TSTP Solution File: MGT026+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : MGT026+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 : n022.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 0.15s 0.50s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 12
% Syntax : Number of formulae : 124 ( 15 unt; 0 def)
% Number of atoms : 439 ( 77 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 502 ( 187 ~; 219 |; 71 &)
% ( 2 <=>; 23 =>; 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 : 177 ( 169 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f178,plain,
$false,
inference(unit_resulting_resolution,[],[f66,f80,f78,f65,f154,f173,f64]) ).
fof(f64,plain,
! [X2,X3,X0,X1] :
( zero != cardinality_at_time(X1,X2)
| ~ environment(X0)
| ~ subpopulation(X3,X0,X2)
| ~ greater(cardinality_at_time(X3,X2),zero)
| selection_favors(X3,X1,X2)
| ~ subpopulation(X1,X0,X2) ),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( ~ subpopulation(X1,X0,X2)
| selection_favors(X3,X1,X2)
| zero != cardinality_at_time(X1,X2)
| ~ environment(X0)
| ~ greater(cardinality_at_time(X3,X2),zero)
| ~ subpopulation(X3,X0,X2) ),
inference(rectify,[],[f30]) ).
fof(f30,plain,
! [X2,X1,X0,X3] :
( ~ subpopulation(X1,X2,X0)
| selection_favors(X3,X1,X0)
| zero != cardinality_at_time(X1,X0)
| ~ environment(X2)
| ~ greater(cardinality_at_time(X3,X0),zero)
| ~ subpopulation(X3,X2,X0) ),
inference(flattening,[],[f29]) ).
fof(f29,plain,
! [X2,X3,X1,X0] :
( selection_favors(X3,X1,X0)
| ~ environment(X2)
| ~ subpopulation(X3,X2,X0)
| ~ greater(cardinality_at_time(X3,X0),zero)
| ~ subpopulation(X1,X2,X0)
| zero != cardinality_at_time(X1,X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,plain,
! [X2,X3,X1,X0] :
( ( environment(X2)
& subpopulation(X3,X2,X0)
& greater(cardinality_at_time(X3,X0),zero)
& subpopulation(X1,X2,X0)
& zero = cardinality_at_time(X1,X0) )
=> selection_favors(X3,X1,X0) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X3,X2,X0,X1] :
( ( subpopulation(X2,X0,X3)
& subpopulation(X1,X0,X3)
& environment(X0)
& greater(cardinality_at_time(X1,X3),zero)
& zero = cardinality_at_time(X2,X3) )
=> selection_favors(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp2_favour_members) ).
fof(f173,plain,
zero = cardinality_at_time(first_movers,sK1),
inference(subsumption_resolution,[],[f172,f66]) ).
fof(f172,plain,
( zero = cardinality_at_time(first_movers,sK1)
| ~ environment(sK0) ),
inference(duplicate_literal_removal,[],[f171]) ).
fof(f171,plain,
( zero = cardinality_at_time(first_movers,sK1)
| ~ environment(sK0)
| zero = cardinality_at_time(first_movers,sK1) ),
inference(resolution,[],[f169,f161]) ).
fof(f161,plain,
( subpopulations(first_movers,efficient_producers,sK0,sK1)
| zero = cardinality_at_time(first_movers,sK1) ),
inference(subsumption_resolution,[],[f160,f66]) ).
fof(f160,plain,
( ~ environment(sK0)
| subpopulations(first_movers,efficient_producers,sK0,sK1)
| zero = cardinality_at_time(first_movers,sK1) ),
inference(resolution,[],[f159,f68]) ).
fof(f68,plain,
in_environment(sK0,sK1),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
( in_environment(sK0,sK1)
& greater(sK1,critical_point(sK0))
& environment(sK0)
& ~ selection_favors(efficient_producers,first_movers,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f49,f50]) ).
fof(f50,plain,
( ? [X0,X1] :
( in_environment(X0,X1)
& greater(X1,critical_point(X0))
& environment(X0)
& ~ selection_favors(efficient_producers,first_movers,X1) )
=> ( in_environment(sK0,sK1)
& greater(sK1,critical_point(sK0))
& environment(sK0)
& ~ selection_favors(efficient_producers,first_movers,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f49,plain,
? [X0,X1] :
( in_environment(X0,X1)
& greater(X1,critical_point(X0))
& environment(X0)
& ~ selection_favors(efficient_producers,first_movers,X1) ),
inference(rectify,[],[f34]) ).
