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

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : MGT027+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n013.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 07:57:09 EDT 2024

% Result   : Theorem 0.14s 0.38s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   92 (  18 unt;   0 def)
%            Number of atoms       :  319 (  26 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  365 ( 138   ~; 142   |;  65   &)
%                                         (   2 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-4 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :  126 ( 111   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f182,plain,
    $false,
    inference(subsumption_resolution,[],[f176,f171]) ).

fof(f171,plain,
    ~ subpopulations(first_movers,efficient_producers,sK1,sK2(sK1)),
    inference(superposition,[],[f140,f149]) ).

fof(f149,plain,
    sK2(sK1) = sK3(sK2(sK1)),
    inference(subsumption_resolution,[],[f148,f44]) ).

fof(f44,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])],[f17,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(f17,plain,
    ? [X0] :
      ( ! [X1] :
          ( ~ contracts_from(X1,first_movers)
          | ~ greater(X1,appear(efficient_producers,X0)) )
      & stable(X0)
      & environment(X0) ),
    inference(flattening,[],[f16]) ).

fof(f16,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/sandbox/benchmark/theBenchmark.p',prove_l9) ).

fof(f148,plain,
    ( ~ environment(sK1)
    | sK2(sK1) = sK3(sK2(sK1)) ),
    inference(subsumption_resolution,[],[f147,f140]) ).

fof(f147,plain,
    ( subpopulations(first_movers,efficient_producers,sK1,sK3(sK2(sK1)))
    | ~ environment(sK1)
    | sK2(sK1) = sK3(sK2(sK1)) ),
    inference(duplicate_literal_removal,[],[f146]) ).

fof(f146,plain,
    ( subpopulations(first_movers,efficient_producers,sK1,sK3(sK2(sK1)))
    | ~ environment(sK1)
    | sK2(sK1) = sK3(sK2(sK1))
    | sK2(sK1) = sK3(sK2(sK1)) ),
    inference(resolution,[],[f145,f121]) ).

fof(f121,plain,
    ( in_environment(sK1,sK3(sK2(sK1)))
    | sK2(sK1) = sK3(sK2(sK1)) ),
    inference(subsumption_resolution,[],[f120,f44]) ).

fof(f120,plain,
    ( in_environment(sK1,sK3(sK2(sK1)))
    | sK2(sK1) = sK3(sK2(sK1))
    | ~ environment(sK1) ),
    inference(subsumption_resolution,[],[f119,f45]) ).

fof(f45,plain,
    stable(sK1),
    inference(cnf_transformation,[],[f35]) ).

fof(f119,plain,
    ( in_environment(sK1,sK3(sK2(sK1)))
    | sK2(sK1) = sK3(sK2(sK1))
    | ~ stable(sK1)
    | ~ environment(sK1) ),
    inference(resolution,[],[f92,f76]) ).

fof(f76,plain,
    in_environment(sK1,sK2(sK1)),
    inference(unit_resulting_resolution,[],[f44,f45,f62,f65,f59]) ).

fof(f59,plain,
    ! [X2,X0,X1] :
      ( ~ greater(X2,X1)
      | in_environment(X0,X2)
      | ~ in_environment(X0,X1)
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( in_environment(X0,X2)
      | ~ greater(X2,X1)
      | ~ in_environment(X0,X1)
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(flattening,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1,X2] :
      ( in_environment(X0,X2)
      | ~ greater(X2,X1)
      | ~ in_environment(X0,X1)
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,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/sandbox/benchmark/theBenchmark.p',mp_long_stable_environments) ).

fof(f65,plain,
    greater(sK2(sK1),appear(efficient_producers,sK1)),
    inference(unit_resulting_resolution,[],[f44,f45,f47]) ).

fof(f47,plain,
    ! [X0] :
      ( ~ stable(X0)
      | greater(sK2(X0),appear(efficient_producers,X0))
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0] :
      ( ( ! [X2] :
            ( greater(zero,growth_rate(first_movers,X2))
            | ~ greater_or_equal(X2,sK2(X0))
            | ~ subpopulations(first_movers,efficient_producers,X0,X2) )
        & greater(sK2(X0),appear(efficient_producers,X0)) )
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f19,f36]) ).

fof(f36,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,sK2(X0))
            | ~ subpopulations(first_movers,efficient_producers,X0,X2) )
        & greater(sK2(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/sandbox/benchmark/theBenchmark.p',l10) ).

fof(f62,plain,
    in_environment(sK1,appear(efficient_producers,sK1)),
    inference(unit_resulting_resolution,[],[f44,f45,f50]) ).

fof(f50,plain,
    ! [X0] :
      ( ~ stable(X0)
      | in_environment(X0,appear(efficient_producers,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/sandbox/benchmark/theBenchmark.p',mp_EP_in_stable_environments) ).

fof(f92,plain,
    ! [X0] :
      ( ~ in_environment(X0,sK2(sK1))
      | in_environment(X0,sK3(sK2(sK1)))
      | sK2(sK1) = sK3(sK2(sK1))
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(resolution,[],[f85,f59]) ).

