TSTP Solution File: MGT034+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : MGT034+2 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.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 : 600s
% DateTime : Sun Jul 17 22:22:58 EDT 2022
% Result : Theorem 0.74s 1.01s
% Output : Refutation 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : MGT034+2 : TPTP v8.1.0. Released v2.0.0.
% 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n019.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 : 600
% 0.13/0.34 % DateTime : Thu Jun 9 10:25:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.43/1.00 ============================== Prover9 ===============================
% 0.43/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.00 Process 19744 was started by sandbox on n019.cluster.edu,
% 0.43/1.00 Thu Jun 9 10:25:25 2022
% 0.43/1.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_19591_n019.cluster.edu".
% 0.43/1.00 ============================== end of head ===========================
% 0.43/1.00
% 0.43/1.00 ============================== INPUT =================================
% 0.43/1.00
% 0.43/1.00 % Reading from file /tmp/Prover9_19591_n019.cluster.edu
% 0.43/1.00
% 0.43/1.00 set(prolog_style_variables).
% 0.43/1.00 set(auto2).
% 0.43/1.00 % set(auto2) -> set(auto).
% 0.43/1.00 % set(auto) -> set(auto_inference).
% 0.43/1.00 % set(auto) -> set(auto_setup).
% 0.43/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.00 % set(auto) -> set(auto_limits).
% 0.43/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.00 % set(auto) -> set(auto_denials).
% 0.43/1.00 % set(auto) -> set(auto_process).
% 0.43/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.00 % set(auto2) -> assign(stats, some).
% 0.43/1.00 % set(auto2) -> clear(echo_input).
% 0.43/1.00 % set(auto2) -> set(quiet).
% 0.43/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.00 % set(auto2) -> clear(print_given).
% 0.43/1.00 assign(lrs_ticks,-1).
% 0.43/1.00 assign(sos_limit,10000).
% 0.43/1.00 assign(order,kbo).
% 0.43/1.00 set(lex_order_vars).
% 0.43/1.00 clear(print_given).
% 0.43/1.00
% 0.43/1.00 % formulas(sos). % not echoed (21 formulas)
% 0.43/1.00
% 0.43/1.00 ============================== end of input ==========================
% 0.43/1.00
% 0.43/1.00 % From the command line: assign(max_seconds, 300).
% 0.43/1.00
% 0.43/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.00
% 0.43/1.00 % Formulas that are not ordinary clauses:
% 0.43/1.00 1 (all E all S1 all S2 all T (environment(E) & subpopulations(S1,S2,E,T) & greater(growth_rate(S2,T),growth_rate(S1,T)) -> selection_favors(S2,S1,T))) # label(mp1_high_growth_rates) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 2 (all E all T (environment(E) & subpopulations(first_movers,efficient_producers,E,T) -> -decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))))) # label(l3) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 3 (all E (environment(E) & in_environment(E,critical_point(E)) -> subpopulations(first_movers,efficient_producers,E,critical_point(E)))) # label(mp_critical_point_means_FM_and_EP) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 4 (all E (environment(E) & in_environment(E,appear(efficient_producers,E)) -> subpopulations(first_movers,efficient_producers,E,appear(efficient_producers,E)))) # label(mp_FM_and_EP_when_EP_appears) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 5 (all T (decreases(difference(founding_rate(first_movers,T),founding_rate(efficient_producers,T))) & -decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) -> decreases(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T))))) # label(mp_difference_between_founding_rates) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 6 (all E all T all To (environment(E) & in_environment(E,To) & greater_or_equal(difference(growth_rate(first_movers,To),growth_rate(efficient_producers,To)),zero) & greater_or_equal(T,appear(efficient_producers,E)) & greater(To,T) -> (decreases(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T))) -> greater(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)),zero)))) # label(mp_decreasing_function) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 7 (all T (greater(zero,difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T))) <-> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)))) # label(mp_negative_growth_rate_difference) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 8 (all T (greater(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)),zero) <-> greater(growth_rate(first_movers,T),growth_rate(efficient_producers,T)))) # label(mp_positive_growth_rate_difference) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 9 (all E all T1 all T2 all T (environment(E) & in_environment(E,T1) & in_environment(E,T2) & greater_or_equal(T2,T) & greater_or_equal(T,T1) -> in_environment(E,T))) # label(mp_durations_are_time_intervals) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 10 (all E (environment(E) -> in_environment(E,start_time(E)))) # label(mp_opening_time_in_duration) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 11 (all E (environment(E) -> greater_or_equal(appear(first_movers,E),start_time(E)))) # label(mp_no_FM_before_opening) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 12 (all E all T (environment(E) & in_environment(E,critical_point(E)) & greater_or_equal(T,appear(efficient_producers,E)) & greater(critical_point(E),T) -> in_environment(E,T))) # label(mp_critical_time_points) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 13 (all E all 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))) # label(mp_contains_FM_and_EP) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 14 (all E all T (environment(E) & subpopulations(first_movers,efficient_producers,E,T) -> subpopulations(efficient_producers,first_movers,E,T))) # label(mp_symmetry_of_subpopulations) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 15 (all E all T (environment(E) & subpopulations(first_movers,efficient_producers,E,T) -> greater_or_equal(T,appear(efficient_producers,E)))) # label(mp_FM_and_EP_members_EP_appeared) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 16 (all X all Y (greater_or_equal(X,Y) <-> greater(X,Y) | X = Y)) # label(mp_greater_or_equal) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 17 (all E all T (environment(E) & subpopulations(first_movers,efficient_producers,E,T) & -greater(zero,difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T))) -> greater_or_equal(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)),zero))) # label(mp_relationship_of_growth_rates) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 18 (all E all 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)))))) # label(d1) # label(hypothesis) # label(non_clause). [assumption].
