TSTP Solution File: MGT035+2 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : MGT035+2 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n031.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 11:35:20 EDT 2023
% Result : Theorem 4.69s 2.12s
% Output : Refutation 4.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 40
% Syntax : Number of formulae : 62 ( 1 unt; 20 typ; 0 def)
% Number of atoms : 203 ( 21 equ; 0 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 635 ( 12 ~; 15 |; 84 &; 462 @)
% ( 2 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 4 con; 0-4 aty)
% Number of variables : 103 ( 0 ^; 96 !; 7 ?; 103 :)
% Comments :
%------------------------------------------------------------------------------
thf(environment_type,type,
environment: $i > $o ).
thf(stable_type,type,
stable: $i > $o ).
thf(in_environment_type,type,
in_environment: $i > $i > $o ).
thf(subpopulations_type,type,
subpopulations: $i > $i > $i > $i > $o ).
thf(first_movers_type,type,
first_movers: $i ).
thf(efficient_producers_type,type,
efficient_producers: $i ).
thf(greater_or_equal_type,type,
greater_or_equal: $i > $i > $o ).
thf(outcompetes_type,type,
outcompetes: $i > $i > $i > $o ).
thf(greater_type,type,
greater: $i > $i > $o ).
thf(sum_type,type,
sum: $i > $i > $i ).
thf(constant_type,type,
constant: $i > $o ).
thf(increases_type,type,
increases: $i > $o ).
thf(decreases_type,type,
decreases: $i > $o ).
thf(subpopulation_type,type,
subpopulation: $i > $i > $i > $o ).
thf(number_of_organizations_type,type,
number_of_organizations: $i > $i > $i ).
thf(zero_type,type,
zero: $i ).
thf(equilibrium_type,type,
equilibrium: $i > $i ).
thf(resources_type,type,
resources: $i > $i > $i ).
thf(growth_rate_type,type,
growth_rate: $i > $i > $i ).
thf(cardinality_at_time_type,type,
cardinality_at_time: $i > $i > $i ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B ) )
=> ( in_environment @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_in_environment) ).
thf(57,plain,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B ) )
=> ( in_environment @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( environment @ B )
& ( in_environment @ B @ C )
& ( subpopulation @ A @ B @ C )
& ( greater @ ( cardinality_at_time @ A @ C ) @ zero ) )
=> ( ( ( constant @ ( cardinality_at_time @ A @ C ) )
=> ( ( growth_rate @ A @ C )
= zero ) )
& ( ( increases @ ( cardinality_at_time @ A @ C ) )
=> ( greater @ ( growth_rate @ A @ C ) @ zero ) )
& ( ( decreases @ ( cardinality_at_time @ A @ C ) )
=> ( greater @ zero @ ( growth_rate @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_growth_rate) ).
thf(106,plain,
! [A: $i,B: $i,C: $i] :
( ( ( environment @ B )
& ( in_environment @ B @ C )
& ( subpopulation @ A @ B @ C )
& ( greater @ ( cardinality_at_time @ A @ C ) @ zero ) )
=> ( ( ( constant @ ( cardinality_at_time @ A @ C ) )
=> ( ( growth_rate @ A @ C )
= zero ) )
& ( ( increases @ ( cardinality_at_time @ A @ C ) )
=> ( greater @ ( growth_rate @ A @ C ) @ zero ) )
& ( ( decreases @ ( cardinality_at_time @ A @ C ) )
=> ( greater @ zero @ ( growth_rate @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( greater_or_equal @ B @ ( equilibrium @ A ) ) )
=> ~ ( greater @ ( equilibrium @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_equilibrium) ).
thf(74,plain,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( greater_or_equal @ B @ ( equilibrium @ A ) ) )
=> ~ ( greater @ ( equilibrium @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( in_environment @ A @ B )
& ( greater @ ( number_of_organizations @ A @ B ) @ zero ) )
=> ( ( ( greater @ ( equilibrium @ A ) @ B )
=> ( decreases @ ( resources @ A @ B ) ) )
& ( ~ ( greater @ ( equilibrium @ A ) @ B )
=> ( constant @ ( resources @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a4) ).
thf(64,plain,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( in_environment @ A @ B )
& ( greater @ ( number_of_organizations @ A @ B ) @ zero ) )
=> ( ( ( greater @ ( equilibrium @ A ) @ B )
=> ( decreases @ ( resources @ A @ B ) ) )
& ( ~ ( greater @ ( equilibrium @ A ) @ B )
=> ( constant @ ( resources @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(14,axiom,
! [A: $i] :
( ( ( environment @ A )
& ( stable @ A ) )
=> ? [B: $i] :
( ( in_environment @ A @ B )
& ( greater_or_equal @ B @ ( equilibrium @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a5) ).
