%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : SEV398^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% Computer : n018.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 15:58:55 EDT 2024

% Result   : Theorem 2.73s 1.55s
% Output   : Refutation 2.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    1
% Syntax   : Number of formulae    :    4 (   1 unt;   0 typ;   0 def)
%            Number of atoms       :   34 (   3 equ;   0 cnn)
%            Maximal formula atoms :    7 (   8 avg)
%            Number of connectives :   86 (   2   ~;   0   |;   6   &;  60   @)
%                                         (   0 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   8 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   2 usr;   1 con; 0-2 aty)
%            Number of variables   :   27 (   0   ^  27   !;   0   ?;  27   :)

% Comments : 
%------------------------------------------------------------------------------
thf(a_type,type,
    a: $tType ).

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

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

thf(1,conjecture,
    ( ( ! [A: a > $o,B: a > $o] :
          ( ! [C: a] :
              ( ( A @ C )
             => ( B @ C ) )
         => ! [C: a] :
              ( ( cF @ B @ C )
             => ( cF @ A @ C ) ) )
      & ! [A: a > $o] :
          ( ! [B: a] :
              ( ( A @ B )
             => ( cF @ ( cG @ A ) @ B ) )
          & ! [B: a] :
              ( ( A @ B )
             => ( cG @ ( cF @ A ) @ B ) ) ) )
   => ! [A: a > $o,B: a] :
        ( ( cF @ ( cG @ ( cF @ A ) ) @ B )
        = ( cF @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM67A_pme) ).

thf(2,negated_conjecture,
    ~ ( ( ! [A: a > $o,B: a > $o] :
            ( ! [C: a] :
                ( ( A @ C )
               => ( B @ C ) )
           => ! [C: a] :
                ( ( cF @ B @ C )
               => ( cF @ A @ C ) ) )
        & ! [A: a > $o] :
            ( ! [B: a] :
                ( ( A @ B )
               => ( cF @ ( cG @ A ) @ B ) )
            & ! [B: a] :
                ( ( A @ B )
               => ( cG @ ( cF @ A ) @ B ) ) ) )
     => ! [A: a > $o,B: a] :
          ( ( cF @ ( cG @ ( cF @ A ) ) @ B )
          = ( cF @ A @ B ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(17,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SEV398^5 : TPTP v8.2.0. Released v4.0.0.
% 0.04/0.12  % Command  : run_Leo-III %s %d THM
% 0.12/0.33  % Computer : n018.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 19:41:40 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.94/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.18/0.95  % [INFO] 	 Parsing done (96ms). 
% 1.23/0.96  % [INFO] 	 Running in sequential loop mode. 
% 1.63/1.16  % [INFO] 	 eprover registered as external prover. 
% 1.63/1.16  % [INFO] 	 Scanning for conjecture ... 
% 1.71/1.22  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.85/1.24  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.85/1.24  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.85/1.24  % [INFO] 	 Type checking passed. 
% 1.88/1.24  % [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 ... 
% 2.73/1.55  % External prover 'e' found a proof!
% 2.73/1.55  % [INFO] 	 Killing All external provers ... 
% 2.73/1.55  % Time passed: 1021ms (effective reasoning time: 584ms)
% 2.73/1.55  % 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)>
% 2.73/1.55  % Axioms used in derivation (0): 
% 2.73/1.55  % No. of inferences in proof: 4
% 2.73/1.55  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1021 ms resp. 584 ms w/o parsing
% 2.73/1.57  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.73/1.57  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------