TSTP Solution File: MGT025-1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : MGT025-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s

% Computer : n022.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Aug 31 17:51:25 EDT 2022

% Result   : Unsatisfiable 0.18s 0.50s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   46
% Syntax   : Number of formulae    :  133 (  10 unt;   0 def)
%            Number of atoms       :  451 (  31 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :  570 ( 252   ~; 297   |;   0   &)
%                                         (  21 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   31 (  29 usr;  22 prp; 0-4 aty)
%            Number of functors    :   12 (  12 usr;   8 con; 0-2 aty)
%            Number of variables   :   84 (  84   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f201,plain,
    $false,
    inference(avatar_sat_refutation,[],[f52,f61,f70,f80,f82,f88,f94,f105,f135,f140,f145,f146,f147,f148,f149,f151,f164,f169,f174,f181,f185,f190,f191,f195,f196,f200]) ).

fof(f200,plain,
    ( ~ spl3_7
    | ~ spl3_8
    | ~ spl3_19 ),
    inference(avatar_split_clause,[],[f199,f162,f77,f73]) ).

fof(f73,plain,
    ( spl3_7
  <=> environment(sk1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).

fof(f77,plain,
    ( spl3_8
  <=> in_environment(sk1,sk2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).

fof(f162,plain,
    ( spl3_19
  <=> ! [X0] :
        ( ~ subpopulation(first_movers,X0,sk2)
        | ~ environment(X0)
        | ~ in_environment(X0,sk2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_19])]) ).

fof(f199,plain,
    ( ~ environment(sk1)
    | ~ spl3_8
    | ~ spl3_19 ),
    inference(resolution,[],[f198,f79]) ).

fof(f79,plain,
    ( in_environment(sk1,sk2)
    | ~ spl3_8 ),
    inference(avatar_component_clause,[],[f77]) ).

fof(f198,plain,
    ( ! [X0] :
        ( ~ in_environment(X0,sk2)
        | ~ environment(X0) )
    | ~ spl3_19 ),
    inference(duplicate_literal_removal,[],[f197]) ).

fof(f197,plain,
    ( ! [X0] :
        ( ~ environment(X0)
        | ~ environment(X0)
        | ~ in_environment(X0,sk2)
        | ~ in_environment(X0,sk2) )
    | ~ spl3_19 ),
    inference(resolution,[],[f163,f4]) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( subpopulation(first_movers,X0,X1)
      | ~ environment(X0)
      | ~ in_environment(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_subpopulations_30) ).

fof(f163,plain,
    ( ! [X0] :
        ( ~ subpopulation(first_movers,X0,sk2)
        | ~ environment(X0)
        | ~ in_environment(X0,sk2) )
    | ~ spl3_19 ),
    inference(avatar_component_clause,[],[f162]) ).

fof(f196,plain,
    ( spl3_2
    | ~ spl3_18
    | spl3_19
    | ~ spl3_9 ),
    inference(avatar_split_clause,[],[f175,f85,f162,f142,f49]) ).

fof(f49,plain,
    ( spl3_2
  <=> greater(sF0,zero) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

fof(f142,plain,
    ( spl3_18
  <=> increases(cardinality_at_time(first_movers,sk2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_18])]) ).

fof(f85,plain,
    ( spl3_9
  <=> greater(cardinality_at_time(first_movers,sk2),zero) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).

fof(f175,plain,
    ( ! [X0] :
        ( ~ subpopulation(first_movers,X0,sk2)
        | ~ environment(X0)
        | ~ increases(cardinality_at_time(first_movers,sk2))
        | greater(sF0,zero)
        | ~ in_environment(X0,sk2) )
    | ~ spl3_9 ),
    inference(forward_demodulation,[],[f171,f37]) ).

fof(f37,plain,
    growth_rate(first_movers,sk2) = sF0,
    introduced(function_definition,[]) ).

fof(f171,plain,
    ( ! [X0] :
        ( ~ increases(cardinality_at_time(first_movers,sk2))
        | ~ environment(X0)
        | greater(growth_rate(first_movers,sk2),zero)
        | ~ in_environment(X0,sk2)
        | ~ subpopulation(first_movers,X0,sk2) )
    | ~ spl3_9 ),
    inference(resolution,[],[f15,f87]) ).

fof(f87,plain,
    ( greater(cardinality_at_time(first_movers,sk2),zero)
    | ~ spl3_9 ),
    inference(avatar_component_clause,[],[f85]) ).

