TSTP Solution File: MGT027+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : MGT027+1 : TPTP v8.2.0. Released v2.0.0.
% 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 : n020.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 : Tue May 21 00:42:11 EDT 2024

% Result   : Theorem 0.56s 0.74s
% Output   : Refutation 0.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :   20
% Syntax   : Number of formulae    :  134 (   4 unt;   0 def)
%            Number of atoms       :  542 (  13 equ)
%            Maximal formula atoms :    9 (   4 avg)
%            Number of connectives :  753 ( 345   ~; 321   |;  59   &)
%                                         (  10 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   17 (  15 usr;   9 prp; 0-4 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :  170 ( 158   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f481,plain,
    $false,
    inference(avatar_sat_refutation,[],[f158,f164,f185,f215,f224,f376,f416,f431,f480]) ).

fof(f480,plain,
    ( ~ spl3_5
    | spl3_24
    | ~ spl3_27 ),
    inference(avatar_contradiction_clause,[],[f479]) ).

fof(f479,plain,
    ( $false
    | ~ spl3_5
    | spl3_24
    | ~ spl3_27 ),
    inference(subsumption_resolution,[],[f478,f148]) ).

fof(f148,plain,
    ( greater(sK0(sK1),appear(efficient_producers,sK1))
    | ~ spl3_5 ),
    inference(avatar_component_clause,[],[f147]) ).

fof(f147,plain,
    ( spl3_5
  <=> greater(sK0(sK1),appear(efficient_producers,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

fof(f478,plain,
    ( ~ greater(sK0(sK1),appear(efficient_producers,sK1))
    | spl3_24
    | ~ spl3_27 ),
    inference(forward_demodulation,[],[f375,f415]) ).

fof(f415,plain,
    ( sK0(sK1) = sK2(sK0(sK1))
    | ~ spl3_27 ),
    inference(avatar_component_clause,[],[f413]) ).

fof(f413,plain,
    ( spl3_27
  <=> sK0(sK1) = sK2(sK0(sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_27])]) ).

fof(f375,plain,
    ( ~ greater(sK2(sK0(sK1)),appear(efficient_producers,sK1))
    | spl3_24 ),
    inference(avatar_component_clause,[],[f373]) ).

fof(f373,plain,
    ( spl3_24
  <=> greater(sK2(sK0(sK1)),appear(efficient_producers,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_24])]) ).

fof(f431,plain,
    ( ~ spl3_4
    | ~ spl3_24 ),
    inference(avatar_contradiction_clause,[],[f430]) ).

fof(f430,plain,
    ( $false
    | ~ spl3_4
    | ~ spl3_24 ),
    inference(subsumption_resolution,[],[f429,f43]) ).

fof(f43,plain,
    environment(sK1),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ( ! [X1] :
        ( ~ contracts_from(X1,first_movers)
        | ~ greater(X1,appear(efficient_producers,sK1)) )
    & stable(sK1)
    & environment(sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f21,f34]) ).

fof(f34,plain,
    ( ? [X0] :
        ( ! [X1] :
            ( ~ contracts_from(X1,first_movers)
            | ~ greater(X1,appear(efficient_producers,X0)) )
        & stable(X0)
        & environment(X0) )
   => ( ! [X1] :
          ( ~ contracts_from(X1,first_movers)
          | ~ greater(X1,appear(efficient_producers,sK1)) )
      & stable(sK1)
      & environment(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f21,plain,
    ? [X0] :
      ( ! [X1] :
          ( ~ contracts_from(X1,first_movers)
          | ~ greater(X1,appear(efficient_producers,X0)) )
      & stable(X0)
      & environment(X0) ),
    inference(flattening,[],[f20]) ).

fof(f20,plain,
    ? [X0] :
      ( ! [X1] :
          ( ~ contracts_from(X1,first_movers)
          | ~ greater(X1,appear(efficient_producers,X0)) )
      & stable(X0)
      & environment(X0) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X0] :
        ( ( stable(X0)
          & environment(X0) )
       => ? [X1] :
            ( contracts_from(X1,first_movers)
            & greater(X1,appear(efficient_producers,X0)) ) ),
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X0] :
      ( ( stable(X0)
        & environment(X0) )
     => ? [X1] :
          ( contracts_from(X1,first_movers)
          & greater(X1,appear(efficient_producers,X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l9) ).

fof(f429,plain,
    ( ~ environment(sK1)
    | ~ spl3_4
    | ~ spl3_24 ),
    inference(subsumption_resolution,[],[f427,f44]) ).

fof(f44,plain,
    stable(sK1),
    inference(cnf_transformation,[],[f35]) ).

fof(f427,plain,
    ( ~ stable(sK1)
    | ~ environment(sK1)
    | ~ spl3_4
    | ~ spl3_24 ),
    inference(resolution,[],[f420,f46]) ).

