TSTP Solution File: MGT037+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : MGT037+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 22:22:59 EDT 2022
% Result : Theorem 0.75s 1.03s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : MGT037+1 : TPTP v8.1.0. Released v2.0.0.
% 0.08/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n018.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 08:57:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.75/1.02 ============================== Prover9 ===============================
% 0.75/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.75/1.02 Process 7299 was started by sandbox2 on n018.cluster.edu,
% 0.75/1.02 Thu Jun 9 08:57:38 2022
% 0.75/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_7146_n018.cluster.edu".
% 0.75/1.02 ============================== end of head ===========================
% 0.75/1.02
% 0.75/1.02 ============================== INPUT =================================
% 0.75/1.02
% 0.75/1.02 % Reading from file /tmp/Prover9_7146_n018.cluster.edu
% 0.75/1.02
% 0.75/1.02 set(prolog_style_variables).
% 0.75/1.02 set(auto2).
% 0.75/1.02 % set(auto2) -> set(auto).
% 0.75/1.02 % set(auto) -> set(auto_inference).
% 0.75/1.02 % set(auto) -> set(auto_setup).
% 0.75/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.75/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.75/1.02 % set(auto) -> set(auto_limits).
% 0.75/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.75/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.75/1.02 % set(auto) -> set(auto_denials).
% 0.75/1.02 % set(auto) -> set(auto_process).
% 0.75/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.75/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.75/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.75/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.75/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.75/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.75/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.75/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.75/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.75/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.75/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.75/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.75/1.02 % set(auto2) -> assign(stats, some).
% 0.75/1.02 % set(auto2) -> clear(echo_input).
% 0.75/1.02 % set(auto2) -> set(quiet).
% 0.75/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.75/1.02 % set(auto2) -> clear(print_given).
% 0.75/1.02 assign(lrs_ticks,-1).
% 0.75/1.02 assign(sos_limit,10000).
% 0.75/1.02 assign(order,kbo).
% 0.75/1.02 set(lex_order_vars).
% 0.75/1.02 clear(print_given).
% 0.75/1.02
% 0.75/1.02 % formulas(sos). % not echoed (16 formulas)
% 0.75/1.02
% 0.75/1.02 ============================== end of input ==========================
% 0.75/1.02
% 0.75/1.02 % From the command line: assign(max_seconds, 300).
% 0.75/1.02
% 0.75/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.75/1.02
% 0.75/1.02 % Formulas that are not ordinary clauses:
% 0.75/1.02 1 (all E all T (environment(E) & greater_or_equal(T,appear(efficient_producers,E)) & cardinality_at_time(efficient_producers,T) = zero -> (exists To (greater(To,appear(efficient_producers,E)) & in_environment(E,To) & greater(T,To) & greater(zero,growth_rate(efficient_producers,To)))))) # label(mp_previous_negative_growth) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 2 (all E all T (environment(E) & in_environment(E,T) & greater(appear(an_organisation,E),T) -> number_of_organizations(E,T) = zero)) # label(mp_start_of_organizations) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 3 (all E all T (environment(E) & in_environment(E,T) & -decreases(number_of_organizations(E,T)) -> (exists X (subpopulation(X,E,T) & greater(cardinality_at_time(X,T),zero) & -greater(zero,growth_rate(X,T)))))) # label(mp_non_decreasing) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 4 (all E all T all X (environment(E) & in_environment(E,T) & number_of_organizations(E,T) = zero & subpopulation(X,E,T) -> cardinality_at_time(X,T) = zero)) # label(mp_no_members) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 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].
% 0.75/1.02 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].
% 0.75/1.02 7 (all E all T (environment(E) & in_environment(E,T) -> 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].
% 0.75/1.02 8 (all X (constant(X) -> -decreases(X))) # label(mp_constant_not_decrease) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 9 (all E all T (environment(E) & in_environment(E,T) -> greater_or_equal(T,appear(an_organisation,E)) | greater(appear(an_organisation,E),T))) # label(mp_environment_inequality) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.02 10 (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].
% 0.75/1.02 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].
% 0.75/1.02 12 (all E all T (environment(E) & in_environment(E,T) -> (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].
% 0.75/1.02 13 (all E all S1 all S2 all T (environment(E) & in_environment(E,T) & -greater(zero,growth_rate(S1,T)) & greater(resilience(S2),resilience(S1)) -> -greater(zero,growth_rate(S2,T)))) # label(a12) # label(hypothesis) # label(non_clause). [assumption].
