%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT025+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 : n010.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 08:00:38 AM UTC 2026
% Result : Theorem 4.44s 2.57s
% Output : Refutation 4.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 8
% Syntax : Number of formulae : 18 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 108 ( 20 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 358 ( 2 ~; 14 |; 51 &; 266 @)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 4 con; 0-4 aty)
% Number of variables : 42 ( 0 ^; 42 !; 0 ?; 42 :)
% 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(constant_decl,type,
constant: $i > $o ).
thf(number_of_organizations_decl,type,
number_of_organizations: $i > $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(subpopulation_decl,type,
subpopulation: $i > $i > $i > $o ).
thf(cardinality_at_time_decl,type,
cardinality_at_time: $i > $i > $i ).
thf(sum_decl,type,
sum: $i > $i > $i ).
thf(in_environment_decl,type,
in_environment: $i > $i > $o ).
thf(increases_decl,type,
increases: $i > $o ).
thf(decreases_decl,type,
decreases: $i > $o ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( B @ ( A @ number_of_organizations ) @ constant )
& ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( ( ( B @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
& ( zero @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) ) )
| ( ( B @ ( efficient_producers @ growth_rate ) @ ( zero @ greater ) )
& ( zero @ ( B @ ( first_movers @ growth_rate ) @ greater ) ) )
| ( ( ( B @ ( efficient_producers @ growth_rate ) )
= zero )
& ( ( B @ ( first_movers @ growth_rate ) )
= zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l7) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( B @ ( A @ number_of_organizations ) @ constant )
& ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( ( ( B @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
& ( zero @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) ) )
| ( ( B @ ( efficient_producers @ growth_rate ) @ ( zero @ greater ) )
& ( zero @ ( B @ ( first_movers @ growth_rate ) @ greater ) ) )
| ( ( ( B @ ( efficient_producers @ growth_rate ) )
= zero )
& ( ( B @ ( first_movers @ growth_rate ) )
= zero ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(10,plain,
~ ! [A: $i,B: $i] :
( ( ( B @ ( A @ number_of_organizations ) @ constant )
& ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( ( ( B @ ( first_movers @ growth_rate ) @ ( zero @ greater ) )
& ( zero @ ( B @ ( efficient_producers @ growth_rate ) @ greater ) ) )
| ( ( B @ ( efficient_producers @ growth_rate ) @ ( zero @ greater ) )
& ( zero @ ( B @ ( first_movers @ growth_rate ) @ greater ) ) )
| ( ( ( B @ ( efficient_producers @ growth_rate ) )
= zero )
& ( ( B @ ( first_movers @ growth_rate ) )
= zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( ( B @ ( A @ ( efficient_producers @ subpopulation ) ) )
& ( B @ ( A @ ( first_movers @ subpopulation ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_subpopulations) ).
thf(29,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( ( B @ ( A @ ( efficient_producers @ subpopulation ) ) )
& ( B @ ( A @ ( first_movers @ subpopulation ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ constant )
& ( A
= ( C @ ( B @ sum ) ) ) )
=> ( ( ( C @ increases )
& ( B @ decreases ) )
| ( ( C @ decreases )
& ( B @ increases ) )
| ( ( C @ constant )
& ( B @ constant ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase) ).
thf(33,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ constant )
& ( A
= ( C @ ( B @ sum ) ) ) )
=> ( ( ( C @ increases )
& ( B @ decreases ) )
| ( ( C @ decreases )
& ( B @ increases ) )
| ( ( C @ constant )
& ( B @ constant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( zero @ ( C @ ( B @ cardinality_at_time ) @ greater ) )
& ( C @ ( A @ ( B @ subpopulation ) ) )
& ( A @ environment ) )
=> ( ( B = first_movers )
| ( B = efficient_producers ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a9) ).
