TSTP Solution File: GRP123-2.003 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GRP123-2.003 : TPTP v8.1.2. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n018.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 : Tue Apr 30 20:19:17 EDT 2024

% Result   : Unsatisfiable 0.12s 0.36s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   62 (  19 unt;   0 def)
%            Number of atoms       :  135 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  146 (  73   ~;  67   |;   0   &)
%                                         (   6 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   10 (   9 usr;   7 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   62 (  62   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f7,axiom,
    group_element(e_1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    group_element(e_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    group_element(e_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ~ equalish(e_1,e_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ~ equalish(e_1,e_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f16,axiom,
    ! [X,Y] :
      ( ~ group_element(X)
      | ~ group_element(Y)
      | product(X,Y,e_1)
      | product(X,Y,e_2)
      | product(X,Y,e_3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f18,axiom,
    ! [X,W,Y,Z] :
      ( ~ product(X,W,Y)
      | ~ product(X,Z,Y)
      | equalish(W,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f19,axiom,
    ! [W,Y,X,Z] :
      ( ~ product(W,Y,X)
      | ~ product(Z,Y,X)
      | equalish(W,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f20,axiom,
    ! [X] : product(X,X,X),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f22,negated_conjecture,
    ! [X1,Y1,Z1,X2,Y2,Z2] :
      ( ~ product(X1,Y1,Z1)
      | ~ product(X2,Y2,Z1)
      | ~ product(Z2,Y1,X1)
      | ~ product(Z2,Y2,X2)
      | equalish(Y1,Y2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f30,plain,
    group_element(e_1),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f31,plain,
    group_element(e_2),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f32,plain,
    group_element(e_3),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f33,plain,
    ~ equalish(e_1,e_2),
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f34,plain,
    ~ equalish(e_1,e_3),
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ~ group_element(X0)
      | ~ group_element(X1)
      | product(X0,X1,e_1)
      | product(X0,X1,e_2)
      | product(X0,X1,e_3) ),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f42,plain,
    ! [W,Z] :
      ( ! [X,Y] :
          ( ~ product(X,W,Y)
          | ~ product(X,Z,Y) )
      | equalish(W,Z) ),
    inference(miniscoping,[status(esa)],[f18]) ).

fof(f43,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(X0,X1,X2)
      | ~ product(X0,X3,X2)
      | equalish(X1,X3) ),
    inference(cnf_transformation,[status(esa)],[f42]) ).

fof(f44,plain,
    ! [W,Z] :
      ( ! [Y,X] :
          ( ~ product(W,Y,X)
          | ~ product(Z,Y,X) )
      | equalish(W,Z) ),
    inference(miniscoping,[status(esa)],[f19]) ).

fof(f45,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(X0,X1,X2)
      | ~ product(X3,X1,X2)
      | equalish(X0,X3) ),
    inference(cnf_transformation,[status(esa)],[f44]) ).

fof(f46,plain,
    ! [X0] : product(X0,X0,X0),
    inference(cnf_transformation,[status(esa)],[f20]) ).

fof(f49,plain,
    ! [Y1,Y2] :
      ( ! [X2,Z2] :
          ( ! [X1] :
              ( ! [Z1] :
                  ( ~ product(X1,Y1,Z1)
                  | ~ product(X2,Y2,Z1) )
              | ~ product(Z2,Y1,X1) )
          | ~ product(Z2,Y2,X2) )
      | equalish(Y1,Y2) ),
    inference(miniscoping,[status(esa)],[f22]) ).

fof(f50,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ product(X0,X1,X2)
      | ~ product(X3,X4,X2)
      | ~ product(X5,X1,X0)
      | ~ product(X5,X4,X3)
      | equalish(X1,X4) ),
    inference(cnf_transformation,[status(esa)],[f49]) ).

fof(f51,plain,
    ! [X0] :
      ( ~ group_element(X0)
      | product(X0,e_1,e_1)
      | product(X0,e_1,e_2)
      | product(X0,e_1,e_3) ),
    inference(resolution,[status(thm)],[f30,f39]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( ~ product(e_1,X0,X1)
      | ~ product(e_2,X0,X1) ),
    inference(resolution,[status(thm)],[f33,f45]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( ~ product(X0,e_1,X1)
      | ~ product(X0,e_2,X1) ),
    inference(resolution,[status(thm)],[f33,f43]) ).

fof(f57,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(X0,e_1,X1)
      | ~ product(X2,e_2,X1)
      | ~ product(X3,e_1,X0)
      | ~ product(X3,e_2,X2) ),
    inference(resolution,[status(thm)],[f33,f50]) ).

fof(f59,plain,
    ! [X0] :
      ( ~ product(X0,e_1,e_2)
      | ~ product(e_2,e_1,X0) ),
    inference(resolution,[status(thm)],[f57,f46]) ).

