TSTP Solution File: MGT034+2 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : MGT034+2 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 09:14:22 EDT 2023
% Result : Theorem 3.44s 1.16s
% Output : CNFRefutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 18
% Syntax : Number of formulae : 180 ( 21 unt; 0 def)
% Number of atoms : 587 ( 33 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 714 ( 307 ~; 287 |; 83 &)
% ( 6 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% 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 : 267 ( 0 sgn; 168 !; 6 ?)
% 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/sandbox/benchmark/theBenchmark.p',mp1_high_growth_rates) ).
fof(f2,axiom,
! [X0,X3] :
( ( subpopulations(first_movers,efficient_producers,X0,X3)
& environment(X0) )
=> ~ decreases(difference(disbanding_rate(first_movers,X3),disbanding_rate(efficient_producers,X3))) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',mp_FM_and_EP_when_EP_appears) ).
fof(f5,axiom,
! [X3] :
( ( ~ decreases(difference(disbanding_rate(first_movers,X3),disbanding_rate(efficient_producers,X3)))
& decreases(difference(founding_rate(first_movers,X3),founding_rate(efficient_producers,X3))) )
=> decreases(difference(growth_rate(first_movers,X3),growth_rate(efficient_producers,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_difference_between_founding_rates) ).
fof(f6,axiom,
! [X0,X3,X4] :
( ( greater(X4,X3)
& greater_or_equal(X3,appear(efficient_producers,X0))
& greater_or_equal(difference(growth_rate(first_movers,X4),growth_rate(efficient_producers,X4)),zero)
& in_environment(X0,X4)
& environment(X0) )
=> ( decreases(difference(growth_rate(first_movers,X3),growth_rate(efficient_producers,X3)))
=> greater(difference(growth_rate(first_movers,X3),growth_rate(efficient_producers,X3)),zero) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_decreasing_function) ).
fof(f7,axiom,
! [X3] :
( greater(zero,difference(growth_rate(first_movers,X3),growth_rate(efficient_producers,X3)))
<=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_negative_growth_rate_difference) ).
fof(f8,axiom,
! [X3] :
( greater(difference(growth_rate(first_movers,X3),growth_rate(efficient_producers,X3)),zero)
<=> greater(growth_rate(first_movers,X3),growth_rate(efficient_producers,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_positive_growth_rate_difference) ).
fof(f12,axiom,
! [X0,X3] :
( ( greater(critical_point(X0),X3)
& greater_or_equal(X3,appear(efficient_producers,X0))
& in_environment(X0,critical_point(X0))
& environment(X0) )
=> in_environment(X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_critical_time_points) ).
fof(f14,axiom,
! [X0,X3] :
( ( subpopulations(first_movers,efficient_producers,X0,X3)
& environment(X0) )
=> subpopulations(efficient_producers,first_movers,X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations) ).
fof(f15,axiom,
! [X0,X3] :
( ( subpopulations(first_movers,efficient_producers,X0,X3)
& environment(X0) )
=> greater_or_equal(X3,appear(efficient_producers,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_FM_and_EP_members_EP_appeared) ).
fof(f16,axiom,
! [X7,X8] :
( greater_or_equal(X7,X8)
<=> ( X7 = X8
| greater(X7,X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal) ).
fof(f17,axiom,
! [X0,X3] :
( ( ~ greater(zero,difference(growth_rate(first_movers,X3),growth_rate(efficient_producers,X3)))
& subpopulations(first_movers,efficient_producers,X0,X3)
& environment(X0) )
=> greater_or_equal(difference(growth_rate(first_movers,X3),growth_rate(efficient_producers,X3)),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_relationship_of_growth_rates) ).
fof(f18,axiom,
! [X0,X9] :
( ( critical_point(X0) = X9
& environment(X0) )
=> ( ! [X3] :
( ( greater(X3,X9)
& subpopulations(first_movers,efficient_producers,X0,X3) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) )
& ~ greater(growth_rate(efficient_producers,X9),growth_rate(first_movers,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
fof(f19,axiom,
! [X0,X5,X6,X3] :
( ( greater_or_equal(X6,X3)
& greater_or_equal(X3,X5)
& subpopulations(first_movers,efficient_producers,X0,X6)
& subpopulations(first_movers,efficient_producers,X0,X5)
& environment(X0) )
=> subpopulations(first_movers,efficient_producers,X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a10) ).
