TSTP Solution File: GRP123-9.003 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : GRP123-9.003 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n013.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 12:10:29 EDT 2023

% Result   : Unsatisfiable 0.12s 0.35s
% Output   : CNFRefutation 0.19s
% 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(f3,axiom,
    group_element(e_1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

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

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

fof(f7,axiom,
    ~ equalish(e_1,e_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ~ equalish(e_2,e_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,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(f14,axiom,
    ! [X,W,Y,Z] :
      ( ~ product1(X,W,Y)
      | ~ product1(X,Z,Y)
      | equalish(W,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ! [W,Y,X,Z] :
      ( ~ product1(W,Y,X)
      | ~ product1(Z,Y,X)
      | equalish(W,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f16,axiom,
    ! [X] : product1(X,X,X),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f18,axiom,
    ! [X,Y,W,Z] :
      ( ~ product2(X,Y,W)
      | ~ product2(X,Y,Z)
      | equalish(W,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f19,axiom,
    ! [X,W,Y,Z] :
      ( ~ product2(X,W,Y)
      | ~ product2(X,Z,Y)
      | equalish(W,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f21,axiom,
    ! [X] : product2(X,X,X),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f22,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(f25,plain,
    group_element(e_1),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f26,plain,
    group_element(e_2),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f27,plain,
    group_element(e_3),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f28,plain,
    ~ equalish(e_1,e_2),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f29,plain,
    ~ equalish(e_1,e_3),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f31,plain,
    ~ equalish(e_2,e_3),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f34,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)],[f12]) ).

fof(f37,plain,
    ! [W,Z] :
      ( ! [X,Y] :
          ( ~ product1(X,W,Y)
          | ~ product1(X,Z,Y) )
      | equalish(W,Z) ),
    inference(miniscoping,[status(esa)],[f14]) ).

fof(f38,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product1(X0,X1,X2)
      | ~ product1(X0,X3,X2)
      | equalish(X1,X3) ),
    inference(cnf_transformation,[status(esa)],[f37]) ).

fof(f39,plain,
    ! [W,Z] :
      ( ! [Y,X] :
          ( ~ product1(W,Y,X)
          | ~ product1(Z,Y,X) )
      | equalish(W,Z) ),
    inference(miniscoping,[status(esa)],[f15]) ).

fof(f40,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product1(X0,X1,X2)
      | ~ product1(X3,X1,X2)
      | equalish(X0,X3) ),
    inference(cnf_transformation,[status(esa)],[f39]) ).

fof(f41,plain,
    ! [X0] : product1(X0,X0,X0),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f43,plain,
    ! [W,Z] :
      ( ! [X,Y] :
          ( ~ product2(X,Y,W)
          | ~ product2(X,Y,Z) )
      | equalish(W,Z) ),
    inference(miniscoping,[status(esa)],[f18]) ).

fof(f44,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product2(X0,X1,X2)
      | ~ product2(X0,X1,X3)
      | equalish(X2,X3) ),
    inference(cnf_transformation,[status(esa)],[f43]) ).

fof(f45,plain,
    ! [W,Z] :
      ( ! [X,Y] :
          ( ~ product2(X,W,Y)
          | ~ product2(X,Z,Y) )
      | equalish(W,Z) ),
    inference(miniscoping,[status(esa)],[f19]) ).

fof(f46,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product2(X0,X1,X2)
      | ~ product2(X0,X3,X2)
      | equalish(X1,X3) ),
    inference(cnf_transformation,[status(esa)],[f45]) ).

fof(f49,plain,
    ! [X0] : product2(X0,X0,X0),
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f50,plain,
    ! [X,Y,Z2] :
      ( ! [Z1] :
          ( ~ product1(X,Y,Z1)
          | ~ product1(Z1,Y,Z2) )
      | product2(Z2,X,Y) ),
    inference(miniscoping,[status(esa)],[f22]) ).

fof(f51,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product1(X0,X1,X2)
      | ~ product1(X2,X1,X3)
      | product2(X3,X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f50]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( ~ product1(X0,X1,X1)
      | product2(X1,X0,X1) ),
    inference(resolution,[status(thm)],[f41,f51]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( ~ product1(e_1,X0,X1)
      | ~ product1(e_2,X0,X1) ),
    inference(resolution,[status(thm)],[f28,f40]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( ~ product2(X0,e_1,X1)
      | ~ product2(X0,e_3,X1) ),
    inference(resolution,[status(thm)],[f29,f46]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( ~ product1(X0,e_1,X1)
      | ~ product1(X0,e_3,X1) ),
    inference(resolution,[status(thm)],[f29,f38]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( ~ product2(X0,e_2,X1)
      | ~ product2(X0,e_3,X1) ),
    inference(resolution,[status(thm)],[f31,f46]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( ~ product2(X0,X1,e_2)
      | ~ product2(X0,X1,e_3) ),
    inference(resolution,[status(thm)],[f31,f44]) ).

fof(f109,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)],[f34,f27]) ).

fof(f121,plain,
    ~ product2(e_3,e_1,e_3),
    inference(resolution,[status(thm)],[f70,f49]) ).

fof(f127,plain,
    ~ product1(e_1,e_3,e_3),
    inference(resolution,[status(thm)],[f121,f52]) ).

fof(f144,plain,
    ~ product2(e_3,e_2,e_3),
    inference(resolution,[status(thm)],[f82,f49]) ).

fof(f148,plain,
    ~ product1(e_2,e_3,e_3),
    inference(resolution,[status(thm)],[f144,f52]) ).

