TSTP Solution File: CAT011-4 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : CAT011-4 : 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 18:59:52 EDT 2024

% Result   : Unsatisfiable 4.16s 2.65s
% Output   : Refutation 4.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   33 (  11 unt;   6 typ;   0 def)
%            Number of atoms       :   47 (  16 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  142 (  22   ~;  20   |;   0   &; 100   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   38 (   0   ^  38   !;   0   ?;  38   :)

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

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

thf(equivalent_type,type,
    equivalent: $i > $i > $o ).

thf(there_exists_type,type,
    there_exists: $i > $o ).

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

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

thf(12,axiom,
    ! [A: $i] :
      ( ( compose @ ( codomain @ A ) @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_codomain) ).

thf(42,plain,
    ! [A: $i] :
      ( ( compose @ ( codomain @ A ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

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

thf(14,plain,
    ( ( domain @ ( domain @ a ) )
   != ( domain @ a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(9,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( there_exists @ ( domain @ A ) )
      | ( ( domain @ A )
       != ( codomain @ B ) )
      | ( there_exists @ ( compose @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_codomain_composition2) ).

thf(35,plain,
    ! [B: $i,A: $i] :
      ( ~ ( there_exists @ ( domain @ A ) )
      | ( ( domain @ A )
       != ( codomain @ B ) )
      | ( there_exists @ ( compose @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

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

thf(28,plain,
    ! [A: $i] :
      ( ~ ( there_exists @ ( codomain @ A ) )
      | ( there_exists @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(10,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( compose @ A @ ( compose @ B @ C ) )
      = ( compose @ ( compose @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_compose) ).

thf(38,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( compose @ A @ ( compose @ B @ C ) )
      = ( compose @ ( compose @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(8,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( there_exists @ ( compose @ A @ B ) )
      | ( ( domain @ A )
        = ( codomain @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_codomain_composition1) ).

thf(32,plain,
    ! [B: $i,A: $i] :
      ( ~ ( there_exists @ ( compose @ A @ B ) )
      | ( ( domain @ A )
        = ( codomain @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(2,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( equivalent @ A @ B )
      | ( there_exists @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_implies_existence1) ).

thf(17,plain,
    ! [B: $i,A: $i] :
      ( ~ ( equivalent @ A @ B )
      | ( there_exists @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( there_exists @ A )
      | ( A != B )
      | ( equivalent @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_and_equality_implies_equivalence1) ).

thf(22,plain,
    ! [B: $i,A: $i] :
      ( ~ ( there_exists @ A )
      | ( A != B )
      | ( equivalent @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(13,axiom,
    there_exists @ ( domain @ a ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assume_domain_exists) ).

thf(44,plain,
    there_exists @ ( domain @ a ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(11,axiom,
    ! [A: $i] :
      ( ( compose @ A @ ( domain @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_domain) ).

thf(40,plain,
    ! [A: $i] :
      ( ( compose @ A @ ( domain @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(5,axiom,
    ! [A: $i] :
      ( ~ ( there_exists @ ( domain @ A ) )
      | ( there_exists @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_has_elements) ).

thf(26,plain,
    ! [A: $i] :
      ( ~ ( there_exists @ ( domain @ A ) )
      | ( there_exists @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(7,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( there_exists @ ( compose @ A @ B ) )
      | ( there_exists @ ( domain @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_implies_domain) ).

thf(30,plain,
    ! [B: $i,A: $i] :
      ( ~ ( there_exists @ ( compose @ A @ B ) )
      | ( there_exists @ ( domain @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(3,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( equivalent @ A @ B )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_implies_existence2) ).

thf(19,plain,
    ! [B: $i,A: $i] :
      ( ~ ( equivalent @ A @ B )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(46,plain,
    $false,
    inference(e,[status(thm)],[42,14,35,28,38,32,17,22,44,40,26,30,19]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : CAT011-4 : TPTP v8.2.0. Released v1.0.0.
% 0.13/0.14  % Command  : run_Leo-III %s %d
% 0.13/0.35  % Computer : n006.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 : Sat May 18 11:33:54 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 1.17/1.15  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.61/1.34  % [INFO] 	 Parsing done (183ms). 
% 1.61/1.35  % [INFO] 	 Running in sequential loop mode. 
% 2.35/1.80  % [INFO] 	 eprover registered as external prover. 
% 2.35/1.80  % [INFO] 	 cvc4 registered as external prover. 
% 2.35/1.81  % [INFO] 	 Scanning for conjecture ... 
% 2.59/1.91  % [INFO] 	 Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ... 
% 2.59/1.94  % [INFO] 	 Axiom selection finished. Selected 12 axioms (removed 0 axioms). 
% 2.59/1.97  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 2.59/1.97  % [INFO] 	 Type checking passed. 
% 2.76/1.98  % [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 ... 
% 4.16/2.64  % External prover 'e' found a proof!
% 4.16/2.64  % [INFO] 	 Killing All external provers ... 
% 4.16/2.64  % Time passed: 2110ms (effective reasoning time: 1287ms)
% 4.16/2.65  % Axioms used in derivation (12): compose_codomain, domain_codomain_composition2, compose_domain, assume_domain_exists, equivalence_implies_existence1, equivalence_implies_existence2, codomain_has_elements, existence_and_equality_implies_equivalence1, associativity_of_compose, domain_codomain_composition1, composition_implies_domain, domain_has_elements
% 4.16/2.65  % No. of inferences in proof: 27
% 4.16/2.65  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2110 ms resp. 1287 ms w/o parsing
% 4.31/2.70  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.31/2.70  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------