fof(f15,axiom,
    ! [X2,X0,X1] :
      ( ~ greater(cardinality_at_time(X2,X1),zero)
      | ~ subpopulation(X2,X0,X1)
      | greater(growth_rate(X2,X1),zero)
      | ~ environment(X0)
      | ~ in_environment(X0,X1)
      | ~ increases(cardinality_at_time(X2,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_41) ).

fof(f195,plain,
    ( ~ spl3_7
    | ~ spl3_8
    | ~ spl3_20 ),
    inference(avatar_split_clause,[],[f194,f167,f77,f73]) ).

fof(f167,plain,
    ( spl3_20
  <=> ! [X1] :
        ( ~ subpopulation(efficient_producers,X1,sk2)
        | ~ environment(X1)
        | ~ in_environment(X1,sk2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_20])]) ).

fof(f194,plain,
    ( ~ environment(sk1)
    | ~ spl3_8
    | ~ spl3_20 ),
    inference(resolution,[],[f193,f79]) ).

fof(f193,plain,
    ( ! [X0] :
        ( ~ in_environment(X0,sk2)
        | ~ environment(X0) )
    | ~ spl3_20 ),
    inference(duplicate_literal_removal,[],[f192]) ).

fof(f192,plain,
    ( ! [X0] :
        ( ~ environment(X0)
        | ~ environment(X0)
        | ~ in_environment(X0,sk2)
        | ~ in_environment(X0,sk2) )
    | ~ spl3_20 ),
    inference(resolution,[],[f168,f5]) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( subpopulation(efficient_producers,X0,X1)
      | ~ environment(X0)
      | ~ in_environment(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_subpopulations_31) ).

fof(f168,plain,
    ( ! [X1] :
        ( ~ subpopulation(efficient_producers,X1,sk2)
        | ~ environment(X1)
        | ~ in_environment(X1,sk2) )
    | ~ spl3_20 ),
    inference(avatar_component_clause,[],[f167]) ).

fof(f191,plain,
    ( ~ spl3_12
    | spl3_4
    | spl3_19
    | ~ spl3_9 ),
    inference(avatar_split_clause,[],[f186,f85,f162,f58,f115]) ).

fof(f115,plain,
    ( spl3_12
  <=> decreases(cardinality_at_time(first_movers,sk2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).

fof(f58,plain,
    ( spl3_4
  <=> greater(zero,sF0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

fof(f186,plain,
    ( ! [X0] :
        ( ~ subpopulation(first_movers,X0,sk2)
        | ~ in_environment(X0,sk2)
        | greater(zero,sF0)
        | ~ environment(X0)
        | ~ decreases(cardinality_at_time(first_movers,sk2)) )
    | ~ spl3_9 ),
    inference(forward_demodulation,[],[f182,f37]) ).

fof(f182,plain,
    ( ! [X0] :
        ( ~ in_environment(X0,sk2)
        | ~ subpopulation(first_movers,X0,sk2)
        | ~ decreases(cardinality_at_time(first_movers,sk2))
        | ~ environment(X0)
        | greater(zero,growth_rate(first_movers,sk2)) )
    | ~ spl3_9 ),
    inference(resolution,[],[f16,f87]) ).

fof(f16,axiom,
    ! [X2,X0,X1] :
      ( ~ greater(cardinality_at_time(X2,X1),zero)
      | ~ decreases(cardinality_at_time(X2,X1))
      | ~ in_environment(X0,X1)
      | ~ environment(X0)
      | ~ subpopulation(X2,X0,X1)
      | greater(zero,growth_rate(X2,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_42) ).

fof(f190,plain,
    ( spl3_4
    | ~ spl3_6
    | ~ spl3_21 ),
    inference(avatar_contradiction_clause,[],[f189]) ).

fof(f189,plain,
    ( $false
    | spl3_4
    | ~ spl3_6
    | ~ spl3_21 ),
    inference(resolution,[],[f180,f170]) ).

fof(f170,plain,
    ( ~ greater(zero,zero)
    | spl3_4
    | ~ spl3_6 ),
    inference(superposition,[],[f60,f68]) ).

fof(f68,plain,
    ( zero = sF0
    | ~ spl3_6 ),
    inference(avatar_component_clause,[],[f67]) ).

fof(f67,plain,
    ( spl3_6
  <=> zero = sF0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).

