TSTP Solution File: MGT034-2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : MGT034-2 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %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 : 600s
% DateTime : Sun Jul 17 22:22:57 EDT 2022
% Result : Unsatisfiable 0.73s 1.01s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : MGT034-2 : TPTP v8.1.0. Released v2.4.0.
% 0.09/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 9 08:05:49 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.69/0.98 ============================== Prover9 ===============================
% 0.69/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.69/0.98 Process 24533 was started by sandbox on n017.cluster.edu,
% 0.69/0.98 Thu Jun 9 08:05:49 2022
% 0.69/0.98 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_24380_n017.cluster.edu".
% 0.69/0.98 ============================== end of head ===========================
% 0.69/0.98
% 0.69/0.98 ============================== INPUT =================================
% 0.69/0.98
% 0.69/0.98 % Reading from file /tmp/Prover9_24380_n017.cluster.edu
% 0.69/0.98
% 0.69/0.98 set(prolog_style_variables).
% 0.69/0.98 set(auto2).
% 0.69/0.98 % set(auto2) -> set(auto).
% 0.69/0.98 % set(auto) -> set(auto_inference).
% 0.69/0.98 % set(auto) -> set(auto_setup).
% 0.69/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.69/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.69/0.98 % set(auto) -> set(auto_limits).
% 0.69/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.69/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.69/0.98 % set(auto) -> set(auto_denials).
% 0.69/0.98 % set(auto) -> set(auto_process).
% 0.69/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.69/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.69/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.69/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.69/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.69/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.69/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.69/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.69/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.69/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.69/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.69/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.69/0.98 % set(auto2) -> assign(stats, some).
% 0.69/0.98 % set(auto2) -> clear(echo_input).
% 0.69/0.98 % set(auto2) -> set(quiet).
% 0.69/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.69/0.98 % set(auto2) -> clear(print_given).
% 0.69/0.98 assign(lrs_ticks,-1).
% 0.69/0.98 assign(sos_limit,10000).
% 0.69/0.98 assign(order,kbo).
% 0.69/0.98 set(lex_order_vars).
% 0.69/0.98 clear(print_given).
% 0.69/0.98
% 0.69/0.98 % formulas(sos). % not echoed (30 formulas)
% 0.69/0.98
% 0.69/0.98 ============================== end of input ==========================
% 0.69/0.98
% 0.69/0.98 % From the command line: assign(max_seconds, 300).
% 0.69/0.98
% 0.69/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.69/0.98
% 0.69/0.98 % Formulas that are not ordinary clauses:
% 0.69/0.98
% 0.69/0.98 ============================== end of process non-clausal formulas ===
% 0.69/0.98
% 0.69/0.98 ============================== PROCESS INITIAL CLAUSES ===============
% 0.69/0.98
% 0.69/0.98 ============================== PREDICATE ELIMINATION =================
% 0.69/0.98 1 -environment(A) | B != critical_point(A) | -greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)) # label(d1_54) # label(hypothesis). [assumption].
% 0.69/0.98 2 environment(sk1) # label(prove_t3_58) # label(negated_conjecture). [assumption].
% 0.69/0.98 Derived: A != critical_point(sk1) | -greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)). [resolve(1,a,2,a)].
% 0.69/0.98 3 -environment(A) | -subpopulations(first_movers,efficient_producers,A,B) | -decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B))) # label(l3_34) # label(axiom). [assumption].
% 0.69/0.98 Derived: -subpopulations(first_movers,efficient_producers,sk1,A) | -decreases(difference(disbanding_rate(first_movers,A),disbanding_rate(efficient_producers,A))). [resolve(3,a,2,a)].
% 0.69/0.98 4 -environment(A) | in_environment(A,start_time(A)) # label(mp_opening_time_in_duration_44) # label(axiom). [assumption].
% 0.69/0.98 Derived: in_environment(sk1,start_time(sk1)). [resolve(4,a,2,a)].
