TSTP Solution File: MGT026+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : MGT026+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 22:22:55 EDT 2022
% Result : Theorem 0.43s 1.01s
% Output : Refutation 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MGT026+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n027.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 : 600
% 0.12/0.33 % DateTime : Thu Jun 9 12:55:42 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.43/1.01 ============================== Prover9 ===============================
% 0.43/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.01 Process 21616 was started by sandbox2 on n027.cluster.edu,
% 0.43/1.01 Thu Jun 9 12:55:43 2022
% 0.43/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_21299_n027.cluster.edu".
% 0.43/1.01 ============================== end of head ===========================
% 0.43/1.01
% 0.43/1.01 ============================== INPUT =================================
% 0.43/1.01
% 0.43/1.01 % Reading from file /tmp/Prover9_21299_n027.cluster.edu
% 0.43/1.01
% 0.43/1.01 set(prolog_style_variables).
% 0.43/1.01 set(auto2).
% 0.43/1.01 % set(auto2) -> set(auto).
% 0.43/1.01 % set(auto) -> set(auto_inference).
% 0.43/1.01 % set(auto) -> set(auto_setup).
% 0.43/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.01 % set(auto) -> set(auto_limits).
% 0.43/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.01 % set(auto) -> set(auto_denials).
% 0.43/1.01 % set(auto) -> set(auto_process).
% 0.43/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.01 % set(auto2) -> assign(stats, some).
% 0.43/1.01 % set(auto2) -> clear(echo_input).
% 0.43/1.01 % set(auto2) -> set(quiet).
% 0.43/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.01 % set(auto2) -> clear(print_given).
% 0.43/1.01 assign(lrs_ticks,-1).
% 0.43/1.01 assign(sos_limit,10000).
% 0.43/1.01 assign(order,kbo).
% 0.43/1.01 set(lex_order_vars).
% 0.43/1.01 clear(print_given).
% 0.43/1.01
% 0.43/1.01 % formulas(sos). % not echoed (11 formulas)
% 0.43/1.01
% 0.43/1.01 ============================== end of input ==========================
% 0.43/1.01
% 0.43/1.01 % From the command line: assign(max_seconds, 300).
% 0.43/1.01
% 0.43/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.01
% 0.43/1.01 % Formulas that are not ordinary clauses:
% 0.43/1.01 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].
% 0.43/1.01 2 (all E all S1 all S2 all T (environment(E) & subpopulation(S1,E,T) & subpopulation(S2,E,T) & greater(cardinality_at_time(S1,T),zero) & cardinality_at_time(S2,T) = zero -> selection_favors(S1,S2,T))) # label(mp2_favour_members) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 3 (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_non_empty_fm_and_ep) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 4 (all E all T (environment(E) & in_environment(E,T) -> greater_or_equal(cardinality_at_time(first_movers,T),zero))) # label(mp_first_movers_exist) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 5 (all E all T (environment(E) & in_environment(E,T) -> subpopulation(first_movers,E,T) & subpopulation(efficient_producers,E,T))) # label(mp_subpopulations) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 6 (all E (environment(E) -> greater_or_equal(critical_point(E),appear(efficient_producers,E)))) # label(mp_critical_point_after_EP) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 7 (all X all Y all Z (greater(X,Y) & greater(Y,Z) -> greater(X,Z))) # label(mp_greater_transitivity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 8 (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].
% 0.43/1.01 9 (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].
% 0.43/1.01 10 (all E all T (environment(E) & in_environment(E,T) & greater_or_equal(T,appear(efficient_producers,E)) -> greater(cardinality_at_time(efficient_producers,T),zero))) # label(t6) # label(hypothesis) # label(non_clause). [assumption].
% 0.43/1.01 11 -(all E all T (environment(E) & in_environment(E,T) & greater(T,critical_point(E)) -> selection_favors(efficient_producers,first_movers,T))) # label(prove_l8) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/1.01
% 0.43/1.01 ============================== end of process non-clausal formulas ===
% 0.43/1.01
% 0.43/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.43/1.01
% 0.43/1.01 ============================== PREDICATE ELIMINATION =================
% 0.43/1.01 12 -environment(A) | critical_point(A) != B | -greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)) # label(d1) # label(hypothesis). [clausify(9)].
% 0.43/1.01 13 environment(c1) # label(prove_l8) # label(negated_conjecture). [clausify(11)].