% 0.43/1.00 19 (all E all T1 all T2 all T (environment(E) & subpopulations(first_movers,efficient_producers,E,T1) & subpopulations(first_movers,efficient_producers,E,T2) & greater_or_equal(T,T1) & greater_or_equal(T2,T) -> subpopulations(first_movers,efficient_producers,E,T))) # label(a10) # label(hypothesis) # label(non_clause). [assumption].
% 0.43/1.00 20 (all E all T (environment(E) & subpopulations(first_movers,efficient_producers,E,T) -> decreases(difference(founding_rate(first_movers,T),founding_rate(efficient_producers,T))))) # label(a12) # label(hypothesis) # label(non_clause). [assumption].
% 0.43/1.00 21 -(all E all T (environment(E) & in_environment(E,critical_point(E)) & greater_or_equal(T,appear(efficient_producers,E)) & greater(critical_point(E),T) -> selection_favors(first_movers,efficient_producers,T))) # label(prove_t3) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/1.00
% 0.43/1.00 ============================== end of process non-clausal formulas ===
% 0.43/1.00
% 0.43/1.00 ============================== PROCESS INITIAL CLAUSES ===============
% 0.43/1.00
% 0.43/1.00 ============================== PREDICATE ELIMINATION =================
% 0.43/1.00 22 -environment(A) | critical_point(A) != B | -greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)) # label(d1) # label(hypothesis). [clausify(18)].
% 0.43/1.00 23 environment(c1) # label(prove_t3) # label(negated_conjecture). [clausify(21)].
% 0.43/1.00 Derived: critical_point(c1) != A | -greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)). [resolve(22,a,23,a)].
% 0.43/1.00 24 -environment(A) | -subpopulations(first_movers,efficient_producers,A,B) | -decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B))) # label(l3) # label(axiom). [clausify(2)].
% 0.43/1.00 Derived: -subpopulations(first_movers,efficient_producers,c1,A) | -decreases(difference(disbanding_rate(first_movers,A),disbanding_rate(efficient_producers,A))). [resolve(24,a,23,a)].
% 0.43/1.00 25 -environment(A) | in_environment(A,start_time(A)) # label(mp_opening_time_in_duration) # label(axiom). [clausify(10)].
% 0.43/1.00 Derived: in_environment(c1,start_time(c1)). [resolve(25,a,23,a)].
% 0.43/1.00 26 -environment(A) | greater_or_equal(appear(first_movers,A),start_time(A)) # label(mp_no_FM_before_opening) # label(axiom). [clausify(11)].
% 0.43/1.00 Derived: greater_or_equal(appear(first_movers,c1),start_time(c1)). [resolve(26,a,23,a)].
% 0.43/1.00 27 -environment(A) | -in_environment(A,critical_point(A)) | subpopulations(first_movers,efficient_producers,A,critical_point(A)) # label(mp_critical_point_means_FM_and_EP) # label(axiom). [clausify(3)].
% 0.43/1.00 Derived: -in_environment(c1,critical_point(c1)) | subpopulations(first_movers,efficient_producers,c1,critical_point(c1)). [resolve(27,a,23,a)].
% 0.43/1.00 28 -environment(A) | -subpopulations(first_movers,efficient_producers,A,B) | subpopulations(efficient_producers,first_movers,A,B) # label(mp_symmetry_of_subpopulations) # label(axiom). [clausify(14)].
% 0.43/1.00 Derived: -subpopulations(first_movers,efficient_producers,c1,A) | subpopulations(efficient_producers,first_movers,c1,A). [resolve(28,a,23,a)].
