%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT023-2 : 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 : n019.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 08:00:37 AM UTC 2026
% Result : Unsatisfiable 4.62s 2.88s
% Output : Refutation 4.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 17
% Syntax : Number of formulae : 35 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 137 ( 6 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 658 ( 88 ~; 102 |; 0 &; 468 @)
% ( 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 : 17 ( 15 usr; 4 con; 0-4 aty)
% Number of variables : 60 ( 0 ^; 60 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(environment_decl,type,
environment: $i > $o ).
thf(sk5_decl,type,
sk5: $i ).
thf(stable_decl,type,
stable: $i > $o ).
thf(in_environment_decl,type,
in_environment: $i > $i > $o ).
thf(critical_point_decl,type,
critical_point: $i > $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(sk1_decl,type,
sk1: $i > $i > $i ).
thf(sk2_decl,type,
sk2: $i > $i ).
thf(greater_or_equal_decl,type,
greater_or_equal: $i > $i > $o ).
thf(greater_decl,type,
greater: $i > $i > $o ).
thf(growth_rate_decl,type,
growth_rate: $i > $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i ).
thf(sk4_decl,type,
sk4: $i > $i ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( A @ sk2 @ ( A @ in_environment ) )
| ( B @ ( A @ ( B @ sk1 ) @ greater_or_equal ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_20) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( A @ sk2 @ ( A @ in_environment ) )
| ( B @ ( A @ ( B @ sk1 ) @ greater_or_equal ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( A @ sk2 @ ( A @ in_environment ) )
| ( A @ ( B @ sk1 ) @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_19) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( A @ sk2 @ ( A @ in_environment ) )
| ( A @ ( B @ sk1 ) @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ sk4 @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_31) ).
thf(49,plain,
! [A: $i] :
( ( A @ sk4 @ ( A @ in_environment ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1,negated_conjecture,
sk5 @ environment,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l5_33) ).
thf(18,plain,
sk5 @ environment,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ critical_point ) )
| ( B @ ( A @ ( B @ sk3 ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ( B @ ( first_movers @ growth_rate ) @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_29) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ critical_point ) )
| ( B @ ( A @ ( B @ sk3 ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ( B @ ( first_movers @ growth_rate ) @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(3,negated_conjecture,
~ ( sk5 @ critical_point @ ( sk5 @ in_environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l5_35) ).
thf(20,plain,
~ ( sk5 @ critical_point @ ( sk5 @ in_environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ critical_point ) )
| ~ ( A @ ( B @ sk3 ) @ ( first_movers @ growth_rate ) @ ( A @ ( B @ sk3 ) @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ( B @ ( first_movers @ growth_rate ) @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_30) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ critical_point ) )
| ~ ( A @ ( B @ sk3 ) @ ( first_movers @ growth_rate ) @ ( A @ ( B @ sk3 ) @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ( B @ ( first_movers @ growth_rate ) @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( first_movers @ growth_rate ) @ ( C @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ sk2 @ ( C @ greater ) )
| ~ ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ( A @ ( B @ sk1 ) @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_22) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( first_movers @ growth_rate ) @ ( C @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ sk2 @ ( C @ greater ) )
| ~ ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ( A @ ( B @ sk1 ) @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( first_movers @ growth_rate ) @ ( C @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ sk2 @ ( C @ greater ) )
| ~ ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ ( B @ sk1 ) @ ( first_movers @ growth_rate ) @ ( A @ ( B @ sk1 ) @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_27) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( first_movers @ growth_rate ) @ ( C @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ sk2 @ ( C @ greater ) )
| ~ ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ ( B @ sk1 ) @ ( first_movers @ growth_rate ) @ ( A @ ( B @ sk1 ) @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( first_movers @ growth_rate ) @ ( C @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ sk2 @ ( C @ greater ) )
| ~ ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ( B @ ( A @ ( B @ sk1 ) @ greater_or_equal ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_24) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( first_movers @ growth_rate ) @ ( C @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ sk2 @ ( C @ greater ) )
| ~ ( C @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ( B @ ( A @ ( B @ sk1 ) @ greater_or_equal ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( A @ sk2 @ ( A @ in_environment ) )
| ~ ( A @ ( B @ sk1 ) @ ( first_movers @ growth_rate ) @ ( A @ ( B @ sk1 ) @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_25) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( A @ sk2 @ ( A @ in_environment ) )
| ~ ( A @ ( B @ sk1 ) @ ( first_movers @ growth_rate ) @ ( A @ ( B @ sk1 ) @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( B
= ( A @ critical_point ) )
| ( A @ ( B @ sk3 ) @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( B @ ( A @ in_environment ) )
| ( B @ ( first_movers @ growth_rate ) @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_28) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ critical_point ) )
| ( A @ ( B @ sk3 ) @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( B @ ( A @ in_environment ) )
| ( B @ ( first_movers @ growth_rate ) @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ~ ( A @ sk2 @ ( first_movers @ growth_rate ) @ ( A @ sk2 @ ( efficient_producers @ growth_rate ) @ greater ) )
| ( A @ ( B @ sk1 ) @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_21) ).
