      & ( quasi_total @ C @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(9,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( in @ A @ B )
        & ( empty @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

thf(73,plain,
    ! [A: $i,B: $i] :
      ~ ( ( in @ A @ B )
        & ( empty @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(6,axiom,
    ? [A: $i] :
      ( ( relation @ A )
      & ( relation_empty_yielding @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).

thf(64,plain,
    ? [A: $i] :
      ( ( relation @ A )
      & ( relation_empty_yielding @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(40,axiom,
    ! [A: $i] :
      ( ( empty @ A )
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

thf(176,plain,
    ! [A: $i] :
      ( ( empty @ A )
     => ( A = empty_set ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(31,axiom,
    ! [A: $i] :
      ( ( subset @ A @ empty_set )
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).

thf(130,plain,
    ! [A: $i] :
      ( ( subset @ A @ empty_set )
     => ( A = empty_set ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(46,axiom,
    ( ( empty @ empty_set )
    & ( relation @ empty_set )
    & ( relation_empty_yielding @ empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).

thf(194,plain,
    ( ( empty @ empty_set )
    & ( relation @ empty_set )
    & ( relation_empty_yielding @ empty_set ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(7,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( relation_of2 @ C @ A @ B )
     => ( ( relation_dom_as_subset @ A @ B @ C )
        = ( relation_dom @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).

thf(67,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( relation_of2 @ C @ A @ B )
     => ( ( relation_dom_as_subset @ A @ B @ C )
        = ( relation_dom @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(34,axiom,
    ? [A: $i] :
      ( ( relation @ A )
      & ( empty @ A )
      & ( function @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).

thf(154,plain,
    ? [A: $i] :
      ( ( relation @ A )
      & ( empty @ A )
      & ( function @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(35,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( relation_of2_as_subset @ C @ A @ B )
    <=> ( relation_of2 @ C @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).

thf(158,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( relation_of2_as_subset @ C @ A @ B )
       => ( relation_of2 @ C @ A @ B ) )
      & ( ( relation_of2 @ C @ A @ B )
       => ( relation_of2_as_subset @ C @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ~ ( ( empty @ A )
        & ( A != B )
        & ( empty @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).

thf(58,plain,
    ! [A: $i,B: $i] :
      ~ ( ( empty @ A )
        & ( A != B )
        & ( empty @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(20,axiom,
    ! [A: $i] :
      ~ ( empty @ ( powerset @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).

thf(100,plain,
    ! [A: $i] :
      ~ ( empty @ ( powerset @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(41,axiom,
    ! [A: $i] :
      ( ( empty @ A )
     => ( function @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).

thf(179,plain,
    ! [A: $i] :
      ( ( empty @ A )
     => ( function @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(22,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( in @ A @ B )
        & ( element @ B @ ( powerset @ C ) ) )
     => ( element @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).

thf(106,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)],[22]) ).

thf(28,axiom,
    ( ( empty @ empty_set )
    & ( relation @ empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).

thf(121,plain,
    ( ( empty @ empty_set )
    & ( relation @ empty_set ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(13,axiom,
    ! [A: $i,B: $i] :
      ( ( element @ A @ B )
     => ( ( empty @ B )
        | ( in @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).

thf(84,plain,
    ! [A: $i,B: $i] :
      ( ( element @ A @ B )
     => ( ( empty @ B )
        | ( in @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(15,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( relation_of2 @ C @ A @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).

thf(89,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( relation_of2 @ C @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(32,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( relation_of2_as_subset @ C @ A @ B )
     => ( ( ( ( B = empty_set )
           => ( A = empty_set ) )
         => ( ( quasi_total @ C @ A @ B )
          <=> ( A
              = ( relation_dom_as_subset @ A @ B @ C ) ) ) )
        & ( ( B = empty_set )
         => ( ( A = empty_set )
            | ( ( quasi_total @ C @ A @ B )
            <=> ( C = empty_set ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_2) ).

thf(133,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( relation_of2_as_subset @ C @ A @ B )
     => ( ( ( ( B = empty_set )
           => ( A = empty_set ) )
         => ( ( ( quasi_total @ C @ A @ B )
             => ( A
                = ( relation_dom_as_subset @ A @ B @ C ) ) )
            & ( ( A
                = ( relation_dom_as_subset @ A @ B @ C ) )
             => ( quasi_total @ C @ A @ B ) ) ) )
        & ( ( B = empty_set )
         => ( ( A = empty_set )
            | ( ( ( quasi_total @ C @ A @ B )
               => ( C = empty_set ) )
              & ( ( C = empty_set )
               => ( quasi_total @ C @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(8,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( in @ A @ B )
        & ( element @ B @ ( powerset @ C ) )
        & ( empty @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).

