TSTP Solution File: GRP124-4.004 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : GRP124-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n004.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 : Sun May  5 05:46:02 EDT 2024

% Result   : Unsatisfiable 0.62s 0.79s
% Output   : Refutation 0.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   69
% Syntax   : Number of formulae    :  251 (  29 unt;   0 def)
%            Number of atoms       :  739 (   0 equ)
%            Maximal formula atoms :   11 (   2 avg)
%            Number of connectives :  791 ( 303   ~; 438   |;   0   &)
%                                         (  50 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   54 (  53 usr;  51 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :   60 (  60   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f971,plain,
    $false,
    inference(avatar_sat_refutation,[],[f86,f106,f138,f167,f196,f198,f200,f234,f239,f241,f243,f317,f330,f389,f412,f423,f425,f446,f473,f487,f506,f508,f509,f511,f513,f540,f558,f573,f581,f599,f600,f608,f623,f624,f633,f641,f656,f674,f675,f690,f708,f710,f718,f720,f735,f737,f775,f788,f800,f814,f846,f866,f900,f929,f930,f938,f948,f959,f970]) ).

fof(f970,plain,
    ( spl0_65
    | spl0_64
    | spl0_63
    | spl0_32
    | ~ spl0_22
    | ~ spl0_8
    | ~ spl0_12 ),
    inference(avatar_split_clause,[],[f961,f127,f111,f169,f223,f461,f465,f469]) ).

fof(f469,plain,
    ( spl0_65
  <=> product(e_2,e_3,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f465,plain,
    ( spl0_64
  <=> product(e_1,e_3,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f461,plain,
    ( spl0_63
  <=> product(e_3,e_3,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f223,plain,
    ( spl0_32
  <=> equalish(e_4,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f169,plain,
    ( spl0_22
  <=> group_element(e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f111,plain,
    ( spl0_8
  <=> group_element(e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f127,plain,
    ( spl0_12
  <=> product(e_3,e_1,e_4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f961,plain,
    ( ~ group_element(e_1)
    | ~ group_element(e_3)
    | equalish(e_4,e_3)
    | product(e_3,e_3,e_1)
    | product(e_1,e_3,e_1)
    | product(e_2,e_3,e_1)
    | ~ spl0_12 ),
    inference(resolution,[],[f129,f80]) ).

fof(f80,plain,
    ! [X0,X1] :
      ( ~ product(X0,X1,e_4)
      | ~ group_element(X1)
      | ~ group_element(X0)
      | equalish(e_4,X0)
      | product(e_3,X0,X1)
      | product(e_1,X0,X1)
      | product(e_2,X0,X1) ),
    inference(resolution,[],[f78,f23]) ).

fof(f23,axiom,
    ! [X0] : product(X0,X0,X0),
    file('/export/starexec/sandbox2/tmp/tmp.2b1NMynG8x/Vampire---4.8_3784',product_idempotence) ).

fof(f78,plain,
    ! [X2,X0,X1] :
      ( ~ product(e_4,e_4,X2)
      | product(e_1,X0,X1)
      | ~ group_element(X1)
      | ~ group_element(X0)
      | equalish(e_4,X0)
      | product(e_3,X0,X1)
      | ~ product(X0,X1,X2)
      | product(e_2,X0,X1) ),
    inference(resolution,[],[f41,f23]) ).

fof(f41,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ product(e_4,X2,X3)
      | product(e_2,X0,X1)
      | product(e_1,X0,X1)
      | ~ group_element(X1)
      | ~ group_element(X0)
      | equalish(X2,X0)
      | product(e_3,X0,X1)
      | ~ product(X0,X1,X4)
      | ~ product(X2,X3,X4) ),
    inference(resolution,[],[f1,f24]) ).

fof(f24,axiom,
    ! [X8,X6,X9,X7,X4,X5] :
      ( ~ product(X9,X7,X8)
      | equalish(X4,X7)
      | ~ product(X9,X4,X5)
      | ~ product(X7,X8,X6)
      | ~ product(X4,X5,X6) ),
    file('/export/starexec/sandbox2/tmp/tmp.2b1NMynG8x/Vampire---4.8_3784',qg2_1) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( product(e_4,X0,X1)
      | product(e_3,X0,X1)
      | product(e_2,X0,X1)
      | product(e_1,X0,X1)
      | ~ group_element(X1)
      | ~ group_element(X0) ),
    file('/export/starexec/sandbox2/tmp/tmp.2b1NMynG8x/Vampire---4.8_3784',row_surjectivity) ).

fof(f129,plain,
    ( product(e_3,e_1,e_4)
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f127]) ).

fof(f959,plain,
    ( spl0_40
    | spl0_39
    | spl0_38
    | spl0_52
    | ~ spl0_15
    | ~ spl0_22
    | ~ spl0_27 ),
    inference(avatar_split_clause,[],[f950,f189,f169,f140,f353,f262,f266,f270]) ).

fof(f270,plain,
    ( spl0_40
  <=> product(e_2,e_2,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f266,plain,
    ( spl0_39
  <=> product(e_1,e_2,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f262,plain,
    ( spl0_38
  <=> product(e_3,e_2,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f353,plain,
    ( spl0_52
  <=> equalish(e_4,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f140,plain,
    ( spl0_15
  <=> group_element(e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f189,plain,
    ( spl0_27
  <=> product(e_2,e_3,e_4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f950,plain,
    ( ~ group_element(e_3)
    | ~ group_element(e_2)
    | equalish(e_4,e_2)
    | product(e_3,e_2,e_3)
    | product(e_1,e_2,e_3)
    | product(e_2,e_2,e_3)
    | ~ spl0_27 ),
    inference(resolution,[],[f191,f80]) ).

fof(f191,plain,
    ( product(e_2,e_3,e_4)
    | ~ spl0_27 ),
    inference(avatar_component_clause,[],[f189]) ).

fof(f948,plain,
    ( ~ spl0_19
    | spl0_36
    | ~ spl0_25 ),
    inference(avatar_split_clause,[],[f947,f181,f254,f156]) ).

fof(f156,plain,
    ( spl0_19
  <=> product(e_3,e_2,e_4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f254,plain,
    ( spl0_36
  <=> equalish(e_2,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f181,plain,
    ( spl0_25
  <=> product(e_2,e_4,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f947,plain,
    ( equalish(e_2,e_3)
    | ~ product(e_3,e_2,e_4)
    | ~ spl0_25 ),
    inference(resolution,[],[f183,f29]) ).

fof(f29,plain,
    ! [X2,X0,X1] :
      ( ~ product(X1,X2,X0)
      | equalish(X1,X0)
      | ~ product(X0,X1,X2) ),
    inference(resolution,[],[f27,f23]) ).