fof(f60,plain,
    ( ~ greater(zero,sF0)
    | spl3_4 ),
    inference(avatar_component_clause,[],[f58]) ).

fof(f180,plain,
    ( greater(zero,zero)
    | ~ spl3_21 ),
    inference(avatar_component_clause,[],[f178]) ).

fof(f178,plain,
    ( spl3_21
  <=> greater(zero,zero) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_21])]) ).

fof(f185,plain,
    ( ~ spl3_15
    | spl3_20
    | spl3_1
    | ~ spl3_10 ),
    inference(avatar_split_clause,[],[f184,f91,f45,f167,f127]) ).

fof(f127,plain,
    ( spl3_15
  <=> decreases(cardinality_at_time(efficient_producers,sk2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_15])]) ).

fof(f45,plain,
    ( spl3_1
  <=> greater(zero,sF1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f91,plain,
    ( spl3_10
  <=> greater(cardinality_at_time(efficient_producers,sk2),zero) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).

fof(f184,plain,
    ( ! [X1] :
        ( greater(zero,sF1)
        | ~ environment(X1)
        | ~ in_environment(X1,sk2)
        | ~ decreases(cardinality_at_time(efficient_producers,sk2))
        | ~ subpopulation(efficient_producers,X1,sk2) )
    | ~ spl3_10 ),
    inference(forward_demodulation,[],[f183,f38]) ).

fof(f38,plain,
    growth_rate(efficient_producers,sk2) = sF1,
    introduced(function_definition,[]) ).

fof(f183,plain,
    ( ! [X1] :
        ( ~ environment(X1)
        | greater(zero,growth_rate(efficient_producers,sk2))
        | ~ in_environment(X1,sk2)
        | ~ subpopulation(efficient_producers,X1,sk2)
        | ~ decreases(cardinality_at_time(efficient_producers,sk2)) )
    | ~ spl3_10 ),
    inference(resolution,[],[f16,f93]) ).

fof(f93,plain,
    ( greater(cardinality_at_time(efficient_producers,sk2),zero)
    | ~ spl3_10 ),
    inference(avatar_component_clause,[],[f91]) ).

fof(f181,plain,
    ( ~ spl3_18
    | spl3_21
    | spl3_19
    | ~ spl3_6
    | ~ spl3_9 ),
    inference(avatar_split_clause,[],[f176,f85,f67,f162,f178,f142]) ).

fof(f176,plain,
    ( ! [X0] :
        ( ~ in_environment(X0,sk2)
        | ~ subpopulation(first_movers,X0,sk2)
        | greater(zero,zero)
        | ~ increases(cardinality_at_time(first_movers,sk2))
        | ~ environment(X0) )
    | ~ spl3_6
    | ~ spl3_9 ),
    inference(forward_demodulation,[],[f175,f68]) ).

fof(f174,plain,
    ( ~ spl3_17
    | spl3_3
    | spl3_20
    | ~ spl3_10 ),
    inference(avatar_split_clause,[],[f173,f91,f167,f54,f137]) ).

fof(f137,plain,
    ( spl3_17
  <=> increases(cardinality_at_time(efficient_producers,sk2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_17])]) ).

fof(f54,plain,
    ( spl3_3
  <=> greater(sF1,zero) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

fof(f173,plain,
    ( ! [X1] :
        ( ~ environment(X1)
        | ~ in_environment(X1,sk2)
        | ~ subpopulation(efficient_producers,X1,sk2)
        | greater(sF1,zero)
        | ~ increases(cardinality_at_time(efficient_producers,sk2)) )
    | ~ spl3_10 ),
    inference(forward_demodulation,[],[f172,f38]) ).

fof(f172,plain,
    ( ! [X1] :
        ( greater(growth_rate(efficient_producers,sk2),zero)
        | ~ environment(X1)
        | ~ in_environment(X1,sk2)
        | ~ increases(cardinality_at_time(efficient_producers,sk2))
        | ~ subpopulation(efficient_producers,X1,sk2) )
    | ~ spl3_10 ),
    inference(resolution,[],[f15,f93]) ).

fof(f169,plain,
    ( ~ spl3_14
    | spl3_20
    | spl3_5
    | ~ spl3_10 ),
    inference(avatar_split_clause,[],[f165,f91,f63,f167,f123]) ).

fof(f123,plain,
    ( spl3_14
  <=> constant(cardinality_at_time(efficient_producers,sk2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).

