%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : MGT039+2 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:02:39 PM UTC 2026
% Result : Theorem 0.14s 0.47s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 37
% Syntax : Number of formulae : 286 ( 31 unt; 19 def)
% Number of atoms : 832 ( 41 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 991 ( 445 ~; 454 |; 53 &)
% ( 20 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 31 ( 29 usr; 20 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 186 ( 0 sgn 179 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2,X3] :
( ( environment(X0)
& subpopulations(X1,X2,X0,X3)
& greater(growth_rate(X2,X3),growth_rate(X1,X3)) )
=> selection_favors(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp1_high_growth_rates) ).
fof(f2,axiom,
! [X0,X1,X2,X3] :
( ( environment(X0)
& subpopulation(X1,X0,X3)
& subpopulation(X2,X0,X3)
& greater(cardinality_at_time(X1,X3),zero)
& cardinality_at_time(X2,X3) = zero )
=> selection_favors(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp2_favour_members) ).
fof(f3,axiom,
! [X0] :
( ( observational_period(X0)
& propagation_strategy(first_movers)
& propagation_strategy(efficient_producers)
& ! [X1] :
( ( environment(X1)
& in_environment(X0,X1) )
=> selection_favors(efficient_producers,first_movers,end_time(X1)) ) )
=> selection_favors(efficient_producers,first_movers,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp3_favoured_trategy) ).
fof(f4,axiom,
! [X0] :
( ( observational_period(X0)
& slow_change(X0) )
=> ! [X1] :
( ( environment(X1)
& in_environment(X0,X1) )
=> ? [X2] :
( in_environment(X1,X2)
& greater(X2,critical_point(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp4_critical_point) ).
fof(f5,axiom,
propagation_strategy(first_movers),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_organizational_sets1) ).
fof(f6,axiom,
propagation_strategy(efficient_producers),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_organizational_sets2) ).
fof(f7,axiom,
! [X0,X1] :
( ( environment(X0)
& greater_or_equal(X1,start_time(X0))
& greater_or_equal(end_time(X0),X1) )
=> in_environment(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_in_environment) ).
fof(f8,axiom,
! [X0,X1] :
( ( environment(X0)
& in_environment(X0,X1) )
=> greater_or_equal(end_time(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_environment_end_point) ).
fof(f9,axiom,
! [X0,X1] :
( ( environment(X0)
& in_environment(X0,X1)
& greater(cardinality_at_time(first_movers,X1),zero)
& greater(cardinality_at_time(efficient_producers,X1),zero) )
=> subpopulations(first_movers,efficient_producers,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_contains_FM_and_EP) ).
fof(f10,axiom,
! [X0,X1] :
( ( environment(X0)
& in_environment(X0,X1) )
=> greater_or_equal(cardinality_at_time(first_movers,X1),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_exist) ).
fof(f11,axiom,
! [X0,X1] :
( ( environment(X0)
& in_environment(X0,X1) )
=> ( subpopulation(first_movers,X0,X1)
& subpopulation(efficient_producers,X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_subpopulations) ).
fof(f12,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(f13,axiom,
! [X0] :
( environment(X0)
=> greater_or_equal(critical_point(X0),start_time(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_of_critical_point) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( greater(X0,X1)
& greater(X1,X2) )
=> greater(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_transitivity) ).
fof(f16,axiom,
! [X0,X1] :
( greater_or_equal(X0,X1)
<=> ( greater(X0,X1)
| X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal) ).
fof(f17,axiom,
! [X0,X1] :
( ( environment(X0)
& X1 = critical_point(X0) )
=> ( ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& ! [X2] :
( ( subpopulations(first_movers,efficient_producers,X0,X2)
& greater(X2,X1) )
=> greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
fof(f18,axiom,
! [X0,X1] :
( ( environment(X0)
& in_environment(X0,X1)
& greater_or_equal(X1,appear(efficient_producers,X0)) )
=> greater(cardinality_at_time(efficient_producers,X1),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6) ).
fof(f19,conjecture,
! [X0] :
( ( observational_period(X0)
& slow_change(X0) )
=> selection_favors(efficient_producers,first_movers,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t8) ).
fof(f20,negated_conjecture,
~ ! [X0] :
( ( observational_period(X0)
& slow_change(X0) )
=> selection_favors(efficient_producers,first_movers,X0) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1,X2,X3] :
( selection_favors(X2,X1,X3)
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3)) ),
inference(ennf_transformation,[],[f1]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( selection_favors(X2,X1,X3)
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3)) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( selection_favors(X1,X2,X3)
| ~ environment(X0)
| ~ subpopulation(X1,X0,X3)
| ~ subpopulation(X2,X0,X3)
| ~ greater(cardinality_at_time(X1,X3),zero)
| zero != cardinality_at_time(X2,X3) ),
inference(ennf_transformation,[],[f2]) ).
fof(f24,plain,
! [X0,X1,X2,X3] :
( selection_favors(X1,X2,X3)
| ~ environment(X0)
| ~ subpopulation(X1,X0,X3)
| ~ subpopulation(X2,X0,X3)
| ~ greater(cardinality_at_time(X1,X3),zero)
| zero != cardinality_at_time(X2,X3) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0] :
( selection_favors(efficient_producers,first_movers,X0)
| ~ observational_period(X0)
| ~ propagation_strategy(first_movers)
| ~ propagation_strategy(efficient_producers)
| ? [X1] :
( ~ selection_favors(efficient_producers,first_movers,end_time(X1))
& environment(X1)
& in_environment(X0,X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f26,plain,
! [X0] :
( selection_favors(efficient_producers,first_movers,X0)
| ~ observational_period(X0)
| ~ propagation_strategy(first_movers)
| ~ propagation_strategy(efficient_producers)
| ? [X1] :
( ~ selection_favors(efficient_producers,first_movers,end_time(X1))
& environment(X1)
& in_environment(X0,X1) ) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
! [X0] :
( ! [X1] :
( ? [X2] :
( in_environment(X1,X2)
& greater(X2,critical_point(X1)) )
| ~ environment(X1)
| ~ in_environment(X0,X1) )
| ~ observational_period(X0)
| ~ slow_change(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f28,plain,
! [X0] :
( ! [X1] :
( ? [X2] :
( in_environment(X1,X2)
& greater(X2,critical_point(X1)) )
| ~ environment(X1)
| ~ in_environment(X0,X1) )
| ~ observational_period(X0)
| ~ slow_change(X0) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ environment(X0)
| ~ greater_or_equal(X1,start_time(X0))
| ~ greater_or_equal(end_time(X0),X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f30,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ environment(X0)
| ~ greater_or_equal(X1,start_time(X0))
| ~ greater_or_equal(end_time(X0),X1) ),
inference(flattening,[],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( greater_or_equal(end_time(X0),X1)
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f32,plain,
! [X0,X1] :
( greater_or_equal(end_time(X0),X1)
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(flattening,[],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero) ),
inference(ennf_transformation,[],[f9]) ).