% 0.69/0.98 5 -environment(A) | greater_or_equal(appear(first_movers,A),start_time(A)) # label(mp_no_FM_before_opening_45) # label(axiom). [assumption].
% 0.69/0.98 Derived: greater_or_equal(appear(first_movers,sk1),start_time(sk1)). [resolve(5,a,2,a)].
% 0.69/0.98 6 -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_35) # label(axiom). [assumption].
% 0.69/0.98 Derived: -in_environment(sk1,critical_point(sk1)) | subpopulations(first_movers,efficient_producers,sk1,critical_point(sk1)). [resolve(6,a,2,a)].
% 0.69/0.98 7 -environment(A) | -subpopulations(first_movers,efficient_producers,A,B) | subpopulations(efficient_producers,first_movers,A,B) # label(mp_symmetry_of_subpopulations_48) # label(axiom). [assumption].
% 0.69/0.98 Derived: -subpopulations(first_movers,efficient_producers,sk1,A) | subpopulations(efficient_producers,first_movers,sk1,A). [resolve(7,a,2,a)].
% 0.69/0.98 8 -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_49) # label(axiom). [assumption].
% 0.69/0.98 Derived: -subpopulations(first_movers,efficient_producers,sk1,A) | greater_or_equal(A,appear(efficient_producers,sk1)). [resolve(8,a,2,a)].
% 0.69/0.98 9 -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_36) # label(axiom). [assumption].
% 0.69/0.98 Derived: -in_environment(sk1,appear(efficient_producers,sk1)) | subpopulations(first_movers,efficient_producers,sk1,appear(efficient_producers,sk1)). [resolve(9,a,2,a)].
% 0.69/0.98 10 -environment(A) | -subpopulations(first_movers,efficient_producers,A,B) | decreases(difference(founding_rate(first_movers,B),founding_rate(efficient_producers,B))) # label(a12_57) # label(hypothesis). [assumption].
% 0.69/0.98 Derived: -subpopulations(first_movers,efficient_producers,sk1,A) | decreases(difference(founding_rate(first_movers,A),founding_rate(efficient_producers,A))). [resolve(10,a,2,a)].
% 0.69/0.98 11 -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_43) # label(axiom). [assumption].
% 0.69/0.98 Derived: -in_environment(sk1,A) | -in_environment(sk1,B) | -greater_or_equal(B,C) | -greater_or_equal(C,A) | in_environment(sk1,C). [resolve(11,a,2,a)].
% 0.69/0.98 12 -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_33) # label(axiom). [assumption].
% 0.69/0.98 Derived: -subpopulations(A,B,sk1,C) | -greater(growth_rate(B,C),growth_rate(A,C)) | selection_favors(B,A,C). [resolve(12,a,2,a)].
% 0.69/0.98 13 -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_46) # label(axiom). [assumption].
% 0.69/0.98 Derived: -in_environment(sk1,critical_point(sk1)) | -greater_or_equal(A,appear(efficient_producers,sk1)) | -greater(critical_point(sk1),A) | in_environment(sk1,A). [resolve(13,a,2,a)].
% 0.69/0.98 14 -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_47) # label(axiom). [assumption].
% 0.69/0.98 Derived: -in_environment(sk1,A) | -greater(cardinality_at_time(first_movers,A),zero) | -greater(cardinality_at_time(efficient_producers,A),zero) | subpopulations(first_movers,efficient_producers,sk1,A). [resolve(14,a,2,a)].
% 0.69/0.98 15 -environment(A) | B != critical_point(A) | -subpopulations(first_movers,efficient_producers,A,C) | -greater(C,B) | greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C)) # label(d1_55) # label(hypothesis). [assumption].
% 0.69/0.98 Derived: A != critical_point(sk1) | -subpopulations(first_movers,efficient_producers,sk1,B) | -greater(B,A) | greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)). [resolve(15,a,2,a)].
% 0.69/0.98 16 -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_56) # label(hypothesis). [assumption].