fof(f34,plain,
? [X1,X0] :
( in_environment(X1,X0)
& greater(X0,critical_point(X1))
& environment(X1)
& ~ selection_favors(efficient_producers,first_movers,X0) ),
inference(flattening,[],[f33]) ).
fof(f33,plain,
? [X1,X0] :
( ~ selection_favors(efficient_producers,first_movers,X0)
& greater(X0,critical_point(X1))
& environment(X1)
& in_environment(X1,X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,plain,
~ ! [X1,X0] :
( ( greater(X0,critical_point(X1))
& environment(X1)
& in_environment(X1,X0) )
=> selection_favors(efficient_producers,first_movers,X0) ),
inference(rectify,[],[f12]) ).
fof(f12,negated_conjecture,
~ ! [X3,X0] :
( ( environment(X0)
& greater(X3,critical_point(X0))
& in_environment(X0,X3) )
=> selection_favors(efficient_producers,first_movers,X3) ),
inference(negated_conjecture,[],[f11]) ).
fof(f11,conjecture,
! [X3,X0] :
( ( environment(X0)
& greater(X3,critical_point(X0))
& in_environment(X0,X3) )
=> selection_favors(efficient_producers,first_movers,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l8) ).
fof(f159,plain,
! [X0] :
( ~ in_environment(X0,sK1)
| subpopulations(first_movers,efficient_producers,X0,sK1)
| zero = cardinality_at_time(first_movers,sK1)
| ~ environment(X0) ),
inference(resolution,[],[f155,f85]) ).
fof(f85,plain,
( greater(cardinality_at_time(first_movers,sK1),zero)
| zero = cardinality_at_time(first_movers,sK1) ),
inference(resolution,[],[f79,f59]) ).
fof(f59,plain,
! [X0,X1] :
( ~ greater_or_equal(X1,X0)
| X0 = X1
| greater(X1,X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0,X1] :
( ( greater(X1,X0)
| X0 = X1
| ~ greater_or_equal(X1,X0) )
& ( greater_or_equal(X1,X0)
| ( ~ greater(X1,X0)
& X0 != X1 ) ) ),
inference(rectify,[],[f44]) ).
fof(f44,plain,
! [X1,X0] :
( ( greater(X0,X1)
| X0 = X1
| ~ greater_or_equal(X0,X1) )
& ( greater_or_equal(X0,X1)
| ( ~ greater(X0,X1)
& X0 != X1 ) ) ),
inference(flattening,[],[f43]) ).
fof(f43,plain,
! [X1,X0] :
( ( greater(X0,X1)
| X0 = X1
| ~ greater_or_equal(X0,X1) )
& ( greater_or_equal(X0,X1)
| ( ~ greater(X0,X1)
& X0 != X1 ) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f13,plain,
! [X1,X0] :
( ( greater(X0,X1)
| X0 = X1 )
<=> greater_or_equal(X0,X1) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X4,X5] :
( greater_or_equal(X4,X5)
<=> ( greater(X4,X5)
| X4 = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal) ).
fof(f79,plain,
greater_or_equal(cardinality_at_time(first_movers,sK1),zero),
inference(subsumption_resolution,[],[f76,f66]) ).
fof(f76,plain,
( ~ environment(sK0)
| greater_or_equal(cardinality_at_time(first_movers,sK1),zero) ),
inference(resolution,[],[f68,f63]) ).
fof(f63,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| greater_or_equal(cardinality_at_time(first_movers,X1),zero) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( ~ environment(X0)
| greater_or_equal(cardinality_at_time(first_movers,X1),zero)
| ~ in_environment(X0,X1) ),
inference(flattening,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( greater_or_equal(cardinality_at_time(first_movers,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,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] :
( ( environment(X0)
& in_environment(X0,X3) )
=> greater_or_equal(cardinality_at_time(first_movers,X3),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_exist) ).
fof(f155,plain,
! [X0] :
( ~ greater(cardinality_at_time(first_movers,sK1),zero)
| ~ in_environment(X0,sK1)
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,sK1) ),
inference(resolution,[],[f154,f69]) ).
fof(f69,plain,
! [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)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0,X1] :
( ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(rectify,[],[f41]) ).
