%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT022-2 : 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 3.29s 2.51s
% Output : Refutation 3.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 10
% Syntax : Number of formulae : 21 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 228 ( 24 ~; 26 |; 0 &; 178 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 14 usr; 5 con; 0-4 aty)
% Number of variables : 18 ( 0 ^; 18 !; 0 ?; 18 :)
% 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(decreases_decl,type,
decreases: $i > $o ).
thf(resources_decl,type,
resources: $i > $i > $i ).
thf(constant_decl,type,
constant: $i > $o ).
thf(difference_decl,type,
difference: $i > $i > $i ).
thf(disbanding_rate_decl,type,
disbanding_rate: $i > $i > $i ).
thf(increases_decl,type,
increases: $i > $o ).
thf(greater_decl,type,
greater: $i > $i > $o ).
thf(resilience_decl,type,
resilience: $i > $i ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ disbanding_rate ) @ ( D @ ( B @ disbanding_rate ) @ difference ) @ constant )
| ~ ( D @ ( A @ resources ) @ constant )
| ~ ( B @ resilience @ ( C @ resilience @ greater ) )
| ~ ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a6_3) ).
thf(25,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ disbanding_rate ) @ ( D @ ( B @ disbanding_rate ) @ difference ) @ constant )
| ~ ( D @ ( A @ resources ) @ constant )
| ~ ( B @ resilience @ ( C @ resilience @ greater ) )
| ~ ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(2,negated_conjecture,
sk2 @ ( sk1 @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l4_6) ).
thf(14,plain,
sk2 @ ( sk1 @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [A: $i] :
( ~ ( A @ decreases )
| ~ ( A @ constant ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_constant_not_decrease_1) ).
thf(21,plain,
! [A: $i] :
( ~ ( A @ decreases )
| ~ ( A @ constant ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(6,negated_conjecture,
( ( sk2 @ ( efficient_producers @ disbanding_rate ) @ ( sk2 @ ( first_movers @ disbanding_rate ) @ difference ) @ decreases )
| ~ ( sk2 @ ( efficient_producers @ disbanding_rate ) @ ( sk2 @ ( first_movers @ disbanding_rate ) @ difference ) @ increases ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l4_10) ).
thf(13,plain,
( ( sk2 @ ( efficient_producers @ disbanding_rate ) @ ( sk2 @ ( first_movers @ disbanding_rate ) @ difference ) @ decreases )
| ~ ( sk2 @ ( efficient_producers @ disbanding_rate ) @ ( sk2 @ ( first_movers @ disbanding_rate ) @ difference ) @ increases ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,axiom,
first_movers @ resilience @ ( efficient_producers @ resilience @ greater ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2_4) ).
thf(27,plain,
first_movers @ resilience @ ( efficient_producers @ resilience @ greater ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1,negated_conjecture,
sk1 @ environment,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l4_5) ).
thf(12,plain,
sk1 @ environment,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,negated_conjecture,
( ( sk2 @ ( efficient_producers @ disbanding_rate ) @ ( sk2 @ ( first_movers @ disbanding_rate ) @ difference ) @ decreases )
| ( sk2 @ ( sk1 @ resources ) @ decreases ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l4_8) ).
thf(16,plain,
( ( sk2 @ ( efficient_producers @ disbanding_rate ) @ ( sk2 @ ( first_movers @ disbanding_rate ) @ difference ) @ decreases )
| ( sk2 @ ( sk1 @ resources ) @ decreases ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,negated_conjecture,
( ( sk2 @ ( sk1 @ resources ) @ constant )
| ~ ( sk2 @ ( efficient_producers @ disbanding_rate ) @ ( sk2 @ ( first_movers @ disbanding_rate ) @ difference ) @ increases ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l4_9) ).
thf(11,plain,
( ( sk2 @ ( sk1 @ resources ) @ constant )
| ~ ( sk2 @ ( efficient_producers @ disbanding_rate ) @ ( sk2 @ ( first_movers @ disbanding_rate ) @ difference ) @ increases ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ disbanding_rate ) @ ( D @ ( B @ disbanding_rate ) @ difference ) @ increases )
| ~ ( D @ ( A @ resources ) @ decreases )
| ~ ( B @ resilience @ ( C @ resilience @ greater ) )
| ~ ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a6_2) ).
thf(23,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ disbanding_rate ) @ ( D @ ( B @ disbanding_rate ) @ difference ) @ increases )
| ~ ( D @ ( A @ resources ) @ decreases )
| ~ ( B @ resilience @ ( C @ resilience @ greater ) )
| ~ ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
| ~ ( A @ environment ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,negated_conjecture,
( ( sk2 @ ( sk1 @ resources ) @ constant )
| ( sk2 @ ( sk1 @ resources ) @ decreases ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l4_7) ).
thf(15,plain,
( ( sk2 @ ( sk1 @ resources ) @ constant )
| ( sk2 @ ( sk1 @ resources ) @ decreases ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(28,plain,
$false,
inference(e,[status(thm)],[25,14,21,13,27,12,16,11,23,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT022-2 : TPTP v9.3.1. Released v2.4.0.
% 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
% 0.11/0.38 % Computer : n001.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 00:10:28 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 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
% 0.87/0.92 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.10/1.08 % [INFO] Parsing done (158ms).
% 1.10/1.10 % [INFO] Running in sequential loop mode.
% 1.74/1.51 % [INFO] eprover registered as external prover.
% 1.74/1.52 % [INFO] Scanning for conjecture ...
% 1.90/1.66 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.02/1.71 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.02/1.74 % [INFO] Problem is propositional (TPTP CNF).
% 2.02/1.74 % [INFO] Type checking passed.
% 2.02/1.75 % [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 ...
% 3.29/2.50 % External prover 'e' found a proof!
% 3.29/2.51 % [INFO] Killing All external provers ...
% 3.29/2.51 % Time passed: 2024ms (effective reasoning time: 1401ms)
% 3.29/2.51 % Axioms used in derivation (4): a6_3, mp_constant_not_decrease_1, a2_4, a6_2
% 3.29/2.51 % No. of inferences in proof: 21
% 3.29/2.51 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2024 ms resp. 1401 ms w/o parsing
% 3.29/2.57 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.29/2.57 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------