TSTP Solution File: MGT025+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : MGT025+1 : TPTP v8.1.2. 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n005.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 : Sun May  5 07:56:37 EDT 2024

% Result   : Theorem 0.56s 0.74s
% Output   : Refutation 0.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   20
% Syntax   : Number of formulae    :  152 (  11 unt;   0 def)
%            Number of atoms       :  529 (  43 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  576 ( 199   ~; 270   |;  73   &)
%                                         (  13 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   24 (  22 usr;  14 prp; 0-4 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :  128 ( 124   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f286,plain,
    $false,
    inference(avatar_sat_refutation,[],[f70,f79,f88,f134,f148,f168,f171,f172,f180,f184,f188,f202,f236,f249,f271,f274,f280,f282,f285]) ).

fof(f285,plain,
    ( ~ spl3_2
    | spl3_5
    | ~ spl3_14 ),
    inference(avatar_contradiction_clause,[],[f284]) ).

fof(f284,plain,
    ( $false
    | ~ spl3_2
    | spl3_5
    | ~ spl3_14 ),
    inference(subsumption_resolution,[],[f283,f279]) ).

fof(f279,plain,
    ( greater(zero,zero)
    | ~ spl3_14 ),
    inference(avatar_component_clause,[],[f277]) ).

fof(f277,plain,
    ( spl3_14
  <=> greater(zero,zero) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).

fof(f283,plain,
    ( ~ greater(zero,zero)
    | ~ spl3_2
    | spl3_5 ),
    inference(superposition,[],[f83,f68]) ).

fof(f68,plain,
    ( zero = growth_rate(first_movers,sK1)
    | ~ spl3_2 ),
    inference(avatar_component_clause,[],[f67]) ).

fof(f67,plain,
    ( spl3_2
  <=> zero = growth_rate(first_movers,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

fof(f83,plain,
    ( ~ greater(zero,growth_rate(first_movers,sK1))
    | spl3_5 ),
    inference(avatar_component_clause,[],[f81]) ).

fof(f81,plain,
    ( spl3_5
  <=> greater(zero,growth_rate(first_movers,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

fof(f282,plain,
    ( spl3_14
    | ~ spl3_2
    | ~ spl3_4 ),
    inference(avatar_split_clause,[],[f281,f76,f67,f277]) ).

fof(f76,plain,
    ( spl3_4
  <=> greater(growth_rate(first_movers,sK1),zero) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

fof(f281,plain,
    ( greater(zero,zero)
    | ~ spl3_2
    | ~ spl3_4 ),
    inference(forward_demodulation,[],[f77,f68]) ).

fof(f77,plain,
    ( greater(growth_rate(first_movers,sK1),zero)
    | ~ spl3_4 ),
    inference(avatar_component_clause,[],[f76]) ).

fof(f280,plain,
    ( ~ spl3_13
    | spl3_8
    | spl3_14
    | ~ spl3_2 ),
    inference(avatar_split_clause,[],[f275,f67,f277,f114,f244]) ).

fof(f244,plain,
    ( spl3_13
  <=> increases(cardinality_at_time(first_movers,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).

fof(f114,plain,
    ( spl3_8
  <=> ! [X0] :
        ( ~ in_environment(X0,sK1)
        | ~ environment(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).

fof(f275,plain,
    ( ! [X0] :
        ( greater(zero,zero)
        | ~ in_environment(X0,sK1)
        | ~ environment(X0)
        | ~ increases(cardinality_at_time(first_movers,sK1)) )
    | ~ spl3_2 ),
    inference(forward_demodulation,[],[f203,f68]) ).

fof(f203,plain,
    ! [X0] :
      ( ~ in_environment(X0,sK1)
      | ~ environment(X0)
      | ~ increases(cardinality_at_time(first_movers,sK1))
      | greater(growth_rate(first_movers,sK1),zero) ),
    inference(subsumption_resolution,[],[f106,f41]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( subpopulation(first_movers,X0,X1)
      | ~ in_environment(X0,X1)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ( subpopulation(efficient_producers,X0,X1)
        & subpopulation(first_movers,X0,X1) )
      | ~ in_environment(X0,X1)
      | ~ environment(X0) ),
    inference(flattening,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ( subpopulation(efficient_producers,X0,X1)
        & subpopulation(first_movers,X0,X1) )
      | ~ in_environment(X0,X1)
      | ~ environment(X0) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( ( in_environment(X0,X1)
        & environment(X0) )
     => ( subpopulation(efficient_producers,X0,X1)
        & subpopulation(first_movers,X0,X1) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X2] :
      ( ( in_environment(X0,X2)
        & environment(X0) )
     => ( subpopulation(efficient_producers,X0,X2)
        & subpopulation(first_movers,X0,X2) ) ),
    file('/export/starexec/sandbox/tmp/tmp.wL6Q2pBBUR/Vampire---4.8_16384',mp_subpopulations) ).

