%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT037+1 : TPTP v9.3.1. Released v2.0.0.
% 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 : n003.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 08:00:41 AM UTC 2026
% Result : Theorem 6.35s 3.59s
% Output : Refutation 6.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 16
% Syntax : Number of formulae : 34 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 145 ( 16 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 490 ( 18 ~; 6 |; 66 &; 361 @)
% ( 0 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 5 con; 0-3 aty)
% Number of variables : 72 ( 0 ^; 68 !; 4 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
thf(environment_decl,type,
environment: $i > $o ).
thf(in_environment_decl,type,
in_environment: $i > $i > $o ).
thf(greater_or_equal_decl,type,
greater_or_equal: $i > $i > $o ).
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(cardinality_at_time_decl,type,
cardinality_at_time: $i > $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(constant_decl,type,
constant: $i > $o ).
thf(decreases_decl,type,
decreases: $i > $o ).
thf(subpopulation_decl,type,
subpopulation: $i > $i > $i > $o ).
thf(first_movers_decl,type,
first_movers: $i ).
thf(number_of_organizations_decl,type,
number_of_organizations: $i > $i > $i ).
thf(growth_rate_decl,type,
growth_rate: $i > $i > $i ).
thf(an_organisation_decl,type,
an_organisation: $i ).
thf(equilibrium_decl,type,
equilibrium: $i > $i ).
thf(resources_decl,type,
resources: $i > $i > $i ).
thf(resilience_decl,type,
resilience: $i > $i ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( ( zero @ ( B @ ( A @ number_of_organizations ) @ greater ) )
& ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( ( ~ ( B @ ( A @ equilibrium @ greater ) )
=> ( B @ ( A @ resources ) @ constant ) )
& ( ( B @ ( A @ equilibrium @ greater ) )
=> ( B @ ( A @ resources ) @ decreases ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3) ).
thf(56,plain,
! [A: $i,B: $i] :
( ( ( zero @ ( B @ ( A @ number_of_organizations ) @ greater ) )
& ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( ( ~ ( B @ ( A @ equilibrium @ greater ) )
=> ( B @ ( A @ resources ) @ constant ) )
& ( ( B @ ( A @ equilibrium @ greater ) )
=> ( B @ ( A @ resources ) @ decreases ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ constant )
=> ~ ( A @ decreases ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_constant_not_decrease) ).
thf(24,plain,
! [A: $i] :
( ( A @ constant )
=> ~ ( A @ decreases ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ resilience @ ( C @ resilience @ greater ) )
& ~ ( D @ ( B @ growth_rate ) @ ( zero @ greater ) )
& ( D @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ~ ( D @ ( C @ growth_rate ) @ ( zero @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a12) ).
thf(60,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ resilience @ ( C @ resilience @ greater ) )
& ~ ( D @ ( B @ growth_rate ) @ ( zero @ greater ) )
& ( D @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ~ ( D @ ( C @ growth_rate ) @ ( zero @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( ( B @ ( efficient_producers @ cardinality_at_time ) )
= zero )
& ( A @ ( efficient_producers @ appear ) @ ( B @ greater_or_equal ) )
& ( A @ environment ) )
=> ? [C: $i] :
( ( C @ ( efficient_producers @ growth_rate ) @ ( zero @ greater ) )
& ( C @ ( B @ greater ) )
& ( C @ ( A @ in_environment ) )
& ( A @ ( efficient_producers @ appear ) @ ( C @ greater ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_previous_negative_growth) ).
thf(33,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( efficient_producers @ cardinality_at_time ) )
= zero )
& ( A @ ( efficient_producers @ appear ) @ ( B @ greater_or_equal ) )
& ( A @ environment ) )
=> ? [C: $i] :
( ( C @ ( efficient_producers @ growth_rate ) @ ( zero @ greater ) )
& ( C @ ( B @ greater ) )
& ( C @ ( A @ in_environment ) )
& ( A @ ( efficient_producers @ appear ) @ ( C @ greater ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( ( ( B @ ( A @ resources ) @ constant )
=> ( B @ ( A @ number_of_organizations ) @ constant ) )
& ( ( B @ ( A @ resources ) @ decreases )
=> ~ ( B @ ( A @ number_of_organizations ) @ decreases ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a6) ).
thf(64,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( ( ( B @ ( A @ resources ) @ constant )
=> ( B @ ( A @ number_of_organizations ) @ constant ) )
& ( ( B @ ( A @ resources ) @ decreases )
=> ~ ( B @ ( A @ number_of_organizations ) @ decreases ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( an_organisation @ appear ) @ ( B @ greater_or_equal ) )
& ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( zero @ ( B @ ( A @ number_of_organizations ) @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
thf(54,plain,
! [A: $i,B: $i] :
( ( ( A @ ( an_organisation @ appear ) @ ( B @ greater_or_equal ) )
& ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( zero @ ( B @ ( A @ number_of_organizations ) @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( ( B @ ( A @ ( efficient_producers @ subpopulation ) ) )
& ( B @ ( A @ ( first_movers @ subpopulation ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_subpopulations) ).
thf(26,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( ( B @ ( A @ ( efficient_producers @ subpopulation ) ) )
& ( B @ ( A @ ( first_movers @ subpopulation ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(17,axiom,
first_movers @ resilience @ ( efficient_producers @ resilience @ greater ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
thf(75,plain,
first_movers @ resilience @ ( efficient_producers @ resilience @ greater ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ cardinality_at_time ) )
= zero )
=> ~ ( B @ ( A @ growth_rate ) @ ( zero @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_empty_not_decreasing) ).