fof(f27,plain,
    ! [X2,X3,X0,X1] :
      ( ~ product(X1,X1,X3)
      | ~ product(X1,X0,X2)
      | equalish(X0,X1)
      | ~ product(X0,X2,X3) ),
    inference(resolution,[],[f23,f24]) ).

fof(f183,plain,
    ( product(e_2,e_4,e_3)
    | ~ spl0_25 ),
    inference(avatar_component_clause,[],[f181]) ).

fof(f938,plain,
    ( ~ spl0_65
    | spl0_41
    | ~ spl0_59 ),
    inference(avatar_split_clause,[],[f937,f408,f275,f469]) ).

fof(f275,plain,
    ( spl0_41
  <=> equalish(e_3,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f408,plain,
    ( spl0_59
  <=> product(e_3,e_1,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f937,plain,
    ( equalish(e_3,e_2)
    | ~ product(e_2,e_3,e_1)
    | ~ spl0_59 ),
    inference(resolution,[],[f410,f29]) ).

fof(f410,plain,
    ( product(e_3,e_1,e_2)
    | ~ spl0_59 ),
    inference(avatar_component_clause,[],[f408]) ).

fof(f930,plain,
    ( spl0_59
    | spl0_52
    | ~ spl0_8
    | ~ spl0_15
    | spl0_58
    | spl0_57
    | ~ spl0_11 ),
    inference(avatar_split_clause,[],[f882,f123,f400,f404,f140,f111,f353,f408]) ).

fof(f404,plain,
    ( spl0_58
  <=> product(e_1,e_1,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f400,plain,
    ( spl0_57
  <=> product(e_2,e_1,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

fof(f123,plain,
    ( spl0_11
  <=> product(e_2,e_4,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f882,plain,
    ( product(e_2,e_1,e_2)
    | product(e_1,e_1,e_2)
    | ~ group_element(e_2)
    | ~ group_element(e_1)
    | equalish(e_4,e_2)
    | product(e_3,e_1,e_2)
    | ~ spl0_11 ),
    inference(resolution,[],[f125,f44]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ~ product(X1,e_4,X0)
      | product(e_2,X0,X1)
      | product(e_1,X0,X1)
      | ~ group_element(X1)
      | ~ group_element(X0)
      | equalish(e_4,X1)
      | product(e_3,X0,X1) ),
    inference(resolution,[],[f1,f29]) ).

fof(f125,plain,
    ( product(e_2,e_4,e_1)
    | ~ spl0_11 ),
    inference(avatar_component_clause,[],[f123]) ).

fof(f929,plain,
    ( spl0_42
    | ~ spl0_58 ),
    inference(avatar_split_clause,[],[f922,f404,f289]) ).

fof(f289,plain,
    ( spl0_42
  <=> equalish(e_2,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f922,plain,
    ( equalish(e_2,e_1)
    | ~ spl0_58 ),
    inference(resolution,[],[f406,f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ~ product(X1,X1,X0)
      | equalish(X0,X1) ),
    inference(resolution,[],[f20,f23]) ).

fof(f20,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ product(X0,X1,X3)
      | equalish(X2,X3)
      | ~ product(X0,X1,X2) ),
    file('/export/starexec/sandbox2/tmp/tmp.2b1NMynG8x/Vampire---4.8_3784',product_total_function2) ).

fof(f406,plain,
    ( product(e_1,e_1,e_2)
    | ~ spl0_58 ),
    inference(avatar_component_clause,[],[f404]) ).

fof(f900,plain,
    ( spl0_34
    | spl0_33
    | spl0_31
    | spl0_45
    | ~ spl0_8
    | ~ spl0_22
    | ~ spl0_28 ),
    inference(avatar_split_clause,[],[f891,f193,f169,f111,f301,f219,f227,f231]) ).

fof(f231,plain,
    ( spl0_34
  <=> product(e_2,e_1,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f227,plain,
    ( spl0_33
  <=> product(e_1,e_1,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f219,plain,
    ( spl0_31
  <=> product(e_3,e_1,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f301,plain,
    ( spl0_45
  <=> equalish(e_4,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f193,plain,
    ( spl0_28
  <=> product(e_1,e_3,e_4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f891,plain,
    ( ~ group_element(e_3)
    | ~ group_element(e_1)
    | equalish(e_4,e_1)
    | product(e_3,e_1,e_3)
    | product(e_1,e_1,e_3)
    | product(e_2,e_1,e_3)
    | ~ spl0_28 ),
    inference(resolution,[],[f195,f80]) ).

fof(f195,plain,
    ( product(e_1,e_3,e_4)
    | ~ spl0_28 ),
    inference(avatar_component_clause,[],[f193]) ).

fof(f866,plain,
    ( spl0_45
    | ~ spl0_14 ),
    inference(avatar_split_clause,[],[f857,f135,f301]) ).

fof(f135,plain,
    ( spl0_14
  <=> product(e_1,e_1,e_4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f857,plain,
    ( equalish(e_4,e_1)
    | ~ spl0_14 ),
    inference(resolution,[],[f137,f32]) ).

fof(f137,plain,
    ( product(e_1,e_1,e_4)
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f135]) ).

fof(f846,plain,
    ( spl0_48
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f838,f400,f314]) ).

fof(f314,plain,
    ( spl0_48
  <=> equalish(e_1,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f838,plain,
    ( equalish(e_1,e_2)
    | ~ spl0_57 ),
    inference(resolution,[],[f402,f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ~ product(X1,X0,X1)
      | equalish(X0,X1) ),
    inference(resolution,[],[f21,f23]) ).

fof(f21,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ product(X0,X3,X1)
      | equalish(X2,X3)
      | ~ product(X0,X2,X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.2b1NMynG8x/Vampire---4.8_3784',product_right_cancellation) ).

fof(f402,plain,
    ( product(e_2,e_1,e_2)
    | ~ spl0_57 ),
    inference(avatar_component_clause,[],[f400]) ).

fof(f814,plain,
    ( ~ spl0_21
    | spl0_42
    | ~ spl0_11 ),
    inference(avatar_split_clause,[],[f809,f123,f289,f164]) ).

fof(f164,plain,
    ( spl0_21
  <=> product(e_1,e_2,e_4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f809,plain,
    ( equalish(e_2,e_1)
    | ~ product(e_1,e_2,e_4)
    | ~ spl0_11 ),
    inference(resolution,[],[f125,f29]) ).

fof(f800,plain,
    ( spl0_45
    | ~ spl0_10 ),
    inference(avatar_split_clause,[],[f791,f119,f301]) ).

fof(f119,plain,
    ( spl0_10
  <=> product(e_1,e_4,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f791,plain,
    ( equalish(e_4,e_1)
    | ~ spl0_10 ),
    inference(resolution,[],[f121,f33]) ).

