TSTP Solution File: GRP123-6.003 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : GRP123-6.003 : TPTP v8.1.2. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n028.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 12:10:28 EDT 2023

% Result   : Unsatisfiable 0.10s 0.33s
% Output   : CNFRefutation 0.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   76 (  24 unt;   0 def)
%            Number of atoms       :  160 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  173 (  89   ~;  78   |;   0   &)
%                                         (   6 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   11 (  10 usr;   7 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   85 (;  85   !;   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,
    group_element(e_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ~ equalish(e_1,e_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ~ equalish(e_1,e_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ~ equalish(e_2,e_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,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(f12,axiom,
    ! [X,W,Y,Z] :
      ( ~ product1(X,W,Y)
      | ~ product1(X,Z,Y)
      | equalish(W,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f13,axiom,
    ! [W,Y,X,Z] :
      ( ~ product1(W,Y,X)
      | ~ product1(Z,Y,X)
      | equalish(W,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f14,axiom,
    ! [X] : product1(X,X,X),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f16,axiom,
    ! [X,Y,W,Z] :
      ( ~ product2(X,Y,W)
      | ~ product2(X,Y,Z)
      | equalish(W,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f17,axiom,
    ! [X,W,Y,Z] :
      ( ~ product2(X,W,Y)
      | ~ product2(X,Z,Y)
      | equalish(W,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f19,axiom,
    ! [X] : product2(X,X,X),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f20,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(f21,plain,
    group_element(e_1),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f22,plain,
    group_element(e_2),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f23,plain,
    group_element(e_3),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f24,plain,
    ~ equalish(e_1,e_2),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f25,plain,
    ~ equalish(e_1,e_3),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f27,plain,
    ~ equalish(e_2,e_3),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f30,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)],[f10]) ).

fof(f33,plain,
    ! [W,Z] :
      ( ! [X,Y] :
          ( ~ product1(X,W,Y)
          | ~ product1(X,Z,Y) )
      | equalish(W,Z) ),
    inference(miniscoping,[status(esa)],[f12]) ).

fof(f34,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product1(X0,X1,X2)
      | ~ product1(X0,X3,X2)
      | equalish(X1,X3) ),
    inference(cnf_transformation,[status(esa)],[f33]) ).

fof(f35,plain,
    ! [W,Z] :
      ( ! [Y,X] :
          ( ~ product1(W,Y,X)
          | ~ product1(Z,Y,X) )
      | equalish(W,Z) ),
    inference(miniscoping,[status(esa)],[f13]) ).

fof(f36,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product1(X0,X1,X2)
      | ~ product1(X3,X1,X2)
      | equalish(X0,X3) ),
    inference(cnf_transformation,[status(esa)],[f35]) ).

fof(f37,plain,
    ! [X0] : product1(X0,X0,X0),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f39,plain,
    ! [W,Z] :
      ( ! [X,Y] :
          ( ~ product2(X,Y,W)
          | ~ product2(X,Y,Z) )
      | equalish(W,Z) ),
    inference(miniscoping,[status(esa)],[f16]) ).

fof(f40,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product2(X0,X1,X2)
      | ~ product2(X0,X1,X3)
      | equalish(X2,X3) ),
    inference(cnf_transformation,[status(esa)],[f39]) ).

fof(f41,plain,
    ! [W,Z] :
      ( ! [X,Y] :
          ( ~ product2(X,W,Y)
          | ~ product2(X,Z,Y) )
      | equalish(W,Z) ),
    inference(miniscoping,[status(esa)],[f17]) ).

fof(f42,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product2(X0,X1,X2)
      | ~ product2(X0,X3,X2)
      | equalish(X1,X3) ),
    inference(cnf_transformation,[status(esa)],[f41]) ).

fof(f45,plain,
    ! [X0] : product2(X0,X0,X0),
    inference(cnf_transformation,[status(esa)],[f19]) ).

fof(f46,plain,
    ! [X,Y,Z2] :
      ( ! [Z1] :
          ( ~ product1(X,Y,Z1)
          | ~ product1(Z1,Y,Z2) )
      | product2(Z2,X,Y) ),
    inference(miniscoping,[status(esa)],[f20]) ).

