%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : MGT034+2 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n017.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 : Fri Sep 25 02:12:27 PM UTC 2026
% Result : Theorem 1.73s 1.21s
% Output : CNFRefutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 17
% Syntax : Number of formulae : 164 ( 21 unt; 0 def)
% Number of atoms : 526 ( 33 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 664 ( 302 ~; 291 |; 51 &)
% ( 3 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 239 ( 0 sgn 235 !; 4 ?; 96 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2,X3] :
( ( greater(growth_rate(X2,X3),growth_rate(X1,X3))
& subpopulations(X1,X2,X0,X3)
& environment(X0) )
=> selection_favors(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp1_high_growth_rates) ).
fof(f2,axiom,
! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3) ).
fof(f3,axiom,
! [X0] :
( ( in_environment(X0,critical_point(X0))
& environment(X0) )
=> subpopulations(first_movers,efficient_producers,X0,critical_point(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_critical_point_means_FM_and_EP) ).
fof(f4,axiom,
! [X0] :
( ( in_environment(X0,appear(efficient_producers,X0))
& environment(X0) )
=> subpopulations(first_movers,efficient_producers,X0,appear(efficient_producers,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_FM_and_EP_when_EP_appears) ).
fof(f5,axiom,
! [X0] :
( ( ~ decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
& decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0))) )
=> decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_difference_between_founding_rates) ).
fof(f6,axiom,
! [X0,X1,X2] :
( ( greater(X2,X1)
& greater_or_equal(X1,appear(efficient_producers,X0))
& greater_or_equal(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)),zero)
& in_environment(X0,X2)
& environment(X0) )
=> ( decreases(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
=> greater(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_decreasing_function) ).
fof(f7,axiom,
! [X0] :
( greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
<=> greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_negative_growth_rate_difference) ).
fof(f8,axiom,
! [X0] :
( greater(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
<=> greater(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_positive_growth_rate_difference) ).
fof(f12,axiom,
! [X0,X1] :
( ( greater(critical_point(X0),X1)
& greater_or_equal(X1,appear(efficient_producers,X0))
& in_environment(X0,critical_point(X0))
& environment(X0) )
=> in_environment(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_critical_time_points) ).
fof(f14,axiom,
! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> subpopulations(efficient_producers,first_movers,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations) ).
fof(f15,axiom,
! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> greater_or_equal(X1,appear(efficient_producers,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_FM_and_EP_members_EP_appeared) ).
fof(f16,axiom,
! [X0,X1] :
( greater_or_equal(X0,X1)
<=> ( X0 = X1
| greater(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal) ).
fof(f17,axiom,
! [X0,X1] :
( ( ~ greater(zero,difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_relationship_of_growth_rates) ).
fof(f18,axiom,
! [X0,X1] :
( ( X1 = critical_point(X0)
& 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)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
fof(f19,axiom,
! [X0,X1,X2,X3] :
( ( greater_or_equal(X2,X3)
& greater_or_equal(X3,X1)
& subpopulations(first_movers,efficient_producers,X0,X2)
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> subpopulations(first_movers,efficient_producers,X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a10) ).
fof(f20,axiom,
! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a12) ).
fof(f21,conjecture,
! [X0,X1] :
( ( greater(critical_point(X0),X1)
& greater_or_equal(X1,appear(efficient_producers,X0))
& in_environment(X0,critical_point(X0))
& environment(X0) )
=> selection_favors(first_movers,efficient_producers,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t3) ).
fof(f22,negated_conjecture,
~ ! [X0,X1] :
( ( greater(critical_point(X0),X1)
& greater_or_equal(X1,appear(efficient_producers,X0))
& in_environment(X0,critical_point(X0))
& environment(X0) )
=> selection_favors(first_movers,efficient_producers,X1) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,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(ennf_transformation,[],[f18]) ).
fof(f24,plain,
! [X0,X1] :
( critical_point(X0) != X1
| ~ environment(X0)
| ( ! [X2] :
( ~ greater(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( ~ greater_or_equal(X2,X3)
| ~ greater_or_equal(X3,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,X3) ),
inference(ennf_transformation,[],[f19]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( ~ greater_or_equal(X2,X3)
| ~ greater_or_equal(X3,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,X3) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1))) ),
inference(ennf_transformation,[],[f20]) ).
