TSTP Solution File: MGT025+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : MGT025+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 22:22:54 EDT 2022
% Result : Theorem 0.75s 1.05s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : MGT025+1 : TPTP v8.1.0. Released v2.0.0.
% 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.15/0.35 % Computer : n019.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Thu Jun 9 08:54:25 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.75/1.04 ============================== Prover9 ===============================
% 0.75/1.04 Prover9 (32) version 2009-11A, November 2009.
% 0.75/1.04 Process 30240 was started by sandbox2 on n019.cluster.edu,
% 0.75/1.04 Thu Jun 9 08:54:25 2022
% 0.75/1.04 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_30086_n019.cluster.edu".
% 0.75/1.04 ============================== end of head ===========================
% 0.75/1.04
% 0.75/1.04 ============================== INPUT =================================
% 0.75/1.04
% 0.75/1.04 % Reading from file /tmp/Prover9_30086_n019.cluster.edu
% 0.75/1.04
% 0.75/1.04 set(prolog_style_variables).
% 0.75/1.04 set(auto2).
% 0.75/1.04 % set(auto2) -> set(auto).
% 0.75/1.04 % set(auto) -> set(auto_inference).
% 0.75/1.04 % set(auto) -> set(auto_setup).
% 0.75/1.04 % set(auto_setup) -> set(predicate_elim).
% 0.75/1.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.75/1.04 % set(auto) -> set(auto_limits).
% 0.75/1.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.75/1.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.75/1.04 % set(auto) -> set(auto_denials).
% 0.75/1.04 % set(auto) -> set(auto_process).
% 0.75/1.04 % set(auto2) -> assign(new_constants, 1).
% 0.75/1.04 % set(auto2) -> assign(fold_denial_max, 3).
% 0.75/1.04 % set(auto2) -> assign(max_weight, "200.000").
% 0.75/1.04 % set(auto2) -> assign(max_hours, 1).
% 0.75/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.75/1.04 % set(auto2) -> assign(max_seconds, 0).
% 0.75/1.04 % set(auto2) -> assign(max_minutes, 5).
% 0.75/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.75/1.04 % set(auto2) -> set(sort_initial_sos).
% 0.75/1.04 % set(auto2) -> assign(sos_limit, -1).
% 0.75/1.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.75/1.04 % set(auto2) -> assign(max_megs, 400).
% 0.75/1.04 % set(auto2) -> assign(stats, some).
% 0.75/1.04 % set(auto2) -> clear(echo_input).
% 0.75/1.04 % set(auto2) -> set(quiet).
% 0.75/1.04 % set(auto2) -> clear(print_initial_clauses).
% 0.75/1.04 % set(auto2) -> clear(print_given).
% 0.75/1.04 assign(lrs_ticks,-1).
% 0.75/1.04 assign(sos_limit,10000).
% 0.75/1.04 assign(order,kbo).
% 0.75/1.04 set(lex_order_vars).
% 0.75/1.04 clear(print_given).
% 0.75/1.04
% 0.75/1.04 % formulas(sos). % not echoed (8 formulas)
% 0.75/1.04
% 0.75/1.04 ============================== end of input ==========================
% 0.75/1.04
% 0.75/1.04 % From the command line: assign(max_seconds, 300).
% 0.75/1.04
% 0.75/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.75/1.04
% 0.75/1.04 % Formulas that are not ordinary clauses:
% 0.75/1.04 1 (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) -> number_of_organizations(E,T) = sum(cardinality_at_time(first_movers,T),cardinality_at_time(efficient_producers,T)))) # label(mp_only_members) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.04 2 (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].
