0.05/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.05/0.10 % Command : tptp2X_and_run_prover9 %d %s 0.09/0.30 % Computer : n029.cluster.edu 0.09/0.30 % Model : x86_64 x86_64 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.30 % Memory : 8042.1875MB 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64 0.09/0.30 % CPULimit : 960 0.09/0.30 % DateTime : Thu Jul 2 06:46:01 EDT 2020 0.09/0.30 % CPUTime : 0.70/1.02 ============================== Prover9 =============================== 0.70/1.02 Prover9 (32) version 2009-11A, November 2009. 0.70/1.02 Process 8390 was started by sandbox2 on n029.cluster.edu, 0.70/1.02 Thu Jul 2 06:46:01 2020 0.70/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_8220_n029.cluster.edu". 0.70/1.02 ============================== end of head =========================== 0.70/1.02 0.70/1.02 ============================== INPUT ================================= 0.70/1.02 0.70/1.02 % Reading from file /tmp/Prover9_8220_n029.cluster.edu 0.70/1.02 0.70/1.02 set(prolog_style_variables). 0.70/1.02 set(auto2). 0.70/1.02 % set(auto2) -> set(auto). 0.70/1.02 % set(auto) -> set(auto_inference). 0.70/1.02 % set(auto) -> set(auto_setup). 0.70/1.02 % set(auto_setup) -> set(predicate_elim). 0.70/1.02 % set(auto_setup) -> assign(eq_defs, unfold). 0.70/1.02 % set(auto) -> set(auto_limits). 0.70/1.02 % set(auto_limits) -> assign(max_weight, "100.000"). 0.70/1.02 % set(auto_limits) -> assign(sos_limit, 20000). 0.70/1.02 % set(auto) -> set(auto_denials). 0.70/1.02 % set(auto) -> set(auto_process). 0.70/1.02 % set(auto2) -> assign(new_constants, 1). 0.70/1.02 % set(auto2) -> assign(fold_denial_max, 3). 0.70/1.02 % set(auto2) -> assign(max_weight, "200.000"). 0.70/1.02 % set(auto2) -> assign(max_hours, 1). 0.70/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.70/1.02 % set(auto2) -> assign(max_seconds, 0). 0.70/1.02 % set(auto2) -> assign(max_minutes, 5). 0.70/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.70/1.02 % set(auto2) -> set(sort_initial_sos). 0.70/1.02 % set(auto2) -> assign(sos_limit, -1). 0.70/1.02 % set(auto2) -> assign(lrs_ticks, 3000). 0.70/1.02 % set(auto2) -> assign(max_megs, 400). 0.70/1.02 % set(auto2) -> assign(stats, some). 0.70/1.02 % set(auto2) -> clear(echo_input). 0.70/1.02 % set(auto2) -> set(quiet). 0.70/1.02 % set(auto2) -> clear(print_initial_clauses). 0.70/1.02 % set(auto2) -> clear(print_given). 0.70/1.02 assign(lrs_ticks,-1). 0.70/1.02 assign(sos_limit,10000). 0.70/1.02 assign(order,kbo). 0.70/1.02 set(lex_order_vars). 0.70/1.02 clear(print_given). 0.70/1.02 0.70/1.02 % formulas(sos). % not echoed (16 formulas) 0.70/1.02 0.70/1.02 ============================== end of input ========================== 0.70/1.02 0.70/1.02 % From the command line: assign(max_seconds, 960). 0.70/1.02 0.70/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.70/1.02 0.70/1.02 % Formulas that are not ordinary clauses: 0.70/1.02 1 (all E all T (in_environment(E,T) & environment(E) -> subpopulation(first_movers,E,T) & subpopulation(efficient_producers,E,T))) # label(mp_subpopulations) # label(axiom) # label(non_clause). [assumption]. 0.70/1.02 2 (all E all S1 all S2 all T (in_environment(E,T) & -greater(zero,growth_rate(S1,T)) & greater(resilience(S2),resilience(S1)) & environment(E) -> -greater(zero,growth_rate(S2,T)))) # label(a12) # label(hypothesis) # label(non_clause). [assumption]. 0.70/1.02 3 (all E all T (in_environment(E,T) & environment(E) -> (decreases(resources(E,T)) -> -decreases(number_of_organizations(E,T))) & (constant(resources(E,T)) -> constant(number_of_organizations(E,T))))) # label(a6) # label(hypothesis) # label(non_clause). [assumption]. 0.70/1.02 4 (all E all X all T (environment(E) & greater(cardinality_at_time(X,T),zero) & subpopulation(X,E,T) -> first_movers = X | X = efficient_producers)) # label(a9) # label(hypothesis) # label(non_clause). [assumption]. 