fof(f63,plain,
    ( spl3_5
  <=> zero = sF1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

fof(f165,plain,
    ( ! [X1] :
        ( zero = sF1
        | ~ subpopulation(efficient_producers,X1,sk2)
        | ~ constant(cardinality_at_time(efficient_producers,sk2))
        | ~ in_environment(X1,sk2)
        | ~ environment(X1) )
    | ~ spl3_10 ),
    inference(forward_demodulation,[],[f159,f38]) ).

fof(f159,plain,
    ( ! [X1] :
        ( ~ in_environment(X1,sk2)
        | zero = growth_rate(efficient_producers,sk2)
        | ~ constant(cardinality_at_time(efficient_producers,sk2))
        | ~ subpopulation(efficient_producers,X1,sk2)
        | ~ environment(X1) )
    | ~ spl3_10 ),
    inference(resolution,[],[f14,f93]) ).

fof(f14,axiom,
    ! [X2,X0,X1] :
      ( ~ greater(cardinality_at_time(X2,X1),zero)
      | ~ in_environment(X0,X1)
      | ~ constant(cardinality_at_time(X2,X1))
      | ~ environment(X0)
      | ~ subpopulation(X2,X0,X1)
      | zero = growth_rate(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_40) ).

fof(f164,plain,
    ( ~ spl3_16
    | spl3_6
    | spl3_19
    | ~ spl3_9 ),
    inference(avatar_split_clause,[],[f160,f85,f162,f67,f132]) ).

fof(f132,plain,
    ( spl3_16
  <=> constant(cardinality_at_time(first_movers,sk2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_16])]) ).

fof(f160,plain,
    ( ! [X0] :
        ( ~ subpopulation(first_movers,X0,sk2)
        | zero = sF0
        | ~ in_environment(X0,sk2)
        | ~ environment(X0)
        | ~ constant(cardinality_at_time(first_movers,sk2)) )
    | ~ spl3_9 ),
    inference(forward_demodulation,[],[f158,f37]) ).

fof(f158,plain,
    ( ! [X0] :
        ( ~ in_environment(X0,sk2)
        | ~ constant(cardinality_at_time(first_movers,sk2))
        | ~ subpopulation(first_movers,X0,sk2)
        | ~ environment(X0)
        | zero = growth_rate(first_movers,sk2) )
    | ~ spl3_9 ),
    inference(resolution,[],[f14,f87]) ).

fof(f151,plain,
    spl3_13,
    inference(avatar_contradiction_clause,[],[f150]) ).

fof(f150,plain,
    ( $false
    | spl3_13 ),
    inference(resolution,[],[f121,f41]) ).

fof(f41,plain,
    constant(sF2),
    inference(definition_folding,[],[f23,f40]) ).

fof(f40,plain,
    number_of_organizations(sk1,sk2) = sF2,
    introduced(function_definition,[]) ).

fof(f23,axiom,
    constant(number_of_organizations(sk1,sk2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l7_49) ).

fof(f121,plain,
    ( ~ constant(sF2)
    | spl3_13 ),
    inference(avatar_component_clause,[],[f119]) ).

fof(f119,plain,
    ( spl3_13
  <=> constant(sF2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).

fof(f149,plain,
    ( spl3_16
    | spl3_18
    | ~ spl3_13
    | spl3_12
    | ~ spl3_11 ),
    inference(avatar_split_clause,[],[f106,f102,f115,f119,f142,f132]) ).

fof(f102,plain,
    ( spl3_11
  <=> sF2 = sum(cardinality_at_time(first_movers,sk2),cardinality_at_time(efficient_producers,sk2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_11])]) ).

fof(f106,plain,
    ( decreases(cardinality_at_time(first_movers,sk2))
    | ~ constant(sF2)
    | increases(cardinality_at_time(first_movers,sk2))
    | constant(cardinality_at_time(first_movers,sk2))
    | ~ spl3_11 ),
    inference(superposition,[],[f27,f104]) ).

fof(f104,plain,
    ( sF2 = sum(cardinality_at_time(first_movers,sk2),cardinality_at_time(efficient_producers,sk2))
    | ~ spl3_11 ),
    inference(avatar_component_clause,[],[f102]) ).

fof(f27,plain,
    ! [X2,X1] :
      ( ~ constant(sum(X1,X2))
      | decreases(X1)
      | constant(X1)
      | increases(X1) ),
    inference(equality_resolution,[],[f6]) ).

