%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.15
% Problem  : SEV282^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d SAT

% Computer : n029.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 : Mon Jun 24 15:59:55 EDT 2024

% Result   : Theorem 2.38s 1.52s
% Output   : Refutation 2.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    3
% Syntax   : Number of formulae    :    9 (   7 unt;   0 typ;   2 def)
%            Number of atoms       :   15 (   3 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   38 (   9   ~;   0   |;   4   &;  21   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   18 (  18   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   18 (   8   ^   4   !;   6   ?;  18   :)

% 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(sk1_type,type,
    sk1: ( ( $i > $o ) > $o ) > $o ).

thf(1,conjecture,
    cNAT @ cZERO,
    file('/export/starexec/sandbox/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(6,plain,
    ( sk1
    @ ^ [A: $i > $o] :
        ~ ? [B: $i] : ( A @ B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(4,plain,
    ~ ( sk1
      @ ^ [A: $i > $o] :
          ~ ? [B: $i] : ( A @ B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(7,plain,
    $false,
    inference(rewrite,[status(thm)],[6,4]) ).

thf(8,plain,
    $false,
    inference(simp,[status(thm)],[7]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SEV282^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% 0.04/0.12  % Command  : run_Leo-III %s %d SAT
% 0.12/0.33  % Computer : n029.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Fri Jun 21 19:11:54 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.99/0.90  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.15/1.02  % [INFO] 	 Parsing done (117ms). 
% 1.15/1.03  % [INFO] 	 Running in sequential loop mode. 
% 1.71/1.23  % [INFO] 	 nitpick registered as external prover. 
% 1.71/1.24  % [INFO] 	 Scanning for conjecture ... 
% 1.77/1.30  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.77/1.32  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.77/1.32  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.77/1.32  % [INFO] 	 Type checking passed. 
% 1.99/1.32  % [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 ... 
% 2.38/1.51  % [INFO] 	 Killing All external provers ... 
% 2.38/1.52  % Time passed: 992ms (effective reasoning time: 481ms)
% 2.38/1.52  % 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)>
% 2.38/1.52  % Axioms used in derivation (0): 
% 2.38/1.52  % No. of inferences in proof: 7
% 2.38/1.52  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 992 ms resp. 481 ms w/o parsing
% 2.55/1.54  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.55/1.54  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------