fof(f121,plain,
    ( product(e_1,e_4,e_1)
    | ~ spl0_10 ),
    inference(avatar_component_clause,[],[f119]) ).

fof(f788,plain,
    ( ~ spl0_50
    | spl0_35
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f787,f297,f236,f345]) ).

fof(f345,plain,
    ( spl0_50
  <=> product(e_1,e_3,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f236,plain,
    ( spl0_35
  <=> equalish(e_3,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f297,plain,
    ( spl0_44
  <=> product(e_3,e_2,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f787,plain,
    ( equalish(e_3,e_1)
    | ~ product(e_1,e_3,e_2)
    | ~ spl0_44 ),
    inference(resolution,[],[f299,f29]) ).

fof(f299,plain,
    ( product(e_3,e_2,e_1)
    | ~ spl0_44 ),
    inference(avatar_component_clause,[],[f297]) ).

fof(f775,plain,
    ( spl0_47
    | spl0_46
    | spl0_44
    | spl0_52
    | ~ spl0_15
    | ~ spl0_8
    | ~ spl0_13 ),
    inference(avatar_split_clause,[],[f766,f131,f111,f140,f353,f297,f305,f309]) ).

fof(f309,plain,
    ( spl0_47
  <=> product(e_2,e_2,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f305,plain,
    ( spl0_46
  <=> product(e_1,e_2,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f131,plain,
    ( spl0_13
  <=> product(e_2,e_1,e_4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f766,plain,
    ( ~ group_element(e_1)
    | ~ group_element(e_2)
    | equalish(e_4,e_2)
    | product(e_3,e_2,e_1)
    | product(e_1,e_2,e_1)
    | product(e_2,e_2,e_1)
    | ~ spl0_13 ),
    inference(resolution,[],[f133,f80]) ).

fof(f133,plain,
    ( product(e_2,e_1,e_4)
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f131]) ).

fof(f737,plain,
    ~ spl0_52,
    inference(avatar_contradiction_clause,[],[f736]) ).

fof(f736,plain,
    ( $false
    | ~ spl0_52 ),
    inference(resolution,[],[f355,f17]) ).

fof(f17,axiom,
    ~ equalish(e_4,e_2),
    file('/export/starexec/sandbox2/tmp/tmp.2b1NMynG8x/Vampire---4.8_3784',e_4_is_not_e_2) ).

fof(f355,plain,
    ( equalish(e_4,e_2)
    | ~ spl0_52 ),
    inference(avatar_component_clause,[],[f353]) ).

fof(f735,plain,
    ( spl0_36
    | ~ spl0_51 ),
    inference(avatar_split_clause,[],[f728,f349,f254]) ).

fof(f349,plain,
    ( spl0_51
  <=> product(e_3,e_3,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f728,plain,
    ( equalish(e_2,e_3)
    | ~ spl0_51 ),
    inference(resolution,[],[f351,f32]) ).

fof(f351,plain,
    ( product(e_3,e_3,e_2)
    | ~ spl0_51 ),
    inference(avatar_component_clause,[],[f349]) ).

fof(f720,plain,
    ~ spl0_48,
    inference(avatar_contradiction_clause,[],[f719]) ).

fof(f719,plain,
    ( $false
    | ~ spl0_48 ),
    inference(resolution,[],[f316,f7]) ).

fof(f7,axiom,
    ~ equalish(e_1,e_2),
    file('/export/starexec/sandbox2/tmp/tmp.2b1NMynG8x/Vampire---4.8_3784',e_1_is_not_e_2) ).

fof(f316,plain,
    ( equalish(e_1,e_2)
    | ~ spl0_48 ),
    inference(avatar_component_clause,[],[f314]) ).

fof(f718,plain,
    ( ~ spl0_34
    | spl0_48
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f717,f345,f314,f231]) ).

fof(f717,plain,
    ( equalish(e_1,e_2)
    | ~ product(e_2,e_1,e_3)
    | ~ spl0_50 ),
    inference(resolution,[],[f347,f29]) ).

fof(f347,plain,
    ( product(e_1,e_3,e_2)
    | ~ spl0_50 ),
    inference(avatar_component_clause,[],[f345]) ).

fof(f710,plain,
    ( spl0_49
    | spl0_50
    | spl0_51
    | spl0_52
    | ~ spl0_22
    | ~ spl0_15
    | ~ spl0_19 ),
    inference(avatar_split_clause,[],[f691,f156,f140,f169,f353,f349,f345,f341]) ).

fof(f341,plain,
    ( spl0_49
  <=> product(e_2,e_3,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f691,plain,
    ( ~ group_element(e_2)
    | ~ group_element(e_3)
    | equalish(e_4,e_2)
    | product(e_3,e_3,e_2)
    | product(e_1,e_3,e_2)
    | product(e_2,e_3,e_2)
    | ~ spl0_19 ),
    inference(resolution,[],[f158,f94]) ).

fof(f94,plain,
    ! [X0,X1] :
      ( ~ product(X0,X1,e_4)
      | ~ group_element(X1)
      | ~ group_element(X0)
      | equalish(e_4,X1)
      | product(e_3,X0,X1)
      | product(e_1,X0,X1)
      | product(e_2,X0,X1) ),
    inference(resolution,[],[f92,f23]) ).

fof(f92,plain,
    ! [X2,X0,X1] :
      ( ~ product(e_4,e_4,X2)
      | product(e_1,X0,X1)
      | ~ group_element(X1)
      | ~ group_element(X0)
      | equalish(e_4,X1)
      | product(e_3,X0,X1)
      | ~ product(X0,X1,X2)
      | product(e_2,X0,X1) ),
    inference(resolution,[],[f42,f23]) ).

fof(f42,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ product(e_4,X3,X2)
      | product(e_2,X0,X1)
      | product(e_1,X0,X1)
      | ~ group_element(X1)
      | ~ group_element(X0)
      | equalish(X2,X1)
      | product(e_3,X0,X1)
      | ~ product(X0,X1,X4)
      | ~ product(X3,X2,X4) ),
    inference(resolution,[],[f1,f25]) ).

fof(f25,axiom,
    ! [X8,X6,X9,X7,X4,X5] :
      ( ~ product(X9,X7,X8)
      | equalish(X5,X8)
      | ~ product(X9,X4,X5)
      | ~ product(X7,X8,X6)
      | ~ product(X4,X5,X6) ),
    file('/export/starexec/sandbox2/tmp/tmp.2b1NMynG8x/Vampire---4.8_3784',qg2_2) ).

fof(f158,plain,
    ( product(e_3,e_2,e_4)
    | ~ spl0_19 ),
    inference(avatar_component_clause,[],[f156]) ).

