TSTP Solution File: MGT028-1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : MGT028-1 : 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 : n026.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 17:50:58 EDT 2022

% Result   : Unsatisfiable 0.21s 0.51s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   58 (   8 unt;   0 def)
%            Number of atoms       :  240 (   0 equ)
%            Maximal formula atoms :    8 (   4 avg)
%            Number of connectives :  350 ( 168   ~; 182   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-4 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-2 aty)
%            Number of variables   :   52 (  52   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f85,plain,
    $false,
    inference(subsumption_resolution,[],[f84,f72]) ).

fof(f72,plain,
    greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))),
    inference(resolution,[],[f70,f57]) ).

fof(f57,plain,
    ( ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
    | greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
    inference(subsumption_resolution,[],[f56,f11]) ).

fof(f11,axiom,
    stable(sk4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l10_11) ).

fof(f56,plain,
    ( ~ stable(sk4)
    | ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
    | greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
    inference(subsumption_resolution,[],[f54,f10]) ).

fof(f10,axiom,
    environment(sk4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l10_10) ).

fof(f54,plain,
    ( ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
    | ~ environment(sk4)
    | ~ stable(sk4)
    | greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
    inference(resolution,[],[f53,f9]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( ~ greater_or_equal(X1,sk3(X0))
      | ~ environment(X0)
      | greater(zero,growth_rate(first_movers,X1))
      | ~ stable(X0)
      | ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l11_9) ).

fof(f53,plain,
    greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4)),
    inference(subsumption_resolution,[],[f52,f42]) ).

fof(f42,plain,
    greater(sk2(sk4),appear(efficient_producers,sk4)),
    inference(subsumption_resolution,[],[f41,f10]) ).

fof(f41,plain,
    ( ~ environment(sk4)
    | greater(sk2(sk4),appear(efficient_producers,sk4)) ),
    inference(resolution,[],[f40,f11]) ).

fof(f40,plain,
    ! [X0] :
      ( ~ stable(X0)
      | greater(sk2(X0),appear(efficient_producers,X0))
      | ~ environment(X0) ),
    inference(subsumption_resolution,[],[f39,f33]) ).

fof(f33,plain,
    ! [X1] :
      ( ~ stable(X1)
      | greater(zero,growth_rate(first_movers,sk1(sk3(X1),X1)))
      | greater(sk2(X1),appear(efficient_producers,X1))
      | ~ environment(X1) ),
    inference(duplicate_literal_removal,[],[f31]) ).

fof(f31,plain,
    ! [X1] :
      ( greater(sk2(X1),appear(efficient_producers,X1))
      | ~ environment(X1)
      | greater(sk2(X1),appear(efficient_producers,X1))
      | greater(zero,growth_rate(first_movers,sk1(sk3(X1),X1)))
      | ~ environment(X1)
      | ~ stable(X1)
      | ~ stable(X1) ),
    inference(resolution,[],[f29,f26]) ).

fof(f26,plain,
    ! [X0] :
      ( ~ subpopulations(first_movers,efficient_producers,X0,sk1(sk3(X0),X0))
      | greater(zero,growth_rate(first_movers,sk1(sk3(X0),X0)))
      | greater(sk2(X0),appear(efficient_producers,X0))
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(duplicate_literal_removal,[],[f24]) ).

fof(f24,plain,
    ! [X0] :
      ( ~ stable(X0)
      | ~ environment(X0)
      | ~ stable(X0)
      | greater(zero,growth_rate(first_movers,sk1(sk3(X0),X0)))
      | ~ subpopulations(first_movers,efficient_producers,X0,sk1(sk3(X0),X0))
      | greater(sk2(X0),appear(efficient_producers,X0))
      | ~ environment(X0) ),
    inference(resolution,[],[f23,f9]) ).

fof(f23,plain,
    ! [X0] :
      ( greater_or_equal(sk1(sk3(X0),X0),sk3(X0))
      | greater(sk2(X0),appear(efficient_producers,X0))
      | ~ environment(X0)
      | ~ stable(X0) ),
    inference(duplicate_literal_removal,[],[f22]) ).

fof(f22,plain,
    ! [X0] :
      ( ~ stable(X0)
      | greater(sk2(X0),appear(efficient_producers,X0))
      | ~ stable(X0)
      | ~ environment(X0)
      | greater_or_equal(sk1(sk3(X0),X0),sk3(X0))
      | ~ environment(X0) ),
    inference(resolution,[],[f2,f7]) ).

