TSTP Solution File: GRP710+1 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : GRP710+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n002.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 11:15:14 EDT 2023

% Result   : Theorem 2.77s 1.70s
% Output   : Refutation 2.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   17 (  11 unt;   3 typ;   0 def)
%            Number of atoms       :   17 (  16 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   61 (   2   ~;   0   |;   3   &;  56   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   32 (   0   ^;  26   !;   6   ?;  32   :)

% Comments : 
%------------------------------------------------------------------------------
thf(mult_type,type,
    mult: $i > $i > $i ).

thf(unit_type,type,
    unit: $i ).

thf(i_type,type,
    i: $i > $i ).

thf(4,axiom,
    ! [A: $i] :
      ( ( mult @ unit @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).

thf(14,plain,
    ! [A: $i] :
      ( ( mult @ unit @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ( mult @ A @ ( i @ A ) )
      = unit ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).

thf(20,plain,
    ! [A: $i] :
      ( ( mult @ A @ ( i @ A ) )
      = unit ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(5,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( mult @ C @ ( mult @ B @ ( mult @ B @ A ) ) )
      = ( mult @ ( mult @ ( mult @ C @ B ) @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).

thf(17,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( mult @ C @ ( mult @ B @ ( mult @ B @ A ) ) )
      = ( mult @ ( mult @ ( mult @ C @ B ) @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(3,axiom,
    ! [A: $i] :
      ( ( mult @ A @ unit )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).

thf(11,plain,
    ! [A: $i] :
      ( ( mult @ A @ unit )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(7,axiom,
    ! [A: $i] :
      ( ( mult @ ( i @ A ) @ A )
      = unit ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).

thf(23,plain,
    ! [A: $i] :
      ( ( mult @ ( i @ A ) @ A )
      = unit ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(1,conjecture,
    ( ! [A: $i,B: $i] :
      ? [C: $i] :
        ( ( mult @ A @ C )
        = B )
    & ! [A: $i,B: $i] :
      ? [C: $i] :
        ( ( mult @ C @ B )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

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

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

thf(30,plain,
    $false,
    inference(e,[status(thm)],[14,20,17,11,23,8]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP710+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.37  % Computer : n002.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Fri May 19 02:05:52 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 0.90/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.06/0.98  % [INFO] 	 Parsing done (114ms). 
% 1.06/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.52/1.21  % [INFO] 	 eprover registered as external prover. 
% 1.52/1.21  % [INFO] 	 cvc4 registered as external prover. 
% 1.52/1.22  % [INFO] 	 Scanning for conjecture ... 
% 1.78/1.27  % [INFO] 	 Found a conjecture and 5 axioms. Running axiom selection ... 
% 1.78/1.29  % [INFO] 	 Axiom selection finished. Selected 5 axioms (removed 0 axioms). 
% 1.78/1.30  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.78/1.31  % [INFO] 	 Type checking passed. 
% 1.78/1.31  % [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 ... 
% 2.77/1.69  % External prover 'e' found a proof!
% 2.77/1.69  % [INFO] 	 Killing All external provers ... 
% 2.77/1.70  % Time passed: 1149ms (effective reasoning time: 701ms)
% 2.77/1.70  % 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)>
% 2.77/1.70  % Axioms used in derivation (5): f03, f02, f05, f04, f01
% 2.77/1.70  % No. of inferences in proof: 14
% 2.77/1.70  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1149 ms resp. 701 ms w/o parsing
% 2.89/1.76  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.89/1.76  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------