TSTP Solution File: MGT036-2 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : MGT036-2 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n028.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 : Wed Aug 31 17:51:03 EDT 2022

% Result   : Unsatisfiable 0.17s 0.50s
% Output   : Refutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   64 (   7 unt;   0 def)
%            Number of atoms       :  200 (   0 equ)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :  284 ( 148   ~; 127   |;   0   &)
%                                         (   9 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   16 (  15 usr;  10 prp; 0-4 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   93 (  93   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f165,plain,
    $false,
    inference(avatar_sat_refutation,[],[f37,f39,f60,f114,f125,f128,f137,f139,f144,f164]) ).

fof(f164,plain,
    ( ~ spl0_5
    | spl0_10 ),
    inference(avatar_split_clause,[],[f162,f76,f51]) ).

fof(f51,plain,
    ( spl0_5
  <=> subpopulations(efficient_producers,first_movers,sk1,sk2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f76,plain,
    ( spl0_10
  <=> greater(zero,growth_rate(efficient_producers,sk2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f162,plain,
    ( ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
    | spl0_10 ),
    inference(resolution,[],[f160,f12]) ).

fof(f12,axiom,
    environment(sk1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t5_12) ).

fof(f160,plain,
    ( ! [X0] :
        ( ~ environment(X0)
        | ~ subpopulations(efficient_producers,first_movers,X0,sk2) )
    | spl0_10 ),
    inference(resolution,[],[f154,f14]) ).

fof(f14,axiom,
    outcompetes(first_movers,efficient_producers,sk2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t5_14) ).

fof(f154,plain,
    ( ! [X2,X3] :
        ( ~ outcompetes(X3,efficient_producers,sk2)
        | ~ subpopulations(efficient_producers,X3,X2,sk2)
        | ~ environment(X2) )
    | spl0_10 ),
    inference(resolution,[],[f77,f9]) ).

fof(f9,axiom,
    ! [X2,X3,X0,X1] :
      ( greater(zero,growth_rate(X1,X3))
      | ~ environment(X0)
      | ~ outcompetes(X2,X1,X3)
      | ~ subpopulations(X1,X2,X0,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_9) ).

fof(f77,plain,
    ( ~ greater(zero,growth_rate(efficient_producers,sk2))
    | spl0_10 ),
    inference(avatar_component_clause,[],[f76]) ).

fof(f144,plain,
    ( ~ spl0_3
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f142,f135,f27]) ).

fof(f27,plain,
    ( spl0_3
  <=> subpopulations(first_movers,efficient_producers,sk1,sk2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f135,plain,
    ( spl0_17
  <=> ! [X1] :
        ( ~ environment(X1)
        | ~ in_environment(X1,sk2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f142,plain,
    ( ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
    | ~ spl0_17 ),
    inference(resolution,[],[f141,f12]) ).

fof(f141,plain,
    ( ! [X0] :
        ( ~ environment(X0)
        | ~ subpopulations(first_movers,efficient_producers,X0,sk2) )
    | ~ spl0_17 ),
    inference(duplicate_literal_removal,[],[f140]) ).

fof(f140,plain,
    ( ! [X0] :
        ( ~ environment(X0)
        | ~ subpopulations(first_movers,efficient_producers,X0,sk2)
        | ~ environment(X0) )
    | ~ spl0_17 ),
    inference(resolution,[],[f136,f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( in_environment(X0,X1)
      | ~ environment(X0)
      | ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_occur_2) ).

fof(f136,plain,
    ( ! [X1] :
        ( ~ in_environment(X1,sk2)
        | ~ environment(X1) )
    | ~ spl0_17 ),
    inference(avatar_component_clause,[],[f135]) ).

fof(f139,plain,
    ( ~ spl0_10
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f138,f132,f76]) ).