fof(f41,plain,
! [X1,X0] :
( ~ greater(cardinality_at_time(efficient_producers,X0),zero)
| subpopulations(first_movers,efficient_producers,X1,X0)
| ~ greater(cardinality_at_time(first_movers,X0),zero)
| ~ in_environment(X1,X0)
| ~ environment(X1) ),
inference(flattening,[],[f40]) ).
fof(f40,plain,
! [X1,X0] :
( subpopulations(first_movers,efficient_producers,X1,X0)
| ~ greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ in_environment(X1,X0)
| ~ greater(cardinality_at_time(first_movers,X0),zero)
| ~ environment(X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,plain,
! [X1,X0] :
( ( greater(cardinality_at_time(efficient_producers,X0),zero)
& in_environment(X1,X0)
& greater(cardinality_at_time(first_movers,X0),zero)
& environment(X1) )
=> subpopulations(first_movers,efficient_producers,X1,X0) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X3,X0] :
( ( greater(cardinality_at_time(first_movers,X3),zero)
& environment(X0)
& greater(cardinality_at_time(efficient_producers,X3),zero)
& in_environment(X0,X3) )
=> subpopulations(first_movers,efficient_producers,X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep) ).
fof(f169,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| zero = cardinality_at_time(first_movers,sK1)
| ~ environment(X0) ),
inference(subsumption_resolution,[],[f166,f65]) ).
fof(f166,plain,
! [X0] :
( zero = cardinality_at_time(first_movers,sK1)
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0)
| selection_favors(efficient_producers,first_movers,sK1) ),
inference(resolution,[],[f165,f55]) ).
fof(f55,plain,
! [X2,X3,X0,X1] :
( ~ greater(growth_rate(X3,X1),growth_rate(X2,X1))
| ~ environment(X0)
| selection_favors(X3,X2,X1)
| ~ subpopulations(X2,X3,X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X1,X2,X3] :
( ~ subpopulations(X2,X3,X0,X1)
| ~ environment(X0)
| ~ greater(growth_rate(X3,X1),growth_rate(X2,X1))
| selection_favors(X3,X2,X1) ),
inference(rectify,[],[f32]) ).
fof(f32,plain,
! [X2,X0,X1,X3] :
( ~ subpopulations(X1,X3,X2,X0)
| ~ environment(X2)
| ~ greater(growth_rate(X3,X0),growth_rate(X1,X0))
| selection_favors(X3,X1,X0) ),
inference(flattening,[],[f31]) ).
fof(f31,plain,
! [X1,X0,X3,X2] :
( selection_favors(X3,X1,X0)
| ~ environment(X2)
| ~ subpopulations(X1,X3,X2,X0)
| ~ greater(growth_rate(X3,X0),growth_rate(X1,X0)) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,plain,
! [X1,X0,X3,X2] :
( ( environment(X2)
& subpopulations(X1,X3,X2,X0)
& greater(growth_rate(X3,X0),growth_rate(X1,X0)) )
=> selection_favors(X3,X1,X0) ),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X3,X1,X0,X2] :
( ( 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(f165,plain,
( greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1))
| zero = cardinality_at_time(first_movers,sK1) ),
inference(subsumption_resolution,[],[f164,f139]) ).
fof(f139,plain,
greater(sK1,appear(efficient_producers,sK0)),
inference(backward_demodulation,[],[f67,f136]) ).
fof(f136,plain,
appear(efficient_producers,sK0) = critical_point(sK0),
inference(subsumption_resolution,[],[f135,f80]) ).
fof(f135,plain,
( ~ subpopulation(first_movers,sK0,sK1)
| appear(efficient_producers,sK0) = critical_point(sK0) ),
inference(subsumption_resolution,[],[f134,f66]) ).
fof(f134,plain,
( appear(efficient_producers,sK0) = critical_point(sK0)
| ~ environment(sK0)
| ~ subpopulation(first_movers,sK0,sK1) ),
inference(resolution,[],[f133,f78]) ).
fof(f133,plain,
! [X1] :
( ~ subpopulation(efficient_producers,X1,sK1)
| ~ environment(X1)
| ~ subpopulation(first_movers,X1,sK1)
| appear(efficient_producers,sK0) = critical_point(sK0) ),
inference(subsumption_resolution,[],[f131,f65]) ).