fof(f46,plain,
    ! [X0] :
      ( in_environment(X0,appear(efficient_producers,X0))
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0] :
      ( in_environment(X0,appear(efficient_producers,X0))
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(flattening,[],[f22]) ).

fof(f22,plain,
    ! [X0] :
      ( in_environment(X0,appear(efficient_producers,X0))
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( ( stable(X0)
        & environment(X0) )
     => in_environment(X0,appear(efficient_producers,X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_EP_in_stable_environments) ).

fof(f420,plain,
    ( ~ in_environment(sK1,appear(efficient_producers,sK1))
    | ~ spl3_4
    | ~ spl3_24 ),
    inference(resolution,[],[f374,f145]) ).

fof(f145,plain,
    ( ! [X0] :
        ( ~ greater(sK2(sK0(sK1)),X0)
        | ~ in_environment(sK1,X0) )
    | ~ spl3_4 ),
    inference(avatar_component_clause,[],[f144]) ).

fof(f144,plain,
    ( spl3_4
  <=> ! [X0] :
        ( ~ greater(sK2(sK0(sK1)),X0)
        | ~ in_environment(sK1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

fof(f374,plain,
    ( greater(sK2(sK0(sK1)),appear(efficient_producers,sK1))
    | ~ spl3_24 ),
    inference(avatar_component_clause,[],[f373]) ).

fof(f416,plain,
    ( spl3_3
    | spl3_27
    | ~ spl3_5
    | spl3_10
    | spl3_24 ),
    inference(avatar_split_clause,[],[f411,f373,f182,f147,f413,f141]) ).

fof(f141,plain,
    ( spl3_3
  <=> ! [X1] :
        ( ~ in_environment(X1,sK0(sK1))
        | ~ environment(X1)
        | ~ stable(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

fof(f182,plain,
    ( spl3_10
  <=> contracts_from(sK0(sK1),first_movers) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).

fof(f411,plain,
    ( ! [X0] :
        ( sK0(sK1) = sK2(sK0(sK1))
        | ~ in_environment(X0,sK0(sK1))
        | ~ stable(X0)
        | ~ environment(X0) )
    | ~ spl3_5
    | spl3_10
    | spl3_24 ),
    inference(subsumption_resolution,[],[f410,f183]) ).

fof(f183,plain,
    ( ~ contracts_from(sK0(sK1),first_movers)
    | spl3_10 ),
    inference(avatar_component_clause,[],[f182]) ).

fof(f410,plain,
    ( ! [X0] :
        ( sK0(sK1) = sK2(sK0(sK1))
        | contracts_from(sK0(sK1),first_movers)
        | ~ in_environment(X0,sK0(sK1))
        | ~ stable(X0)
        | ~ environment(X0) )
    | ~ spl3_5
    | spl3_24 ),
    inference(subsumption_resolution,[],[f407,f148]) ).

fof(f407,plain,
    ( ! [X0] :
        ( sK0(sK1) = sK2(sK0(sK1))
        | ~ greater(sK0(sK1),appear(efficient_producers,sK1))
        | contracts_from(sK0(sK1),first_movers)
        | ~ in_environment(X0,sK0(sK1))
        | ~ stable(X0)
        | ~ environment(X0) )
    | spl3_24 ),
    inference(resolution,[],[f396,f50]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( greater_or_equal(sK2(X1),X1)
      | contracts_from(X1,first_movers)
      | ~ in_environment(X0,X1)
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( contracts_from(X1,first_movers)
      | ( ~ greater(zero,growth_rate(first_movers,sK2(X1)))
        & greater_or_equal(sK2(X1),X1)
        & greater(cardinality_at_time(first_movers,sK2(X1)),zero) )
      | ~ in_environment(X0,X1)
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f29,f36]) ).

fof(f36,plain,
    ! [X1] :
      ( ? [X2] :
          ( ~ greater(zero,growth_rate(first_movers,X2))
          & greater_or_equal(X2,X1)
          & greater(cardinality_at_time(first_movers,X2),zero) )
     => ( ~ greater(zero,growth_rate(first_movers,sK2(X1)))
        & greater_or_equal(sK2(X1),X1)
        & greater(cardinality_at_time(first_movers,sK2(X1)),zero) ) ),
    introduced(choice_axiom,[]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( contracts_from(X1,first_movers)
      | ? [X2] :
          ( ~ greater(zero,growth_rate(first_movers,X2))
          & greater_or_equal(X2,X1)
          & greater(cardinality_at_time(first_movers,X2),zero) )
      | ~ in_environment(X0,X1)
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(flattening,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( contracts_from(X1,first_movers)
      | ? [X2] :
          ( ~ greater(zero,growth_rate(first_movers,X2))
          & greater_or_equal(X2,X1)
          & greater(cardinality_at_time(first_movers,X2),zero) )
      | ~ in_environment(X0,X1)
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( greater_or_equal(X2,X1)
              & greater(cardinality_at_time(first_movers,X2),zero) )
           => greater(zero,growth_rate(first_movers,X2)) )
        & in_environment(X0,X1)
        & stable(X0)
        & environment(X0) )
     => contracts_from(X1,first_movers) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_contracts_from) ).