thf(76,plain,
! [A: $i] :
( ( ( environment @ A )
& ( stable @ A ) )
=> ? [B: $i] :
( ( in_environment @ A @ B )
& ( greater_or_equal @ B @ ( equilibrium @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
! [A: $i,B: $i] :
~ ( ( greater @ A @ B )
& ( greater @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp6_2) ).
thf(35,plain,
! [A: $i,B: $i] :
~ ( ( greater @ A @ B )
& ( greater @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in_environment @ A @ B )
& ( in_environment @ A @ C ) )
=> ( ( greater @ C @ B )
| ( C = B )
| ( greater @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_times_in_environment) ).
thf(67,plain,
! [A: $i,B: $i,C: $i] :
( ( ( in_environment @ A @ B )
& ( in_environment @ A @ C ) )
=> ( ( greater @ C @ B )
| ( C = B )
| ( greater @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(16,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(82,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)],[16]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B ) )
=> ( greater @ ( number_of_organizations @ A @ B ) @ zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_environment_not_empty) ).
thf(62,plain,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B ) )
=> ( greater @ ( number_of_organizations @ A @ B ) @ zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( environment @ A )
& ( subpopulation @ B @ A @ C )
& ( greater @ ( cardinality_at_time @ B @ C ) @ zero ) )
=> ( ( B = efficient_producers )
| ( B = first_movers ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a11) ).
thf(111,plain,
! [A: $i,B: $i,C: $i] :
( ( ( environment @ A )
& ( subpopulation @ B @ A @ C )
& ( greater @ ( cardinality_at_time @ B @ C ) @ zero ) )
=> ( ( B = efficient_producers )
| ( B = first_movers ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( environment @ A )
& ( subpopulations @ B @ C @ A @ D ) )
=> ( ( ( greater_or_equal @ ( growth_rate @ C @ D ) @ zero )
& ( greater @ zero @ ( growth_rate @ B @ D ) ) )
<=> ( outcompetes @ C @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
thf(70,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( environment @ A )
& ( subpopulations @ B @ C @ A @ D ) )
=> ( ( ( ( greater_or_equal @ ( growth_rate @ C @ D ) @ zero )
& ( greater @ zero @ ( growth_rate @ B @ D ) ) )
=> ( outcompetes @ C @ B @ D ) )
& ( ( outcompetes @ C @ B @ D )
=> ( ( greater_or_equal @ ( growth_rate @ C @ D ) @ zero )
& ( greater @ zero @ ( growth_rate @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(4,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(33,plain,
! [A: $i,B: $i,C: $i] :
( ( ( greater @ A @ B )
& ( greater @ B @ C ) )
=> ( greater @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( greater @ A @ B )
& ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp6_1) ).
thf(28,plain,
! [A: $i,B: $i] :
~ ( ( greater @ A @ B )
& ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A
= ( sum @ B @ C ) )
& ( constant @ A ) )
=> ( ( ( constant @ B )
& ( constant @ C ) )
| ( ( increases @ B )
& ( decreases @ C ) )
| ( ( decreases @ B )
& ( increases @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_abc_sum_increase) ).
thf(38,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A
= ( sum @ B @ C ) )
& ( constant @ A ) )
=> ( ( ( constant @ B )
& ( constant @ C ) )
| ( ( increases @ B )
& ( decreases @ C ) )
| ( ( decreases @ B )
& ( increases @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( environment @ A )
& ( stable @ A ) )
=> ? [B: $i] :
( ( in_environment @ A @ B )
& ! [C: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
& ( greater_or_equal @ C @ B ) )
=> ( outcompetes @ efficient_producers @ first_movers @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t4) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( environment @ A )
& ( stable @ A ) )
=> ? [B: $i] :
( ( in_environment @ A @ B )
& ! [C: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
& ( greater_or_equal @ C @ B ) )
=> ( outcompetes @ efficient_producers @ first_movers @ C ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(22,plain,
~ ! [A: $i] :
( ( ( environment @ A )
& ( stable @ A ) )
=> ? [B: $i] :
( ( in_environment @ A @ B )
& ! [C: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
& ( greater_or_equal @ C @ B ) )
=> ( outcompetes @ efficient_producers @ first_movers @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,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_FM_and_EP_organisational) ).
thf(59,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)],[8]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B ) )
=> ( ( greater @ ( cardinality_at_time @ first_movers @ B ) @ zero )
& ( greater @ ( cardinality_at_time @ efficient_producers @ B ) @ zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_positive_number_of_organizations) ).
