TSTP Solution File: GRP129-1.003 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GRP129-1.003 : TPTP v8.1.2. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n007.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 20:19:26 EDT 2024

% Result   : Unsatisfiable 0.19s 0.47s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   41
% Syntax   : Number of formulae    :  243 (  19 unt;   0 def)
%            Number of atoms       :  656 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  774 ( 361   ~; 386   |;   0   &)
%                                         (  27 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   31 (  30 usr;  28 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   87 (  87   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    group_element(e_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    group_element(e_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    group_element(e_3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ~ equalish(e_1,e_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ~ equalish(e_1,e_3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ~ equalish(e_2,e_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ~ equalish(e_2,e_3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ~ equalish(e_3,e_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ~ equalish(e_3,e_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [X,Y] :
      ( ~ group_element(X)
      | ~ group_element(Y)
      | product(X,Y,e_1)
      | product(X,Y,e_2)
      | product(X,Y,e_3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [X,Y,W,Z] :
      ( ~ product(X,Y,W)
      | ~ product(X,Y,Z)
      | equalish(W,Z) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [X,W,Y,Z] :
      ( ~ product(X,W,Y)
      | ~ product(X,Z,Y)
      | equalish(W,Z) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f13,axiom,
    ! [W,Y,X,Z] :
      ( ~ product(W,Y,X)
      | ~ product(Z,Y,X)
      | equalish(W,Z) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f14,negated_conjecture,
    ! [Y,X,Z1,Z2] :
      ( ~ product(Y,X,Z1)
      | ~ product(X,Z1,Z2)
      | product(Z1,Y,Z2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f15,plain,
    group_element(e_1),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f16,plain,
    group_element(e_2),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f17,plain,
    group_element(e_3),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f18,plain,
    ~ equalish(e_1,e_2),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f19,plain,
    ~ equalish(e_1,e_3),
    inference(cnf_transformation,[status(esa)],[f5]) ).

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

fof(f21,plain,
    ~ equalish(e_2,e_3),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f22,plain,
    ~ equalish(e_3,e_1),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f23,plain,
    ~ equalish(e_3,e_2),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ~ group_element(X0)
      | ~ group_element(X1)
      | product(X0,X1,e_1)
      | product(X0,X1,e_2)
      | product(X0,X1,e_3) ),
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f25,plain,
    ! [W,Z] :
      ( ! [X,Y] :
          ( ~ product(X,Y,W)
          | ~ product(X,Y,Z) )
      | equalish(W,Z) ),
    inference(miniscoping,[status(esa)],[f11]) ).

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

fof(f27,plain,
    ! [W,Z] :
      ( ! [X,Y] :
          ( ~ product(X,W,Y)
          | ~ product(X,Z,Y) )
      | equalish(W,Z) ),
    inference(miniscoping,[status(esa)],[f12]) ).

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

fof(f29,plain,
    ! [W,Z] :
      ( ! [Y,X] :
          ( ~ product(W,Y,X)
          | ~ product(Z,Y,X) )
      | equalish(W,Z) ),
    inference(miniscoping,[status(esa)],[f13]) ).

fof(f30,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product(X0,X1,X2)
      | ~ product(X3,X1,X2)
      | equalish(X0,X3) ),
    inference(cnf_transformation,[status(esa)],[f29]) ).

fof(f31,plain,
    ! [Y,Z1,Z2] :
      ( ! [X] :
          ( ~ product(Y,X,Z1)
          | ~ product(X,Z1,Z2) )
      | product(Z1,Y,Z2) ),
    inference(miniscoping,[status(esa)],[f14]) ).

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

fof(f33,plain,
    ! [X0] :
      ( ~ group_element(X0)
      | product(e_3,X0,e_1)
      | product(e_3,X0,e_2)
      | product(e_3,X0,e_3) ),
    inference(resolution,[status(thm)],[f24,f17]) ).

fof(f34,plain,
    ! [X0] :
      ( ~ group_element(X0)
      | product(e_2,X0,e_1)
      | product(e_2,X0,e_2)
      | product(e_2,X0,e_3) ),
    inference(resolution,[status(thm)],[f24,f16]) ).

fof(f35,plain,
    ! [X0] :
      ( ~ group_element(X0)
      | product(e_1,X0,e_1)
      | product(e_1,X0,e_2)
      | product(e_1,X0,e_3) ),
    inference(resolution,[status(thm)],[f24,f15]) ).

fof(f36,plain,
    ( spl0_0
  <=> product(e_3,e_3,e_1) ),
    introduced(split_symbol_definition) ).

fof(f37,plain,
    ( product(e_3,e_3,e_1)
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f36]) ).

fof(f39,plain,
    ( spl0_1
  <=> product(e_3,e_3,e_2) ),
    introduced(split_symbol_definition) ).

fof(f40,plain,
    ( product(e_3,e_3,e_2)
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f39]) ).

fof(f42,plain,
    ( spl0_2
  <=> product(e_3,e_3,e_3) ),
    introduced(split_symbol_definition) ).

fof(f43,plain,
    ( product(e_3,e_3,e_3)
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f42]) ).

fof(f45,plain,
    ( product(e_3,e_3,e_1)
    | product(e_3,e_3,e_2)
    | product(e_3,e_3,e_3) ),
    inference(resolution,[status(thm)],[f33,f17]) ).

fof(f46,plain,
    ( spl0_0
    | spl0_1
    | spl0_2 ),
    inference(split_clause,[status(thm)],[f45,f36,f39,f42]) ).