thf(70,plain,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( in @ A @ B )
        & ( element @ B @ ( powerset @ C ) )
        & ( empty @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(45,axiom,
    ! [A: $i,B: $i] : ( subset @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

thf(192,plain,
    ! [A: $i] : ( subset @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(29,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).

thf(124,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(18,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
     => ( relation @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).

thf(96,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
     => ( relation @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(42,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( relation_of2_as_subset @ C @ A @ B )
     => ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).

thf(181,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( relation_of2_as_subset @ C @ A @ B )
     => ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(14,axiom,
    ! [A: $i] :
      ( ~ ( empty @ A )
     => ? [B: $i] :
          ( ( element @ B @ ( powerset @ A ) )
          & ~ ( empty @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).

thf(86,plain,
    ! [A: $i] :
      ( ~ ( empty @ A )
     => ? [B: $i] :
          ( ( element @ B @ ( powerset @ A ) )
          & ~ ( empty @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(44,axiom,
    ? [A: $i] :
      ( ( relation @ A )
      & ( function @ A )
      & ( one_to_one @ A )
      & ( empty @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_partfun1) ).

thf(187,plain,
    ? [A: $i] :
      ( ( relation @ A )
      & ( function @ A )
      & ( one_to_one @ A )
      & ( empty @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(25,axiom,
    ! [A: $i] :
      ( ( ~ ( empty @ A )
        & ( relation @ A ) )
     => ~ ( empty @ ( relation_dom @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).

thf(113,plain,
    ! [A: $i] :
      ( ( ~ ( empty @ A )
        & ( relation @ A ) )
     => ~ ( empty @ ( relation_dom @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

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

thf(81,plain,
    ? [A: $i] :
      ~ ( empty @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(10,axiom,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ( element @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).

thf(76,plain,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ( element @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(19,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( relation_of2 @ C @ A @ B )
     => ( element @ ( relation_dom_as_subset @ A @ B @ C ) @ ( powerset @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relset_1) ).

thf(98,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( relation_of2 @ C @ A @ B )
     => ( element @ ( relation_dom_as_subset @ A @ B @ C ) @ ( powerset @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(21,axiom,
    ! [A: $i] :
      ( ( empty @ A )
     => ( ( empty @ ( relation_dom @ A ) )
        & ( relation @ ( relation_dom @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).

thf(103,plain,
    ! [A: $i] :
      ( ( empty @ A )
     => ( ( empty @ ( relation_dom @ A ) )
        & ( relation @ ( relation_dom @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(16,axiom,
    ? [A: $i] :
      ( ~ ( empty @ A )
      & ( relation @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).

thf(91,plain,
    ? [A: $i] :
      ( ~ ( empty @ A )
      & ( relation @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(47,axiom,
    ? [A: $i] :
      ( ( relation @ A )
      & ( function @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).

thf(198,plain,
    ? [A: $i] :
      ( ( relation @ A )
      & ( function @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(23,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( empty @ A )
        & ~ ( empty @ B ) )
     => ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).

thf(108,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( empty @ A )
        & ~ ( empty @ B ) )
     => ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(1,conjecture,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( function @ D )
        & ( quasi_total @ D @ A @ B )
        & ( relation_of2_as_subset @ D @ A @ B ) )
     => ( ( subset @ B @ C )
       => ( ( ( B = empty_set )
            & ( A != empty_set ) )
          | ( ( function @ D )
            & ( quasi_total @ D @ A @ C )
            & ( relation_of2_as_subset @ D @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_2) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i,C: $i,D: $i] :
        ( ( ( function @ D )
          & ( quasi_total @ D @ A @ B )
          & ( relation_of2_as_subset @ D @ A @ B ) )
       => ( ( subset @ B @ C )
         => ( ( ( B = empty_set )
              & ( A != empty_set ) )
            | ( ( function @ D )
              & ( quasi_total @ D @ A @ C )
              & ( relation_of2_as_subset @ D @ A @ C ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(48,plain,
    ~ ! [A: $i,B: $i,C: $i,D: $i] :
        ( ( ( function @ D )
          & ( quasi_total @ D @ A @ B )
          & ( relation_of2_as_subset @ D @ A @ B ) )
       => ( ( subset @ B @ C )
         => ( ( ( B = empty_set )
              & ( A != empty_set ) )
            | ( ( function @ D )
              & ( quasi_total @ D @ A @ C )
              & ( relation_of2_as_subset @ D @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(33,axiom,
    ? [A: $i] :
      ( ( relation @ A )
      & ( relation_empty_yielding @ A )
      & ( function @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_funct_1) ).

