%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : MGT028-1 : 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 : n002.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 02:12:25 PM UTC 2026
% Result : Unsatisfiable 1.97s 1.30s
% Output : CNFRefutation 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 18
% Syntax : Number of formulae : 89 ( 15 unt; 5 def)
% Number of atoms : 380 ( 5 equ)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 379 ( 178 ~; 201 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 13 ( 11 usr; 6 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 89 ( 0 sgn 89 !; 0 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( greater(sk2(X0),appear(efficient_producers,X0))
| subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth_1) ).
fof(f2,axiom,
! [X0,X1] :
( greater(sk2(X0),appear(efficient_producers,X0))
| greater_or_equal(sk1(X1,X0),X1)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth_2) ).
fof(f3,axiom,
! [X2,X0,X1] :
( greater(zero,growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth_3) ).
fof(f4,axiom,
! [X2,X0,X1] :
( greater(zero,growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater_or_equal(sk1(X1,X0),X1)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth_4) ).
fof(f5,axiom,
! [X0,X1] :
( greater(sk2(X0),appear(efficient_producers,X0))
| ~ greater(zero,growth_rate(first_movers,sk1(X1,X0)))
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth_5) ).
fof(f6,axiom,
! [X2,X0,X1] :
( greater(zero,growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(zero,growth_rate(first_movers,sk1(X1,X0)))
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_negative_growth_6) ).
fof(f7,axiom,
! [X0] :
( in_environment(X0,sk3(X0))
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l11_7) ).
fof(f9,axiom,
! [X0,X1] :
( greater(zero,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',l11_9) ).
fof(f10,negated_conjecture,
environment(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l10_10) ).
fof(f11,negated_conjecture,
stable(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l10_11) ).
fof(f12,negated_conjecture,
! [X0] :
( subpopulations(first_movers,efficient_producers,sk4,sk5(X0))
| ~ greater(X0,appear(efficient_producers,sk4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l10_12) ).
fof(f13,negated_conjecture,
! [X0] :
( greater_or_equal(sk5(X0),X0)
| ~ greater(X0,appear(efficient_producers,sk4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l10_13) ).
fof(f14,negated_conjecture,
! [X0] :
( ~ greater(zero,growth_rate(first_movers,sk5(X0)))
| ~ greater(X0,appear(efficient_producers,sk4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l10_14) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( greater(sk2(X0),appear(efficient_producers,X0))
| subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ stable(X0)
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(sk1(X1,X0),X1)
| greater(sk2(X0),appear(efficient_producers,X0))
| ~ stable(X0)
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(zero,growth_rate(first_movers,X1))
| subpopulations(first_movers,efficient_producers,X0,sk1(X2,X0))
| ~ stable(X0)
| ~ environment(X0)
| ~ in_environment(X0,X2)
| ~ greater_or_equal(X1,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(zero,growth_rate(first_movers,X1))
| greater_or_equal(sk1(X2,X0),X2)
| ~ stable(X0)
| ~ environment(X0)
| ~ in_environment(X0,X2)
| ~ greater_or_equal(X1,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( greater(sk2(X1),appear(efficient_producers,X1))
| ~ stable(X1)
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater(zero,growth_rate(first_movers,sk1(X0,X1))) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(zero,growth_rate(first_movers,X2))
| ~ stable(X1)
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater_or_equal(X2,sk2(X1))
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater(zero,growth_rate(first_movers,sk1(X0,X1))) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_69,plain,
! [X0: $i] :
( in_environment(X0,sk3(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( greater(zero,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,[],[f9]) ).
tcf(c_72,negated_conjecture,
environment(sk4),
inference(cnf_transformation,[],[f10]) ).
tcf(c_73,negated_conjecture,
stable(sk4),
inference(cnf_transformation,[],[f11]) ).
tcf(c_74,negated_conjecture,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,sk4,sk5(X0))
| ~ greater(X0,appear(efficient_producers,sk4)) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_75,negated_conjecture,
! [X0: $i] :
( greater_or_equal(sk5(X0),X0)
| ~ greater(X0,appear(efficient_producers,sk4)) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_76,negated_conjecture,
! [X0: $i] :
( ~ greater(X0,appear(efficient_producers,sk4))
| ~ greater(zero,growth_rate(first_movers,sk5(X0))) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_203,plain,
! [X0: $i] :
( greater(zero,growth_rate(first_movers,X0))
| ~ stable(sk4)
| ~ greater_or_equal(X0,sk3(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0) ),
inference(resolution,[status(thm)],[c_71,c_72]) ).
