TSTP Solution File: MGT032+2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : MGT032+2 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n021.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 13:06:05 EDT 2022
% Result : Theorem 1.70s 1.90s
% Output : Refutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 14 ( 8 unt; 0 nHn; 14 RR)
% Number of literals : 26 ( 0 equ; 13 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 10 ( 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('MGT032+2.p',unknown),
[] ).
cnf(2,axiom,
( ~ environment(A)
| ~ stable(A)
| in_environment(A,dollar_f1(A)) ),
file('MGT032+2.p',unknown),
[] ).
cnf(3,axiom,
( ~ environment(A)
| ~ stable(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ greater_or_e_qual(B,dollar_f1(A))
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)) ),
file('MGT032+2.p',unknown),
[] ).
cnf(4,axiom,
( ~ in_environment(dollar_c1,A)
| subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f2(A)) ),
file('MGT032+2.p',unknown),
[] ).
cnf(5,axiom,
( ~ in_environment(dollar_c1,A)
| greater_or_e_qual(dollar_f2(A),A) ),
file('MGT032+2.p',unknown),
[] ).
cnf(6,axiom,
( ~ in_environment(dollar_c1,A)
| ~ selection_favors(efficient_producers,first_movers,dollar_f2(A)) ),
file('MGT032+2.p',unknown),
[] ).
cnf(7,axiom,
environment(dollar_c1),
file('MGT032+2.p',unknown),
[] ).
cnf(8,axiom,
stable(dollar_c1),
file('MGT032+2.p',unknown),
[] ).
cnf(9,plain,
in_environment(dollar_c1,dollar_f1(dollar_c1)),
inference(hyper,[status(thm)],[8,2,7]),
[iquote('hyper,8,2,7')] ).
cnf(10,plain,
greater_or_e_qual(dollar_f2(dollar_f1(dollar_c1)),dollar_f1(dollar_c1)),
inference(hyper,[status(thm)],[9,5]),
[iquote('hyper,9,5')] ).
cnf(11,plain,
subpopulations(first_movers,efficient_producers,dollar_c1,dollar_f2(dollar_f1(dollar_c1))),
inference(hyper,[status(thm)],[9,4]),
[iquote('hyper,9,4')] ).
cnf(12,plain,
greater(growth_rate(efficient_producers,dollar_f2(dollar_f1(dollar_c1))),growth_rate(first_movers,dollar_f2(dollar_f1(dollar_c1)))),
inference(hyper,[status(thm)],[11,3,7,8,10]),
[iquote('hyper,11,3,7,8,10')] ).
cnf(13,plain,
selection_favors(efficient_producers,first_movers,dollar_f2(dollar_f1(dollar_c1))),
inference(hyper,[status(thm)],[12,1,7,11]),
[iquote('hyper,12,1,7,11')] ).
cnf(14,plain,
$false,
inference(hyper,[status(thm)],[13,6,9]),
[iquote('hyper,13,6,9')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : MGT032+2 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 03:58:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.70/1.90 ----- Otter 3.3f, August 2004 -----
% 1.70/1.90 The process was started by sandbox on n021.cluster.edu,
% 1.70/1.90 Wed Jul 27 03:58:23 2022
% 1.70/1.90 The command was "./otter". The process ID is 32254.
% 1.70/1.90
% 1.70/1.90 set(prolog_style_variables).
% 1.70/1.90 set(auto).
% 1.70/1.90 dependent: set(auto1).
% 1.70/1.90 dependent: set(process_input).
% 1.70/1.90 dependent: clear(print_kept).
% 1.70/1.90 dependent: clear(print_new_demod).
% 1.70/1.90 dependent: clear(print_back_demod).
% 1.70/1.90 dependent: clear(print_back_sub).
% 1.70/1.90 dependent: set(control_memory).
% 1.70/1.90 dependent: assign(max_mem, 12000).
% 1.70/1.90 dependent: assign(pick_given_ratio, 4).
% 1.70/1.90 dependent: assign(stats_level, 1).
% 1.70/1.90 dependent: assign(max_seconds, 10800).
% 1.70/1.90 clear(print_given).
% 1.70/1.90
% 1.70/1.90 formula_list(usable).
% 1.70/1.90 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)).
% 1.70/1.90 all E (environment(E)&stable(E)-> (exists To (in_environment(E,To)& (all T (subpopulations(first_movers,efficient_producers,E,T)&greater_or_e_qual(T,To)->greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))))))).
% 1.70/1.90 -(all E (environment(E)&stable(E)-> (exists To (in_environment(E,To)& (all T (subpopulations(first_movers,efficient_producers,E,T)&greater_or_e_qual(T,To)->selection_favors(efficient_producers,first_movers,T))))))).
% 1.70/1.90 end_of_list.