fof(f20,axiom,
! [X0,X3] :
( ( subpopulations(first_movers,efficient_producers,X0,X3)
& environment(X0) )
=> decreases(difference(founding_rate(first_movers,X3),founding_rate(efficient_producers,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a12) ).
fof(f21,conjecture,
! [X0,X3] :
( ( greater(critical_point(X0),X3)
& greater_or_equal(X3,appear(efficient_producers,X0))
& in_environment(X0,critical_point(X0))
& environment(X0) )
=> selection_favors(first_movers,efficient_producers,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t3) ).
fof(f22,negated_conjecture,
~ ! [X0,X3] :
( ( greater(critical_point(X0),X3)
& greater_or_equal(X3,appear(efficient_producers,X0))
& in_environment(X0,critical_point(X0))
& environment(X0) )
=> selection_favors(first_movers,efficient_producers,X3) ),
inference(negated_conjecture,[],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
inference(rectify,[],[f2]) ).
fof(f24,plain,
! [X0] :
( ( ~ decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
& decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0))) )
=> decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))) ),
inference(rectify,[],[f5]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( greater(X2,X1)
& greater_or_equal(X1,appear(efficient_producers,X0))
& greater_or_equal(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)),zero)
& in_environment(X0,X2)
& environment(X0) )
=> ( decreases(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
=> greater(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero) ) ),
inference(rectify,[],[f6]) ).
fof(f26,plain,
! [X0] :
( greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
<=> greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
inference(rectify,[],[f7]) ).
fof(f27,plain,
! [X0] :
( greater(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
<=> greater(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)) ),
inference(rectify,[],[f8]) ).
fof(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) )
=> in_environment(X0,X1) ),
inference(rectify,[],[f12]) ).
fof(f31,plain,
! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> subpopulations(efficient_producers,first_movers,X0,X1) ),
inference(rectify,[],[f14]) ).
fof(f32,plain,
! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> greater_or_equal(X1,appear(efficient_producers,X0)) ),
inference(rectify,[],[f15]) ).
fof(f33,plain,
! [X0,X1] :
( greater_or_equal(X0,X1)
<=> ( X0 = X1
| greater(X0,X1) ) ),
inference(rectify,[],[f16]) ).
fof(f34,plain,
! [X0,X1] :
( ( ~ greater(zero,difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero) ),
inference(rectify,[],[f17]) ).
fof(f35,plain,
! [X0,X1] :
( ( critical_point(X0) = X1
& environment(X0) )
=> ( ! [X2] :
( ( greater(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ) ),
inference(rectify,[],[f18]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( ( greater_or_equal(X2,X3)
& greater_or_equal(X3,X1)
& subpopulations(first_movers,efficient_producers,X0,X2)
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> subpopulations(first_movers,efficient_producers,X0,X3) ),
inference(rectify,[],[f19]) ).
fof(f37,plain,
! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1))) ),
inference(rectify,[],[f20]) ).
fof(f38,plain,
~ ! [X0,X1] :
( ( greater(critical_point(X0),X1)
& greater_or_equal(X1,appear(efficient_producers,X0))
& in_environment(X0,critical_point(X0))
& environment(X0) )
=> selection_favors(first_movers,efficient_producers,X1) ),
inference(rectify,[],[f22]) ).
fof(f39,plain,
! [X0,X1,X2,X3] :
( selection_favors(X2,X1,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f40,plain,
! [X0,X1,X2,X3] :
( selection_favors(X2,X1,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f42,plain,
! [X0,X1] :
( ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
! [X0] :
( subpopulations(first_movers,efficient_producers,X0,critical_point(X0))
| ~ in_environment(X0,critical_point(X0))
| ~ environment(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f44,plain,
! [X0] :
( subpopulations(first_movers,efficient_producers,X0,critical_point(X0))
| ~ in_environment(X0,critical_point(X0))
| ~ environment(X0) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
! [X0] :
( subpopulations(first_movers,efficient_producers,X0,appear(efficient_producers,X0))
| ~ in_environment(X0,appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f46,plain,
! [X0] :
( subpopulations(first_movers,efficient_producers,X0,appear(efficient_producers,X0))
| ~ in_environment(X0,appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0] :
( decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| ~ decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0))) ),
inference(ennf_transformation,[],[f24]) ).