fof(f47,plain,
    ( spl0_3
  <=> product(e_3,e_2,e_1) ),
    introduced(split_symbol_definition) ).

fof(f48,plain,
    ( product(e_3,e_2,e_1)
    | ~ spl0_3 ),
    inference(component_clause,[status(thm)],[f47]) ).

fof(f50,plain,
    ( spl0_4
  <=> product(e_3,e_2,e_2) ),
    introduced(split_symbol_definition) ).

fof(f51,plain,
    ( product(e_3,e_2,e_2)
    | ~ spl0_4 ),
    inference(component_clause,[status(thm)],[f50]) ).

fof(f53,plain,
    ( spl0_5
  <=> product(e_3,e_2,e_3) ),
    introduced(split_symbol_definition) ).

fof(f54,plain,
    ( product(e_3,e_2,e_3)
    | ~ spl0_5 ),
    inference(component_clause,[status(thm)],[f53]) ).

fof(f56,plain,
    ( product(e_3,e_2,e_1)
    | product(e_3,e_2,e_2)
    | product(e_3,e_2,e_3) ),
    inference(resolution,[status(thm)],[f33,f16]) ).

fof(f57,plain,
    ( spl0_3
    | spl0_4
    | spl0_5 ),
    inference(split_clause,[status(thm)],[f56,f47,f50,f53]) ).

fof(f58,plain,
    ( spl0_6
  <=> product(e_3,e_1,e_1) ),
    introduced(split_symbol_definition) ).

fof(f59,plain,
    ( product(e_3,e_1,e_1)
    | ~ spl0_6 ),
    inference(component_clause,[status(thm)],[f58]) ).

fof(f61,plain,
    ( spl0_7
  <=> product(e_3,e_1,e_2) ),
    introduced(split_symbol_definition) ).

fof(f62,plain,
    ( product(e_3,e_1,e_2)
    | ~ spl0_7 ),
    inference(component_clause,[status(thm)],[f61]) ).

fof(f64,plain,
    ( spl0_8
  <=> product(e_3,e_1,e_3) ),
    introduced(split_symbol_definition) ).

fof(f65,plain,
    ( product(e_3,e_1,e_3)
    | ~ spl0_8 ),
    inference(component_clause,[status(thm)],[f64]) ).

fof(f67,plain,
    ( product(e_3,e_1,e_1)
    | product(e_3,e_1,e_2)
    | product(e_3,e_1,e_3) ),
    inference(resolution,[status(thm)],[f33,f15]) ).

fof(f68,plain,
    ( spl0_6
    | spl0_7
    | spl0_8 ),
    inference(split_clause,[status(thm)],[f67,f58,f61,f64]) ).

fof(f69,plain,
    ( spl0_9
  <=> product(e_2,e_3,e_1) ),
    introduced(split_symbol_definition) ).

fof(f70,plain,
    ( product(e_2,e_3,e_1)
    | ~ spl0_9 ),
    inference(component_clause,[status(thm)],[f69]) ).

fof(f72,plain,
    ( spl0_10
  <=> product(e_2,e_3,e_2) ),
    introduced(split_symbol_definition) ).

fof(f73,plain,
    ( product(e_2,e_3,e_2)
    | ~ spl0_10 ),
    inference(component_clause,[status(thm)],[f72]) ).

fof(f75,plain,
    ( spl0_11
  <=> product(e_2,e_3,e_3) ),
    introduced(split_symbol_definition) ).

fof(f76,plain,
    ( product(e_2,e_3,e_3)
    | ~ spl0_11 ),
    inference(component_clause,[status(thm)],[f75]) ).

fof(f78,plain,
    ( product(e_2,e_3,e_1)
    | product(e_2,e_3,e_2)
    | product(e_2,e_3,e_3) ),
    inference(resolution,[status(thm)],[f34,f17]) ).

fof(f79,plain,
    ( spl0_9
    | spl0_10
    | spl0_11 ),
    inference(split_clause,[status(thm)],[f78,f69,f72,f75]) ).

fof(f80,plain,
    ( spl0_12
  <=> product(e_2,e_2,e_1) ),
    introduced(split_symbol_definition) ).

fof(f81,plain,
    ( product(e_2,e_2,e_1)
    | ~ spl0_12 ),
    inference(component_clause,[status(thm)],[f80]) ).

fof(f83,plain,
    ( spl0_13
  <=> product(e_2,e_2,e_2) ),
    introduced(split_symbol_definition) ).

fof(f84,plain,
    ( product(e_2,e_2,e_2)
    | ~ spl0_13 ),
    inference(component_clause,[status(thm)],[f83]) ).

fof(f86,plain,
    ( spl0_14
  <=> product(e_2,e_2,e_3) ),
    introduced(split_symbol_definition) ).

fof(f87,plain,
    ( product(e_2,e_2,e_3)
    | ~ spl0_14 ),
    inference(component_clause,[status(thm)],[f86]) ).

fof(f89,plain,
    ( product(e_2,e_2,e_1)
    | product(e_2,e_2,e_2)
    | product(e_2,e_2,e_3) ),
    inference(resolution,[status(thm)],[f34,f16]) ).

fof(f90,plain,
    ( spl0_12
    | spl0_13
    | spl0_14 ),
    inference(split_clause,[status(thm)],[f89,f80,f83,f86]) ).

fof(f91,plain,
    ( spl0_15
  <=> product(e_2,e_1,e_1) ),
    introduced(split_symbol_definition) ).