% 0.43/1.00 29 -environment(A) | -subpopulations(first_movers,efficient_producers,A,B) | greater_or_equal(B,appear(efficient_producers,A)) # label(mp_FM_and_EP_members_EP_appeared) # label(axiom). [clausify(15)].
% 0.43/1.00 Derived: -subpopulations(first_movers,efficient_producers,c1,A) | greater_or_equal(A,appear(efficient_producers,c1)). [resolve(29,a,23,a)].
% 0.43/1.00 30 -environment(A) | -in_environment(A,appear(efficient_producers,A)) | subpopulations(first_movers,efficient_producers,A,appear(efficient_producers,A)) # label(mp_FM_and_EP_when_EP_appears) # label(axiom). [clausify(4)].
% 0.43/1.00 Derived: -in_environment(c1,appear(efficient_producers,c1)) | subpopulations(first_movers,efficient_producers,c1,appear(efficient_producers,c1)). [resolve(30,a,23,a)].
% 0.43/1.00 31 -environment(A) | -subpopulations(first_movers,efficient_producers,A,B) | decreases(difference(founding_rate(first_movers,B),founding_rate(efficient_producers,B))) # label(a12) # label(hypothesis). [clausify(20)].
% 0.43/1.00 Derived: -subpopulations(first_movers,efficient_producers,c1,A) | decreases(difference(founding_rate(first_movers,A),founding_rate(efficient_producers,A))). [resolve(31,a,23,a)].
% 0.43/1.00 32 -environment(A) | -in_environment(A,B) | -in_environment(A,C) | -greater_or_equal(C,D) | -greater_or_equal(D,B) | in_environment(A,D) # label(mp_durations_are_time_intervals) # label(axiom). [clausify(9)].
% 0.43/1.00 Derived: -in_environment(c1,A) | -in_environment(c1,B) | -greater_or_equal(B,C) | -greater_or_equal(C,A) | in_environment(c1,C). [resolve(32,a,23,a)].
% 0.43/1.00 33 -environment(A) | -subpopulations(B,C,A,D) | -greater(growth_rate(C,D),growth_rate(B,D)) | selection_favors(C,B,D) # label(mp1_high_growth_rates) # label(axiom). [clausify(1)].
% 0.43/1.00 Derived: -subpopulations(A,B,c1,C) | -greater(growth_rate(B,C),growth_rate(A,C)) | selection_favors(B,A,C). [resolve(33,a,23,a)].
% 0.43/1.00 34 -environment(A) | -in_environment(A,critical_point(A)) | -greater_or_equal(B,appear(efficient_producers,A)) | -greater(critical_point(A),B) | in_environment(A,B) # label(mp_critical_time_points) # label(axiom). [clausify(12)].
% 0.43/1.00 Derived: -in_environment(c1,critical_point(c1)) | -greater_or_equal(A,appear(efficient_producers,c1)) | -greater(critical_point(c1),A) | in_environment(c1,A). [resolve(34,a,23,a)].
% 0.43/1.00 35 -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) # label(mp_contains_FM_and_EP) # label(axiom). [clausify(13)].
% 0.74/1.01 Derived: -in_environment(c1,A) | -greater(cardinality_at_time(first_movers,A),zero) | -greater(cardinality_at_time(efficient_producers,A),zero) | subpopulations(first_movers,efficient_producers,c1,A). [resolve(35,a,23,a)].
% 0.74/1.01 36 -environment(A) | critical_point(A) != B | -subpopulations(first_movers,efficient_producers,A,C) | -greater(C,B) | greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C)) # label(d1) # label(hypothesis). [clausify(18)].
% 0.74/1.01 Derived: critical_point(c1) != A | -subpopulations(first_movers,efficient_producers,c1,B) | -greater(B,A) | greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)). [resolve(36,a,23,a)].
% 0.74/1.01 37 -environment(A) | -subpopulations(first_movers,efficient_producers,A,B) | -subpopulations(first_movers,efficient_producers,A,C) | -greater_or_equal(D,B) | -greater_or_equal(C,D) | subpopulations(first_movers,efficient_producers,A,D) # label(a10) # label(hypothesis). [clausify(19)].
% 0.74/1.01 Derived: -subpopulations(first_movers,efficient_producers,c1,A) | -subpopulations(first_movers,efficient_producers,c1,B) | -greater_or_equal(C,A) | -greater_or_equal(B,C) | subpopulations(first_movers,efficient_producers,c1,C). [resolve(37,a,23,a)].
% 0.74/1.01 38 -environment(A) | -subpopulations(first_movers,efficient_producers,A,B) | greater(zero,difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B))) | greater_or_equal(difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B)),zero) # label(mp_relationship_of_growth_rates) # label(axiom). [clausify(17)].