fof(f48,plain,
! [X0] :
( decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| ~ decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0))) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
! [X0,X1,X2] :
( greater(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ decreases(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ greater(X2,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ greater_or_equal(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)),zero)
| ~ in_environment(X0,X2)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f50,plain,
! [X0,X1,X2] :
( greater(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ decreases(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ greater(X2,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ greater_or_equal(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)),zero)
| ~ in_environment(X0,X2)
| ~ environment(X0) ),
inference(flattening,[],[f49]) ).
fof(f55,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ greater(critical_point(X0),X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,critical_point(X0))
| ~ environment(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f56,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ greater(critical_point(X0),X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,critical_point(X0))
| ~ environment(X0) ),
inference(flattening,[],[f55]) ).
fof(f59,plain,
! [X0,X1] :
( subpopulations(efficient_producers,first_movers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f60,plain,
! [X0,X1] :
( subpopulations(efficient_producers,first_movers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f59]) ).
fof(f61,plain,
! [X0,X1] :
( greater_or_equal(X1,appear(efficient_producers,X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f62,plain,
! [X0,X1] :
( greater_or_equal(X1,appear(efficient_producers,X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0,X1] :
( greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| greater(zero,difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f64,plain,
! [X0,X1] :
( greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| greater(zero,difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f63]) ).
fof(f65,plain,
! [X0,X1] :
( ( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) )
| critical_point(X0) != X1
| ~ environment(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f66,plain,
! [X0,X1] :
( ( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) )
| critical_point(X0) != X1
| ~ environment(X0) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0,X1,X2,X3] :
( subpopulations(first_movers,efficient_producers,X0,X3)
| ~ greater_or_equal(X2,X3)
| ~ greater_or_equal(X3,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f68,plain,
! [X0,X1,X2,X3] :
( subpopulations(first_movers,efficient_producers,X0,X3)
| ~ greater_or_equal(X2,X3)
| ~ greater_or_equal(X3,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f70,plain,
! [X0,X1] :
( decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
? [X0,X1] :
( ~ selection_favors(first_movers,efficient_producers,X1)
& greater(critical_point(X0),X1)
& greater_or_equal(X1,appear(efficient_producers,X0))
& in_environment(X0,critical_point(X0))
& environment(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f72,plain,
? [X0,X1] :
( ~ selection_favors(first_movers,efficient_producers,X1)
& greater(critical_point(X0),X1)
& greater_or_equal(X1,appear(efficient_producers,X0))
& in_environment(X0,critical_point(X0))
& environment(X0) ),
inference(flattening,[],[f71]) ).
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)) )
& ( 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,[],[f26]) ).
fof(f74,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,[],[f27]) ).
fof(f75,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,[],[f33]) ).
fof(f76,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,[],[f75]) ).
fof(f77,plain,
( ? [X0,X1] :
( ~ selection_favors(first_movers,efficient_producers,X1)
& greater(critical_point(X0),X1)
& greater_or_equal(X1,appear(efficient_producers,X0))
& in_environment(X0,critical_point(X0))
& environment(X0) )
=> ( ~ selection_favors(first_movers,efficient_producers,sK1)
& greater(critical_point(sK0),sK1)
& greater_or_equal(sK1,appear(efficient_producers,sK0))
& in_environment(sK0,critical_point(sK0))
& environment(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
( ~ selection_favors(first_movers,efficient_producers,sK1)
& greater(critical_point(sK0),sK1)
& greater_or_equal(sK1,appear(efficient_producers,sK0))
& in_environment(sK0,critical_point(sK0))
& environment(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f72,f77]) ).
fof(f79,plain,
! [X2,X3,X0,X1] :
( selection_favors(X2,X1,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f80,plain,
! [X0,X1] :
( ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f81,plain,
! [X0] :
( subpopulations(first_movers,efficient_producers,X0,critical_point(X0))
| ~ in_environment(X0,critical_point(X0))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f82,plain,
! [X0] :
( subpopulations(first_movers,efficient_producers,X0,appear(efficient_producers,X0))
| ~ in_environment(X0,appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f83,plain,
! [X0] :
( decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| ~ decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0))) ),
inference(cnf_transformation,[],[f48]) ).
fof(f84,plain,
! [X2,X0,X1] :
( greater(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ decreases(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ greater(X2,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ greater_or_equal(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)),zero)
| ~ in_environment(X0,X2)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f85,plain,
! [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(cnf_transformation,[],[f73]) ).
fof(f87,plain,
! [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(cnf_transformation,[],[f74]) ).
