%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ALG272^5 : TPTP v8.2.0. Bugfixed v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n010.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 18:14:41 EDT 2024

% Result   : Theorem 23.76s 5.97s
% Output   : Refutation 23.88s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    6
% Syntax   : Number of formulae    :    9 (   6 unt;   3 typ;   2 def)
%            Number of atoms       :   26 (  13 equ;   0 cnn)
%            Maximal formula atoms :    1 (   4 avg)
%            Number of connectives :   58 (   2   ~;   0   |;  10   &;  46   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   18 (  18   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   22 (   4   ^  16   !;   2   ?;  22   :)

% Comments : 
%------------------------------------------------------------------------------
thf(g_type,type,
    g: $tType ).

thf(cGROUP1_type,type,
    cGROUP1: ( g > g > g ) > g > $o ).

thf(cGROUP1_def,definition,
    ( cGROUP1
    = ( ^ [A: g > g > g,B: g] :
          ( ( cGRP_ASSOC @ A )
          & ( cGRP_UNIT @ A @ B )
          & ( cGRP_INVERSE @ A @ B ) ) ) ) ).

thf(cGROUP2_type,type,
    cGROUP2: ( g > g > g ) > g > $o ).

thf(cGROUP2_def,definition,
    ( cGROUP2
    = ( ^ [A: g > g > g,B: g] :
          ( ( cGRP_ASSOC @ A )
          & ( cGRP_LEFT_UNIT @ A @ B )
          & ( cGRP_LEFT_INVERSE @ A @ B ) ) ) ) ).

thf(1,conjecture,
    ! [A: g > g > g,B: g] :
      ( ( cGROUP1 @ A @ B )
      = ( cGROUP2 @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEQUIV_01_02) ).

thf(2,negated_conjecture,
    ~ ! [A: g > g > g,B: g] :
        ( ( cGROUP1 @ A @ B )
        = ( cGROUP2 @ A @ B ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(1662,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : ALG272^5 : TPTP v8.2.0. Bugfixed v5.3.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.15/0.38  % Computer : n010.cluster.edu
% 0.15/0.38  % Model    : x86_64 x86_64
% 0.15/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38  % Memory   : 8042.1875MB
% 0.15/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38  % CPULimit : 300
% 0.15/0.38  % WCLimit  : 300
% 0.15/0.38  % DateTime : Sat May 18 22:36:39 EDT 2024
% 0.15/0.38  % CPUTime  : 
% 1.34/1.23  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.63/1.44  % [INFO] 	 Parsing done (211ms). 
% 1.63/1.46  % [INFO] 	 Running in sequential loop mode. 
% 2.55/1.95  % [INFO] 	 eprover registered as external prover. 
% 2.55/1.95  % [INFO] 	 cvc4 registered as external prover. 
% 2.55/1.96  % [INFO] 	 Scanning for conjecture ... 
% 2.96/2.11  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 3.03/2.15  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 3.03/2.15  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 3.03/2.16  % [INFO] 	 Type checking passed. 
% 3.03/2.16  % [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 ... 
% 23.76/5.97  % External prover 'e' found a proof!
% 23.76/5.97  % [INFO] 	 Killing All external provers ... 
% 23.76/5.97  % Time passed: 5399ms (effective reasoning time: 4502ms)
% 23.76/5.97  % 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)>
% 23.76/5.97  % Axioms used in derivation (0): 
% 23.76/5.97  % No. of inferences in proof: 4
% 23.76/5.97  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5399 ms resp. 4502 ms w/o parsing
% 23.88/6.01  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 23.88/6.01  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------