TSTP Solution File: MGT036+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : MGT036+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n010.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 13:06:07 EDT 2022
% Result : Theorem 1.62s 1.81s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 10
% Syntax : Number of clauses : 16 ( 10 unt; 0 nHn; 16 RR)
% Number of literals : 31 ( 0 equ; 16 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| subpopulations(efficient_producers,first_movers,A,B) ),
file('MGT036+1.p',unknown),
[] ).
cnf(2,axiom,
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| in_environment(A,B) ),
file('MGT036+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ greater_or_e_qual(growth_rate(A,B),zero)
| ~ greater(zero,growth_rate(A,B)) ),
file('MGT036+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| greater_or_e_qual(growth_rate(C,D),zero)
| ~ outcompetes(C,B,D) ),
file('MGT036+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| greater(zero,growth_rate(B,D))
| ~ outcompetes(C,B,D) ),
file('MGT036+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ environment(A)
| ~ in_environment(A,B)
| greater(zero,growth_rate(C,B))
| ~ greater(resilience(D),resilience(C))
| ~ greater(zero,growth_rate(D,B)) ),
file('MGT036+1.p',unknown),
[] ).
cnf(11,axiom,
greater(resilience(efficient_producers),resilience(first_movers)),
file('MGT036+1.p',unknown),
[] ).
cnf(12,axiom,
environment(dollar_c2),
file('MGT036+1.p',unknown),
[] ).
cnf(13,axiom,
subpopulations(first_movers,efficient_producers,dollar_c2,dollar_c1),
file('MGT036+1.p',unknown),
[] ).
cnf(14,axiom,
outcompetes(first_movers,efficient_producers,dollar_c1),
file('MGT036+1.p',unknown),
[] ).
cnf(16,plain,
in_environment(dollar_c2,dollar_c1),
inference(hyper,[status(thm)],[13,2,12]),
[iquote('hyper,13,2,12')] ).
cnf(17,plain,
subpopulations(efficient_producers,first_movers,dollar_c2,dollar_c1),
inference(hyper,[status(thm)],[13,1,12]),
[iquote('hyper,13,1,12')] ).
cnf(18,plain,
greater(zero,growth_rate(efficient_producers,dollar_c1)),
inference(hyper,[status(thm)],[17,9,12,14]),
[iquote('hyper,17,9,12,14')] ).
cnf(19,plain,
greater_or_e_qual(growth_rate(first_movers,dollar_c1),zero),
inference(hyper,[status(thm)],[17,8,12,14]),
[iquote('hyper,17,8,12,14')] ).
cnf(20,plain,
greater(zero,growth_rate(first_movers,dollar_c1)),
inference(hyper,[status(thm)],[18,10,12,16,11]),
[iquote('hyper,18,10,12,16,11')] ).
cnf(23,plain,
$false,
inference(hyper,[status(thm)],[20,5,19]),
[iquote('hyper,20,5,19')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : MGT036+1 : TPTP v8.1.0. Released v2.0.0.
% 0.04/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n010.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 03:53:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.62/1.81 ----- Otter 3.3f, August 2004 -----
% 1.62/1.81 The process was started by sandbox on n010.cluster.edu,
% 1.62/1.81 Wed Jul 27 03:53:55 2022
% 1.62/1.81 The command was "./otter". The process ID is 19972.
% 1.62/1.81
% 1.62/1.81 set(prolog_style_variables).
% 1.62/1.81 set(auto).
% 1.62/1.81 dependent: set(auto1).
% 1.62/1.81 dependent: set(process_input).
% 1.62/1.81 dependent: clear(print_kept).
% 1.62/1.81 dependent: clear(print_new_demod).
% 1.62/1.81 dependent: clear(print_back_demod).
% 1.62/1.81 dependent: clear(print_back_sub).
% 1.62/1.81 dependent: set(control_memory).
% 1.62/1.81 dependent: assign(max_mem, 12000).
% 1.62/1.81 dependent: assign(pick_given_ratio, 4).
% 1.62/1.81 dependent: assign(stats_level, 1).
% 1.62/1.81 dependent: assign(max_seconds, 10800).
% 1.62/1.81 clear(print_given).
% 1.62/1.81
% 1.62/1.81 formula_list(usable).
% 1.62/1.81 all E T (environment(E)&subpopulations(first_movers,efficient_producers,E,T)->subpopulations(efficient_producers,first_movers,E,T)).
