%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SYN057^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n004.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 08:10:05 EDT 2024

% Result   : Theorem 3.32s 2.33s
% Output   : Refutation 3.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    6
% Syntax   : Number of formulae    :    9 (   1 unt;   5 typ;   0 def)
%            Number of atoms       :   40 (   0 equ;   0 cnn)
%            Maximal formula atoms :   13 (  10 avg)
%            Number of connectives :   89 (  14   ~;   0   |;  18   &;  39   @)
%                                         (   0 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   5 usr;   1 con; 0-1 aty)
%            Number of variables   :   18 (   0   ^  12   !;   6   ?;  18   :)

% Comments : 
%------------------------------------------------------------------------------
thf(cI_type,type,
    cI: $i > $o ).

thf(cJ_type,type,
    cJ: $i > $o ).

thf(cH_type,type,
    cH: $i > $o ).

thf(cG_type,type,
    cG: $i > $o ).

thf(cF_type,type,
    cF: $i > $o ).

thf(1,conjecture,
    ( ( ? [A: $i] :
          ( ( cF @ A )
          & ~ ( cG @ A ) )
      & ! [A: $i] :
          ( ( cF @ A )
         => ( cH @ A ) )
      & ! [A: $i] :
          ( ( ( cJ @ A )
            & ( cI @ A ) )
         => ( cF @ A ) )
      & ( ? [A: $i] :
            ( ( cH @ A )
            & ~ ( cG @ A ) )
       => ! [A: $i] :
            ( ( cI @ A )
           => ~ ( cH @ A ) ) ) )
   => ! [A: $i] :
        ( ( cJ @ A )
       => ~ ( cI @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPELL27) ).

thf(2,negated_conjecture,
    ~ ( ( ? [A: $i] :
            ( ( cF @ A )
            & ~ ( cG @ A ) )
        & ! [A: $i] :
            ( ( cF @ A )
           => ( cH @ A ) )
        & ! [A: $i] :
            ( ( ( cJ @ A )
              & ( cI @ A ) )
           => ( cF @ A ) )
        & ( ? [A: $i] :
              ( ( cH @ A )
              & ~ ( cG @ A ) )
         => ! [A: $i] :
              ( ( cI @ A )
             => ~ ( cH @ A ) ) ) )
     => ! [A: $i] :
          ( ( cJ @ A )
         => ~ ( cI @ A ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ( ? [A: $i] :
            ( ( cF @ A )
            & ~ ( cG @ A ) )
        & ! [A: $i] :
            ( ( cF @ A )
           => ( cH @ A ) )
        & ! [A: $i] :
            ( ( ( cJ @ A )
              & ( cI @ A ) )
           => ( cF @ A ) )
        & ( ? [A: $i] :
              ( ( cH @ A )
              & ~ ( cG @ A ) )
         => ! [A: $i] :
              ( ( cI @ A )
             => ~ ( cH @ A ) ) ) )
     => ! [A: $i] :
          ( ( cJ @ A )
         => ~ ( cI @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(13,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SYN057^5 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.13  % Command  : run_Leo-III %s %d
% 0.12/0.34  % Computer : n004.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Mon May 20 15:37:39 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 1.06/1.06  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.47/1.23  % [INFO] 	 Parsing done (173ms). 
% 1.51/1.25  % [INFO] 	 Running in sequential loop mode. 
% 2.02/1.68  % [INFO] 	 eprover registered as external prover. 
% 2.02/1.68  % [INFO] 	 cvc4 registered as external prover. 
% 2.02/1.69  % [INFO] 	 Scanning for conjecture ... 
% 2.37/1.79  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.44/1.83  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.44/1.83  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.44/1.84  % [INFO] 	 Type checking passed. 
% 2.44/1.85  % [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 ... 
% 3.32/2.32  % External prover 'e' found a proof!
% 3.32/2.33  % [INFO] 	 Killing All external provers ... 
% 3.32/2.33  % Time passed: 1824ms (effective reasoning time: 1074ms)
% 3.32/2.33  % 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)>
% 3.32/2.33  % Axioms used in derivation (0): 
% 3.32/2.33  % No. of inferences in proof: 4
% 3.32/2.33  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1824 ms resp. 1074 ms w/o parsing
% 3.71/2.43  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.71/2.43  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------