fof(f396,plain,
    ( ! [X0] :
        ( ~ greater_or_equal(sK2(sK0(sK1)),X0)
        | sK2(sK0(sK1)) = X0
        | ~ greater(X0,appear(efficient_producers,sK1)) )
    | spl3_24 ),
    inference(resolution,[],[f379,f52]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( greater(X0,X1)
      | X0 = X1
      | ~ greater_or_equal(X0,X1) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ( greater_or_equal(X0,X1)
        | ( X0 != X1
          & ~ greater(X0,X1) ) )
      & ( X0 = X1
        | greater(X0,X1)
        | ~ greater_or_equal(X0,X1) ) ),
    inference(flattening,[],[f38]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ( greater_or_equal(X0,X1)
        | ( X0 != X1
          & ~ greater(X0,X1) ) )
      & ( X0 = X1
        | greater(X0,X1)
        | ~ greater_or_equal(X0,X1) ) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( greater_or_equal(X0,X1)
    <=> ( X0 = X1
        | greater(X0,X1) ) ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X5,X6] :
      ( greater_or_equal(X5,X6)
    <=> ( X5 = X6
        | greater(X5,X6) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal) ).

fof(f379,plain,
    ( ! [X0] :
        ( ~ greater(sK2(sK0(sK1)),X0)
        | ~ greater(X0,appear(efficient_producers,sK1)) )
    | spl3_24 ),
    inference(resolution,[],[f375,f55]) ).

fof(f55,plain,
    ! [X2,X0,X1] :
      ( greater(X0,X2)
      | ~ greater(X1,X2)
      | ~ greater(X0,X1) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ! [X0,X1,X2] :
      ( greater(X0,X2)
      | ~ greater(X1,X2)
      | ~ greater(X0,X1) ),
    inference(flattening,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1,X2] :
      ( greater(X0,X2)
      | ~ greater(X1,X2)
      | ~ greater(X0,X1) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0,X1,X2] :
      ( ( greater(X1,X2)
        & greater(X0,X1) )
     => greater(X0,X2) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X5,X6,X7] :
      ( ( greater(X6,X7)
        & greater(X5,X6) )
     => greater(X5,X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_transitivity) ).

fof(f376,plain,
    ( spl3_4
    | ~ spl3_24
    | spl3_7 ),
    inference(avatar_split_clause,[],[f371,f155,f373,f144]) ).

fof(f155,plain,
    ( spl3_7
  <=> greater(cardinality_at_time(efficient_producers,sK2(sK0(sK1))),zero) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).

fof(f371,plain,
    ( ! [X0] :
        ( ~ greater(sK2(sK0(sK1)),appear(efficient_producers,sK1))
        | ~ greater(sK2(sK0(sK1)),X0)
        | ~ in_environment(sK1,X0) )
    | spl3_7 ),
    inference(subsumption_resolution,[],[f370,f43]) ).

fof(f370,plain,
    ( ! [X0] :
        ( ~ greater(sK2(sK0(sK1)),appear(efficient_producers,sK1))
        | ~ greater(sK2(sK0(sK1)),X0)
        | ~ in_environment(sK1,X0)
        | ~ environment(sK1) )
    | spl3_7 ),
    inference(resolution,[],[f334,f44]) ).

fof(f334,plain,
    ( ! [X0,X1] :
        ( ~ stable(X0)
        | ~ greater(sK2(sK0(sK1)),appear(efficient_producers,X0))
        | ~ greater(sK2(sK0(sK1)),X1)
        | ~ in_environment(X0,X1)
        | ~ environment(X0) )
    | spl3_7 ),
    inference(duplicate_literal_removal,[],[f333]) ).

fof(f333,plain,
    ( ! [X0,X1] :
        ( ~ environment(X0)
        | ~ greater(sK2(sK0(sK1)),appear(efficient_producers,X0))
        | ~ greater(sK2(sK0(sK1)),X1)
        | ~ in_environment(X0,X1)
        | ~ stable(X0)
        | ~ environment(X0) )
    | spl3_7 ),
    inference(resolution,[],[f304,f47]) ).