fof(f6,axiom,
    ! [X2,X0,X1] :
      ( ~ constant(X0)
      | constant(X1)
      | decreases(X1)
      | increases(X1)
      | sum(X1,X2) != X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_32) ).

fof(f148,plain,
    ( spl3_16
    | ~ spl3_13
    | spl3_17
    | spl3_18
    | ~ spl3_11 ),
    inference(avatar_split_clause,[],[f111,f102,f142,f137,f119,f132]) ).

fof(f111,plain,
    ( increases(cardinality_at_time(first_movers,sk2))
    | increases(cardinality_at_time(efficient_producers,sk2))
    | ~ constant(sF2)
    | constant(cardinality_at_time(first_movers,sk2))
    | ~ spl3_11 ),
    inference(superposition,[],[f33,f104]) ).

fof(f33,plain,
    ! [X2,X1] :
      ( ~ constant(sum(X1,X2))
      | constant(X1)
      | increases(X1)
      | increases(X2) ),
    inference(equality_resolution,[],[f7]) ).

fof(f7,axiom,
    ! [X2,X0,X1] :
      ( sum(X1,X2) != X0
      | increases(X2)
      | increases(X1)
      | ~ constant(X0)
      | constant(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_33) ).

fof(f147,plain,
    ( spl3_17
    | spl3_14
    | spl3_18
    | ~ spl3_13
    | ~ spl3_11 ),
    inference(avatar_split_clause,[],[f112,f102,f119,f142,f123,f137]) ).

fof(f112,plain,
    ( ~ constant(sF2)
    | increases(cardinality_at_time(first_movers,sk2))
    | constant(cardinality_at_time(efficient_producers,sk2))
    | increases(cardinality_at_time(efficient_producers,sk2))
    | ~ spl3_11 ),
    inference(superposition,[],[f34,f104]) ).

fof(f34,plain,
    ! [X2,X1] :
      ( ~ constant(sum(X1,X2))
      | increases(X2)
      | constant(X2)
      | increases(X1) ),
    inference(equality_resolution,[],[f11]) ).

fof(f11,axiom,
    ! [X2,X0,X1] :
      ( increases(X1)
      | sum(X1,X2) != X0
      | constant(X2)
      | ~ constant(X0)
      | increases(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_37) ).

fof(f146,plain,
    ( ~ spl3_13
    | spl3_15
    | spl3_17
    | spl3_14
    | ~ spl3_11 ),
    inference(avatar_split_clause,[],[f108,f102,f123,f137,f127,f119]) ).

fof(f108,plain,
    ( constant(cardinality_at_time(efficient_producers,sk2))
    | increases(cardinality_at_time(efficient_producers,sk2))
    | decreases(cardinality_at_time(efficient_producers,sk2))
    | ~ constant(sF2)
    | ~ spl3_11 ),
    inference(superposition,[],[f29,f104]) ).

fof(f29,plain,
    ! [X2,X1] :
      ( ~ constant(sum(X1,X2))
      | constant(X2)
      | decreases(X2)
      | increases(X2) ),
    inference(equality_resolution,[],[f13]) ).

fof(f13,axiom,
    ! [X2,X0,X1] :
      ( decreases(X2)
      | constant(X2)
      | increases(X2)
      | sum(X1,X2) != X0
      | ~ constant(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_39) ).

fof(f145,plain,
    ( spl3_18
    | spl3_14
    | ~ spl3_13
    | spl3_12
    | ~ spl3_11 ),
    inference(avatar_split_clause,[],[f107,f102,f115,f119,f123,f142]) ).

fof(f107,plain,
    ( decreases(cardinality_at_time(first_movers,sk2))
    | ~ constant(sF2)
    | constant(cardinality_at_time(efficient_producers,sk2))
    | increases(cardinality_at_time(first_movers,sk2))
    | ~ spl3_11 ),
    inference(superposition,[],[f28,f104]) ).

fof(f28,plain,
    ! [X2,X1] :
      ( ~ constant(sum(X1,X2))
      | increases(X1)
      | decreases(X1)
      | constant(X2) ),
    inference(equality_resolution,[],[f10]) ).

fof(f10,axiom,
    ! [X2,X0,X1] :
      ( increases(X1)
      | decreases(X1)
      | ~ constant(X0)
      | constant(X2)
      | sum(X1,X2) != X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_36) ).

fof(f140,plain,
    ( ~ spl3_13
    | spl3_15
    | spl3_16
    | spl3_17
    | ~ spl3_11 ),
    inference(avatar_split_clause,[],[f110,f102,f137,f132,f127,f119]) ).