fof(f7,axiom,
    ! [X0] :
      ( in_environment(X0,sk3(X0))
      | ~ stable(X0)
      | ~ environment(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l11_7) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( ~ in_environment(X0,X1)
      | greater(sk2(X0),appear(efficient_producers,X0))
      | greater_or_equal(sk1(X1,X0),X1)
      | ~ environment(X0)
      | ~ stable(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_negative_growth_2) ).

fof(f29,plain,
    ! [X0] :
      ( subpopulations(first_movers,efficient_producers,X0,sk1(sk3(X0),X0))
      | greater(sk2(X0),appear(efficient_producers,X0))
      | ~ environment(X0)
      | ~ stable(X0) ),
    inference(duplicate_literal_removal,[],[f28]) ).

fof(f28,plain,
    ! [X0] :
      ( subpopulations(first_movers,efficient_producers,X0,sk1(sk3(X0),X0))
      | ~ environment(X0)
      | ~ stable(X0)
      | ~ stable(X0)
      | greater(sk2(X0),appear(efficient_producers,X0))
      | ~ environment(X0) ),
    inference(resolution,[],[f1,f7]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( ~ in_environment(X0,X1)
      | ~ environment(X0)
      | greater(sk2(X0),appear(efficient_producers,X0))
      | subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
      | ~ stable(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_negative_growth_1) ).

fof(f39,plain,
    ! [X0] :
      ( ~ greater(zero,growth_rate(first_movers,sk1(sk3(X0),X0)))
      | greater(sk2(X0),appear(efficient_producers,X0))
      | ~ environment(X0)
      | ~ stable(X0) ),
    inference(duplicate_literal_removal,[],[f38]) ).

fof(f38,plain,
    ! [X0] :
      ( ~ stable(X0)
      | greater(sk2(X0),appear(efficient_producers,X0))
      | ~ environment(X0)
      | ~ greater(zero,growth_rate(first_movers,sk1(sk3(X0),X0)))
      | ~ environment(X0)
      | ~ stable(X0) ),
    inference(resolution,[],[f5,f7]) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( ~ in_environment(X0,X1)
      | ~ greater(zero,growth_rate(first_movers,sk1(X1,X0)))
      | ~ stable(X0)
      | greater(sk2(X0),appear(efficient_producers,X0))
      | ~ environment(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_negative_growth_5) ).

fof(f52,plain,
    ( greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4))
    | ~ greater(sk2(sk4),appear(efficient_producers,sk4)) ),
    inference(duplicate_literal_removal,[],[f51]) ).

fof(f51,plain,
    ( ~ greater(sk2(sk4),appear(efficient_producers,sk4))
    | greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4))
    | ~ greater(sk2(sk4),appear(efficient_producers,sk4)) ),
    inference(resolution,[],[f50,f13]) ).

fof(f13,axiom,
    ! [X0] :
      ( greater_or_equal(sk5(X0),X0)
      | ~ greater(X0,appear(efficient_producers,sk4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l10_13) ).

fof(f50,plain,
    ! [X0] :
      ( ~ greater_or_equal(sk5(X0),sk2(sk4))
      | greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4))
      | ~ greater(X0,appear(efficient_producers,sk4)) ),
    inference(subsumption_resolution,[],[f49,f14]) ).

fof(f14,axiom,
    ! [X0] :
      ( ~ greater(zero,growth_rate(first_movers,sk5(X0)))
      | ~ greater(X0,appear(efficient_producers,sk4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l10_14) ).

fof(f49,plain,
    ! [X0] :
      ( greater(zero,growth_rate(first_movers,sk5(X0)))
      | ~ greater(X0,appear(efficient_producers,sk4))
      | ~ greater_or_equal(sk5(X0),sk2(sk4))
      | greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4)) ),
    inference(subsumption_resolution,[],[f48,f11]) ).

fof(f48,plain,
    ! [X0] :
      ( ~ greater_or_equal(sk5(X0),sk2(sk4))
      | greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4))
      | ~ stable(sk4)
      | greater(zero,growth_rate(first_movers,sk5(X0)))
      | ~ greater(X0,appear(efficient_producers,sk4)) ),
    inference(subsumption_resolution,[],[f45,f10]) ).

