%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET646^3 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% 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 : Tue May 21 03:06:40 EDT 2024

% Result   : Theorem 2.62s 1.66s
% Output   : Refutation 2.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   10 (   5 unt;   3 typ;   3 def)
%            Number of atoms       :   20 (   5 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   23 (   2   ~;   1   |;   1   &;  18   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   22 (  22   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   3 usr;   2 con; 0-4 aty)
%            Number of variables   :   20 (  14   ^   6   !;   0   ?;  20   :)

% 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(pair_rel_type,type,
    pair_rel: $i > $i > $i > $i > $o ).

thf(pair_rel_def,definition,
    ( pair_rel
    = ( ^ [A: $i,B: $i,C: $i,D: $i] :
          ( ( C = A )
          | ( D = B ) ) ) ) ).

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,B: $i] :
      ( sub_rel @ ( pair_rel @ A @ B )
      @ ( cartesian_product
        @ ^ [C: $i] : $true
        @ ^ [C: $i] : $true ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i] :
        ( sub_rel @ ( pair_rel @ A @ B )
        @ ( 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
% 0.06/0.11  % Problem  : SET646^3 : TPTP v8.2.0. Released v3.6.0.
% 0.06/0.13  % Command  : run_Leo-III %s %d
% 0.12/0.32  % Computer : n024.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Mon May 20 12:37:24 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.86/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.23/1.04  % [INFO] 	 Parsing done (194ms). 
% 1.43/1.05  % [INFO] 	 Running in sequential loop mode. 
% 1.92/1.33  % [INFO] 	 nitpick registered as external prover. 
% 1.92/1.34  % [INFO] 	 Scanning for conjecture ... 
% 2.27/1.47  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.27/1.50  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.27/1.50  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.27/1.51  % [INFO] 	 Type checking passed. 
% 2.27/1.51  % [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 ... 
% 2.62/1.65  % [INFO] 	 Killing All external provers ... 
% 2.62/1.66  % Time passed: 1225ms (effective reasoning time: 599ms)
% 2.62/1.66  % 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)>
% 2.62/1.66  % Axioms used in derivation (0): 
% 2.62/1.66  % No. of inferences in proof: 4
% 2.62/1.66  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1225 ms resp. 599 ms w/o parsing
% 2.67/1.70  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.67/1.70  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------