% 1.70/1.90
% 1.70/1.90 -------> usable clausifies to:
% 1.70/1.90
% 1.70/1.90 list(usable).
% 1.70/1.90 0 [] -environment(E)| -subpopulations(S1,S2,E,T)| -greater(growth_rate(S2,T),growth_rate(S1,T))|selection_favors(S2,S1,T).
% 1.70/1.90 0 [] -environment(E)| -stable(E)|in_environment(E,$f1(E)).
% 1.70/1.90 0 [] -environment(E)| -stable(E)| -subpopulations(first_movers,efficient_producers,E,T)| -greater_or_e_qual(T,$f1(E))|greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)).
% 1.70/1.90 0 [] environment($c1).
% 1.70/1.90 0 [] stable($c1).
% 1.70/1.90 0 [] -in_environment($c1,To)|subpopulations(first_movers,efficient_producers,$c1,$f2(To)).
% 1.70/1.90 0 [] -in_environment($c1,To)|greater_or_e_qual($f2(To),To).
% 1.70/1.90 0 [] -in_environment($c1,To)| -selection_favors(efficient_producers,first_movers,$f2(To)).
% 1.70/1.90 end_of_list.
% 1.70/1.90
% 1.70/1.90 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=5.
% 1.70/1.90
% 1.70/1.90 This is a Horn set without equality. The strategy will
% 1.70/1.90 be hyperresolution, with satellites in sos and nuclei
% 1.70/1.90 in usable.
% 1.70/1.90
% 1.70/1.90 dependent: set(hyper_res).
% 1.70/1.90 dependent: clear(order_hyper).
% 1.70/1.90
% 1.70/1.90 ------------> process usable:
% 1.70/1.90 ** 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).
% 1.70/1.90 ** KEPT (pick-wt=8): 2 [] -environment(A)| -stable(A)|in_environment(A,$f1(A)).
% 1.70/1.90 ** KEPT (pick-wt=20): 3 [] -environment(A)| -stable(A)| -subpopulations(first_movers,efficient_producers,A,B)| -greater_or_e_qual(B,$f1(A))|greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)).
% 1.70/1.90 ** KEPT (pick-wt=9): 4 [] -in_environment($c1,A)|subpopulations(first_movers,efficient_producers,$c1,$f2(A)).
% 1.70/1.90 ** KEPT (pick-wt=7): 5 [] -in_environment($c1,A)|greater_or_e_qual($f2(A),A).
% 1.70/1.90 ** KEPT (pick-wt=8): 6 [] -in_environment($c1,A)| -selection_favors(efficient_producers,first_movers,$f2(A)).
% 1.70/1.90
% 1.70/1.90 ------------> process sos:
% 1.70/1.90 ** KEPT (pick-wt=2): 7 [] environment($c1).
% 1.70/1.90 ** KEPT (pick-wt=2): 8 [] stable($c1).
% 1.70/1.90
% 1.70/1.90 ======= end of input processing =======
% 1.70/1.90
% 1.70/1.90 =========== start of search ===========
% 1.70/1.90
% 1.70/1.90 -------- PROOF --------
% 1.70/1.90
% 1.70/1.90 -----> EMPTY CLAUSE at 0.00 sec ----> 14 [hyper,13,6,9] $F.
% 1.70/1.90
% 1.70/1.90 Length of proof is 5. Level of proof is 4.
% 1.70/1.90
% 1.70/1.90 ---------------- PROOF ----------------
% 1.70/1.90 % SZS status Theorem
% 1.70/1.90 % SZS output start Refutation
% See solution above
% 1.70/1.90 ------------ end of proof -------------
% 1.70/1.90
% 1.70/1.90
% 1.70/1.90 Search stopped by max_proofs option.
% 1.70/1.90
% 1.70/1.90
% 1.70/1.90 Search stopped by max_proofs option.
% 1.70/1.90
% 1.70/1.90 ============ end of search ============
% 1.70/1.90
% 1.70/1.90 -------------- statistics -------------
% 1.70/1.90 clauses given 7
% 1.70/1.90 clauses generated 6
% 1.70/1.90 clauses kept 13
% 1.70/1.90 clauses forward subsumed 0
% 1.70/1.90 clauses back subsumed 0
% 1.70/1.90 Kbytes malloced 976
% 1.70/1.90
% 1.70/1.90 ----------- times (seconds) -----------
% 1.70/1.90 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.70/1.90 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.70/1.90 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.70/1.90
% 1.70/1.90 That finishes the proof of the theorem.
% 1.70/1.90
% 1.70/1.90 Process 32254 finished Wed Jul 27 03:58:24 2022
% 1.70/1.90 Otter interrupted
% 1.70/1.90 PROOF FOUND
%------------------------------------------------------------------------------