% 1.62/1.81 all E T (environment(E)&subpopulations(first_movers,efficient_producers,E,T)->in_environment(E,T)).
% 1.62/1.81 all E S1 S2 T ((environment(E)&subpopulations(S1,S2,E,T)->greater_or_e_qual(growth_rate(S1,T),zero))<-> -greater(zero,growth_rate(S1,T))).
% 1.62/1.81 all E S1 S2 T (environment(E)&subpopulations(S1,S2,E,T)-> (greater_or_e_qual(growth_rate(S2,T),zero)&greater(zero,growth_rate(S1,T))<->outcompetes(S2,S1,T))).
% 1.62/1.81 all E S1 S2 T (environment(E)&in_environment(E,T)& -greater(zero,growth_rate(S1,T))&greater(resilience(S2),resilience(S1))-> -greater(zero,growth_rate(S2,T))).
% 1.62/1.81 greater(resilience(efficient_producers),resilience(first_movers)).
% 1.62/1.81 -(all E T (environment(E)&subpopulations(first_movers,efficient_producers,E,T)-> -outcompetes(first_movers,efficient_producers,T))).
% 1.62/1.81 end_of_list.
% 1.62/1.81
% 1.62/1.81 -------> usable clausifies to:
% 1.62/1.81
% 1.62/1.81 list(usable).
% 1.62/1.81 0 [] -environment(E)| -subpopulations(first_movers,efficient_producers,E,T)|subpopulations(efficient_producers,first_movers,E,T).
% 1.62/1.81 0 [] -environment(E)| -subpopulations(first_movers,efficient_producers,E,T)|in_environment(E,T).
% 1.62/1.81 0 [] environment(E)| -greater(zero,growth_rate(S1,T)).
% 1.62/1.81 0 [] subpopulations(S1,S2,E,T)| -greater(zero,growth_rate(S1,T)).
% 1.62/1.81 0 [] -greater_or_e_qual(growth_rate(S1,T),zero)| -greater(zero,growth_rate(S1,T)).
% 1.62/1.81 0 [] -environment(E)| -subpopulations(S1,S2,E,T)|greater_or_e_qual(growth_rate(S1,T),zero)|greater(zero,growth_rate(S1,T)).
% 1.62/1.81 0 [] -environment(E)| -subpopulations(S1,S2,E,T)| -greater_or_e_qual(growth_rate(S2,T),zero)| -greater(zero,growth_rate(S1,T))|outcompetes(S2,S1,T).
% 1.62/1.81 0 [] -environment(E)| -subpopulations(S1,S2,E,T)|greater_or_e_qual(growth_rate(S2,T),zero)| -outcompetes(S2,S1,T).
% 1.62/1.81 0 [] -environment(E)| -subpopulations(S1,S2,E,T)|greater(zero,growth_rate(S1,T))| -outcompetes(S2,S1,T).
% 1.62/1.81 0 [] -environment(E)| -in_environment(E,T)|greater(zero,growth_rate(S1,T))| -greater(resilience(S2),resilience(S1))| -greater(zero,growth_rate(S2,T)).
% 1.62/1.81 0 [] greater(resilience(efficient_producers),resilience(first_movers)).
% 1.62/1.81 0 [] environment($c2).
% 1.62/1.81 0 [] subpopulations(first_movers,efficient_producers,$c2,$c1).
% 1.62/1.81 0 [] outcompetes(first_movers,efficient_producers,$c1).
% 1.62/1.81 end_of_list.
% 1.62/1.81
% 1.62/1.81 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.62/1.81
% 1.62/1.81 This is a non-Horn set without equality. The strategy will
% 1.62/1.81 be ordered hyper_res, unit deletion, and factoring, with
% 1.62/1.81 satellites in sos and with nuclei in usable.
% 1.62/1.81
% 1.62/1.81 dependent: set(hyper_res).
% 1.62/1.81 dependent: set(factor).
% 1.62/1.81 dependent: set(unit_deletion).
% 1.62/1.81
% 1.62/1.81 ------------> process usable:
% 1.62/1.81 ** KEPT (pick-wt=12): 1 [] -environment(A)| -subpopulations(first_movers,efficient_producers,A,B)|subpopulations(efficient_producers,first_movers,A,B).