fof(f92,plain,
    ( product(e_2,e_1,e_1)
    | ~ spl0_15 ),
    inference(component_clause,[status(thm)],[f91]) ).

fof(f94,plain,
    ( spl0_16
  <=> product(e_2,e_1,e_2) ),
    introduced(split_symbol_definition) ).

fof(f95,plain,
    ( product(e_2,e_1,e_2)
    | ~ spl0_16 ),
    inference(component_clause,[status(thm)],[f94]) ).

fof(f96,plain,
    ( ~ product(e_2,e_1,e_2)
    | spl0_16 ),
    inference(component_clause,[status(thm)],[f94]) ).

fof(f97,plain,
    ( spl0_17
  <=> product(e_2,e_1,e_3) ),
    introduced(split_symbol_definition) ).

fof(f98,plain,
    ( product(e_2,e_1,e_3)
    | ~ spl0_17 ),
    inference(component_clause,[status(thm)],[f97]) ).

fof(f100,plain,
    ( product(e_2,e_1,e_1)
    | product(e_2,e_1,e_2)
    | product(e_2,e_1,e_3) ),
    inference(resolution,[status(thm)],[f34,f15]) ).

fof(f101,plain,
    ( spl0_15
    | spl0_16
    | spl0_17 ),
    inference(split_clause,[status(thm)],[f100,f91,f94,f97]) ).

fof(f102,plain,
    ( spl0_18
  <=> product(e_1,e_3,e_1) ),
    introduced(split_symbol_definition) ).

fof(f103,plain,
    ( product(e_1,e_3,e_1)
    | ~ spl0_18 ),
    inference(component_clause,[status(thm)],[f102]) ).

fof(f105,plain,
    ( spl0_19
  <=> product(e_1,e_3,e_2) ),
    introduced(split_symbol_definition) ).

fof(f106,plain,
    ( product(e_1,e_3,e_2)
    | ~ spl0_19 ),
    inference(component_clause,[status(thm)],[f105]) ).

fof(f108,plain,
    ( spl0_20
  <=> product(e_1,e_3,e_3) ),
    introduced(split_symbol_definition) ).

fof(f109,plain,
    ( product(e_1,e_3,e_3)
    | ~ spl0_20 ),
    inference(component_clause,[status(thm)],[f108]) ).

fof(f111,plain,
    ( product(e_1,e_3,e_1)
    | product(e_1,e_3,e_2)
    | product(e_1,e_3,e_3) ),
    inference(resolution,[status(thm)],[f35,f17]) ).

fof(f112,plain,
    ( spl0_18
    | spl0_19
    | spl0_20 ),
    inference(split_clause,[status(thm)],[f111,f102,f105,f108]) ).

fof(f113,plain,
    ( spl0_21
  <=> product(e_1,e_2,e_1) ),
    introduced(split_symbol_definition) ).

fof(f114,plain,
    ( product(e_1,e_2,e_1)
    | ~ spl0_21 ),
    inference(component_clause,[status(thm)],[f113]) ).

fof(f116,plain,
    ( spl0_22
  <=> product(e_1,e_2,e_2) ),
    introduced(split_symbol_definition) ).

fof(f117,plain,
    ( product(e_1,e_2,e_2)
    | ~ spl0_22 ),
    inference(component_clause,[status(thm)],[f116]) ).

fof(f119,plain,
    ( spl0_23
  <=> product(e_1,e_2,e_3) ),
    introduced(split_symbol_definition) ).

fof(f120,plain,
    ( product(e_1,e_2,e_3)
    | ~ spl0_23 ),
    inference(component_clause,[status(thm)],[f119]) ).

fof(f122,plain,
    ( product(e_1,e_2,e_1)
    | product(e_1,e_2,e_2)
    | product(e_1,e_2,e_3) ),
    inference(resolution,[status(thm)],[f35,f16]) ).

fof(f123,plain,
    ( spl0_21
    | spl0_22
    | spl0_23 ),
    inference(split_clause,[status(thm)],[f122,f113,f116,f119]) ).

fof(f124,plain,
    ( spl0_24
  <=> product(e_1,e_1,e_1) ),
    introduced(split_symbol_definition) ).

fof(f125,plain,
    ( product(e_1,e_1,e_1)
    | ~ spl0_24 ),
    inference(component_clause,[status(thm)],[f124]) ).

fof(f127,plain,
    ( spl0_25
  <=> product(e_1,e_1,e_2) ),
    introduced(split_symbol_definition) ).

fof(f128,plain,
    ( product(e_1,e_1,e_2)
    | ~ spl0_25 ),
    inference(component_clause,[status(thm)],[f127]) ).

fof(f130,plain,
    ( spl0_26
  <=> product(e_1,e_1,e_3) ),
    introduced(split_symbol_definition) ).

fof(f131,plain,
    ( product(e_1,e_1,e_3)
    | ~ spl0_26 ),
    inference(component_clause,[status(thm)],[f130]) ).

fof(f133,plain,
    ( product(e_1,e_1,e_1)
    | product(e_1,e_1,e_2)
    | product(e_1,e_1,e_3) ),
    inference(resolution,[status(thm)],[f35,f15]) ).

fof(f134,plain,
    ( spl0_24
    | spl0_25
    | spl0_26 ),
    inference(split_clause,[status(thm)],[f133,f124,f127,f130]) ).

fof(f138,plain,
    ! [X0] :
      ( ~ product(e_1,e_3,X0)
      | product(e_3,e_3,X0)
      | ~ spl0_8 ),
    inference(resolution,[status(thm)],[f65,f32]) ).

