%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : LCL588^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% Computer : n026.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 : Mon Jun 24 11:14:44 EDT 2024

% Result   : Theorem 2.95s 1.89s
% Output   : Refutation 3.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of formulae    :    8 (   5 unt;   0 typ;   4 def)
%            Number of atoms       :   47 (   4 equ;   0 cnn)
%            Maximal formula atoms :   14 (   5 avg)
%            Number of connectives :   58 (   5   ~;   3   |;   2   &;  45   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (  10 usr;   4 con; 0-3 aty)
%            Number of variables   :   13 (   7   ^   4   !;   2   ?;  13   :)

% Comments : 
%------------------------------------------------------------------------------
thf(mimpl_type,type,
    mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mimpl_def,definition,
    ( mimpl
    = ( ^ [A: $i > $o] : ( mor @ ( mnot @ A ) ) ) ) ).

thf(mbox_type,type,
    mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mbox_def,definition,
    ( mbox
    = ( ^ [A: $i > $i > $o,B: $i > $o,C: $i] :
        ! [D: $i] :
          ( ( A @ C @ D )
         => ( B @ D ) ) ) ) ).

thf(mdia_type,type,
    mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mdia_def,definition,
    ( mdia
    = ( ^ [A: $i > $i > $o,B: $i > $o,C: $i] :
        ? [D: $i] :
          ( ( A @ C @ D )
          & ( B @ D ) ) ) ) ).

thf(individuals_type,type,
    individuals: $tType ).

thf(mvalid_type,type,
    mvalid: ( $i > $o ) > $o ).

thf(mvalid_def,definition,
    ( mvalid
    = ( '!' @ $i ) ) ).

thf(a_type,type,
    a: $i > $o ).

thf(b_type,type,
    b: $i > $o ).

thf(r_type,type,
    r: $i > $i > $o ).

thf(1,conjecture,
    mvalid @ ( mimpl @ ( mimpl @ ( mdia @ r @ a ) @ ( mbox @ r @ b ) ) @ ( mbox @ r @ ( mimpl @ a @ b ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).

thf(2,negated_conjecture,
    ~ ( mvalid @ ( mimpl @ ( mimpl @ ( mdia @ r @ a ) @ ( mbox @ r @ b ) ) @ ( mbox @ r @ ( mimpl @ a @ b ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ! [A: $i] :
        ( ~ ( ~ ? [B: $i] :
                  ( ( r @ A @ B )
                  & ( a @ B ) )
            | ! [B: $i] :
                ( ( r @ A @ B )
               => ( b @ B ) ) )
        | ! [B: $i] :
            ( ( r @ A @ B )
           => ( ~ ( a @ B )
              | ( b @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(8,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14  % Problem  : LCL588^1 : TPTP v8.2.0. Released v3.6.0.
% 0.14/0.14  % Command  : run_Leo-III %s %d THM
% 0.15/0.36  % Computer : n026.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 : Sat Jun 22 16:08:10 EDT 2024
% 0.15/0.37  % CPUTime  : 
% 1.04/0.99  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.50/1.20  % [INFO] 	 Parsing done (210ms). 
% 1.50/1.21  % [INFO] 	 Running in sequential loop mode. 
% 1.95/1.49  % [INFO] 	 eprover registered as external prover. 
% 2.02/1.50  % [INFO] 	 Scanning for conjecture ... 
% 2.13/1.60  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.13/1.61  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.13/1.62  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.13/1.62  % [INFO] 	 Type checking passed. 
% 2.13/1.62  % [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 ... 
% 2.95/1.89  % External prover 'e' found a proof!
% 2.95/1.89  % [INFO] 	 Killing All external provers ... 
% 2.95/1.89  % Time passed: 1323ms (effective reasoning time: 673ms)
% 2.95/1.89  % 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)>
% 2.95/1.89  % Axioms used in derivation (0): 
% 2.95/1.89  % No. of inferences in proof: 4
% 2.95/1.89  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1323 ms resp. 673 ms w/o parsing
% 3.02/1.92  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.02/1.92  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------