TSTP Solution File: GRP124-7.004 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GRP124-7.004 : TPTP v8.1.2. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n029.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 20:19:20 EDT 2024

% Result   : Unsatisfiable 0.19s 0.41s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   48
% Syntax   : Number of formulae    :  196 (  51 unt;   0 def)
%            Number of atoms       :  416 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  416 ( 196   ~; 195   |;   0   &)
%                                         (  25 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   30 (  29 usr;  26 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :   87 (  87   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f11,axiom,
    group_element(e_1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    group_element(e_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f14,axiom,
    group_element(e_4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ~ equalish(e_1,e_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f16,axiom,
    ~ equalish(e_1,e_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f17,axiom,
    ~ equalish(e_1,e_4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f18,axiom,
    ~ equalish(e_2,e_1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f19,axiom,
    ~ equalish(e_2,e_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f20,axiom,
    ~ equalish(e_2,e_4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f21,axiom,
    ~ equalish(e_3,e_1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f22,axiom,
    ~ equalish(e_3,e_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f23,axiom,
    ~ equalish(e_3,e_4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f24,axiom,
    ~ equalish(e_4,e_1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f25,axiom,
    ~ equalish(e_4,e_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f26,axiom,
    ~ equalish(e_4,e_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f27,axiom,
    ! [X,Y] :
      ( ~ group_element(X)
      | ~ group_element(Y)
      | product1(X,Y,e_1)
      | product1(X,Y,e_2)
      | product1(X,Y,e_3)
      | product1(X,Y,e_4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f28,axiom,
    ! [X,Y,W,Z] :
      ( ~ product1(X,Y,W)
      | ~ product1(X,Y,Z)
      | equalish(W,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f29,axiom,
    ! [X,W,Y,Z] :
      ( ~ product1(X,W,Y)
      | ~ product1(X,Z,Y)
      | equalish(W,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f30,axiom,
    ! [W,Y,X,Z] :
      ( ~ product1(W,Y,X)
      | ~ product1(Z,Y,X)
      | equalish(W,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f31,axiom,
    ! [X] : product1(X,X,X),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f33,axiom,
    ! [X,Y,W,Z] :
      ( ~ product2(X,Y,W)
      | ~ product2(X,Y,Z)
      | equalish(W,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f37,negated_conjecture,
    ! [X,Y,Z1,Z2] :
      ( ~ product1(X,Y,Z1)
      | ~ product1(Z1,X,Z2)
      | product2(Z2,Y,X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f49,plain,
    group_element(e_1),
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f50,plain,
    group_element(e_2),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f51,plain,
    group_element(e_3),
    inference(cnf_transformation,[status(esa)],[f13]) ).

fof(f52,plain,
    group_element(e_4),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f53,plain,
    ~ equalish(e_1,e_2),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f54,plain,
    ~ equalish(e_1,e_3),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f55,plain,
    ~ equalish(e_1,e_4),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f56,plain,
    ~ equalish(e_2,e_1),
    inference(cnf_transformation,[status(esa)],[f18]) ).

fof(f57,plain,
    ~ equalish(e_2,e_3),
    inference(cnf_transformation,[status(esa)],[f19]) ).

fof(f58,plain,
    ~ equalish(e_2,e_4),
    inference(cnf_transformation,[status(esa)],[f20]) ).

fof(f59,plain,
    ~ equalish(e_3,e_1),
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f60,plain,
    ~ equalish(e_3,e_2),
    inference(cnf_transformation,[status(esa)],[f22]) ).

fof(f61,plain,
    ~ equalish(e_3,e_4),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f62,plain,
    ~ equalish(e_4,e_1),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f63,plain,
    ~ equalish(e_4,e_2),
    inference(cnf_transformation,[status(esa)],[f25]) ).

fof(f64,plain,
    ~ equalish(e_4,e_3),
    inference(cnf_transformation,[status(esa)],[f26]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( ~ group_element(X0)
      | ~ group_element(X1)
      | product1(X0,X1,e_1)
      | product1(X0,X1,e_2)
      | product1(X0,X1,e_3)
      | product1(X0,X1,e_4) ),
    inference(cnf_transformation,[status(esa)],[f27]) ).