0.70/1.02 5 (all E all T (environment(E) & greater_or_equal(T,appear(efficient_producers,E)) & cardinality_at_time(efficient_producers,T) = zero -> (exists To (greater(zero,growth_rate(efficient_producers,To)) & greater(T,To) & in_environment(E,To) & greater(To,appear(efficient_producers,E)))))) # label(mp_previous_negative_growth) # label(axiom) # label(non_clause). [assumption]. 0.70/1.02 6 (all S all T (cardinality_at_time(S,T) = zero -> -greater(zero,growth_rate(S,T)))) # label(mp_empty_not_decreasing) # label(axiom) # label(non_clause). [assumption]. 0.70/1.02 7 (all E all T (environment(E) & in_environment(E,T) & greater(number_of_organizations(E,T),zero) -> (greater(equilibrium(E),T) -> decreases(resources(E,T))) & (-greater(equilibrium(E),T) -> constant(resources(E,T))))) # label(a3) # label(hypothesis) # label(non_clause). [assumption]. 0.70/1.02 8 (all X (constant(X) -> -decreases(X))) # label(mp_constant_not_decrease) # label(axiom) # label(non_clause). [assumption]. 0.70/1.02 9 (all E all T (in_environment(E,T) & environment(E) -> cardinality_at_time(efficient_producers,T) = zero | greater(cardinality_at_time(efficient_producers,T),zero))) # label(mp_efficient_producers_exist) # label(axiom) # label(non_clause). [assumption]. 0.70/1.02 10 (all E all T all X (subpopulation(X,E,T) & number_of_organizations(E,T) = zero & in_environment(E,T) & environment(E) -> cardinality_at_time(X,T) = zero)) # label(mp_no_members) # label(axiom) # label(non_clause). [assumption]. 0.70/1.02 11 (all E all T (environment(E) & in_environment(E,T) & greater_or_equal(T,appear(an_organisation,E)) -> greater(number_of_organizations(E,T),zero))) # label(a1) # label(hypothesis) # label(non_clause). [assumption]. 0.70/1.02 12 (all E all T (environment(E) & in_environment(E,T) & greater(appear(an_organisation,E),T) -> zero = number_of_organizations(E,T))) # label(mp_start_of_organizations) # label(axiom) # label(non_clause). [assumption]. 0.70/1.02 13 (all E all T (environment(E) & -decreases(number_of_organizations(E,T)) & in_environment(E,T) -> (exists X (subpopulation(X,E,T) & -greater(zero,growth_rate(X,T)) & greater(cardinality_at_time(X,T),zero))))) # label(mp_non_decreasing) # label(axiom) # label(non_clause). [assumption]. 0.70/1.02 14 (all E all T (environment(E) & in_environment(E,T) -> greater(appear(an_organisation,E),T) | greater_or_equal(T,appear(an_organisation,E)))) # label(mp_environment_inequality) # label(axiom) # label(non_clause). [assumption]. 0.70/1.02 15 -(all E all T (environment(E) & greater_or_equal(T,appear(efficient_producers,E)) & in_environment(E,T) -> greater(cardinality_at_time(efficient_producers,T),zero))) # label(prove_t6) # label(negated_conjecture) # label(non_clause). [assumption]. 0.70/1.02 0.70/1.02 ============================== end of process non-clausal formulas === 0.70/1.02 0.70/1.02 ============================== PROCESS INITIAL CLAUSES =============== 0.70/1.02 0.70/1.02 ============================== PREDICATE ELIMINATION ================= 0.70/1.02 16 -in_environment(A,B) | -environment(A) | -decreases(resources(A,B)) | -decreases(number_of_organizations(A,B)) # label(a6) # label(hypothesis). [clausify(3)]. 0.70/1.02 17 environment(c1) # label(prove_t6) # label(negated_conjecture). [clausify(15)]. 0.70/1.02 Derived: -in_environment(c1,A) | -decreases(resources(c1,A)) | -decreases(number_of_organizations(c1,A)). [resolve(16,b,17,a)]. 0.70/1.02 18 -in_environment(A,B) | -environment(A) | subpopulation(first_movers,A,B) # label(mp_subpopulations) # label(axiom). [clausify(1)]. 0.70/1.02 Derived: -in_environment(c1,A) | subpopulation(first_movers,c1,A). [resolve(18,b,17,a)]. 0.70/1.02 19 -in_environment(A,B) | -environment(A) | subpopulation(efficient_producers,A,B) # label(mp_subpopulations) # label(axiom). [clausify(1)]. 0.70/1.02 Derived: -in_environment(c1,A) | subpopulation(efficient_producers,c1,A). [resolve(19,b,17,a)]. 0.70/1.02 20 -in_environment(A,B) | -environment(A) | -constant(resources(A,B)) | constant(number_of_organizations(A,B)) # label(a6) # label(hypothesis). [clausify(3)]. 