thf(103,plain,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B ) )
=> ( ( greater @ ( cardinality_at_time @ first_movers @ B ) @ zero )
& ( greater @ ( cardinality_at_time @ efficient_producers @ B ) @ zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( in_environment @ A @ B ) )
=> ( ( ( decreases @ ( resources @ A @ B ) )
=> ~ ( decreases @ ( number_of_organizations @ A @ B ) ) )
& ( ( constant @ ( resources @ A @ B ) )
=> ( constant @ ( number_of_organizations @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a7) ).
thf(91,plain,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( in_environment @ A @ B ) )
=> ( ( ( decreases @ ( resources @ A @ B ) )
=> ~ ( decreases @ ( number_of_organizations @ A @ B ) ) )
& ( ( constant @ ( resources @ A @ B ) )
=> ( constant @ ( number_of_organizations @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(15,axiom,
! [A: $i] :
( ( ( environment @ A )
& ( stable @ A ) )
=> ? [B: $i] :
( ( in_environment @ A @ B )
& ! [C: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
& ( greater_or_equal @ C @ B ) )
=> ( greater @ ( growth_rate @ efficient_producers @ C ) @ ( growth_rate @ first_movers @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1) ).
thf(79,plain,
! [A: $i] :
( ( ( environment @ A )
& ( stable @ A ) )
=> ? [B: $i] :
( ( in_environment @ A @ B )
& ! [C: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
& ( greater_or_equal @ C @ B ) )
=> ( greater @ ( growth_rate @ efficient_producers @ C ) @ ( growth_rate @ first_movers @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( environment @ A )
& ( subpopulation @ B @ A @ C )
& ( ( greater @ ( cardinality_at_time @ B @ C ) @ zero )
=> ( ( B = efficient_producers )
| ( B = first_movers ) ) ) )
=> ( ( number_of_organizations @ A @ C )
= ( sum @ ( cardinality_at_time @ first_movers @ C ) @ ( cardinality_at_time @ efficient_producers @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_only_members) ).
thf(94,plain,
! [A: $i,B: $i,C: $i] :
( ( ( environment @ A )
& ( subpopulation @ B @ A @ C )
& ( ( greater @ ( cardinality_at_time @ B @ C ) @ zero )
=> ( ( B = efficient_producers )
| ( B = first_movers ) ) ) )
=> ( ( number_of_organizations @ A @ C )
= ( sum @ ( cardinality_at_time @ first_movers @ C ) @ ( cardinality_at_time @ efficient_producers @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(145,plain,
$false,
inference(cvc4,[status(thm)],[57,106,74,64,76,35,67,82,62,111,70,33,28,38,22,59,103,91,79,94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : MGT035+2 : TPTP v8.1.2. Released v2.0.0.
% 0.14/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n031.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Fri May 19 00:06:11 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.94/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/1.00 % [INFO] Parsing done (137ms).
% 1.23/1.01 % [INFO] Running in sequential loop mode.
% 1.77/1.22 % [INFO] eprover registered as external prover.
% 1.77/1.22 % [INFO] cvc4 registered as external prover.
% 1.87/1.23 % [INFO] Scanning for conjecture ...
% 1.90/1.29 % [INFO] Found a conjecture and 19 axioms. Running axiom selection ...
% 2.12/1.34 % [INFO] Axiom selection finished. Selected 19 axioms (removed 0 axioms).
% 2.36/1.39 % [INFO] Problem is first-order (TPTP FOF).
% 2.36/1.39 % [INFO] Type checking passed.
% 2.36/1.40 % [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 ...
% 4.69/2.11 % External prover 'cvc4' found a proof!
% 4.69/2.11 % [INFO] Killing All external provers ...
% 4.69/2.12 % Time passed: 1579ms (effective reasoning time: 1104ms)
% 4.69/2.12 % 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)>
% 4.69/2.12 % Axioms used in derivation (19): l1, mp_time_point_in_environment, mp_growth_rate, mp_FM_and_EP_organisational, mp_only_members, mp6_2, mp_greater_or_equal, mp_equilibrium, a5, a4, mp_positive_number_of_organizations, a11, mp_times_in_environment, mp_environment_not_empty, mp6_1, d2, mp_greater_transitivity, mp_abc_sum_increase, a7
% 4.69/2.12 % No. of inferences in proof: 42
% 4.69/2.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1579 ms resp. 1104 ms w/o parsing
% 4.77/2.16 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.77/2.16 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------