tcf(c_205,plain,
! [X0: $i] :
( greater(zero,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_203,c_73,c_203]) ).
tcf(c_206,plain,
! [X0: $i] :
( greater(zero,growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sk3(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0) ),
inference(renaming,[status(thm)],[c_205]) ).
tcf(c_217,plain,
( in_environment(sk4,sk3(sk4))
| ~ stable(sk4) ),
inference(resolution,[status(thm)],[c_69,c_72]) ).
tcf(c_218,plain,
in_environment(sk4,sk3(sk4)),
inference(global_subsumption_just,[status(thm)],[c_217,c_73,c_217]) ).
tcf(c_223,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X0))
| greater_or_equal(sk1(X1,sk4),X1)
| ~ stable(sk4)
| ~ in_environment(sk4,X1)
| ~ greater_or_equal(X0,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0) ),
inference(resolution,[status(thm)],[c_66,c_72]) ).
tcf(c_225,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X0))
| greater_or_equal(sk1(X1,sk4),X1)
| ~ subpopulations(first_movers,efficient_producers,sk4,X0)
| ~ greater_or_equal(X0,sk2(sk4))
| ~ in_environment(sk4,X1) ),
inference(global_subsumption_just,[status(thm)],[c_223,c_73,c_223]) ).
tcf(c_226,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X0))
| greater_or_equal(sk1(X1,sk4),X1)
| ~ in_environment(sk4,X1)
| ~ greater_or_equal(X0,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0) ),
inference(renaming,[status(thm)],[c_225]) ).
tcf(c_243,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X0))
| subpopulations(first_movers,efficient_producers,sk4,sk1(X1,sk4))
| ~ stable(sk4)
| ~ in_environment(sk4,X1)
| ~ greater_or_equal(X0,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0) ),
inference(resolution,[status(thm)],[c_65,c_72]) ).
tcf(c_245,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X0))
| subpopulations(first_movers,efficient_producers,sk4,sk1(X1,sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0)
| ~ greater_or_equal(X0,sk2(sk4))
| ~ in_environment(sk4,X1) ),
inference(global_subsumption_just,[status(thm)],[c_243,c_73,c_243]) ).
tcf(c_246,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X0))
| subpopulations(first_movers,efficient_producers,sk4,sk1(X1,sk4))
| ~ in_environment(sk4,X1)
| ~ greater_or_equal(X0,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0) ),
inference(renaming,[status(thm)],[c_245]) ).
tcf(c_263,plain,
! [X0: $i] :
( greater_or_equal(sk1(X0,sk4),X0)
| greater(sk2(sk4),appear(efficient_producers,sk4))
| ~ stable(sk4)
| ~ in_environment(sk4,X0) ),
inference(resolution,[status(thm)],[c_64,c_72]) ).
tcf(c_265,plain,
! [X0: $i] :
( greater_or_equal(sk1(X0,sk4),X0)
| greater(sk2(sk4),appear(efficient_producers,sk4))
| ~ in_environment(sk4,X0) ),
inference(global_subsumption_just,[status(thm)],[c_263,c_73,c_263]) ).
tcf(c_277,plain,
! [X0: $i] :
( greater(sk2(sk4),appear(efficient_producers,sk4))
| subpopulations(first_movers,efficient_producers,sk4,sk1(X0,sk4))
| ~ stable(sk4)
| ~ in_environment(sk4,X0) ),
inference(resolution,[status(thm)],[c_63,c_72]) ).
tcf(c_279,plain,
! [X0: $i] :
( greater(sk2(sk4),appear(efficient_producers,sk4))
| subpopulations(first_movers,efficient_producers,sk4,sk1(X0,sk4))
| ~ in_environment(sk4,X0) ),
inference(global_subsumption_just,[status(thm)],[c_277,c_73,c_277]) ).
tcf(c_291,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X1))
| ~ stable(sk4)
| ~ in_environment(sk4,X0)
| ~ greater_or_equal(X1,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X1)
| ~ greater(zero,growth_rate(first_movers,sk1(X0,sk4))) ),
inference(resolution,[status(thm)],[c_68,c_72]) ).
