TSTP Solution File: MGT022+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : MGT022+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 : n020.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun May  5 07:57:06 EDT 2024

% Result   : Theorem 0.10s 0.34s
% Output   : Refutation 0.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   44 (   9 unt;   0 def)
%            Number of atoms       :  148 (   0 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  158 (  54   ~;  50   |;  37   &)
%                                         (   0 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   1 prp; 0-4 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   51 (  43   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f47,plain,
    $false,
    inference(subsumption_resolution,[],[f46,f39]) ).

fof(f39,plain,
    constant(resources(sK1,sK2)),
    inference(subsumption_resolution,[],[f38,f34]) ).

fof(f34,plain,
    ( ~ increases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)))
    | constant(resources(sK1,sK2)) ),
    inference(resolution,[],[f20,f23]) ).

fof(f23,plain,
    ( sP0(sK2,sK1)
    | constant(resources(sK1,sK2)) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ( ( ( decreases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)))
        & constant(resources(sK1,sK2)) )
      | sP0(sK2,sK1) )
    & subpopulations(first_movers,efficient_producers,sK1,sK2)
    & environment(sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f14,f17]) ).

fof(f17,plain,
    ( ? [X0,X1] :
        ( ( ( decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
            & constant(resources(X0,X1)) )
          | sP0(X1,X0) )
        & subpopulations(first_movers,efficient_producers,X0,X1)
        & environment(X0) )
   => ( ( ( decreases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)))
          & constant(resources(sK1,sK2)) )
        | sP0(sK2,sK1) )
      & subpopulations(first_movers,efficient_producers,sK1,sK2)
      & environment(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f14,plain,
    ? [X0,X1] :
      ( ( ( decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
          & constant(resources(X0,X1)) )
        | sP0(X1,X0) )
      & subpopulations(first_movers,efficient_producers,X0,X1)
      & environment(X0) ),
    inference(definition_folding,[],[f9,f13]) ).

fof(f13,plain,
    ! [X1,X0] :
      ( ( ~ increases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
        & decreases(resources(X0,X1)) )
      | ~ sP0(X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f9,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,[],[f8]) ).

fof(f8,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,plain,
    ~ ! [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))) ) ) ),
    inference(rectify,[],[f5]) ).

fof(f5,negated_conjecture,
    ~ ! [X1,X4] :
        ( ( subpopulations(first_movers,efficient_producers,X1,X4)
          & environment(X1) )
       => ( ( constant(resources(X1,X4))
           => ~ decreases(difference(disbanding_rate(first_movers,X4),disbanding_rate(efficient_producers,X4))) )
          & ( decreases(resources(X1,X4))
           => increases(difference(disbanding_rate(first_movers,X4),disbanding_rate(efficient_producers,X4))) ) ) ),
    inference(negated_conjecture,[],[f4]) ).

fof(f4,conjecture,
    ! [X1,X4] :
      ( ( subpopulations(first_movers,efficient_producers,X1,X4)
        & environment(X1) )
     => ( ( constant(resources(X1,X4))
         => ~ decreases(difference(disbanding_rate(first_movers,X4),disbanding_rate(efficient_producers,X4))) )
        & ( decreases(resources(X1,X4))
         => increases(difference(disbanding_rate(first_movers,X4),disbanding_rate(efficient_producers,X4))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l4) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | ~ increases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( ( ~ increases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
        & decreases(resources(X1,X0)) )
      | ~ sP0(X0,X1) ),
    inference(rectify,[],[f15]) ).

fof(f15,plain,
    ! [X1,X0] :
      ( ( ~ increases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
        & decreases(resources(X0,X1)) )
      | ~ sP0(X1,X0) ),
    inference(nnf_transformation,[],[f13]) ).

fof(f38,plain,
    ( increases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)))
    | constant(resources(sK1,sK2)) ),
    inference(resolution,[],[f37,f30]) ).

fof(f30,plain,
    ( decreases(resources(sK1,sK2))
    | constant(resources(sK1,sK2)) ),
    inference(resolution,[],[f19,f23]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | decreases(resources(X1,X0)) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f37,plain,
    ( ~ decreases(resources(sK1,sK2))
    | increases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2))) ),
    inference(subsumption_resolution,[],[f36,f21]) ).

fof(f21,plain,
    environment(sK1),
    inference(cnf_transformation,[],[f18]) ).

fof(f36,plain,
    ( ~ decreases(resources(sK1,sK2))
    | increases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)))
    | ~ environment(sK1) ),
    inference(subsumption_resolution,[],[f35,f25]) ).

fof(f25,plain,
    greater(resilience(efficient_producers),resilience(first_movers)),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    greater(resilience(efficient_producers),resilience(first_movers)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).

fof(f35,plain,
    ( ~ decreases(resources(sK1,sK2))
    | ~ greater(resilience(efficient_producers),resilience(first_movers))
    | increases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)))
    | ~ environment(sK1) ),
    inference(resolution,[],[f26,f22]) ).

fof(f22,plain,
    subpopulations(first_movers,efficient_producers,sK1,sK2),
    inference(cnf_transformation,[],[f18]) ).

fof(f26,plain,
    ! [X2,X3,X0,X1] :
      ( ~ subpopulations(X1,X2,X0,X3)
      | ~ decreases(resources(X0,X3))
      | ~ greater(resilience(X2),resilience(X1))
      | increases(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3)))
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f11]) ).

