TSTP Solution File: MGT034+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : MGT034+2 : 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 : n019.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 Apr 30 13:54:35 EDT 2024
% Result : Theorem 0.22s 0.39s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 19
% Syntax : Number of formulae : 142 ( 24 unt; 0 def)
% Number of atoms : 461 ( 35 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 519 ( 200 ~; 198 |; 83 &)
% ( 7 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 188 ( 182 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f411,plain,
$false,
inference(subsumption_resolution,[],[f409,f400]) ).
fof(f400,plain,
~ greater(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)),zero),
inference(unit_resulting_resolution,[],[f390,f95]) ).
fof(f95,plain,
! [X0] :
( ~ greater(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
| greater(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0] :
( ( greater(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
| ~ greater(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)) )
& ( greater(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))
| ~ greater(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0] :
( greater(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
<=> greater(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X3] :
( greater(difference(growth_rate(first_movers,X3),growth_rate(efficient_producers,X3)),zero)
<=> greater(growth_rate(first_movers,X3),growth_rate(efficient_producers,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_positive_growth_rate_difference) ).
fof(f390,plain,
~ greater(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)),
inference(unit_resulting_resolution,[],[f79,f83,f370,f108]) ).
fof(f108,plain,
! [X2,X3,X0,X1] :
( ~ subpopulations(X1,X2,X0,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| selection_favors(X2,X1,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1,X2,X3] :
( selection_favors(X2,X1,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(flattening,[],[f71]) ).
fof(f71,plain,
! [X0,X1,X2,X3] :
( selection_favors(X2,X1,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1,X2,X3] :
( ( greater(growth_rate(X2,X3),growth_rate(X1,X3))
& subpopulations(X1,X2,X0,X3)
& environment(X0) )
=> selection_favors(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp1_high_growth_rates) ).
fof(f370,plain,
subpopulations(efficient_producers,first_movers,sK0,sK1),
inference(unit_resulting_resolution,[],[f79,f360,f100]) ).
fof(f100,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| subpopulations(efficient_producers,first_movers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( subpopulations(efficient_producers,first_movers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f61]) ).
fof(f61,plain,
! [X0,X1] :
( subpopulations(efficient_producers,first_movers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> subpopulations(efficient_producers,first_movers,X0,X1) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X0,X3] :
( ( subpopulations(first_movers,efficient_producers,X0,X3)
& environment(X0) )
=> subpopulations(efficient_producers,first_movers,X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations) ).
fof(f360,plain,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(unit_resulting_resolution,[],[f79,f144,f142,f322,f113]) ).
fof(f113,plain,
! [X3,X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater_or_equal(X3,X1)
| subpopulations(first_movers,efficient_producers,X0,X3)
| ~ environment(X0)
| ~ sP2(X0,X3) ),
inference(general_splitting,[],[f87,f112_D]) ).
fof(f112,plain,
! [X2,X3,X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,X3)
| sP2(X0,X3) ),
inference(cnf_transformation,[],[f112_D]) ).
fof(f112_D,plain,
! [X3,X0] :
( ! [X2] :
( ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,X3) )
<=> ~ sP2(X0,X3) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP2])]) ).
fof(f87,plain,
! [X2,X3,X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,X3)
| ~ greater_or_equal(X2,X3)
| ~ greater_or_equal(X3,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X1,X2,X3] :
( subpopulations(first_movers,efficient_producers,X0,X3)
| ~ greater_or_equal(X2,X3)
| ~ greater_or_equal(X3,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f45]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( subpopulations(first_movers,efficient_producers,X0,X3)
| ~ greater_or_equal(X2,X3)
| ~ greater_or_equal(X3,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( ( greater_or_equal(X2,X3)
& greater_or_equal(X3,X1)
& subpopulations(first_movers,efficient_producers,X0,X2)
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> subpopulations(first_movers,efficient_producers,X0,X3) ),
inference(rectify,[],[f19]) ).
fof(f19,axiom,
! [X0,X5,X6,X3] :
( ( greater_or_equal(X6,X3)
& greater_or_equal(X3,X5)
& subpopulations(first_movers,efficient_producers,X0,X6)
& subpopulations(first_movers,efficient_producers,X0,X5)
& environment(X0) )
=> subpopulations(first_movers,efficient_producers,X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a10) ).
fof(f322,plain,
greater_or_equal(sK1,critical_point(sK0)),
inference(superposition,[],[f81,f321]) ).