% 0.74/1.01 Derived: -subpopulations(first_movers,efficient_producers,c1,A) | greater(zero,difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A))) | greater_or_equal(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)),zero). [resolve(38,a,23,a)].
% 0.74/1.01 39 -environment(A) | -in_environment(A,B) | -greater_or_equal(difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B)),zero) | -greater_or_equal(C,appear(efficient_producers,A)) | -greater(B,C) | -decreases(difference(growth_rate(first_movers,C),growth_rate(efficient_producers,C))) | greater(difference(growth_rate(first_movers,C),growth_rate(efficient_producers,C)),zero) # label(mp_decreasing_function) # label(axiom). [clausify(6)].
% 0.74/1.01 Derived: -in_environment(c1,A) | -greater_or_equal(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)),zero) | -greater_or_equal(B,appear(efficient_producers,c1)) | -greater(A,B) | -decreases(difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B))) | greater(difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B)),zero). [resolve(39,a,23,a)].
% 0.74/1.01
% 0.74/1.01 ============================== end predicate elimination =============
% 0.74/1.01
% 0.74/1.01 Auto_denials: (non-Horn, no changes).
% 0.74/1.01
% 0.74/1.01 Term ordering decisions:
% 0.74/1.01 Function symbol KB weights: efficient_producers=1. first_movers=1. zero=1. c1=1. c2=1. growth_rate=1. difference=1. appear=1. founding_rate=1. cardinality_at_time=1. disbanding_rate=1. critical_point=1. start_time=1.
% 0.74/1.01
% 0.74/1.01 ============================== end of process initial clauses ========
% 0.74/1.01
% 0.74/1.01 ============================== CLAUSES FOR SEARCH ====================
% 0.74/1.01
% 0.74/1.01 ============================== end of clauses for search =============
% 0.74/1.01
% 0.74/1.01 ============================== SEARCH ================================
% 0.74/1.01
% 0.74/1.01 % Starting search at 0.01 seconds.
% 0.74/1.01
% 0.74/1.01 ============================== PROOF =================================
% 0.74/1.01 % SZS status Theorem
% 0.74/1.01 % SZS output start Refutation
% 0.74/1.01
% 0.74/1.01 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.74/1.01 % Length of proof is 92.
% 0.74/1.01 % Level of proof is 21.
% 0.74/1.01 % Maximum clause weight is 37.000.
% 0.74/1.01 % Given clauses 134.
% 0.74/1.01
% 0.74/1.01 1 (all E all S1 all S2 all T (environment(E) & subpopulations(S1,S2,E,T) & greater(growth_rate(S2,T),growth_rate(S1,T)) -> selection_favors(S2,S1,T))) # label(mp1_high_growth_rates) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 2 (all E all T (environment(E) & subpopulations(first_movers,efficient_producers,E,T) -> -decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))))) # label(l3) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 3 (all E (environment(E) & in_environment(E,critical_point(E)) -> subpopulations(first_movers,efficient_producers,E,critical_point(E)))) # label(mp_critical_point_means_FM_and_EP) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 4 (all E (environment(E) & in_environment(E,appear(efficient_producers,E)) -> subpopulations(first_movers,efficient_producers,E,appear(efficient_producers,E)))) # label(mp_FM_and_EP_when_EP_appears) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 5 (all T (decreases(difference(founding_rate(first_movers,T),founding_rate(efficient_producers,T))) & -decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) -> decreases(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T))))) # label(mp_difference_between_founding_rates) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 6 (all E all T all To (environment(E) & in_environment(E,To) & greater_or_equal(difference(growth_rate(first_movers,To),growth_rate(efficient_producers,To)),zero) & greater_or_equal(T,appear(efficient_producers,E)) & greater(To,T) -> (decreases(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T))) -> greater(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)),zero)))) # label(mp_decreasing_function) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 7 (all T (greater(zero,difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T))) <-> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)))) # label(mp_negative_growth_rate_difference) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 8 (all T (greater(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)),zero) <-> greater(growth_rate(first_movers,T),growth_rate(efficient_producers,T)))) # label(mp_positive_growth_rate_difference) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 12 (all E all T (environment(E) & in_environment(E,critical_point(E)) & greater_or_equal(T,appear(efficient_producers,E)) & greater(critical_point(E),T) -> in_environment(E,T))) # label(mp_critical_time_points) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 14 (all E all T (environment(E) & subpopulations(first_movers,efficient_producers,E,T) -> subpopulations(efficient_producers,first_movers,E,T))) # label(mp_symmetry_of_subpopulations) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 15 (all E all T (environment(E) & subpopulations(first_movers,efficient_producers,E,T) -> greater_or_equal(T,appear(efficient_producers,E)))) # label(mp_FM_and_EP_members_EP_appeared) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 16 (all X all Y (greater_or_equal(X,Y) <-> greater(X,Y) | X = Y)) # label(mp_greater_or_equal) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 17 (all E all T (environment(E) & subpopulations(first_movers,efficient_producers,E,T) & -greater(zero,difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T))) -> greater_or_equal(difference(growth_rate(first_movers,T),growth_rate(efficient_producers,T)),zero))) # label(mp_relationship_of_growth_rates) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 18 (all E all 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)))))) # label(d1) # label(hypothesis) # label(non_clause). [assumption].