fof(f110,plain,
    ( increases(cardinality_at_time(efficient_producers,sk2))
    | constant(cardinality_at_time(first_movers,sk2))
    | decreases(cardinality_at_time(efficient_producers,sk2))
    | ~ constant(sF2)
    | ~ spl3_11 ),
    inference(superposition,[],[f31,f104]) ).

fof(f31,plain,
    ! [X2,X1] :
      ( ~ constant(sum(X1,X2))
      | constant(X1)
      | decreases(X2)
      | increases(X2) ),
    inference(equality_resolution,[],[f9]) ).

fof(f9,axiom,
    ! [X2,X0,X1] :
      ( decreases(X2)
      | sum(X1,X2) != X0
      | increases(X2)
      | ~ constant(X0)
      | constant(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_35) ).

fof(f135,plain,
    ( spl3_16
    | ~ spl3_13
    | spl3_12
    | spl3_15
    | ~ spl3_11 ),
    inference(avatar_split_clause,[],[f113,f102,f127,f115,f119,f132]) ).

fof(f113,plain,
    ( decreases(cardinality_at_time(efficient_producers,sk2))
    | decreases(cardinality_at_time(first_movers,sk2))
    | ~ constant(sF2)
    | constant(cardinality_at_time(first_movers,sk2))
    | ~ spl3_11 ),
    inference(superposition,[],[f35,f104]) ).

fof(f35,plain,
    ! [X2,X1] :
      ( ~ constant(sum(X1,X2))
      | decreases(X1)
      | decreases(X2)
      | constant(X1) ),
    inference(equality_resolution,[],[f8]) ).

fof(f8,axiom,
    ! [X2,X0,X1] :
      ( decreases(X1)
      | sum(X1,X2) != X0
      | ~ constant(X0)
      | decreases(X2)
      | constant(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_34) ).

fof(f105,plain,
    ( ~ spl3_7
    | spl3_11
    | ~ spl3_8 ),
    inference(avatar_split_clause,[],[f100,f77,f102,f73]) ).

fof(f100,plain,
    ( sF2 = sum(cardinality_at_time(first_movers,sk2),cardinality_at_time(efficient_producers,sk2))
    | ~ environment(sk1)
    | ~ spl3_8 ),
    inference(forward_demodulation,[],[f99,f40]) ).

fof(f99,plain,
    ( number_of_organizations(sk1,sk2) = sum(cardinality_at_time(first_movers,sk2),cardinality_at_time(efficient_producers,sk2))
    | ~ environment(sk1)
    | ~ spl3_8 ),
    inference(resolution,[],[f98,f79]) ).

fof(f98,plain,
    ! [X0,X1] :
      ( ~ in_environment(X0,X1)
      | sum(cardinality_at_time(first_movers,X1),cardinality_at_time(efficient_producers,X1)) = number_of_organizations(X0,X1)
      | ~ environment(X0) ),
    inference(duplicate_literal_removal,[],[f97]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( ~ in_environment(X0,X1)
      | ~ environment(X0)
      | sum(cardinality_at_time(first_movers,X1),cardinality_at_time(efficient_producers,X1)) = number_of_organizations(X0,X1)
      | ~ environment(X0) ),
    inference(resolution,[],[f32,f5]) ).

fof(f32,plain,
    ! [X2,X0] :
      ( ~ subpopulation(efficient_producers,X0,X2)
      | number_of_organizations(X0,X2) = sum(cardinality_at_time(first_movers,X2),cardinality_at_time(efficient_producers,X2))
      | ~ environment(X0) ),
    inference(equality_resolution,[],[f2]) ).

fof(f2,axiom,
    ! [X2,X0,X1] :
      ( ~ subpopulation(X1,X0,X2)
      | number_of_organizations(X0,X2) = sum(cardinality_at_time(first_movers,X2),cardinality_at_time(efficient_producers,X2))
      | ~ environment(X0)
      | efficient_producers != X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_only_members_28) ).

fof(f94,plain,
    ( spl3_10
    | ~ spl3_7 ),
    inference(avatar_split_clause,[],[f89,f73,f91]) ).

fof(f89,plain,
    ( ~ environment(sk1)
    | greater(cardinality_at_time(efficient_producers,sk2),zero) ),
    inference(resolution,[],[f18,f22]) ).

