%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : MGT027-1 : 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 : n014.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 02:12:24 PM UTC 2026
% Result : Unsatisfiable 2.72s 1.30s
% Output : CNFRefutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 20
% Syntax : Number of formulae : 109 ( 18 unt; 5 def)
% Number of atoms : 475 ( 43 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 543 ( 271 ~; 272 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 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 : 15 ( 13 usr; 7 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 122 ( 0 sgn 122 !; 0 ?; 97 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( contracts_from(X1,first_movers)
| greater(cardinality_at_time(first_movers,sk1(X1,X0)),zero)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_contracts_from_24) ).
fof(f2,axiom,
! [X0,X1] :
( contracts_from(X1,first_movers)
| greater_or_equal(sk1(X1,X0),X1)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_contracts_from_25) ).
fof(f3,axiom,
! [X0,X1] :
( contracts_from(X1,first_movers)
| ~ 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_contracts_from_26) ).
fof(f4,axiom,
! [X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep_27) ).
fof(f5,axiom,
! [X2,X0,X1] :
( in_environment(X0,X2)
| ~ greater(X2,X1)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_long_stable_environments_28) ).
fof(f6,axiom,
! [X0] :
( in_environment(X0,appear(efficient_producers,X0))
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_EP_in_stable_environments_29) ).
fof(f7,axiom,
! [X2,X0,X1] :
( greater(X0,X2)
| ~ greater(X1,X2)
| ~ greater(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_transitivity_30) ).
fof(f8,axiom,
! [X0,X1] :
( X0 = X1
| greater(X0,X1)
| ~ greater_or_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_31) ).
fof(f9,axiom,
! [X0,X1] :
( greater_or_equal(X0,X1)
| ~ greater(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_32) ).
fof(f11,axiom,
! [X0,X1] :
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_34) ).
fof(f12,axiom,
! [X0] :
( greater(sk2(X0),appear(efficient_producers,X0))
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l10_35) ).
fof(f13,axiom,
! [X0,X1] :
( greater(zero,growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l10_36) ).
fof(f14,negated_conjecture,
environment(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l9_37) ).
fof(f15,negated_conjecture,
stable(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l9_38) ).
fof(f16,negated_conjecture,
! [X0] :
( ~ contracts_from(X0,first_movers)
| ~ greater(X0,appear(efficient_producers,sk3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l9_39) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( contracts_from(X1,first_movers)
| greater(cardinality_at_time(first_movers,sk1(X1,X0)),zero)
| ~ stable(X0)
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( contracts_from(X1,first_movers)
| greater_or_equal(sk1(X1,X0),X1)
| ~ stable(X0)
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( contracts_from(X0,first_movers)
| ~ stable(X1)
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater(zero,growth_rate(first_movers,sk1(X0,X1))) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( subpopulations(first_movers,efficient_producers,X1,X0)
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater(cardinality_at_time(first_movers,X0),zero) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( in_environment(X0,X2)
| ~ stable(X0)
| ~ environment(X0)
| ~ greater(X2,X1)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_70,plain,
! [X0: $i] :
( in_environment(X0,appear(efficient_producers,X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(X0,X2)
| ~ greater(X1,X2)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( greater(X0,X1)
| ( X0 = X1 )
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater_or_equal(X0,appear(efficient_producers,X1)) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_76,plain,
! [X0: $i] :
( greater(sk2(X0),appear(efficient_producers,X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X1))
| ~ stable(X0)
| ~ environment(X0)
| ~ greater_or_equal(X1,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_78,negated_conjecture,
environment(sk3),
inference(cnf_transformation,[],[f14]) ).
tcf(c_79,negated_conjecture,
stable(sk3),
inference(cnf_transformation,[],[f15]) ).
tcf(c_80,negated_conjecture,
! [X0: $i] :
( ~ contracts_from(X0,first_movers)
| ~ greater(X0,appear(efficient_producers,sk3)) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( greater(zero,growth_rate(first_movers,X2))
| ~ stable(X0)
| ~ environment(X1)
| ~ environment(X0)
| ~ in_environment(X1,X3)
| ~ greater_or_equal(X2,sk2(X0))
| ~ greater(cardinality_at_time(efficient_producers,X3),zero)
| ~ greater(cardinality_at_time(first_movers,X3),zero)
| ( efficient_producers != efficient_producers )
| ( first_movers != first_movers )
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_77,c_68]) ).
