TSTP Solution File: SET011-1 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SET011-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n006.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 03:00:44 EDT 2024

% Result   : Unsatisfiable 3.60s 2.14s
% Output   : Refutation 3.93s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   29
% Syntax   : Number of formulae    :   48 (   7 unt;  11 typ;   0 def)
%            Number of atoms       :  101 (   0 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  434 (  48   ~;  64   |;   0   &; 322   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   18 (  18   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (  11 usr;   5 con; 0-3 aty)
%            Number of variables   :   98 (   0   ^  98   !;   0   ?;  98   :)

% Comments : 
%------------------------------------------------------------------------------
thf(intersection_type,type,
    intersection: $i > $i > $i > $o ).

thf(a_type,type,
    a: $i ).

thf(b_type,type,
    b: $i ).

thf(aD_aDb_type,type,
    aD_aDb: $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(difference_type,type,
    difference: $i > $i > $i > $o ).

thf(k_type,type,
    k: $i > $i > $i > $i ).

thf(aDb_type,type,
    aDb: $i ).

thf(h_type,type,
    h: $i > $i > $i > $i ).

thf(6,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( member @ A @ B )
      | ~ ( difference @ B @ C @ D )
      | ( member @ A @ D )
      | ( member @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_difference_or_set2) ).

thf(29,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( member @ A @ B )
      | ~ ( difference @ B @ C @ D )
      | ( member @ A @ D )
      | ( member @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

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

thf(41,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( intersection @ A @ B @ C )
      | ~ ( member @ D @ B )
      | ~ ( member @ D @ A )
      | ( member @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(15,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ ( h @ A @ B @ C ) @ C )
      | ~ ( member @ ( h @ A @ B @ C ) @ B )
      | ~ ( member @ ( h @ A @ B @ C ) @ A )
      | ( intersection @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_axiom3) ).

thf(45,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ ( h @ A @ B @ C ) @ C )
      | ~ ( member @ ( h @ A @ B @ C ) @ B )
      | ~ ( member @ ( h @ A @ B @ C ) @ A )
      | ( intersection @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(5,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ ( k @ A @ B @ C ) @ C )
      | ~ ( member @ ( k @ A @ B @ C ) @ A )
      | ( member @ ( k @ A @ B @ C ) @ B )
      | ( difference @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_axiom3) ).

thf(27,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ ( k @ A @ B @ C ) @ C )
      | ~ ( member @ ( k @ A @ B @ C ) @ A )
      | ( member @ ( k @ A @ B @ C ) @ B )
      | ( difference @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

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

thf(49,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( intersection @ A @ B @ C )
      | ~ ( member @ D @ C )
      | ( member @ D @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(11,axiom,
    difference @ a @ aDb @ aD_aDb,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_minus_aDb) ).

thf(39,plain,
    difference @ a @ aDb @ aD_aDb,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(9,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( difference @ A @ B @ C )
      | ~ ( member @ D @ C )
      | ( member @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_difference) ).

thf(35,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( difference @ A @ B @ C )
      | ~ ( member @ D @ C )
      | ( member @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(7,axiom,
    ! [B: $i,A: $i] :
      ( ( subset @ A @ B )
      | ( member @ ( member_of_1_not_of_2 @ A @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsets_axiom1) ).

thf(31,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)],[7]) ).

thf(14,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( member @ ( h @ A @ B @ C ) @ C )
      | ( intersection @ A @ B @ C )
      | ( member @ ( h @ A @ B @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_axiom2) ).

thf(43,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( member @ ( h @ A @ B @ C ) @ C )
      | ( intersection @ A @ B @ C )
      | ( member @ ( h @ A @ B @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(16,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( member @ ( h @ A @ B @ C ) @ C )
      | ( intersection @ A @ B @ C )
      | ( member @ ( h @ A @ B @ C ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_axiom1) ).

