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

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---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 : n018.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 03:06:40 EDT 2024

% Result   : Theorem 2.91s 1.88s
% Output   : Refutation 3.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   31 (  11 unt;  10 typ;   5 def)
%            Number of atoms       :   46 (   7 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  101 (  12   ~;   7   |;   5   &;  69   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   52 (  52   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   4 con; 0-4 aty)
%            Number of variables   :   42 (  12   ^  26   !;   4   ?;  42   :)

% 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(sk1_type,type,
    sk1: $i > $i > $o ).

thf(sk2_type,type,
    sk2: $i > $o ).

thf(sk3_type,type,
    sk3: $i > $o ).

thf(sk4_type,type,
    sk4: $i ).

thf(sk5_type,type,
    sk5: $i ).

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(5,plain,
    sk1 @ sk4 @ sk5,
    inference(cnf,[status(esa)],[3]) ).

thf(6,plain,
    ! [B: $i,A: $i] :
      ( ~ ( sk1 @ B @ A )
      | ( sk3 @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(8,plain,
    ! [B: $i,A: $i] :
      ( ~ ( sk1 @ B @ A )
      | ( sk3 @ A ) ),
    inference(simp,[status(thm)],[6]) ).

thf(13,plain,
    ! [B: $i,A: $i] :
      ( ( sk3 @ A )
      | ( ( sk1 @ sk4 @ sk5 )
       != ( sk1 @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[5,8]) ).

thf(14,plain,
    sk3 @ sk5,
    inference(pattern_uni,[status(thm)],[13:[bind(A,$thf( sk5 )),bind(B,$thf( sk4 ))]]) ).

thf(4,plain,
    ( ~ ( sk2 @ sk4 )
    | ~ ( sk3 @ sk5 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(7,plain,
    ! [B: $i,A: $i] :
      ( ~ ( sk1 @ A @ B )
      | ( sk2 @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(9,plain,
    ! [B: $i,A: $i] :
      ( ( sk2 @ A )
      | ( ( sk1 @ sk4 @ sk5 )
       != ( sk1 @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[5,7]) ).

thf(10,plain,
    sk2 @ sk4,
    inference(pattern_uni,[status(thm)],[9:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 ))]]) ).

thf(11,plain,
    ( ~ $true
    | ~ ( sk3 @ sk5 ) ),
    inference(rewrite,[status(thm)],[4,10]) ).

thf(12,plain,
    ~ ( sk3 @ sk5 ),
    inference(simp,[status(thm)],[11]) ).

thf(15,plain,
    $false,
    inference(rewrite,[status(thm)],[14,12]) ).

thf(16,plain,
    $false,
    inference(simp,[status(thm)],[15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem  : SET649^3 : TPTP v8.2.0. Released v3.6.0.
% 0.13/0.13  % Command  : run_Leo-III %s %d
% 0.13/0.34  % Computer : n018.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Mon May 20 11:35:23 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.80/0.82  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.22/0.99  % [INFO] 	 Parsing done (173ms). 
% 1.22/1.02  % [INFO] 	 Running in sequential loop mode. 
% 1.65/1.29  % [INFO] 	 nitpick registered as external prover. 
% 1.65/1.30  % [INFO] 	 Scanning for conjecture ... 
% 1.92/1.44  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.13/1.47  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.13/1.47  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.13/1.47  % [INFO] 	 Type checking passed. 
% 2.13/1.48  % [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 ... 
% 2.91/1.88  % [INFO] 	 Killing All external provers ... 
% 2.91/1.88  % Time passed: 1409ms (effective reasoning time: 859ms)
% 2.91/1.88  % 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)>
% 2.91/1.88  % Axioms used in derivation (0): 
% 2.91/1.88  % No. of inferences in proof: 16
% 2.91/1.88  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1409 ms resp. 859 ms w/o parsing
% 3.11/1.93  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.11/1.93  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------