TSTP Solution File: MGT028+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : MGT028+1 : 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 : 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 17:50:58 EDT 2022
% Result : Theorem 0.21s 0.50s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of formulae : 94 ( 6 unt; 0 def)
% Number of atoms : 479 ( 2 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 662 ( 277 ~; 277 |; 81 &)
% ( 6 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 7 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 158 ( 130 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f129,plain,
$false,
inference(avatar_sat_refutation,[],[f53,f76,f100,f107,f113,f119,f124,f128]) ).
fof(f128,plain,
( ~ spl7_2
| ~ spl7_3
| ~ spl7_5 ),
inference(avatar_contradiction_clause,[],[f127]) ).
fof(f127,plain,
( $false
| ~ spl7_2
| ~ spl7_3
| ~ spl7_5 ),
inference(subsumption_resolution,[],[f126,f94]) ).
fof(f94,plain,
( in_environment(sK1,sK0(sK1))
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f93,plain,
( spl7_5
<=> in_environment(sK1,sK0(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_5])]) ).
fof(f126,plain,
( ~ in_environment(sK1,sK0(sK1))
| ~ spl7_2
| ~ spl7_3 ),
inference(duplicate_literal_removal,[],[f125]) ).
fof(f125,plain,
( ~ in_environment(sK1,sK0(sK1))
| ~ in_environment(sK1,sK0(sK1))
| ~ spl7_2
| ~ spl7_3 ),
inference(resolution,[],[f75,f52]) ).
fof(f52,plain,
( ! [X0] :
( greater_or_equal(sK4(sK1,X0),X0)
| ~ in_environment(sK1,X0) )
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f51,plain,
( spl7_2
<=> ! [X0] :
( ~ in_environment(sK1,X0)
| greater_or_equal(sK4(sK1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_2])]) ).
fof(f75,plain,
( ! [X0] :
( ~ greater_or_equal(sK4(sK1,X0),sK0(sK1))
| ~ in_environment(sK1,X0) )
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f74,plain,
( spl7_3
<=> ! [X0] :
( ~ greater_or_equal(sK4(sK1,X0),sK0(sK1))
| ~ in_environment(sK1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_3])]) ).
fof(f124,plain,
( ~ spl7_1
| ~ spl7_6 ),
inference(avatar_split_clause,[],[f121,f105,f47]) ).
fof(f47,plain,
( spl7_1
<=> greater(sK3(sK1),sF5) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_1])]) ).
fof(f105,plain,
( spl7_6
<=> ! [X0] :
( ~ greater(X0,sF5)
| ~ greater_or_equal(sK2(X0),sK3(sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_6])]) ).
fof(f121,plain,
( ~ greater(sK3(sK1),sF5)
| ~ spl7_6 ),
inference(duplicate_literal_removal,[],[f120]) ).
fof(f120,plain,
( ~ greater(sK3(sK1),sF5)
| ~ greater(sK3(sK1),sF5)
| ~ spl7_6 ),
inference(resolution,[],[f106,f39]) ).
fof(f39,plain,
! [X1] :
( greater_or_equal(sK2(X1),X1)
| ~ greater(X1,sF5) ),
inference(definition_folding,[],[f29,f37]) ).
fof(f37,plain,
appear(efficient_producers,sK1) = sF5,
introduced(function_definition,[]) ).
fof(f29,plain,
! [X1] :
( greater_or_equal(sK2(X1),X1)
| ~ greater(X1,appear(efficient_producers,sK1)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
( ! [X1] :
( ( subpopulations(first_movers,efficient_producers,sK1,sK2(X1))
& greater_or_equal(sK2(X1),X1)
& ~ greater(zero,growth_rate(first_movers,sK2(X1))) )
| ~ greater(X1,appear(efficient_producers,sK1)) )
& environment(sK1)
& stable(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f13,f17,f16]) ).