% 0.74/1.01 19 (all E all T1 all T2 all T (environment(E) & subpopulations(first_movers,efficient_producers,E,T1) & subpopulations(first_movers,efficient_producers,E,T2) & greater_or_equal(T,T1) & greater_or_equal(T2,T) -> subpopulations(first_movers,efficient_producers,E,T))) # label(a10) # label(hypothesis) # label(non_clause). [assumption].
% 0.74/1.01 20 (all E all T (environment(E) & subpopulations(first_movers,efficient_producers,E,T) -> decreases(difference(founding_rate(first_movers,T),founding_rate(efficient_producers,T))))) # label(a12) # label(hypothesis) # label(non_clause). [assumption].
% 0.74/1.01 21 -(all E all T (environment(E) & in_environment(E,critical_point(E)) & greater_or_equal(T,appear(efficient_producers,E)) & greater(critical_point(E),T) -> selection_favors(first_movers,efficient_producers,T))) # label(prove_t3) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.74/1.01 22 -environment(A) | critical_point(A) != B | -greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)) # label(d1) # label(hypothesis). [clausify(18)].
% 0.74/1.01 23 environment(c1) # label(prove_t3) # label(negated_conjecture). [clausify(21)].
% 0.74/1.01 24 -environment(A) | -subpopulations(first_movers,efficient_producers,A,B) | -decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B))) # label(l3) # label(axiom). [clausify(2)].
% 0.74/1.01 27 -environment(A) | -in_environment(A,critical_point(A)) | subpopulations(first_movers,efficient_producers,A,critical_point(A)) # label(mp_critical_point_means_FM_and_EP) # label(axiom). [clausify(3)].
% 0.74/1.01 28 -environment(A) | -subpopulations(first_movers,efficient_producers,A,B) | subpopulations(efficient_producers,first_movers,A,B) # label(mp_symmetry_of_subpopulations) # label(axiom). [clausify(14)].
% 0.74/1.01 29 -environment(A) | -subpopulations(first_movers,efficient_producers,A,B) | greater_or_equal(B,appear(efficient_producers,A)) # label(mp_FM_and_EP_members_EP_appeared) # label(axiom). [clausify(15)].
% 0.74/1.01 30 -environment(A) | -in_environment(A,appear(efficient_producers,A)) | subpopulations(first_movers,efficient_producers,A,appear(efficient_producers,A)) # label(mp_FM_and_EP_when_EP_appears) # label(axiom). [clausify(4)].
% 0.74/1.01 31 -environment(A) | -subpopulations(first_movers,efficient_producers,A,B) | decreases(difference(founding_rate(first_movers,B),founding_rate(efficient_producers,B))) # label(a12) # label(hypothesis). [clausify(20)].
% 0.74/1.01 33 -environment(A) | -subpopulations(B,C,A,D) | -greater(growth_rate(C,D),growth_rate(B,D)) | selection_favors(C,B,D) # label(mp1_high_growth_rates) # label(axiom). [clausify(1)].
% 0.74/1.01 34 -environment(A) | -in_environment(A,critical_point(A)) | -greater_or_equal(B,appear(efficient_producers,A)) | -greater(critical_point(A),B) | in_environment(A,B) # label(mp_critical_time_points) # label(axiom). [clausify(12)].
% 0.74/1.01 37 -environment(A) | -subpopulations(first_movers,efficient_producers,A,B) | -subpopulations(first_movers,efficient_producers,A,C) | -greater_or_equal(D,B) | -greater_or_equal(C,D) | subpopulations(first_movers,efficient_producers,A,D) # label(a10) # label(hypothesis). [clausify(19)].
% 0.74/1.01 38 -environment(A) | -subpopulations(first_movers,efficient_producers,A,B) | greater(zero,difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B))) | greater_or_equal(difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B)),zero) # label(mp_relationship_of_growth_rates) # label(axiom). [clausify(17)].