fof(f66,plain,
    ! [W,Z] :
      ( ! [X,Y] :
          ( ~ product1(X,Y,W)
          | ~ product1(X,Y,Z) )
      | equalish(W,Z) ),
    inference(miniscoping,[status(esa)],[f28]) ).

fof(f67,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product1(X0,X1,X2)
      | ~ product1(X0,X1,X3)
      | equalish(X2,X3) ),
    inference(cnf_transformation,[status(esa)],[f66]) ).

fof(f68,plain,
    ! [W,Z] :
      ( ! [X,Y] :
          ( ~ product1(X,W,Y)
          | ~ product1(X,Z,Y) )
      | equalish(W,Z) ),
    inference(miniscoping,[status(esa)],[f29]) ).

fof(f69,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product1(X0,X1,X2)
      | ~ product1(X0,X3,X2)
      | equalish(X1,X3) ),
    inference(cnf_transformation,[status(esa)],[f68]) ).

fof(f70,plain,
    ! [W,Z] :
      ( ! [Y,X] :
          ( ~ product1(W,Y,X)
          | ~ product1(Z,Y,X) )
      | equalish(W,Z) ),
    inference(miniscoping,[status(esa)],[f30]) ).

fof(f71,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product1(X0,X1,X2)
      | ~ product1(X3,X1,X2)
      | equalish(X0,X3) ),
    inference(cnf_transformation,[status(esa)],[f70]) ).

fof(f72,plain,
    ! [X0] : product1(X0,X0,X0),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f74,plain,
    ! [W,Z] :
      ( ! [X,Y] :
          ( ~ product2(X,Y,W)
          | ~ product2(X,Y,Z) )
      | equalish(W,Z) ),
    inference(miniscoping,[status(esa)],[f33]) ).

fof(f75,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product2(X0,X1,X2)
      | ~ product2(X0,X1,X3)
      | equalish(X2,X3) ),
    inference(cnf_transformation,[status(esa)],[f74]) ).

fof(f81,plain,
    ! [X,Y,Z2] :
      ( ! [Z1] :
          ( ~ product1(X,Y,Z1)
          | ~ product1(Z1,X,Z2) )
      | product2(Z2,Y,X) ),
    inference(miniscoping,[status(esa)],[f37]) ).

fof(f82,plain,
    ! [X0,X1,X2,X3] :
      ( ~ product1(X0,X1,X2)
      | ~ product1(X2,X0,X3)
      | product2(X3,X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f81]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( ~ product1(X0,X0,X1)
      | product2(X1,X0,X0) ),
    inference(resolution,[status(thm)],[f72,f82]) ).

fof(f84,plain,
    ! [X0] : product2(X0,X0,X0),
    inference(resolution,[status(thm)],[f83,f72]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( ~ product1(X0,X0,X1)
      | equalish(X0,X1) ),
    inference(resolution,[status(thm)],[f67,f72]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( ~ product1(X0,X1,X0)
      | equalish(X0,X1) ),
    inference(resolution,[status(thm)],[f69,f72]) ).

fof(f89,plain,
    ! [X0,X1] :
      ( ~ product1(X0,X1,X1)
      | equalish(X1,X0) ),
    inference(resolution,[status(thm)],[f71,f72]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( ~ product2(X0,X0,X1)
      | equalish(X0,X1) ),
    inference(resolution,[status(thm)],[f75,f84]) ).

fof(f97,plain,
    ! [X0] :
      ( ~ group_element(X0)
      | product1(e_4,X0,e_1)
      | product1(e_4,X0,e_2)
      | product1(e_4,X0,e_3)
      | product1(e_4,X0,e_4) ),
    inference(resolution,[status(thm)],[f65,f52]) ).