fof(f16,plain,
( ? [X0] :
( ! [X1] :
( ? [X2] :
( subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X1)
& ~ greater(zero,growth_rate(first_movers,X2)) )
| ~ greater(X1,appear(efficient_producers,X0)) )
& environment(X0)
& stable(X0) )
=> ( ! [X1] :
( ? [X2] :
( subpopulations(first_movers,efficient_producers,sK1,X2)
& greater_or_equal(X2,X1)
& ~ greater(zero,growth_rate(first_movers,X2)) )
| ~ greater(X1,appear(efficient_producers,sK1)) )
& environment(sK1)
& stable(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
! [X1] :
( ? [X2] :
( subpopulations(first_movers,efficient_producers,sK1,X2)
& greater_or_equal(X2,X1)
& ~ greater(zero,growth_rate(first_movers,X2)) )
=> ( subpopulations(first_movers,efficient_producers,sK1,sK2(X1))
& greater_or_equal(sK2(X1),X1)
& ~ greater(zero,growth_rate(first_movers,sK2(X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f13,plain,
? [X0] :
( ! [X1] :
( ? [X2] :
( subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X1)
& ~ greater(zero,growth_rate(first_movers,X2)) )
| ~ greater(X1,appear(efficient_producers,X0)) )
& environment(X0)
& stable(X0) ),
inference(flattening,[],[f12]) ).
fof(f12,plain,
? [X0] :
( ! [X1] :
( ~ greater(X1,appear(efficient_producers,X0))
| ? [X2] :
( ~ greater(zero,growth_rate(first_movers,X2))
& greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) ) )
& stable(X0)
& environment(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,plain,
~ ! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X1] :
( greater(X1,appear(efficient_producers,X0))
& ! [X2] :
( ( greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> greater(zero,growth_rate(first_movers,X2)) ) ) ),
inference(rectify,[],[f4]) ).
fof(f4,negated_conjecture,
~ ! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X4] :
( greater(X4,appear(efficient_producers,X0))
& ! [X2] :
( ( greater_or_equal(X2,X4)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> greater(zero,growth_rate(first_movers,X2)) ) ) ),
inference(negated_conjecture,[],[f3]) ).
fof(f3,conjecture,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X4] :
( greater(X4,appear(efficient_producers,X0))
& ! [X2] :
( ( greater_or_equal(X2,X4)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> greater(zero,growth_rate(first_movers,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l10) ).
fof(f106,plain,
( ! [X0] :
( ~ greater_or_equal(sK2(X0),sK3(sK1))
| ~ greater(X0,sF5) )
| ~ spl7_6 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f119,plain,
( spl7_6
| ~ spl7_4 ),
inference(avatar_split_clause,[],[f118,f90,f105]) ).
fof(f90,plain,
( spl7_4
<=> ! [X1] :
( greater(zero,growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,sK3(sK1))
| ~ subpopulations(first_movers,efficient_producers,sK1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_4])]) ).
fof(f118,plain,
( ! [X0] :
( ~ greater_or_equal(sK2(X0),sK3(sK1))
| ~ greater(X0,sF5) )
| ~ spl7_4 ),
inference(subsumption_resolution,[],[f117,f41]) ).
fof(f41,plain,
! [X1] :
( ~ greater(zero,sF6(X1))
| ~ greater(X1,sF5) ),
inference(definition_folding,[],[f28,f37,f40]) ).
fof(f40,plain,
! [X1] : growth_rate(first_movers,sK2(X1)) = sF6(X1),
introduced(function_definition,[]) ).
fof(f28,plain,
! [X1] :
( ~ greater(zero,growth_rate(first_movers,sK2(X1)))
| ~ greater(X1,appear(efficient_producers,sK1)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f117,plain,
( ! [X0] :
( ~ greater(X0,sF5)
| greater(zero,sF6(X0))
| ~ greater_or_equal(sK2(X0),sK3(sK1)) )
| ~ spl7_4 ),
inference(resolution,[],[f116,f38]) ).
fof(f38,plain,
! [X1] :
( subpopulations(first_movers,efficient_producers,sK1,sK2(X1))
| ~ greater(X1,sF5) ),
inference(definition_folding,[],[f30,f37]) ).
