%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYN732+1 : TPTP v8.2.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n008.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 08:19:15 EDT 2024

% Result   : Theorem 2.10s 1.35s
% Output   : Refutation 2.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   13 (   6 unt;   3 typ;   0 def)
%            Number of atoms       :   26 (   0 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   71 (   5   ~;   4   |;   0   &;  50   @)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   3 usr;   1 con; 0-2 aty)
%            Number of variables   :   33 (   0   ^  19   !;  14   ?;  33   :)

% Comments : 
%------------------------------------------------------------------------------
thf(p_type,type,
    p: $i > $i > $o ).

thf(q_type,type,
    q: $i > $i > $o ).

thf(sk2_type,type,
    sk2: $i > $i ).

thf(1,conjecture,
    ( ! [A: $i] :
        ( ! [B: $i] : ( p @ B @ A )
       => ! [B: $i] : ( q @ B @ A ) )
   => ? [A: $i] :
        ( ? [B: $i] : ( p @ B @ A )
       => ? [B: $i] :
            ( ( p @ A @ B )
            | ( q @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',x3411) ).

thf(2,negated_conjecture,
    ~ ( ! [A: $i] :
          ( ! [B: $i] : ( p @ B @ A )
         => ! [B: $i] : ( q @ B @ A ) )
     => ? [A: $i] :
          ( ? [B: $i] : ( p @ B @ A )
         => ? [B: $i] :
              ( ( p @ A @ B )
              | ( q @ B @ A ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ! [A: $i] :
          ( ! [B: $i] : ( p @ B @ A )
         => ! [B: $i] : ( q @ B @ A ) )
     => ? [A: $i] :
          ( ? [B: $i] : ( p @ B @ A )
         => ? [B: $i] :
              ( ( p @ A @ B )
              | ( q @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    ~ ( ! [A: $i] :
          ( ! [B: $i] : ( p @ B @ A )
         => ! [B: $i] : ( q @ B @ A ) )
     => ( ! [A: $i] :
          ? [B: $i] : ( p @ B @ A )
       => ( ? [A: $i,B: $i] : ( p @ A @ B )
          | ? [A: $i,B: $i] : ( q @ B @ A ) ) ) ),
    inference(miniscope,[status(thm)],[3]) ).

thf(7,plain,
    ! [A: $i] : ( p @ ( sk2 @ A ) @ A ),
    inference(cnf,[status(esa)],[4]) ).

thf(11,plain,
    ! [A: $i] : ( p @ ( sk2 @ A ) @ A ),
    inference(simp,[status(thm)],[7]) ).

thf(6,plain,
    ! [B: $i,A: $i] :
      ~ ( p @ A @ B ),
    inference(cnf,[status(esa)],[4]) ).

thf(10,plain,
    ! [B: $i,A: $i] :
      ~ ( p @ A @ B ),
    inference(simp,[status(thm)],[6]) ).

thf(12,plain,
    $false,
    inference(rewrite,[status(thm)],[11,10]) ).

thf(13,plain,
    $false,
    inference(simp,[status(thm)],[12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11  % Problem  : SYN732+1 : TPTP v8.2.0. Released v2.5.0.
% 0.04/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n008.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon May 20 13:58:54 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.87/0.77  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.03/0.86  % [INFO] 	 Parsing done (88ms). 
% 1.03/0.86  % [INFO] 	 Running in sequential loop mode. 
% 1.39/1.06  % [INFO] 	 nitpick registered as external prover. 
% 1.39/1.07  % [INFO] 	 Scanning for conjecture ... 
% 1.53/1.11  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.53/1.13  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.53/1.13  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.53/1.14  % [INFO] 	 Type checking passed. 
% 1.53/1.14  % [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 ... 
% 2.10/1.35  % [INFO] 	 Killing All external provers ... 
% 2.10/1.35  % Time passed: 900ms (effective reasoning time: 478ms)
% 2.10/1.35  % 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)>
% 2.10/1.35  % Axioms used in derivation (0): 
% 2.10/1.35  % No. of inferences in proof: 10
% 2.10/1.35  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 900 ms resp. 478 ms w/o parsing
% 2.22/1.37  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.22/1.37  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------