TSTP Solution File: GRP132-2.002 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : GRP132-2.002 : TPTP v8.1.2. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n019.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 : Wed May 31 12:10:40 EDT 2023

% Result   : Unsatisfiable 0.12s 0.36s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   67 (   7 unt;   0 def)
%            Number of atoms       :  169 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  205 ( 103   ~;  94   |;   0   &)
%                                         (   8 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   12 (  11 usr;   9 prp; 0-3 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   62 (;  62   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    group_element(e_1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    group_element(e_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ~ equalish(e_1,e_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [X,Y] :
      ( ~ group_element(X)
      | ~ group_element(Y)
      | product(X,Y,e_1)
      | product(X,Y,e_2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [X,W,Y,Z] :
      ( ~ product(X,W,Y)
      | ~ product(X,Z,Y)
      | equalish(W,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [W,Y,X,Z] :
      ( ~ product(W,Y,X)
      | ~ product(Z,Y,X)
      | equalish(W,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f13,negated_conjecture,
    ! [X1,Y1,Z1,X2,Y2,Z2] :
      ( ~ product(X1,Y1,Z1)
      | ~ product(X2,Y2,Z1)
      | ~ product(Z2,X1,Y1)
      | ~ product(Z2,X2,Y2)
      | equalish(Y1,Y2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f18,plain,
    group_element(e_1),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f19,plain,
    group_element(e_2),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f20,plain,
    ~ equalish(e_1,e_2),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ~ group_element(X0)
      | ~ group_element(X1)
      | product(X0,X1,e_1)
      | product(X0,X1,e_2) ),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f25,plain,
    ! [W,Z] :
      ( ! [X,Y] :
          ( ~ product(X,W,Y)
          | ~ product(X,Z,Y) )
      | equalish(W,Z) ),
    inference(miniscoping,[status(esa)],[f10]) ).

fof(f26,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(X0,X1,X2)
      | ~ product(X0,X3,X2)
      | equalish(X1,X3) ),
    inference(cnf_transformation,[status(esa)],[f25]) ).

fof(f27,plain,
    ! [W,Z] :
      ( ! [Y,X] :
          ( ~ product(W,Y,X)
          | ~ product(Z,Y,X) )
      | equalish(W,Z) ),
    inference(miniscoping,[status(esa)],[f11]) ).

fof(f28,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(X0,X1,X2)
      | ~ product(X3,X1,X2)
      | equalish(X0,X3) ),
    inference(cnf_transformation,[status(esa)],[f27]) ).

fof(f31,plain,
    ! [Y1,Y2] :
      ( ! [X2,Z2] :
          ( ! [X1] :
              ( ! [Z1] :
                  ( ~ product(X1,Y1,Z1)
                  | ~ product(X2,Y2,Z1) )
              | ~ product(Z2,X1,Y1) )
          | ~ product(Z2,X2,Y2) )
      | equalish(Y1,Y2) ),
    inference(miniscoping,[status(esa)],[f13]) ).

fof(f32,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ product(X0,X1,X2)
      | ~ product(X3,X4,X2)
      | ~ product(X5,X0,X1)
      | ~ product(X5,X3,X4)
      | equalish(X1,X4) ),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ~ product(e_1,X0,X1)
      | ~ product(e_2,X0,X1) ),
    inference(resolution,[status(thm)],[f20,f28]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ~ product(X0,e_1,X1)
      | ~ product(X0,e_2,X1) ),
    inference(resolution,[status(thm)],[f20,f26]) ).

fof(f36,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(X0,e_1,X1)
      | ~ product(X2,e_2,X1)
      | ~ product(X3,X0,e_1)
      | ~ product(X3,X2,e_2) ),
    inference(resolution,[status(thm)],[f20,f32]) ).

fof(f43,plain,
    ! [X0] :
      ( ~ group_element(X0)
      | product(X0,e_2,e_1)
      | product(X0,e_2,e_2) ),
    inference(resolution,[status(thm)],[f22,f19]) ).

fof(f44,plain,
    ! [X0] :
      ( ~ group_element(X0)
      | product(X0,e_1,e_1)
      | product(X0,e_1,e_2) ),
    inference(resolution,[status(thm)],[f22,f18]) ).

fof(f45,plain,
    ( spl0_0
  <=> product(e_2,e_2,e_1) ),
    introduced(split_symbol_definition) ).

fof(f46,plain,
    ( product(e_2,e_2,e_1)
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f45]) ).

fof(f48,plain,
    ( spl0_1
  <=> product(e_2,e_2,e_2) ),
    introduced(split_symbol_definition) ).

fof(f49,plain,
    ( product(e_2,e_2,e_2)
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f48]) ).

fof(f51,plain,
    ( product(e_2,e_2,e_1)
    | product(e_2,e_2,e_2) ),
    inference(resolution,[status(thm)],[f43,f19]) ).

fof(f52,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f51,f45,f48]) ).

fof(f53,plain,
    ( spl0_2
  <=> product(e_1,e_2,e_1) ),
    introduced(split_symbol_definition) ).

fof(f54,plain,
    ( product(e_1,e_2,e_1)
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f53]) ).

fof(f56,plain,
    ( spl0_3
  <=> product(e_1,e_2,e_2) ),
    introduced(split_symbol_definition) ).

fof(f57,plain,
    ( product(e_1,e_2,e_2)
    | ~ spl0_3 ),
    inference(component_clause,[status(thm)],[f56]) ).

fof(f59,plain,
    ( product(e_1,e_2,e_1)
    | product(e_1,e_2,e_2) ),
    inference(resolution,[status(thm)],[f43,f18]) ).

fof(f60,plain,
    ( spl0_2
    | spl0_3 ),
    inference(split_clause,[status(thm)],[f59,f53,f56]) ).