fof(f30,plain,
! [X1] :
( subpopulations(first_movers,efficient_producers,sK1,sK2(X1))
| ~ greater(X1,appear(efficient_producers,sK1)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f116,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,sK1,sK2(X0))
| greater(zero,sF6(X0))
| ~ greater_or_equal(sK2(X0),sK3(sK1)) )
| ~ spl7_4 ),
inference(superposition,[],[f91,f40]) ).
fof(f91,plain,
( ! [X1] :
( greater(zero,growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,sK3(sK1))
| ~ subpopulations(first_movers,efficient_producers,sK1,X1) )
| ~ spl7_4 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f113,plain,
( spl7_4
| spl7_4
| ~ spl7_2
| ~ spl7_5 ),
inference(avatar_split_clause,[],[f112,f93,f51,f90,f90]) ).
fof(f112,plain,
( ! [X0,X1] :
( greater(zero,growth_rate(first_movers,X0))
| ~ subpopulations(first_movers,efficient_producers,sK1,X0)
| ~ subpopulations(first_movers,efficient_producers,sK1,X1)
| ~ greater_or_equal(X0,sK3(sK1))
| ~ greater_or_equal(X1,sK3(sK1))
| greater(zero,growth_rate(first_movers,X1)) )
| ~ spl7_2
| ~ spl7_5 ),
inference(subsumption_resolution,[],[f111,f27]) ).
fof(f27,plain,
environment(sK1),
inference(cnf_transformation,[],[f18]) ).
fof(f111,plain,
( ! [X0,X1] :
( ~ greater_or_equal(X1,sK3(sK1))
| ~ subpopulations(first_movers,efficient_producers,sK1,X0)
| greater(zero,growth_rate(first_movers,X1))
| greater(zero,growth_rate(first_movers,X0))
| ~ subpopulations(first_movers,efficient_producers,sK1,X1)
| ~ environment(sK1)
| ~ greater_or_equal(X0,sK3(sK1)) )
| ~ spl7_2
| ~ spl7_5 ),
inference(subsumption_resolution,[],[f110,f94]) ).
fof(f110,plain,
( ! [X0,X1] :
( greater(zero,growth_rate(first_movers,X0))
| ~ subpopulations(first_movers,efficient_producers,sK1,X0)
| ~ greater_or_equal(X1,sK3(sK1))
| greater(zero,growth_rate(first_movers,X1))
| ~ subpopulations(first_movers,efficient_producers,sK1,X1)
| ~ in_environment(sK1,sK0(sK1))
| ~ environment(sK1)
| ~ greater_or_equal(X0,sK3(sK1)) )
| ~ spl7_2 ),
inference(subsumption_resolution,[],[f109,f26]) ).
fof(f26,plain,
stable(sK1),
inference(cnf_transformation,[],[f18]) ).
fof(f109,plain,
( ! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,sK1,X1)
| ~ stable(sK1)
| greater(zero,growth_rate(first_movers,X1))
| greater(zero,growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sK3(sK1))
| ~ subpopulations(first_movers,efficient_producers,sK1,X0)
| ~ in_environment(sK1,sK0(sK1))
| ~ environment(sK1)
| ~ greater_or_equal(X1,sK3(sK1)) )
| ~ spl7_2 ),
inference(duplicate_literal_removal,[],[f108]) ).
fof(f108,plain,
( ! [X0,X1] :
( ~ stable(sK1)
| ~ subpopulations(first_movers,efficient_producers,sK1,X0)
| ~ subpopulations(first_movers,efficient_producers,sK1,X1)
| ~ in_environment(sK1,sK0(sK1))
| ~ greater_or_equal(X0,sK3(sK1))
| ~ greater_or_equal(X1,sK3(sK1))
| ~ in_environment(sK1,sK0(sK1))
| greater(zero,growth_rate(first_movers,X0))
| greater(zero,growth_rate(first_movers,X1))
| ~ environment(sK1) )
| ~ spl7_2 ),
inference(resolution,[],[f52,f79]) ).