fof(f92,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ greater(critical_point(X0),X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,critical_point(X0))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f94,plain,
! [X0,X1] :
( subpopulations(efficient_producers,first_movers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f95,plain,
! [X0,X1] :
( greater_or_equal(X1,appear(efficient_producers,X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f96,plain,
! [X0,X1] :
( X0 = X1
| greater(X0,X1)
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f97,plain,
! [X0,X1] :
( greater_or_equal(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f98,plain,
! [X0,X1] :
( greater_or_equal(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f76]) ).
fof(f99,plain,
! [X0,X1] :
( greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| greater(zero,difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f100,plain,
! [X0,X1] :
( ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| critical_point(X0) != X1
| ~ environment(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f102,plain,
! [X2,X3,X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,X3)
| ~ greater_or_equal(X2,X3)
| ~ greater_or_equal(X3,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f103,plain,
! [X0,X1] :
( decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f104,plain,
environment(sK0),
inference(cnf_transformation,[],[f78]) ).
fof(f105,plain,
in_environment(sK0,critical_point(sK0)),
inference(cnf_transformation,[],[f78]) ).
fof(f106,plain,
greater_or_equal(sK1,appear(efficient_producers,sK0)),
inference(cnf_transformation,[],[f78]) ).
fof(f107,plain,
greater(critical_point(sK0),sK1),
inference(cnf_transformation,[],[f78]) ).
fof(f108,plain,
~ selection_favors(first_movers,efficient_producers,sK1),
inference(cnf_transformation,[],[f78]) ).
fof(f109,plain,
! [X1] : greater_or_equal(X1,X1),
inference(equality_resolution,[],[f98]) ).
fof(f111,plain,
! [X0] :
( ~ greater(growth_rate(efficient_producers,critical_point(X0)),growth_rate(first_movers,critical_point(X0)))
| ~ environment(X0) ),
inference(equality_resolution,[],[f100]) ).
cnf(c_49,plain,
( ~ greater(growth_rate(X0,X1),growth_rate(X2,X1))
| ~ subpopulations(X2,X0,X3,X1)
| ~ environment(X3)
| selection_favors(X0,X2,X1) ),
inference(cnf_transformation,[],[f79]) ).
cnf(c_50,plain,
( ~ decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| ~ subpopulations(first_movers,efficient_producers,X1,X0)
| ~ environment(X1) ),
inference(cnf_transformation,[],[f80]) ).
cnf(c_51,plain,
( ~ in_environment(X0,critical_point(X0))
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,critical_point(X0)) ),
inference(cnf_transformation,[],[f81]) ).
cnf(c_52,plain,
( ~ in_environment(X0,appear(efficient_producers,X0))
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,appear(efficient_producers,X0)) ),
inference(cnf_transformation,[],[f82]) ).
cnf(c_53,plain,
( ~ decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0)))
| decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))) ),
inference(cnf_transformation,[],[f83]) ).
cnf(c_54,plain,
( ~ greater_or_equal(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
| ~ decreases(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ greater_or_equal(X1,appear(efficient_producers,X2))
| ~ greater(X0,X1)
| ~ in_environment(X2,X0)
| ~ environment(X2)
| greater(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero) ),
inference(cnf_transformation,[],[f84]) ).
cnf(c_56,plain,
( ~ 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,[],[f85]) ).
cnf(c_58,plain,
( ~ 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,[],[f87]) ).
cnf(c_62,plain,
( ~ greater_or_equal(X0,appear(efficient_producers,X1))
| ~ greater(critical_point(X1),X0)
| ~ in_environment(X1,critical_point(X1))
| ~ environment(X1)
| in_environment(X1,X0) ),
inference(cnf_transformation,[],[f92]) ).
cnf(c_64,plain,
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| subpopulations(efficient_producers,first_movers,X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
cnf(c_65,plain,
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater_or_equal(X1,appear(efficient_producers,X0)) ),
inference(cnf_transformation,[],[f95]) ).
cnf(c_66,plain,
greater_or_equal(X0,X0),
inference(cnf_transformation,[],[f109]) ).
cnf(c_67,plain,
( ~ greater(X0,X1)
| greater_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
cnf(c_68,plain,
( ~ greater_or_equal(X0,X1)
| X0 = X1
| greater(X0,X1) ),
inference(cnf_transformation,[],[f96]) ).