fof(f11,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( constant(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3)))
          | ~ constant(resources(X0,X3)) )
        & ( increases(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3)))
          | ~ decreases(resources(X0,X3)) ) )
      | ~ greater(resilience(X2),resilience(X1))
      | ~ subpopulations(X1,X2,X0,X3)
      | ~ environment(X0) ),
    inference(flattening,[],[f10]) ).

fof(f10,plain,
    ! [X0,X1,X2,X3] :
      ( ( ( constant(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3)))
          | ~ constant(resources(X0,X3)) )
        & ( increases(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3)))
          | ~ decreases(resources(X0,X3)) ) )
      | ~ greater(resilience(X2),resilience(X1))
      | ~ subpopulations(X1,X2,X0,X3)
      | ~ environment(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,plain,
    ! [X0,X1,X2,X3] :
      ( ( greater(resilience(X2),resilience(X1))
        & subpopulations(X1,X2,X0,X3)
        & environment(X0) )
     => ( ( constant(resources(X0,X3))
         => constant(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3))) )
        & ( decreases(resources(X0,X3))
         => increases(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3))) ) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X1,X2,X3,X4] :
      ( ( greater(resilience(X3),resilience(X2))
        & subpopulations(X2,X3,X1,X4)
        & environment(X1) )
     => ( ( constant(resources(X1,X4))
         => constant(difference(disbanding_rate(X2,X4),disbanding_rate(X3,X4))) )
        & ( decreases(resources(X1,X4))
         => increases(difference(disbanding_rate(X2,X4),disbanding_rate(X3,X4))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a5) ).

fof(f46,plain,
    ~ constant(resources(sK1,sK2)),
    inference(resolution,[],[f44,f28]) ).

fof(f28,plain,
    ! [X0] :
      ( ~ decreases(X0)
      | ~ constant(X0) ),
    inference(cnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X0] :
      ( ~ decreases(X0)
      | ~ constant(X0) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] :
      ( constant(X0)
     => ~ decreases(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_constant_not_decrease) ).

fof(f44,plain,
    decreases(resources(sK1,sK2)),
    inference(resolution,[],[f43,f32]) ).

fof(f32,plain,
    ( ~ constant(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)))
    | decreases(resources(sK1,sK2)) ),
    inference(resolution,[],[f29,f28]) ).

fof(f29,plain,
    ( decreases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)))
    | decreases(resources(sK1,sK2)) ),
    inference(resolution,[],[f19,f24]) ).

fof(f24,plain,
    ( sP0(sK2,sK1)
    | decreases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2))) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f43,plain,
    constant(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2))),
    inference(subsumption_resolution,[],[f42,f21]) ).

fof(f42,plain,
    ( constant(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)))
    | ~ environment(sK1) ),
    inference(subsumption_resolution,[],[f41,f25]) ).

fof(f41,plain,
    ( ~ greater(resilience(efficient_producers),resilience(first_movers))
    | constant(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)))
    | ~ environment(sK1) ),
    inference(subsumption_resolution,[],[f40,f39]) ).

fof(f40,plain,
    ( ~ constant(resources(sK1,sK2))
    | ~ greater(resilience(efficient_producers),resilience(first_movers))
    | constant(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)))
    | ~ environment(sK1) ),
    inference(resolution,[],[f27,f22]) ).

fof(f27,plain,
    ! [X2,X3,X0,X1] :
      ( ~ subpopulations(X1,X2,X0,X3)
      | ~ constant(resources(X0,X3))
      | ~ greater(resilience(X2),resilience(X1))
      | constant(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3)))
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f11]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem    : MGT022+1 : TPTP v8.1.2. Released v2.0.0.
% 0.02/0.11  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.32  % Computer : n020.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   : Fri May  3 20:05:38 EDT 2024
% 0.10/0.32  % CPUTime    : 
% 0.10/0.32  % (28137)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.34  % (28143)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.10/0.34  % (28138)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.10/0.34  % (28141)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.10/0.34  % (28142)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.10/0.34  % (28144)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.10/0.34  % (28140)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.10/0.34  % (28139)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.10/0.34  % (28142)First to succeed.
% 0.10/0.34  % (28143)Also succeeded, but the first one will report.
% 0.10/0.34  TRYING [1]
% 0.10/0.34  Detected minimum model sizes of [1,1,1,1]
% 0.10/0.34  Detected maximum model sizes of [max,2,1,1]
% 0.10/0.34  % (28140)Also succeeded, but the first one will report.
% 0.10/0.34  TRYING [1]
% 0.10/0.34  TRYING [1,1,1,1]
% 0.10/0.34  Detected minimum model sizes of [1,1,1,1]
% 0.10/0.34  Detected maximum model sizes of [max,2,1,1]
% 0.10/0.34  TRYING [1,1,1,1]
% 0.10/0.34  TRYING [2,1,1,1]
% 0.10/0.34  TRYING [2]
% 0.10/0.34  TRYING [2]
% 0.10/0.34  TRYING [2,1,1,1]
% 0.10/0.34  % (28142)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-28137"
% 0.10/0.34  TRYING [3,1,1,1]
% 0.10/0.34  % (28142)Refutation found. Thanks to Tanya!
% 0.10/0.34  % SZS status Theorem for theBenchmark
% 0.10/0.34  % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.34  % (28142)------------------------------
% 0.10/0.34  % (28142)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.10/0.34  % (28142)Termination reason: Refutation
% 0.10/0.34  
% 0.10/0.34  % (28142)Memory used [KB]: 751
% 0.10/0.34  % (28142)Time elapsed: 0.003 s
% 0.10/0.34  % (28142)Instructions burned: 4 (million)
% 0.10/0.34  % (28137)Success in time 0.017 s
%------------------------------------------------------------------------------