fof(f131,plain,
! [X1] :
( selection_favors(efficient_producers,first_movers,sK1)
| ~ subpopulation(efficient_producers,X1,sK1)
| ~ environment(X1)
| ~ subpopulation(first_movers,X1,sK1)
| appear(efficient_producers,sK0) = critical_point(sK0) ),
inference(duplicate_literal_removal,[],[f128]) ).
fof(f128,plain,
! [X1] :
( ~ subpopulation(efficient_producers,X1,sK1)
| selection_favors(efficient_producers,first_movers,sK1)
| appear(efficient_producers,sK0) = critical_point(sK0)
| appear(efficient_producers,sK0) = critical_point(sK0)
| ~ subpopulation(first_movers,X1,sK1)
| ~ environment(X1) ),
inference(resolution,[],[f123,f99]) ).
fof(f99,plain,
( greater(cardinality_at_time(efficient_producers,sK1),zero)
| appear(efficient_producers,sK0) = critical_point(sK0) ),
inference(subsumption_resolution,[],[f98,f68]) ).
fof(f98,plain,
( greater(cardinality_at_time(efficient_producers,sK1),zero)
| ~ in_environment(sK0,sK1)
| appear(efficient_producers,sK0) = critical_point(sK0) ),
inference(subsumption_resolution,[],[f96,f66]) ).
fof(f96,plain,
( appear(efficient_producers,sK0) = critical_point(sK0)
| greater(cardinality_at_time(efficient_producers,sK1),zero)
| ~ environment(sK0)
| ~ in_environment(sK0,sK1) ),
inference(resolution,[],[f95,f70]) ).
fof(f70,plain,
! [X0,X1] :
( ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ environment(X0)
| ~ in_environment(X0,X1)
| greater(cardinality_at_time(efficient_producers,X1),zero) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ environment(X0)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,X1) ),
inference(flattening,[],[f23]) ).
fof(f23,plain,
! [X1,X0] :
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0)) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
! [X1,X0] :
( ( environment(X0)
& in_environment(X0,X1)
& greater_or_equal(X1,appear(efficient_producers,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/sandbox2/benchmark/theBenchmark.p',t6) ).
fof(f95,plain,
( greater_or_equal(sK1,appear(efficient_producers,sK0))
| appear(efficient_producers,sK0) = critical_point(sK0) ),
inference(resolution,[],[f93,f58]) ).
fof(f58,plain,
! [X0,X1] :
( ~ greater(X1,X0)
| greater_or_equal(X1,X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f93,plain,
( greater(sK1,appear(efficient_producers,sK0))
| appear(efficient_producers,sK0) = critical_point(sK0) ),
inference(resolution,[],[f91,f67]) ).
fof(f91,plain,
! [X0] :
( ~ greater(X0,critical_point(sK0))
| greater(X0,appear(efficient_producers,sK0))
| appear(efficient_producers,sK0) = critical_point(sK0) ),
inference(resolution,[],[f87,f62]) ).
fof(f62,plain,
! [X2,X0,X1] :
( ~ greater(X1,X2)
| ~ greater(X0,X1)
| greater(X0,X2) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ~ greater(X1,X2)
| greater(X0,X2)
| ~ greater(X0,X1) ),
inference(rectify,[],[f39]) ).
fof(f39,plain,
! [X1,X0,X2] :
( ~ greater(X0,X2)
| greater(X1,X2)
| ~ greater(X1,X0) ),
inference(flattening,[],[f38]) ).
fof(f38,plain,
! [X0,X2,X1] :
( greater(X1,X2)
| ~ greater(X1,X0)
| ~ greater(X0,X2) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0,X2,X1] :
( ( greater(X1,X0)
& greater(X0,X2) )
=> greater(X1,X2) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X5,X4,X6] :
( ( greater(X4,X5)
& greater(X5,X6) )
=> greater(X4,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_transitivity) ).
fof(f87,plain,
( greater(critical_point(sK0),appear(efficient_producers,sK0))
| appear(efficient_producers,sK0) = critical_point(sK0) ),
inference(resolution,[],[f74,f59]) ).
fof(f74,plain,
greater_or_equal(critical_point(sK0),appear(efficient_producers,sK0)),
inference(resolution,[],[f66,f56]) ).
fof(f56,plain,
! [X0] :
( ~ environment(X0)
| greater_or_equal(critical_point(X0),appear(efficient_producers,X0)) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,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/sandbox2/benchmark/theBenchmark.p',mp_critical_point_after_EP) ).