% 0.75/1.02 14 (all E all X all T (environment(E) & subpopulation(X,E,T) & greater(cardinality_at_time(X,T),zero) -> X = efficient_producers | X = first_movers)) # label(a9) # label(hypothesis) # label(non_clause). [assumption].
% 0.75/1.02 15 -(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(prove_t6) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.75/1.02
% 0.75/1.02 ============================== end of process non-clausal formulas ===
% 0.75/1.02
% 0.75/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.75/1.02
% 0.75/1.02 ============================== PREDICATE ELIMINATION =================
% 0.75/1.02 16 -environment(A) | -in_environment(A,B) | -decreases(resources(A,B)) | -decreases(number_of_organizations(A,B)) # label(a6) # label(hypothesis). [clausify(12)].
% 0.75/1.02 17 environment(c1) # label(prove_t6) # label(negated_conjecture). [clausify(15)].
% 0.75/1.02 Derived: -in_environment(c1,A) | -decreases(resources(c1,A)) | -decreases(number_of_organizations(c1,A)). [resolve(16,a,17,a)].
% 0.75/1.02 18 -environment(A) | -in_environment(A,B) | subpopulation(first_movers,A,B) # label(mp_subpopulations) # label(axiom). [clausify(5)].
% 0.75/1.02 Derived: -in_environment(c1,A) | subpopulation(first_movers,c1,A). [resolve(18,a,17,a)].
% 0.75/1.02 19 -environment(A) | -in_environment(A,B) | subpopulation(efficient_producers,A,B) # label(mp_subpopulations) # label(axiom). [clausify(5)].
% 0.75/1.02 Derived: -in_environment(c1,A) | subpopulation(efficient_producers,c1,A). [resolve(19,a,17,a)].
% 0.75/1.02 20 -environment(A) | -in_environment(A,B) | -constant(resources(A,B)) | constant(number_of_organizations(A,B)) # label(a6) # label(hypothesis). [clausify(12)].
% 0.75/1.02 Derived: -in_environment(c1,A) | -constant(resources(c1,A)) | constant(number_of_organizations(c1,A)). [resolve(20,a,17,a)].
% 0.75/1.02 21 -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(2)].
% 0.75/1.02 Derived: -in_environment(c1,A) | -greater(appear(an_organisation,c1),A) | number_of_organizations(c1,A) = zero. [resolve(21,a,17,a)].
% 0.75/1.02 22 -environment(A) | -in_environment(A,B) | decreases(number_of_organizations(A,B)) | subpopulation(f2(A,B),A,B) # label(mp_non_decreasing) # label(axiom). [clausify(3)].
% 0.75/1.02 Derived: -in_environment(c1,A) | decreases(number_of_organizations(c1,A)) | subpopulation(f2(c1,A),c1,A). [resolve(22,a,17,a)].
% 0.75/1.02 23 -environment(A) | -in_environment(A,B) | cardinality_at_time(efficient_producers,B) = zero | greater(cardinality_at_time(efficient_producers,B),zero) # label(mp_efficient_producers_exist) # label(axiom). [clausify(7)].
% 0.75/1.02 Derived: -in_environment(c1,A) | cardinality_at_time(efficient_producers,A) = zero | greater(cardinality_at_time(efficient_producers,A),zero). [resolve(23,a,17,a)].
% 0.75/1.02 24 -environment(A) | -in_environment(A,B) | greater_or_equal(B,appear(an_organisation,A)) | greater(appear(an_organisation,A),B) # label(mp_environment_inequality) # label(axiom). [clausify(9)].
% 0.75/1.02 Derived: -in_environment(c1,A) | greater_or_equal(A,appear(an_organisation,c1)) | greater(appear(an_organisation,c1),A). [resolve(24,a,17,a)].
% 0.75/1.02 25 -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)].
% 0.75/1.02 Derived: -in_environment(c1,A) | -greater_or_equal(A,appear(an_organisation,c1)) | greater(number_of_organizations(c1,A),zero). [resolve(25,a,17,a)].
% 0.75/1.02 26 -environment(A) | -in_environment(A,B) | decreases(number_of_organizations(A,B)) | greater(cardinality_at_time(f2(A,B),B),zero) # label(mp_non_decreasing) # label(axiom). [clausify(3)].
