%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU459^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n002.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 03:42:13 EDT 2024

% Result   : Theorem 2.80s 1.83s
% Output   : Refutation 2.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   14 (   6 unt;   5 typ;   2 def)
%            Number of atoms       :   13 (   2 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   25 (   3   ~;   2   |;   0   &;  19   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   24 (  24   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   4 con; 0-3 aty)
%            Number of variables   :    8 (   4   ^   4   !;   0   ?;   8   :)

% Comments : 
%------------------------------------------------------------------------------
thf(infl_type,type,
    infl: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).

thf(infl_def,definition,
    ( infl
    = ( ^ [A: ( $i > $i > $o ) > $i > $i > $o] :
        ! [B: $i > $i > $o] : ( subrel @ B @ ( A @ B ) ) ) ) ).

thf(sc_type,type,
    sc: ( $i > $i > $o ) > $i > $i > $o ).

thf(sc_def,definition,
    ( sc
    = ( ^ [A: $i > $i > $o,B: $i,C: $i] :
          ( ( A @ C @ B )
          | ( A @ B @ C ) ) ) ) ).

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

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

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

thf(1,conjecture,
    infl @ sc,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_closure_op_is_inflationary) ).

thf(2,negated_conjecture,
    ~ ( infl @ sc ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(6,plain,
    sk1 @ sk2 @ sk3,
    inference(cnf,[status(esa)],[3]) ).

thf(4,plain,
    ~ ( sk1 @ sk2 @ sk3 ),
    inference(cnf,[status(esa)],[3]) ).

thf(7,plain,
    $false,
    inference(rewrite,[status(thm)],[6,4]) ).

thf(8,plain,
    $false,
    inference(simp,[status(thm)],[7]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU459^1 : TPTP v8.2.0. Released v3.6.0.
% 0.12/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.37  % Computer : n002.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Sun May 19 15:57:54 EDT 2024
% 0.15/0.37  % CPUTime  : 
% 0.99/0.94  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.38/1.11  % [INFO] 	 Parsing done (162ms). 
% 1.38/1.12  % [INFO] 	 Running in sequential loop mode. 
% 1.93/1.37  % [INFO] 	 nitpick registered as external prover. 
% 1.93/1.38  % [INFO] 	 Scanning for conjecture ... 
% 2.28/1.55  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.28/1.57  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.28/1.57  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.28/1.58  % [INFO] 	 Type checking passed. 
% 2.28/1.58  % [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 ... 
% 2.80/1.83  % [INFO] 	 Killing All external provers ... 
% 2.80/1.83  % Time passed: 1305ms (effective reasoning time: 702ms)
% 2.80/1.83  % 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)>
% 2.80/1.83  % Axioms used in derivation (0): 
% 2.80/1.83  % No. of inferences in proof: 7
% 2.80/1.83  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1305 ms resp. 702 ms w/o parsing
% 2.80/1.86  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.80/1.86  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------