fof(f321,plain,
critical_point(sK0) = appear(efficient_producers,sK0),
inference(subsumption_resolution,[],[f319,f251]) ).
fof(f251,plain,
( ~ greater(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1))
| critical_point(sK0) = appear(efficient_producers,sK0) ),
inference(subsumption_resolution,[],[f250,f79]) ).
fof(f250,plain,
( critical_point(sK0) = appear(efficient_producers,sK0)
| ~ greater(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1))
| ~ environment(sK0) ),
inference(subsumption_resolution,[],[f249,f83]) ).
fof(f249,plain,
( critical_point(sK0) = appear(efficient_producers,sK0)
| ~ greater(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1))
| selection_favors(first_movers,efficient_producers,sK1)
| ~ environment(sK0) ),
inference(resolution,[],[f244,f108]) ).
fof(f244,plain,
( subpopulations(efficient_producers,first_movers,sK0,sK1)
| critical_point(sK0) = appear(efficient_producers,sK0) ),
inference(subsumption_resolution,[],[f237,f79]) ).
fof(f237,plain,
( critical_point(sK0) = appear(efficient_producers,sK0)
| subpopulations(efficient_producers,first_movers,sK0,sK1)
| ~ environment(sK0) ),
inference(resolution,[],[f234,f100]) ).
fof(f234,plain,
( subpopulations(first_movers,efficient_producers,sK0,sK1)
| critical_point(sK0) = appear(efficient_producers,sK0) ),
inference(subsumption_resolution,[],[f231,f81]) ).
fof(f231,plain,
( ~ greater_or_equal(sK1,appear(efficient_producers,sK0))
| subpopulations(first_movers,efficient_producers,sK0,sK1)
| critical_point(sK0) = appear(efficient_producers,sK0) ),
inference(resolution,[],[f222,f144]) ).
fof(f222,plain,
! [X0] :
( ~ sP2(sK0,X0)
| ~ greater_or_equal(X0,appear(efficient_producers,sK0))
| subpopulations(first_movers,efficient_producers,sK0,X0)
| critical_point(sK0) = appear(efficient_producers,sK0) ),
inference(subsumption_resolution,[],[f217,f79]) ).
fof(f217,plain,
! [X0] :
( critical_point(sK0) = appear(efficient_producers,sK0)
| ~ greater_or_equal(X0,appear(efficient_producers,sK0))
| subpopulations(first_movers,efficient_producers,sK0,X0)
| ~ environment(sK0)
| ~ sP2(sK0,X0) ),
inference(resolution,[],[f210,f113]) ).
fof(f210,plain,
( subpopulations(first_movers,efficient_producers,sK0,appear(efficient_producers,sK0))
| critical_point(sK0) = appear(efficient_producers,sK0) ),
inference(subsumption_resolution,[],[f208,f79]) ).
fof(f208,plain,
( critical_point(sK0) = appear(efficient_producers,sK0)
| subpopulations(first_movers,efficient_producers,sK0,appear(efficient_producers,sK0))
| ~ environment(sK0) ),
inference(resolution,[],[f206,f91]) ).
fof(f91,plain,
! [X0] :
( ~ in_environment(X0,appear(efficient_producers,X0))
| subpopulations(first_movers,efficient_producers,X0,appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0] :
( subpopulations(first_movers,efficient_producers,X0,appear(efficient_producers,X0))
| ~ in_environment(X0,appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(flattening,[],[f51]) ).
fof(f51,plain,
! [X0] :
( subpopulations(first_movers,efficient_producers,X0,appear(efficient_producers,X0))
| ~ in_environment(X0,appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ( in_environment(X0,appear(efficient_producers,X0))
& environment(X0) )
=> subpopulations(first_movers,efficient_producers,X0,appear(efficient_producers,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_FM_and_EP_when_EP_appears) ).
fof(f206,plain,
( in_environment(sK0,appear(efficient_producers,sK0))
| critical_point(sK0) = appear(efficient_producers,sK0) ),
inference(resolution,[],[f205,f158]) ).
fof(f158,plain,
( greater(critical_point(sK0),appear(efficient_producers,sK0))
| critical_point(sK0) = appear(efficient_producers,sK0) ),
inference(resolution,[],[f151,f103]) ).
