%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : MGT034-2 : 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 02:12:27 PM UTC 2026
% Result : Unsatisfiable 4.17s 1.30s
% Output : CNFRefutation 4.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 23
% Syntax : Number of formulae : 115 ( 20 unt; 0 def)
% Number of atoms : 322 ( 28 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 412 ( 205 ~; 207 |; 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 : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 132 ( 0 sgn 132 !; 0 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp1_high_growth_rates_33) ).
fof(f2,axiom,
! [X0,X1] :
( ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_34) ).
fof(f3,axiom,
! [X0] :
( subpopulations(first_movers,efficient_producers,X0,critical_point(X0))
| ~ in_environment(X0,critical_point(X0))
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_critical_point_means_FM_and_EP_35) ).
fof(f4,axiom,
! [X0] :
( subpopulations(first_movers,efficient_producers,X0,appear(efficient_producers,X0))
| ~ in_environment(X0,appear(efficient_producers,X0))
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_FM_and_EP_when_EP_appears_36) ).
fof(f5,axiom,
! [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))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_difference_between_founding_rates_37) ).
fof(f6,axiom,
! [X2,X0,X1] :
( greater(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)),zero)
| ~ decreases(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)))
| ~ greater(X1,X2)
| ~ greater_or_equal(X2,appear(efficient_producers,X0))
| ~ greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_decreasing_function_38) ).
fof(f7,axiom,
! [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))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_negative_growth_rate_difference_39) ).
fof(f9,axiom,
! [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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_positive_growth_rate_difference_41) ).
fof(f14,axiom,
! [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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_critical_time_points_46) ).
fof(f16,axiom,
! [X0,X1] :
( subpopulations(efficient_producers,first_movers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations_48) ).
fof(f17,axiom,
! [X0,X1] :
( greater_or_equal(X1,appear(efficient_producers,X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_FM_and_EP_members_EP_appeared_49) ).
fof(f18,axiom,
! [X0,X1] :
( X0 = X1
| greater(X0,X1)
| ~ greater_or_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_50) ).
fof(f19,axiom,
! [X0,X1] :
( greater_or_equal(X0,X1)
| ~ greater(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_51) ).
fof(f20,axiom,
! [X0,X1] :
( greater_or_equal(X0,X1)
| X0 != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_52) ).
fof(f21,axiom,
! [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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_relationship_of_growth_rates_53) ).
fof(f22,axiom,
! [X0,X1] :
( ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| X1 != critical_point(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_54) ).
fof(f23,plain,
! [X0,X1] :
( ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| critical_point(X0) != X1
| ~ environment(X0) ),
inference(reorient_equations,[],[f22]) ).
fof(f26,axiom,
! [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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a10_56) ).
fof(f27,axiom,
! [X0,X1] :
( decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a12_57) ).
fof(f28,negated_conjecture,
environment(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t3_58) ).
fof(f29,negated_conjecture,
in_environment(sk1,critical_point(sk1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t3_59) ).
fof(f30,negated_conjecture,
greater_or_equal(sk2,appear(efficient_producers,sk1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t3_60) ).
fof(f31,negated_conjecture,
greater(critical_point(sk1),sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t3_61) ).
fof(f32,negated_conjecture,
~ selection_favors(first_movers,efficient_producers,sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t3_62) ).
fof(f33,plain,
! [X0] :
( ~ greater(growth_rate(efficient_producers,critical_point(X0)),growth_rate(first_movers,critical_point(X0)))
| ~ environment(X0) ),
inference(equality_resolution,[],[f23]) ).
fof(f35,plain,
! [X1] : greater_or_equal(X1,X1),
inference(equality_resolution,[],[f20]) ).
