%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : NUM706^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n019.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  7 08:00:36 EDT 2024

% Result   : Theorem 2.36s 1.50s
% Output   : Refutation 2.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   14 (  10 unt;   4 typ;   0 def)
%            Number of atoms       :   10 (   9 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :   20 (   4   ~;   0   |;   0   &;  16   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   2 avg)
%            Number of types       :    1 (   1 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3 usr;   3 con; 0-2 aty)
%            Number of variables   :    4 (   0   ^   4   !;   0   ?;   4   :)

% Comments : 
%------------------------------------------------------------------------------
thf(nat_type,type,
    nat: $tType ).

thf(x_type,type,
    x: nat ).

thf(ts_type,type,
    ts: nat > nat > nat ).

thf(n_1_type,type,
    n_1: nat ).

thf(1,conjecture,
    ( x
    = ( ts @ x @ n_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz28e) ).

thf(2,negated_conjecture,
    ( x
   != ( ts @ x @ n_1 ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(4,plain,
    ( x
   != ( ts @ x @ n_1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(5,plain,
    ( ( ts @ x @ n_1 )
   != x ),
    inference(lifteq,[status(thm)],[4]) ).

thf(3,axiom,
    ! [A: nat] :
      ( ( ts @ A @ n_1 )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz28a) ).

thf(6,plain,
    ! [A: nat] :
      ( ( ts @ A @ n_1 )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(7,plain,
    ! [A: nat] :
      ( ( ts @ A @ n_1 )
      = A ),
    inference(cnf,[status(esa)],[6]) ).

thf(8,plain,
    ! [A: nat] :
      ( ( ts @ A @ n_1 )
      = A ),
    inference(lifteq,[status(thm)],[7]) ).

thf(9,plain,
    x != x,
    inference(rewrite,[status(thm)],[5,8]) ).

thf(10,plain,
    $false,
    inference(simp,[status(thm)],[9]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM706^1 : TPTP v8.1.2. Released v3.7.0.
% 0.12/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n019.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
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Mon May  6 12:29:39 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.84/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.24/0.96  % [INFO] 	 Parsing done (108ms). 
% 1.24/0.96  % [INFO] 	 Running in sequential loop mode. 
% 1.66/1.17  % [INFO] 	 eprover registered as external prover. 
% 1.66/1.17  % [INFO] 	 cvc4 registered as external prover. 
% 1.66/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.76/1.21  % [INFO] 	 Found a conjecture and 1 axioms. Running axiom selection ... 
% 1.76/1.23  % [INFO] 	 Axiom selection finished. Selected 1 axioms (removed 0 axioms). 
% 1.83/1.24  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.83/1.24  % [INFO] 	 Type checking passed. 
% 1.83/1.25  % [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 ... 
% 2.36/1.49  % [INFO] 	 Killing All external provers ... 
% 2.36/1.49  % Time passed: 975ms (effective reasoning time: 526ms)
% 2.36/1.49  % 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)>
% 2.36/1.50  % Axioms used in derivation (1): satz28a
% 2.36/1.50  % No. of inferences in proof: 10
% 2.36/1.50  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 975 ms resp. 526 ms w/o parsing
% 2.63/1.56  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.63/1.56  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------