%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : MGT039+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 : n015.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 08:00:42 AM UTC 2026
% Result : Theorem 4.14s 2.59s
% Output : Refutation 4.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 12
% Syntax : Number of formulae : 26 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 89 ( 3 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 234 ( 4 ~; 3 |; 34 &; 167 @)
% ( 1 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 41 ( 0 ^; 39 !; 2 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
thf(observational_period_decl,type,
observational_period: $i > $o ).
thf(slow_change_decl,type,
slow_change: $i > $o ).
thf(selection_favors_decl,type,
selection_favors: $i > $i > $i > $o ).
thf(efficient_producers_decl,type,
efficient_producers: $i ).
thf(first_movers_decl,type,
first_movers: $i ).
thf(propagation_strategy_decl,type,
propagation_strategy: $i > $o ).
thf(environment_decl,type,
environment: $i > $o ).
thf(in_environment_decl,type,
in_environment: $i > $i > $o ).
thf(end_time_decl,type,
end_time: $i > $i ).
thf(greater_decl,type,
greater: $i > $i > $o ).
thf(critical_point_decl,type,
critical_point: $i > $i ).
thf(greater_or_equal_decl,type,
greater_or_equal: $i > $i > $o ).
thf(start_time_decl,type,
start_time: $i > $i ).
thf(4,axiom,
! [A: $i] :
( ( ( A @ slow_change )
& ( A @ observational_period ) )
=> ! [B: $i] :
( ( ( B @ ( A @ in_environment ) )
& ( B @ environment ) )
=> ? [C: $i] :
( ( B @ critical_point @ ( C @ greater ) )
& ( C @ ( B @ in_environment ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp4_critical_point) ).
thf(24,plain,
! [A: $i] :
( ( ( A @ slow_change )
& ( A @ observational_period ) )
=> ! [B: $i] :
( ( ( B @ ( A @ in_environment ) )
& ( B @ environment ) )
=> ? [C: $i] :
( ( B @ critical_point @ ( C @ greater ) )
& ( C @ ( B @ in_environment ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ slow_change )
& ( A @ observational_period ) )
=> ( A @ ( first_movers @ ( efficient_producers @ selection_favors ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t8) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ slow_change )
& ( A @ observational_period ) )
=> ( A @ ( first_movers @ ( efficient_producers @ selection_favors ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(14,plain,
~ ! [A: $i] :
( ( ( A @ slow_change )
& ( A @ observational_period ) )
=> ( A @ ( first_movers @ ( efficient_producers @ selection_favors ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
efficient_producers @ propagation_strategy,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_organizational_sets2) ).
thf(29,plain,
efficient_producers @ propagation_strategy,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ~ ( A @ end_time @ ( B @ greater ) )
& ( A @ start_time @ ( B @ greater ) )
& ( A @ environment ) )
=> ( B @ ( A @ end_time @ greater_or_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_beginning_and_ending) ).
thf(48,plain,
! [A: $i,B: $i] :
( ( ~ ( A @ end_time @ ( B @ greater ) )
& ( A @ start_time @ ( B @ greater ) )
& ( A @ environment ) )
=> ( B @ ( A @ end_time @ greater_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ( A @ critical_point @ ( B @ greater ) )
& ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( B @ ( first_movers @ ( efficient_producers @ selection_favors ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l8) ).
thf(50,plain,
! [A: $i,B: $i] :
( ( ( A @ critical_point @ ( B @ greater ) )
& ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( B @ ( first_movers @ ( efficient_producers @ selection_favors ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
first_movers @ propagation_strategy,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_organizational_sets1) ).
thf(28,plain,
first_movers @ propagation_strategy,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,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(38,plain,
! [A: $i,B: $i] :
( ( ( ( A = B )
| ( B @ ( A @ greater ) ) )
=> ( B @ ( A @ greater_or_equal ) ) )
& ( ( B @ ( A @ greater_or_equal ) )
=> ( ( A = B )
| ( B @ ( A @ greater ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( B @ ( A @ end_time @ greater_or_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_environment_end_point) ).
thf(32,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ in_environment ) )
& ( A @ environment ) )
=> ( B @ ( A @ end_time @ greater_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ environment )
=> ( A @ start_time @ ( A @ critical_point @ greater_or_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_of_critical_point) ).
thf(34,plain,
! [A: $i] :
( ( A @ environment )
=> ( A @ start_time @ ( A @ critical_point @ greater_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,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(36,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ greater ) )
& ( B @ ( A @ greater ) ) )
=> ( C @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ end_time @ greater_or_equal ) )
& ( A @ start_time @ ( B @ greater_or_equal ) )
& ( A @ environment ) )
=> ( B @ ( A @ in_environment ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_in_environment) ).
thf(30,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ end_time @ greater_or_equal ) )
& ( A @ start_time @ ( B @ greater_or_equal ) )
& ( A @ environment ) )
=> ( B @ ( A @ in_environment ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
! [A: $i] :
( ( ! [B: $i] :
( ( ( B @ ( A @ in_environment ) )
& ( B @ environment ) )
=> ( B @ end_time @ ( first_movers @ ( efficient_producers @ selection_favors ) ) ) )
& ( efficient_producers @ propagation_strategy )
& ( first_movers @ propagation_strategy )
& ( A @ observational_period ) )
=> ( A @ ( first_movers @ ( efficient_producers @ selection_favors ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp3_favoured_trategy) ).
thf(19,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( ( B @ ( A @ in_environment ) )
& ( B @ environment ) )
=> ( B @ end_time @ ( first_movers @ ( efficient_producers @ selection_favors ) ) ) )
& ( efficient_producers @ propagation_strategy )
& ( first_movers @ propagation_strategy )
& ( A @ observational_period ) )
=> ( A @ ( first_movers @ ( efficient_producers @ selection_favors ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(57,plain,
$false,
inference(e,[status(thm)],[24,14,29,48,50,28,38,32,34,36,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT039+1 : 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
% 0.13/0.40 % Computer : n015.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 00:10:13 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 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
% 0.85/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.35/1.21 % [INFO] Parsing done (202ms).
% 1.35/1.22 % [INFO] Running in sequential loop mode.
% 1.98/1.63 % [INFO] eprover registered as external prover.
% 1.98/1.64 % [INFO] Scanning for conjecture ...
% 2.17/1.74 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 2.17/1.78 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 2.37/1.81 % [INFO] Problem is first-order (TPTP FOF).
% 2.37/1.82 % [INFO] Type checking passed.
% 2.37/1.82 % [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 ...
% 4.14/2.58 % External prover 'e' found a proof!
% 4.14/2.58 % [INFO] Killing All external provers ...
% 4.14/2.58 % Time passed: 2030ms (effective reasoning time: 1353ms)
% 4.14/2.58 % 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)>
% 4.14/2.58 % Axioms used in derivation (11): mp3_favoured_trategy, mp_time_of_critical_point, mp_time_in_environment, mp_organizational_sets1, mp4_critical_point, mp_organizational_sets2, mp_beginning_and_ending, mp_greater_transitivity, mp_greater_or_equal, mp_environment_end_point, l8
% 4.14/2.58 % No. of inferences in proof: 26
% 4.14/2.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2030 ms resp. 1353 ms w/o parsing
% 4.42/2.64 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.42/2.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------