%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU561^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n012.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 03:42:42 EDT 2024

% Result   : Theorem 2.10s 1.43s
% Output   : Refutation 2.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   18 (   9 unt;   6 typ;   2 def)
%            Number of atoms       :   25 (   7 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   37 (   4   ~;   0   |;   0   &;  24   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   13 (   2   ^  11   !;   0   ?;  13   :)

% Comments : 
%------------------------------------------------------------------------------
thf(in_type,type,
    in: $i > $i > $o ).

thf(subset_type,type,
    subset: $i > $i > $o ).

thf(subset_def,definition,
    ( subset
    = ( ^ [A: $i,B: $i] :
        ! [C: $i] :
          ( ( in @ C @ A )
         => ( in @ C @ B ) ) ) ) ).

thf(subsetI1_type,type,
    subsetI1: $o ).

thf(subsetI1_def,definition,
    ( subsetI1
    = ( ! [A: $i,B: $i] :
          ( ! [C: $i] :
              ( ( in @ C @ A )
             => ( in @ C @ B ) )
         => ( subset @ A @ B ) ) ) ) ).

thf(sk1_type,type,
    sk1: $i ).

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

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

thf(1,conjecture,
    ( subsetI1
   => ! [A: $i,B: $i] :
        ( ( A = B )
       => ( subset @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset1) ).

thf(2,negated_conjecture,
    ~ ( subsetI1
     => ! [A: $i,B: $i] :
          ( ( A = B )
         => ( subset @ A @ B ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

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

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

thf(6,plain,
    sk1 = sk2,
    inference(cnf,[status(esa)],[3]) ).

thf(7,plain,
    sk2 = sk1,
    inference(lifteq,[status(thm)],[6]) ).

thf(8,plain,
    ~ ( in @ sk3 @ sk1 ),
    inference(rewrite,[status(thm)],[4,7]) ).

thf(9,plain,
    $false,
    inference(rewrite,[status(thm)],[5,8]) ).

thf(10,plain,
    $false,
    inference(simp,[status(thm)],[9]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SEU561^2 : TPTP v8.2.0. Released v3.7.0.
% 0.10/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.34  % Computer : n012.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Sun May 19 15:44:24 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.86/0.82  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.15/0.93  % [INFO] 	 Parsing done (106ms). 
% 1.22/0.93  % [INFO] 	 Running in sequential loop mode. 
% 1.49/1.14  % [INFO] 	 nitpick registered as external prover. 
% 1.49/1.15  % [INFO] 	 Scanning for conjecture ... 
% 1.66/1.20  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.66/1.22  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.66/1.22  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.66/1.23  % [INFO] 	 Type checking passed. 
% 1.66/1.23  % [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 ... 
% 2.10/1.42  % [INFO] 	 Killing All external provers ... 
% 2.10/1.43  % Time passed: 937ms (effective reasoning time: 487ms)
% 2.10/1.43  % 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)>
% 2.10/1.43  % Axioms used in derivation (0): 
% 2.10/1.43  % No. of inferences in proof: 10
% 2.10/1.43  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 937 ms resp. 487 ms w/o parsing
% 2.29/1.45  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.29/1.45  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------