fof(f106,plain,
    ! [X0] :
      ( ~ in_environment(X0,sK1)
      | ~ subpopulation(first_movers,X0,sK1)
      | ~ environment(X0)
      | ~ increases(cardinality_at_time(first_movers,sK1))
      | greater(growth_rate(first_movers,sK1),zero) ),
    inference(resolution,[],[f90,f47]) ).

fof(f47,plain,
    ! [X2,X0,X1] :
      ( ~ greater(cardinality_at_time(X0,X2),zero)
      | ~ in_environment(X1,X2)
      | ~ subpopulation(X0,X1,X2)
      | ~ environment(X1)
      | ~ increases(cardinality_at_time(X0,X2))
      | greater(growth_rate(X0,X2),zero) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ( ( greater(zero,growth_rate(X0,X2))
          | ~ decreases(cardinality_at_time(X0,X2)) )
        & ( greater(growth_rate(X0,X2),zero)
          | ~ increases(cardinality_at_time(X0,X2)) )
        & ( zero = growth_rate(X0,X2)
          | ~ constant(cardinality_at_time(X0,X2)) ) )
      | ~ greater(cardinality_at_time(X0,X2),zero)
      | ~ subpopulation(X0,X1,X2)
      | ~ in_environment(X1,X2)
      | ~ environment(X1) ),
    inference(flattening,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( ( ( greater(zero,growth_rate(X0,X2))
          | ~ decreases(cardinality_at_time(X0,X2)) )
        & ( greater(growth_rate(X0,X2),zero)
          | ~ increases(cardinality_at_time(X0,X2)) )
        & ( zero = growth_rate(X0,X2)
          | ~ constant(cardinality_at_time(X0,X2)) ) )
      | ~ greater(cardinality_at_time(X0,X2),zero)
      | ~ subpopulation(X0,X1,X2)
      | ~ in_environment(X1,X2)
      | ~ environment(X1) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X0,X1,X2] :
      ( ( greater(cardinality_at_time(X0,X2),zero)
        & subpopulation(X0,X1,X2)
        & in_environment(X1,X2)
        & environment(X1) )
     => ( ( decreases(cardinality_at_time(X0,X2))
         => greater(zero,growth_rate(X0,X2)) )
        & ( increases(cardinality_at_time(X0,X2))
         => greater(growth_rate(X0,X2),zero) )
        & ( constant(cardinality_at_time(X0,X2))
         => zero = growth_rate(X0,X2) ) ) ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X1,X0,X2] :
      ( ( greater(cardinality_at_time(X1,X2),zero)
        & subpopulation(X1,X0,X2)
        & in_environment(X0,X2)
        & environment(X0) )
     => ( ( decreases(cardinality_at_time(X1,X2))
         => greater(zero,growth_rate(X1,X2)) )
        & ( increases(cardinality_at_time(X1,X2))
         => greater(growth_rate(X1,X2),zero) )
        & ( constant(cardinality_at_time(X1,X2))
         => zero = growth_rate(X1,X2) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.wL6Q2pBBUR/Vampire---4.8_16384',mp_growth_rate) ).

fof(f90,plain,
    greater(cardinality_at_time(first_movers,sK1),zero),
    inference(unit_resulting_resolution,[],[f36,f37,f39]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ environment(X0)
      | greater(cardinality_at_time(first_movers,X1),zero) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ( greater(cardinality_at_time(efficient_producers,X1),zero)
        & greater(cardinality_at_time(first_movers,X1),zero) )
      | ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ environment(X0) ),
    inference(flattening,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ( greater(cardinality_at_time(efficient_producers,X1),zero)
        & greater(cardinality_at_time(first_movers,X1),zero) )
      | ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ environment(X0) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f11,plain,
    ! [X0,X1] :
      ( ( subpopulations(first_movers,efficient_producers,X0,X1)
        & environment(X0) )
     => ( greater(cardinality_at_time(efficient_producers,X1),zero)
        & greater(cardinality_at_time(first_movers,X1),zero) ) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X2] :
      ( ( subpopulations(first_movers,efficient_producers,X0,X2)
        & environment(X0) )
     => ( greater(cardinality_at_time(efficient_producers,X2),zero)
        & greater(cardinality_at_time(first_movers,X2),zero) ) ),
    file('/export/starexec/sandbox/tmp/tmp.wL6Q2pBBUR/Vampire---4.8_16384',mp_non_zero_producers) ).

