TSTP Solution File: SET647^3 by Leo-III-SAT---1.7.15

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%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.15
% Problem  : SET647^3 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d SAT

% Computer : n024.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 Jun 24 14:45:29 EDT 2024

% Result   : Theorem 3.05s 1.92s
% Output   : Refutation 3.05s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   18 (  10 unt;   0 typ;   5 def)
%            Number of atoms       :   39 (   7 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   84 (  11   ~;   5   |;   2   &;  59   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   21 (  21   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9 usr;   3 con; 0-4 aty)
%            Number of variables   :   35 (  12   ^  19   !;   4   ?;  35   :)

% 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 ).

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

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

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

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

thf(5,plain,
    sk1 @ sk3 @ sk4,
    inference(cnf,[status(esa)],[3]) ).

thf(6,plain,
    ! [B: $i,A: $i] :
      ( ~ ( sk1 @ A @ B )
      | ( sk2 @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(10,plain,
    ! [B: $i,A: $i] :
      ( ( sk2 @ A )
      | ( ( sk1 @ sk3 @ sk4 )
       != ( sk1 @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[5,6]) ).

thf(11,plain,
    sk2 @ sk3,
    inference(pattern_uni,[status(thm)],[10:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).

thf(4,plain,
    ! [A: $i] :
      ( ~ ( sk2 @ sk3 )
      | ~ ( sk1 @ A @ sk4 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(7,plain,
    ! [A: $i] :
      ( ~ ( sk2 @ sk3 )
      | ~ ( sk1 @ A @ sk4 ) ),
    inference(simp,[status(thm)],[4]) ).

thf(8,plain,
    ! [A: $i] :
      ( ~ ( sk2 @ sk3 )
      | ( ( sk1 @ sk3 @ sk4 )
       != ( sk1 @ A @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[5,7]) ).

thf(9,plain,
    ~ ( sk2 @ sk3 ),
    inference(pattern_uni,[status(thm)],[8:[bind(A,$thf( sk3 ))]]) ).

thf(12,plain,
    $false,
    inference(rewrite,[status(thm)],[11,9]) ).

thf(13,plain,
    $false,
    inference(simp,[status(thm)],[12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11  % Problem  : SET647^3 : TPTP v8.2.0. Released v3.6.0.
% 0.02/0.11  % Command  : run_Leo-III %s %d SAT
% 0.11/0.32  % Computer : n024.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Sun Jun 23 14:47:40 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.97/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.28/1.07  % [INFO] 	 Parsing done (192ms). 
% 1.28/1.08  % [INFO] 	 Running in sequential loop mode. 
% 1.93/1.37  % [INFO] 	 nitpick registered as external prover. 
% 1.93/1.38  % [INFO] 	 Scanning for conjecture ... 
% 2.24/1.51  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.31/1.53  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.31/1.53  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.31/1.54  % [INFO] 	 Type checking passed. 
% 2.31/1.54  % [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 ... 
% 3.05/1.91  % [INFO] 	 Killing All external provers ... 
% 3.05/1.92  % Time passed: 1466ms (effective reasoning time: 827ms)
% 3.05/1.92  % 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)>
% 3.05/1.92  % Axioms used in derivation (0): 
% 3.05/1.92  % No. of inferences in proof: 13
% 3.05/1.92  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1466 ms resp. 827 ms w/o parsing
% 3.05/1.97  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.05/1.97  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------