% 0.75/1.04 3 (all A all B all C (A = sum(B,C) & constant(A) -> constant(B) & constant(C) | increases(B) & decreases(C) | decreases(B) & increases(C))) # label(mp_abc_sum_increase) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.04 4 (all X all E all T (environment(E) & in_environment(E,T) & subpopulation(X,E,T) & greater(cardinality_at_time(X,T),zero) -> (constant(cardinality_at_time(X,T)) -> growth_rate(X,T) = zero) & (increases(cardinality_at_time(X,T)) -> greater(growth_rate(X,T),zero)) & (decreases(cardinality_at_time(X,T)) -> greater(zero,growth_rate(X,T))))) # label(mp_growth_rate) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.04 5 (all E all T (environment(E) & subpopulations(first_movers,efficient_producers,E,T) -> greater(cardinality_at_time(first_movers,T),zero) & greater(cardinality_at_time(efficient_producers,T),zero))) # label(mp_non_zero_producers) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.04 6 (all E all T (environment(E) & subpopulations(first_movers,efficient_producers,E,T) -> in_environment(E,T))) # label(mp_time_point_occur) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.04 7 (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].
% 0.75/1.04 8 -(all E all T (environment(E) & subpopulations(first_movers,efficient_producers,E,T) & constant(number_of_organizations(E,T)) -> growth_rate(first_movers,T) = zero & growth_rate(efficient_producers,T) = zero | greater(growth_rate(first_movers,T),zero) & greater(zero,growth_rate(efficient_producers,T)) | greater(growth_rate(efficient_producers,T),zero) & greater(zero,growth_rate(first_movers,T)))) # label(prove_l7) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.75/1.04
% 0.75/1.04 ============================== end of process non-clausal formulas ===
% 0.75/1.04
% 0.75/1.04 ============================== PROCESS INITIAL CLAUSES ===============
% 0.75/1.04
% 0.75/1.04 ============================== PREDICATE ELIMINATION =================
% 0.75/1.04 9 -environment(A) | -in_environment(A,B) | subpopulation(first_movers,A,B) # label(mp_subpopulations) # label(axiom). [clausify(2)].
% 0.75/1.04 10 environment(c1) # label(prove_l7) # label(negated_conjecture). [clausify(8)].
% 0.75/1.04 Derived: -in_environment(c1,A) | subpopulation(first_movers,c1,A). [resolve(9,a,10,a)].
% 0.75/1.04 11 -environment(A) | -in_environment(A,B) | subpopulation(efficient_producers,A,B) # label(mp_subpopulations) # label(axiom). [clausify(2)].
% 0.75/1.04 Derived: -in_environment(c1,A) | subpopulation(efficient_producers,c1,A). [resolve(11,a,10,a)].
% 0.75/1.04 12 -environment(A) | -subpopulations(first_movers,efficient_producers,A,B) | in_environment(A,B) # label(mp_time_point_occur) # label(axiom). [clausify(6)].
% 0.75/1.04 Derived: -subpopulations(first_movers,efficient_producers,c1,A) | in_environment(c1,A). [resolve(12,a,10,a)].
% 0.75/1.04 13 -environment(A) | -subpopulations(first_movers,efficient_producers,A,B) | greater(cardinality_at_time(first_movers,B),zero) # label(mp_non_zero_producers) # label(axiom). [clausify(5)].
% 0.75/1.04 Derived: -subpopulations(first_movers,efficient_producers,c1,A) | greater(cardinality_at_time(first_movers,A),zero). [resolve(13,a,10,a)].
% 0.75/1.04 14 -environment(A) | -subpopulations(first_movers,efficient_producers,A,B) | greater(cardinality_at_time(efficient_producers,B),zero) # label(mp_non_zero_producers) # label(axiom). [clausify(5)].
% 0.75/1.04 Derived: -subpopulations(first_movers,efficient_producers,c1,A) | greater(cardinality_at_time(efficient_producers,A),zero). [resolve(14,a,10,a)].
% 0.75/1.04 15 -environment(A) | -subpopulation(B,A,C) | -greater(cardinality_at_time(B,C),zero) | efficient_producers = B | first_movers = B # label(a9) # label(hypothesis). [clausify(7)].
% 0.75/1.04 Derived: -subpopulation(A,c1,B) | -greater(cardinality_at_time(A,B),zero) | efficient_producers = A | first_movers = A. [resolve(15,a,10,a)].
