%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEV282^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n003.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 04:10:17 EDT 2024

% Result   : Theorem 3.39s 1.71s
% Output   : Refutation 3.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of formulae    :    8 (   4 unt;   2 typ;   2 def)
%            Number of atoms       :   12 (   3 equ;   0 cnn)
%            Maximal formula atoms :    2 (   2 avg)
%            Number of connectives :   31 (   6   ~;   0   |;   4   &;  17   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   21 (  21   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   14 (   6   ^   4   !;   4   ?;  14   :)

% Comments : 
%------------------------------------------------------------------------------
thf(cNAT_type,type,
    cNAT: ( ( $i > $o ) > $o ) > $o ).

thf(cNAT_def,definition,
    ( cNAT
    = ( ^ [A: ( $i > $o ) > $o] :
        ! [B: ( ( $i > $o ) > $o ) > $o] :
          ( ( ( B @ cZERO )
            & ! [C: ( $i > $o ) > $o] :
                ( ( B @ C )
               => ( B @ ( cSUCC @ C ) ) ) )
         => ( B @ A ) ) ) ) ).

thf(cZERO_type,type,
    cZERO: ( $i > $o ) > $o ).

thf(cZERO_def,definition,
    ( cZERO
    = ( ^ [A: $i > $o] :
          ~ ? [B: $i] : ( A @ B ) ) ) ).

thf(1,conjecture,
    cNAT @ cZERO,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTTTP6100) ).

thf(2,negated_conjecture,
    ~ ( cNAT @ cZERO ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ! [A: ( ( $i > $o ) > $o ) > $o] :
        ( ( ( A
            @ ^ [B: $i > $o] :
                ~ ? [C: $i] : ( B @ C ) )
          & ! [B: ( $i > $o ) > $o] :
              ( ( A @ B )
             => ( A
                @ ^ [C: $i > $o] :
                  ? [D: $i] :
                    ( ( C @ D )
                    & ( B
                      @ ^ [E: $i] :
                          ( ( E != D )
                          & ( C @ E ) ) ) ) ) ) )
       => ( A
          @ ^ [B: $i > $o] :
              ~ ? [C: $i] : ( B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(7,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEV282^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n003.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 : Sun May 19 18:58:39 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.97/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.20/0.96  % [INFO] 	 Parsing done (101ms). 
% 1.20/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.65/1.17  % [INFO] 	 eprover registered as external prover. 
% 1.65/1.18  % [INFO] 	 cvc4 registered as external prover. 
% 1.65/1.18  % [INFO] 	 Scanning for conjecture ... 
% 1.82/1.24  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.82/1.25  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.82/1.25  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.82/1.25  % [INFO] 	 Type checking passed. 
% 1.82/1.26  % [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 ... 
% 3.39/1.70  % External prover 'e' found a proof!
% 3.39/1.71  % [INFO] 	 Killing All external provers ... 
% 3.39/1.71  % Time passed: 1182ms (effective reasoning time: 731ms)
% 3.39/1.71  % 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)>
% 3.39/1.71  % Axioms used in derivation (0): 
% 3.39/1.71  % No. of inferences in proof: 4
% 3.39/1.71  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1182 ms resp. 731 ms w/o parsing
% 3.73/1.78  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.73/1.78  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------