%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : MGT030-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:12:26 PM UTC 2026
% Result : Unsatisfiable 3.00s 1.32s
% Output : CNFRefutation 3.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 64 ( 5 unt; 0 def)
% Number of atoms : 238 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 332 ( 158 ~; 174 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 3 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn 76 !; 0 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in_environment(X0,sk2(X0))
| subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_1) ).
fof(f2,axiom,
! [X0,X1] :
( in_environment(X0,sk2(X0))
| greater_or_equal(sk1(X1,X0),X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_2) ).
fof(f3,axiom,
! [X0,X1] :
( ~ greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0)))
| subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_3) ).
fof(f4,axiom,
! [X2,X0,X1] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_4) ).
fof(f5,axiom,
! [X0,X1] :
( ~ greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0)))
| greater_or_equal(sk1(X1,X0),X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_5) ).
fof(f6,axiom,
! [X2,X0,X1] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater_or_equal(sk1(X1,X0),X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_6) ).
fof(f7,axiom,
! [X0,X1] :
( in_environment(X0,sk2(X0))
| ~ greater(growth_rate(efficient_producers,sk1(X1,X0)),growth_rate(first_movers,sk1(X1,X0)))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_7) ).
fof(f8,axiom,
! [X0,X1] :
( ~ greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0)))
| ~ greater(growth_rate(efficient_producers,sk1(X1,X0)),growth_rate(first_movers,sk1(X1,X0)))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_8) ).
fof(f9,axiom,
! [X2,X0,X1] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(growth_rate(efficient_producers,sk1(X1,X0)),growth_rate(first_movers,sk1(X1,X0)))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_9) ).
fof(f10,axiom,
! [X0] :
( in_environment(X0,sk3(X0))
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_10) ).
fof(f11,axiom,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,sk3(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_11) ).
fof(f12,negated_conjecture,
environment(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l12_12) ).
fof(f13,negated_conjecture,
stable(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l12_13) ).
fof(f14,negated_conjecture,
! [X0] :
( subpopulations(first_movers,efficient_producers,sk4,sk5(X0))
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ in_environment(sk4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l12_14) ).
fof(f15,negated_conjecture,
! [X0] :
( greater(sk5(X0),X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ in_environment(sk4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l12_15) ).
fof(f16,negated_conjecture,
! [X0] :
( ~ greater(growth_rate(efficient_producers,sk5(X0)),growth_rate(first_movers,sk5(X0)))
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ in_environment(sk4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l12_16) ).
tcf(c_65,plain,
! [X0: $i] :
( in_environment(X0,sk3(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ stable(X0)
| ~ environment(X0)
| ~ greater_or_equal(X1,sk3(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_67,negated_conjecture,
environment(sk4),
inference(cnf_transformation,[],[f12]) ).
tcf(c_68,negated_conjecture,
stable(sk4),
inference(cnf_transformation,[],[f13]) ).
tcf(c_69,negated_conjecture,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,sk4,sk5(X0))
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ in_environment(sk4,X0) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_70,negated_conjecture,
! [X0: $i] :
( greater(sk5(X0),X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ in_environment(sk4,X0) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_71,negated_conjecture,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ in_environment(sk4,X0)
| ~ greater(growth_rate(efficient_producers,sk5(X0)),growth_rate(first_movers,sk5(X0))) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater(growth_rate(efficient_producers,sk2(X1)),growth_rate(first_movers,sk2(X1)))
| ~ greater(growth_rate(efficient_producers,sk1(X0,X1)),growth_rate(first_movers,sk1(X0,X1))) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( in_environment(X1,sk2(X1))
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater(growth_rate(efficient_producers,sk1(X0,X1)),growth_rate(first_movers,sk1(X0,X1))) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater(X2,sk2(X1))
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater(growth_rate(efficient_producers,sk1(X0,X1)),growth_rate(first_movers,sk1(X0,X1))) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| subpopulations(first_movers,efficient_producers,X0,sk1(X2,X0))
| ~ environment(X0)
| ~ in_environment(X0,X2)
| ~ greater(X1,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0))) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( in_environment(X0,sk2(X0))
| subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater_or_equal(sk1(X2,X0),X2)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0)
| ~ in_environment(X0,X2)
| ~ greater(X1,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(sk1(X1,X0),X1)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0))) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( in_environment(X0,sk2(X0))
| greater_or_equal(sk1(X1,X0),X1)
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_217,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ environment(sk4)
| ~ greater_or_equal(X0,sk3(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0) ),
inference(resolution,[status(thm)],[c_66,c_68]) ).