% 0.75/1.02 Derived: -in_environment(c1,A) | decreases(number_of_organizations(c1,A)) | greater(cardinality_at_time(f2(c1,A),A),zero). [resolve(26,a,17,a)].
% 0.75/1.02 27 -environment(A) | -in_environment(A,B) | decreases(number_of_organizations(A,B)) | -greater(zero,growth_rate(f2(A,B),B)) # label(mp_non_decreasing) # label(axiom). [clausify(3)].
% 0.75/1.02 Derived: -in_environment(c1,A) | decreases(number_of_organizations(c1,A)) | -greater(zero,growth_rate(f2(c1,A),A)). [resolve(27,a,17,a)].
% 0.75/1.02 28 -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(1)].
% 0.75/1.02 Derived: -greater_or_equal(A,appear(efficient_producers,c1)) | cardinality_at_time(efficient_producers,A) != zero | in_environment(c1,f1(c1,A)). [resolve(28,a,17,a)].
% 0.75/1.02 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(1)].
% 0.75/1.02 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)].
% 0.75/1.02 30 -environment(A) | -subpopulation(B,A,C) | -greater(cardinality_at_time(B,C),zero) | B = efficient_producers | first_movers = B # label(a9) # label(hypothesis). [clausify(14)].
% 0.75/1.02 Derived: -subpopulation(A,c1,B) | -greater(cardinality_at_time(A,B),zero) | A = efficient_producers | first_movers = A. [resolve(30,a,17,a)].
% 0.75/1.02 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(10)].
% 0.75/1.02 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)].
% 0.75/1.02 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(10)].
% 0.75/1.02 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)].
% 0.75/1.02 33 -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(1)].
% 0.75/1.02 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(33,a,17,a)].
% 0.75/1.02 34 -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(1)].
% 0.75/1.02 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(34,a,17,a)].
% 0.75/1.02 35 -environment(A) | -in_environment(A,B) | number_of_organizations(A,B) != zero | -subpopulation(C,A,B) | cardinality_at_time(C,B) = zero # label(mp_no_members) # label(axiom). [clausify(4)].
% 0.75/1.03 Derived: -in_environment(c1,A) | number_of_organizations(c1,A) != zero | -subpopulation(B,c1,A) | cardinality_at_time(B,A) = zero. [resolve(35,a,17,a)].
% 0.75/1.03 36 -environment(A) | -in_environment(A,B) | greater(zero,growth_rate(C,B)) | -greater(resilience(D),resilience(C)) | -greater(zero,growth_rate(D,B)) # label(a12) # label(hypothesis). [clausify(13)].
% 0.75/1.03 Derived: -in_environment(c1,A) | greater(zero,growth_rate(B,A)) | -greater(resilience(C),resilience(B)) | -greater(zero,growth_rate(C,A)). [resolve(36,a,17,a)].
% 0.75/1.03
% 0.75/1.03 ============================== end predicate elimination =============
% 0.75/1.03
% 0.75/1.03 Auto_denials: (non-Horn, no changes).
% 0.75/1.03
% 0.75/1.03 Term ordering decisions:
% 0.75/1.03 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.
% 0.75/1.03
% 0.75/1.03 ============================== end of process initial clauses ========
% 0.75/1.03
% 0.75/1.03 ============================== CLAUSES FOR SEARCH ====================
% 0.75/1.03
% 0.75/1.03 ============================== end of clauses for search =============
% 0.75/1.03
% 0.75/1.03 ============================== SEARCH ================================
% 0.75/1.03
% 0.75/1.03 % Starting search at 0.02 seconds.
% 0.75/1.03
% 0.75/1.03 ============================== PROOF =================================
% 0.75/1.03 % SZS status Theorem
% 0.75/1.03 % SZS output start Refutation
% 0.75/1.03
% 0.75/1.03 % Proof 1 at 0.03 (+ 0.00) seconds.
% 0.75/1.03 % Length of proof is 95.
% 0.75/1.03 % Level of proof is 24.
% 0.75/1.03 % Maximum clause weight is 31.000.
% 0.75/1.03 % Given clauses 93.
