%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYN406+1 : TPTP v8.2.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n009.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 08:18:25 EDT 2024

% Result   : Theorem 2.37s 1.49s
% Output   : Refutation 2.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   18 (   6 unt;   4 typ;   0 def)
%            Number of atoms       :   38 (   2 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   66 (  12   ~;   5   |;   9   &;  34   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   14 (   0   ^   8   !;   6   ?;  14   :)

% Comments : 
%------------------------------------------------------------------------------
thf(f_type,type,
    f: $i > $o ).

thf(g_type,type,
    g: $i > $o ).

thf(h_type,type,
    h: $i > $o ).

thf(sk1_type,type,
    sk1: $i ).

thf(1,conjecture,
    ( ( ! [A: $i] :
          ( ( f @ A )
         => ( g @ A ) )
      & ? [A: $i] :
          ( ( f @ A )
          & ( h @ A ) ) )
   => ? [A: $i] :
        ( ( g @ A )
        & ( h @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kalish240) ).

thf(2,negated_conjecture,
    ~ ( ( ! [A: $i] :
            ( ( f @ A )
           => ( g @ A ) )
        & ? [A: $i] :
            ( ( f @ A )
            & ( h @ A ) ) )
     => ? [A: $i] :
          ( ( g @ A )
          & ( h @ A ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ( ! [A: $i] :
            ( ( f @ A )
           => ( g @ A ) )
        & ? [A: $i] :
            ( ( f @ A )
            & ( h @ A ) ) )
     => ? [A: $i] :
          ( ( g @ A )
          & ( h @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

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

thf(4,plain,
    ! [A: $i] :
      ( ~ ( g @ A )
      | ~ ( h @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(8,plain,
    ! [A: $i] :
      ( ~ ( g @ A )
      | ~ ( h @ A ) ),
    inference(simp,[status(thm)],[4]) ).

thf(11,plain,
    ! [A: $i] :
      ( ~ ( g @ A )
      | ( ( h @ sk1 )
       != ( h @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[5,8]) ).

thf(12,plain,
    ~ ( g @ sk1 ),
    inference(pattern_uni,[status(thm)],[11:[bind(A,$thf( sk1 ))]]) ).

thf(6,plain,
    f @ sk1,
    inference(cnf,[status(esa)],[3]) ).

thf(7,plain,
    ! [A: $i] :
      ( ~ ( f @ A )
      | ( g @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(9,plain,
    ! [A: $i] :
      ( ( g @ A )
      | ( ( f @ sk1 )
       != ( f @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[6,7]) ).

thf(10,plain,
    g @ sk1,
    inference(pattern_uni,[status(thm)],[9:[bind(A,$thf( sk1 ))]]) ).

thf(17,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[12,10]) ).

thf(18,plain,
    $false,
    inference(simp,[status(thm)],[17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SYN406+1 : TPTP v8.2.0. Released v2.0.0.
% 0.10/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n009.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Mon May 20 14:06:54 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.88/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.15/0.95  % [INFO] 	 Parsing done (94ms). 
% 1.15/0.96  % [INFO] 	 Running in sequential loop mode. 
% 1.46/1.15  % [INFO] 	 nitpick registered as external prover. 
% 1.46/1.16  % [INFO] 	 Scanning for conjecture ... 
% 1.66/1.20  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.75/1.22  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.75/1.22  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.75/1.23  % [INFO] 	 Type checking passed. 
% 1.80/1.23  % [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 ... 
% 2.37/1.48  % [INFO] 	 Killing All external provers ... 
% 2.37/1.49  % Time passed: 962ms (effective reasoning time: 521ms)
% 2.37/1.49  % 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)>
% 2.37/1.49  % Axioms used in derivation (0): 
% 2.37/1.49  % No. of inferences in proof: 14
% 2.37/1.49  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 962 ms resp. 521 ms w/o parsing
% 2.51/1.55  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.51/1.55  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------