TSTP Solution File: SET649^3 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SET649^3 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n009.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 03:03:25 EDT 2024

% Result   : Theorem 3.61s 2.14s
% Output   : Refutation 3.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   14 (   6 unt;   5 typ;   5 def)
%            Number of atoms       :   23 (   5 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   57 (   2   ~;   0   |;   5   &;  42   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   48 (  48   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   1 con; 0-4 aty)
%            Number of variables   :   32 (  12   ^  16   !;   4   ?;  32   :)

% Comments : 
%------------------------------------------------------------------------------
thf(subset_type,type,
    subset: ( $i > $o ) > ( $i > $o ) > $o ).

thf(subset_def,definition,
    ( subset
    = ( ^ [A: $i > $o,B: $i > $o] :
        ! [C: $i] :
          ( ( A @ C )
         => ( B @ C ) ) ) ) ).

thf(cartesian_product_type,type,
    cartesian_product: ( $i > $o ) > ( $i > $o ) > $i > $i > $o ).

thf(cartesian_product_def,definition,
    ( cartesian_product
    = ( ^ [A: $i > $o,B: $i > $o,C: $i,D: $i] :
          ( ( A @ C )
          & ( B @ D ) ) ) ) ).

thf(sub_rel_type,type,
    sub_rel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).

thf(sub_rel_def,definition,
    ( sub_rel
    = ( ^ [A: $i > $i > $o,B: $i > $i > $o] :
        ! [C: $i,D: $i] :
          ( ( A @ C @ D )
         => ( B @ C @ D ) ) ) ) ).

thf(rel_codomain_type,type,
    rel_codomain: ( $i > $i > $o ) > $i > $o ).

thf(rel_codomain_def,definition,
    ( rel_codomain
    = ( ^ [A: $i > $i > $o,B: $i] :
        ? [C: $i] : ( A @ C @ B ) ) ) ).

thf(rel_domain_type,type,
    rel_domain: ( $i > $i > $o ) > $i > $o ).

thf(rel_domain_def,definition,
    ( rel_domain
    = ( ^ [A: $i > $i > $o,B: $i] :
        ? [C: $i] : ( A @ B @ C ) ) ) ).

thf(1,conjecture,
    ! [A: $i > $i > $o,B: $i > $o,C: $i > $o] :
      ( ( ( subset @ ( rel_domain @ A ) @ B )
        & ( subset @ ( rel_codomain @ A ) @ C ) )
     => ( sub_rel @ A @ ( cartesian_product @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).

thf(2,negated_conjecture,
    ~ ! [A: $i > $i > $o,B: $i > $o,C: $i > $o] :
        ( ( ( subset @ ( rel_domain @ A ) @ B )
          & ( subset @ ( rel_codomain @ A ) @ C ) )
       => ( sub_rel @ A @ ( cartesian_product @ B @ C ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ! [A: $i > $i > $o,B: $i > $o,C: $i > $o] :
        ( ( ! [D: $i] :
              ( ? [E: $i] : ( A @ D @ E )
             => ( B @ D ) )
          & ! [D: $i] :
              ( ? [E: $i] : ( A @ E @ D )
             => ( C @ D ) ) )
       => ! [D: $i,E: $i] :
            ( ( A @ D @ E )
           => ( ( B @ D )
              & ( C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(9,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : SET649^3 : TPTP v8.2.0. Released v3.6.0.
% 0.09/0.11  % Command  : run_Leo-III %s %d
% 0.10/0.31  % Computer : n009.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Mon May 20 11:35:24 EDT 2024
% 0.10/0.31  % CPUTime  : 
% 0.94/0.90  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.34/1.15  % [INFO] 	 Parsing done (241ms). 
% 1.34/1.16  % [INFO] 	 Running in sequential loop mode. 
% 2.06/1.50  % [INFO] 	 eprover registered as external prover. 
% 2.06/1.50  % [INFO] 	 cvc4 registered as external prover. 
% 2.06/1.51  % [INFO] 	 Scanning for conjecture ... 
% 2.40/1.66  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.57/1.69  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.57/1.69  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.57/1.70  % [INFO] 	 Type checking passed. 
% 2.57/1.70  % [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 ... 
% 3.61/2.14  % External prover 'e' found a proof!
% 3.61/2.14  % [INFO] 	 Killing All external provers ... 
% 3.61/2.14  % Time passed: 1692ms (effective reasoning time: 975ms)
% 3.61/2.14  % 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)>
% 3.61/2.14  % Axioms used in derivation (0): 
% 3.61/2.14  % No. of inferences in proof: 4
% 3.61/2.14  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1692 ms resp. 975 ms w/o parsing
% 3.61/2.18  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.61/2.18  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------