%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT034-2 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n013.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 : Sun Sep 27 08:00:40 AM UTC 2026
% Result : Unsatisfiable 6.58s 4.04s
% Output : Refutation 7.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 30
% Syntax : Number of formulae : 61 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 181 ( 8 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 876 ( 120 ~; 120 |; 0 &; 636 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 6 con; 0-4 aty)
% Number of variables : 98 ( 0 ^; 98 !; 0 ?; 98 :)
% Comments :
%------------------------------------------------------------------------------
thf(environment_decl,type,
environment: $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(in_environment_decl,type,
in_environment: $i > $i > $o ).
thf(critical_point_decl,type,
critical_point: $i > $i ).
thf(greater_or_equal_decl,type,
greater_or_equal: $i > $i > $o ).
thf(sk2_decl,type,
sk2: $i ).
thf(appear_decl,type,
appear: $i > $i > $i ).
thf(efficient_producers_decl,type,
efficient_producers: $i ).
thf(greater_decl,type,
greater: $i > $i > $o ).
thf(selection_favors_decl,type,
selection_favors: $i > $i > $i > $o ).
thf(first_movers_decl,type,
first_movers: $i ).
thf(start_time_decl,type,
start_time: $i > $i ).
thf(subpopulations_decl,type,
subpopulations: $i > $i > $i > $i > $o ).
thf(decreases_decl,type,
decreases: $i > $o ).
thf(difference_decl,type,
difference: $i > $i > $i ).
thf(founding_rate_decl,type,
founding_rate: $i > $i > $i ).
thf(cardinality_at_time_decl,type,
cardinality_at_time: $i > $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(growth_rate_decl,type,
growth_rate: $i > $i > $i ).
thf(disbanding_rate_decl,type,
disbanding_rate: $i > $i > $i ).
thf(28,axiom,
! [A: $i] :
( ( A @ critical_point @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ critical_point @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_critical_point_means_FM_and_EP_35) ).
thf(88,plain,
! [A: $i] :
( ( A @ critical_point @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ critical_point @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ greater_or_equal ) )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_52) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ greater_or_equal ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ start_time @ ( A @ ( first_movers @ appear ) @ greater_or_equal ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_no_FM_before_opening_45) ).
thf(37,plain,
! [A: $i] :
( ( A @ start_time @ ( A @ ( first_movers @ appear ) @ greater_or_equal ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ ( efficient_producers @ growth_rate ) @ ( A @ ( first_movers @ growth_rate ) @ difference ) @ decreases )
| ( A @ ( efficient_producers @ disbanding_rate ) @ ( A @ ( first_movers @ disbanding_rate ) @ difference ) @ decreases )
| ~ ( A @ ( efficient_producers @ founding_rate ) @ ( A @ ( first_movers @ founding_rate ) @ difference ) @ decreases ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_difference_between_founding_rates_37) ).
thf(78,plain,
! [A: $i] :
( ( A @ ( efficient_producers @ growth_rate ) @ ( A @ ( first_movers @ growth_rate ) @ difference ) @ decreases )
| ( A @ ( efficient_producers @ disbanding_rate ) @ ( A @ ( first_movers @ disbanding_rate ) @ difference ) @ decreases )
| ~ ( A @ ( efficient_producers @ founding_rate ) @ ( A @ ( first_movers @ founding_rate ) @ difference ) @ decreases ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ( zero @ ( C @ ( efficient_producers @ growth_rate ) @ ( C @ ( first_movers @ growth_rate ) @ difference ) @ greater ) )
| ~ ( C @ ( efficient_producers @ growth_rate ) @ ( C @ ( first_movers @ growth_rate ) @ difference ) @ decreases )
| ~ ( C @ ( B @ greater ) )
| ~ ( A @ ( efficient_producers @ appear ) @ ( C @ greater_or_equal ) )
| ~ ( zero @ ( B @ ( efficient_producers @ growth_rate ) @ ( B @ ( first_movers @ growth_rate ) @ difference ) @ greater_or_equal ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_decreasing_function_38) ).