% 1.62/1.81 ** KEPT (pick-wt=10): 2 [] -environment(A)| -subpopulations(first_movers,efficient_producers,A,B)|in_environment(A,B).
% 1.62/1.81 ** KEPT (pick-wt=7): 3 [] environment(A)| -greater(zero,growth_rate(B,C)).
% 1.62/1.81 ** KEPT (pick-wt=10): 4 [] subpopulations(A,B,C,D)| -greater(zero,growth_rate(A,D)).
% 1.62/1.81 ** KEPT (pick-wt=10): 5 [] -greater_or_e_qual(growth_rate(A,B),zero)| -greater(zero,growth_rate(A,B)).
% 1.62/1.81 ** KEPT (pick-wt=17): 6 [] -environment(A)| -subpopulations(B,C,A,D)|greater_or_e_qual(growth_rate(B,D),zero)|greater(zero,growth_rate(B,D)).
% 1.62/1.81 ** KEPT (pick-wt=21): 7 [] -environment(A)| -subpopulations(B,C,A,D)| -greater_or_e_qual(growth_rate(C,D),zero)| -greater(zero,growth_rate(B,D))|outcompetes(C,B,D).
% 1.62/1.81 ** KEPT (pick-wt=16): 8 [] -environment(A)| -subpopulations(B,C,A,D)|greater_or_e_qual(growth_rate(C,D),zero)| -outcompetes(C,B,D).
% 1.62/1.81 ** KEPT (pick-wt=16): 9 [] -environment(A)| -subpopulations(B,C,A,D)|greater(zero,growth_rate(B,D))| -outcompetes(C,B,D).
% 1.62/1.81 ** KEPT (pick-wt=20): 10 [] -environment(A)| -in_environment(A,B)|greater(zero,growth_rate(C,B))| -greater(resilience(D),resilience(C))| -greater(zero,growth_rate(D,B)).
% 1.62/1.81
% 1.62/1.81 ------------> process sos:
% 1.62/1.81 ** KEPT (pick-wt=5): 11 [] greater(resilience(efficient_producers),resilience(first_movers)).
% 1.62/1.81 ** KEPT (pick-wt=2): 12 [] environment($c2).
% 1.62/1.81 ** KEPT (pick-wt=5): 13 [] subpopulations(first_movers,efficient_producers,$c2,$c1).
% 1.62/1.81 ** KEPT (pick-wt=4): 14 [] outcompetes(first_movers,efficient_producers,$c1).
% 1.62/1.81
% 1.62/1.81 ======= end of input processing =======
% 1.62/1.81
% 1.62/1.81 =========== start of search ===========
% 1.62/1.81
% 1.62/1.81 -------- PROOF --------
% 1.62/1.81
% 1.62/1.81 -----> EMPTY CLAUSE at 0.00 sec ----> 23 [hyper,20,5,19] $F.
% 1.62/1.81
% 1.62/1.81 Length of proof is 5. Level of proof is 3.
% 1.62/1.81
% 1.62/1.81 ---------------- PROOF ----------------
% 1.62/1.81 % SZS status Theorem
% 1.62/1.81 % SZS output start Refutation
% See solution above
% 1.62/1.81 ------------ end of proof -------------
% 1.62/1.81
% 1.62/1.81
% 1.62/1.81 Search stopped by max_proofs option.
% 1.62/1.81
% 1.62/1.81
% 1.62/1.81 Search stopped by max_proofs option.
% 1.62/1.81
% 1.62/1.81 ============ end of search ============
% 1.62/1.81
% 1.62/1.81 -------------- statistics -------------
% 1.62/1.81 clauses given 11
% 1.62/1.81 clauses generated 14
% 1.62/1.81 clauses kept 22
% 1.62/1.81 clauses forward subsumed 5
% 1.62/1.81 clauses back subsumed 4
% 1.62/1.81 Kbytes malloced 976
% 1.62/1.81
% 1.62/1.81 ----------- times (seconds) -----------
% 1.62/1.81 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.62/1.81 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.62/1.81 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.62/1.81
% 1.62/1.81 That finishes the proof of the theorem.
% 1.62/1.81
% 1.62/1.81 Process 19972 finished Wed Jul 27 03:53:56 2022
% 1.62/1.81 Otter interrupted
% 1.62/1.81 PROOF FOUND
%------------------------------------------------------------------------------