fof(f47,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product1(X0,X1,X2)
      | ~ product1(X2,X1,X3)
      | product2(X3,X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f46]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( ~ product1(X0,X1,X1)
      | product2(X1,X0,X1) ),
    inference(resolution,[status(thm)],[f37,f47]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( ~ product1(e_1,X0,X1)
      | ~ product1(e_2,X0,X1) ),
    inference(resolution,[status(thm)],[f24,f36]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( ~ product2(X0,e_1,X1)
      | ~ product2(X0,e_3,X1) ),
    inference(resolution,[status(thm)],[f25,f42]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( ~ product1(X0,e_1,X1)
      | ~ product1(X0,e_3,X1) ),
    inference(resolution,[status(thm)],[f25,f34]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( ~ product2(X0,e_2,X1)
      | ~ product2(X0,e_3,X1) ),
    inference(resolution,[status(thm)],[f27,f42]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( ~ product2(X0,X1,e_2)
      | ~ product2(X0,X1,e_3) ),
    inference(resolution,[status(thm)],[f27,f40]) ).

fof(f105,plain,
    ! [X0] :
      ( ~ group_element(X0)
      | product1(X0,e_3,e_1)
      | product1(X0,e_3,e_2)
      | product1(X0,e_3,e_3) ),
    inference(resolution,[status(thm)],[f30,f23]) ).

fof(f111,plain,
    ~ product2(e_3,e_1,e_3),
    inference(resolution,[status(thm)],[f66,f45]) ).

fof(f131,plain,
    ~ product1(e_1,e_3,e_3),
    inference(resolution,[status(thm)],[f111,f48]) ).

fof(f143,plain,
    ~ product2(e_3,e_2,e_3),
    inference(resolution,[status(thm)],[f78,f45]) ).

fof(f148,plain,
    ~ product1(e_2,e_3,e_3),
    inference(resolution,[status(thm)],[f143,f48]) ).

fof(f152,plain,
    ! [X0,X1,X2] :
      ( ~ product2(X0,X1,e_2)
      | ~ product1(X1,e_3,X2)
      | ~ product1(X2,e_3,X0) ),
    inference(resolution,[status(thm)],[f79,f47]) ).

fof(f171,plain,
    ( spl0_3
  <=> product1(e_2,e_3,e_1) ),
    introduced(split_symbol_definition) ).

fof(f172,plain,
    ( product1(e_2,e_3,e_1)
    | ~ spl0_3 ),
    inference(component_clause,[status(thm)],[f171]) ).

fof(f174,plain,
    ( spl0_4
  <=> product1(e_2,e_3,e_2) ),
    introduced(split_symbol_definition) ).

fof(f175,plain,
    ( product1(e_2,e_3,e_2)
    | ~ spl0_4 ),
    inference(component_clause,[status(thm)],[f174]) ).

fof(f177,plain,
    ( spl0_5
  <=> product1(e_2,e_3,e_3) ),
    introduced(split_symbol_definition) ).

fof(f178,plain,
    ( product1(e_2,e_3,e_3)
    | ~ spl0_5 ),
    inference(component_clause,[status(thm)],[f177]) ).

fof(f180,plain,
    ( product1(e_2,e_3,e_1)
    | product1(e_2,e_3,e_2)
    | product1(e_2,e_3,e_3) ),
    inference(resolution,[status(thm)],[f105,f22]) ).

fof(f181,plain,
    ( spl0_3
    | spl0_4
    | spl0_5 ),
    inference(split_clause,[status(thm)],[f180,f171,f174,f177]) ).

fof(f182,plain,
    ( spl0_6
  <=> product1(e_1,e_3,e_1) ),
    introduced(split_symbol_definition) ).

fof(f183,plain,
    ( product1(e_1,e_3,e_1)
    | ~ spl0_6 ),
    inference(component_clause,[status(thm)],[f182]) ).

