%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT035-2 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 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 : Sun Sep 27 08:00:40 AM UTC 2026
% Result : Unsatisfiable 44.26s 15.69s
% Output : Refutation 37.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 45
% Syntax : Number of formulae : 182 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 663 ( 100 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 2118 ( 375 ~; 421 |; 0 &;1322 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 6 con; 0-4 aty)
% Number of variables : 322 ( 0 ^; 322 !; 0 ?; 322 :)
% Comments :
%------------------------------------------------------------------------------
thf(environment_decl,type,
environment: $i > $o ).
thf(sk3_decl,type,
sk3: $i ).
thf(stable_decl,type,
stable: $i > $o ).
thf(in_environment_decl,type,
in_environment: $i > $i > $o ).
thf(subpopulations_decl,type,
subpopulations: $i > $i > $i > $i > $o ).
thf(first_movers_decl,type,
first_movers: $i ).
thf(efficient_producers_decl,type,
efficient_producers: $i ).
thf(sk4_decl,type,
sk4: $i > $i ).
thf(greater_or_equal_decl,type,
greater_or_equal: $i > $i > $o ).
thf(outcompetes_decl,type,
outcompetes: $i > $i > $i > $o ).
thf(greater_decl,type,
greater: $i > $i > $o ).
thf(sum_decl,type,
sum: $i > $i > $i ).
thf(constant_decl,type,
constant: $i > $o ).
thf(increases_decl,type,
increases: $i > $o ).
thf(decreases_decl,type,
decreases: $i > $o ).
thf(cardinality_at_time_decl,type,
cardinality_at_time: $i > $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(resources_decl,type,
resources: $i > $i > $i ).
thf(number_of_organizations_decl,type,
number_of_organizations: $i > $i > $i ).
thf(equilibrium_decl,type,
equilibrium: $i > $i ).
thf(growth_rate_decl,type,
growth_rate: $i > $i > $i ).
thf(subpopulation_decl,type,
subpopulation: $i > $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i > $i ).
thf(sk2_decl,type,
sk2: $i > $i ).
thf(1,negated_conjecture,
sk3 @ environment,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t4_76) ).
thf(47,plain,
sk3 @ environment,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ sk1 @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a5_69) ).
thf(117,plain,
! [A: $i] :
( ( A @ sk1 @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(118,plain,
! [A: $i] :
( ( A @ sk1 @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
inference(cnf,[status(esa)],[117]) ).
thf(175,plain,
! [A: $i] :
( ( ( sk3 @ environment )
!= ( A @ environment ) )
| ( A @ sk1 @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47,118]) ).
thf(176,plain,
! [A: $i] :
( ( ( sk3 @ environment )
!= ( A @ environment ) )
| ( A @ sk1 @ ( A @ in_environment ) )
| ~ ( A @ stable ) ),
inference(simp,[status(thm)],[175]) ).
thf(177,plain,
( ( sk3 @ sk1 @ ( sk3 @ in_environment ) )
| ~ ( sk3 @ stable ) ),
inference(pattern_uni,[status(thm)],[176:[bind(A,$thf( sk3 ))]]) ).
thf(2,negated_conjecture,
sk3 @ stable,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t4_77) ).
thf(48,plain,
sk3 @ stable,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(181,plain,
( ( sk3 @ sk1 @ ( sk3 @ in_environment ) )
| ~ $true ),
inference(rewrite,[status(thm)],[177,48]) ).
thf(182,plain,
sk3 @ sk1 @ ( sk3 @ in_environment ),
inference(simp,[status(thm)],[181]) ).
thf(3,negated_conjecture,
! [A: $i] :
( ( A @ sk4 @ ( sk3 @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ ( sk3 @ in_environment ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t4_78) ).
thf(49,plain,
! [A: $i] :
( ( A @ sk4 @ ( sk3 @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ ( sk3 @ in_environment ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(52,plain,
! [A: $i] :
( ( A @ sk4 @ ( sk3 @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ ( sk3 @ in_environment ) ) ),
inference(cnf,[status(esa)],[49]) ).
thf(183,plain,
! [A: $i] :
( ( ( sk3 @ sk1 @ ( sk3 @ in_environment ) )
!= ( A @ ( sk3 @ in_environment ) ) )
| ( A @ sk4 @ ( sk3 @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[182,52]) ).
thf(184,plain,
! [A: $i] :
( ( ( sk3 @ sk1 @ ( sk3 @ in_environment ) )
!= ( A @ ( sk3 @ in_environment ) ) )
| ( A @ sk4 @ ( sk3 @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) ) ),
inference(simp,[status(thm)],[183]) ).
thf(185,plain,
sk3 @ sk1 @ sk4 @ ( sk3 @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ),
inference(pattern_uni,[status(thm)],[184:[bind(A,$thf( sk3 @ sk1 ))]]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = first_movers )
| ( B = efficient_producers )
| ~ ( zero @ ( C @ ( B @ cardinality_at_time ) @ greater ) )
| ~ ( C @ ( A @ ( B @ subpopulation ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a11_73) ).