tcf(c_79,plain,
! [X0: $i] :
( ~ environment(X0)
| ~ greater(growth_rate(efficient_producers,critical_point(X0)),growth_rate(first_movers,critical_point(X0))) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subpopulations(first_movers,efficient_producers,X0,X3)
| ~ environment(X0)
| ~ greater_or_equal(X3,X2)
| ~ greater_or_equal(X1,X3)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] :
( decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1)))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_83,negated_conjecture,
environment(sk1),
inference(cnf_transformation,[],[f28]) ).
tcf(c_84,negated_conjecture,
in_environment(sk1,critical_point(sk1)),
inference(cnf_transformation,[],[f29]) ).
tcf(c_85,negated_conjecture,
greater_or_equal(sk2,appear(efficient_producers,sk1)),
inference(cnf_transformation,[],[f30]) ).
tcf(c_86,negated_conjecture,
greater(critical_point(sk1),sk2),
inference(cnf_transformation,[],[f31]) ).
tcf(c_87,negated_conjecture,
~ selection_favors(first_movers,efficient_producers,sk2),
inference(cnf_transformation,[],[f32]) ).
tcf(c_88,plain,
! [X0: $i] : greater_or_equal(X0,X0),
inference(cnf_transformation,[],[f35]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] :
( greater(X0,X1)
| ( X0 = X1 )
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| greater(zero,difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_92,plain,
! [X0: $i] :
( greater(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))
| ~ greater(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_94,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] :
( in_environment(X1,X0)
| ~ environment(X1)
| ~ in_environment(X1,critical_point(X1))
| ~ greater(critical_point(X1),X0)
| ~ greater_or_equal(X0,appear(efficient_producers,X1)) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_97,plain,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,X0,critical_point(X0))
| ~ environment(X0)
| ~ in_environment(X0,critical_point(X0)) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( subpopulations(efficient_producers,first_movers,X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ environment(X2)
| ~ in_environment(X2,X0)
| ~ greater(X0,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X2))
| ~ decreases(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ greater_or_equal(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_101,plain,
! [X0: $i] :
( decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| ~ decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0))) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_102,plain,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,X0,appear(efficient_producers,X0))
| ~ environment(X0)
| ~ in_environment(X0,appear(efficient_producers,X0)) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(X1,appear(efficient_producers,X0))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( selection_favors(X0,X2,X1)
| ~ environment(X3)
| ~ subpopulations(X2,X0,X3,X1)
| ~ greater(growth_rate(X0,X1),growth_rate(X2,X1)) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i] :
( ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X0)
| ~ decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_133,plain,
! [X0: $i] :
( ~ greater(growth_rate(efficient_producers,critical_point(X0)),growth_rate(first_movers,critical_point(X0)))
| ~ environment(X0) ),
inference(prop_impl_just,[status(thm)],[c_79]) ).
tcf(c_134,plain,
! [X0: $i] :
( ~ environment(X0)
| ~ greater(growth_rate(efficient_producers,critical_point(X0)),growth_rate(first_movers,critical_point(X0))) ),
inference(renaming,[status(thm)],[c_133]) ).
tcf(c_519,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ environment(X3)
| ~ subpopulations(X2,X0,X3,X1)
| ~ greater(growth_rate(X0,X1),growth_rate(X2,X1))
| ( X2 != efficient_producers )
| ( X1 != sk2 )
| ( X0 != first_movers ) ),
inference(resolution_lifted,[status(thm)],[c_104,c_87]) ).
tcf(c_520,plain,
! [X0: $i] :
( ~ environment(X0)
| ~ subpopulations(efficient_producers,first_movers,X0,sk2)
| ~ greater(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)) ),
inference(unflattening,[status(thm)],[c_519]) ).
tcf(c_534,plain,
! [X0: $i] :
( ~ subpopulations(efficient_producers,first_movers,X0,sk2)
| ~ greater(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2))
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_520,c_83]) ).
tcf(c_535,plain,
( ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ greater(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)) ),
inference(unflattening,[status(thm)],[c_534]) ).