fof(f34,plain,
! [X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( greater_or_equal(cardinality_at_time(first_movers,X1),zero)
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f36,plain,
! [X0,X1] :
( greater_or_equal(cardinality_at_time(first_movers,X1),zero)
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
! [X0,X1] :
( ( subpopulation(first_movers,X0,X1)
& subpopulation(efficient_producers,X0,X1) )
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f38,plain,
! [X0,X1] :
( ( subpopulation(first_movers,X0,X1)
& subpopulation(efficient_producers,X0,X1) )
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
! [X0] :
( greater_or_equal(critical_point(X0),appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f40,plain,
! [X0] :
( greater_or_equal(critical_point(X0),start_time(X0))
| ~ environment(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f41,plain,
! [X0,X1,X2] :
( greater(X0,X2)
| ~ greater(X0,X1)
| ~ greater(X1,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f42,plain,
! [X0,X1,X2] :
( greater(X0,X2)
| ~ greater(X0,X1)
| ~ greater(X1,X2) ),
inference(flattening,[],[f41]) ).
fof(f45,plain,
! [X0,X1] :
( ( ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(X2,X1) ) )
| ~ environment(X0)
| critical_point(X0) != X1 ),
inference(ennf_transformation,[],[f17]) ).
fof(f46,plain,
! [X0,X1] :
( ( ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(X2,X1) ) )
| ~ environment(X0)
| critical_point(X0) != X1 ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( 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,[],[f18]) ).
fof(f48,plain,
! [X0,X1] :
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0)) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
? [X0] :
( ~ selection_favors(efficient_producers,first_movers,X0)
& observational_period(X0)
& slow_change(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f50,plain,
? [X0] :
( ~ selection_favors(efficient_producers,first_movers,X0)
& observational_period(X0)
& slow_change(X0) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
! [X0] :
( selection_favors(efficient_producers,first_movers,X0)
| ~ observational_period(X0)
| ~ propagation_strategy(first_movers)
| ~ propagation_strategy(efficient_producers)
| ( ~ selection_favors(efficient_producers,first_movers,end_time(sK0(X0)))
& environment(sK0(X0))
& in_environment(X0,sK0(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f26]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( ( in_environment(X1,sK1(X1))
& greater(sK1(X1),critical_point(X1)) )
| ~ environment(X1)
| ~ in_environment(X0,X1) )
| ~ observational_period(X0)
| ~ slow_change(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X1))],[f28]) ).
fof(f53,plain,
! [X0,X1] :
( ( greater_or_equal(X0,X1)
| ( ~ greater(X0,X1)
& X0 != X1 ) )
& ( greater(X0,X1)
| X0 = X1
| ~ greater_or_equal(X0,X1) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f54,plain,
! [X0,X1] :
( ( greater_or_equal(X0,X1)
| ( ~ greater(X0,X1)
& X0 != X1 ) )
& ( greater(X0,X1)
| X0 = X1
| ~ greater_or_equal(X0,X1) ) ),
inference(flattening,[],[f53]) ).
fof(f55,plain,
( ~ selection_favors(efficient_producers,first_movers,sK2)
& observational_period(sK2)
& slow_change(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f50]) ).
fof(f56,plain,
! [X2,X3,X0,X1] :
( ~ environment(X0)
| selection_favors(X2,X1,X3)
| ~ subpopulations(X1,X2,X0,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f57,plain,
! [X2,X3,X0,X1] :
( ~ environment(X0)
| selection_favors(X1,X2,X3)
| ~ subpopulation(X1,X0,X3)
| ~ subpopulation(X2,X0,X3)
| ~ greater(cardinality_at_time(X1,X3),zero)
| zero != cardinality_at_time(X2,X3) ),
inference(cnf_transformation,[],[f24]) ).
fof(f58,plain,
! [X0] :
( selection_favors(efficient_producers,first_movers,X0)
| ~ observational_period(X0)
| ~ propagation_strategy(first_movers)
| ~ propagation_strategy(efficient_producers)
| in_environment(X0,sK0(X0)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f59,plain,
! [X0] :
( selection_favors(efficient_producers,first_movers,X0)
| ~ observational_period(X0)
| ~ propagation_strategy(first_movers)
| ~ propagation_strategy(efficient_producers)
| environment(sK0(X0)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f60,plain,
! [X0] :
( selection_favors(efficient_producers,first_movers,X0)
| ~ observational_period(X0)
| ~ propagation_strategy(first_movers)
| ~ propagation_strategy(efficient_producers)
| ~ selection_favors(efficient_producers,first_movers,end_time(sK0(X0))) ),
inference(cnf_transformation,[],[f51]) ).
fof(f61,plain,
! [X0,X1] :
( ~ slow_change(X0)
| ~ environment(X1)
| ~ in_environment(X0,X1)
| ~ observational_period(X0)
| greater(sK1(X1),critical_point(X1)) ),
inference(cnf_transformation,[],[f52]) ).
fof(f62,plain,
! [X0,X1] :
( ~ slow_change(X0)
| ~ environment(X1)
| ~ in_environment(X0,X1)
| ~ observational_period(X0)
| in_environment(X1,sK1(X1)) ),
inference(cnf_transformation,[],[f52]) ).
fof(f63,plain,
propagation_strategy(first_movers),
inference(cnf_transformation,[],[f5]) ).
fof(f64,plain,
propagation_strategy(efficient_producers),
inference(cnf_transformation,[],[f6]) ).
fof(f65,plain,
! [X0,X1] :
( ~ environment(X0)
| in_environment(X0,X1)
| ~ greater_or_equal(X1,start_time(X0))
| ~ greater_or_equal(end_time(X0),X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f66,plain,
! [X0,X1] :
( ~ environment(X0)
| greater_or_equal(end_time(X0),X1)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f67,plain,
! [X0,X1] :
( ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,X1)
| ~ in_environment(X0,X1)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero) ),
inference(cnf_transformation,[],[f34]) ).
fof(f68,plain,
! [X0,X1] :
( ~ environment(X0)
| greater_or_equal(cardinality_at_time(first_movers,X1),zero)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f69,plain,
! [X0,X1] :
( ~ environment(X0)
| subpopulation(efficient_producers,X0,X1)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f70,plain,
! [X0,X1] :
( ~ environment(X0)
| subpopulation(first_movers,X0,X1)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f71,plain,
! [X0] :
( ~ environment(X0)
| greater_or_equal(critical_point(X0),appear(efficient_producers,X0)) ),
inference(cnf_transformation,[],[f39]) ).
fof(f72,plain,
! [X0] :
( ~ environment(X0)
| greater_or_equal(critical_point(X0),start_time(X0)) ),
inference(cnf_transformation,[],[f40]) ).
fof(f73,plain,
! [X2,X0,X1] :
( ~ greater(X0,X1)
| greater(X0,X2)
| ~ greater(X1,X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f75,plain,
! [X0,X1] :
( ~ greater_or_equal(X0,X1)
| X0 = X1
| greater(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f76,plain,
! [X0,X1] :
( X0 != X1
| greater_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f77,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| greater_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f78,plain,
! [X2,X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(X2,X1)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| critical_point(X0) != X1 ),
inference(cnf_transformation,[],[f46]) ).
fof(f80,plain,
! [X0,X1] :
( ~ environment(X0)
| greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ in_environment(X0,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0)) ),
inference(cnf_transformation,[],[f48]) ).
fof(f81,plain,
slow_change(sK2),
inference(cnf_transformation,[],[f55]) ).
