%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : MGT023-2 : 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 : n015.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 02:12:23 PM UTC 2026
% Result : Unsatisfiable 0.92s 1.29s
% Output : CNFRefutation 0.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 22
% Syntax : Number of formulae : 124 ( 19 unt; 5 def)
% Number of atoms : 536 ( 51 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 600 ( 278 ~; 322 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 16 ( 14 usr; 9 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 140 ( 0 sgn 140 !; 0 ?; 104 :)
% 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_19) ).
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_20) ).
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_21) ).
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_22) ).
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_23) ).
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_24) ).
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_25) ).
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_26) ).
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_27) ).
fof(f10,axiom,
! [X0,X1] :
( X1 = critical_point(X0)
| subpopulations(first_movers,efficient_producers,X0,sk3(X1,X0))
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_28) ).
fof(f11,plain,
! [X0,X1] :
( critical_point(X0) = X1
| subpopulations(first_movers,efficient_producers,X0,sk3(X1,X0))
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,axiom,
! [X0,X1] :
( X1 = critical_point(X0)
| greater(sk3(X1,X0),X1)
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_29) ).
fof(f13,plain,
! [X0,X1] :
( critical_point(X0) = X1
| greater(sk3(X1,X0),X1)
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,axiom,
! [X0,X1] :
( X1 = critical_point(X0)
| ~ greater(growth_rate(efficient_producers,sk3(X1,X0)),growth_rate(first_movers,sk3(X1,X0)))
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_30) ).
fof(f15,plain,
! [X0,X1] :
( critical_point(X0) = X1
| ~ greater(growth_rate(efficient_producers,sk3(X1,X0)),growth_rate(first_movers,sk3(X1,X0)))
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,axiom,
! [X0] :
( in_environment(X0,sk4(X0))
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_31) ).
fof(f17,axiom,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,sk4(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_32) ).
fof(f18,negated_conjecture,
environment(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5_33) ).
fof(f19,negated_conjecture,
stable(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5_34) ).
fof(f20,negated_conjecture,
~ in_environment(sk5,critical_point(sk5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5_35) ).
tcf(c_66,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_67,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_68,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_69,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_70,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_71,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_72,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_73,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_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] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| subpopulations(first_movers,efficient_producers,X0,sk3(X1,X0))
| ( critical_point(X0) = X1 )
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( greater(sk3(X1,X0),X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ( critical_point(X0) = X1 )
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ( critical_point(X1) = X0 )
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater(growth_rate(efficient_producers,sk3(X0,X1)),growth_rate(first_movers,sk3(X0,X1))) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_78,plain,
! [X0: $i] :
( in_environment(X0,sk4(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ stable(X0)
| ~ environment(X0)
| ~ greater_or_equal(X1,sk4(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_80,negated_conjecture,
environment(sk5),
inference(cnf_transformation,[],[f18]) ).
tcf(c_81,negated_conjecture,
stable(sk5),
inference(cnf_transformation,[],[f19]) ).
tcf(c_82,negated_conjecture,
~ in_environment(sk5,critical_point(sk5)),
inference(cnf_transformation,[],[f20]) ).
tcf(c_371,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0)
| ~ greater_or_equal(X1,sk4(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ( X0 != sk5 ) ),
inference(resolution_lifted,[status(thm)],[c_79,c_81]) ).
tcf(c_372,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ environment(sk5)
| ~ greater_or_equal(X0,sk4(sk5))
| ~ subpopulations(first_movers,efficient_producers,sk5,X0) ),
inference(unflattening,[status(thm)],[c_371]) ).
tcf(c_374,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ subpopulations(first_movers,efficient_producers,sk5,X0)
| ~ greater_or_equal(X0,sk4(sk5)) ),
inference(global_subsumption_just,[status(thm)],[c_372,c_80,c_372]) ).
tcf(c_375,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sk4(sk5))
| ~ subpopulations(first_movers,efficient_producers,sk5,X0) ),
inference(renaming,[status(thm)],[c_374]) ).
