%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU620^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n006.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 03:38:38 EDT 2024

% Result   : Theorem 2.08s 1.42s
% Output   : Refutation 2.20s
% 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       :   41 (   4 equ;   0 cnn)
%            Maximal formula atoms :    2 (   5 avg)
%            Number of connectives :   49 (   2   ~;   0   |;   2   &;  43   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   7 con; 0-2 aty)
%            Number of variables   :   11 (   3   ^   6   !;   2   ?;  11   :)

% Comments : 
%------------------------------------------------------------------------------
thf(iskpair_type,type,
    iskpair: $i > $o ).

thf(iskpair_def,definition,
    ( iskpair
    = ( ^ [A: $i] :
        ? [B: $i] :
          ( ( in @ B @ ( setunion @ A ) )
          & ? [C: $i] :
              ( ( in @ C @ ( setunion @ A ) )
              & ( A
                = ( setadjoin @ ( setadjoin @ B @ emptyset ) @ ( setadjoin @ ( setadjoin @ B @ ( setadjoin @ C @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).

thf(kpairiskpair_type,type,
    kpairiskpair: $o ).

thf(kpairiskpair_def,definition,
    ( kpairiskpair
    = ( ! [A: $i,B: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ) ) ).

thf(kpair_type,type,
    kpair: $i > $i > $i ).

thf(kpair_def,definition,
    ( kpair
    = ( ^ [A: $i,B: $i] : ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ) ).

thf(1,conjecture,
    ( kpairiskpair
   => ! [A: $i,B: $i] : ( iskpair @ ( kpair @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairp) ).

thf(2,negated_conjecture,
    ~ ( kpairiskpair
     => ! [A: $i,B: $i] : ( iskpair @ ( kpair @ A @ B ) ) ),
    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
% 0.10/0.12  % Problem  : SEU620^2 : TPTP v8.2.0. Released v3.7.0.
% 0.10/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n006.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Sun May 19 17:49:54 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.93/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.10/0.99  % [INFO] 	 Parsing done (113ms). 
% 1.10/1.00  % [INFO] 	 Running in sequential loop mode. 
% 1.60/1.22  % [INFO] 	 eprover registered as external prover. 
% 1.60/1.22  % [INFO] 	 cvc4 registered as external prover. 
% 1.60/1.23  % [INFO] 	 Scanning for conjecture ... 
% 1.69/1.29  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.69/1.31  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.69/1.31  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.69/1.31  % [INFO] 	 Type checking passed. 
% 1.69/1.32  % [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 ... 
% 2.08/1.41  % [INFO] 	 Killing All external provers ... 
% 2.08/1.41  % Time passed: 888ms (effective reasoning time: 408ms)
% 2.08/1.41  % 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)>
% 2.08/1.41  % Axioms used in derivation (0): 
% 2.08/1.41  % No. of inferences in proof: 4
% 2.08/1.42  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 888 ms resp. 408 ms w/o parsing
% 2.20/1.44  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.20/1.44  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------