fof(f708,plain,
    ( spl0_41
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f700,f341,f275]) ).

fof(f700,plain,
    ( equalish(e_3,e_2)
    | ~ spl0_49 ),
    inference(resolution,[],[f343,f33]) ).

fof(f343,plain,
    ( product(e_2,e_3,e_2)
    | ~ spl0_49 ),
    inference(avatar_component_clause,[],[f341]) ).

fof(f690,plain,
    ( spl0_48
    | ~ spl0_47 ),
    inference(avatar_split_clause,[],[f683,f309,f314]) ).

fof(f683,plain,
    ( equalish(e_1,e_2)
    | ~ spl0_47 ),
    inference(resolution,[],[f311,f32]) ).

fof(f311,plain,
    ( product(e_2,e_2,e_1)
    | ~ spl0_47 ),
    inference(avatar_component_clause,[],[f309]) ).

fof(f675,plain,
    ( spl0_44
    | spl0_45
    | ~ spl0_15
    | ~ spl0_8
    | spl0_46
    | spl0_47
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f658,f148,f309,f305,f111,f140,f301,f297]) ).

fof(f148,plain,
    ( spl0_17
  <=> product(e_1,e_4,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f658,plain,
    ( product(e_2,e_2,e_1)
    | product(e_1,e_2,e_1)
    | ~ group_element(e_1)
    | ~ group_element(e_2)
    | equalish(e_4,e_1)
    | product(e_3,e_2,e_1)
    | ~ spl0_17 ),
    inference(resolution,[],[f150,f44]) ).

fof(f150,plain,
    ( product(e_1,e_4,e_2)
    | ~ spl0_17 ),
    inference(avatar_component_clause,[],[f148]) ).

fof(f674,plain,
    ( spl0_42
    | ~ spl0_46 ),
    inference(avatar_split_clause,[],[f666,f305,f289]) ).

fof(f666,plain,
    ( equalish(e_2,e_1)
    | ~ spl0_46 ),
    inference(resolution,[],[f307,f33]) ).

fof(f307,plain,
    ( product(e_1,e_2,e_1)
    | ~ spl0_46 ),
    inference(avatar_component_clause,[],[f305]) ).

fof(f656,plain,
    ( spl0_41
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f649,f270,f275]) ).

fof(f649,plain,
    ( equalish(e_3,e_2)
    | ~ spl0_40 ),
    inference(resolution,[],[f272,f32]) ).

fof(f272,plain,
    ( product(e_2,e_2,e_3)
    | ~ spl0_40 ),
    inference(avatar_component_clause,[],[f270]) ).

fof(f641,plain,
    ( ~ spl0_39
    | spl0_42
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f640,f469,f289,f266]) ).

fof(f640,plain,
    ( equalish(e_2,e_1)
    | ~ product(e_1,e_2,e_3)
    | ~ spl0_65 ),
    inference(resolution,[],[f471,f29]) ).

fof(f471,plain,
    ( product(e_2,e_3,e_1)
    | ~ spl0_65 ),
    inference(avatar_component_clause,[],[f469]) ).

fof(f633,plain,
    ( spl0_35
    | ~ spl0_64 ),
    inference(avatar_split_clause,[],[f625,f465,f236]) ).

fof(f625,plain,
    ( equalish(e_3,e_1)
    | ~ spl0_64 ),
    inference(resolution,[],[f467,f33]) ).

fof(f467,plain,
    ( product(e_1,e_3,e_1)
    | ~ spl0_64 ),
    inference(avatar_component_clause,[],[f465]) ).

fof(f624,plain,
    ( spl0_63
    | spl0_45
    | ~ spl0_22
    | ~ spl0_8
    | spl0_64
    | spl0_65
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f542,f177,f469,f465,f111,f169,f301,f461]) ).

fof(f177,plain,
    ( spl0_24
  <=> product(e_1,e_4,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f542,plain,
    ( product(e_2,e_3,e_1)
    | product(e_1,e_3,e_1)
    | ~ group_element(e_1)
    | ~ group_element(e_3)
    | equalish(e_4,e_1)
    | product(e_3,e_3,e_1)
    | ~ spl0_24 ),
    inference(resolution,[],[f179,f44]) ).

fof(f179,plain,
    ( product(e_1,e_4,e_3)
    | ~ spl0_24 ),
    inference(avatar_component_clause,[],[f177]) ).

fof(f623,plain,
    ( spl0_29
    | ~ spl0_63 ),
    inference(avatar_split_clause,[],[f616,f461,f211]) ).

fof(f211,plain,
    ( spl0_29
  <=> equalish(e_1,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f616,plain,
    ( equalish(e_1,e_3)
    | ~ spl0_63 ),
    inference(resolution,[],[f463,f32]) ).

fof(f463,plain,
    ( product(e_3,e_3,e_1)
    | ~ spl0_63 ),
    inference(avatar_component_clause,[],[f461]) ).

fof(f608,plain,
    ( ~ spl0_59
    | spl0_29
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f607,f266,f211,f408]) ).

fof(f607,plain,
    ( equalish(e_1,e_3)
    | ~ product(e_3,e_1,e_2)
    | ~ spl0_39 ),
    inference(resolution,[],[f268,f29]) ).

fof(f268,plain,
    ( product(e_1,e_2,e_3)
    | ~ spl0_39 ),
    inference(avatar_component_clause,[],[f266]) ).

fof(f600,plain,
    ( spl0_38
    | spl0_32
    | ~ spl0_15
    | ~ spl0_22
    | spl0_39
    | spl0_40
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f583,f144,f270,f266,f169,f140,f223,f262]) ).

fof(f144,plain,
    ( spl0_16
  <=> product(e_3,e_4,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f583,plain,
    ( product(e_2,e_2,e_3)
    | product(e_1,e_2,e_3)
    | ~ group_element(e_3)
    | ~ group_element(e_2)
    | equalish(e_4,e_3)
    | product(e_3,e_2,e_3)
    | ~ spl0_16 ),
    inference(resolution,[],[f146,f44]) ).

fof(f146,plain,
    ( product(e_3,e_4,e_2)
    | ~ spl0_16 ),
    inference(avatar_component_clause,[],[f144]) ).

fof(f599,plain,
    ( spl0_36
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f591,f262,f254]) ).

fof(f591,plain,
    ( equalish(e_2,e_3)
    | ~ spl0_38 ),
    inference(resolution,[],[f264,f33]) ).

fof(f264,plain,
    ( product(e_3,e_2,e_3)
    | ~ spl0_38 ),
    inference(avatar_component_clause,[],[f262]) ).

