TSTP Solution File: MGT039+2 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : MGT039+2 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:35:23 EDT 2023
% Result : Theorem 3.50s 1.84s
% Output : Refutation 3.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 38
% Syntax : Number of formulae : 59 ( 5 unt; 19 typ; 0 def)
% Number of atoms : 149 ( 7 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 460 ( 6 ~; 3 |; 64 &; 345 @)
% ( 1 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 19 usr; 4 con; 0-4 aty)
% Number of variables : 77 ( 0 ^; 75 !; 2 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
thf(observational_period_type,type,
observational_period: $i > $o ).
thf(slow_change_type,type,
slow_change: $i > $o ).
thf(selection_favors_type,type,
selection_favors: $i > $i > $i > $o ).
thf(efficient_producers_type,type,
efficient_producers: $i ).
thf(first_movers_type,type,
first_movers: $i ).
thf(greater_type,type,
greater: $i > $i > $o ).
thf(environment_type,type,
environment: $i > $o ).
thf(greater_or_equal_type,type,
greater_or_equal: $i > $i > $o ).
thf(start_time_type,type,
start_time: $i > $i ).
thf(end_time_type,type,
end_time: $i > $i ).
thf(in_environment_type,type,
in_environment: $i > $i > $o ).
thf(critical_point_type,type,
critical_point: $i > $i ).
thf(growth_rate_type,type,
growth_rate: $i > $i > $i ).
thf(subpopulations_type,type,
subpopulations: $i > $i > $i > $i > $o ).
thf(cardinality_at_time_type,type,
cardinality_at_time: $i > $i > $i ).
thf(zero_type,type,
zero: $i ).
thf(propagation_strategy_type,type,
propagation_strategy: $i > $o ).
thf(appear_type,type,
appear: $i > $i > $i ).
thf(subpopulation_type,type,
subpopulation: $i > $i > $i > $o ).
thf(19,axiom,
! [A: $i] :
( ( ( observational_period @ A )
& ( propagation_strategy @ first_movers )
& ( propagation_strategy @ efficient_producers )
& ! [B: $i] :
( ( ( environment @ B )
& ( in_environment @ A @ B ) )
=> ( selection_favors @ efficient_producers @ first_movers @ ( end_time @ B ) ) ) )
=> ( selection_favors @ efficient_producers @ first_movers @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp3_favoured_trategy) ).
thf(69,plain,
! [A: $i] :
( ( ( observational_period @ A )
& ( propagation_strategy @ first_movers )
& ( propagation_strategy @ efficient_producers )
& ! [B: $i] :
( ( ( environment @ B )
& ( in_environment @ A @ B ) )
=> ( selection_favors @ efficient_producers @ first_movers @ ( end_time @ B ) ) ) )
=> ( selection_favors @ efficient_producers @ first_movers @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(13,axiom,
! [A: $i] :
( ( environment @ A )
=> ( greater_or_equal @ ( critical_point @ A ) @ ( appear @ efficient_producers @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_critical_point_after_EP) ).
thf(56,plain,
! [A: $i] :
( ( environment @ A )
=> ( greater_or_equal @ ( critical_point @ A ) @ ( appear @ efficient_producers @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
! [A: $i] :
( ( environment @ A )
=> ( greater_or_equal @ ( critical_point @ A ) @ ( start_time @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_of_critical_point) ).
thf(29,plain,
! [A: $i] :
( ( environment @ A )
=> ( greater_or_equal @ ( critical_point @ A ) @ ( start_time @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( in_environment @ A @ B ) )
=> ( ( subpopulation @ first_movers @ A @ B )
& ( subpopulation @ efficient_producers @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_subpopulations) ).
