TSTP Solution File: GRP124-3.004 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GRP124-3.004 : TPTP v8.1.2. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n024.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 05:53:31 EDT 2024

% Result   : Unsatisfiable 0.17s 0.37s
% Output   : Refutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   58
% Syntax   : Number of formulae    :  211 (  36 unt;   0 def)
%            Number of atoms       :  467 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  461 ( 205   ~; 220   |;   0   &)
%                                         (  36 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   40 (  39 usr;  37 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :   44 (  44   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1022,plain,
    $false,
    inference(avatar_sat_refutation,[],[f138,f155,f172,f192,f213,f230,f247,f268,f285,f302,f317,f420,f440,f471,f500,f521,f571,f595,f608,f621,f633,f666,f676,f687,f708,f725,f750,f793,f806,f829,f857,f869,f886,f908,f957,f969,f982,f1017,f1021]) ).

fof(f1021,plain,
    ( ~ spl0_35
    | ~ spl0_26 ),
    inference(avatar_split_clause,[],[f1020,f215,f257]) ).

fof(f257,plain,
    ( spl0_35
  <=> product(e_1,e_3,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f215,plain,
    ( spl0_26
  <=> product(e_3,e_2,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f1020,plain,
    ( ~ product(e_1,e_3,e_2)
    | ~ spl0_26 ),
    inference(subsumption_resolution,[],[f988,f27]) ).

fof(f27,axiom,
    ~ equalish(e_1,e_3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).

fof(f988,plain,
    ( ~ product(e_1,e_3,e_2)
    | equalish(e_1,e_3)
    | ~ spl0_26 ),
    inference(resolution,[],[f217,f110]) ).

fof(f110,plain,
    ! [X2,X0,X1] :
      ( ~ product(X1,X2,X0)
      | ~ product(X0,X1,X2)
      | equalish(X0,X1) ),
    inference(resolution,[],[f98,f42]) ).

fof(f42,axiom,
    ! [X0] : product(X0,X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).

fof(f98,plain,
    ! [X2,X3,X0,X1] :
      ( ~ product(X0,X3,X3)
      | ~ product(X0,X1,X2)
      | ~ product(X1,X2,X3)
      | equalish(X3,X1) ),
    inference(resolution,[],[f43,f42]) ).

fof(f43,axiom,
    ! [X8,X6,X9,X7,X4,X5] :
      ( ~ product(X6,X7,X4)
      | ~ product(X5,X8,X9)
      | ~ product(X5,X6,X7)
      | ~ product(X8,X9,X4)
      | equalish(X6,X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg2_1) ).

fof(f217,plain,
    ( product(e_3,e_2,e_1)
    | ~ spl0_26 ),
    inference(avatar_component_clause,[],[f215]) ).

fof(f1017,plain,
    ( ~ spl0_24
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f1016,f270,f206]) ).

fof(f206,plain,
    ( spl0_24
  <=> product(e_1,e_2,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f270,plain,
    ( spl0_38
  <=> product(e_2,e_3,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f1016,plain,
    ( ~ product(e_1,e_2,e_3)
    | ~ spl0_38 ),
    inference(subsumption_resolution,[],[f1006,f26]) ).

fof(f26,axiom,
    ~ equalish(e_1,e_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).

fof(f1006,plain,
    ( ~ product(e_1,e_2,e_3)
    | equalish(e_1,e_2)
    | ~ spl0_38 ),
    inference(resolution,[],[f272,f110]) ).

fof(f272,plain,
    ( product(e_2,e_3,e_1)
    | ~ spl0_38 ),
    inference(avatar_component_clause,[],[f270]) ).

fof(f982,plain,
    ( ~ spl0_30
    | ~ spl0_11 ),
    inference(avatar_split_clause,[],[f981,f135,f232]) ).

fof(f232,plain,
    ( spl0_30
  <=> product(e_4,e_2,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f135,plain,
    ( spl0_11
  <=> product(e_2,e_1,e_4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f981,plain,
    ( ~ product(e_4,e_2,e_1)
    | ~ spl0_11 ),
    inference(subsumption_resolution,[],[f977,f35]) ).

fof(f35,axiom,
    ~ equalish(e_4,e_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_1) ).

fof(f977,plain,
    ( ~ product(e_4,e_2,e_1)
    | equalish(e_4,e_1)
    | ~ spl0_11 ),
    inference(resolution,[],[f137,f112]) ).