fof(f103,plain,
! [X0,X1] :
( ~ greater_or_equal(X0,X1)
| greater(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( ( greater_or_equal(X0,X1)
| ( X0 != X1
& ~ greater(X0,X1) ) )
& ( X0 = X1
| greater(X0,X1)
| ~ greater_or_equal(X0,X1) ) ),
inference(flattening,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( ( greater_or_equal(X0,X1)
| ( X0 != X1
& ~ greater(X0,X1) ) )
& ( X0 = X1
| greater(X0,X1)
| ~ greater_or_equal(X0,X1) ) ),
inference(nnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0,X1] :
( greater_or_equal(X0,X1)
<=> ( X0 = X1
| greater(X0,X1) ) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X7,X8] :
( greater_or_equal(X7,X8)
<=> ( X7 = X8
| greater(X7,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal) ).
fof(f151,plain,
greater_or_equal(critical_point(sK0),appear(efficient_producers,sK0)),
inference(unit_resulting_resolution,[],[f79,f142,f99]) ).
fof(f99,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater_or_equal(X1,appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1] :
( greater_or_equal(X1,appear(efficient_producers,X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f59]) ).
fof(f59,plain,
! [X0,X1] :
( greater_or_equal(X1,appear(efficient_producers,X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> greater_or_equal(X1,appear(efficient_producers,X0)) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X0,X3] :
( ( subpopulations(first_movers,efficient_producers,X0,X3)
& environment(X0) )
=> greater_or_equal(X3,appear(efficient_producers,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_FM_and_EP_members_EP_appeared) ).
fof(f205,plain,
( ~ greater(critical_point(sK0),appear(efficient_producers,sK0))
| in_environment(sK0,appear(efficient_producers,sK0)) ),
inference(subsumption_resolution,[],[f204,f79]) ).
fof(f204,plain,
( in_environment(sK0,appear(efficient_producers,sK0))
| ~ greater(critical_point(sK0),appear(efficient_producers,sK0))
| ~ environment(sK0) ),
inference(resolution,[],[f192,f80]) ).
fof(f80,plain,
in_environment(sK0,critical_point(sK0)),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
( ~ selection_favors(first_movers,efficient_producers,sK1)
& greater(critical_point(sK0),sK1)
& greater_or_equal(sK1,appear(efficient_producers,sK0))
& in_environment(sK0,critical_point(sK0))
& environment(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f40,f73]) ).
fof(f73,plain,
( ? [X0,X1] :
( ~ selection_favors(first_movers,efficient_producers,X1)
& greater(critical_point(X0),X1)
& greater_or_equal(X1,appear(efficient_producers,X0))
& in_environment(X0,critical_point(X0))
& environment(X0) )
=> ( ~ selection_favors(first_movers,efficient_producers,sK1)
& greater(critical_point(sK0),sK1)
& greater_or_equal(sK1,appear(efficient_producers,sK0))
& in_environment(sK0,critical_point(sK0))
& environment(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
? [X0,X1] :
( ~ selection_favors(first_movers,efficient_producers,X1)
& greater(critical_point(X0),X1)
& greater_or_equal(X1,appear(efficient_producers,X0))
& in_environment(X0,critical_point(X0))
& environment(X0) ),
inference(flattening,[],[f39]) ).
fof(f39,plain,
? [X0,X1] :
( ~ selection_favors(first_movers,efficient_producers,X1)
& greater(critical_point(X0),X1)
& greater_or_equal(X1,appear(efficient_producers,X0))
& in_environment(X0,critical_point(X0))
& environment(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,plain,
~ ! [X0,X1] :
( ( greater(critical_point(X0),X1)
& greater_or_equal(X1,appear(efficient_producers,X0))
& in_environment(X0,critical_point(X0))
& environment(X0) )
=> selection_favors(first_movers,efficient_producers,X1) ),
inference(rectify,[],[f22]) ).
fof(f22,negated_conjecture,
~ ! [X0,X3] :
( ( greater(critical_point(X0),X3)
& greater_or_equal(X3,appear(efficient_producers,X0))
& in_environment(X0,critical_point(X0))
& environment(X0) )
=> selection_favors(first_movers,efficient_producers,X3) ),
inference(negated_conjecture,[],[f21]) ).
fof(f21,conjecture,
! [X0,X3] :
( ( greater(critical_point(X0),X3)
& greater_or_equal(X3,appear(efficient_producers,X0))
& in_environment(X0,critical_point(X0))
& environment(X0) )
=> selection_favors(first_movers,efficient_producers,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t3) ).