fof(f82,plain,
observational_period(sK2),
inference(cnf_transformation,[],[f55]) ).
fof(f83,plain,
~ selection_favors(efficient_producers,first_movers,sK2),
inference(cnf_transformation,[],[f55]) ).
fof(f84,plain,
! [X0] :
( selection_favors(efficient_producers,first_movers,X0)
| ~ observational_period(X0)
| ~ propagation_strategy(efficient_producers)
| in_environment(X0,sK0(X0)) ),
inference(forward_subsumption_resolution,[],[f58,f63]) ).
fof(f85,plain,
! [X0] :
( selection_favors(efficient_producers,first_movers,X0)
| ~ observational_period(X0)
| ~ propagation_strategy(efficient_producers)
| environment(sK0(X0)) ),
inference(forward_subsumption_resolution,[],[f59,f63]) ).
fof(f86,plain,
! [X0] :
( selection_favors(efficient_producers,first_movers,X0)
| ~ observational_period(X0)
| ~ propagation_strategy(efficient_producers)
| ~ selection_favors(efficient_producers,first_movers,end_time(sK0(X0))) ),
inference(forward_subsumption_resolution,[],[f60,f63]) ).
fof(f87,plain,
! [X0] :
( ~ observational_period(X0)
| selection_favors(efficient_producers,first_movers,X0)
| in_environment(X0,sK0(X0)) ),
inference(forward_subsumption_resolution,[],[f84,f64]) ).
fof(f88,plain,
! [X0] :
( ~ observational_period(X0)
| selection_favors(efficient_producers,first_movers,X0)
| environment(sK0(X0)) ),
inference(forward_subsumption_resolution,[],[f85,f64]) ).
fof(f89,plain,
! [X0] :
( ~ observational_period(X0)
| selection_favors(efficient_producers,first_movers,X0)
| ~ selection_favors(efficient_producers,first_movers,end_time(sK0(X0))) ),
inference(forward_subsumption_resolution,[],[f86,f64]) ).
fof(f90,plain,
! [X0] : greater_or_equal(X0,X0),
inference(equality_resolution,[],[f76]) ).
fof(f92,plain,
( selection_favors(efficient_producers,first_movers,sK2)
| environment(sK0(sK2)) ),
inference(resolution,[],[f88,f82]) ).
fof(f93,plain,
environment(sK0(sK2)),
inference(forward_subsumption_resolution,[],[f92,f83]) ).
fof(f94,plain,
! [X0] :
( ~ in_environment(sK0(sK2),X0)
| subpopulation(first_movers,sK0(sK2),X0) ),
inference(resolution,[],[f93,f70]) ).
fof(f95,plain,
! [X0] :
( ~ in_environment(sK0(sK2),X0)
| subpopulation(efficient_producers,sK0(sK2),X0) ),
inference(resolution,[],[f93,f69]) ).
fof(f96,plain,
! [X0] :
( ~ in_environment(sK0(sK2),X0)
| greater_or_equal(end_time(sK0(sK2)),X0) ),
inference(resolution,[],[f93,f66]) ).
fof(f97,plain,
greater_or_equal(critical_point(sK0(sK2)),appear(efficient_producers,sK0(sK2))),
inference(resolution,[],[f93,f71]) ).
fof(f98,plain,
greater_or_equal(critical_point(sK0(sK2)),start_time(sK0(sK2))),
inference(resolution,[],[f93,f72]) ).
fof(f99,plain,
! [X0] :
( ~ in_environment(sK0(sK2),X0)
| greater_or_equal(cardinality_at_time(first_movers,X0),zero) ),
inference(resolution,[],[f68,f93]) ).
fof(f100,plain,
( critical_point(sK0(sK2)) = start_time(sK0(sK2))
| greater(critical_point(sK0(sK2)),start_time(sK0(sK2))) ),
inference(resolution,[],[f98,f75]) ).
fof(f102,definition,
( spl3_1
<=> greater(critical_point(sK0(sK2)),start_time(sK0(sK2))) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f104,plain,
( greater(critical_point(sK0(sK2)),start_time(sK0(sK2)))
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f106,definition,
( spl3_2
<=> critical_point(sK0(sK2)) = start_time(sK0(sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f108,plain,
( critical_point(sK0(sK2)) = start_time(sK0(sK2))
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f109,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f100,f106,f102]) ).
fof(f110,plain,
( selection_favors(efficient_producers,first_movers,sK2)
| in_environment(sK2,sK0(sK2)) ),
inference(resolution,[],[f87,f82]) ).
fof(f111,plain,
in_environment(sK2,sK0(sK2)),
inference(forward_subsumption_resolution,[],[f110,f83]) ).
fof(f112,plain,
( selection_favors(efficient_producers,first_movers,sK2)
| ~ selection_favors(efficient_producers,first_movers,end_time(sK0(sK2))) ),
inference(resolution,[],[f89,f82]) ).
fof(f113,plain,
~ selection_favors(efficient_producers,first_movers,end_time(sK0(sK2))),
inference(forward_subsumption_resolution,[],[f112,f83]) ).
fof(f116,plain,
! [X0] :
( ~ environment(X0)
| ~ in_environment(sK2,X0)
| ~ observational_period(sK2)
| in_environment(X0,sK1(X0)) ),
inference(resolution,[],[f62,f81]) ).
fof(f117,plain,
! [X0] :
( ~ environment(X0)
| ~ in_environment(sK2,X0)
| in_environment(X0,sK1(X0)) ),
inference(forward_subsumption_resolution,[],[f116,f82]) ).
fof(f118,plain,
( critical_point(sK0(sK2)) = appear(efficient_producers,sK0(sK2))
| greater(critical_point(sK0(sK2)),appear(efficient_producers,sK0(sK2))) ),
inference(resolution,[],[f97,f75]) ).
fof(f120,definition,
( spl3_3
<=> greater(critical_point(sK0(sK2)),appear(efficient_producers,sK0(sK2))) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f122,plain,
( greater(critical_point(sK0(sK2)),appear(efficient_producers,sK0(sK2)))
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f124,definition,
( spl3_4
<=> critical_point(sK0(sK2)) = appear(efficient_producers,sK0(sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f126,plain,
( critical_point(sK0(sK2)) = appear(efficient_producers,sK0(sK2))
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f127,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[],[f118,f124,f120]) ).
fof(f128,plain,
! [X0] :
( ~ greater_or_equal(X0,start_time(sK0(sK2)))
| in_environment(sK0(sK2),X0)
| ~ greater_or_equal(end_time(sK0(sK2)),X0) ),
inference(resolution,[],[f65,f93]) ).
fof(f132,plain,
! [X0] :
( ~ environment(X0)
| ~ in_environment(sK2,X0)
| ~ observational_period(sK2)
| greater(sK1(X0),critical_point(X0)) ),
inference(resolution,[],[f61,f81]) ).
fof(f133,plain,
! [X0] :
( ~ environment(X0)
| ~ in_environment(sK2,X0)
| greater(sK1(X0),critical_point(X0)) ),
inference(forward_subsumption_resolution,[],[f132,f82]) ).
fof(f134,plain,
( ~ in_environment(sK2,sK0(sK2))
| in_environment(sK0(sK2),sK1(sK0(sK2))) ),
inference(resolution,[],[f117,f93]) ).