thf(129,plain,
! [C: $i,B: $i,A: $i] :
( ( B = first_movers )
| ( B = efficient_producers )
| ~ ( zero @ ( C @ ( B @ cardinality_at_time ) @ greater ) )
| ~ ( C @ ( A @ ( B @ subpopulation ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(35,axiom,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( efficient_producers @ cardinality_at_time ) @ greater ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_positive_number_of_organizations_55) ).
thf(134,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( efficient_producers @ cardinality_at_time ) @ greater ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ decreases )
| ( B @ increases )
| ( B @ constant )
| ~ ( A @ constant )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_43) ).
thf(64,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ decreases )
| ( B @ increases )
| ( B @ constant )
| ~ ( A @ constant )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ( zero @ ( B @ ( C @ growth_rate ) @ greater ) )
| ~ ( B @ ( C @ cardinality_at_time ) @ increases )
| ~ ( zero @ ( B @ ( C @ cardinality_at_time ) @ greater ) )
| ~ ( B @ ( A @ ( C @ subpopulation ) ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_52) ).
thf(108,plain,
! [C: $i,B: $i,A: $i] :
( ( zero @ ( B @ ( C @ growth_rate ) @ greater ) )
| ~ ( B @ ( C @ cardinality_at_time ) @ increases )
| ~ ( zero @ ( B @ ( C @ cardinality_at_time ) @ greater ) )
| ~ ( B @ ( A @ ( C @ subpopulation ) ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ greater ) )
| ~ ( B @ ( A @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp6_2_57) ).
thf(54,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ greater ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ greater ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(cnf,[status(esa)],[54]) ).
thf(37,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ number_of_organizations ) )
= ( C @ ( efficient_producers @ cardinality_at_time ) @ ( C @ ( first_movers @ cardinality_at_time ) @ sum ) ) )
| ( zero @ ( C @ ( B @ cardinality_at_time ) @ greater ) )
| ~ ( C @ ( A @ ( B @ subpopulation ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_only_members_38) ).
thf(138,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ number_of_organizations ) )
= ( C @ ( efficient_producers @ cardinality_at_time ) @ ( C @ ( first_movers @ cardinality_at_time ) @ sum ) ) )
| ( zero @ ( C @ ( B @ cardinality_at_time ) @ greater ) )
| ~ ( C @ ( A @ ( B @ subpopulation ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ increases )
| ( C @ decreases )
| ( C @ constant )
| ~ ( A @ constant )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_50) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ increases )
| ( C @ decreases )
| ( C @ constant )
| ~ ( A @ constant )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ growth_rate ) @ ( zero @ greater ) )
| ~ ( B @ ( C @ cardinality_at_time ) @ decreases )
| ~ ( zero @ ( B @ ( C @ cardinality_at_time ) @ greater ) )
| ~ ( B @ ( A @ ( C @ subpopulation ) ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_53) ).
thf(115,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ growth_rate ) @ ( zero @ greater ) )
| ~ ( B @ ( C @ cardinality_at_time ) @ decreases )
| ~ ( zero @ ( B @ ( C @ cardinality_at_time ) @ greater ) )
| ~ ( B @ ( A @ ( C @ subpopulation ) ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ sk2 @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_74) ).
thf(119,plain,
! [A: $i] :
( ( A @ sk2 @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(120,plain,
! [A: $i] :
( ( A @ sk2 @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
inference(cnf,[status(esa)],[119]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ decreases )
| ( B @ increases )
| ( C @ constant )
| ~ ( A @ constant )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_47) ).
thf(56,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ decreases )
| ( B @ increases )
| ( C @ constant )
| ~ ( A @ constant )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(38,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ greater_or_equal ) )
| ~ ( B @ ( A @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_61) ).
thf(141,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ greater_or_equal ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(142,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ greater_or_equal ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(cnf,[status(esa)],[141]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ greater ) )
| ~ ( B @ ( A @ greater_or_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_60) ).
thf(110,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ greater ) )
| ~ ( B @ ( A @ greater_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ resources ) @ decreases )
| ~ ( B @ ( A @ equilibrium @ greater ) )
| ~ ( zero @ ( B @ ( A @ number_of_organizations ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a4_67) ).
thf(125,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ resources ) @ decreases )
| ~ ( B @ ( A @ equilibrium @ greater ) )
| ~ ( zero @ ( B @ ( A @ number_of_organizations ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(5,negated_conjecture,
! [A: $i] :
( ~ ( A @ sk4 @ ( first_movers @ ( efficient_producers @ outcompetes ) ) )
| ~ ( A @ ( sk3 @ in_environment ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t4_80) ).
thf(46,plain,
! [A: $i] :
( ~ ( A @ sk4 @ ( first_movers @ ( efficient_producers @ outcompetes ) ) )
| ~ ( A @ ( sk3 @ in_environment ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(209,plain,
! [A: $i] :
( ( ( sk3 @ environment )
!= ( A @ environment ) )
| ( A @ sk2 @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47,120]) ).
