TSTP Solution File: GRP124-9.004 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : GRP124-9.004 : TPTP v8.2.0. 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 : n013.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 : Mon May 20 21:06:43 EDT 2024

% Result   : Unsatisfiable 0.58s 0.74s
% Output   : Refutation 0.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   45
% Syntax   : Number of formulae    :  147 (  29 unt;   0 def)
%            Number of atoms       :  380 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  391 ( 158   ~; 209   |;   0   &)
%                                         (  24 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   29 (  28 usr;  25 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :   53 (  53   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f531,plain,
    $false,
    inference(avatar_sat_refutation,[],[f64,f103,f105,f107,f120,f122,f166,f203,f210,f276,f293,f326,f338,f348,f350,f358,f365,f367,f426,f457,f498,f506,f513,f523,f530]) ).

fof(f530,plain,
    ~ spl0_35,
    inference(avatar_contradiction_clause,[],[f529]) ).

fof(f529,plain,
    ( $false
    | ~ spl0_35 ),
    inference(resolution,[],[f528,f7]) ).

fof(f7,axiom,
    ~ equalish(e_1,e_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).

fof(f528,plain,
    ( equalish(e_1,e_2)
    | ~ spl0_35 ),
    inference(resolution,[],[f448,f36]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ~ product1(X0,X1,X1)
      | equalish(X0,X1) ),
    inference(resolution,[],[f22,f23]) ).

fof(f23,axiom,
    ! [X0] : product1(X0,X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_idempotence) ).

fof(f22,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ product1(X3,X1,X0)
      | equalish(X2,X3)
      | ~ product1(X2,X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_left_cancellation) ).

fof(f448,plain,
    ( product1(e_1,e_2,e_2)
    | ~ spl0_35 ),
    inference(avatar_component_clause,[],[f446]) ).

fof(f446,plain,
    ( spl0_35
  <=> product1(e_1,e_2,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f523,plain,
    ~ spl0_37,
    inference(avatar_contradiction_clause,[],[f522]) ).

fof(f522,plain,
    ( $false
    | ~ spl0_37 ),
    inference(resolution,[],[f521,f7]) ).

fof(f521,plain,
    ( equalish(e_1,e_2)
    | ~ spl0_37 ),
    inference(resolution,[],[f456,f38]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ~ product2(X1,X1,X0)
      | equalish(X0,X1) ),
    inference(resolution,[],[f25,f28]) ).

fof(f28,axiom,
    ! [X0] : product2(X0,X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_idempotence) ).

fof(f25,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ product2(X0,X1,X3)
      | equalish(X2,X3)
      | ~ product2(X0,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_total_function2) ).

fof(f456,plain,
    ( product2(e_2,e_2,e_1)
    | ~ spl0_37 ),
    inference(avatar_component_clause,[],[f454]) ).

fof(f454,plain,
    ( spl0_37
  <=> product2(e_2,e_2,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f513,plain,
    ( ~ spl0_8
    | ~ spl0_29 ),
    inference(avatar_contradiction_clause,[],[f512]) ).

fof(f512,plain,
    ( $false
    | ~ spl0_8
    | ~ spl0_29 ),
    inference(resolution,[],[f507,f11]) ).

fof(f11,axiom,
    ~ equalish(e_2,e_3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).

fof(f507,plain,
    ( equalish(e_2,e_3)
    | ~ spl0_8
    | ~ spl0_29 ),
    inference(resolution,[],[f292,f381]) ).

fof(f381,plain,
    ( ! [X0] :
        ( ~ product1(e_4,X0,e_1)
        | equalish(X0,e_3) )
    | ~ spl0_8 ),
    inference(resolution,[],[f102,f21]) ).

fof(f21,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ product1(X0,X3,X1)
      | equalish(X2,X3)
      | ~ product1(X0,X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_right_cancellation) ).

fof(f102,plain,
    ( product1(e_4,e_3,e_1)
    | ~ spl0_8 ),
    inference(avatar_component_clause,[],[f100]) ).

fof(f100,plain,
    ( spl0_8
  <=> product1(e_4,e_3,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f292,plain,
    ( product1(e_4,e_2,e_1)
    | ~ spl0_29 ),
    inference(avatar_component_clause,[],[f290]) ).