tcf(c_310,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X0))
| ~ stable(X1)
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater_or_equal(X0,sk2(X1))
| ~ greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater(cardinality_at_time(first_movers,X0),zero) ),
inference(unflattening,[status(thm)],[c_309]) ).
tcf(c_340,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ stable(X2)
| ~ environment(X2)
| ~ in_environment(X2,X0)
| ~ greater(X1,appear(efficient_producers,sk3))
| ~ greater(zero,growth_rate(first_movers,sk1(X0,X2)))
| ( first_movers != first_movers )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_67,c_80]) ).
tcf(c_341,plain,
! [X0: $i,X1: $i] :
( ~ stable(X1)
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater(X0,appear(efficient_producers,sk3))
| ~ greater(zero,growth_rate(first_movers,sk1(X0,X1))) ),
inference(unflattening,[status(thm)],[c_340]) ).
tcf(c_358,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater_or_equal(sk1(X0,X2),X0)
| ~ stable(X2)
| ~ environment(X2)
| ~ in_environment(X2,X0)
| ~ greater(X1,appear(efficient_producers,sk3))
| ( first_movers != first_movers )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_66,c_80]) ).
tcf(c_359,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(sk1(X0,X1),X0)
| ~ stable(X1)
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater(X0,appear(efficient_producers,sk3)) ),
inference(unflattening,[status(thm)],[c_358]) ).
tcf(c_376,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(cardinality_at_time(first_movers,sk1(X0,X2)),zero)
| ~ stable(X2)
| ~ environment(X2)
| ~ in_environment(X2,X0)
| ~ greater(X1,appear(efficient_producers,sk3))
| ( first_movers != first_movers )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_65,c_80]) ).
tcf(c_377,plain,
! [X0: $i,X1: $i] :
( greater(cardinality_at_time(first_movers,sk1(X0,X1)),zero)
| ~ stable(X1)
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater(X0,appear(efficient_producers,sk3)) ),
inference(unflattening,[status(thm)],[c_376]) ).
tcf(c_409,plain,
! [X0: $i] :
( greater(sk2(X0),appear(efficient_producers,X0))
| ~ environment(X0)
| ( X0 != sk3 ) ),
inference(resolution_lifted,[status(thm)],[c_76,c_79]) ).
tcf(c_410,plain,
( greater(sk2(sk3),appear(efficient_producers,sk3))
| ~ environment(sk3) ),
inference(unflattening,[status(thm)],[c_409]) ).
tcf(c_411,plain,
greater(sk2(sk3),appear(efficient_producers,sk3)),
inference(global_subsumption_just,[status(thm)],[c_410,c_78,c_410]) ).
tcf(c_416,plain,
! [X0: $i] :
( in_environment(X0,appear(efficient_producers,X0))
| ~ environment(X0)
| ( X0 != sk3 ) ),
inference(resolution_lifted,[status(thm)],[c_70,c_79]) ).
tcf(c_417,plain,
( in_environment(sk3,appear(efficient_producers,sk3))
| ~ environment(sk3) ),
inference(unflattening,[status(thm)],[c_416]) ).
tcf(c_418,plain,
in_environment(sk3,appear(efficient_producers,sk3)),
inference(global_subsumption_just,[status(thm)],[c_417,c_78,c_417]) ).
tcf(c_423,plain,
! [X0: $i,X1: $i,X2: $i] :
( in_environment(X0,X2)
| ~ environment(X0)
| ~ greater(X2,X1)
| ~ in_environment(X0,X1)
| ( X0 != sk3 ) ),
inference(resolution_lifted,[status(thm)],[c_69,c_79]) ).
tcf(c_424,plain,
! [X0: $i,X1: $i] :
( in_environment(sk3,X0)
| ~ environment(sk3)
| ~ in_environment(sk3,X1)
| ~ greater(X0,X1) ),
inference(unflattening,[status(thm)],[c_423]) ).
tcf(c_425,plain,
! [X0: $i,X1: $i] :
( in_environment(sk3,X0)
| ~ greater(X0,X1)
| ~ in_environment(sk3,X1) ),
inference(global_subsumption_just,[status(thm)],[c_424,c_78,c_424]) ).
tcf(c_426,plain,
! [X0: $i,X1: $i] :
( in_environment(sk3,X0)
| ~ in_environment(sk3,X1)
| ~ greater(X0,X1) ),
inference(renaming,[status(thm)],[c_425]) ).