% 0.69/0.98 Derived: -subpopulations(first_movers,efficient_producers,sk1,A) | -subpopulations(first_movers,efficient_producers,sk1,B) | -greater_or_equal(C,A) | -greater_or_equal(B,C) | subpopulations(first_movers,efficient_producers,sk1,C). [resolve(16,a,2,a)].
% 0.69/0.98 17 -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_53) # label(axiom). [assumption].
% 0.73/1.01 Derived: -subpopulations(first_movers,efficient_producers,sk1,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(17,a,2,a)].
% 0.73/1.01 18 -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_38) # label(axiom). [assumption].
% 0.73/1.01 Derived: -in_environment(sk1,A) | -greater_or_equal(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)),zero) | -greater_or_equal(B,appear(efficient_producers,sk1)) | -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(18,a,2,a)].
% 0.73/1.01
% 0.73/1.01 ============================== end predicate elimination =============
% 0.73/1.01
% 0.73/1.01 Auto_denials: (non-Horn, no changes).
% 0.73/1.01
% 0.73/1.01 Term ordering decisions:
% 0.73/1.01 Function symbol KB weights: sk1=1. efficient_producers=1. first_movers=1. zero=1. sk2=1. growth_rate=1. difference=1. appear=1. founding_rate=1. cardinality_at_time=1. disbanding_rate=1. critical_point=1. start_time=1.
% 0.73/1.01
% 0.73/1.01 ============================== end of process initial clauses ========
% 0.73/1.01
% 0.73/1.01 ============================== CLAUSES FOR SEARCH ====================
% 0.73/1.01
% 0.73/1.01 ============================== end of clauses for search =============
% 0.73/1.01
% 0.73/1.01 ============================== SEARCH ================================
% 0.73/1.01
% 0.73/1.01 % Starting search at 0.02 seconds.
% 0.73/1.01
% 0.73/1.01 ============================== PROOF =================================
% 0.73/1.01 % SZS status Unsatisfiable
% 0.73/1.01 % SZS output start Refutation
% 0.73/1.01
% 0.73/1.01 % Proof 1 at 0.04 (+ 0.00) seconds.
% 0.73/1.01 % Length of proof is 76.
% 0.73/1.01 % Level of proof is 20.
% 0.73/1.01 % Maximum clause weight is 37.000.
% 0.73/1.01 % Given clauses 134.
% 0.73/1.01
% 0.73/1.01 1 -environment(A) | B != critical_point(A) | -greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)) # label(d1_54) # label(hypothesis). [assumption].
% 0.73/1.01 2 environment(sk1) # label(prove_t3_58) # label(negated_conjecture). [assumption].
% 0.73/1.01 3 -environment(A) | -subpopulations(first_movers,efficient_producers,A,B) | -decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B))) # label(l3_34) # label(axiom). [assumption].
% 0.73/1.01 6 -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_35) # label(axiom). [assumption].
% 0.73/1.01 7 -environment(A) | -subpopulations(first_movers,efficient_producers,A,B) | subpopulations(efficient_producers,first_movers,A,B) # label(mp_symmetry_of_subpopulations_48) # label(axiom). [assumption].
% 0.73/1.01 8 -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_49) # label(axiom). [assumption].
% 0.73/1.01 9 -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_36) # label(axiom). [assumption].
% 0.73/1.01 10 -environment(A) | -subpopulations(first_movers,efficient_producers,A,B) | decreases(difference(founding_rate(first_movers,B),founding_rate(efficient_producers,B))) # label(a12_57) # label(hypothesis). [assumption].
% 0.73/1.01 12 -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_33) # label(axiom). [assumption].
% 0.73/1.01 13 -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_46) # label(axiom). [assumption].
% 0.73/1.01 16 -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_56) # label(hypothesis). [assumption].
% 0.73/1.01 17 -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_53) # label(axiom). [assumption].
% 0.73/1.01 18 -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_38) # label(axiom). [assumption].