fof(f192,plain,
! [X0] :
( ~ in_environment(X0,critical_point(X0))
| in_environment(X0,appear(efficient_producers,X0))
| ~ greater(critical_point(X0),appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(resolution,[],[f98,f111]) ).
fof(f111,plain,
! [X1] : greater_or_equal(X1,X1),
inference(equality_resolution,[],[f105]) ).
fof(f105,plain,
! [X0,X1] :
( greater_or_equal(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f78]) ).
fof(f98,plain,
! [X0,X1] :
( ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ greater(critical_point(X0),X1)
| in_environment(X0,X1)
| ~ in_environment(X0,critical_point(X0))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ greater(critical_point(X0),X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,critical_point(X0))
| ~ environment(X0) ),
inference(flattening,[],[f57]) ).
fof(f57,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ greater(critical_point(X0),X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,critical_point(X0))
| ~ environment(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1] :
( ( greater(critical_point(X0),X1)
& greater_or_equal(X1,appear(efficient_producers,X0))
& in_environment(X0,critical_point(X0))
& environment(X0) )
=> in_environment(X0,X1) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X0,X3] :
( ( greater(critical_point(X0),X3)
& greater_or_equal(X3,appear(efficient_producers,X0))
& in_environment(X0,critical_point(X0))
& environment(X0) )
=> in_environment(X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_critical_time_points) ).
fof(f319,plain,
( critical_point(sK0) = appear(efficient_producers,sK0)
| greater(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)) ),
inference(resolution,[],[f318,f95]) ).
fof(f318,plain,
( greater(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)),zero)
| critical_point(sK0) = appear(efficient_producers,sK0) ),
inference(resolution,[],[f317,f268]) ).
fof(f268,plain,
( decreases(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)))
| critical_point(sK0) = appear(efficient_producers,sK0) ),
inference(subsumption_resolution,[],[f266,f245]) ).
fof(f245,plain,
( ~ decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| critical_point(sK0) = appear(efficient_producers,sK0) ),
inference(subsumption_resolution,[],[f238,f79]) ).
fof(f238,plain,
( critical_point(sK0) = appear(efficient_producers,sK0)
| ~ decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| ~ environment(sK0) ),
inference(resolution,[],[f234,f101]) ).
fof(f101,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,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,[],[f63]) ).
fof(f63,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,[],[f34]) ).
fof(f34,plain,
! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X0,X3] :
( ( subpopulations(first_movers,efficient_producers,X0,X3)
& environment(X0) )
=> ~ decreases(difference(disbanding_rate(first_movers,X3),disbanding_rate(efficient_producers,X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3) ).
fof(f266,plain,
( decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| decreases(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)))
| critical_point(sK0) = appear(efficient_producers,sK0) ),
inference(resolution,[],[f92,f243]) ).
fof(f243,plain,
( decreases(difference(founding_rate(first_movers,sK1),founding_rate(efficient_producers,sK1)))
| critical_point(sK0) = appear(efficient_producers,sK0) ),
inference(subsumption_resolution,[],[f235,f79]) ).
fof(f235,plain,
( critical_point(sK0) = appear(efficient_producers,sK0)
| decreases(difference(founding_rate(first_movers,sK1),founding_rate(efficient_producers,sK1)))
| ~ environment(sK0) ),
inference(resolution,[],[f234,f86]) ).
fof(f86,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1)))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X1] :
( decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f43]) ).
fof(f43,plain,
! [X0,X1] :
( decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1))) ),
inference(rectify,[],[f20]) ).
fof(f20,axiom,
! [X0,X3] :
( ( subpopulations(first_movers,efficient_producers,X0,X3)
& environment(X0) )
=> decreases(difference(founding_rate(first_movers,X3),founding_rate(efficient_producers,X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a12) ).
fof(f92,plain,
! [X0] :
( ~ decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0)))
| decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] :
( decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| ~ decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0))) ),
inference(flattening,[],[f53]) ).
fof(f53,plain,
! [X0] :
( decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| ~ decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0))) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0] :
( ( ~ decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
& decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0))) )
=> decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X3] :
( ( ~ decreases(difference(disbanding_rate(first_movers,X3),disbanding_rate(efficient_producers,X3)))
& decreases(difference(founding_rate(first_movers,X3),founding_rate(efficient_producers,X3))) )
=> decreases(difference(growth_rate(first_movers,X3),growth_rate(efficient_producers,X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_difference_between_founding_rates) ).
