TSTP Solution File: GRP126-3.004 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GRP126-3.004 : 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 : n027.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 05:53:35 EDT 2024

% Result   : Unsatisfiable 0.20s 0.40s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   52
% Syntax   : Number of formulae    :  163 (  32 unt;   0 def)
%            Number of atoms       :  380 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  389 ( 172   ~; 192   |;   0   &)
%                                         (  25 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   32 (  31 usr;  26 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   41 (  41   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f975,plain,
    $false,
    inference(avatar_sat_refutation,[],[f133,f167,f194,f228,f243,f298,f310,f444,f461,f468,f598,f607,f640,f647,f654,f673,f680,f790,f794,f797,f805,f808,f818,f850,f898,f974]) ).

fof(f974,plain,
    ( ~ spl0_10
    | ~ spl0_23
    | spl0_43 ),
    inference(avatar_contradiction_clause,[],[f973]) ).

fof(f973,plain,
    ( $false
    | ~ spl0_10
    | ~ spl0_23
    | spl0_43 ),
    inference(subsumption_resolution,[],[f972,f288]) ).

fof(f288,plain,
    ( ~ product(e_4,e_3,e_2)
    | spl0_43 ),
    inference(avatar_component_clause,[],[f287]) ).

fof(f287,plain,
    ( spl0_43
  <=> product(e_4,e_3,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f972,plain,
    ( product(e_4,e_3,e_2)
    | ~ spl0_10
    | ~ spl0_23 ),
    inference(resolution,[],[f822,f193]) ).

fof(f193,plain,
    ( product(e_1,e_2,e_4)
    | ~ spl0_23 ),
    inference(avatar_component_clause,[],[f191]) ).

fof(f191,plain,
    ( spl0_23
  <=> product(e_1,e_2,e_4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f822,plain,
    ( ! [X0] :
        ( ~ product(e_1,e_2,X0)
        | product(X0,e_3,e_2) )
    | ~ spl0_10 ),
    inference(resolution,[],[f128,f43]) ).

fof(f43,axiom,
    ! [X0,X1,X4,X5] :
      ( ~ product(X1,X0,X5)
      | ~ product(X0,X1,X4)
      | product(X4,X5,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg4) ).

fof(f128,plain,
    ( product(e_2,e_1,e_3)
    | ~ spl0_10 ),
    inference(avatar_component_clause,[],[f126]) ).

fof(f126,plain,
    ( spl0_10
  <=> product(e_2,e_1,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f898,plain,
    ~ spl0_45,
    inference(avatar_contradiction_clause,[],[f897]) ).

fof(f897,plain,
    ( $false
    | ~ spl0_45 ),
    inference(subsumption_resolution,[],[f896,f37]) ).

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

fof(f896,plain,
    ( equalish(e_4,e_3)
    | ~ spl0_45 ),
    inference(resolution,[],[f297,f47]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( ~ product(X0,X1,X0)
      | equalish(X0,X1) ),
    inference(resolution,[],[f40,f42]) ).

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

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(f297,plain,
    ( product(e_4,e_3,e_4)
    | ~ spl0_45 ),
    inference(avatar_component_clause,[],[f295]) ).

fof(f295,plain,
    ( spl0_45
  <=> product(e_4,e_3,e_4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f850,plain,
    ( ~ spl0_17
    | ~ spl0_43 ),
    inference(avatar_contradiction_clause,[],[f849]) ).

fof(f849,plain,
    ( $false
    | ~ spl0_17
    | ~ spl0_43 ),
    inference(subsumption_resolution,[],[f843,f32]) ).