cnf(c_69,plain,
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater(zero,difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero) ),
inference(cnf_transformation,[],[f99]) ).
cnf(c_71,plain,
( ~ greater(growth_rate(efficient_producers,critical_point(X0)),growth_rate(first_movers,critical_point(X0)))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f111]) ).
cnf(c_72,plain,
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X1,X3)
| ~ greater_or_equal(X3,X2)
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,X3) ),
inference(cnf_transformation,[],[f102]) ).
cnf(c_73,plain,
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1))) ),
inference(cnf_transformation,[],[f103]) ).
cnf(c_74,negated_conjecture,
~ selection_favors(first_movers,efficient_producers,sK1),
inference(cnf_transformation,[],[f108]) ).
cnf(c_75,negated_conjecture,
greater(critical_point(sK0),sK1),
inference(cnf_transformation,[],[f107]) ).
cnf(c_76,negated_conjecture,
greater_or_equal(sK1,appear(efficient_producers,sK0)),
inference(cnf_transformation,[],[f106]) ).
cnf(c_77,negated_conjecture,
in_environment(sK0,critical_point(sK0)),
inference(cnf_transformation,[],[f105]) ).
cnf(c_78,negated_conjecture,
environment(sK0),
inference(cnf_transformation,[],[f104]) ).
cnf(c_113,plain,
( ~ environment(X0)
| ~ greater(growth_rate(efficient_producers,critical_point(X0)),growth_rate(first_movers,critical_point(X0))) ),
inference(prop_impl_just,[status(thm)],[c_71]) ).
cnf(c_114,plain,
( ~ greater(growth_rate(efficient_producers,critical_point(X0)),growth_rate(first_movers,critical_point(X0)))
| ~ environment(X0) ),
inference(renaming,[status(thm)],[c_113]) ).
cnf(c_546,plain,
( X0 != first_movers
| X1 != sK1
| X2 != efficient_producers
| ~ greater(growth_rate(X0,X1),growth_rate(X2,X1))
| ~ subpopulations(X2,X0,X3,X1)
| ~ environment(X3) ),
inference(resolution_lifted,[status(thm)],[c_49,c_74]) ).
cnf(c_547,plain,
( ~ greater(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1))
| ~ subpopulations(efficient_producers,first_movers,X0,sK1)
| ~ environment(X0) ),
inference(unflattening,[status(thm)],[c_546]) ).
cnf(c_576,plain,
( X0 != sK0
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ greater(critical_point(X0),X1)
| ~ in_environment(X0,critical_point(X0))
| in_environment(X0,X1) ),
inference(resolution_lifted,[status(thm)],[c_62,c_78]) ).
cnf(c_577,plain,
( ~ greater_or_equal(X0,appear(efficient_producers,sK0))
| ~ greater(critical_point(sK0),X0)
| ~ in_environment(sK0,critical_point(sK0))
| in_environment(sK0,X0) ),
inference(unflattening,[status(thm)],[c_576]) ).
cnf(c_579,plain,
( ~ greater(critical_point(sK0),X0)
| ~ greater_or_equal(X0,appear(efficient_producers,sK0))
| in_environment(sK0,X0) ),
inference(global_subsumption_just,[status(thm)],[c_577,c_77,c_577]) ).
cnf(c_580,plain,
( ~ greater_or_equal(X0,appear(efficient_producers,sK0))
| ~ greater(critical_point(sK0),X0)
| in_environment(sK0,X0) ),
inference(renaming,[status(thm)],[c_579]) ).
cnf(c_591,plain,
( X0 != sK0
| ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(resolution_lifted,[status(thm)],[c_50,c_78]) ).
cnf(c_592,plain,
( ~ decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(unflattening,[status(thm)],[c_591]) ).
cnf(c_600,plain,
( X0 != sK0
| ~ greater(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1))
| ~ subpopulations(efficient_producers,first_movers,X0,sK1) ),
inference(resolution_lifted,[status(thm)],[c_547,c_78]) ).
cnf(c_601,plain,
( ~ greater(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1))
| ~ subpopulations(efficient_producers,first_movers,sK0,sK1) ),
inference(unflattening,[status(thm)],[c_600]) ).
cnf(c_608,plain,
( X0 != sK0
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1))) ),
inference(resolution_lifted,[status(thm)],[c_73,c_78]) ).
cnf(c_609,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,X0)
| decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0))) ),
inference(unflattening,[status(thm)],[c_608]) ).