thf(210,plain,
! [A: $i] :
( ( ( sk3 @ environment )
!= ( A @ environment ) )
| ( A @ sk2 @ ( A @ in_environment ) )
| ~ ( A @ stable ) ),
inference(simp,[status(thm)],[209]) ).
thf(211,plain,
( ( sk3 @ sk2 @ ( sk3 @ in_environment ) )
| ~ ( sk3 @ stable ) ),
inference(pattern_uni,[status(thm)],[210:[bind(A,$thf( sk3 ))]]) ).
thf(218,plain,
( ( sk3 @ sk2 @ ( sk3 @ in_environment ) )
| ~ $true ),
inference(rewrite,[status(thm)],[211,48]) ).
thf(219,plain,
sk3 @ sk2 @ ( sk3 @ in_environment ),
inference(simp,[status(thm)],[218]) ).
thf(4,negated_conjecture,
! [A: $i] :
( ( A @ ( A @ sk4 @ greater_or_equal ) )
| ~ ( A @ ( sk3 @ in_environment ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t4_79) ).
thf(50,plain,
! [A: $i] :
( ( A @ ( A @ sk4 @ greater_or_equal ) )
| ~ ( A @ ( sk3 @ in_environment ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(53,plain,
! [A: $i] :
( ( A @ ( A @ sk4 @ greater_or_equal ) )
| ~ ( A @ ( sk3 @ in_environment ) ) ),
inference(cnf,[status(esa)],[50]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ equilibrium @ greater ) )
| ~ ( A @ equilibrium @ ( B @ greater_or_equal ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_equilibrium_63) ).
thf(123,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ equilibrium @ greater ) )
| ~ ( A @ equilibrium @ ( B @ greater_or_equal ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(124,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ equilibrium @ greater ) )
| ~ ( A @ equilibrium @ ( B @ greater_or_equal ) )
| ~ ( A @ environment ) ),
inference(cnf,[status(esa)],[123]) ).
thf(231,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ environment )
!= ( A @ environment ) )
| ~ ( B @ ( A @ equilibrium @ greater ) )
| ~ ( A @ equilibrium @ ( B @ greater_or_equal ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47,124]) ).
thf(232,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ environment )
!= ( A @ environment ) )
| ~ ( B @ ( A @ equilibrium @ greater ) )
| ~ ( A @ equilibrium @ ( B @ greater_or_equal ) ) ),
inference(simp,[status(thm)],[231]) ).
thf(233,plain,
! [A: $i] :
( ~ ( A @ ( sk3 @ equilibrium @ greater ) )
| ~ ( sk3 @ equilibrium @ ( A @ greater_or_equal ) ) ),
inference(pattern_uni,[status(thm)],[232:[bind(A,$thf( sk3 ))]]) ).
thf(245,plain,
! [A: $i] :
( ~ ( A @ ( sk3 @ equilibrium @ greater ) )
| ~ ( sk3 @ equilibrium @ ( A @ greater_or_equal ) ) ),
inference(simp,[status(thm)],[233]) ).
thf(259,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk4 @ greater_or_equal ) )
!= ( sk3 @ equilibrium @ ( B @ greater_or_equal ) ) )
| ~ ( B @ ( sk3 @ equilibrium @ greater ) )
| ~ $true
| ~ ( A @ ( sk3 @ in_environment ) ) ),
inference(paramod_ordered,[status(thm)],[53,245]) ).
thf(260,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ sk4 @ greater_or_equal ) )
!= ( sk3 @ equilibrium @ ( B @ greater_or_equal ) ) )
| ~ ( B @ ( sk3 @ equilibrium @ greater ) )
| ~ ( A @ ( sk3 @ in_environment ) ) ),
inference(simp,[status(thm)],[259]) ).
thf(261,plain,
( ~ ( sk3 @ equilibrium @ sk4 @ ( sk3 @ equilibrium @ greater ) )
| ~ ( sk3 @ equilibrium @ ( sk3 @ in_environment ) ) ),
inference(pattern_uni,[status(thm)],[260:[bind(A,$thf( sk3 @ equilibrium )),bind(B,$thf( sk3 @ equilibrium @ sk4 ))]]) ).
thf(274,plain,
( ( ( sk3 @ sk2 @ ( sk3 @ in_environment ) )
!= ( sk3 @ equilibrium @ ( sk3 @ in_environment ) ) )
| ~ ( sk3 @ equilibrium @ sk4 @ ( sk3 @ equilibrium @ greater ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[219,261]) ).
thf(275,plain,
( ( ( sk3 @ sk2 @ ( sk3 @ in_environment ) )
!= ( sk3 @ equilibrium @ ( sk3 @ in_environment ) ) )
| ~ ( sk3 @ equilibrium @ sk4 @ ( sk3 @ equilibrium @ greater ) ) ),
inference(simp,[status(thm)],[274]) ).