fof(f85,plain,
    ( greater(sK3(sK2(sK1)),sK2(sK1))
    | sK2(sK1) = sK3(sK2(sK1)) ),
    inference(resolution,[],[f82,f56]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( ~ greater_or_equal(X0,X1)
      | greater(X0,X1)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f43]) ).

fof(f43,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,[],[f42]) ).

fof(f42,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,[],[f13]) ).

fof(f13,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/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal) ).

fof(f82,plain,
    greater_or_equal(sK3(sK2(sK1)),sK2(sK1)),
    inference(unit_resulting_resolution,[],[f78,f52]) ).

fof(f52,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | greater_or_equal(sK3(X0),X0) ),
    inference(cnf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X0] :
      ( ( ~ greater(zero,growth_rate(first_movers,sK3(X0)))
        & greater_or_equal(sK3(X0),X0)
        & greater(cardinality_at_time(first_movers,sK3(X0)),zero) )
      | ~ sP0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f39,f40]) ).

fof(f40,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ greater(zero,growth_rate(first_movers,X1))
          & greater_or_equal(X1,X0)
          & greater(cardinality_at_time(first_movers,X1),zero) )
     => ( ~ greater(zero,growth_rate(first_movers,sK3(X0)))
        & greater_or_equal(sK3(X0),X0)
        & greater(cardinality_at_time(first_movers,sK3(X0)),zero) ) ),
    introduced(choice_axiom,[]) ).

fof(f39,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ greater(zero,growth_rate(first_movers,X1))
          & greater_or_equal(X1,X0)
          & greater(cardinality_at_time(first_movers,X1),zero) )
      | ~ sP0(X0) ),
    inference(rectify,[],[f38]) ).

fof(f38,plain,
    ! [X1] :
      ( ? [X2] :
          ( ~ greater(zero,growth_rate(first_movers,X2))
          & greater_or_equal(X2,X1)
          & greater(cardinality_at_time(first_movers,X2),zero) )
      | ~ sP0(X1) ),
    inference(nnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X1] :
      ( ? [X2] :
          ( ~ greater(zero,growth_rate(first_movers,X2))
          & greater_or_equal(X2,X1)
          & greater(cardinality_at_time(first_movers,X2),zero) )
      | ~ sP0(X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f78,plain,
    sP0(sK2(sK1)),
    inference(unit_resulting_resolution,[],[f44,f45,f67,f76,f54]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( ~ in_environment(X0,X1)
      | sP0(X1)
      | contracts_from(X1,first_movers)
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( contracts_from(X1,first_movers)
      | sP0(X1)
      | ~ in_environment(X0,X1)
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(definition_folding,[],[f25,f32]) ).

fof(f25,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,[],[f24]) ).

fof(f24,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/sandbox/benchmark/theBenchmark.p',mp_contracts_from) ).

fof(f67,plain,
    ~ contracts_from(sK2(sK1),first_movers),
    inference(unit_resulting_resolution,[],[f65,f46]) ).

fof(f46,plain,
    ! [X1] :
      ( ~ contracts_from(X1,first_movers)
      | ~ greater(X1,appear(efficient_producers,sK1)) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f145,plain,
    ! [X0] :
      ( ~ in_environment(X0,sK3(sK2(sK1)))
      | subpopulations(first_movers,efficient_producers,X0,sK3(sK2(sK1)))
      | ~ environment(X0)
      | sK2(sK1) = sK3(sK2(sK1)) ),
    inference(subsumption_resolution,[],[f144,f81]) ).

fof(f81,plain,
    greater(cardinality_at_time(first_movers,sK3(sK2(sK1))),zero),
    inference(unit_resulting_resolution,[],[f78,f51]) ).

fof(f51,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | greater(cardinality_at_time(first_movers,sK3(X0)),zero) ),
    inference(cnf_transformation,[],[f41]) ).

fof(f144,plain,
    ! [X0] :
      ( subpopulations(first_movers,efficient_producers,X0,sK3(sK2(sK1)))
      | ~ greater(cardinality_at_time(first_movers,sK3(sK2(sK1))),zero)
      | ~ in_environment(X0,sK3(sK2(sK1)))
      | ~ environment(X0)
      | sK2(sK1) = sK3(sK2(sK1)) ),
    inference(resolution,[],[f55,f124]) ).

fof(f124,plain,
    ( greater(cardinality_at_time(efficient_producers,sK3(sK2(sK1))),zero)
    | sK2(sK1) = sK3(sK2(sK1)) ),
    inference(duplicate_literal_removal,[],[f122]) ).

fof(f122,plain,
    ( sK2(sK1) = sK3(sK2(sK1))
    | greater(cardinality_at_time(efficient_producers,sK3(sK2(sK1))),zero)
    | sK2(sK1) = sK3(sK2(sK1)) ),
    inference(resolution,[],[f121,f106]) ).

fof(f106,plain,
    ( ~ in_environment(sK1,sK3(sK2(sK1)))
    | greater(cardinality_at_time(efficient_producers,sK3(sK2(sK1))),zero)
    | sK2(sK1) = sK3(sK2(sK1)) ),
    inference(subsumption_resolution,[],[f105,f44]) ).

