TSTP Solution File: MGT026+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : MGT026+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 : n004.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 13:54:09 EDT 2024
% Result : Theorem 0.15s 0.39s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 12
% Syntax : Number of formulae : 103 ( 16 unt; 0 def)
% Number of atoms : 343 ( 55 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 379 ( 139 ~; 158 |; 59 &)
% ( 2 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 136 ( 130 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f157,plain,
$false,
inference(subsumption_resolution,[],[f156,f46]) ).
fof(f46,plain,
greater(sK1,critical_point(sK0)),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
( ~ selection_favors(efficient_producers,first_movers,sK1)
& greater(sK1,critical_point(sK0))
& in_environment(sK0,sK1)
& environment(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f22,f40]) ).
fof(f40,plain,
( ? [X0,X1] :
( ~ selection_favors(efficient_producers,first_movers,X1)
& greater(X1,critical_point(X0))
& in_environment(X0,X1)
& environment(X0) )
=> ( ~ selection_favors(efficient_producers,first_movers,sK1)
& greater(sK1,critical_point(sK0))
& in_environment(sK0,sK1)
& environment(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
? [X0,X1] :
( ~ selection_favors(efficient_producers,first_movers,X1)
& greater(X1,critical_point(X0))
& in_environment(X0,X1)
& environment(X0) ),
inference(flattening,[],[f21]) ).
fof(f21,plain,
? [X0,X1] :
( ~ selection_favors(efficient_producers,first_movers,X1)
& greater(X1,critical_point(X0))
& in_environment(X0,X1)
& environment(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,plain,
~ ! [X0,X1] :
( ( greater(X1,critical_point(X0))
& in_environment(X0,X1)
& environment(X0) )
=> selection_favors(efficient_producers,first_movers,X1) ),
inference(rectify,[],[f12]) ).
fof(f12,negated_conjecture,
~ ! [X0,X3] :
( ( greater(X3,critical_point(X0))
& in_environment(X0,X3)
& environment(X0) )
=> selection_favors(efficient_producers,first_movers,X3) ),
inference(negated_conjecture,[],[f11]) ).
fof(f11,conjecture,
! [X0,X3] :
( ( greater(X3,critical_point(X0))
& in_environment(X0,X3)
& environment(X0) )
=> selection_favors(efficient_producers,first_movers,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l8) ).
fof(f156,plain,
~ greater(sK1,critical_point(sK0)),
inference(forward_demodulation,[],[f153,f147]) ).
fof(f147,plain,
critical_point(sK0) = appear(efficient_producers,sK0),
inference(unit_resulting_resolution,[],[f140,f94]) ).
fof(f94,plain,
( greater(cardinality_at_time(efficient_producers,sK1),zero)
| critical_point(sK0) = appear(efficient_producers,sK0) ),
inference(subsumption_resolution,[],[f93,f44]) ).
fof(f44,plain,
environment(sK0),
inference(cnf_transformation,[],[f41]) ).
fof(f93,plain,
( greater(cardinality_at_time(efficient_producers,sK1),zero)
| ~ environment(sK0)
| critical_point(sK0) = appear(efficient_producers,sK0) ),
inference(subsumption_resolution,[],[f91,f45]) ).
fof(f45,plain,
in_environment(sK0,sK1),
inference(cnf_transformation,[],[f41]) ).
fof(f91,plain,
( greater(cardinality_at_time(efficient_producers,sK1),zero)
| ~ in_environment(sK0,sK1)
| ~ environment(sK0)
| critical_point(sK0) = appear(efficient_producers,sK0) ),
inference(resolution,[],[f48,f87]) ).
fof(f87,plain,
( greater_or_equal(sK1,appear(efficient_producers,sK0))
| critical_point(sK0) = appear(efficient_producers,sK0) ),
inference(resolution,[],[f85,f57]) ).
fof(f57,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| greater_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,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,[],[f42]) ).