fof(f37,plain,
    subpopulations(first_movers,efficient_producers,sK0,sK1),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ? [X0,X1] :
      ( ( ~ greater(zero,growth_rate(first_movers,X1))
        | ~ greater(growth_rate(efficient_producers,X1),zero) )
      & ( ~ greater(zero,growth_rate(efficient_producers,X1))
        | ~ greater(growth_rate(first_movers,X1),zero) )
      & ( zero != growth_rate(efficient_producers,X1)
        | zero != growth_rate(first_movers,X1) )
      & constant(number_of_organizations(X0,X1))
      & subpopulations(first_movers,efficient_producers,X0,X1)
      & environment(X0) ),
    inference(flattening,[],[f18]) ).

fof(f18,plain,
    ? [X0,X1] :
      ( ( ~ greater(zero,growth_rate(first_movers,X1))
        | ~ greater(growth_rate(efficient_producers,X1),zero) )
      & ( ~ greater(zero,growth_rate(efficient_producers,X1))
        | ~ greater(growth_rate(first_movers,X1),zero) )
      & ( zero != growth_rate(efficient_producers,X1)
        | zero != growth_rate(first_movers,X1) )
      & constant(number_of_organizations(X0,X1))
      & subpopulations(first_movers,efficient_producers,X0,X1)
      & environment(X0) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,plain,
    ~ ! [X0,X1] :
        ( ( constant(number_of_organizations(X0,X1))
          & subpopulations(first_movers,efficient_producers,X0,X1)
          & environment(X0) )
       => ( ( greater(zero,growth_rate(first_movers,X1))
            & greater(growth_rate(efficient_producers,X1),zero) )
          | ( greater(zero,growth_rate(efficient_producers,X1))
            & greater(growth_rate(first_movers,X1),zero) )
          | ( zero = growth_rate(efficient_producers,X1)
            & zero = growth_rate(first_movers,X1) ) ) ),
    inference(rectify,[],[f9]) ).

fof(f9,negated_conjecture,
    ~ ! [X0,X2] :
        ( ( constant(number_of_organizations(X0,X2))
          & subpopulations(first_movers,efficient_producers,X0,X2)
          & environment(X0) )
       => ( ( greater(zero,growth_rate(first_movers,X2))
            & greater(growth_rate(efficient_producers,X2),zero) )
          | ( greater(zero,growth_rate(efficient_producers,X2))
            & greater(growth_rate(first_movers,X2),zero) )
          | ( zero = growth_rate(efficient_producers,X2)
            & zero = growth_rate(first_movers,X2) ) ) ),
    inference(negated_conjecture,[],[f8]) ).

fof(f8,conjecture,
    ! [X0,X2] :
      ( ( constant(number_of_organizations(X0,X2))
        & subpopulations(first_movers,efficient_producers,X0,X2)
        & environment(X0) )
     => ( ( greater(zero,growth_rate(first_movers,X2))
          & greater(growth_rate(efficient_producers,X2),zero) )
        | ( greater(zero,growth_rate(efficient_producers,X2))
          & greater(growth_rate(first_movers,X2),zero) )
        | ( zero = growth_rate(efficient_producers,X2)
          & zero = growth_rate(first_movers,X2) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.wL6Q2pBBUR/Vampire---4.8_16384',prove_l7) ).

fof(f36,plain,
    environment(sK0),
    inference(cnf_transformation,[],[f19]) ).

fof(f274,plain,
    ( spl3_1
    | spl3_7
    | spl3_13 ),
    inference(avatar_contradiction_clause,[],[f273]) ).

fof(f273,plain,
    ( $false
    | spl3_1
    | spl3_7
    | spl3_13 ),
    inference(subsumption_resolution,[],[f272,f38]) ).

fof(f38,plain,
    constant(number_of_organizations(sK0,sK1)),
    inference(cnf_transformation,[],[f19]) ).

fof(f272,plain,
    ( ~ constant(number_of_organizations(sK0,sK1))
    | spl3_1
    | spl3_7
    | spl3_13 ),
    inference(forward_demodulation,[],[f257,f97]) ).

fof(f97,plain,
    number_of_organizations(sK0,sK1) = sum(cardinality_at_time(first_movers,sK1),cardinality_at_time(efficient_producers,sK1)),
    inference(unit_resulting_resolution,[],[f36,f95,f56]) ).

fof(f56,plain,
    ! [X2,X0] :
      ( ~ subpopulation(first_movers,X0,X2)
      | ~ environment(X0)
      | number_of_organizations(X0,X2) = sum(cardinality_at_time(first_movers,X2),cardinality_at_time(efficient_producers,X2)) ),
    inference(equality_resolution,[],[f45]) ).