fof(f112,plain,
    ! [X2,X0,X1] :
      ( ~ product(X1,X2,X0)
      | ~ product(X0,X1,X2)
      | equalish(X0,X2) ),
    inference(resolution,[],[f99,f42]) ).

fof(f99,plain,
    ! [X2,X3,X0,X1] :
      ( ~ product(X0,X3,X3)
      | ~ product(X0,X1,X2)
      | ~ product(X1,X2,X3)
      | equalish(X3,X2) ),
    inference(resolution,[],[f44,f42]) ).

fof(f44,axiom,
    ! [X8,X6,X9,X7,X4,X5] :
      ( ~ product(X6,X7,X4)
      | ~ product(X5,X8,X9)
      | ~ product(X5,X6,X7)
      | ~ product(X8,X9,X4)
      | equalish(X7,X9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg2_2) ).

fof(f137,plain,
    ( product(e_2,e_1,e_4)
    | ~ spl0_11 ),
    inference(avatar_component_clause,[],[f135]) ).

fof(f969,plain,
    ~ spl0_44,
    inference(avatar_contradiction_clause,[],[f968]) ).

fof(f968,plain,
    ( $false
    | ~ spl0_44 ),
    inference(subsumption_resolution,[],[f967,f34]) ).

fof(f34,axiom,
    ~ equalish(e_3,e_4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_4) ).

fof(f967,plain,
    ( equalish(e_3,e_4)
    | ~ spl0_44 ),
    inference(resolution,[],[f297,f50]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( ~ product(X0,X1,X1)
      | equalish(X1,X0) ),
    inference(resolution,[],[f41,f42]) ).

fof(f41,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ product(X3,X1,X0)
      | ~ product(X2,X1,X0)
      | equalish(X3,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).

fof(f297,plain,
    ( product(e_4,e_3,e_3)
    | ~ spl0_44 ),
    inference(avatar_component_clause,[],[f295]) ).

fof(f295,plain,
    ( spl0_44
  <=> product(e_4,e_3,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f957,plain,
    ~ spl0_45,
    inference(avatar_contradiction_clause,[],[f956]) ).

fof(f956,plain,
    ( $false
    | ~ spl0_45 ),
    inference(subsumption_resolution,[],[f955,f37]) ).

fof(f37,axiom,
    ~ equalish(e_4,e_3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_3) ).

fof(f955,plain,
    ( equalish(e_4,e_3)
    | ~ spl0_45 ),
    inference(resolution,[],[f301,f48]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( ~ product(X0,X1,X0)
      | equalish(X0,X1) ),
    inference(resolution,[],[f40,f42]) ).

fof(f40,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ product(X0,X3,X1)
      | ~ product(X0,X2,X1)
      | equalish(X3,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).

fof(f301,plain,
    ( product(e_4,e_3,e_4)
    | ~ spl0_45 ),
    inference(avatar_component_clause,[],[f299]) ).

fof(f299,plain,
    ( spl0_45
  <=> product(e_4,e_3,e_4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f908,plain,
    ( ~ spl0_42
    | ~ spl0_15 ),
    inference(avatar_split_clause,[],[f907,f152,f287]) ).

fof(f287,plain,
    ( spl0_42
  <=> product(e_4,e_3,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f152,plain,
    ( spl0_15
  <=> product(e_3,e_1,e_4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f907,plain,
    ( ~ product(e_4,e_3,e_1)
    | ~ spl0_15 ),
    inference(subsumption_resolution,[],[f903,f35]) ).

fof(f903,plain,
    ( ~ product(e_4,e_3,e_1)
    | equalish(e_4,e_1)
    | ~ spl0_15 ),
    inference(resolution,[],[f154,f112]) ).

fof(f154,plain,
    ( product(e_3,e_1,e_4)
    | ~ spl0_15 ),
    inference(avatar_component_clause,[],[f152]) ).

fof(f886,plain,
    ( ~ spl0_32
    | ~ spl0_41 ),
    inference(avatar_split_clause,[],[f885,f282,f240]) ).

fof(f240,plain,
    ( spl0_32
  <=> product(e_4,e_2,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f282,plain,
    ( spl0_41
  <=> product(e_2,e_3,e_4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f885,plain,
    ( ~ product(e_4,e_2,e_3)
    | ~ spl0_41 ),
    inference(subsumption_resolution,[],[f875,f36]) ).

