TSTP Solution File: MGT020+1 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : MGT020+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.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 11:35:15 EDT 2023
% Result : Theorem 2.97s 1.68s
% Output : Refutation 3.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 23
% Syntax : Number of formulae : 36 ( 1 unt; 12 typ; 0 def)
% Number of atoms : 88 ( 2 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 331 ( 6 ~; 2 |; 33 &; 261 @)
% ( 0 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 3 con; 0-4 aty)
% Number of variables : 54 ( 0 ^; 54 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(environment_type,type,
environment: $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_type,type,
greater: $i > $i > $o ).
thf(disbanding_rate_type,type,
disbanding_rate: $i > $i > $i ).
thf(decreases_type,type,
decreases: $i > $o ).
thf(difference_type,type,
difference: $i > $i > $i ).
thf(in_environment_type,type,
in_environment: $i > $i > $o ).
thf(initial_FM_EP_type,type,
initial_FM_EP: $i > $i ).
thf(greater_or_equal_type,type,
greater_or_equal: $i > $i > $o ).
thf(start_time_type,type,
start_time: $i > $i ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( environment @ A )
& ( greater_or_equal @ B @ ( start_time @ A ) )
& ( greater @ C @ B )
& ( in_environment @ A @ C ) )
=> ( in_environment @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_times_in_order) ).
thf(29,plain,
! [A: $i,B: $i,C: $i] :
( ( ( environment @ A )
& ( greater_or_equal @ B @ ( start_time @ A ) )
& ( greater @ C @ B )
& ( in_environment @ A @ C ) )
=> ( in_environment @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B ) )
=> ( greater @ ( disbanding_rate @ first_movers @ B ) @ ( disbanding_rate @ efficient_producers @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l2) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B ) )
=> ( greater @ ( disbanding_rate @ first_movers @ B ) @ ( disbanding_rate @ efficient_producers @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
~ ! [A: $i,B: $i] :
( ( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B ) )
=> ( greater @ ( disbanding_rate @ first_movers @ B ) @ ( disbanding_rate @ efficient_producers @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [A: $i] :
( ( environment @ A )
=> ( greater_or_equal @ ( initial_FM_EP @ A ) @ ( start_time @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_initial_time) ).
thf(27,plain,
! [A: $i] :
( ( environment @ A )
=> ( greater_or_equal @ ( initial_FM_EP @ A ) @ ( start_time @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B )
& ( subpopulations @ first_movers @ efficient_producers @ A @ C )
& ( greater_or_equal @ D @ B )
& ( greater_or_equal @ C @ D ) )
=> ( subpopulations @ first_movers @ efficient_producers @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a10) ).
thf(39,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B )
& ( subpopulations @ first_movers @ efficient_producers @ A @ C )
& ( greater_or_equal @ D @ B )
& ( greater_or_equal @ C @ D ) )
=> ( subpopulations @ first_movers @ efficient_producers @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( environment @ A )
& ( greater_or_equal @ B @ C )
& ( greater_or_equal @ D @ B )
& ( subpopulations @ first_movers @ efficient_producers @ A @ D )
& ( greater @ ( disbanding_rate @ first_movers @ C ) @ ( disbanding_rate @ efficient_producers @ C ) ) )
=> ( ~ ( decreases @ ( difference @ ( disbanding_rate @ first_movers @ B ) @ ( disbanding_rate @ efficient_producers @ B ) ) )
=> ( greater @ ( disbanding_rate @ first_movers @ D ) @ ( disbanding_rate @ efficient_producers @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_positive_function_difference) ).