tcf(c_293,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X1))
| ~ greater(zero,growth_rate(first_movers,sk1(X0,sk4)))
| ~ subpopulations(first_movers,efficient_producers,sk4,X1)
| ~ greater_or_equal(X1,sk2(sk4))
| ~ in_environment(sk4,X0) ),
inference(global_subsumption_just,[status(thm)],[c_291,c_73,c_291]) ).
tcf(c_294,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X1))
| ~ in_environment(sk4,X0)
| ~ greater_or_equal(X1,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X1)
| ~ greater(zero,growth_rate(first_movers,sk1(X0,sk4))) ),
inference(renaming,[status(thm)],[c_293]) ).
tcf(c_311,plain,
! [X0: $i] :
( greater(sk2(sk4),appear(efficient_producers,sk4))
| ~ stable(sk4)
| ~ in_environment(sk4,X0)
| ~ greater(zero,growth_rate(first_movers,sk1(X0,sk4))) ),
inference(resolution,[status(thm)],[c_67,c_72]) ).
tcf(c_313,plain,
! [X0: $i] :
( greater(sk2(sk4),appear(efficient_producers,sk4))
| ~ greater(zero,growth_rate(first_movers,sk1(X0,sk4)))
| ~ in_environment(sk4,X0) ),
inference(global_subsumption_just,[status(thm)],[c_311,c_73,c_311]) ).
tcf(c_314,plain,
! [X0: $i] :
( greater(sk2(sk4),appear(efficient_producers,sk4))
| ~ in_environment(sk4,X0)
| ~ greater(zero,growth_rate(first_movers,sk1(X0,sk4))) ),
inference(renaming,[status(thm)],[c_313]) ).
tcf(c_353,plain,
! [X0: $i] :
( greater(zero,growth_rate(first_movers,X0))
| subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4))
| ~ greater_or_equal(X0,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0) ),
inference(resolution,[status(thm)],[c_218,c_246]) ).
tcf(c_367,plain,
! [X0: $i] :
( greater(zero,growth_rate(first_movers,X0))
| greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4))
| ~ greater_or_equal(X0,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0) ),
inference(resolution,[status(thm)],[c_218,c_226]) ).
tcf(c_381,plain,
( greater(sk2(sk4),appear(efficient_producers,sk4))
| ~ greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(resolution,[status(thm)],[c_218,c_314]) ).
tcf(c_388,plain,
! [X0: $i] :
( greater(zero,growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sk2(sk4))
| ~ subpopulations(first_movers,efficient_producers,sk4,X0)
| ~ greater(zero,growth_rate(first_movers,sk1(sk3(sk4),sk4))) ),
inference(resolution,[status(thm)],[c_218,c_294]) ).
tcf(c_402,plain,
( greater(sk2(sk4),appear(efficient_producers,sk4))
| subpopulations(first_movers,efficient_producers,sk4,sk1(sk3(sk4),sk4)) ),
inference(resolution,[status(thm)],[c_218,c_279]) ).
tcf(c_409,plain,
( greater(sk2(sk4),appear(efficient_producers,sk4))
| greater_or_equal(sk1(sk3(sk4),sk4),sk3(sk4)) ),
inference(resolution,[status(thm)],[c_218,c_265]) ).
tcf(c_488,definition,
iPr_def_10 = sk3(sk4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_489,definition,
iPr_def_11 = sk1(iPr_def_10,sk4),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_490,definition,
iPr_def_12 = sk2(sk4),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_491,definition,
iPr_def_13 = appear(efficient_producers,sk4),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_492,definition,
iPr_def_14 = growth_rate(first_movers,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_493,plain,
( greater_or_equal(iPr_def_11,iPr_def_10)
| greater(iPr_def_12,iPr_def_13) ),
inference(demodulation,[status(thm)],[c_409,c_491,c_490,c_488,c_489]) ).
tcf(c_494,plain,
( greater(iPr_def_12,iPr_def_13)
| subpopulations(first_movers,efficient_producers,sk4,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_402]) ).
tcf(c_495,plain,
! [X0: $i] :
( greater(zero,growth_rate(first_movers,X0))
| ~ greater(zero,iPr_def_14)
| ~ greater_or_equal(X0,iPr_def_12)
| ~ subpopulations(first_movers,efficient_producers,sk4,X0) ),
inference(demodulation,[status(thm)],[c_388,c_492]) ).