tcf(c_219,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0)
| ~ greater_or_equal(X0,sk3(sk4)) ),
inference(global_subsumption_just,[status(thm)],[c_217,c_67,c_217]) ).
tcf(c_220,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sk3(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0) ),
inference(renaming,[status(thm)],[c_219]) ).
tcf(c_231,plain,
( in_environment(sk4,sk3(sk4))
| ~ environment(sk4) ),
inference(resolution,[status(thm)],[c_65,c_68]) ).
tcf(c_241,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,sk1(sk3(sk4),X0)),growth_rate(first_movers,sk1(sk3(sk4),X0)))
| ~ environment(X0)
| ~ in_environment(X0,sk3(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),X0))
| ~ greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0))) ),
inference(resolution,[status(thm)],[c_79,c_220]) ).
tcf(c_253,plain,
! [X0: $i] :
( ~ environment(X0)
| ~ in_environment(X0,sk3(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),X0))
| ~ greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_241,c_72]) ).
tcf(c_259,plain,
! [X0: $i] :
( in_environment(X0,sk2(X0))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),X0)),growth_rate(first_movers,sk1(sk3(sk4),X0)))
| ~ environment(X0)
| ~ in_environment(X0,sk3(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),X0)) ),
inference(resolution,[status(thm)],[c_80,c_220]) ).
tcf(c_271,plain,
! [X0: $i] :
( in_environment(X0,sk2(X0))
| ~ environment(X0)
| ~ in_environment(X0,sk3(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_259,c_73]) ).
tcf(c_277,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| greater(growth_rate(efficient_producers,sk1(sk3(sk4),X0)),growth_rate(first_movers,sk1(sk3(sk4),X0)))
| ~ environment(X0)
| ~ in_environment(X0,sk3(sk4))
| ~ greater(X1,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),X0)) ),
inference(resolution,[status(thm)],[c_78,c_220]) ).
tcf(c_293,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0)
| ~ in_environment(X0,sk3(sk4))
| ~ greater(X1,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_277,c_74]) ).
tcf(c_315,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ in_environment(sk4,sk3(sk4))
| ~ greater(X0,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0)
| ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)) ),
inference(resolution,[status(thm)],[c_293,c_67]) ).
tcf(c_317,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0)
| ~ greater(X0,sk2(sk4)) ),
inference(global_subsumption_just,[status(thm)],[c_315,c_67,c_231,c_315]) ).
tcf(c_318,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0)
| ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)) ),
inference(renaming,[status(thm)],[c_317]) ).
tcf(c_332,plain,
( in_environment(sk4,sk2(sk4))
| ~ in_environment(sk4,sk3(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)) ),
inference(resolution,[status(thm)],[c_271,c_67]) ).
tcf(c_333,plain,
( in_environment(sk4,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)) ),
inference(global_subsumption_just,[status(thm)],[c_332,c_67,c_231,c_332]) ).
tcf(c_341,plain,
( ~ in_environment(sk4,sk3(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
| ~ greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4))) ),
inference(resolution,[status(thm)],[c_253,c_67]) ).
tcf(c_350,plain,
! [X0: $i,X1: $i] :
( subpopulations(first_movers,efficient_producers,sk4,sk1(X1,sk4))
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ in_environment(sk4,X1)
| ~ greater(X0,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0) ),
inference(resolution,[status(thm)],[c_75,c_67]) ).
tcf(c_367,plain,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,sk4,sk1(X0,sk4))
| ~ in_environment(sk4,X0)
| ~ greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4))) ),
inference(resolution,[status(thm)],[c_76,c_67]) ).
tcf(c_378,plain,
! [X0: $i] :
( in_environment(sk4,sk2(sk4))
| subpopulations(first_movers,efficient_producers,sk4,sk1(X0,sk4))
| ~ in_environment(sk4,X0) ),
inference(resolution,[status(thm)],[c_77,c_67]) ).
tcf(c_389,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(sk4,X0)
| ~ greater(X1,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X1)
| ~ greater(growth_rate(efficient_producers,sk1(X0,sk4)),growth_rate(first_movers,sk1(X0,sk4))) ),
inference(resolution,[status(thm)],[c_74,c_67]) ).
tcf(c_538,plain,
! [X0: $i] :
( ~ iPr_def_10
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_389]) ).