% 0.75/1.04 16 -environment(A) | -subpopulation(B,A,C) | efficient_producers != B | sum(cardinality_at_time(first_movers,C),cardinality_at_time(efficient_producers,C)) = number_of_organizations(A,C) # label(mp_only_members) # label(axiom). [clausify(1)].
% 0.75/1.04 Derived: -subpopulation(A,c1,B) | efficient_producers != A | sum(cardinality_at_time(first_movers,B),cardinality_at_time(efficient_producers,B)) = number_of_organizations(c1,B). [resolve(16,a,10,a)].
% 0.75/1.04 17 -environment(A) | -subpopulation(B,A,C) | first_movers != B | sum(cardinality_at_time(first_movers,C),cardinality_at_time(efficient_producers,C)) = number_of_organizations(A,C) # label(mp_only_members) # label(axiom). [clausify(1)].
% 0.75/1.04 Derived: -subpopulation(A,c1,B) | first_movers != A | sum(cardinality_at_time(first_movers,B),cardinality_at_time(efficient_producers,B)) = number_of_organizations(c1,B). [resolve(17,a,10,a)].
% 0.75/1.04 18 -environment(A) | -subpopulation(B,A,C) | greater(cardinality_at_time(B,C),zero) | sum(cardinality_at_time(first_movers,C),cardinality_at_time(efficient_producers,C)) = number_of_organizations(A,C) # label(mp_only_members) # label(axiom). [clausify(1)].
% 0.75/1.04 Derived: -subpopulation(A,c1,B) | greater(cardinality_at_time(A,B),zero) | sum(cardinality_at_time(first_movers,B),cardinality_at_time(efficient_producers,B)) = number_of_organizations(c1,B). [resolve(18,a,10,a)].
% 0.75/1.04 19 -environment(A) | -in_environment(A,B) | -subpopulation(C,A,B) | -greater(cardinality_at_time(C,B),zero) | -constant(cardinality_at_time(C,B)) | growth_rate(C,B) = zero # label(mp_growth_rate) # label(axiom). [clausify(4)].
% 0.75/1.04 Derived: -in_environment(c1,A) | -subpopulation(B,c1,A) | -greater(cardinality_at_time(B,A),zero) | -constant(cardinality_at_time(B,A)) | growth_rate(B,A) = zero. [resolve(19,a,10,a)].
% 0.75/1.05 20 -environment(A) | -in_environment(A,B) | -subpopulation(C,A,B) | -greater(cardinality_at_time(C,B),zero) | -increases(cardinality_at_time(C,B)) | greater(growth_rate(C,B),zero) # label(mp_growth_rate) # label(axiom). [clausify(4)].
% 0.75/1.05 Derived: -in_environment(c1,A) | -subpopulation(B,c1,A) | -greater(cardinality_at_time(B,A),zero) | -increases(cardinality_at_time(B,A)) | greater(growth_rate(B,A),zero). [resolve(20,a,10,a)].
% 0.75/1.05 21 -environment(A) | -in_environment(A,B) | -subpopulation(C,A,B) | -greater(cardinality_at_time(C,B),zero) | -decreases(cardinality_at_time(C,B)) | greater(zero,growth_rate(C,B)) # label(mp_growth_rate) # label(axiom). [clausify(4)].
% 0.75/1.05 Derived: -in_environment(c1,A) | -subpopulation(B,c1,A) | -greater(cardinality_at_time(B,A),zero) | -decreases(cardinality_at_time(B,A)) | greater(zero,growth_rate(B,A)). [resolve(21,a,10,a)].
% 0.75/1.05
% 0.75/1.05 ============================== end predicate elimination =============
% 0.75/1.05
% 0.75/1.05 Auto_denials: (non-Horn, no changes).
% 0.75/1.05
% 0.75/1.05 Term ordering decisions:
% 0.75/1.05 Function symbol KB weights: efficient_producers=1. first_movers=1. zero=1. c1=1. c2=1. cardinality_at_time=1. sum=1. number_of_organizations=1. growth_rate=1.
