TSTP Solution File: GRP123-7.003 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GRP123-7.003 : TPTP v8.1.2. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n021.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 20:19:18 EDT 2024

% Result   : Unsatisfiable 0.13s 0.37s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   95 (  28 unt;   0 def)
%            Number of atoms       :  198 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  201 (  98   ~;  94   |;   0   &)
%                                         (   9 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   14 (  13 usr;  10 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   81 (  81   !;   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(f12,axiom,
    ~ equalish(e_2,e_1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f13,axiom,
    ~ equalish(e_2,e_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f14,axiom,
    ~ equalish(e_3,e_1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ~ equalish(e_3,e_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f16,axiom,
    ! [X,Y] :
      ( ~ group_element(X)
      | ~ group_element(Y)
      | product1(X,Y,e_1)
      | product1(X,Y,e_2)
      | product1(X,Y,e_3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f17,axiom,
    ! [X,Y,W,Z] :
      ( ~ product1(X,Y,W)
      | ~ product1(X,Y,Z)
      | equalish(W,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f18,axiom,
    ! [X,W,Y,Z] :
      ( ~ product1(X,W,Y)
      | ~ product1(X,Z,Y)
      | equalish(W,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f19,axiom,
    ! [W,Y,X,Z] :
      ( ~ product1(W,Y,X)
      | ~ product1(Z,Y,X)
      | equalish(W,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f20,axiom,
    ! [X] : product1(X,X,X),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f22,axiom,
    ! [X,Y,W,Z] :
      ( ~ product2(X,Y,W)
      | ~ product2(X,Y,Z)
      | equalish(W,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f26,negated_conjecture,
    ! [X,Y,Z1,Z2] :
      ( ~ product1(X,Y,Z1)
      | ~ product1(Z1,Y,Z2)
      | product2(Z2,X,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f34,plain,
    group_element(e_1),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f35,plain,
    group_element(e_2),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f36,plain,
    group_element(e_3),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f37,plain,
    ~ equalish(e_1,e_2),
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f38,plain,
    ~ equalish(e_1,e_3),
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f39,plain,
    ~ equalish(e_2,e_1),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f40,plain,
    ~ equalish(e_2,e_3),
    inference(cnf_transformation,[status(esa)],[f13]) ).

fof(f41,plain,
    ~ equalish(e_3,e_1),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f42,plain,
    ~ equalish(e_3,e_2),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( ~ group_element(X0)
      | ~ group_element(X1)
      | product1(X0,X1,e_1)
      | product1(X0,X1,e_2)
      | product1(X0,X1,e_3) ),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f44,plain,
    ! [W,Z] :
      ( ! [X,Y] :
          ( ~ product1(X,Y,W)
          | ~ product1(X,Y,Z) )
      | equalish(W,Z) ),
    inference(miniscoping,[status(esa)],[f17]) ).

fof(f45,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product1(X0,X1,X2)
      | ~ product1(X0,X1,X3)
      | equalish(X2,X3) ),
    inference(cnf_transformation,[status(esa)],[f44]) ).

fof(f46,plain,
    ! [W,Z] :
      ( ! [X,Y] :
          ( ~ product1(X,W,Y)
          | ~ product1(X,Z,Y) )
      | equalish(W,Z) ),
    inference(miniscoping,[status(esa)],[f18]) ).

fof(f47,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product1(X0,X1,X2)
      | ~ product1(X0,X3,X2)
      | equalish(X1,X3) ),
    inference(cnf_transformation,[status(esa)],[f46]) ).

fof(f48,plain,
    ! [W,Z] :
      ( ! [Y,X] :
          ( ~ product1(W,Y,X)
          | ~ product1(Z,Y,X) )
      | equalish(W,Z) ),
    inference(miniscoping,[status(esa)],[f19]) ).

fof(f49,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product1(X0,X1,X2)
      | ~ product1(X3,X1,X2)
      | equalish(X0,X3) ),
    inference(cnf_transformation,[status(esa)],[f48]) ).

fof(f50,plain,
    ! [X0] : product1(X0,X0,X0),
    inference(cnf_transformation,[status(esa)],[f20]) ).

fof(f52,plain,
    ! [W,Z] :
      ( ! [X,Y] :
          ( ~ product2(X,Y,W)
          | ~ product2(X,Y,Z) )
      | equalish(W,Z) ),
    inference(miniscoping,[status(esa)],[f22]) ).

fof(f53,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product2(X0,X1,X2)
      | ~ product2(X0,X1,X3)
      | equalish(X2,X3) ),
    inference(cnf_transformation,[status(esa)],[f52]) ).

fof(f59,plain,
    ! [X,Y,Z2] :
      ( ! [Z1] :
          ( ~ product1(X,Y,Z1)
          | ~ product1(Z1,Y,Z2) )
      | product2(Z2,X,Y) ),
    inference(miniscoping,[status(esa)],[f26]) ).

fof(f60,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product1(X0,X1,X2)
      | ~ product1(X2,X1,X3)
      | product2(X3,X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f59]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( ~ product1(X0,X1,X1)
      | product2(X1,X0,X1) ),
    inference(resolution,[status(thm)],[f50,f60]) ).