fof(f135,plain,
in_environment(sK0(sK2),sK1(sK0(sK2))),
inference(forward_subsumption_resolution,[],[f134,f111]) ).
fof(f138,plain,
! [X0] :
( ~ greater_or_equal(X0,appear(efficient_producers,sK0(sK2)))
| ~ in_environment(sK0(sK2),X0)
| greater(cardinality_at_time(efficient_producers,X0),zero) ),
inference(resolution,[],[f80,f93]) ).
fof(f139,plain,
subpopulation(first_movers,sK0(sK2),sK1(sK0(sK2))),
inference(resolution,[],[f94,f135]) ).
fof(f140,plain,
! [X2,X0,X1] :
( ~ greater(growth_rate(X0,X2),growth_rate(X1,X2))
| ~ subpopulations(X1,X0,sK0(sK2),X2)
| selection_favors(X0,X1,X2) ),
inference(resolution,[],[f56,f93]) ).
fof(f141,plain,
! [X0] :
( ~ in_environment(sK0(sK2),X0)
| subpopulations(first_movers,efficient_producers,sK0(sK2),X0)
| ~ greater(cardinality_at_time(first_movers,X0),zero)
| ~ greater(cardinality_at_time(efficient_producers,X0),zero) ),
inference(resolution,[],[f67,f93]) ).
fof(f142,plain,
subpopulation(efficient_producers,sK0(sK2),sK1(sK0(sK2))),
inference(resolution,[],[f95,f135]) ).
fof(f143,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,sK0(sK2),X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| critical_point(sK0(sK2)) != X1 ),
inference(resolution,[],[f78,f93]) ).
fof(f144,plain,
! [X2,X0,X1] :
( ~ greater(cardinality_at_time(X0,X2),zero)
| ~ subpopulation(X0,sK0(sK2),X2)
| ~ subpopulation(X1,sK0(sK2),X2)
| selection_favors(X0,X1,X2)
| zero != cardinality_at_time(X1,X2) ),
inference(resolution,[],[f57,f93]) ).
fof(f145,plain,
greater_or_equal(end_time(sK0(sK2)),sK1(sK0(sK2))),
inference(resolution,[],[f96,f135]) ).
fof(f146,plain,
( ~ in_environment(sK2,sK0(sK2))
| greater(sK1(sK0(sK2)),critical_point(sK0(sK2))) ),
inference(resolution,[],[f133,f93]) ).
fof(f147,plain,
greater(sK1(sK0(sK2)),critical_point(sK0(sK2))),
inference(forward_subsumption_resolution,[],[f146,f111]) ).
fof(f148,plain,
! [X0] :
( ~ greater(critical_point(sK0(sK2)),X0)
| greater(sK1(sK0(sK2)),X0) ),
inference(resolution,[],[f147,f73]) ).
fof(f149,plain,
greater_or_equal(sK1(sK0(sK2)),critical_point(sK0(sK2))),
inference(resolution,[],[f147,f77]) ).
fof(f150,plain,
greater_or_equal(cardinality_at_time(first_movers,sK1(sK0(sK2))),zero),
inference(resolution,[],[f99,f135]) ).
fof(f151,plain,
( end_time(sK0(sK2)) = sK1(sK0(sK2))
| greater(end_time(sK0(sK2)),sK1(sK0(sK2))) ),
inference(resolution,[],[f145,f75]) ).
fof(f153,definition,
( spl3_5
<=> greater(end_time(sK0(sK2)),sK1(sK0(sK2))) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f155,plain,
( greater(end_time(sK0(sK2)),sK1(sK0(sK2)))
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f157,definition,
( spl3_6
<=> end_time(sK0(sK2)) = sK1(sK0(sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
fof(f159,plain,
( end_time(sK0(sK2)) = sK1(sK0(sK2))
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f160,plain,
( spl3_5
| spl3_6 ),
inference(avatar_split_clause,[],[f151,f157,f153]) ).
fof(f165,definition,
( spl3_7
<=> greater_or_equal(end_time(sK0(sK2)),critical_point(sK0(sK2))) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
fof(f166,plain,
( greater_or_equal(end_time(sK0(sK2)),critical_point(sK0(sK2)))
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f167,plain,
( ~ greater_or_equal(end_time(sK0(sK2)),critical_point(sK0(sK2)))
| spl3_7 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f173,plain,
( zero = cardinality_at_time(first_movers,sK1(sK0(sK2)))
| greater(cardinality_at_time(first_movers,sK1(sK0(sK2))),zero) ),
inference(resolution,[],[f150,f75]) ).
fof(f175,definition,
( spl3_9
<=> greater(cardinality_at_time(first_movers,sK1(sK0(sK2))),zero) ),
introduced(definition,[new_symbols(definition,[spl3_9])],[avatar_definition]) ).
fof(f177,plain,
( greater(cardinality_at_time(first_movers,sK1(sK0(sK2))),zero)
| ~ spl3_9 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f179,definition,
( spl3_10
<=> zero = cardinality_at_time(first_movers,sK1(sK0(sK2))) ),
introduced(definition,[new_symbols(definition,[spl3_10])],[avatar_definition]) ).
fof(f181,plain,
( zero = cardinality_at_time(first_movers,sK1(sK0(sK2)))
| ~ spl3_10 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f182,plain,
( spl3_9
| spl3_10 ),
inference(avatar_split_clause,[],[f173,f179,f175]) ).
fof(f200,plain,
( subpopulations(first_movers,efficient_producers,sK0(sK2),sK1(sK0(sK2)))
| ~ greater(cardinality_at_time(first_movers,sK1(sK0(sK2))),zero)
| ~ greater(cardinality_at_time(efficient_producers,sK1(sK0(sK2))),zero) ),
inference(resolution,[],[f141,f135]) ).
fof(f201,plain,
( subpopulations(first_movers,efficient_producers,sK0(sK2),sK1(sK0(sK2)))
| ~ greater(cardinality_at_time(efficient_producers,sK1(sK0(sK2))),zero)
| ~ spl3_9 ),
inference(forward_subsumption_resolution,[],[f200,f177]) ).
fof(f203,definition,
( spl3_14
<=> greater(cardinality_at_time(efficient_producers,sK1(sK0(sK2))),zero) ),
introduced(definition,[new_symbols(definition,[spl3_14])],[avatar_definition]) ).
fof(f204,plain,
( greater(cardinality_at_time(efficient_producers,sK1(sK0(sK2))),zero)
| ~ spl3_14 ),
inference(avatar_component_clause,[],[f203]) ).
fof(f205,plain,
( ~ greater(cardinality_at_time(efficient_producers,sK1(sK0(sK2))),zero)
| spl3_14 ),
inference(avatar_component_clause,[],[f203]) ).
fof(f207,definition,
( spl3_15
<=> subpopulations(first_movers,efficient_producers,sK0(sK2),sK1(sK0(sK2))) ),
introduced(definition,[new_symbols(definition,[spl3_15])],[avatar_definition]) ).
fof(f210,plain,
( ~ spl3_14
| spl3_15
| ~ spl3_9 ),
inference(avatar_split_clause,[],[f201,f175,f207,f203]) ).