% 0.75/1.05
% 0.75/1.05 ============================== end of process initial clauses ========
% 0.75/1.05
% 0.75/1.05 ============================== CLAUSES FOR SEARCH ====================
% 0.75/1.05
% 0.75/1.05 ============================== end of clauses for search =============
% 0.75/1.05
% 0.75/1.05 ============================== SEARCH ================================
% 0.75/1.05
% 0.75/1.05 % Starting search at 0.01 seconds.
% 0.75/1.05
% 0.75/1.05 ============================== PROOF =================================
% 0.75/1.05 % SZS status Theorem
% 0.75/1.05 % SZS output start Refutation
% 0.75/1.05
% 0.75/1.05 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.75/1.05 % Length of proof is 99.
% 0.75/1.05 % Level of proof is 22.
% 0.75/1.05 % Maximum clause weight is 21.000.
% 0.75/1.05 % Given clauses 88.
% 0.75/1.05
% 0.75/1.05 1 (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) -> number_of_organizations(E,T) = sum(cardinality_at_time(first_movers,T),cardinality_at_time(efficient_producers,T)))) # label(mp_only_members) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.05 2 (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].
% 0.75/1.05 3 (all A all B all C (A = sum(B,C) & constant(A) -> constant(B) & constant(C) | increases(B) & decreases(C) | decreases(B) & increases(C))) # label(mp_abc_sum_increase) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.05 4 (all X all E all T (environment(E) & in_environment(E,T) & subpopulation(X,E,T) & greater(cardinality_at_time(X,T),zero) -> (constant(cardinality_at_time(X,T)) -> growth_rate(X,T) = zero) & (increases(cardinality_at_time(X,T)) -> greater(growth_rate(X,T),zero)) & (decreases(cardinality_at_time(X,T)) -> greater(zero,growth_rate(X,T))))) # label(mp_growth_rate) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.05 5 (all E all T (environment(E) & subpopulations(first_movers,efficient_producers,E,T) -> greater(cardinality_at_time(first_movers,T),zero) & greater(cardinality_at_time(efficient_producers,T),zero))) # label(mp_non_zero_producers) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.05 6 (all E all T (environment(E) & subpopulations(first_movers,efficient_producers,E,T) -> in_environment(E,T))) # label(mp_time_point_occur) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.05 8 -(all E all T (environment(E) & subpopulations(first_movers,efficient_producers,E,T) & constant(number_of_organizations(E,T)) -> growth_rate(first_movers,T) = zero & growth_rate(efficient_producers,T) = zero | greater(growth_rate(first_movers,T),zero) & greater(zero,growth_rate(efficient_producers,T)) | greater(growth_rate(efficient_producers,T),zero) & greater(zero,growth_rate(first_movers,T)))) # label(prove_l7) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.75/1.05 9 -environment(A) | -in_environment(A,B) | subpopulation(first_movers,A,B) # label(mp_subpopulations) # label(axiom). [clausify(2)].
% 0.75/1.05 10 environment(c1) # label(prove_l7) # label(negated_conjecture). [clausify(8)].
% 0.75/1.05 11 -environment(A) | -in_environment(A,B) | subpopulation(efficient_producers,A,B) # label(mp_subpopulations) # label(axiom). [clausify(2)].
% 0.75/1.05 12 -environment(A) | -subpopulations(first_movers,efficient_producers,A,B) | in_environment(A,B) # label(mp_time_point_occur) # label(axiom). [clausify(6)].
% 0.75/1.05 13 -environment(A) | -subpopulations(first_movers,efficient_producers,A,B) | greater(cardinality_at_time(first_movers,B),zero) # label(mp_non_zero_producers) # label(axiom). [clausify(5)].
% 0.75/1.05 14 -environment(A) | -subpopulations(first_movers,efficient_producers,A,B) | greater(cardinality_at_time(efficient_producers,B),zero) # label(mp_non_zero_producers) # label(axiom). [clausify(5)].
