%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT036-2 : 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 : n020.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 : Unsatisfiable 3.65s 2.56s
% Output : Refutation 3.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 14
% Syntax : Number of formulae : 29 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 77 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 330 ( 48 ~; 48 |; 0 &; 234 @)
% ( 0 <=>; 0 =>; 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 : 14 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 70 ( 0 ^; 70 !; 0 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(environment_decl,type,
environment: $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
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(sk2_decl,type,
sk2: $i ).
thf(outcompetes_decl,type,
outcompetes: $i > $i > $i > $o ).
thf(in_environment_decl,type,
in_environment: $i > $i > $o ).
thf(greater_decl,type,
greater: $i > $i > $o ).
thf(zero_decl,type,
zero: $i ).
thf(growth_rate_decl,type,
growth_rate: $i > $i > $i ).
thf(greater_or_equal_decl,type,
greater_or_equal: $i > $i > $o ).
thf(resilience_decl,type,
resilience: $i > $i ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ in_environment ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_occur_2) ).
thf(20,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)],[5]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( zero @ ( B @ ( A @ growth_rate ) @ greater_or_equal ) )
| ~ ( B @ ( C @ ( D @ ( A @ subpopulations ) ) ) )
| ~ ( C @ environment )
| ( B @ ( A @ growth_rate ) @ ( zero @ greater ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_growth_rate_relationships_6) ).
thf(28,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( zero @ ( B @ ( A @ growth_rate ) @ greater_or_equal ) )
| ~ ( B @ ( C @ ( D @ ( A @ subpopulations ) ) ) )
| ~ ( C @ environment )
| ( B @ ( A @ growth_rate ) @ ( zero @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ growth_rate ) @ ( zero @ greater ) )
| ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_growth_rate_relationships_3) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ growth_rate ) @ ( zero @ greater ) )
| ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ ( C @ subpopulations ) ) ) )
| ~ ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations_1) ).
thf(18,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ ( C @ subpopulations ) ) ) )
| ~ ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,negated_conjecture,
sk2 @ ( sk1 @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t5_13) ).
thf(16,plain,
sk2 @ ( sk1 @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ growth_rate ) @ ( zero @ greater ) )
| ~ ( zero @ ( B @ ( A @ growth_rate ) @ greater_or_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_growth_rate_relationships_5) ).
thf(26,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ growth_rate ) @ ( zero @ greater ) )
| ~ ( zero @ ( B @ ( A @ growth_rate ) @ greater_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,negated_conjecture,
sk1 @ environment,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t5_12) ).
thf(15,plain,
sk1 @ environment,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ growth_rate ) @ ( zero @ greater ) )
| ( D @ ( C @ ( B @ ( A @ subpopulations ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_growth_rate_relationships_4) ).
thf(24,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ growth_rate ) @ ( zero @ greater ) )
| ( D @ ( C @ ( B @ ( A @ subpopulations ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ growth_rate ) @ ( zero @ greater ) )
| ~ ( C @ resilience @ ( D @ resilience @ greater ) )
| ( B @ ( C @ growth_rate ) @ ( zero @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a13_11) ).
thf(37,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ growth_rate ) @ ( zero @ greater ) )
| ~ ( C @ resilience @ ( D @ resilience @ greater ) )
| ( B @ ( C @ growth_rate ) @ ( zero @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(3,negated_conjecture,
sk2 @ ( efficient_producers @ ( first_movers @ outcompetes ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t5_14) ).
thf(17,plain,
sk2 @ ( efficient_producers @ ( first_movers @ outcompetes ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,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/sandbox2/benchmark/theBenchmark.p',d2_8) ).
thf(32,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)],[11]) ).
thf(12,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/sandbox2/benchmark/theBenchmark.p',d2_9) ).
thf(34,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)],[12]) ).
thf(13,axiom,
first_movers @ resilience @ ( efficient_producers @ resilience @ greater ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2_10) ).
thf(36,plain,
first_movers @ resilience @ ( efficient_producers @ resilience @ greater ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10,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/sandbox2/benchmark/theBenchmark.p',d2_7) ).
thf(30,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)],[10]) ).
thf(39,plain,
$false,
inference(e,[status(thm)],[20,28,22,18,16,26,15,24,37,17,32,34,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT036-2 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.08 % 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
% 0.14/0.62 % Computer : n020.cluster.edu
% 0.14/0.62 % Model : x86_64 x86_64
% 0.14/0.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.62 % Memory : 8046.5625MB
% 0.14/0.62 % OS : Linux 6.8.0-71-generic
% 0.14/0.62 % CPULimit : 300
% 0.14/0.62 % WCLimit : 300
% 0.14/0.62 % DateTime : Sat Sep 26 00:07:20 UTC 2026
% 0.14/0.62 % CPUTime :
% 0.14/0.62 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
% 0.93/1.18 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/1.37 % [INFO] Parsing done (195ms).
% 1.22/1.39 % [INFO] Running in sequential loop mode.
% 2.04/1.80 % [INFO] eprover registered as external prover.
% 2.04/1.81 % [INFO] Scanning for conjecture ...
% 2.23/1.90 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 2.23/1.94 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 2.23/1.97 % [INFO] Problem is propositional (TPTP CNF).
% 2.23/1.97 % [INFO] Type checking passed.
% 2.23/1.98 % [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 ...
% 3.65/2.56 % External prover 'e' found a proof!
% 3.65/2.56 % [INFO] Killing All external provers ...
% 3.65/2.56 % Time passed: 1815ms (effective reasoning time: 1161ms)
% 3.65/2.56 % Axioms used in derivation (11): d2_7, mp_growth_rate_relationships_5, d2_9, mp_growth_rate_relationships_6, mp_growth_rate_relationships_3, mp_growth_rate_relationships_4, mp_symmetry_of_subpopulations_1, mp_time_point_occur_2, a13_11, d2_8, a2_10
% 3.65/2.56 % No. of inferences in proof: 29
% 3.65/2.56 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1815 ms resp. 1161 ms w/o parsing
% 3.96/2.61 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.96/2.61 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------