TSTP Solution File: SET013-1 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SET013-1 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n018.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 03:00:46 EDT 2024

% Result   : Unsatisfiable 3.93s 2.36s
% Output   : Refutation 3.99s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   29
% Syntax   : Number of formulae    :   49 (   7 unt;  10 typ;   0 def)
%            Number of atoms       :   81 (   0 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :  288 (  42   ~;  42   |;   0   &; 204   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   13 (  13   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (  10 usr;   4 con; 0-2 aty)
%            Number of variables   :   84 (   0   ^  84   !;   0   ?;  84   :)

% Comments : 
%------------------------------------------------------------------------------
thf(equal_sets_type,type,
    equal_sets: $i > $i > $o ).

thf(intersection_type,type,
    intersection: $i > $i > $i ).

thf(as_type,type,
    as: $i ).

thf(bs_type,type,
    bs: $i ).

thf(member_type,type,
    member: $i > $i > $o ).

thf(member_of_1_not_of_2_type,type,
    member_of_1_not_of_2: $i > $i > $i ).

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

thf(union_type,type,
    union: $i > $i > $i ).

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

thf(complement_type,type,
    complement: $i > $i ).

thf(18,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( equal_sets @ A @ B )
      | ( subset @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_equal_sets_are_subsets2) ).

thf(53,plain,
    ! [B: $i,A: $i] :
      ( ~ ( equal_sets @ A @ B )
      | ( subset @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(15,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ A @ B )
      | ~ ( member @ A @ C )
      | ( member @ A @ ( intersection @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_both_is_member_of_intersection) ).

thf(48,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ A @ B )
      | ~ ( member @ A @ C )
      | ( member @ A @ ( intersection @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(16,axiom,
    ! [A: $i] : ( equal_sets @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_for_set_equal) ).

thf(50,plain,
    ! [A: $i] : ( equal_sets @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(12,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( equal_sets @ A @ B )
      | ~ ( equal_sets @ B @ C )
      | ( equal_sets @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_for_set_equal) ).

thf(42,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( equal_sets @ A @ B )
      | ~ ( equal_sets @ B @ C )
      | ( equal_sets @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(3,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ A @ B )
      | ~ ( subset @ B @ C )
      | ( member @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',membership_in_subsets) ).

thf(24,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ A @ B )
      | ~ ( subset @ B @ C )
      | ( member @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(1,negated_conjecture,
    ~ ( equal_sets @ ( intersection @ as @ bs ) @ ( intersection @ bs @ as ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutativity) ).

thf(20,plain,
    ~ ( equal_sets @ ( intersection @ as @ bs ) @ ( intersection @ bs @ as ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

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

thf(46,plain,
    ! [B: $i,A: $i] :
      ( ~ ( subset @ A @ B )
      | ~ ( subset @ B @ A )
      | ( equal_sets @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(5,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ A @ ( union @ B @ C ) )
      | ( member @ A @ B )
      | ( member @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_union_is_member_of_one_set) ).

thf(28,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ A @ ( union @ B @ C ) )
      | ( member @ A @ B )
      | ( member @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(10,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ A @ B )
      | ( member @ A @ ( union @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_set2_is_member_of_union) ).

thf(38,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ A @ B )
      | ( member @ A @ ( union @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(7,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( member @ A @ B )
      | ~ ( member @ A @ ( complement @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_member_of_set_and_complement) ).

thf(32,plain,
    ! [B: $i,A: $i] :
      ( ~ ( member @ A @ B )
      | ~ ( member @ A @ ( complement @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(8,axiom,
    ! [B: $i,A: $i] :
      ( ( subset @ A @ B )
      | ( member @ ( member_of_1_not_of_2 @ A @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_axiom1) ).

thf(34,plain,
    ! [B: $i,A: $i] :
      ( ( subset @ A @ B )
      | ( member @ ( member_of_1_not_of_2 @ A @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(2,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( member @ ( member_of_1_not_of_2 @ A @ B ) @ B )
      | ( subset @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_axiom2) ).