fof(f47,plain,
    ! [X2,X0,X1] :
      ( in_environment(X0,X2)
      | ~ greater(X2,X1)
      | ~ in_environment(X0,X1)
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( in_environment(X0,X2)
      | ~ greater(X2,X1)
      | ~ in_environment(X0,X1)
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(flattening,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( in_environment(X0,X2)
      | ~ greater(X2,X1)
      | ~ in_environment(X0,X1)
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X0,X1,X2] :
      ( ( greater(X2,X1)
        & in_environment(X0,X1)
        & stable(X0)
        & environment(X0) )
     => in_environment(X0,X2) ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X3,X4] :
      ( ( greater(X4,X3)
        & in_environment(X0,X3)
        & stable(X0)
        & environment(X0) )
     => in_environment(X0,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_long_stable_environments) ).

fof(f304,plain,
    ( ! [X0] :
        ( ~ in_environment(X0,sK2(sK0(sK1)))
        | ~ environment(X0)
        | ~ greater(sK2(sK0(sK1)),appear(efficient_producers,X0)) )
    | spl3_7 ),
    inference(resolution,[],[f231,f53]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( greater_or_equal(X0,X1)
      | ~ greater(X0,X1) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f231,plain,
    ( ! [X0] :
        ( ~ greater_or_equal(sK2(sK0(sK1)),appear(efficient_producers,X0))
        | ~ in_environment(X0,sK2(sK0(sK1)))
        | ~ environment(X0) )
    | spl3_7 ),
    inference(resolution,[],[f157,f40]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( greater(cardinality_at_time(efficient_producers,X1),zero)
      | ~ greater_or_equal(X1,appear(efficient_producers,X0))
      | ~ in_environment(X0,X1)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( greater(cardinality_at_time(efficient_producers,X1),zero)
      | ~ greater_or_equal(X1,appear(efficient_producers,X0))
      | ~ in_environment(X0,X1)
      | ~ environment(X0) ),
    inference(flattening,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( greater(cardinality_at_time(efficient_producers,X1),zero)
      | ~ greater_or_equal(X1,appear(efficient_producers,X0))
      | ~ in_environment(X0,X1)
      | ~ environment(X0) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f11,plain,
    ! [X0,X1] :
      ( ( greater_or_equal(X1,appear(efficient_producers,X0))
        & in_environment(X0,X1)
        & environment(X0) )
     => greater(cardinality_at_time(efficient_producers,X1),zero) ),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X2] :
      ( ( greater_or_equal(X2,appear(efficient_producers,X0))
        & in_environment(X0,X2)
        & environment(X0) )
     => greater(cardinality_at_time(efficient_producers,X2),zero) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6) ).

fof(f157,plain,
    ( ~ greater(cardinality_at_time(efficient_producers,sK2(sK0(sK1))),zero)
    | spl3_7 ),
    inference(avatar_component_clause,[],[f155]) ).

fof(f224,plain,
    ( ~ spl3_5
    | ~ spl3_10 ),
    inference(avatar_contradiction_clause,[],[f223]) ).

fof(f223,plain,
    ( $false
    | ~ spl3_5
    | ~ spl3_10 ),
    inference(subsumption_resolution,[],[f222,f148]) ).

fof(f222,plain,
    ( ~ greater(sK0(sK1),appear(efficient_producers,sK1))
    | ~ spl3_10 ),
    inference(resolution,[],[f184,f45]) ).

fof(f45,plain,
    ! [X1] :
      ( ~ contracts_from(X1,first_movers)
      | ~ greater(X1,appear(efficient_producers,sK1)) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f184,plain,
    ( contracts_from(sK0(sK1),first_movers)
    | ~ spl3_10 ),
    inference(avatar_component_clause,[],[f182]) ).

fof(f215,plain,
    ( ~ spl3_3
    | ~ spl3_5 ),
    inference(avatar_contradiction_clause,[],[f214]) ).

fof(f214,plain,
    ( $false
    | ~ spl3_3
    | ~ spl3_5 ),
    inference(subsumption_resolution,[],[f213,f43]) ).

fof(f213,plain,
    ( ~ environment(sK1)
    | ~ spl3_3
    | ~ spl3_5 ),
    inference(subsumption_resolution,[],[f212,f44]) ).

fof(f212,plain,
    ( ~ stable(sK1)
    | ~ environment(sK1)
    | ~ spl3_3
    | ~ spl3_5 ),
    inference(subsumption_resolution,[],[f210,f148]) ).

fof(f210,plain,
    ( ~ greater(sK0(sK1),appear(efficient_producers,sK1))
    | ~ stable(sK1)
    | ~ environment(sK1)
    | ~ spl3_3 ),
    inference(resolution,[],[f207,f46]) ).