fof(f67,plain,
    ~ product(e_2,e_1,e_2),
    inference(resolution,[status(thm)],[f55,f46]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( ~ product(e_1,X0,X1)
      | ~ product(e_3,X0,X1) ),
    inference(resolution,[status(thm)],[f34,f45]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( ~ product(X0,e_1,X1)
      | ~ product(X0,e_3,X1) ),
    inference(resolution,[status(thm)],[f34,f43]) ).

fof(f82,plain,
    ~ product(e_3,e_1,e_3),
    inference(resolution,[status(thm)],[f70,f46]) ).

fof(f115,plain,
    ( spl0_0
  <=> product(e_3,e_1,e_1) ),
    introduced(split_symbol_definition) ).

fof(f116,plain,
    ( product(e_3,e_1,e_1)
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f115]) ).

fof(f118,plain,
    ( spl0_1
  <=> product(e_3,e_1,e_2) ),
    introduced(split_symbol_definition) ).

fof(f119,plain,
    ( product(e_3,e_1,e_2)
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f118]) ).

fof(f121,plain,
    ( spl0_2
  <=> product(e_3,e_1,e_3) ),
    introduced(split_symbol_definition) ).

fof(f122,plain,
    ( product(e_3,e_1,e_3)
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f121]) ).

fof(f124,plain,
    ( product(e_3,e_1,e_1)
    | product(e_3,e_1,e_2)
    | product(e_3,e_1,e_3) ),
    inference(resolution,[status(thm)],[f51,f32]) ).

fof(f125,plain,
    ( spl0_0
    | spl0_1
    | spl0_2 ),
    inference(split_clause,[status(thm)],[f124,f115,f118,f121]) ).

fof(f126,plain,
    ( spl0_3
  <=> product(e_2,e_1,e_1) ),
    introduced(split_symbol_definition) ).

fof(f127,plain,
    ( product(e_2,e_1,e_1)
    | ~ spl0_3 ),
    inference(component_clause,[status(thm)],[f126]) ).

fof(f129,plain,
    ( spl0_4
  <=> product(e_2,e_1,e_2) ),
    introduced(split_symbol_definition) ).

fof(f130,plain,
    ( product(e_2,e_1,e_2)
    | ~ spl0_4 ),
    inference(component_clause,[status(thm)],[f129]) ).

fof(f132,plain,
    ( spl0_5
  <=> product(e_2,e_1,e_3) ),
    introduced(split_symbol_definition) ).

fof(f133,plain,
    ( product(e_2,e_1,e_3)
    | ~ spl0_5 ),
    inference(component_clause,[status(thm)],[f132]) ).

fof(f135,plain,
    ( product(e_2,e_1,e_1)
    | product(e_2,e_1,e_2)
    | product(e_2,e_1,e_3) ),
    inference(resolution,[status(thm)],[f51,f31]) ).

fof(f136,plain,
    ( spl0_3
    | spl0_4
    | spl0_5 ),
    inference(split_clause,[status(thm)],[f135,f126,f129,f132]) ).

fof(f148,plain,
    ( $false
    | ~ spl0_4 ),
    inference(forward_subsumption_resolution,[status(thm)],[f130,f67]) ).

fof(f149,plain,
    ~ spl0_4,
    inference(contradiction_clause,[status(thm)],[f148]) ).

fof(f150,plain,
    ( $false
    | ~ spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f122,f82]) ).

fof(f151,plain,
    ~ spl0_2,
    inference(contradiction_clause,[status(thm)],[f150]) ).

fof(f163,plain,
    ( ~ product(e_1,e_1,e_1)
    | ~ spl0_3 ),
    inference(resolution,[status(thm)],[f127,f54]) ).

fof(f164,plain,
    ( $false
    | ~ spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f163,f46]) ).

fof(f165,plain,
    ~ spl0_3,
    inference(contradiction_clause,[status(thm)],[f164]) ).

fof(f168,plain,
    ( ~ product(e_1,e_1,e_1)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f116,f69]) ).

fof(f169,plain,
    ( $false
    | ~ spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f168,f46]) ).

fof(f170,plain,
    ~ spl0_0,
    inference(contradiction_clause,[status(thm)],[f169]) ).

fof(f172,plain,
    ( ~ product(e_3,e_1,e_2)
    | ~ spl0_5 ),
    inference(resolution,[status(thm)],[f133,f59]) ).

fof(f173,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f172,f119]) ).

fof(f174,plain,
    ( ~ spl0_1
    | ~ spl0_5 ),
    inference(contradiction_clause,[status(thm)],[f173]) ).

fof(f175,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f125,f136,f149,f151,f165,f170,f174]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12  % Problem  : GRP123-2.003 : TPTP v8.1.2. Released v1.2.0.
% 0.09/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34  % Computer : n018.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Tue Apr 30 00:30:28 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  % Drodi V3.6.0
% 0.12/0.36  % Refutation found
% 0.12/0.36  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.36  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.37  % Elapsed time: 0.019087 seconds
% 0.12/0.37  % CPU time: 0.069450 seconds
% 0.12/0.37  % Total memory used: 3.835 MB
% 0.12/0.37  % Net memory used: 3.676 MB
%------------------------------------------------------------------------------