fof(f45,plain,
    ! [X2,X0,X1] :
      ( ~ environment(X0)
      | ~ subpopulation(X1,X0,X2)
      | first_movers != X1
      | number_of_organizations(X0,X2) = sum(cardinality_at_time(first_movers,X2),cardinality_at_time(efficient_producers,X2)) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( number_of_organizations(X0,X2) = sum(cardinality_at_time(first_movers,X2),cardinality_at_time(efficient_producers,X2))
      | ( first_movers != X1
        & efficient_producers != X1
        & greater(cardinality_at_time(X1,X2),zero) )
      | ~ subpopulation(X1,X0,X2)
      | ~ environment(X0) ),
    inference(flattening,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( number_of_organizations(X0,X2) = sum(cardinality_at_time(first_movers,X2),cardinality_at_time(efficient_producers,X2))
      | ( first_movers != X1
        & efficient_producers != X1
        & greater(cardinality_at_time(X1,X2),zero) )
      | ~ subpopulation(X1,X0,X2)
      | ~ environment(X0) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1,X2] :
      ( ( ( greater(cardinality_at_time(X1,X2),zero)
         => ( first_movers = X1
            | efficient_producers = X1 ) )
        & subpopulation(X1,X0,X2)
        & environment(X0) )
     => number_of_organizations(X0,X2) = sum(cardinality_at_time(first_movers,X2),cardinality_at_time(efficient_producers,X2)) ),
    file('/export/starexec/sandbox/tmp/tmp.wL6Q2pBBUR/Vampire---4.8_16384',mp_only_members) ).

fof(f95,plain,
    subpopulation(first_movers,sK0,sK1),
    inference(unit_resulting_resolution,[],[f36,f89,f41]) ).

fof(f89,plain,
    in_environment(sK0,sK1),
    inference(unit_resulting_resolution,[],[f36,f37,f55]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ environment(X0)
      | in_environment(X0,X1) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( in_environment(X0,X1)
      | ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ environment(X0) ),
    inference(flattening,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( in_environment(X0,X1)
      | ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ environment(X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( ( subpopulations(first_movers,efficient_producers,X0,X1)
        & environment(X0) )
     => in_environment(X0,X1) ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X2] :
      ( ( subpopulations(first_movers,efficient_producers,X0,X2)
        & environment(X0) )
     => in_environment(X0,X2) ),
    file('/export/starexec/sandbox/tmp/tmp.wL6Q2pBBUR/Vampire---4.8_16384',mp_time_point_occur) ).

fof(f257,plain,
    ( ~ constant(sum(cardinality_at_time(first_movers,sK1),cardinality_at_time(efficient_producers,sK1)))
    | spl3_1
    | spl3_7
    | spl3_13 ),
    inference(unit_resulting_resolution,[],[f124,f245,f251,f61]) ).

fof(f61,plain,
    ! [X2,X1] :
      ( ~ constant(sum(X1,X2))
      | constant(X2)
      | increases(X1)
      | sP2(X2,X1) ),
    inference(equality_resolution,[],[f51]) ).

fof(f51,plain,
    ! [X2,X0,X1] :
      ( sum(X1,X2) != X0
      | ~ constant(X0)
      | constant(X2)
      | increases(X1)
      | sP2(X2,X1) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( ( increases(X2)
        & decreases(X1) )
      | ( decreases(X2)
        & increases(X1) )
      | ( constant(X2)
        & constant(X1) )
      | ~ constant(X0)
      | sum(X1,X2) != X0 ),
    inference(flattening,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1,X2] :
      ( ( increases(X2)
        & decreases(X1) )
      | ( decreases(X2)
        & increases(X1) )
      | ( constant(X2)
        & constant(X1) )
      | ~ constant(X0)
      | sum(X1,X2) != X0 ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X0,X1,X2] :
      ( ( constant(X0)
        & sum(X1,X2) = X0 )
     => ( ( increases(X2)
          & decreases(X1) )
        | ( decreases(X2)
          & increases(X1) )
        | ( constant(X2)
          & constant(X1) ) ) ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X3,X4,X5] :
      ( ( constant(X3)
        & sum(X4,X5) = X3 )
     => ( ( increases(X5)
          & decreases(X4) )
        | ( decreases(X5)
          & increases(X4) )
        | ( constant(X5)
          & constant(X4) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.wL6Q2pBBUR/Vampire---4.8_16384',mp_abc_sum_increase) ).

fof(f251,plain,
    ( ! [X0] : ~ sP2(X0,cardinality_at_time(first_movers,sK1))
    | spl3_7 ),
    inference(unit_resulting_resolution,[],[f112,f49]) ).

fof(f49,plain,
    ! [X2,X1] :
      ( ~ sP2(X2,X1)
      | decreases(X1) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f112,plain,
    ( ~ decreases(cardinality_at_time(first_movers,sK1))
    | spl3_7 ),
    inference(avatar_component_clause,[],[f110]) ).

fof(f110,plain,
    ( spl3_7
  <=> decreases(cardinality_at_time(first_movers,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).

fof(f245,plain,
    ( ~ increases(cardinality_at_time(first_movers,sK1))
    | spl3_13 ),
    inference(avatar_component_clause,[],[f244]) ).