fof(f42,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,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( greater_or_equal(X0,X1)
<=> ( X0 = X1
| greater(X0,X1) ) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X4,X5] :
( greater_or_equal(X4,X5)
<=> ( X4 = X5
| greater(X4,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal) ).
fof(f85,plain,
( greater(sK1,appear(efficient_producers,sK0))
| critical_point(sK0) = appear(efficient_producers,sK0) ),
inference(resolution,[],[f82,f46]) ).
fof(f82,plain,
! [X0] :
( ~ greater(X0,critical_point(sK0))
| greater(X0,appear(efficient_producers,sK0))
| critical_point(sK0) = appear(efficient_producers,sK0) ),
inference(resolution,[],[f75,f59]) ).
fof(f59,plain,
! [X2,X0,X1] :
( ~ greater(X1,X2)
| greater(X0,X2)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1,X2] :
( greater(X0,X2)
| ~ greater(X1,X2)
| ~ greater(X0,X1) ),
inference(flattening,[],[f34]) ).
fof(f34,plain,
! [X0,X1,X2] :
( greater(X0,X2)
| ~ greater(X1,X2)
| ~ greater(X0,X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( greater(X1,X2)
& greater(X0,X1) )
=> greater(X0,X2) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X4,X5,X6] :
( ( greater(X5,X6)
& greater(X4,X5) )
=> greater(X4,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_transitivity) ).
fof(f75,plain,
( greater(critical_point(sK0),appear(efficient_producers,sK0))
| critical_point(sK0) = appear(efficient_producers,sK0) ),
inference(resolution,[],[f56,f67]) ).
fof(f67,plain,
greater_or_equal(critical_point(sK0),appear(efficient_producers,sK0)),
inference(unit_resulting_resolution,[],[f44,f51]) ).
fof(f51,plain,
! [X0] :
( ~ environment(X0)
| greater_or_equal(critical_point(X0),appear(efficient_producers,X0)) ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0] :
( greater_or_equal(critical_point(X0),appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( environment(X0)
=> greater_or_equal(critical_point(X0),appear(efficient_producers,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_critical_point_after_EP) ).
fof(f56,plain,
! [X0,X1] :
( ~ greater_or_equal(X0,X1)
| greater(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f43]) ).
fof(f48,plain,
! [X0,X1] :
( ~ greater_or_equal(X1,appear(efficient_producers,X0))
| greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f23]) ).
fof(f23,plain,
! [X0,X1] :
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,plain,
! [X0,X1] :
( ( greater_or_equal(X1,appear(efficient_producers,X0))
& in_environment(X0,X1)
& environment(X0) )
=> greater(cardinality_at_time(efficient_producers,X1),zero) ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X0,X3] :
( ( greater_or_equal(X3,appear(efficient_producers,X0))
& in_environment(X0,X3)
& environment(X0) )
=> greater(cardinality_at_time(efficient_producers,X3),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6) ).
fof(f140,plain,
~ greater(cardinality_at_time(efficient_producers,sK1),zero),
inference(unit_resulting_resolution,[],[f44,f71,f47,f69,f131,f60]) ).
fof(f60,plain,
! [X2,X3,X0,X1] :
( ~ subpopulation(X2,X0,X3)
| zero != cardinality_at_time(X2,X3)
| ~ greater(cardinality_at_time(X1,X3),zero)
| selection_favors(X1,X2,X3)
| ~ subpopulation(X1,X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0,X1,X2,X3] :
( selection_favors(X1,X2,X3)
| zero != cardinality_at_time(X2,X3)
| ~ greater(cardinality_at_time(X1,X3),zero)
| ~ subpopulation(X2,X0,X3)
| ~ subpopulation(X1,X0,X3)
| ~ environment(X0) ),
inference(flattening,[],[f36]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( selection_favors(X1,X2,X3)
| zero != cardinality_at_time(X2,X3)
| ~ greater(cardinality_at_time(X1,X3),zero)
| ~ subpopulation(X2,X0,X3)
| ~ subpopulation(X1,X0,X3)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1,X2,X3] :
( ( zero = cardinality_at_time(X2,X3)
& greater(cardinality_at_time(X1,X3),zero)
& subpopulation(X2,X0,X3)
& subpopulation(X1,X0,X3)
& environment(X0) )
=> selection_favors(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp2_favour_members) ).