thf(61,plain,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( in_environment @ A @ B ) )
=> ( ( subpopulation @ first_movers @ A @ B )
& ( subpopulation @ efficient_producers @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( observational_period @ A )
& ( slow_change @ A ) )
=> ( selection_favors @ efficient_producers @ first_movers @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t8) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( observational_period @ A )
& ( slow_change @ A ) )
=> ( selection_favors @ efficient_producers @ first_movers @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ! [A: $i] :
( ( ( observational_period @ A )
& ( slow_change @ A ) )
=> ( selection_favors @ efficient_producers @ first_movers @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( environment @ A )
& ( subpopulations @ B @ C @ A @ D )
& ( greater @ ( growth_rate @ C @ D ) @ ( growth_rate @ B @ D ) ) )
=> ( selection_favors @ C @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp1_high_growth_rates) ).
thf(53,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( environment @ A )
& ( subpopulations @ B @ C @ A @ D )
& ( greater @ ( growth_rate @ C @ D ) @ ( growth_rate @ B @ D ) ) )
=> ( selection_favors @ C @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(20,axiom,
! [A: $i] :
( ( ( observational_period @ A )
& ( slow_change @ A ) )
=> ! [B: $i] :
( ( ( environment @ B )
& ( in_environment @ A @ B ) )
=> ? [C: $i] :
( ( in_environment @ B @ C )
& ( greater @ C @ ( critical_point @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp4_critical_point) ).
thf(73,plain,
! [A: $i] :
( ( ( observational_period @ A )
& ( slow_change @ A ) )
=> ! [B: $i] :
( ( ( environment @ B )
& ( in_environment @ A @ B ) )
=> ? [C: $i] :
( ( in_environment @ B @ C )
& ( greater @ C @ ( critical_point @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( in_environment @ A @ B )
& ( greater @ ( cardinality_at_time @ first_movers @ B ) @ zero )
& ( greater @ ( cardinality_at_time @ efficient_producers @ B ) @ zero ) )
=> ( subpopulations @ first_movers @ efficient_producers @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_contains_FM_and_EP) ).
thf(64,plain,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( in_environment @ A @ B )
& ( greater @ ( cardinality_at_time @ first_movers @ B ) @ zero )
& ( greater @ ( cardinality_at_time @ efficient_producers @ B ) @ zero ) )
=> ( subpopulations @ first_movers @ efficient_producers @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(17,axiom,
propagation_strategy @ efficient_producers,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_organizational_sets2) ).
thf(66,plain,
propagation_strategy @ efficient_producers,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( environment @ A )
& ( subpopulation @ B @ A @ D )
& ( subpopulation @ C @ A @ D )
& ( greater @ ( cardinality_at_time @ B @ D ) @ zero )
& ( ( cardinality_at_time @ C @ D )
= zero ) )
=> ( selection_favors @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp2_favour_members) ).
thf(58,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( environment @ A )
& ( subpopulation @ B @ A @ D )
& ( subpopulation @ C @ A @ D )
& ( greater @ ( cardinality_at_time @ B @ D ) @ zero )
& ( ( cardinality_at_time @ C @ D )
= zero ) )
=> ( selection_favors @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( in_environment @ A @ B ) )
=> ( greater_or_equal @ ( cardinality_at_time @ first_movers @ B ) @ zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_exist) ).
thf(51,plain,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( in_environment @ A @ B ) )
=> ( greater_or_equal @ ( cardinality_at_time @ first_movers @ B ) @ zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( greater @ B @ ( start_time @ A ) )
& ~ ( greater @ B @ ( end_time @ A ) ) )
=> ( greater_or_equal @ ( end_time @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_beginning_and_ending) ).
thf(42,plain,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( greater @ B @ ( start_time @ A ) )
& ~ ( greater @ B @ ( end_time @ A ) ) )
=> ( greater_or_equal @ ( end_time @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( greater @ A @ B )
& ( greater @ B @ C ) )
=> ( greater @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_transitivity) ).
