TSTP Solution File: TOP005-2 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : TOP005-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n031.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 12:38:39 EDT 2023

% Result   : Unsatisfiable 2.67s 1.55s
% Output   : Refutation 2.83s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   36 (   5 unt;  11 typ;   0 def)
%            Number of atoms       :   61 (   0 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  246 (  34   ~;  36   |;   0   &; 176   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (  17   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (  11 usr;   3 con; 0-3 aty)
%            Number of variables   :   54 (   0   ^;  54   !;   0   ?;  54   :)

% Comments : 
%------------------------------------------------------------------------------
thf(subset_collections_type,type,
    subset_collections: $i > $i > $o ).

thf(g_type,type,
    g: $i ).

thf(top_of_basis_type,type,
    top_of_basis: $i > $i ).

thf(f_type,type,
    f: $i ).

thf(element_of_collection_type,type,
    element_of_collection: $i > $i > $o ).

thf(union_of_members_type,type,
    union_of_members: $i > $i ).

thf(element_of_set_type,type,
    element_of_set: $i > $i > $o ).

thf(f1_type,type,
    f1: $i > $i > $i ).

thf(f10_type,type,
    f10: $i > $i > $i > $i ).

thf(subset_sets_type,type,
    subset_sets: $i > $i > $o ).

thf(f11_type,type,
    f11: $i > $i > $i ).

thf(7,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( element_of_collection @ A @ ( top_of_basis @ B ) )
      | ~ ( element_of_set @ C @ A )
      | ( subset_sets @ ( f10 @ B @ A @ C ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_39) ).

thf(24,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( element_of_collection @ A @ ( top_of_basis @ B ) )
      | ~ ( element_of_set @ C @ A )
      | ( subset_sets @ ( f10 @ B @ A @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(2,negated_conjecture,
    ~ ( element_of_collection @ ( union_of_members @ g ) @ ( top_of_basis @ f ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_1e_3) ).

thf(14,plain,
    ~ ( element_of_collection @ ( union_of_members @ g ) @ ( top_of_basis @ f ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(5,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( element_of_collection @ A @ ( top_of_basis @ B ) )
      | ~ ( element_of_set @ C @ A )
      | ( element_of_set @ C @ ( f10 @ B @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_37) ).

thf(20,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( element_of_collection @ A @ ( top_of_basis @ B ) )
      | ~ ( element_of_set @ C @ A )
      | ( element_of_set @ C @ ( f10 @ B @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(9,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( element_of_collection @ A @ ( top_of_basis @ B ) )
      | ~ ( element_of_set @ ( f11 @ B @ A ) @ C )
      | ~ ( element_of_collection @ C @ B )
      | ~ ( subset_sets @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_41) ).

thf(28,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( element_of_collection @ A @ ( top_of_basis @ B ) )
      | ~ ( element_of_set @ ( f11 @ B @ A ) @ C )
      | ~ ( element_of_collection @ C @ B )
      | ~ ( subset_sets @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(1,negated_conjecture,
    subset_collections @ g @ ( top_of_basis @ f ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_1e_2) ).

thf(13,plain,
    subset_collections @ g @ ( top_of_basis @ f ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(6,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( element_of_collection @ A @ ( top_of_basis @ B ) )
      | ~ ( element_of_set @ C @ A )
      | ( element_of_collection @ ( f10 @ B @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_38) ).

thf(22,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( element_of_collection @ A @ ( top_of_basis @ B ) )
      | ~ ( element_of_set @ C @ A )
      | ( element_of_collection @ ( f10 @ B @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(4,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( element_of_set @ A @ ( union_of_members @ B ) )
      | ( element_of_collection @ ( f1 @ B @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_of_members_2) ).

thf(18,plain,
    ! [B: $i,A: $i] :
      ( ~ ( element_of_set @ A @ ( union_of_members @ B ) )
      | ( element_of_collection @ ( f1 @ B @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(3,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( element_of_set @ A @ ( union_of_members @ B ) )
      | ( element_of_set @ A @ ( f1 @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_of_members_1) ).

thf(16,plain,
    ! [B: $i,A: $i] :
      ( ~ ( element_of_set @ A @ ( union_of_members @ B ) )
      | ( element_of_set @ A @ ( f1 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(8,axiom,
    ! [B: $i,A: $i] :
      ( ( element_of_collection @ A @ ( top_of_basis @ B ) )
      | ( element_of_set @ ( f11 @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_40) ).

thf(26,plain,
    ! [B: $i,A: $i] :
      ( ( element_of_collection @ A @ ( top_of_basis @ B ) )
      | ( element_of_set @ ( f11 @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(10,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( subset_sets @ A @ B )
      | ~ ( element_of_set @ C @ A )
      | ( element_of_set @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_theory_19) ).

thf(30,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( subset_sets @ A @ B )
      | ~ ( element_of_set @ C @ A )
      | ( element_of_set @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(11,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( subset_sets @ A @ B )
      | ~ ( element_of_collection @ B @ C )
      | ( subset_sets @ A @ ( union_of_members @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_theory_20) ).

thf(32,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( subset_sets @ A @ B )
      | ~ ( element_of_collection @ B @ C )
      | ( subset_sets @ A @ ( union_of_members @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(12,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( subset_collections @ A @ B )
      | ~ ( element_of_collection @ C @ A )
      | ( element_of_collection @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_theory_21) ).

thf(34,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( subset_collections @ A @ B )
      | ~ ( element_of_collection @ C @ A )
      | ( element_of_collection @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(36,plain,
    $false,
    inference(e,[status(thm)],[24,14,20,28,13,22,18,16,26,30,32,34]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : TOP005-2 : TPTP v8.1.2. Released v1.0.0.
% 0.08/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n031.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu May 18 20:31:11 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.95/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.15/0.97  % [INFO] 	 Parsing done (120ms). 
% 1.15/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.67/1.16  % [INFO] 	 eprover registered as external prover. 
% 1.67/1.17  % [INFO] 	 cvc4 registered as external prover. 
% 1.67/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.67/1.22  % [INFO] 	 Found a conjecture and 10 axioms. Running axiom selection ... 
% 1.82/1.24  % [INFO] 	 Axiom selection finished. Selected 10 axioms (removed 0 axioms). 
% 1.82/1.26  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.82/1.26  % [INFO] 	 Type checking passed. 
% 1.82/1.26  % [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 ... 
% 2.67/1.54  % External prover 'e' found a proof!
% 2.67/1.55  % [INFO] 	 Killing All external provers ... 
% 2.67/1.55  % Time passed: 1015ms (effective reasoning time: 563ms)
% 2.67/1.55  % 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)>
% 2.67/1.55  % Axioms used in derivation (10): topology_generated_37, topology_generated_40, topology_generated_39, union_of_members_2, set_theory_20, topology_generated_38, union_of_members_1, topology_generated_41, set_theory_19, set_theory_21
% 2.67/1.55  % No. of inferences in proof: 25
% 2.67/1.55  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1015 ms resp. 563 ms w/o parsing
% 2.83/1.58  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.83/1.58  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------