%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT022+2 : 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 : n013.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 3.43s 2.55s
% Output : Refutation 3.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 10 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 39 ( 0 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 181 ( 7 ~; 0 |; 12 &; 145 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 12 usr; 3 con; 0-4 aty)
% Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% 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(decreases_decl,type,
decreases: $i > $o ).
thf(resources_decl,type,
resources: $i > $i > $i ).
thf(increases_decl,type,
increases: $i > $o ).
thf(difference_decl,type,
difference: $i > $i > $i ).
thf(disbanding_rate_decl,type,
disbanding_rate: $i > $i > $i ).
thf(constant_decl,type,
constant: $i > $o ).
thf(greater_decl,type,
greater: $i > $i > $o ).
thf(resilience_decl,type,
resilience: $i > $i ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( ( ( B @ ( A @ resources ) @ constant )
=> ~ ( B @ ( efficient_producers @ disbanding_rate ) @ ( B @ ( first_movers @ disbanding_rate ) @ difference ) @ decreases ) )
& ( ( B @ ( A @ resources ) @ decreases )
=> ( B @ ( efficient_producers @ disbanding_rate ) @ ( B @ ( first_movers @ disbanding_rate ) @ difference ) @ increases ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l4) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( ( ( B @ ( A @ resources ) @ constant )
=> ~ ( B @ ( efficient_producers @ disbanding_rate ) @ ( B @ ( first_movers @ disbanding_rate ) @ difference ) @ decreases ) )
& ( ( B @ ( A @ resources ) @ decreases )
=> ( B @ ( efficient_producers @ disbanding_rate ) @ ( B @ ( first_movers @ disbanding_rate ) @ difference ) @ increases ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: $i,B: $i] :
( ( ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( ( ( B @ ( A @ resources ) @ constant )
=> ~ ( B @ ( efficient_producers @ disbanding_rate ) @ ( B @ ( first_movers @ disbanding_rate ) @ difference ) @ decreases ) )
& ( ( B @ ( A @ resources ) @ decreases )
=> ( B @ ( efficient_producers @ disbanding_rate ) @ ( B @ ( first_movers @ disbanding_rate ) @ difference ) @ increases ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ constant )
=> ~ ( A @ decreases ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_constant_not_decrease) ).
thf(14,plain,
! [A: $i] :
( ( A @ constant )
=> ~ ( A @ decreases ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ resilience @ ( C @ resilience @ greater ) )
& ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( ( ( D @ ( A @ resources ) @ constant )
=> ( D @ ( C @ disbanding_rate ) @ ( D @ ( B @ disbanding_rate ) @ difference ) @ constant ) )
& ( ( D @ ( A @ resources ) @ decreases )
=> ( D @ ( C @ disbanding_rate ) @ ( D @ ( B @ disbanding_rate ) @ difference ) @ increases ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a6) ).
thf(16,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ resilience @ ( C @ resilience @ greater ) )
& ( D @ ( A @ ( C @ ( B @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( ( ( D @ ( A @ resources ) @ constant )
=> ( D @ ( C @ disbanding_rate ) @ ( D @ ( B @ disbanding_rate ) @ difference ) @ constant ) )
& ( ( D @ ( A @ resources ) @ decreases )
=> ( D @ ( C @ disbanding_rate ) @ ( D @ ( B @ disbanding_rate ) @ difference ) @ increases ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
first_movers @ resilience @ ( efficient_producers @ resilience @ greater ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
thf(20,plain,
first_movers @ resilience @ ( efficient_producers @ resilience @ greater ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,plain,
$false,
inference(e,[status(thm)],[6,14,16,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT022+2 : TPTP v9.3.1. Released v2.0.0.
% 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
% 0.15/0.62 % Computer : n013.cluster.edu
% 0.15/0.62 % Model : x86_64 x86_64
% 0.15/0.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.62 % Memory : 8046.5625MB
% 0.15/0.62 % OS : Linux 6.8.0-71-generic
% 0.15/0.62 % CPULimit : 300
% 0.15/0.62 % WCLimit : 300
% 0.15/0.62 % DateTime : Sat Sep 26 00:03:39 UTC 2026
% 0.15/0.62 % CPUTime :
% 0.15/0.62 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
% 1.02/1.22 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.35/1.41 % [INFO] Parsing done (186ms).
% 1.35/1.42 % [INFO] Running in sequential loop mode.
% 1.94/1.82 % [INFO] eprover registered as external prover.
% 1.94/1.83 % [INFO] Scanning for conjecture ...
% 2.10/1.94 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.10/1.98 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.10/2.00 % [INFO] Problem is first-order (TPTP FOF).
% 2.10/2.00 % [INFO] Type checking passed.
% 2.10/2.01 % [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 ...
% 3.43/2.55 % External prover 'e' found a proof!
% 3.43/2.55 % [INFO] Killing All external provers ...
% 3.43/2.55 % Time passed: 1779ms (effective reasoning time: 1122ms)
% 3.43/2.55 % 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)>
% 3.43/2.55 % Axioms used in derivation (3): mp_constant_not_decrease, a6, a2
% 3.43/2.55 % No. of inferences in proof: 10
% 3.43/2.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1779 ms resp. 1122 ms w/o parsing
% 3.43/2.59 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.43/2.59 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------