fof(f62,plain,
    ! [X0] : product2(X0,X0,X0),
    inference(resolution,[status(thm)],[f61,f50]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( ~ product1(X0,X0,X1)
      | equalish(X1,X0) ),
    inference(resolution,[status(thm)],[f45,f50]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( ~ product1(X0,X1,X0)
      | equalish(X1,X0) ),
    inference(resolution,[status(thm)],[f47,f50]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( ~ product1(X0,X1,X1)
      | equalish(X0,X1) ),
    inference(resolution,[status(thm)],[f49,f50]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( ~ product2(X0,X0,X1)
      | equalish(X1,X0) ),
    inference(resolution,[status(thm)],[f53,f62]) ).

fof(f75,plain,
    ! [X0] :
      ( ~ group_element(X0)
      | product1(e_3,X0,e_1)
      | product1(e_3,X0,e_2)
      | product1(e_3,X0,e_3) ),
    inference(resolution,[status(thm)],[f43,f36]) ).

fof(f76,plain,
    ! [X0] :
      ( ~ group_element(X0)
      | product1(e_2,X0,e_1)
      | product1(e_2,X0,e_2)
      | product1(e_2,X0,e_3) ),
    inference(resolution,[status(thm)],[f43,f35]) ).

fof(f103,plain,
    ( spl0_6
  <=> product1(e_3,e_1,e_1) ),
    introduced(split_symbol_definition) ).

fof(f104,plain,
    ( product1(e_3,e_1,e_1)
    | ~ spl0_6 ),
    inference(component_clause,[status(thm)],[f103]) ).

fof(f106,plain,
    ( spl0_7
  <=> product1(e_3,e_1,e_2) ),
    introduced(split_symbol_definition) ).

fof(f107,plain,
    ( product1(e_3,e_1,e_2)
    | ~ spl0_7 ),
    inference(component_clause,[status(thm)],[f106]) ).

fof(f109,plain,
    ( spl0_8
  <=> product1(e_3,e_1,e_3) ),
    introduced(split_symbol_definition) ).

fof(f110,plain,
    ( product1(e_3,e_1,e_3)
    | ~ spl0_8 ),
    inference(component_clause,[status(thm)],[f109]) ).

fof(f112,plain,
    ( product1(e_3,e_1,e_1)
    | product1(e_3,e_1,e_2)
    | product1(e_3,e_1,e_3) ),
    inference(resolution,[status(thm)],[f75,f34]) ).

fof(f113,plain,
    ( spl0_6
    | spl0_7
    | spl0_8 ),
    inference(split_clause,[status(thm)],[f112,f103,f106,f109]) ).

fof(f115,plain,
    ( equalish(e_1,e_3)
    | ~ spl0_8 ),
    inference(resolution,[status(thm)],[f110,f65]) ).

fof(f116,plain,
    ( $false
    | ~ spl0_8 ),
    inference(forward_subsumption_resolution,[status(thm)],[f115,f38]) ).

fof(f117,plain,
    ~ spl0_8,
    inference(contradiction_clause,[status(thm)],[f116]) ).

fof(f118,plain,
    ! [X0] :
      ( ~ product1(X0,e_1,e_2)
      | equalish(X0,e_3)
      | ~ spl0_7 ),
    inference(resolution,[status(thm)],[f107,f49]) ).

fof(f121,plain,
    ! [X0] :
      ( ~ product1(X0,e_1,e_3)
      | product2(e_2,X0,e_1)
      | ~ spl0_7 ),
    inference(resolution,[status(thm)],[f107,f60]) ).

fof(f128,plain,
    ( equalish(e_3,e_1)
    | ~ spl0_6 ),
    inference(resolution,[status(thm)],[f104,f67]) ).

fof(f129,plain,
    ( $false
    | ~ spl0_6 ),
    inference(forward_subsumption_resolution,[status(thm)],[f128,f41]) ).

fof(f130,plain,
    ~ spl0_6,
    inference(contradiction_clause,[status(thm)],[f129]) ).

fof(f155,plain,
    ( spl0_10
  <=> product1(e_2,e_3,e_2) ),
    introduced(split_symbol_definition) ).

fof(f156,plain,
    ( product1(e_2,e_3,e_2)
    | ~ spl0_10 ),
    inference(component_clause,[status(thm)],[f155]) ).

fof(f158,plain,
    ( spl0_11
  <=> product1(e_2,e_3,e_3) ),
    introduced(split_symbol_definition) ).

fof(f159,plain,
    ( product1(e_2,e_3,e_3)
    | ~ spl0_11 ),
    inference(component_clause,[status(thm)],[f158]) ).

fof(f169,plain,
    ( spl0_14
  <=> product1(e_2,e_2,e_3) ),
    introduced(split_symbol_definition) ).

fof(f170,plain,
    ( product1(e_2,e_2,e_3)
    | ~ spl0_14 ),
    inference(component_clause,[status(thm)],[f169]) ).