fof(f98,plain,
    ! [X0] :
      ( ~ group_element(X0)
      | product1(e_3,X0,e_1)
      | product1(e_3,X0,e_2)
      | product1(e_3,X0,e_3)
      | product1(e_3,X0,e_4) ),
    inference(resolution,[status(thm)],[f65,f51]) ).

fof(f99,plain,
    ! [X0] :
      ( ~ group_element(X0)
      | product1(e_2,X0,e_1)
      | product1(e_2,X0,e_2)
      | product1(e_2,X0,e_3)
      | product1(e_2,X0,e_4) ),
    inference(resolution,[status(thm)],[f65,f50]) ).

fof(f119,plain,
    ( spl0_4
  <=> product1(e_4,e_3,e_1) ),
    introduced(split_symbol_definition) ).

fof(f120,plain,
    ( product1(e_4,e_3,e_1)
    | ~ spl0_4 ),
    inference(component_clause,[status(thm)],[f119]) ).

fof(f122,plain,
    ( spl0_5
  <=> product1(e_4,e_3,e_2) ),
    introduced(split_symbol_definition) ).

fof(f123,plain,
    ( product1(e_4,e_3,e_2)
    | ~ spl0_5 ),
    inference(component_clause,[status(thm)],[f122]) ).

fof(f125,plain,
    ( spl0_6
  <=> product1(e_4,e_3,e_3) ),
    introduced(split_symbol_definition) ).

fof(f126,plain,
    ( product1(e_4,e_3,e_3)
    | ~ spl0_6 ),
    inference(component_clause,[status(thm)],[f125]) ).

fof(f128,plain,
    ( spl0_7
  <=> product1(e_4,e_3,e_4) ),
    introduced(split_symbol_definition) ).

fof(f129,plain,
    ( product1(e_4,e_3,e_4)
    | ~ spl0_7 ),
    inference(component_clause,[status(thm)],[f128]) ).

fof(f131,plain,
    ( product1(e_4,e_3,e_1)
    | product1(e_4,e_3,e_2)
    | product1(e_4,e_3,e_3)
    | product1(e_4,e_3,e_4) ),
    inference(resolution,[status(thm)],[f97,f51]) ).

fof(f132,plain,
    ( spl0_4
    | spl0_5
    | spl0_6
    | spl0_7 ),
    inference(split_clause,[status(thm)],[f131,f119,f122,f125,f128]) ).

fof(f136,plain,
    ( spl0_9
  <=> product1(e_4,e_2,e_2) ),
    introduced(split_symbol_definition) ).

fof(f137,plain,
    ( product1(e_4,e_2,e_2)
    | ~ spl0_9 ),
    inference(component_clause,[status(thm)],[f136]) ).

fof(f142,plain,
    ( spl0_11
  <=> product1(e_4,e_2,e_4) ),
    introduced(split_symbol_definition) ).

fof(f143,plain,
    ( product1(e_4,e_2,e_4)
    | ~ spl0_11 ),
    inference(component_clause,[status(thm)],[f142]) ).

fof(f147,plain,
    ( spl0_12
  <=> product1(e_4,e_1,e_1) ),
    introduced(split_symbol_definition) ).

fof(f148,plain,
    ( product1(e_4,e_1,e_1)
    | ~ spl0_12 ),
    inference(component_clause,[status(thm)],[f147]) ).

fof(f150,plain,
    ( spl0_13
  <=> product1(e_4,e_1,e_2) ),
    introduced(split_symbol_definition) ).

fof(f151,plain,
    ( product1(e_4,e_1,e_2)
    | ~ spl0_13 ),
    inference(component_clause,[status(thm)],[f150]) ).

fof(f153,plain,
    ( spl0_14
  <=> product1(e_4,e_1,e_3) ),
    introduced(split_symbol_definition) ).

fof(f154,plain,
    ( product1(e_4,e_1,e_3)
    | ~ spl0_14 ),
    inference(component_clause,[status(thm)],[f153]) ).

fof(f156,plain,
    ( spl0_15
  <=> product1(e_4,e_1,e_4) ),
    introduced(split_symbol_definition) ).

