TSTP Solution File: MGT023+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : MGT023+1 : TPTP v8.1.0. Released v2.0.0.
% 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 : n009.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 17:50:56 EDT 2022

% Result   : Theorem 0.19s 0.45s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   49 (   6 unt;   0 def)
%            Number of atoms       :  226 (  18 equ)
%            Maximal formula atoms :   11 (   4 avg)
%            Number of connectives :  297 ( 120   ~; 118   |;  46   &)
%                                         (   2 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   3 prp; 0-4 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   67 (  56   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f73,plain,
    $false,
    inference(avatar_sat_refutation,[],[f63,f70,f72]) ).

fof(f72,plain,
    spl3_2,
    inference(avatar_contradiction_clause,[],[f71]) ).

fof(f71,plain,
    ( $false
    | spl3_2 ),
    inference(resolution,[],[f62,f20]) ).

fof(f20,plain,
    stable(sK0),
    inference(cnf_transformation,[],[f13]) ).

fof(f13,plain,
    ( ~ in_environment(sK0,critical_point(sK0))
    & stable(sK0)
    & environment(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f12]) ).

fof(f12,plain,
    ( ? [X0] :
        ( ~ in_environment(X0,critical_point(X0))
        & stable(X0)
        & environment(X0) )
   => ( ~ in_environment(sK0,critical_point(sK0))
      & stable(sK0)
      & environment(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f9,plain,
    ? [X0] :
      ( ~ in_environment(X0,critical_point(X0))
      & stable(X0)
      & environment(X0) ),
    inference(flattening,[],[f8]) ).

fof(f8,plain,
    ? [X0] :
      ( ~ in_environment(X0,critical_point(X0))
      & environment(X0)
      & stable(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,negated_conjecture,
    ~ ! [X0] :
        ( ( environment(X0)
          & stable(X0) )
       => in_environment(X0,critical_point(X0)) ),
    inference(negated_conjecture,[],[f3]) ).

fof(f3,conjecture,
    ! [X0] :
      ( ( environment(X0)
        & stable(X0) )
     => in_environment(X0,critical_point(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5) ).

fof(f62,plain,
    ( ~ stable(sK0)
    | spl3_2 ),
    inference(avatar_component_clause,[],[f60]) ).

fof(f60,plain,
    ( spl3_2
  <=> stable(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

fof(f70,plain,
    spl3_1,
    inference(avatar_contradiction_clause,[],[f69]) ).

fof(f69,plain,
    ( $false
    | spl3_1 ),
    inference(resolution,[],[f58,f19]) ).

fof(f19,plain,
    environment(sK0),
    inference(cnf_transformation,[],[f13]) ).

fof(f58,plain,
    ( ~ environment(sK0)
    | spl3_1 ),
    inference(avatar_component_clause,[],[f56]) ).

fof(f56,plain,
    ( spl3_1
  <=> environment(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f63,plain,
    ( ~ spl3_1
    | ~ spl3_2 ),
    inference(avatar_split_clause,[],[f54,f60,f56]) ).

fof(f54,plain,
    ( ~ stable(sK0)
    | ~ environment(sK0) ),
    inference(resolution,[],[f52,f21]) ).

fof(f21,plain,
    ~ in_environment(sK0,critical_point(sK0)),
    inference(cnf_transformation,[],[f13]) ).

fof(f52,plain,
    ! [X0] :
      ( in_environment(X0,critical_point(X0))
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(duplicate_literal_removal,[],[f50]) ).

fof(f50,plain,
    ! [X0] :
      ( ~ environment(X0)
      | ~ environment(X0)
      | ~ stable(X0)
      | in_environment(X0,critical_point(X0))
      | ~ stable(X0) ),
    inference(resolution,[],[f47,f23]) ).

fof(f23,plain,
    ! [X0] :
      ( in_environment(X0,sK1(X0))
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0] :
      ( ~ environment(X0)
      | ~ stable(X0)
      | ( ! [X2] :
            ( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
            | ~ greater(X2,sK1(X0))
            | ~ subpopulations(first_movers,efficient_producers,X0,X2) )
        & in_environment(X0,sK1(X0))
        & ~ greater(growth_rate(efficient_producers,sK1(X0)),growth_rate(first_movers,sK1(X0))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f11,f14]) ).