fof(f212,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0(sK2),sK1(sK0(sK2)))
| greater(growth_rate(efficient_producers,sK1(sK0(sK2))),growth_rate(first_movers,sK1(sK0(sK2))))
| critical_point(sK0(sK2)) != critical_point(sK0(sK2)) ),
inference(resolution,[],[f143,f147]) ).
fof(f213,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0(sK2),sK1(sK0(sK2)))
| greater(growth_rate(efficient_producers,sK1(sK0(sK2))),growth_rate(first_movers,sK1(sK0(sK2)))) ),
inference(trivial_inequality_removal,[],[f212]) ).
fof(f215,definition,
( spl3_16
<=> greater(growth_rate(efficient_producers,sK1(sK0(sK2))),growth_rate(first_movers,sK1(sK0(sK2)))) ),
introduced(definition,[new_symbols(definition,[spl3_16])],[avatar_definition]) ).
fof(f217,plain,
( greater(growth_rate(efficient_producers,sK1(sK0(sK2))),growth_rate(first_movers,sK1(sK0(sK2))))
| ~ spl3_16 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f218,plain,
( spl3_16
| ~ spl3_15 ),
inference(avatar_split_clause,[],[f213,f207,f215]) ).
fof(f229,plain,
( ! [X0] :
( ~ greater(sK1(sK0(sK2)),X0)
| greater(end_time(sK0(sK2)),X0) )
| ~ spl3_5 ),
inference(resolution,[],[f155,f73]) ).
fof(f236,definition,
( spl3_20
<=> greater(growth_rate(efficient_producers,end_time(sK0(sK2))),growth_rate(first_movers,end_time(sK0(sK2)))) ),
introduced(definition,[new_symbols(definition,[spl3_20])],[avatar_definition]) ).
fof(f238,plain,
( greater(growth_rate(efficient_producers,end_time(sK0(sK2))),growth_rate(first_movers,end_time(sK0(sK2))))
| ~ spl3_20 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f240,definition,
( spl3_21
<=> subpopulations(first_movers,efficient_producers,sK0(sK2),end_time(sK0(sK2))) ),
introduced(definition,[new_symbols(definition,[spl3_21])],[avatar_definition]) ).
fof(f241,plain,
( subpopulations(first_movers,efficient_producers,sK0(sK2),end_time(sK0(sK2)))
| ~ spl3_21 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f242,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0(sK2),end_time(sK0(sK2)))
| spl3_21 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f262,plain,
( greater(sK1(sK0(sK2)),appear(efficient_producers,sK0(sK2)))
| ~ spl3_3 ),
inference(resolution,[],[f148,f122]) ).
fof(f265,plain,
( greater_or_equal(sK1(sK0(sK2)),appear(efficient_producers,sK0(sK2)))
| ~ spl3_3 ),
inference(resolution,[],[f262,f77]) ).
fof(f266,plain,
( ~ in_environment(sK0(sK2),sK1(sK0(sK2)))
| greater(cardinality_at_time(efficient_producers,sK1(sK0(sK2))),zero)
| ~ spl3_3 ),
inference(resolution,[],[f265,f138]) ).
fof(f268,plain,
( greater(cardinality_at_time(efficient_producers,sK1(sK0(sK2))),zero)
| ~ spl3_3 ),
inference(forward_subsumption_resolution,[],[f266,f135]) ).
fof(f278,plain,
( greater_or_equal(sK1(sK0(sK2)),appear(efficient_producers,sK0(sK2)))
| ~ spl3_4 ),
inference(superposition,[],[f149,f126]) ).
fof(f287,plain,
( ~ in_environment(sK0(sK2),sK1(sK0(sK2)))
| greater(cardinality_at_time(efficient_producers,sK1(sK0(sK2))),zero)
| ~ spl3_4 ),
inference(resolution,[],[f278,f138]) ).
fof(f289,plain,
( greater(cardinality_at_time(efficient_producers,sK1(sK0(sK2))),zero)
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f287,f135]) ).
fof(f290,plain,
( $false
| ~ spl3_4
| spl3_14 ),
inference(forward_subsumption_resolution,[],[f289,f205]) ).
fof(f291,plain,
( ~ spl3_4
| spl3_14 ),
inference(avatar_contradiction_clause,[],[f290]) ).
fof(f292,plain,
( spl3_14
| ~ spl3_3 ),
inference(avatar_split_clause,[],[f268,f120,f203]) ).
fof(f293,plain,
( ! [X0] :
( ~ subpopulation(efficient_producers,sK0(sK2),sK1(sK0(sK2)))
| ~ subpopulation(X0,sK0(sK2),sK1(sK0(sK2)))
| selection_favors(efficient_producers,X0,sK1(sK0(sK2)))
| zero != cardinality_at_time(X0,sK1(sK0(sK2))) )
| ~ spl3_14 ),
inference(resolution,[],[f204,f144]) ).
fof(f297,plain,
( ! [X0] :
( ~ subpopulation(X0,sK0(sK2),sK1(sK0(sK2)))
| selection_favors(efficient_producers,X0,sK1(sK0(sK2)))
| zero != cardinality_at_time(X0,sK1(sK0(sK2))) )
| ~ spl3_14 ),
inference(forward_subsumption_resolution,[],[f293,f142]) ).
fof(f312,plain,
( greater(end_time(sK0(sK2)),critical_point(sK0(sK2)))
| ~ spl3_5 ),
inference(resolution,[],[f229,f147]) ).
fof(f313,plain,
( greater(end_time(sK0(sK2)),appear(efficient_producers,sK0(sK2)))
| ~ spl3_3
| ~ spl3_5 ),
inference(resolution,[],[f229,f262]) ).
fof(f315,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0(sK2),end_time(sK0(sK2)))
| greater(growth_rate(efficient_producers,end_time(sK0(sK2))),growth_rate(first_movers,end_time(sK0(sK2))))
| critical_point(sK0(sK2)) != critical_point(sK0(sK2))
| ~ spl3_5 ),
inference(resolution,[],[f312,f143]) ).
fof(f317,plain,
( greater_or_equal(end_time(sK0(sK2)),critical_point(sK0(sK2)))
| ~ spl3_5 ),
inference(resolution,[],[f312,f77]) ).
fof(f318,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0(sK2),end_time(sK0(sK2)))
| greater(growth_rate(efficient_producers,end_time(sK0(sK2))),growth_rate(first_movers,end_time(sK0(sK2))))
| ~ spl3_5 ),
inference(trivial_inequality_removal,[],[f315]) ).
fof(f319,plain,
( $false
| ~ spl3_5
| spl3_7 ),
inference(forward_subsumption_resolution,[],[f317,f167]) ).
fof(f320,plain,
( ~ spl3_5
| spl3_7 ),
inference(avatar_contradiction_clause,[],[f319]) ).
fof(f321,plain,
( spl3_20
| ~ spl3_21
| ~ spl3_5 ),
inference(avatar_split_clause,[],[f318,f153,f240,f236]) ).
fof(f327,definition,
( spl3_25
<=> greater_or_equal(end_time(sK0(sK2)),start_time(sK0(sK2))) ),
introduced(definition,[new_symbols(definition,[spl3_25])],[avatar_definition]) ).