% 0.75/1.05 16 -environment(A) | -subpopulation(B,A,C) | efficient_producers != B | sum(cardinality_at_time(first_movers,C),cardinality_at_time(efficient_producers,C)) = number_of_organizations(A,C) # label(mp_only_members) # label(axiom). [clausify(1)].
% 0.75/1.05 19 -environment(A) | -in_environment(A,B) | -subpopulation(C,A,B) | -greater(cardinality_at_time(C,B),zero) | -constant(cardinality_at_time(C,B)) | growth_rate(C,B) = zero # label(mp_growth_rate) # label(axiom). [clausify(4)].
% 0.75/1.05 20 -environment(A) | -in_environment(A,B) | -subpopulation(C,A,B) | -greater(cardinality_at_time(C,B),zero) | -increases(cardinality_at_time(C,B)) | greater(growth_rate(C,B),zero) # label(mp_growth_rate) # label(axiom). [clausify(4)].
% 0.75/1.05 21 -environment(A) | -in_environment(A,B) | -subpopulation(C,A,B) | -greater(cardinality_at_time(C,B),zero) | -decreases(cardinality_at_time(C,B)) | greater(zero,growth_rate(C,B)) # label(mp_growth_rate) # label(axiom). [clausify(4)].
% 0.75/1.05 22 constant(number_of_organizations(c1,c2)) # label(prove_l7) # label(negated_conjecture). [clausify(8)].
% 0.75/1.05 23 subpopulations(first_movers,efficient_producers,c1,c2) # label(prove_l7) # label(negated_conjecture). [clausify(8)].
% 0.75/1.05 24 growth_rate(first_movers,c2) != zero | growth_rate(efficient_producers,c2) != zero # label(prove_l7) # label(negated_conjecture). [clausify(8)].
% 0.75/1.05 25 -greater(growth_rate(first_movers,c2),zero) | -greater(zero,growth_rate(efficient_producers,c2)) # label(prove_l7) # label(negated_conjecture). [clausify(8)].
% 0.75/1.05 26 -greater(growth_rate(efficient_producers,c2),zero) | -greater(zero,growth_rate(first_movers,c2)) # label(prove_l7) # label(negated_conjecture). [clausify(8)].
% 0.75/1.05 27 sum(A,B) != C | -constant(C) | constant(A) | increases(A) | decreases(A) # label(mp_abc_sum_increase) # label(axiom). [clausify(3)].
% 0.75/1.05 28 sum(A,B) != C | -constant(C) | constant(A) | increases(A) | increases(B) # label(mp_abc_sum_increase) # label(axiom). [clausify(3)].
% 0.75/1.05 29 sum(A,B) != C | -constant(C) | constant(A) | decreases(B) | decreases(A) # label(mp_abc_sum_increase) # label(axiom). [clausify(3)].
% 0.75/1.05 30 sum(A,B) != C | -constant(C) | constant(A) | decreases(B) | increases(B) # label(mp_abc_sum_increase) # label(axiom). [clausify(3)].
% 0.75/1.05 31 sum(A,B) != C | -constant(C) | constant(B) | increases(A) | decreases(A) # label(mp_abc_sum_increase) # label(axiom). [clausify(3)].
% 0.75/1.05 33 sum(A,B) != C | -constant(C) | constant(B) | decreases(B) | decreases(A) # label(mp_abc_sum_increase) # label(axiom). [clausify(3)].
% 0.75/1.05 34 sum(A,B) != C | -constant(C) | constant(B) | decreases(B) | increases(B) # label(mp_abc_sum_increase) # label(axiom). [clausify(3)].
% 0.75/1.05 35 -in_environment(c1,A) | subpopulation(first_movers,c1,A). [resolve(9,a,10,a)].
% 0.75/1.05 36 -in_environment(c1,A) | subpopulation(efficient_producers,c1,A). [resolve(11,a,10,a)].
% 0.75/1.05 37 -subpopulations(first_movers,efficient_producers,c1,A) | in_environment(c1,A). [resolve(12,a,10,a)].
