%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU930^5 : TPTP v8.2.0. Released v4.0.0.
% 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 : Tue May 21 03:40:29 EDT 2024

% Result   : Theorem 2.54s 1.56s
% Output   : Refutation 2.88s
% 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 :   35 (   2   ~;   0   |;   3   &;  21   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   6 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   2 usr;   1 con; 0-2 aty)
%            Number of variables   :   12 (   6   ^   6   !;   0   ?;  12   :)

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

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

thf(1,conjecture,
    ( ( ( ^ [A: $i] : ( f @ ( g @ A ) ) )
      = ( ^ [A: $i] : ( g @ ( f @ A ) ) ) )
   => ! [A: $i] :
        ( ( ( ( g @ A )
            = A )
          & ! [B: $i] :
              ( ( ( g @ B )
                = B )
             => ( B = A ) ) )
       => ( ( f @ A )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM171A_pme) ).

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

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

thf(13,plain,
    $false,
    inference(cvc4,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU930^5 : TPTP v8.2.0. Released v4.0.0.
% 0.13/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.36  % Computer : n010.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Sun May 19 15:23:54 EDT 2024
% 0.14/0.36  % CPUTime  : 
% 0.96/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.20/0.95  % [INFO] 	 Parsing done (100ms). 
% 1.25/0.95  % [INFO] 	 Running in sequential loop mode. 
% 1.64/1.17  % [INFO] 	 eprover registered as external prover. 
% 1.64/1.17  % [INFO] 	 cvc4 registered as external prover. 
% 1.64/1.18  % [INFO] 	 Scanning for conjecture ... 
% 1.73/1.23  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.83/1.25  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.83/1.25  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.83/1.25  % [INFO] 	 Type checking passed. 
% 1.83/1.26  % [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 ... 
% 2.54/1.56  % External prover 'cvc4' found a proof!
% 2.54/1.56  % [INFO] 	 Killing All external provers ... 
% 2.54/1.56  % Time passed: 1047ms (effective reasoning time: 600ms)
% 2.54/1.56  % 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)>
% 2.54/1.56  % Axioms used in derivation (0): 
% 2.54/1.56  % No. of inferences in proof: 4
% 2.54/1.56  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1047 ms resp. 600 ms w/o parsing
% 2.88/1.63  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.88/1.63  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------