fof(f22,axiom,
    subpopulations(first_movers,efficient_producers,sk1,sk2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l7_48) ).

fof(f18,axiom,
    ! [X0,X1] :
      ( ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ environment(X0)
      | greater(cardinality_at_time(efficient_producers,X1),zero) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_non_zero_producers_44) ).

fof(f88,plain,
    ( spl3_9
    | ~ spl3_7 ),
    inference(avatar_split_clause,[],[f83,f73,f85]) ).

fof(f83,plain,
    ( ~ environment(sk1)
    | greater(cardinality_at_time(first_movers,sk2),zero) ),
    inference(resolution,[],[f17,f22]) ).

fof(f17,axiom,
    ! [X0,X1] :
      ( ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ environment(X0)
      | greater(cardinality_at_time(first_movers,X1),zero) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_non_zero_producers_43) ).

fof(f82,plain,
    spl3_7,
    inference(avatar_contradiction_clause,[],[f81]) ).

fof(f81,plain,
    ( $false
    | spl3_7 ),
    inference(resolution,[],[f75,f21]) ).

fof(f21,axiom,
    environment(sk1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l7_47) ).

fof(f75,plain,
    ( ~ environment(sk1)
    | spl3_7 ),
    inference(avatar_component_clause,[],[f73]) ).

fof(f80,plain,
    ( ~ spl3_7
    | spl3_8 ),
    inference(avatar_split_clause,[],[f71,f77,f73]) ).

fof(f71,plain,
    ( in_environment(sk1,sk2)
    | ~ environment(sk1) ),
    inference(resolution,[],[f19,f22]) ).

fof(f19,axiom,
    ! [X0,X1] :
      ( ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | in_environment(X0,X1)
      | ~ environment(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_point_occur_45) ).

fof(f70,plain,
    ( ~ spl3_5
    | ~ spl3_6 ),
    inference(avatar_split_clause,[],[f42,f67,f63]) ).

fof(f42,plain,
    ( zero != sF0
    | zero != sF1 ),
    inference(definition_folding,[],[f24,f37,f38]) ).

fof(f24,axiom,
    ( zero != growth_rate(efficient_producers,sk2)
    | zero != growth_rate(first_movers,sk2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l7_50) ).

fof(f61,plain,
    ( ~ spl3_3
    | ~ spl3_4 ),
    inference(avatar_split_clause,[],[f39,f58,f54]) ).

fof(f39,plain,
    ( ~ greater(zero,sF0)
    | ~ greater(sF1,zero) ),
    inference(definition_folding,[],[f26,f38,f37]) ).

fof(f26,axiom,
    ( ~ greater(zero,growth_rate(first_movers,sk2))
    | ~ greater(growth_rate(efficient_producers,sk2),zero) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l7_52) ).

fof(f52,plain,
    ( ~ spl3_1
    | ~ spl3_2 ),
    inference(avatar_split_clause,[],[f43,f49,f45]) ).

fof(f43,plain,
    ( ~ greater(sF0,zero)
    | ~ greater(zero,sF1) ),
    inference(definition_folding,[],[f25,f37,f38]) ).

fof(f25,axiom,
    ( ~ greater(zero,growth_rate(efficient_producers,sk2))
    | ~ greater(growth_rate(first_movers,sk2),zero) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l7_51) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11  % Problem    : MGT025-1 : TPTP v8.1.0. Released v2.4.0.
% 0.09/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.33  % Computer : n022.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Tue Aug 30 03:16:11 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.18/0.49  % (17715)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.18/0.50  % (17701)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.18/0.50  % (17701)First to succeed.
% 0.18/0.50  % (17702)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.18/0.50  % (17703)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.18/0.50  % (17701)Refutation found. Thanks to Tanya!
% 0.18/0.50  % SZS status Unsatisfiable for theBenchmark
% 0.18/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.50  % (17701)------------------------------
% 0.18/0.50  % (17701)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.50  % (17701)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.50  % (17701)Termination reason: Refutation
% 0.18/0.50  
% 0.18/0.50  % (17701)Memory used [KB]: 5500
% 0.18/0.50  % (17701)Time elapsed: 0.110 s
% 0.18/0.50  % (17701)Instructions burned: 4 (million)
% 0.18/0.50  % (17701)------------------------------
% 0.18/0.50  % (17701)------------------------------
% 0.18/0.50  % (17688)Success in time 0.158 s
%------------------------------------------------------------------------------