fof(f123,plain,
! [X2,X3] :
( ~ greater(cardinality_at_time(X3,sK1),zero)
| ~ subpopulation(first_movers,X2,sK1)
| appear(efficient_producers,sK0) = critical_point(sK0)
| ~ environment(X2)
| selection_favors(X3,first_movers,sK1)
| ~ subpopulation(X3,X2,sK1) ),
inference(trivial_inequality_removal,[],[f122]) ).
fof(f122,plain,
! [X2,X3] :
( zero != zero
| ~ greater(cardinality_at_time(X3,sK1),zero)
| appear(efficient_producers,sK0) = critical_point(sK0)
| ~ environment(X2)
| ~ subpopulation(X3,X2,sK1)
| selection_favors(X3,first_movers,sK1)
| ~ subpopulation(first_movers,X2,sK1) ),
inference(superposition,[],[f64,f117]) ).
fof(f117,plain,
( zero = cardinality_at_time(first_movers,sK1)
| appear(efficient_producers,sK0) = critical_point(sK0) ),
inference(subsumption_resolution,[],[f116,f66]) ).
fof(f116,plain,
( zero = cardinality_at_time(first_movers,sK1)
| appear(efficient_producers,sK0) = critical_point(sK0)
| ~ environment(sK0) ),
inference(duplicate_literal_removal,[],[f115]) ).
fof(f115,plain,
( appear(efficient_producers,sK0) = critical_point(sK0)
| appear(efficient_producers,sK0) = critical_point(sK0)
| zero = cardinality_at_time(first_movers,sK1)
| zero = cardinality_at_time(first_movers,sK1)
| ~ environment(sK0) ),
inference(resolution,[],[f113,f106]) ).
fof(f106,plain,
( subpopulations(first_movers,efficient_producers,sK0,sK1)
| appear(efficient_producers,sK0) = critical_point(sK0)
| zero = cardinality_at_time(first_movers,sK1) ),
inference(subsumption_resolution,[],[f105,f66]) ).
fof(f105,plain,
( appear(efficient_producers,sK0) = critical_point(sK0)
| zero = cardinality_at_time(first_movers,sK1)
| ~ environment(sK0)
| subpopulations(first_movers,efficient_producers,sK0,sK1) ),
inference(resolution,[],[f104,f68]) ).
fof(f104,plain,
! [X0] :
( ~ in_environment(X0,sK1)
| zero = cardinality_at_time(first_movers,sK1)
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,sK1)
| appear(efficient_producers,sK0) = critical_point(sK0) ),
inference(resolution,[],[f100,f85]) ).
fof(f100,plain,
! [X0] :
( ~ greater(cardinality_at_time(first_movers,sK1),zero)
| subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0)
| appear(efficient_producers,sK0) = critical_point(sK0)
| ~ in_environment(X0,sK1) ),
inference(resolution,[],[f99,f69]) ).
fof(f113,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| zero = cardinality_at_time(first_movers,sK1)
| ~ environment(X0)
| appear(efficient_producers,sK0) = critical_point(sK0) ),
inference(subsumption_resolution,[],[f110,f65]) ).
fof(f110,plain,
! [X0] :
( zero = cardinality_at_time(first_movers,sK1)
| selection_favors(efficient_producers,first_movers,sK1)
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0)
| appear(efficient_producers,sK0) = critical_point(sK0) ),
inference(resolution,[],[f109,f55]) ).
fof(f109,plain,
( greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1))
| appear(efficient_producers,sK0) = critical_point(sK0)
| zero = cardinality_at_time(first_movers,sK1) ),
inference(subsumption_resolution,[],[f108,f66]) ).
fof(f108,plain,
( ~ environment(sK0)
| appear(efficient_producers,sK0) = critical_point(sK0)
| greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1))
| zero = cardinality_at_time(first_movers,sK1) ),
inference(subsumption_resolution,[],[f107,f67]) ).
fof(f107,plain,
( appear(efficient_producers,sK0) = critical_point(sK0)
| ~ greater(sK1,critical_point(sK0))
| ~ environment(sK0)
| zero = cardinality_at_time(first_movers,sK1)
| greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1)) ),
inference(resolution,[],[f106,f73]) ).
fof(f73,plain,
! [X2,X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,critical_point(X0))
| ~ environment(X0) ),
inference(equality_resolution,[],[f60]) ).