fof(f142,plain,
    ! [X0] :
      ( ~ product(e_1,e_2,X0)
      | product(e_2,e_3,X0)
      | ~ spl0_7 ),
    inference(resolution,[status(thm)],[f62,f32]) ).

fof(f146,plain,
    ! [X0] :
      ( ~ product(e_1,e_1,X0)
      | product(e_1,e_3,X0)
      | ~ spl0_6 ),
    inference(resolution,[status(thm)],[f59,f32]) ).

fof(f150,plain,
    ! [X0] :
      ( ~ product(e_2,e_3,X0)
      | product(e_3,e_3,X0)
      | ~ spl0_5 ),
    inference(resolution,[status(thm)],[f54,f32]) ).

fof(f154,plain,
    ! [X0] :
      ( ~ product(e_2,e_2,X0)
      | product(e_2,e_3,X0)
      | ~ spl0_4 ),
    inference(resolution,[status(thm)],[f51,f32]) ).

fof(f158,plain,
    ! [X0] :
      ( ~ product(e_2,e_1,X0)
      | product(e_1,e_3,X0)
      | ~ spl0_3 ),
    inference(resolution,[status(thm)],[f48,f32]) ).

fof(f165,plain,
    ! [X0] :
      ( ~ product(e_1,e_3,X0)
      | product(e_3,e_2,X0)
      | ~ spl0_17 ),
    inference(resolution,[status(thm)],[f98,f32]) ).

fof(f169,plain,
    ! [X0] :
      ( ~ product(e_1,e_2,X0)
      | product(e_2,e_2,X0)
      | ~ spl0_16 ),
    inference(resolution,[status(thm)],[f95,f32]) ).

fof(f173,plain,
    ! [X0] :
      ( ~ product(e_1,e_1,X0)
      | product(e_1,e_2,X0)
      | ~ spl0_15 ),
    inference(resolution,[status(thm)],[f92,f32]) ).

fof(f177,plain,
    ! [X0] :
      ( ~ product(e_2,e_3,X0)
      | product(e_3,e_2,X0)
      | ~ spl0_14 ),
    inference(resolution,[status(thm)],[f87,f32]) ).

fof(f184,plain,
    ! [X0] :
      ( ~ product(e_2,e_1,X0)
      | product(e_1,e_2,X0)
      | ~ spl0_12 ),
    inference(resolution,[status(thm)],[f81,f32]) ).

fof(f188,plain,
    ! [X0] :
      ( ~ product(e_3,e_3,X0)
      | product(e_3,e_2,X0)
      | ~ spl0_11 ),
    inference(resolution,[status(thm)],[f76,f32]) ).

fof(f189,plain,
    ( product(e_3,e_3,e_2)
    | ~ spl0_10
    | ~ spl0_5 ),
    inference(resolution,[status(thm)],[f73,f150]) ).

fof(f193,plain,
    ! [X0] :
      ( ~ product(e_3,e_2,X0)
      | product(e_2,e_2,X0)
      | ~ spl0_10 ),
    inference(resolution,[status(thm)],[f73,f32]) ).

fof(f194,plain,
    ! [X0] :
      ( ~ product(X0,e_3,e_2)
      | equalish(e_3,X0)
      | ~ spl0_10
      | ~ spl0_5 ),
    inference(resolution,[status(thm)],[f189,f30]) ).

fof(f198,plain,
    ( equalish(e_3,e_2)
    | ~ spl0_5
    | ~ spl0_10 ),
    inference(resolution,[status(thm)],[f194,f73]) ).

fof(f199,plain,
    ( $false
    | ~ spl0_5
    | ~ spl0_10 ),
    inference(forward_subsumption_resolution,[status(thm)],[f198,f23]) ).

fof(f200,plain,
    ( ~ spl0_5
    | ~ spl0_10 ),
    inference(contradiction_clause,[status(thm)],[f199]) ).

fof(f201,plain,
    ( product(e_3,e_2,e_3)
    | ~ spl0_11
    | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f188,f43]) ).

fof(f202,plain,
    ( spl0_5
    | ~ spl0_11
    | ~ spl0_2 ),
    inference(split_clause,[status(thm)],[f201,f53,f75,f42]) ).

fof(f203,plain,
    ( product(e_3,e_2,e_3)
    | ~ spl0_11
    | ~ spl0_14 ),
    inference(resolution,[status(thm)],[f76,f177]) ).

fof(f204,plain,
    ( spl0_5
    | ~ spl0_11
    | ~ spl0_14 ),
    inference(split_clause,[status(thm)],[f203,f53,f75,f86]) ).

fof(f205,plain,
    ( product(e_2,e_3,e_2)
    | ~ spl0_13
    | ~ spl0_4 ),
    inference(resolution,[status(thm)],[f84,f154]) ).

fof(f207,plain,
    ! [X0] :
      ( ~ product(e_2,X0,e_2)
      | equalish(e_3,X0)
      | ~ spl0_13
      | ~ spl0_4 ),
    inference(resolution,[status(thm)],[f205,f28]) ).

fof(f212,plain,
    ( equalish(e_3,e_2)
    | ~ spl0_4
    | ~ spl0_13 ),
    inference(resolution,[status(thm)],[f207,f84]) ).

fof(f213,plain,
    ( $false
    | ~ spl0_4
    | ~ spl0_13 ),
    inference(forward_subsumption_resolution,[status(thm)],[f212,f23]) ).