fof(f124,plain,
    ( ~ constant(cardinality_at_time(efficient_producers,sK1))
    | spl3_1 ),
    inference(unit_resulting_resolution,[],[f36,f89,f96,f65,f91,f48]) ).

fof(f48,plain,
    ! [X2,X0,X1] :
      ( ~ greater(cardinality_at_time(X0,X2),zero)
      | ~ in_environment(X1,X2)
      | ~ subpopulation(X0,X1,X2)
      | ~ environment(X1)
      | ~ constant(cardinality_at_time(X0,X2))
      | zero = growth_rate(X0,X2) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f91,plain,
    greater(cardinality_at_time(efficient_producers,sK1),zero),
    inference(unit_resulting_resolution,[],[f36,f37,f40]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ environment(X0)
      | greater(cardinality_at_time(efficient_producers,X1),zero) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f65,plain,
    ( zero != growth_rate(efficient_producers,sK1)
    | spl3_1 ),
    inference(avatar_component_clause,[],[f63]) ).

fof(f63,plain,
    ( spl3_1
  <=> zero = growth_rate(efficient_producers,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f96,plain,
    subpopulation(efficient_producers,sK0,sK1),
    inference(unit_resulting_resolution,[],[f36,f89,f42]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( subpopulation(efficient_producers,X0,X1)
      | ~ in_environment(X0,X1)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f271,plain,
    ( spl3_7
    | spl3_9
    | spl3_13 ),
    inference(avatar_contradiction_clause,[],[f270]) ).

fof(f270,plain,
    ( $false
    | spl3_7
    | spl3_9
    | spl3_13 ),
    inference(subsumption_resolution,[],[f269,f38]) ).

fof(f269,plain,
    ( ~ constant(number_of_organizations(sK0,sK1))
    | spl3_7
    | spl3_9
    | spl3_13 ),
    inference(superposition,[],[f260,f97]) ).

fof(f260,plain,
    ( ! [X0] : ~ constant(sum(cardinality_at_time(first_movers,sK1),X0))
    | spl3_7
    | spl3_9
    | spl3_13 ),
    inference(unit_resulting_resolution,[],[f121,f245,f251,f59]) ).

fof(f59,plain,
    ! [X2,X1] :
      ( ~ constant(sum(X1,X2))
      | constant(X1)
      | increases(X1)
      | sP2(X2,X1) ),
    inference(equality_resolution,[],[f53]) ).

fof(f53,plain,
    ! [X2,X0,X1] :
      ( sum(X1,X2) != X0
      | ~ constant(X0)
      | constant(X1)
      | increases(X1)
      | sP2(X2,X1) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f121,plain,
    ( ~ constant(cardinality_at_time(first_movers,sK1))
    | spl3_9 ),
    inference(avatar_component_clause,[],[f119]) ).

fof(f119,plain,
    ( spl3_9
  <=> constant(cardinality_at_time(first_movers,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).

fof(f249,plain,
    ( ~ spl3_13
    | spl3_8
    | spl3_4 ),
    inference(avatar_split_clause,[],[f248,f76,f114,f244]) ).

fof(f248,plain,
    ( ! [X0] :
        ( ~ in_environment(X0,sK1)
        | ~ environment(X0)
        | ~ increases(cardinality_at_time(first_movers,sK1)) )
    | spl3_4 ),
    inference(subsumption_resolution,[],[f203,f78]) ).

fof(f78,plain,
    ( ~ greater(growth_rate(first_movers,sK1),zero)
    | spl3_4 ),
    inference(avatar_component_clause,[],[f76]) ).

fof(f236,plain,
    ( spl3_10
    | spl3_1
    | spl3_11 ),
    inference(avatar_split_clause,[],[f235,f175,f63,f131]) ).

fof(f131,plain,
    ( spl3_10
  <=> decreases(cardinality_at_time(efficient_producers,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).

fof(f175,plain,
    ( spl3_11
  <=> increases(cardinality_at_time(efficient_producers,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_11])]) ).

fof(f235,plain,
    ( decreases(cardinality_at_time(efficient_producers,sK1))
    | spl3_1
    | spl3_11 ),
    inference(subsumption_resolution,[],[f226,f189]) ).

fof(f189,plain,
    ( ! [X0] : ~ sP2(cardinality_at_time(efficient_producers,sK1),X0)
    | spl3_11 ),
    inference(unit_resulting_resolution,[],[f177,f50]) ).

fof(f50,plain,
    ! [X2,X1] :
      ( ~ sP2(X2,X1)
      | increases(X2) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f177,plain,
    ( ~ increases(cardinality_at_time(efficient_producers,sK1))
    | spl3_11 ),
    inference(avatar_component_clause,[],[f175]) ).

