%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT024-1 : 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 : n001.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 4.46s 2.57s
% Output : Refutation 4.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 21
% Syntax : Number of formulae : 43 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 169 ( 20 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 706 ( 102 ~; 126 |; 0 &; 478 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 6 con; 0-4 aty)
% Number of variables : 60 ( 0 ^; 60 !; 0 ?; 60 :)
% 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_or_equal_decl,type,
greater_or_equal: $i > $i > $o ).
thf(equilibrium_decl,type,
equilibrium: $i > $i ).
thf(growth_rate_decl,type,
growth_rate: $i > $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(greater_decl,type,
greater: $i > $i > $o ).
thf(constant_decl,type,
constant: $i > $o ).
thf(number_of_organizations_decl,type,
number_of_organizations: $i > $i > $i ).
thf(in_environment_decl,type,
in_environment: $i > $i > $o ).
thf(resources_decl,type,
resources: $i > $i > $i ).
thf(decreases_decl,type,
decreases: $i > $o ).
thf(17,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_occur_24) ).
thf(57,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)],[17]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ( B @ ( efficient_producers @ growth_rate ) @ ( zero @ greater ) )
| ( ( B @ ( first_movers @ growth_rate ) )
= zero )
| ~ ( B @ ( A @ number_of_organizations ) @ constant )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l7_33) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ( B @ ( efficient_producers @ growth_rate ) @ ( zero @ greater ) )
| ( ( B @ ( first_movers @ growth_rate ) )
= zero )
| ~ ( B @ ( A @ number_of_organizations ) @ constant )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ resources ) @ constant )
| ( B @ ( A @ equilibrium @ greater ) )
| ~ ( zero @ ( B @ ( A @ number_of_organizations ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3_28) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ resources ) @ constant )
| ( B @ ( A @ equilibrium @ greater ) )
| ~ ( zero @ ( B @ ( A @ number_of_organizations ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ equilibrium @ greater ) )
| ~ ( A @ equilibrium @ ( B @ greater_or_equal ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_equilibrium_26) ).
thf(41,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ equilibrium @ greater ) )
| ~ ( A @ equilibrium @ ( B @ greater_or_equal ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( B @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
| ( zero @ ( B @ ( first_movers @ growth_rate ) @ greater ) )
| ( ( B @ ( efficient_producers @ growth_rate ) )
= zero )
| ~ ( B @ ( A @ number_of_organizations ) @ constant )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l7_36) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( B @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
| ( zero @ ( B @ ( first_movers @ growth_rate ) @ greater ) )
| ( ( B @ ( efficient_producers @ growth_rate ) )
= zero )
| ~ ( B @ ( A @ number_of_organizations ) @ constant )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( A @ number_of_organizations ) @ greater ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_positive_number_of_organizations_25) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( A @ number_of_organizations ) @ greater ) )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ number_of_organizations ) @ constant )
| ~ ( B @ ( A @ resources ) @ constant )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a6_30) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ number_of_organizations ) @ constant )
| ~ ( B @ ( A @ resources ) @ constant )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ number_of_organizations ) @ decreases )
| ~ ( B @ ( A @ resources ) @ decreases )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a6_29) ).
thf(62,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ number_of_organizations ) @ decreases )
| ~ ( B @ ( A @ resources ) @ decreases )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(6,negated_conjecture,
( ~ ( sk2 @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
| ~ ( zero @ ( sk2 @ ( efficient_producers @ growth_rate ) @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l6_44) ).
thf(24,plain,
( ~ ( sk2 @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
| ~ ( zero @ ( sk2 @ ( efficient_producers @ growth_rate ) @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(2,negated_conjecture,
sk2 @ ( sk1 @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l6_40) ).
thf(25,plain,
sk2 @ ( sk1 @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
| ( zero @ ( B @ ( first_movers @ growth_rate ) @ greater ) )
| ( ( B @ ( first_movers @ growth_rate ) )
= zero )
| ~ ( B @ ( A @ number_of_organizations ) @ constant )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l7_32) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( B @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
| ( zero @ ( B @ ( first_movers @ growth_rate ) @ greater ) )
| ( ( B @ ( first_movers @ growth_rate ) )
= zero )
| ~ ( B @ ( A @ number_of_organizations ) @ constant )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ( zero @ ( B @ ( first_movers @ growth_rate ) @ greater ) )
| ( ( B @ ( first_movers @ growth_rate ) )
= zero )
| ~ ( B @ ( A @ number_of_organizations ) @ constant )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l7_31) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ( zero @ ( B @ ( first_movers @ growth_rate ) @ greater ) )
| ( ( B @ ( first_movers @ growth_rate ) )
= zero )
| ~ ( B @ ( A @ number_of_organizations ) @ constant )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ( B @ ( efficient_producers @ growth_rate ) @ ( zero @ greater ) )
| ( ( B @ ( efficient_producers @ growth_rate ) )
= zero )
| ~ ( B @ ( A @ number_of_organizations ) @ constant )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l7_37) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ( B @ ( efficient_producers @ growth_rate ) @ ( zero @ greater ) )
| ( ( B @ ( efficient_producers @ growth_rate ) )
= zero )
| ~ ( B @ ( A @ number_of_organizations ) @ constant )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(5,negated_conjecture,
( ~ ( sk2 @ ( efficient_producers @ growth_rate ) @ ( zero @ greater ) )
| ~ ( zero @ ( sk2 @ ( first_movers @ growth_rate ) @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l6_43) ).