fof(f290,plain,
    ( spl0_29
  <=> product1(e_4,e_2,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f506,plain,
    ~ spl0_36,
    inference(avatar_contradiction_clause,[],[f505]) ).

fof(f505,plain,
    ( $false
    | ~ spl0_36 ),
    inference(resolution,[],[f503,f10]) ).

fof(f10,axiom,
    ~ equalish(e_2,e_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).

fof(f503,plain,
    ( equalish(e_2,e_1)
    | ~ spl0_36 ),
    inference(resolution,[],[f452,f34]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ~ product1(X1,X0,X1)
      | equalish(X0,X1) ),
    inference(resolution,[],[f21,f23]) ).

fof(f452,plain,
    ( product1(e_1,e_2,e_1)
    | ~ spl0_36 ),
    inference(avatar_component_clause,[],[f450]) ).

fof(f450,plain,
    ( spl0_36
  <=> product1(e_1,e_2,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f498,plain,
    ( ~ spl0_26
    | ~ spl0_34 ),
    inference(avatar_contradiction_clause,[],[f497]) ).

fof(f497,plain,
    ( $false
    | ~ spl0_26
    | ~ spl0_34 ),
    inference(resolution,[],[f492,f9]) ).

fof(f9,axiom,
    ~ equalish(e_1,e_4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_4) ).

fof(f492,plain,
    ( equalish(e_1,e_4)
    | ~ spl0_26
    | ~ spl0_34 ),
    inference(resolution,[],[f444,f384]) ).

fof(f384,plain,
    ( ! [X0] :
        ( ~ product1(X0,e_2,e_3)
        | equalish(X0,e_4) )
    | ~ spl0_26 ),
    inference(resolution,[],[f280,f22]) ).

fof(f280,plain,
    ( product1(e_4,e_2,e_3)
    | ~ spl0_26 ),
    inference(avatar_component_clause,[],[f278]) ).

fof(f278,plain,
    ( spl0_26
  <=> product1(e_4,e_2,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f444,plain,
    ( product1(e_1,e_2,e_3)
    | ~ spl0_34 ),
    inference(avatar_component_clause,[],[f442]) ).

fof(f442,plain,
    ( spl0_34
  <=> product1(e_1,e_2,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f457,plain,
    ( spl0_34
    | spl0_35
    | spl0_36
    | spl0_37
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f438,f424,f454,f450,f446,f442]) ).

fof(f424,plain,
    ( spl0_31
  <=> ! [X0] :
        ( product2(e_2,X0,e_1)
        | ~ group_element(X0)
        | product1(e_1,X0,e_1)
        | product1(e_1,X0,e_2)
        | product1(e_1,X0,e_3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f438,plain,
    ( product2(e_2,e_2,e_1)
    | product1(e_1,e_2,e_1)
    | product1(e_1,e_2,e_2)
    | product1(e_1,e_2,e_3)
    | ~ spl0_31 ),
    inference(resolution,[],[f425,f4]) ).

fof(f4,axiom,
    group_element(e_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).

fof(f425,plain,
    ( ! [X0] :
        ( ~ group_element(X0)
        | product2(e_2,X0,e_1)
        | product1(e_1,X0,e_1)
        | product1(e_1,X0,e_2)
        | product1(e_1,X0,e_3) )
    | ~ spl0_31 ),
    inference(avatar_component_clause,[],[f424]) ).

fof(f426,plain,
    ( ~ spl0_23
    | spl0_31
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f422,f269,f424,f265]) ).

fof(f265,plain,
    ( spl0_23
  <=> group_element(e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f269,plain,
    ( spl0_24
  <=> product1(e_4,e_1,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f422,plain,
    ( ! [X0] :
        ( product2(e_2,X0,e_1)
        | product1(e_1,X0,e_3)
        | product1(e_1,X0,e_2)
        | product1(e_1,X0,e_1)
        | ~ group_element(X0)
        | ~ group_element(e_1) )
    | ~ spl0_24 ),
    inference(resolution,[],[f372,f19]) ).

fof(f19,axiom,
    ! [X0,X1] :
      ( product1(X0,X1,e_4)
      | product1(X0,X1,e_3)
      | product1(X0,X1,e_2)
      | product1(X0,X1,e_1)
      | ~ group_element(X1)
      | ~ group_element(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_total_function1) ).