fof(f328,plain,
( greater_or_equal(end_time(sK0(sK2)),start_time(sK0(sK2)))
| ~ spl3_25 ),
inference(avatar_component_clause,[],[f327]) ).
fof(f329,plain,
( ~ greater_or_equal(end_time(sK0(sK2)),start_time(sK0(sK2)))
| spl3_25 ),
inference(avatar_component_clause,[],[f327]) ).
fof(f344,plain,
( in_environment(sK0(sK2),end_time(sK0(sK2)))
| ~ spl3_6 ),
inference(superposition,[],[f135,f159]) ).
fof(f354,plain,
( greater(cardinality_at_time(efficient_producers,end_time(sK0(sK2))),zero)
| ~ spl3_6
| ~ spl3_14 ),
inference(superposition,[],[f204,f159]) ).
fof(f371,plain,
( subpopulations(first_movers,efficient_producers,sK0(sK2),end_time(sK0(sK2)))
| ~ greater(cardinality_at_time(first_movers,end_time(sK0(sK2))),zero)
| ~ greater(cardinality_at_time(efficient_producers,end_time(sK0(sK2))),zero)
| ~ spl3_6 ),
inference(resolution,[],[f344,f141]) ).
fof(f377,plain,
( ~ greater(cardinality_at_time(first_movers,end_time(sK0(sK2))),zero)
| ~ greater(cardinality_at_time(efficient_producers,end_time(sK0(sK2))),zero)
| ~ spl3_6
| spl3_21 ),
inference(forward_subsumption_resolution,[],[f371,f242]) ).
fof(f378,plain,
( ~ greater(cardinality_at_time(first_movers,end_time(sK0(sK2))),zero)
| ~ spl3_6
| ~ spl3_14
| spl3_21 ),
inference(forward_subsumption_resolution,[],[f377,f354]) ).
fof(f397,plain,
( ~ greater_or_equal(end_time(sK0(sK2)),critical_point(sK0(sK2)))
| ~ spl3_2
| spl3_25 ),
inference(superposition,[],[f329,f108]) ).
fof(f398,plain,
( $false
| ~ spl3_2
| ~ spl3_7
| spl3_25 ),
inference(forward_subsumption_resolution,[],[f397,f166]) ).
fof(f399,plain,
( ~ spl3_2
| ~ spl3_7
| spl3_25 ),
inference(avatar_contradiction_clause,[],[f398]) ).
fof(f426,plain,
( in_environment(sK0(sK2),end_time(sK0(sK2)))
| ~ greater_or_equal(end_time(sK0(sK2)),end_time(sK0(sK2)))
| ~ spl3_25 ),
inference(resolution,[],[f328,f128]) ).
fof(f442,plain,
( selection_favors(efficient_producers,first_movers,sK1(sK0(sK2)))
| zero != cardinality_at_time(first_movers,sK1(sK0(sK2)))
| ~ spl3_14 ),
inference(resolution,[],[f297,f139]) ).
fof(f446,plain,
( selection_favors(efficient_producers,first_movers,sK1(sK0(sK2)))
| ~ spl3_10
| ~ spl3_14 ),
inference(forward_subsumption_resolution,[],[f442,f181]) ).
fof(f448,plain,
( selection_favors(efficient_producers,first_movers,end_time(sK0(sK2)))
| ~ spl3_6
| ~ spl3_10
| ~ spl3_14 ),
inference(forward_demodulation,[],[f446,f159]) ).
fof(f458,plain,
( $false
| ~ spl3_6
| ~ spl3_10
| ~ spl3_14 ),
inference(forward_subsumption_resolution,[],[f448,f113]) ).
fof(f459,plain,
( ~ spl3_6
| ~ spl3_10
| ~ spl3_14 ),
inference(avatar_contradiction_clause,[],[f458]) ).
fof(f460,plain,
( greater(cardinality_at_time(first_movers,end_time(sK0(sK2))),zero)
| ~ spl3_6
| ~ spl3_9 ),
inference(forward_demodulation,[],[f177,f159]) ).
fof(f463,plain,
( greater(growth_rate(efficient_producers,end_time(sK0(sK2))),growth_rate(first_movers,end_time(sK0(sK2))))
| ~ spl3_6
| ~ spl3_16 ),
inference(forward_demodulation,[],[f217,f159]) ).
fof(f467,plain,
( $false
| ~ spl3_6
| ~ spl3_9
| ~ spl3_14
| spl3_21 ),
inference(forward_subsumption_resolution,[],[f460,f378]) ).
fof(f468,plain,
( ~ spl3_6
| ~ spl3_9
| ~ spl3_14
| spl3_21 ),
inference(avatar_contradiction_clause,[],[f467]) ).
fof(f471,plain,
( spl3_20
| ~ spl3_6
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f463,f215,f157,f236]) ).
fof(f520,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0(sK2),end_time(sK0(sK2)))
| selection_favors(efficient_producers,first_movers,end_time(sK0(sK2)))
| ~ spl3_20 ),
inference(resolution,[],[f238,f140]) ).
fof(f537,plain,
( selection_favors(efficient_producers,first_movers,end_time(sK0(sK2)))
| ~ spl3_20
| ~ spl3_21 ),
inference(forward_subsumption_resolution,[],[f520,f241]) ).
fof(f538,plain,
( $false
| ~ spl3_20
| ~ spl3_21 ),
inference(forward_subsumption_resolution,[],[f537,f113]) ).
fof(f539,plain,
( ~ spl3_20
| ~ spl3_21 ),
inference(avatar_contradiction_clause,[],[f538]) ).
fof(f541,definition,
( spl3_38
<=> greater(end_time(sK0(sK2)),start_time(sK0(sK2))) ),
introduced(definition,[new_symbols(definition,[spl3_38])],[avatar_definition]) ).
fof(f542,plain,
( ~ greater(end_time(sK0(sK2)),start_time(sK0(sK2)))
| spl3_38 ),
inference(avatar_component_clause,[],[f541]) ).
fof(f543,plain,
( greater(end_time(sK0(sK2)),start_time(sK0(sK2)))
| ~ spl3_38 ),
inference(avatar_component_clause,[],[f541]) ).
fof(f549,plain,
( in_environment(sK0(sK2),end_time(sK0(sK2)))
| ~ spl3_25 ),
inference(forward_subsumption_resolution,[],[f426,f90]) ).
fof(f559,plain,
( subpopulations(first_movers,efficient_producers,sK0(sK2),end_time(sK0(sK2)))
| ~ greater(cardinality_at_time(first_movers,end_time(sK0(sK2))),zero)
| ~ greater(cardinality_at_time(efficient_producers,end_time(sK0(sK2))),zero)
| ~ spl3_25 ),
inference(resolution,[],[f549,f141]) ).
fof(f560,plain,
( greater_or_equal(cardinality_at_time(first_movers,end_time(sK0(sK2))),zero)
| ~ spl3_25 ),
inference(resolution,[],[f549,f99]) ).
fof(f562,plain,
( subpopulation(efficient_producers,sK0(sK2),end_time(sK0(sK2)))
| ~ spl3_25 ),
inference(resolution,[],[f549,f95]) ).
