TSTP Solution File: GRP001+6 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : GRP001+6 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n032.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 11:12:58 EDT 2023

% Result   : Theorem 2.51s 1.50s
% Output   : Refutation 2.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    3
% Syntax   : Number of formulae    :    6 (   1 unt;   2 typ;   0 def)
%            Number of atoms       :   49 (   0 equ;   0 cnn)
%            Maximal formula atoms :   16 (  12 avg)
%            Number of connectives :  197 (   2   ~;   0   |;  30   &; 150   @)
%                                         (   0 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (  14 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   2 usr;   1 con; 0-3 aty)
%            Number of variables   :   72 (   0   ^;  69   !;   3   ?;  72   :)

% Comments : 
%------------------------------------------------------------------------------
thf(product_type,type,
    product: $i > $i > $i > $o ).

thf(inverse_type,type,
    inverse: $i > $i ).

thf(1,conjecture,
    ! [A: $i] :
      ( ( ! [B: $i,C: $i] :
          ? [D: $i] : ( product @ B @ C @ D )
        & ! [B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
            ( ( ( product @ B @ C @ E )
              & ( product @ C @ D @ F )
              & ( product @ E @ D @ G ) )
           => ( product @ B @ F @ G ) )
        & ! [B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
            ( ( ( product @ B @ C @ E )
              & ( product @ C @ D @ F )
              & ( product @ B @ F @ G ) )
           => ( product @ E @ D @ G ) )
        & ! [B: $i] : ( product @ B @ A @ B )
        & ! [B: $i] : ( product @ A @ B @ B )
        & ! [B: $i] : ( product @ B @ ( inverse @ B ) @ A )
        & ! [B: $i] : ( product @ ( inverse @ B ) @ B @ A ) )
     => ( ! [B: $i] : ( product @ B @ B @ A )
       => ! [B: $i,C: $i,D: $i] :
            ( ( product @ B @ C @ D )
           => ( product @ C @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ( ( ! [B: $i,C: $i] :
            ? [D: $i] : ( product @ B @ C @ D )
          & ! [B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
              ( ( ( product @ B @ C @ E )
                & ( product @ C @ D @ F )
                & ( product @ E @ D @ G ) )
             => ( product @ B @ F @ G ) )
          & ! [B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
              ( ( ( product @ B @ C @ E )
                & ( product @ C @ D @ F )
                & ( product @ B @ F @ G ) )
             => ( product @ E @ D @ G ) )
          & ! [B: $i] : ( product @ B @ A @ B )
          & ! [B: $i] : ( product @ A @ B @ B )
          & ! [B: $i] : ( product @ B @ ( inverse @ B ) @ A )
          & ! [B: $i] : ( product @ ( inverse @ B ) @ B @ A ) )
       => ( ! [B: $i] : ( product @ B @ B @ A )
         => ! [B: $i,C: $i,D: $i] :
              ( ( product @ B @ C @ D )
             => ( product @ C @ B @ D ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ! [A: $i] :
        ( ( ! [B: $i,C: $i] :
            ? [D: $i] : ( product @ B @ C @ D )
          & ! [B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
              ( ( ( product @ B @ C @ E )
                & ( product @ C @ D @ F )
                & ( product @ E @ D @ G ) )
             => ( product @ B @ F @ G ) )
          & ! [B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
              ( ( ( product @ B @ C @ E )
                & ( product @ C @ D @ F )
                & ( product @ B @ F @ G ) )
             => ( product @ E @ D @ G ) )
          & ! [B: $i] : ( product @ B @ A @ B )
          & ! [B: $i] : ( product @ A @ B @ B )
          & ! [B: $i] : ( product @ B @ ( inverse @ B ) @ A )
          & ! [B: $i] : ( product @ ( inverse @ B ) @ B @ A ) )
       => ( ! [B: $i] : ( product @ B @ B @ A )
         => ! [B: $i,C: $i,D: $i] :
              ( ( product @ B @ C @ D )
             => ( product @ C @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(24,plain,
    $false,
    inference(e,[status(thm)],[3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08  % Problem  : GRP001+6 : TPTP v8.1.2. Released v3.1.0.
% 0.02/0.10  % Command  : run_Leo-III %s %d
% 0.11/0.29  % Computer : n032.cluster.edu
% 0.11/0.29  % Model    : x86_64 x86_64
% 0.11/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29  % Memory   : 8042.1875MB
% 0.11/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29  % CPULimit : 300
% 0.11/0.29  % WCLimit  : 300
% 0.11/0.29  % DateTime : Fri May 19 01:46:12 EDT 2023
% 0.11/0.29  % CPUTime  : 
% 0.75/0.74  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 0.84/0.86  % [INFO] 	 Parsing done (119ms). 
% 1.06/0.87  % [INFO] 	 Running in sequential loop mode. 
% 1.31/1.06  % [INFO] 	 eprover registered as external prover. 
% 1.31/1.06  % [INFO] 	 cvc4 registered as external prover. 
% 1.31/1.07  % [INFO] 	 Scanning for conjecture ... 
% 1.49/1.13  % [INFO] 	 Found a conjecture and 0 axioms. Running axiom selection ... 
% 1.49/1.15  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.49/1.16  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.49/1.16  % [INFO] 	 Type checking passed. 
% 1.49/1.16  % [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 ... 
% 2.26/1.47  % External prover 'e' found a proof!
% 2.26/1.47  % [INFO] 	 Killing All external provers ... 
% 2.26/1.47  % Time passed: 1050ms (effective reasoning time: 598ms)
% 2.26/1.47  % 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)>
% 2.51/1.50  % Axioms used in derivation (0): 
% 2.51/1.50  % No. of inferences in proof: 4
% 2.51/1.50  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1050 ms resp. 598 ms w/o parsing
% 2.51/1.53  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.51/1.53  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------