fof(f581,plain,
    ( ~ spl0_44
    | spl0_36
    | ~ spl0_34 ),
    inference(avatar_split_clause,[],[f580,f231,f254,f297]) ).

fof(f580,plain,
    ( equalish(e_2,e_3)
    | ~ product(e_3,e_2,e_1)
    | ~ spl0_34 ),
    inference(resolution,[],[f233,f29]) ).

fof(f233,plain,
    ( product(e_2,e_1,e_3)
    | ~ spl0_34 ),
    inference(avatar_component_clause,[],[f231]) ).

fof(f573,plain,
    ( spl0_35
    | ~ spl0_33 ),
    inference(avatar_split_clause,[],[f566,f227,f236]) ).

fof(f566,plain,
    ( equalish(e_3,e_1)
    | ~ spl0_33 ),
    inference(resolution,[],[f229,f32]) ).

fof(f229,plain,
    ( product(e_1,e_1,e_3)
    | ~ spl0_33 ),
    inference(avatar_component_clause,[],[f227]) ).

fof(f558,plain,
    ( spl0_29
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f550,f219,f211]) ).

fof(f550,plain,
    ( equalish(e_1,e_3)
    | ~ spl0_31 ),
    inference(resolution,[],[f221,f33]) ).

fof(f221,plain,
    ( product(e_3,e_1,e_3)
    | ~ spl0_31 ),
    inference(avatar_component_clause,[],[f219]) ).

fof(f540,plain,
    ~ spl0_45,
    inference(avatar_contradiction_clause,[],[f539]) ).

fof(f539,plain,
    ( $false
    | ~ spl0_45 ),
    inference(resolution,[],[f303,f16]) ).

fof(f16,axiom,
    ~ equalish(e_4,e_1),
    file('/export/starexec/sandbox2/tmp/tmp.2b1NMynG8x/Vampire---4.8_3784',e_4_is_not_e_1) ).

fof(f303,plain,
    ( equalish(e_4,e_1)
    | ~ spl0_45 ),
    inference(avatar_component_clause,[],[f301]) ).

fof(f513,plain,
    ~ spl0_42,
    inference(avatar_contradiction_clause,[],[f512]) ).

fof(f512,plain,
    ( $false
    | ~ spl0_42 ),
    inference(resolution,[],[f291,f10]) ).

fof(f10,axiom,
    ~ equalish(e_2,e_1),
    file('/export/starexec/sandbox2/tmp/tmp.2b1NMynG8x/Vampire---4.8_3784',e_2_is_not_e_1) ).

fof(f291,plain,
    ( equalish(e_2,e_1)
    | ~ spl0_42 ),
    inference(avatar_component_clause,[],[f289]) ).

fof(f511,plain,
    ~ spl0_41,
    inference(avatar_contradiction_clause,[],[f510]) ).

fof(f510,plain,
    ( $false
    | ~ spl0_41 ),
    inference(resolution,[],[f277,f14]) ).

fof(f14,axiom,
    ~ equalish(e_3,e_2),
    file('/export/starexec/sandbox2/tmp/tmp.2b1NMynG8x/Vampire---4.8_3784',e_3_is_not_e_2) ).

fof(f277,plain,
    ( equalish(e_3,e_2)
    | ~ spl0_41 ),
    inference(avatar_component_clause,[],[f275]) ).

fof(f509,plain,
    ( ~ spl0_27
    | spl0_41
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f434,f144,f275,f189]) ).

fof(f434,plain,
    ( equalish(e_3,e_2)
    | ~ product(e_2,e_3,e_4)
    | ~ spl0_16 ),
    inference(resolution,[],[f146,f29]) ).

fof(f508,plain,
    ~ spl0_35,
    inference(avatar_contradiction_clause,[],[f507]) ).

fof(f507,plain,
    ( $false
    | ~ spl0_35 ),
    inference(resolution,[],[f238,f13]) ).

fof(f13,axiom,
    ~ equalish(e_3,e_1),
    file('/export/starexec/sandbox2/tmp/tmp.2b1NMynG8x/Vampire---4.8_3784',e_3_is_not_e_1) ).

fof(f238,plain,
    ( equalish(e_3,e_1)
    | ~ spl0_35 ),
    inference(avatar_component_clause,[],[f236]) ).

fof(f506,plain,
    ( spl0_32
    | ~ spl0_26 ),
    inference(avatar_split_clause,[],[f497,f185,f223]) ).

fof(f185,plain,
    ( spl0_26
  <=> product(e_3,e_3,e_4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f497,plain,
    ( equalish(e_4,e_3)
    | ~ spl0_26 ),
    inference(resolution,[],[f187,f32]) ).

fof(f187,plain,
    ( product(e_3,e_3,e_4)
    | ~ spl0_26 ),
    inference(avatar_component_clause,[],[f185]) ).

fof(f487,plain,
    ( spl0_51
    | spl0_52
    | ~ spl0_22
    | ~ spl0_15
    | spl0_50
    | spl0_49
    | ~ spl0_25 ),
    inference(avatar_split_clause,[],[f475,f181,f341,f345,f140,f169,f353,f349]) ).

fof(f475,plain,
    ( product(e_2,e_3,e_2)
    | product(e_1,e_3,e_2)
    | ~ group_element(e_2)
    | ~ group_element(e_3)
    | equalish(e_4,e_2)
    | product(e_3,e_3,e_2)
    | ~ spl0_25 ),
    inference(resolution,[],[f183,f44]) ).

fof(f473,plain,
    ( ~ spl0_12
    | spl0_29
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f455,f177,f211,f127]) ).

fof(f455,plain,
    ( equalish(e_1,e_3)
    | ~ product(e_3,e_1,e_4)
    | ~ spl0_24 ),
    inference(resolution,[],[f179,f29]) ).

fof(f446,plain,
    ( spl0_32
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f437,f173,f223]) ).

fof(f173,plain,
    ( spl0_23
  <=> product(e_3,e_4,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f437,plain,
    ( equalish(e_4,e_3)
    | ~ spl0_23 ),
    inference(resolution,[],[f175,f33]) ).

fof(f175,plain,
    ( product(e_3,e_4,e_3)
    | ~ spl0_23 ),
    inference(avatar_component_clause,[],[f173]) ).

fof(f425,plain,
    ~ spl0_36,
    inference(avatar_contradiction_clause,[],[f424]) ).

fof(f424,plain,
    ( $false
    | ~ spl0_36 ),
    inference(resolution,[],[f256,f11]) ).

fof(f11,axiom,
    ~ equalish(e_2,e_3),
    file('/export/starexec/sandbox2/tmp/tmp.2b1NMynG8x/Vampire---4.8_3784',e_2_is_not_e_3) ).

fof(f256,plain,
    ( equalish(e_2,e_3)
    | ~ spl0_36 ),
    inference(avatar_component_clause,[],[f254]) ).

