TSTP Solution File: MGT024-1 by Leo-III---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : MGT024-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n023.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 : Tue May 7 07:57:26 EDT 2024
% Result : Unsatisfiable 3.64s 1.96s
% Output : Refutation 3.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 37
% Syntax : Number of formulae : 59 ( 7 unt; 16 typ; 0 def)
% Number of atoms : 169 ( 20 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 706 ( 102 ~; 126 |; 0 &; 478 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 6 con; 0-4 aty)
% Number of variables : 60 ( 0 ^ 60 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(environment_type,type,
environment: $i > $o ).
thf(sk1_type,type,
sk1: $i ).
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(sk2_type,type,
sk2: $i ).
thf(greater_or_equal_type,type,
greater_or_equal: $i > $i > $o ).
thf(equilibrium_type,type,
equilibrium: $i > $i ).
thf(growth_rate_type,type,
growth_rate: $i > $i > $i ).
thf(zero_type,type,
zero: $i ).
thf(greater_type,type,
greater: $i > $i > $o ).
thf(constant_type,type,
constant: $i > $o ).
thf(number_of_organizations_type,type,
number_of_organizations: $i > $i > $i ).
thf(in_environment_type,type,
in_environment: $i > $i > $o ).
thf(resources_type,type,
resources: $i > $i > $i ).
thf(decreases_type,type,
decreases: $i > $o ).
thf(17,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ( in_environment @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_occur_24) ).
thf(57,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ( in_environment @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( constant @ ( number_of_organizations @ A @ B ) )
| ( ( growth_rate @ first_movers @ B )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ B ) )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7_33) ).
thf(38,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( constant @ ( number_of_organizations @ A @ B ) )
| ( ( growth_rate @ first_movers @ B )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ B ) )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ~ ( greater @ ( number_of_organizations @ A @ B ) @ zero )
| ( greater @ ( equilibrium @ A ) @ B )
| ( constant @ ( resources @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3_28) ).
thf(53,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ~ ( greater @ ( number_of_organizations @ A @ B ) @ zero )
| ( greater @ ( equilibrium @ A ) @ B )
| ( constant @ ( resources @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( greater_or_equal @ B @ ( equilibrium @ A ) )
| ~ ( greater @ ( equilibrium @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_equilibrium_26) ).
thf(41,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( greater_or_equal @ B @ ( equilibrium @ A ) )
| ~ ( greater @ ( equilibrium @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( constant @ ( number_of_organizations @ A @ B ) )
| ( ( growth_rate @ efficient_producers @ B )
= zero )
| ( greater @ ( growth_rate @ first_movers @ B ) @ zero )
| ( greater @ zero @ ( growth_rate @ first_movers @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7_36) ).
thf(35,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( constant @ ( number_of_organizations @ A @ B ) )
| ( ( growth_rate @ efficient_producers @ B )
= zero )
| ( greater @ ( growth_rate @ first_movers @ B ) @ zero )
| ( greater @ zero @ ( growth_rate @ first_movers @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
! [B: $i,A: $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_positive_number_of_organizations_25) ).
thf(48,plain,
! [B: $i,A: $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)],[13]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ~ ( constant @ ( resources @ A @ B ) )
| ( constant @ ( number_of_organizations @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a6_30) ).
thf(43,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ~ ( constant @ ( resources @ A @ B ) )
| ( constant @ ( number_of_organizations @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ~ ( decreases @ ( resources @ A @ B ) )
| ~ ( decreases @ ( number_of_organizations @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a6_29) ).
thf(62,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ~ ( decreases @ ( resources @ A @ B ) )
| ~ ( decreases @ ( number_of_organizations @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(6,negated_conjecture,
( ~ ( greater @ ( growth_rate @ efficient_producers @ sk2 ) @ zero )
| ~ ( greater @ zero @ ( growth_rate @ first_movers @ sk2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l6_44) ).
thf(24,plain,
( ~ ( greater @ ( growth_rate @ efficient_producers @ sk2 ) @ zero )
| ~ ( greater @ zero @ ( growth_rate @ first_movers @ sk2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(2,negated_conjecture,
subpopulations @ first_movers @ efficient_producers @ sk1 @ sk2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l6_40) ).
thf(25,plain,
subpopulations @ first_movers @ efficient_producers @ sk1 @ sk2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( constant @ ( number_of_organizations @ A @ B ) )
| ( ( growth_rate @ first_movers @ B )
= zero )
| ( greater @ ( growth_rate @ first_movers @ B ) @ zero )
| ( greater @ zero @ ( growth_rate @ first_movers @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7_32) ).
thf(32,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( constant @ ( number_of_organizations @ A @ B ) )
| ( ( growth_rate @ first_movers @ B )
= zero )
| ( greater @ ( growth_rate @ first_movers @ B ) @ zero )
| ( greater @ zero @ ( growth_rate @ first_movers @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( constant @ ( number_of_organizations @ A @ B ) )
| ( ( growth_rate @ first_movers @ B )
= zero )
| ( greater @ ( growth_rate @ first_movers @ B ) @ zero )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7_31) ).
thf(45,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( constant @ ( number_of_organizations @ A @ B ) )
| ( ( growth_rate @ first_movers @ B )
= zero )
| ( greater @ ( growth_rate @ first_movers @ B ) @ zero )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( constant @ ( number_of_organizations @ A @ B ) )
| ( ( growth_rate @ efficient_producers @ B )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ B ) )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7_37) ).