fof(f28,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1))) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
? [X0,X1] :
( greater(critical_point(X0),X1)
& greater_or_equal(X1,appear(efficient_producers,X0))
& in_environment(X0,critical_point(X0))
& environment(X0)
& ~ selection_favors(first_movers,efficient_producers,X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f30,plain,
? [X0,X1] :
( greater(critical_point(X0),X1)
& greater_or_equal(X1,appear(efficient_producers,X0))
& in_environment(X0,critical_point(X0))
& environment(X0)
& ~ selection_favors(first_movers,efficient_producers,X1) ),
inference(flattening,[],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( greater(zero,difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero) ),
inference(ennf_transformation,[],[f17]) ).
fof(f32,plain,
! [X0,X1] :
( greater(zero,difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero) ),
inference(flattening,[],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| subpopulations(efficient_producers,first_movers,X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f34,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| subpopulations(efficient_producers,first_movers,X0,X1) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( ~ greater(critical_point(X0),X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,critical_point(X0))
| ~ environment(X0)
| in_environment(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f36,plain,
! [X0,X1] :
( ~ greater(critical_point(X0),X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,critical_point(X0))
| ~ environment(X0)
| in_environment(X0,X1) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
! [X0] :
( ~ in_environment(X0,critical_point(X0))
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,critical_point(X0)) ),
inference(ennf_transformation,[],[f3]) ).
fof(f38,plain,
! [X0] :
( ~ in_environment(X0,critical_point(X0))
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,critical_point(X0)) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater_or_equal(X1,appear(efficient_producers,X0)) ),
inference(ennf_transformation,[],[f15]) ).
fof(f40,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater_or_equal(X1,appear(efficient_producers,X0)) ),
inference(flattening,[],[f39]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ~ greater(X2,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ greater_or_equal(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)),zero)
| ~ in_environment(X0,X2)
| ~ environment(X0)
| ~ decreases(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| greater(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero) ),
inference(ennf_transformation,[],[f6]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ greater(X2,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ greater_or_equal(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)),zero)
| ~ in_environment(X0,X2)
| ~ environment(X0)
| ~ decreases(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| greater(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
! [X0] :
( decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| ~ decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0)))
| decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))) ),
inference(ennf_transformation,[],[f5]) ).
fof(f46,plain,
! [X0] :
( decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| ~ decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0)))
| decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [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) ),
inference(ennf_transformation,[],[f1]) ).
fof(f48,plain,
! [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) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
! [X0] :
( ~ in_environment(X0,appear(efficient_producers,X0))
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,appear(efficient_producers,X0)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f50,plain,
! [X0] :
( ~ in_environment(X0,appear(efficient_producers,X0))
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,appear(efficient_producers,X0)) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
inference(ennf_transformation,[],[f2]) ).
fof(f52,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
inference(flattening,[],[f51]) ).
fof(f53,plain,
( greater(critical_point(sK0),sK1)
& greater_or_equal(sK1,appear(efficient_producers,sK0))
& in_environment(sK0,critical_point(sK0))
& environment(sK0)
& ~ selection_favors(first_movers,efficient_producers,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f30]) ).
fof(f54,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,[],[f16]) ).
fof(f55,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,[],[f54]) ).
fof(f56,plain,
! [X0] :
( ( ~ greater(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
| greater(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)) )
& ( ~ greater(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))
| greater(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f57,plain,
! [X0] :
( ( ~ greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) )
& ( ~ greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f59,plain,
! [X0,X1] :
( critical_point(X0) != X1
| ~ environment(X0)
| ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f60,plain,
! [X2,X3,X0,X1] :
( ~ greater_or_equal(X2,X3)
| ~ greater_or_equal(X3,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,X3) ),
inference(cnf_transformation,[],[f26]) ).
fof(f61,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1))) ),
inference(cnf_transformation,[],[f28]) ).
fof(f62,plain,
greater(critical_point(sK0),sK1),
inference(cnf_transformation,[],[f53]) ).
fof(f63,plain,
greater_or_equal(sK1,appear(efficient_producers,sK0)),
inference(cnf_transformation,[],[f53]) ).
