%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : GRP001^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n021.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 May 20 20:59:24 EDT 2024

% Result   : Theorem 3.35s 2.16s
% Output   : Refutation 3.45s
% 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       :   16 (  15 equ;   0 cnn)
%            Maximal formula atoms :    5 (   4 avg)
%            Number of connectives :   68 (   2   ~;   0   |;   9   &;  54   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   7 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   2 usr;   2 con; 0-2 aty)
%            Number of variables   :   24 (   0   ^  24   !;   0   ?;  24   :)

% Comments : 
%------------------------------------------------------------------------------
thf(cP_type,type,
    cP: $i > $i > $i ).

thf(e_type,type,
    e: $i ).

thf(1,conjecture,
    ( ( ! [A: $i] :
          ( ( cP @ e @ A )
          = A )
      & ! [A: $i] :
          ( ( cP @ A @ e )
          = A )
      & ! [A: $i] :
          ( ( cP @ A @ A )
          = e )
      & ! [A: $i,B: $i,C: $i] :
          ( ( cP @ ( cP @ A @ B ) @ C )
          = ( cP @ A @ ( cP @ B @ C ) ) ) )
   => ! [A: $i,B: $i] :
        ( ( cP @ A @ B )
        = ( cP @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_COMM2) ).

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

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

thf(22,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09  % Problem  : GRP001^5 : TPTP v8.2.0. Released v4.0.0.
% 0.08/0.12  % Command  : run_Leo-III %s %d
% 0.11/0.32  % Computer : n021.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Sun May 19 05:47:39 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 1.02/0.94  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.29/1.10  % [INFO] 	 Parsing done (159ms). 
% 1.29/1.12  % [INFO] 	 Running in sequential loop mode. 
% 1.85/1.48  % [INFO] 	 eprover registered as external prover. 
% 1.85/1.49  % [INFO] 	 cvc4 registered as external prover. 
% 1.85/1.49  % [INFO] 	 Scanning for conjecture ... 
% 2.10/1.58  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.10/1.62  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.10/1.62  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.10/1.62  % [INFO] 	 Type checking passed. 
% 2.10/1.63  % [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 ... 
% 3.35/2.15  % External prover 'e' found a proof!
% 3.35/2.15  % [INFO] 	 Killing All external provers ... 
% 3.35/2.15  % Time passed: 1684ms (effective reasoning time: 1029ms)
% 3.35/2.15  % 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)>
% 3.35/2.15  % Axioms used in derivation (0): 
% 3.35/2.16  % No. of inferences in proof: 4
% 3.35/2.16  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1684 ms resp. 1029 ms w/o parsing
% 3.45/2.19  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.45/2.19  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------