fof(f214,plain,
    ( ~ spl0_4
    | ~ spl0_13 ),
    inference(contradiction_clause,[status(thm)],[f213]) ).

fof(f215,plain,
    ( product(e_3,e_3,e_3)
    | ~ spl0_11
    | ~ spl0_5 ),
    inference(resolution,[status(thm)],[f76,f150]) ).

fof(f217,plain,
    ! [X0] :
      ( ~ product(e_3,X0,e_3)
      | equalish(e_3,X0)
      | ~ spl0_11
      | ~ spl0_5 ),
    inference(resolution,[status(thm)],[f215,f28]) ).

fof(f221,plain,
    ( product(e_3,e_3,e_1)
    | ~ spl0_9
    | ~ spl0_5 ),
    inference(resolution,[status(thm)],[f70,f150]) ).

fof(f221_001,plain,
    ( product(e_3,e_3,e_1)
    | ~ spl0_9
    | ~ spl0_5 ),
    inference(resolution,[status(thm)],[f70,f150]) ).

fof(f225,plain,
    ! [X0] :
      ( ~ product(e_3,e_1,X0)
      | product(e_1,e_2,X0)
      | ~ spl0_9 ),
    inference(resolution,[status(thm)],[f70,f32]) ).

fof(f229,plain,
    ! [X0] :
      ( ~ product(e_1,e_3,X0)
      | product(e_3,e_1,X0)
      | ~ spl0_26 ),
    inference(resolution,[status(thm)],[f131,f32]) ).

fof(f233,plain,
    ! [X0] :
      ( ~ product(e_1,e_2,X0)
      | product(e_2,e_1,X0)
      | ~ spl0_25 ),
    inference(resolution,[status(thm)],[f128,f32]) ).

fof(f241,plain,
    ! [X0] :
      ( ~ product(e_2,e_3,X0)
      | product(e_3,e_1,X0)
      | ~ spl0_23 ),
    inference(resolution,[status(thm)],[f120,f32]) ).

fof(f242,plain,
    ( product(e_2,e_2,e_2)
    | ~ spl0_22
    | ~ spl0_16 ),
    inference(resolution,[status(thm)],[f117,f169]) ).

fof(f242_002,plain,
    ( product(e_2,e_2,e_2)
    | ~ spl0_22
    | ~ spl0_16 ),
    inference(resolution,[status(thm)],[f117,f169]) ).

fof(f243,plain,
    ( product(e_2,e_3,e_2)
    | ~ spl0_22
    | ~ spl0_7 ),
    inference(resolution,[status(thm)],[f117,f142]) ).

fof(f244,plain,
    ( spl0_10
    | ~ spl0_22
    | ~ spl0_7 ),
    inference(split_clause,[status(thm)],[f243,f72,f116,f61]) ).

fof(f249,plain,
    ( product(e_1,e_2,e_2)
    | ~ spl0_25
    | ~ spl0_15 ),
    inference(resolution,[status(thm)],[f128,f173]) ).

fof(f250,plain,
    ( spl0_22
    | ~ spl0_25
    | ~ spl0_15 ),
    inference(split_clause,[status(thm)],[f249,f116,f127,f91]) ).

fof(f251,plain,
    ( product(e_1,e_2,e_2)
    | ~ spl0_12
    | ~ spl0_16 ),
    inference(resolution,[status(thm)],[f184,f95]) ).

fof(f252,plain,
    ( spl0_22
    | ~ spl0_12
    | ~ spl0_16 ),
    inference(split_clause,[status(thm)],[f251,f116,f80,f94]) ).

fof(f264,plain,
    ( product(e_3,e_3,e_3)
    | ~ spl0_20
    | ~ spl0_8 ),
    inference(resolution,[status(thm)],[f109,f138]) ).

fof(f265,plain,
    ( product(e_3,e_2,e_3)
    | ~ spl0_20
    | ~ spl0_17 ),
    inference(resolution,[status(thm)],[f109,f165]) ).

fof(f266,plain,
    ( spl0_5
    | ~ spl0_20
    | ~ spl0_17 ),
    inference(split_clause,[status(thm)],[f265,f53,f108,f97]) ).

fof(f267,plain,
    ( product(e_1,e_3,e_3)
    | ~ spl0_26
    | ~ spl0_6 ),
    inference(resolution,[status(thm)],[f131,f146]) ).

fof(f268,plain,
    ( spl0_20
    | ~ spl0_26
    | ~ spl0_6 ),
    inference(split_clause,[status(thm)],[f267,f108,f130,f58]) ).

fof(f269,plain,
    ( product(e_1,e_3,e_3)
    | ~ spl0_17
    | ~ spl0_3 ),
    inference(resolution,[status(thm)],[f98,f158]) ).

fof(f270,plain,
    ( spl0_20
    | ~ spl0_17
    | ~ spl0_3 ),
    inference(split_clause,[status(thm)],[f269,f108,f97,f47]) ).

fof(f274,plain,
    ! [X0] :
      ( ~ product(e_3,e_2,X0)
      | product(e_2,e_1,X0)
      | ~ spl0_19 ),
    inference(resolution,[status(thm)],[f106,f32]) ).

fof(f278,plain,
    ! [X0] :
      ( ~ product(e_3,e_1,X0)
      | product(e_1,e_1,X0)
      | ~ spl0_18 ),
    inference(resolution,[status(thm)],[f103,f32]) ).