fof(f131,plain,
zero = cardinality_at_time(first_movers,sK1),
inference(subsumption_resolution,[],[f130,f128]) ).
fof(f128,plain,
( greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1))
| zero = cardinality_at_time(first_movers,sK1) ),
inference(subsumption_resolution,[],[f127,f44]) ).
fof(f127,plain,
( zero = cardinality_at_time(first_movers,sK1)
| greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1))
| ~ environment(sK0) ),
inference(subsumption_resolution,[],[f125,f46]) ).
fof(f125,plain,
( zero = cardinality_at_time(first_movers,sK1)
| ~ greater(sK1,critical_point(sK0))
| greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1))
| ~ environment(sK0) ),
inference(resolution,[],[f123,f62]) ).
fof(f62,plain,
! [X2,X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(X2,critical_point(X0))
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ environment(X0) ),
inference(equality_resolution,[],[f50]) ).
fof(f50,plain,
! [X2,X0,X1] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| critical_point(X0) != X1
| ~ environment(X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,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,[],[f25]) ).
fof(f25,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,[],[f15]) ).
fof(f15,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,[],[f9]) ).
fof(f9,axiom,
! [X0,X7] :
( ( critical_point(X0) = X7
& environment(X0) )
=> ( ! [X3] :
( ( greater(X3,X7)
& subpopulations(first_movers,efficient_producers,X0,X3) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) )
& ~ greater(growth_rate(efficient_producers,X7),growth_rate(first_movers,X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
fof(f123,plain,
( subpopulations(first_movers,efficient_producers,sK0,sK1)
| zero = cardinality_at_time(first_movers,sK1) ),
inference(subsumption_resolution,[],[f120,f79]) ).
fof(f79,plain,
( greater(cardinality_at_time(first_movers,sK1),zero)
| zero = cardinality_at_time(first_movers,sK1) ),
inference(resolution,[],[f77,f56]) ).
fof(f77,plain,
greater_or_equal(cardinality_at_time(first_movers,sK1),zero),
inference(unit_resulting_resolution,[],[f44,f45,f52]) ).
fof(f52,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| greater_or_equal(cardinality_at_time(first_movers,X1),zero)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1] :
( greater_or_equal(cardinality_at_time(first_movers,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( greater_or_equal(cardinality_at_time(first_movers,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0,X1] :
( ( in_environment(X0,X1)
& environment(X0) )
=> greater_or_equal(cardinality_at_time(first_movers,X1),zero) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X0,X3] :
( ( in_environment(X0,X3)
& environment(X0) )
=> greater_or_equal(cardinality_at_time(first_movers,X3),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_exist) ).
fof(f120,plain,
( zero = cardinality_at_time(first_movers,sK1)
| ~ greater(cardinality_at_time(first_movers,sK1),zero)
| subpopulations(first_movers,efficient_producers,sK0,sK1) ),
inference(resolution,[],[f119,f99]) ).
fof(f99,plain,
( ~ greater(cardinality_at_time(efficient_producers,sK1),zero)
| ~ greater(cardinality_at_time(first_movers,sK1),zero)
| subpopulations(first_movers,efficient_producers,sK0,sK1) ),
inference(subsumption_resolution,[],[f98,f44]) ).
fof(f98,plain,
( ~ greater(cardinality_at_time(efficient_producers,sK1),zero)
| ~ greater(cardinality_at_time(first_movers,sK1),zero)
| subpopulations(first_movers,efficient_producers,sK0,sK1)
| ~ environment(sK0) ),
inference(resolution,[],[f53,f45]) ).
