TSTP Solution File: GRP775+1 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : GRP775+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n009.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 11:15:22 EDT 2023

% Result   : Theorem 3.37s 1.82s
% Output   : Refutation 3.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   18 (   5 unt;   4 typ;   0 def)
%            Number of atoms       :   44 (  24 equ;   0 cnn)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :  146 (   2   ~;   0   |;  17   &; 114   @)
%                                         (   5 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   1 con; 0-2 aty)
%            Number of variables   :   29 (   0   ^;  26   !;   3   ?;  29   :)

% Comments : 
%------------------------------------------------------------------------------
thf(d_type,type,
    d: $i > $i > $o ).

thf(product_type,type,
    product: $i > $i > $i ).

thf(l_type,type,
    l: $i > $i > $o ).

thf(r_type,type,
    r: $i > $i > $o ).

thf(3,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( product @ ( product @ C @ B ) @ A )
      = ( product @ C @ ( product @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos01) ).

thf(18,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( product @ ( product @ C @ B ) @ A )
      = ( product @ C @ ( product @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(1,conjecture,
    ! [A: $i,B: $i] :
      ( ( d @ A @ B )
    <=> ( ( ( product @ A @ ( product @ B @ A ) )
          = A )
        & ( ( product @ B @ ( product @ A @ B ) )
          = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

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

thf(8,plain,
    ~ ! [A: $i,B: $i] :
        ( ( ( d @ A @ B )
         => ( ( ( product @ A @ ( product @ B @ A ) )
              = A )
            & ( ( product @ B @ ( product @ A @ B ) )
              = B ) ) )
        & ( ( ( ( product @ A @ ( product @ B @ A ) )
              = A )
            & ( ( product @ B @ ( product @ A @ B ) )
              = B ) )
         => ( d @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(7,axiom,
    ! [A: $i,B: $i] :
      ( ( d @ A @ B )
    <=> ? [C: $i] :
          ( ( r @ A @ C )
          & ( l @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos05) ).

thf(42,plain,
    ! [A: $i,B: $i] :
      ( ( ( d @ A @ B )
       => ? [C: $i] :
            ( ( r @ A @ C )
            & ( l @ C @ B ) ) )
      & ( ? [C: $i] :
            ( ( r @ A @ C )
            & ( l @ C @ B ) )
       => ( d @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ( ( l @ A @ B )
    <=> ( ( ( product @ A @ B )
          = A )
        & ( ( product @ B @ A )
          = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).

thf(24,plain,
    ! [A: $i,B: $i] :
      ( ( ( l @ A @ B )
       => ( ( ( product @ A @ B )
            = A )
          & ( ( product @ B @ A )
            = B ) ) )
      & ( ( ( ( product @ A @ B )
            = A )
          & ( ( product @ B @ A )
            = B ) )
       => ( l @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(4,axiom,
    ! [A: $i] :
      ( ( product @ A @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos02) ).

thf(21,plain,
    ! [A: $i] :
      ( ( product @ A @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(6,axiom,
    ! [A: $i,B: $i] :
      ( ( r @ A @ B )
    <=> ( ( ( product @ A @ B )
          = B )
        & ( ( product @ B @ A )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos04) ).

thf(33,plain,
    ! [A: $i,B: $i] :
      ( ( ( r @ A @ B )
       => ( ( ( product @ A @ B )
            = B )
          & ( ( product @ B @ A )
            = A ) ) )
      & ( ( ( ( product @ A @ B )
            = B )
          & ( ( product @ B @ A )
            = A ) )
       => ( r @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(59,plain,
    $false,
    inference(cvc4,[status(thm)],[18,8,42,24,21,33]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : GRP775+1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n009.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Fri May 19 02:03:48 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 0.91/0.93  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.17/1.05  % [INFO] 	 Parsing done (116ms). 
% 1.17/1.06  % [INFO] 	 Running in sequential loop mode. 
% 1.69/1.25  % [INFO] 	 eprover registered as external prover. 
% 1.69/1.26  % [INFO] 	 cvc4 registered as external prover. 
% 1.69/1.26  % [INFO] 	 Scanning for conjecture ... 
% 1.80/1.31  % [INFO] 	 Found a conjecture and 5 axioms. Running axiom selection ... 
% 1.80/1.34  % [INFO] 	 Axiom selection finished. Selected 5 axioms (removed 0 axioms). 
% 1.98/1.35  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.98/1.35  % [INFO] 	 Type checking passed. 
% 1.98/1.35  % [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 ... 
% 3.37/1.82  % External prover 'cvc4' found a proof!
% 3.37/1.82  % [INFO] 	 Killing All external provers ... 
% 3.37/1.82  % Time passed: 1252ms (effective reasoning time: 760ms)
% 3.37/1.82  % 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)>
% 3.37/1.82  % Axioms used in derivation (5): sos03, sos02, sos05, sos04, sos01
% 3.37/1.82  % No. of inferences in proof: 14
% 3.37/1.82  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1252 ms resp. 760 ms w/o parsing
% 3.37/1.85  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.37/1.85  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------