fof(f36,axiom,
    ~ equalish(e_4,e_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_2) ).

fof(f875,plain,
    ( ~ product(e_4,e_2,e_3)
    | equalish(e_4,e_2)
    | ~ spl0_41 ),
    inference(resolution,[],[f284,f110]) ).

fof(f284,plain,
    ( product(e_2,e_3,e_4)
    | ~ spl0_41 ),
    inference(avatar_component_clause,[],[f282]) ).

fof(f869,plain,
    ~ spl0_40,
    inference(avatar_contradiction_clause,[],[f868]) ).

fof(f868,plain,
    ( $false
    | ~ spl0_40 ),
    inference(subsumption_resolution,[],[f867,f33]) ).

fof(f33,axiom,
    ~ equalish(e_3,e_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).

fof(f867,plain,
    ( equalish(e_3,e_2)
    | ~ spl0_40 ),
    inference(resolution,[],[f280,f50]) ).

fof(f280,plain,
    ( product(e_2,e_3,e_3)
    | ~ spl0_40 ),
    inference(avatar_component_clause,[],[f278]) ).

fof(f278,plain,
    ( spl0_40
  <=> product(e_2,e_3,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f857,plain,
    ~ spl0_39,
    inference(avatar_contradiction_clause,[],[f856]) ).

fof(f856,plain,
    ( $false
    | ~ spl0_39 ),
    inference(subsumption_resolution,[],[f855,f30]) ).

fof(f30,axiom,
    ~ equalish(e_2,e_3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).

fof(f855,plain,
    ( equalish(e_2,e_3)
    | ~ spl0_39 ),
    inference(resolution,[],[f276,f48]) ).

fof(f276,plain,
    ( product(e_2,e_3,e_2)
    | ~ spl0_39 ),
    inference(avatar_component_clause,[],[f274]) ).

fof(f274,plain,
    ( spl0_39
  <=> product(e_2,e_3,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f829,plain,
    ~ spl0_33,
    inference(avatar_contradiction_clause,[],[f828]) ).

fof(f828,plain,
    ( $false
    | ~ spl0_33 ),
    inference(subsumption_resolution,[],[f827,f36]) ).

fof(f827,plain,
    ( equalish(e_4,e_2)
    | ~ spl0_33 ),
    inference(resolution,[],[f246,f48]) ).

fof(f246,plain,
    ( product(e_4,e_2,e_4)
    | ~ spl0_33 ),
    inference(avatar_component_clause,[],[f244]) ).

fof(f244,plain,
    ( spl0_33
  <=> product(e_4,e_2,e_4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f806,plain,
    ( ~ spl0_18
    | ~ spl0_37 ),
    inference(avatar_contradiction_clause,[],[f805]) ).

fof(f805,plain,
    ( $false
    | ~ spl0_18
    | ~ spl0_37 ),
    inference(subsumption_resolution,[],[f804,f37]) ).

fof(f804,plain,
    ( equalish(e_4,e_3)
    | ~ spl0_18
    | ~ spl0_37 ),
    inference(subsumption_resolution,[],[f800,f167]) ).

fof(f167,plain,
    ( product(e_4,e_1,e_3)
    | ~ spl0_18 ),
    inference(avatar_component_clause,[],[f165]) ).

fof(f165,plain,
    ( spl0_18
  <=> product(e_4,e_1,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f800,plain,
    ( ~ product(e_4,e_1,e_3)
    | equalish(e_4,e_3)
    | ~ spl0_37 ),
    inference(resolution,[],[f267,f112]) ).

fof(f267,plain,
    ( product(e_1,e_3,e_4)
    | ~ spl0_37 ),
    inference(avatar_component_clause,[],[f265]) ).

fof(f265,plain,
    ( spl0_37
  <=> product(e_1,e_3,e_4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f793,plain,
    ~ spl0_36,
    inference(avatar_contradiction_clause,[],[f792]) ).

fof(f792,plain,
    ( $false
    | ~ spl0_36 ),
    inference(subsumption_resolution,[],[f791,f32]) ).

fof(f32,axiom,
    ~ equalish(e_3,e_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).

fof(f791,plain,
    ( equalish(e_3,e_1)
    | ~ spl0_36 ),
    inference(resolution,[],[f263,f50]) ).