% 0.74/1.01 39 -environment(A) | -in_environment(A,B) | -greater_or_equal(difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B)),zero) | -greater_or_equal(C,appear(efficient_producers,A)) | -greater(B,C) | -decreases(difference(growth_rate(first_movers,C),growth_rate(efficient_producers,C))) | greater(difference(growth_rate(first_movers,C),growth_rate(efficient_producers,C)),zero) # label(mp_decreasing_function) # label(axiom). [clausify(6)].
% 0.74/1.01 40 in_environment(c1,critical_point(c1)) # label(prove_t3) # label(negated_conjecture). [clausify(21)].
% 0.74/1.01 41 greater(critical_point(c1),c2) # label(prove_t3) # label(negated_conjecture). [clausify(21)].
% 0.74/1.01 42 greater_or_equal(c2,appear(efficient_producers,c1)) # label(prove_t3) # label(negated_conjecture). [clausify(21)].
% 0.74/1.01 43 -selection_favors(first_movers,efficient_producers,c2) # label(prove_t3) # label(negated_conjecture). [clausify(21)].
% 0.74/1.01 44 greater_or_equal(A,B) | -greater(A,B) # label(mp_greater_or_equal) # label(axiom). [clausify(16)].
% 0.74/1.01 45 greater_or_equal(A,B) | B != A # label(mp_greater_or_equal) # label(axiom). [clausify(16)].
% 0.74/1.01 46 -greater_or_equal(A,B) | greater(A,B) | B = A # label(mp_greater_or_equal) # label(axiom). [clausify(16)].
% 0.74/1.01 47 -greater(zero,difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A))) | greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)) # label(mp_negative_growth_rate_difference) # label(axiom). [clausify(7)].
% 0.74/1.01 49 -greater(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)),zero) | greater(growth_rate(first_movers,A),growth_rate(efficient_producers,A)) # label(mp_positive_growth_rate_difference) # label(axiom). [clausify(8)].
% 0.74/1.01 51 -decreases(difference(founding_rate(first_movers,A),founding_rate(efficient_producers,A))) | decreases(difference(disbanding_rate(first_movers,A),disbanding_rate(efficient_producers,A))) | decreases(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A))) # label(mp_difference_between_founding_rates) # label(axiom). [clausify(5)].
% 0.74/1.01 52 critical_point(c1) != A | -greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)). [resolve(22,a,23,a)].
% 0.74/1.01 53 -subpopulations(first_movers,efficient_producers,c1,A) | -decreases(difference(disbanding_rate(first_movers,A),disbanding_rate(efficient_producers,A))). [resolve(24,a,23,a)].
% 0.74/1.01 56 -in_environment(c1,critical_point(c1)) | subpopulations(first_movers,efficient_producers,c1,critical_point(c1)). [resolve(27,a,23,a)].
% 0.74/1.01 57 subpopulations(first_movers,efficient_producers,c1,critical_point(c1)). [copy(56),unit_del(a,40)].
% 0.74/1.01 58 -subpopulations(first_movers,efficient_producers,c1,A) | subpopulations(efficient_producers,first_movers,c1,A). [resolve(28,a,23,a)].
% 0.74/1.01 59 -subpopulations(first_movers,efficient_producers,c1,A) | greater_or_equal(A,appear(efficient_producers,c1)). [resolve(29,a,23,a)].
% 0.74/1.01 60 -in_environment(c1,appear(efficient_producers,c1)) | subpopulations(first_movers,efficient_producers,c1,appear(efficient_producers,c1)). [resolve(30,a,23,a)].
% 0.74/1.01 61 -subpopulations(first_movers,efficient_producers,c1,A) | decreases(difference(founding_rate(first_movers,A),founding_rate(efficient_producers,A))). [resolve(31,a,23,a)].
% 0.74/1.01 63 -subpopulations(A,B,c1,C) | -greater(growth_rate(B,C),growth_rate(A,C)) | selection_favors(B,A,C). [resolve(33,a,23,a)].
% 0.74/1.01 64 -in_environment(c1,critical_point(c1)) | -greater_or_equal(A,appear(efficient_producers,c1)) | -greater(critical_point(c1),A) | in_environment(c1,A). [resolve(34,a,23,a)].
% 0.74/1.01 65 -greater_or_equal(A,appear(efficient_producers,c1)) | -greater(critical_point(c1),A) | in_environment(c1,A). [copy(64),unit_del(a,40)].
% 0.74/1.01 68 -subpopulations(first_movers,efficient_producers,c1,A) | -subpopulations(first_movers,efficient_producers,c1,B) | -greater_or_equal(C,A) | -greater_or_equal(B,C) | subpopulations(first_movers,efficient_producers,c1,C). [resolve(37,a,23,a)].