fof(f423,plain,
    ~ spl0_32,
    inference(avatar_contradiction_clause,[],[f422]) ).

fof(f422,plain,
    ( $false
    | ~ spl0_32 ),
    inference(resolution,[],[f225,f18]) ).

fof(f18,axiom,
    ~ equalish(e_4,e_3),
    file('/export/starexec/sandbox2/tmp/tmp.2b1NMynG8x/Vampire---4.8_3784',e_4_is_not_e_3) ).

fof(f225,plain,
    ( equalish(e_4,e_3)
    | ~ spl0_32 ),
    inference(avatar_component_clause,[],[f223]) ).

fof(f412,plain,
    ( spl0_57
    | spl0_58
    | spl0_59
    | spl0_45
    | ~ spl0_8
    | ~ spl0_15
    | ~ spl0_21 ),
    inference(avatar_split_clause,[],[f391,f164,f140,f111,f301,f408,f404,f400]) ).

fof(f391,plain,
    ( ~ group_element(e_2)
    | ~ group_element(e_1)
    | equalish(e_4,e_1)
    | product(e_3,e_1,e_2)
    | product(e_1,e_1,e_2)
    | product(e_2,e_1,e_2)
    | ~ spl0_21 ),
    inference(resolution,[],[f166,f80]) ).

fof(f166,plain,
    ( product(e_1,e_2,e_4)
    | ~ spl0_21 ),
    inference(avatar_component_clause,[],[f164]) ).

fof(f389,plain,
    ( spl0_52
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f376,f160,f353]) ).

fof(f160,plain,
    ( spl0_20
  <=> product(e_2,e_2,e_4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f376,plain,
    ( equalish(e_4,e_2)
    | ~ spl0_20 ),
    inference(resolution,[],[f162,f32]) ).

fof(f162,plain,
    ( product(e_2,e_2,e_4)
    | ~ spl0_20 ),
    inference(avatar_component_clause,[],[f160]) ).

fof(f330,plain,
    ~ spl0_18,
    inference(avatar_contradiction_clause,[],[f329]) ).

fof(f329,plain,
    ( $false
    | ~ spl0_18 ),
    inference(resolution,[],[f320,f17]) ).

fof(f320,plain,
    ( equalish(e_4,e_2)
    | ~ spl0_18 ),
    inference(resolution,[],[f154,f33]) ).

fof(f154,plain,
    ( product(e_2,e_4,e_2)
    | ~ spl0_18 ),
    inference(avatar_component_clause,[],[f152]) ).

fof(f152,plain,
    ( spl0_18
  <=> product(e_2,e_4,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f317,plain,
    ( ~ spl0_13
    | spl0_48
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f287,f148,f314,f131]) ).

fof(f287,plain,
    ( equalish(e_1,e_2)
    | ~ product(e_2,e_1,e_4)
    | ~ spl0_17 ),
    inference(resolution,[],[f150,f29]) ).

fof(f243,plain,
    ~ spl0_29,
    inference(avatar_contradiction_clause,[],[f242]) ).

fof(f242,plain,
    ( $false
    | ~ spl0_29 ),
    inference(resolution,[],[f213,f8]) ).

fof(f8,axiom,
    ~ equalish(e_1,e_3),
    file('/export/starexec/sandbox2/tmp/tmp.2b1NMynG8x/Vampire---4.8_3784',e_1_is_not_e_3) ).

fof(f213,plain,
    ( equalish(e_1,e_3)
    | ~ spl0_29 ),
    inference(avatar_component_clause,[],[f211]) ).

fof(f241,plain,
    spl0_8,
    inference(avatar_contradiction_clause,[],[f240]) ).

fof(f240,plain,
    ( $false
    | spl0_8 ),
    inference(resolution,[],[f113,f3]) ).

fof(f3,axiom,
    group_element(e_1),
    file('/export/starexec/sandbox2/tmp/tmp.2b1NMynG8x/Vampire---4.8_3784',element_1) ).

fof(f113,plain,
    ( ~ group_element(e_1)
    | spl0_8 ),
    inference(avatar_component_clause,[],[f111]) ).

fof(f239,plain,
    ( ~ spl0_28
    | spl0_35
    | ~ spl0_9 ),
    inference(avatar_split_clause,[],[f209,f115,f236,f193]) ).

fof(f115,plain,
    ( spl0_9
  <=> product(e_3,e_4,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f209,plain,
    ( equalish(e_3,e_1)
    | ~ product(e_1,e_3,e_4)
    | ~ spl0_9 ),
    inference(resolution,[],[f117,f29]) ).

fof(f117,plain,
    ( product(e_3,e_4,e_1)
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f115]) ).

fof(f234,plain,
    ( spl0_31
    | spl0_32
    | ~ spl0_8
    | ~ spl0_22
    | spl0_33
    | spl0_34
    | ~ spl0_9 ),
    inference(avatar_split_clause,[],[f202,f115,f231,f227,f169,f111,f223,f219]) ).

fof(f202,plain,
    ( product(e_2,e_1,e_3)
    | product(e_1,e_1,e_3)
    | ~ group_element(e_3)
    | ~ group_element(e_1)
    | equalish(e_4,e_3)
    | product(e_3,e_1,e_3)
    | ~ spl0_9 ),
    inference(resolution,[],[f117,f44]) ).

fof(f200,plain,
    spl0_22,
    inference(avatar_contradiction_clause,[],[f199]) ).

fof(f199,plain,
    ( $false
    | spl0_22 ),
    inference(resolution,[],[f171,f5]) ).

fof(f5,axiom,
    group_element(e_3),
    file('/export/starexec/sandbox2/tmp/tmp.2b1NMynG8x/Vampire---4.8_3784',element_3) ).

fof(f171,plain,
    ( ~ group_element(e_3)
    | spl0_22 ),
    inference(avatar_component_clause,[],[f169]) ).

fof(f198,plain,
    spl0_15,
    inference(avatar_contradiction_clause,[],[f197]) ).

fof(f197,plain,
    ( $false
    | spl0_15 ),
    inference(resolution,[],[f142,f4]) ).

fof(f4,axiom,
    group_element(e_2),
    file('/export/starexec/sandbox2/tmp/tmp.2b1NMynG8x/Vampire---4.8_3784',element_2) ).

fof(f142,plain,
    ( ~ group_element(e_2)
    | spl0_15 ),
    inference(avatar_component_clause,[],[f140]) ).

fof(f196,plain,
    ( ~ spl0_22
    | spl0_23
    | spl0_24
    | spl0_25
    | spl0_26
    | spl0_27
    | spl0_28
    | ~ spl0_7 ),
    inference(avatar_split_clause,[],[f109,f104,f193,f189,f185,f181,f177,f173,f169]) ).