fof(f282,plain,
    ! [X0] :
      ( ~ product(e_3,e_2,X0)
      | product(e_2,e_3,X0)
      | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f40,f32]) ).

fof(f286,plain,
    ! [X0] :
      ( ~ product(e_3,e_1,X0)
      | product(e_1,e_3,X0)
      | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f37,f32]) ).

fof(f299,plain,
    ( equalish(e_3,e_2)
    | ~ spl0_11
    | ~ spl0_5 ),
    inference(resolution,[status(thm)],[f217,f54]) ).

fof(f300,plain,
    ( $false
    | ~ spl0_11
    | ~ spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f299,f23]) ).

fof(f301,plain,
    ( ~ spl0_11
    | ~ spl0_5 ),
    inference(contradiction_clause,[status(thm)],[f300]) ).

fof(f303,plain,
    ! [X0] :
      ( ~ product(e_3,X0,e_3)
      | equalish(e_3,X0)
      | ~ spl0_20
      | ~ spl0_8 ),
    inference(resolution,[status(thm)],[f264,f28]) ).

fof(f310,plain,
    ( equalish(e_3,e_1)
    | ~ spl0_20
    | ~ spl0_8 ),
    inference(resolution,[status(thm)],[f303,f65]) ).

fof(f311,plain,
    ( $false
    | ~ spl0_20
    | ~ spl0_8 ),
    inference(forward_subsumption_resolution,[status(thm)],[f310,f22]) ).

fof(f312,plain,
    ( ~ spl0_20
    | ~ spl0_8 ),
    inference(contradiction_clause,[status(thm)],[f311]) ).

fof(f313,plain,
    ( product(e_2,e_1,e_3)
    | ~ spl0_25
    | ~ spl0_23 ),
    inference(resolution,[status(thm)],[f233,f120]) ).

fof(f314,plain,
    ( spl0_17
    | ~ spl0_25
    | ~ spl0_23 ),
    inference(split_clause,[status(thm)],[f313,f97,f127,f119]) ).

fof(f319,plain,
    ( product(e_2,e_1,e_2)
    | ~ spl0_22
    | ~ spl0_25 ),
    inference(resolution,[status(thm)],[f117,f233]) ).

fof(f327,plain,
    ! [X0] :
      ( ~ product(e_2,X0,e_2)
      | equalish(e_1,X0)
      | ~ spl0_22
      | ~ spl0_25 ),
    inference(resolution,[status(thm)],[f319,f28]) ).

fof(f336,plain,
    ( product(e_2,e_1,e_1)
    | ~ spl0_25
    | ~ spl0_21 ),
    inference(resolution,[status(thm)],[f233,f114]) ).

fof(f337,plain,
    ( spl0_15
    | ~ spl0_25
    | ~ spl0_21 ),
    inference(split_clause,[status(thm)],[f336,f91,f127,f113]) ).

fof(f338,plain,
    ( equalish(e_1,e_2)
    | ~ spl0_16
    | ~ spl0_22
    | ~ spl0_25 ),
    inference(resolution,[status(thm)],[f242,f327]) ).

fof(f339,plain,
    ( $false
    | ~ spl0_16
    | ~ spl0_22
    | ~ spl0_25 ),
    inference(forward_subsumption_resolution,[status(thm)],[f338,f18]) ).

fof(f340,plain,
    ( ~ spl0_16
    | ~ spl0_22
    | ~ spl0_25 ),
    inference(contradiction_clause,[status(thm)],[f339]) ).

fof(f341,plain,
    ( $false
    | ~ spl0_22
    | ~ spl0_25
    | spl0_16 ),
    inference(forward_subsumption_resolution,[status(thm)],[f96,f319]) ).

fof(f342,plain,
    ( ~ spl0_22
    | ~ spl0_25
    | spl0_16 ),
    inference(contradiction_clause,[status(thm)],[f341]) ).

fof(f345,plain,
    ( product(e_3,e_2,e_1)
    | ~ spl0_17
    | ~ spl0_18 ),
    inference(resolution,[status(thm)],[f165,f103]) ).

fof(f346,plain,
    ( spl0_3
    | ~ spl0_17
    | ~ spl0_18 ),
    inference(split_clause,[status(thm)],[f345,f47,f97,f102]) ).

fof(f347,plain,
    ( product(e_1,e_3,e_1)
    | ~ spl0_6
    | ~ spl0_24 ),
    inference(resolution,[status(thm)],[f146,f125]) ).

fof(f348,plain,
    ( spl0_18
    | ~ spl0_6
    | ~ spl0_24 ),
    inference(split_clause,[status(thm)],[f347,f102,f58,f124]) ).

fof(f351,plain,
    ( product(e_3,e_1,e_1)
    | ~ spl0_23
    | ~ spl0_9 ),
    inference(resolution,[status(thm)],[f241,f70]) ).

fof(f352,plain,
    ( spl0_6
    | ~ spl0_23
    | ~ spl0_9 ),
    inference(split_clause,[status(thm)],[f351,f58,f119,f69]) ).

fof(f353,plain,
    ( product(e_1,e_2,e_1)
    | ~ spl0_15
    | ~ spl0_24 ),
    inference(resolution,[status(thm)],[f173,f125]) ).

fof(f368,plain,
    ( product(e_2,e_2,e_1)
    | ~ spl0_3
    | ~ spl0_10 ),
    inference(resolution,[status(thm)],[f48,f193]) ).