tcf(c_559,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subpopulations(first_movers,efficient_producers,X0,X3)
| ~ greater_or_equal(X3,X2)
| ~ greater_or_equal(X1,X3)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_81,c_83]) ).
tcf(c_560,plain,
! [X0: $i,X1: $i,X2: $i] :
( subpopulations(first_movers,efficient_producers,sk1,X2)
| ~ greater_or_equal(X2,X1)
| ~ greater_or_equal(X0,X2)
| ~ subpopulations(first_movers,efficient_producers,sk1,X1)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(unflattening,[status(thm)],[c_559]) ).
tcf(c_588,plain,
! [X0: $i] :
( ~ greater(growth_rate(efficient_producers,critical_point(X0)),growth_rate(first_movers,critical_point(X0)))
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_134,c_83]) ).
tcf(c_589,plain,
~ greater(growth_rate(efficient_producers,critical_point(sk1)),growth_rate(first_movers,critical_point(sk1))),
inference(unflattening,[status(thm)],[c_588]) ).
tcf(c_593,plain,
! [X0: $i,X1: $i] :
( decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_82,c_83]) ).
tcf(c_594,plain,
! [X0: $i] :
( decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0)))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(unflattening,[status(thm)],[c_593]) ).
tcf(c_602,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| greater(zero,difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_90,c_83]) ).
tcf(c_603,plain,
! [X0: $i] :
( greater_or_equal(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
| greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(unflattening,[status(thm)],[c_602]) ).
tcf(c_614,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(X1,appear(efficient_producers,X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_103,c_83]) ).
tcf(c_615,plain,
! [X0: $i] :
( greater_or_equal(X0,appear(efficient_producers,sk1))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(unflattening,[status(thm)],[c_614]) ).
tcf(c_623,plain,
! [X0: $i,X1: $i] :
( subpopulations(efficient_producers,first_movers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_98,c_83]) ).
tcf(c_624,plain,
! [X0: $i] :
( subpopulations(efficient_producers,first_movers,sk1,X0)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(unflattening,[status(thm)],[c_623]) ).
tcf(c_632,plain,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,X0,appear(efficient_producers,X0))
| ~ in_environment(X0,appear(efficient_producers,X0))
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_102,c_83]) ).
tcf(c_633,plain,
( subpopulations(first_movers,efficient_producers,sk1,appear(efficient_producers,sk1))
| ~ in_environment(sk1,appear(efficient_producers,sk1)) ),
inference(unflattening,[status(thm)],[c_632]) ).
tcf(c_640,plain,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,X0,critical_point(X0))
| ~ in_environment(X0,critical_point(X0))
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_97,c_83]) ).
tcf(c_641,plain,
( subpopulations(first_movers,efficient_producers,sk1,critical_point(sk1))
| ~ in_environment(sk1,critical_point(sk1)) ),
inference(unflattening,[status(thm)],[c_640]) ).
tcf(c_642,plain,
subpopulations(first_movers,efficient_producers,sk1,critical_point(sk1)),
inference(global_subsumption_just,[status(thm)],[c_641,c_84,c_641]) ).
tcf(c_647,plain,
! [X0: $i,X1: $i] :
( in_environment(X0,X1)
| ~ in_environment(X0,critical_point(X0))
| ~ greater(critical_point(X0),X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_96,c_83]) ).
tcf(c_648,plain,
! [X0: $i] :
( in_environment(sk1,X0)
| ~ in_environment(sk1,critical_point(sk1))
| ~ greater(critical_point(sk1),X0)
| ~ greater_or_equal(X0,appear(efficient_producers,sk1)) ),
inference(unflattening,[status(thm)],[c_647]) ).
tcf(c_650,plain,
! [X0: $i] :
( in_environment(sk1,X0)
| ~ greater_or_equal(X0,appear(efficient_producers,sk1))
| ~ greater(critical_point(sk1),X0) ),
inference(global_subsumption_just,[status(thm)],[c_648,c_84,c_648]) ).