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)],[f83,f51]) ).

fof(f175,plain,
    ( spl0_3
  <=> product1(e_2,e_3,e_1) ),
    introduced(split_symbol_definition) ).

fof(f176,plain,
    ( product1(e_2,e_3,e_1)
    | ~ spl0_3 ),
    inference(component_clause,[status(thm)],[f175]) ).

fof(f178,plain,
    ( spl0_4
  <=> product1(e_2,e_3,e_2) ),
    introduced(split_symbol_definition) ).

fof(f179,plain,
    ( product1(e_2,e_3,e_2)
    | ~ spl0_4 ),
    inference(component_clause,[status(thm)],[f178]) ).

fof(f181,plain,
    ( spl0_5
  <=> product1(e_2,e_3,e_3) ),
    introduced(split_symbol_definition) ).

fof(f182,plain,
    ( product1(e_2,e_3,e_3)
    | ~ spl0_5 ),
    inference(component_clause,[status(thm)],[f181]) ).

fof(f184,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)],[f109,f26]) ).

fof(f185,plain,
    ( spl0_3
    | spl0_4
    | spl0_5 ),
    inference(split_clause,[status(thm)],[f184,f175,f178,f181]) ).

fof(f186,plain,
    ( spl0_6
  <=> product1(e_1,e_3,e_1) ),
    introduced(split_symbol_definition) ).

fof(f187,plain,
    ( product1(e_1,e_3,e_1)
    | ~ spl0_6 ),
    inference(component_clause,[status(thm)],[f186]) ).

fof(f189,plain,
    ( spl0_7
  <=> product1(e_1,e_3,e_2) ),
    introduced(split_symbol_definition) ).

fof(f190,plain,
    ( product1(e_1,e_3,e_2)
    | ~ spl0_7 ),
    inference(component_clause,[status(thm)],[f189]) ).

fof(f192,plain,
    ( spl0_8
  <=> product1(e_1,e_3,e_3) ),
    introduced(split_symbol_definition) ).

fof(f193,plain,
    ( product1(e_1,e_3,e_3)
    | ~ spl0_8 ),
    inference(component_clause,[status(thm)],[f192]) ).

fof(f195,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)],[f109,f25]) ).

fof(f196,plain,
    ( spl0_6
    | spl0_7
    | spl0_8 ),
    inference(split_clause,[status(thm)],[f195,f186,f189,f192]) ).

fof(f197,plain,
    ( $false
    | ~ spl0_8 ),
    inference(forward_subsumption_resolution,[status(thm)],[f193,f127]) ).

fof(f198,plain,
    ~ spl0_8,
    inference(contradiction_clause,[status(thm)],[f197]) ).

fof(f199,plain,
    ( $false
    | ~ spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f182,f148]) ).

fof(f200,plain,
    ~ spl0_5,
    inference(contradiction_clause,[status(thm)],[f199]) ).

fof(f397,plain,
    ! [X0] :
      ( ~ product2(e_2,X0,e_2)
      | ~ product1(X0,e_3,e_1)
      | ~ spl0_7 ),
    inference(resolution,[status(thm)],[f190,f152]) ).

fof(f409,plain,
    ( ~ product1(e_1,e_1,e_1)
    | ~ spl0_6 ),
    inference(resolution,[status(thm)],[f187,f73]) ).

fof(f410,plain,
    ( $false
    | ~ spl0_6 ),
    inference(forward_subsumption_resolution,[status(thm)],[f409,f41]) ).

fof(f411,plain,
    ~ spl0_6,
    inference(contradiction_clause,[status(thm)],[f410]) ).

fof(f417,plain,
    ( ~ product1(e_1,e_3,e_2)
    | ~ spl0_4 ),
    inference(resolution,[status(thm)],[f179,f56]) ).

fof(f418,plain,
    ( $false
    | ~ spl0_7
    | ~ spl0_4 ),
    inference(forward_subsumption_resolution,[status(thm)],[f417,f190]) ).

fof(f419,plain,
    ( ~ spl0_7
    | ~ spl0_4 ),
    inference(contradiction_clause,[status(thm)],[f418]) ).

fof(f422,plain,
    ( ~ product2(e_2,e_2,e_2)
    | ~ spl0_3
    | ~ spl0_7 ),
    inference(resolution,[status(thm)],[f176,f397]) ).

fof(f423,plain,
    ( $false
    | ~ spl0_3
    | ~ spl0_7 ),
    inference(forward_subsumption_resolution,[status(thm)],[f422,f49]) ).

fof(f424,plain,
    ( ~ spl0_3
    | ~ spl0_7 ),
    inference(contradiction_clause,[status(thm)],[f423]) ).

fof(f425,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f185,f196,f198,f200,f411,f419,f424]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP123-9.003 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34  % Computer : n013.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 11:22:35 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  % Drodi V3.5.1
% 0.12/0.35  % Refutation found
% 0.12/0.35  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.35  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.37  % Elapsed time: 0.021452 seconds
% 0.19/0.37  % CPU time: 0.057824 seconds
% 0.19/0.37  % Memory used: 2.289 MB
%------------------------------------------------------------------------------