%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU922^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n028.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 03:40:27 EDT 2024

% Result   : Theorem 3.09s 2.07s
% Output   : Refutation 3.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of formulae    :    8 (   1 unt;   4 typ;   0 def)
%            Number of atoms       :   10 (   3 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   44 (   2   ~;   0   |;   0   &;  36   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :    6 (   6   ^   0   !;   0   ?;   6   :)

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

thf(f_type,type,
    f: $i > $i ).

thf(g_type,type,
    g: $i > $i ).

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

thf(1,conjecture,
    ( ( ( ^ [A: $i] : ( f @ ( g @ A ) ) )
      = ( ^ [A: $i] : ( g @ ( f @ A ) ) ) )
   => ( ( cP @ ( f @ ( f @ ( g @ a ) ) ) )
     => ( cP @ ( g @ ( f @ ( f @ a ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM128_pme) ).

thf(2,negated_conjecture,
    ~ ( ( ( ^ [A: $i] : ( f @ ( g @ A ) ) )
        = ( ^ [A: $i] : ( g @ ( f @ A ) ) ) )
     => ( ( cP @ ( f @ ( f @ ( g @ a ) ) ) )
       => ( cP @ ( g @ ( f @ ( f @ a ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ( ( ^ [A: $i] : ( f @ ( g @ A ) ) )
        = ( ^ [A: $i] : ( g @ ( f @ A ) ) ) )
     => ( ( cP @ ( f @ ( f @ ( g @ a ) ) ) )
       => ( cP @ ( g @ ( f @ ( f @ a ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(9,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem  : SEU922^5 : TPTP v8.2.0. Released v4.0.0.
% 0.05/0.13  % Command  : run_Leo-III %s %d
% 0.12/0.33  % Computer : n028.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sun May 19 15:37:39 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.99/0.97  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.27/1.12  % [INFO] 	 Parsing done (156ms). 
% 1.36/1.14  % [INFO] 	 Running in sequential loop mode. 
% 1.83/1.50  % [INFO] 	 eprover registered as external prover. 
% 1.83/1.51  % [INFO] 	 cvc4 registered as external prover. 
% 1.83/1.51  % [INFO] 	 Scanning for conjecture ... 
% 2.03/1.59  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.03/1.62  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.03/1.62  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.03/1.63  % [INFO] 	 Type checking passed. 
% 2.03/1.63  % [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 ... 
% 3.09/2.07  % External prover 'e' found a proof!
% 3.09/2.07  % [INFO] 	 Killing All external provers ... 
% 3.09/2.07  % Time passed: 1584ms (effective reasoning time: 926ms)
% 3.09/2.07  % 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)>
% 3.09/2.07  % Axioms used in derivation (0): 
% 3.09/2.07  % No. of inferences in proof: 4
% 3.09/2.07  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1584 ms resp. 926 ms w/o parsing
% 3.19/2.16  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.19/2.16  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------