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 v2.0.0.
% 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 11:35:17 EDT 2023
% Result : Theorem 3.29s 1.81s
% Output : Refutation 3.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 25
% Syntax : Number of formulae : 38 ( 1 unt; 14 typ; 0 def)
% Number of atoms : 96 ( 7 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 323 ( 4 ~; 3 |; 43 &; 247 @)
% ( 1 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 4 con; 0-4 aty)
% Number of variables : 56 ( 0 ^; 56 !; 0 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(environment_type,type,
environment: $i > $o ).
thf(in_environment_type,type,
in_environment: $i > $i > $o ).
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(6,axiom,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( in_environment @ A @ B ) )
=> ( greater_or_equal @ ( cardinality_at_time @ first_movers @ B ) @ zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_exist) ).
thf(25,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)],[6]) ).
thf(4,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/sandbox/benchmark/theBenchmark.p',mp2_favour_members) ).
thf(20,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)],[4]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( in_environment @ A @ B )
& ( greater @ B @ ( critical_point @ A ) ) )
=> ( selection_favors @ efficient_producers @ first_movers @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l8) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( environment @ A )
& ( in_environment @ A @ B )
& ( greater @ B @ ( critical_point @ A ) ) )
=> ( selection_favors @ efficient_producers @ first_movers @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
~ ! [A: $i,B: $i] :
( ( ( environment @ A )
& ( in_environment @ A @ B )
& ( greater @ B @ ( critical_point @ A ) ) )
=> ( selection_favors @ efficient_producers @ first_movers @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ( in_environment @ A @ B ) )
=> ( ( subpopulation @ first_movers @ A @ B )
& ( subpopulation @ efficient_producers @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_subpopulations) ).
thf(27,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)],[7]) ).
thf(3,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/sandbox/benchmark/theBenchmark.p',mp1_high_growth_rates) ).
thf(18,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)],[3]) ).
thf(12,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/sandbox/benchmark/theBenchmark.p',t6) ).
thf(50,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)],[12]) ).
thf(11,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/sandbox/benchmark/theBenchmark.p',d1) ).
thf(43,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)],[11]) ).
thf(5,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/sandbox/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep) ).
thf(23,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)],[5]) ).
thf(8,axiom,
! [A: $i] :
( ( environment @ A )
=> ( greater_or_equal @ ( critical_point @ A ) @ ( appear @ efficient_producers @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_critical_point_after_EP) ).
thf(30,plain,
! [A: $i] :
( ( environment @ A )
=> ( greater_or_equal @ ( critical_point @ A ) @ ( appear @ efficient_producers @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( greater @ A @ B )
& ( greater @ B @ C ) )
=> ( greater @ A @ C ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal) ).
thf(34,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)],[10]) ).
thf(52,plain,
$false,
inference(e,[status(thm)],[25,20,13,27,18,50,43,23,30,32,34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MGT026+1 : TPTP v8.1.2. Released v2.0.0.
% 0.07/0.16 % 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/sandbox/benchmark/theBenchmark.p ...
% 1.36/0.99 % [INFO] Parsing done (132ms).
% 1.36/1.00 % [INFO] Running in sequential loop mode.
% 1.65/1.21 % [INFO] eprover registered as external prover.
% 1.65/1.21 % [INFO] cvc4 registered as external prover.
% 1.65/1.22 % [INFO] Scanning for conjecture ...
% 1.95/1.28 % [INFO] Found a conjecture and 10 axioms. Running axiom selection ...
% 1.95/1.31 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 1.95/1.33 % [INFO] Problem is first-order (TPTP FOF).
% 1.95/1.34 % [INFO] Type checking passed.
% 1.95/1.34 % [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 ...
% 3.17/1.76 % External prover 'e' found a proof!
% 3.17/1.76 % [INFO] Killing All external provers ...
% 3.29/1.81 % Time passed: 1281ms (effective reasoning time: 806ms)
% 3.29/1.81 % 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)>
% 3.29/1.81 % Axioms used in derivation (10): mp1_high_growth_rates, mp_subpopulations, t6, mp_non_empty_fm_and_ep, mp_first_movers_exist, mp_critical_point_after_EP, d1, mp_greater_transitivity, mp_greater_or_equal, mp2_favour_members
% 3.29/1.81 % No. of inferences in proof: 24
% 3.29/1.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1281 ms resp. 806 ms w/o parsing
% 3.57/1.85 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.57/1.85 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------