thf(280,plain,
( ( ( sk3 @ sk2 )
!= ( sk3 @ equilibrium ) )
| ( sk3 != sk3 )
| ~ ( sk3 @ equilibrium @ sk4 @ ( sk3 @ equilibrium @ greater ) ) ),
inference(simp,[status(thm)],[275]) ).
thf(284,plain,
( ( ( sk3 @ sk2 )
!= ( sk3 @ equilibrium ) )
| ~ ( sk3 @ equilibrium @ sk4 @ ( sk3 @ equilibrium @ greater ) ) ),
inference(simp,[status(thm)],[280]) ).
thf(226,plain,
! [A: $i] :
( ( ( sk3 @ sk2 @ ( sk3 @ in_environment ) )
!= ( A @ ( sk3 @ in_environment ) ) )
| ( A @ ( A @ sk4 @ greater_or_equal ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[219,53]) ).
thf(227,plain,
! [A: $i] :
( ( ( sk3 @ sk2 @ ( sk3 @ in_environment ) )
!= ( A @ ( sk3 @ in_environment ) ) )
| ( A @ ( A @ sk4 @ greater_or_equal ) ) ),
inference(simp,[status(thm)],[226]) ).
thf(228,plain,
sk3 @ sk2 @ ( sk3 @ sk2 @ sk4 @ greater_or_equal ),
inference(pattern_uni,[status(thm)],[227:[bind(A,$thf( sk3 @ sk2 ))]]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ( B @ ( first_movers @ growth_rate ) @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ sk2 @ ( B @ greater_or_equal ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_75) ).
thf(121,plain,
! [B: $i,A: $i] :
( ( B @ ( first_movers @ growth_rate ) @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ sk2 @ ( B @ greater_or_equal ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ decreases )
| ( C @ decreases )
| ( B @ constant )
| ~ ( A @ constant )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_45) ).
thf(84,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ decreases )
| ( C @ decreases )
| ( B @ constant )
| ~ ( A @ constant )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ greater_or_equal ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_62) ).
thf(147,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ greater_or_equal ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(34,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( efficient_producers @ subpopulation ) ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_FM_and_EP_organisational_42) ).
thf(132,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( efficient_producers @ subpopulation ) ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(21,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ outcompetes ) ) )
| ~ ( D @ ( B @ growth_rate ) @ ( zero @ greater ) )
| ~ ( zero @ ( D @ ( C @ growth_rate ) @ greater_or_equal ) )
| ~ ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_64) ).
thf(102,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ outcompetes ) ) )
| ~ ( D @ ( B @ growth_rate ) @ ( zero @ greater ) )
| ~ ( zero @ ( D @ ( C @ growth_rate ) @ greater_or_equal ) )
| ~ ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( B @ ( A @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp6_1_56) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( B @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ greater ) )
| ~ ( C @ ( B @ greater ) )
| ~ ( B @ ( A @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_transitivity_58) ).
thf(92,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ greater ) )
| ~ ( C @ ( B @ greater ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(276,plain,
( ( ( sk3 @ sk1 @ ( sk3 @ in_environment ) )
!= ( sk3 @ equilibrium @ ( sk3 @ in_environment ) ) )
| ~ ( sk3 @ equilibrium @ sk4 @ ( sk3 @ equilibrium @ greater ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[182,261]) ).
thf(277,plain,
( ( ( sk3 @ sk1 @ ( sk3 @ in_environment ) )
!= ( sk3 @ equilibrium @ ( sk3 @ in_environment ) ) )
| ~ ( sk3 @ equilibrium @ sk4 @ ( sk3 @ equilibrium @ greater ) ) ),
inference(simp,[status(thm)],[276]) ).
thf(281,plain,
( ( ( sk3 @ sk1 )
!= ( sk3 @ equilibrium ) )
| ( sk3 != sk3 )
| ~ ( sk3 @ equilibrium @ sk4 @ ( sk3 @ equilibrium @ greater ) ) ),
inference(simp,[status(thm)],[277]) ).
thf(285,plain,
( ( ( sk3 @ sk1 )
!= ( sk3 @ equilibrium ) )
| ~ ( sk3 @ equilibrium @ sk4 @ ( sk3 @ equilibrium @ greater ) ) ),
inference(simp,[status(thm)],[281]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ greater ) )
| ( C = B )
| ( B @ ( C @ greater ) )
| ~ ( C @ ( A @ in_environment ) )
| ~ ( B @ ( A @ in_environment ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_times_in_environment_59) ).
thf(156,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ greater ) )
| ( C = B )
| ( B @ ( C @ greater ) )
| ~ ( C @ ( A @ in_environment ) )
| ~ ( B @ ( A @ in_environment ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(186,plain,
! [A: $i] :
( ( ( sk3 @ sk1 @ ( sk3 @ in_environment ) )
!= ( A @ ( sk3 @ in_environment ) ) )
| ( A @ ( A @ sk4 @ greater_or_equal ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[182,53]) ).