fof(f60,plain,
! [X2,X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,X1)
| critical_point(X0) != X1 ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X1] :
( ~ environment(X0)
| ( ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& ! [X2] :
( ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,X1) ) )
| critical_point(X0) != X1 ),
inference(rectify,[],[f36]) ).
fof(f36,plain,
! [X1,X0] :
( ~ environment(X1)
| ( ~ greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
& ! [X2] :
( ~ subpopulations(first_movers,efficient_producers,X1,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,X0) ) )
| critical_point(X1) != X0 ),
inference(flattening,[],[f35]) ).
fof(f35,plain,
! [X1,X0] :
( ( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,X0)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) )
& ~ greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) )
| critical_point(X1) != X0
| ~ environment(X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,plain,
! [X1,X0] :
( ( critical_point(X1) = X0
& environment(X1) )
=> ( ! [X2] :
( ( greater(X2,X0)
& subpopulations(first_movers,efficient_producers,X1,X2) )
=> greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
& ~ greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X7,X0] :
( ( environment(X0)
& critical_point(X0) = X7 )
=> ( ! [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/sandbox2/benchmark/theBenchmark.p',d1) ).
fof(f67,plain,
greater(sK1,critical_point(sK0)),
inference(cnf_transformation,[],[f51]) ).
fof(f164,plain,
( greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1))
| ~ greater(sK1,appear(efficient_producers,sK0))
| zero = cardinality_at_time(first_movers,sK1) ),
inference(forward_demodulation,[],[f163,f136]) ).
fof(f163,plain,
( greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1))
| zero = cardinality_at_time(first_movers,sK1)
| ~ greater(sK1,critical_point(sK0)) ),
inference(subsumption_resolution,[],[f162,f66]) ).
fof(f162,plain,
( greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1))
| ~ environment(sK0)
| zero = cardinality_at_time(first_movers,sK1)
| ~ greater(sK1,critical_point(sK0)) ),
inference(resolution,[],[f161,f73]) ).
fof(f154,plain,
greater(cardinality_at_time(efficient_producers,sK1),zero),
inference(subsumption_resolution,[],[f153,f68]) ).
fof(f153,plain,
( greater(cardinality_at_time(efficient_producers,sK1),zero)
| ~ in_environment(sK0,sK1) ),
inference(subsumption_resolution,[],[f151,f66]) ).
fof(f151,plain,
( ~ environment(sK0)
| ~ in_environment(sK0,sK1)
| greater(cardinality_at_time(efficient_producers,sK1),zero) ),
inference(resolution,[],[f142,f70]) ).
fof(f142,plain,
greater_or_equal(sK1,appear(efficient_producers,sK0)),
inference(backward_demodulation,[],[f82,f136]) ).
fof(f82,plain,
greater_or_equal(sK1,critical_point(sK0)),
inference(resolution,[],[f67,f58]) ).
fof(f65,plain,
~ selection_favors(efficient_producers,first_movers,sK1),
inference(cnf_transformation,[],[f51]) ).
fof(f78,plain,
subpopulation(efficient_producers,sK0,sK1),
inference(subsumption_resolution,[],[f77,f66]) ).
fof(f77,plain,
( subpopulation(efficient_producers,sK0,sK1)
| ~ environment(sK0) ),
inference(resolution,[],[f68,f53]) ).
fof(f53,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| subpopulation(efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( ~ environment(X0)
| ~ in_environment(X0,X1)
| ( subpopulation(first_movers,X0,X1)
& subpopulation(efficient_producers,X0,X1) ) ),
inference(flattening,[],[f25]) ).
fof(f25,plain,
! [X1,X0] :
( ( subpopulation(first_movers,X0,X1)
& subpopulation(efficient_producers,X0,X1) )
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,plain,
! [X1,X0] :
( ( environment(X0)
& in_environment(X0,X1) )
=> ( subpopulation(first_movers,X0,X1)
& subpopulation(efficient_producers,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/sandbox2/benchmark/theBenchmark.p',mp_subpopulations) ).
fof(f80,plain,
subpopulation(first_movers,sK0,sK1),
inference(subsumption_resolution,[],[f75,f66]) ).
fof(f75,plain,
( ~ environment(sK0)
| subpopulation(first_movers,sK0,sK1) ),
inference(resolution,[],[f68,f54]) ).
fof(f54,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| subpopulation(first_movers,X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f66,plain,
environment(sK0),
inference(cnf_transformation,[],[f51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : MGT026+1 : TPTP v8.1.0. Released v2.0.0.