0.70/1.02 Derived: -in_environment(c1,A) | -constant(resources(c1,A)) | constant(number_of_organizations(c1,A)). [resolve(20,b,17,a)]. 0.70/1.02 21 -in_environment(A,B) | -environment(A) | cardinality_at_time(efficient_producers,B) = zero | greater(cardinality_at_time(efficient_producers,B),zero) # label(mp_efficient_producers_exist) # label(axiom). [clausify(9)]. 0.70/1.02 Derived: -in_environment(c1,A) | cardinality_at_time(efficient_producers,A) = zero | greater(cardinality_at_time(efficient_producers,A),zero). [resolve(21,b,17,a)]. 0.70/1.02 22 -environment(A) | -in_environment(A,B) | -greater_or_equal(B,appear(an_organisation,A)) | greater(number_of_organizations(A,B),zero) # label(a1) # label(hypothesis). [clausify(11)]. 0.70/1.02 Derived: -in_environment(c1,A) | -greater_or_equal(A,appear(an_organisation,c1)) | greater(number_of_organizations(c1,A),zero). [resolve(22,a,17,a)]. 0.70/1.02 23 -environment(A) | -in_environment(A,B) | -greater(appear(an_organisation,A),B) | number_of_organizations(A,B) = zero # label(mp_start_of_organizations) # label(axiom). [clausify(12)]. 0.70/1.02 Derived: -in_environment(c1,A) | -greater(appear(an_organisation,c1),A) | number_of_organizations(c1,A) = zero. [resolve(23,a,17,a)]. 0.70/1.02 24 -environment(A) | decreases(number_of_organizations(A,B)) | -in_environment(A,B) | subpopulation(f2(A,B),A,B) # label(mp_non_decreasing) # label(axiom). [clausify(13)]. 0.70/1.02 Derived: decreases(number_of_organizations(c1,A)) | -in_environment(c1,A) | subpopulation(f2(c1,A),c1,A). [resolve(24,a,17,a)]. 0.70/1.02 25 -environment(A) | -in_environment(A,B) | greater(appear(an_organisation,A),B) | greater_or_equal(B,appear(an_organisation,A)) # label(mp_environment_inequality) # label(axiom). [clausify(14)]. 0.70/1.02 Derived: -in_environment(c1,A) | greater(appear(an_organisation,c1),A) | greater_or_equal(A,appear(an_organisation,c1)). [resolve(25,a,17,a)]. 0.70/1.02 26 -environment(A) | decreases(number_of_organizations(A,B)) | -in_environment(A,B) | -greater(zero,growth_rate(f2(A,B),B)) # label(mp_non_decreasing) # label(axiom). [clausify(13)]. 0.70/1.02 Derived: decreases(number_of_organizations(c1,A)) | -in_environment(c1,A) | -greater(zero,growth_rate(f2(c1,A),A)). [resolve(26,a,17,a)]. 0.70/1.02 27 -environment(A) | decreases(number_of_organizations(A,B)) | -in_environment(A,B) | greater(cardinality_at_time(f2(A,B),B),zero) # label(mp_non_decreasing) # label(axiom). [clausify(13)]. 0.70/1.02 Derived: decreases(number_of_organizations(c1,A)) | -in_environment(c1,A) | greater(cardinality_at_time(f2(c1,A),A),zero). [resolve(27,a,17,a)]. 0.70/1.02 28 -environment(A) | -greater(cardinality_at_time(B,C),zero) | -subpopulation(B,A,C) | B = first_movers | B = efficient_producers # label(a9) # label(hypothesis). [clausify(4)]. 0.70/1.02 Derived: -greater(cardinality_at_time(A,B),zero) | -subpopulation(A,c1,B) | A = first_movers | A = efficient_producers. [resolve(28,a,17,a)]. 0.70/1.02 29 -environment(A) | -greater_or_equal(B,appear(efficient_producers,A)) | cardinality_at_time(efficient_producers,B) != zero | greater(B,f1(A,B)) # label(mp_previous_negative_growth) # label(axiom). [clausify(5)]. 0.70/1.02 Derived: -greater_or_equal(A,appear(efficient_producers,c1)) | cardinality_at_time(efficient_producers,A) != zero | greater(A,f1(c1,A)). [resolve(29,a,17,a)]. 0.70/1.02 30 -environment(A) | -greater_or_equal(B,appear(efficient_producers,A)) | cardinality_at_time(efficient_producers,B) != zero | in_environment(A,f1(A,B)) # label(mp_previous_negative_growth) # label(axiom). [clausify(5)]. 0.70/1.02 Derived: -greater_or_equal(A,appear(efficient_producers,c1)) | cardinality_at_time(efficient_producers,A) != zero | in_environment(c1,f1(c1,A)). [resolve(30,a,17,a)]. 0.70/1.02 31 -environment(A) | -in_environment(A,B) | -greater(number_of_organizations(A,B),zero) | -greater(equilibrium(A),B) | decreases(resources(A,B)) # label(a3) # label(hypothesis). [clausify(7)]. 