TSTP Solution File: MGT020+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : MGT020+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 13:06:01 EDT 2022
% Result : Theorem 1.74s 1.96s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 23 ( 11 unt; 5 nHn; 23 RR)
% Number of literals : 48 ( 4 equ; 22 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B))) ),
file('MGT020+1.p',unknown),
[] ).
cnf(2,axiom,
( ~ environment(A)
| ~ in_environment(A,initial_FM_EP(A))
| subpopulations(first_movers,efficient_producers,A,initial_FM_EP(A)) ),
file('MGT020+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| greater_or_e_qual(B,initial_FM_EP(A)) ),
file('MGT020+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ environment(A)
| ~ greater_or_e_qual(B,C)
| ~ greater_or_e_qual(D,B)
| ~ subpopulations(first_movers,efficient_producers,A,D)
| ~ greater(disbanding_rate(first_movers,C),disbanding_rate(efficient_producers,C))
| decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| greater(disbanding_rate(first_movers,D),disbanding_rate(efficient_producers,D)) ),
file('MGT020+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| in_environment(A,B) ),
file('MGT020+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ environment(A)
| greater_or_e_qual(initial_FM_EP(A),start_time(A)) ),
file('MGT020+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ environment(A)
| ~ greater_or_e_qual(B,start_time(A))
| ~ greater(C,B)
| ~ in_environment(A,C)
| in_environment(A,B) ),
file('MGT020+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ greater_or_e_qual(A,B)
| greater(A,B)
| A = B ),
file('MGT020+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ environment(A)
| greater(disbanding_rate(first_movers,initial_FM_EP(A)),disbanding_rate(efficient_producers,initial_FM_EP(A))) ),
file('MGT020+1.p',unknown),
[] ).
cnf(12,axiom,
~ greater(disbanding_rate(first_movers,dollar_c1),disbanding_rate(efficient_producers,dollar_c1)),
file('MGT020+1.p',unknown),
[] ).
cnf(15,axiom,
environment(dollar_c2),
file('MGT020+1.p',unknown),
[] ).
cnf(16,axiom,
subpopulations(first_movers,efficient_producers,dollar_c2,dollar_c1),
file('MGT020+1.p',unknown),
[] ).
cnf(17,plain,
greater(disbanding_rate(first_movers,initial_FM_EP(dollar_c2)),disbanding_rate(efficient_producers,initial_FM_EP(dollar_c2))),
inference(hyper,[status(thm)],[15,10]),
[iquote('hyper,15,10')] ).
cnf(18,plain,
greater_or_e_qual(initial_FM_EP(dollar_c2),start_time(dollar_c2)),
inference(hyper,[status(thm)],[15,6]),
[iquote('hyper,15,6')] ).
cnf(20,plain,
in_environment(dollar_c2,dollar_c1),
inference(hyper,[status(thm)],[16,5,15]),
[iquote('hyper,16,5,15')] ).
cnf(21,plain,
greater_or_e_qual(dollar_c1,initial_FM_EP(dollar_c2)),
inference(hyper,[status(thm)],[16,3,15]),
[iquote('hyper,16,3,15')] ).
cnf(28,plain,
( greater(dollar_c1,initial_FM_EP(dollar_c2))
| initial_FM_EP(dollar_c2) = dollar_c1 ),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[21,9])]),
[iquote('hyper,21,9,flip.2')] ).
cnf(47,plain,
( initial_FM_EP(dollar_c2) = dollar_c1
| in_environment(dollar_c2,initial_FM_EP(dollar_c2)) ),
inference(hyper,[status(thm)],[28,7,15,18,20]),
[iquote('hyper,28,7,15,18,20')] ).
cnf(70,plain,
( initial_FM_EP(dollar_c2) = dollar_c1
| subpopulations(first_movers,efficient_producers,dollar_c2,initial_FM_EP(dollar_c2)) ),
inference(hyper,[status(thm)],[47,2,15]),
[iquote('hyper,47,2,15')] ).
cnf(217,plain,
subpopulations(first_movers,efficient_producers,dollar_c2,initial_FM_EP(dollar_c2)),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[70,2]),15,20])]),
[iquote('para_from,70.1.1,2.2.2,unit_del,15,20,factor_simp')] ).
cnf(219,plain,
greater_or_e_qual(initial_FM_EP(dollar_c2),initial_FM_EP(dollar_c2)),
inference(hyper,[status(thm)],[217,3,15]),
[iquote('hyper,217,3,15')] ).