fof(f79,plain,
! [X2,X3,X0,X1] :
( ~ greater_or_equal(sK4(X0,X2),sK0(X0))
| greater(zero,growth_rate(first_movers,X3))
| ~ environment(X0)
| ~ greater_or_equal(X1,sK3(X0))
| greater(zero,growth_rate(first_movers,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X3)
| ~ greater_or_equal(X3,sK3(X0))
| ~ stable(X0)
| ~ in_environment(X0,X2)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(duplicate_literal_removal,[],[f77]) ).
fof(f77,plain,
! [X2,X3,X0,X1] :
( ~ stable(X0)
| greater(zero,growth_rate(first_movers,X3))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X3)
| greater(zero,growth_rate(first_movers,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ stable(X0)
| ~ environment(X0)
| ~ greater_or_equal(sK4(X0,X2),sK0(X0))
| ~ environment(X0)
| ~ greater_or_equal(X1,sK3(X0))
| ~ greater_or_equal(X3,sK3(X0))
| ~ in_environment(X0,X2)
| ~ stable(X0)
| ~ in_environment(X0,X2) ),
inference(resolution,[],[f65,f36]) ).
fof(f36,plain,
! [X2,X3,X0] :
( subpopulations(first_movers,efficient_producers,X0,sK4(X0,X3))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,sK3(X0))
| ~ stable(X0)
| greater(zero,growth_rate(first_movers,X2))
| ~ environment(X0)
| ~ in_environment(X0,X3) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0] :
( ( ! [X2] :
( greater(zero,growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,sK3(X0)) )
& greater(sK3(X0),appear(efficient_producers,X0)) )
| ~ stable(X0)
| ~ environment(X0)
| ! [X3] :
( ( subpopulations(first_movers,efficient_producers,X0,sK4(X0,X3))
& greater_or_equal(sK4(X0,X3),X3)
& ~ greater(zero,growth_rate(first_movers,sK4(X0,X3))) )
| ~ in_environment(X0,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f19,f21,f20]) ).
fof(f20,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( greater(zero,growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,X1) )
& greater(X1,appear(efficient_producers,X0)) )
=> ( ! [X2] :
( greater(zero,growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,sK3(X0)) )
& greater(sK3(X0),appear(efficient_producers,X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
! [X0,X3] :
( ? [X4] :
( subpopulations(first_movers,efficient_producers,X0,X4)
& greater_or_equal(X4,X3)
& ~ greater(zero,growth_rate(first_movers,X4)) )
=> ( subpopulations(first_movers,efficient_producers,X0,sK4(X0,X3))
& greater_or_equal(sK4(X0,X3),X3)
& ~ greater(zero,growth_rate(first_movers,sK4(X0,X3))) ) ),
introduced(choice_axiom,[]) ).
fof(f19,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( greater(zero,growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,X1) )
& greater(X1,appear(efficient_producers,X0)) )
| ~ stable(X0)
| ~ environment(X0)
| ! [X3] :
( ? [X4] :
( subpopulations(first_movers,efficient_producers,X0,X4)
& greater_or_equal(X4,X3)
& ~ greater(zero,growth_rate(first_movers,X4)) )
| ~ in_environment(X0,X3) ) ),
inference(rectify,[],[f11]) ).
fof(f11,plain,
! [X0] :
( ? [X3] :
( ! [X4] :
( greater(zero,growth_rate(first_movers,X4))
| ~ subpopulations(first_movers,efficient_producers,X0,X4)
| ~ greater_or_equal(X4,X3) )
& greater(X3,appear(efficient_producers,X0)) )
| ~ stable(X0)
| ~ environment(X0)
| ! [X1] :
( ? [X2] :
( subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X1)
& ~ greater(zero,growth_rate(first_movers,X2)) )
| ~ in_environment(X0,X1) ) ),
inference(flattening,[],[f10]) ).