fof(f263,plain,
    ( product(e_1,e_3,e_3)
    | ~ spl0_36 ),
    inference(avatar_component_clause,[],[f261]) ).

fof(f261,plain,
    ( spl0_36
  <=> product(e_1,e_3,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f750,plain,
    ~ spl0_31,
    inference(avatar_contradiction_clause,[],[f749]) ).

fof(f749,plain,
    ( $false
    | ~ spl0_31 ),
    inference(subsumption_resolution,[],[f748,f31]) ).

fof(f31,axiom,
    ~ equalish(e_2,e_4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_4) ).

fof(f748,plain,
    ( equalish(e_2,e_4)
    | ~ spl0_31 ),
    inference(resolution,[],[f238,f50]) ).

fof(f238,plain,
    ( product(e_4,e_2,e_2)
    | ~ spl0_31 ),
    inference(avatar_component_clause,[],[f236]) ).

fof(f236,plain,
    ( spl0_31
  <=> product(e_4,e_2,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f725,plain,
    ( ~ spl0_10
    | ~ spl0_35 ),
    inference(avatar_split_clause,[],[f724,f257,f131]) ).

fof(f131,plain,
    ( spl0_10
  <=> product(e_2,e_1,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f724,plain,
    ( ~ product(e_2,e_1,e_3)
    | ~ spl0_35 ),
    inference(subsumption_resolution,[],[f714,f29]) ).

fof(f29,axiom,
    ~ equalish(e_2,e_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).

fof(f714,plain,
    ( ~ product(e_2,e_1,e_3)
    | equalish(e_2,e_1)
    | ~ spl0_35 ),
    inference(resolution,[],[f259,f110]) ).

fof(f259,plain,
    ( product(e_1,e_3,e_2)
    | ~ spl0_35 ),
    inference(avatar_component_clause,[],[f257]) ).

fof(f708,plain,
    ~ spl0_34,
    inference(avatar_contradiction_clause,[],[f707]) ).

fof(f707,plain,
    ( $false
    | ~ spl0_34 ),
    inference(subsumption_resolution,[],[f706,f27]) ).

fof(f706,plain,
    ( equalish(e_1,e_3)
    | ~ spl0_34 ),
    inference(resolution,[],[f255,f48]) ).

fof(f255,plain,
    ( product(e_1,e_3,e_1)
    | ~ spl0_34 ),
    inference(avatar_component_clause,[],[f253]) ).

fof(f253,plain,
    ( spl0_34
  <=> product(e_1,e_3,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f687,plain,
    ( ~ spl0_43
    | ~ spl0_29 ),
    inference(avatar_split_clause,[],[f686,f227,f291]) ).

fof(f291,plain,
    ( spl0_43
  <=> product(e_4,e_3,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f227,plain,
    ( spl0_29
  <=> product(e_3,e_2,e_4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f686,plain,
    ( ~ product(e_4,e_3,e_2)
    | ~ spl0_29 ),
    inference(subsumption_resolution,[],[f683,f36]) ).

fof(f683,plain,
    ( ~ product(e_4,e_3,e_2)
    | equalish(e_4,e_2)
    | ~ spl0_29 ),
    inference(resolution,[],[f229,f112]) ).

fof(f229,plain,
    ( product(e_3,e_2,e_4)
    | ~ spl0_29 ),
    inference(avatar_component_clause,[],[f227]) ).

fof(f676,plain,
    ~ spl0_28,
    inference(avatar_contradiction_clause,[],[f675]) ).

fof(f675,plain,
    ( $false
    | ~ spl0_28 ),
    inference(subsumption_resolution,[],[f674,f33]) ).

fof(f674,plain,
    ( equalish(e_3,e_2)
    | ~ spl0_28 ),
    inference(resolution,[],[f225,f48]) ).

fof(f225,plain,
    ( product(e_3,e_2,e_3)
    | ~ spl0_28 ),
    inference(avatar_component_clause,[],[f223]) ).

fof(f223,plain,
    ( spl0_28
  <=> product(e_3,e_2,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f666,plain,
    ~ spl0_27,
    inference(avatar_contradiction_clause,[],[f665]) ).

fof(f665,plain,
    ( $false
    | ~ spl0_27 ),
    inference(subsumption_resolution,[],[f664,f30]) ).