fof(f207,plain,
    ( ! [X0] :
        ( ~ in_environment(sK1,X0)
        | ~ greater(sK0(sK1),X0) )
    | ~ spl3_3 ),
    inference(subsumption_resolution,[],[f206,f43]) ).

fof(f206,plain,
    ( ! [X0] :
        ( ~ environment(sK1)
        | ~ greater(sK0(sK1),X0)
        | ~ in_environment(sK1,X0) )
    | ~ spl3_3 ),
    inference(resolution,[],[f196,f44]) ).

fof(f196,plain,
    ( ! [X0,X1] :
        ( ~ stable(X0)
        | ~ environment(X0)
        | ~ greater(sK0(sK1),X1)
        | ~ in_environment(X0,X1) )
    | ~ spl3_3 ),
    inference(duplicate_literal_removal,[],[f195]) ).

fof(f195,plain,
    ( ! [X0,X1] :
        ( ~ environment(X0)
        | ~ stable(X0)
        | ~ greater(sK0(sK1),X1)
        | ~ in_environment(X0,X1)
        | ~ stable(X0)
        | ~ environment(X0) )
    | ~ spl3_3 ),
    inference(resolution,[],[f142,f47]) ).

fof(f142,plain,
    ( ! [X1] :
        ( ~ in_environment(X1,sK0(sK1))
        | ~ environment(X1)
        | ~ stable(X1) )
    | ~ spl3_3 ),
    inference(avatar_component_clause,[],[f141]) ).

fof(f185,plain,
    ( spl3_3
    | spl3_10
    | spl3_6 ),
    inference(avatar_split_clause,[],[f178,f151,f182,f141]) ).

fof(f151,plain,
    ( spl3_6
  <=> greater(cardinality_at_time(first_movers,sK2(sK0(sK1))),zero) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).

fof(f178,plain,
    ( ! [X0] :
        ( contracts_from(sK0(sK1),first_movers)
        | ~ in_environment(X0,sK0(sK1))
        | ~ stable(X0)
        | ~ environment(X0) )
    | spl3_6 ),
    inference(resolution,[],[f153,f49]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( greater(cardinality_at_time(first_movers,sK2(X1)),zero)
      | contracts_from(X1,first_movers)
      | ~ in_environment(X0,X1)
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f153,plain,
    ( ~ greater(cardinality_at_time(first_movers,sK2(sK0(sK1))),zero)
    | spl3_6 ),
    inference(avatar_component_clause,[],[f151]) ).

fof(f164,plain,
    spl3_5,
    inference(avatar_contradiction_clause,[],[f163]) ).

fof(f163,plain,
    ( $false
    | spl3_5 ),
    inference(subsumption_resolution,[],[f162,f43]) ).

fof(f162,plain,
    ( ~ environment(sK1)
    | spl3_5 ),
    inference(subsumption_resolution,[],[f159,f44]) ).

fof(f159,plain,
    ( ~ stable(sK1)
    | ~ environment(sK1)
    | spl3_5 ),
    inference(resolution,[],[f149,f41]) ).

fof(f41,plain,
    ! [X0] :
      ( greater(sK0(X0),appear(efficient_producers,X0))
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0] :
      ( ( ! [X2] :
            ( greater(zero,growth_rate(first_movers,X2))
            | ~ greater_or_equal(X2,sK0(X0))
            | ~ subpopulations(first_movers,efficient_producers,X0,X2) )
        & greater(sK0(X0),appear(efficient_producers,X0)) )
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f19,f32]) ).

fof(f32,plain,
    ! [X0] :
      ( ? [X1] :
          ( ! [X2] :
              ( greater(zero,growth_rate(first_movers,X2))
              | ~ greater_or_equal(X2,X1)
              | ~ subpopulations(first_movers,efficient_producers,X0,X2) )
          & greater(X1,appear(efficient_producers,X0)) )
     => ( ! [X2] :
            ( greater(zero,growth_rate(first_movers,X2))
            | ~ greater_or_equal(X2,sK0(X0))
            | ~ subpopulations(first_movers,efficient_producers,X0,X2) )
        & greater(sK0(X0),appear(efficient_producers,X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f19,plain,
    ! [X0] :
      ( ? [X1] :
          ( ! [X2] :
              ( greater(zero,growth_rate(first_movers,X2))
              | ~ greater_or_equal(X2,X1)
              | ~ subpopulations(first_movers,efficient_producers,X0,X2) )
          & greater(X1,appear(efficient_producers,X0)) )
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(flattening,[],[f18]) ).