tcf(c_386,plain,
! [X0: $i] :
( in_environment(X0,sk4(X0))
| ~ environment(X0)
| ( X0 != sk5 ) ),
inference(resolution_lifted,[status(thm)],[c_78,c_81]) ).
tcf(c_387,plain,
( in_environment(sk5,sk4(sk5))
| ~ environment(sk5) ),
inference(unflattening,[status(thm)],[c_386]) ).
tcf(c_388,plain,
in_environment(sk5,sk4(sk5)),
inference(global_subsumption_just,[status(thm)],[c_387,c_80,c_387]) ).
tcf(c_397,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ subpopulations(first_movers,efficient_producers,sk5,X2)
| ~ greater(growth_rate(efficient_producers,sk2(X1)),growth_rate(first_movers,sk2(X1)))
| ( sk4(sk5) != X0 )
| ( sk1(X0,X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_70,c_375]) ).
tcf(c_398,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,sk1(sk4(sk5),X0)),growth_rate(first_movers,sk1(sk4(sk5),X0)))
| ~ environment(X0)
| ~ in_environment(X0,sk4(sk5))
| ~ subpopulations(first_movers,efficient_producers,sk5,sk1(sk4(sk5),X0))
| ~ greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0))) ),
inference(unflattening,[status(thm)],[c_397]) ).
tcf(c_410,plain,
! [X0: $i] :
( ~ environment(X0)
| ~ in_environment(X0,sk4(sk5))
| ~ subpopulations(first_movers,efficient_producers,sk5,sk1(sk4(sk5),X0))
| ~ greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_398,c_73]) ).
tcf(c_416,plain,
! [X0: $i,X1: $i,X2: $i] :
( in_environment(X1,sk2(X1))
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ subpopulations(first_movers,efficient_producers,sk5,X2)
| ( sk4(sk5) != X0 )
| ( sk1(X0,X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_67,c_375]) ).
tcf(c_417,plain,
! [X0: $i] :
( in_environment(X0,sk2(X0))
| greater(growth_rate(efficient_producers,sk1(sk4(sk5),X0)),growth_rate(first_movers,sk1(sk4(sk5),X0)))
| ~ environment(X0)
| ~ in_environment(X0,sk4(sk5))
| ~ subpopulations(first_movers,efficient_producers,sk5,sk1(sk4(sk5),X0)) ),
inference(unflattening,[status(thm)],[c_416]) ).
tcf(c_429,plain,
! [X0: $i] :
( in_environment(X0,sk2(X0))
| ~ environment(X0)
| ~ in_environment(X0,sk4(sk5))
| ~ subpopulations(first_movers,efficient_producers,sk5,sk1(sk4(sk5),X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_417,c_72]) ).
tcf(c_435,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3))
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater(X3,sk2(X1))
| ~ subpopulations(first_movers,efficient_producers,sk5,X2)
| ~ subpopulations(first_movers,efficient_producers,X1,X3)
| ( sk4(sk5) != X0 )
| ( sk1(X0,X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_71,c_375]) ).
tcf(c_436,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| greater(growth_rate(efficient_producers,sk1(sk4(sk5),X0)),growth_rate(first_movers,sk1(sk4(sk5),X0)))
| ~ environment(X0)
| ~ in_environment(X0,sk4(sk5))
| ~ greater(X1,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,sk5,sk1(sk4(sk5),X0)) ),
inference(unflattening,[status(thm)],[c_435]) ).
tcf(c_452,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0)
| ~ in_environment(X0,sk4(sk5))
| ~ greater(X1,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,sk5,sk1(sk4(sk5),X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_436,c_74]) ).
tcf(c_474,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(X0,sk4(sk5))
| ~ greater(X1,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,sk5,sk1(sk4(sk5),X0))
| ( X0 != sk5 ) ),
inference(resolution_lifted,[status(thm)],[c_452,c_80]) ).
