TSTP Solution File: SEU167+3 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SEU167+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n017.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 11:57:21 EDT 2023

% Result   : Theorem 2.61s 1.59s
% Output   : Refutation 2.95s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   17 (   7 unt;   3 typ;   0 def)
%            Number of atoms       :   28 (   0 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   96 (   4   ~;   0   |;   7   &;  78   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   3 usr;   1 con; 0-2 aty)
%            Number of variables   :   31 (   0   ^;  27   !;   4   ?;  31   :)

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

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

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

thf(7,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( subset @ A @ B )
        & ( subset @ B @ C ) )
     => ( subset @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).

thf(24,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( subset @ A @ B )
        & ( subset @ B @ C ) )
     => ( subset @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(4,axiom,
    ? [A: $i] :
      ~ ( empty @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).

thf(14,plain,
    ? [A: $i] :
      ~ ( empty @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(5,axiom,
    ! [A: $i,B: $i] : ( subset @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

thf(17,plain,
    ! [A: $i] : ( subset @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(3,axiom,
    ? [A: $i] : ( empty @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

thf(12,plain,
    ? [A: $i] : ( empty @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(1,conjecture,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( subset @ A @ B )
        & ( subset @ C @ D ) )
     => ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).

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

thf(8,plain,
    ~ ! [A: $i,B: $i,C: $i,D: $i] :
        ( ( ( subset @ A @ B )
          & ( subset @ C @ D ) )
       => ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(6,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( subset @ A @ B )
     => ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
        & ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).

thf(19,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( subset @ A @ B )
     => ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
        & ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(28,plain,
    $false,
    inference(e,[status(thm)],[24,14,17,12,8,19]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SEU167+3 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n017.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 12:18:16 EDT 2023
% 0.16/0.36  % CPUTime  : 
% 0.85/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.15/0.97  % [INFO] 	 Parsing done (106ms). 
% 1.15/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.46/1.18  % [INFO] 	 eprover registered as external prover. 
% 1.46/1.18  % [INFO] 	 cvc4 registered as external prover. 
% 1.67/1.18  % [INFO] 	 Scanning for conjecture ... 
% 1.75/1.23  % [INFO] 	 Found a conjecture and 5 axioms. Running axiom selection ... 
% 1.83/1.26  % [INFO] 	 Axiom selection finished. Selected 5 axioms (removed 0 axioms). 
% 1.83/1.27  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.83/1.27  % [INFO] 	 Type checking passed. 
% 1.83/1.27  % [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 ... 
% 2.61/1.59  % External prover 'e' found a proof!
% 2.61/1.59  % [INFO] 	 Killing All external provers ... 
% 2.61/1.59  % Time passed: 1060ms (effective reasoning time: 609ms)
% 2.61/1.59  % 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)>
% 2.61/1.59  % Axioms used in derivation (5): t118_zfmisc_1, t1_xboole_1, reflexivity_r1_tarski, rc1_xboole_0, rc2_xboole_0
% 2.61/1.59  % No. of inferences in proof: 14
% 2.61/1.59  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1060 ms resp. 609 ms w/o parsing
% 2.95/1.66  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.95/1.66  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------