fof(f157,plain,
    ( product1(e_4,e_1,e_4)
    | ~ spl0_15 ),
    inference(component_clause,[status(thm)],[f156]) ).

fof(f159,plain,
    ( product1(e_4,e_1,e_1)
    | product1(e_4,e_1,e_2)
    | product1(e_4,e_1,e_3)
    | product1(e_4,e_1,e_4) ),
    inference(resolution,[status(thm)],[f97,f49]) ).

fof(f160,plain,
    ( spl0_12
    | spl0_13
    | spl0_14
    | spl0_15 ),
    inference(split_clause,[status(thm)],[f159,f147,f150,f153,f156]) ).

fof(f162,plain,
    ( equalish(e_4,e_1)
    | ~ spl0_15 ),
    inference(resolution,[status(thm)],[f157,f87]) ).

fof(f163,plain,
    ( $false
    | ~ spl0_15 ),
    inference(forward_subsumption_resolution,[status(thm)],[f162,f62]) ).

fof(f164,plain,
    ~ spl0_15,
    inference(contradiction_clause,[status(thm)],[f163]) ).

fof(f165,plain,
    ! [X0] :
      ( ~ product1(X0,e_1,e_3)
      | equalish(e_4,X0)
      | ~ spl0_14 ),
    inference(resolution,[status(thm)],[f154,f71]) ).

fof(f168,plain,
    ! [X0] :
      ( ~ product1(e_3,e_4,X0)
      | product2(X0,e_1,e_4)
      | ~ spl0_14 ),
    inference(resolution,[status(thm)],[f154,f82]) ).

fof(f175,plain,
    ( equalish(e_1,e_4)
    | ~ spl0_12 ),
    inference(resolution,[status(thm)],[f148,f89]) ).

fof(f176,plain,
    ( $false
    | ~ spl0_12 ),
    inference(forward_subsumption_resolution,[status(thm)],[f175,f55]) ).

fof(f177,plain,
    ~ spl0_12,
    inference(contradiction_clause,[status(thm)],[f176]) ).

fof(f178,plain,
    ! [X0] :
      ( ~ product1(X0,e_1,e_2)
      | equalish(e_4,X0)
      | ~ spl0_13 ),
    inference(resolution,[status(thm)],[f151,f71]) ).

fof(f179,plain,
    ! [X0] :
      ( ~ product1(e_4,X0,e_2)
      | equalish(e_1,X0)
      | ~ spl0_13 ),
    inference(resolution,[status(thm)],[f151,f69]) ).

fof(f183,plain,
    ( equalish(e_4,e_2)
    | ~ spl0_11 ),
    inference(resolution,[status(thm)],[f143,f87]) ).

fof(f184,plain,
    ( $false
    | ~ spl0_11 ),
    inference(forward_subsumption_resolution,[status(thm)],[f183,f63]) ).

fof(f185,plain,
    ~ spl0_11,
    inference(contradiction_clause,[status(thm)],[f184]) ).

fof(f190,plain,
    ( equalish(e_2,e_4)
    | ~ spl0_9 ),
    inference(resolution,[status(thm)],[f137,f89]) ).

fof(f191,plain,
    ( $false
    | ~ spl0_9 ),
    inference(forward_subsumption_resolution,[status(thm)],[f190,f58]) ).

fof(f192,plain,
    ~ spl0_9,
    inference(contradiction_clause,[status(thm)],[f191]) ).

fof(f198,plain,
    ( equalish(e_4,e_3)
    | ~ spl0_7 ),
    inference(resolution,[status(thm)],[f129,f87]) ).

fof(f199,plain,
    ( $false
    | ~ spl0_7 ),
    inference(forward_subsumption_resolution,[status(thm)],[f198,f64]) ).

fof(f200,plain,
    ~ spl0_7,
    inference(contradiction_clause,[status(thm)],[f199]) ).

fof(f201,plain,
    ( equalish(e_3,e_4)
    | ~ spl0_6 ),
    inference(resolution,[status(thm)],[f126,f89]) ).