tcf(c_541,plain,
! [X0: $i] :
( ~ iPr_def_12
| ~ in_environment(sk4,X0)
| subpopulations(first_movers,efficient_producers,sk4,sk1(X0,sk4)) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_350]) ).
tcf(c_542,plain,
( iPr_def_12
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_350]) ).
tcf(c_549,plain,
( in_environment(sk4,sk2(sk4))
| subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
| ~ in_environment(sk4,sk3(sk4)) ),
inference(instantiation,[status(thm)],[c_378]) ).
tcf(c_553,plain,
( greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| ~ in_environment(sk4,sk2(sk4))
| ~ greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4)))) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_554,plain,
( greater(sk5(sk2(sk4)),sk2(sk4))
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| ~ in_environment(sk4,sk2(sk4)) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_555,plain,
( subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4)))
| greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4)))
| ~ in_environment(sk4,sk2(sk4)) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_561,plain,
( subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
| ~ in_environment(sk4,sk3(sk4))
| ~ greater(growth_rate(efficient_producers,sk2(sk4)),growth_rate(first_movers,sk2(sk4))) ),
inference(instantiation,[status(thm)],[c_367]) ).
tcf(c_565,plain,
( greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4))))
| ~ iPr_def_10
| ~ greater(sk5(sk2(sk4)),sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4))) ),
inference(instantiation,[status(thm)],[c_538]) ).
tcf(c_568,plain,
( subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
| ~ iPr_def_12
| ~ in_environment(sk4,sk3(sk4)) ),
inference(instantiation,[status(thm)],[c_541]) ).
tcf(c_579,plain,
( greater(growth_rate(efficient_producers,sk5(sk2(sk4))),growth_rate(first_movers,sk5(sk2(sk4))))
| ~ greater(sk5(sk2(sk4)),sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,sk5(sk2(sk4)))
| ~ subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)) ),
inference(instantiation,[status(thm)],[c_318]) ).
tcf(c_580,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_579,c_568,c_565,c_561,c_553,c_554,c_555,c_549,c_542,c_341,c_333,c_231,c_67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT030-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.38 % Computer : n001.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Thu Sep 24 01:11:06 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 3.00/1.32 % SZS status Started for theBenchmark.p
% 3.00/1.32 % SZS status Unsatisfiable for theBenchmark.p
% 3.00/1.32
% 3.00/1.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.00/1.32
% 3.00/1.32 % ------ iProver source info
% 3.00/1.32
% 3.00/1.32 % git: date: 2026-07-19 20:42:38 +0200
% 3.00/1.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.00/1.32 % git: non_committed_changes: false
% 3.00/1.32
% 3.00/1.32 % ------ Parsing...% successful
% 3.00/1.32
% 3.00/1.32
% 3.00/1.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.00/1.32
% 3.00/1.32 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.00/1.32
% 3.00/1.32 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.00/1.32 % ------ Proving...
% 3.00/1.32 % ------ Problem Properties
% 3.00/1.32
% 3.00/1.32 %
% 3.00/1.32 % clauses 16
% 3.00/1.32 % conjectures 3
% 3.00/1.32 % EPR 2
% 3.00/1.32 % Horn 11
% 3.00/1.32 % unary 1
% 3.00/1.32 % binary 4
% 3.00/1.32 % lits 44
% 3.00/1.32 % lits eq 0
% 3.00/1.32 % fd_pure 0
% 3.00/1.32 % fd_pseudo 0
% 3.00/1.32 % fd_cond 0
% 3.00/1.32 % fd_pseudo_cond 0
% 3.00/1.32 % AC symbols 0
% 3.00/1.32
% 3.00/1.32 % ------ Schedule dynamic 5 is on
% 3.00/1.32
% 3.00/1.32 % ------ no equalities: superposition off
% 3.00/1.32
% 3.00/1.32 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.00/1.32
% 3.00/1.32
% 3.00/1.32 % ------
% 3.00/1.32 % Current options:
% 3.00/1.32 % ------
% 3.00/1.32
% 3.00/1.32
% 3.00/1.32 %
% 3.00/1.32
% 3.00/1.32 % ------ Proving...
% 3.00/1.32 %
% 3.00/1.32
% 3.00/1.32 % SZS status Unsatisfiable for theBenchmark.p
% 3.00/1.32
% 3.00/1.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.00/1.32
% 3.00/1.32
%------------------------------------------------------------------------------