tcf(c_651,plain,
! [X0: $i] :
( in_environment(sk1,X0)
| ~ greater(critical_point(sk1),X0)
| ~ greater_or_equal(X0,appear(efficient_producers,sk1)) ),
inference(renaming,[status(thm)],[c_650]) ).
tcf(c_662,plain,
! [X0: $i,X1: $i] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_105,c_83]) ).
tcf(c_663,plain,
! [X0: $i] :
( ~ subpopulations(first_movers,efficient_producers,sk1,X0)
| ~ decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))) ),
inference(unflattening,[status(thm)],[c_662]) ).
tcf(c_671,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)),zero)
| ~ in_environment(X0,X1)
| ~ greater(X1,X2)
| ~ greater_or_equal(X2,appear(efficient_producers,X0))
| ~ decreases(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)))
| ~ greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_100,c_83]) ).
tcf(c_672,plain,
! [X0: $i,X1: $i] :
( greater(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ in_environment(sk1,X0)
| ~ greater(X0,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,sk1))
| ~ decreases(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ greater_or_equal(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero) ),
inference(unflattening,[status(thm)],[c_671]) ).
tcf(c_731,plain,
! [X0: $i] :
( ~ greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
inference(prop_impl_just,[status(thm)],[c_94]) ).
tcf(c_732,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))) ),
inference(renaming,[status(thm)],[c_731]) ).
tcf(c_741,plain,
! [X0: $i] :
( ~ subpopulations(first_movers,efficient_producers,sk1,X0)
| decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0))) ),
inference(prop_impl_just,[status(thm)],[c_594]) ).
tcf(c_742,plain,
! [X0: $i] :
( decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0)))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(renaming,[status(thm)],[c_741]) ).
tcf(c_755,plain,
! [X0: $i] :
( greater_or_equal(X0,appear(efficient_producers,sk1))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(prop_impl_just,[status(thm)],[c_615]) ).
tcf(c_757,plain,
! [X0: $i] :
( subpopulations(efficient_producers,first_movers,sk1,X0)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(prop_impl_just,[status(thm)],[c_624]) ).
tcf(c_763,plain,
( subpopulations(first_movers,efficient_producers,sk1,appear(efficient_producers,sk1))
| ~ in_environment(sk1,appear(efficient_producers,sk1)) ),
inference(prop_impl_just,[status(thm)],[c_633]) ).
tcf(c_819,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| greater_or_equal(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(bin_hyper_res,[status(thm)],[c_603,c_732]) ).
tcf(c_1737,plain,
( in_environment(sk1,appear(efficient_producers,sk1))
| ~ greater(critical_point(sk1),appear(efficient_producers,sk1)) ),
inference(superposition,[status(thm)],[c_88,c_651]) ).
tcf(c_1745,plain,
greater_or_equal(critical_point(sk1),sk2),
inference(superposition,[status(thm)],[c_86,c_95]) ).
tcf(c_1764,plain,
greater_or_equal(critical_point(sk1),appear(efficient_producers,sk1)),
inference(superposition,[status(thm)],[c_642,c_755]) ).
tcf(c_1766,plain,
( greater(critical_point(sk1),appear(efficient_producers,sk1))
| ( appear(efficient_producers,sk1) = critical_point(sk1) ) ),
inference(superposition,[status(thm)],[c_1764,c_89]) ).
tcf(c_1847,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| greater(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
| ~ in_environment(sk1,X1)
| ~ greater(X1,X0)
| ~ greater_or_equal(X0,appear(efficient_producers,sk1))
| ~ subpopulations(first_movers,efficient_producers,sk1,X1)
| ~ decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))) ),
inference(superposition,[status(thm)],[c_819,c_672]) ).