% 0.74/1.01 69 -subpopulations(first_movers,efficient_producers,c1,A) | greater(zero,difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A))) | greater_or_equal(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)),zero). [resolve(38,a,23,a)].
% 0.74/1.01 70 -in_environment(c1,A) | -greater_or_equal(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)),zero) | -greater_or_equal(B,appear(efficient_producers,c1)) | -greater(A,B) | -decreases(difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B))) | greater(difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B)),zero). [resolve(39,a,23,a)].
% 0.74/1.01 72 -subpopulations(first_movers,efficient_producers,c1,A) | -greater_or_equal(B,A) | -greater_or_equal(A,B) | subpopulations(first_movers,efficient_producers,c1,B). [factor(68,a,b)].
% 0.74/1.01 73 greater_or_equal(critical_point(c1),c2). [resolve(44,b,41,a)].
% 0.74/1.01 74 greater_or_equal(A,A). [xx_res(45,b)].
% 0.74/1.01 76 -greater(growth_rate(efficient_producers,critical_point(c1)),growth_rate(first_movers,critical_point(c1))). [ur(52,a,xx)].
% 0.74/1.01 80 greater_or_equal(critical_point(c1),appear(efficient_producers,c1)). [resolve(59,a,57,a)].
% 0.74/1.01 90 -subpopulations(first_movers,efficient_producers,c1,A) | -greater_or_equal(B,A) | -greater_or_equal(critical_point(c1),B) | subpopulations(first_movers,efficient_producers,c1,B). [resolve(68,b,57,a)].
% 0.74/1.01 91 greater(zero,difference(growth_rate(first_movers,critical_point(c1)),growth_rate(efficient_producers,critical_point(c1)))) | greater_or_equal(difference(growth_rate(first_movers,critical_point(c1)),growth_rate(efficient_producers,critical_point(c1))),zero). [resolve(69,a,57,a)].
% 0.74/1.01 93 -greater_or_equal(difference(growth_rate(first_movers,critical_point(c1)),growth_rate(efficient_producers,critical_point(c1))),zero) | -greater_or_equal(A,appear(efficient_producers,c1)) | -greater(critical_point(c1),A) | -decreases(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A))) | greater(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)),zero). [resolve(70,a,40,a)].
% 0.74/1.01 96 -greater_or_equal(A,critical_point(c1)) | -greater_or_equal(critical_point(c1),A) | subpopulations(first_movers,efficient_producers,c1,A). [resolve(72,a,57,a)].
% 0.74/1.01 99 -greater(zero,difference(growth_rate(first_movers,critical_point(c1)),growth_rate(efficient_producers,critical_point(c1)))). [ur(47,b,76,a)].
% 0.74/1.01 100 greater_or_equal(difference(growth_rate(first_movers,critical_point(c1)),growth_rate(efficient_producers,critical_point(c1))),zero). [back_unit_del(91),unit_del(a,99)].
% 0.74/1.01 101 -greater_or_equal(A,appear(efficient_producers,c1)) | -greater(critical_point(c1),A) | -decreases(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A))) | greater(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)),zero). [back_unit_del(93),unit_del(a,100)].
% 0.74/1.01 102 -greater(critical_point(c1),appear(efficient_producers,c1)) | in_environment(c1,appear(efficient_producers,c1)). [resolve(74,a,65,a)].
% 0.74/1.01 109 greater(critical_point(c1),appear(efficient_producers,c1)) | appear(efficient_producers,c1) = critical_point(c1). [resolve(80,a,46,a)].
% 0.74/1.01 124 appear(efficient_producers,c1) = critical_point(c1) | in_environment(c1,appear(efficient_producers,c1)). [resolve(109,a,102,a)].
% 0.74/1.01 136 appear(efficient_producers,c1) = critical_point(c1) | subpopulations(first_movers,efficient_producers,c1,appear(efficient_producers,c1)). [resolve(124,b,60,a)].
% 0.74/1.01 138 -greater_or_equal(c2,critical_point(c1)) | subpopulations(first_movers,efficient_producers,c1,c2). [resolve(96,b,73,a)].
% 0.74/1.01 150 -greater_or_equal(A,appear(efficient_producers,c1)) | -greater_or_equal(critical_point(c1),A) | subpopulations(first_movers,efficient_producers,c1,A) | appear(efficient_producers,c1) = critical_point(c1). [resolve(90,a,136,b)].
% 0.74/1.01 155 -decreases(difference(growth_rate(first_movers,c2),growth_rate(efficient_producers,c2))) | greater(difference(growth_rate(first_movers,c2),growth_rate(efficient_producers,c2)),zero). [resolve(101,a,42,a),unit_del(a,41)].