tcf(c_475,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ in_environment(sk5,sk4(sk5))
| ~ greater(X0,sk2(sk5))
| ~ subpopulations(first_movers,efficient_producers,sk5,X0)
| ~ subpopulations(first_movers,efficient_producers,sk5,sk1(sk4(sk5),sk5)) ),
inference(unflattening,[status(thm)],[c_474]) ).
tcf(c_477,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ subpopulations(first_movers,efficient_producers,sk5,sk1(sk4(sk5),sk5))
| ~ subpopulations(first_movers,efficient_producers,sk5,X0)
| ~ greater(X0,sk2(sk5)) ),
inference(global_subsumption_just,[status(thm)],[c_475,c_80,c_387,c_475]) ).
tcf(c_478,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,sk2(sk5))
| ~ subpopulations(first_movers,efficient_producers,sk5,X0)
| ~ subpopulations(first_movers,efficient_producers,sk5,sk1(sk4(sk5),sk5)) ),
inference(renaming,[status(thm)],[c_477]) ).
tcf(c_492,plain,
! [X0: $i] :
( in_environment(X0,sk2(X0))
| ~ in_environment(X0,sk4(sk5))
| ~ subpopulations(first_movers,efficient_producers,sk5,sk1(sk4(sk5),X0))
| ( X0 != sk5 ) ),
inference(resolution_lifted,[status(thm)],[c_429,c_80]) ).
tcf(c_493,plain,
( in_environment(sk5,sk2(sk5))
| ~ in_environment(sk5,sk4(sk5))
| ~ subpopulations(first_movers,efficient_producers,sk5,sk1(sk4(sk5),sk5)) ),
inference(unflattening,[status(thm)],[c_492]) ).
tcf(c_494,plain,
( in_environment(sk5,sk2(sk5))
| ~ subpopulations(first_movers,efficient_producers,sk5,sk1(sk4(sk5),sk5)) ),
inference(global_subsumption_just,[status(thm)],[c_493,c_80,c_387,c_493]) ).
tcf(c_502,plain,
! [X0: $i] :
( ~ in_environment(X0,sk4(sk5))
| ~ subpopulations(first_movers,efficient_producers,sk5,sk1(sk4(sk5),X0))
| ~ greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0)))
| ( X0 != sk5 ) ),
inference(resolution_lifted,[status(thm)],[c_410,c_80]) ).
tcf(c_503,plain,
( ~ in_environment(sk5,sk4(sk5))
| ~ subpopulations(first_movers,efficient_producers,sk5,sk1(sk4(sk5),sk5))
| ~ greater(growth_rate(efficient_producers,sk2(sk5)),growth_rate(first_movers,sk2(sk5))) ),
inference(unflattening,[status(thm)],[c_502]) ).
tcf(c_504,plain,
( ~ greater(growth_rate(efficient_producers,sk2(sk5)),growth_rate(first_movers,sk2(sk5)))
| ~ subpopulations(first_movers,efficient_producers,sk5,sk1(sk4(sk5),sk5)) ),
inference(global_subsumption_just,[status(thm)],[c_503,c_80,c_387,c_503]) ).
tcf(c_505,plain,
( ~ subpopulations(first_movers,efficient_producers,sk5,sk1(sk4(sk5),sk5))
| ~ greater(growth_rate(efficient_producers,sk2(sk5)),growth_rate(first_movers,sk2(sk5))) ),
inference(renaming,[status(thm)],[c_504]) ).
tcf(c_512,plain,
! [X0: $i,X1: $i] :
( greater(sk3(X1,X0),X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ( critical_point(X0) = X1 )
| ~ in_environment(X0,X1)
| ( X0 != sk5 ) ),
inference(resolution_lifted,[status(thm)],[c_76,c_80]) ).
tcf(c_513,plain,
! [X0: $i] :
( greater(sk3(X0,sk5),X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ( critical_point(sk5) = X0 )
| ~ in_environment(sk5,X0) ),
inference(unflattening,[status(thm)],[c_512]) ).