fof(f317,plain,
( ~ decreases(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)))
| greater(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)),zero) ),
inference(subsumption_resolution,[],[f316,f80]) ).
fof(f316,plain,
( greater(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)),zero)
| ~ decreases(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)))
| ~ in_environment(sK0,critical_point(sK0)) ),
inference(subsumption_resolution,[],[f313,f82]) ).
fof(f82,plain,
greater(critical_point(sK0),sK1),
inference(cnf_transformation,[],[f74]) ).
fof(f313,plain,
( ~ greater(critical_point(sK0),sK1)
| greater(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)),zero)
| ~ decreases(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)))
| ~ in_environment(sK0,critical_point(sK0)) ),
inference(resolution,[],[f307,f269]) ).
fof(f269,plain,
greater_or_equal(difference(growth_rate(first_movers,critical_point(sK0)),growth_rate(efficient_producers,critical_point(sK0))),zero),
inference(unit_resulting_resolution,[],[f79,f142,f179,f102]) ).
fof(f102,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater(zero,difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| greater(zero,difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| greater(zero,difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1] :
( ( ~ greater(zero,difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero) ),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X0,X3] :
( ( ~ greater(zero,difference(growth_rate(first_movers,X3),growth_rate(efficient_producers,X3)))
& subpopulations(first_movers,efficient_producers,X0,X3)
& environment(X0) )
=> greater_or_equal(difference(growth_rate(first_movers,X3),growth_rate(efficient_producers,X3)),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_relationship_of_growth_rates) ).
fof(f179,plain,
~ greater(zero,difference(growth_rate(first_movers,critical_point(sK0)),growth_rate(efficient_producers,critical_point(sK0)))),
inference(unit_resulting_resolution,[],[f141,f93]) ).
fof(f93,plain,
! [X0] :
( ~ greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0] :
( ( greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| ~ greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) )
& ( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))) ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0] :
( greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
<=> greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X3] :
( greater(zero,difference(growth_rate(first_movers,X3),growth_rate(efficient_producers,X3)))
<=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_negative_growth_rate_difference) ).
fof(f141,plain,
~ greater(growth_rate(efficient_producers,critical_point(sK0)),growth_rate(first_movers,critical_point(sK0))),
inference(unit_resulting_resolution,[],[f79,f110]) ).
fof(f110,plain,
! [X0] :
( ~ greater(growth_rate(efficient_producers,critical_point(X0)),growth_rate(first_movers,critical_point(X0)))
| ~ environment(X0) ),
inference(equality_resolution,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| critical_point(X0) != X1
| ~ environment(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X1] :
( ( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) )
| critical_point(X0) != X1
| ~ environment(X0) ),
inference(flattening,[],[f41]) ).
fof(f41,plain,
! [X0,X1] :
( ( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) )
| critical_point(X0) != X1
| ~ environment(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( ( critical_point(X0) = X1
& environment(X0) )
=> ( ! [X2] :
( ( greater(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X0,X9] :
( ( critical_point(X0) = X9
& environment(X0) )
=> ( ! [X3] :
( ( greater(X3,X9)
& subpopulations(first_movers,efficient_producers,X0,X3) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) )
& ~ greater(growth_rate(efficient_producers,X9),growth_rate(first_movers,X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
fof(f307,plain,
! [X0] :
( ~ greater_or_equal(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
| ~ greater(X0,sK1)
| greater(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)),zero)
| ~ decreases(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)))
| ~ in_environment(sK0,X0) ),
inference(subsumption_resolution,[],[f304,f79]) ).
fof(f304,plain,
! [X0] :
( ~ decreases(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)))
| ~ greater(X0,sK1)
| greater(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)),zero)
| ~ greater_or_equal(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
| ~ in_environment(sK0,X0)
| ~ environment(sK0) ),
inference(resolution,[],[f106,f81]) ).
fof(f106,plain,
! [X2,X0,X1] :
( ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ decreases(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ greater(X2,X1)
| greater(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ greater_or_equal(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)),zero)
| ~ in_environment(X0,X2)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1,X2] :
( greater(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ decreases(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ greater(X2,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ greater_or_equal(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)),zero)
| ~ in_environment(X0,X2)
| ~ environment(X0) ),
inference(flattening,[],[f67]) ).
