TSTP Solution File: CAT010-10 by Leo-III---1.7.12

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%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : CAT010-10 : TPTP v8.2.0. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n004.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 18:59:51 EDT 2024

% Result   : Unsatisfiable 3.10s 1.62s
% Output   : Refutation 3.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   27
% Syntax   : Number of formulae    :   44 (  33 unt;  11 typ;   0 def)
%            Number of atoms       :   33 (  32 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :  204 (   2   ~;   0   |;   0   &; 202   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   19 (  19   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  11 usr;   4 con; 0-4 aty)
%            Number of variables   :   54 (   0   ^  54   !;   0   ?;  54   :)

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

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

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

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

thf(ifeq_type,type,
    ifeq: $i > $i > $i > $i > $i ).

thf(ifeq2_type,type,
    ifeq2: $i > $i > $i > $i > $i ).

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

thf(true_type,type,
    true: $i ).

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

thf(ifeq3_type,type,
    ifeq3: $i > $i > $i > $i > $i ).

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

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

thf(48,plain,
    ! [A: $i] :
      ( ( compose @ ( codomain @ A ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(13,axiom,
    ! [A: $i] :
      ( ( ifeq @ ( there_exists @ ( codomain @ A ) ) @ true @ ( there_exists @ A ) @ true )
      = true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_has_elements) ).

thf(42,plain,
    ! [A: $i] :
      ( ( ifeq @ ( there_exists @ ( codomain @ A ) ) @ true @ ( there_exists @ A ) @ true )
      = true ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(4,axiom,
    ! [B: $i,A: $i] :
      ( ( ifeq @ ( equivalent @ A @ B ) @ true @ ( there_exists @ A ) @ true )
      = true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_implies_existence1) ).

thf(24,plain,
    ! [B: $i,A: $i] :
      ( ( ifeq @ ( equivalent @ A @ B ) @ true @ ( there_exists @ A ) @ true )
      = true ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(2,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ifeq @ A @ A @ B @ C )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_002) ).

thf(20,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ifeq @ A @ A @ B @ C )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(15,axiom,
    ! [B: $i,A: $i] :
      ( ( ifeq @ ( there_exists @ ( compose @ A @ B ) ) @ true @ ( there_exists @ ( domain @ A ) ) @ true )
      = true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_implies_domain) ).

thf(46,plain,
    ! [B: $i,A: $i] :
      ( ( ifeq @ ( there_exists @ ( compose @ A @ B ) ) @ true @ ( there_exists @ ( domain @ A ) ) @ true )
      = true ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ( ifeq @ ( there_exists @ A ) @ true @ ( equivalent @ A @ A ) @ true )
      = true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_and_equality_implies_equivalence1) ).

thf(28,plain,
    ! [A: $i] :
      ( ( ifeq @ ( there_exists @ A ) @ true @ ( equivalent @ A @ A ) @ true )
      = true ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(11,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)],[11]) ).

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

thf(17,plain,
    ( ( codomain @ ( compose @ a @ b ) )
   != ( codomain @ a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(8,axiom,
    ! [A: $i] :
      ( ( ifeq @ ( there_exists @ ( domain @ A ) ) @ true @ ( there_exists @ A ) @ true )
      = true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_has_elements) ).

thf(32,plain,
    ! [A: $i] :
      ( ( ifeq @ ( there_exists @ ( domain @ A ) ) @ true @ ( there_exists @ A ) @ true )
      = true ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ( compose @ A @ ( domain @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_domain) ).

thf(34,plain,
    ! [A: $i] :
      ( ( compose @ A @ ( domain @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(3,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ifeq2 @ A @ A @ B @ C )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).

thf(22,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ifeq2 @ A @ A @ B @ C )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(14,axiom,
    ! [B: $i,A: $i] :
      ( ( ifeq2 @ ( there_exists @ ( compose @ A @ B ) ) @ true @ ( domain @ A ) @ ( codomain @ B ) )
      = ( codomain @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_codomain_composition1) ).

thf(44,plain,
    ! [B: $i,A: $i] :
      ( ( ifeq2 @ ( there_exists @ ( compose @ A @ B ) ) @ true @ ( domain @ A ) @ ( codomain @ B ) )
      = ( codomain @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(12,axiom,
    ( ( there_exists @ ( compose @ a @ b ) )
    = true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_exists) ).

thf(40,plain,
    ( ( there_exists @ ( compose @ a @ b ) )
    = true ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(5,axiom,
    ! [B: $i,A: $i] :
      ( ( ifeq2 @ ( equivalent @ A @ B ) @ true @ A @ B )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_implies_existence2) ).

thf(26,plain,
    ! [B: $i,A: $i] :
      ( ( ifeq2 @ ( equivalent @ A @ B ) @ true @ A @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(10,axiom,
    ! [B: $i,A: $i] :
      ( ( ifeq @ ( there_exists @ ( domain @ A ) ) @ true @ ( ifeq3 @ ( domain @ A ) @ ( codomain @ B ) @ ( there_exists @ ( compose @ A @ B ) ) @ true ) @ true )
      = true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_codomain_composition2) ).

thf(36,plain,
    ! [B: $i,A: $i] :
      ( ( ifeq @ ( there_exists @ ( domain @ A ) ) @ true @ ( ifeq3 @ ( domain @ A ) @ ( codomain @ B ) @ ( there_exists @ ( compose @ A @ B ) ) @ true ) @ true )
      = true ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(7,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ifeq3 @ A @ A @ B @ C )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).

thf(30,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ifeq3 @ A @ A @ B @ C )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(65,plain,
    $false,
    inference(e,[status(thm)],[48,42,24,20,46,28,38,17,32,34,22,44,40,26,36,30]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : CAT010-10 : TPTP v8.2.0. Released v7.3.0.
% 0.12/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n004.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 11:45:09 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.81/0.78  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.07/0.88  % [INFO] 	 Parsing done (99ms). 
% 1.07/0.89  % [INFO] 	 Running in sequential loop mode. 
% 1.39/1.10  % [INFO] 	 eprover registered as external prover. 
% 1.54/1.10  % [INFO] 	 cvc4 registered as external prover. 
% 1.54/1.10  % [INFO] 	 Scanning for conjecture ... 
% 1.54/1.15  % [INFO] 	 Found a conjecture (or negated_conjecture) and 15 axioms. Running axiom selection ... 
% 1.77/1.19  % [INFO] 	 Axiom selection finished. Selected 15 axioms (removed 0 axioms). 
% 1.77/1.21  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 1.77/1.21  % [INFO] 	 Type checking passed. 
% 1.77/1.21  % [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 ... 
% 3.10/1.62  % External prover 'e' found a proof!
% 3.10/1.62  % [INFO] 	 Killing All external provers ... 
% 3.10/1.62  % Time passed: 1117ms (effective reasoning time: 727ms)
% 3.10/1.62  % Axioms used in derivation (15): ifeq_axiom_001, ifeq_axiom, ab_exists, compose_codomain, domain_codomain_composition2, compose_domain, equivalence_implies_existence1, equivalence_implies_existence2, codomain_has_elements, associativity_of_compose, domain_codomain_composition1, composition_implies_domain, domain_has_elements, existence_and_equality_implies_equivalence1, ifeq_axiom_002
% 3.10/1.62  % No. of inferences in proof: 33
% 3.10/1.62  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1117 ms resp. 727 ms w/o parsing
% 3.10/1.65  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.10/1.65  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------