%------------------------------------------------------------------------------
% File     : SnakeForV---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_uns --cores 0 -t %d %s

% Computer : n008.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 17:51:04 EDT 2022

% Result   : Theorem 0.19s 0.50s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   37 (   8 unt;   0 def)
%            Number of atoms       :  126 (   0 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  143 (  54   ~;  45   |;  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   :   78 (  66   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f54,plain,
    $false,
    inference(subsumption_resolution,[],[f53,f24]) ).

fof(f24,plain,
    environment(sK1),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ( greater(zero,growth_rate(efficient_producers,sK0))
    & environment(sK1)
    & subpopulations(first_movers,efficient_producers,sK1,sK0)
    & greater_or_equal(growth_rate(first_movers,sK0),zero) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f15]) ).

fof(f15,plain,
    ( ? [X0,X1] :
        ( greater(zero,growth_rate(efficient_producers,X0))
        & environment(X1)
        & subpopulations(first_movers,efficient_producers,X1,X0)
        & greater_or_equal(growth_rate(first_movers,X0),zero) )
   => ( greater(zero,growth_rate(efficient_producers,sK0))
      & environment(sK1)
      & subpopulations(first_movers,efficient_producers,sK1,sK0)
      & greater_or_equal(growth_rate(first_movers,sK0),zero) ) ),
    introduced(choice_axiom,[]) ).

fof(f6,plain,
    ? [X0,X1] :
      ( greater(zero,growth_rate(efficient_producers,X0))
      & environment(X1)
      & subpopulations(first_movers,efficient_producers,X1,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(f53,plain,
    ~ environment(sK1),
    inference(resolution,[],[f52,f34]) ).

fof(f34,plain,
    subpopulations(efficient_producers,first_movers,sK1,sK0),
    inference(subsumption_resolution,[],[f33,f24]) ).

fof(f33,plain,
    ( subpopulations(efficient_producers,first_movers,sK1,sK0)
    | ~ environment(sK1) ),
    inference(resolution,[],[f27,f23]) ).

fof(f23,plain,
    subpopulations(first_movers,efficient_producers,sK1,sK0),
    inference(cnf_transformation,[],[f16]) ).

fof(f27,plain,
    ! [X2,X3,X0,X1] :
      ( ~ subpopulations(X3,X2,X1,X0)
      | subpopulations(X2,X3,X1,X0)
      | ~ environment(X1) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1,X2,X3] :
      ( subpopulations(X2,X3,X1,X0)
      | ~ environment(X1)
      | ~ subpopulations(X3,X2,X1,X0) ),
    inference(rectify,[],[f13]) ).

fof(f13,plain,
    ! [X0,X3,X2,X1] :
      ( subpopulations(X2,X1,X3,X0)
      | ~ environment(X3)
      | ~ subpopulations(X1,X2,X3,X0) ),
    inference(flattening,[],[f12]) ).

fof(f12,plain,
    ! [X0,X3,X2,X1] :
      ( subpopulations(X2,X1,X3,X0)
      | ~ subpopulations(X1,X2,X3,X0)
      | ~ environment(X3) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,plain,
    ! [X0,X3,X2,X1] :
      ( ( subpopulations(X1,X2,X3,X0)
        & environment(X3) )
     => subpopulations(X2,X1,X3,X0) ),
    inference(rectify,[],[f1]) ).

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

fof(f52,plain,
    ! [X0] :
      ( ~ subpopulations(efficient_producers,first_movers,X0,sK0)
      | ~ environment(X0) ),
    inference(subsumption_resolution,[],[f51,f32]) ).

fof(f32,plain,
    ~ outcompetes(first_movers,efficient_producers,sK0),
    inference(subsumption_resolution,[],[f31,f24]) ).

fof(f31,plain,
    ( ~ outcompetes(first_movers,efficient_producers,sK0)
    | ~ environment(sK1) ),
    inference(resolution,[],[f26,f23]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ outcompetes(first_movers,efficient_producers,X1)
      | ~ environment(X0) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ~ environment(X0)
      | ~ subpopulations(first_movers,efficient_producers,X0,X1)
      | ~ outcompetes(first_movers,efficient_producers,X1) ),
    inference(rectify,[],[f14]) ).

fof(f14,plain,
    ! [X1,X0] :
      ( ~ environment(X1)
      | ~ subpopulations(first_movers,efficient_producers,X1,X0)
      | ~ outcompetes(first_movers,efficient_producers,X0) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,plain,
    ~ ? [X0,X1] :
        ( outcompetes(first_movers,efficient_producers,X0)
        & environment(X1)
        & subpopulations(first_movers,efficient_producers,X1,X0) ),
    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(f51,plain,
    ! [X0] :
      ( ~ subpopulations(efficient_producers,first_movers,X0,sK0)
      | outcompetes(first_movers,efficient_producers,sK0)
      | ~ environment(X0) ),
    inference(resolution,[],[f50,f22]) ).