fof(f18,plain,
    ! [X0] :
      ( ? [X1] :
          ( ! [X2] :
              ( greater(zero,growth_rate(first_movers,X2))
              | ~ greater_or_equal(X2,X1)
              | ~ subpopulations(first_movers,efficient_producers,X0,X2) )
          & greater(X1,appear(efficient_producers,X0)) )
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0] :
      ( ( stable(X0)
        & environment(X0) )
     => ? [X1] :
          ( ! [X2] :
              ( ( greater_or_equal(X2,X1)
                & subpopulations(first_movers,efficient_producers,X0,X2) )
             => greater(zero,growth_rate(first_movers,X2)) )
          & greater(X1,appear(efficient_producers,X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l10) ).

fof(f149,plain,
    ( ~ greater(sK0(sK1),appear(efficient_producers,sK1))
    | spl3_5 ),
    inference(avatar_component_clause,[],[f147]) ).

fof(f158,plain,
    ( spl3_3
    | spl3_4
    | ~ spl3_5
    | ~ spl3_6
    | ~ spl3_7 ),
    inference(avatar_split_clause,[],[f139,f155,f151,f147,f144,f141]) ).

fof(f139,plain,
    ! [X0,X1] :
      ( ~ greater(cardinality_at_time(efficient_producers,sK2(sK0(sK1))),zero)
      | ~ greater(cardinality_at_time(first_movers,sK2(sK0(sK1))),zero)
      | ~ greater(sK0(sK1),appear(efficient_producers,sK1))
      | ~ greater(sK2(sK0(sK1)),X0)
      | ~ in_environment(sK1,X0)
      | ~ in_environment(X1,sK0(sK1))
      | ~ stable(X1)
      | ~ environment(X1) ),
    inference(subsumption_resolution,[],[f137,f45]) ).

fof(f137,plain,
    ! [X0,X1] :
      ( ~ greater(cardinality_at_time(efficient_producers,sK2(sK0(sK1))),zero)
      | ~ greater(cardinality_at_time(first_movers,sK2(sK0(sK1))),zero)
      | ~ greater(sK0(sK1),appear(efficient_producers,sK1))
      | ~ greater(sK2(sK0(sK1)),X0)
      | ~ in_environment(sK1,X0)
      | contracts_from(sK0(sK1),first_movers)
      | ~ in_environment(X1,sK0(sK1))
      | ~ stable(X1)
      | ~ environment(X1) ),
    inference(resolution,[],[f125,f50]) ).

fof(f125,plain,
    ! [X0,X1] :
      ( ~ greater_or_equal(sK2(X0),sK0(sK1))
      | ~ greater(cardinality_at_time(efficient_producers,sK2(X0)),zero)
      | ~ greater(cardinality_at_time(first_movers,sK2(X0)),zero)
      | ~ greater(X0,appear(efficient_producers,sK1))
      | ~ greater(sK2(X0),X1)
      | ~ in_environment(sK1,X1) ),
    inference(subsumption_resolution,[],[f124,f43]) ).

fof(f124,plain,
    ! [X0,X1] :
      ( ~ greater(X0,appear(efficient_producers,sK1))
      | ~ greater(cardinality_at_time(efficient_producers,sK2(X0)),zero)
      | ~ greater(cardinality_at_time(first_movers,sK2(X0)),zero)
      | ~ greater_or_equal(sK2(X0),sK0(sK1))
      | ~ greater(sK2(X0),X1)
      | ~ in_environment(sK1,X1)
      | ~ environment(sK1) ),
    inference(subsumption_resolution,[],[f123,f44]) ).

fof(f123,plain,
    ! [X0,X1] :
      ( ~ greater(X0,appear(efficient_producers,sK1))
      | ~ greater(cardinality_at_time(efficient_producers,sK2(X0)),zero)
      | ~ greater(cardinality_at_time(first_movers,sK2(X0)),zero)
      | ~ greater_or_equal(sK2(X0),sK0(sK1))
      | ~ greater(sK2(X0),X1)
      | ~ in_environment(sK1,X1)
      | ~ stable(sK1)
      | ~ environment(sK1) ),
    inference(resolution,[],[f100,f47]) ).

fof(f100,plain,
    ! [X0] :
      ( ~ in_environment(sK1,sK2(X0))
      | ~ greater(X0,appear(efficient_producers,sK1))
      | ~ greater(cardinality_at_time(efficient_producers,sK2(X0)),zero)
      | ~ greater(cardinality_at_time(first_movers,sK2(X0)),zero)
      | ~ greater_or_equal(sK2(X0),sK0(sK1)) ),
    inference(subsumption_resolution,[],[f99,f43]) ).