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

fof(f843,plain,
    ( equalish(e_3,e_1)
    | ~ spl0_17
    | ~ spl0_43 ),
    inference(resolution,[],[f158,f701]) ).

fof(f701,plain,
    ( ! [X0] :
        ( ~ product(e_4,X0,e_2)
        | equalish(e_3,X0) )
    | ~ spl0_43 ),
    inference(resolution,[],[f289,f40]) ).

fof(f289,plain,
    ( product(e_4,e_3,e_2)
    | ~ spl0_43 ),
    inference(avatar_component_clause,[],[f287]) ).

fof(f158,plain,
    ( product(e_4,e_1,e_2)
    | ~ spl0_17 ),
    inference(avatar_component_clause,[],[f156]) ).

fof(f156,plain,
    ( spl0_17
  <=> product(e_4,e_1,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f818,plain,
    ( ~ spl0_32
    | ~ spl0_69 ),
    inference(avatar_contradiction_clause,[],[f817]) ).

fof(f817,plain,
    ( $false
    | ~ spl0_32
    | ~ spl0_69 ),
    inference(subsumption_resolution,[],[f813,f6]) ).

fof(f6,axiom,
    greater(e_2,e_0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_greater_e_0) ).

fof(f813,plain,
    ( ~ greater(e_2,e_0)
    | ~ spl0_32
    | ~ spl0_69 ),
    inference(resolution,[],[f530,f237]) ).

fof(f237,plain,
    ( ! [X1] :
        ( ~ cycle(e_2,X1)
        | ~ greater(X1,e_0) )
    | ~ spl0_32 ),
    inference(avatar_component_clause,[],[f236]) ).

fof(f236,plain,
    ( spl0_32
  <=> ! [X1] :
        ( ~ cycle(e_2,X1)
        | ~ greater(X1,e_0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f530,plain,
    ( cycle(e_2,e_2)
    | ~ spl0_69 ),
    inference(avatar_component_clause,[],[f528]) ).

fof(f528,plain,
    ( spl0_69
  <=> cycle(e_2,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f808,plain,
    ( spl0_68
    | spl0_69
    | spl0_70
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f807,f236,f532,f528,f524]) ).

fof(f524,plain,
    ( spl0_68
  <=> cycle(e_2,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f532,plain,
    ( spl0_70
  <=> cycle(e_2,e_0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

fof(f807,plain,
    ( cycle(e_2,e_0)
    | cycle(e_2,e_2)
    | cycle(e_2,e_1)
    | ~ spl0_32 ),
    inference(subsumption_resolution,[],[f806,f23]) ).

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

fof(f806,plain,
    ( cycle(e_2,e_0)
    | ~ group_element(e_2)
    | cycle(e_2,e_2)
    | cycle(e_2,e_1)
    | ~ spl0_32 ),
    inference(subsumption_resolution,[],[f803,f7]) ).

fof(f7,axiom,
    greater(e_3,e_0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_greater_e_0) ).

fof(f803,plain,
    ( ~ greater(e_3,e_0)
    | cycle(e_2,e_0)
    | ~ group_element(e_2)
    | cycle(e_2,e_2)
    | cycle(e_2,e_1)
    | ~ spl0_32 ),
    inference(resolution,[],[f237,f16]) ).

fof(f16,axiom,
    ! [X0] :
      ( cycle(X0,e_3)
      | cycle(X0,e_0)
      | ~ group_element(X0)
      | cycle(X0,e_2)
      | cycle(X0,e_1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cycle2) ).

fof(f805,plain,
    ( ~ spl0_32
    | ~ spl0_68 ),
    inference(avatar_contradiction_clause,[],[f804]) ).

fof(f804,plain,
    ( $false
    | ~ spl0_32
    | ~ spl0_68 ),
    inference(subsumption_resolution,[],[f802,f5]) ).

fof(f5,axiom,
    greater(e_1,e_0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_greater_e_0) ).

fof(f802,plain,
    ( ~ greater(e_1,e_0)
    | ~ spl0_32
    | ~ spl0_68 ),
    inference(resolution,[],[f237,f526]) ).

fof(f526,plain,
    ( cycle(e_2,e_1)
    | ~ spl0_68 ),
    inference(avatar_component_clause,[],[f524]) ).

fof(f797,plain,
    ~ spl0_74,
    inference(avatar_contradiction_clause,[],[f796]) ).

fof(f796,plain,
    ( $false
    | ~ spl0_74 ),
    inference(subsumption_resolution,[],[f795,f37]) ).