fof(f10,plain,
! [X0] :
( ? [X3] :
( ! [X4] :
( greater(zero,growth_rate(first_movers,X4))
| ~ subpopulations(first_movers,efficient_producers,X0,X4)
| ~ greater_or_equal(X4,X3) )
& greater(X3,appear(efficient_producers,X0)) )
| ! [X1] :
( ? [X2] :
( ~ greater(zero,growth_rate(first_movers,X2))
& greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
| ~ in_environment(X0,X1) )
| ~ stable(X0)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,plain,
! [X0] :
( ( ? [X1] :
( ! [X2] :
( ( greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> greater(zero,growth_rate(first_movers,X2)) )
& in_environment(X0,X1) )
& stable(X0)
& environment(X0) )
=> ? [X3] :
( ! [X4] :
( ( subpopulations(first_movers,efficient_producers,X0,X4)
& greater_or_equal(X4,X3) )
=> greater(zero,growth_rate(first_movers,X4)) )
& greater(X3,appear(efficient_producers,X0)) ) ),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( ( ? [X1] :
( ! [X2] :
( ( greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> greater(zero,growth_rate(first_movers,X2)) )
& in_environment(X0,X1) )
& stable(X0)
& environment(X0) )
=> ? [X3] :
( greater(X3,appear(efficient_producers,X0))
& ! [X2] :
( ( subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X3) )
=> greater(zero,growth_rate(first_movers,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_negative_growth) ).
fof(f65,plain,
! [X8,X6,X7,X5] :
( ~ subpopulations(first_movers,efficient_producers,X8,sK4(X5,X7))
| ~ subpopulations(first_movers,efficient_producers,X5,X6)
| ~ in_environment(X5,X7)
| ~ greater_or_equal(sK4(X5,X7),sK0(X8))
| ~ stable(X5)
| ~ environment(X5)
| ~ environment(X8)
| greater(zero,growth_rate(first_movers,X6))
| ~ stable(X8)
| ~ greater_or_equal(X6,sK3(X5)) ),
inference(resolution,[],[f34,f25]) ).
fof(f25,plain,
! [X2,X0] :
( greater(zero,growth_rate(first_movers,X2))
| ~ environment(X0)
| ~ stable(X0)
| ~ greater_or_equal(X2,sK0(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2) ),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0] :
( ~ environment(X0)
| ~ stable(X0)
| ( ! [X2] :
( ( greater(zero,growth_rate(first_movers,X2))
& greater(growth_rate(efficient_producers,X2),zero) )
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,sK0(X0)) )
& in_environment(X0,sK0(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f14]) ).
fof(f14,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( ( greater(zero,growth_rate(first_movers,X2))
& greater(growth_rate(efficient_producers,X2),zero) )
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,X1) )
& in_environment(X0,X1) )
=> ( ! [X2] :
( ( greater(zero,growth_rate(first_movers,X2))
& greater(growth_rate(efficient_producers,X2),zero) )
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,sK0(X0)) )
& in_environment(X0,sK0(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f9,plain,
! [X0] :
( ~ environment(X0)
| ~ stable(X0)
| ? [X1] :
( ! [X2] :
( ( greater(zero,growth_rate(first_movers,X2))
& greater(growth_rate(efficient_producers,X2),zero) )
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,X1) )
& in_environment(X0,X1) ) ),
inference(flattening,[],[f8]) ).
fof(f8,plain,
! [X0] :
( ? [X1] :
( in_environment(X0,X1)
& ! [X2] :
( ( greater(zero,growth_rate(first_movers,X2))
& greater(growth_rate(efficient_producers,X2),zero) )
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,X1) ) )
| ~ stable(X0)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,plain,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X1] :
( in_environment(X0,X1)
& ! [X2] :
( ( subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X1) )
=> ( greater(zero,growth_rate(first_movers,X2))
& greater(growth_rate(efficient_producers,X2),zero) ) ) ) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X4] :
( in_environment(X0,X4)
& ! [X2] :
( ( subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X4) )
=> ( greater(zero,growth_rate(first_movers,X2))
& greater(growth_rate(efficient_producers,X2),zero) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l11) ).
fof(f34,plain,
! [X2,X3,X0] :
( ~ greater(zero,growth_rate(first_movers,sK4(X0,X3)))
| ~ stable(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ environment(X0)
| greater(zero,growth_rate(first_movers,X2))
| ~ in_environment(X0,X3)
| ~ greater_or_equal(X2,sK3(X0)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f107,plain,
( spl7_2
| spl7_6 ),
inference(avatar_split_clause,[],[f103,f105,f51]) ).