% 0.43/1.01 Derived: critical_point(c1) != A | -greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)). [resolve(12,a,13,a)].
% 0.43/1.01 14 -environment(A) | greater_or_equal(critical_point(A),appear(efficient_producers,A)) # label(mp_critical_point_after_EP) # label(axiom). [clausify(6)].
% 0.43/1.01 Derived: greater_or_equal(critical_point(c1),appear(efficient_producers,c1)). [resolve(14,a,13,a)].
% 0.43/1.01 15 -environment(A) | -in_environment(A,B) | subpopulation(first_movers,A,B) # label(mp_subpopulations) # label(axiom). [clausify(5)].
% 0.43/1.01 Derived: -in_environment(c1,A) | subpopulation(first_movers,c1,A). [resolve(15,a,13,a)].
% 0.43/1.01 16 -environment(A) | -in_environment(A,B) | subpopulation(efficient_producers,A,B) # label(mp_subpopulations) # label(axiom). [clausify(5)].
% 0.43/1.01 Derived: -in_environment(c1,A) | subpopulation(efficient_producers,c1,A). [resolve(16,a,13,a)].
% 0.43/1.01 17 -environment(A) | -in_environment(A,B) | greater_or_equal(cardinality_at_time(first_movers,B),zero) # label(mp_first_movers_exist) # label(axiom). [clausify(4)].
% 0.43/1.01 Derived: -in_environment(c1,A) | greater_or_equal(cardinality_at_time(first_movers,A),zero). [resolve(17,a,13,a)].
% 0.43/1.01 18 -environment(A) | -in_environment(A,B) | -greater_or_equal(B,appear(efficient_producers,A)) | greater(cardinality_at_time(efficient_producers,B),zero) # label(t6) # label(hypothesis). [clausify(10)].
% 0.43/1.01 Derived: -in_environment(c1,A) | -greater_or_equal(A,appear(efficient_producers,c1)) | greater(cardinality_at_time(efficient_producers,A),zero). [resolve(18,a,13,a)].
% 0.43/1.01 19 -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)].
% 0.43/1.01 Derived: -subpopulations(A,B,c1,C) | -greater(growth_rate(B,C),growth_rate(A,C)) | selection_favors(B,A,C). [resolve(19,a,13,a)].
% 0.43/1.01 20 -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_non_empty_fm_and_ep) # label(axiom). [clausify(3)].
% 0.43/1.01 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(20,a,13,a)].
% 0.43/1.01 21 -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(9)].
% 0.43/1.01 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(21,a,13,a)].
% 0.43/1.01 22 -environment(A) | -subpopulation(B,A,C) | -subpopulation(D,A,C) | -greater(cardinality_at_time(B,C),zero) | cardinality_at_time(D,C) != zero | selection_favors(B,D,C) # label(mp2_favour_members) # label(axiom). [clausify(2)].
% 0.43/1.01 Derived: -subpopulation(A,c1,B) | -subpopulation(C,c1,B) | -greater(cardinality_at_time(A,B),zero) | cardinality_at_time(C,B) != zero | selection_favors(A,C,B). [resolve(22,a,13,a)].
% 0.43/1.01
% 0.43/1.01 ============================== end predicate elimination =============
% 0.43/1.01
% 0.43/1.01 Auto_denials: (non-Horn, no changes).
% 0.43/1.01
% 0.43/1.01 Term ordering decisions:
% 0.43/1.01
% 0.43/1.01 % Assigning unary symbol critical_point kb_weight 0 and highest precedence (16).
% 0.43/1.01 Function symbol KB weights: efficient_producers=1. first_movers=1. zero=1. c1=1. c2=1. cardinality_at_time=1. growth_rate=1. appear=1. critical_point=0.
% 0.43/1.01
% 0.43/1.01 ============================== end of process initial clauses ========
% 0.43/1.01
% 0.43/1.01 ============================== CLAUSES FOR SEARCH ====================
% 0.43/1.01
% 0.43/1.01 ============================== end of clauses for search =============
% 0.43/1.01
% 0.43/1.01 ============================== SEARCH ================================
% 0.43/1.01
% 0.43/1.01 % Starting search at 0.01 seconds.