fof(f372,plain,
    ( ! [X0] :
        ( ~ product1(e_1,X0,e_4)
        | product2(e_2,X0,e_1) )
    | ~ spl0_24 ),
    inference(resolution,[],[f271,f29]) ).

fof(f29,axiom,
    ! [X0,X1,X4,X5] :
      ( ~ product1(X4,X0,X5)
      | product2(X5,X1,X0)
      | ~ product1(X0,X1,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg2a) ).

fof(f271,plain,
    ( product1(e_4,e_1,e_2)
    | ~ spl0_24 ),
    inference(avatar_component_clause,[],[f269]) ).

fof(f367,plain,
    spl0_23,
    inference(avatar_contradiction_clause,[],[f366]) ).

fof(f366,plain,
    ( $false
    | spl0_23 ),
    inference(resolution,[],[f267,f3]) ).

fof(f3,axiom,
    group_element(e_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).

fof(f267,plain,
    ( ~ group_element(e_1)
    | spl0_23 ),
    inference(avatar_component_clause,[],[f265]) ).

fof(f365,plain,
    ~ spl0_25,
    inference(avatar_contradiction_clause,[],[f364]) ).

fof(f364,plain,
    ( $false
    | ~ spl0_25 ),
    inference(resolution,[],[f363,f16]) ).

fof(f16,axiom,
    ~ equalish(e_4,e_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_1) ).

fof(f363,plain,
    ( equalish(e_4,e_1)
    | ~ spl0_25 ),
    inference(resolution,[],[f275,f36]) ).

fof(f275,plain,
    ( product1(e_4,e_1,e_1)
    | ~ spl0_25 ),
    inference(avatar_component_clause,[],[f273]) ).

fof(f273,plain,
    ( spl0_25
  <=> product1(e_4,e_1,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f358,plain,
    ~ spl0_28,
    inference(avatar_contradiction_clause,[],[f357]) ).

fof(f357,plain,
    ( $false
    | ~ spl0_28 ),
    inference(resolution,[],[f356,f17]) ).

fof(f17,axiom,
    ~ equalish(e_4,e_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_2) ).

fof(f356,plain,
    ( equalish(e_4,e_2)
    | ~ spl0_28 ),
    inference(resolution,[],[f288,f36]) ).

fof(f288,plain,
    ( product1(e_4,e_2,e_2)
    | ~ spl0_28 ),
    inference(avatar_component_clause,[],[f286]) ).

fof(f286,plain,
    ( spl0_28
  <=> product1(e_4,e_2,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f350,plain,
    spl0_27,
    inference(avatar_contradiction_clause,[],[f349]) ).

fof(f349,plain,
    ( $false
    | spl0_27 ),
    inference(resolution,[],[f284,f4]) ).

fof(f284,plain,
    ( ~ group_element(e_2)
    | spl0_27 ),
    inference(avatar_component_clause,[],[f282]) ).

fof(f282,plain,
    ( spl0_27
  <=> group_element(e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f348,plain,
    ( ~ spl0_16
    | ~ spl0_29 ),
    inference(avatar_contradiction_clause,[],[f347]) ).

fof(f347,plain,
    ( $false
    | ~ spl0_16
    | ~ spl0_29 ),
    inference(resolution,[],[f346,f15]) ).

fof(f15,axiom,
    ~ equalish(e_3,e_4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_4) ).

fof(f346,plain,
    ( equalish(e_3,e_4)
    | ~ spl0_16
    | ~ spl0_29 ),
    inference(resolution,[],[f339,f161]) ).

fof(f161,plain,
    ( product1(e_3,e_2,e_1)
    | ~ spl0_16 ),
    inference(avatar_component_clause,[],[f159]) ).

fof(f159,plain,
    ( spl0_16
  <=> product1(e_3,e_2,e_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f339,plain,
    ( ! [X0] :
        ( ~ product1(X0,e_2,e_1)
        | equalish(X0,e_4) )
    | ~ spl0_29 ),
    inference(resolution,[],[f292,f22]) ).

fof(f338,plain,
    ( ~ spl0_22
    | ~ spl0_26 ),
    inference(avatar_contradiction_clause,[],[f337]) ).