tcf(c_527,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| subpopulations(first_movers,efficient_producers,X0,sk3(X1,X0))
| ( critical_point(X0) = X1 )
| ~ in_environment(X0,X1)
| ( X0 != sk5 ) ),
inference(resolution_lifted,[status(thm)],[c_75,c_80]) ).
tcf(c_528,plain,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,sk5,sk3(X0,sk5))
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ( critical_point(sk5) = X0 )
| ~ in_environment(sk5,X0) ),
inference(unflattening,[status(thm)],[c_527]) ).
tcf(c_542,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))
| ~ in_environment(X0,X2)
| ~ greater(X1,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ( X0 != sk5 ) ),
inference(resolution_lifted,[status(thm)],[c_69,c_80]) ).
tcf(c_543,plain,
! [X0: $i,X1: $i] :
( subpopulations(first_movers,efficient_producers,sk5,sk1(X1,sk5))
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ in_environment(sk5,X1)
| ~ greater(X0,sk2(sk5))
| ~ subpopulations(first_movers,efficient_producers,sk5,X0) ),
inference(unflattening,[status(thm)],[c_542]) ).
tcf(c_560,plain,
! [X0: $i,X1: $i] :
( subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ in_environment(X0,X1)
| ~ greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0)))
| ( X0 != sk5 ) ),
inference(resolution_lifted,[status(thm)],[c_68,c_80]) ).
tcf(c_561,plain,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,sk5,sk1(X0,sk5))
| ~ in_environment(sk5,X0)
| ~ greater(growth_rate(efficient_producers,sk2(sk5)),growth_rate(first_movers,sk2(sk5))) ),
inference(unflattening,[status(thm)],[c_560]) ).
tcf(c_572,plain,
! [X0: $i,X1: $i] :
( in_environment(X0,sk2(X0))
| subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ in_environment(X0,X1)
| ( X0 != sk5 ) ),
inference(resolution_lifted,[status(thm)],[c_66,c_80]) ).
tcf(c_573,plain,
! [X0: $i] :
( in_environment(sk5,sk2(sk5))
| subpopulations(first_movers,efficient_producers,sk5,sk1(X0,sk5))
| ~ in_environment(sk5,X0) ),
inference(unflattening,[status(thm)],[c_572]) ).
tcf(c_584,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ( critical_point(X0) = X1 )
| ~ in_environment(X0,X1)
| ~ greater(growth_rate(efficient_producers,sk3(X1,X0)),growth_rate(first_movers,sk3(X1,X0)))
| ( X0 != sk5 ) ),
inference(resolution_lifted,[status(thm)],[c_77,c_80]) ).
tcf(c_585,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ( critical_point(sk5) = X0 )
| ~ in_environment(sk5,X0)
| ~ greater(growth_rate(efficient_producers,sk3(X0,sk5)),growth_rate(first_movers,sk3(X0,sk5))) ),
inference(unflattening,[status(thm)],[c_584]) ).
tcf(c_599,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ in_environment(X0,X1)
| ~ 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)))
| ( X0 != sk5 ) ),
inference(resolution_lifted,[status(thm)],[c_74,c_80]) ).
tcf(c_600,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(sk5,X0)
| ~ greater(X1,sk2(sk5))
| ~ subpopulations(first_movers,efficient_producers,sk5,X1)
| ~ greater(growth_rate(efficient_producers,sk1(X0,sk5)),growth_rate(first_movers,sk1(X0,sk5))) ),
inference(unflattening,[status(thm)],[c_599]) ).
tcf(c_617,plain,
! [X0: $i,X1: $i] :
( ~ in_environment(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)))
| ( X0 != sk5 ) ),
inference(resolution_lifted,[status(thm)],[c_73,c_80]) ).
tcf(c_618,plain,
! [X0: $i] :
( ~ in_environment(sk5,X0)
| ~ greater(growth_rate(efficient_producers,sk2(sk5)),growth_rate(first_movers,sk2(sk5)))
| ~ greater(growth_rate(efficient_producers,sk1(X0,sk5)),growth_rate(first_movers,sk1(X0,sk5))) ),
inference(unflattening,[status(thm)],[c_617]) ).