thf(25,plain,
! [A: $i,B: $i,C: $i] :
( ( ( greater @ A @ B )
& ( greater @ B @ C ) )
=> ( greater @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( B
= ( critical_point @ A ) ) )
=> ( ~ ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
& ! [C: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
& ( greater @ C @ B ) )
=> ( greater @ ( growth_rate @ efficient_producers @ C ) @ ( growth_rate @ first_movers @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
thf(44,plain,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( B
= ( critical_point @ A ) ) )
=> ( ~ ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
& ! [C: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
& ( greater @ C @ B ) )
=> ( greater @ ( growth_rate @ efficient_producers @ C ) @ ( growth_rate @ first_movers @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( greater_or_equal @ B @ ( start_time @ A ) )
& ( greater_or_equal @ ( end_time @ A ) @ B ) )
=> ( in_environment @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_in_environment) ).
thf(27,plain,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( greater_or_equal @ B @ ( start_time @ A ) )
& ( greater_or_equal @ ( end_time @ A ) @ B ) )
=> ( in_environment @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( in_environment @ A @ B )
& ( greater_or_equal @ B @ ( appear @ efficient_producers @ A ) ) )
=> ( greater @ ( cardinality_at_time @ efficient_producers @ B ) @ zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6) ).
thf(67,plain,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( in_environment @ A @ B )
& ( greater_or_equal @ B @ ( appear @ efficient_producers @ A ) ) )
=> ( greater @ ( cardinality_at_time @ efficient_producers @ B ) @ zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( greater_or_equal @ A @ B )
<=> ( ( greater @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal) ).
thf(31,plain,
! [A: $i,B: $i] :
( ( ( greater_or_equal @ A @ B )
=> ( ( greater @ A @ B )
| ( A = B ) ) )
& ( ( ( greater @ A @ B )
| ( A = B ) )
=> ( greater_or_equal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( in_environment @ A @ B ) )
=> ( greater_or_equal @ ( end_time @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_environment_end_point) ).
thf(40,plain,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( in_environment @ A @ B ) )
=> ( greater_or_equal @ ( end_time @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
propagation_strategy @ first_movers,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_organizational_sets1) ).
thf(55,plain,
propagation_strategy @ first_movers,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(76,plain,
$false,
inference(cvc4,[status(thm)],[69,56,29,61,21,53,73,64,66,58,51,42,25,44,27,67,31,40,55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MGT039+2 : TPTP v8.1.2. Released v2.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n009.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 23:38:03 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.92/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/0.96 % [INFO] Parsing done (123ms).
% 1.21/0.97 % [INFO] Running in sequential loop mode.
% 1.77/1.17 % [INFO] eprover registered as external prover.
% 1.77/1.17 % [INFO] cvc4 registered as external prover.
% 1.77/1.17 % [INFO] Scanning for conjecture ...
% 1.93/1.23 % [INFO] Found a conjecture and 18 axioms. Running axiom selection ...
% 2.03/1.27 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 2.03/1.31 % [INFO] Problem is first-order (TPTP FOF).
% 2.03/1.32 % [INFO] Type checking passed.
% 2.03/1.32 % [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 ...
% 3.50/1.83 % External prover 'cvc4' found a proof!
% 3.50/1.83 % [INFO] Killing All external provers ...
% 3.50/1.84 % Time passed: 1319ms (effective reasoning time: 863ms)
% 3.50/1.84 % 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)>
% 3.50/1.84 % Axioms used in derivation (18): mp1_high_growth_rates, mp3_favoured_trategy, mp_subpopulations, t6, mp_organizational_sets1, mp4_critical_point, mp_organizational_sets2, mp_greater_transitivity, mp_greater_or_equal, mp2_favour_members, mp_time_of_critical_point, mp_contains_FM_and_EP, mp_first_movers_exist, mp_time_in_environment, mp_environment_end_point, mp_critical_point_after_EP, mp_beginning_and_ending, d1
% 3.50/1.84 % No. of inferences in proof: 40
% 3.50/1.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1319 ms resp. 863 ms w/o parsing
% 3.70/1.88 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.70/1.88 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------