thf(22,plain,
    ! [B: $i,A: $i] :
      ( ~ ( member @ ( member_of_1_not_of_2 @ A @ B ) @ B )
      | ( subset @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(13,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ A @ ( intersection @ B @ C ) )
      | ( member @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set1) ).

thf(44,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ A @ ( intersection @ B @ C ) )
      | ( member @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(11,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( equal_sets @ A @ B )
      | ( subset @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_equal_sets_are_subsets1) ).

thf(40,plain,
    ! [B: $i,A: $i] :
      ( ~ ( equal_sets @ A @ B )
      | ( subset @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(4,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ A @ B )
      | ( member @ A @ ( union @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_set1_is_member_of_union) ).

thf(26,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ A @ B )
      | ( member @ A @ ( union @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(19,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( equal_sets @ A @ B )
      | ( equal_sets @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_for_set_equal) ).

thf(55,plain,
    ! [B: $i,A: $i] :
      ( ~ ( equal_sets @ A @ B )
      | ( equal_sets @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(9,axiom,
    ! [B: $i,A: $i] :
      ( ( member @ A @ B )
      | ( member @ A @ ( complement @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_set_or_complement) ).

thf(36,plain,
    ! [B: $i,A: $i] :
      ( ( member @ A @ B )
      | ( member @ A @ ( complement @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(6,axiom,
    ! [A: $i] :
      ~ ( member @ A @ empty_set ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).

thf(30,plain,
    ! [A: $i] :
      ~ ( member @ A @ empty_set ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(17,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ A @ ( intersection @ B @ C ) )
      | ( member @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set2) ).

thf(51,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ A @ ( intersection @ B @ C ) )
      | ( member @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(60,plain,
    $false,
    inference(cvc4,[status(thm)],[53,48,50,42,24,20,46,28,38,32,34,22,44,40,26,55,36,30,51]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10  % Problem  : SET013-1 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.09/0.13  % Command  : run_Leo-III %s %d
% 0.13/0.33  % Computer : n018.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Mon May 20 12:08:09 EDT 2024
% 0.13/0.33  % CPUTime  : 
% 1.01/0.97  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.30/1.14  % [INFO] 	 Parsing done (172ms). 
% 1.30/1.15  % [INFO] 	 Running in sequential loop mode. 
% 1.95/1.52  % [INFO] 	 eprover registered as external prover. 
% 1.95/1.52  % [INFO] 	 cvc4 registered as external prover. 
% 2.01/1.53  % [INFO] 	 Scanning for conjecture ... 
% 2.17/1.62  % [INFO] 	 Found a conjecture (or negated_conjecture) and 21 axioms. Running axiom selection ... 
% 2.17/1.67  % [INFO] 	 Axiom selection finished. Selected 18 axioms (removed 3 axioms). 
% 2.35/1.70  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.35/1.70  % [INFO] 	 Type checking passed. 
% 2.35/1.71  % [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 ... 
% 3.93/2.36  % External prover 'cvc4' found a proof!
% 3.93/2.36  % [INFO] 	 Killing All external provers ... 
% 3.93/2.36  % Time passed: 1874ms (effective reasoning time: 1201ms)
% 3.93/2.36  % Axioms used in derivation (18): member_of_intersection_is_member_of_set2, reflexivity_for_set_equal, set_equal_sets_are_subsets2, subsets_are_set_equal_sets, member_of_intersection_is_member_of_set1, set_equal_sets_are_subsets1, transitivity_for_set_equal, member_of_set_or_complement, symmetry_for_set_equal, member_of_set1_is_member_of_union, member_of_union_is_member_of_one_set, not_member_of_set_and_complement, subsets_axiom2, empty_set, member_of_set2_is_member_of_union, member_of_both_is_member_of_intersection, membership_in_subsets, subsets_axiom1
% 3.93/2.36  % No. of inferences in proof: 39
% 3.93/2.36  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1874 ms resp. 1201 ms w/o parsing
% 3.99/2.41  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.99/2.41  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------