thf(84,plain,
! [C: $i,B: $i,A: $i] :
( ( zero @ ( C @ ( efficient_producers @ growth_rate ) @ ( C @ ( first_movers @ growth_rate ) @ difference ) @ greater ) )
| ~ ( C @ ( efficient_producers @ growth_rate ) @ ( C @ ( first_movers @ growth_rate ) @ difference ) @ decreases )
| ~ ( C @ ( B @ greater ) )
| ~ ( A @ ( efficient_producers @ appear ) @ ( C @ greater_or_equal ) )
| ~ ( zero @ ( B @ ( efficient_producers @ growth_rate ) @ ( B @ ( first_movers @ growth_rate ) @ difference ) @ greater_or_equal ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(22,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ selection_favors ) ) )
| ~ ( D @ ( B @ growth_rate ) @ ( D @ ( C @ growth_rate ) @ greater ) )
| ~ ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp1_high_growth_rates_33) ).
thf(74,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ selection_favors ) ) )
| ~ ( D @ ( B @ growth_rate ) @ ( D @ ( C @ growth_rate ) @ greater ) )
| ~ ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ ( efficient_producers @ growth_rate ) @ ( A @ ( first_movers @ growth_rate ) @ greater ) )
| ~ ( zero @ ( A @ ( efficient_producers @ growth_rate ) @ ( A @ ( first_movers @ growth_rate ) @ difference ) @ greater ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_positive_growth_rate_difference_41) ).
thf(60,plain,
! [A: $i] :
( ( A @ ( efficient_producers @ growth_rate ) @ ( A @ ( first_movers @ growth_rate ) @ greater ) )
| ~ ( zero @ ( A @ ( efficient_producers @ growth_rate ) @ ( A @ ( first_movers @ growth_rate ) @ difference ) @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( first_movers @ ( efficient_producers @ subpopulations ) ) ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations_48) ).
thf(92,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( first_movers @ ( efficient_producers @ subpopulations ) ) ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ greater ) )
| ~ ( B @ ( A @ greater_or_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_50) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ greater ) )
| ~ ( B @ ( A @ greater_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( B @ ( efficient_producers @ founding_rate ) @ ( B @ ( first_movers @ founding_rate ) @ difference ) @ decreases )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a12_57) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( B @ ( efficient_producers @ founding_rate ) @ ( B @ ( first_movers @ founding_rate ) @ difference ) @ decreases )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,negated_conjecture,
~ ( sk2 @ ( efficient_producers @ ( first_movers @ selection_favors ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t3_62) ).
thf(31,plain,
~ ( sk2 @ ( efficient_producers @ ( first_movers @ selection_favors ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ in_environment ) )
| ~ ( B @ ( D @ greater_or_equal ) )
| ~ ( D @ ( C @ greater_or_equal ) )
| ~ ( C @ ( A @ in_environment ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_durations_are_time_intervals_43) ).
thf(51,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ in_environment ) )
| ~ ( B @ ( D @ greater_or_equal ) )
| ~ ( D @ ( C @ greater_or_equal ) )
| ~ ( C @ ( A @ in_environment ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( efficient_producers @ growth_rate ) @ ( B @ ( first_movers @ growth_rate ) @ difference ) @ greater_or_equal ) )
| ( B @ ( efficient_producers @ growth_rate ) @ ( B @ ( first_movers @ growth_rate ) @ difference ) @ ( zero @ greater ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_relationship_of_growth_rates_53) ).
thf(90,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( efficient_producers @ growth_rate ) @ ( B @ ( first_movers @ growth_rate ) @ difference ) @ greater_or_equal ) )
| ( B @ ( efficient_producers @ growth_rate ) @ ( B @ ( first_movers @ growth_rate ) @ difference ) @ ( zero @ greater ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ start_time @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_opening_time_in_duration_44) ).
thf(70,plain,
! [A: $i] :
( ( A @ start_time @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(2,negated_conjecture,
sk1 @ critical_point @ ( sk1 @ in_environment ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t3_59) ).