thf(23,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( environment @ A )
& ( greater_or_equal @ B @ C )
& ( greater_or_equal @ D @ B )
& ( subpopulations @ first_movers @ efficient_producers @ A @ D )
& ( greater @ ( disbanding_rate @ first_movers @ C ) @ ( disbanding_rate @ efficient_producers @ C ) ) )
=> ( ~ ( decreases @ ( difference @ ( disbanding_rate @ first_movers @ B ) @ ( disbanding_rate @ efficient_producers @ B ) ) )
=> ( greater @ ( disbanding_rate @ first_movers @ D ) @ ( disbanding_rate @ efficient_producers @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( environment @ A )
=> ( ( ( in_environment @ A @ ( initial_FM_EP @ A ) )
=> ( subpopulations @ first_movers @ efficient_producers @ A @ ( initial_FM_EP @ A ) ) )
& ( ( subpopulations @ first_movers @ efficient_producers @ A @ B )
=> ( greater_or_equal @ B @ ( initial_FM_EP @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_point) ).
thf(19,plain,
! [A: $i,B: $i] :
( ( environment @ A )
=> ( ( ( in_environment @ A @ ( initial_FM_EP @ A ) )
=> ( subpopulations @ first_movers @ efficient_producers @ A @ ( initial_FM_EP @ A ) ) )
& ( ( subpopulations @ first_movers @ efficient_producers @ A @ B )
=> ( greater_or_equal @ B @ ( initial_FM_EP @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,axiom,
! [A: $i] :
( ( environment @ A )
=> ( greater @ ( disbanding_rate @ first_movers @ ( initial_FM_EP @ A ) ) @ ( disbanding_rate @ efficient_producers @ ( initial_FM_EP @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a8) ).
thf(37,plain,
! [A: $i] :
( ( environment @ A )
=> ( greater @ ( disbanding_rate @ first_movers @ ( initial_FM_EP @ A ) ) @ ( disbanding_rate @ efficient_producers @ ( initial_FM_EP @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(6,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_occurs) ).
thf(25,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)],[6]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B ) )
=> ~ ( decreases @ ( difference @ ( disbanding_rate @ first_movers @ B ) @ ( disbanding_rate @ efficient_producers @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3) ).
thf(17,plain,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( subpopulations @ first_movers @ efficient_producers @ A @ B ) )
=> ~ ( decreases @ ( difference @ ( disbanding_rate @ first_movers @ B ) @ ( disbanding_rate @ efficient_producers @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,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(32,plain,
! [A: $i,B: $i,C: $i] :
( ( ( greater @ A @ B )
& ( greater @ B @ C ) )
=> ( greater @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,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(34,plain,
! [A: $i,B: $i] :
( ( greater_or_equal @ A @ B )
=> ( ( greater @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(41,plain,
$false,
inference(e,[status(thm)],[29,13,27,39,23,19,37,25,17,32,34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : MGT020+1 : TPTP v8.1.2. Released v2.0.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n015.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % 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 23:57:08 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.83/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/0.96 % [INFO] Parsing done (127ms).
% 1.24/0.97 % [INFO] Running in sequential loop mode.
% 1.71/1.17 % [INFO] eprover registered as external prover.
% 1.71/1.18 % [INFO] cvc4 registered as external prover.
% 1.71/1.18 % [INFO] Scanning for conjecture ...
% 1.87/1.24 % [INFO] Found a conjecture and 10 axioms. Running axiom selection ...
% 1.87/1.26 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 1.87/1.29 % [INFO] Problem is first-order (TPTP FOF).
% 1.87/1.29 % [INFO] Type checking passed.
% 1.87/1.29 % [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 ...
% 2.97/1.68 % External prover 'e' found a proof!
% 2.97/1.68 % [INFO] Killing All external provers ...
% 2.97/1.68 % Time passed: 1164ms (effective reasoning time: 702ms)
% 2.97/1.68 % 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)>
% 2.97/1.68 % Axioms used in derivation (10): l3, mp_times_in_order, mp_time_point_occurs, mp_positive_function_difference, a10, a8, mp_initial_time, mp_greater_or_equal, mp_greater_transitivity, mp_earliest_time_point
% 2.97/1.68 % No. of inferences in proof: 24
% 2.97/1.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1164 ms resp. 702 ms w/o parsing
% 3.33/1.77 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.33/1.77 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------