fof(f795,plain,
    ( equalish(e_4,e_3)
    | ~ spl0_74 ),
    inference(resolution,[],[f793,f3]) ).

fof(f3,axiom,
    next(e_2,e_3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_then_e_3) ).

fof(f793,plain,
    ( ! [X0] :
        ( ~ next(e_2,X0)
        | equalish(e_4,X0) )
    | ~ spl0_74 ),
    inference(avatar_component_clause,[],[f792]) ).

fof(f792,plain,
    ( spl0_74
  <=> ! [X0] :
        ( ~ next(e_2,X0)
        | equalish(e_4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f794,plain,
    ( spl0_32
    | spl0_74
    | ~ spl0_11 ),
    inference(avatar_split_clause,[],[f608,f130,f792,f236]) ).

fof(f130,plain,
    ( spl0_11
  <=> product(e_2,e_1,e_4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f608,plain,
    ( ! [X0,X1] :
        ( ~ next(e_2,X0)
        | ~ cycle(e_2,X1)
        | equalish(e_4,X0)
        | ~ greater(X1,e_0) )
    | ~ spl0_11 ),
    inference(resolution,[],[f132,f21]) ).

fof(f21,axiom,
    ! [X2,X0,X1,X6] :
      ( ~ product(X0,e_1,X2)
      | ~ next(X0,X6)
      | ~ cycle(X0,X1)
      | equalish(X2,X6)
      | ~ greater(X1,e_0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cycle7) ).

fof(f132,plain,
    ( product(e_2,e_1,e_4)
    | ~ spl0_11 ),
    inference(avatar_component_clause,[],[f130]) ).

fof(f790,plain,
    ( ~ spl0_11
    | ~ spl0_70 ),
    inference(avatar_contradiction_clause,[],[f789]) ).

fof(f789,plain,
    ( $false
    | ~ spl0_11
    | ~ spl0_70 ),
    inference(subsumption_resolution,[],[f788,f13]) ).

fof(f13,axiom,
    greater(e_4,e_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_greater_e_2) ).

fof(f788,plain,
    ( ~ greater(e_4,e_2)
    | ~ spl0_11
    | ~ spl0_70 ),
    inference(resolution,[],[f539,f132]) ).

fof(f539,plain,
    ( ! [X0] :
        ( ~ product(e_2,e_1,X0)
        | ~ greater(X0,e_2) )
    | ~ spl0_70 ),
    inference(resolution,[],[f534,f20]) ).

fof(f20,axiom,
    ! [X0,X1] :
      ( ~ cycle(X0,e_0)
      | ~ greater(X1,X0)
      | ~ product(X0,e_1,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cycle6) ).

fof(f534,plain,
    ( cycle(e_2,e_0)
    | ~ spl0_70 ),
    inference(avatar_component_clause,[],[f532]) ).

fof(f680,plain,
    ~ spl0_31,
    inference(avatar_contradiction_clause,[],[f679]) ).

fof(f679,plain,
    ( $false
    | ~ spl0_31 ),
    inference(subsumption_resolution,[],[f678,f36]) ).

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

fof(f678,plain,
    ( equalish(e_4,e_2)
    | ~ spl0_31 ),
    inference(resolution,[],[f227,f47]) ).

fof(f227,plain,
    ( product(e_4,e_2,e_4)
    | ~ spl0_31 ),
    inference(avatar_component_clause,[],[f225]) ).

fof(f225,plain,
    ( spl0_31
  <=> product(e_4,e_2,e_4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f673,plain,
    ~ spl0_44,
    inference(avatar_contradiction_clause,[],[f672]) ).

fof(f672,plain,
    ( $false
    | ~ spl0_44 ),
    inference(subsumption_resolution,[],[f671,f34]) ).

