%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU919^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n007.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 03:44:14 EDT 2024

% Result   : Theorem 2.70s 1.91s
% Output   : Refutation 2.85s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   16 (   9 unt;   4 typ;   0 def)
%            Number of atoms       :   20 (   9 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   74 (   6   ~;   0   |;   0   &;  62   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 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 @ ( g @ a ) ) )
     => ( cP @ ( g @ ( f @ a ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM127_pme) ).

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

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

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

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

thf(8,plain,
    ( ( cP @ ( g @ ( f @ a ) ) )
   != ( cP @ ( f @ ( g @ a ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5,4]) ).

thf(9,plain,
    ( ( g @ ( f @ a ) )
   != ( f @ ( g @ a ) ) ),
    inference(simp,[status(thm)],[8]) ).

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

thf(14,plain,
    ( ( f @ ( g @ a ) )
   != ( f @ ( g @ a ) ) ),
    inference(rewrite,[status(thm)],[9,10]) ).

thf(15,plain,
    $false,
    inference(simp,[status(thm)],[14]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10  % Problem  : SEU919^5 : TPTP v8.2.0. Released v4.0.0.
% 0.08/0.12  % Command  : run_Leo-III %s %d
% 0.11/0.32  % Computer : n007.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
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Sun May 19 17:12:39 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.79/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.22/1.00  % [INFO] 	 Parsing done (154ms). 
% 1.22/1.02  % [INFO] 	 Running in sequential loop mode. 
% 1.68/1.37  % [INFO] 	 nitpick registered as external prover. 
% 1.68/1.38  % [INFO] 	 Scanning for conjecture ... 
% 1.91/1.45  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.93/1.48  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.93/1.48  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.93/1.49  % [INFO] 	 Type checking passed. 
% 1.93/1.49  % [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 ... 
% 2.70/1.90  % [INFO] 	 Killing All external provers ... 
% 2.70/1.91  % Time passed: 1453ms (effective reasoning time: 883ms)
% 2.70/1.91  % 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)>
% 2.70/1.91  % Axioms used in derivation (0): 
% 2.70/1.91  % No. of inferences in proof: 12
% 2.70/1.91  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1453 ms resp. 883 ms w/o parsing
% 2.85/1.99  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.85/1.99  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------