fof(f337,plain,
    ( $false
    | ~ spl0_22
    | ~ spl0_26 ),
    inference(resolution,[],[f336,f10]) ).

fof(f336,plain,
    ( equalish(e_2,e_1)
    | ~ spl0_22
    | ~ spl0_26 ),
    inference(resolution,[],[f296,f280]) ).

fof(f296,plain,
    ( ! [X0] :
        ( ~ product1(e_4,X0,e_3)
        | equalish(X0,e_1) )
    | ~ spl0_22 ),
    inference(resolution,[],[f263,f21]) ).

fof(f263,plain,
    ( product1(e_4,e_1,e_3)
    | ~ spl0_22 ),
    inference(avatar_component_clause,[],[f261]) ).

fof(f261,plain,
    ( spl0_22
  <=> product1(e_4,e_1,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f326,plain,
    ~ spl0_17,
    inference(avatar_contradiction_clause,[],[f325]) ).

fof(f325,plain,
    ( $false
    | ~ spl0_17 ),
    inference(resolution,[],[f324,f14]) ).

fof(f14,axiom,
    ~ equalish(e_3,e_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).

fof(f324,plain,
    ( equalish(e_3,e_2)
    | ~ spl0_17 ),
    inference(resolution,[],[f165,f38]) ).

fof(f165,plain,
    ( product2(e_2,e_2,e_3)
    | ~ spl0_17 ),
    inference(avatar_component_clause,[],[f163]) ).

fof(f163,plain,
    ( spl0_17
  <=> product2(e_2,e_2,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f293,plain,
    ( spl0_26
    | ~ spl0_27
    | spl0_28
    | spl0_29
    | ~ spl0_3 ),
    inference(avatar_split_clause,[],[f258,f62,f290,f286,f282,f278]) ).

fof(f62,plain,
    ( spl0_3
  <=> ! [X0] :
        ( product1(e_4,X0,e_3)
        | product2(e_4,X0,e_4)
        | ~ group_element(X0)
        | product1(e_4,X0,e_1)
        | product1(e_4,X0,e_2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f258,plain,
    ( product1(e_4,e_2,e_1)
    | product1(e_4,e_2,e_2)
    | ~ group_element(e_2)
    | product1(e_4,e_2,e_3)
    | ~ spl0_3 ),
    inference(resolution,[],[f256,f17]) ).

fof(f256,plain,
    ( ! [X0] :
        ( equalish(e_4,X0)
        | product1(e_4,X0,e_1)
        | product1(e_4,X0,e_2)
        | ~ group_element(X0)
        | product1(e_4,X0,e_3) )
    | ~ spl0_3 ),
    inference(resolution,[],[f126,f28]) ).

fof(f126,plain,
    ( ! [X0,X1] :
        ( ~ product2(e_4,X1,e_4)
        | ~ group_element(X0)
        | product1(e_4,X0,e_1)
        | product1(e_4,X0,e_2)
        | equalish(X1,X0)
        | product1(e_4,X0,e_3) )
    | ~ spl0_3 ),
    inference(resolution,[],[f63,f26]) ).

fof(f26,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ product2(X0,X3,X1)
      | equalish(X2,X3)
      | ~ product2(X0,X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_right_cancellation) ).

fof(f63,plain,
    ( ! [X0] :
        ( product2(e_4,X0,e_4)
        | product1(e_4,X0,e_3)
        | ~ group_element(X0)
        | product1(e_4,X0,e_1)
        | product1(e_4,X0,e_2) )
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f62]) ).

fof(f276,plain,
    ( spl0_22
    | ~ spl0_23
    | spl0_24
    | spl0_25
    | ~ spl0_3 ),
    inference(avatar_split_clause,[],[f257,f62,f273,f269,f265,f261]) ).

fof(f257,plain,
    ( product1(e_4,e_1,e_1)
    | product1(e_4,e_1,e_2)
    | ~ group_element(e_1)
    | product1(e_4,e_1,e_3)
    | ~ spl0_3 ),
    inference(resolution,[],[f256,f16]) ).

fof(f210,plain,
    ~ spl0_15,
    inference(avatar_contradiction_clause,[],[f209]) ).