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

fof(f671,plain,
    ( equalish(e_3,e_4)
    | ~ spl0_44 ),
    inference(resolution,[],[f293,f49]) ).

fof(f49,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(f293,plain,
    ( product(e_4,e_3,e_3)
    | ~ spl0_44 ),
    inference(avatar_component_clause,[],[f291]) ).

fof(f291,plain,
    ( spl0_44
  <=> product(e_4,e_3,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f654,plain,
    ( ~ spl0_22
    | ~ spl0_30 ),
    inference(avatar_contradiction_clause,[],[f653]) ).

fof(f653,plain,
    ( $false
    | ~ spl0_22
    | ~ spl0_30 ),
    inference(subsumption_resolution,[],[f648,f28]) ).

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

fof(f648,plain,
    ( equalish(e_1,e_4)
    | ~ spl0_22
    | ~ spl0_30 ),
    inference(resolution,[],[f223,f470]) ).

fof(f470,plain,
    ( ! [X0] :
        ( ~ product(X0,e_2,e_3)
        | equalish(e_1,X0) )
    | ~ spl0_22 ),
    inference(resolution,[],[f189,f41]) ).

fof(f189,plain,
    ( product(e_1,e_2,e_3)
    | ~ spl0_22 ),
    inference(avatar_component_clause,[],[f187]) ).

fof(f187,plain,
    ( spl0_22
  <=> product(e_1,e_2,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f223,plain,
    ( product(e_4,e_2,e_3)
    | ~ spl0_30 ),
    inference(avatar_component_clause,[],[f221]) ).

fof(f221,plain,
    ( spl0_30
  <=> product(e_4,e_2,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f647,plain,
    ~ spl0_29,
    inference(avatar_contradiction_clause,[],[f646]) ).

fof(f646,plain,
    ( $false
    | ~ spl0_29 ),
    inference(subsumption_resolution,[],[f645,f31]) ).

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

fof(f645,plain,
    ( equalish(e_2,e_4)
    | ~ spl0_29 ),
    inference(resolution,[],[f219,f49]) ).

fof(f219,plain,
    ( product(e_4,e_2,e_2)
    | ~ spl0_29 ),
    inference(avatar_component_clause,[],[f217]) ).

fof(f217,plain,
    ( spl0_29
  <=> product(e_4,e_2,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f640,plain,
    ( ~ spl0_28
    | ~ spl0_42 ),
    inference(avatar_contradiction_clause,[],[f639]) ).

fof(f639,plain,
    ( $false
    | ~ spl0_28
    | ~ spl0_42 ),
    inference(subsumption_resolution,[],[f637,f30]) ).

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

fof(f637,plain,
    ( equalish(e_2,e_3)
    | ~ spl0_28
    | ~ spl0_42 ),
    inference(resolution,[],[f479,f285]) ).

fof(f285,plain,
    ( product(e_4,e_3,e_1)
    | ~ spl0_42 ),
    inference(avatar_component_clause,[],[f283]) ).

fof(f283,plain,
    ( spl0_42
  <=> product(e_4,e_3,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f479,plain,
    ( ! [X0] :
        ( ~ product(e_4,X0,e_1)
        | equalish(e_2,X0) )
    | ~ spl0_28 ),
    inference(resolution,[],[f215,f40]) ).

fof(f215,plain,
    ( product(e_4,e_2,e_1)
    | ~ spl0_28 ),
    inference(avatar_component_clause,[],[f213]) ).

fof(f213,plain,
    ( spl0_28
  <=> product(e_4,e_2,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f607,plain,
    ( ~ spl0_10
    | ~ spl0_18 ),
    inference(avatar_contradiction_clause,[],[f606]) ).

fof(f606,plain,
    ( $false
    | ~ spl0_10
    | ~ spl0_18 ),
    inference(subsumption_resolution,[],[f600,f31]) ).

fof(f600,plain,
    ( equalish(e_2,e_4)
    | ~ spl0_10
    | ~ spl0_18 ),
    inference(resolution,[],[f162,f371]) ).

fof(f371,plain,
    ( ! [X0] :
        ( ~ product(X0,e_1,e_3)
        | equalish(e_2,X0) )
    | ~ spl0_10 ),
    inference(resolution,[],[f128,f41]) ).

fof(f162,plain,
    ( product(e_4,e_1,e_3)
    | ~ spl0_18 ),
    inference(avatar_component_clause,[],[f160]) ).

fof(f160,plain,
    ( spl0_18
  <=> product(e_4,e_1,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f598,plain,
    ~ spl0_19,
    inference(avatar_contradiction_clause,[],[f597]) ).

fof(f597,plain,
    ( $false
    | ~ spl0_19 ),
    inference(subsumption_resolution,[],[f596,f35]) ).