% 0.75/1.03
% 0.75/1.03 1 (all E all T (environment(E) & greater_or_equal(T,appear(efficient_producers,E)) & cardinality_at_time(efficient_producers,T) = zero -> (exists To (greater(To,appear(efficient_producers,E)) & in_environment(E,To) & greater(T,To) & greater(zero,growth_rate(efficient_producers,To)))))) # label(mp_previous_negative_growth) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.03 2 (all E all T (environment(E) & in_environment(E,T) & greater(appear(an_organisation,E),T) -> number_of_organizations(E,T) = zero)) # label(mp_start_of_organizations) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.03 3 (all E all T (environment(E) & in_environment(E,T) & -decreases(number_of_organizations(E,T)) -> (exists X (subpopulation(X,E,T) & greater(cardinality_at_time(X,T),zero) & -greater(zero,growth_rate(X,T)))))) # label(mp_non_decreasing) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.03 4 (all E all T all X (environment(E) & in_environment(E,T) & number_of_organizations(E,T) = zero & subpopulation(X,E,T) -> cardinality_at_time(X,T) = zero)) # label(mp_no_members) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.03 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].
% 0.75/1.03 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].
% 0.75/1.03 7 (all E all T (environment(E) & in_environment(E,T) -> 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].
% 0.75/1.03 8 (all X (constant(X) -> -decreases(X))) # label(mp_constant_not_decrease) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.03 9 (all E all T (environment(E) & in_environment(E,T) -> greater_or_equal(T,appear(an_organisation,E)) | greater(appear(an_organisation,E),T))) # label(mp_environment_inequality) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.03 10 (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].
% 0.75/1.03 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].
% 0.75/1.03 12 (all E all T (environment(E) & in_environment(E,T) -> (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].
% 0.75/1.03 13 (all E all S1 all S2 all T (environment(E) & in_environment(E,T) & -greater(zero,growth_rate(S1,T)) & greater(resilience(S2),resilience(S1)) -> -greater(zero,growth_rate(S2,T)))) # label(a12) # label(hypothesis) # label(non_clause). [assumption].
% 0.75/1.03 14 (all E all X all T (environment(E) & subpopulation(X,E,T) & greater(cardinality_at_time(X,T),zero) -> X = efficient_producers | X = first_movers)) # label(a9) # label(hypothesis) # label(non_clause). [assumption].
% 0.75/1.03 15 -(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(prove_t6) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.75/1.03 16 -environment(A) | -in_environment(A,B) | -decreases(resources(A,B)) | -decreases(number_of_organizations(A,B)) # label(a6) # label(hypothesis). [clausify(12)].
% 0.75/1.03 17 environment(c1) # label(prove_t6) # label(negated_conjecture). [clausify(15)].
% 0.75/1.03 19 -environment(A) | -in_environment(A,B) | subpopulation(efficient_producers,A,B) # label(mp_subpopulations) # label(axiom). [clausify(5)].
% 0.75/1.03 20 -environment(A) | -in_environment(A,B) | -constant(resources(A,B)) | constant(number_of_organizations(A,B)) # label(a6) # label(hypothesis). [clausify(12)].
% 0.75/1.03 21 -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(2)].
% 0.75/1.03 22 -environment(A) | -in_environment(A,B) | decreases(number_of_organizations(A,B)) | subpopulation(f2(A,B),A,B) # label(mp_non_decreasing) # label(axiom). [clausify(3)].
% 0.75/1.03 23 -environment(A) | -in_environment(A,B) | cardinality_at_time(efficient_producers,B) = zero | greater(cardinality_at_time(efficient_producers,B),zero) # label(mp_efficient_producers_exist) # label(axiom). [clausify(7)].
% 0.75/1.03 24 -environment(A) | -in_environment(A,B) | greater_or_equal(B,appear(an_organisation,A)) | greater(appear(an_organisation,A),B) # label(mp_environment_inequality) # label(axiom). [clausify(9)].
% 0.75/1.03 25 -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)].
% 0.75/1.03 26 -environment(A) | -in_environment(A,B) | decreases(number_of_organizations(A,B)) | greater(cardinality_at_time(f2(A,B),B),zero) # label(mp_non_decreasing) # label(axiom). [clausify(3)].
% 0.75/1.03 27 -environment(A) | -in_environment(A,B) | decreases(number_of_organizations(A,B)) | -greater(zero,growth_rate(f2(A,B),B)) # label(mp_non_decreasing) # label(axiom). [clausify(3)].
% 0.75/1.03 28 -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(1)].
% 0.75/1.03 30 -environment(A) | -subpopulation(B,A,C) | -greater(cardinality_at_time(B,C),zero) | B = efficient_producers | first_movers = B # label(a9) # label(hypothesis). [clausify(14)].