fof(f209,plain,
    ( $false
    | ~ spl0_15 ),
    inference(resolution,[],[f208,f14]) ).

fof(f208,plain,
    ( equalish(e_3,e_2)
    | ~ spl0_15 ),
    inference(resolution,[],[f157,f36]) ).

fof(f157,plain,
    ( product1(e_3,e_2,e_2)
    | ~ spl0_15 ),
    inference(avatar_component_clause,[],[f155]) ).

fof(f155,plain,
    ( spl0_15
  <=> product1(e_3,e_2,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f203,plain,
    ~ spl0_14,
    inference(avatar_contradiction_clause,[],[f202]) ).

fof(f202,plain,
    ( $false
    | ~ spl0_14 ),
    inference(resolution,[],[f200,f11]) ).

fof(f200,plain,
    ( equalish(e_2,e_3)
    | ~ spl0_14 ),
    inference(resolution,[],[f153,f34]) ).

fof(f153,plain,
    ( product1(e_3,e_2,e_3)
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f151]) ).

fof(f151,plain,
    ( spl0_14
  <=> product1(e_3,e_2,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f166,plain,
    ( spl0_14
    | spl0_15
    | spl0_16
    | spl0_17
    | ~ spl0_9 ),
    inference(avatar_split_clause,[],[f130,f118,f163,f159,f155,f151]) ).

fof(f118,plain,
    ( spl0_9
  <=> ! [X0] :
        ( product2(e_2,X0,e_3)
        | ~ group_element(X0)
        | product1(e_3,X0,e_1)
        | product1(e_3,X0,e_2)
        | product1(e_3,X0,e_3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f130,plain,
    ( product2(e_2,e_2,e_3)
    | product1(e_3,e_2,e_1)
    | product1(e_3,e_2,e_2)
    | product1(e_3,e_2,e_3)
    | ~ spl0_9 ),
    inference(resolution,[],[f119,f4]) ).

fof(f119,plain,
    ( ! [X0] :
        ( ~ group_element(X0)
        | product2(e_2,X0,e_3)
        | product1(e_3,X0,e_1)
        | product1(e_3,X0,e_2)
        | product1(e_3,X0,e_3) )
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f118]) ).

fof(f122,plain,
    spl0_5,
    inference(avatar_contradiction_clause,[],[f121]) ).

fof(f121,plain,
    ( $false
    | spl0_5 ),
    inference(resolution,[],[f90,f5]) ).

fof(f5,axiom,
    group_element(e_3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).

fof(f90,plain,
    ( ~ group_element(e_3)
    | spl0_5 ),
    inference(avatar_component_clause,[],[f88]) ).

fof(f88,plain,
    ( spl0_5
  <=> group_element(e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f120,plain,
    ( ~ spl0_5
    | spl0_9
    | ~ spl0_7 ),
    inference(avatar_split_clause,[],[f116,f96,f118,f88]) ).

fof(f96,plain,
    ( spl0_7
  <=> product1(e_4,e_3,e_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f116,plain,
    ( ! [X0] :
        ( product2(e_2,X0,e_3)
        | product1(e_3,X0,e_3)
        | product1(e_3,X0,e_2)
        | product1(e_3,X0,e_1)
        | ~ group_element(X0)
        | ~ group_element(e_3) )
    | ~ spl0_7 ),
    inference(resolution,[],[f111,f19]) ).

fof(f111,plain,
    ( ! [X0] :
        ( ~ product1(e_3,X0,e_4)
        | product2(e_2,X0,e_3) )
    | ~ spl0_7 ),
    inference(resolution,[],[f98,f29]) ).

fof(f98,plain,
    ( product1(e_4,e_3,e_2)
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f96]) ).

fof(f107,plain,
    ~ spl0_6,
    inference(avatar_contradiction_clause,[],[f106]) ).

fof(f106,plain,
    ( $false
    | ~ spl0_6 ),
    inference(resolution,[],[f94,f18]) ).

fof(f18,axiom,
    ~ equalish(e_4,e_3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_3) ).

fof(f94,plain,
    ( equalish(e_4,e_3)
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f92]) ).

fof(f92,plain,
    ( spl0_6
  <=> equalish(e_4,e_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f105,plain,
    spl0_1,
    inference(avatar_contradiction_clause,[],[f104]) ).