fof(f174,plain,
    ( spl0_15
  <=> product1(e_2,e_1,e_1) ),
    introduced(split_symbol_definition) ).

fof(f175,plain,
    ( product1(e_2,e_1,e_1)
    | ~ spl0_15 ),
    inference(component_clause,[status(thm)],[f174]) ).

fof(f177,plain,
    ( spl0_16
  <=> product1(e_2,e_1,e_2) ),
    introduced(split_symbol_definition) ).

fof(f178,plain,
    ( product1(e_2,e_1,e_2)
    | ~ spl0_16 ),
    inference(component_clause,[status(thm)],[f177]) ).

fof(f180,plain,
    ( spl0_17
  <=> product1(e_2,e_1,e_3) ),
    introduced(split_symbol_definition) ).

fof(f181,plain,
    ( product1(e_2,e_1,e_3)
    | ~ spl0_17 ),
    inference(component_clause,[status(thm)],[f180]) ).

fof(f183,plain,
    ( product1(e_2,e_1,e_1)
    | product1(e_2,e_1,e_2)
    | product1(e_2,e_1,e_3) ),
    inference(resolution,[status(thm)],[f76,f34]) ).

fof(f184,plain,
    ( spl0_15
    | spl0_16
    | spl0_17 ),
    inference(split_clause,[status(thm)],[f183,f174,f177,f180]) ).

fof(f185,plain,
    ( product2(e_2,e_2,e_1)
    | ~ spl0_17
    | ~ spl0_7 ),
    inference(resolution,[status(thm)],[f181,f121]) ).

fof(f190,plain,
    ( equalish(e_2,e_3)
    | ~ spl0_16
    | ~ spl0_7 ),
    inference(resolution,[status(thm)],[f178,f118]) ).

fof(f191,plain,
    ( $false
    | ~ spl0_16
    | ~ spl0_7 ),
    inference(forward_subsumption_resolution,[status(thm)],[f190,f40]) ).

fof(f192,plain,
    ( ~ spl0_16
    | ~ spl0_7 ),
    inference(contradiction_clause,[status(thm)],[f191]) ).

fof(f193,plain,
    ( equalish(e_2,e_1)
    | ~ spl0_15 ),
    inference(resolution,[status(thm)],[f175,f67]) ).

fof(f194,plain,
    ( $false
    | ~ spl0_15 ),
    inference(forward_subsumption_resolution,[status(thm)],[f193,f39]) ).

fof(f195,plain,
    ~ spl0_15,
    inference(contradiction_clause,[status(thm)],[f194]) ).

fof(f199,plain,
    ( equalish(e_3,e_2)
    | ~ spl0_14 ),
    inference(resolution,[status(thm)],[f170,f63]) ).

fof(f200,plain,
    ( $false
    | ~ spl0_14 ),
    inference(forward_subsumption_resolution,[status(thm)],[f199,f42]) ).

fof(f201,plain,
    ~ spl0_14,
    inference(contradiction_clause,[status(thm)],[f200]) ).

fof(f205,plain,
    ( equalish(e_2,e_3)
    | ~ spl0_11 ),
    inference(resolution,[status(thm)],[f159,f67]) ).

fof(f206,plain,
    ( $false
    | ~ spl0_11 ),
    inference(forward_subsumption_resolution,[status(thm)],[f205,f40]) ).

fof(f207,plain,
    ~ spl0_11,
    inference(contradiction_clause,[status(thm)],[f206]) ).

fof(f209,plain,
    ( equalish(e_3,e_2)
    | ~ spl0_10 ),
    inference(resolution,[status(thm)],[f156,f65]) ).

fof(f210,plain,
    ( $false
    | ~ spl0_10 ),
    inference(forward_subsumption_resolution,[status(thm)],[f209,f42]) ).

fof(f211,plain,
    ~ spl0_10,
    inference(contradiction_clause,[status(thm)],[f210]) ).

fof(f218,plain,
    ( equalish(e_1,e_2)
    | ~ spl0_17
    | ~ spl0_7 ),
    inference(resolution,[status(thm)],[f185,f69]) ).

fof(f219,plain,
    ( $false
    | ~ spl0_17
    | ~ spl0_7 ),
    inference(forward_subsumption_resolution,[status(thm)],[f218,f37]) ).

fof(f220,plain,
    ( ~ spl0_17
    | ~ spl0_7 ),
    inference(contradiction_clause,[status(thm)],[f219]) ).

fof(f221,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f113,f117,f130,f184,f192,f195,f201,f207,f211,f220]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : GRP123-7.003 : TPTP v8.1.2. Released v1.2.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n021.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Tue Apr 30 00:23:55 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  % Drodi V3.6.0
% 0.13/0.37  % Refutation found
% 0.13/0.37  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.37  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.38  % Elapsed time: 0.023372 seconds
% 0.13/0.38  % CPU time: 0.085938 seconds
% 0.13/0.38  % Total memory used: 3.332 MB
% 0.13/0.38  % Net memory used: 3.175 MB
%------------------------------------------------------------------------------