fof(f99,plain,
    ! [X0] :
      ( ~ greater_or_equal(sK2(X0),sK0(sK1))
      | ~ greater(X0,appear(efficient_producers,sK1))
      | ~ greater(cardinality_at_time(efficient_producers,sK2(X0)),zero)
      | ~ greater(cardinality_at_time(first_movers,sK2(X0)),zero)
      | ~ in_environment(sK1,sK2(X0))
      | ~ environment(sK1) ),
    inference(resolution,[],[f98,f48]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ greater(cardinality_at_time(efficient_producers,X1),zero)
      | ~ greater(cardinality_at_time(first_movers,X1),zero)
      | ~ in_environment(X0,X1)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ greater(cardinality_at_time(efficient_producers,X1),zero)
      | ~ greater(cardinality_at_time(first_movers,X1),zero)
      | ~ in_environment(X0,X1)
      | ~ environment(X0) ),
    inference(flattening,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ greater(cardinality_at_time(efficient_producers,X1),zero)
      | ~ greater(cardinality_at_time(first_movers,X1),zero)
      | ~ in_environment(X0,X1)
      | ~ environment(X0) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( ( greater(cardinality_at_time(efficient_producers,X1),zero)
        & greater(cardinality_at_time(first_movers,X1),zero)
        & in_environment(X0,X1)
        & environment(X0) )
     => subpopulations(first_movers,efficient_producers,X0,X1) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X2] :
      ( ( greater(cardinality_at_time(efficient_producers,X2),zero)
        & greater(cardinality_at_time(first_movers,X2),zero)
        & in_environment(X0,X2)
        & environment(X0) )
     => subpopulations(first_movers,efficient_producers,X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep) ).

fof(f98,plain,
    ! [X0] :
      ( ~ subpopulations(first_movers,efficient_producers,sK1,sK2(X0))
      | ~ greater_or_equal(sK2(X0),sK0(sK1))
      | ~ greater(X0,appear(efficient_producers,sK1)) ),
    inference(subsumption_resolution,[],[f97,f43]) ).

fof(f97,plain,
    ! [X0] :
      ( ~ greater_or_equal(sK2(X0),sK0(sK1))
      | ~ subpopulations(first_movers,efficient_producers,sK1,sK2(X0))
      | ~ greater(X0,appear(efficient_producers,sK1))
      | ~ environment(sK1) ),
    inference(resolution,[],[f84,f44]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( ~ stable(X1)
      | ~ greater_or_equal(sK2(X0),sK0(X1))
      | ~ subpopulations(first_movers,efficient_producers,X1,sK2(X0))
      | ~ greater(X0,appear(efficient_producers,sK1))
      | ~ environment(X1) ),
    inference(resolution,[],[f81,f42]) ).

fof(f42,plain,
    ! [X2,X0] :
      ( greater(zero,growth_rate(first_movers,X2))
      | ~ greater_or_equal(X2,sK0(X0))
      | ~ subpopulations(first_movers,efficient_producers,X0,X2)
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f81,plain,
    ! [X0] :
      ( ~ greater(zero,growth_rate(first_movers,sK2(X0)))
      | ~ greater(X0,appear(efficient_producers,sK1)) ),
    inference(subsumption_resolution,[],[f80,f43]) ).

fof(f80,plain,
    ! [X0] :
      ( ~ greater(X0,appear(efficient_producers,sK1))
      | ~ greater(zero,growth_rate(first_movers,sK2(X0)))
      | ~ environment(sK1) ),
    inference(subsumption_resolution,[],[f79,f44]) ).

fof(f79,plain,
    ! [X0] :
      ( ~ greater(X0,appear(efficient_producers,sK1))
      | ~ greater(zero,growth_rate(first_movers,sK2(X0)))
      | ~ stable(sK1)
      | ~ environment(sK1) ),
    inference(duplicate_literal_removal,[],[f77]) ).

fof(f77,plain,
    ! [X0] :
      ( ~ greater(X0,appear(efficient_producers,sK1))
      | ~ greater(X0,appear(efficient_producers,sK1))
      | ~ greater(zero,growth_rate(first_movers,sK2(X0)))
      | ~ stable(sK1)
      | ~ environment(sK1) ),
    inference(resolution,[],[f74,f46]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( ~ in_environment(sK1,X1)
      | ~ greater(X0,appear(efficient_producers,sK1))
      | ~ greater(X0,X1)
      | ~ greater(zero,growth_rate(first_movers,sK2(X0))) ),
    inference(subsumption_resolution,[],[f73,f43]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( ~ greater(zero,growth_rate(first_movers,sK2(X0)))
      | ~ greater(X0,appear(efficient_producers,sK1))
      | ~ greater(X0,X1)
      | ~ in_environment(sK1,X1)
      | ~ environment(sK1) ),
    inference(subsumption_resolution,[],[f61,f44]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( ~ greater(zero,growth_rate(first_movers,sK2(X0)))
      | ~ greater(X0,appear(efficient_producers,sK1))
      | ~ greater(X0,X1)
      | ~ in_environment(sK1,X1)
      | ~ stable(sK1)
      | ~ environment(sK1) ),
    inference(resolution,[],[f59,f47]) ).