% 0.73/1.01 19 in_environment(sk1,critical_point(sk1)) # label(prove_t3_59) # label(negated_conjecture). [assumption].
% 0.73/1.01 20 greater(critical_point(sk1),sk2) # label(prove_t3_61) # label(negated_conjecture). [assumption].
% 0.73/1.01 21 greater_or_equal(sk2,appear(efficient_producers,sk1)) # label(prove_t3_60) # label(negated_conjecture). [assumption].
% 0.73/1.01 22 -selection_favors(first_movers,efficient_producers,sk2) # label(prove_t3_62) # label(negated_conjecture). [assumption].
% 0.73/1.01 23 -greater(A,B) | greater_or_equal(A,B) # label(mp_greater_or_equal_51) # label(axiom). [assumption].
% 0.73/1.01 24 A != B | greater_or_equal(A,B) # label(mp_greater_or_equal_52) # label(axiom). [assumption].
% 0.73/1.01 25 -greater_or_equal(A,B) | greater(A,B) | A = B # label(mp_greater_or_equal_50) # label(axiom). [assumption].
% 0.73/1.01 26 -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_39) # label(axiom). [assumption].
% 0.73/1.01 28 -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_41) # label(axiom). [assumption].
% 0.73/1.01 30 -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_37) # label(axiom). [assumption].
% 0.73/1.01 31 A != critical_point(sk1) | -greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)). [resolve(1,a,2,a)].
% 0.73/1.01 32 critical_point(sk1) != A | -greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)). [copy(31),flip(a)].
% 0.73/1.01 33 -subpopulations(first_movers,efficient_producers,sk1,A) | -decreases(difference(disbanding_rate(first_movers,A),disbanding_rate(efficient_producers,A))). [resolve(3,a,2,a)].
% 0.73/1.01 36 -in_environment(sk1,critical_point(sk1)) | subpopulations(first_movers,efficient_producers,sk1,critical_point(sk1)). [resolve(6,a,2,a)].
% 0.73/1.01 37 subpopulations(first_movers,efficient_producers,sk1,critical_point(sk1)). [copy(36),unit_del(a,19)].
% 0.73/1.01 38 -subpopulations(first_movers,efficient_producers,sk1,A) | subpopulations(efficient_producers,first_movers,sk1,A). [resolve(7,a,2,a)].
% 0.73/1.01 39 -subpopulations(first_movers,efficient_producers,sk1,A) | greater_or_equal(A,appear(efficient_producers,sk1)). [resolve(8,a,2,a)].
% 0.73/1.01 40 -in_environment(sk1,appear(efficient_producers,sk1)) | subpopulations(first_movers,efficient_producers,sk1,appear(efficient_producers,sk1)). [resolve(9,a,2,a)].
% 0.73/1.01 41 -subpopulations(first_movers,efficient_producers,sk1,A) | decreases(difference(founding_rate(first_movers,A),founding_rate(efficient_producers,A))). [resolve(10,a,2,a)].
% 0.73/1.01 43 -subpopulations(A,B,sk1,C) | -greater(growth_rate(B,C),growth_rate(A,C)) | selection_favors(B,A,C). [resolve(12,a,2,a)].
% 0.73/1.01 44 -in_environment(sk1,critical_point(sk1)) | -greater_or_equal(A,appear(efficient_producers,sk1)) | -greater(critical_point(sk1),A) | in_environment(sk1,A). [resolve(13,a,2,a)].
% 0.73/1.01 45 -greater_or_equal(A,appear(efficient_producers,sk1)) | -greater(critical_point(sk1),A) | in_environment(sk1,A). [copy(44),unit_del(a,19)].
% 0.73/1.01 49 -subpopulations(first_movers,efficient_producers,sk1,A) | -subpopulations(first_movers,efficient_producers,sk1,B) | -greater_or_equal(C,A) | -greater_or_equal(B,C) | subpopulations(first_movers,efficient_producers,sk1,C). [resolve(16,a,2,a)].