fof(f45,plain,
    ! [X0] :
      ( ~ greater(X0,appear(efficient_producers,sk4))
      | greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4))
      | greater(zero,growth_rate(first_movers,sk5(X0)))
      | ~ environment(sk4)
      | ~ greater_or_equal(sk5(X0),sk2(sk4))
      | ~ stable(sk4) ),
    inference(resolution,[],[f44,f12]) ).

fof(f12,axiom,
    ! [X0] :
      ( subpopulations(first_movers,efficient_producers,sk4,sk5(X0))
      | ~ greater(X0,appear(efficient_producers,sk4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l10_12) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ environment(X0)
      | ~ stable(X0)
      | greater(zero,growth_rate(first_movers,X1))
      | greater_or_equal(sk1(sk3(X0),X0),sk3(X0))
      | ~ greater_or_equal(X1,sk2(X0)) ),
    inference(duplicate_literal_removal,[],[f43]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( greater_or_equal(sk1(sk3(X0),X0),sk3(X0))
      | ~ environment(X0)
      | ~ stable(X0)
      | ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ stable(X0)
      | ~ greater_or_equal(X1,sk2(X0))
      | greater(zero,growth_rate(first_movers,X1))
      | ~ environment(X0) ),
    inference(resolution,[],[f4,f7]) ).

fof(f4,axiom,
    ! [X2,X0,X1] :
      ( ~ in_environment(X0,X1)
      | ~ environment(X0)
      | ~ subpopulations(first_movers,efficient_producers,X0,X2)
      | ~ greater_or_equal(X2,sk2(X0))
      | ~ stable(X0)
      | greater_or_equal(sk1(X1,X0),X1)
      | greater(zero,growth_rate(first_movers,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_negative_growth_4) ).

fof(f70,plain,
    subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)),
    inference(subsumption_resolution,[],[f69,f10]) ).

fof(f69,plain,
    ( subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
    | ~ environment(sk4) ),
    inference(subsumption_resolution,[],[f68,f11]) ).

fof(f68,plain,
    ( ~ stable(sk4)
    | ~ environment(sk4)
    | subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)) ),
    inference(subsumption_resolution,[],[f67,f42]) ).

fof(f67,plain,
    ( ~ greater(sk2(sk4),appear(efficient_producers,sk4))
    | subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
    | ~ stable(sk4)
    | ~ environment(sk4) ),
    inference(duplicate_literal_removal,[],[f66]) ).

fof(f66,plain,
    ( ~ environment(sk4)
    | ~ greater(sk2(sk4),appear(efficient_producers,sk4))
    | ~ stable(sk4)
    | ~ greater(sk2(sk4),appear(efficient_producers,sk4))
    | subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)) ),
    inference(resolution,[],[f65,f12]) ).

fof(f65,plain,
    ! [X0] :
      ( ~ subpopulations(first_movers,efficient_producers,X0,sk5(sk2(X0)))
      | ~ greater(sk2(X0),appear(efficient_producers,sk4))
      | ~ environment(X0)
      | subpopulations(first_movers,efficient_producers,X0,sk1(sk3(X0),X0))
      | ~ stable(X0) ),
    inference(subsumption_resolution,[],[f64,f14]) ).

fof(f64,plain,
    ! [X0] :
      ( subpopulations(first_movers,efficient_producers,X0,sk1(sk3(X0),X0))
      | greater(zero,growth_rate(first_movers,sk5(sk2(X0))))
      | ~ greater(sk2(X0),appear(efficient_producers,sk4))
      | ~ subpopulations(first_movers,efficient_producers,X0,sk5(sk2(X0)))
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(resolution,[],[f63,f13]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( ~ greater_or_equal(X1,sk2(X0))
      | ~ stable(X0)
      | subpopulations(first_movers,efficient_producers,X0,sk1(sk3(X0),X0))
      | ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ environment(X0)
      | greater(zero,growth_rate(first_movers,X1)) ),
    inference(duplicate_literal_removal,[],[f62]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( ~ environment(X0)
      | ~ greater_or_equal(X1,sk2(X0))
      | ~ environment(X0)
      | ~ stable(X0)
      | subpopulations(first_movers,efficient_producers,X0,sk1(sk3(X0),X0))
      | ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | greater(zero,growth_rate(first_movers,X1))
      | ~ stable(X0) ),
    inference(resolution,[],[f3,f7]) ).