thf(187,plain,
! [A: $i] :
( ( ( sk3 @ sk1 @ ( sk3 @ in_environment ) )
!= ( A @ ( sk3 @ in_environment ) ) )
| ( A @ ( A @ sk4 @ greater_or_equal ) ) ),
inference(simp,[status(thm)],[186]) ).
thf(188,plain,
sk3 @ sk1 @ ( sk3 @ sk1 @ sk4 @ greater_or_equal ),
inference(pattern_uni,[status(thm)],[187:[bind(A,$thf( sk3 @ sk1 ))]]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( first_movers @ cardinality_at_time ) @ greater ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_positive_number_of_organizations_54) ).
thf(96,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( first_movers @ cardinality_at_time ) @ greater ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(51,plain,
! [A: $i] :
( ~ ( A @ sk4 @ ( first_movers @ ( efficient_producers @ outcompetes ) ) )
| ~ ( A @ ( sk3 @ in_environment ) ) ),
inference(cnf,[status(esa)],[46]) ).
thf(223,plain,
! [A: $i] :
( ( ( sk3 @ sk2 @ ( sk3 @ in_environment ) )
!= ( A @ ( sk3 @ in_environment ) ) )
| ~ ( A @ sk4 @ ( first_movers @ ( efficient_producers @ outcompetes ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[219,51]) ).
thf(224,plain,
! [A: $i] :
( ( ( sk3 @ sk2 @ ( sk3 @ in_environment ) )
!= ( A @ ( sk3 @ in_environment ) ) )
| ~ ( A @ sk4 @ ( first_movers @ ( efficient_producers @ outcompetes ) ) ) ),
inference(simp,[status(thm)],[223]) ).
thf(225,plain,
~ ( sk3 @ sk2 @ sk4 @ ( first_movers @ ( efficient_producers @ outcompetes ) ) ),
inference(pattern_uni,[status(thm)],[224:[bind(A,$thf( sk3 @ sk2 ))]]) ).
thf(189,plain,
! [A: $i] :
( ( ( sk3 @ sk1 @ ( sk3 @ in_environment ) )
!= ( A @ ( sk3 @ in_environment ) ) )
| ~ ( A @ sk4 @ ( first_movers @ ( efficient_producers @ outcompetes ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[182,51]) ).
thf(190,plain,
! [A: $i] :
( ( ( sk3 @ sk1 @ ( sk3 @ in_environment ) )
!= ( A @ ( sk3 @ in_environment ) ) )
| ~ ( A @ sk4 @ ( first_movers @ ( efficient_producers @ outcompetes ) ) ) ),
inference(simp,[status(thm)],[189]) ).
thf(191,plain,
~ ( sk3 @ sk1 @ sk4 @ ( first_movers @ ( efficient_producers @ outcompetes ) ) ),
inference(pattern_uni,[status(thm)],[190:[bind(A,$thf( sk3 @ sk1 ))]]) ).
thf(57,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ decreases )
| ( B @ increases )
| ( C @ constant )
| ~ ( A @ constant )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
inference(cnf,[status(esa)],[56]) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ decreases )
| ( B @ increases )
| ( C @ constant )
| ~ ( A @ constant )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
inference(lifteq,[status(thm)],[57]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( A @ decreases )
| ( A @ increases )
| ( B @ constant )
| ~ ( B @ ( A @ sum ) @ constant ) ),
inference(simp,[status(thm)],[58]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ increases )
| ( B @ increases )
| ( C @ constant )
| ~ ( A @ constant )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_48) ).
thf(68,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ increases )
| ( B @ increases )
| ( C @ constant )
| ~ ( A @ constant )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(69,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ increases )
| ( B @ increases )
| ( C @ constant )
| ~ ( A @ constant )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
inference(cnf,[status(esa)],[68]) ).
thf(70,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ increases )
| ( B @ increases )
| ( C @ constant )
| ~ ( A @ constant )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
inference(lifteq,[status(thm)],[69]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ( B @ increases )
| ( A @ increases )
| ( B @ constant )
| ~ ( B @ ( A @ sum ) @ constant ) ),
inference(simp,[status(thm)],[70]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ number_of_organizations ) )
= ( C @ ( efficient_producers @ cardinality_at_time ) @ ( C @ ( first_movers @ cardinality_at_time ) @ sum ) ) )
| ( B != efficient_producers )
| ~ ( C @ ( A @ ( B @ subpopulation ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_only_members_39) ).
thf(159,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ number_of_organizations ) )
= ( C @ ( efficient_producers @ cardinality_at_time ) @ ( C @ ( first_movers @ cardinality_at_time ) @ sum ) ) )
| ( B != efficient_producers )
| ~ ( C @ ( A @ ( B @ subpopulation ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( A @ number_of_organizations ) @ greater ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_environment_not_empty_37) ).