tcf(c_496,plain,
( greater(iPr_def_12,iPr_def_13)
| ~ greater(zero,iPr_def_14) ),
inference(demodulation,[status(thm)],[c_381]) ).
tcf(c_497,plain,
! [X0: $i] :
( greater_or_equal(iPr_def_11,iPr_def_10)
| greater(zero,growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,iPr_def_12)
| ~ subpopulations(first_movers,efficient_producers,sk4,X0) ),
inference(demodulation,[status(thm)],[c_367]) ).
tcf(c_498,plain,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,sk4,iPr_def_11)
| greater(zero,growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,iPr_def_12)
| ~ subpopulations(first_movers,efficient_producers,sk4,X0) ),
inference(demodulation,[status(thm)],[c_353]) ).
tcf(c_499,plain,
! [X0: $i] :
( greater(zero,growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,iPr_def_10)
| ~ subpopulations(first_movers,efficient_producers,sk4,X0) ),
inference(demodulation,[status(thm)],[c_206]) ).
tcf(c_500,negated_conjecture,
! [X0: $i] :
( ~ greater(X0,iPr_def_13)
| ~ greater(zero,growth_rate(first_movers,sk5(X0))) ),
inference(demodulation,[status(thm)],[c_76]) ).
tcf(c_501,negated_conjecture,
! [X0: $i] :
( greater_or_equal(sk5(X0),X0)
| ~ greater(X0,iPr_def_13) ),
inference(demodulation,[status(thm)],[c_75]) ).
tcf(c_502,negated_conjecture,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,sk4,sk5(X0))
| ~ greater(X0,iPr_def_13) ),
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_823,plain,
( greater(iPr_def_12,iPr_def_13)
| greater(zero,growth_rate(first_movers,iPr_def_11))
| ~ greater_or_equal(iPr_def_11,iPr_def_10) ),
inference(superposition,[status(thm)],[c_494,c_499]) ).
tcf(c_824,plain,
( greater(iPr_def_12,iPr_def_13)
| greater(zero,iPr_def_14)
| ~ greater_or_equal(iPr_def_11,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_823,c_492]) ).
tcf(c_828,plain,
greater(iPr_def_12,iPr_def_13),
inference(global_subsumption_just,[status(thm)],[c_824,c_493,c_496,c_824]) ).
tcf(c_838,plain,
! [X0: $i] :
( greater_or_equal(iPr_def_11,iPr_def_10)
| greater(zero,growth_rate(first_movers,sk5(X0)))
| ~ greater(X0,iPr_def_13)
| ~ greater_or_equal(sk5(X0),iPr_def_12) ),
inference(superposition,[status(thm)],[c_502,c_497]) ).
tcf(c_844,plain,
! [X0: $i] :
( greater_or_equal(iPr_def_11,iPr_def_10)
| ~ greater_or_equal(sk5(X0),iPr_def_12)
| ~ greater(X0,iPr_def_13) ),
inference(global_subsumption_just,[status(thm)],[c_838,c_500,c_838]) ).
tcf(c_845,plain,
! [X0: $i] :
( greater_or_equal(iPr_def_11,iPr_def_10)
| ~ greater(X0,iPr_def_13)
| ~ greater_or_equal(sk5(X0),iPr_def_12) ),
inference(renaming,[status(thm)],[c_844]) ).
tcf(c_853,plain,
( greater_or_equal(iPr_def_11,iPr_def_10)
| ~ greater(iPr_def_12,iPr_def_13) ),
inference(superposition,[status(thm)],[c_501,c_845]) ).
tcf(c_854,plain,
greater_or_equal(iPr_def_11,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_853,c_828]) ).
tcf(c_863,plain,
! [X0: $i] :
( greater(zero,growth_rate(first_movers,sk5(X0)))
| ~ greater(zero,iPr_def_14)
| ~ greater(X0,iPr_def_13)
| ~ greater_or_equal(sk5(X0),iPr_def_12) ),
inference(superposition,[status(thm)],[c_502,c_495]) ).
tcf(c_869,plain,
! [X0: $i] :
( ~ greater_or_equal(sk5(X0),iPr_def_12)
| ~ greater(X0,iPr_def_13)
| ~ greater(zero,iPr_def_14) ),
inference(global_subsumption_just,[status(thm)],[c_863,c_500,c_863]) ).