0.70/1.02 Derived: -in_environment(c1,A) | -greater(number_of_organizations(c1,A),zero) | -greater(equilibrium(c1),A) | decreases(resources(c1,A)). [resolve(31,a,17,a)]. 0.70/1.02 32 -environment(A) | -in_environment(A,B) | -greater(number_of_organizations(A,B),zero) | greater(equilibrium(A),B) | constant(resources(A,B)) # label(a3) # label(hypothesis). [clausify(7)]. 0.70/1.02 Derived: -in_environment(c1,A) | -greater(number_of_organizations(c1,A),zero) | greater(equilibrium(c1),A) | constant(resources(c1,A)). [resolve(32,a,17,a)]. 0.70/1.02 33 -environment(A) | -greater_or_equal(B,appear(efficient_producers,A)) | cardinality_at_time(efficient_producers,B) != zero | greater(zero,growth_rate(efficient_producers,f1(A,B))) # label(mp_previous_negative_growth) # label(axiom). [clausify(5)]. 0.70/1.02 Derived: -greater_or_equal(A,appear(efficient_producers,c1)) | cardinality_at_time(efficient_producers,A) != zero | greater(zero,growth_rate(efficient_producers,f1(c1,A))). [resolve(33,a,17,a)]. 0.70/1.02 34 -environment(A) | -greater_or_equal(B,appear(efficient_producers,A)) | cardinality_at_time(efficient_producers,B) != zero | greater(f1(A,B),appear(efficient_producers,A)) # label(mp_previous_negative_growth) # label(axiom). [clausify(5)]. 0.70/1.02 Derived: -greater_or_equal(A,appear(efficient_producers,c1)) | cardinality_at_time(efficient_producers,A) != zero | greater(f1(c1,A),appear(efficient_producers,c1)). [resolve(34,a,17,a)]. 0.70/1.02 35 -subpopulation(A,B,C) | number_of_organizations(B,C) != zero | -in_environment(B,C) | -environment(B) | cardinality_at_time(A,C) = zero # label(mp_no_members) # label(axiom). [clausify(10)]. 0.70/1.03 Derived: -subpopulation(A,c1,B) | number_of_organizations(c1,B) != zero | -in_environment(c1,B) | cardinality_at_time(A,B) = zero. [resolve(35,d,17,a)]. 0.70/1.03 36 -in_environment(A,B) | greater(zero,growth_rate(C,B)) | -greater(resilience(D),resilience(C)) | -environment(A) | -greater(zero,growth_rate(D,B)) # label(a12) # label(hypothesis). [clausify(2)]. 0.70/1.03 Derived: -in_environment(c1,A) | greater(zero,growth_rate(B,A)) | -greater(resilience(C),resilience(B)) | -greater(zero,growth_rate(C,A)). [resolve(36,d,17,a)]. 0.70/1.03 0.70/1.03 ============================== end predicate elimination ============= 0.70/1.03 0.70/1.03 Auto_denials: (non-Horn, no changes). 0.70/1.03 0.70/1.03 Term ordering decisions: 0.70/1.03 Function symbol KB weights: zero=1. efficient_producers=1. an_organisation=1. first_movers=1. c1=1. c2=1. appear=1. cardinality_at_time=1. number_of_organizations=1. growth_rate=1. resources=1. f1=1. f2=1. resilience=1. equilibrium=1. 0.70/1.03 0.70/1.03 ============================== end of process initial clauses ======== 0.70/1.03 0.70/1.03 ============================== CLAUSES FOR SEARCH ==================== 0.70/1.03 0.70/1.03 ============================== end of clauses for search ============= 0.70/1.03 0.70/1.03 ============================== SEARCH ================================ 0.70/1.03 0.70/1.03 % Starting search at 0.01 seconds. 0.70/1.03 0.70/1.03 ============================== PROOF ================================= 0.70/1.03 % SZS status Theorem 0.70/1.03 % SZS output start Refutation 0.70/1.03 0.70/1.03 % Proof 1 at 0.02 (+ 0.00) seconds. 0.70/1.03 % Length of proof is 95. 0.70/1.03 % Level of proof is 24. 0.70/1.03 % Maximum clause weight is 31.000. 0.70/1.03 % Given clauses 93. 0.70/1.03 0.70/1.03 1 (all E all T (in_environment(E,T) & environment(E) -> subpopulation(first_movers,E,T) & subpopulation(efficient_producers,E,T))) # label(mp_subpopulations) # label(axiom) # label(non_clause). [assumption]. 0.70/1.03 2 (all E all S1 all S2 all T (in_environment(E,T) & -greater(zero,growth_rate(S1,T)) & greater(resilience(S2),resilience(S1)) & environment(E) -> -greater(zero,growth_rate(S2,T)))) # label(a12) # label(hypothesis) # label(non_clause). [assumption]. 