%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT020+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 : 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 08:00:36 AM UTC 2026
% Result : Theorem 3.99s 7.69s
% Output : Refutation 4.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 11
% Syntax : Number of formulae : 24 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 88 ( 2 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 331 ( 6 ~; 2 |; 33 &; 261 @)
% ( 0 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 3 con; 0-4 aty)
% Number of variables : 54 ( 0 ^; 54 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(environment_decl,type,
environment: $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(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(5,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( 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 ) )
=> ( ~ ( B @ ( efficient_producers @ disbanding_rate ) @ ( B @ ( first_movers @ disbanding_rate ) @ difference ) @ decreases )
=> ( D @ ( efficient_producers @ disbanding_rate ) @ ( D @ ( first_movers @ disbanding_rate ) @ greater ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_positive_function_difference) ).
thf(25,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( 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 ) )
=> ( ~ ( B @ ( efficient_producers @ disbanding_rate ) @ ( B @ ( first_movers @ disbanding_rate ) @ difference ) @ decreases )
=> ( D @ ( efficient_producers @ disbanding_rate ) @ ( D @ ( first_movers @ disbanding_rate ) @ greater ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ greater ) )
& ( B @ ( A @ greater ) ) )
=> ( C @ ( A @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_transitivity) ).
thf(34,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ greater ) )
& ( B @ ( A @ greater ) ) )
=> ( C @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( B @ ( A @ in_environment ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_point_occurs) ).
thf(27,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( B @ ( A @ in_environment ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ environment )
=> ( A @ initial_FM_EP @ ( efficient_producers @ disbanding_rate ) @ ( A @ initial_FM_EP @ ( first_movers @ disbanding_rate ) @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a8) ).
thf(39,plain,
! [A: $i] :
( ( A @ environment )
=> ( A @ initial_FM_EP @ ( efficient_producers @ disbanding_rate ) @ ( A @ initial_FM_EP @ ( first_movers @ disbanding_rate ) @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ~ ( B @ ( efficient_producers @ disbanding_rate ) @ ( B @ ( first_movers @ disbanding_rate ) @ difference ) @ decreases ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3) ).
thf(18,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ~ ( B @ ( efficient_producers @ disbanding_rate ) @ ( B @ ( first_movers @ disbanding_rate ) @ difference ) @ decreases ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ in_environment ) )
& ( B @ ( C @ greater ) )
& ( A @ start_time @ ( B @ greater_or_equal ) )
& ( A @ environment ) )
=> ( B @ ( A @ in_environment ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_times_in_order) ).
thf(31,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ in_environment ) )
& ( B @ ( C @ greater ) )
& ( A @ start_time @ ( B @ greater_or_equal ) )
& ( A @ environment ) )
=> ( B @ ( A @ in_environment ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ greater_or_equal ) )
=> ( ( A = B )
| ( B @ ( A @ greater ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal) ).
thf(36,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ greater_or_equal ) )
=> ( ( A = B )
| ( B @ ( A @ greater ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A @ environment )
=> ( ( ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
=> ( A @ initial_FM_EP @ ( B @ greater_or_equal ) ) )
& ( ( A @ initial_FM_EP @ ( A @ in_environment ) )
=> ( A @ initial_FM_EP @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_point) ).
thf(20,plain,
! [A: $i,B: $i] :
( ( A @ environment )
=> ( ( ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
=> ( A @ initial_FM_EP @ ( B @ greater_or_equal ) ) )
& ( ( A @ initial_FM_EP @ ( A @ in_environment ) )
=> ( A @ initial_FM_EP @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ environment )
=> ( A @ start_time @ ( A @ initial_FM_EP @ greater_or_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_initial_time) ).
thf(29,plain,
! [A: $i] :
( ( A @ environment )
=> ( A @ start_time @ ( A @ initial_FM_EP @ greater_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( B @ ( efficient_producers @ disbanding_rate ) @ ( B @ ( first_movers @ disbanding_rate ) @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l2) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( B @ ( efficient_producers @ disbanding_rate ) @ ( B @ ( first_movers @ disbanding_rate ) @ greater ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
~ ! [A: $i,B: $i] :
( ( ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( B @ ( efficient_producers @ disbanding_rate ) @ ( B @ ( first_movers @ disbanding_rate ) @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( 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 ) )
=> ( D @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a10) ).
thf(41,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( 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 ) )
=> ( D @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(43,plain,
$false,
inference(e,[status(thm)],[25,34,27,39,18,31,36,20,29,13,41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT020+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
% 0.11/5.60 % Computer : n014.cluster.edu
% 0.11/5.60 % Model : x86_64 x86_64
% 0.11/5.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.60 % Memory : 8046.5625MB
% 0.11/5.60 % OS : Linux 6.8.0-71-generic
% 0.11/5.61 % CPULimit : 300
% 0.11/5.61 % WCLimit : 300
% 0.11/5.61 % DateTime : Sat Sep 26 00:03:53 UTC 2026
% 0.11/5.61 % CPUTime :
% 0.11/5.61 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
% 1.02/6.20 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/6.41 % [INFO] Parsing done (207ms).
% 1.21/6.42 % [INFO] Running in sequential loop mode.
% 2.18/6.83 % [INFO] eprover registered as external prover.
% 2.18/6.84 % [INFO] Scanning for conjecture ...
% 2.40/6.95 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 2.40/6.99 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 2.64/7.03 % [INFO] Problem is first-order (TPTP FOF).
% 2.64/7.04 % [INFO] Type checking passed.
% 2.64/7.04 % [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 ...
% 3.99/7.69 % External prover 'e' found a proof!
% 3.99/7.69 % [INFO] Killing All external provers ...
% 3.99/7.69 % Time passed: 1935ms (effective reasoning time: 1257ms)
% 3.99/7.69 % 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)>
% 3.99/7.69 % Axioms used in derivation (10): l3, mp_times_in_order, mp_time_point_occurs, mp_positive_function_difference, a10, a8, mp_initial_time, mp_greater_or_equal, mp_greater_transitivity, mp_earliest_time_point
% 3.99/7.69 % No. of inferences in proof: 24
% 3.99/7.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1935 ms resp. 1257 ms w/o parsing
% 4.30/7.75 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.30/7.75 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------