thf(33,plain,
sk1 @ critical_point @ ( sk1 @ in_environment ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( zero @ ( B @ ( efficient_producers @ cardinality_at_time ) @ greater ) )
| ~ ( zero @ ( B @ ( first_movers @ cardinality_at_time ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_contains_FM_and_EP_47) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( zero @ ( B @ ( efficient_producers @ cardinality_at_time ) @ greater ) )
| ~ ( zero @ ( B @ ( first_movers @ cardinality_at_time ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( first_movers @ growth_rate ) @ ( C @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( B @ ( C @ greater ) )
| ~ ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ( B
!= ( A @ critical_point ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_55) ).
thf(64,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( first_movers @ growth_rate ) @ ( C @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( B @ ( C @ greater ) )
| ~ ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ( B
!= ( A @ critical_point ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1,negated_conjecture,
sk1 @ environment,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t3_58) ).
thf(32,plain,
sk1 @ environment,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(3,negated_conjecture,
sk1 @ ( efficient_producers @ appear ) @ ( sk2 @ greater_or_equal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t3_60) ).
thf(34,plain,
sk1 @ ( efficient_producers @ appear ) @ ( sk2 @ greater_or_equal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( D @ ( C @ greater_or_equal ) )
| ~ ( B @ ( D @ greater_or_equal ) )
| ~ ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a10_56) ).
thf(49,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( D @ ( C @ greater_or_equal ) )
| ~ ( B @ ( D @ greater_or_equal ) )
| ~ ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ in_environment ) )
| ~ ( B @ ( A @ critical_point @ greater ) )
| ~ ( A @ ( efficient_producers @ appear ) @ ( B @ greater_or_equal ) )
| ~ ( A @ critical_point @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_critical_time_points_46) ).
thf(86,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ in_environment ) )
| ~ ( B @ ( A @ critical_point @ greater ) )
| ~ ( A @ ( efficient_producers @ appear ) @ ( B @ greater_or_equal ) )
| ~ ( A @ critical_point @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( efficient_producers @ disbanding_rate ) @ ( B @ ( first_movers @ disbanding_rate ) @ difference ) @ decreases )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_34) ).
thf(76,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( efficient_producers @ disbanding_rate ) @ ( B @ ( first_movers @ disbanding_rate ) @ difference ) @ decreases )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ greater_or_equal ) )
| ~ ( B @ ( A @ greater ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_51) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ greater_or_equal ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( first_movers @ growth_rate ) @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ( B
!= ( A @ critical_point ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_54) ).
thf(80,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( first_movers @ growth_rate ) @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ( B
!= ( A @ critical_point ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(4,negated_conjecture,
sk2 @ ( sk1 @ critical_point @ greater ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t3_61) ).
thf(35,plain,
sk2 @ ( sk1 @ critical_point @ greater ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(21,axiom,
! [A: $i] :
( ( zero @ ( A @ ( efficient_producers @ growth_rate ) @ ( A @ ( first_movers @ growth_rate ) @ difference ) @ greater ) )
| ~ ( A @ ( efficient_producers @ growth_rate ) @ ( A @ ( first_movers @ growth_rate ) @ greater ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_positive_growth_rate_difference_42) ).
thf(72,plain,
! [A: $i] :
( ( zero @ ( A @ ( efficient_producers @ growth_rate ) @ ( A @ ( first_movers @ growth_rate ) @ difference ) @ greater ) )
| ~ ( A @ ( efficient_producers @ growth_rate ) @ ( A @ ( first_movers @ growth_rate ) @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( A @ ( efficient_producers @ appear ) @ ( B @ greater_or_equal ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_FM_and_EP_members_EP_appeared_49) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( A @ ( efficient_producers @ appear ) @ ( B @ greater_or_equal ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ ( efficient_producers @ growth_rate ) @ ( A @ ( first_movers @ growth_rate ) @ difference ) @ ( zero @ greater ) )
| ~ ( A @ ( first_movers @ growth_rate ) @ ( A @ ( efficient_producers @ growth_rate ) @ greater ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_negative_growth_rate_difference_40) ).