fof(f67,plain,
! [X0,X1,X2] :
( greater(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ decreases(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ greater(X2,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ greater_or_equal(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)),zero)
| ~ in_environment(X0,X2)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ( greater(X2,X1)
& greater_or_equal(X1,appear(efficient_producers,X0))
& greater_or_equal(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)),zero)
& in_environment(X0,X2)
& environment(X0) )
=> ( decreases(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
=> greater(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X0,X3,X4] :
( ( greater(X4,X3)
& greater_or_equal(X3,appear(efficient_producers,X0))
& greater_or_equal(difference(growth_rate(first_movers,X4),growth_rate(efficient_producers,X4)),zero)
& in_environment(X0,X4)
& environment(X0) )
=> ( decreases(difference(growth_rate(first_movers,X3),growth_rate(efficient_producers,X3)))
=> greater(difference(growth_rate(first_movers,X3),growth_rate(efficient_producers,X3)),zero) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_decreasing_function) ).
fof(f81,plain,
greater_or_equal(sK1,appear(efficient_producers,sK0)),
inference(cnf_transformation,[],[f74]) ).
fof(f142,plain,
subpopulations(first_movers,efficient_producers,sK0,critical_point(sK0)),
inference(unit_resulting_resolution,[],[f79,f80,f90]) ).
fof(f90,plain,
! [X0] :
( ~ in_environment(X0,critical_point(X0))
| subpopulations(first_movers,efficient_producers,X0,critical_point(X0))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0] :
( subpopulations(first_movers,efficient_producers,X0,critical_point(X0))
| ~ in_environment(X0,critical_point(X0))
| ~ environment(X0) ),
inference(flattening,[],[f49]) ).
fof(f49,plain,
! [X0] :
( subpopulations(first_movers,efficient_producers,X0,critical_point(X0))
| ~ in_environment(X0,critical_point(X0))
| ~ environment(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( ( in_environment(X0,critical_point(X0))
& environment(X0) )
=> subpopulations(first_movers,efficient_producers,X0,critical_point(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_critical_point_means_FM_and_EP) ).
fof(f144,plain,
sP2(sK0,sK1),
inference(unit_resulting_resolution,[],[f118,f142,f112]) ).
fof(f118,plain,
greater_or_equal(critical_point(sK0),sK1),
inference(unit_resulting_resolution,[],[f82,f104]) ).
fof(f104,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| greater_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f83,plain,
~ selection_favors(first_movers,efficient_producers,sK1),
inference(cnf_transformation,[],[f74]) ).
fof(f79,plain,
environment(sK0),
inference(cnf_transformation,[],[f74]) ).
fof(f409,plain,
greater(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)),zero),
inference(unit_resulting_resolution,[],[f79,f80,f82,f81,f269,f405,f106]) ).
fof(f405,plain,
decreases(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1))),
inference(subsumption_resolution,[],[f404,f371]) ).
fof(f371,plain,
~ decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))),
inference(unit_resulting_resolution,[],[f79,f360,f101]) ).
fof(f404,plain,
( decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| decreases(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1))) ),
inference(resolution,[],[f368,f92]) ).
fof(f368,plain,
decreases(difference(founding_rate(first_movers,sK1),founding_rate(efficient_producers,sK1))),
inference(unit_resulting_resolution,[],[f79,f360,f86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MGT034+2 : TPTP v8.1.2. Released v2.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n019.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Apr 30 03:38:59 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (13356)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (13359)WARNING: value z3 for option sas not known
% 0.15/0.38 % (13358)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (13362)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.38 % (13361)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.38 % (13357)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (13360)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (13359)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38 % (13363)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.38 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 % (13363)First to succeed.
% 0.22/0.39 % (13363)Refutation found. Thanks to Tanya!
% 0.22/0.39 % SZS status Theorem for theBenchmark
% 0.22/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.39 % (13363)------------------------------
% 0.22/0.39 % (13363)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.39 % (13363)Termination reason: Refutation
% 0.22/0.39
% 0.22/0.39 % (13363)Memory used [KB]: 941
% 0.22/0.39 % (13363)Time elapsed: 0.015 s
% 0.22/0.39 % (13363)Instructions burned: 23 (million)
% 0.22/0.39 % (13363)------------------------------
% 0.22/0.39 % (13363)------------------------------
% 0.22/0.39 % (13356)Success in time 0.024 s
%------------------------------------------------------------------------------