% 0.73/1.01 50 -subpopulations(first_movers,efficient_producers,sk1,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(17,a,2,a)].
% 0.73/1.01 51 -in_environment(sk1,A) | -greater_or_equal(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)),zero) | -greater_or_equal(B,appear(efficient_producers,sk1)) | -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(18,a,2,a)].
% 0.73/1.01 53 -subpopulations(first_movers,efficient_producers,sk1,A) | -greater_or_equal(B,A) | -greater_or_equal(A,B) | subpopulations(first_movers,efficient_producers,sk1,B). [factor(49,a,b)].
% 0.73/1.01 54 greater_or_equal(critical_point(sk1),sk2). [resolve(23,a,20,a)].
% 0.73/1.01 55 greater_or_equal(A,A). [xx_res(24,a)].
% 0.73/1.01 57 -greater(growth_rate(efficient_producers,critical_point(sk1)),growth_rate(first_movers,critical_point(sk1))). [ur(32,a,xx)].
% 0.73/1.01 61 greater_or_equal(critical_point(sk1),appear(efficient_producers,sk1)). [resolve(39,a,37,a)].
% 0.73/1.01 71 -subpopulations(first_movers,efficient_producers,sk1,A) | -greater_or_equal(B,A) | -greater_or_equal(critical_point(sk1),B) | subpopulations(first_movers,efficient_producers,sk1,B). [resolve(49,b,37,a)].
% 0.73/1.01 72 greater(zero,difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1)))) | greater_or_equal(difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))),zero). [resolve(50,a,37,a)].
% 0.73/1.01 74 -greater_or_equal(difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))),zero) | -greater_or_equal(A,appear(efficient_producers,sk1)) | -greater(critical_point(sk1),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(51,a,19,a)].
% 0.73/1.01 77 -greater_or_equal(A,critical_point(sk1)) | -greater_or_equal(critical_point(sk1),A) | subpopulations(first_movers,efficient_producers,sk1,A). [resolve(53,a,37,a)].
% 0.73/1.01 80 -greater(zero,difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1)))). [ur(26,b,57,a)].
% 0.73/1.01 81 greater_or_equal(difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))),zero). [back_unit_del(72),unit_del(a,80)].
% 0.73/1.01 82 -greater_or_equal(A,appear(efficient_producers,sk1)) | -greater(critical_point(sk1),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(74),unit_del(a,81)].
% 0.73/1.01 83 -greater(critical_point(sk1),appear(efficient_producers,sk1)) | in_environment(sk1,appear(efficient_producers,sk1)). [resolve(55,a,45,a)].
% 0.73/1.01 90 greater(critical_point(sk1),appear(efficient_producers,sk1)) | appear(efficient_producers,sk1) = critical_point(sk1). [resolve(61,a,25,a),flip(b)].
% 0.73/1.01 105 appear(efficient_producers,sk1) = critical_point(sk1) | in_environment(sk1,appear(efficient_producers,sk1)). [resolve(90,a,83,a)].
% 0.73/1.01 117 appear(efficient_producers,sk1) = critical_point(sk1) | subpopulations(first_movers,efficient_producers,sk1,appear(efficient_producers,sk1)). [resolve(105,b,40,a)].
% 0.73/1.01 119 -greater_or_equal(sk2,critical_point(sk1)) | subpopulations(first_movers,efficient_producers,sk1,sk2). [resolve(77,b,54,a)].
% 0.73/1.01 131 -greater_or_equal(A,appear(efficient_producers,sk1)) | -greater_or_equal(critical_point(sk1),A) | subpopulations(first_movers,efficient_producers,sk1,A) | appear(efficient_producers,sk1) = critical_point(sk1). [resolve(71,a,117,b)].
% 0.73/1.01 136 -decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2))) | greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero). [resolve(82,a,21,a),unit_del(a,20)].