fof(f202,plain,
    ( $false
    | ~ spl0_6 ),
    inference(forward_subsumption_resolution,[status(thm)],[f201,f61]) ).

fof(f203,plain,
    ~ spl0_6,
    inference(contradiction_clause,[status(thm)],[f202]) ).

fof(f212,plain,
    ( spl0_16
  <=> product1(e_3,e_4,e_1) ),
    introduced(split_symbol_definition) ).

fof(f213,plain,
    ( product1(e_3,e_4,e_1)
    | ~ spl0_16 ),
    inference(component_clause,[status(thm)],[f212]) ).

fof(f215,plain,
    ( spl0_17
  <=> product1(e_3,e_4,e_2) ),
    introduced(split_symbol_definition) ).

fof(f216,plain,
    ( product1(e_3,e_4,e_2)
    | ~ spl0_17 ),
    inference(component_clause,[status(thm)],[f215]) ).

fof(f218,plain,
    ( spl0_18
  <=> product1(e_3,e_4,e_3) ),
    introduced(split_symbol_definition) ).

fof(f219,plain,
    ( product1(e_3,e_4,e_3)
    | ~ spl0_18 ),
    inference(component_clause,[status(thm)],[f218]) ).

fof(f221,plain,
    ( spl0_19
  <=> product1(e_3,e_4,e_4) ),
    introduced(split_symbol_definition) ).

fof(f222,plain,
    ( product1(e_3,e_4,e_4)
    | ~ spl0_19 ),
    inference(component_clause,[status(thm)],[f221]) ).

fof(f224,plain,
    ( product1(e_3,e_4,e_1)
    | product1(e_3,e_4,e_2)
    | product1(e_3,e_4,e_3)
    | product1(e_3,e_4,e_4) ),
    inference(resolution,[status(thm)],[f98,f52]) ).

fof(f225,plain,
    ( spl0_16
    | spl0_17
    | spl0_18
    | spl0_19 ),
    inference(split_clause,[status(thm)],[f224,f212,f215,f218,f221]) ).

fof(f235,plain,
    ( spl0_23
  <=> product1(e_3,e_3,e_4) ),
    introduced(split_symbol_definition) ).

fof(f236,plain,
    ( product1(e_3,e_3,e_4)
    | ~ spl0_23 ),
    inference(component_clause,[status(thm)],[f235]) ).

fof(f243,plain,
    ( spl0_25
  <=> product1(e_3,e_2,e_2) ),
    introduced(split_symbol_definition) ).

fof(f244,plain,
    ( product1(e_3,e_2,e_2)
    | ~ spl0_25 ),
    inference(component_clause,[status(thm)],[f243]) ).

fof(f246,plain,
    ( spl0_26
  <=> product1(e_3,e_2,e_3) ),
    introduced(split_symbol_definition) ).

fof(f247,plain,
    ( product1(e_3,e_2,e_3)
    | ~ spl0_26 ),
    inference(component_clause,[status(thm)],[f246]) ).

fof(f254,plain,
    ( spl0_28
  <=> product1(e_3,e_1,e_1) ),
    introduced(split_symbol_definition) ).

fof(f255,plain,
    ( product1(e_3,e_1,e_1)
    | ~ spl0_28 ),
    inference(component_clause,[status(thm)],[f254]) ).

fof(f257,plain,
    ( spl0_29
  <=> product1(e_3,e_1,e_2) ),
    introduced(split_symbol_definition) ).

fof(f258,plain,
    ( product1(e_3,e_1,e_2)
    | ~ spl0_29 ),
    inference(component_clause,[status(thm)],[f257]) ).

fof(f260,plain,
    ( spl0_30
  <=> product1(e_3,e_1,e_3) ),
    introduced(split_symbol_definition) ).

fof(f261,plain,
    ( product1(e_3,e_1,e_3)
    | ~ spl0_30 ),
    inference(component_clause,[status(thm)],[f260]) ).

fof(f263,plain,
    ( spl0_31
  <=> product1(e_3,e_1,e_4) ),
    introduced(split_symbol_definition) ).