thf(26,plain,
! [B: $i,A: $i] :
( ~ ( A @ sk2 @ ( first_movers @ growth_rate ) @ ( A @ sk2 @ ( efficient_producers @ growth_rate ) @ greater ) )
| ( A @ ( B @ sk1 ) @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ~ ( A @ sk2 @ ( first_movers @ growth_rate ) @ ( A @ sk2 @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ ( B @ sk1 ) @ ( first_movers @ growth_rate ) @ ( A @ ( B @ sk1 ) @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_26) ).
thf(36,plain,
! [B: $i,A: $i] :
( ~ ( A @ sk2 @ ( first_movers @ growth_rate ) @ ( A @ sk2 @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ ( B @ sk1 ) @ ( first_movers @ growth_rate ) @ ( A @ ( B @ sk1 ) @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( A @ sk2 @ ( first_movers @ growth_rate ) @ ( A @ sk2 @ ( efficient_producers @ growth_rate ) @ greater ) )
| ( B @ ( A @ ( B @ sk1 ) @ greater_or_equal ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds_23) ).
thf(30,plain,
! [B: $i,A: $i] :
( ~ ( A @ sk2 @ ( first_movers @ growth_rate ) @ ( A @ sk2 @ ( efficient_producers @ growth_rate ) @ greater ) )
| ( B @ ( A @ ( B @ sk1 ) @ greater_or_equal ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( B @ ( first_movers @ growth_rate ) @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ sk4 @ ( B @ greater_or_equal ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_32) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( B @ ( first_movers @ growth_rate ) @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ~ ( A @ sk4 @ ( B @ greater_or_equal ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ stable )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(2,negated_conjecture,
sk5 @ stable,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l5_34) ).
thf(19,plain,
sk5 @ stable,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(53,plain,
$false,
inference(e,[status(thm)],[24,22,49,18,43,20,46,28,38,32,34,40,26,36,30,51,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT023-2 : 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
% 0.14/0.39 % Computer : n019.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sat Sep 26 00:04:34 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 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
% 1.29/1.26 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.76/1.56 % [INFO] Parsing done (302ms).
% 1.76/1.58 % [INFO] Running in sequential loop mode.
% 2.92/2.17 % [INFO] eprover registered as external prover.
% 2.92/2.17 % [INFO] Scanning for conjecture ...
% 3.02/2.25 % [INFO] Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ...
% 3.02/2.28 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 3.22/2.31 % [INFO] Problem is propositional (TPTP CNF).
% 3.22/2.31 % [INFO] Type checking passed.
% 3.22/2.32 % [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 ...
% 4.62/2.87 % External prover 'e' found a proof!
% 4.62/2.88 % [INFO] Killing All external provers ...
% 4.62/2.88 % Time passed: 2272ms (effective reasoning time: 1282ms)
% 4.62/2.88 % Axioms used in derivation (14): mp_earliest_time_growth_rate_exceeds_25, l1_32, l1_31, mp_earliest_time_growth_rate_exceeds_24, d1_28, mp_earliest_time_growth_rate_exceeds_19, d1_29, mp_earliest_time_growth_rate_exceeds_23, mp_earliest_time_growth_rate_exceeds_21, mp_earliest_time_growth_rate_exceeds_26, d1_30, mp_earliest_time_growth_rate_exceeds_22, mp_earliest_time_growth_rate_exceeds_27, mp_earliest_time_growth_rate_exceeds_20
% 4.62/2.88 % No. of inferences in proof: 35
% 4.62/2.88 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2272 ms resp. 1282 ms w/o parsing
% 4.91/2.94 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.91/2.94 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------