tcf(c_436,plain,
! [X0: $i,X1: $i] :
( greater(cardinality_at_time(first_movers,sk1(X1,X0)),zero)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(X1,appear(efficient_producers,sk3))
| ( X0 != sk3 ) ),
inference(resolution_lifted,[status(thm)],[c_377,c_79]) ).
tcf(c_437,plain,
! [X0: $i] :
( greater(cardinality_at_time(first_movers,sk1(X0,sk3)),zero)
| ~ environment(sk3)
| ~ in_environment(sk3,X0)
| ~ greater(X0,appear(efficient_producers,sk3)) ),
inference(unflattening,[status(thm)],[c_436]) ).
tcf(c_439,plain,
! [X0: $i] :
( greater(cardinality_at_time(first_movers,sk1(X0,sk3)),zero)
| ~ greater(X0,appear(efficient_producers,sk3))
| ~ in_environment(sk3,X0) ),
inference(global_subsumption_just,[status(thm)],[c_437,c_78,c_437]) ).
tcf(c_440,plain,
! [X0: $i] :
( greater(cardinality_at_time(first_movers,sk1(X0,sk3)),zero)
| ~ in_environment(sk3,X0)
| ~ greater(X0,appear(efficient_producers,sk3)) ),
inference(renaming,[status(thm)],[c_439]) ).
tcf(c_451,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(sk1(X1,X0),X1)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(X1,appear(efficient_producers,sk3))
| ( X0 != sk3 ) ),
inference(resolution_lifted,[status(thm)],[c_359,c_79]) ).
tcf(c_452,plain,
! [X0: $i] :
( greater_or_equal(sk1(X0,sk3),X0)
| ~ environment(sk3)
| ~ in_environment(sk3,X0)
| ~ greater(X0,appear(efficient_producers,sk3)) ),
inference(unflattening,[status(thm)],[c_451]) ).
tcf(c_454,plain,
! [X0: $i] :
( greater_or_equal(sk1(X0,sk3),X0)
| ~ greater(X0,appear(efficient_producers,sk3))
| ~ in_environment(sk3,X0) ),
inference(global_subsumption_just,[status(thm)],[c_452,c_78,c_452]) ).
tcf(c_455,plain,
! [X0: $i] :
( greater_or_equal(sk1(X0,sk3),X0)
| ~ in_environment(sk3,X0)
| ~ greater(X0,appear(efficient_producers,sk3)) ),
inference(renaming,[status(thm)],[c_454]) ).
tcf(c_466,plain,
! [X0: $i,X1: $i] :
( ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(X1,appear(efficient_producers,sk3))
| ~ greater(zero,growth_rate(first_movers,sk1(X1,X0)))
| ( X0 != sk3 ) ),
inference(resolution_lifted,[status(thm)],[c_341,c_79]) ).
tcf(c_467,plain,
! [X0: $i] :
( ~ environment(sk3)
| ~ in_environment(sk3,X0)
| ~ greater(X0,appear(efficient_producers,sk3))
| ~ greater(zero,growth_rate(first_movers,sk1(X0,sk3))) ),
inference(unflattening,[status(thm)],[c_466]) ).
tcf(c_469,plain,
! [X0: $i] :
( ~ greater(zero,growth_rate(first_movers,sk1(X0,sk3)))
| ~ greater(X0,appear(efficient_producers,sk3))
| ~ in_environment(sk3,X0) ),
inference(global_subsumption_just,[status(thm)],[c_467,c_78,c_467]) ).
tcf(c_470,plain,
! [X0: $i] :
( ~ in_environment(sk3,X0)
| ~ greater(X0,appear(efficient_producers,sk3))
| ~ greater(zero,growth_rate(first_movers,sk1(X0,sk3))) ),
inference(renaming,[status(thm)],[c_469]) ).
tcf(c_481,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X1))
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater_or_equal(X1,sk2(X0))
| ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ( X0 != sk3 ) ),
inference(resolution_lifted,[status(thm)],[c_310,c_79]) ).
tcf(c_482,plain,
! [X0: $i] :
( greater(zero,growth_rate(first_movers,X0))
| ~ environment(sk3)
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(X0,sk2(sk3))
| ~ greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater(cardinality_at_time(first_movers,X0),zero) ),
inference(unflattening,[status(thm)],[c_481]) ).