fof(f185,plain,
    ( spl0_7
  <=> product1(e_1,e_3,e_2) ),
    introduced(split_symbol_definition) ).

fof(f186,plain,
    ( product1(e_1,e_3,e_2)
    | ~ spl0_7 ),
    inference(component_clause,[status(thm)],[f185]) ).

fof(f188,plain,
    ( spl0_8
  <=> product1(e_1,e_3,e_3) ),
    introduced(split_symbol_definition) ).

fof(f189,plain,
    ( product1(e_1,e_3,e_3)
    | ~ spl0_8 ),
    inference(component_clause,[status(thm)],[f188]) ).

fof(f191,plain,
    ( product1(e_1,e_3,e_1)
    | product1(e_1,e_3,e_2)
    | product1(e_1,e_3,e_3) ),
    inference(resolution,[status(thm)],[f105,f21]) ).

fof(f192,plain,
    ( spl0_6
    | spl0_7
    | spl0_8 ),
    inference(split_clause,[status(thm)],[f191,f182,f185,f188]) ).

fof(f193,plain,
    ( $false
    | ~ spl0_8 ),
    inference(forward_subsumption_resolution,[status(thm)],[f189,f131]) ).

fof(f194,plain,
    ~ spl0_8,
    inference(contradiction_clause,[status(thm)],[f193]) ).

fof(f195,plain,
    ( $false
    | ~ spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f178,f148]) ).

fof(f196,plain,
    ~ spl0_5,
    inference(contradiction_clause,[status(thm)],[f195]) ).

fof(f393,plain,
    ! [X0] :
      ( ~ product2(e_2,X0,e_2)
      | ~ product1(X0,e_3,e_1)
      | ~ spl0_7 ),
    inference(resolution,[status(thm)],[f186,f152]) ).

fof(f405,plain,
    ( ~ product1(e_1,e_1,e_1)
    | ~ spl0_6 ),
    inference(resolution,[status(thm)],[f183,f69]) ).

fof(f406,plain,
    ( $false
    | ~ spl0_6 ),
    inference(forward_subsumption_resolution,[status(thm)],[f405,f37]) ).

fof(f407,plain,
    ~ spl0_6,
    inference(contradiction_clause,[status(thm)],[f406]) ).

fof(f413,plain,
    ( ~ product1(e_1,e_3,e_2)
    | ~ spl0_4 ),
    inference(resolution,[status(thm)],[f175,f52]) ).

fof(f414,plain,
    ( $false
    | ~ spl0_7
    | ~ spl0_4 ),
    inference(forward_subsumption_resolution,[status(thm)],[f413,f186]) ).

fof(f415,plain,
    ( ~ spl0_7
    | ~ spl0_4 ),
    inference(contradiction_clause,[status(thm)],[f414]) ).

fof(f418,plain,
    ( ~ product2(e_2,e_2,e_2)
    | ~ spl0_3
    | ~ spl0_7 ),
    inference(resolution,[status(thm)],[f172,f393]) ).

fof(f419,plain,
    ( $false
    | ~ spl0_3
    | ~ spl0_7 ),
    inference(forward_subsumption_resolution,[status(thm)],[f418,f45]) ).

fof(f420,plain,
    ( ~ spl0_3
    | ~ spl0_7 ),
    inference(contradiction_clause,[status(thm)],[f419]) ).

fof(f421,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f181,f192,f194,f196,f407,f415,f420]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11  % Problem  : GRP123-6.003 : TPTP v8.1.2. Released v1.2.0.
% 0.05/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31  % Computer : n028.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit : 300
% 0.10/0.32  % WCLimit  : 300
% 0.10/0.32  % DateTime : Tue May 30 11:42:02 EDT 2023
% 0.10/0.32  % CPUTime  : 
% 0.10/0.32  % Drodi V3.5.1
% 0.10/0.33  % Refutation found
% 0.10/0.33  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.33  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.56  % Elapsed time: 0.023114 seconds
% 0.16/0.56  % CPU time: 0.017697 seconds
% 0.16/0.56  % Memory used: 676.378 KB
%------------------------------------------------------------------------------