fof(f664,plain,
    ( equalish(e_2,e_3)
    | ~ spl0_27 ),
    inference(resolution,[],[f221,f50]) ).

fof(f221,plain,
    ( product(e_3,e_2,e_2)
    | ~ spl0_27 ),
    inference(avatar_component_clause,[],[f219]) ).

fof(f219,plain,
    ( spl0_27
  <=> product(e_3,e_2,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f633,plain,
    ~ spl0_23,
    inference(avatar_contradiction_clause,[],[f632]) ).

fof(f632,plain,
    ( $false
    | ~ spl0_23 ),
    inference(subsumption_resolution,[],[f631,f29]) ).

fof(f631,plain,
    ( equalish(e_2,e_1)
    | ~ spl0_23 ),
    inference(resolution,[],[f204,f50]) ).

fof(f204,plain,
    ( product(e_1,e_2,e_2)
    | ~ spl0_23 ),
    inference(avatar_component_clause,[],[f202]) ).

fof(f202,plain,
    ( spl0_23
  <=> product(e_1,e_2,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f621,plain,
    ( ~ spl0_17
    | ~ spl0_25 ),
    inference(avatar_contradiction_clause,[],[f620]) ).

fof(f620,plain,
    ( $false
    | ~ spl0_17
    | ~ spl0_25 ),
    inference(subsumption_resolution,[],[f619,f36]) ).

fof(f619,plain,
    ( equalish(e_4,e_2)
    | ~ spl0_17
    | ~ spl0_25 ),
    inference(subsumption_resolution,[],[f615,f163]) ).

fof(f163,plain,
    ( product(e_4,e_1,e_2)
    | ~ spl0_17 ),
    inference(avatar_component_clause,[],[f161]) ).

fof(f161,plain,
    ( spl0_17
  <=> product(e_4,e_1,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f615,plain,
    ( ~ product(e_4,e_1,e_2)
    | equalish(e_4,e_2)
    | ~ spl0_25 ),
    inference(resolution,[],[f212,f112]) ).

fof(f212,plain,
    ( product(e_1,e_2,e_4)
    | ~ spl0_25 ),
    inference(avatar_component_clause,[],[f210]) ).

fof(f210,plain,
    ( spl0_25
  <=> product(e_1,e_2,e_4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f608,plain,
    ( ~ spl0_13
    | ~ spl0_24 ),
    inference(avatar_contradiction_clause,[],[f607]) ).

fof(f607,plain,
    ( $false
    | ~ spl0_13
    | ~ spl0_24 ),
    inference(subsumption_resolution,[],[f606,f33]) ).

fof(f606,plain,
    ( equalish(e_3,e_2)
    | ~ spl0_13
    | ~ spl0_24 ),
    inference(subsumption_resolution,[],[f602,f146]) ).

fof(f146,plain,
    ( product(e_3,e_1,e_2)
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f144]) ).

fof(f144,plain,
    ( spl0_13
  <=> product(e_3,e_1,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f602,plain,
    ( ~ product(e_3,e_1,e_2)
    | equalish(e_3,e_2)
    | ~ spl0_24 ),
    inference(resolution,[],[f208,f112]) ).

fof(f208,plain,
    ( product(e_1,e_2,e_3)
    | ~ spl0_24 ),
    inference(avatar_component_clause,[],[f206]) ).

fof(f595,plain,
    ~ spl0_22,
    inference(avatar_contradiction_clause,[],[f594]) ).

fof(f594,plain,
    ( $false
    | ~ spl0_22 ),
    inference(subsumption_resolution,[],[f593,f26]) ).

fof(f593,plain,
    ( equalish(e_1,e_2)
    | ~ spl0_22 ),
    inference(resolution,[],[f200,f48]) ).

fof(f200,plain,
    ( product(e_1,e_2,e_1)
    | ~ spl0_22 ),
    inference(avatar_component_clause,[],[f198]) ).

fof(f198,plain,
    ( spl0_22
  <=> product(e_1,e_2,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f571,plain,
    ~ spl0_19,
    inference(avatar_contradiction_clause,[],[f570]) ).

fof(f570,plain,
    ( $false
    | ~ spl0_19 ),
    inference(subsumption_resolution,[],[f565,f35]) ).

