%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.10
% Problem  : SET640^3 : TPTP v8.1.2. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n017.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  7 10:50:14 EDT 2024

% Result   : Theorem 2.64s 1.73s
% Output   : Refutation 2.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of formulae    :    8 (   4 unt;   2 typ;   2 def)
%            Number of atoms       :   16 (   2 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   24 (   2   ~;   0   |;   1   &;  18   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   26 (  26   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   2 usr;   2 con; 0-4 aty)
%            Number of variables   :   16 (  10   ^   6   !;   0   ?;  16   :)

% Comments : 
%------------------------------------------------------------------------------
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(1,conjecture,
    ! [A: $i > $i > $o,B: $i > $i > $o] :
      ( ( sub_rel @ A @ B )
     => ( sub_rel @ A
        @ ( cartesian_product
          @ ^ [C: $i] : $true
          @ ^ [C: $i] : $true ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).

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

thf(3,plain,
    ~ $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    $false,
    inference(simp,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem  : SET640^3 : TPTP v8.1.2. Released v3.6.0.
% 0.08/0.10  % Command  : run_Leo-III %s %d
% 0.08/0.29  % Computer : n017.cluster.edu
% 0.08/0.29  % Model    : x86_64 x86_64
% 0.08/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29  % Memory   : 8042.1875MB
% 0.08/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29  % CPULimit : 300
% 0.08/0.29  % WCLimit  : 300
% 0.08/0.29  % DateTime : Mon May  6 20:47:53 EDT 2024
% 0.08/0.29  % CPUTime  : 
% 0.94/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.38/1.09  % [INFO] 	 Parsing done (224ms). 
% 1.38/1.10  % [INFO] 	 Running in sequential loop mode. 
% 2.00/1.39  % [INFO] 	 nitpick registered as external prover. 
% 2.00/1.40  % [INFO] 	 Scanning for conjecture ... 
% 2.27/1.54  % [INFO] 	 Found a conjecture and 0 axioms. Running axiom selection ... 
% 2.35/1.57  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.35/1.57  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.35/1.57  % [INFO] 	 Type checking passed. 
% 2.35/1.58  % [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 ... 
% 2.64/1.72  % [INFO] 	 Killing All external provers ... 
% 2.64/1.73  % Time passed: 1315ms (effective reasoning time: 620ms)
% 2.64/1.73  % 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)>
% 2.64/1.73  % Axioms used in derivation (0): 
% 2.64/1.73  % No. of inferences in proof: 4
% 2.64/1.73  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1315 ms resp. 620 ms w/o parsing
% 2.80/1.78  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.80/1.78  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------