fof(f373,plain,
    ! [X0] :
      ( ~ product(X0,e_2,e_1)
      | equalish(e_2,X0)
      | ~ spl0_3
      | ~ spl0_10 ),
    inference(resolution,[status(thm)],[f368,f30]) ).

fof(f383,plain,
    ! [X0] :
      ( ~ product(e_1,X0,e_1)
      | equalish(e_2,X0)
      | ~ spl0_15
      | ~ spl0_24 ),
    inference(resolution,[status(thm)],[f353,f28]) ).

fof(f393,plain,
    ( product(e_2,e_2,e_2)
    | ~ spl0_4
    | ~ spl0_10 ),
    inference(resolution,[status(thm)],[f51,f193]) ).

fof(f394,plain,
    ( spl0_13
    | ~ spl0_4
    | ~ spl0_10 ),
    inference(split_clause,[status(thm)],[f393,f83,f50,f72]) ).

fof(f395,plain,
    ( product(e_2,e_1,e_2)
    | ~ spl0_4
    | ~ spl0_19 ),
    inference(resolution,[status(thm)],[f51,f274]) ).

fof(f403,plain,
    ( product(e_1,e_3,e_3)
    | ~ spl0_8
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f65,f286]) ).

fof(f404,plain,
    ( spl0_20
    | ~ spl0_8
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f403,f108,f64,f36]) ).

fof(f442,plain,
    ! [X0] :
      ( ~ product(X0,e_3,e_1)
      | equalish(e_3,X0)
      | ~ spl0_9
      | ~ spl0_5 ),
    inference(resolution,[status(thm)],[f221,f30]) ).

fof(f449,plain,
    ( equalish(e_3,e_1)
    | ~ spl0_9
    | ~ spl0_5
    | ~ spl0_18 ),
    inference(resolution,[status(thm)],[f442,f103]) ).

fof(f450,plain,
    ( $false
    | ~ spl0_9
    | ~ spl0_5
    | ~ spl0_18 ),
    inference(forward_subsumption_resolution,[status(thm)],[f449,f22]) ).

fof(f451,plain,
    ( ~ spl0_9
    | ~ spl0_5
    | ~ spl0_18 ),
    inference(contradiction_clause,[status(thm)],[f450]) ).

fof(f452,plain,
    ( product(e_2,e_1,e_1)
    | ~ spl0_3
    | ~ spl0_19 ),
    inference(resolution,[status(thm)],[f48,f274]) ).

fof(f453,plain,
    ( spl0_15
    | ~ spl0_3
    | ~ spl0_19 ),
    inference(split_clause,[status(thm)],[f452,f91,f47,f105]) ).

fof(f455,plain,
    ( equalish(e_2,e_3)
    | ~ spl0_10
    | ~ spl0_3 ),
    inference(resolution,[status(thm)],[f373,f48]) ).

fof(f456,plain,
    ( $false
    | ~ spl0_10
    | ~ spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f455,f21]) ).

fof(f457,plain,
    ( ~ spl0_10
    | ~ spl0_3 ),
    inference(contradiction_clause,[status(thm)],[f456]) ).

fof(f458,plain,
    ( product(e_1,e_2,e_3)
    | ~ spl0_9
    | ~ spl0_8 ),
    inference(resolution,[status(thm)],[f225,f65]) ).

fof(f459,plain,
    ( spl0_23
    | ~ spl0_9
    | ~ spl0_8 ),
    inference(split_clause,[status(thm)],[f458,f119,f69,f64]) ).

fof(f460,plain,
    ( product(e_2,e_3,e_2)
    | ~ spl0_4
    | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f51,f282]) ).

fof(f461,plain,
    ( spl0_10
    | ~ spl0_4
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f460,f72,f50,f39]) ).

fof(f466,plain,
    ( product(e_1,e_2,e_1)
    | ~ spl0_15
    | ~ spl0_12 ),
    inference(resolution,[status(thm)],[f92,f184]) ).

fof(f469,plain,
    ( product(e_1,e_3,e_1)
    | ~ spl0_6
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f59,f286]) ).

fof(f469_003,plain,
    ( product(e_1,e_3,e_1)
    | ~ spl0_6
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f59,f286]) ).

fof(f472,plain,
    ! [X0] :
      ( ~ product(e_1,e_2,X0)
      | equalish(e_1,X0)
      | ~ spl0_15
      | ~ spl0_12 ),
    inference(resolution,[status(thm)],[f466,f26]) ).

fof(f474,plain,
    ! [X0] :
      ( ~ product(X0,e_3,e_1)
      | equalish(e_1,X0)
      | ~ spl0_6
      | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f469,f30]) ).

fof(f482,plain,
    ( product(e_2,e_3,e_3)
    | ~ spl0_14
    | ~ spl0_4 ),
    inference(resolution,[status(thm)],[f87,f154]) ).

fof(f483,plain,
    ( spl0_11
    | ~ spl0_14
    | ~ spl0_4 ),
    inference(split_clause,[status(thm)],[f482,f75,f86,f50]) ).

fof(f492,plain,
    ( equalish(e_1,e_2)
    | ~ spl0_9
    | ~ spl0_6
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f70,f474]) ).

fof(f493,plain,
    ( $false
    | ~ spl0_9
    | ~ spl0_6
    | ~ spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f492,f18]) ).

fof(f494,plain,
    ( ~ spl0_9
    | ~ spl0_6
    | ~ spl0_0 ),
    inference(contradiction_clause,[status(thm)],[f493]) ).