fof(f565,plain,
    ( equalish(e_4,e_1)
    | ~ spl0_19 ),
    inference(resolution,[],[f171,f48]) ).

fof(f171,plain,
    ( product(e_4,e_1,e_4)
    | ~ spl0_19 ),
    inference(avatar_component_clause,[],[f169]) ).

fof(f169,plain,
    ( spl0_19
  <=> product(e_4,e_1,e_4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f521,plain,
    ~ spl0_16,
    inference(avatar_contradiction_clause,[],[f520]) ).

fof(f520,plain,
    ( $false
    | ~ spl0_16 ),
    inference(subsumption_resolution,[],[f512,f28]) ).

fof(f28,axiom,
    ~ equalish(e_1,e_4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_4) ).

fof(f512,plain,
    ( equalish(e_1,e_4)
    | ~ spl0_16 ),
    inference(resolution,[],[f159,f50]) ).

fof(f159,plain,
    ( product(e_4,e_1,e_1)
    | ~ spl0_16 ),
    inference(avatar_component_clause,[],[f157]) ).

fof(f157,plain,
    ( spl0_16
  <=> product(e_4,e_1,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f500,plain,
    ( ~ spl0_38
    | ~ spl0_13 ),
    inference(avatar_split_clause,[],[f499,f144,f270]) ).

fof(f499,plain,
    ( ~ product(e_2,e_3,e_1)
    | ~ spl0_13 ),
    inference(subsumption_resolution,[],[f495,f29]) ).

fof(f495,plain,
    ( ~ product(e_2,e_3,e_1)
    | equalish(e_2,e_1)
    | ~ spl0_13 ),
    inference(resolution,[],[f146,f112]) ).

fof(f471,plain,
    ~ spl0_14,
    inference(avatar_contradiction_clause,[],[f470]) ).

fof(f470,plain,
    ( $false
    | ~ spl0_14 ),
    inference(subsumption_resolution,[],[f465,f32]) ).

fof(f465,plain,
    ( equalish(e_3,e_1)
    | ~ spl0_14 ),
    inference(resolution,[],[f150,f48]) ).

fof(f150,plain,
    ( product(e_3,e_1,e_3)
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f148]) ).

fof(f148,plain,
    ( spl0_14
  <=> product(e_3,e_1,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f440,plain,
    ~ spl0_12,
    inference(avatar_contradiction_clause,[],[f439]) ).

fof(f439,plain,
    ( $false
    | ~ spl0_12 ),
    inference(subsumption_resolution,[],[f431,f27]) ).

fof(f431,plain,
    ( equalish(e_1,e_3)
    | ~ spl0_12 ),
    inference(resolution,[],[f142,f50]) ).

fof(f142,plain,
    ( product(e_3,e_1,e_1)
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f140]) ).

fof(f140,plain,
    ( spl0_12
  <=> product(e_3,e_1,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f420,plain,
    ( ~ spl0_26
    | ~ spl0_10 ),
    inference(avatar_split_clause,[],[f419,f131,f215]) ).

fof(f419,plain,
    ( ~ product(e_3,e_2,e_1)
    | ~ spl0_10 ),
    inference(subsumption_resolution,[],[f415,f32]) ).

fof(f415,plain,
    ( ~ product(e_3,e_2,e_1)
    | equalish(e_3,e_1)
    | ~ spl0_10 ),
    inference(resolution,[],[f133,f112]) ).

fof(f133,plain,
    ( product(e_2,e_1,e_3)
    | ~ spl0_10 ),
    inference(avatar_component_clause,[],[f131]) ).

fof(f317,plain,
    ~ spl0_9,
    inference(avatar_contradiction_clause,[],[f316]) ).

fof(f316,plain,
    ( $false
    | ~ spl0_9 ),
    inference(subsumption_resolution,[],[f311,f29]) ).

fof(f311,plain,
    ( equalish(e_2,e_1)
    | ~ spl0_9 ),
    inference(resolution,[],[f129,f48]) ).

fof(f129,plain,
    ( product(e_2,e_1,e_2)
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f127]) ).

fof(f127,plain,
    ( spl0_9
  <=> product(e_2,e_1,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f302,plain,
    ( spl0_42
    | spl0_43
    | spl0_44
    | spl0_45 ),
    inference(avatar_split_clause,[],[f251,f299,f295,f291,f287]) ).