thf(150,plain,
    ? [A: $i] :
      ( ( relation @ A )
      & ( relation_empty_yielding @ A )
      & ( function @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(37,axiom,
    empty @ empty_set,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).

thf(168,plain,
    empty @ empty_set,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(43,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] :
      ( ( relation_of2 @ C @ A @ B )
      & ( relation @ C )
      & ( function @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_partfun1) ).

thf(183,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] :
      ( ( relation_of2 @ C @ A @ B )
      & ( relation @ C )
      & ( function @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(30,axiom,
    ? [A: $i] :
      ( ( relation @ A )
      & ( function @ A )
      & ( one_to_one @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).

thf(126,plain,
    ? [A: $i] :
      ( ( relation @ A )
      & ( function @ A )
      & ( one_to_one @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(17,axiom,
    ! [A: $i] :
      ( ( empty @ A )
     => ( relation @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).

thf(94,plain,
    ! [A: $i] :
      ( ( empty @ A )
     => ( relation @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(36,axiom,
    ! [A: $i,B: $i] :
      ( ( element @ A @ ( powerset @ B ) )
    <=> ( subset @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).

thf(163,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)],[36]) ).

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

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

thf(205,plain,
    $false,
    inference(cvc4,[status(thm)],[115,56,174,110,78,117,169,73,64,176,130,194,67,154,158,58,100,179,106,121,84,89,133,70,192,124,96,181,86,187,113,81,76,98,103,91,198,108,48,150,168,183,126,94,163,62]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU291+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n021.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 13:01:13 EDT 2023
% 0.16/0.36  % CPUTime  : 
% 0.91/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.20/0.98  % [INFO] 	 Parsing done (136ms). 
% 1.40/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.73/1.19  % [INFO] 	 eprover registered as external prover. 
% 1.73/1.19  % [INFO] 	 cvc4 registered as external prover. 
% 1.73/1.20  % [INFO] 	 Scanning for conjecture ... 
% 1.93/1.26  % [INFO] 	 Found a conjecture and 51 axioms. Running axiom selection ... 
% 2.00/1.31  % [INFO] 	 Axiom selection finished. Selected 45 axioms (removed 6 axioms). 
% 2.21/1.35  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.21/1.36  % [INFO] 	 Type checking passed. 
% 2.21/1.36  % [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 ... 
% 4.07/2.00  % External prover 'cvc4' found a proof!
% 4.07/2.00  % [INFO] 	 Killing All external provers ... 
% 4.07/2.00  % Time passed: 1486ms (effective reasoning time: 1008ms)
% 4.07/2.00  % 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)>
% 4.07/2.00  % Axioms used in derivation (45): redefinition_m2_relset_1, fc4_subset_1, rc1_funct_1, t5_subset, existence_m1_relset_1, rc4_funct_1, t4_subset, fc5_relat_1, d1_funct_2, rc2_xboole_0, antisymmetry_r2_hidden, t3_xboole_1, dt_k4_relset_1, fc1_xboole_0, fc4_relat_1, t1_subset, rc2_partfun1, rc3_funct_1, dt_m2_relset_1, cc1_relat_1, t16_relset_1, rc3_relat_1, t6_boole, rc2_subset_1, t7_boole, cc1_funct_1, fc1_subset_1, rc2_funct_1, rc1_subset_1, rc1_funct_2, cc2_funct_1, t3_subset, cc1_relset_1, existence_m1_subset_1, rc2_relat_1, existence_m2_relset_1, rc1_relat_1, reflexivity_r1_tarski, t8_boole, rc1_xboole_0, t2_subset, fc7_relat_1, fc12_relat_1, rc1_partfun1, redefinition_k4_relset_1
% 4.07/2.00  % No. of inferences in proof: 94
% 4.07/2.00  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1486 ms resp. 1008 ms w/o parsing
% 4.45/2.05  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.45/2.05  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------