TSTP Solution File: MGT026+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : MGT026+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n028.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 : Wed Jul 27 13:06:04 EDT 2022
% Result : Theorem 1.76s 1.98s
% Output : Refutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of clauses : 32 ( 16 unt; 5 nHn; 31 RR)
% Number of literals : 68 ( 6 equ; 32 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| selection_favors(C,B,D) ),
file('MGT026+1.p',unknown),
[] ).
cnf(2,axiom,
( ~ 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('MGT026+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ 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('MGT026+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ environment(A)
| ~ in_environment(A,B)
| greater_or_e_qual(cardinality_at_time(first_movers,B),zero) ),
file('MGT026+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ environment(A)
| ~ in_environment(A,B)
| subpopulation(first_movers,A,B) ),
file('MGT026+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ environment(A)
| ~ in_environment(A,B)
| subpopulation(efficient_producers,A,B) ),
file('MGT026+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ environment(A)
| greater_or_e_qual(critical_point(A),appear(efficient_producers,A)) ),
file('MGT026+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ greater(A,B)
| ~ greater(B,C)
| greater(A,C) ),
file('MGT026+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ greater_or_e_qual(A,B)
| greater(A,B)
| A = B ),
file('MGT026+1.p',unknown),
[] ).
cnf(10,axiom,
( greater_or_e_qual(A,B)
| ~ greater(A,B) ),
file('MGT026+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ 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('MGT026+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ environment(A)
| ~ in_environment(A,B)
| ~ greater_or_e_qual(B,appear(efficient_producers,A))
| greater(cardinality_at_time(efficient_producers,B),zero) ),
file('MGT026+1.p',unknown),
[] ).
cnf(15,axiom,
~ selection_favors(efficient_producers,first_movers,dollar_c1),
file('MGT026+1.p',unknown),
[] ).
cnf(17,axiom,
A = A,
file('MGT026+1.p',unknown),
[] ).
cnf(18,axiom,
environment(dollar_c2),
file('MGT026+1.p',unknown),
[] ).
cnf(19,axiom,
in_environment(dollar_c2,dollar_c1),
file('MGT026+1.p',unknown),
[] ).
cnf(20,axiom,
greater(dollar_c1,critical_point(dollar_c2)),
file('MGT026+1.p',unknown),
[] ).
cnf(22,plain,
greater_or_e_qual(critical_point(dollar_c2),appear(efficient_producers,dollar_c2)),
inference(hyper,[status(thm)],[18,7]),
[iquote('hyper,18,7')] ).
cnf(24,plain,
subpopulation(efficient_producers,dollar_c2,dollar_c1),
inference(hyper,[status(thm)],[19,6,18]),
[iquote('hyper,19,6,18')] ).
cnf(25,plain,
subpopulation(first_movers,dollar_c2,dollar_c1),
inference(hyper,[status(thm)],[19,5,18]),
[iquote('hyper,19,5,18')] ).
cnf(26,plain,
greater_or_e_qual(cardinality_at_time(first_movers,dollar_c1),zero),
inference(hyper,[status(thm)],[19,4,18]),
[iquote('hyper,19,4,18')] ).
cnf(32,plain,
( greater(dollar_c1,A)
| ~ greater_or_e_qual(critical_point(dollar_c2),A)
| greater(critical_point(dollar_c2),A) ),
inference(para_into,[status(thm),theory(equality)],[20,9]),
[iquote('para_into,20.1.2,9.3.1')] ).
cnf(48,plain,
( greater(cardinality_at_time(first_movers,dollar_c1),zero)
| cardinality_at_time(first_movers,dollar_c1) = zero ),
inference(hyper,[status(thm)],[26,9]),
[iquote('hyper,26,9')] ).
cnf(67,plain,
( greater(dollar_c1,appear(efficient_producers,dollar_c2))
| greater(critical_point(dollar_c2),appear(efficient_producers,dollar_c2)) ),
inference(hyper,[status(thm)],[32,22]),
[iquote('hyper,32,22')] ).
cnf(156,plain,
greater(dollar_c1,appear(efficient_producers,dollar_c2)),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[67,8,20])]),
[iquote('hyper,67,8,20,factor_simp')] ).
cnf(157,plain,
greater_or_e_qual(dollar_c1,appear(efficient_producers,dollar_c2)),
inference(hyper,[status(thm)],[156,10]),
[iquote('hyper,156,10')] ).
cnf(162,plain,
greater(cardinality_at_time(efficient_producers,dollar_c1),zero),
inference(hyper,[status(thm)],[157,14,18,19]),
[iquote('hyper,157,14,18,19')] ).
