%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SYN365+1 : TPTP v8.1.2. Released v2.0.0.
% 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 : Fri May 19 12:28:31 EDT 2023

% Result   : Theorem 2.74s 1.56s
% Output   : Refutation 2.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of formulae    :    8 (   1 unt;   4 typ;   0 def)
%            Number of atoms       :   28 (   0 equ;   0 cnn)
%            Maximal formula atoms :    9 (   7 avg)
%            Number of connectives :   71 (   2   ~;   0   |;  12   &;  45   @)
%                                         (   0 <=>;  12  =>;   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     :    5 (   4 usr;   1 con; 0-2 aty)
%            Number of variables   :   15 (   0   ^;   9   !;   6   ?;  15   :)

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

thf(big_r_type,type,
    big_r: $i > $i > $o ).

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

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

thf(1,conjecture,
    ( ( ! [A: $i] :
        ? [B: $i] :
          ( ( big_p @ A )
         => ( ( big_r @ A @ ( g @ ( h @ B ) ) )
            & ( big_p @ B ) ) )
      & ! [A: $i] :
          ( ( big_p @ A )
         => ( ( big_p @ ( g @ A ) )
            & ( big_p @ ( h @ A ) ) ) ) )
   => ! [A: $i] :
        ( ( big_p @ A )
       => ? [B: $i] :
            ( ( big_r @ A @ B )
            & ( big_p @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2116) ).

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

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

thf(19,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SYN365+1 : TPTP v8.1.2. Released v2.0.0.
% 0.12/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n004.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 : Thu May 18 19:25:10 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 0.97/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.23/0.95  % [INFO] 	 Parsing done (102ms). 
% 1.23/0.96  % [INFO] 	 Running in sequential loop mode. 
% 1.48/1.15  % [INFO] 	 eprover registered as external prover. 
% 1.48/1.15  % [INFO] 	 cvc4 registered as external prover. 
% 1.48/1.15  % [INFO] 	 Scanning for conjecture ... 
% 1.67/1.20  % [INFO] 	 Found a conjecture and 0 axioms. Running axiom selection ... 
% 1.77/1.23  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.77/1.23  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.77/1.23  % [INFO] 	 Type checking passed. 
% 1.77/1.23  % [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 ... 
% 2.74/1.56  % External prover 'e' found a proof!
% 2.74/1.56  % [INFO] 	 Killing All external provers ... 
% 2.74/1.56  % Time passed: 1031ms (effective reasoning time: 595ms)
% 2.74/1.56  % 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)>
% 2.74/1.56  % Axioms used in derivation (0): 
% 2.74/1.56  % No. of inferences in proof: 4
% 2.74/1.56  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1031 ms resp. 595 ms w/o parsing
% 2.74/1.58  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.74/1.58  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------