TSTP Solution File: GRP131-1.002 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GRP131-1.002 : TPTP v8.1.2. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n027.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 20:19:28 EDT 2024

% Result   : Unsatisfiable 0.13s 0.36s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   71 (   7 unt;   0 def)
%            Number of atoms       :  176 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  213 ( 108   ~;  97   |;   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(f1,axiom,
    group_element(e_1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    group_element(e_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ~ equalish(e_1,e_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,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(f7,axiom,
    ! [X,W,Y,Z] :
      ( ~ product(X,W,Y)
      | ~ product(X,Z,Y)
      | equalish(W,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f10,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(f11,plain,
    group_element(e_1),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f12,plain,
    group_element(e_2),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f13,plain,
    ~ equalish(e_1,e_2),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( ~ group_element(X0)
      | ~ group_element(X1)
      | product(X0,X1,e_1)
      | product(X0,X1,e_2) ),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f18,plain,
    ! [W,Z] :
      ( ! [X,Y] :
          ( ~ product(X,W,Y)
          | ~ product(X,Z,Y) )
      | equalish(W,Z) ),
    inference(miniscoping,[status(esa)],[f7]) ).

fof(f19,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(X0,X1,X2)
      | ~ product(X0,X3,X2)
      | equalish(X1,X3) ),
    inference(cnf_transformation,[status(esa)],[f18]) ).

fof(f20,plain,
    ! [W,Z] :
      ( ! [Y,X] :
          ( ~ product(W,Y,X)
          | ~ product(Z,Y,X) )
      | equalish(W,Z) ),
    inference(miniscoping,[status(esa)],[f8]) ).

fof(f21,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(X0,X1,X2)
      | ~ product(X3,X1,X2)
      | equalish(X0,X3) ),
    inference(cnf_transformation,[status(esa)],[f20]) ).

fof(f24,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)],[f10]) ).

fof(f25,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)],[f24]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ~ product(e_1,X0,X1)
      | ~ product(e_2,X0,X1) ),
    inference(resolution,[status(thm)],[f13,f21]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ~ product(X0,e_1,X1)
      | ~ product(X0,e_2,X1) ),
    inference(resolution,[status(thm)],[f13,f19]) ).

fof(f29,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)],[f13,f25]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ~ product(X0,e_1,X1)
      | ~ product(X1,e_2,X1)
      | ~ product(X1,e_1,X0) ),
    inference(factoring,[status(esa)],[f29]) ).

fof(f37,plain,
    ! [X0] :
      ( ~ group_element(X0)
      | product(X0,e_2,e_1)
      | product(X0,e_2,e_2) ),
    inference(resolution,[status(thm)],[f15,f12]) ).

fof(f38,plain,
    ! [X0] :
      ( ~ group_element(X0)
      | product(X0,e_1,e_1)
      | product(X0,e_1,e_2) ),
    inference(resolution,[status(thm)],[f15,f11]) ).

fof(f39,plain,
    ( spl0_0
  <=> product(e_2,e_2,e_1) ),
    introduced(split_symbol_definition) ).

fof(f40,plain,
    ( product(e_2,e_2,e_1)
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f39]) ).

fof(f42,plain,
    ( spl0_1
  <=> product(e_2,e_2,e_2) ),
    introduced(split_symbol_definition) ).

fof(f43,plain,
    ( product(e_2,e_2,e_2)
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f42]) ).

fof(f45,plain,
    ( product(e_2,e_2,e_1)
    | product(e_2,e_2,e_2) ),
    inference(resolution,[status(thm)],[f37,f12]) ).

fof(f46,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f45,f39,f42]) ).

fof(f47,plain,
    ( spl0_2
  <=> product(e_1,e_2,e_1) ),
    introduced(split_symbol_definition) ).

fof(f48,plain,
    ( product(e_1,e_2,e_1)
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f47]) ).

fof(f50,plain,
    ( spl0_3
  <=> product(e_1,e_2,e_2) ),
    introduced(split_symbol_definition) ).

fof(f51,plain,
    ( product(e_1,e_2,e_2)
    | ~ spl0_3 ),
    inference(component_clause,[status(thm)],[f50]) ).

fof(f53,plain,
    ( product(e_1,e_2,e_1)
    | product(e_1,e_2,e_2) ),
    inference(resolution,[status(thm)],[f37,f11]) ).

fof(f54,plain,
    ( spl0_2
    | spl0_3 ),
    inference(split_clause,[status(thm)],[f53,f47,f50]) ).

fof(f55,plain,
    ( spl0_4
  <=> product(e_2,e_1,e_1) ),
    introduced(split_symbol_definition) ).

fof(f56,plain,
    ( product(e_2,e_1,e_1)
    | ~ spl0_4 ),
    inference(component_clause,[status(thm)],[f55]) ).

fof(f58,plain,
    ( spl0_5
  <=> product(e_2,e_1,e_2) ),
    introduced(split_symbol_definition) ).

fof(f59,plain,
    ( product(e_2,e_1,e_2)
    | ~ spl0_5 ),
    inference(component_clause,[status(thm)],[f58]) ).

fof(f61,plain,
    ( product(e_2,e_1,e_1)
    | product(e_2,e_1,e_2) ),
    inference(resolution,[status(thm)],[f38,f12]) ).