fof(f496,plain,
    ( product(e_1,e_3,e_1)
    | ~ spl0_15
    | ~ spl0_3 ),
    inference(resolution,[status(thm)],[f92,f158]) ).

fof(f497,plain,
    ( spl0_18
    | ~ spl0_15
    | ~ spl0_3 ),
    inference(split_clause,[status(thm)],[f496,f102,f91,f47]) ).

fof(f500,plain,
    ( spl0_18
    | ~ spl0_6
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f469,f102,f58,f36]) ).

fof(f503,plain,
    ( spl0_16
    | ~ spl0_4
    | ~ spl0_19 ),
    inference(split_clause,[status(thm)],[f395,f94,f50,f105]) ).

fof(f510,plain,
    ( product(e_1,e_3,e_2)
    | ~ spl0_16
    | ~ spl0_3 ),
    inference(resolution,[status(thm)],[f95,f158]) ).

fof(f511,plain,
    ( spl0_19
    | ~ spl0_16
    | ~ spl0_3 ),
    inference(split_clause,[status(thm)],[f510,f105,f94,f47]) ).

fof(f512,plain,
    ! [X0] :
      ( ~ product(e_3,e_1,X0)
      | product(e_1,e_2,X0)
      | ~ spl0_9 ),
    inference(resolution,[status(thm)],[f70,f32]) ).

fof(f516,plain,
    ( product(e_1,e_1,e_1)
    | ~ spl0_6
    | ~ spl0_18 ),
    inference(resolution,[status(thm)],[f59,f278]) ).

fof(f517,plain,
    ( spl0_24
    | ~ spl0_6
    | ~ spl0_18 ),
    inference(split_clause,[status(thm)],[f516,f124,f58,f102]) ).

fof(f537,plain,
    ( product(e_3,e_1,e_1)
    | ~ spl0_18
    | ~ spl0_26 ),
    inference(resolution,[status(thm)],[f103,f229]) ).

fof(f538,plain,
    ( spl0_6
    | ~ spl0_18
    | ~ spl0_26 ),
    inference(split_clause,[status(thm)],[f537,f58,f102,f130]) ).

fof(f543,plain,
    ( equalish(e_2,e_1)
    | ~ spl0_15
    | ~ spl0_24 ),
    inference(resolution,[status(thm)],[f383,f125]) ).

fof(f544,plain,
    ( $false
    | ~ spl0_15
    | ~ spl0_24 ),
    inference(forward_subsumption_resolution,[status(thm)],[f543,f20]) ).

fof(f545,plain,
    ( ~ spl0_15
    | ~ spl0_24 ),
    inference(contradiction_clause,[status(thm)],[f544]) ).

fof(f548,plain,
    ( product(e_3,e_2,e_1)
    | ~ spl0_9
    | ~ spl0_14 ),
    inference(resolution,[status(thm)],[f70,f177]) ).

fof(f549,plain,
    ( spl0_3
    | ~ spl0_9
    | ~ spl0_14 ),
    inference(split_clause,[status(thm)],[f548,f47,f69,f86]) ).

fof(f562,plain,
    ( product(e_1,e_2,e_2)
    | ~ spl0_9
    | ~ spl0_7 ),
    inference(resolution,[status(thm)],[f512,f62]) ).

fof(f563,plain,
    ( spl0_22
    | ~ spl0_9
    | ~ spl0_7 ),
    inference(split_clause,[status(thm)],[f562,f116,f69,f61]) ).

fof(f564,plain,
    ( spl0_0
    | ~ spl0_9
    | ~ spl0_5 ),
    inference(split_clause,[status(thm)],[f221,f36,f69,f53]) ).

fof(f569,plain,
    ( product(e_1,e_2,e_3)
    | ~ spl0_26
    | ~ spl0_15 ),
    inference(resolution,[status(thm)],[f131,f173]) ).

fof(f574,plain,
    ( equalish(e_1,e_3)
    | ~ spl0_12
    | ~ spl0_26
    | ~ spl0_15 ),
    inference(resolution,[status(thm)],[f472,f569]) ).

fof(f575,plain,
    ( $false
    | ~ spl0_12
    | ~ spl0_26
    | ~ spl0_15 ),
    inference(forward_subsumption_resolution,[status(thm)],[f574,f19]) ).

fof(f576,plain,
    ( ~ spl0_12
    | ~ spl0_26
    | ~ spl0_15 ),
    inference(contradiction_clause,[status(thm)],[f575]) ).

fof(f577,plain,
    ( spl0_13
    | ~ spl0_22
    | ~ spl0_16 ),
    inference(split_clause,[status(thm)],[f242,f83,f116,f94]) ).

fof(f578,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f46,f57,f68,f79,f90,f101,f112,f123,f134,f200,f202,f204,f214,f244,f250,f252,f266,f268,f270,f301,f312,f314,f337,f340,f342,f346,f348,f352,f394,f404,f451,f453,f457,f459,f461,f483,f494,f497,f500,f503,f511,f517,f538,f545,f549,f563,f564,f576,f577]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : GRP129-1.003 : TPTP v8.1.2. Released v1.2.0.
% 0.12/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35  % Computer : n007.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 00:22:32 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  % Drodi V3.6.0
% 0.19/0.47  % Refutation found
% 0.19/0.47  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.19/0.47  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.48  % Elapsed time: 0.132913 seconds
% 0.19/0.48  % CPU time: 0.991788 seconds
% 0.19/0.48  % Total memory used: 14.146 MB
% 0.19/0.48  % Net memory used: 12.848 MB
%------------------------------------------------------------------------------