fof(f132,plain,
    ( spl0_16
  <=> ! [X0] :
        ( ~ greater(zero,growth_rate(X0,sk2))
        | ~ greater(resilience(X0),resilience(first_movers)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f138,plain,
    ( ~ greater(zero,growth_rate(efficient_producers,sk2))
    | ~ spl0_16 ),
    inference(resolution,[],[f133,f10]) ).

fof(f10,axiom,
    greater(resilience(efficient_producers),resilience(first_movers)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2_10) ).

fof(f133,plain,
    ( ! [X0] :
        ( ~ greater(resilience(X0),resilience(first_movers))
        | ~ greater(zero,growth_rate(X0,sk2)) )
    | ~ spl0_16 ),
    inference(avatar_component_clause,[],[f132]) ).

fof(f137,plain,
    ( spl0_16
    | spl0_17
    | spl0_15 ),
    inference(avatar_split_clause,[],[f129,f122,f135,f132]) ).

fof(f122,plain,
    ( spl0_15
  <=> greater(zero,growth_rate(first_movers,sk2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f129,plain,
    ( ! [X0,X1] :
        ( ~ environment(X1)
        | ~ greater(zero,growth_rate(X0,sk2))
        | ~ in_environment(X1,sk2)
        | ~ greater(resilience(X0),resilience(first_movers)) )
    | spl0_15 ),
    inference(resolution,[],[f124,f11]) ).

fof(f11,axiom,
    ! [X2,X3,X0,X1] :
      ( greater(zero,growth_rate(X2,X1))
      | ~ greater(resilience(X3),resilience(X2))
      | ~ in_environment(X0,X1)
      | ~ greater(zero,growth_rate(X3,X1))
      | ~ environment(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a13_11) ).

fof(f124,plain,
    ( ~ greater(zero,growth_rate(first_movers,sk2))
    | spl0_15 ),
    inference(avatar_component_clause,[],[f122]) ).

fof(f128,plain,
    ( ~ spl0_15
    | spl0_14 ),
    inference(avatar_split_clause,[],[f126,f118,f122]) ).

fof(f118,plain,
    ( spl0_14
  <=> subpopulations(first_movers,first_movers,sk1,sk2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f126,plain,
    ( ~ greater(zero,growth_rate(first_movers,sk2))
    | spl0_14 ),
    inference(resolution,[],[f120,f4]) ).

fof(f4,axiom,
    ! [X2,X3,X0,X1] :
      ( subpopulations(X0,X1,X2,X3)
      | ~ greater(zero,growth_rate(X0,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_growth_rate_relationships_4) ).

fof(f120,plain,
    ( ~ subpopulations(first_movers,first_movers,sk1,sk2)
    | spl0_14 ),
    inference(avatar_component_clause,[],[f118]) ).

fof(f125,plain,
    ( ~ spl0_14
    | ~ spl0_15
    | ~ spl0_5
    | ~ spl0_13 ),
    inference(avatar_split_clause,[],[f115,f112,f51,f122,f118]) ).

fof(f112,plain,
    ( spl0_13
  <=> ! [X0,X1] :
        ( ~ outcompetes(X0,X1,sk2)
        | ~ subpopulations(X1,X0,sk1,sk2)
        | ~ greater(zero,growth_rate(X0,sk2))
        | ~ subpopulations(X0,first_movers,sk1,sk2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f115,plain,
    ( ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
    | ~ greater(zero,growth_rate(first_movers,sk2))
    | ~ subpopulations(first_movers,first_movers,sk1,sk2)
    | ~ spl0_13 ),
    inference(resolution,[],[f113,f14]) ).

fof(f113,plain,
    ( ! [X0,X1] :
        ( ~ outcompetes(X0,X1,sk2)
        | ~ subpopulations(X1,X0,sk1,sk2)
        | ~ subpopulations(X0,first_movers,sk1,sk2)
        | ~ greater(zero,growth_rate(X0,sk2)) )
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f112]) ).