% 0.75/1.03 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(10)].
% 0.75/1.03 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(10)].
% 0.75/1.03 34 -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(1)].
% 0.75/1.03 35 -environment(A) | -in_environment(A,B) | number_of_organizations(A,B) != zero | -subpopulation(C,A,B) | cardinality_at_time(C,B) = zero # label(mp_no_members) # label(axiom). [clausify(4)].
% 0.75/1.03 36 -environment(A) | -in_environment(A,B) | greater(zero,growth_rate(C,B)) | -greater(resilience(D),resilience(C)) | -greater(zero,growth_rate(D,B)) # label(a12) # label(hypothesis). [clausify(13)].
% 0.75/1.03 37 in_environment(c1,c2) # label(prove_t6) # label(negated_conjecture). [clausify(15)].
% 0.75/1.03 38 greater(resilience(efficient_producers),resilience(first_movers)) # label(a2) # label(hypothesis). [assumption].
% 0.75/1.03 39 greater_or_equal(c2,appear(efficient_producers,c1)) # label(prove_t6) # label(negated_conjecture). [clausify(15)].
% 0.75/1.03 40 -constant(A) | -decreases(A) # label(mp_constant_not_decrease) # label(axiom). [clausify(8)].
% 0.75/1.03 41 -greater(cardinality_at_time(efficient_producers,c2),zero) # label(prove_t6) # label(negated_conjecture). [clausify(15)].
% 0.75/1.03 42 cardinality_at_time(A,B) != zero | -greater(zero,growth_rate(A,B)) # label(mp_empty_not_decreasing) # label(axiom). [clausify(6)].
% 0.75/1.03 43 -in_environment(c1,A) | -decreases(resources(c1,A)) | -decreases(number_of_organizations(c1,A)). [resolve(16,a,17,a)].
% 0.75/1.03 45 -in_environment(c1,A) | subpopulation(efficient_producers,c1,A). [resolve(19,a,17,a)].
% 0.75/1.03 46 -in_environment(c1,A) | -constant(resources(c1,A)) | constant(number_of_organizations(c1,A)). [resolve(20,a,17,a)].
% 0.75/1.03 47 -in_environment(c1,A) | -greater(appear(an_organisation,c1),A) | number_of_organizations(c1,A) = zero. [resolve(21,a,17,a)].
% 0.75/1.03 48 -in_environment(c1,A) | decreases(number_of_organizations(c1,A)) | subpopulation(f2(c1,A),c1,A). [resolve(22,a,17,a)].
% 0.75/1.03 49 -in_environment(c1,A) | cardinality_at_time(efficient_producers,A) = zero | greater(cardinality_at_time(efficient_producers,A),zero). [resolve(23,a,17,a)].
% 0.75/1.03 50 -in_environment(c1,A) | greater_or_equal(A,appear(an_organisation,c1)) | greater(appear(an_organisation,c1),A). [resolve(24,a,17,a)].
% 0.75/1.03 51 -in_environment(c1,A) | -greater_or_equal(A,appear(an_organisation,c1)) | greater(number_of_organizations(c1,A),zero). [resolve(25,a,17,a)].
% 0.75/1.03 52 -in_environment(c1,A) | decreases(number_of_organizations(c1,A)) | greater(cardinality_at_time(f2(c1,A),A),zero). [resolve(26,a,17,a)].
% 0.75/1.03 53 -in_environment(c1,A) | decreases(number_of_organizations(c1,A)) | -greater(zero,growth_rate(f2(c1,A),A)). [resolve(27,a,17,a)].
% 0.75/1.03 54 -greater_or_equal(A,appear(efficient_producers,c1)) | cardinality_at_time(efficient_producers,A) != zero | in_environment(c1,f1(c1,A)). [resolve(28,a,17,a)].
% 0.75/1.03 56 -subpopulation(A,c1,B) | -greater(cardinality_at_time(A,B),zero) | A = efficient_producers | first_movers = A. [resolve(30,a,17,a)].
% 0.75/1.03 57 -subpopulation(A,c1,B) | -greater(cardinality_at_time(A,B),zero) | efficient_producers = A | first_movers = A. [copy(56),flip(c)].
% 0.75/1.03 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)].
% 0.75/1.03 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)].
% 0.75/1.03 61 -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(34,a,17,a)].