% 0.43/1.01
% 0.43/1.01 ============================== PROOF =================================
% 0.43/1.01 % SZS status Theorem
% 0.43/1.01 % SZS output start Refutation
% 0.43/1.01
% 0.43/1.01 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.43/1.01 % Length of proof is 66.
% 0.43/1.01 % Level of proof is 17.
% 0.43/1.01 % Maximum clause weight is 25.000.
% 0.43/1.01 % Given clauses 69.
% 0.43/1.01
% 0.43/1.01 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].
% 0.43/1.01 2 (all E all S1 all S2 all T (environment(E) & subpopulation(S1,E,T) & subpopulation(S2,E,T) & greater(cardinality_at_time(S1,T),zero) & cardinality_at_time(S2,T) = zero -> selection_favors(S1,S2,T))) # label(mp2_favour_members) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 3 (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_non_empty_fm_and_ep) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 4 (all E all T (environment(E) & in_environment(E,T) -> greater_or_equal(cardinality_at_time(first_movers,T),zero))) # label(mp_first_movers_exist) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 5 (all E all T (environment(E) & in_environment(E,T) -> subpopulation(first_movers,E,T) & subpopulation(efficient_producers,E,T))) # label(mp_subpopulations) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 6 (all E (environment(E) -> greater_or_equal(critical_point(E),appear(efficient_producers,E)))) # label(mp_critical_point_after_EP) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 7 (all X all Y all Z (greater(X,Y) & greater(Y,Z) -> greater(X,Z))) # label(mp_greater_transitivity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 8 (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].
% 0.43/1.01 9 (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].
% 0.43/1.01 10 (all E all T (environment(E) & in_environment(E,T) & greater_or_equal(T,appear(efficient_producers,E)) -> greater(cardinality_at_time(efficient_producers,T),zero))) # label(t6) # label(hypothesis) # label(non_clause). [assumption].
% 0.43/1.01 11 -(all E all T (environment(E) & in_environment(E,T) & greater(T,critical_point(E)) -> selection_favors(efficient_producers,first_movers,T))) # label(prove_l8) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/1.01 13 environment(c1) # label(prove_l8) # label(negated_conjecture). [clausify(11)].
% 0.43/1.01 14 -environment(A) | greater_or_equal(critical_point(A),appear(efficient_producers,A)) # label(mp_critical_point_after_EP) # label(axiom). [clausify(6)].
% 0.43/1.01 15 -environment(A) | -in_environment(A,B) | subpopulation(first_movers,A,B) # label(mp_subpopulations) # label(axiom). [clausify(5)].
% 0.43/1.01 16 -environment(A) | -in_environment(A,B) | subpopulation(efficient_producers,A,B) # label(mp_subpopulations) # label(axiom). [clausify(5)].
% 0.43/1.01 17 -environment(A) | -in_environment(A,B) | greater_or_equal(cardinality_at_time(first_movers,B),zero) # label(mp_first_movers_exist) # label(axiom). [clausify(4)].
% 0.43/1.01 18 -environment(A) | -in_environment(A,B) | -greater_or_equal(B,appear(efficient_producers,A)) | greater(cardinality_at_time(efficient_producers,B),zero) # label(t6) # label(hypothesis). [clausify(10)].
% 0.43/1.01 19 -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)].
% 0.43/1.01 20 -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_non_empty_fm_and_ep) # label(axiom). [clausify(3)].
% 0.43/1.01 21 -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(9)].
% 0.43/1.01 22 -environment(A) | -subpopulation(B,A,C) | -subpopulation(D,A,C) | -greater(cardinality_at_time(B,C),zero) | cardinality_at_time(D,C) != zero | selection_favors(B,D,C) # label(mp2_favour_members) # label(axiom). [clausify(2)].
% 0.43/1.01 23 in_environment(c1,c2) # label(prove_l8) # label(negated_conjecture). [clausify(11)].
% 0.43/1.01 24 greater(c2,critical_point(c1)) # label(prove_l8) # label(negated_conjecture). [clausify(11)].
% 0.43/1.01 25 -selection_favors(efficient_producers,first_movers,c2) # label(prove_l8) # label(negated_conjecture). [clausify(11)].
% 0.43/1.01 26 greater_or_equal(A,B) | -greater(A,B) # label(mp_greater_or_equal) # label(axiom). [clausify(8)].
% 0.43/1.01 28 -greater(A,B) | -greater(B,C) | greater(A,C) # label(mp_greater_transitivity) # label(axiom). [clausify(7)].
