TSTP Solution File: MGT036+3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : MGT036+3 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n017.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 1.66s 1.88s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 7
% Syntax : Number of clauses : 10 ( 7 unt; 0 nHn; 10 RR)
% Number of literals : 18 ( 0 equ; 9 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| subpopulations(C,B,A,D) ),
file('MGT036+3.p',unknown),
[] ).
cnf(2,axiom,
( ~ 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) ),
file('MGT036+3.p',unknown),
[] ).
cnf(5,axiom,
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ outcompetes(first_movers,efficient_producers,B) ),
file('MGT036+3.p',unknown),
[] ).
cnf(6,axiom,
environment(dollar_c2),
file('MGT036+3.p',unknown),
[] ).
cnf(7,axiom,
subpopulations(first_movers,efficient_producers,dollar_c2,dollar_c1),
file('MGT036+3.p',unknown),
[] ).
cnf(8,axiom,
greater_or_e_qual(growth_rate(first_movers,dollar_c1),zero),
file('MGT036+3.p',unknown),
[] ).
cnf(9,axiom,
greater(zero,growth_rate(efficient_producers,dollar_c1)),
file('MGT036+3.p',unknown),
[] ).
cnf(10,plain,
subpopulations(efficient_producers,first_movers,dollar_c2,dollar_c1),
inference(hyper,[status(thm)],[7,1,6]),
[iquote('hyper,7,1,6')] ).
cnf(11,plain,
outcompetes(first_movers,efficient_producers,dollar_c1),
inference(hyper,[status(thm)],[10,2,6,8,9]),
[iquote('hyper,10,2,6,8,9')] ).
cnf(12,plain,
$false,
inference(hyper,[status(thm)],[11,5,6,7]),
[iquote('hyper,11,5,6,7')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : MGT036+3 : TPTP v8.1.0. Released v2.0.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n017.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 03:23:03 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.66/1.87 ----- Otter 3.3f, August 2004 -----
% 1.66/1.87 The process was started by sandbox2 on n017.cluster.edu,
% 1.66/1.87 Wed Jul 27 03:23:03 2022
% 1.66/1.87 The command was "./otter". The process ID is 19834.
% 1.66/1.87
% 1.66/1.87 set(prolog_style_variables).
% 1.66/1.87 set(auto).
% 1.66/1.87 dependent: set(auto1).
% 1.66/1.87 dependent: set(process_input).
% 1.66/1.87 dependent: clear(print_kept).
% 1.66/1.87 dependent: clear(print_new_demod).
% 1.66/1.87 dependent: clear(print_back_demod).
% 1.66/1.87 dependent: clear(print_back_sub).
% 1.66/1.87 dependent: set(control_memory).
% 1.66/1.87 dependent: assign(max_mem, 12000).
% 1.66/1.87 dependent: assign(pick_given_ratio, 4).
% 1.66/1.87 dependent: assign(stats_level, 1).
% 1.66/1.87 dependent: assign(max_seconds, 10800).
% 1.66/1.87 clear(print_given).
% 1.66/1.87
% 1.66/1.87 formula_list(usable).
% 1.66/1.87 all E S1 S2 T (environment(E)&subpopulations(S1,S2,E,T)->subpopulations(S2,S1,E,T)).
% 1.66/1.87 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))).
% 1.66/1.87 exists E T (environment(E)&subpopulations(first_movers,efficient_producers,E,T)&greater_or_e_qual(growth_rate(first_movers,T),zero)&greater(zero,growth_rate(efficient_producers,T))).
% 1.66/1.88 -(exists E T (environment(E)&subpopulations(first_movers,efficient_producers,E,T)&outcompetes(first_movers,efficient_producers,T))).
% 1.66/1.88 end_of_list.
% 1.66/1.88
% 1.66/1.88 -------> usable clausifies to:
% 1.66/1.88
% 1.66/1.88 list(usable).
% 1.66/1.88 0 [] -environment(E)| -subpopulations(S1,S2,E,T)|subpopulations(S2,S1,E,T).
% 1.66/1.88 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).
% 1.66/1.88 0 [] -environment(E)| -subpopulations(S1,S2,E,T)|greater_or_e_qual(growth_rate(S2,T),zero)| -outcompetes(S2,S1,T).
% 1.66/1.88 0 [] -environment(E)| -subpopulations(S1,S2,E,T)|greater(zero,growth_rate(S1,T))| -outcompetes(S2,S1,T).