fof(f62,plain,
    ( spl0_4
    | spl0_5 ),
    inference(split_clause,[status(thm)],[f61,f55,f58]) ).

fof(f63,plain,
    ( spl0_6
  <=> product(e_1,e_1,e_1) ),
    introduced(split_symbol_definition) ).

fof(f64,plain,
    ( product(e_1,e_1,e_1)
    | ~ spl0_6 ),
    inference(component_clause,[status(thm)],[f63]) ).

fof(f66,plain,
    ( spl0_7
  <=> product(e_1,e_1,e_2) ),
    introduced(split_symbol_definition) ).

fof(f67,plain,
    ( product(e_1,e_1,e_2)
    | ~ spl0_7 ),
    inference(component_clause,[status(thm)],[f66]) ).

fof(f69,plain,
    ( product(e_1,e_1,e_1)
    | product(e_1,e_1,e_2) ),
    inference(resolution,[status(thm)],[f38,f11]) ).

fof(f70,plain,
    ( spl0_6
    | spl0_7 ),
    inference(split_clause,[status(thm)],[f69,f63,f66]) ).

fof(f71,plain,
    ! [X0] :
      ( ~ product(X0,e_1,e_1)
      | ~ product(e_1,e_1,X0)
      | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f48,f31]) ).

fof(f78,plain,
    ( ~ product(e_1,e_2,e_1)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f40,f26]) ).

fof(f79,plain,
    ( $false
    | ~ spl0_2
    | ~ spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f78,f48]) ).

fof(f80,plain,
    ( ~ spl0_2
    | ~ spl0_0 ),
    inference(contradiction_clause,[status(thm)],[f79]) ).

fof(f83,plain,
    ( ~ product(e_1,e_1,e_1)
    | ~ spl0_4 ),
    inference(resolution,[status(thm)],[f56,f26]) ).

fof(f84,plain,
    ( $false
    | ~ spl0_6
    | ~ spl0_4 ),
    inference(forward_subsumption_resolution,[status(thm)],[f83,f64]) ).

fof(f85,plain,
    ( ~ spl0_6
    | ~ spl0_4 ),
    inference(contradiction_clause,[status(thm)],[f84]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( ~ product(X0,e_1,X1)
      | ~ product(e_2,e_2,X1)
      | ~ product(e_1,e_1,X0)
      | ~ spl0_3 ),
    inference(resolution,[status(thm)],[f51,f29]) ).

fof(f88,plain,
    ( ~ product(e_1,e_1,e_2)
    | ~ spl0_3 ),
    inference(resolution,[status(thm)],[f51,f27]) ).

fof(f92,plain,
    ( ~ product(e_1,e_2,e_2)
    | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f43,f26]) ).

fof(f93,plain,
    ( $false
    | ~ spl0_3
    | ~ spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f92,f51]) ).

fof(f94,plain,
    ( ~ spl0_3
    | ~ spl0_1 ),
    inference(contradiction_clause,[status(thm)],[f93]) ).

fof(f100,plain,
    ( ~ product(e_2,e_1,e_2)
    | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f43,f27]) ).

fof(f102,plain,
    ( ~ product(e_2,e_1,e_1)
    | ~ spl0_7
    | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f67,f71]) ).

fof(f106,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f59,f100]) ).

fof(f107,plain,
    ( ~ spl0_1
    | ~ spl0_5 ),
    inference(contradiction_clause,[status(thm)],[f106]) ).

fof(f112,plain,
    ( $false
    | ~ spl0_7
    | ~ spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f88,f67]) ).

fof(f113,plain,
    ( ~ spl0_7
    | ~ spl0_3 ),
    inference(contradiction_clause,[status(thm)],[f112]) ).

fof(f131,plain,
    ( $false
    | ~ spl0_4
    | ~ spl0_7
    | ~ spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f102,f56]) ).

fof(f132,plain,
    ( ~ spl0_4
    | ~ spl0_7
    | ~ spl0_2 ),
    inference(contradiction_clause,[status(thm)],[f131]) ).

fof(f136,plain,
    ! [X0] :
      ( ~ product(X0,e_1,e_1)
      | ~ product(e_1,e_1,X0)
      | ~ spl0_0
      | ~ spl0_3 ),
    inference(resolution,[status(thm)],[f40,f86]) ).

fof(f141,plain,
    ( ~ product(e_1,e_1,e_1)
    | ~ spl0_6
    | ~ spl0_0
    | ~ spl0_3 ),
    inference(resolution,[status(thm)],[f64,f136]) ).

fof(f142,plain,
    ( ~ spl0_6
    | ~ spl0_0
    | ~ spl0_3 ),
    inference(split_clause,[status(thm)],[f141,f63,f39,f50]) ).

fof(f147,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f46,f54,f62,f70,f80,f85,f94,f107,f113,f132,f142]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : GRP131-1.002 : TPTP v8.1.2. Released v1.2.0.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35  % Computer : n027.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Tue Apr 30 00:59:17 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  % Drodi V3.6.0
% 0.13/0.36  % Refutation found
% 0.13/0.36  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.36  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.37  % Elapsed time: 0.021744 seconds
% 0.21/0.37  % CPU time: 0.069423 seconds
% 0.21/0.37  % Total memory used: 2.794 MB
% 0.21/0.37  % Net memory used: 2.732 MB
%------------------------------------------------------------------------------