thf(48,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ cardinality_at_time ) )
= zero )
=> ~ ( B @ ( A @ growth_rate ) @ ( zero @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( A @ ( efficient_producers @ appear ) @ ( B @ greater_or_equal ) )
& ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( zero @ ( B @ ( efficient_producers @ cardinality_at_time ) @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t6) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( A @ ( efficient_producers @ appear ) @ ( B @ greater_or_equal ) )
& ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( zero @ ( B @ ( efficient_producers @ cardinality_at_time ) @ greater ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(18,plain,
~ ! [A: $i,B: $i] :
( ( ( A @ ( efficient_producers @ appear ) @ ( B @ greater_or_equal ) )
& ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( zero @ ( B @ ( efficient_producers @ cardinality_at_time ) @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( an_organisation @ appear ) @ greater ) )
& ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( ( B @ ( A @ number_of_organizations ) )
= zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_start_of_organizations) ).
thf(72,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( an_organisation @ appear ) @ greater ) )
& ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( ( B @ ( A @ number_of_organizations ) )
= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ number_of_organizations ) @ decreases )
& ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ? [C: $i] :
( ~ ( B @ ( C @ growth_rate ) @ ( zero @ greater ) )
& ( zero @ ( B @ ( C @ cardinality_at_time ) @ greater ) )
& ( B @ ( A @ ( C @ subpopulation ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_non_decreasing) ).
thf(43,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ number_of_organizations ) @ decreases )
& ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ? [C: $i] :
( ~ ( B @ ( C @ growth_rate ) @ ( zero @ greater ) )
& ( zero @ ( B @ ( C @ cardinality_at_time ) @ greater ) )
& ( B @ ( A @ ( C @ subpopulation ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ subpopulation ) ) )
& ( ( B @ ( A @ number_of_organizations ) )
= zero )
& ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( ( B @ ( C @ cardinality_at_time ) )
= zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_no_members) ).
thf(30,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ subpopulation ) ) )
& ( ( B @ ( A @ number_of_organizations ) )
= zero )
& ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( ( B @ ( C @ cardinality_at_time ) )
= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( ( zero @ ( B @ ( efficient_producers @ cardinality_at_time ) @ greater ) )
| ( ( B @ ( efficient_producers @ cardinality_at_time ) )
= zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_efficient_producers_exist) ).
thf(51,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( ( zero @ ( B @ ( efficient_producers @ cardinality_at_time ) @ greater ) )
| ( ( B @ ( efficient_producers @ cardinality_at_time ) )
= zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( zero @ ( C @ ( B @ cardinality_at_time ) @ greater ) )
& ( C @ ( A @ ( B @ subpopulation ) ) )
& ( A @ environment ) )
=> ( ( B = first_movers )
| ( B = efficient_producers ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a9) ).
thf(68,plain,
! [A: $i,B: $i,C: $i] :
( ( ( zero @ ( C @ ( B @ cardinality_at_time ) @ greater ) )
& ( C @ ( A @ ( B @ subpopulation ) ) )
& ( A @ environment ) )
=> ( ( B = first_movers )
| ( B = efficient_producers ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( ( B @ ( A @ ( an_organisation @ appear ) @ greater ) )
| ( A @ ( an_organisation @ appear ) @ ( B @ greater_or_equal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_environment_inequality) ).
thf(62,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( ( B @ ( A @ ( an_organisation @ appear ) @ greater ) )
| ( A @ ( an_organisation @ appear ) @ ( B @ greater_or_equal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(76,plain,
$false,
inference(e,[status(thm)],[56,24,60,33,64,54,26,75,48,18,72,43,30,51,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT037+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.07 % 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
% 0.12/0.38 % Computer : n003.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 26 00:09:23 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 0.90/1.03 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.63/1.34 % [INFO] Parsing done (309ms).
% 1.63/1.37 % [INFO] Running in sequential loop mode.
% 2.78/1.98 % [INFO] eprover registered as external prover.
% 2.78/1.99 % [INFO] Scanning for conjecture ...
% 3.32/2.16 % [INFO] Found a conjecture (or negated_conjecture) and 15 axioms. Running axiom selection ...
% 3.40/2.28 % [INFO] Axiom selection finished. Selected 15 axioms (removed 0 axioms).
% 3.60/2.36 % [INFO] Problem is first-order (TPTP FOF).
% 3.60/2.37 % [INFO] Type checking passed.
% 3.60/2.38 % [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 ...
% 6.35/3.58 % External prover 'e' found a proof!
% 6.35/3.58 % [INFO] Killing All external provers ...
% 6.35/3.58 % Time passed: 3093ms (effective reasoning time: 2209ms)
% 6.35/3.58 % Solved by 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)>
% 6.35/3.59 % Axioms used in derivation (15): mp_non_decreasing, a6, mp_empty_not_decreasing, mp_environment_inequality, a9, mp_constant_not_decrease, mp_start_of_organizations, a3, a1, a2, mp_previous_negative_growth, mp_no_members, mp_subpopulations, a12, mp_efficient_producers_exist
% 6.35/3.59 % No. of inferences in proof: 34
% 6.35/3.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3093 ms resp. 2209 ms w/o parsing
% 6.74/3.68 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.74/3.68 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------