% 0.43/1.01 29 -greater_or_equal(A,B) | greater(A,B) | B = A # label(mp_greater_or_equal) # label(axiom). [clausify(8)].
% 0.43/1.01 31 greater_or_equal(critical_point(c1),appear(efficient_producers,c1)). [resolve(14,a,13,a)].
% 0.43/1.01 32 -in_environment(c1,A) | subpopulation(first_movers,c1,A). [resolve(15,a,13,a)].
% 0.43/1.01 33 -in_environment(c1,A) | subpopulation(efficient_producers,c1,A). [resolve(16,a,13,a)].
% 0.43/1.01 34 -in_environment(c1,A) | greater_or_equal(cardinality_at_time(first_movers,A),zero). [resolve(17,a,13,a)].
% 0.43/1.01 35 -in_environment(c1,A) | -greater_or_equal(A,appear(efficient_producers,c1)) | greater(cardinality_at_time(efficient_producers,A),zero). [resolve(18,a,13,a)].
% 0.43/1.01 36 -subpopulations(A,B,c1,C) | -greater(growth_rate(B,C),growth_rate(A,C)) | selection_favors(B,A,C). [resolve(19,a,13,a)].
% 0.43/1.01 37 -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(20,a,13,a)].
% 0.43/1.01 38 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(21,a,13,a)].
% 0.43/1.01 39 -subpopulation(A,c1,B) | -subpopulation(C,c1,B) | -greater(cardinality_at_time(A,B),zero) | cardinality_at_time(C,B) != zero | selection_favors(A,C,B). [resolve(22,a,13,a)].
% 0.43/1.01 41 greater_or_equal(c2,critical_point(c1)). [resolve(26,b,24,a)].
% 0.43/1.01 43 -greater(critical_point(c1),A) | greater(c2,A). [resolve(28,a,24,a)].
% 0.43/1.01 46 greater(critical_point(c1),appear(efficient_producers,c1)) | appear(efficient_producers,c1) = critical_point(c1). [resolve(31,a,29,a)].
% 0.43/1.01 47 subpopulation(first_movers,c1,c2). [resolve(32,a,23,a)].
% 0.43/1.01 48 subpopulation(efficient_producers,c1,c2). [resolve(33,a,23,a)].
% 0.43/1.01 49 greater_or_equal(cardinality_at_time(first_movers,c2),zero). [resolve(34,a,23,a)].
% 0.43/1.01 50 -greater_or_equal(c2,appear(efficient_producers,c1)) | greater(cardinality_at_time(efficient_producers,c2),zero). [resolve(35,a,23,a)].
% 0.43/1.01 51 -greater(cardinality_at_time(first_movers,c2),zero) | -greater(cardinality_at_time(efficient_producers,c2),zero) | subpopulations(first_movers,efficient_producers,c1,c2). [resolve(37,a,23,a)].
% 0.43/1.01 53 -subpopulation(A,c1,c2) | -greater(cardinality_at_time(A,c2),zero) | cardinality_at_time(first_movers,c2) != zero | selection_favors(A,first_movers,c2). [resolve(47,a,39,b)].
% 0.43/1.01 58 greater(cardinality_at_time(first_movers,c2),zero) | cardinality_at_time(first_movers,c2) = zero. [resolve(49,a,29,a),flip(b)].
% 0.43/1.01 61 appear(efficient_producers,c1) = critical_point(c1) | greater(c2,appear(efficient_producers,c1)). [resolve(46,a,43,a)].
% 0.43/1.01 64 -greater(cardinality_at_time(efficient_producers,c2),zero) | subpopulations(first_movers,efficient_producers,c1,c2) | cardinality_at_time(first_movers,c2) = zero. [resolve(51,a,58,a)].
% 0.43/1.01 67 appear(efficient_producers,c1) = critical_point(c1) | greater_or_equal(c2,appear(efficient_producers,c1)). [resolve(61,b,26,b)].
% 0.43/1.01 68 appear(efficient_producers,c1) = critical_point(c1) | greater(cardinality_at_time(efficient_producers,c2),zero). [resolve(67,b,50,a)].
% 0.43/1.01 73 -greater(cardinality_at_time(efficient_producers,c2),zero) | cardinality_at_time(first_movers,c2) != zero. [resolve(53,a,48,a),unit_del(c,25)].