fof(f14,plain,
    ! [X0] :
      ( ? [X1] :
          ( ! [X2] :
              ( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
              | ~ greater(X2,X1)
              | ~ subpopulations(first_movers,efficient_producers,X0,X2) )
          & in_environment(X0,X1)
          & ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) )
     => ( ! [X2] :
            ( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
            | ~ greater(X2,sK1(X0))
            | ~ subpopulations(first_movers,efficient_producers,X0,X2) )
        & in_environment(X0,sK1(X0))
        & ~ greater(growth_rate(efficient_producers,sK1(X0)),growth_rate(first_movers,sK1(X0))) ) ),
    introduced(choice_axiom,[]) ).

fof(f11,plain,
    ! [X0] :
      ( ~ environment(X0)
      | ~ stable(X0)
      | ? [X1] :
          ( ! [X2] :
              ( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
              | ~ greater(X2,X1)
              | ~ subpopulations(first_movers,efficient_producers,X0,X2) )
          & in_environment(X0,X1)
          & ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ) ),
    inference(flattening,[],[f10]) ).

fof(f10,plain,
    ! [X0] :
      ( ? [X1] :
          ( ! [X2] :
              ( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
              | ~ greater(X2,X1)
              | ~ subpopulations(first_movers,efficient_producers,X0,X2) )
          & ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
          & in_environment(X0,X1) )
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] :
      ( ( stable(X0)
        & environment(X0) )
     => ? [X1] :
          ( ! [X2] :
              ( ( greater(X2,X1)
                & subpopulations(first_movers,efficient_producers,X0,X2) )
             => greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
          & ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
          & in_environment(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12) ).

fof(f47,plain,
    ! [X1] :
      ( ~ in_environment(X1,sK1(X1))
      | ~ stable(X1)
      | in_environment(X1,critical_point(X1))
      | ~ environment(X1) ),
    inference(duplicate_literal_removal,[],[f39]) ).

fof(f39,plain,
    ! [X1] :
      ( ~ environment(X1)
      | ~ in_environment(X1,sK1(X1))
      | ~ stable(X1)
      | ~ environment(X1)
      | in_environment(X1,critical_point(X1))
      | ~ stable(X1) ),
    inference(superposition,[],[f23,f37]) ).

fof(f37,plain,
    ! [X0] :
      ( critical_point(X0) = sK1(X0)
      | ~ in_environment(X0,sK1(X0))
      | ~ environment(X0)
      | ~ stable(X0) ),
    inference(duplicate_literal_removal,[],[f36]) ).

fof(f36,plain,
    ! [X0] :
      ( ~ stable(X0)
      | ~ stable(X0)
      | ~ environment(X0)
      | critical_point(X0) = sK1(X0)
      | ~ stable(X0)
      | ~ environment(X0)
      | ~ environment(X0)
      | ~ in_environment(X0,sK1(X0))
      | ~ environment(X0)
      | critical_point(X0) = sK1(X0)
      | ~ in_environment(X0,sK1(X0)) ),
    inference(resolution,[],[f34,f29]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( greater(sK2(X0,sK1(X1)),sK1(X1))
      | ~ in_environment(X0,sK1(X1))
      | ~ environment(X0)
      | ~ environment(X1)
      | critical_point(X0) = sK1(X1)
      | ~ stable(X1) ),
    inference(resolution,[],[f27,f22]) ).

fof(f22,plain,
    ! [X0] :
      ( ~ greater(growth_rate(efficient_producers,sK1(X0)),growth_rate(first_movers,sK1(X0)))
      | ~ environment(X0)
      | ~ stable(X0) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
      | ~ environment(X0)
      | greater(sK2(X0,X1),X1)
      | critical_point(X0) = X1
      | ~ in_environment(X0,X1) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
      | ~ in_environment(X0,X1)
      | ( greater(sK2(X0,X1),X1)
        & subpopulations(first_movers,efficient_producers,X0,sK2(X0,X1))
        & ~ greater(growth_rate(efficient_producers,sK2(X0,X1)),growth_rate(first_movers,sK2(X0,X1))) )
      | critical_point(X0) = X1
      | ~ environment(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f16,f17]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( greater(X2,X1)
          & subpopulations(first_movers,efficient_producers,X0,X2)
          & ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
     => ( greater(sK2(X0,X1),X1)
        & subpopulations(first_movers,efficient_producers,X0,sK2(X0,X1))
        & ~ greater(growth_rate(efficient_producers,sK2(X0,X1)),growth_rate(first_movers,sK2(X0,X1))) ) ),
    introduced(choice_axiom,[]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
      | ~ in_environment(X0,X1)
      | ? [X2] :
          ( greater(X2,X1)
          & subpopulations(first_movers,efficient_producers,X0,X2)
          & ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
      | critical_point(X0) = X1
      | ~ environment(X0) ),
    inference(rectify,[],[f7]) ).