cnf(242,plain,
decreases(difference(disbanding_rate(first_movers,initial_FM_EP(dollar_c2)),disbanding_rate(efficient_producers,initial_FM_EP(dollar_c2)))),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[219,4,15,21,16,17]),12]),
[iquote('hyper,219,4,15,21,16,17,unit_del,12')] ).
cnf(254,plain,
$false,
inference(hyper,[status(thm)],[242,1,15,217]),
[iquote('hyper,242,1,15,217')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : MGT020+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n028.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 04:11:33 EDT 2022
% 0.18/0.33 % CPUTime :
% 1.74/1.95 ----- Otter 3.3f, August 2004 -----
% 1.74/1.95 The process was started by sandbox on n028.cluster.edu,
% 1.74/1.95 Wed Jul 27 04:11:33 2022
% 1.74/1.95 The command was "./otter". The process ID is 15483.
% 1.74/1.95
% 1.74/1.95 set(prolog_style_variables).
% 1.74/1.95 set(auto).
% 1.74/1.95 dependent: set(auto1).
% 1.74/1.95 dependent: set(process_input).
% 1.74/1.95 dependent: clear(print_kept).
% 1.74/1.95 dependent: clear(print_new_demod).
% 1.74/1.95 dependent: clear(print_back_demod).
% 1.74/1.95 dependent: clear(print_back_sub).
% 1.74/1.95 dependent: set(control_memory).
% 1.74/1.95 dependent: assign(max_mem, 12000).
% 1.74/1.95 dependent: assign(pick_given_ratio, 4).
% 1.74/1.95 dependent: assign(stats_level, 1).
% 1.74/1.95 dependent: assign(max_seconds, 10800).
% 1.74/1.95 clear(print_given).
% 1.74/1.95
% 1.74/1.95 formula_list(usable).
% 1.74/1.95 all A (A=A).
% 1.74/1.95 all E T (environment(E)&subpopulations(first_movers,efficient_producers,E,T)-> -decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))).
% 1.74/1.95 all E T (environment(E)-> (in_environment(E,initial_FM_EP(E))->subpopulations(first_movers,efficient_producers,E,initial_FM_EP(E)))& (subpopulations(first_movers,efficient_producers,E,T)->greater_or_e_qual(T,initial_FM_EP(E)))).
% 1.74/1.95 all E T T1 T2 (environment(E)&greater_or_e_qual(T,T1)&greater_or_e_qual(T2,T)&subpopulations(first_movers,efficient_producers,E,T2)&greater(disbanding_rate(first_movers,T1),disbanding_rate(efficient_producers,T1))-> (-decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))->greater(disbanding_rate(first_movers,T2),disbanding_rate(efficient_producers,T2)))).
% 1.74/1.95 all E T (environment(E)&subpopulations(first_movers,efficient_producers,E,T)->in_environment(E,T)).
% 1.74/1.95 all E (environment(E)->greater_or_e_qual(initial_FM_EP(E),start_time(E))).
% 1.74/1.95 all E T1 T2 (environment(E)&greater_or_e_qual(T1,start_time(E))&greater(T2,T1)&in_environment(E,T2)->in_environment(E,T1)).
% 1.74/1.95 all X Y Z (greater(X,Y)&greater(Y,Z)->greater(X,Z)).
% 1.74/1.95 all X Y (greater_or_e_qual(X,Y)->greater(X,Y)|X=Y).
% 1.74/1.95 all E (environment(E)->greater(disbanding_rate(first_movers,initial_FM_EP(E)),disbanding_rate(efficient_producers,initial_FM_EP(E)))).
% 1.74/1.95 all E T1 T2 T (environment(E)&subpopulations(first_movers,efficient_producers,E,T1)&subpopulations(first_movers,efficient_producers,E,T2)&greater_or_e_qual(T,T1)&greater_or_e_qual(T2,T)->subpopulations(first_movers,efficient_producers,E,T)).
% 1.74/1.95 -(all E T (environment(E)&subpopulations(first_movers,efficient_producers,E,T)->greater(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))).
% 1.74/1.95 end_of_list.
% 1.74/1.95
% 1.74/1.95 -------> usable clausifies to:
% 1.74/1.95
% 1.74/1.95 list(usable).
% 1.74/1.95 0 [] A=A.