tcf(c_1894,plain,
! [X0: $i,X1: $i] :
( subpopulations(first_movers,efficient_producers,sk1,X1)
| ~ greater_or_equal(X0,X1)
| ~ in_environment(sk1,appear(efficient_producers,sk1))
| ~ greater_or_equal(X1,appear(efficient_producers,sk1))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(superposition,[status(thm)],[c_763,c_560]) ).
tcf(c_1926,plain,
( in_environment(sk1,appear(efficient_producers,sk1))
| ( appear(efficient_producers,sk1) = critical_point(sk1) ) ),
inference(superposition,[status(thm)],[c_1766,c_1737]) ).
tcf(c_2001,plain,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,sk1,X0)
| ~ greater_or_equal(critical_point(sk1),X0)
| ~ in_environment(sk1,appear(efficient_producers,sk1))
| ~ greater_or_equal(X0,appear(efficient_producers,sk1)) ),
inference(superposition,[status(thm)],[c_642,c_1894]) ).
tcf(c_2027,plain,
( subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ greater_or_equal(critical_point(sk1),sk2)
| ~ in_environment(sk1,appear(efficient_producers,sk1)) ),
inference(superposition,[status(thm)],[c_85,c_2001]) ).
tcf(c_2030,plain,
( subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ in_environment(sk1,appear(efficient_producers,sk1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2027,c_1745]) ).
tcf(c_2037,plain,
( subpopulations(first_movers,efficient_producers,sk1,sk2)
| ( appear(efficient_producers,sk1) = critical_point(sk1) ) ),
inference(superposition,[status(thm)],[c_1926,c_2030]) ).
tcf(c_2146,plain,
! [X0: $i] :
( decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(superposition,[status(thm)],[c_742,c_101]) ).
tcf(c_2166,plain,
( subpopulations(efficient_producers,first_movers,sk1,sk2)
| ( appear(efficient_producers,sk1) = critical_point(sk1) ) ),
inference(superposition,[status(thm)],[c_2037,c_757]) ).
tcf(c_3375,plain,
! [X0: $i] :
( ~ subpopulations(first_movers,efficient_producers,sk1,X0)
| decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))) ),
inference(global_subsumption_just,[status(thm)],[c_2146,c_663,c_2146]) ).
tcf(c_3376,plain,
! [X0: $i] :
( decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(renaming,[status(thm)],[c_3375]) ).
tcf(c_4196,plain,
( greater(growth_rate(efficient_producers,critical_point(sk1)),growth_rate(first_movers,critical_point(sk1)))
| greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero)
| ~ in_environment(sk1,critical_point(sk1))
| ~ greater_or_equal(sk2,appear(efficient_producers,sk1))
| ~ subpopulations(first_movers,efficient_producers,sk1,critical_point(sk1))
| ~ decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2))) ),
inference(superposition,[status(thm)],[c_86,c_1847]) ).
tcf(c_4197,plain,
( greater(growth_rate(efficient_producers,critical_point(sk1)),growth_rate(first_movers,critical_point(sk1)))
| greater(difference(growth_rate(first_movers,appear(efficient_producers,sk1)),growth_rate(efficient_producers,appear(efficient_producers,sk1))),zero)
| ( appear(efficient_producers,sk1) = critical_point(sk1) )
| ~ in_environment(sk1,critical_point(sk1))
| ~ subpopulations(first_movers,efficient_producers,sk1,critical_point(sk1))
| ~ greater_or_equal(appear(efficient_producers,sk1),appear(efficient_producers,sk1))
| ~ decreases(difference(growth_rate(first_movers,appear(efficient_producers,sk1)),growth_rate(efficient_producers,appear(efficient_producers,sk1)))) ),
inference(superposition,[status(thm)],[c_1766,c_1847]) ).
tcf(c_4203,plain,
( greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero)
| ~ decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4196,c_589,c_84,c_85,c_642]) ).