% 0.75/1.03 62 -in_environment(c1,A) | number_of_organizations(c1,A) != zero | -subpopulation(B,c1,A) | cardinality_at_time(B,A) = zero. [resolve(35,a,17,a)].
% 0.75/1.03 63 -in_environment(c1,A) | greater(zero,growth_rate(B,A)) | -greater(resilience(C),resilience(B)) | -greater(zero,growth_rate(C,A)). [resolve(36,a,17,a)].
% 0.75/1.03 70 cardinality_at_time(efficient_producers,c2) = zero. [resolve(49,a,37,a),unit_del(b,41)].
% 0.75/1.03 75 in_environment(c1,f1(c1,c2)). [resolve(54,a,39,a),rewrite([70(3)]),xx(a)].
% 0.75/1.03 80 greater(zero,growth_rate(efficient_producers,f1(c1,c2))). [resolve(61,a,39,a),rewrite([70(3)]),xx(a)].
% 0.75/1.03 84 greater(zero,growth_rate(A,f1(c1,c2))) | -greater(resilience(B),resilience(A)) | -greater(zero,growth_rate(B,f1(c1,c2))). [resolve(75,a,63,a)].
% 0.75/1.03 85 -greater(number_of_organizations(c1,f1(c1,c2)),zero) | greater(equilibrium(c1),f1(c1,c2)) | constant(resources(c1,f1(c1,c2))). [resolve(75,a,59,a)].
% 0.75/1.03 86 -greater(number_of_organizations(c1,f1(c1,c2)),zero) | -greater(equilibrium(c1),f1(c1,c2)) | decreases(resources(c1,f1(c1,c2))). [resolve(75,a,58,a)].
% 0.75/1.03 87 decreases(number_of_organizations(c1,f1(c1,c2))) | -greater(zero,growth_rate(f2(c1,f1(c1,c2)),f1(c1,c2))). [resolve(75,a,53,a)].
% 0.75/1.03 88 decreases(number_of_organizations(c1,f1(c1,c2))) | greater(cardinality_at_time(f2(c1,f1(c1,c2)),f1(c1,c2)),zero). [resolve(75,a,52,a)].
% 0.75/1.03 89 greater_or_equal(f1(c1,c2),appear(an_organisation,c1)) | greater(appear(an_organisation,c1),f1(c1,c2)). [resolve(75,a,50,a)].
% 0.75/1.03 91 decreases(number_of_organizations(c1,f1(c1,c2))) | subpopulation(f2(c1,f1(c1,c2)),c1,f1(c1,c2)). [resolve(75,a,48,a)].
% 0.75/1.03 92 -greater(appear(an_organisation,c1),f1(c1,c2)) | number_of_organizations(c1,f1(c1,c2)) = zero. [resolve(75,a,47,a)].
% 0.75/1.03 93 -constant(resources(c1,f1(c1,c2))) | constant(number_of_organizations(c1,f1(c1,c2))). [resolve(75,a,46,a)].
% 0.75/1.03 94 subpopulation(efficient_producers,c1,f1(c1,c2)). [resolve(75,a,45,a)].
% 0.75/1.03 96 -decreases(resources(c1,f1(c1,c2))) | -decreases(number_of_organizations(c1,f1(c1,c2))). [resolve(75,a,43,a)].
% 0.75/1.03 97 number_of_organizations(c1,f1(c1,c2)) != zero | cardinality_at_time(efficient_producers,f1(c1,c2)) = zero. [resolve(94,a,62,c),unit_del(a,75)].
% 0.75/1.03 99 cardinality_at_time(efficient_producers,f1(c1,c2)) != zero. [resolve(80,a,42,b)].
% 0.75/1.03 100 number_of_organizations(c1,f1(c1,c2)) != zero. [back_unit_del(97),unit_del(b,99)].
% 0.75/1.03 102 -greater(appear(an_organisation,c1),f1(c1,c2)). [back_unit_del(92),unit_del(b,100)].
% 0.75/1.03 103 greater_or_equal(f1(c1,c2),appear(an_organisation,c1)). [back_unit_del(89),unit_del(b,102)].
% 0.75/1.03 104 greater(number_of_organizations(c1,f1(c1,c2)),zero). [resolve(103,a,51,b),unit_del(a,75)].
% 0.75/1.03 105 -greater(equilibrium(c1),f1(c1,c2)) | decreases(resources(c1,f1(c1,c2))). [back_unit_del(86),unit_del(a,104)].