fof(f251,plain,
    ( product(e_4,e_3,e_4)
    | product(e_4,e_3,e_3)
    | product(e_4,e_3,e_2)
    | product(e_4,e_3,e_1) ),
    inference(resolution,[],[f107,f25]) ).

fof(f25,axiom,
    group_element(e_4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).

fof(f107,plain,
    ! [X0] :
      ( ~ group_element(X0)
      | product(X0,e_3,e_4)
      | product(X0,e_3,e_3)
      | product(X0,e_3,e_2)
      | product(X0,e_3,e_1) ),
    inference(resolution,[],[f38,f24]) ).

fof(f24,axiom,
    group_element(e_3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).

fof(f38,axiom,
    ! [X0,X1] :
      ( ~ group_element(X1)
      | ~ group_element(X0)
      | product(X0,X1,e_4)
      | product(X0,X1,e_3)
      | product(X0,X1,e_2)
      | product(X0,X1,e_1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).

fof(f285,plain,
    ( spl0_38
    | spl0_39
    | spl0_40
    | spl0_41 ),
    inference(avatar_split_clause,[],[f249,f282,f278,f274,f270]) ).

fof(f249,plain,
    ( product(e_2,e_3,e_4)
    | product(e_2,e_3,e_3)
    | product(e_2,e_3,e_2)
    | product(e_2,e_3,e_1) ),
    inference(resolution,[],[f107,f23]) ).

fof(f23,axiom,
    group_element(e_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).

fof(f268,plain,
    ( spl0_34
    | spl0_35
    | spl0_36
    | spl0_37 ),
    inference(avatar_split_clause,[],[f248,f265,f261,f257,f253]) ).

fof(f248,plain,
    ( product(e_1,e_3,e_4)
    | product(e_1,e_3,e_3)
    | product(e_1,e_3,e_2)
    | product(e_1,e_3,e_1) ),
    inference(resolution,[],[f107,f22]) ).

fof(f22,axiom,
    group_element(e_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).

fof(f247,plain,
    ( spl0_30
    | spl0_31
    | spl0_32
    | spl0_33 ),
    inference(avatar_split_clause,[],[f196,f244,f240,f236,f232]) ).

fof(f196,plain,
    ( product(e_4,e_2,e_4)
    | product(e_4,e_2,e_3)
    | product(e_4,e_2,e_2)
    | product(e_4,e_2,e_1) ),
    inference(resolution,[],[f106,f25]) ).

fof(f106,plain,
    ! [X0] :
      ( ~ group_element(X0)
      | product(X0,e_2,e_4)
      | product(X0,e_2,e_3)
      | product(X0,e_2,e_2)
      | product(X0,e_2,e_1) ),
    inference(resolution,[],[f38,f23]) ).

fof(f230,plain,
    ( spl0_26
    | spl0_27
    | spl0_28
    | spl0_29 ),
    inference(avatar_split_clause,[],[f195,f227,f223,f219,f215]) ).

fof(f195,plain,
    ( product(e_3,e_2,e_4)
    | product(e_3,e_2,e_3)
    | product(e_3,e_2,e_2)
    | product(e_3,e_2,e_1) ),
    inference(resolution,[],[f106,f24]) ).

fof(f213,plain,
    ( spl0_22
    | spl0_23
    | spl0_24
    | spl0_25 ),
    inference(avatar_split_clause,[],[f193,f210,f206,f202,f198]) ).

fof(f193,plain,
    ( product(e_1,e_2,e_4)
    | product(e_1,e_2,e_3)
    | product(e_1,e_2,e_2)
    | product(e_1,e_2,e_1) ),
    inference(resolution,[],[f106,f22]) ).

fof(f192,plain,
    ~ spl0_8,
    inference(avatar_contradiction_clause,[],[f191]) ).

fof(f191,plain,
    ( $false
    | ~ spl0_8 ),
    inference(subsumption_resolution,[],[f183,f26]) ).

fof(f183,plain,
    ( equalish(e_1,e_2)
    | ~ spl0_8 ),
    inference(resolution,[],[f125,f50]) ).

fof(f125,plain,
    ( product(e_2,e_1,e_1)
    | ~ spl0_8 ),
    inference(avatar_component_clause,[],[f123]) ).