0.70/1.03 3 (all E all T (in_environment(E,T) & environment(E) -> (decreases(resources(E,T)) -> -decreases(number_of_organizations(E,T))) & (constant(resources(E,T)) -> constant(number_of_organizations(E,T))))) # label(a6) # label(hypothesis) # label(non_clause). [assumption]. 0.70/1.03 4 (all E all X all T (environment(E) & greater(cardinality_at_time(X,T),zero) & subpopulation(X,E,T) -> first_movers = X | X = efficient_producers)) # label(a9) # label(hypothesis) # label(non_clause). [assumption]. 0.70/1.03 5 (all E all T (environment(E) & greater_or_equal(T,appear(efficient_producers,E)) & cardinality_at_time(efficient_producers,T) = zero -> (exists To (greater(zero,growth_rate(efficient_producers,To)) & greater(T,To) & in_environment(E,To) & greater(To,appear(efficient_producers,E)))))) # label(mp_previous_negative_growth) # label(axiom) # label(non_clause). [assumption]. 0.70/1.03 6 (all S all T (cardinality_at_time(S,T) = zero -> -greater(zero,growth_rate(S,T)))) # label(mp_empty_not_decreasing) # label(axiom) # label(non_clause). [assumption]. 0.70/1.03 7 (all E all T (environment(E) & in_environment(E,T) & greater(number_of_organizations(E,T),zero) -> (greater(equilibrium(E),T) -> decreases(resources(E,T))) & (-greater(equilibrium(E),T) -> constant(resources(E,T))))) # label(a3) # label(hypothesis) # label(non_clause). [assumption]. 0.70/1.03 8 (all X (constant(X) -> -decreases(X))) # label(mp_constant_not_decrease) # label(axiom) # label(non_clause). [assumption]. 0.70/1.03 9 (all E all T (in_environment(E,T) & environment(E) -> cardinality_at_time(efficient_producers,T) = zero | greater(cardinality_at_time(efficient_producers,T),zero))) # label(mp_efficient_producers_exist) # label(axiom) # label(non_clause). [assumption]. 0.70/1.03 10 (all E all T all X (subpopulation(X,E,T) & number_of_organizations(E,T) = zero & in_environment(E,T) & environment(E) -> cardinality_at_time(X,T) = zero)) # label(mp_no_members) # label(axiom) # label(non_clause). [assumption]. 0.70/1.03 11 (all E all T (environment(E) & in_environment(E,T) & greater_or_equal(T,appear(an_organisation,E)) -> greater(number_of_organizations(E,T),zero))) # label(a1) # label(hypothesis) # label(non_clause). [assumption]. 0.70/1.03 12 (all E all T (environment(E) & in_environment(E,T) & greater(appear(an_organisation,E),T) -> zero = number_of_organizations(E,T))) # label(mp_start_of_organizations) # label(axiom) # label(non_clause). [assumption]. 0.70/1.03 13 (all E all T (environment(E) & -decreases(number_of_organizations(E,T)) & in_environment(E,T) -> (exists X (subpopulation(X,E,T) & -greater(zero,growth_rate(X,T)) & greater(cardinality_at_time(X,T),zero))))) # label(mp_non_decreasing) # label(axiom) # label(non_clause). [assumption]. 0.70/1.03 14 (all E all T (environment(E) & in_environment(E,T) -> greater(appear(an_organisation,E),T) | greater_or_equal(T,appear(an_organisation,E)))) # label(mp_environment_inequality) # label(axiom) # label(non_clause). [assumption]. 0.70/1.03 15 -(all E all T (environment(E) & greater_or_equal(T,appear(efficient_producers,E)) & in_environment(E,T) -> greater(cardinality_at_time(efficient_producers,T),zero))) # label(prove_t6) # label(negated_conjecture) # label(non_clause). [assumption]. 0.70/1.03 16 -in_environment(A,B) | -environment(A) | -decreases(resources(A,B)) | -decreases(number_of_organizations(A,B)) # label(a6) # label(hypothesis). [clausify(3)]. 0.70/1.03 17 environment(c1) # label(prove_t6) # label(negated_conjecture). [clausify(15)]. 0.70/1.03 19 -in_environment(A,B) | -environment(A) | subpopulation(efficient_producers,A,B) # label(mp_subpopulations) # label(axiom). [clausify(1)]. 0.70/1.03 20 -in_environment(A,B) | -environment(A) | -constant(resources(A,B)) | constant(number_of_organizations(A,B)) # label(a6) # label(hypothesis). [clausify(3)]. 