tcf(c_4212,plain,
( greater(difference(growth_rate(first_movers,appear(efficient_producers,sk1)),growth_rate(efficient_producers,appear(efficient_producers,sk1))),zero)
| ( appear(efficient_producers,sk1) = critical_point(sk1) )
| ~ decreases(difference(growth_rate(first_movers,appear(efficient_producers,sk1)),growth_rate(efficient_producers,appear(efficient_producers,sk1)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4197,c_589,c_84,c_642,c_88]) ).
tcf(c_4322,plain,
( greater(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2))
| ~ decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2))) ),
inference(superposition,[status(thm)],[c_4203,c_92]) ).
tcf(c_4349,plain,
( greater(growth_rate(first_movers,appear(efficient_producers,sk1)),growth_rate(efficient_producers,appear(efficient_producers,sk1)))
| ( appear(efficient_producers,sk1) = critical_point(sk1) )
| ~ decreases(difference(growth_rate(first_movers,appear(efficient_producers,sk1)),growth_rate(efficient_producers,appear(efficient_producers,sk1)))) ),
inference(superposition,[status(thm)],[c_4212,c_92]) ).
tcf(c_4404,plain,
( greater(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2))
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2) ),
inference(superposition,[status(thm)],[c_3376,c_4322]) ).
tcf(c_4460,plain,
appear(efficient_producers,sk1) = critical_point(sk1),
inference(global_subsumption_just,[status(thm)],[c_4349,c_535,c_2037,c_2166,c_4404]) ).
tcf(c_4505,plain,
( subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ in_environment(sk1,critical_point(sk1)) ),
inference(demodulation,[status(thm)],[c_2030,c_4460]) ).
tcf(c_4522,plain,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(forward_subsumption_resolution,[status(thm)],[c_4505,c_84]) ).
tcf(c_4597,plain,
subpopulations(efficient_producers,first_movers,sk1,sk2),
inference(superposition,[status(thm)],[c_4522,c_757]) ).
tcf(c_4614,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4597,c_4522,c_4404,c_535]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT034-2 : 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 : 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 01:09:51 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...
% 4.17/1.30 % SZS status Started for theBenchmark.p
% 4.17/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 4.17/1.30
% 4.17/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.17/1.30
% 4.17/1.30 % ------ iProver source info
% 4.17/1.30
% 4.17/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 4.17/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.17/1.30 % git: non_committed_changes: false
% 4.17/1.30
% 4.17/1.30 % ------ Parsing...% successful
% 4.17/1.30
% 4.17/1.30
% 4.17/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.17/1.30
% 4.17/1.30 % ------ 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 %
% 4.17/1.30
% 4.17/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.17/1.30
% 4.17/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.17/1.30 % ------ Proving...
% 4.17/1.30 % ------ Problem Properties
% 4.17/1.30
% 4.17/1.30 %
% 4.17/1.30 % clauses 25
% 4.17/1.30 % conjectures 3
% 4.17/1.30 % EPR 6
% 4.17/1.30 % Horn 22
% 4.17/1.30 % unary 6
% 4.17/1.30 % binary 11
% 4.17/1.30 % lits 59
% 4.17/1.30 % lits eq 1
% 4.17/1.30 % fd_pure 0
% 4.17/1.30 % fd_pseudo 0
% 4.17/1.30 % fd_cond 0
% 4.17/1.30 % fd_pseudo_cond 1
% 4.17/1.30 % AC symbols 0
% 4.17/1.30
% 4.17/1.30 % ------ Schedule dynamic 5 is on
% 4.17/1.30
% 4.17/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.17/1.30
% 4.17/1.30
% 4.17/1.30 % ------
% 4.17/1.30 % Current options:
% 4.17/1.30 % ------
% 4.17/1.30
% 4.17/1.30
% 4.17/1.30 %
% 4.17/1.30
% 4.17/1.30 % ------ Proving...
% 4.17/1.30 %
% 4.17/1.30
% 4.17/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 4.17/1.30
% 4.17/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.17/1.30
% 4.17/1.30
%------------------------------------------------------------------------------