fof(f105,plain,
    ( greater(cardinality_at_time(efficient_producers,sK3(sK2(sK1))),zero)
    | ~ in_environment(sK1,sK3(sK2(sK1)))
    | ~ environment(sK1)
    | sK2(sK1) = sK3(sK2(sK1)) ),
    inference(resolution,[],[f49,f99]) ).

fof(f99,plain,
    ( greater_or_equal(sK3(sK2(sK1)),appear(efficient_producers,sK1))
    | sK2(sK1) = sK3(sK2(sK1)) ),
    inference(resolution,[],[f91,f57]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( ~ greater(X0,X1)
      | greater_or_equal(X0,X1) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f91,plain,
    ( greater(sK3(sK2(sK1)),appear(efficient_producers,sK1))
    | sK2(sK1) = sK3(sK2(sK1)) ),
    inference(resolution,[],[f85,f69]) ).

fof(f69,plain,
    ! [X0] :
      ( ~ greater(X0,sK2(sK1))
      | greater(X0,appear(efficient_producers,sK1)) ),
    inference(resolution,[],[f65,f60]) ).

fof(f60,plain,
    ! [X2,X0,X1] :
      ( ~ greater(X1,X2)
      | greater(X0,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/sandbox/benchmark/theBenchmark.p',mp_greater_transitivity) ).

fof(f49,plain,
    ! [X0,X1] :
      ( ~ greater_or_equal(X1,appear(efficient_producers,X0))
      | greater(cardinality_at_time(efficient_producers,X1),zero)
      | ~ in_environment(X0,X1)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,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,[],[f20]) ).

fof(f20,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/sandbox/benchmark/theBenchmark.p',t6) ).

fof(f55,plain,
    ! [X0,X1] :
      ( ~ greater(cardinality_at_time(efficient_producers,X1),zero)
      | subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ 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,[],[f12]) ).

fof(f12,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/sandbox/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep) ).

fof(f140,plain,
    ~ subpopulations(first_movers,efficient_producers,sK1,sK3(sK2(sK1))),
    inference(unit_resulting_resolution,[],[f44,f45,f82,f80,f48]) ).

fof(f48,plain,
    ! [X2,X0] :
      ( ~ subpopulations(first_movers,efficient_producers,X0,X2)
      | ~ greater_or_equal(X2,sK2(X0))
      | greater(zero,growth_rate(first_movers,X2))
      | ~ stable(X0)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f80,plain,
    ~ greater(zero,growth_rate(first_movers,sK3(sK2(sK1)))),
    inference(unit_resulting_resolution,[],[f78,f53]) ).

fof(f53,plain,
    ! [X0] :
      ( ~ greater(zero,growth_rate(first_movers,sK3(X0)))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f41]) ).

fof(f176,plain,
    subpopulations(first_movers,efficient_producers,sK1,sK2(sK1)),
    inference(unit_resulting_resolution,[],[f44,f76,f102,f151,f55]) ).

fof(f151,plain,
    greater(cardinality_at_time(first_movers,sK2(sK1)),zero),
    inference(superposition,[],[f81,f149]) ).

fof(f102,plain,
    greater(cardinality_at_time(efficient_producers,sK2(sK1)),zero),
    inference(unit_resulting_resolution,[],[f44,f76,f68,f49]) ).

fof(f68,plain,
    greater_or_equal(sK2(sK1),appear(efficient_producers,sK1)),
    inference(unit_resulting_resolution,[],[f65,f57]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : MGT027+1 : TPTP v8.1.2. Released v2.0.0.
% 0.06/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34  % Computer : n013.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Fri May  3 20:05:23 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (11083)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36  % (11087)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.36  TRYING [1]
% 0.14/0.36  TRYING [2]
% 0.14/0.36  TRYING [3]
% 0.14/0.36  TRYING [4]
% 0.14/0.37  % (11086)WARNING: value z3 for option sas not known
% 0.14/0.37  % (11084)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37  % (11085)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37  % (11088)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.37  % (11090)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.37  % (11089)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.37  % (11086)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37  TRYING [5]
% 0.14/0.37  TRYING [1]
% 0.14/0.37  % (11090)First to succeed.
% 0.14/0.37  TRYING [2]
% 0.14/0.37  % (11090)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-11083"
% 0.14/0.38  % (11090)Refutation found. Thanks to Tanya!
% 0.14/0.38  % SZS status Theorem for theBenchmark
% 0.14/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.38  % (11090)------------------------------
% 0.14/0.38  % (11090)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.38  % (11090)Termination reason: Refutation
% 0.14/0.38  
% 0.14/0.38  % (11090)Memory used [KB]: 844
% 0.14/0.38  % (11090)Time elapsed: 0.009 s
% 0.14/0.38  % (11090)Instructions burned: 11 (million)
% 0.14/0.38  % (11083)Success in time 0.026 s
%------------------------------------------------------------------------------