fof(f61,plain,
    ( spl0_4
  <=> product(e_2,e_1,e_1) ),
    introduced(split_symbol_definition) ).

fof(f62,plain,
    ( product(e_2,e_1,e_1)
    | ~ spl0_4 ),
    inference(component_clause,[status(thm)],[f61]) ).

fof(f64,plain,
    ( spl0_5
  <=> product(e_2,e_1,e_2) ),
    introduced(split_symbol_definition) ).

fof(f65,plain,
    ( product(e_2,e_1,e_2)
    | ~ spl0_5 ),
    inference(component_clause,[status(thm)],[f64]) ).

fof(f67,plain,
    ( product(e_2,e_1,e_1)
    | product(e_2,e_1,e_2) ),
    inference(resolution,[status(thm)],[f44,f19]) ).

fof(f68,plain,
    ( spl0_4
    | spl0_5 ),
    inference(split_clause,[status(thm)],[f67,f61,f64]) ).

fof(f69,plain,
    ( spl0_6
  <=> product(e_1,e_1,e_1) ),
    introduced(split_symbol_definition) ).

fof(f70,plain,
    ( product(e_1,e_1,e_1)
    | ~ spl0_6 ),
    inference(component_clause,[status(thm)],[f69]) ).

fof(f72,plain,
    ( spl0_7
  <=> product(e_1,e_1,e_2) ),
    introduced(split_symbol_definition) ).

fof(f73,plain,
    ( product(e_1,e_1,e_2)
    | ~ spl0_7 ),
    inference(component_clause,[status(thm)],[f72]) ).

fof(f75,plain,
    ( product(e_1,e_1,e_1)
    | product(e_1,e_1,e_2) ),
    inference(resolution,[status(thm)],[f44,f18]) ).

fof(f76,plain,
    ( spl0_6
    | spl0_7 ),
    inference(split_clause,[status(thm)],[f75,f69,f72]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( ~ product(X0,e_1,e_1)
      | ~ product(X1,X0,e_1)
      | ~ product(X1,e_1,e_2)
      | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f54,f36]) ).

fof(f78,plain,
    ( ~ product(e_1,e_1,e_1)
    | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f54,f34]) ).

fof(f79,plain,
    ( $false
    | ~ spl0_6
    | ~ spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f78,f70]) ).

fof(f80,plain,
    ( ~ spl0_6
    | ~ spl0_2 ),
    inference(contradiction_clause,[status(thm)],[f79]) ).

fof(f84,plain,
    ( ~ product(e_2,e_1,e_1)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f46,f34]) ).

fof(f85,plain,
    ( $false
    | ~ spl0_4
    | ~ spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f84,f62]) ).

fof(f86,plain,
    ( ~ spl0_4
    | ~ spl0_0 ),
    inference(contradiction_clause,[status(thm)],[f85]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( ~ product(X0,e_1,e_2)
      | ~ product(X1,X0,e_1)
      | ~ product(X1,e_1,e_2)
      | ~ spl0_3 ),
    inference(resolution,[status(thm)],[f57,f36]) ).

fof(f94,plain,
    ! [X0] :
      ( ~ product(X0,e_1,e_2)
      | ~ product(e_2,X0,e_1)
      | ~ spl0_5
      | ~ spl0_3 ),
    inference(resolution,[status(thm)],[f65,f88]) ).

fof(f97,plain,
    ( ~ product(e_1,e_2,e_2)
    | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f49,f33]) ).

fof(f98,plain,
    ( $false
    | ~ spl0_3
    | ~ spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f97,f57]) ).

fof(f99,plain,
    ( ~ spl0_3
    | ~ spl0_1 ),
    inference(contradiction_clause,[status(thm)],[f98]) ).

fof(f100,plain,
    ( ~ product(e_1,e_1,e_2)
    | ~ spl0_5 ),
    inference(resolution,[status(thm)],[f65,f33]) ).

fof(f101,plain,
    ( ~ spl0_7
    | ~ spl0_5 ),
    inference(split_clause,[status(thm)],[f100,f72,f64]) ).

fof(f103,plain,
    ( ~ product(e_2,e_1,e_2)
    | ~ spl0_0
    | ~ spl0_5
    | ~ spl0_3 ),
    inference(resolution,[status(thm)],[f46,f94]) ).

fof(f104,plain,
    ( $false
    | ~ spl0_0
    | ~ spl0_5
    | ~ spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f103,f65]) ).

fof(f105,plain,
    ( ~ spl0_0
    | ~ spl0_5
    | ~ spl0_3 ),
    inference(contradiction_clause,[status(thm)],[f104]) ).

fof(f110,plain,
    ! [X0] :
      ( ~ product(X0,e_1,e_1)
      | ~ product(e_1,X0,e_1)
      | ~ spl0_7
      | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f73,f77]) ).

fof(f113,plain,
    ( ~ product(e_1,e_2,e_1)
    | ~ spl0_4
    | ~ spl0_7
    | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f62,f110]) ).

fof(f114,plain,
    ( ~ spl0_2
    | ~ spl0_4
    | ~ spl0_7 ),
    inference(split_clause,[status(thm)],[f113,f53,f61,f72]) ).

fof(f116,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f52,f60,f68,f76,f80,f86,f99,f101,f105,f114]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP132-2.002 : TPTP v8.1.2. Released v1.2.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34  % Computer : n019.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 May 30 11:31:25 EDT 2023
% 0.12/0.35  % CPUTime  : 
% 0.12/0.35  % Drodi V3.5.1
% 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
% 0.20/0.58  % Elapsed time: 0.014207 seconds
% 0.20/0.58  % CPU time: 0.037437 seconds
% 0.20/0.58  % Memory used: 1.991 MB
%------------------------------------------------------------------------------