TSTP Solution File: MGT021+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : MGT021+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 : n029.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 00:42:08 EDT 2024

% Result   : Theorem 0.47s 0.65s
% Output   : Refutation 0.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   57 (   8 unt;   0 def)
%            Number of atoms       :  182 (   0 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :  221 (  96   ~;  87   |;  23   &)
%                                         (   2 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   10 (   9 usr;   3 prp; 0-4 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-2 aty)
%            Number of variables   :   64 (  58   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f65,plain,
    $false,
    inference(avatar_sat_refutation,[],[f49,f59,f64]) ).

fof(f64,plain,
    spl2_1,
    inference(avatar_contradiction_clause,[],[f63]) ).

fof(f63,plain,
    ( $false
    | spl2_1 ),
    inference(subsumption_resolution,[],[f62,f27]) ).

fof(f27,plain,
    environment(sK0),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ( decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
    & subpopulations(first_movers,efficient_producers,sK0,sK1)
    & environment(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f15,f21]) ).

fof(f21,plain,
    ( ? [X0,X1] :
        ( decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
        & subpopulations(first_movers,efficient_producers,X0,X1)
        & environment(X0) )
   => ( decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
      & subpopulations(first_movers,efficient_producers,sK0,sK1)
      & environment(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f15,plain,
    ? [X0,X1] :
      ( decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
      & subpopulations(first_movers,efficient_producers,X0,X1)
      & environment(X0) ),
    inference(flattening,[],[f14]) ).

fof(f14,plain,
    ? [X0,X1] :
      ( decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
      & subpopulations(first_movers,efficient_producers,X0,X1)
      & environment(X0) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,negated_conjecture,
    ~ ! [X0,X1] :
        ( ( subpopulations(first_movers,efficient_producers,X0,X1)
          & environment(X0) )
       => ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
    inference(negated_conjecture,[],[f7]) ).

fof(f7,conjecture,
    ! [X0,X1] :
      ( ( subpopulations(first_movers,efficient_producers,X0,X1)
        & environment(X0) )
     => ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l3) ).

fof(f62,plain,
    ( ~ environment(sK0)
    | spl2_1 ),
    inference(subsumption_resolution,[],[f61,f55]) ).

fof(f55,plain,
    ( constant(resources(sK0,sK1))
    | spl2_1 ),
    inference(subsumption_resolution,[],[f54,f44]) ).

fof(f44,plain,
    ( ~ greater(equilibrium(sK0),sK1)
    | spl2_1 ),
    inference(avatar_component_clause,[],[f42]) ).

fof(f42,plain,
    ( spl2_1
  <=> greater(equilibrium(sK0),sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).

fof(f54,plain,
    ( constant(resources(sK0,sK1))
    | greater(equilibrium(sK0),sK1) ),
    inference(subsumption_resolution,[],[f53,f27]) ).

fof(f53,plain,
    ( constant(resources(sK0,sK1))
    | ~ environment(sK0)
    | greater(equilibrium(sK0),sK1) ),
    inference(resolution,[],[f52,f28]) ).

fof(f28,plain,
    subpopulations(first_movers,efficient_producers,sK0,sK1),
    inference(cnf_transformation,[],[f22]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | constant(resources(X0,X1))
      | ~ environment(X0)
      | greater(equilibrium(X0),X1) ),
    inference(subsumption_resolution,[],[f51,f31]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | in_environment(X0,X1)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( in_environment(X0,X1)
      | ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ environment(X0) ),
    inference(flattening,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( in_environment(X0,X1)
      | ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ environment(X0) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( ( subpopulations(first_movers,efficient_producers,X0,X1)
        & environment(X0) )
     => in_environment(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_in_environment) ).