fof(f123,plain,
    ( spl0_8
  <=> product(e_2,e_1,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f172,plain,
    ( spl0_16
    | spl0_17
    | spl0_18
    | spl0_19 ),
    inference(avatar_split_clause,[],[f121,f169,f165,f161,f157]) ).

fof(f121,plain,
    ( product(e_4,e_1,e_4)
    | product(e_4,e_1,e_3)
    | product(e_4,e_1,e_2)
    | product(e_4,e_1,e_1) ),
    inference(resolution,[],[f105,f25]) ).

fof(f105,plain,
    ! [X0] :
      ( ~ group_element(X0)
      | product(X0,e_1,e_4)
      | product(X0,e_1,e_3)
      | product(X0,e_1,e_2)
      | product(X0,e_1,e_1) ),
    inference(resolution,[],[f38,f22]) ).

fof(f155,plain,
    ( spl0_12
    | spl0_13
    | spl0_14
    | spl0_15 ),
    inference(avatar_split_clause,[],[f120,f152,f148,f144,f140]) ).

fof(f120,plain,
    ( product(e_3,e_1,e_4)
    | product(e_3,e_1,e_3)
    | product(e_3,e_1,e_2)
    | product(e_3,e_1,e_1) ),
    inference(resolution,[],[f105,f24]) ).

fof(f138,plain,
    ( spl0_8
    | spl0_9
    | spl0_10
    | spl0_11 ),
    inference(avatar_split_clause,[],[f119,f135,f131,f127,f123]) ).

fof(f119,plain,
    ( product(e_2,e_1,e_4)
    | product(e_2,e_1,e_3)
    | product(e_2,e_1,e_2)
    | product(e_2,e_1,e_1) ),
    inference(resolution,[],[f105,f23]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : GRP124-3.004 : TPTP v8.1.2. Released v1.2.0.
% 0.11/0.12  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.33  % Computer : n024.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 300
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Fri May  3 20:40:38 EDT 2024
% 0.11/0.33  % CPUTime    : 
% 0.11/0.33  % (5261)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.35  % (5263)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.17/0.35  % (5267)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.17/0.35  % (5262)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.17/0.35  % (5265)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.17/0.35  % (5266)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.17/0.35  % (5264)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.17/0.35  % (5268)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.17/0.35  Detected minimum model sizes of [1]
% 0.17/0.35  Detected maximum model sizes of [5]
% 0.17/0.35  TRYING [1]
% 0.17/0.35  TRYING [2]
% 0.17/0.35  Detected minimum model sizes of [1]
% 0.17/0.35  Detected maximum model sizes of [5]
% 0.17/0.35  TRYING [1]
% 0.17/0.35  Detected minimum model sizes of [1]
% 0.17/0.35  Detected maximum model sizes of [5]
% 0.17/0.35  Detected minimum model sizes of [1]
% 0.17/0.35  TRYING [1]
% 0.17/0.35  Detected maximum model sizes of [5]
% 0.17/0.35  TRYING [1]
% 0.17/0.35  TRYING [2]
% 0.17/0.35  TRYING [2]
% 0.17/0.35  TRYING [2]
% 0.17/0.35  TRYING [3]
% 0.17/0.35  TRYING [3]
% 0.17/0.35  TRYING [3]
% 0.17/0.35  TRYING [3]
% 0.17/0.36  TRYING [4]
% 0.17/0.36  TRYING [4]
% 0.17/0.36  TRYING [4]
% 0.17/0.36  TRYING [4]
% 0.17/0.36  TRYING [5]
% 0.17/0.37  TRYING [5]
% 0.17/0.37  TRYING [5]
% 0.17/0.37  TRYING [5]
% 0.17/0.37  % (5267)First to succeed.
% 0.17/0.37  % (5267)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-5261"
% 0.17/0.37  % (5267)Refutation found. Thanks to Tanya!
% 0.17/0.37  % SZS status Unsatisfiable for theBenchmark
% 0.17/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.37  % (5267)------------------------------
% 0.17/0.37  % (5267)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.17/0.37  % (5267)Termination reason: Refutation
% 0.17/0.37  
% 0.17/0.37  % (5267)Memory used [KB]: 1087
% 0.17/0.37  % (5267)Time elapsed: 0.023 s
% 0.17/0.37  % (5267)Instructions burned: 44 (million)
% 0.17/0.37  % (5261)Success in time 0.037 s
%------------------------------------------------------------------------------