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

fof(f596,plain,
    ( equalish(e_4,e_1)
    | ~ spl0_19 ),
    inference(resolution,[],[f166,f47]) ).

fof(f166,plain,
    ( product(e_4,e_1,e_4)
    | ~ spl0_19 ),
    inference(avatar_component_clause,[],[f164]) ).

fof(f164,plain,
    ( spl0_19
  <=> product(e_4,e_1,e_4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f468,plain,
    ~ spl0_21,
    inference(avatar_contradiction_clause,[],[f467]) ).

fof(f467,plain,
    ( $false
    | ~ spl0_21 ),
    inference(subsumption_resolution,[],[f466,f29]) ).

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

fof(f466,plain,
    ( equalish(e_2,e_1)
    | ~ spl0_21 ),
    inference(resolution,[],[f185,f49]) ).

fof(f185,plain,
    ( product(e_1,e_2,e_2)
    | ~ spl0_21 ),
    inference(avatar_component_clause,[],[f183]) ).

fof(f183,plain,
    ( spl0_21
  <=> product(e_1,e_2,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f461,plain,
    ~ spl0_20,
    inference(avatar_contradiction_clause,[],[f460]) ).

fof(f460,plain,
    ( $false
    | ~ spl0_20 ),
    inference(subsumption_resolution,[],[f459,f26]) ).

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

fof(f459,plain,
    ( equalish(e_1,e_2)
    | ~ spl0_20 ),
    inference(resolution,[],[f181,f47]) ).

fof(f181,plain,
    ( product(e_1,e_2,e_1)
    | ~ spl0_20 ),
    inference(avatar_component_clause,[],[f179]) ).

fof(f179,plain,
    ( spl0_20
  <=> product(e_1,e_2,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f444,plain,
    ~ spl0_16,
    inference(avatar_contradiction_clause,[],[f443]) ).

fof(f443,plain,
    ( $false
    | ~ spl0_16 ),
    inference(subsumption_resolution,[],[f435,f28]) ).

fof(f435,plain,
    ( equalish(e_1,e_4)
    | ~ spl0_16 ),
    inference(resolution,[],[f154,f49]) ).

fof(f154,plain,
    ( product(e_4,e_1,e_1)
    | ~ spl0_16 ),
    inference(avatar_component_clause,[],[f152]) ).

fof(f152,plain,
    ( spl0_16
  <=> product(e_4,e_1,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f310,plain,
    ~ spl0_9,
    inference(avatar_contradiction_clause,[],[f309]) ).

fof(f309,plain,
    ( $false
    | ~ spl0_9 ),
    inference(subsumption_resolution,[],[f304,f29]) ).

fof(f304,plain,
    ( equalish(e_2,e_1)
    | ~ spl0_9 ),
    inference(resolution,[],[f124,f47]) ).

fof(f124,plain,
    ( product(e_2,e_1,e_2)
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f122]) ).

fof(f122,plain,
    ( spl0_9
  <=> product(e_2,e_1,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f298,plain,
    ( spl0_42
    | spl0_43
    | spl0_44
    | spl0_45 ),
    inference(avatar_split_clause,[],[f247,f295,f291,f287,f283]) ).

fof(f247,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,[],[f96,f25]) ).