0.70/1.03 21 -in_environment(A,B) | -environment(A) | cardinality_at_time(efficient_producers,B) = zero | greater(cardinality_at_time(efficient_producers,B),zero) # label(mp_efficient_producers_exist) # label(axiom). [clausify(9)]. 0.70/1.03 22 -environment(A) | -in_environment(A,B) | -greater_or_equal(B,appear(an_organisation,A)) | greater(number_of_organizations(A,B),zero) # label(a1) # label(hypothesis). [clausify(11)]. 0.70/1.03 23 -environment(A) | -in_environment(A,B) | -greater(appear(an_organisation,A),B) | number_of_organizations(A,B) = zero # label(mp_start_of_organizations) # label(axiom). [clausify(12)]. 0.70/1.03 24 -environment(A) | decreases(number_of_organizations(A,B)) | -in_environment(A,B) | subpopulation(f2(A,B),A,B) # label(mp_non_decreasing) # label(axiom). [clausify(13)]. 0.70/1.03 25 -environment(A) | -in_environment(A,B) | greater(appear(an_organisation,A),B) | greater_or_equal(B,appear(an_organisation,A)) # label(mp_environment_inequality) # label(axiom). [clausify(14)]. 0.70/1.03 26 -environment(A) | decreases(number_of_organizations(A,B)) | -in_environment(A,B) | -greater(zero,growth_rate(f2(A,B),B)) # label(mp_non_decreasing) # label(axiom). [clausify(13)]. 0.70/1.03 27 -environment(A) | decreases(number_of_organizations(A,B)) | -in_environment(A,B) | greater(cardinality_at_time(f2(A,B),B),zero) # label(mp_non_decreasing) # label(axiom). [clausify(13)]. 0.70/1.03 28 -environment(A) | -greater(cardinality_at_time(B,C),zero) | -subpopulation(B,A,C) | B = first_movers | B = efficient_producers # label(a9) # label(hypothesis). [clausify(4)]. 0.70/1.03 30 -environment(A) | -greater_or_equal(B,appear(efficient_producers,A)) | cardinality_at_time(efficient_producers,B) != zero | in_environment(A,f1(A,B)) # label(mp_previous_negative_growth) # label(axiom). [clausify(5)]. 0.70/1.03 31 -environment(A) | -in_environment(A,B) | -greater(number_of_organizations(A,B),zero) | -greater(equilibrium(A),B) | decreases(resources(A,B)) # label(a3) # label(hypothesis). [clausify(7)]. 0.70/1.03 32 -environment(A) | -in_environment(A,B) | -greater(number_of_organizations(A,B),zero) | greater(equilibrium(A),B) | constant(resources(A,B)) # label(a3) # label(hypothesis). [clausify(7)]. 0.70/1.03 33 -environment(A) | -greater_or_equal(B,appear(efficient_producers,A)) | cardinality_at_time(efficient_producers,B) != zero | greater(zero,growth_rate(efficient_producers,f1(A,B))) # label(mp_previous_negative_growth) # label(axiom). [clausify(5)]. 0.70/1.03 35 -subpopulation(A,B,C) | number_of_organizations(B,C) != zero | -in_environment(B,C) | -environment(B) | cardinality_at_time(A,C) = zero # label(mp_no_members) # label(axiom). [clausify(10)]. 0.70/1.03 36 -in_environment(A,B) | greater(zero,growth_rate(C,B)) | -greater(resilience(D),resilience(C)) | -environment(A) | -greater(zero,growth_rate(D,B)) # label(a12) # label(hypothesis). [clausify(2)]. 0.70/1.03 37 in_environment(c1,c2) # label(prove_t6) # label(negated_conjecture). [clausify(15)]. 0.70/1.03 38 greater(resilience(efficient_producers),resilience(first_movers)) # label(a2) # label(hypothesis). [assumption]. 0.70/1.03 39 greater_or_equal(c2,appear(efficient_producers,c1)) # label(prove_t6) # label(negated_conjecture). [clausify(15)]. 0.70/1.03 40 -constant(A) | -decreases(A) # label(mp_constant_not_decrease) # label(axiom). [clausify(8)]. 0.70/1.03 41 -greater(cardinality_at_time(efficient_producers,c2),zero) # label(prove_t6) # label(negated_conjecture). [clausify(15)]. 0.70/1.03 42 cardinality_at_time(A,B) != zero | -greater(zero,growth_rate(A,B)) # label(mp_empty_not_decreasing) # label(axiom). [clausify(6)]. 0.70/1.03 43 -in_environment(c1,A) | -decreases(resources(c1,A)) | -decreases(number_of_organizations(c1,A)). [resolve(16,b,17,a)]. 0.70/1.03 45 -in_environment(c1,A) | subpopulation(efficient_producers,c1,A). [resolve(19,b,17,a)]. 0.70/1.03 46 -in_environment(c1,A) | -constant(resources(c1,A)) | constant(number_of_organizations(c1,A)). [resolve(20,b,17,a)]. 