% 0.74/1.01 160 subpopulations(first_movers,efficient_producers,c1,c2) | appear(efficient_producers,c1) = critical_point(c1). [resolve(150,a,42,a),unit_del(a,73)].
% 0.74/1.01 169 appear(efficient_producers,c1) = critical_point(c1) | decreases(difference(founding_rate(first_movers,c2),founding_rate(efficient_producers,c2))). [resolve(160,a,61,a)].
% 0.74/1.01 170 appear(efficient_producers,c1) = critical_point(c1) | subpopulations(efficient_producers,first_movers,c1,c2). [resolve(160,a,58,a)].
% 0.74/1.01 171 appear(efficient_producers,c1) = critical_point(c1) | -decreases(difference(disbanding_rate(first_movers,c2),disbanding_rate(efficient_producers,c2))). [resolve(160,a,53,a)].
% 0.74/1.01 172 appear(efficient_producers,c1) = critical_point(c1) | -greater(growth_rate(first_movers,c2),growth_rate(efficient_producers,c2)). [resolve(170,b,63,a),unit_del(c,43)].
% 0.74/1.01 175 appear(efficient_producers,c1) = critical_point(c1) | decreases(difference(disbanding_rate(first_movers,c2),disbanding_rate(efficient_producers,c2))) | decreases(difference(growth_rate(first_movers,c2),growth_rate(efficient_producers,c2))). [resolve(169,b,51,a)].
% 0.74/1.01 182 appear(efficient_producers,c1) = critical_point(c1) | decreases(difference(growth_rate(first_movers,c2),growth_rate(efficient_producers,c2))). [resolve(175,b,171,b),merge(c)].
% 0.74/1.01 183 appear(efficient_producers,c1) = critical_point(c1) | greater(difference(growth_rate(first_movers,c2),growth_rate(efficient_producers,c2)),zero). [resolve(182,b,155,a)].
% 0.74/1.01 184 appear(efficient_producers,c1) = critical_point(c1) | greater(growth_rate(first_movers,c2),growth_rate(efficient_producers,c2)). [resolve(183,b,49,a)].
% 0.74/1.01 186 appear(efficient_producers,c1) = critical_point(c1). [resolve(184,b,172,b),merge(b)].
% 0.74/1.01 194 greater_or_equal(c2,critical_point(c1)). [back_rewrite(42),rewrite([186(4)])].
% 0.74/1.01 196 subpopulations(first_movers,efficient_producers,c1,c2). [back_unit_del(138),unit_del(a,194)].
% 0.74/1.01 205 decreases(difference(founding_rate(first_movers,c2),founding_rate(efficient_producers,c2))). [resolve(196,a,61,a)].
% 0.74/1.01 206 subpopulations(efficient_producers,first_movers,c1,c2). [resolve(196,a,58,a)].
% 0.74/1.01 207 -decreases(difference(disbanding_rate(first_movers,c2),disbanding_rate(efficient_producers,c2))). [resolve(196,a,53,a)].
% 0.74/1.01 208 -greater(growth_rate(first_movers,c2),growth_rate(efficient_producers,c2)). [resolve(206,a,63,a),unit_del(b,43)].
% 0.74/1.01 209 decreases(difference(growth_rate(first_movers,c2),growth_rate(efficient_producers,c2))). [resolve(205,a,51,a),unit_del(a,207)].
% 0.74/1.01 210 greater(difference(growth_rate(first_movers,c2),growth_rate(efficient_producers,c2)),zero). [back_unit_del(155),unit_del(a,209)].
% 0.74/1.01 211 $F. [ur(49,b,208,a),unit_del(a,210)].
% 0.74/1.01
% 0.74/1.01 % SZS output end Refutation
% 0.74/1.01 ============================== end of proof ==========================
% 0.74/1.01
% 0.74/1.01 ============================== STATISTICS ============================
% 0.74/1.01
% 0.74/1.01 Given=134. Generated=338. Kept=169. proofs=1.
% 0.74/1.01 Usable=76. Sos=17. Demods=1. Limbo=0, Disabled=123. Hints=0.
% 0.74/1.01 Megabytes=0.31.
% 0.74/1.01 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.74/1.01
% 0.74/1.01 ============================== end of statistics =====================
% 0.74/1.01
% 0.74/1.01 ============================== end of search =========================
% 0.74/1.01
% 0.74/1.01 THEOREM PROVED
% 0.74/1.01 % SZS status Theorem
% 0.74/1.01
% 0.74/1.01 Exiting with 1 proof.
% 0.74/1.01
% 0.74/1.01 Process 19744 exit (max_proofs) Thu Jun 9 10:25:25 2022
% 0.74/1.01 Prover9 interrupted
%------------------------------------------------------------------------------