TSTP Solution File: SEU263+1 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SEU263+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n013.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 11:57:54 EDT 2023

% Result   : Theorem 3.21s 1.69s
% Output   : Refutation 3.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   39 (   9 unt;   9 typ;   0 def)
%            Number of atoms       :   66 (   0 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  231 (   2   ~;   0   |;   9   &; 193   @)
%                                         (   3 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   16 (  16   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   9 usr;   1 con; 0-3 aty)
%            Number of variables   :   81 (   0   ^;  75   !;   6   ?;  81   :)

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

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

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

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

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

thf(5,axiom,
    ! [A: $i] :
    ? [B: $i] : ( element @ B @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).

thf(24,plain,
    ! [A: $i] :
    ? [B: $i] : ( element @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(14,axiom,
    ! [A: $i,B: $i] : ( subset @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

thf(52,plain,
    ! [A: $i] : ( subset @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(3,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(20,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
     => ( relation @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(9,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( relation_of2_as_subset @ C @ A @ B )
     => ( ( subset @ ( relation_dom @ C ) @ A )
        & ( subset @ ( relation_rng @ C ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_relset_1) ).

thf(38,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( relation_of2_as_subset @ C @ A @ B )
     => ( ( subset @ ( relation_dom @ C ) @ A )
        & ( subset @ ( relation_rng @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(10,axiom,
    ! [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(41,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)],[10]) ).

thf(12,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(45,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)],[12]) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( relation_of2 @ C @ A @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).

thf(22,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( relation_of2 @ C @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(15,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(54,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( subset @ A @ B )
        & ( subset @ B @ C ) )
     => ( subset @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(11,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(43,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)],[11]) ).

thf(6,axiom,
    ! [A: $i,B: $i] :
      ( ( element @ A @ ( powerset @ B ) )
    <=> ( subset @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).

thf(26,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)],[6]) ).

thf(8,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(36,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(13,axiom,
    ! [A: $i] :
      ( ( relation @ A )
     => ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relat_1) ).

thf(50,plain,
    ! [A: $i] :
      ( ( relation @ A )
     => ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(1,conjecture,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( relation_of2_as_subset @ D @ C @ A )
     => ( ( subset @ ( relation_rng @ D ) @ B )
       => ( relation_of2_as_subset @ D @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relset_1) ).

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

thf(16,plain,
    ~ ! [A: $i,B: $i,C: $i,D: $i] :
        ( ( relation_of2_as_subset @ D @ C @ A )
       => ( ( subset @ ( relation_rng @ D ) @ B )
         => ( relation_of2_as_subset @ D @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(7,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( relation_of2 @ C @ A @ B )
    <=> ( subset @ C @ ( cartesian_product2 @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relset_1) ).

thf(31,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( relation_of2 @ C @ A @ B )
       => ( subset @ C @ ( cartesian_product2 @ A @ B ) ) )
      & ( ( subset @ C @ ( cartesian_product2 @ A @ B ) )
       => ( relation_of2 @ C @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(59,plain,
    $false,
    inference(cvc4,[status(thm)],[24,52,20,38,41,45,22,54,43,26,36,50,16,31]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU263+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14  % Command  : run_Leo-III %s %d
% 0.13/0.35  % Computer : n013.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu May 18 13:10:37 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.92/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.17/0.95  % [INFO] 	 Parsing done (113ms). 
% 1.17/0.96  % [INFO] 	 Running in sequential loop mode. 
% 1.63/1.14  % [INFO] 	 eprover registered as external prover. 
% 1.63/1.14  % [INFO] 	 cvc4 registered as external prover. 
% 1.63/1.15  % [INFO] 	 Scanning for conjecture ... 
% 1.70/1.20  % [INFO] 	 Found a conjecture and 19 axioms. Running axiom selection ... 
% 1.89/1.23  % [INFO] 	 Axiom selection finished. Selected 13 axioms (removed 6 axioms). 
% 1.89/1.25  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.89/1.26  % [INFO] 	 Type checking passed. 
% 2.01/1.26  % [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 ... 
% 3.21/1.68  % External prover 'cvc4' found a proof!
% 3.21/1.68  % [INFO] 	 Killing All external provers ... 
% 3.21/1.69  % Time passed: 1170ms (effective reasoning time: 724ms)
% 3.21/1.69  % 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)>
% 3.21/1.69  % Axioms used in derivation (13): redefinition_m2_relset_1, dt_m2_relset_1, t1_xboole_1, existence_m1_relset_1, existence_m2_relset_1, t21_relat_1, t12_relset_1, t3_subset, cc1_relset_1, existence_m1_subset_1, d1_relset_1, t119_zfmisc_1, reflexivity_r1_tarski
% 3.21/1.69  % No. of inferences in proof: 30
% 3.21/1.69  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1170 ms resp. 724 ms w/o parsing
% 3.25/1.72  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.25/1.72  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------