fof(f226,plain,
    ( decreases(cardinality_at_time(efficient_producers,sK1))
    | sP2(cardinality_at_time(efficient_producers,sK1),cardinality_at_time(first_movers,sK1))
    | spl3_1 ),
    inference(subsumption_resolution,[],[f225,f124]) ).

fof(f225,plain,
    ( constant(cardinality_at_time(efficient_producers,sK1))
    | decreases(cardinality_at_time(efficient_producers,sK1))
    | sP2(cardinality_at_time(efficient_producers,sK1),cardinality_at_time(first_movers,sK1)) ),
    inference(subsumption_resolution,[],[f217,f38]) ).

fof(f217,plain,
    ( ~ constant(number_of_organizations(sK0,sK1))
    | constant(cardinality_at_time(efficient_producers,sK1))
    | decreases(cardinality_at_time(efficient_producers,sK1))
    | sP2(cardinality_at_time(efficient_producers,sK1),cardinality_at_time(first_movers,sK1)) ),
    inference(superposition,[],[f60,f97]) ).

fof(f60,plain,
    ! [X2,X1] :
      ( ~ constant(sum(X1,X2))
      | constant(X2)
      | decreases(X2)
      | sP2(X2,X1) ),
    inference(equality_resolution,[],[f52]) ).

fof(f52,plain,
    ! [X2,X0,X1] :
      ( sum(X1,X2) != X0
      | ~ constant(X0)
      | constant(X2)
      | decreases(X2)
      | sP2(X2,X1) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f202,plain,
    ~ spl3_8,
    inference(avatar_contradiction_clause,[],[f201]) ).

fof(f201,plain,
    ( $false
    | ~ spl3_8 ),
    inference(subsumption_resolution,[],[f195,f36]) ).

fof(f195,plain,
    ( ~ environment(sK0)
    | ~ spl3_8 ),
    inference(resolution,[],[f115,f89]) ).

fof(f115,plain,
    ( ! [X0] :
        ( ~ in_environment(X0,sK1)
        | ~ environment(X0) )
    | ~ spl3_8 ),
    inference(avatar_component_clause,[],[f114]) ).

fof(f188,plain,
    ( ~ spl3_11
    | spl3_6 ),
    inference(avatar_split_clause,[],[f187,f85,f175]) ).

fof(f85,plain,
    ( spl3_6
  <=> greater(growth_rate(efficient_producers,sK1),zero) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).

fof(f187,plain,
    ( ~ increases(cardinality_at_time(efficient_producers,sK1))
    | spl3_6 ),
    inference(unit_resulting_resolution,[],[f36,f89,f96,f91,f87,f47]) ).

fof(f87,plain,
    ( ~ greater(growth_rate(efficient_producers,sK1),zero)
    | spl3_6 ),
    inference(avatar_component_clause,[],[f85]) ).

fof(f184,plain,
    ( ~ spl3_2
    | spl3_4
    | ~ spl3_5 ),
    inference(avatar_contradiction_clause,[],[f183]) ).

fof(f183,plain,
    ( $false
    | ~ spl3_2
    | spl3_4
    | ~ spl3_5 ),
    inference(subsumption_resolution,[],[f182,f181]) ).

fof(f181,plain,
    ( ~ greater(zero,zero)
    | ~ spl3_2
    | spl3_4 ),
    inference(superposition,[],[f78,f68]) ).

fof(f182,plain,
    ( greater(zero,zero)
    | ~ spl3_2
    | ~ spl3_5 ),
    inference(superposition,[],[f82,f68]) ).

fof(f82,plain,
    ( greater(zero,growth_rate(first_movers,sK1))
    | ~ spl3_5 ),
    inference(avatar_component_clause,[],[f81]) ).

fof(f180,plain,
    ( spl3_2
    | ~ spl3_9 ),
    inference(avatar_split_clause,[],[f179,f119,f67]) ).

fof(f179,plain,
    ( zero = growth_rate(first_movers,sK1)
    | ~ spl3_9 ),
    inference(unit_resulting_resolution,[],[f36,f89,f95,f90,f120,f48]) ).

fof(f120,plain,
    ( constant(cardinality_at_time(first_movers,sK1))
    | ~ spl3_9 ),
    inference(avatar_component_clause,[],[f119]) ).

fof(f172,plain,
    ( spl3_5
    | ~ spl3_7 ),
    inference(avatar_split_clause,[],[f149,f110,f81]) ).

fof(f149,plain,
    ( greater(zero,growth_rate(first_movers,sK1))
    | ~ spl3_7 ),
    inference(unit_resulting_resolution,[],[f36,f89,f95,f90,f111,f46]) ).