fof(f104,plain,
    ( spl0_7
  <=> ! [X0] :
        ( ~ group_element(X0)
        | product(e_1,X0,e_4)
        | product(e_2,X0,e_4)
        | product(e_3,X0,e_4)
        | product(e_2,e_4,X0)
        | product(e_1,e_4,X0)
        | product(e_3,e_4,X0)
        | equalish(e_4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f109,plain,
    ( product(e_1,e_3,e_4)
    | product(e_2,e_3,e_4)
    | product(e_3,e_3,e_4)
    | product(e_2,e_4,e_3)
    | product(e_1,e_4,e_3)
    | product(e_3,e_4,e_3)
    | ~ group_element(e_3)
    | ~ spl0_7 ),
    inference(resolution,[],[f105,f18]) ).

fof(f105,plain,
    ( ! [X0] :
        ( equalish(e_4,X0)
        | product(e_1,X0,e_4)
        | product(e_2,X0,e_4)
        | product(e_3,X0,e_4)
        | product(e_2,e_4,X0)
        | product(e_1,e_4,X0)
        | product(e_3,e_4,X0)
        | ~ group_element(X0) )
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f104]) ).

fof(f167,plain,
    ( ~ spl0_15
    | spl0_16
    | spl0_17
    | spl0_18
    | spl0_19
    | spl0_20
    | spl0_21
    | ~ spl0_7 ),
    inference(avatar_split_clause,[],[f108,f104,f164,f160,f156,f152,f148,f144,f140]) ).

fof(f108,plain,
    ( product(e_1,e_2,e_4)
    | product(e_2,e_2,e_4)
    | product(e_3,e_2,e_4)
    | product(e_2,e_4,e_2)
    | product(e_1,e_4,e_2)
    | product(e_3,e_4,e_2)
    | ~ group_element(e_2)
    | ~ spl0_7 ),
    inference(resolution,[],[f105,f17]) ).

fof(f138,plain,
    ( ~ spl0_8
    | spl0_9
    | spl0_10
    | spl0_11
    | spl0_12
    | spl0_13
    | spl0_14
    | ~ spl0_7 ),
    inference(avatar_split_clause,[],[f107,f104,f135,f131,f127,f123,f119,f115,f111]) ).

fof(f107,plain,
    ( product(e_1,e_1,e_4)
    | product(e_2,e_1,e_4)
    | product(e_3,e_1,e_4)
    | product(e_2,e_4,e_1)
    | product(e_1,e_4,e_1)
    | product(e_3,e_4,e_1)
    | ~ group_element(e_1)
    | ~ spl0_7 ),
    inference(resolution,[],[f105,f16]) ).

fof(f106,plain,
    ( ~ spl0_1
    | spl0_7 ),
    inference(avatar_split_clause,[],[f101,f104,f53]) ).

fof(f53,plain,
    ( spl0_1
  <=> group_element(e_4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f101,plain,
    ! [X0] :
      ( ~ group_element(X0)
      | ~ group_element(e_4)
      | equalish(e_4,X0)
      | product(e_3,e_4,X0)
      | product(e_1,e_4,X0)
      | product(e_2,e_4,X0)
      | product(e_3,X0,e_4)
      | product(e_2,X0,e_4)
      | product(e_1,X0,e_4) ),
    inference(duplicate_literal_removal,[],[f100]) ).

fof(f100,plain,
    ! [X0] :
      ( ~ group_element(X0)
      | ~ group_element(e_4)
      | equalish(e_4,X0)
      | product(e_3,e_4,X0)
      | product(e_1,e_4,X0)
      | product(e_2,e_4,X0)
      | product(e_3,X0,e_4)
      | product(e_2,X0,e_4)
      | product(e_1,X0,e_4)
      | ~ group_element(e_4)
      | ~ group_element(X0) ),
    inference(resolution,[],[f94,f1]) ).

fof(f86,plain,
    spl0_1,
    inference(avatar_contradiction_clause,[],[f85]) ).

fof(f85,plain,
    ( $false
    | spl0_1 ),
    inference(resolution,[],[f55,f6]) ).

fof(f6,axiom,
    group_element(e_4),
    file('/export/starexec/sandbox2/tmp/tmp.2b1NMynG8x/Vampire---4.8_3784',element_4) ).