fof(f51,plain,
    ! [X0,X1] :
      ( greater(equilibrium(X0),X1)
      | constant(resources(X0,X1))
      | ~ in_environment(X0,X1)
      | ~ environment(X0)
      | ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
    inference(duplicate_literal_removal,[],[f50]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( greater(equilibrium(X0),X1)
      | constant(resources(X0,X1))
      | ~ in_environment(X0,X1)
      | ~ environment(X0)
      | ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ environment(X0) ),
    inference(resolution,[],[f24,f30]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( greater(number_of_organizations(X0,X1),zero)
      | ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( greater(number_of_organizations(X0,X1),zero)
      | ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ environment(X0) ),
    inference(flattening,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( greater(number_of_organizations(X0,X1),zero)
      | ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ environment(X0) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( ( subpopulations(first_movers,efficient_producers,X0,X1)
        & environment(X0) )
     => greater(number_of_organizations(X0,X1),zero) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_environment_not_empty) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ~ greater(number_of_organizations(X0,X1),zero)
      | greater(equilibrium(X0),X1)
      | constant(resources(X0,X1))
      | ~ in_environment(X0,X1)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f11]) ).

fof(f11,plain,
    ! [X0,X1] :
      ( ( ( constant(resources(X0,X1))
          | greater(equilibrium(X0),X1) )
        & ( decreases(resources(X0,X1))
          | ~ greater(equilibrium(X0),X1) ) )
      | ~ greater(number_of_organizations(X0,X1),zero)
      | ~ in_environment(X0,X1)
      | ~ environment(X0) ),
    inference(flattening,[],[f10]) ).

fof(f10,plain,
    ! [X0,X1] :
      ( ( ( constant(resources(X0,X1))
          | greater(equilibrium(X0),X1) )
        & ( decreases(resources(X0,X1))
          | ~ greater(equilibrium(X0),X1) ) )
      | ~ greater(number_of_organizations(X0,X1),zero)
      | ~ in_environment(X0,X1)
      | ~ environment(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( ( greater(number_of_organizations(X0,X1),zero)
        & in_environment(X0,X1)
        & environment(X0) )
     => ( ( ~ greater(equilibrium(X0),X1)
         => constant(resources(X0,X1)) )
        & ( greater(equilibrium(X0),X1)
         => decreases(resources(X0,X1)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3) ).

fof(f61,plain,
    ( ~ constant(resources(sK0,sK1))
    | ~ environment(sK0) ),
    inference(resolution,[],[f60,f28]) ).

fof(f60,plain,
    ! [X0] :
      ( ~ subpopulations(first_movers,efficient_producers,X0,sK1)
      | ~ constant(resources(X0,sK1))
      | ~ environment(X0) ),
    inference(resolution,[],[f26,f29]) ).

fof(f29,plain,
    decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))),
    inference(cnf_transformation,[],[f22]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
      | ~ constant(resources(X0,X1))
      | ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( ( ( ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
          | ~ constant(resources(X0,X1)) )
        & ( increases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
          | ~ decreases(resources(X0,X1)) ) )
      | ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ environment(X0) ),
    inference(flattening,[],[f12]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( ( ( ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
          | ~ constant(resources(X0,X1)) )
        & ( increases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
          | ~ decreases(resources(X0,X1)) ) )
      | ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ environment(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( ( subpopulations(first_movers,efficient_producers,X0,X1)
        & environment(X0) )
     => ( ( constant(resources(X0,X1))
         => ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) )
        & ( decreases(resources(X0,X1))
         => increases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4) ).

fof(f59,plain,
    ~ spl2_2,
    inference(avatar_split_clause,[],[f58,f46]) ).

fof(f46,plain,
    ( spl2_2
  <=> decreases(resources(sK0,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

fof(f58,plain,
    ~ decreases(resources(sK0,sK1)),
    inference(subsumption_resolution,[],[f57,f27]) ).

fof(f57,plain,
    ( ~ decreases(resources(sK0,sK1))
    | ~ environment(sK0) ),
    inference(resolution,[],[f56,f28]) ).

