TSTP Solution File: CAT012-1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : CAT012-1 : 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 : Mon May 20 18:59:53 EDT 2024

% Result   : Unsatisfiable 2.85s 1.80s
% Output   : Refutation 3.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   26
% Syntax   : Number of formulae    :   46 (  15 unt;   7 typ;   0 def)
%            Number of atoms       :   93 (   4 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  342 (  56   ~;  54   |;   0   &; 232   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   2 con; 0-3 aty)
%            Number of variables   :  104 (   0   ^ 104   !;   0   ?; 104   :)

% Comments : 
%------------------------------------------------------------------------------
thf(codomain_type,type,
    codomain: $i > $i ).

thf(domain_type,type,
    domain: $i > $i ).

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

thf(defined_type,type,
    defined: $i > $i > $o ).

thf(identity_map_type,type,
    identity_map: $i > $o ).

thf(product_type,type,
    product: $i > $i > $i > $o ).

thf(compose_type,type,
    compose: $i > $i > $i ).

thf(18,axiom,
    ! [A: $i] : ( product @ ( codomain @ A ) @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_on_codomain) ).

thf(52,plain,
    ! [A: $i] : ( product @ ( codomain @ A ) @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(7,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( defined @ D @ C )
      | ( defined @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',category_theory_axiom3) ).

thf(33,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( defined @ D @ C )
      | ( defined @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(19,axiom,
    ! [A: $i] : ( defined @ A @ ( domain @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mapping_from_x_to_its_domain) ).

thf(53,plain,
    ! [A: $i] : ( defined @ A @ ( domain @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(15,axiom,
    ! [A: $i] : ( identity_map @ ( codomain @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_is_an_identity_map) ).

thf(49,plain,
    ! [A: $i] : ( identity_map @ ( codomain @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

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

thf(39,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ A @ B @ D )
      | ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(8,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ D @ C @ E )
      | ~ ( product @ D @ A @ F )
      | ( product @ F @ B @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',category_theory_axiom5) ).

thf(35,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ D @ C @ E )
      | ~ ( product @ D @ A @ F )
      | ( product @ F @ B @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

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

thf(48,plain,
    ! [A: $i] : ( product @ A @ ( domain @ A ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(2,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( defined @ A @ B )
      | ~ ( identity_map @ A )
      | ( product @ A @ B @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity1) ).

thf(23,plain,
    ! [B: $i,A: $i] :
      ( ~ ( defined @ A @ B )
      | ~ ( identity_map @ A )
      | ( product @ A @ B @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(17,axiom,
    ! [A: $i] : ( identity_map @ ( domain @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_is_an_identity_map) ).

thf(51,plain,
    ! [A: $i] : ( identity_map @ ( domain @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(11,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ C @ D @ E )
      | ~ ( product @ B @ D @ F )
      | ( product @ A @ F @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',category_theory_axiom2) ).

thf(42,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ C @ D @ E )
      | ~ ( product @ B @ D @ F )
      | ( product @ A @ F @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(9,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( defined @ A @ B )
      | ~ ( defined @ B @ C )
      | ~ ( identity_map @ B )
      | ( defined @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',category_theory_axiom6) ).

thf(37,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( defined @ A @ B )
      | ~ ( defined @ B @ C )
      | ~ ( identity_map @ B )
      | ( defined @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(3,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ( defined @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associative_property1) ).

thf(25,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ( defined @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(1,negated_conjecture,
    ( ( codomain @ ( domain @ a ) )
   != ( domain @ a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_codomain_of_domain_is_domain) ).

thf(20,plain,
    ( ( codomain @ ( domain @ a ) )
   != ( domain @ a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(13,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ B @ D @ E )
      | ~ ( defined @ C @ D )
      | ( defined @ A @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',category_theory_axiom1) ).

thf(46,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ B @ D @ E )
      | ~ ( defined @ C @ D )
      | ( defined @ A @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(5,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( defined @ A @ B )
      | ~ ( identity_map @ B )
      | ( product @ A @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity2) ).

thf(29,plain,
    ! [B: $i,A: $i] :
      ( ~ ( defined @ A @ B )
      | ~ ( identity_map @ B )
      | ( product @ A @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(12,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( defined @ C @ D )
      | ( defined @ B @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associative_property2) ).

thf(44,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( defined @ C @ D )
      | ( defined @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(4,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( defined @ A @ B )
      | ( product @ A @ B @ ( compose @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_composition) ).

thf(27,plain,
    ! [B: $i,A: $i] :
      ( ~ ( defined @ A @ B )
      | ( product @ A @ B @ ( compose @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

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

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

thf(6,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ D @ A @ E )
      | ~ ( defined @ D @ C )
      | ( defined @ E @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',category_theory_axiom4) ).

thf(31,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( product @ A @ B @ C )
      | ~ ( product @ D @ A @ E )
      | ~ ( defined @ D @ C )
      | ( defined @ E @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(54,plain,
    $false,
    inference(e,[status(thm)],[52,33,53,49,39,35,48,23,51,42,37,25,20,46,29,44,27,50,31]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : CAT012-1 : TPTP v8.2.0. Released v1.0.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n006.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 : Sat May 18 11:45:54 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.93/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.21/1.01  % [INFO] 	 Parsing done (122ms). 
% 1.21/1.02  % [INFO] 	 Running in sequential loop mode. 
% 1.65/1.25  % [INFO] 	 eprover registered as external prover. 
% 1.65/1.25  % [INFO] 	 cvc4 registered as external prover. 
% 1.65/1.26  % [INFO] 	 Scanning for conjecture ... 
% 1.77/1.31  % [INFO] 	 Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ... 
% 1.92/1.35  % [INFO] 	 Axiom selection finished. Selected 18 axioms (removed 0 axioms). 
% 2.00/1.38  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.00/1.38  % [INFO] 	 Type checking passed. 
% 2.00/1.39  % [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 ... 
% 2.85/1.79  % External prover 'e' found a proof!
% 2.85/1.79  % [INFO] 	 Killing All external provers ... 
% 2.85/1.79  % Time passed: 1275ms (effective reasoning time: 765ms)
% 2.85/1.79  % Axioms used in derivation (18): category_theory_axiom5, domain_is_an_identity_map, category_theory_axiom1, codomain_is_an_identity_map, identity2, category_theory_axiom4, closure_of_composition, mapping_from_x_to_its_domain, mapping_from_codomain_of_x_to_x, associative_property1, product_on_codomain, category_theory_axiom3, category_theory_axiom6, associative_property2, identity1, category_theory_axiom2, product_on_domain, composition_is_well_defined
% 2.85/1.79  % No. of inferences in proof: 39
% 2.85/1.80  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1275 ms resp. 765 ms w/o parsing
% 3.15/1.86  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.15/1.86  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------