fof(f55,plain,
    ( ~ group_element(e_4)
    | spl0_1 ),
    inference(avatar_component_clause,[],[f53]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : GRP124-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.07/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.36  % Computer : n004.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Fri May  3 20:51:38 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  This is a CNF_UNS_EPR_NEQ_NHN problem
% 0.15/0.36  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.2b1NMynG8x/Vampire---4.8_3784
% 0.62/0.77  % (3943)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.62/0.77  % (3945)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.62/0.77  % (3946)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.62/0.77  % (3947)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.62/0.77  % (3949)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.62/0.77  % (3948)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.62/0.77  % (3944)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.62/0.77  % (3945)Refutation not found, incomplete strategy% (3945)------------------------------
% 0.62/0.77  % (3945)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.62/0.77  % (3946)Refutation not found, incomplete strategy% (3946)------------------------------
% 0.62/0.77  % (3946)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.62/0.77  % (3946)Termination reason: Refutation not found, incomplete strategy
% 0.62/0.77  
% 0.62/0.77  % (3946)Memory used [KB]: 949
% 0.62/0.77  % (3946)Time elapsed: 0.002 s
% 0.62/0.77  % (3946)Instructions burned: 2 (million)
% 0.62/0.77  % (3945)Termination reason: Refutation not found, incomplete strategy
% 0.62/0.77  
% 0.62/0.77  % (3945)Memory used [KB]: 948
% 0.62/0.77  % (3950)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.62/0.77  % (3948)Refutation not found, incomplete strategy% (3948)------------------------------
% 0.62/0.77  % (3948)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.62/0.77  % (3948)Termination reason: Refutation not found, incomplete strategy
% 0.62/0.77  
% 0.62/0.77  % (3948)Memory used [KB]: 949
% 0.62/0.77  % (3948)Time elapsed: 0.002 s
% 0.62/0.77  % (3948)Instructions burned: 2 (million)
% 0.62/0.77  % (3945)Time elapsed: 0.002 s
% 0.62/0.77  % (3945)Instructions burned: 2 (million)
% 0.62/0.77  % (3946)------------------------------
% 0.62/0.77  % (3946)------------------------------
% 0.62/0.77  % (3948)------------------------------
% 0.62/0.77  % (3948)------------------------------
% 0.62/0.77  % (3945)------------------------------
% 0.62/0.77  % (3945)------------------------------
% 0.62/0.77  % (3950)Refutation not found, incomplete strategy% (3950)------------------------------
% 0.62/0.77  % (3950)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.62/0.77  % (3950)Termination reason: Refutation not found, incomplete strategy
% 0.62/0.77  
% 0.62/0.77  % (3950)Memory used [KB]: 949
% 0.62/0.77  % (3950)Time elapsed: 0.002 s
% 0.62/0.77  % (3950)Instructions burned: 2 (million)
% 0.62/0.77  % (3943)Refutation not found, incomplete strategy% (3943)------------------------------
% 0.62/0.77  % (3943)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.62/0.77  % (3943)Termination reason: Refutation not found, incomplete strategy
% 0.62/0.77  
% 0.62/0.77  % (3943)Memory used [KB]: 974
% 0.62/0.77  % (3943)Time elapsed: 0.002 s
% 0.62/0.77  % (3943)Instructions burned: 4 (million)
% 0.62/0.77  % (3943)------------------------------
% 0.62/0.77  % (3943)------------------------------
% 0.62/0.77  % (3950)------------------------------
% 0.62/0.77  % (3950)------------------------------
% 0.62/0.77  % (3952)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on Vampire---4 for (2995ds/50Mi)
% 0.62/0.77  % (3951)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2995ds/55Mi)
% 0.62/0.77  % (3953)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/208Mi)
% 0.62/0.77  % (3954)lrs-1011_1:1_sil=4000:plsq=on:plsqr=32,1:sp=frequency:plsql=on:nwc=10.0:i=52:aac=none:afr=on:ss=axioms:er=filter:sgt=16:rawr=on:etr=on:lma=on_0 on Vampire---4 for (2995ds/52Mi)
% 0.62/0.77  % (3953)Refutation not found, incomplete strategy% (3953)------------------------------
% 0.62/0.77  % (3953)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.62/0.77  % (3953)Termination reason: Refutation not found, incomplete strategy
% 0.62/0.77  
% 0.62/0.77  % (3953)Memory used [KB]: 969
% 0.62/0.77  % (3953)Time elapsed: 0.003 s
% 0.62/0.77  % (3953)Instructions burned: 3 (million)
% 0.62/0.77  % (3953)------------------------------
% 0.62/0.77  % (3953)------------------------------
% 0.62/0.77  % (3951)Refutation not found, incomplete strategy% (3951)------------------------------
% 0.62/0.77  % (3951)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.62/0.77  % (3951)Termination reason: Refutation not found, incomplete strategy
% 0.62/0.77  
% 0.62/0.77  % (3951)Memory used [KB]: 1038
% 0.62/0.77  % (3951)Time elapsed: 0.004 s
% 0.62/0.77  % (3951)Instructions burned: 5 (million)
% 0.62/0.77  % (3951)------------------------------
% 0.62/0.77  % (3951)------------------------------
% 0.62/0.78  % (3956)lrs+1011_87677:1048576_sil=8000:sos=on:spb=non_intro:nwc=10.0:kmz=on:i=42:ep=RS:nm=0:ins=1:uhcvi=on:rawr=on:fde=unused:afp=2000:afq=1.444:plsq=on:nicw=on_0 on Vampire---4 for (2995ds/42Mi)
% 0.62/0.78  % (3955)lrs-1010_1:1_to=lpo:sil=2000:sp=reverse_arity:sos=on:urr=ec_only:i=518:sd=2:bd=off:ss=axioms:sgt=16_0 on Vampire---4 for (2995ds/518Mi)
% 0.62/0.78  % (3957)dis+1011_1258907:1048576_bsr=unit_only:to=lpo:drc=off:sil=2000:tgt=full:fde=none:sp=frequency:spb=goal:rnwc=on:nwc=6.70083:sac=on:newcnf=on:st=2:i=243:bs=unit_only:sd=3:afp=300:awrs=decay:awrsf=218:nm=16:ins=3:afq=3.76821:afr=on:ss=axioms:sgt=5:rawr=on:add=off:bsd=on_0 on Vampire---4 for (2995ds/243Mi)
% 0.62/0.78  % (3947)Instruction limit reached!
% 0.62/0.78  % (3947)------------------------------
% 0.62/0.78  % (3947)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.62/0.78  % (3947)Termination reason: Unknown
% 0.62/0.78  % (3947)Termination phase: Saturation
% 0.62/0.78  
% 0.62/0.78  % (3947)Memory used [KB]: 1141
% 0.62/0.78  % (3947)Time elapsed: 0.017 s
% 0.62/0.78  % (3947)Instructions burned: 35 (million)
% 0.62/0.78  % (3947)------------------------------
% 0.62/0.78  % (3947)------------------------------
% 0.62/0.78  % (3952)Instruction limit reached!
% 0.62/0.78  % (3952)------------------------------
% 0.62/0.78  % (3952)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.62/0.78  % (3952)Termination reason: Unknown
% 0.62/0.78  % (3952)Termination phase: Saturation
% 0.62/0.78  
% 0.62/0.78  % (3952)Memory used [KB]: 1197
% 0.62/0.78  % (3952)Time elapsed: 0.013 s
% 0.62/0.78  % (3952)Instructions burned: 52 (million)
% 0.62/0.78  % (3952)------------------------------
% 0.62/0.78  % (3952)------------------------------
% 0.62/0.79  % (3958)lrs+1011_2:9_sil=2000:lsd=10:newcnf=on:i=117:sd=2:awrs=decay:ss=included:amm=off:ep=R_0 on Vampire---4 for (2995ds/117Mi)
% 0.62/0.79  % (3959)dis+1011_11:1_sil=2000:avsq=on:i=143:avsqr=1,16:ep=RS:rawr=on:aac=none:lsd=100:mep=off:fde=none:newcnf=on:bsr=unit_only_0 on Vampire---4 for (2995ds/143Mi)
% 0.62/0.79  % (3944)First to succeed.
% 0.62/0.79  % (3944)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3942"
% 0.62/0.79  % (3944)Refutation found. Thanks to Tanya!
% 0.62/0.79  % SZS status Unsatisfiable for Vampire---4
% 0.62/0.79  % SZS output start Proof for Vampire---4
% See solution above
% 0.62/0.80  % (3944)------------------------------
% 0.62/0.80  % (3944)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.62/0.80  % (3944)Termination reason: Refutation
% 0.62/0.80  
% 0.62/0.80  % (3944)Memory used [KB]: 1327
% 0.62/0.80  % (3944)Time elapsed: 0.026 s
% 0.62/0.80  % (3944)Instructions burned: 45 (million)
% 0.62/0.80  % (3942)Success in time 0.423 s
% 0.62/0.80  % Vampire---4.8 exiting
%------------------------------------------------------------------------------