fof(f104,plain,
    ( $false
    | spl0_1 ),
    inference(resolution,[],[f56,f6]) ).

fof(f6,axiom,
    group_element(e_4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).

fof(f56,plain,
    ( ~ group_element(e_4)
    | spl0_1 ),
    inference(avatar_component_clause,[],[f54]) ).

fof(f54,plain,
    ( spl0_1
  <=> group_element(e_4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f103,plain,
    ( ~ spl0_5
    | spl0_6
    | spl0_7
    | spl0_8
    | ~ spl0_3 ),
    inference(avatar_split_clause,[],[f86,f62,f100,f96,f92,f88]) ).

fof(f86,plain,
    ( product1(e_4,e_3,e_1)
    | product1(e_4,e_3,e_2)
    | equalish(e_4,e_3)
    | ~ group_element(e_3)
    | ~ spl0_3 ),
    inference(duplicate_literal_removal,[],[f84]) ).

fof(f84,plain,
    ( product1(e_4,e_3,e_1)
    | product1(e_4,e_3,e_2)
    | equalish(e_4,e_3)
    | ~ group_element(e_3)
    | equalish(e_4,e_3)
    | ~ spl0_3 ),
    inference(resolution,[],[f79,f36]) ).

fof(f79,plain,
    ( ! [X0] :
        ( product1(e_4,X0,e_3)
        | product1(e_4,X0,e_1)
        | product1(e_4,X0,e_2)
        | equalish(e_4,X0)
        | ~ group_element(X0) )
    | ~ spl0_3 ),
    inference(resolution,[],[f70,f28]) ).

fof(f70,plain,
    ( ! [X0,X1] :
        ( ~ product2(e_4,X1,e_4)
        | ~ group_element(X0)
        | product1(e_4,X0,e_1)
        | product1(e_4,X0,e_2)
        | equalish(X1,X0)
        | product1(e_4,X0,e_3) )
    | ~ spl0_3 ),
    inference(resolution,[],[f63,f26]) ).

fof(f64,plain,
    ( ~ spl0_1
    | spl0_3 ),
    inference(avatar_split_clause,[],[f49,f62,f54]) ).