thf(64,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( constant @ ( number_of_organizations @ A @ B ) )
| ( ( growth_rate @ efficient_producers @ B )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ B ) )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(5,negated_conjecture,
( ~ ( greater @ ( growth_rate @ first_movers @ sk2 ) @ zero )
| ~ ( greater @ zero @ ( growth_rate @ efficient_producers @ sk2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l6_43) ).
thf(22,plain,
( ~ ( greater @ ( growth_rate @ first_movers @ sk2 ) @ zero )
| ~ ( greater @ zero @ ( growth_rate @ efficient_producers @ sk2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( constant @ ( number_of_organizations @ A @ B ) )
| ( ( growth_rate @ efficient_producers @ B )
= zero )
| ( greater @ ( growth_rate @ first_movers @ B ) @ zero )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7_35) ).
thf(59,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( constant @ ( number_of_organizations @ A @ B ) )
| ( ( growth_rate @ efficient_producers @ B )
= zero )
| ( greater @ ( growth_rate @ first_movers @ B ) @ zero )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(4,negated_conjecture,
( ( ( growth_rate @ first_movers @ sk2 )
!= zero )
| ( ( growth_rate @ efficient_producers @ sk2 )
!= zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l6_42) ).
thf(27,plain,
( ( ( growth_rate @ first_movers @ sk2 )
!= zero )
| ( ( growth_rate @ efficient_producers @ sk2 )
!= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( constant @ ( number_of_organizations @ A @ B ) )
| ( ( growth_rate @ first_movers @ B )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ B ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7_34) ).
thf(50,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( constant @ ( number_of_organizations @ A @ B ) )
| ( ( growth_rate @ first_movers @ B )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ B ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( constant @ ( number_of_organizations @ A @ B ) )
| ( ( growth_rate @ efficient_producers @ B )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ B ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7_38) ).
thf(67,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( constant @ ( number_of_organizations @ A @ B ) )
| ( ( growth_rate @ efficient_producers @ B )
= zero )
| ( greater @ zero @ ( growth_rate @ efficient_producers @ B ) )
| ( greater @ zero @ ( growth_rate @ first_movers @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(3,negated_conjecture,
greater_or_equal @ sk2 @ ( equilibrium @ sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l6_41) ).
thf(26,plain,
greater_or_equal @ sk2 @ ( equilibrium @ sk1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ~ ( greater @ ( number_of_organizations @ A @ B ) @ zero )
| ~ ( greater @ ( equilibrium @ A ) @ B )
| ( decreases @ ( resources @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3_27) ).
thf(55,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ~ ( greater @ ( number_of_organizations @ A @ B ) @ zero )
| ~ ( greater @ ( equilibrium @ A ) @ B )
| ( decreases @ ( resources @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1,negated_conjecture,
environment @ sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l6_39) ).
thf(23,plain,
environment @ sk1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(70,plain,
$false,
inference(e,[status(thm)],[57,38,53,41,35,48,43,62,24,25,32,45,64,22,59,27,50,67,26,55,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.15 % Problem : MGT024-1 : TPTP v8.1.2. Released v2.4.0.
% 0.15/0.18 % Command : run_Leo-III %s %d
% 0.18/0.40 % Computer : n023.cluster.edu
% 0.18/0.40 % Model : x86_64 x86_64
% 0.18/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.40 % Memory : 8042.1875MB
% 0.18/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.40 % CPULimit : 300
% 0.18/0.40 % WCLimit : 300
% 0.18/0.40 % DateTime : Mon May 6 15:29:24 EDT 2024
% 0.18/0.40 % CPUTime :
% 0.90/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.17/1.01 % [INFO] Parsing done (128ms).
% 1.35/1.01 % [INFO] Running in sequential loop mode.
% 1.79/1.25 % [INFO] eprover registered as external prover.
% 1.79/1.25 % [INFO] cvc4 registered as external prover.
% 1.79/1.25 % [INFO] Scanning for conjecture ...
% 1.79/1.33 % [INFO] Found a conjecture and 15 axioms. Running axiom selection ...
% 2.02/1.38 % [INFO] Axiom selection finished. Selected 15 axioms (removed 0 axioms).
% 2.22/1.41 % [INFO] Problem is propositional (TPTP CNF).
% 2.22/1.41 % [INFO] Type checking passed.
% 2.22/1.42 % [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 ...
% 3.64/1.92 % External prover 'e' found a proof!
% 3.64/1.93 % [INFO] Killing All external provers ...
% 3.64/1.93 % Time passed: 1376ms (effective reasoning time: 907ms)
% 3.64/1.93 % 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)>
% 3.64/1.93 % Axioms used in derivation (15): l7_38, l7_33, a6_29, mp_time_point_occur_24, l7_31, mp_equilibrium_26, l7_34, l7_36, mp_positive_number_of_organizations_25, l7_37, a3_27, a3_28, a6_30, l7_35, l7_32
% 3.64/1.93 % No. of inferences in proof: 43
% 3.64/1.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1376 ms resp. 907 ms w/o parsing
% 3.86/2.03 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.86/2.03 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------