% 0.73/1.01 141 subpopulations(first_movers,efficient_producers,sk1,sk2) | appear(efficient_producers,sk1) = critical_point(sk1). [resolve(131,a,21,a),unit_del(a,54)].
% 0.73/1.01 150 appear(efficient_producers,sk1) = critical_point(sk1) | decreases(difference(founding_rate(first_movers,sk2),founding_rate(efficient_producers,sk2))). [resolve(141,a,41,a)].
% 0.73/1.01 151 appear(efficient_producers,sk1) = critical_point(sk1) | subpopulations(efficient_producers,first_movers,sk1,sk2). [resolve(141,a,38,a)].
% 0.73/1.01 152 appear(efficient_producers,sk1) = critical_point(sk1) | -decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))). [resolve(141,a,33,a)].
% 0.73/1.01 153 appear(efficient_producers,sk1) = critical_point(sk1) | -greater(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)). [resolve(151,b,43,a),unit_del(c,22)].
% 0.73/1.01 156 appear(efficient_producers,sk1) = critical_point(sk1) | decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))) | decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2))). [resolve(150,b,30,a)].
% 0.73/1.01 163 appear(efficient_producers,sk1) = critical_point(sk1) | decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2))). [resolve(156,b,152,b),merge(c)].
% 0.73/1.01 164 appear(efficient_producers,sk1) = critical_point(sk1) | greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero). [resolve(163,b,136,a)].
% 0.73/1.01 165 appear(efficient_producers,sk1) = critical_point(sk1) | greater(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)). [resolve(164,b,28,a)].
% 0.73/1.01 167 appear(efficient_producers,sk1) = critical_point(sk1). [resolve(165,b,153,b),merge(b)].
% 0.73/1.01 175 greater_or_equal(sk2,critical_point(sk1)). [back_rewrite(21),rewrite([167(4)])].
% 0.73/1.01 177 subpopulations(first_movers,efficient_producers,sk1,sk2). [back_unit_del(119),unit_del(a,175)].
% 0.73/1.01 186 decreases(difference(founding_rate(first_movers,sk2),founding_rate(efficient_producers,sk2))). [resolve(177,a,41,a)].
% 0.73/1.01 187 subpopulations(efficient_producers,first_movers,sk1,sk2). [resolve(177,a,38,a)].
% 0.73/1.01 188 -decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))). [resolve(177,a,33,a)].
% 0.73/1.01 189 -greater(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)). [resolve(187,a,43,a),unit_del(b,22)].
% 0.73/1.01 190 decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2))). [resolve(186,a,30,a),unit_del(a,188)].
% 0.73/1.01 191 greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero). [back_unit_del(136),unit_del(a,190)].
% 0.73/1.01 192 $F. [ur(28,b,189,a),unit_del(a,191)].
% 0.73/1.01
% 0.73/1.01 % SZS output end Refutation
% 0.73/1.01 ============================== end of proof ==========================
% 0.73/1.01
% 0.73/1.01 ============================== STATISTICS ============================
% 0.73/1.01
% 0.73/1.01 Given=134. Generated=338. Kept=169. proofs=1.
% 0.73/1.01 Usable=76. Sos=17. Demods=1. Limbo=0, Disabled=123. Hints=0.
% 0.73/1.01 Megabytes=0.28.
% 0.73/1.01 User_CPU=0.04, System_CPU=0.00, Wall_clock=0.
% 0.73/1.01
% 0.73/1.01 ============================== end of statistics =====================
% 0.73/1.01
% 0.73/1.01 ============================== end of search =========================
% 0.73/1.01
% 0.73/1.01 THEOREM PROVED
% 0.73/1.01 % SZS status Unsatisfiable
% 0.73/1.01
% 0.73/1.01 Exiting with 1 proof.
% 0.73/1.01
% 0.73/1.01 Process 24533 exit (max_proofs) Thu Jun 9 08:05:49 2022
% 0.73/1.01 Prover9 interrupted
%------------------------------------------------------------------------------