tcf(c_484,plain,
! [X0: $i] :
( greater(zero,growth_rate(first_movers,X0))
| ~ greater(cardinality_at_time(first_movers,X0),zero)
| ~ greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater_or_equal(X0,sk2(sk3))
| ~ in_environment(sk3,X0) ),
inference(global_subsumption_just,[status(thm)],[c_482,c_78,c_482]) ).
tcf(c_485,plain,
! [X0: $i] :
( greater(zero,growth_rate(first_movers,X0))
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(X0,sk2(sk3))
| ~ greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater(cardinality_at_time(first_movers,X0),zero) ),
inference(renaming,[status(thm)],[c_484]) ).
tcf(c_521,plain,
! [X0: $i,X1: $i] :
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ in_environment(X0,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ( X0 != sk3 ) ),
inference(resolution_lifted,[status(thm)],[c_75,c_78]) ).
tcf(c_522,plain,
! [X0: $i] :
( greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(X0,appear(efficient_producers,sk3)) ),
inference(unflattening,[status(thm)],[c_521]) ).
tcf(c_540,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(X1,X2)
| ( X1 = X2 )
| ~ in_environment(sk3,X0)
| ~ greater(X0,appear(efficient_producers,sk3))
| ( X0 != X2 )
| ( sk1(X0,sk3) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_72,c_455]) ).
tcf(c_541,plain,
! [X0: $i] :
( greater(sk1(X0,sk3),X0)
| ( sk1(X0,sk3) = X0 )
| ~ in_environment(sk3,X0)
| ~ greater(X0,appear(efficient_producers,sk3)) ),
inference(unflattening,[status(thm)],[c_540]) ).
tcf(c_573,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ in_environment(sk3,X1)
| ~ greater(X0,X2)
| ( X0 != X1 )
| ( appear(efficient_producers,sk3) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_73,c_522]) ).
tcf(c_574,plain,
! [X0: $i] :
( greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ in_environment(sk3,X0)
| ~ greater(X0,appear(efficient_producers,sk3)) ),
inference(unflattening,[status(thm)],[c_573]) ).
tcf(c_606,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X1))
| ~ in_environment(sk3,X1)
| ~ in_environment(sk3,X0)
| ~ greater(X0,appear(efficient_producers,sk3))
| ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ( sk2(sk3) != X0 )
| ( sk1(X0,sk3) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_455,c_485]) ).
tcf(c_607,plain,
( greater(zero,growth_rate(first_movers,sk1(sk2(sk3),sk3)))
| ~ in_environment(sk3,sk2(sk3))
| ~ greater(sk2(sk3),appear(efficient_producers,sk3))
| ~ in_environment(sk3,sk1(sk2(sk3),sk3))
| ~ greater(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),zero)
| ~ greater(cardinality_at_time(first_movers,sk1(sk2(sk3),sk3)),zero) ),
inference(unflattening,[status(thm)],[c_606]) ).
tcf(c_608,plain,
( greater(zero,growth_rate(first_movers,sk1(sk2(sk3),sk3)))
| ~ in_environment(sk3,sk2(sk3))
| ~ greater(cardinality_at_time(first_movers,sk1(sk2(sk3),sk3)),zero)
| ~ greater(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),zero)
| ~ in_environment(sk3,sk1(sk2(sk3),sk3)) ),
inference(global_subsumption_just,[status(thm)],[c_607,c_78,c_410,c_607]) ).
tcf(c_609,plain,
( greater(zero,growth_rate(first_movers,sk1(sk2(sk3),sk3)))
| ~ in_environment(sk3,sk2(sk3))
| ~ in_environment(sk3,sk1(sk2(sk3),sk3))
| ~ greater(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),zero)
| ~ greater(cardinality_at_time(first_movers,sk1(sk2(sk3),sk3)),zero) ),
inference(renaming,[status(thm)],[c_608]) ).
tcf(c_823,definition,
iPr_def_13 = sk2(sk3),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_824,definition,
iPr_def_14 = sk1(iPr_def_13,sk3),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_825,definition,
iPr_def_15 = cardinality_at_time(first_movers,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_826,definition,
iPr_def_16 = cardinality_at_time(efficient_producers,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_827,definition,
iPr_def_17 = growth_rate(first_movers,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_833,plain,
( greater(zero,iPr_def_17)
| ~ greater(iPr_def_16,zero)
| ~ greater(iPr_def_15,zero)
| ~ in_environment(sk3,iPr_def_14)
| ~ in_environment(sk3,iPr_def_13) ),
inference(demodulation,[status(thm)],[c_609,c_827,c_826,c_823,c_824,c_825]) ).