fof(f64,plain,
in_environment(sK0,critical_point(sK0)),
inference(cnf_transformation,[],[f53]) ).
fof(f65,plain,
environment(sK0),
inference(cnf_transformation,[],[f53]) ).
fof(f66,plain,
~ selection_favors(first_movers,efficient_producers,sK1),
inference(cnf_transformation,[],[f53]) ).
fof(f67,plain,
! [X0,X1] :
( ~ greater_or_equal(X0,X1)
| X0 = X1
| greater(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f68,plain,
! [X0,X1] :
( X0 != X1
| greater_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f69,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| greater_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f70,plain,
! [X0,X1] :
( greater(zero,difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero) ),
inference(cnf_transformation,[],[f32]) ).
fof(f71,plain,
! [X0] :
( ~ greater(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
| greater(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)) ),
inference(cnf_transformation,[],[f56]) ).
fof(f73,plain,
! [X0] :
( ~ greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f75,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| subpopulations(efficient_producers,first_movers,X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f76,plain,
! [X0,X1] :
( ~ greater(critical_point(X0),X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,critical_point(X0))
| ~ environment(X0)
| in_environment(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f77,plain,
! [X0] :
( ~ in_environment(X0,critical_point(X0))
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,critical_point(X0)) ),
inference(cnf_transformation,[],[f38]) ).
fof(f78,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater_or_equal(X1,appear(efficient_producers,X0)) ),
inference(cnf_transformation,[],[f40]) ).
fof(f80,plain,
! [X2,X0,X1] :
( ~ greater(X2,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ greater_or_equal(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)),zero)
| ~ in_environment(X0,X2)
| ~ environment(X0)
| ~ decreases(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| greater(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero) ),
inference(cnf_transformation,[],[f44]) ).
fof(f81,plain,
! [X0] :
( decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| ~ decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0)))
| decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))) ),
inference(cnf_transformation,[],[f46]) ).
fof(f82,plain,
! [X2,X3,X0,X1] :
( ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| selection_favors(X2,X1,X3) ),
inference(cnf_transformation,[],[f48]) ).
fof(f83,plain,
! [X0] :
( ~ in_environment(X0,appear(efficient_producers,X0))
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,appear(efficient_producers,X0)) ),
inference(cnf_transformation,[],[f50]) ).
fof(f84,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
inference(cnf_transformation,[],[f52]) ).
fof(f85,plain,
! [X0] :
( ~ environment(X0)
| ~ greater(growth_rate(efficient_producers,critical_point(X0)),growth_rate(first_movers,critical_point(X0))) ),
inference(equality_resolution,[],[f59]) ).
fof(f87,plain,
! [X1] : greater_or_equal(X1,X1),
inference(equality_resolution,[],[f68]) ).
tcf(c_49,plain,
! [X0: $i] :
( ~ environment(X0)
| ~ greater(growth_rate(efficient_producers,critical_point(X0)),growth_rate(first_movers,critical_point(X0))) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subpopulations(first_movers,efficient_producers,X0,X3)
| ~ environment(X0)
| ~ greater_or_equal(X3,X2)
| ~ greater_or_equal(X1,X3)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1)))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_53,negated_conjecture,
~ selection_favors(first_movers,efficient_producers,sK1),
inference(cnf_transformation,[],[f66]) ).
tcf(c_54,negated_conjecture,
environment(sK0),
inference(cnf_transformation,[],[f65]) ).
tcf(c_55,negated_conjecture,
in_environment(sK0,critical_point(sK0)),
inference(cnf_transformation,[],[f64]) ).
tcf(c_56,negated_conjecture,
greater_or_equal(sK1,appear(efficient_producers,sK0)),
inference(cnf_transformation,[],[f63]) ).
