%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEV019^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n029.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 04:09:49 EDT 2024

% Result   : Theorem 2.63s 1.58s
% Output   : Refutation 2.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    3
% Syntax   : Number of formulae    :    6 (   1 unt;   2 typ;   0 def)
%            Number of atoms       :   25 (   3 equ;   0 cnn)
%            Maximal formula atoms :    7 (   6 avg)
%            Number of connectives :   83 (   2   ~;   0   |;  15   &;  54   @)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   9 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1 usr;   1 con; 0-2 aty)
%            Number of variables   :   33 (   0   ^  27   !;   6   ?;  33   :)

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

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

thf(1,conjecture,
    ( ! [A: a] :
      ? [B: a > $o] :
        ( ? [C: a] : ( B @ C )
        & ! [C: a] :
            ( ( B @ C )
           => ! [D: a] :
                ( ( B @ D )
                = ( cQ @ C @ D ) ) )
        & ( B @ A ) )
   => ( ! [A: a] : ( cQ @ A @ A )
      & ! [A: a,B: a] :
          ( ( cQ @ A @ B )
         => ( cQ @ B @ A ) )
      & ! [A: a,B: a,C: a] :
          ( ( ( cQ @ A @ B )
            & ( cQ @ B @ C ) )
         => ( cQ @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM559_pme) ).

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

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

thf(14,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEV019^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n029.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 19:03:39 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.83/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.15/0.97  % [INFO] 	 Parsing done (102ms). 
% 1.15/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.45/1.17  % [INFO] 	 eprover registered as external prover. 
% 1.45/1.17  % [INFO] 	 cvc4 registered as external prover. 
% 1.45/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.78/1.23  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.88/1.25  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.88/1.25  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.88/1.25  % [INFO] 	 Type checking passed. 
% 1.88/1.26  % [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 ... 
% 2.63/1.58  % External prover 'e' found a proof!
% 2.63/1.58  % [INFO] 	 Killing All external provers ... 
% 2.63/1.58  % Time passed: 1057ms (effective reasoning time: 604ms)
% 2.63/1.58  % 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)>
% 2.63/1.58  % Axioms used in derivation (0): 
% 2.63/1.58  % No. of inferences in proof: 4
% 2.63/1.58  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1057 ms resp. 604 ms w/o parsing
% 2.63/1.60  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.63/1.60  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------