0.70/1.03 47 -in_environment(c1,A) | cardinality_at_time(efficient_producers,A) = zero | greater(cardinality_at_time(efficient_producers,A),zero). [resolve(21,b,17,a)]. 0.70/1.03 48 -in_environment(c1,A) | -greater_or_equal(A,appear(an_organisation,c1)) | greater(number_of_organizations(c1,A),zero). [resolve(22,a,17,a)]. 0.70/1.03 49 -in_environment(c1,A) | -greater(appear(an_organisation,c1),A) | number_of_organizations(c1,A) = zero. [resolve(23,a,17,a)]. 0.70/1.03 50 decreases(number_of_organizations(c1,A)) | -in_environment(c1,A) | subpopulation(f2(c1,A),c1,A). [resolve(24,a,17,a)]. 0.70/1.03 51 -in_environment(c1,A) | greater(appear(an_organisation,c1),A) | greater_or_equal(A,appear(an_organisation,c1)). [resolve(25,a,17,a)]. 0.70/1.03 52 decreases(number_of_organizations(c1,A)) | -in_environment(c1,A) | -greater(zero,growth_rate(f2(c1,A),A)). [resolve(26,a,17,a)]. 0.70/1.03 53 decreases(number_of_organizations(c1,A)) | -in_environment(c1,A) | greater(cardinality_at_time(f2(c1,A),A),zero). [resolve(27,a,17,a)]. 0.70/1.03 54 -greater(cardinality_at_time(A,B),zero) | -subpopulation(A,c1,B) | A = first_movers | A = efficient_producers. [resolve(28,a,17,a)]. 0.70/1.03 55 -greater(cardinality_at_time(A,B),zero) | -subpopulation(A,c1,B) | first_movers = A | efficient_producers = A. [copy(54),flip(c),flip(d)]. 0.70/1.03 57 -greater_or_equal(A,appear(efficient_producers,c1)) | cardinality_at_time(efficient_producers,A) != zero | in_environment(c1,f1(c1,A)). [resolve(30,a,17,a)]. 0.70/1.03 58 -in_environment(c1,A) | -greater(number_of_organizations(c1,A),zero) | -greater(equilibrium(c1),A) | decreases(resources(c1,A)). [resolve(31,a,17,a)]. 0.70/1.03 59 -in_environment(c1,A) | -greater(number_of_organizations(c1,A),zero) | greater(equilibrium(c1),A) | constant(resources(c1,A)). [resolve(32,a,17,a)]. 0.70/1.03 60 -greater_or_equal(A,appear(efficient_producers,c1)) | cardinality_at_time(efficient_producers,A) != zero | greater(zero,growth_rate(efficient_producers,f1(c1,A))). [resolve(33,a,17,a)]. 0.70/1.03 62 -subpopulation(A,c1,B) | number_of_organizations(c1,B) != zero | -in_environment(c1,B) | cardinality_at_time(A,B) = zero. [resolve(35,d,17,a)]. 0.70/1.03 63 -in_environment(c1,A) | greater(zero,growth_rate(B,A)) | -greater(resilience(C),resilience(B)) | -greater(zero,growth_rate(C,A)). [resolve(36,d,17,a)]. 0.70/1.03 68 cardinality_at_time(efficient_producers,c2) = zero. [resolve(47,a,37,a),unit_del(b,41)]. 0.70/1.03 76 in_environment(c1,f1(c1,c2)). [resolve(57,a,39,a),rewrite([68(3)]),xx(a)]. 0.70/1.03 79 greater(zero,growth_rate(efficient_producers,f1(c1,c2))). [resolve(60,a,39,a),rewrite([68(3)]),xx(a)]. 0.70/1.03 84 greater(zero,growth_rate(A,f1(c1,c2))) | -greater(resilience(B),resilience(A)) | -greater(zero,growth_rate(B,f1(c1,c2))). [resolve(76,a,63,a)]. 0.70/1.03 85 -greater(number_of_organizations(c1,f1(c1,c2)),zero) | greater(equilibrium(c1),f1(c1,c2)) | constant(resources(c1,f1(c1,c2))). [resolve(76,a,59,a)]. 0.70/1.03 86 -greater(number_of_organizations(c1,f1(c1,c2)),zero) | -greater(equilibrium(c1),f1(c1,c2)) | decreases(resources(c1,f1(c1,c2))). [resolve(76,a,58,a)]. 0.70/1.03 87 decreases(number_of_organizations(c1,f1(c1,c2))) | greater(cardinality_at_time(f2(c1,f1(c1,c2)),f1(c1,c2)),zero). [resolve(76,a,53,b)]. 0.70/1.03 88 decreases(number_of_organizations(c1,f1(c1,c2))) | -greater(zero,growth_rate(f2(c1,f1(c1,c2)),f1(c1,c2))). [resolve(76,a,52,b)]. 0.70/1.03 89 greater(appear(an_organisation,c1),f1(c1,c2)) | greater_or_equal(f1(c1,c2),appear(an_organisation,c1)). [resolve(76,a,51,a)]. 0.70/1.03 90 decreases(number_of_organizations(c1,f1(c1,c2))) | subpopulation(f2(c1,f1(c1,c2)),c1,f1(c1,c2)). [resolve(76,a,50,b)]. 0.70/1.03 91 -greater(appear(an_organisation,c1),f1(c1,c2)) | number_of_organizations(c1,f1(c1,c2)) = zero. [resolve(76,a,49,a)]. 0.70/1.03 93 -constant(resources(c1,f1(c1,c2))) | constant(number_of_organizations(c1,f1(c1,c2))). [resolve(76,a,46,a)]. 0.70/1.03 94 subpopulation(efficient_producers,c1,f1(c1,c2)). [resolve(76,a,45,a)]. 