fof(f563,plain,
( subpopulation(first_movers,sK0(sK2),end_time(sK0(sK2)))
| ~ spl3_25 ),
inference(resolution,[],[f549,f94]) ).
fof(f564,plain,
( ~ greater(cardinality_at_time(first_movers,end_time(sK0(sK2))),zero)
| ~ greater(cardinality_at_time(efficient_producers,end_time(sK0(sK2))),zero)
| spl3_21
| ~ spl3_25 ),
inference(forward_subsumption_resolution,[],[f559,f242]) ).
fof(f566,definition,
( spl3_42
<=> greater(cardinality_at_time(efficient_producers,end_time(sK0(sK2))),zero) ),
introduced(definition,[new_symbols(definition,[spl3_42])],[avatar_definition]) ).
fof(f567,plain,
( greater(cardinality_at_time(efficient_producers,end_time(sK0(sK2))),zero)
| ~ spl3_42 ),
inference(avatar_component_clause,[],[f566]) ).
fof(f568,plain,
( ~ greater(cardinality_at_time(efficient_producers,end_time(sK0(sK2))),zero)
| spl3_42 ),
inference(avatar_component_clause,[],[f566]) ).
fof(f570,definition,
( spl3_43
<=> greater(cardinality_at_time(first_movers,end_time(sK0(sK2))),zero) ),
introduced(definition,[new_symbols(definition,[spl3_43])],[avatar_definition]) ).
fof(f573,plain,
( ~ spl3_42
| ~ spl3_43
| spl3_21
| ~ spl3_25 ),
inference(avatar_split_clause,[],[f564,f327,f240,f570,f566]) ).
fof(f608,plain,
( greater_or_equal(end_time(sK0(sK2)),start_time(sK0(sK2)))
| ~ spl3_38 ),
inference(resolution,[],[f543,f77]) ).
fof(f610,plain,
( zero = cardinality_at_time(first_movers,end_time(sK0(sK2)))
| greater(cardinality_at_time(first_movers,end_time(sK0(sK2))),zero)
| ~ spl3_25 ),
inference(resolution,[],[f560,f75]) ).
fof(f612,definition,
( spl3_47
<=> zero = cardinality_at_time(first_movers,end_time(sK0(sK2))) ),
introduced(definition,[new_symbols(definition,[spl3_47])],[avatar_definition]) ).
fof(f614,plain,
( zero = cardinality_at_time(first_movers,end_time(sK0(sK2)))
| ~ spl3_47 ),
inference(avatar_component_clause,[],[f612]) ).
fof(f615,plain,
( spl3_43
| spl3_47
| ~ spl3_25 ),
inference(avatar_split_clause,[],[f610,f327,f612,f570]) ).
fof(f620,plain,
( ! [X0] :
( ~ greater(critical_point(sK0(sK2)),X0)
| greater(end_time(sK0(sK2)),X0) )
| ~ spl3_5 ),
inference(resolution,[],[f312,f73]) ).
fof(f630,plain,
( greater_or_equal(end_time(sK0(sK2)),appear(efficient_producers,sK0(sK2)))
| ~ spl3_3
| ~ spl3_5 ),
inference(resolution,[],[f313,f77]) ).
fof(f631,plain,
( ~ in_environment(sK0(sK2),end_time(sK0(sK2)))
| greater(cardinality_at_time(efficient_producers,end_time(sK0(sK2))),zero)
| ~ spl3_3
| ~ spl3_5 ),
inference(resolution,[],[f630,f138]) ).
fof(f633,plain,
( greater(cardinality_at_time(efficient_producers,end_time(sK0(sK2))),zero)
| ~ spl3_3
| ~ spl3_5
| ~ spl3_25 ),
inference(forward_subsumption_resolution,[],[f631,f549]) ).
fof(f634,plain,
( $false
| ~ spl3_3
| ~ spl3_5
| ~ spl3_25
| spl3_42 ),
inference(forward_subsumption_resolution,[],[f633,f568]) ).
fof(f635,plain,
( ~ spl3_3
| ~ spl3_5
| ~ spl3_25
| spl3_42 ),
inference(avatar_contradiction_clause,[],[f634]) ).
fof(f637,plain,
( ! [X0] :
( ~ subpopulation(efficient_producers,sK0(sK2),end_time(sK0(sK2)))
| ~ subpopulation(X0,sK0(sK2),end_time(sK0(sK2)))
| selection_favors(efficient_producers,X0,end_time(sK0(sK2)))
| zero != cardinality_at_time(X0,end_time(sK0(sK2))) )
| ~ spl3_42 ),
inference(resolution,[],[f567,f144]) ).
fof(f641,plain,
( ! [X0] :
( ~ subpopulation(X0,sK0(sK2),end_time(sK0(sK2)))
| selection_favors(efficient_producers,X0,end_time(sK0(sK2)))
| zero != cardinality_at_time(X0,end_time(sK0(sK2))) )
| ~ spl3_25
| ~ spl3_42 ),
inference(forward_subsumption_resolution,[],[f637,f562]) ).
fof(f644,plain,
( greater(end_time(sK0(sK2)),start_time(sK0(sK2)))
| ~ spl3_1
| ~ spl3_5 ),
inference(resolution,[],[f620,f104]) ).
fof(f648,plain,
( selection_favors(efficient_producers,first_movers,end_time(sK0(sK2)))
| zero != cardinality_at_time(first_movers,end_time(sK0(sK2)))
| ~ spl3_25
| ~ spl3_42 ),
inference(resolution,[],[f641,f563]) ).
fof(f649,plain,
( zero != cardinality_at_time(first_movers,end_time(sK0(sK2)))
| ~ spl3_25
| ~ spl3_42 ),
inference(forward_subsumption_resolution,[],[f648,f113]) ).
fof(f650,plain,
( $false
| ~ spl3_25
| ~ spl3_42
| ~ spl3_47 ),
inference(forward_subsumption_resolution,[],[f649,f614]) ).
fof(f651,plain,
( ~ spl3_25
| ~ spl3_42
| ~ spl3_47 ),
inference(avatar_contradiction_clause,[],[f650]) ).
fof(f659,plain,
( greater_or_equal(end_time(sK0(sK2)),appear(efficient_producers,sK0(sK2)))
| ~ spl3_4
| ~ spl3_7 ),
inference(superposition,[],[f166,f126]) ).
fof(f710,plain,
( ~ in_environment(sK0(sK2),end_time(sK0(sK2)))
| greater(cardinality_at_time(efficient_producers,end_time(sK0(sK2))),zero)
| ~ spl3_4
| ~ spl3_7 ),
inference(resolution,[],[f659,f138]) ).
fof(f712,plain,
( greater(cardinality_at_time(efficient_producers,end_time(sK0(sK2))),zero)
| ~ spl3_4
| ~ spl3_7
| ~ spl3_25 ),
inference(forward_subsumption_resolution,[],[f710,f549]) ).
fof(f713,plain,
( $false
| ~ spl3_4
| ~ spl3_7
| ~ spl3_25
| spl3_42 ),
inference(forward_subsumption_resolution,[],[f712,f568]) ).
fof(f714,plain,
( ~ spl3_4
| ~ spl3_7
| ~ spl3_25
| spl3_42 ),
inference(avatar_contradiction_clause,[],[f713]) ).