% 1.74/1.95 0 [] -environment(E)| -subpopulations(first_movers,efficient_producers,E,T)| -decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))).
% 1.74/1.95 0 [] -environment(E)| -in_environment(E,initial_FM_EP(E))|subpopulations(first_movers,efficient_producers,E,initial_FM_EP(E)).
% 1.74/1.95 0 [] -environment(E)| -subpopulations(first_movers,efficient_producers,E,T)|greater_or_e_qual(T,initial_FM_EP(E)).
% 1.74/1.95 0 [] -environment(E)| -greater_or_e_qual(T,T1)| -greater_or_e_qual(T2,T)| -subpopulations(first_movers,efficient_producers,E,T2)| -greater(disbanding_rate(first_movers,T1),disbanding_rate(efficient_producers,T1))|decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))|greater(disbanding_rate(first_movers,T2),disbanding_rate(efficient_producers,T2)).
% 1.74/1.95 0 [] -environment(E)| -subpopulations(first_movers,efficient_producers,E,T)|in_environment(E,T).
% 1.74/1.95 0 [] -environment(E)|greater_or_e_qual(initial_FM_EP(E),start_time(E)).
% 1.74/1.95 0 [] -environment(E)| -greater_or_e_qual(T1,start_time(E))| -greater(T2,T1)| -in_environment(E,T2)|in_environment(E,T1).
% 1.74/1.95 0 [] -greater(X,Y)| -greater(Y,Z)|greater(X,Z).
% 1.74/1.95 0 [] -greater_or_e_qual(X,Y)|greater(X,Y)|X=Y.
% 1.74/1.95 0 [] -environment(E)|greater(disbanding_rate(first_movers,initial_FM_EP(E)),disbanding_rate(efficient_producers,initial_FM_EP(E))).
% 1.74/1.95 0 [] -environment(E)| -subpopulations(first_movers,efficient_producers,E,T1)| -subpopulations(first_movers,efficient_producers,E,T2)| -greater_or_e_qual(T,T1)| -greater_or_e_qual(T2,T)|subpopulations(first_movers,efficient_producers,E,T).
% 1.74/1.95 0 [] environment($c2).
% 1.74/1.95 0 [] subpopulations(first_movers,efficient_producers,$c2,$c1).
% 1.74/1.96 0 [] -greater(disbanding_rate(first_movers,$c1),disbanding_rate(efficient_producers,$c1)).
% 1.74/1.96 end_of_list.
% 1.74/1.96
% 1.74/1.96 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 1.74/1.96
% 1.74/1.96 This ia a non-Horn set with equality. The strategy will be
% 1.74/1.96 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.74/1.96 deletion, with positive clauses in sos and nonpositive
% 1.74/1.96 clauses in usable.
% 1.74/1.96
% 1.74/1.96 dependent: set(knuth_bendix).
% 1.74/1.96 dependent: set(anl_eq).
% 1.74/1.96 dependent: set(para_from).
% 1.74/1.96 dependent: set(para_into).
% 1.74/1.96 dependent: clear(para_from_right).
% 1.74/1.96 dependent: clear(para_into_right).
% 1.74/1.96 dependent: set(para_from_vars).
% 1.74/1.96 dependent: set(eq_units_both_ways).
% 1.74/1.96 dependent: set(dynamic_demod_all).
% 1.74/1.96 dependent: set(dynamic_demod).
% 1.74/1.96 dependent: set(order_eq).
% 1.74/1.96 dependent: set(back_demod).
% 1.74/1.96 dependent: set(lrpo).
% 1.74/1.96 dependent: set(hyper_res).
% 1.74/1.96 dependent: set(unit_deletion).
% 1.74/1.96 dependent: set(factor).
% 1.74/1.96
% 1.74/1.96 ------------> process usable:
% 1.74/1.96 ** KEPT (pick-wt=15): 1 [] -environment(A)| -subpopulations(first_movers,efficient_producers,A,B)| -decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B))).
% 1.74/1.96 ** KEPT (pick-wt=12): 2 [] -environment(A)| -in_environment(A,initial_FM_EP(A))|subpopulations(first_movers,efficient_producers,A,initial_FM_EP(A)).
% 1.74/1.96 ** KEPT (pick-wt=11): 3 [] -environment(A)| -subpopulations(first_movers,efficient_producers,A,B)|greater_or_e_qual(B,initial_FM_EP(A)).