cnf(173,plain,
( subpopulations(first_movers,efficient_producers,dollar_c2,dollar_c1)
| cardinality_at_time(first_movers,dollar_c1) = zero ),
inference(hyper,[status(thm)],[162,3,18,19,48]),
[iquote('hyper,162,3,18,19,48')] ).
cnf(182,plain,
subpopulations(first_movers,efficient_producers,dollar_c2,dollar_c1),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[173,2,18,24,25,162]),15]),
[iquote('hyper,173,2,18,24,25,162,unit_del,15')] ).
cnf(183,plain,
greater(growth_rate(efficient_producers,dollar_c1),growth_rate(first_movers,dollar_c1)),
inference(hyper,[status(thm)],[182,13,18,17,20]),
[iquote('hyper,182,13,18,17,20')] ).
cnf(193,plain,
selection_favors(efficient_producers,first_movers,dollar_c1),
inference(hyper,[status(thm)],[183,1,18,182]),
[iquote('hyper,183,1,18,182')] ).
cnf(194,plain,
$false,
inference(binary,[status(thm)],[193,15]),
[iquote('binary,193.1,15.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MGT026+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 04:12:03 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.76/1.97 ----- Otter 3.3f, August 2004 -----
% 1.76/1.97 The process was started by sandbox on n028.cluster.edu,
% 1.76/1.97 Wed Jul 27 04:12:03 2022
% 1.76/1.97 The command was "./otter". The process ID is 17852.
% 1.76/1.97
% 1.76/1.97 set(prolog_style_variables).
% 1.76/1.97 set(auto).
% 1.76/1.97 dependent: set(auto1).
% 1.76/1.97 dependent: set(process_input).
% 1.76/1.97 dependent: clear(print_kept).
% 1.76/1.97 dependent: clear(print_new_demod).
% 1.76/1.97 dependent: clear(print_back_demod).
% 1.76/1.97 dependent: clear(print_back_sub).
% 1.76/1.97 dependent: set(control_memory).
% 1.76/1.97 dependent: assign(max_mem, 12000).
% 1.76/1.97 dependent: assign(pick_given_ratio, 4).
% 1.76/1.97 dependent: assign(stats_level, 1).
% 1.76/1.97 dependent: assign(max_seconds, 10800).
% 1.76/1.97 clear(print_given).
% 1.76/1.97
% 1.76/1.97 formula_list(usable).
% 1.76/1.97 all A (A=A).
% 1.76/1.97 all E S1 S2 T (environment(E)&subpopulations(S1,S2,E,T)&greater(growth_rate(S2,T),growth_rate(S1,T))->selection_favors(S2,S1,T)).
% 1.76/1.97 all E S1 S2 T (environment(E)&subpopulation(S1,E,T)&subpopulation(S2,E,T)&greater(cardinality_at_time(S1,T),zero)&cardinality_at_time(S2,T)=zero->selection_favors(S1,S2,T)).
% 1.76/1.97 all E T (environment(E)&in_environment(E,T)&greater(cardinality_at_time(first_movers,T),zero)&greater(cardinality_at_time(efficient_producers,T),zero)->subpopulations(first_movers,efficient_producers,E,T)).
% 1.76/1.97 all E T (environment(E)&in_environment(E,T)->greater_or_e_qual(cardinality_at_time(first_movers,T),zero)).
% 1.76/1.97 all E T (environment(E)&in_environment(E,T)->subpopulation(first_movers,E,T)&subpopulation(efficient_producers,E,T)).
% 1.76/1.97 all E (environment(E)->greater_or_e_qual(critical_point(E),appear(efficient_producers,E))).
% 1.76/1.97 all X Y Z (greater(X,Y)&greater(Y,Z)->greater(X,Z)).
% 1.76/1.97 all X Y (greater_or_e_qual(X,Y)<->greater(X,Y)|X=Y).
% 1.76/1.97 all E Tc (environment(E)&Tc=critical_point(E)-> -greater(growth_rate(efficient_producers,Tc),growth_rate(first_movers,Tc))& (all T (subpopulations(first_movers,efficient_producers,E,T)&greater(T,Tc)->greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))))).
% 1.76/1.97 all E T (environment(E)&in_environment(E,T)&greater_or_e_qual(T,appear(efficient_producers,E))->greater(cardinality_at_time(efficient_producers,T),zero)).