fof(f114,plain,
    ( ~ spl0_5
    | spl0_13 ),
    inference(avatar_split_clause,[],[f109,f112,f51]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( ~ outcompetes(X0,X1,sk2)
      | ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
      | ~ subpopulations(X0,first_movers,sk1,sk2)
      | ~ greater(zero,growth_rate(X0,sk2))
      | ~ subpopulations(X1,X0,sk1,sk2) ),
    inference(resolution,[],[f107,f14]) ).

fof(f107,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ outcompetes(X3,X4,X2)
      | ~ subpopulations(X1,X3,sk1,X2)
      | ~ greater(zero,growth_rate(X1,X2))
      | ~ outcompetes(X1,X0,X2)
      | ~ subpopulations(X0,X1,sk1,X2)
      | ~ subpopulations(X4,X3,sk1,X2) ),
    inference(resolution,[],[f106,f12]) ).

fof(f106,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ environment(X0)
      | ~ subpopulations(X5,X1,sk1,X3)
      | ~ subpopulations(X1,X2,sk1,X3)
      | ~ subpopulations(X4,X2,X0,X3)
      | ~ greater(zero,growth_rate(X1,X3))
      | ~ outcompetes(X1,X5,X3)
      | ~ outcompetes(X2,X4,X3) ),
    inference(duplicate_literal_removal,[],[f104]) ).

fof(f104,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ subpopulations(X4,X2,X0,X3)
      | ~ outcompetes(X1,X5,X3)
      | ~ subpopulations(X1,X2,sk1,X3)
      | ~ subpopulations(X1,X2,sk1,X3)
      | ~ environment(X0)
      | ~ subpopulations(X5,X1,sk1,X3)
      | ~ greater(zero,growth_rate(X1,X3))
      | ~ outcompetes(X2,X4,X3) ),
    inference(resolution,[],[f101,f12]) ).

fof(f101,plain,
    ! [X10,X11,X8,X9,X7,X12,X13] :
      ( ~ environment(X11)
      | ~ environment(X13)
      | ~ subpopulations(X7,X10,sk1,X9)
      | ~ subpopulations(X7,X10,X11,X9)
      | ~ outcompetes(X10,X12,X9)
      | ~ outcompetes(X7,X8,X9)
      | ~ subpopulations(X12,X10,X13,X9)
      | ~ greater(zero,growth_rate(X7,X9))
      | ~ subpopulations(X8,X7,sk1,X9) ),
    inference(resolution,[],[f49,f8]) ).

fof(f8,axiom,
    ! [X2,X3,X0,X1] :
      ( greater_or_equal(growth_rate(X2,X3),zero)
      | ~ subpopulations(X1,X2,X0,X3)
      | ~ environment(X0)
      | ~ outcompetes(X2,X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_8) ).

fof(f49,plain,
    ! [X2,X3,X1,X4,X5] :
      ( ~ greater_or_equal(growth_rate(X4,X3),zero)
      | ~ outcompetes(X2,X1,X3)
      | ~ subpopulations(X2,X4,sk1,X3)
      | ~ greater(zero,growth_rate(X2,X3))
      | ~ subpopulations(X2,X4,X5,X3)
      | ~ subpopulations(X1,X2,sk1,X3)
      | ~ environment(X5) ),
    inference(resolution,[],[f46,f7]) ).

fof(f7,axiom,
    ! [X2,X3,X0,X1] :
      ( outcompetes(X2,X1,X3)
      | ~ greater(zero,growth_rate(X1,X3))
      | ~ greater_or_equal(growth_rate(X2,X3),zero)
      | ~ environment(X0)
      | ~ subpopulations(X1,X2,X0,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_7) ).

fof(f46,plain,
    ! [X2,X3,X0,X1] :
      ( ~ outcompetes(X3,X1,X2)
      | ~ subpopulations(X0,X1,sk1,X2)
      | ~ subpopulations(X1,X3,sk1,X2)
      | ~ outcompetes(X1,X0,X2) ),
    inference(resolution,[],[f44,f12]) ).