% 1.74/1.96 ** KEPT (pick-wt=35): 4 [] -environment(A)| -greater_or_e_qual(B,C)| -greater_or_e_qual(D,B)| -subpopulations(first_movers,efficient_producers,A,D)| -greater(disbanding_rate(first_movers,C),disbanding_rate(efficient_producers,C))|decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))|greater(disbanding_rate(first_movers,D),disbanding_rate(efficient_producers,D)).
% 1.74/1.96 ** KEPT (pick-wt=10): 5 [] -environment(A)| -subpopulations(first_movers,efficient_producers,A,B)|in_environment(A,B).
% 1.74/1.96 ** KEPT (pick-wt=7): 6 [] -environment(A)|greater_or_e_qual(initial_FM_EP(A),start_time(A)).
% 1.74/1.96 ** KEPT (pick-wt=15): 7 [] -environment(A)| -greater_or_e_qual(B,start_time(A))| -greater(C,B)| -in_environment(A,C)|in_environment(A,B).
% 1.74/1.96 ** KEPT (pick-wt=9): 8 [] -greater(A,B)| -greater(B,C)|greater(A,C).
% 1.74/1.96 ** KEPT (pick-wt=9): 9 [] -greater_or_e_qual(A,B)|greater(A,B)|A=B.
% 1.74/1.96 ** KEPT (pick-wt=11): 10 [] -environment(A)|greater(disbanding_rate(first_movers,initial_FM_EP(A)),disbanding_rate(efficient_producers,initial_FM_EP(A))).
% 1.74/1.96 ** KEPT (pick-wt=23): 11 [] -environment(A)| -subpopulations(first_movers,efficient_producers,A,B)| -subpopulations(first_movers,efficient_producers,A,C)| -greater_or_e_qual(D,B)| -greater_or_e_qual(C,D)|subpopulations(first_movers,efficient_producers,A,D).
% 1.74/1.96 ** KEPT (pick-wt=7): 12 [] -greater(disbanding_rate(first_movers,$c1),disbanding_rate(efficient_producers,$c1)).
% 1.74/1.96
% 1.74/1.96 ------------> process sos:
% 1.74/1.96 ** KEPT (pick-wt=3): 14 [] A=A.
% 1.74/1.96 ** KEPT (pick-wt=2): 15 [] environment($c2).
% 1.74/1.96 ** KEPT (pick-wt=5): 16 [] subpopulations(first_movers,efficient_producers,$c2,$c1).
% 1.74/1.96 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] A=A.
% 1.74/1.96
% 1.74/1.96 ======= end of input processing =======
% 1.74/1.96
% 1.74/1.96 =========== start of search ===========
% 1.74/1.96
% 1.74/1.96 -------- PROOF --------
% 1.74/1.96
% 1.74/1.96 -----> EMPTY CLAUSE at 0.01 sec ----> 254 [hyper,242,1,15,217] $F.
% 1.74/1.96
% 1.74/1.96 Length of proof is 10. Level of proof is 7.
% 1.74/1.96
% 1.74/1.96 ---------------- PROOF ----------------
% 1.74/1.96 % SZS status Theorem
% 1.74/1.96 % SZS output start Refutation
% See solution above
% 1.74/1.96 ------------ end of proof -------------
% 1.74/1.96
% 1.74/1.96
% 1.74/1.96 Search stopped by max_proofs option.
% 1.74/1.96
% 1.74/1.96
% 1.74/1.96 Search stopped by max_proofs option.
% 1.74/1.96
% 1.74/1.96 ============ end of search ============
% 1.74/1.96
% 1.74/1.96 -------------- statistics -------------
% 1.74/1.96 clauses given 40
% 1.74/1.96 clauses generated 487
% 1.74/1.96 clauses kept 253
% 1.74/1.96 clauses forward subsumed 236
% 1.74/1.96 clauses back subsumed 86
% 1.74/1.96 Kbytes malloced 976
% 1.74/1.96
% 1.74/1.96 ----------- times (seconds) -----------
% 1.74/1.96 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.74/1.96 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.74/1.96 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.74/1.96
% 1.74/1.96 That finishes the proof of the theorem.
% 1.74/1.96
% 1.74/1.96 Process 15483 finished Wed Jul 27 04:11:35 2022
% 1.74/1.96 Otter interrupted
% 1.74/1.96 PROOF FOUND
%------------------------------------------------------------------------------