% 1.76/1.97 -(all E T (environment(E)&in_environment(E,T)&greater(T,critical_point(E))->selection_favors(efficient_producers,first_movers,T))).
% 1.76/1.97 end_of_list.
% 1.76/1.97
% 1.76/1.97 -------> usable clausifies to:
% 1.76/1.97
% 1.76/1.97 list(usable).
% 1.76/1.97 0 [] A=A.
% 1.76/1.97 0 [] -environment(E)| -subpopulations(S1,S2,E,T)| -greater(growth_rate(S2,T),growth_rate(S1,T))|selection_favors(S2,S1,T).
% 1.76/1.97 0 [] -environment(E)| -subpopulation(S1,E,T)| -subpopulation(S2,E,T)| -greater(cardinality_at_time(S1,T),zero)|cardinality_at_time(S2,T)!=zero|selection_favors(S1,S2,T).
% 1.76/1.97 0 [] -environment(E)| -in_environment(E,T)| -greater(cardinality_at_time(first_movers,T),zero)| -greater(cardinality_at_time(efficient_producers,T),zero)|subpopulations(first_movers,efficient_producers,E,T).
% 1.76/1.97 0 [] -environment(E)| -in_environment(E,T)|greater_or_e_qual(cardinality_at_time(first_movers,T),zero).
% 1.76/1.97 0 [] -environment(E)| -in_environment(E,T)|subpopulation(first_movers,E,T).
% 1.76/1.97 0 [] -environment(E)| -in_environment(E,T)|subpopulation(efficient_producers,E,T).
% 1.76/1.97 0 [] -environment(E)|greater_or_e_qual(critical_point(E),appear(efficient_producers,E)).
% 1.76/1.97 0 [] -greater(X,Y)| -greater(Y,Z)|greater(X,Z).
% 1.76/1.97 0 [] -greater_or_e_qual(X,Y)|greater(X,Y)|X=Y.
% 1.76/1.97 0 [] greater_or_e_qual(X,Y)| -greater(X,Y).
% 1.76/1.97 0 [] greater_or_e_qual(X,Y)|X!=Y.
% 1.76/1.97 0 [] -environment(E)|Tc!=critical_point(E)| -greater(growth_rate(efficient_producers,Tc),growth_rate(first_movers,Tc)).
% 1.76/1.97 0 [] -environment(E)|Tc!=critical_point(E)| -subpopulations(first_movers,efficient_producers,E,T)| -greater(T,Tc)|greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)).
% 1.76/1.97 0 [] -environment(E)| -in_environment(E,T)| -greater_or_e_qual(T,appear(efficient_producers,E))|greater(cardinality_at_time(efficient_producers,T),zero).
% 1.76/1.97 0 [] environment($c2).
% 1.76/1.97 0 [] in_environment($c2,$c1).
% 1.76/1.97 0 [] greater($c1,critical_point($c2)).
% 1.76/1.97 0 [] -selection_favors(efficient_producers,first_movers,$c1).
% 1.76/1.97 end_of_list.
% 1.76/1.97
% 1.76/1.97 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 1.76/1.97
% 1.76/1.97 This ia a non-Horn set with equality. The strategy will be
% 1.76/1.97 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.76/1.97 deletion, with positive clauses in sos and nonpositive
% 1.76/1.98 clauses in usable.
% 1.76/1.98
% 1.76/1.98 dependent: set(knuth_bendix).
% 1.76/1.98 dependent: set(anl_eq).
% 1.76/1.98 dependent: set(para_from).
% 1.76/1.98 dependent: set(para_into).
% 1.76/1.98 dependent: clear(para_from_right).
% 1.76/1.98 dependent: clear(para_into_right).
% 1.76/1.98 dependent: set(para_from_vars).
% 1.76/1.98 dependent: set(eq_units_both_ways).
% 1.76/1.98 dependent: set(dynamic_demod_all).
% 1.76/1.98 dependent: set(dynamic_demod).
% 1.76/1.98 dependent: set(order_eq).
% 1.76/1.98 dependent: set(back_demod).
% 1.76/1.98 dependent: set(lrpo).
% 1.76/1.98 dependent: set(hyper_res).
% 1.76/1.98 dependent: set(unit_deletion).
% 1.76/1.98 dependent: set(factor).
% 1.76/1.98
% 1.76/1.98 ------------> process usable:
% 1.76/1.98 ** KEPT (pick-wt=18): 1 [] -environment(A)| -subpopulations(B,C,A,D)| -greater(growth_rate(C,D),growth_rate(B,D))|selection_favors(C,B,D).