tcf(c_836,plain,
! [X0: $i] :
( greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater(X0,iPr_def_10)
| ~ in_environment(sk3,X0) ),
inference(demodulation,[status(thm)],[c_574]) ).
tcf(c_838,plain,
! [X0: $i] :
( greater(sk1(X0,sk3),X0)
| ( sk1(X0,sk3) = X0 )
| ~ greater(X0,iPr_def_10)
| ~ in_environment(sk3,X0) ),
inference(demodulation,[status(thm)],[c_541]) ).
tcf(c_839,plain,
! [X0: $i] :
( ~ greater(X0,iPr_def_10)
| ~ in_environment(sk3,X0)
| ~ greater(zero,growth_rate(first_movers,sk1(X0,sk3))) ),
inference(demodulation,[status(thm)],[c_470]) ).
tcf(c_840,plain,
! [X0: $i] :
( greater(cardinality_at_time(first_movers,sk1(X0,sk3)),zero)
| ~ greater(X0,iPr_def_10)
| ~ in_environment(sk3,X0) ),
inference(demodulation,[status(thm)],[c_440]) ).
tcf(c_841,plain,
! [X0: $i,X1: $i] :
( in_environment(sk3,X0)
| ~ in_environment(sk3,X1)
| ~ greater(X0,X1) ),
inference(demodulation,[status(thm)],[c_426]) ).
tcf(c_842,plain,
in_environment(sk3,iPr_def_10),
inference(demodulation,[status(thm)],[c_418]) ).
tcf(c_843,plain,
greater(iPr_def_13,iPr_def_10),
inference(demodulation,[status(thm)],[c_411]) ).
tcf(c_1179,plain,
( in_environment(sk3,iPr_def_13)
| ~ in_environment(sk3,iPr_def_10) ),
inference(superposition,[status(thm)],[c_843,c_841]) ).
tcf(c_1180,plain,
in_environment(sk3,iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_1179,c_842]) ).
tcf(c_1214,plain,
( ~ greater(iPr_def_13,iPr_def_10)
| ~ in_environment(sk3,iPr_def_13)
| ~ greater(zero,growth_rate(first_movers,iPr_def_14)) ),
inference(superposition,[status(thm)],[c_824,c_839]) ).
tcf(c_1215,plain,
( greater(cardinality_at_time(first_movers,iPr_def_14),zero)
| ~ greater(iPr_def_13,iPr_def_10)
| ~ in_environment(sk3,iPr_def_13) ),
inference(superposition,[status(thm)],[c_824,c_840]) ).
tcf(c_1216,plain,
( greater(iPr_def_15,zero)
| ~ greater(iPr_def_13,iPr_def_10)
| ~ in_environment(sk3,iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_1215,c_825]) ).
tcf(c_1217,plain,
greater(iPr_def_15,zero),
inference(forward_subsumption_resolution,[status(thm)],[c_1216,c_843,c_1180]) ).
tcf(c_1218,plain,
( ~ greater(iPr_def_13,iPr_def_10)
| ~ greater(zero,iPr_def_17)
| ~ in_environment(sk3,iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_1214,c_827]) ).
tcf(c_1219,plain,
~ greater(zero,iPr_def_17),
inference(forward_subsumption_resolution,[status(thm)],[c_1218,c_843,c_1180]) ).
tcf(c_1252,plain,
( greater(iPr_def_16,zero)
| ~ greater(iPr_def_14,iPr_def_10)
| ~ in_environment(sk3,iPr_def_14) ),
inference(superposition,[status(thm)],[c_826,c_836]) ).
tcf(c_1381,plain,
( greater(iPr_def_14,iPr_def_13)
| ( sk1(iPr_def_13,sk3) = iPr_def_13 )
| ~ greater(iPr_def_13,iPr_def_10)
| ~ in_environment(sk3,iPr_def_13) ),
inference(superposition,[status(thm)],[c_824,c_838]) ).
tcf(c_1384,plain,
( greater(iPr_def_14,iPr_def_13)
| ( iPr_def_13 = iPr_def_14 )
| ~ greater(iPr_def_13,iPr_def_10)
| ~ in_environment(sk3,iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_1381,c_824]) ).