thf(113,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( A @ number_of_organizations ) @ greater ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ increases )
| ( B @ increases )
| ( B @ constant )
| ~ ( A @ constant )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_44) ).
thf(76,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ increases )
| ( B @ increases )
| ( B @ constant )
| ~ ( A @ constant )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ number_of_organizations ) @ decreases )
| ~ ( B @ ( A @ resources ) @ decreases )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a7_71) ).
thf(98,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ number_of_organizations ) @ decreases )
| ~ ( B @ ( A @ resources ) @ decreases )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(255,plain,
! [A: $i] :
( ( ( sk3 @ sk2 @ ( sk3 @ sk2 @ sk4 @ greater_or_equal ) )
!= ( sk3 @ equilibrium @ ( A @ greater_or_equal ) ) )
| ~ ( A @ ( sk3 @ equilibrium @ greater ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[228,245]) ).
thf(256,plain,
! [A: $i] :
( ( ( sk3 @ sk2 @ ( sk3 @ sk2 @ sk4 @ greater_or_equal ) )
!= ( sk3 @ equilibrium @ ( A @ greater_or_equal ) ) )
| ~ ( A @ ( sk3 @ equilibrium @ greater ) ) ),
inference(simp,[status(thm)],[255]) ).
thf(265,plain,
! [A: $i] :
( ( ( sk3 @ sk2 )
!= ( sk3 @ equilibrium ) )
| ( ( sk3 @ sk2 @ sk4 )
!= A )
| ~ ( A @ ( sk3 @ equilibrium @ greater ) ) ),
inference(simp,[status(thm)],[256]) ).
thf(267,plain,
( ( ( sk3 @ sk2 )
!= ( sk3 @ equilibrium ) )
| ~ ( sk3 @ sk2 @ sk4 @ ( sk3 @ equilibrium @ greater ) ) ),
inference(simp,[status(thm)],[265]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ increases )
| ( C @ decreases )
| ( B @ constant )
| ~ ( A @ constant )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_46) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ increases )
| ( C @ decreases )
| ( B @ constant )
| ~ ( A @ constant )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(40,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ number_of_organizations ) @ constant )
| ~ ( B @ ( A @ resources ) @ constant )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a7_72) ).
thf(145,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ number_of_organizations ) @ constant )
| ~ ( B @ ( A @ resources ) @ constant )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( B @ ( A @ greater ) ) ),
inference(cnf,[status(esa)],[60]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ greater ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[61]) ).
thf(63,plain,
! [A: $i] :
~ ( A @ ( A @ greater ) ),
inference(simp,[status(thm)],[62]) ).
thf(148,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ greater_or_equal ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[147]) ).
thf(149,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ greater_or_equal ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[148]) ).
thf(150,plain,
! [A: $i] : ( A @ ( A @ greater_or_equal ) ),
inference(simp,[status(thm)],[149]) ).
thf(65,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ decreases )
| ( B @ increases )
| ( B @ constant )
| ~ ( A @ constant )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
inference(cnf,[status(esa)],[64]) ).
thf(66,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ decreases )
| ( B @ increases )
| ( B @ constant )
| ~ ( A @ constant )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
inference(lifteq,[status(thm)],[65]) ).
thf(67,plain,
! [B: $i,A: $i] :
( ( A @ decreases )
| ( A @ increases )
| ( A @ constant )
| ~ ( B @ ( A @ sum ) @ constant ) ),
inference(simp,[status(thm)],[66]) ).
thf(32,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ growth_rate ) @ ( zero @ greater ) )
| ~ ( D @ ( B @ ( C @ outcompetes ) ) )
| ~ ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_66) ).
thf(127,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ growth_rate ) @ ( zero @ greater ) )
| ~ ( D @ ( B @ ( C @ outcompetes ) ) )
| ~ ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(43,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( zero @ ( D @ ( C @ growth_rate ) @ greater_or_equal ) )
| ~ ( D @ ( B @ ( C @ outcompetes ) ) )
| ~ ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_65) ).
thf(154,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( zero @ ( D @ ( C @ growth_rate ) @ greater_or_equal ) )
| ~ ( D @ ( B @ ( C @ outcompetes ) ) )
| ~ ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ decreases )
| ( C @ decreases )
| ( C @ constant )
| ~ ( A @ constant )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_49) ).
thf(72,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ decreases )
| ( C @ decreases )
| ( C @ constant )
| ~ ( A @ constant )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(39,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( first_movers @ subpopulation ) ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_FM_and_EP_organisational_41) ).
thf(143,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( first_movers @ subpopulation ) ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(85,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ decreases )
| ( C @ decreases )
| ( B @ constant )
| ~ ( A @ constant )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
inference(cnf,[status(esa)],[84]) ).
thf(86,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ decreases )
| ( C @ decreases )
| ( B @ constant )
| ~ ( A @ constant )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
inference(lifteq,[status(thm)],[85]) ).