% 0.05/0.10 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.10/0.30 % Computer : n022.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue Aug 30 03:15:56 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.15/0.46 % (16529)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.15/0.48 % (16538)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)
% 0.15/0.48 % (16546)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.15/0.48 % (16545)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)
% 0.15/0.49 % (16530)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.15/0.49 % (16537)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)
% 0.15/0.49 % (16537)Instruction limit reached!
% 0.15/0.49 % (16537)------------------------------
% 0.15/0.49 % (16537)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.15/0.49 % (16523)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.15/0.49 % (16537)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.15/0.49 % (16537)Termination reason: Unknown
% 0.15/0.49 % (16537)Termination phase: Saturation
% 0.15/0.49
% 0.15/0.49 % (16537)Memory used [KB]: 5884
% 0.15/0.49 % (16537)Time elapsed: 0.003 s
% 0.15/0.49 % (16537)Instructions burned: 3 (million)
% 0.15/0.49 % (16546)First to succeed.
% 0.15/0.49 % (16537)------------------------------
% 0.15/0.49 % (16537)------------------------------
% 0.15/0.49 % (16538)Instruction limit reached!
% 0.15/0.49 % (16538)------------------------------
% 0.15/0.49 % (16538)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.15/0.49 % (16538)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.15/0.49 % (16538)Termination reason: Unknown
% 0.15/0.49 % (16538)Termination phase: Saturation
% 0.15/0.49
% 0.15/0.49 % (16538)Memory used [KB]: 6012
% 0.15/0.49 % (16538)Time elapsed: 0.075 s
% 0.15/0.49 % (16538)Instructions burned: 7 (million)
% 0.15/0.49 % (16538)------------------------------
% 0.15/0.49 % (16538)------------------------------
% 0.15/0.50 % (16524)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.15/0.50 % (16528)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.15/0.50 % (16526)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.15/0.50 % (16524)Refutation not found, incomplete strategy% (16524)------------------------------
% 0.15/0.50 % (16524)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.15/0.50 % (16524)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.15/0.50 % (16524)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.50
% 0.15/0.50 % (16524)Memory used [KB]: 6012
% 0.15/0.50 % (16524)Time elapsed: 0.131 s
% 0.15/0.50 % (16524)Instructions burned: 3 (million)
% 0.15/0.50 % (16524)------------------------------
% 0.15/0.50 % (16524)------------------------------
% 0.15/0.50 % (16526)Refutation not found, incomplete strategy% (16526)------------------------------
% 0.15/0.50 % (16526)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.15/0.50 % (16526)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.15/0.50 % (16526)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.50
% 0.15/0.50 % (16526)Memory used [KB]: 6012
% 0.15/0.50 % (16526)Time elapsed: 0.127 s
% 0.15/0.50 % (16526)Instructions burned: 3 (million)
% 0.15/0.50 % (16526)------------------------------
% 0.15/0.50 % (16526)------------------------------
% 0.15/0.50 % (16528)Refutation not found, incomplete strategy% (16528)------------------------------
% 0.15/0.50 % (16528)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.15/0.50 % (16528)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.15/0.50 % (16528)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.50
% 0.15/0.50 % (16528)Memory used [KB]: 1535
% 0.15/0.50 % (16528)Time elapsed: 0.132 s
% 0.15/0.50 % (16528)Instructions burned: 4 (million)
% 0.15/0.50 % (16528)------------------------------
% 0.15/0.50 % (16528)------------------------------
% 0.15/0.50 % (16530)Also succeeded, but the first one will report.
% 0.15/0.50 % (16546)Refutation found. Thanks to Tanya!
% 0.15/0.50 % SZS status Theorem for theBenchmark
% 0.15/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.50 % (16546)------------------------------
% 0.15/0.50 % (16546)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.15/0.50 % (16546)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.15/0.50 % (16546)Termination reason: Refutation
% 0.15/0.50
% 0.15/0.50 % (16546)Memory used [KB]: 1535
% 0.15/0.50 % (16546)Time elapsed: 0.070 s
% 0.15/0.50 % (16546)Instructions burned: 8 (million)
% 0.15/0.50 % (16546)------------------------------
% 0.15/0.50 % (16546)------------------------------
% 0.15/0.50 % (16522)Success in time 0.192 s
%------------------------------------------------------------------------------