tcf(c_1385,plain,
( greater(iPr_def_14,iPr_def_13)
| ( iPr_def_13 = iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1384,c_843,c_1180]) ).
tcf(c_1407,plain,
! [X0: $i] :
( greater(iPr_def_14,X0)
| ( iPr_def_13 = iPr_def_14 )
| ~ greater(iPr_def_13,X0) ),
inference(superposition,[status(thm)],[c_1385,c_71]) ).
tcf(c_1408,plain,
( in_environment(sk3,iPr_def_14)
| ( iPr_def_13 = iPr_def_14 )
| ~ in_environment(sk3,iPr_def_13) ),
inference(superposition,[status(thm)],[c_1385,c_841]) ).
tcf(c_1409,plain,
( in_environment(sk3,iPr_def_14)
| ( iPr_def_13 = iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1408,c_1180]) ).
tcf(c_1481,plain,
( ~ in_environment(sk3,iPr_def_14)
| ~ greater(iPr_def_14,iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_1252,c_833,c_1180,c_1217,c_1219,c_1252]) ).
tcf(c_1482,plain,
( ~ greater(iPr_def_14,iPr_def_10)
| ~ in_environment(sk3,iPr_def_14) ),
inference(renaming,[status(thm)],[c_1481]) ).
tcf(c_1491,plain,
( ( iPr_def_13 = iPr_def_14 )
| ~ greater(iPr_def_14,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1409,c_1482]) ).
tcf(c_1505,plain,
( greater(iPr_def_14,iPr_def_10)
| ( iPr_def_13 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_843,c_1407]) ).
tcf(c_1508,plain,
iPr_def_13 = iPr_def_14,
inference(global_subsumption_just,[status(thm)],[c_1505,c_1491,c_1505]) ).
tcf(c_1512,plain,
( ~ greater(iPr_def_13,iPr_def_10)
| ~ in_environment(sk3,iPr_def_13) ),
inference(demodulation,[status(thm)],[c_1482,c_1508]) ).
tcf(c_1519,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1512,c_843,c_1180]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT027-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.39 % Computer : n014.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Thu Sep 24 01:04:19 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 0.11/0.44
% 0.11/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.44
% 0.11/0.44 % Detected problem language: tptp
% 0.11/0.46 % Proving...
% 2.72/1.30 % SZS status Started for theBenchmark.p
% 2.72/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 2.72/1.30
% 2.72/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.72/1.30
% 2.72/1.30 % ------ iProver source info
% 2.72/1.30
% 2.72/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 2.72/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.72/1.30 % git: non_committed_changes: false
% 2.72/1.30
% 2.72/1.30 % ------ Parsing...% successful
% 2.72/1.30
% 2.72/1.30
% 2.72/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.72/1.30
% 2.72/1.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 6 0s sf_e pe_s pe_e %
% 2.72/1.30
% 2.72/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.72/1.30
% 2.72/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.72/1.30 % ------ Proving...
% 2.72/1.30 % ------ Problem Properties
% 2.72/1.30
% 2.72/1.30 %
% 2.72/1.30 % clauses 25
% 2.72/1.30 % conjectures 0
% 2.72/1.30 % EPR 8
% 2.72/1.30 % Horn 24
% 2.72/1.30 % unary 15
% 2.72/1.30 % binary 0
% 2.72/1.30 % lits 51
% 2.72/1.30 % lits eq 13
% 2.72/1.30 % fd_pure 0
% 2.72/1.30 % fd_pseudo 0
% 2.72/1.30 % fd_cond 0
% 2.72/1.30 % fd_pseudo_cond 0
% 2.72/1.30 % AC symbols 0
% 2.72/1.30
% 2.72/1.30 % ------ Schedule dynamic 5 is on
% 2.72/1.30
% 2.72/1.30 % ------ no conjectures: strip conj schedule
% 2.72/1.30
% 2.72/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.72/1.30
% 2.72/1.30
% 2.72/1.30 % ------
% 2.72/1.30 % Current options:
% 2.72/1.30 % ------
% 2.72/1.30
% 2.72/1.30
% 2.72/1.30 %
% 2.72/1.30
% 2.72/1.30 % ------ Proving...
% 2.72/1.30 %
% 2.72/1.30
% 2.72/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 2.72/1.30
% 2.72/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.72/1.31
% 2.72/1.31
%------------------------------------------------------------------------------