% 1.76/1.98 ** KEPT (pick-wt=24): 2 [] -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).
% 1.76/1.98 ** KEPT (pick-wt=20): 3 [] -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).
% 1.76/1.98 ** KEPT (pick-wt=10): 4 [] -environment(A)| -in_environment(A,B)|greater_or_e_qual(cardinality_at_time(first_movers,B),zero).
% 1.76/1.98 ** KEPT (pick-wt=9): 5 [] -environment(A)| -in_environment(A,B)|subpopulation(first_movers,A,B).
% 1.76/1.98 ** KEPT (pick-wt=9): 6 [] -environment(A)| -in_environment(A,B)|subpopulation(efficient_producers,A,B).
% 1.76/1.98 ** KEPT (pick-wt=8): 7 [] -environment(A)|greater_or_e_qual(critical_point(A),appear(efficient_producers,A)).
% 1.76/1.98 ** KEPT (pick-wt=9): 8 [] -greater(A,B)| -greater(B,C)|greater(A,C).
% 1.76/1.98 ** KEPT (pick-wt=9): 9 [] -greater_or_e_qual(A,B)|greater(A,B)|A=B.
% 1.76/1.98 ** KEPT (pick-wt=6): 10 [] greater_or_e_qual(A,B)| -greater(A,B).
% 1.76/1.98 ** KEPT (pick-wt=6): 11 [] greater_or_e_qual(A,B)|A!=B.
% 1.76/1.98 ** KEPT (pick-wt=13): 12 [] -environment(A)|B!=critical_point(A)| -greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)).
% 1.76/1.98 ** KEPT (pick-wt=21): 13 [] -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)).
% 1.76/1.98 ** KEPT (pick-wt=15): 14 [] -environment(A)| -in_environment(A,B)| -greater_or_e_qual(B,appear(efficient_producers,A))|greater(cardinality_at_time(efficient_producers,B),zero).
% 1.76/1.98 ** KEPT (pick-wt=4): 15 [] -selection_favors(efficient_producers,first_movers,$c1).
% 1.76/1.98
% 1.76/1.98 ------------> process sos:
% 1.76/1.98 ** KEPT (pick-wt=3): 17 [] A=A.
% 1.76/1.98 ** KEPT (pick-wt=2): 18 [] environment($c2).
% 1.76/1.98 ** KEPT (pick-wt=3): 19 [] in_environment($c2,$c1).
% 1.76/1.98 ** KEPT (pick-wt=4): 20 [] greater($c1,critical_point($c2)).
% 1.76/1.98 Following clause subsumed by 17 during input processing: 0 [copy,17,flip.1] A=A.
% 1.76/1.98
% 1.76/1.98 ======= end of input processing =======
% 1.76/1.98
% 1.76/1.98 =========== start of search ===========
% 1.76/1.98
% 1.76/1.98 -------- PROOF --------
% 1.76/1.98
% 1.76/1.98 ----> UNIT CONFLICT at 0.01 sec ----> 194 [binary,193.1,15.1] $F.
% 1.76/1.98
% 1.76/1.98 Length of proof is 14. Level of proof is 9.
% 1.76/1.98
% 1.76/1.98 ---------------- PROOF ----------------
% 1.76/1.98 % SZS status Theorem
% 1.76/1.98 % SZS output start Refutation
% See solution above
% 1.76/1.98 ------------ end of proof -------------
% 1.76/1.98
% 1.76/1.98
% 1.76/1.98 Search stopped by max_proofs option.
% 1.76/1.98
% 1.76/1.98
% 1.76/1.98 Search stopped by max_proofs option.
% 1.76/1.98
% 1.76/1.98 ============ end of search ============
% 1.76/1.98
% 1.76/1.98 -------------- statistics -------------
% 1.76/1.98 clauses given 42
% 1.76/1.98 clauses generated 364
% 1.76/1.98 clauses kept 193
% 1.76/1.98 clauses forward subsumed 187
% 1.76/1.98 clauses back subsumed 6
% 1.76/1.98 Kbytes malloced 976
% 1.76/1.98
% 1.76/1.98 ----------- times (seconds) -----------
% 1.76/1.98 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.76/1.98 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.76/1.98 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.76/1.98
% 1.76/1.98 That finishes the proof of the theorem.
% 1.76/1.98
% 1.76/1.98 Process 17852 finished Wed Jul 27 04:12:05 2022
% 1.76/1.98 Otter interrupted
% 1.76/1.98 PROOF FOUND
%------------------------------------------------------------------------------