tcf(c_865,plain,
! [X0: $i] :
( ~ iPr_def_10
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,sk2(sk5))
| ~ subpopulations(first_movers,efficient_producers,sk5,X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_600]) ).
tcf(c_868,plain,
! [X0: $i] :
( ~ iPr_def_12
| ~ in_environment(sk5,X0)
| subpopulations(first_movers,efficient_producers,sk5,sk1(X0,sk5)) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_543]) ).
tcf(c_869,plain,
( iPr_def_12
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_543]) ).
tcf(c_871,definition,
iPr_def_14 = growth_rate(efficient_producers,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_872,definition,
iPr_def_15 = growth_rate(first_movers,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_873,definition,
iPr_def_16 = critical_point(sk5),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_874,definition,
iPr_def_17 = sk4(sk5),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_875,definition,
iPr_def_18 = sk1(iPr_def_17,sk5),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_877,plain,
! [X0: $i] :
( ~ greater(iPr_def_14,iPr_def_15)
| ~ in_environment(sk5,X0)
| ~ greater(growth_rate(efficient_producers,sk1(X0,sk5)),growth_rate(first_movers,sk1(X0,sk5))) ),
inference(demodulation,[status(thm)],[c_618,c_872,c_871]) ).
tcf(c_881,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ( iPr_def_16 = X0 )
| ~ in_environment(sk5,X0)
| ~ greater(growth_rate(efficient_producers,sk3(X0,sk5)),growth_rate(first_movers,sk3(X0,sk5))) ),
inference(demodulation,[status(thm)],[c_585,c_873]) ).
tcf(c_882,plain,
! [X0: $i] :
( in_environment(sk5,iPr_def_13)
| subpopulations(first_movers,efficient_producers,sk5,sk1(X0,sk5))
| ~ in_environment(sk5,X0) ),
inference(demodulation,[status(thm)],[c_573]) ).
tcf(c_883,plain,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,sk5,sk1(X0,sk5))
| ~ greater(iPr_def_14,iPr_def_15)
| ~ in_environment(sk5,X0) ),
inference(demodulation,[status(thm)],[c_561]) ).
tcf(c_884,plain,
( iPr_def_12
| iPr_def_10 ),
inference(demodulation,[status(thm)],[c_869]) ).
tcf(c_885,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ iPr_def_10
| ~ greater(X0,iPr_def_13)
| ~ subpopulations(first_movers,efficient_producers,sk5,X0) ),
inference(demodulation,[status(thm)],[c_865]) ).
tcf(c_886,plain,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,sk5,sk1(X0,sk5))
| ~ iPr_def_12
| ~ in_environment(sk5,X0) ),
inference(demodulation,[status(thm)],[c_868]) ).
tcf(c_887,plain,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,sk5,sk3(X0,sk5))
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ( iPr_def_16 = X0 )
| ~ in_environment(sk5,X0) ),
inference(demodulation,[status(thm)],[c_528]) ).
tcf(c_888,plain,
! [X0: $i] :
( greater(sk3(X0,sk5),X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ( iPr_def_16 = X0 )
| ~ in_environment(sk5,X0) ),
inference(demodulation,[status(thm)],[c_513]) ).
tcf(c_889,plain,
( ~ greater(iPr_def_14,iPr_def_15)
| ~ subpopulations(first_movers,efficient_producers,sk5,iPr_def_18) ),
inference(demodulation,[status(thm)],[c_505,c_874,c_875]) ).
tcf(c_890,plain,
( in_environment(sk5,iPr_def_13)
| ~ subpopulations(first_movers,efficient_producers,sk5,iPr_def_18) ),
inference(demodulation,[status(thm)],[c_494]) ).
tcf(c_891,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,iPr_def_13)
| ~ subpopulations(first_movers,efficient_producers,sk5,iPr_def_18)
| ~ subpopulations(first_movers,efficient_producers,sk5,X0) ),
inference(demodulation,[status(thm)],[c_478]) ).