fof(f7,plain,
    ! [X1,X0] :
      ( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
      | ~ in_environment(X1,X0)
      | ? [X2] :
          ( greater(X2,X0)
          & subpopulations(first_movers,efficient_producers,X1,X2)
          & ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
      | critical_point(X1) = X0
      | ~ environment(X1) ),
    inference(flattening,[],[f6]) ).

fof(f6,plain,
    ! [X1,X0] :
      ( critical_point(X1) = X0
      | greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
      | ? [X2] :
          ( ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
          & greater(X2,X0)
          & subpopulations(first_movers,efficient_producers,X1,X2) )
      | ~ in_environment(X1,X0)
      | ~ environment(X1) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,plain,
    ! [X1,X0] :
      ( ( ~ greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
        & ! [X2] :
            ( ( greater(X2,X0)
              & subpopulations(first_movers,efficient_producers,X1,X2) )
           => greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
        & in_environment(X1,X0)
        & environment(X1) )
     => critical_point(X1) = X0 ),
    inference(rectify,[],[f1]) ).

fof(f1,axiom,
    ! [X1,X0] :
      ( ( ! [X2] :
            ( ( greater(X2,X1)
              & subpopulations(first_movers,efficient_producers,X0,X2) )
           => greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
        & in_environment(X0,X1)
        & ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
        & environment(X0) )
     => critical_point(X0) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ~ greater(sK2(X0,sK1(X1)),sK1(X0))
      | ~ environment(X0)
      | ~ environment(X1)
      | ~ stable(X1)
      | ~ in_environment(X0,sK1(X1))
      | critical_point(X0) = sK1(X1)
      | ~ stable(X0) ),
    inference(resolution,[],[f33,f22]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
      | critical_point(X0) = X1
      | ~ stable(X0)
      | ~ environment(X0)
      | ~ greater(sK2(X0,X1),sK1(X0))
      | ~ in_environment(X0,X1) ),
    inference(duplicate_literal_removal,[],[f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ~ in_environment(X0,X1)
      | ~ in_environment(X0,X1)
      | ~ environment(X0)
      | greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
      | critical_point(X0) = X1
      | ~ environment(X0)
      | ~ environment(X0)
      | greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
      | critical_point(X0) = X1
      | ~ stable(X0)
      | ~ greater(sK2(X0,X1),sK1(X0)) ),
    inference(resolution,[],[f31,f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( subpopulations(first_movers,efficient_producers,X0,sK2(X0,X1))
      | critical_point(X0) = X1
      | ~ environment(X0)
      | ~ in_environment(X0,X1)
      | greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f31,plain,
    ! [X3,X4,X5] :
      ( ~ subpopulations(first_movers,efficient_producers,X5,sK2(X4,X3))
      | ~ environment(X4)
      | ~ environment(X5)
      | ~ stable(X5)
      | ~ greater(sK2(X4,X3),sK1(X5))
      | greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3))
      | critical_point(X4) = X3
      | ~ in_environment(X4,X3) ),
    inference(resolution,[],[f25,f24]) ).

fof(f24,plain,
    ! [X2,X0] :
      ( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
      | ~ stable(X0)
      | ~ subpopulations(first_movers,efficient_producers,X0,X2)
      | ~ greater(X2,sK1(X0))
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ~ greater(growth_rate(efficient_producers,sK2(X0,X1)),growth_rate(first_movers,sK2(X0,X1)))
      | greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
      | critical_point(X0) = X1
      | ~ in_environment(X0,X1)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : MGT023+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.33  % Computer : n009.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Tue Aug 30 03:11:20 EDT 2022
% 0.12/0.33  % CPUTime    : 
% 0.19/0.44  % (29601)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.19/0.44  % (29593)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.44  % (29601)First to succeed.
% 0.19/0.45  % (29593)Also succeeded, but the first one will report.
% 0.19/0.45  % (29601)Refutation found. Thanks to Tanya!
% 0.19/0.45  % SZS status Theorem for theBenchmark
% 0.19/0.45  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.45  % (29601)------------------------------
% 0.19/0.45  % (29601)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.45  % (29601)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.45  % (29601)Termination reason: Refutation
% 0.19/0.45  
% 0.19/0.45  % (29601)Memory used [KB]: 6012
% 0.19/0.45  % (29601)Time elapsed: 0.050 s
% 0.19/0.45  % (29601)Instructions burned: 2 (million)
% 0.19/0.45  % (29601)------------------------------
% 0.19/0.45  % (29601)------------------------------
% 0.19/0.45  % (29578)Success in time 0.119 s
%------------------------------------------------------------------------------