% 0.75/1.03 106 greater(equilibrium(c1),f1(c1,c2)) | constant(resources(c1,f1(c1,c2))). [back_unit_del(85),unit_del(a,104)].
% 0.75/1.03 110 constant(resources(c1,f1(c1,c2))) | decreases(resources(c1,f1(c1,c2))). [resolve(106,a,105,a)].
% 0.75/1.03 111 decreases(resources(c1,f1(c1,c2))) | constant(number_of_organizations(c1,f1(c1,c2))). [resolve(110,a,93,a)].
% 0.75/1.03 113 decreases(resources(c1,f1(c1,c2))) | -decreases(number_of_organizations(c1,f1(c1,c2))). [resolve(111,b,40,a)].
% 0.75/1.03 117 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)) = efficient_producers | f2(c1,f1(c1,c2)) = first_movers. [resolve(91,b,57,a),flip(c),flip(d)].
% 0.75/1.03 118 greater(zero,growth_rate(first_movers,f1(c1,c2))). [resolve(84,b,38,a),unit_del(b,80)].
% 0.75/1.03 131 decreases(number_of_organizations(c1,f1(c1,c2))) | f2(c1,f1(c1,c2)) = efficient_producers | f2(c1,f1(c1,c2)) = first_movers. [resolve(117,b,88,b),merge(d)].
% 0.75/1.03 132 f2(c1,f1(c1,c2)) = efficient_producers | f2(c1,f1(c1,c2)) = first_movers | decreases(resources(c1,f1(c1,c2))). [resolve(131,a,113,b)].
% 0.75/1.03 133 f2(c1,f1(c1,c2)) = efficient_producers | f2(c1,f1(c1,c2)) = first_movers | -decreases(number_of_organizations(c1,f1(c1,c2))). [resolve(132,c,96,a)].
% 0.75/1.03 134 f2(c1,f1(c1,c2)) = efficient_producers | f2(c1,f1(c1,c2)) = first_movers. [resolve(133,c,131,a),merge(c),merge(d)].
% 0.75/1.03 135 f2(c1,f1(c1,c2)) = efficient_producers | decreases(number_of_organizations(c1,f1(c1,c2))). [para(134(b,1),87(b,2,1)),unit_del(c,118)].
% 0.75/1.03 136 f2(c1,f1(c1,c2)) = efficient_producers | decreases(resources(c1,f1(c1,c2))). [resolve(135,b,113,b)].
% 0.75/1.03 137 f2(c1,f1(c1,c2)) = efficient_producers | -decreases(number_of_organizations(c1,f1(c1,c2))). [resolve(136,b,96,a)].
% 0.75/1.03 138 f2(c1,f1(c1,c2)) = efficient_producers. [resolve(137,b,135,b),merge(b)].
% 0.75/1.03 139 decreases(number_of_organizations(c1,f1(c1,c2))). [back_rewrite(87),rewrite([138(12)]),unit_del(b,80)].
% 0.75/1.03 140 decreases(resources(c1,f1(c1,c2))). [back_unit_del(113),unit_del(b,139)].
% 0.75/1.03 141 $F. [back_unit_del(96),unit_del(a,140),unit_del(b,139)].
% 0.75/1.03
% 0.75/1.03 % SZS output end Refutation
% 0.75/1.03 ============================== end of proof ==========================
% 0.75/1.03
% 0.75/1.03 ============================== STATISTICS ============================
% 0.75/1.03
% 0.75/1.03 Given=93. Generated=127. Kept=103. proofs=1.
% 0.75/1.03 Usable=75. Sos=1. Demods=2. Limbo=2, Disabled=72. Hints=0.
% 0.75/1.03 Megabytes=0.21.
% 0.75/1.03 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.75/1.04
% 0.75/1.04 ============================== end of statistics =====================
% 0.75/1.04
% 0.75/1.04 ============================== end of search =========================
% 0.75/1.04
% 0.75/1.04 THEOREM PROVED
% 0.75/1.04 % SZS status Theorem
% 0.75/1.04
% 0.75/1.04 Exiting with 1 proof.
% 0.75/1.04
% 0.75/1.04 Process 7299 exit (max_proofs) Thu Jun 9 08:57:38 2022
% 0.75/1.04 Prover9 interrupted
%------------------------------------------------------------------------------