%------------------------------------------------------------------------------
% File     : Leo-III-SAT---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 : n022.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 03:44:15 EDT 2024

% Result   : Theorem 2.81s 1.74s
% Output   : Refutation 3.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   16 (   9 unt;   4 typ;   0 def)
%            Number of atoms       :   18 (   6 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   75 (   5   ~;   0   |;   0   &;  64   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 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   :   11 (  10   ^   1   !;   0   ?;  11   :)

% 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(5,plain,
    cP @ ( f @ ( f @ ( g @ a ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(4,plain,
    ~ ( cP @ ( g @ ( f @ ( f @ a ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(6,plain,
    ( ( ^ [A: $i] : ( f @ ( g @ A ) ) )
    = ( ^ [A: $i] : ( g @ ( f @ A ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(7,plain,
    ( ( ^ [A: $i] : ( g @ ( f @ A ) ) )
    = ( ^ [A: $i] : ( f @ ( g @ A ) ) ) ),
    inference(lifteq,[status(thm)],[6]) ).

thf(8,plain,
    ! [A: $i] :
      ( ( g @ ( f @ A ) )
      = ( f @ ( g @ A ) ) ),
    inference(func_ext,[status(esa)],[7]) ).

thf(11,plain,
    ~ ( cP @ ( f @ ( g @ ( f @ a ) ) ) ),
    inference(rewrite,[status(thm)],[4,8]) ).

thf(17,plain,
    ~ ( cP @ ( f @ ( f @ ( g @ a ) ) ) ),
    inference(rewrite,[status(thm)],[11,8]) ).

thf(18,plain,
    $false,
    inference(rewrite,[status(thm)],[5,17]) ).

thf(19,plain,
    $false,
    inference(simp,[status(thm)],[18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU922^5 : TPTP v8.2.0. Released v4.0.0.
% 0.14/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n022.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Sun May 19 15:37:39 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.99/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.20/0.99  % [INFO] 	 Parsing done (109ms). 
% 1.20/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.69/1.22  % [INFO] 	 nitpick registered as external prover. 
% 1.69/1.23  % [INFO] 	 Scanning for conjecture ... 
% 1.78/1.29  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.78/1.32  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.78/1.32  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.78/1.33  % [INFO] 	 Type checking passed. 
% 2.05/1.33  % [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 ... 
% 2.81/1.73  % [INFO] 	 Killing All external provers ... 
% 2.81/1.74  % Time passed: 1200ms (effective reasoning time: 734ms)
% 2.81/1.74  % 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)>
% 2.81/1.74  % Axioms used in derivation (0): 
% 2.81/1.74  % No. of inferences in proof: 12
% 2.81/1.74  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1200 ms resp. 734 ms w/o parsing
% 3.03/1.82  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.03/1.82  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------