fof(f264,plain,
    ( product1(e_3,e_1,e_4)
    | ~ spl0_31 ),
    inference(component_clause,[status(thm)],[f263]) ).

fof(f266,plain,
    ( product1(e_3,e_1,e_1)
    | product1(e_3,e_1,e_2)
    | product1(e_3,e_1,e_3)
    | product1(e_3,e_1,e_4) ),
    inference(resolution,[status(thm)],[f98,f49]) ).

fof(f267,plain,
    ( spl0_28
    | spl0_29
    | spl0_30
    | spl0_31 ),
    inference(split_clause,[status(thm)],[f266,f254,f257,f260,f263]) ).

fof(f310,plain,
    ( spl0_44
  <=> product1(e_2,e_1,e_1) ),
    introduced(split_symbol_definition) ).

fof(f311,plain,
    ( product1(e_2,e_1,e_1)
    | ~ spl0_44 ),
    inference(component_clause,[status(thm)],[f310]) ).

fof(f313,plain,
    ( spl0_45
  <=> product1(e_2,e_1,e_2) ),
    introduced(split_symbol_definition) ).

fof(f314,plain,
    ( product1(e_2,e_1,e_2)
    | ~ spl0_45 ),
    inference(component_clause,[status(thm)],[f313]) ).

fof(f316,plain,
    ( spl0_46
  <=> product1(e_2,e_1,e_3) ),
    introduced(split_symbol_definition) ).

fof(f317,plain,
    ( product1(e_2,e_1,e_3)
    | ~ spl0_46 ),
    inference(component_clause,[status(thm)],[f316]) ).

fof(f319,plain,
    ( spl0_47
  <=> product1(e_2,e_1,e_4) ),
    introduced(split_symbol_definition) ).

fof(f320,plain,
    ( product1(e_2,e_1,e_4)
    | ~ spl0_47 ),
    inference(component_clause,[status(thm)],[f319]) ).

fof(f322,plain,
    ( product1(e_2,e_1,e_1)
    | product1(e_2,e_1,e_2)
    | product1(e_2,e_1,e_3)
    | product1(e_2,e_1,e_4) ),
    inference(resolution,[status(thm)],[f99,f49]) ).

fof(f323,plain,
    ( spl0_44
    | spl0_45
    | spl0_46
    | spl0_47 ),
    inference(split_clause,[status(thm)],[f322,f310,f313,f316,f319]) ).

fof(f604,plain,
    ( equalish(e_1,e_3)
    | ~ spl0_13
    | ~ spl0_5 ),
    inference(resolution,[status(thm)],[f179,f123]) ).

fof(f605,plain,
    ( $false
    | ~ spl0_13
    | ~ spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f604,f54]) ).

fof(f606,plain,
    ( ~ spl0_13
    | ~ spl0_5 ),
    inference(contradiction_clause,[status(thm)],[f605]) ).

fof(f627,plain,
    ! [X0] :
      ( ~ product1(X0,e_1,e_4)
      | equalish(e_3,X0)
      | ~ spl0_31 ),
    inference(resolution,[status(thm)],[f264,f71]) ).

fof(f630,plain,
    ! [X0] :
      ( ~ product1(e_4,e_3,X0)
      | product2(X0,e_1,e_3)
      | ~ spl0_31 ),
    inference(resolution,[status(thm)],[f264,f82]) ).

fof(f631,plain,
    ( product2(e_1,e_1,e_3)
    | ~ spl0_31
    | ~ spl0_4 ),
    inference(resolution,[status(thm)],[f630,f120]) ).

fof(f634,plain,
    ( equalish(e_1,e_3)
    | ~ spl0_31
    | ~ spl0_4 ),
    inference(resolution,[status(thm)],[f631,f91]) ).

fof(f635,plain,
    ( $false
    | ~ spl0_31
    | ~ spl0_4 ),
    inference(forward_subsumption_resolution,[status(thm)],[f634,f54]) ).

fof(f636,plain,
    ( ~ spl0_31
    | ~ spl0_4 ),
    inference(contradiction_clause,[status(thm)],[f635]) ).