cnf(c_617,plain,
( X0 != sK0
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X1,X3)
| ~ greater_or_equal(X3,X2)
| subpopulations(first_movers,efficient_producers,X0,X3) ),
inference(resolution_lifted,[status(thm)],[c_72,c_78]) ).
cnf(c_618,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,X0)
| ~ subpopulations(first_movers,efficient_producers,sK0,X1)
| ~ greater_or_equal(X0,X2)
| ~ greater_or_equal(X2,X1)
| subpopulations(first_movers,efficient_producers,sK0,X2) ),
inference(unflattening,[status(thm)],[c_617]) ).
cnf(c_634,plain,
( X0 != sK0
| ~ greater(growth_rate(efficient_producers,critical_point(X0)),growth_rate(first_movers,critical_point(X0))) ),
inference(resolution_lifted,[status(thm)],[c_114,c_78]) ).
cnf(c_635,plain,
~ greater(growth_rate(efficient_producers,critical_point(sK0)),growth_rate(first_movers,critical_point(sK0))),
inference(unflattening,[status(thm)],[c_634]) ).
cnf(c_651,plain,
( X0 != sK0
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater(zero,difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero) ),
inference(resolution_lifted,[status(thm)],[c_69,c_78]) ).
cnf(c_652,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,X0)
| greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| greater_or_equal(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero) ),
inference(unflattening,[status(thm)],[c_651]) ).
cnf(c_663,plain,
( X0 != sK0
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater_or_equal(X1,appear(efficient_producers,X0)) ),
inference(resolution_lifted,[status(thm)],[c_65,c_78]) ).
cnf(c_664,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,X0)
| greater_or_equal(X0,appear(efficient_producers,sK0)) ),
inference(unflattening,[status(thm)],[c_663]) ).
cnf(c_672,plain,
( X0 != sK0
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| subpopulations(efficient_producers,first_movers,X0,X1) ),
inference(resolution_lifted,[status(thm)],[c_64,c_78]) ).
cnf(c_673,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,X0)
| subpopulations(efficient_producers,first_movers,sK0,X0) ),
inference(unflattening,[status(thm)],[c_672]) ).
cnf(c_708,plain,
( X0 != sK0
| ~ in_environment(X0,appear(efficient_producers,X0))
| subpopulations(first_movers,efficient_producers,X0,appear(efficient_producers,X0)) ),
inference(resolution_lifted,[status(thm)],[c_52,c_78]) ).
cnf(c_709,plain,
( ~ in_environment(sK0,appear(efficient_producers,sK0))
| subpopulations(first_movers,efficient_producers,sK0,appear(efficient_producers,sK0)) ),
inference(unflattening,[status(thm)],[c_708]) ).
cnf(c_716,plain,
( X0 != sK0
| ~ in_environment(X0,critical_point(X0))
| subpopulations(first_movers,efficient_producers,X0,critical_point(X0)) ),
inference(resolution_lifted,[status(thm)],[c_51,c_78]) ).
cnf(c_717,plain,
( ~ in_environment(sK0,critical_point(sK0))
| subpopulations(first_movers,efficient_producers,sK0,critical_point(sK0)) ),
inference(unflattening,[status(thm)],[c_716]) ).
cnf(c_718,plain,
subpopulations(first_movers,efficient_producers,sK0,critical_point(sK0)),
inference(global_subsumption_just,[status(thm)],[c_717,c_77,c_717]) ).
cnf(c_723,plain,
( X0 != sK0
| ~ greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ decreases(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)))
| ~ greater_or_equal(X2,appear(efficient_producers,X0))
| ~ greater(X1,X2)
| ~ in_environment(X0,X1)
| greater(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)),zero) ),
inference(resolution_lifted,[status(thm)],[c_54,c_78]) ).
cnf(c_724,plain,
( ~ greater_or_equal(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
| ~ decreases(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ greater_or_equal(X1,appear(efficient_producers,sK0))
| ~ greater(X0,X1)
| ~ in_environment(sK0,X0)
| greater(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero) ),
inference(unflattening,[status(thm)],[c_723]) ).
cnf(c_789,plain,
( 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(prop_impl_just,[status(thm)],[c_56]) ).
cnf(c_790,plain,
( ~ 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(renaming,[status(thm)],[c_789]) ).
cnf(c_799,plain,
( decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0)))
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(prop_impl_just,[status(thm)],[c_609]) ).