thf(47,plain,
! [A: $i] :
( ( A @ ( efficient_producers @ growth_rate ) @ ( A @ ( first_movers @ growth_rate ) @ difference ) @ ( zero @ greater ) )
| ~ ( A @ ( first_movers @ growth_rate ) @ ( A @ ( efficient_producers @ growth_rate ) @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ ( efficient_producers @ appear ) @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ ( efficient_producers @ appear ) @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_FM_and_EP_when_EP_appears_36) ).
thf(68,plain,
! [A: $i] :
( ( A @ ( efficient_producers @ appear ) @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ ( efficient_producers @ appear ) @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ ( first_movers @ growth_rate ) @ ( A @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ ( efficient_producers @ growth_rate ) @ ( A @ ( first_movers @ growth_rate ) @ difference ) @ ( zero @ greater ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_negative_growth_rate_difference_39) ).
thf(62,plain,
! [A: $i] :
( ( A @ ( first_movers @ growth_rate ) @ ( A @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ ( efficient_producers @ growth_rate ) @ ( A @ ( first_movers @ growth_rate ) @ difference ) @ ( zero @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(100,plain,
$false,
inference(e,[status(thm)],[88,56,37,78,84,74,60,92,53,41,31,51,90,70,33,45,64,32,34,49,86,76,39,80,35,72,43,47,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : MGT034-2 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.22/0.49 % Computer : n013.cluster.edu
% 0.22/0.49 % Model : x86_64 x86_64
% 0.22/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.49 % Memory : 8046.5625MB
% 0.22/0.49 % OS : Linux 6.8.0-71-generic
% 0.22/0.49 % CPULimit : 300
% 0.22/0.49 % WCLimit : 300
% 0.22/0.49 % DateTime : Sat Sep 26 00:05:07 UTC 2026
% 0.22/0.50 % CPUTime :
% 0.22/0.50 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.38/1.36 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.85/1.69 % [INFO] Parsing done (322ms).
% 2.17/1.71 % [INFO] Running in sequential loop mode.
% 3.09/2.33 % [INFO] eprover registered as external prover.
% 3.09/2.34 % [INFO] Scanning for conjecture ...
% 3.44/2.51 % [INFO] Found a conjecture (or negated_conjecture) and 25 axioms. Running axiom selection ...
% 3.61/2.63 % [INFO] Axiom selection finished. Selected 25 axioms (removed 0 axioms).
% 3.85/2.72 % [INFO] Problem is propositional (TPTP CNF).
% 3.85/2.74 % [INFO] Type checking passed.
% 3.85/2.74 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 6.58/4.03 % External prover 'e' found a proof!
% 6.58/4.03 % [INFO] Killing All external provers ...
% 6.58/4.03 % Time passed: 3316ms (effective reasoning time: 2309ms)
% 6.58/4.04 % Axioms used in derivation (25): mp_relationship_of_growth_rates_53, a12_57, mp_positive_growth_rate_difference_42, mp_critical_time_points_46, mp_greater_or_equal_52, mp_no_FM_before_opening_45, a10_56, l3_34, mp_FM_and_EP_members_EP_appeared_49, d1_54, mp_contains_FM_and_EP_47, mp_difference_between_founding_rates_37, mp_durations_are_time_intervals_43, mp_greater_or_equal_50, mp_opening_time_in_duration_44, mp_symmetry_of_subpopulations_48, mp_FM_and_EP_when_EP_appears_36, mp_positive_growth_rate_difference_41, mp_greater_or_equal_51, mp_negative_growth_rate_difference_40, d1_55, mp_decreasing_function_38, mp_critical_point_means_FM_and_EP_35, mp1_high_growth_rates_33, mp_negative_growth_rate_difference_39
% 6.58/4.04 % No. of inferences in proof: 61
% 6.58/4.04 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3316 ms resp. 2309 ms w/o parsing
% 7.51/4.16 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.51/4.16 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------