fof(f53,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f30]) ).
fof(f30,plain,
! [X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( ( greater(cardinality_at_time(efficient_producers,X1),zero)
& greater(cardinality_at_time(first_movers,X1),zero)
& in_environment(X0,X1)
& environment(X0) )
=> subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X0,X3] :
( ( greater(cardinality_at_time(efficient_producers,X3),zero)
& greater(cardinality_at_time(first_movers,X3),zero)
& in_environment(X0,X3)
& environment(X0) )
=> subpopulations(first_movers,efficient_producers,X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep) ).
fof(f119,plain,
( greater(cardinality_at_time(efficient_producers,sK1),zero)
| zero = cardinality_at_time(first_movers,sK1) ),
inference(subsumption_resolution,[],[f118,f45]) ).
fof(f118,plain,
( greater(cardinality_at_time(efficient_producers,sK1),zero)
| ~ in_environment(sK0,sK1)
| zero = cardinality_at_time(first_movers,sK1) ),
inference(resolution,[],[f116,f65]) ).
fof(f65,plain,
greater_or_equal(sK1,critical_point(sK0)),
inference(unit_resulting_resolution,[],[f46,f57]) ).
fof(f116,plain,
! [X0] :
( ~ greater_or_equal(X0,critical_point(sK0))
| greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ in_environment(sK0,X0)
| zero = cardinality_at_time(first_movers,sK1) ),
inference(subsumption_resolution,[],[f114,f44]) ).
fof(f114,plain,
! [X0] :
( ~ greater_or_equal(X0,critical_point(sK0))
| greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ in_environment(sK0,X0)
| ~ environment(sK0)
| zero = cardinality_at_time(first_movers,sK1) ),
inference(superposition,[],[f48,f108]) ).
fof(f108,plain,
( critical_point(sK0) = appear(efficient_producers,sK0)
| zero = cardinality_at_time(first_movers,sK1) ),
inference(subsumption_resolution,[],[f107,f105]) ).
fof(f105,plain,
( greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1))
| zero = cardinality_at_time(first_movers,sK1)
| critical_point(sK0) = appear(efficient_producers,sK0) ),
inference(subsumption_resolution,[],[f104,f44]) ).
fof(f104,plain,
( critical_point(sK0) = appear(efficient_producers,sK0)
| zero = cardinality_at_time(first_movers,sK1)
| greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1))
| ~ environment(sK0) ),
inference(subsumption_resolution,[],[f102,f46]) ).
fof(f102,plain,
( critical_point(sK0) = appear(efficient_producers,sK0)
| zero = cardinality_at_time(first_movers,sK1)
| ~ greater(sK1,critical_point(sK0))
| greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1))
| ~ environment(sK0) ),
inference(resolution,[],[f101,f62]) ).
fof(f101,plain,
( subpopulations(first_movers,efficient_producers,sK0,sK1)
| critical_point(sK0) = appear(efficient_producers,sK0)
| zero = cardinality_at_time(first_movers,sK1) ),
inference(resolution,[],[f100,f79]) ).
fof(f100,plain,
( ~ greater(cardinality_at_time(first_movers,sK1),zero)
| subpopulations(first_movers,efficient_producers,sK0,sK1)
| critical_point(sK0) = appear(efficient_producers,sK0) ),
inference(resolution,[],[f99,f94]) ).
fof(f107,plain,
( critical_point(sK0) = appear(efficient_producers,sK0)
| zero = cardinality_at_time(first_movers,sK1)
| ~ greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1)) ),
inference(subsumption_resolution,[],[f106,f44]) ).
fof(f106,plain,
( critical_point(sK0) = appear(efficient_producers,sK0)
| zero = cardinality_at_time(first_movers,sK1)
| ~ greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1))
| ~ environment(sK0) ),
inference(subsumption_resolution,[],[f103,f47]) ).