cnf(c_800,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,X0)
| decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0))) ),
inference(renaming,[status(thm)],[c_799]) ).
cnf(c_805,plain,
( ~ greater(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1))
| ~ subpopulations(efficient_producers,first_movers,sK0,sK1) ),
inference(prop_impl_just,[status(thm)],[c_601]) ).
cnf(c_811,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,X0)
| greater_or_equal(X0,appear(efficient_producers,sK0)) ),
inference(prop_impl_just,[status(thm)],[c_664]) ).
cnf(c_813,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,X0)
| subpopulations(efficient_producers,first_movers,sK0,X0) ),
inference(prop_impl_just,[status(thm)],[c_673]) ).
cnf(c_821,plain,
( ~ in_environment(sK0,appear(efficient_producers,sK0))
| subpopulations(first_movers,efficient_producers,sK0,appear(efficient_producers,sK0)) ),
inference(prop_impl_just,[status(thm)],[c_709]) ).
cnf(c_882,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,X0)
| greater_or_equal(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
inference(bin_hyper_res,[status(thm)],[c_652,c_790]) ).
cnf(c_1888,plain,
( ~ greater(critical_point(sK0),appear(efficient_producers,sK0))
| in_environment(sK0,appear(efficient_producers,sK0)) ),
inference(superposition,[status(thm)],[c_66,c_580]) ).
cnf(c_1895,plain,
greater_or_equal(critical_point(sK0),sK1),
inference(superposition,[status(thm)],[c_75,c_67]) ).
cnf(c_1913,plain,
greater_or_equal(critical_point(sK0),appear(efficient_producers,sK0)),
inference(superposition,[status(thm)],[c_718,c_811]) ).
cnf(c_1915,plain,
( appear(efficient_producers,sK0) = critical_point(sK0)
| greater(critical_point(sK0),appear(efficient_producers,sK0)) ),
inference(superposition,[status(thm)],[c_1913,c_68]) ).
cnf(c_2001,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,X0)
| ~ greater_or_equal(critical_point(sK0),X1)
| ~ greater_or_equal(X1,X0)
| subpopulations(first_movers,efficient_producers,sK0,X1) ),
inference(superposition,[status(thm)],[c_718,c_618]) ).
cnf(c_2018,plain,
( ~ decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| ~ subpopulations(first_movers,efficient_producers,sK0,X1)
| ~ greater_or_equal(X0,appear(efficient_producers,sK0))
| ~ greater(X1,X0)
| ~ in_environment(sK0,X1)
| greater(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(superposition,[status(thm)],[c_882,c_724]) ).
cnf(c_2071,plain,
( appear(efficient_producers,sK0) = critical_point(sK0)
| in_environment(sK0,appear(efficient_producers,sK0)) ),
inference(superposition,[status(thm)],[c_1915,c_1888]) ).
cnf(c_2116,plain,
( ~ greater_or_equal(X0,appear(efficient_producers,sK0))
| ~ in_environment(sK0,appear(efficient_producers,sK0))
| ~ greater_or_equal(critical_point(sK0),X0)
| subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(superposition,[status(thm)],[c_821,c_2001]) ).
cnf(c_2117,plain,
( ~ greater_or_equal(critical_point(sK0),X0)
| ~ greater_or_equal(X0,critical_point(sK0))
| subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(superposition,[status(thm)],[c_718,c_2001]) ).
cnf(c_2299,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,X0)
| decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))) ),
inference(superposition,[status(thm)],[c_800,c_53]) ).
cnf(c_2709,plain,
( ~ in_environment(sK0,appear(efficient_producers,sK0))
| ~ greater_or_equal(critical_point(sK0),sK1)
| subpopulations(first_movers,efficient_producers,sK0,sK1) ),
inference(superposition,[status(thm)],[c_76,c_2116]) ).
cnf(c_2713,plain,
( ~ in_environment(sK0,appear(efficient_producers,sK0))
| subpopulations(first_movers,efficient_producers,sK0,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2709,c_1895]) ).
cnf(c_2720,plain,
( appear(efficient_producers,sK0) = critical_point(sK0)
| subpopulations(first_movers,efficient_producers,sK0,sK1) ),
inference(superposition,[status(thm)],[c_2071,c_2713]) ).
cnf(c_3170,plain,
( decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(global_subsumption_just,[status(thm)],[c_2299,c_592,c_2299]) ).