tcf(c_892,plain,
in_environment(sk5,iPr_def_17),
inference(demodulation,[status(thm)],[c_388]) ).
tcf(c_893,negated_conjecture,
~ in_environment(sk5,iPr_def_16),
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_1297,plain,
( in_environment(sk5,iPr_def_13)
| subpopulations(first_movers,efficient_producers,sk5,iPr_def_18)
| ~ in_environment(sk5,iPr_def_17) ),
inference(superposition,[status(thm)],[c_875,c_882]) ).
tcf(c_1298,plain,
( subpopulations(first_movers,efficient_producers,sk5,iPr_def_18)
| ~ iPr_def_12
| ~ in_environment(sk5,iPr_def_17) ),
inference(superposition,[status(thm)],[c_875,c_886]) ).
tcf(c_1299,plain,
( subpopulations(first_movers,efficient_producers,sk5,iPr_def_18)
| ~ iPr_def_12 ),
inference(forward_subsumption_resolution,[status(thm)],[c_1298,c_892]) ).
tcf(c_1302,plain,
( in_environment(sk5,iPr_def_13)
| subpopulations(first_movers,efficient_producers,sk5,iPr_def_18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1297,c_892]) ).
tcf(c_1310,plain,
( in_environment(sk5,iPr_def_13)
| ~ iPr_def_12 ),
inference(superposition,[status(thm)],[c_1299,c_890]) ).
tcf(c_1315,plain,
in_environment(sk5,iPr_def_13),
inference(global_subsumption_just,[status(thm)],[c_1310,c_890,c_1302]) ).
tcf(c_1327,plain,
( subpopulations(first_movers,efficient_producers,sk5,iPr_def_18)
| ~ greater(iPr_def_14,iPr_def_15)
| ~ in_environment(sk5,iPr_def_17) ),
inference(superposition,[status(thm)],[c_875,c_883]) ).
tcf(c_1328,plain,
( subpopulations(first_movers,efficient_producers,sk5,iPr_def_18)
| ~ greater(iPr_def_14,iPr_def_15) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1327,c_892]) ).
tcf(c_1344,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ subpopulations(first_movers,efficient_producers,sk5,X0)
| ~ greater(X0,iPr_def_13) ),
inference(global_subsumption_just,[status(thm)],[c_885,c_884,c_885,c_891,c_1299]) ).
tcf(c_1345,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,iPr_def_13)
| ~ subpopulations(first_movers,efficient_producers,sk5,X0) ),
inference(renaming,[status(thm)],[c_1344]) ).
tcf(c_1366,plain,
~ greater(iPr_def_14,iPr_def_15),
inference(global_subsumption_just,[status(thm)],[c_877,c_889,c_1328]) ).
tcf(c_1377,plain,
( greater(sk3(iPr_def_13,sk5),iPr_def_13)
| greater(growth_rate(efficient_producers,iPr_def_13),iPr_def_15)
| ( iPr_def_13 = iPr_def_16 )
| ~ in_environment(sk5,iPr_def_13) ),
inference(superposition,[status(thm)],[c_872,c_888]) ).
tcf(c_1379,plain,
( greater(iPr_def_14,iPr_def_15)
| greater(sk3(iPr_def_13,sk5),iPr_def_13)
| ( iPr_def_13 = iPr_def_16 )
| ~ in_environment(sk5,iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_1377,c_871]) ).
tcf(c_1380,plain,
( greater(sk3(iPr_def_13,sk5),iPr_def_13)
| ( iPr_def_13 = iPr_def_16 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1379,c_1366,c_1315]) ).
tcf(c_1448,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ( X0 = iPr_def_16 )
| ~ in_environment(sk5,X0)
| ~ greater(sk3(X0,sk5),iPr_def_13)
| ~ subpopulations(first_movers,efficient_producers,sk5,sk3(X0,sk5)) ),
inference(superposition,[status(thm)],[c_1345,c_881]) ).