fof(f59,plain,
    ! [X0] :
      ( ~ in_environment(sK1,X0)
      | ~ greater(zero,growth_rate(first_movers,sK2(X0)))
      | ~ greater(X0,appear(efficient_producers,sK1)) ),
    inference(subsumption_resolution,[],[f58,f43]) ).

fof(f58,plain,
    ! [X0] :
      ( ~ in_environment(sK1,X0)
      | ~ greater(zero,growth_rate(first_movers,sK2(X0)))
      | ~ environment(sK1)
      | ~ greater(X0,appear(efficient_producers,sK1)) ),
    inference(resolution,[],[f57,f44]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( ~ stable(X1)
      | ~ in_environment(X1,X0)
      | ~ greater(zero,growth_rate(first_movers,sK2(X0)))
      | ~ environment(X1)
      | ~ greater(X0,appear(efficient_producers,sK1)) ),
    inference(resolution,[],[f51,f45]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( contracts_from(X1,first_movers)
      | ~ greater(zero,growth_rate(first_movers,sK2(X1)))
      | ~ in_environment(X0,X1)
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f37]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : MGT027+1 : TPTP v8.2.0. Released v2.0.0.
% 0.03/0.13  % 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
% 0.12/0.34  % Computer : n020.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Sun May 19 00:10:08 EDT 2024
% 0.12/0.34  % CPUTime    : 
% 0.12/0.34  This is a FOF_THM_RFO_SEQ problem
% 0.12/0.34  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
% 0.50/0.73  % (8665)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on theBenchmark for (2996ds/78Mi)
% 0.50/0.73  % (8666)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)
% 0.50/0.73  % (8667)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)
% 0.50/0.73  % (8668)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)
% 0.50/0.73  % (8670)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)
% 0.50/0.73  % (8669)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)
% 0.50/0.73  % (8663)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)
% 0.50/0.73  % (8669)Refutation not found, incomplete strategy% (8669)------------------------------
% 0.50/0.73  % (8669)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.50/0.73  % (8669)Termination reason: Refutation not found, incomplete strategy
% 0.50/0.73  
% 0.50/0.73  % (8669)Memory used [KB]: 1068
% 0.50/0.73  % (8669)Time elapsed: 0.005 s
% 0.50/0.73  % (8669)Instructions burned: 6 (million)
% 0.50/0.73  % (8669)------------------------------
% 0.50/0.73  % (8669)------------------------------
% 0.56/0.73  % (8671)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)
% 0.56/0.73  % (8664)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)
% 0.56/0.74  % (8671)Refutation not found, incomplete strategy% (8671)------------------------------
% 0.56/0.74  % (8671)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.74  % (8671)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.74  
% 0.56/0.74  % (8671)Memory used [KB]: 1041
% 0.56/0.74  % (8671)Time elapsed: 0.004 s
% 0.56/0.74  % (8671)Instructions burned: 4 (million)
% 0.56/0.74  % (8671)------------------------------
% 0.56/0.74  % (8671)------------------------------
% 0.56/0.74  % (8665)First to succeed.
% 0.56/0.74  % (8666)Instruction limit reached!
% 0.56/0.74  % (8666)------------------------------
% 0.56/0.74  % (8666)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.74  % (8666)Termination reason: Unknown
% 0.56/0.74  % (8666)Termination phase: Saturation
% 0.56/0.74  
% 0.56/0.74  % (8666)Memory used [KB]: 1255
% 0.56/0.74  % (8666)Time elapsed: 0.017 s
% 0.56/0.74  % (8666)Instructions burned: 34 (million)
% 0.56/0.74  % (8666)------------------------------
% 0.56/0.74  % (8666)------------------------------
% 0.56/0.74  % (8665)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-8662"
% 0.56/0.74  % (8664)Also succeeded, but the first one will report.
% 0.56/0.74  % (8665)Refutation found. Thanks to Tanya!
% 0.56/0.74  % SZS status Theorem for theBenchmark
% 0.56/0.74  % SZS output start Proof for theBenchmark
% See solution above
% 0.56/0.74  % (8665)------------------------------
% 0.56/0.74  % (8665)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.74  % (8665)Termination reason: Refutation
% 0.56/0.74  
% 0.56/0.74  % (8665)Memory used [KB]: 1251
% 0.56/0.74  % (8665)Time elapsed: 0.017 s
% 0.56/0.74  % (8665)Instructions burned: 47 (million)
% 0.56/0.74  % (8662)Success in time 0.386 s
% 0.56/0.74  % Vampire---4.8 exiting
%------------------------------------------------------------------------------