tcf(c_57,negated_conjecture,
greater(critical_point(sK0),sK1),
inference(cnf_transformation,[],[f62]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_59,plain,
! [X0: $i] : greater_or_equal(X0,X0),
inference(cnf_transformation,[],[f87]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( greater(X0,X1)
| ( X0 = X1 )
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| greater(zero,difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_63,plain,
! [X0: $i] :
( greater(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))
| ~ greater(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_65,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( subpopulations(efficient_producers,first_movers,X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( in_environment(X1,X0)
| ~ environment(X1)
| ~ in_environment(X1,critical_point(X1))
| ~ greater(critical_point(X1),X0)
| ~ greater_or_equal(X0,appear(efficient_producers,X1)) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_68,plain,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,X0,critical_point(X0))
| ~ environment(X0)
| ~ in_environment(X0,critical_point(X0)) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(X1,appear(efficient_producers,X0))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ environment(X2)
| ~ in_environment(X2,X0)
| ~ greater(X0,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X2))
| ~ decreases(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ greater_or_equal(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_72,plain,
! [X0: $i] :
( decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| ~ decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0))) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( selection_favors(X0,X2,X1)
| ~ environment(X3)
| ~ subpopulations(X2,X0,X3,X1)
| ~ greater(growth_rate(X0,X1),growth_rate(X2,X1)) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_74,plain,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,X0,appear(efficient_producers,X0))
| ~ environment(X0)
| ~ in_environment(X0,appear(efficient_producers,X0)) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X0)
| ~ decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_103,plain,
! [X0: $i] :
( ~ environment(X0)
| ~ greater(growth_rate(efficient_producers,critical_point(X0)),growth_rate(first_movers,critical_point(X0))) ),
inference(prop_impl_just,[status(thm)],[c_49]) ).
tcf(c_490,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ environment(X3)
| ~ subpopulations(X0,X1,X3,X2)
| ~ greater(growth_rate(X1,X2),growth_rate(X0,X2))
| ( X2 != sK1 )
| ( X1 != first_movers )
| ( X0 != efficient_producers ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_73]) ).
tcf(c_491,plain,
! [X0: $i] :
( ~ environment(X0)
| ~ subpopulations(efficient_producers,first_movers,X0,sK1)
| ~ greater(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)) ),
inference(unflattening,[status(thm)],[c_490]) ).
tcf(c_505,plain,
! [X0: $i] :
( ~ subpopulations(efficient_producers,first_movers,X0,sK1)
| ~ greater(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_491,c_54]) ).
tcf(c_506,plain,
( ~ subpopulations(efficient_producers,first_movers,sK0,sK1)
| ~ greater(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)) ),
inference(unflattening,[status(thm)],[c_505]) ).
tcf(c_513,plain,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,X0,appear(efficient_producers,X0))
| ~ in_environment(X0,appear(efficient_producers,X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_74,c_54]) ).
tcf(c_514,plain,
( subpopulations(first_movers,efficient_producers,sK0,appear(efficient_producers,sK0))
| ~ in_environment(sK0,appear(efficient_producers,sK0)) ),
inference(unflattening,[status(thm)],[c_513]) ).
tcf(c_521,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(X1,appear(efficient_producers,X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_69,c_54]) ).
tcf(c_522,plain,
! [X0: $i] :
( greater_or_equal(X0,appear(efficient_producers,sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(unflattening,[status(thm)],[c_521]) ).
tcf(c_530,plain,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,X0,critical_point(X0))
| ~ in_environment(X0,critical_point(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_68,c_54]) ).
tcf(c_531,plain,
( subpopulations(first_movers,efficient_producers,sK0,critical_point(sK0))
| ~ in_environment(sK0,critical_point(sK0)) ),
inference(unflattening,[status(thm)],[c_530]) ).
tcf(c_532,plain,
subpopulations(first_movers,efficient_producers,sK0,critical_point(sK0)),
inference(global_subsumption_just,[status(thm)],[c_531,c_55,c_531]) ).
tcf(c_537,plain,
! [X0: $i,X1: $i] :
( subpopulations(efficient_producers,first_movers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_66,c_54]) ).
tcf(c_538,plain,
! [X0: $i] :
( subpopulations(efficient_producers,first_movers,sK0,X0)
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(unflattening,[status(thm)],[c_537]) ).
tcf(c_546,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| greater(zero,difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_61,c_54]) ).
tcf(c_547,plain,
! [X0: $i] :
( greater_or_equal(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
| greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(unflattening,[status(thm)],[c_546]) ).
tcf(c_558,plain,
! [X0: $i,X1: $i] :
( decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_54]) ).
