TSTP Solution File: MGT026-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : MGT026-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n029.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 11:35:17 EDT 2023
% Result : Unsatisfiable 2.99s 1.67s
% Output : Refutation 3.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 34
% Syntax : Number of formulae : 53 ( 9 unt; 16 typ; 0 def)
% Number of atoms : 105 ( 10 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 394 ( 70 ~; 68 |; 0 &; 256 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 6 con; 0-4 aty)
% Number of variables : 66 ( 0 ^; 66 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(environment_type,type,
environment: $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(in_environment_type,type,
in_environment: $i > $i > $o ).
thf(sk2_type,type,
sk2: $i ).
thf(greater_type,type,
greater: $i > $i > $o ).
thf(critical_point_type,type,
critical_point: $i > $i ).
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(subpopulations_type,type,
subpopulations: $i > $i > $i > $i > $o ).
thf(growth_rate_type,type,
growth_rate: $i > $i > $i ).
thf(subpopulation_type,type,
subpopulation: $i > $i > $i > $o ).
thf(cardinality_at_time_type,type,
cardinality_at_time: $i > $i > $i ).
thf(zero_type,type,
zero: $i ).
thf(greater_or_equal_type,type,
greater_or_equal: $i > $i > $o ).
thf(appear_type,type,
appear: $i > $i > $i ).
thf(13,axiom,
! [B: $i,A: $i] :
( ~ ( greater_or_equal @ A @ B )
| ( greater @ A @ B )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_36) ).
thf(41,plain,
! [B: $i,A: $i] :
( ~ ( greater_or_equal @ A @ B )
| ( greater @ A @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( environment @ A )
| ( B
!= ( critical_point @ A ) )
| ~ ( 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_40) ).
thf(54,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( environment @ A )
| ( B
!= ( critical_point @ A ) )
| ~ ( 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)],[17]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( greater @ A @ B )
| ~ ( greater @ B @ C )
| ( greater @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_transitivity_35) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( greater @ A @ B )
| ~ ( greater @ B @ C )
| ( greater @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ( subpopulation @ efficient_producers @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_subpopulations_33) ).
thf(35,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ( subpopulation @ efficient_producers @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulation @ B @ A @ C )
| ~ ( subpopulation @ D @ A @ C )
| ~ ( greater @ ( cardinality_at_time @ B @ C ) @ zero )
| ( ( cardinality_at_time @ D @ C )
!= zero )
| ( selection_favors @ B @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp2_favour_members_29) ).
thf(26,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( subpopulation @ B @ A @ C )
| ~ ( subpopulation @ D @ A @ C )
| ~ ( greater @ ( cardinality_at_time @ B @ C ) @ zero )
| ( ( cardinality_at_time @ D @ C )
!= zero )
| ( selection_favors @ B @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(18,axiom,
! [B: $i,A: $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_41) ).
thf(58,plain,
! [B: $i,A: $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(1,negated_conjecture,
environment @ sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l8_42) ).
thf(19,plain,
environment @ sk1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $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_28) ).
thf(24,plain,
! [D: $i,C: $i,B: $i,A: $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)],[5]) ).
thf(11,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_34) ).
thf(37,plain,
! [A: $i] :
( ~ ( environment @ A )
| ( greater_or_equal @ ( critical_point @ A ) @ ( appear @ efficient_producers @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(2,negated_conjecture,
in_environment @ sk1 @ sk2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l8_43) ).
thf(20,plain,
in_environment @ sk1 @ sk2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ( greater_or_equal @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_38) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( greater_or_equal @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(7,axiom,
! [B: $i,A: $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_non_empty_fm_and_ep_30) ).
thf(29,plain,
! [B: $i,A: $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)],[7]) ).
thf(3,negated_conjecture,
greater @ sk2 @ ( critical_point @ sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l8_44) ).
thf(21,plain,
greater @ sk2 @ ( critical_point @ sk1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ( subpopulation @ first_movers @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_subpopulations_32) ).
thf(33,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( in_environment @ A @ B )
| ( subpopulation @ first_movers @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,negated_conjecture,
~ ( selection_favors @ efficient_producers @ first_movers @ sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l8_45) ).
thf(22,plain,
~ ( selection_favors @ efficient_producers @ first_movers @ sk2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ~ ( greater @ A @ B )
| ( greater_or_equal @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_37) ).
thf(44,plain,
! [B: $i,A: $i] :
( ~ ( greater @ A @ B )
| ( greater_or_equal @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ( B
!= ( critical_point @ A ) )
| ~ ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_39) ).
thf(50,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ( B
!= ( critical_point @ A ) )
| ~ ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(8,axiom,
! [B: $i,A: $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_31) ).
thf(31,plain,
! [B: $i,A: $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)],[8]) ).
thf(60,plain,
$false,
inference(e,[status(thm)],[41,54,39,35,26,58,19,24,37,20,46,29,21,33,22,44,50,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : MGT026-1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.14 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n029.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
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 23:54:29 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.86/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/0.95 % [INFO] Parsing done (113ms).
% 1.22/0.96 % [INFO] Running in sequential loop mode.
% 1.52/1.14 % [INFO] eprover registered as external prover.
% 1.52/1.15 % [INFO] cvc4 registered as external prover.
% 1.52/1.15 % [INFO] Scanning for conjecture ...
% 1.82/1.21 % [INFO] Found a conjecture and 14 axioms. Running axiom selection ...
% 1.82/1.23 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 1.91/1.25 % [INFO] Problem is propositional (TPTP CNF).
% 1.91/1.26 % [INFO] Type checking passed.
% 1.91/1.26 % [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 ...
% 2.99/1.63 % External prover 'e' found a proof!
% 2.99/1.63 % [INFO] Killing All external provers ...
% 2.99/1.63 % Time passed: 1118ms (effective reasoning time: 673ms)
% 2.99/1.63 % 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)>
% 2.99/1.63 % Axioms used in derivation (14): mp_first_movers_exist_31, mp_greater_or_equal_38, mp_subpopulations_33, mp_non_empty_fm_and_ep_30, mp_greater_or_equal_36, mp_subpopulations_32, mp1_high_growth_rates_28, mp_greater_or_equal_37, mp2_favour_members_29, t6_41, mp_greater_transitivity_35, mp_critical_point_after_EP_34, d1_40, d1_39
% 2.99/1.63 % No. of inferences in proof: 37
% 2.99/1.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1118 ms resp. 673 ms w/o parsing
% 3.26/1.70 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.26/1.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------