cnf(c_3171,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,X0)
| decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))) ),
inference(renaming,[status(thm)],[c_3170]) ).
cnf(c_4712,plain,
( ~ decreases(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)))
| ~ subpopulations(first_movers,efficient_producers,sK0,critical_point(sK0))
| ~ greater_or_equal(sK1,appear(efficient_producers,sK0))
| ~ in_environment(sK0,critical_point(sK0))
| greater(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)),zero)
| greater(growth_rate(efficient_producers,critical_point(sK0)),growth_rate(first_movers,critical_point(sK0))) ),
inference(superposition,[status(thm)],[c_75,c_2018]) ).
cnf(c_4717,plain,
( ~ decreases(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)))
| greater(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)),zero) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4712,c_635,c_77,c_76,c_718]) ).
cnf(c_4813,plain,
( ~ decreases(difference(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)))
| greater(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)) ),
inference(superposition,[status(thm)],[c_4717,c_58]) ).
cnf(c_4948,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,sK1)
| greater(growth_rate(first_movers,sK1),growth_rate(efficient_producers,sK1)) ),
inference(superposition,[status(thm)],[c_3171,c_4813]) ).
cnf(c_5050,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,sK1)
| ~ subpopulations(efficient_producers,first_movers,sK0,sK1) ),
inference(superposition,[status(thm)],[c_4948,c_805]) ).
cnf(c_5098,plain,
~ subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_5050,c_813]) ).
cnf(c_5099,plain,
appear(efficient_producers,sK0) = critical_point(sK0),
inference(backward_subsumption_resolution,[status(thm)],[c_2720,c_5098]) ).
cnf(c_5122,plain,
greater_or_equal(sK1,critical_point(sK0)),
inference(demodulation,[status(thm)],[c_76,c_5099]) ).
cnf(c_5195,plain,
( ~ greater_or_equal(critical_point(sK0),sK1)
| ~ greater_or_equal(sK1,critical_point(sK0)) ),
inference(superposition,[status(thm)],[c_2117,c_5098]) ).
cnf(c_5196,plain,
~ greater_or_equal(sK1,critical_point(sK0)),
inference(forward_subsumption_resolution,[status(thm)],[c_5195,c_1895]) ).
cnf(c_5197,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5196,c_5122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT034+2 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 06:27:47 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.44/1.16 % SZS status Started for theBenchmark.p
% 3.44/1.16 % SZS status Theorem for theBenchmark.p
% 3.44/1.16
% 3.44/1.16 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.44/1.16
% 3.44/1.16 ------ iProver source info
% 3.44/1.16
% 3.44/1.16 git: date: 2023-05-31 18:12:56 +0000
% 3.44/1.16 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.44/1.16 git: non_committed_changes: false
% 3.44/1.16 git: last_make_outside_of_git: false
% 3.44/1.16
% 3.44/1.16 ------ Parsing...
% 3.44/1.16 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.44/1.16
% 3.44/1.16 ------ 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
% 3.44/1.16
% 3.44/1.16 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.44/1.16
% 3.44/1.16 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.44/1.16 ------ Proving...
% 3.44/1.16 ------ Problem Properties
% 3.44/1.16
% 3.44/1.16
% 3.44/1.16 clauses 28
% 3.44/1.16 conjectures 3
% 3.44/1.16 EPR 6
% 3.44/1.16 Horn 25
% 3.44/1.16 unary 8
% 3.44/1.16 binary 11
% 3.44/1.16 lits 65
% 3.44/1.16 lits eq 1
% 3.44/1.16 fd_pure 0
% 3.44/1.16 fd_pseudo 0
% 3.44/1.16 fd_cond 0
% 3.44/1.16 fd_pseudo_cond 1
% 3.44/1.16 AC symbols 0
% 3.44/1.16
% 3.44/1.16 ------ Schedule dynamic 5 is on
% 3.44/1.16
% 3.44/1.16 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.44/1.16
% 3.44/1.16
% 3.44/1.16 ------
% 3.44/1.16 Current options:
% 3.44/1.16 ------
% 3.44/1.16
% 3.44/1.16
% 3.44/1.16
% 3.44/1.16
% 3.44/1.16 ------ Proving...
% 3.44/1.16
% 3.44/1.16
% 3.44/1.16 % SZS status Theorem for theBenchmark.p
% 3.44/1.16
% 3.44/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.44/1.17
% 3.44/1.17
%------------------------------------------------------------------------------