tcf(c_559,plain,
! [X0: $i] :
( decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0)))
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(unflattening,[status(thm)],[c_558]) ).
tcf(c_567,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subpopulations(first_movers,efficient_producers,X0,X3)
| ~ greater_or_equal(X3,X2)
| ~ greater_or_equal(X1,X3)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_54]) ).
tcf(c_568,plain,
! [X0: $i,X1: $i,X2: $i] :
( subpopulations(first_movers,efficient_producers,sK0,X2)
| ~ greater_or_equal(X2,X1)
| ~ greater_or_equal(X0,X2)
| ~ subpopulations(first_movers,efficient_producers,sK0,X1)
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(unflattening,[status(thm)],[c_567]) ).
tcf(c_596,plain,
! [X0: $i] :
( ~ greater(growth_rate(efficient_producers,critical_point(X0)),growth_rate(first_movers,critical_point(X0)))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_103,c_54]) ).
tcf(c_597,plain,
~ greater(growth_rate(efficient_producers,critical_point(sK0)),growth_rate(first_movers,critical_point(sK0))),
inference(unflattening,[status(thm)],[c_596]) ).
tcf(c_601,plain,
! [X0: $i,X1: $i] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_75]) ).
tcf(c_602,plain,
! [X0: $i] :
( ~ subpopulations(first_movers,efficient_producers,sK0,X0)
| ~ decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))) ),
inference(unflattening,[status(thm)],[c_601]) ).
tcf(c_610,plain,
! [X0: $i,X1: $i] :
( in_environment(X0,X1)
| ~ in_environment(X0,critical_point(X0))
| ~ greater(critical_point(X0),X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_67]) ).
tcf(c_611,plain,
! [X0: $i] :
( in_environment(sK0,X0)
| ~ in_environment(sK0,critical_point(sK0))
| ~ greater(critical_point(sK0),X0)
| ~ greater_or_equal(X0,appear(efficient_producers,sK0)) ),
inference(unflattening,[status(thm)],[c_610]) ).
tcf(c_613,plain,
! [X0: $i] :
( in_environment(sK0,X0)
| ~ greater_or_equal(X0,appear(efficient_producers,sK0))
| ~ greater(critical_point(sK0),X0) ),
inference(global_subsumption_just,[status(thm)],[c_611,c_55,c_611]) ).
tcf(c_614,plain,
! [X0: $i] :
( in_environment(sK0,X0)
| ~ greater(critical_point(sK0),X0)
| ~ greater_or_equal(X0,appear(efficient_producers,sK0)) ),
inference(renaming,[status(thm)],[c_613]) ).
tcf(c_642,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)),zero)
| ~ in_environment(X0,X1)
| ~ greater(X1,X2)
| ~ greater_or_equal(X2,appear(efficient_producers,X0))
| ~ decreases(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)))
| ~ greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_71]) ).
tcf(c_643,plain,
! [X0: $i,X1: $i] :
( greater(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ in_environment(sK0,X0)
| ~ greater(X0,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,sK0))
| ~ decreases(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ greater_or_equal(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero) ),
inference(unflattening,[status(thm)],[c_642]) ).
tcf(c_706,plain,
! [X0: $i] :
( ~ greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
inference(prop_impl_just,[status(thm)],[c_65]) ).
tcf(c_707,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))) ),
inference(renaming,[status(thm)],[c_706]) ).
tcf(c_714,plain,
! [X0: $i] :
( ~ subpopulations(first_movers,efficient_producers,sK0,X0)
| decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0))) ),
inference(prop_impl_just,[status(thm)],[c_559]) ).
tcf(c_715,plain,
! [X0: $i] :
( decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0)))
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(renaming,[status(thm)],[c_714]) ).
tcf(c_718,plain,
( ~ subpopulations(efficient_producers,first_movers,sK0,sK1)
| ~ greater(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)) ),
inference(prop_impl_just,[status(thm)],[c_506]) ).
tcf(c_722,plain,
( subpopulations(first_movers,efficient_producers,sK0,appear(efficient_producers,sK0))
| ~ in_environment(sK0,appear(efficient_producers,sK0)) ),
inference(prop_impl_just,[status(thm)],[c_514]) ).