fof(f638,plain,
    ( equalish(e_3,e_1)
    | ~ spl0_30 ),
    inference(resolution,[status(thm)],[f261,f87]) ).

fof(f639,plain,
    ( $false
    | ~ spl0_30 ),
    inference(forward_subsumption_resolution,[status(thm)],[f638,f59]) ).

fof(f640,plain,
    ~ spl0_30,
    inference(contradiction_clause,[status(thm)],[f639]) ).

fof(f641,plain,
    ( equalish(e_4,e_3)
    | ~ spl0_29
    | ~ spl0_13 ),
    inference(resolution,[status(thm)],[f258,f178]) ).

fof(f642,plain,
    ( $false
    | ~ spl0_29
    | ~ spl0_13 ),
    inference(forward_subsumption_resolution,[status(thm)],[f641,f64]) ).

fof(f643,plain,
    ( ~ spl0_29
    | ~ spl0_13 ),
    inference(contradiction_clause,[status(thm)],[f642]) ).

fof(f644,plain,
    ( equalish(e_1,e_3)
    | ~ spl0_28 ),
    inference(resolution,[status(thm)],[f255,f89]) ).

fof(f645,plain,
    ( $false
    | ~ spl0_28 ),
    inference(forward_subsumption_resolution,[status(thm)],[f644,f54]) ).

fof(f646,plain,
    ~ spl0_28,
    inference(contradiction_clause,[status(thm)],[f645]) ).

fof(f648,plain,
    ! [X0] :
      ( ~ product1(e_3,X0,e_2)
      | equalish(e_1,X0)
      | ~ spl0_29 ),
    inference(resolution,[status(thm)],[f258,f69]) ).

fof(f675,plain,
    ( equalish(e_3,e_4)
    | ~ spl0_23 ),
    inference(resolution,[status(thm)],[f236,f85]) ).

fof(f676,plain,
    ( $false
    | ~ spl0_23 ),
    inference(forward_subsumption_resolution,[status(thm)],[f675,f61]) ).

fof(f677,plain,
    ~ spl0_23,
    inference(contradiction_clause,[status(thm)],[f676]) ).

fof(f686,plain,
    ( equalish(e_4,e_3)
    | ~ spl0_19 ),
    inference(resolution,[status(thm)],[f222,f89]) ).

fof(f687,plain,
    ( $false
    | ~ spl0_19 ),
    inference(forward_subsumption_resolution,[status(thm)],[f686,f64]) ).

fof(f688,plain,
    ~ spl0_19,
    inference(contradiction_clause,[status(thm)],[f687]) ).

fof(f692,plain,
    ( equalish(e_3,e_4)
    | ~ spl0_18 ),
    inference(resolution,[status(thm)],[f219,f87]) ).

fof(f693,plain,
    ( $false
    | ~ spl0_18 ),
    inference(forward_subsumption_resolution,[status(thm)],[f692,f61]) ).

fof(f694,plain,
    ~ spl0_18,
    inference(contradiction_clause,[status(thm)],[f693]) ).

fof(f697,plain,
    ( equalish(e_1,e_4)
    | ~ spl0_17
    | ~ spl0_29 ),
    inference(resolution,[status(thm)],[f216,f648]) ).

fof(f698,plain,
    ( $false
    | ~ spl0_17
    | ~ spl0_29 ),
    inference(forward_subsumption_resolution,[status(thm)],[f697,f55]) ).

fof(f699,plain,
    ( ~ spl0_17
    | ~ spl0_29 ),
    inference(contradiction_clause,[status(thm)],[f698]) ).

fof(f700,plain,
    ( product2(e_1,e_1,e_4)
    | ~ spl0_16
    | ~ spl0_14 ),
    inference(resolution,[status(thm)],[f213,f168]) ).

fof(f712,plain,
    ( equalish(e_1,e_4)
    | ~ spl0_16
    | ~ spl0_14 ),
    inference(resolution,[status(thm)],[f700,f91]) ).