thf(87,plain,
! [B: $i,A: $i] :
( ( A @ decreases )
| ( B @ decreases )
| ( A @ constant )
| ~ ( B @ ( A @ sum ) @ constant ) ),
inference(simp,[status(thm)],[86]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ number_of_organizations ) )
= ( C @ ( efficient_producers @ cardinality_at_time ) @ ( C @ ( first_movers @ cardinality_at_time ) @ sum ) ) )
| ( B != first_movers )
| ~ ( C @ ( A @ ( B @ subpopulation ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_only_members_40) ).
thf(104,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ number_of_organizations ) )
= ( C @ ( efficient_producers @ cardinality_at_time ) @ ( C @ ( first_movers @ cardinality_at_time ) @ sum ) ) )
| ( B != first_movers )
| ~ ( C @ ( A @ ( B @ subpopulation ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(73,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ decreases )
| ( C @ decreases )
| ( C @ constant )
| ~ ( A @ constant )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
inference(cnf,[status(esa)],[72]) ).
thf(74,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ decreases )
| ( C @ decreases )
| ( C @ constant )
| ~ ( A @ constant )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
inference(lifteq,[status(thm)],[73]) ).
thf(75,plain,
! [B: $i,A: $i] :
( ( A @ decreases )
| ( B @ decreases )
| ( B @ constant )
| ~ ( B @ ( A @ sum ) @ constant ) ),
inference(simp,[status(thm)],[74]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ growth_rate ) )
= zero )
| ~ ( B @ ( C @ cardinality_at_time ) @ constant )
| ~ ( zero @ ( B @ ( C @ cardinality_at_time ) @ greater ) )
| ~ ( B @ ( A @ ( C @ subpopulation ) ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_51) ).
thf(151,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ growth_rate ) )
= zero )
| ~ ( B @ ( C @ cardinality_at_time ) @ constant )
| ~ ( zero @ ( B @ ( C @ cardinality_at_time ) @ greater ) )
| ~ ( B @ ( A @ ( C @ subpopulation ) ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ equilibrium @ ( A @ sk1 @ greater_or_equal ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a5_70) ).
thf(136,plain,
! [A: $i] :
( ( A @ equilibrium @ ( A @ sk1 @ greater_or_equal ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(257,plain,
! [A: $i] :
( ( ( sk3 @ sk1 @ ( sk3 @ sk1 @ sk4 @ greater_or_equal ) )
!= ( sk3 @ equilibrium @ ( A @ greater_or_equal ) ) )
| ~ ( A @ ( sk3 @ equilibrium @ greater ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[188,245]) ).
thf(258,plain,
! [A: $i] :
( ( ( sk3 @ sk1 @ ( sk3 @ sk1 @ sk4 @ greater_or_equal ) )
!= ( sk3 @ equilibrium @ ( A @ greater_or_equal ) ) )
| ~ ( A @ ( sk3 @ equilibrium @ greater ) ) ),
inference(simp,[status(thm)],[257]) ).
thf(266,plain,
! [A: $i] :
( ( ( sk3 @ sk1 )
!= ( sk3 @ equilibrium ) )
| ( ( sk3 @ sk1 @ sk4 )
!= A )
| ~ ( A @ ( sk3 @ equilibrium @ greater ) ) ),
inference(simp,[status(thm)],[258]) ).
thf(268,plain,
( ( ( sk3 @ sk1 )
!= ( sk3 @ equilibrium ) )
| ~ ( sk3 @ sk1 @ sk4 @ ( sk3 @ equilibrium @ greater ) ) ),
inference(simp,[status(thm)],[266]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ increases )
| ( B @ increases )
| ( B @ constant )
| ~ ( A @ constant )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
inference(cnf,[status(esa)],[76]) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ increases )
| ( B @ increases )
| ( B @ constant )
| ~ ( A @ constant )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
inference(lifteq,[status(thm)],[77]) ).
thf(79,plain,
! [B: $i,A: $i] :
( ( B @ increases )
| ( A @ increases )
| ( A @ constant )
| ~ ( B @ ( A @ sum ) @ constant ) ),
inference(simp,[status(thm)],[78]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ in_environment ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_point_in_environment_36) ).
thf(94,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ in_environment ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(198,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ increases )
!= ( A @ increases ) )
| ( A @ increases )
| ( B @ constant )
| ~ ( B @ ( A @ sum ) @ constant ) ),
inference(eqfactor_ordered,[status(thm)],[71]) ).
thf(199,plain,
! [A: $i] :
( ( A @ increases )
| ( A @ constant )
| ~ ( A @ ( A @ sum ) @ constant ) ),
inference(pattern_uni,[status(thm)],[198:[bind(A,$thf( B ))]]) ).
thf(200,plain,
! [A: $i] :
( ( A @ increases )
| ( A @ constant )
| ~ ( A @ ( A @ sum ) @ constant ) ),
inference(simp,[status(thm)],[199]) ).