thf(47,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( member @ ( h @ A @ B @ C ) @ C )
      | ( intersection @ A @ B @ C )
      | ( member @ ( h @ A @ B @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(10,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ ( k @ A @ B @ C ) @ B )
      | ( member @ ( k @ A @ B @ C ) @ C )
      | ( difference @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_axiom1) ).

thf(37,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( member @ ( k @ A @ B @ C ) @ B )
      | ( member @ ( k @ A @ B @ C ) @ C )
      | ( difference @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(4,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( difference @ A @ B @ C )
      | ( member @ ( k @ A @ B @ C ) @ A )
      | ( member @ ( k @ A @ B @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_axiom2) ).

thf(25,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( difference @ A @ B @ C )
      | ( member @ ( k @ A @ B @ C ) @ A )
      | ( member @ ( k @ A @ B @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

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

thf(21,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(8,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( member @ A @ B )
      | ~ ( member @ A @ C )
      | ~ ( difference @ D @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_member_of_difference) ).

thf(33,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( member @ A @ B )
      | ~ ( member @ A @ C )
      | ~ ( difference @ D @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(12,axiom,
    difference @ a @ b @ aDb,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_minus_b) ).

thf(40,plain,
    difference @ a @ b @ aDb,
    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/sandbox/benchmark/theBenchmark.p',membership_in_subsets) ).

thf(23,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(18,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( intersection @ A @ B @ C )
      | ~ ( member @ D @ C )
      | ( member @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set1) ).

thf(51,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( intersection @ A @ B @ C )
      | ~ ( member @ D @ C )
      | ( member @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(1,negated_conjecture,
    ~ ( intersection @ a @ b @ aD_aDb ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_intersection_b_is_aD_aDb) ).

thf(19,plain,
    ~ ( intersection @ a @ b @ aD_aDb ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(53,plain,
    $false,
    inference(e,[status(thm)],[29,41,45,27,49,39,35,31,43,47,37,25,21,33,40,23,51,19]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09  % Problem  : SET011-1 : TPTP v8.2.0. Released v1.0.0.
% 0.04/0.11  % Command  : run_Leo-III %s %d
% 0.11/0.31  % Computer : n006.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Mon May 20 11:33:54 EDT 2024
% 0.11/0.31  % CPUTime  : 
% 0.90/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.23/1.08  % [INFO] 	 Parsing done (167ms). 
% 1.40/1.09  % [INFO] 	 Running in sequential loop mode. 
% 1.83/1.44  % [INFO] 	 eprover registered as external prover. 
% 1.83/1.44  % [INFO] 	 cvc4 registered as external prover. 
% 1.98/1.45  % [INFO] 	 Scanning for conjecture ... 
% 2.07/1.52  % [INFO] 	 Found a conjecture (or negated_conjecture) and 20 axioms. Running axiom selection ... 
% 2.21/1.58  % [INFO] 	 Axiom selection finished. Selected 17 axioms (removed 3 axioms). 
% 2.21/1.61  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.21/1.61  % [INFO] 	 Type checking passed. 
% 2.21/1.62  % [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 ... 
% 3.60/2.14  % External prover 'e' found a proof!
% 3.60/2.14  % [INFO] 	 Killing All external provers ... 
% 3.60/2.14  % Time passed: 1685ms (effective reasoning time: 1044ms)
% 3.60/2.14  % Axioms used in derivation (17): member_of_intersection_is_member_of_set2, a_minus_aDb, member_of_difference_or_set2, difference_axiom3, subsets_axiom2, member_of_both_is_member_of_intersection, difference_axiom2, a_minus_b, member_of_intersection_is_member_of_set1, difference_axiom1, intersection_axiom1, not_member_of_difference, member_of_difference, intersection_axiom3, intersection_axiom2, membership_in_subsets, subsets_axiom1
% 3.60/2.14  % No. of inferences in proof: 37
% 3.60/2.14  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1685 ms resp. 1044 ms w/o parsing
% 3.93/2.25  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.93/2.25  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------