fof(f46,plain,
    ! [X2,X0,X1] :
      ( ~ greater(cardinality_at_time(X0,X2),zero)
      | ~ in_environment(X1,X2)
      | ~ subpopulation(X0,X1,X2)
      | ~ environment(X1)
      | ~ decreases(cardinality_at_time(X0,X2))
      | greater(zero,growth_rate(X0,X2)) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f111,plain,
    ( decreases(cardinality_at_time(first_movers,sK1))
    | ~ spl3_7 ),
    inference(avatar_component_clause,[],[f110]) ).

fof(f171,plain,
    ( spl3_4
    | spl3_6
    | spl3_9 ),
    inference(avatar_contradiction_clause,[],[f170]) ).

fof(f170,plain,
    ( $false
    | spl3_4
    | spl3_6
    | spl3_9 ),
    inference(subsumption_resolution,[],[f169,f38]) ).

fof(f169,plain,
    ( ~ constant(number_of_organizations(sK0,sK1))
    | spl3_4
    | spl3_6
    | spl3_9 ),
    inference(forward_demodulation,[],[f162,f97]) ).

fof(f162,plain,
    ( ~ constant(sum(cardinality_at_time(first_movers,sK1),cardinality_at_time(efficient_producers,sK1)))
    | spl3_4
    | spl3_6
    | spl3_9 ),
    inference(unit_resulting_resolution,[],[f121,f103,f138,f59]) ).

fof(f138,plain,
    ( ! [X0] : ~ sP2(cardinality_at_time(efficient_producers,sK1),X0)
    | spl3_6 ),
    inference(unit_resulting_resolution,[],[f123,f50]) ).

fof(f123,plain,
    ( ~ increases(cardinality_at_time(efficient_producers,sK1))
    | spl3_6 ),
    inference(unit_resulting_resolution,[],[f36,f89,f96,f87,f91,f47]) ).

fof(f103,plain,
    ( ~ increases(cardinality_at_time(first_movers,sK1))
    | spl3_4 ),
    inference(unit_resulting_resolution,[],[f36,f89,f95,f78,f90,f47]) ).

fof(f168,plain,
    ( spl3_6
    | spl3_9
    | spl3_10 ),
    inference(avatar_contradiction_clause,[],[f167]) ).

fof(f167,plain,
    ( $false
    | spl3_6
    | spl3_9
    | spl3_10 ),
    inference(subsumption_resolution,[],[f166,f38]) ).

fof(f166,plain,
    ( ~ constant(number_of_organizations(sK0,sK1))
    | spl3_6
    | spl3_9
    | spl3_10 ),
    inference(forward_demodulation,[],[f164,f97]) ).

fof(f164,plain,
    ( ~ constant(sum(cardinality_at_time(first_movers,sK1),cardinality_at_time(efficient_producers,sK1)))
    | spl3_6
    | spl3_9
    | spl3_10 ),
    inference(unit_resulting_resolution,[],[f121,f133,f138,f58]) ).

fof(f58,plain,
    ! [X2,X1] :
      ( ~ constant(sum(X1,X2))
      | constant(X1)
      | decreases(X2)
      | sP2(X2,X1) ),
    inference(equality_resolution,[],[f54]) ).

fof(f54,plain,
    ! [X2,X0,X1] :
      ( sum(X1,X2) != X0
      | ~ constant(X0)
      | constant(X1)
      | decreases(X2)
      | sP2(X2,X1) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f133,plain,
    ( ~ decreases(cardinality_at_time(efficient_producers,sK1))
    | spl3_10 ),
    inference(avatar_component_clause,[],[f131]) ).

fof(f148,plain,
    ( spl3_7
    | spl3_9
    | spl3_10 ),
    inference(avatar_contradiction_clause,[],[f147]) ).

fof(f147,plain,
    ( $false
    | spl3_7
    | spl3_9
    | spl3_10 ),
    inference(subsumption_resolution,[],[f146,f38]) ).

fof(f146,plain,
    ( ~ constant(number_of_organizations(sK0,sK1))
    | spl3_7
    | spl3_9
    | spl3_10 ),
    inference(forward_demodulation,[],[f145,f97]) ).

fof(f145,plain,
    ( ~ constant(sum(cardinality_at_time(first_movers,sK1),cardinality_at_time(efficient_producers,sK1)))
    | spl3_7
    | spl3_9
    | spl3_10 ),
    inference(unit_resulting_resolution,[],[f133,f121,f135,f58]) ).

fof(f135,plain,
    ( ! [X0] : ~ sP2(X0,cardinality_at_time(first_movers,sK1))
    | spl3_7 ),
    inference(unit_resulting_resolution,[],[f112,f49]) ).

fof(f134,plain,
    ( spl3_3
    | ~ spl3_10
    | spl3_8 ),
    inference(avatar_split_clause,[],[f129,f114,f131,f72]) ).