fof(f103,plain,
! [X0,X1] :
( ~ greater(X0,sF5)
| ~ greater_or_equal(sK2(X0),sK3(sK1))
| ~ in_environment(sK1,X1)
| greater_or_equal(sK4(sK1,X1),X1) ),
inference(subsumption_resolution,[],[f102,f41]) ).
fof(f102,plain,
! [X0,X1] :
( ~ greater_or_equal(sK2(X0),sK3(sK1))
| greater(zero,sF6(X0))
| ~ greater(X0,sF5)
| ~ in_environment(sK1,X1)
| greater_or_equal(sK4(sK1,X1),X1) ),
inference(subsumption_resolution,[],[f101,f27]) ).
fof(f101,plain,
! [X0,X1] :
( ~ in_environment(sK1,X1)
| ~ environment(sK1)
| greater_or_equal(sK4(sK1,X1),X1)
| ~ greater_or_equal(sK2(X0),sK3(sK1))
| greater(zero,sF6(X0))
| ~ greater(X0,sF5) ),
inference(subsumption_resolution,[],[f63,f26]) ).
fof(f63,plain,
! [X0,X1] :
( ~ greater(X0,sF5)
| greater_or_equal(sK4(sK1,X1),X1)
| greater(zero,sF6(X0))
| ~ stable(sK1)
| ~ in_environment(sK1,X1)
| ~ greater_or_equal(sK2(X0),sK3(sK1))
| ~ environment(sK1) ),
inference(resolution,[],[f62,f38]) ).
fof(f62,plain,
! [X2,X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X1,sK2(X0))
| greater(zero,sF6(X0))
| ~ greater_or_equal(sK2(X0),sK3(X1))
| ~ stable(X1)
| greater_or_equal(sK4(X1,X2),X2)
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(superposition,[],[f35,f40]) ).
fof(f35,plain,
! [X2,X3,X0] :
( greater(zero,growth_rate(first_movers,X2))
| ~ stable(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater_or_equal(sK4(X0,X3),X3)
| ~ greater_or_equal(X2,sK3(X0))
| ~ environment(X0)
| ~ in_environment(X0,X3) ),
inference(cnf_transformation,[],[f22]) ).
fof(f100,plain,
spl7_5,
inference(avatar_contradiction_clause,[],[f99]) ).
fof(f99,plain,
( $false
| spl7_5 ),
inference(subsumption_resolution,[],[f98,f26]) ).
fof(f98,plain,
( ~ stable(sK1)
| spl7_5 ),
inference(subsumption_resolution,[],[f97,f27]) ).
fof(f97,plain,
( ~ environment(sK1)
| ~ stable(sK1)
| spl7_5 ),
inference(resolution,[],[f95,f23]) ).
fof(f23,plain,
! [X0] :
( in_environment(X0,sK0(X0))
| ~ environment(X0)
| ~ stable(X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f95,plain,
( ~ in_environment(sK1,sK0(sK1))
| spl7_5 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f76,plain,
( spl7_3
| spl7_1 ),
inference(avatar_split_clause,[],[f72,f47,f74]) ).
fof(f72,plain,
! [X0] :
( greater(sK3(sK1),sF5)
| ~ greater_or_equal(sK4(sK1,X0),sK0(sK1))
| ~ in_environment(sK1,X0) ),
inference(subsumption_resolution,[],[f71,f26]) ).
fof(f71,plain,
! [X0] :
( ~ greater_or_equal(sK4(sK1,X0),sK0(sK1))
| ~ in_environment(sK1,X0)
| greater(sK3(sK1),sF5)
| ~ stable(sK1) ),
inference(subsumption_resolution,[],[f70,f27]) ).
fof(f70,plain,
! [X0] :
( ~ environment(sK1)
| ~ stable(sK1)
| ~ in_environment(sK1,X0)
| greater(sK3(sK1),sF5)
| ~ greater_or_equal(sK4(sK1,X0),sK0(sK1)) ),
inference(superposition,[],[f69,f37]) ).