thf(65,plain,
! [A: $i,B: $i,C: $i] :
( ( ( zero @ ( C @ ( B @ cardinality_at_time ) @ greater ) )
& ( C @ ( A @ ( B @ subpopulation ) ) )
& ( A @ environment ) )
=> ( ( B = first_movers )
| ( B = efficient_producers ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( zero @ ( C @ ( A @ cardinality_at_time ) @ greater ) )
& ( C @ ( B @ ( A @ subpopulation ) ) )
& ( C @ ( B @ in_environment ) )
& ( B @ environment ) )
=> ( ( ( C @ ( A @ cardinality_at_time ) @ decreases )
=> ( C @ ( A @ growth_rate ) @ ( zero @ greater ) ) )
& ( ( C @ ( A @ cardinality_at_time ) @ increases )
=> ( zero @ ( C @ ( A @ growth_rate ) @ greater ) ) )
& ( ( C @ ( A @ cardinality_at_time ) @ constant )
=> ( ( C @ ( A @ growth_rate ) )
= zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate) ).
thf(53,plain,
! [A: $i,B: $i,C: $i] :
( ( ( zero @ ( C @ ( A @ cardinality_at_time ) @ greater ) )
& ( C @ ( B @ ( A @ subpopulation ) ) )
& ( C @ ( B @ in_environment ) )
& ( B @ environment ) )
=> ( ( ( C @ ( A @ cardinality_at_time ) @ decreases )
=> ( C @ ( A @ growth_rate ) @ ( zero @ greater ) ) )
& ( ( C @ ( A @ cardinality_at_time ) @ increases )
=> ( zero @ ( C @ ( A @ growth_rate ) @ greater ) ) )
& ( ( C @ ( A @ cardinality_at_time ) @ constant )
=> ( ( C @ ( A @ growth_rate ) )
= zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( ( zero @ ( B @ ( efficient_producers @ cardinality_at_time ) @ greater ) )
& ( zero @ ( B @ ( first_movers @ cardinality_at_time ) @ greater ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_non_zero_producers) ).
thf(59,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( efficient_producers @ ( first_movers @ subpopulations ) ) ) )
& ( A @ environment ) )
=> ( ( zero @ ( B @ ( efficient_producers @ cardinality_at_time ) @ greater ) )
& ( zero @ ( B @ ( first_movers @ cardinality_at_time ) @ greater ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,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_occur) ).
thf(63,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)],[8]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ( zero @ ( C @ ( B @ cardinality_at_time ) @ greater ) )
=> ( ( B = first_movers )
| ( B = efficient_producers ) ) )
& ( C @ ( A @ ( B @ subpopulation ) ) )
& ( A @ environment ) )
=> ( ( C @ ( A @ number_of_organizations ) )
= ( C @ ( efficient_producers @ cardinality_at_time ) @ ( C @ ( first_movers @ cardinality_at_time ) @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_only_members) ).
thf(19,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( zero @ ( C @ ( B @ cardinality_at_time ) @ greater ) )
=> ( ( B = first_movers )
| ( B = efficient_producers ) ) )
& ( C @ ( A @ ( B @ subpopulation ) ) )
& ( A @ environment ) )
=> ( ( C @ ( A @ number_of_organizations ) )
= ( C @ ( efficient_producers @ cardinality_at_time ) @ ( C @ ( first_movers @ cardinality_at_time ) @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(69,plain,
$false,
inference(e,[status(thm)],[10,29,33,65,53,59,63,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT025+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
% 0.12/0.39 % Computer : n010.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 00:04:45 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 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 ...
% 1.28/1.18 % [INFO] Parsing done (206ms).
% 1.49/1.20 % [INFO] Running in sequential loop mode.
% 2.20/1.61 % [INFO] eprover registered as external prover.
% 2.20/1.61 % [INFO] Scanning for conjecture ...
% 2.40/1.73 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 2.40/1.77 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 2.66/1.80 % [INFO] Problem is first-order (TPTP FOF).
% 2.66/1.81 % [INFO] Type checking passed.
% 2.66/1.81 % [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 ...
% 4.44/2.57 % External prover 'e' found a proof!
% 4.44/2.57 % [INFO] Killing All external provers ...
% 4.44/2.57 % Time passed: 2032ms (effective reasoning time: 1365ms)
% 4.44/2.57 % 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)>
% 4.44/2.57 % Axioms used in derivation (7): mp_subpopulations, mp_growth_rate, a9, mp_time_point_occur, mp_only_members, mp_abc_sum_increase, mp_non_zero_producers
% 4.44/2.57 % No. of inferences in proof: 18
% 4.44/2.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2032 ms resp. 1365 ms w/o parsing
% 4.72/2.65 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.72/2.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------