0.70/1.03 96 -decreases(resources(c1,f1(c1,c2))) | -decreases(number_of_organizations(c1,f1(c1,c2))). [resolve(76,a,43,a)]. 0.70/1.03 97 number_of_organizations(c1,f1(c1,c2)) != zero | cardinality_at_time(efficient_producers,f1(c1,c2)) = zero. [resolve(94,a,62,a),unit_del(b,76)]. 0.70/1.03 99 cardinality_at_time(efficient_producers,f1(c1,c2)) != zero. [resolve(79,a,42,b)]. 0.70/1.03 100 number_of_organizations(c1,f1(c1,c2)) != zero. [back_unit_del(97),unit_del(b,99)]. 0.70/1.03 102 -greater(appear(an_organisation,c1),f1(c1,c2)). [back_unit_del(91),unit_del(b,100)]. 0.70/1.03 103 greater_or_equal(f1(c1,c2),appear(an_organisation,c1)). [back_unit_del(89),unit_del(a,102)]. 0.70/1.03 104 greater(number_of_organizations(c1,f1(c1,c2)),zero). [resolve(103,a,48,b),unit_del(a,76)]. 0.70/1.03 105 -greater(equilibrium(c1),f1(c1,c2)) | decreases(resources(c1,f1(c1,c2))). [back_unit_del(86),unit_del(a,104)]. 0.70/1.03 106 greater(equilibrium(c1),f1(c1,c2)) | constant(resources(c1,f1(c1,c2))). [back_unit_del(85),unit_del(a,104)]. 0.70/1.03 110 constant(resources(c1,f1(c1,c2))) | decreases(resources(c1,f1(c1,c2))). [resolve(106,a,105,a)]. 0.70/1.03 111 decreases(resources(c1,f1(c1,c2))) | constant(number_of_organizations(c1,f1(c1,c2))). [resolve(110,a,93,a)]. 0.70/1.03 113 decreases(resources(c1,f1(c1,c2))) | -decreases(number_of_organizations(c1,f1(c1,c2))). [resolve(111,b,40,a)]. 0.70/1.03 117 decreases(number_of_organizations(c1,f1(c1,c2))) | -greater(cardinality_at_time(f2(c1,f1(c1,c2)),f1(c1,c2)),zero) | f2(c1,f1(c1,c2)) = first_movers | f2(c1,f1(c1,c2)) = efficient_producers. [resolve(90,b,55,b),flip(c),flip(d)]. 0.70/1.03 118 greater(zero,growth_rate(first_movers,f1(c1,c2))). [resolve(84,b,38,a),unit_del(b,79)]. 0.70/1.03 131 decreases(number_of_organizations(c1,f1(c1,c2))) | f2(c1,f1(c1,c2)) = first_movers | f2(c1,f1(c1,c2)) = efficient_producers. [resolve(117,b,87,b),merge(d)]. 0.70/1.03 132 f2(c1,f1(c1,c2)) = first_movers | f2(c1,f1(c1,c2)) = efficient_producers | decreases(resources(c1,f1(c1,c2))). [resolve(131,a,113,b)]. 0.70/1.03 133 f2(c1,f1(c1,c2)) = first_movers | f2(c1,f1(c1,c2)) = efficient_producers | -decreases(number_of_organizations(c1,f1(c1,c2))). [resolve(132,c,96,a)]. 0.70/1.03 134 f2(c1,f1(c1,c2)) = first_movers | f2(c1,f1(c1,c2)) = efficient_producers. [resolve(133,c,131,a),merge(c),merge(d)]. 0.70/1.03 136 f2(c1,f1(c1,c2)) = efficient_producers | decreases(number_of_organizations(c1,f1(c1,c2))). [para(134(a,1),88(b,2,1)),unit_del(c,118)]. 0.70/1.03 137 f2(c1,f1(c1,c2)) = efficient_producers | decreases(resources(c1,f1(c1,c2))). [resolve(136,b,113,b)]. 0.70/1.03 138 f2(c1,f1(c1,c2)) = efficient_producers | -decreases(number_of_organizations(c1,f1(c1,c2))). [resolve(137,b,96,a)]. 0.70/1.03 139 f2(c1,f1(c1,c2)) = efficient_producers. [resolve(138,b,136,b),merge(b)]. 0.70/1.03 140 decreases(number_of_organizations(c1,f1(c1,c2))). [back_rewrite(88),rewrite([139(12)]),unit_del(b,79)]. 0.70/1.03 141 decreases(resources(c1,f1(c1,c2))). [back_unit_del(113),unit_del(b,140)]. 0.70/1.03 142 $F. [back_unit_del(96),unit_del(a,141),unit_del(b,140)]. 0.70/1.03 0.70/1.03 % SZS output end Refutation 0.70/1.03 ============================== end of proof ========================== 0.70/1.03 0.70/1.03 ============================== STATISTICS ============================ 0.70/1.03 0.70/1.03 Given=93. Generated=127. Kept=104. proofs=1. 0.70/1.03 Usable=75. Sos=1. Demods=2. Limbo=2, Disabled=73. Hints=0. 0.70/1.03 Megabytes=0.21. 0.70/1.03 User_CPU=0.02, System_CPU=0.00, Wall_clock=0. 0.70/1.03 0.70/1.03 ============================== end of statistics ===================== 0.70/1.03 0.70/1.03 ============================== end of search ========================= 0.70/1.03 0.70/1.03 THEOREM PROVED 0.70/1.03 % SZS status Theorem 0.70/1.03 0.70/1.03 Exiting with 1 proof. 0.70/1.03 0.70/1.03 Process 8390 exit (max_proofs) Thu Jul 2 06:46:01 2020 0.70/1.03 Prover9 interrupted 0.70/1.03 EOF