fof(f22,plain,
    greater_or_equal(growth_rate(first_movers,sK0),zero),
    inference(cnf_transformation,[],[f16]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( ~ greater_or_equal(growth_rate(X0,sK0),zero)
      | outcompetes(X0,efficient_producers,sK0)
      | ~ subpopulations(efficient_producers,X0,X1,sK0)
      | ~ environment(X1) ),
    inference(resolution,[],[f30,f25]) ).

fof(f25,plain,
    greater(zero,growth_rate(efficient_producers,sK0)),
    inference(cnf_transformation,[],[f16]) ).

fof(f30,plain,
    ! [X2,X3,X0,X1] :
      ( ~ greater(zero,growth_rate(X1,X0))
      | outcompetes(X3,X1,X0)
      | ~ environment(X2)
      | ~ subpopulations(X1,X3,X2,X0)
      | ~ greater_or_equal(growth_rate(X3,X0),zero) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1,X2,X3] :
      ( ~ environment(X2)
      | ( ( outcompetes(X3,X1,X0)
          | ~ greater(zero,growth_rate(X1,X0))
          | ~ greater_or_equal(growth_rate(X3,X0),zero) )
        & ( ( greater(zero,growth_rate(X1,X0))
            & greater_or_equal(growth_rate(X3,X0),zero) )
          | ~ outcompetes(X3,X1,X0) ) )
      | ~ subpopulations(X1,X3,X2,X0) ),
    inference(rectify,[],[f20]) ).

fof(f20,plain,
    ! [X1,X0,X3,X2] :
      ( ~ environment(X3)
      | ( ( outcompetes(X2,X0,X1)
          | ~ greater(zero,growth_rate(X0,X1))
          | ~ greater_or_equal(growth_rate(X2,X1),zero) )
        & ( ( greater(zero,growth_rate(X0,X1))
            & greater_or_equal(growth_rate(X2,X1),zero) )
          | ~ outcompetes(X2,X0,X1) ) )
      | ~ subpopulations(X0,X2,X3,X1) ),
    inference(flattening,[],[f19]) ).

fof(f19,plain,
    ! [X1,X0,X3,X2] :
      ( ~ environment(X3)
      | ( ( outcompetes(X2,X0,X1)
          | ~ greater(zero,growth_rate(X0,X1))
          | ~ greater_or_equal(growth_rate(X2,X1),zero) )
        & ( ( greater(zero,growth_rate(X0,X1))
            & greater_or_equal(growth_rate(X2,X1),zero) )
          | ~ outcompetes(X2,X0,X1) ) )
      | ~ subpopulations(X0,X2,X3,X1) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f11,plain,
    ! [X1,X0,X3,X2] :
      ( ~ environment(X3)
      | ( outcompetes(X2,X0,X1)
      <=> ( greater(zero,growth_rate(X0,X1))
          & greater_or_equal(growth_rate(X2,X1),zero) ) )
      | ~ subpopulations(X0,X2,X3,X1) ),
    inference(flattening,[],[f10]) ).

fof(f10,plain,
    ! [X0,X2,X1,X3] :
      ( ( outcompetes(X2,X0,X1)
      <=> ( greater(zero,growth_rate(X0,X1))
          & greater_or_equal(growth_rate(X2,X1),zero) ) )
      | ~ environment(X3)
      | ~ subpopulations(X0,X2,X3,X1) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,plain,
    ! [X0,X2,X1,X3] :
      ( ( environment(X3)
        & subpopulations(X0,X2,X3,X1) )
     => ( outcompetes(X2,X0,X1)
      <=> ( greater(zero,growth_rate(X0,X1))
          & greater_or_equal(growth_rate(X2,X1),zero) ) ) ),
    inference(rectify,[],[f2]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : MGT036+3 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n008.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
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 03:23:55 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.50  % (12095)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.19/0.50  % (12087)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.50  % (12087)First to succeed.
% 0.19/0.50  % (12095)Also succeeded, but the first one will report.
% 0.19/0.50  % (12087)Refutation found. Thanks to Tanya!
% 0.19/0.50  % SZS status Theorem for theBenchmark
% 0.19/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.50  % (12087)------------------------------
% 0.19/0.50  % (12087)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (12087)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50  % (12087)Termination reason: Refutation
% 0.19/0.50  
% 0.19/0.50  % (12087)Memory used [KB]: 5884
% 0.19/0.50  % (12087)Time elapsed: 0.062 s
% 0.19/0.50  % (12087)Instructions burned: 1 (million)
% 0.19/0.50  % (12087)------------------------------
% 0.19/0.50  % (12087)------------------------------
% 0.19/0.50  % (12072)Success in time 0.157 s
%------------------------------------------------------------------------------