thf(253,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( A @ decreases )
!= ( B @ decreases ) )
| ( B @ decreases )
| ( B @ constant )
| ~ ( B @ ( A @ sum ) @ constant ) ),
inference(eqfactor_ordered,[status(thm)],[75]) ).
thf(254,plain,
! [A: $i] :
( ( A @ decreases )
| ( A @ constant )
| ~ ( A @ ( A @ sum ) @ constant ) ),
inference(pattern_uni,[status(thm)],[253:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(81,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ increases )
| ( C @ decreases )
| ( B @ constant )
| ~ ( A @ constant )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
inference(cnf,[status(esa)],[80]) ).
thf(82,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ increases )
| ( C @ decreases )
| ( B @ constant )
| ~ ( A @ constant )
| ( A
!= ( C @ ( B @ sum ) ) ) ),
inference(lifteq,[status(thm)],[81]) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( B @ increases )
| ( B @ decreases )
| ( A @ constant )
| ~ ( B @ ( A @ sum ) @ constant ) ),
inference(simp,[status(thm)],[82]) ).
thf(220,plain,
! [A: $i] :
( ( ( sk3 @ sk2 @ ( sk3 @ in_environment ) )
!= ( A @ ( sk3 @ in_environment ) ) )
| ( A @ sk4 @ ( sk3 @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[219,52]) ).
thf(221,plain,
! [A: $i] :
( ( ( sk3 @ sk2 @ ( sk3 @ in_environment ) )
!= ( A @ ( sk3 @ in_environment ) ) )
| ( A @ sk4 @ ( sk3 @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) ) ),
inference(simp,[status(thm)],[220]) ).
thf(222,plain,
sk3 @ sk2 @ sk4 @ ( sk3 @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ),
inference(pattern_uni,[status(thm)],[221:[bind(A,$thf( sk3 @ sk2 ))]]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ resources ) @ constant )
| ( B @ ( A @ equilibrium @ greater ) )
| ~ ( zero @ ( B @ ( A @ number_of_organizations ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a4_68) ).
thf(100,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ resources ) @ constant )
| ( B @ ( A @ equilibrium @ greater ) )
| ~ ( zero @ ( B @ ( A @ number_of_organizations ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(12376,plain,
$false,
inference(e,[status(thm)],[185,129,134,64,108,55,138,88,115,120,56,142,52,110,125,46,284,228,261,121,84,147,132,102,60,117,92,285,156,188,53,141,96,124,225,191,59,118,71,54,49,159,113,219,76,245,98,267,80,123,145,48,63,150,50,67,182,127,154,72,143,87,104,75,119,151,51,136,268,79,94,47,200,68,254,83,222,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT035-2 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.09 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.15/0.40 % Computer : n014.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 00:05:19 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.85/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.31/1.26 % [INFO] Parsing done (256ms).
% 1.31/1.29 % [INFO] Running in sequential loop mode.
% 2.18/1.84 % [INFO] eprover registered as external prover.
% 2.18/1.85 % [INFO] Scanning for conjecture ...
% 2.33/1.98 % [INFO] Found a conjecture (or negated_conjecture) and 40 axioms. Running axiom selection ...
% 2.52/2.06 % [INFO] Axiom selection finished. Selected 40 axioms (removed 0 axioms).
% 2.52/2.12 % [INFO] Problem is propositional (TPTP CNF).
% 2.52/2.13 % [INFO] Type checking passed.
% 2.52/2.13 % [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 ...
% 44.26/15.68 % External prover 'e' found a proof!
% 44.26/15.68 % [INFO] Killing All external provers ...
% 44.26/15.68 % Time passed: 15130ms (effective reasoning time: 14378ms)
% 44.26/15.69 % Axioms used in derivation (40): mp_abc_sum_increase_47, mp_FM_and_EP_organisational_41, mp_positive_number_of_organizations_55, a4_67, mp_abc_sum_increase_49, mp_greater_or_equal_62, mp_only_members_40, l1_75, d2_64, l1_74, mp_greater_or_equal_60, mp_abc_sum_increase_43, mp_growth_rate_51, a11_73, mp_equilibrium_63, mp_positive_number_of_organizations_54, mp_growth_rate_53, d2_65, a4_68, a5_70, mp_growth_rate_52, a5_69, mp_greater_transitivity_58, mp_abc_sum_increase_48, mp_only_members_39, mp_abc_sum_increase_45, mp_environment_not_empty_37, d2_66, mp_abc_sum_increase_44, a7_72, mp_time_point_in_environment_36, a7_71, mp_abc_sum_increase_50, mp_abc_sum_increase_46, mp_FM_and_EP_organisational_42, mp_only_members_38, mp_greater_or_equal_61, mp6_1_56, mp_times_in_environment_59, mp6_2_57
% 44.26/15.69 % No. of inferences in proof: 182
% 44.26/15.69 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 15130 ms resp. 14378 ms w/o parsing
% 37.51/15.85 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 37.51/15.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------