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

fof(f96,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(f243,plain,
    ~ spl0_8,
    inference(avatar_contradiction_clause,[],[f242]) ).

fof(f242,plain,
    ( $false
    | ~ spl0_8 ),
    inference(subsumption_resolution,[],[f234,f26]) ).

fof(f234,plain,
    ( equalish(e_1,e_2)
    | ~ spl0_8 ),
    inference(resolution,[],[f120,f49]) ).

fof(f120,plain,
    ( product(e_2,e_1,e_1)
    | ~ spl0_8 ),
    inference(avatar_component_clause,[],[f118]) ).

fof(f118,plain,
    ( spl0_8
  <=> product(e_2,e_1,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f228,plain,
    ( spl0_28
    | spl0_29
    | spl0_30
    | spl0_31 ),
    inference(avatar_split_clause,[],[f177,f225,f221,f217,f213]) ).

fof(f177,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,[],[f95,f25]) ).

fof(f95,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(f194,plain,
    ( spl0_20
    | spl0_21
    | spl0_22
    | spl0_23 ),
    inference(avatar_split_clause,[],[f174,f191,f187,f183,f179]) ).

fof(f174,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,[],[f95,f22]) ).

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

fof(f167,plain,
    ( spl0_16
    | spl0_17
    | spl0_18
    | spl0_19 ),
    inference(avatar_split_clause,[],[f116,f164,f160,f156,f152]) ).

fof(f116,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,[],[f94,f25]) ).

fof(f94,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(f133,plain,
    ( spl0_8
    | spl0_9
    | spl0_10
    | spl0_11 ),
    inference(avatar_split_clause,[],[f114,f130,f126,f122,f118]) ).

fof(f114,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,[],[f94,f23]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : GRP126-3.004 : TPTP v8.1.2. Released v1.2.0.
% 0.04/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n027.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 20:42:08 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (17342)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.38  % (17344)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.20/0.38  % (17348)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.20/0.38  % (17347)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.20/0.38  % (17346)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.20/0.38  % (17349)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)
% 0.20/0.38  % (17345)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)
% 0.20/0.38  % (17343)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.20/0.38  Detected minimum model sizes of [1]
% 0.20/0.38  Detected maximum model sizes of [5]
% 0.20/0.38  TRYING [1]
% 0.20/0.38  Detected minimum model sizes of [1]
% 0.20/0.38  Detected maximum model sizes of [5]
% 0.20/0.38  Detected minimum model sizes of [1]
% 0.20/0.38  TRYING [1]
% 0.20/0.38  Detected maximum model sizes of [5]
% 0.20/0.38  Detected minimum model sizes of [1]
% 0.20/0.38  TRYING [2]
% 0.20/0.38  TRYING [1]
% 0.20/0.38  Detected maximum model sizes of [5]
% 0.20/0.38  TRYING [1]
% 0.20/0.38  TRYING [2]
% 0.20/0.38  TRYING [2]
% 0.20/0.38  TRYING [2]
% 0.20/0.38  TRYING [3]
% 0.20/0.38  TRYING [3]
% 0.20/0.38  TRYING [3]
% 0.20/0.38  TRYING [3]
% 0.20/0.39  TRYING [4]
% 0.20/0.39  TRYING [4]
% 0.20/0.39  TRYING [4]
% 0.20/0.39  TRYING [4]
% 0.20/0.39  TRYING [5]
% 0.20/0.40  TRYING [5]
% 0.20/0.40  TRYING [5]
% 0.20/0.40  TRYING [5]
% 0.20/0.40  % (17348)First to succeed.
% 0.20/0.40  % (17348)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-17342"
% 0.20/0.40  % (17348)Refutation found. Thanks to Tanya!
% 0.20/0.40  % SZS status Unsatisfiable for theBenchmark
% 0.20/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.40  % (17348)------------------------------
% 0.20/0.40  % (17348)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.40  % (17348)Termination reason: Refutation
% 0.20/0.40  
% 0.20/0.40  % (17348)Memory used [KB]: 1050
% 0.20/0.40  % (17348)Time elapsed: 0.023 s
% 0.20/0.40  % (17348)Instructions burned: 36 (million)
% 0.20/0.40  % (17342)Success in time 0.035 s
%------------------------------------------------------------------------------