tcf(c_870,plain,
! [X0: $i] :
( ~ greater(zero,iPr_def_14)
| ~ greater(X0,iPr_def_13)
| ~ greater_or_equal(sk5(X0),iPr_def_12) ),
inference(renaming,[status(thm)],[c_869]) ).
tcf(c_878,plain,
( ~ greater(iPr_def_12,iPr_def_13)
| ~ greater(zero,iPr_def_14) ),
inference(superposition,[status(thm)],[c_501,c_870]) ).
tcf(c_879,plain,
~ greater(zero,iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_878,c_828]) ).
tcf(c_888,plain,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,sk4,iPr_def_11)
| greater(zero,growth_rate(first_movers,sk5(X0)))
| ~ greater(X0,iPr_def_13)
| ~ greater_or_equal(sk5(X0),iPr_def_12) ),
inference(superposition,[status(thm)],[c_502,c_498]) ).
tcf(c_894,plain,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,sk4,iPr_def_11)
| ~ greater_or_equal(sk5(X0),iPr_def_12)
| ~ greater(X0,iPr_def_13) ),
inference(global_subsumption_just,[status(thm)],[c_888,c_500,c_888]) ).
tcf(c_895,plain,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,sk4,iPr_def_11)
| ~ greater(X0,iPr_def_13)
| ~ greater_or_equal(sk5(X0),iPr_def_12) ),
inference(renaming,[status(thm)],[c_894]) ).
tcf(c_903,plain,
( subpopulations(first_movers,efficient_producers,sk4,iPr_def_11)
| ~ greater(iPr_def_12,iPr_def_13) ),
inference(superposition,[status(thm)],[c_501,c_895]) ).
tcf(c_904,plain,
subpopulations(first_movers,efficient_producers,sk4,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_903,c_828]) ).
tcf(c_905,plain,
( greater(zero,growth_rate(first_movers,iPr_def_11))
| ~ greater_or_equal(iPr_def_11,iPr_def_10) ),
inference(superposition,[status(thm)],[c_904,c_499]) ).
tcf(c_906,plain,
( greater(zero,iPr_def_14)
| ~ greater_or_equal(iPr_def_11,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_905,c_492]) ).
tcf(c_907,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_906,c_879,c_854]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT028-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.38 % Computer : n002.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 01:07:33 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
% 0.12/0.45 % Proving...
% 1.97/1.30 % SZS status Started for theBenchmark.p
% 1.97/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 1.97/1.30
% 1.97/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.97/1.30
% 1.97/1.30 % ------ iProver source info
% 1.97/1.30
% 1.97/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 1.97/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.97/1.30 % git: non_committed_changes: false
% 1.97/1.30
% 1.97/1.30 % ------ Parsing...% successful
% 1.97/1.30
% 1.97/1.30
% 1.97/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.97/1.30
% 1.97/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.97/1.30
% 1.97/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.97/1.30
% 1.97/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.97/1.30 % ------ Proving...
% 1.97/1.30 % ------ Problem Properties
% 1.97/1.30
% 1.97/1.30 %
% 1.97/1.30 % clauses 15
% 1.97/1.30 % conjectures 3
% 1.97/1.30 % EPR 3
% 1.97/1.30 % Horn 11
% 1.97/1.30 % unary 5
% 1.97/1.30 % binary 6
% 1.97/1.30 % lits 32
% 1.97/1.30 % lits eq 5
% 1.97/1.30 % fd_pure 0
% 1.97/1.30 % fd_pseudo 0
% 1.97/1.30 % fd_cond 0
% 1.97/1.30 % fd_pseudo_cond 0
% 1.97/1.30 % AC symbols 0
% 1.97/1.30
% 1.97/1.30 % ------ Schedule dynamic 5 is on
% 1.97/1.30
% 1.97/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.97/1.30
% 1.97/1.30
% 1.97/1.30 % ------
% 1.97/1.30 % Current options:
% 1.97/1.30 % ------
% 1.97/1.30
% 1.97/1.30
% 1.97/1.30 %
% 1.97/1.30
% 1.97/1.30 % ------ Proving...
% 1.97/1.30 %
% 1.97/1.30
% 1.97/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 1.97/1.30
% 1.97/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.97/1.30
% 1.97/1.30
%------------------------------------------------------------------------------