% 1.66/1.88 0 [] environment($c2).
% 1.66/1.88 0 [] subpopulations(first_movers,efficient_producers,$c2,$c1).
% 1.66/1.88 0 [] greater_or_e_qual(growth_rate(first_movers,$c1),zero).
% 1.66/1.88 0 [] greater(zero,growth_rate(efficient_producers,$c1)).
% 1.66/1.88 0 [] -environment(E)| -subpopulations(first_movers,efficient_producers,E,T)| -outcompetes(first_movers,efficient_producers,T).
% 1.66/1.88 end_of_list.
% 1.66/1.88
% 1.66/1.88 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=5.
% 1.66/1.88
% 1.66/1.88 This is a Horn set without equality. The strategy will
% 1.66/1.88 be hyperresolution, with satellites in sos and nuclei
% 1.66/1.88 in usable.
% 1.66/1.88
% 1.66/1.88 dependent: set(hyper_res).
% 1.66/1.88 dependent: clear(order_hyper).
% 1.66/1.88
% 1.66/1.88 ------------> process usable:
% 1.66/1.88 ** KEPT (pick-wt=12): 1 [] -environment(A)| -subpopulations(B,C,A,D)|subpopulations(C,B,A,D).
% 1.66/1.88 ** KEPT (pick-wt=21): 2 [] -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).
% 1.66/1.88 ** KEPT (pick-wt=16): 3 [] -environment(A)| -subpopulations(B,C,A,D)|greater_or_e_qual(growth_rate(C,D),zero)| -outcompetes(C,B,D).
% 1.66/1.88 ** KEPT (pick-wt=16): 4 [] -environment(A)| -subpopulations(B,C,A,D)|greater(zero,growth_rate(B,D))| -outcompetes(C,B,D).
% 1.66/1.88 ** KEPT (pick-wt=11): 5 [] -environment(A)| -subpopulations(first_movers,efficient_producers,A,B)| -outcompetes(first_movers,efficient_producers,B).
% 1.66/1.88
% 1.66/1.88 ------------> process sos:
% 1.66/1.88 ** KEPT (pick-wt=2): 6 [] environment($c2).
% 1.66/1.88 ** KEPT (pick-wt=5): 7 [] subpopulations(first_movers,efficient_producers,$c2,$c1).
% 1.66/1.88 ** KEPT (pick-wt=5): 8 [] greater_or_e_qual(growth_rate(first_movers,$c1),zero).
% 1.66/1.88 ** KEPT (pick-wt=5): 9 [] greater(zero,growth_rate(efficient_producers,$c1)).
% 1.66/1.88
% 1.66/1.88 ======= end of input processing =======
% 1.66/1.88
% 1.66/1.88 =========== start of search ===========
% 1.66/1.88
% 1.66/1.88 -------- PROOF --------
% 1.66/1.88
% 1.66/1.88 -----> EMPTY CLAUSE at 0.00 sec ----> 12 [hyper,11,5,6,7] $F.
% 1.66/1.88
% 1.66/1.88 Length of proof is 2. Level of proof is 2.
% 1.66/1.88
% 1.66/1.88 ---------------- PROOF ----------------
% 1.66/1.88 % SZS status Theorem
% 1.66/1.88 % SZS output start Refutation
% See solution above
% 1.66/1.88 ------------ end of proof -------------
% 1.66/1.88
% 1.66/1.88
% 1.66/1.88 Search stopped by max_proofs option.
% 1.66/1.88
% 1.66/1.88
% 1.66/1.88 Search stopped by max_proofs option.
% 1.66/1.88
% 1.66/1.88 ============ end of search ============
% 1.66/1.88
% 1.66/1.88 -------------- statistics -------------
% 1.66/1.88 clauses given 6
% 1.66/1.88 clauses generated 4
% 1.66/1.88 clauses kept 11
% 1.66/1.88 clauses forward subsumed 1
% 1.66/1.88 clauses back subsumed 0
% 1.66/1.88 Kbytes malloced 976
% 1.66/1.88
% 1.66/1.88 ----------- times (seconds) -----------
% 1.66/1.88 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.66/1.88 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.66/1.88 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.66/1.88
% 1.66/1.88 That finishes the proof of the theorem.
% 1.66/1.88
% 1.66/1.88 Process 19834 finished Wed Jul 27 03:23:04 2022
% 1.66/1.88 Otter interrupted
% 1.66/1.88 PROOF FOUND
%------------------------------------------------------------------------------