fof(f44,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ environment(X2)
      | ~ subpopulations(X0,X1,X2,X3)
      | ~ subpopulations(X1,X4,sk1,X3)
      | ~ outcompetes(X1,X0,X3)
      | ~ outcompetes(X4,X1,X3) ),
    inference(resolution,[],[f41,f12]) ).

fof(f41,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ environment(X4)
      | ~ subpopulations(X1,X0,X3,X2)
      | ~ outcompetes(X0,X1,X2)
      | ~ outcompetes(X5,X0,X2)
      | ~ environment(X3)
      | ~ subpopulations(X0,X5,X4,X2) ),
    inference(resolution,[],[f40,f9]) ).

fof(f40,plain,
    ! [X2,X3,X0,X1] :
      ( ~ greater(zero,growth_rate(X0,X1))
      | ~ outcompetes(X0,X2,X1)
      | ~ subpopulations(X2,X0,X3,X1)
      | ~ environment(X3) ),
    inference(resolution,[],[f5,f8]) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( ~ greater_or_equal(growth_rate(X0,X1),zero)
      | ~ greater(zero,growth_rate(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_growth_rate_relationships_5) ).

fof(f60,plain,
    ( ~ spl0_3
    | ~ spl0_4
    | spl0_5 ),
    inference(avatar_split_clause,[],[f59,f51,f31,f27]) ).

fof(f31,plain,
    ( spl0_4
  <=> environment(sk1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f59,plain,
    ( ~ environment(sk1)
    | ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
    | spl0_5 ),
    inference(resolution,[],[f53,f1]) ).

fof(f1,axiom,
    ! [X2,X3,X0,X1] :
      ( subpopulations(X2,X1,X0,X3)
      | ~ subpopulations(X1,X2,X0,X3)
      | ~ environment(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations_1) ).

fof(f53,plain,
    ( ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
    | spl0_5 ),
    inference(avatar_component_clause,[],[f51]) ).

fof(f39,plain,
    spl0_4,
    inference(avatar_contradiction_clause,[],[f38]) ).

fof(f38,plain,
    ( $false
    | spl0_4 ),
    inference(resolution,[],[f33,f12]) ).

fof(f33,plain,
    ( ~ environment(sk1)
    | spl0_4 ),
    inference(avatar_component_clause,[],[f31]) ).

fof(f37,plain,
    spl0_3,
    inference(avatar_contradiction_clause,[],[f35]) ).

fof(f35,plain,
    ( $false
    | spl0_3 ),
    inference(resolution,[],[f29,f13]) ).

fof(f13,axiom,
    subpopulations(first_movers,efficient_producers,sk1,sk2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t5_13) ).

fof(f29,plain,
    ( ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
    | spl0_3 ),
    inference(avatar_component_clause,[],[f27]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : MGT036-2 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.11/0.32  % Computer : n028.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Tue Aug 30 03:26:48 EDT 2022
% 0.11/0.32  % CPUTime    : 
% 0.17/0.49  % (14901)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=97:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/97Mi)
% 0.17/0.49  % (14884)dis+1011_1:16_fsr=off:nwc=2.0:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.17/0.50  % (14884)First to succeed.
% 0.17/0.50  % (14902)lrs+1011_1:1_aac=none:bsr=unit_only:ep=R:sac=on:sos=all:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.17/0.50  % (14884)Refutation found. Thanks to Tanya!
% 0.17/0.50  % SZS status Unsatisfiable for theBenchmark
% 0.17/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.50  % (14884)------------------------------
% 0.17/0.50  % (14884)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.50  % (14884)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.17/0.50  % (14884)Termination reason: Refutation
% 0.17/0.50  
% 0.17/0.50  % (14884)Memory used [KB]: 6012
% 0.17/0.50  % (14884)Time elapsed: 0.113 s
% 0.17/0.50  % (14884)Instructions burned: 6 (million)
% 0.17/0.50  % (14884)------------------------------
% 0.17/0.50  % (14884)------------------------------
% 0.17/0.50  % (14878)Success in time 0.175 s
%------------------------------------------------------------------------------