% 0.43/1.01 74 cardinality_at_time(first_movers,c2) != zero | appear(efficient_producers,c1) = critical_point(c1). [resolve(73,a,68,b)].
% 0.43/1.01 77 subpopulations(first_movers,efficient_producers,c1,c2) | cardinality_at_time(first_movers,c2) = zero | appear(efficient_producers,c1) = critical_point(c1). [resolve(64,a,68,b)].
% 0.43/1.01 78 cardinality_at_time(first_movers,c2) = zero | appear(efficient_producers,c1) = critical_point(c1) | critical_point(c1) != A | -greater(c2,A) | greater(growth_rate(efficient_producers,c2),growth_rate(first_movers,c2)). [resolve(77,a,38,b)].
% 0.43/1.01 79 cardinality_at_time(first_movers,c2) = zero | appear(efficient_producers,c1) = critical_point(c1) | -greater(growth_rate(efficient_producers,c2),growth_rate(first_movers,c2)). [resolve(77,a,36,a),unit_del(d,25)].
% 0.43/1.01 80 cardinality_at_time(first_movers,c2) = zero | appear(efficient_producers,c1) = critical_point(c1) | greater(growth_rate(efficient_producers,c2),growth_rate(first_movers,c2)). [resolve(78,d,24,a),xx(c)].
% 0.43/1.01 81 cardinality_at_time(first_movers,c2) = zero | appear(efficient_producers,c1) = critical_point(c1). [resolve(80,c,79,c),merge(c),merge(d)].
% 0.43/1.01 83 cardinality_at_time(first_movers,c2) = zero | greater(cardinality_at_time(efficient_producers,c2),zero). [para(81(b,1),50(a,2)),unit_del(b,41)].
% 0.43/1.01 84 cardinality_at_time(first_movers,c2) = zero | subpopulations(first_movers,efficient_producers,c1,c2). [resolve(83,b,64,a),merge(c)].
% 0.43/1.01 89 cardinality_at_time(first_movers,c2) = zero | critical_point(c1) != A | -greater(c2,A) | greater(growth_rate(efficient_producers,c2),growth_rate(first_movers,c2)). [resolve(84,b,38,b)].
% 0.43/1.01 90 cardinality_at_time(first_movers,c2) = zero | -greater(growth_rate(efficient_producers,c2),growth_rate(first_movers,c2)). [resolve(84,b,36,a),unit_del(c,25)].
% 0.43/1.01 91 cardinality_at_time(first_movers,c2) = zero | greater(growth_rate(efficient_producers,c2),growth_rate(first_movers,c2)). [resolve(89,c,24,a),xx(b)].
% 0.43/1.01 92 cardinality_at_time(first_movers,c2) = zero. [resolve(91,b,90,b),merge(b)].
% 0.43/1.01 94 appear(efficient_producers,c1) = critical_point(c1). [back_rewrite(74),rewrite([92(3)]),xx(a)].
% 0.43/1.01 95 -greater(cardinality_at_time(efficient_producers,c2),zero). [back_rewrite(73),rewrite([92(8)]),xx(b)].
% 0.43/1.01 99 $F. [back_rewrite(50),rewrite([94(4)]),unit_del(a,41),unit_del(b,95)].
% 0.43/1.01
% 0.43/1.01 % SZS output end Refutation
% 0.43/1.01 ============================== end of proof ==========================
% 0.43/1.01
% 0.43/1.01 ============================== STATISTICS ============================
% 0.43/1.01
% 0.43/1.01 Given=69. Generated=116. Kept=76. proofs=1.
% 0.43/1.01 Usable=28. Sos=2. Demods=2. Limbo=5, Disabled=69. Hints=0.
% 0.43/1.01 Megabytes=0.13.
% 0.43/1.01 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.43/1.01
% 0.43/1.01 ============================== end of statistics =====================
% 0.43/1.01
% 0.43/1.01 ============================== end of search =========================
% 0.43/1.01
% 0.43/1.01 THEOREM PROVED
% 0.43/1.01 % SZS status Theorem
% 0.43/1.01
% 0.43/1.01 Exiting with 1 proof.
% 0.43/1.01
% 0.43/1.01 Process 21616 exit (max_proofs) Thu Jun 9 12:55:43 2022
% 0.43/1.01 Prover9 interrupted
%------------------------------------------------------------------------------