%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.15
% Problem  : SYO024^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d SAT

% Computer : n028.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 20:53:56 EDT 2024

% Result   : Theorem 2.47s 1.60s
% Output   : Refutation 2.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   14 (   9 unt;   0 typ;   1 def)
%            Number of atoms       :   34 (   5 equ;   6 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   68 (  34   ~;  11   |;   9   &;  12   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   4 usr;   5 con; 0-2 aty)
%            Number of variables   :   16 (  14   ^   2   !;   0   ?;  16   :)

% Comments : 
%------------------------------------------------------------------------------
thf(leibeq_type,type,
    leibeq: ( $o > $o > $o ) > ( $o > $o > $o ) > $o ).

thf(leibeq_def,definition,
    ( leibeq
    = ( ^ [A: $o > $o > $o,B: $o > $o > $o] :
        ! [C: ( $o > $o > $o ) > $o] :
          ( ( C @ A )
         => ( C @ B ) ) ) ) ).

thf(sk1_type,type,
    sk1: ( $o > $o > $o ) > $o ).

thf(sk2_type,type,
    sk2: $o ).

thf(sk3_type,type,
    sk3: $o ).

thf(1,conjecture,
    ( leibeq @ (&)
    @ ^ [A: $o,B: $o] :
        ~ ( ~ A
          | ~ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).

thf(2,negated_conjecture,
    ~ ( leibeq @ (&)
      @ ^ [A: $o,B: $o] :
          ~ ( ~ A
            | ~ B ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(5,plain,
    sk1 @ (&),
    inference(cnf,[status(esa)],[3]) ).

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

thf(6,plain,
    ( ( sk1 @ (&) )
   != ( sk1
      @ ^ [A: $o,B: $o] :
          ~ ( ~ A
            | ~ B ) ) ),
    inference(paramod_ordered,[status(thm)],[5,4]) ).

thf(7,plain,
    ( (&)
   != ( ^ [A: $o,B: $o] :
          ~ ( ~ A
            | ~ B ) ) ),
    inference(simp,[status(thm)],[6]) ).

thf(8,plain,
    ( ( sk2
      & sk3 )
   != ( ~ ( ~ sk2
          | ~ sk3 ) ) ),
    inference(func_ext,[status(esa)],[7]) ).

thf(10,plain,
    ( ( sk2
      & sk3 )
    | ~ ( ~ sk2
        | ~ sk3 ) ),
    inference(bool_ext,[status(thm)],[8]) ).

thf(14,plain,
    ( sk3
    | sk3 ),
    inference(cnf,[status(esa)],[10]) ).

thf(16,plain,
    sk3,
    inference(simp,[status(thm)],[14]) ).

thf(20,plain,
    ( ( sk2
      & $true )
   != ( ~ ( ~ sk2
          | ~ $true ) ) ),
    inference(rewrite,[status(thm)],[8,16]) ).

thf(21,plain,
    $false,
    inference(simp,[status(thm)],[20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SYO024^1 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.12  % Command  : run_Leo-III %s %d SAT
% 0.12/0.33  % Computer : n028.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 : Sun Jun 23 09:15:25 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.98/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.16/1.02  % [INFO] 	 Parsing done (115ms). 
% 1.16/1.03  % [INFO] 	 Running in sequential loop mode. 
% 1.71/1.25  % [INFO] 	 nitpick registered as external prover. 
% 1.76/1.25  % [INFO] 	 Scanning for conjecture ... 
% 1.76/1.30  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.96/1.32  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.96/1.32  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.96/1.32  % [INFO] 	 Type checking passed. 
% 1.96/1.33  % [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 ... 
% 2.47/1.59  % [INFO] 	 Killing All external provers ... 
% 2.47/1.59  % Time passed: 1068ms (effective reasoning time: 556ms)
% 2.47/1.59  % 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)>
% 2.47/1.59  % Axioms used in derivation (0): 
% 2.47/1.59  % No. of inferences in proof: 13
% 2.47/1.60  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1068 ms resp. 556 ms w/o parsing
% 2.47/1.62  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.47/1.62  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------