fof(f3,axiom,
    ! [X2,X0,X1] :
      ( ~ in_environment(X0,X1)
      | subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
      | greater(zero,growth_rate(first_movers,X2))
      | ~ subpopulations(first_movers,efficient_producers,X0,X2)
      | ~ greater_or_equal(X2,sk2(X0))
      | ~ environment(X0)
      | ~ stable(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_negative_growth_3) ).

fof(f84,plain,
    ~ greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))),
    inference(subsumption_resolution,[],[f83,f11]) ).

fof(f83,plain,
    ( ~ stable(sk4)
    | ~ greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
    inference(subsumption_resolution,[],[f82,f42]) ).

fof(f82,plain,
    ( ~ greater(sk2(sk4),appear(efficient_producers,sk4))
    | ~ greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4)))
    | ~ stable(sk4) ),
    inference(subsumption_resolution,[],[f81,f10]) ).

fof(f81,plain,
    ( ~ environment(sk4)
    | ~ stable(sk4)
    | ~ greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4)))
    | ~ greater(sk2(sk4),appear(efficient_producers,sk4)) ),
    inference(duplicate_literal_removal,[],[f80]) ).

fof(f80,plain,
    ( ~ greater(sk2(sk4),appear(efficient_producers,sk4))
    | ~ stable(sk4)
    | ~ environment(sk4)
    | ~ greater(sk2(sk4),appear(efficient_producers,sk4))
    | ~ greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
    inference(resolution,[],[f79,f12]) ).

fof(f79,plain,
    ! [X0] :
      ( ~ subpopulations(first_movers,efficient_producers,X0,sk5(sk2(X0)))
      | ~ greater(sk2(X0),appear(efficient_producers,sk4))
      | ~ environment(X0)
      | ~ stable(X0)
      | ~ greater(zero,growth_rate(first_movers,sk1(sk3(X0),X0))) ),
    inference(subsumption_resolution,[],[f78,f14]) ).

fof(f78,plain,
    ! [X0] :
      ( ~ environment(X0)
      | ~ subpopulations(first_movers,efficient_producers,X0,sk5(sk2(X0)))
      | ~ greater(zero,growth_rate(first_movers,sk1(sk3(X0),X0)))
      | ~ greater(sk2(X0),appear(efficient_producers,sk4))
      | greater(zero,growth_rate(first_movers,sk5(sk2(X0))))
      | ~ stable(X0) ),
    inference(resolution,[],[f77,f13]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( ~ greater_or_equal(X1,sk2(X0))
      | ~ greater(zero,growth_rate(first_movers,sk1(sk3(X0),X0)))
      | greater(zero,growth_rate(first_movers,X1))
      | ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(duplicate_literal_removal,[],[f76]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( ~ stable(X0)
      | ~ environment(X0)
      | ~ environment(X0)
      | ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | greater(zero,growth_rate(first_movers,X1))
      | ~ stable(X0)
      | ~ greater(zero,growth_rate(first_movers,sk1(sk3(X0),X0)))
      | ~ greater_or_equal(X1,sk2(X0)) ),
    inference(resolution,[],[f6,f7]) ).

fof(f6,axiom,
    ! [X2,X0,X1] :
      ( ~ in_environment(X0,X1)
      | ~ greater(zero,growth_rate(first_movers,sk1(X1,X0)))
      | ~ environment(X0)
      | ~ stable(X0)
      | ~ greater_or_equal(X2,sk2(X0))
      | greater(zero,growth_rate(first_movers,X2))
      | ~ subpopulations(first_movers,efficient_producers,X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_negative_growth_6) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : MGT028-1 : TPTP v8.1.0. Released v2.4.0.
% 0.13/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.35  % Computer : n026.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Aug 30 03:29:20 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.21/0.50  % (18505)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.21/0.51  % (18505)First to succeed.
% 0.21/0.51  % (18522)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)
% 0.21/0.51  % (18505)Refutation found. Thanks to Tanya!
% 0.21/0.51  % SZS status Unsatisfiable for theBenchmark
% 0.21/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.51  % (18505)------------------------------
% 0.21/0.51  % (18505)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.51  % (18505)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.51  % (18505)Termination reason: Refutation
% 0.21/0.51  
% 0.21/0.51  % (18505)Memory used [KB]: 1407
% 0.21/0.51  % (18505)Time elapsed: 0.096 s
% 0.21/0.51  % (18505)Instructions burned: 3 (million)
% 0.21/0.51  % (18505)------------------------------
% 0.21/0.51  % (18505)------------------------------
% 0.21/0.51  % (18498)Success in time 0.151 s
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