fof(f713,plain,
    ( $false
    | ~ spl0_16
    | ~ spl0_14 ),
    inference(forward_subsumption_resolution,[status(thm)],[f712,f55]) ).

fof(f714,plain,
    ( ~ spl0_16
    | ~ spl0_14 ),
    inference(contradiction_clause,[status(thm)],[f713]) ).

fof(f735,plain,
    ( equalish(e_2,e_3)
    | ~ spl0_25 ),
    inference(resolution,[status(thm)],[f244,f89]) ).

fof(f736,plain,
    ( $false
    | ~ spl0_25 ),
    inference(forward_subsumption_resolution,[status(thm)],[f735,f57]) ).

fof(f737,plain,
    ~ spl0_25,
    inference(contradiction_clause,[status(thm)],[f736]) ).

fof(f739,plain,
    ( equalish(e_3,e_2)
    | ~ spl0_26 ),
    inference(resolution,[status(thm)],[f247,f87]) ).

fof(f740,plain,
    ( $false
    | ~ spl0_26 ),
    inference(forward_subsumption_resolution,[status(thm)],[f739,f60]) ).

fof(f741,plain,
    ~ spl0_26,
    inference(contradiction_clause,[status(thm)],[f740]) ).

fof(f742,plain,
    ( equalish(e_3,e_2)
    | ~ spl0_31
    | ~ spl0_47 ),
    inference(resolution,[status(thm)],[f627,f320]) ).

fof(f743,plain,
    ( $false
    | ~ spl0_31
    | ~ spl0_47 ),
    inference(forward_subsumption_resolution,[status(thm)],[f742,f60]) ).

fof(f744,plain,
    ( ~ spl0_31
    | ~ spl0_47 ),
    inference(contradiction_clause,[status(thm)],[f743]) ).

fof(f745,plain,
    ( equalish(e_4,e_2)
    | ~ spl0_46
    | ~ spl0_14 ),
    inference(resolution,[status(thm)],[f317,f165]) ).

fof(f746,plain,
    ( $false
    | ~ spl0_46
    | ~ spl0_14 ),
    inference(forward_subsumption_resolution,[status(thm)],[f745,f63]) ).

fof(f747,plain,
    ( ~ spl0_46
    | ~ spl0_14 ),
    inference(contradiction_clause,[status(thm)],[f746]) ).

fof(f749,plain,
    ( equalish(e_2,e_1)
    | ~ spl0_45 ),
    inference(resolution,[status(thm)],[f314,f87]) ).

fof(f750,plain,
    ( $false
    | ~ spl0_45 ),
    inference(forward_subsumption_resolution,[status(thm)],[f749,f56]) ).

fof(f751,plain,
    ~ spl0_45,
    inference(contradiction_clause,[status(thm)],[f750]) ).

fof(f752,plain,
    ( equalish(e_1,e_2)
    | ~ spl0_44 ),
    inference(resolution,[status(thm)],[f311,f89]) ).

fof(f753,plain,
    ( $false
    | ~ spl0_44 ),
    inference(forward_subsumption_resolution,[status(thm)],[f752,f53]) ).

fof(f754,plain,
    ~ spl0_44,
    inference(contradiction_clause,[status(thm)],[f753]) ).

fof(f755,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f132,f160,f164,f177,f185,f192,f200,f203,f225,f267,f323,f606,f636,f640,f643,f646,f677,f688,f694,f699,f714,f737,f741,f744,f747,f751,f754]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : GRP124-7.004 : TPTP v8.1.2. Released v1.2.0.
% 0.03/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33  % Computer : n029.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Tue Apr 30 00:46:04 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  % Drodi V3.6.0
% 0.19/0.41  % Refutation found
% 0.19/0.41  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.19/0.41  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.42  % Elapsed time: 0.082542 seconds
% 0.19/0.42  % CPU time: 0.571147 seconds
% 0.19/0.42  % Total memory used: 18.364 MB
% 0.19/0.42  % Net memory used: 17.257 MB
%------------------------------------------------------------------------------