fof(f49,plain,
    ! [X0] :
      ( product1(e_4,X0,e_3)
      | product1(e_4,X0,e_2)
      | product1(e_4,X0,e_1)
      | ~ group_element(X0)
      | ~ group_element(e_4)
      | product2(e_4,X0,e_4) ),
    inference(resolution,[],[f19,f30]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ~ product1(X0,X1,X0)
      | product2(X0,X1,X0) ),
    inference(resolution,[],[f23,f29]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : GRP124-9.004 : TPTP v8.2.0. Bugfixed v1.2.1.
% 0.10/0.14  % 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
% 0.15/0.35  % Computer : n013.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Sun May 19 04:33:38 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.15/0.35  This is a CNF_UNS_EPR_NEQ_NHN problem
% 0.15/0.35  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/benchmark/theBenchmark.p
% 0.48/0.72  % (14854)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on theBenchmark for (2996ds/56Mi)
% 0.48/0.72  % (14851)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 theBenchmark for (2996ds/34Mi)
% 0.48/0.72  % (14847)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 theBenchmark for (2996ds/34Mi)
% 0.48/0.72  % (14849)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on theBenchmark for (2996ds/78Mi)
% 0.48/0.72  % (14848)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 theBenchmark for (2996ds/51Mi)
% 0.48/0.72  % (14854)Refutation not found, incomplete strategy% (14854)------------------------------
% 0.48/0.72  % (14854)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.48/0.72  % (14854)Termination reason: Refutation not found, incomplete strategy
% 0.48/0.72  
% 0.48/0.72  % (14854)Memory used [KB]: 952
% 0.48/0.72  % (14854)Time elapsed: 0.002 s
% 0.48/0.72  % (14854)Instructions burned: 2 (million)
% 0.48/0.72  % (14847)Refutation not found, incomplete strategy% (14847)------------------------------
% 0.48/0.72  % (14847)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.48/0.72  % (14847)Termination reason: Refutation not found, incomplete strategy
% 0.48/0.72  
% 0.48/0.72  % (14847)Memory used [KB]: 950
% 0.48/0.72  % (14847)Time elapsed: 0.002 s
% 0.48/0.72  % (14847)Instructions burned: 2 (million)
% 0.48/0.72  % (14854)------------------------------
% 0.48/0.72  % (14854)------------------------------
% 0.48/0.72  % (14847)------------------------------
% 0.48/0.72  % (14847)------------------------------
% 0.48/0.73  % (14852)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on theBenchmark for (2996ds/45Mi)
% 0.48/0.73  % (14850)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on theBenchmark for (2996ds/33Mi)
% 0.48/0.73  % (14850)Refutation not found, incomplete strategy% (14850)------------------------------
% 0.48/0.73  % (14850)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.48/0.73  % (14850)Termination reason: Refutation not found, incomplete strategy
% 0.48/0.73  
% 0.48/0.73  % (14850)Memory used [KB]: 950
% 0.48/0.73  % (14850)Time elapsed: 0.003 s
% 0.48/0.73  % (14850)Instructions burned: 2 (million)
% 0.48/0.73  % (14850)------------------------------
% 0.48/0.73  % (14850)------------------------------
% 0.58/0.73  % (14855)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 theBenchmark for (2996ds/55Mi)
% 0.58/0.73  % (14853)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 theBenchmark for (2996ds/83Mi)
% 0.58/0.73  % (14857)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on theBenchmark for (2996ds/208Mi)
% 0.58/0.73  % (14857)Refutation not found, incomplete strategy% (14857)------------------------------
% 0.58/0.73  % (14857)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.73  % (14857)Termination reason: Refutation not found, incomplete strategy
% 0.58/0.73  
% 0.58/0.73  % (14857)Memory used [KB]: 950
% 0.58/0.73  % (14857)Time elapsed: 0.002 s
% 0.58/0.73  % (14857)Instructions burned: 2 (million)
% 0.58/0.73  % (14857)------------------------------
% 0.58/0.73  % (14857)------------------------------
% 0.58/0.73  % (14848)First to succeed.
% 0.58/0.73  % (14851)Instruction limit reached!
% 0.58/0.73  % (14851)------------------------------
% 0.58/0.73  % (14851)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.73  % (14851)Termination reason: Unknown
% 0.58/0.73  % (14851)Termination phase: Saturation
% 0.58/0.73  
% 0.58/0.73  % (14851)Memory used [KB]: 1162
% 0.58/0.73  % (14851)Time elapsed: 0.011 s
% 0.58/0.73  % (14851)Instructions burned: 38 (million)
% 0.58/0.73  % (14851)------------------------------
% 0.58/0.73  % (14851)------------------------------
% 0.58/0.73  % (14855)Refutation not found, incomplete strategy% (14855)------------------------------
% 0.58/0.73  % (14855)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.73  % (14855)Termination reason: Refutation not found, incomplete strategy
% 0.58/0.73  
% 0.58/0.73  % (14855)Memory used [KB]: 1046
% 0.58/0.73  % (14855)Time elapsed: 0.006 s
% 0.58/0.73  % (14855)Instructions burned: 7 (million)
% 0.58/0.73  % (14855)------------------------------
% 0.58/0.73  % (14855)------------------------------
% 0.58/0.73  % (14858)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 theBenchmark for (2996ds/52Mi)
% 0.58/0.73  % (14848)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-14845"
% 0.58/0.74  % (14856)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 theBenchmark for (2996ds/50Mi)
% 0.58/0.74  % (14848)Refutation found. Thanks to Tanya!
% 0.58/0.74  % SZS status Unsatisfiable for theBenchmark
% 0.58/0.74  % SZS output start Proof for theBenchmark
% See solution above
% 0.58/0.74  % (14848)------------------------------
% 0.58/0.74  % (14848)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.74  % (14848)Termination reason: Refutation
% 0.58/0.74  
% 0.58/0.74  % (14848)Memory used [KB]: 1151
% 0.58/0.74  % (14848)Time elapsed: 0.012 s
% 0.58/0.74  % (14848)Instructions burned: 17 (million)
% 0.58/0.74  % (14845)Success in time 0.37 s
% 0.58/0.74  % Vampire---4.8 exiting
%------------------------------------------------------------------------------