%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT020-1 : 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 : n017.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 08:00:36 AM UTC 2026
% Result : Unsatisfiable 5.14s 3.16s
% Output : Refutation 5.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 14
% Syntax : Number of formulae : 29 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 87 ( 2 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 368 ( 58 ~; 58 |; 0 &; 252 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 5 con; 0-4 aty)
% Number of variables : 50 ( 0 ^; 50 !; 0 ?; 50 :)
% 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(greater_decl,type,
greater: $i > $i > $o ).
thf(disbanding_rate_decl,type,
disbanding_rate: $i > $i > $i ).
thf(decreases_decl,type,
decreases: $i > $o ).
thf(difference_decl,type,
difference: $i > $i > $i ).
thf(in_environment_decl,type,
in_environment: $i > $i > $o ).
thf(initial_FM_EP_decl,type,
initial_FM_EP: $i > $i ).
thf(greater_or_equal_decl,type,
greater_or_equal: $i > $i > $o ).
thf(start_time_decl,type,
start_time: $i > $i ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( efficient_producers @ disbanding_rate ) @ ( D @ ( first_movers @ disbanding_rate ) @ greater ) )
| ( B @ ( efficient_producers @ disbanding_rate ) @ ( B @ ( first_movers @ disbanding_rate ) @ difference ) @ decreases )
| ~ ( C @ ( efficient_producers @ disbanding_rate ) @ ( C @ ( first_movers @ disbanding_rate ) @ greater ) )
| ~ ( D @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( B @ ( D @ greater_or_equal ) )
| ~ ( C @ ( B @ greater_or_equal ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_positive_function_difference_25) ).
thf(25,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( efficient_producers @ disbanding_rate ) @ ( D @ ( first_movers @ disbanding_rate ) @ greater ) )
| ( B @ ( efficient_producers @ disbanding_rate ) @ ( B @ ( first_movers @ disbanding_rate ) @ difference ) @ decreases )
| ~ ( C @ ( efficient_producers @ disbanding_rate ) @ ( C @ ( first_movers @ disbanding_rate ) @ greater ) )
| ~ ( D @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( B @ ( D @ greater_or_equal ) )
| ~ ( C @ ( B @ greater_or_equal ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ start_time @ ( A @ initial_FM_EP @ greater_or_equal ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_initial_time_27) ).
thf(29,plain,
! [A: $i] :
( ( A @ start_time @ ( A @ initial_FM_EP @ greater_or_equal ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,negated_conjecture,
~ ( sk2 @ ( efficient_producers @ disbanding_rate ) @ ( sk2 @ ( first_movers @ disbanding_rate ) @ greater ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l2_35) ).
thf(17,plain,
~ ( sk2 @ ( efficient_producers @ disbanding_rate ) @ ( sk2 @ ( first_movers @ disbanding_rate ) @ greater ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,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_occurs_26) ).
thf(27,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)],[8]) ).
thf(12,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_30) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ greater ) )
| ~ ( B @ ( A @ greater_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(4,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/sandbox/benchmark/theBenchmark.p',l3_22) ).
thf(19,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)],[4]) ).
thf(1,negated_conjecture,
sk1 @ environment,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l2_33) ).
thf(15,plain,
sk1 @ environment,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ initial_FM_EP @ ( efficient_producers @ disbanding_rate ) @ ( A @ initial_FM_EP @ ( first_movers @ disbanding_rate ) @ greater ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a8_31) ).
thf(38,plain,
! [A: $i] :
( ( A @ initial_FM_EP @ ( efficient_producers @ disbanding_rate ) @ ( A @ initial_FM_EP @ ( first_movers @ disbanding_rate ) @ greater ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ initial_FM_EP @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ initial_FM_EP @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_point_23) ).
thf(21,plain,
! [A: $i] :
( ( A @ initial_FM_EP @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ initial_FM_EP @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,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_29) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ greater ) )
| ~ ( C @ ( B @ greater ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(2,negated_conjecture,
sk2 @ ( sk1 @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l2_34) ).
thf(16,plain,
sk2 @ ( sk1 @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ in_environment ) )
| ~ ( C @ ( A @ in_environment ) )
| ~ ( B @ ( C @ greater ) )
| ~ ( A @ start_time @ ( B @ greater_or_equal ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_times_in_order_28) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ in_environment ) )
| ~ ( C @ ( A @ in_environment ) )
| ~ ( B @ ( C @ greater ) )
| ~ ( A @ start_time @ ( B @ greater_or_equal ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(14,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/sandbox/benchmark/theBenchmark.p',a10_32) ).
thf(40,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)],[14]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( A @ initial_FM_EP @ ( B @ greater_or_equal ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_point_24) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( A @ initial_FM_EP @ ( B @ greater_or_equal ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(42,plain,
$false,
inference(e,[status(thm)],[25,29,17,27,35,19,15,38,21,33,16,31,40,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : MGT020-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.13 % 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
% 0.24/0.50 % Computer : n017.cluster.edu
% 0.24/0.50 % Model : x86_64 x86_64
% 0.24/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.50 % Memory : 8046.5625MB
% 0.24/0.50 % OS : Linux 6.8.0-71-generic
% 0.24/0.50 % CPULimit : 300
% 0.24/0.50 % WCLimit : 300
% 0.24/0.50 % DateTime : Fri Sep 25 23:59:33 UTC 2026
% 0.28/0.50 % CPUTime :
% 0.28/0.50 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
% 1.14/1.13 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.74/1.41 % [INFO] Parsing done (271ms).
% 1.74/1.43 % [INFO] Running in sequential loop mode.
% 2.47/2.02 % [INFO] eprover registered as external prover.
% 2.47/2.03 % [INFO] Scanning for conjecture ...
% 2.91/2.17 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 3.01/2.22 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 3.01/2.27 % [INFO] Problem is propositional (TPTP CNF).
% 3.01/2.28 % [INFO] Type checking passed.
% 3.01/2.28 % [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 ...
% 5.14/3.15 % External prover 'e' found a proof!
% 5.14/3.15 % [INFO] Killing All external provers ...
% 5.14/3.16 % Time passed: 2503ms (effective reasoning time: 1714ms)
% 5.14/3.16 % Axioms used in derivation (11): a8_31, a10_32, mp_earliest_time_point_23, mp_time_point_occurs_26, mp_greater_or_equal_30, mp_greater_transitivity_29, mp_positive_function_difference_25, mp_times_in_order_28, mp_initial_time_27, mp_earliest_time_point_24, l3_22
% 5.14/3.16 % No. of inferences in proof: 29
% 5.14/3.16 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2503 ms resp. 1714 ms w/o parsing
% 5.24/3.24 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.24/3.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------