tcf(c_1572,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ( X0 = iPr_def_16 )
| ~ in_environment(sk5,X0)
| ~ greater(sk3(X0,sk5),iPr_def_13) ),
inference(superposition,[status(thm)],[c_887,c_1448]) ).
tcf(c_1598,plain,
( greater(growth_rate(efficient_producers,iPr_def_13),iPr_def_15)
| ( iPr_def_13 = iPr_def_16 )
| ~ in_environment(sk5,iPr_def_13)
| ~ greater(sk3(iPr_def_13,sk5),iPr_def_13) ),
inference(superposition,[status(thm)],[c_872,c_1572]) ).
tcf(c_1606,plain,
( greater(iPr_def_14,iPr_def_15)
| ( iPr_def_13 = iPr_def_16 )
| ~ in_environment(sk5,iPr_def_13)
| ~ greater(sk3(iPr_def_13,sk5),iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_1598,c_871]) ).
tcf(c_1607,plain,
( ( iPr_def_13 = iPr_def_16 )
| ~ greater(sk3(iPr_def_13,sk5),iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1606,c_1366,c_1315]) ).
tcf(c_1673,plain,
iPr_def_13 = iPr_def_16,
inference(global_subsumption_just,[status(thm)],[c_1607,c_1380,c_1607]) ).
tcf(c_1685,plain,
~ in_environment(sk5,iPr_def_13),
inference(demodulation,[status(thm)],[c_893,c_1673]) ).
tcf(c_1686,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1685,c_1315]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT023-2 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.02/0.36 % CPULimit : 300
% 0.02/0.36 % WCLimit : 300
% 0.02/0.36 % DateTime : Thu Sep 24 01:05:55 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.02/0.42 Running first-order theorem proving
% 0.02/0.42 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
% 0.02/0.43
% 0.02/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.02/0.43
% 0.02/0.43 % Detected problem language: tptp
% 0.02/0.44 % Proving...
% 0.92/1.29 % SZS status Started for theBenchmark.p
% 0.92/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 0.92/1.29
% 0.92/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.92/1.29
% 0.92/1.29 % ------ iProver source info
% 0.92/1.29
% 0.92/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.92/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.92/1.29 % git: non_committed_changes: false
% 0.92/1.29
% 0.92/1.29 % ------ Parsing...% successful
% 0.92/1.29
% 0.92/1.29
% 0.92/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.92/1.29
% 0.92/1.29 % ------ 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: 4 0s sf_e pe_s pe_e %
% 0.92/1.29
% 0.92/1.29 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.92/1.29
% 0.92/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.92/1.29 % ------ Proving...
% 0.92/1.29 % ------ Problem Properties
% 0.92/1.29
% 0.92/1.29 %
% 0.92/1.29 % clauses 23
% 0.92/1.29 % conjectures 1
% 0.92/1.29 % EPR 6
% 0.92/1.29 % Horn 17
% 0.92/1.29 % unary 8
% 0.92/1.29 % binary 4
% 0.92/1.29 % lits 54
% 0.92/1.29 % lits eq 9
% 0.92/1.29 % fd_pure 0
% 0.92/1.29 % fd_pseudo 0
% 0.92/1.29 % fd_cond 3
% 0.92/1.29 % fd_pseudo_cond 0
% 0.92/1.29 % AC symbols 0
% 0.92/1.29
% 0.92/1.29 % ------ Schedule dynamic 5 is on
% 0.92/1.29
% 0.92/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.92/1.29
% 0.92/1.29
% 0.92/1.29 % ------
% 0.92/1.29 % Current options:
% 0.92/1.29 % ------
% 0.92/1.29
% 0.92/1.29
% 0.92/1.29 %
% 0.92/1.29
% 0.92/1.29 % ------ Proving...
% 0.92/1.29 %
% 0.92/1.29
% 0.92/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 0.92/1.29
% 0.92/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.92/1.29
% 0.92/1.29
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