fof(f72,plain,
    ( spl3_3
  <=> greater(zero,growth_rate(efficient_producers,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

fof(f129,plain,
    ! [X0] :
      ( ~ in_environment(X0,sK1)
      | ~ environment(X0)
      | ~ decreases(cardinality_at_time(efficient_producers,sK1))
      | greater(zero,growth_rate(efficient_producers,sK1)) ),
    inference(subsumption_resolution,[],[f126,f42]) ).

fof(f126,plain,
    ! [X0] :
      ( ~ in_environment(X0,sK1)
      | ~ subpopulation(efficient_producers,X0,sK1)
      | ~ environment(X0)
      | ~ decreases(cardinality_at_time(efficient_producers,sK1))
      | greater(zero,growth_rate(efficient_producers,sK1)) ),
    inference(resolution,[],[f91,f46]) ).

fof(f88,plain,
    ( ~ spl3_5
    | ~ spl3_6 ),
    inference(avatar_split_clause,[],[f33,f85,f81]) ).

fof(f33,plain,
    ( ~ greater(growth_rate(efficient_producers,sK1),zero)
    | ~ greater(zero,growth_rate(first_movers,sK1)) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f79,plain,
    ( ~ spl3_3
    | ~ spl3_4 ),
    inference(avatar_split_clause,[],[f34,f76,f72]) ).

fof(f34,plain,
    ( ~ greater(growth_rate(first_movers,sK1),zero)
    | ~ greater(zero,growth_rate(efficient_producers,sK1)) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f70,plain,
    ( ~ spl3_1
    | ~ spl3_2 ),
    inference(avatar_split_clause,[],[f35,f67,f63]) ).

fof(f35,plain,
    ( zero != growth_rate(first_movers,sK1)
    | zero != growth_rate(efficient_producers,sK1) ),
    inference(cnf_transformation,[],[f19]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : MGT025+1 : TPTP v8.1.2. Released v2.0.0.
% 0.07/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.36  % Computer : n005.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Fri May  3 20:03:23 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.wL6Q2pBBUR/Vampire---4.8_16384
% 0.56/0.74  % (16651)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 Vampire---4 for (2996ds/83Mi)
% 0.56/0.74  % (16645)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 Vampire---4 for (2996ds/34Mi)
% 0.56/0.74  % (16648)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.56/0.74  % (16650)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.56/0.74  % (16649)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 Vampire---4 for (2996ds/34Mi)
% 0.56/0.74  % (16646)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 Vampire---4 for (2996ds/51Mi)
% 0.56/0.74  % (16652)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.56/0.74  % (16648)Refutation not found, incomplete strategy% (16648)------------------------------
% 0.56/0.74  % (16648)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.74  % (16648)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.74  
% 0.56/0.74  % (16648)Memory used [KB]: 961
% 0.56/0.74  % (16648)Time elapsed: 0.003 s
% 0.56/0.74  % (16648)Instructions burned: 3 (million)
% 0.56/0.74  % (16648)------------------------------
% 0.56/0.74  % (16648)------------------------------
% 0.56/0.74  % (16649)Refutation not found, incomplete strategy% (16649)------------------------------
% 0.56/0.74  % (16649)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.74  % (16649)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.74  
% 0.56/0.74  % (16649)Memory used [KB]: 1067
% 0.56/0.74  % (16649)Time elapsed: 0.004 s
% 0.56/0.74  % (16649)Instructions burned: 4 (million)
% 0.56/0.74  % (16645)Refutation not found, incomplete strategy% (16645)------------------------------
% 0.56/0.74  % (16645)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.74  % (16645)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.74  
% 0.56/0.74  % (16645)Memory used [KB]: 1068
% 0.56/0.74  % (16645)Time elapsed: 0.004 s
% 0.56/0.74  % (16645)Instructions burned: 5 (million)
% 0.56/0.74  % (16651)First to succeed.
% 0.56/0.74  % (16649)------------------------------
% 0.56/0.74  % (16649)------------------------------
% 0.56/0.74  % (16645)------------------------------
% 0.56/0.74  % (16645)------------------------------
% 0.56/0.74  % (16650)Also succeeded, but the first one will report.
% 0.56/0.74  % (16651)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-16641"
% 0.56/0.74  % (16651)Refutation found. Thanks to Tanya!
% 0.56/0.74  % SZS status Theorem for Vampire---4
% 0.56/0.74  % SZS output start Proof for Vampire---4
% See solution above
% 0.56/0.75  % (16651)------------------------------
% 0.56/0.75  % (16651)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.75  % (16651)Termination reason: Refutation
% 0.56/0.75  
% 0.56/0.75  % (16651)Memory used [KB]: 1124
% 0.56/0.75  % (16651)Time elapsed: 0.006 s
% 0.56/0.75  % (16651)Instructions burned: 14 (million)
% 0.56/0.75  % (16641)Success in time 0.37 s
% 0.56/0.75  % Vampire---4.8 exiting
%------------------------------------------------------------------------------