tcf(c_730,plain,
! [X0: $i] :
( greater_or_equal(X0,appear(efficient_producers,sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(prop_impl_just,[status(thm)],[c_522]) ).
tcf(c_732,plain,
! [X0: $i] :
( subpopulations(efficient_producers,first_movers,sK0,X0)
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(prop_impl_just,[status(thm)],[c_538]) ).
tcf(c_790,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| greater_or_equal(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(bin_hyper_res,[status(thm)],[c_547,c_707]) ).
tcf(c_1708,plain,
( in_environment(sK0,appear(efficient_producers,sK0))
| ~ greater(critical_point(sK0),appear(efficient_producers,sK0)) ),
inference(superposition,[status(thm)],[c_59,c_614]) ).
tcf(c_1715,plain,
greater_or_equal(critical_point(sK0),sK1),
inference(superposition,[status(thm)],[c_57,c_58]) ).
tcf(c_1735,plain,
greater_or_equal(critical_point(sK0),appear(efficient_producers,sK0)),
inference(superposition,[status(thm)],[c_532,c_730]) ).
tcf(c_1737,plain,
( greater(critical_point(sK0),appear(efficient_producers,sK0))
| ( appear(efficient_producers,sK0) = critical_point(sK0) ) ),
inference(superposition,[status(thm)],[c_1735,c_60]) ).
tcf(c_1795,plain,
! [X0: $i,X1: $i] :
( subpopulations(first_movers,efficient_producers,sK0,X1)
| ~ greater_or_equal(X0,X1)
| ~ greater_or_equal(X1,critical_point(sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(superposition,[status(thm)],[c_532,c_568]) ).
tcf(c_1812,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| greater(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
| ~ in_environment(sK0,X1)
| ~ greater(X1,X0)
| ~ greater_or_equal(X0,appear(efficient_producers,sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,X1)
| ~ decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))) ),
inference(superposition,[status(thm)],[c_790,c_643]) ).
tcf(c_1852,plain,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,sK0,X0)
| ~ greater_or_equal(X0,critical_point(sK0))
| ~ greater_or_equal(critical_point(sK0),X0) ),
inference(superposition,[status(thm)],[c_532,c_1795]) ).
tcf(c_1869,plain,
! [X0: $i,X1: $i] :
( subpopulations(first_movers,efficient_producers,sK0,X1)
| ~ greater_or_equal(X0,X1)
| ~ in_environment(sK0,appear(efficient_producers,sK0))
| ~ greater_or_equal(X1,appear(efficient_producers,sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(superposition,[status(thm)],[c_722,c_568]) ).
tcf(c_1903,plain,
( in_environment(sK0,appear(efficient_producers,sK0))
| ( appear(efficient_producers,sK0) = critical_point(sK0) ) ),
inference(superposition,[status(thm)],[c_1737,c_1708]) ).
tcf(c_1957,plain,
! [X0: $i,X1: $i] :
( subpopulations(first_movers,efficient_producers,sK0,X1)
| ( appear(efficient_producers,sK0) = critical_point(sK0) )
| ~ greater_or_equal(X0,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(superposition,[status(thm)],[c_1903,c_1869]) ).
tcf(c_2083,plain,
( greater(growth_rate(efficient_producers,critical_point(sK0)),growth_rate(first_movers,critical_point(sK0)))
| greater(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)),zero)
| ~ in_environment(sK0,critical_point(sK0))
| ~ greater_or_equal(sK1,appear(efficient_producers,sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,critical_point(sK0))
| ~ decreases(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1))) ),
inference(superposition,[status(thm)],[c_57,c_1812]) ).
tcf(c_2089,plain,
( greater(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)),zero)
| ~ decreases(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2083,c_597,c_55,c_56,c_532]) ).
tcf(c_2185,plain,
! [X0: $i] :
( decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(superposition,[status(thm)],[c_715,c_72]) ).
tcf(c_2245,plain,
( greater(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1))
| ~ decreases(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1))) ),
inference(superposition,[status(thm)],[c_2089,c_63]) ).
tcf(c_2486,plain,
! [X0: $i] :
( ~ subpopulations(first_movers,efficient_producers,sK0,X0)
| decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))) ),
inference(global_subsumption_just,[status(thm)],[c_2185,c_602,c_2185]) ).
