%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SYO258^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n008.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 08:56:15 EDT 2024

% Result   : Theorem 3.01s 2.03s
% Output   : Refutation 3.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   11 (   4 unt;   4 typ;   0 def)
%            Number of atoms       :   16 (   0 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   51 (   2   ~;   0   |;   9   &;  34   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   13 (  13   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   14 (   0   ^   8   !;   6   ?;  14   :)

% Comments : 
%------------------------------------------------------------------------------
thf(a_type,type,
    a: $i ).

thf(cQ_type,type,
    cQ: $i > ( $i > $o ) > $o ).

thf(cP_type,type,
    cP: $i > $i > $o ).

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

thf(1,conjecture,
    ( ( ( cP @ a @ b )
      & ! [A: $i > $o] : ( cQ @ b @ A ) )
   => ? [A: $i > $o] :
      ! [B: $i] :
        ( ( A @ B )
       => ( ? [C: $i] :
              ( ( cP @ B @ C )
              & ( cQ @ C @ A ) )
          & ( A @ a ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBLEDSOE_FENG_6) ).

thf(2,negated_conjecture,
    ~ ( ( ( cP @ a @ b )
        & ! [A: $i > $o] : ( cQ @ b @ A ) )
     => ? [A: $i > $o] :
        ! [B: $i] :
          ( ( A @ B )
         => ( ? [C: $i] :
                ( ( cP @ B @ C )
                & ( cQ @ C @ A ) )
            & ( A @ a ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(5,plain,
    ! [A: $i > $o] : ( A @ ( sk1 @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(9,plain,
    ! [A: $i > $o] : ( A @ ( sk1 @ A ) ),
    inference(simp,[status(thm)],[5]) ).

thf(17,plain,
    $false,
    inference(prim_subst,[status(thm)],[9:[bind(A,$thf( ^ [B: $i] : $false ))]]) ).

thf(19,plain,
    $false,
    inference(simp,[status(thm)],[17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : SYO258^5 : TPTP v8.2.0. Released v4.0.0.
% 0.09/0.11  % Command  : run_Leo-III %s %d
% 0.10/0.30  % Computer : n008.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 300
% 0.10/0.30  % DateTime : Mon May 20 08:39:24 EDT 2024
% 0.10/0.31  % CPUTime  : 
% 0.92/0.89  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.18/1.04  % [INFO] 	 Parsing done (147ms). 
% 1.18/1.05  % [INFO] 	 Running in sequential loop mode. 
% 1.72/1.39  % [INFO] 	 eprover registered as external prover. 
% 1.72/1.39  % [INFO] 	 cvc4 registered as external prover. 
% 1.72/1.40  % [INFO] 	 Scanning for conjecture ... 
% 1.91/1.48  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.97/1.51  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.97/1.51  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.97/1.52  % [INFO] 	 Type checking passed. 
% 1.97/1.52  % [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 ... 
% 3.01/2.03  % [INFO] 	 Killing All external provers ... 
% 3.01/2.03  % Time passed: 1584ms (effective reasoning time: 972ms)
% 3.01/2.03  % 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)>
% 3.01/2.03  % Axioms used in derivation (0): 
% 3.01/2.03  % No. of inferences in proof: 7
% 3.01/2.03  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1584 ms resp. 972 ms w/o parsing
% 3.01/2.06  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.01/2.06  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------