fof(f69,plain,
! [X3,X4] :
( greater(sK3(X3),appear(efficient_producers,X3))
| ~ stable(X3)
| ~ greater_or_equal(sK4(X3,X4),sK0(X3))
| ~ environment(X3)
| ~ in_environment(X3,X4) ),
inference(duplicate_literal_removal,[],[f67]) ).
fof(f67,plain,
! [X3,X4] :
( ~ in_environment(X3,X4)
| greater(sK3(X3),appear(efficient_producers,X3))
| ~ stable(X3)
| ~ environment(X3)
| ~ in_environment(X3,X4)
| ~ environment(X3)
| greater(sK3(X3),appear(efficient_producers,X3))
| ~ stable(X3)
| ~ greater_or_equal(sK4(X3,X4),sK0(X3))
| ~ environment(X3)
| ~ stable(X3) ),
inference(resolution,[],[f60,f33]) ).
fof(f33,plain,
! [X3,X0] :
( subpopulations(first_movers,efficient_producers,X0,sK4(X0,X3))
| ~ in_environment(X0,X3)
| greater(sK3(X0),appear(efficient_producers,X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f60,plain,
! [X2,X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X2,sK4(X0,X1))
| ~ stable(X2)
| greater(sK3(X0),appear(efficient_producers,X0))
| ~ stable(X0)
| ~ environment(X2)
| ~ environment(X0)
| ~ greater_or_equal(sK4(X0,X1),sK0(X2))
| ~ in_environment(X0,X1) ),
inference(resolution,[],[f31,f25]) ).
fof(f31,plain,
! [X3,X0] :
( ~ greater(zero,growth_rate(first_movers,sK4(X0,X3)))
| ~ environment(X0)
| greater(sK3(X0),appear(efficient_producers,X0))
| ~ stable(X0)
| ~ in_environment(X0,X3) ),
inference(cnf_transformation,[],[f22]) ).
fof(f53,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f45,f51,f47]) ).
fof(f45,plain,
! [X0] :
( ~ in_environment(sK1,X0)
| greater_or_equal(sK4(sK1,X0),X0)
| greater(sK3(sK1),sF5) ),
inference(subsumption_resolution,[],[f44,f27]) ).
fof(f44,plain,
! [X0] :
( ~ environment(sK1)
| ~ in_environment(sK1,X0)
| greater(sK3(sK1),sF5)
| greater_or_equal(sK4(sK1,X0),X0) ),
inference(subsumption_resolution,[],[f43,f26]) ).
fof(f43,plain,
! [X0] :
( ~ stable(sK1)
| ~ in_environment(sK1,X0)
| ~ environment(sK1)
| greater(sK3(sK1),sF5)
| greater_or_equal(sK4(sK1,X0),X0) ),
inference(superposition,[],[f32,f37]) ).
fof(f32,plain,
! [X3,X0] :
( greater(sK3(X0),appear(efficient_producers,X0))
| ~ in_environment(X0,X3)
| ~ environment(X0)
| greater_or_equal(sK4(X0,X3),X3)
| ~ stable(X0) ),
inference(cnf_transformation,[],[f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : MGT028+1 : TPTP v8.1.0. Released v2.0.0.
% 0.10/0.13 % 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 : 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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 03:00:15 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.21/0.49 % (14141)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.49 % (14126)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.21/0.49 % (14126)First to succeed.
% 0.21/0.50 % (14126)Refutation found. Thanks to Tanya!
% 0.21/0.50 % SZS status Theorem for theBenchmark
% 0.21/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.50 % (14126)------------------------------
% 0.21/0.50 % (14126)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.50 % (14126)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.50 % (14126)Termination reason: Refutation
% 0.21/0.50
% 0.21/0.50 % (14126)Memory used [KB]: 6012
% 0.21/0.50 % (14126)Time elapsed: 0.075 s
% 0.21/0.50 % (14126)Instructions burned: 5 (million)
% 0.21/0.50 % (14126)------------------------------
% 0.21/0.50 % (14126)------------------------------
% 0.21/0.50 % (14125)Success in time 0.145 s
%------------------------------------------------------------------------------