TSTP Solution File: MGT036+3 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : MGT036+3 : TPTP v8.1.0. Released v2.0.0.
% 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 : n007.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 17:51:31 EDT 2022

% Result   : Theorem 0.20s 0.52s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   37 (   7 unt;   0 def)
%            Number of atoms       :  130 (   0 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  151 (  58   ~;  49   |;  35   &)
%                                         (   4 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-4 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   84 (  72   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f49,plain,
    $false,
    inference(subsumption_resolution,[],[f48,f44]) ).

fof(f44,plain,
    ~ subpopulations(efficient_producers,first_movers,sK1,sK0),
    inference(resolution,[],[f41,f28]) ).

fof(f28,plain,
    environment(sK1),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ( subpopulations(first_movers,efficient_producers,sK1,sK0)
    & environment(sK1)
    & greater(zero,growth_rate(efficient_producers,sK0))
    & greater_or_equal(growth_rate(first_movers,sK0),zero) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f19]) ).

fof(f19,plain,
    ( ? [X0,X1] :
        ( subpopulations(first_movers,efficient_producers,X1,X0)
        & environment(X1)
        & greater(zero,growth_rate(efficient_producers,X0))
        & greater_or_equal(growth_rate(first_movers,X0),zero) )
   => ( subpopulations(first_movers,efficient_producers,sK1,sK0)
      & environment(sK1)
      & greater(zero,growth_rate(efficient_producers,sK0))
      & greater_or_equal(growth_rate(first_movers,sK0),zero) ) ),
    introduced(choice_axiom,[]) ).

fof(f7,plain,
    ? [X0,X1] :
      ( subpopulations(first_movers,efficient_producers,X1,X0)
      & environment(X1)
      & greater(zero,growth_rate(efficient_producers,X0))
      & greater_or_equal(growth_rate(first_movers,X0),zero) ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ? [X3,X0] :
      ( greater(zero,growth_rate(efficient_producers,X3))
      & environment(X0)
      & subpopulations(first_movers,efficient_producers,X0,X3)
      & greater_or_equal(growth_rate(first_movers,X3),zero) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_star) ).

fof(f41,plain,
    ! [X0] :
      ( ~ environment(X0)
      | ~ subpopulations(efficient_producers,first_movers,X0,sK0) ),
    inference(subsumption_resolution,[],[f40,f28]) ).

fof(f40,plain,
    ! [X0] :
      ( ~ subpopulations(efficient_producers,first_movers,X0,sK0)
      | ~ environment(sK1)
      | ~ environment(X0) ),
    inference(resolution,[],[f35,f29]) ).

fof(f29,plain,
    subpopulations(first_movers,efficient_producers,sK1,sK0),
    inference(cnf_transformation,[],[f20]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ~ subpopulations(first_movers,efficient_producers,X1,sK0)
      | ~ environment(X0)
      | ~ subpopulations(efficient_producers,first_movers,X0,sK0)
      | ~ environment(X1) ),
    inference(resolution,[],[f33,f30]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ~ outcompetes(first_movers,efficient_producers,X1)
      | ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ~ environment(X0)
      | ~ outcompetes(first_movers,efficient_producers,X1)
      | ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
    inference(rectify,[],[f14]) ).

fof(f14,plain,
    ! [X1,X0] :
      ( ~ environment(X1)
      | ~ outcompetes(first_movers,efficient_producers,X0)
      | ~ subpopulations(first_movers,efficient_producers,X1,X0) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,plain,
    ~ ? [X0,X1] :
        ( subpopulations(first_movers,efficient_producers,X1,X0)
        & outcompetes(first_movers,efficient_producers,X0)
        & environment(X1) ),
    inference(rectify,[],[f5]) ).

fof(f5,negated_conjecture,
    ~ ? [X3,X0] :
        ( subpopulations(first_movers,efficient_producers,X0,X3)
        & outcompetes(first_movers,efficient_producers,X3)
        & environment(X0) ),
    inference(negated_conjecture,[],[f4]) ).

fof(f4,conjecture,
    ? [X3,X0] :
      ( subpopulations(first_movers,efficient_producers,X0,X3)
      & outcompetes(first_movers,efficient_producers,X3)
      & environment(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t5_star) ).

fof(f33,plain,
    ! [X0] :
      ( outcompetes(first_movers,efficient_producers,sK0)
      | ~ subpopulations(efficient_producers,first_movers,X0,sK0)
      | ~ environment(X0) ),
    inference(resolution,[],[f31,f26]) ).

fof(f26,plain,
    greater_or_equal(growth_rate(first_movers,sK0),zero),
    inference(cnf_transformation,[],[f20]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ~ greater_or_equal(growth_rate(X1,sK0),zero)
      | ~ subpopulations(efficient_producers,X1,X0,sK0)
      | outcompetes(X1,efficient_producers,sK0)
      | ~ environment(X0) ),
    inference(resolution,[],[f22,f27]) ).

fof(f27,plain,
    greater(zero,growth_rate(efficient_producers,sK0)),
    inference(cnf_transformation,[],[f20]) ).

fof(f22,plain,
    ! [X2,X3,X0,X1] :
      ( ~ greater(zero,growth_rate(X2,X3))
      | ~ environment(X0)
      | ~ greater_or_equal(growth_rate(X1,X3),zero)
      | ~ subpopulations(X2,X1,X0,X3)
      | outcompetes(X1,X2,X3) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1,X2,X3] :
      ( ~ environment(X0)
      | ( ( ( greater(zero,growth_rate(X2,X3))
            & greater_or_equal(growth_rate(X1,X3),zero) )
          | ~ outcompetes(X1,X2,X3) )
        & ( outcompetes(X1,X2,X3)
          | ~ greater(zero,growth_rate(X2,X3))
          | ~ greater_or_equal(growth_rate(X1,X3),zero) ) )
      | ~ subpopulations(X2,X1,X0,X3) ),
    inference(rectify,[],[f16]) ).

