%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SYN375+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n001.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 : Fri May 19 12:28:33 EDT 2023

% Result   : Theorem 2.60s 1.60s
% Output   : Refutation 2.99s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    2
% Syntax   : Number of formulae    :    5 (   1 unt;   1 typ;   0 def)
%            Number of atoms       :   25 (   0 equ;   0 cnn)
%            Maximal formula atoms :   16 (   6 avg)
%            Number of connectives :   47 (   2   ~;   0   |;   5   &;  24   @)
%                                         (   6 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    1 (   1   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    2 (   1 usr;   1 con; 0-1 aty)
%            Number of variables   :   22 (   0   ^;  10   !;  12   ?;  22   :)

% Comments : 
%------------------------------------------------------------------------------
thf(big_p_type,type,
    big_p: $i > $o ).

thf(1,conjecture,
    ( ! [A: $i] :
        ( ( big_p @ A )
      <=> ? [B: $i] : ( big_p @ B ) )
  <=> ( ! [A: $i] : ( big_p @ A )
    <=> ? [A: $i] : ( big_p @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2126) ).

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

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

thf(32,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYN375+1 : TPTP v8.1.2. Released v2.0.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.35  % Computer : n001.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Thu May 18 20:07:51 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.95/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.28/0.99  % [INFO] 	 Parsing done (113ms). 
% 1.28/1.00  % [INFO] 	 Running in sequential loop mode. 
% 1.60/1.19  % [INFO] 	 eprover registered as external prover. 
% 1.60/1.20  % [INFO] 	 cvc4 registered as external prover. 
% 1.60/1.20  % [INFO] 	 Scanning for conjecture ... 
% 1.77/1.24  % [INFO] 	 Found a conjecture and 0 axioms. Running axiom selection ... 
% 1.77/1.26  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.77/1.27  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.90/1.27  % [INFO] 	 Type checking passed. 
% 1.90/1.27  % [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 ... 
% 2.60/1.60  % External prover 'e' found a proof!
% 2.60/1.60  % [INFO] 	 Killing All external provers ... 
% 2.60/1.60  % Time passed: 1090ms (effective reasoning time: 596ms)
% 2.60/1.60  % 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)>
% 2.60/1.60  % Axioms used in derivation (0): 
% 2.60/1.60  % No. of inferences in proof: 4
% 2.60/1.60  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1090 ms resp. 596 ms w/o parsing
% 2.99/1.67  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.99/1.67  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------