tcf(c_2487,plain,
! [X0: $i] :
( decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(renaming,[status(thm)],[c_2486]) ).
tcf(c_2493,plain,
( greater(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1))
| ~ subpopulations(first_movers,efficient_producers,sK0,sK1) ),
inference(superposition,[status(thm)],[c_2487,c_2245]) ).
tcf(c_2505,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,sK1)
| ~ subpopulations(efficient_producers,first_movers,sK0,sK1) ),
inference(superposition,[status(thm)],[c_2493,c_718]) ).
tcf(c_2522,plain,
~ subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_2505,c_732]) ).
tcf(c_2523,plain,
( ~ greater_or_equal(sK1,critical_point(sK0))
| ~ greater_or_equal(critical_point(sK0),sK1) ),
inference(superposition,[status(thm)],[c_1852,c_2522]) ).
tcf(c_2524,plain,
~ greater_or_equal(sK1,critical_point(sK0)),
inference(forward_subsumption_resolution,[status(thm)],[c_2523,c_1715]) ).
tcf(c_2935,plain,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,sK0,X0)
| ( appear(efficient_producers,sK0) = critical_point(sK0) )
| ~ greater_or_equal(critical_point(sK0),X0)
| ~ greater_or_equal(X0,appear(efficient_producers,sK0)) ),
inference(superposition,[status(thm)],[c_532,c_1957]) ).
tcf(c_2982,plain,
( subpopulations(first_movers,efficient_producers,sK0,sK1)
| ( appear(efficient_producers,sK0) = critical_point(sK0) )
| ~ greater_or_equal(critical_point(sK0),sK1) ),
inference(superposition,[status(thm)],[c_56,c_2935]) ).
tcf(c_2986,plain,
appear(efficient_producers,sK0) = critical_point(sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_2982,c_2522,c_1715]) ).
tcf(c_3006,plain,
greater_or_equal(sK1,critical_point(sK0)),
inference(demodulation,[status(thm)],[c_56,c_2986]) ).
tcf(c_3007,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3006,c_2524]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT034+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 01:02:16 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 1.73/1.21 % SZS status Started for theBenchmark.p
% 1.73/1.21 % SZS status Theorem for theBenchmark.p
% 1.73/1.21
% 1.73/1.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.73/1.21
% 1.73/1.21 % ------ iProver source info
% 1.73/1.21
% 1.73/1.21 % git: date: 2026-07-19 20:42:38 +0200
% 1.73/1.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.73/1.21 % git: non_committed_changes: false
% 1.73/1.21
% 1.73/1.21 % ------ Parsing...
% 1.73/1.21 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.73/1.21
% 1.73/1.21 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 1.73/1.21
% 1.73/1.21 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.73/1.21
% 1.73/1.21 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.73/1.21 % ------ Proving...
% 1.73/1.21 % ------ Problem Properties
% 1.73/1.21
% 1.73/1.21 %
% 1.73/1.21 % clauses 25
% 1.73/1.21 % conjectures 3
% 1.73/1.21 % EPR 6
% 1.73/1.21 % Horn 22
% 1.73/1.21 % unary 6
% 1.73/1.21 % binary 11
% 1.73/1.21 % lits 59
% 1.73/1.21 % lits eq 1
% 1.73/1.21 % fd_pure 0
% 1.73/1.21 % fd_pseudo 0
% 1.73/1.21 % fd_cond 0
% 1.73/1.21 % fd_pseudo_cond 1
% 1.73/1.21 % AC symbols 0
% 1.73/1.21
% 1.73/1.21 % ------ Schedule dynamic 5 is on
% 1.73/1.21
% 1.73/1.21 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.73/1.21
% 1.73/1.21
% 1.73/1.21 % ------
% 1.73/1.21 % Current options:
% 1.73/1.21 % ------
% 1.73/1.21
% 1.73/1.21
% 1.73/1.21 %
% 1.73/1.21
% 1.73/1.21 % ------ Proving...
% 1.73/1.21 %
% 1.73/1.21
% 1.73/1.21 % SZS status Theorem for theBenchmark.p
% 1.73/1.21
% 1.73/1.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.73/1.22
% 1.73/1.22
%------------------------------------------------------------------------------