thf(22,plain,
( ~ ( sk2 @ ( efficient_producers @ growth_rate ) @ ( zero @ greater ) )
| ~ ( zero @ ( sk2 @ ( first_movers @ growth_rate ) @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ( zero @ ( B @ ( first_movers @ growth_rate ) @ greater ) )
| ( ( B @ ( efficient_producers @ growth_rate ) )
= zero )
| ~ ( B @ ( A @ number_of_organizations ) @ constant )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l7_35) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) )
| ( zero @ ( B @ ( first_movers @ growth_rate ) @ greater ) )
| ( ( B @ ( efficient_producers @ growth_rate ) )
= zero )
| ~ ( B @ ( A @ number_of_organizations ) @ constant )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(4,negated_conjecture,
( ( ( sk2 @ ( efficient_producers @ growth_rate ) )
!= zero )
| ( ( sk2 @ ( first_movers @ growth_rate ) )
!= zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l6_42) ).
thf(27,plain,
( ( ( sk2 @ ( efficient_producers @ growth_rate ) )
!= zero )
| ( ( sk2 @ ( first_movers @ growth_rate ) )
!= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( B @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
| ( B @ ( efficient_producers @ growth_rate ) @ ( zero @ greater ) )
| ( ( B @ ( first_movers @ growth_rate ) )
= zero )
| ~ ( B @ ( A @ number_of_organizations ) @ constant )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l7_34) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( B @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
| ( B @ ( efficient_producers @ growth_rate ) @ ( zero @ greater ) )
| ( ( B @ ( first_movers @ growth_rate ) )
= zero )
| ~ ( B @ ( A @ number_of_organizations ) @ constant )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ( B @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
| ( B @ ( efficient_producers @ growth_rate ) @ ( zero @ greater ) )
| ( ( B @ ( efficient_producers @ growth_rate ) )
= zero )
| ~ ( B @ ( A @ number_of_organizations ) @ constant )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l7_38) ).
thf(67,plain,
! [B: $i,A: $i] :
( ( B @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
| ( B @ ( efficient_producers @ growth_rate ) @ ( zero @ greater ) )
| ( ( B @ ( efficient_producers @ growth_rate ) )
= zero )
| ~ ( B @ ( A @ number_of_organizations ) @ constant )
| ~ ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(3,negated_conjecture,
sk1 @ equilibrium @ ( sk2 @ greater_or_equal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l6_41) ).
thf(26,plain,
sk1 @ equilibrium @ ( sk2 @ greater_or_equal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ resources ) @ decreases )
| ~ ( B @ ( A @ equilibrium @ greater ) )
| ~ ( zero @ ( B @ ( A @ number_of_organizations ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3_27) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ resources ) @ decreases )
| ~ ( B @ ( A @ equilibrium @ greater ) )
| ~ ( zero @ ( B @ ( A @ number_of_organizations ) @ greater ) )
| ~ ( B @ ( A @ in_environment ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1,negated_conjecture,
sk1 @ environment,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l6_39) ).
thf(23,plain,
sk1 @ environment,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(70,plain,
$false,
inference(e,[status(thm)],[57,38,53,41,35,48,43,62,24,25,32,45,64,22,59,27,50,67,26,55,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT024-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.08 % 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
% 0.13/0.39 % Computer : n001.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 00:10:12 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.87/0.97 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.27/1.18 % [INFO] Parsing done (207ms).
% 1.27/1.19 % [INFO] Running in sequential loop mode.
% 1.97/1.60 % [INFO] eprover registered as external prover.
% 2.21/1.60 % [INFO] Scanning for conjecture ...
% 2.39/1.72 % [INFO] Found a conjecture (or negated_conjecture) and 15 axioms. Running axiom selection ...
% 2.59/1.80 % [INFO] Axiom selection finished. Selected 15 axioms (removed 0 axioms).
% 2.59/1.85 % [INFO] Problem is propositional (TPTP CNF).
% 2.59/1.85 % [INFO] Type checking passed.
% 2.59/1.86 % [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 ...
% 4.46/2.56 % External prover 'e' found a proof!
% 4.46/2.57 % [INFO] Killing All external provers ...
% 4.46/2.57 % Time passed: 2037ms (effective reasoning time: 1368ms)
% 4.46/2.57 % Axioms used in derivation (15): l7_38, l7_33, a6_29, mp_time_point_occur_24, l7_31, mp_equilibrium_26, l7_34, l7_36, mp_positive_number_of_organizations_25, l7_37, a3_27, a3_28, a6_30, l7_35, l7_32
% 4.46/2.57 % No. of inferences in proof: 43
% 4.46/2.57 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2037 ms resp. 1368 ms w/o parsing
% 4.77/2.64 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.77/2.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------