fof(f56,plain,
    ! [X0] :
      ( ~ subpopulations(first_movers,efficient_producers,X0,sK1)
      | ~ decreases(resources(X0,sK1))
      | ~ environment(X0) ),
    inference(resolution,[],[f25,f35]) ).

fof(f35,plain,
    ~ increases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))),
    inference(resolution,[],[f29,f32]) ).

fof(f32,plain,
    ! [X0] :
      ( ~ decreases(X0)
      | ~ increases(X0) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0] :
      ( ~ decreases(X0)
      | ~ increases(X0) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,plain,
    ! [X0] :
      ( increases(X0)
     => ~ decreases(X0) ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X2] :
      ( increases(X2)
     => ~ decreases(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_increase_not_decrease) ).

fof(f25,plain,
    ! [X0,X1] :
      ( increases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
      | ~ decreases(resources(X0,X1))
      | ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f49,plain,
    ( ~ spl2_1
    | spl2_2 ),
    inference(avatar_split_clause,[],[f40,f46,f42]) ).

fof(f40,plain,
    ( decreases(resources(sK0,sK1))
    | ~ greater(equilibrium(sK0),sK1) ),
    inference(subsumption_resolution,[],[f39,f27]) ).

fof(f39,plain,
    ( decreases(resources(sK0,sK1))
    | ~ environment(sK0)
    | ~ greater(equilibrium(sK0),sK1) ),
    inference(resolution,[],[f38,f28]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | decreases(resources(X0,X1))
      | ~ environment(X0)
      | ~ greater(equilibrium(X0),X1) ),
    inference(subsumption_resolution,[],[f37,f31]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ~ greater(equilibrium(X0),X1)
      | decreases(resources(X0,X1))
      | ~ in_environment(X0,X1)
      | ~ environment(X0)
      | ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
    inference(duplicate_literal_removal,[],[f36]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ~ greater(equilibrium(X0),X1)
      | decreases(resources(X0,X1))
      | ~ in_environment(X0,X1)
      | ~ environment(X0)
      | ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ environment(X0) ),
    inference(resolution,[],[f23,f30]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ~ greater(number_of_organizations(X0,X1),zero)
      | ~ greater(equilibrium(X0),X1)
      | decreases(resources(X0,X1))
      | ~ in_environment(X0,X1)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f11]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.10  % Problem    : MGT021+1 : TPTP v8.2.0. Released v2.0.0.
% 0.10/0.11  % 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
% 0.10/0.32  % Computer : n029.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit   : 300
% 0.10/0.32  % WCLimit    : 300
% 0.10/0.32  % DateTime   : Sun May 19 00:04:38 EDT 2024
% 0.10/0.32  % CPUTime    : 
% 0.10/0.32  This is a FOF_THM_RFO_SEQ problem
% 0.10/0.32  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
% 0.47/0.64  % (27901)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)
% 0.47/0.65  % (27903)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)
% 0.47/0.65  % (27902)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)
% 0.47/0.65  % (27896)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)
% 0.47/0.65  % (27901)First to succeed.
% 0.47/0.65  % (27898)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on theBenchmark for (2996ds/78Mi)
% 0.47/0.65  % (27901)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-27891"
% 0.47/0.65  % (27903)Also succeeded, but the first one will report.
% 0.47/0.65  % (27901)Refutation found. Thanks to Tanya!
% 0.47/0.65  % SZS status Theorem for theBenchmark
% 0.47/0.65  % SZS output start Proof for theBenchmark
% See solution above
% 0.47/0.65  % (27901)------------------------------
% 0.47/0.65  % (27901)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.47/0.65  % (27901)Termination reason: Refutation
% 0.47/0.65  
% 0.47/0.65  % (27901)Memory used [KB]: 980
% 0.47/0.65  % (27901)Time elapsed: 0.003 s
% 0.47/0.65  % (27901)Instructions burned: 4 (million)
% 0.47/0.65  % (27891)Success in time 0.32 s
% 0.47/0.65  % Vampire---4.8 exiting
%------------------------------------------------------------------------------