fof(f717,plain,
( $false
| spl3_25
| ~ spl3_38 ),
inference(forward_subsumption_resolution,[],[f608,f329]) ).
fof(f718,plain,
( spl3_25
| ~ spl3_38 ),
inference(avatar_contradiction_clause,[],[f717]) ).
fof(f740,plain,
( $false
| ~ spl3_1
| ~ spl3_5
| spl3_38 ),
inference(forward_subsumption_resolution,[],[f644,f542]) ).
fof(f741,plain,
( ~ spl3_1
| ~ spl3_5
| spl3_38 ),
inference(avatar_contradiction_clause,[],[f740]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f109]) ).
cnf(s2,plain,
( spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f127]) ).
cnf(s3,plain,
( spl3_5
| spl3_6 ),
inference(sat_conversion,[],[f160]) ).
cnf(s5,plain,
( spl3_9
| spl3_10 ),
inference(sat_conversion,[],[f182]) ).
cnf(s8,plain,
( ~ spl3_9
| ~ spl3_14
| spl3_15 ),
inference(sat_conversion,[],[f210]) ).
cnf(s9,plain,
( ~ spl3_15
| spl3_16 ),
inference(sat_conversion,[],[f218]) ).
cnf(s14,plain,
( ~ spl3_4
| spl3_14 ),
inference(sat_conversion,[],[f291]) ).
cnf(s15,plain,
( ~ spl3_3
| spl3_14 ),
inference(sat_conversion,[],[f292]) ).
cnf(s16,plain,
( ~ spl3_5
| spl3_7 ),
inference(sat_conversion,[],[f320]) ).
cnf(s17,plain,
( ~ spl3_5
| spl3_20
| ~ spl3_21 ),
inference(sat_conversion,[],[f321]) ).
cnf(s22,plain,
( ~ spl3_2
| ~ spl3_7
| spl3_25 ),
inference(sat_conversion,[],[f399]) ).
cnf(s27,plain,
( ~ spl3_6
| ~ spl3_10
| ~ spl3_14 ),
inference(sat_conversion,[],[f459]) ).
cnf(s28,plain,
( ~ spl3_6
| ~ spl3_9
| ~ spl3_14
| spl3_21 ),
inference(sat_conversion,[],[f468]) ).
cnf(s30,plain,
( ~ spl3_6
| ~ spl3_16
| spl3_20 ),
inference(sat_conversion,[],[f471]) ).
cnf(s33,plain,
( ~ spl3_20
| ~ spl3_21 ),
inference(sat_conversion,[],[f539]) ).
cnf(s36,plain,
( spl3_21
| ~ spl3_25
| ~ spl3_42
| ~ spl3_43 ),
inference(sat_conversion,[],[f573]) ).
cnf(s38,plain,
( ~ spl3_25
| spl3_43
| spl3_47 ),
inference(sat_conversion,[],[f615]) ).
cnf(s39,plain,
( ~ spl3_3
| ~ spl3_5
| ~ spl3_25
| spl3_42 ),
inference(sat_conversion,[],[f635]) ).
cnf(s40,plain,
( ~ spl3_25
| ~ spl3_42
| ~ spl3_47 ),
inference(sat_conversion,[],[f651]) ).
cnf(s43,plain,
( ~ spl3_4
| ~ spl3_7
| ~ spl3_25
| spl3_42 ),
inference(sat_conversion,[],[f714]) ).
cnf(s45,plain,
( spl3_25
| ~ spl3_38 ),
inference(sat_conversion,[],[f718]) ).
cnf(s49,plain,
( ~ spl3_1
| ~ spl3_5
| spl3_38 ),
inference(sat_conversion,[],[f741]) ).
cnf(s50,plain,
( ~ spl3_9
| ~ spl3_6
| ~ spl3_14 ),
inference(rat,[],[s30,s9,s33,s8,s28]) ).
cnf(s51,plain,
( ~ spl3_6
| ~ spl3_14 ),
inference(rat,[],[s50,s5,s27]) ).
cnf(s52,plain,
( ~ spl3_4
| ~ spl3_2 ),
inference(rat,[],[s17,s33,s36,s38,s40,s43,s22,s16,s3,s51,s14]) ).
cnf(s53,plain,
( ~ spl3_25
| ~ spl3_5
| ~ spl3_3 ),
inference(rat,[],[s17,s33,s36,s38,s40,s39]) ).
cnf(s54,plain,
~ spl3_2,
inference(rat,[],[s53,s22,s16,s3,s51,s15,s2,s52]) ).
cnf(s55,plain,
spl3_1,
inference(rat,[],[s1,s54]) ).
cnf(s56,plain,
~ spl3_4,
inference(rat,[],[s17,s33,s36,s38,s40,s43,s45,s16,s49,s3,s51,s14,s55]) ).
cnf(s57,plain,
spl3_3,
inference(rat,[],[s2,s56]) ).
cnf(s58,plain,
spl3_14,
inference(rat,[],[s15,s57]) ).
cnf(s59,plain,
~ spl3_6,
inference(rat,[],[s51,s58]) ).
cnf(s60,plain,
spl3_5,
inference(rat,[],[s3,s59]) ).
cnf(s61,plain,
spl3_38,
inference(rat,[],[s49,s55,s60]) ).
cnf(s63,plain,
~ spl3_25,
inference(rat,[],[s53,s57,s60]) ).
cnf(s64,plain,
$false,
inference(rat,[],[s45,s61,s63]) ).
fof(f742,plain,
$false,
inference(avatar_sat_refutation,[],[s64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT039+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 17:29:31 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.47 % (3825820)Will run a generic schedule for satisfiability detection.
% 0.14/0.47 % (3825825)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2773911836_2999 on theBenchmark for (2999ds/0Mi)
% 0.14/0.47 % TRYING [1]
% 0.14/0.47 % TRYING [2]
% 0.14/0.47 % (3825826)% WARNING: option uhcvi not known.
% 0.14/0.47 % (3825828)dis+10_1_sil=32000:sp=arity:random_seed=2135703177:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.14/0.47 % (3825826)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2738541758:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.14/0.47 % (3825827)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4185499897:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.14/0.47 % (3825830)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1570488484:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.14/0.47 % (3825829)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=698403246:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.14/0.47 % (3825831)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=695488488:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.14/0.47 % TRYING [3]
% 0.14/0.47 % (3825830) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3825820-3825830"...
% 0.14/0.47 % (3825830)...printing done.
% 0.14/0.47 % (3825830)Refutation found. Thanks to Tanya!
% 0.14/0.47 % SZS status Theorem for theBenchmark
% 0.14/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.48 % (3825830)------------------------------
% 0.14/0.48 % (3825830)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.48 % (3825830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.48 % (3825830)CaDiCaL version: 2.1.3
% 0.14/0.48 % (3825830)Termination reason: Refutation
% 0.14/0.48 % (3825830)Time elapsed: 0.021 s
% 0.14/0.48 % (3825830)Peak memory usage: 12 MB
% 0.14/0.48 % (3825830)Instructions burned: 28 (million)
% 0.14/0.48 % (3825820)Success in time 0.059 s
% 0.14/0.48 % Vampire exiting
%------------------------------------------------------------------------------