fof(f16,plain,
    ! [X1,X0,X2,X3] :
      ( ~ environment(X1)
      | ( ( ( greater(zero,growth_rate(X2,X3))
            & greater_or_equal(growth_rate(X0,X3),zero) )
          | ~ outcompetes(X0,X2,X3) )
        & ( outcompetes(X0,X2,X3)
          | ~ greater(zero,growth_rate(X2,X3))
          | ~ greater_or_equal(growth_rate(X0,X3),zero) ) )
      | ~ subpopulations(X2,X0,X1,X3) ),
    inference(flattening,[],[f15]) ).

fof(f15,plain,
    ! [X1,X0,X2,X3] :
      ( ~ environment(X1)
      | ( ( ( greater(zero,growth_rate(X2,X3))
            & greater_or_equal(growth_rate(X0,X3),zero) )
          | ~ outcompetes(X0,X2,X3) )
        & ( outcompetes(X0,X2,X3)
          | ~ greater(zero,growth_rate(X2,X3))
          | ~ greater_or_equal(growth_rate(X0,X3),zero) ) )
      | ~ subpopulations(X2,X0,X1,X3) ),
    inference(nnf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X1,X0,X2,X3] :
      ( ~ environment(X1)
      | ( ( greater(zero,growth_rate(X2,X3))
          & greater_or_equal(growth_rate(X0,X3),zero) )
      <=> outcompetes(X0,X2,X3) )
      | ~ subpopulations(X2,X0,X1,X3) ),
    inference(flattening,[],[f12]) ).

fof(f12,plain,
    ! [X0,X1,X3,X2] :
      ( ( ( greater(zero,growth_rate(X2,X3))
          & greater_or_equal(growth_rate(X0,X3),zero) )
      <=> outcompetes(X0,X2,X3) )
      | ~ environment(X1)
      | ~ subpopulations(X2,X0,X1,X3) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,plain,
    ! [X0,X1,X3,X2] :
      ( ( environment(X1)
        & subpopulations(X2,X0,X1,X3) )
     => ( ( greater(zero,growth_rate(X2,X3))
          & greater_or_equal(growth_rate(X0,X3),zero) )
      <=> outcompetes(X0,X2,X3) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X2,X0,X1,X3] :
      ( ( environment(X0)
        & subpopulations(X1,X2,X0,X3) )
     => ( ( greater(zero,growth_rate(X1,X3))
          & greater_or_equal(growth_rate(X2,X3),zero) )
      <=> outcompetes(X2,X1,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).

fof(f48,plain,
    subpopulations(efficient_producers,first_movers,sK1,sK0),
    inference(resolution,[],[f47,f29]) ).

fof(f47,plain,
    ! [X2,X0,X1] :
      ( ~ subpopulations(X0,X1,sK1,X2)
      | subpopulations(X1,X0,sK1,X2) ),
    inference(resolution,[],[f25,f28]) ).

fof(f25,plain,
    ! [X2,X3,X0,X1] :
      ( ~ environment(X0)
      | ~ subpopulations(X2,X1,X0,X3)
      | subpopulations(X1,X2,X0,X3) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1,X2,X3] :
      ( ~ environment(X0)
      | ~ subpopulations(X2,X1,X0,X3)
      | subpopulations(X1,X2,X0,X3) ),
    inference(rectify,[],[f11]) ).

fof(f11,plain,
    ! [X1,X0,X2,X3] :
      ( ~ environment(X1)
      | ~ subpopulations(X2,X0,X1,X3)
      | subpopulations(X0,X2,X1,X3) ),
    inference(flattening,[],[f10]) ).

fof(f10,plain,
    ! [X0,X2,X3,X1] :
      ( subpopulations(X0,X2,X1,X3)
      | ~ subpopulations(X2,X0,X1,X3)
      | ~ environment(X1) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,plain,
    ! [X0,X2,X3,X1] :
      ( ( subpopulations(X2,X0,X1,X3)
        & environment(X1) )
     => subpopulations(X0,X2,X1,X3) ),
    inference(rectify,[],[f1]) ).

fof(f1,axiom,
    ! [X2,X0,X1,X3] :
      ( ( subpopulations(X1,X2,X0,X3)
        & environment(X0) )
     => subpopulations(X2,X1,X0,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : MGT036+3 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n007.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 30 03:03:15 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.51  % (23735)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.20/0.51  % (23727)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.51  % (23735)First to succeed.
% 0.20/0.51  % (23719)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.51  % (23727)Also succeeded, but the first one will report.
% 0.20/0.52  % (23735)Refutation found. Thanks to Tanya!
% 0.20/0.52  % SZS status Theorem for theBenchmark
% 0.20/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.52  % (23735)------------------------------
% 0.20/0.52  % (23735)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (23735)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52  % (23735)Termination reason: Refutation
% 0.20/0.52  
% 0.20/0.52  % (23735)Memory used [KB]: 895
% 0.20/0.52  % (23735)Time elapsed: 0.061 s
% 0.20/0.52  % (23735)Instructions burned: 2 (million)
% 0.20/0.52  % (23735)------------------------------
% 0.20/0.52  % (23735)------------------------------
% 0.20/0.52  % (23712)Success in time 0.161 s
%------------------------------------------------------------------------------