fof(f103,plain,
( critical_point(sK0) = appear(efficient_producers,sK0)
| zero = cardinality_at_time(first_movers,sK1)
| ~ greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1))
| selection_favors(efficient_producers,first_movers,sK1)
| ~ environment(sK0) ),
inference(resolution,[],[f101,f61]) ).
fof(f61,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,[],[f39]) ).
fof(f39,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,[],[f38]) ).
fof(f38,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/sandbox/benchmark/theBenchmark.p',mp1_high_growth_rates) ).
fof(f130,plain,
( zero = cardinality_at_time(first_movers,sK1)
| ~ greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1)) ),
inference(subsumption_resolution,[],[f129,f44]) ).
fof(f129,plain,
( zero = cardinality_at_time(first_movers,sK1)
| ~ greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1))
| ~ environment(sK0) ),
inference(subsumption_resolution,[],[f126,f47]) ).
fof(f126,plain,
( zero = cardinality_at_time(first_movers,sK1)
| ~ greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1))
| selection_favors(efficient_producers,first_movers,sK1)
| ~ environment(sK0) ),
inference(resolution,[],[f123,f61]) ).
fof(f69,plain,
subpopulation(first_movers,sK0,sK1),
inference(unit_resulting_resolution,[],[f44,f45,f54]) ).
fof(f54,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| subpopulation(first_movers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1] :
( ( subpopulation(efficient_producers,X0,X1)
& subpopulation(first_movers,X0,X1) )
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f32]) ).
fof(f32,plain,
! [X0,X1] :
( ( subpopulation(efficient_producers,X0,X1)
& subpopulation(first_movers,X0,X1) )
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1] :
( ( in_environment(X0,X1)
& environment(X0) )
=> ( subpopulation(efficient_producers,X0,X1)
& subpopulation(first_movers,X0,X1) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X0,X3] :
( ( in_environment(X0,X3)
& environment(X0) )
=> ( subpopulation(efficient_producers,X0,X3)
& subpopulation(first_movers,X0,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_subpopulations) ).
fof(f47,plain,
~ selection_favors(efficient_producers,first_movers,sK1),
inference(cnf_transformation,[],[f41]) ).
fof(f71,plain,
subpopulation(efficient_producers,sK0,sK1),
inference(unit_resulting_resolution,[],[f44,f45,f55]) ).
fof(f55,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| subpopulation(efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f153,plain,
~ greater(sK1,appear(efficient_producers,sK0)),
inference(unit_resulting_resolution,[],[f149,f57]) ).
fof(f149,plain,
~ greater_or_equal(sK1,appear(efficient_producers,sK0)),
inference(unit_resulting_resolution,[],[f44,f45,f140,f48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : MGT026+1 : TPTP v8.1.2. Released v2.0.0.
% 0.14/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n004.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Apr 30 03:32:48 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (10335)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (10338)WARNING: value z3 for option sas not known
% 0.15/0.38 % (10336)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (10337)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 % (10339)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (10338)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 % (10340)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 % (10341)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 % (10342)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]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 % (10342)First to succeed.
% 0.15/0.38 TRYING [3]
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 % (10342)Refutation found. Thanks to Tanya!
% 0.15/0.39 % SZS status Theorem for theBenchmark
% 0.15/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.39 % (10342)------------------------------
% 0.15/0.39 % (10342)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.39 % (10342)Termination reason: Refutation
% 0.15/0.39
% 0.15/0.39 % (10342)Memory used [KB]: 845
% 0.15/0.39 % (10342)Time elapsed: 0.009 s
% 0.15/0.39 % (10342)Instructions burned: 11 (million)
% 0.15/0.39 % (10342)------------------------------
% 0.15/0.39 % (10342)------------------------------
% 0.15/0.39 % (10335)Success in time 0.025 s
%------------------------------------------------------------------------------