TSTP Solution File: SET984+1 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SET984+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n023.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 : Tue May 21 03:04:42 EDT 2024

% Result   : Theorem 2.79s 1.66s
% Output   : Refutation 3.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   31 (  17 unt;   5 typ;   0 def)
%            Number of atoms       :   52 (  30 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  142 (   4   ~;  10   |;   6   &; 112   @)
%                                         (   1 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   54 (   0   ^  50   !;   4   ?;  54   :)

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

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

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

thf(set_intersection2_type,type,
    set_intersection2: $i > $i > $i ).

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

thf(1,conjecture,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( subset @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
     => ( ( ( cartesian_product2 @ A @ B )
          = empty_set )
        | ( ( subset @ A @ C )
          & ( subset @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t138_zfmisc_1) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i,C: $i,D: $i] :
        ( ( subset @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
       => ( ( ( cartesian_product2 @ A @ B )
            = empty_set )
          | ( ( subset @ A @ C )
            & ( subset @ B @ D ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(14,plain,
    ~ ! [A: $i,B: $i,C: $i,D: $i] :
        ( ( subset @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
       => ( ( ( cartesian_product2 @ A @ B )
            = empty_set )
          | ( ( subset @ A @ C )
            & ( subset @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(11,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( cartesian_product2 @ A @ B )
        = ( cartesian_product2 @ C @ D ) )
     => ( ( A = empty_set )
        | ( B = empty_set )
        | ( ( A = C )
          & ( B = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_zfmisc_1) ).

thf(46,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( cartesian_product2 @ A @ B )
        = ( cartesian_product2 @ C @ D ) )
     => ( ( A = empty_set )
        | ( B = empty_set )
        | ( ( A = C )
          & ( B = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(13,axiom,
    ! [A: $i,B: $i] :
      ( ( subset @ A @ B )
     => ( ( set_intersection2 @ A @ B )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).

thf(53,plain,
    ! [A: $i,B: $i] :
      ( ( subset @ A @ B )
     => ( ( set_intersection2 @ A @ B )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(4,axiom,
    empty @ empty_set,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).

thf(22,plain,
    empty @ empty_set,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(8,axiom,
    ! [A: $i,B: $i] : ( subset @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

thf(31,plain,
    ! [A: $i] : ( subset @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(10,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( cartesian_product2 @ ( set_intersection2 @ A @ B ) @ ( set_intersection2 @ C @ D ) )
      = ( set_intersection2 @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_zfmisc_1) ).

thf(43,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( cartesian_product2 @ ( set_intersection2 @ A @ B ) @ ( set_intersection2 @ C @ D ) )
      = ( set_intersection2 @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(7,axiom,
    ? [A: $i] :
      ~ ( empty @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).

thf(28,plain,
    ? [A: $i] :
      ~ ( empty @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(9,axiom,
    ! [A: $i,B: $i] :
      ( ( ( cartesian_product2 @ A @ B )
        = empty_set )
    <=> ( ( A = empty_set )
        | ( B = empty_set ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_zfmisc_1) ).

thf(33,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( cartesian_product2 @ A @ B )
          = empty_set )
       => ( ( A = empty_set )
          | ( B = empty_set ) ) )
      & ( ( ( A = empty_set )
          | ( B = empty_set ) )
       => ( ( cartesian_product2 @ A @ B )
          = empty_set ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(6,axiom,
    ? [A: $i] : ( empty @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).

thf(26,plain,
    ? [A: $i] : ( empty @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ( ( set_intersection2 @ A @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).

thf(23,plain,
    ! [A: $i] :
      ( ( set_intersection2 @ A @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(12,axiom,
    ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).

thf(51,plain,
    ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(3,axiom,
    ! [A: $i,B: $i] :
      ( ( set_intersection2 @ A @ B )
      = ( set_intersection2 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

thf(19,plain,
    ! [A: $i,B: $i] :
      ( ( set_intersection2 @ A @ B )
      = ( set_intersection2 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(56,plain,
    $false,
    inference(e,[status(thm)],[14,46,53,22,31,43,28,33,26,23,51,19]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET984+1 : TPTP v8.2.0. Released v3.2.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.36  % Computer : n023.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Mon May 20 11:57:24 EDT 2024
% 0.14/0.36  % CPUTime  : 
% 0.97/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.15/0.98  % [INFO] 	 Parsing done (107ms). 
% 1.15/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.68/1.18  % [INFO] 	 eprover registered as external prover. 
% 1.68/1.18  % [INFO] 	 cvc4 registered as external prover. 
% 1.68/1.19  % [INFO] 	 Scanning for conjecture ... 
% 1.84/1.24  % [INFO] 	 Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ... 
% 1.84/1.26  % [INFO] 	 Axiom selection finished. Selected 11 axioms (removed 0 axioms). 
% 1.84/1.28  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.84/1.28  % [INFO] 	 Type checking passed. 
% 1.84/1.29  % [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 ... 
% 2.79/1.66  % External prover 'e' found a proof!
% 2.79/1.66  % [INFO] 	 Killing All external provers ... 
% 2.79/1.66  % Time passed: 1134ms (effective reasoning time: 675ms)
% 2.79/1.66  % 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)>
% 2.79/1.66  % Axioms used in derivation (11): t17_xboole_1, idempotence_k3_xboole_0, commutativity_k3_xboole_0, t123_zfmisc_1, rc1_xboole_0, t134_zfmisc_1, rc2_xboole_0, fc1_xboole_0, t113_zfmisc_1, t28_xboole_1, reflexivity_r1_tarski
% 2.79/1.66  % No. of inferences in proof: 26
% 2.79/1.66  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1134 ms resp. 675 ms w/o parsing
% 3.18/1.70  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.18/1.70  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------