% 0.75/1.05 38 -subpopulations(first_movers,efficient_producers,c1,A) | greater(cardinality_at_time(first_movers,A),zero). [resolve(13,a,10,a)].
% 0.75/1.05 39 -subpopulations(first_movers,efficient_producers,c1,A) | greater(cardinality_at_time(efficient_producers,A),zero). [resolve(14,a,10,a)].
% 0.75/1.05 41 -subpopulation(A,c1,B) | efficient_producers != A | sum(cardinality_at_time(first_movers,B),cardinality_at_time(efficient_producers,B)) = number_of_organizations(c1,B). [resolve(16,a,10,a)].
% 0.75/1.05 44 -in_environment(c1,A) | -subpopulation(B,c1,A) | -greater(cardinality_at_time(B,A),zero) | -constant(cardinality_at_time(B,A)) | growth_rate(B,A) = zero. [resolve(19,a,10,a)].
% 0.75/1.05 45 -in_environment(c1,A) | -subpopulation(B,c1,A) | -greater(cardinality_at_time(B,A),zero) | -increases(cardinality_at_time(B,A)) | greater(growth_rate(B,A),zero). [resolve(20,a,10,a)].
% 0.75/1.05 46 -in_environment(c1,A) | -subpopulation(B,c1,A) | -greater(cardinality_at_time(B,A),zero) | -decreases(cardinality_at_time(B,A)) | greater(zero,growth_rate(B,A)). [resolve(21,a,10,a)].
% 0.75/1.05 49 sum(A,B) != number_of_organizations(c1,c2) | constant(A) | increases(A) | decreases(A). [resolve(27,b,22,a)].
% 0.75/1.05 50 sum(A,B) != number_of_organizations(c1,c2) | constant(A) | increases(A) | increases(B). [resolve(28,b,22,a)].
% 0.75/1.05 52 sum(A,B) != number_of_organizations(c1,c2) | constant(A) | decreases(B) | decreases(A). [resolve(29,b,22,a)].
% 0.75/1.05 54 sum(A,B) != number_of_organizations(c1,c2) | constant(A) | decreases(B) | increases(B). [resolve(30,b,22,a)].
% 0.75/1.05 55 sum(A,B) != number_of_organizations(c1,c2) | constant(B) | increases(A) | decreases(A). [resolve(31,b,22,a)].
% 0.75/1.05 57 sum(A,B) != number_of_organizations(c1,c2) | constant(B) | decreases(B) | decreases(A). [resolve(33,b,22,a)].
% 0.75/1.05 58 sum(A,B) != number_of_organizations(c1,c2) | constant(B) | decreases(B) | increases(B). [resolve(34,b,22,a)].
% 0.75/1.05 59 in_environment(c1,c2). [resolve(37,a,23,a)].
% 0.75/1.05 60 greater(cardinality_at_time(first_movers,c2),zero). [resolve(38,a,23,a)].
% 0.75/1.05 61 greater(cardinality_at_time(efficient_producers,c2),zero). [resolve(39,a,23,a)].
% 0.75/1.05 62 subpopulation(efficient_producers,c1,c2). [resolve(59,a,36,a)].
% 0.75/1.05 63 subpopulation(first_movers,c1,c2). [resolve(59,a,35,a)].
% 0.75/1.05 64 -decreases(cardinality_at_time(efficient_producers,c2)) | greater(zero,growth_rate(efficient_producers,c2)). [resolve(62,a,46,b),unit_del(a,59),unit_del(b,61)].
% 0.75/1.05 65 -increases(cardinality_at_time(efficient_producers,c2)) | greater(growth_rate(efficient_producers,c2),zero). [resolve(62,a,45,b),unit_del(a,59),unit_del(b,61)].
% 0.75/1.05 66 -constant(cardinality_at_time(efficient_producers,c2)) | growth_rate(efficient_producers,c2) = zero. [resolve(62,a,44,b),unit_del(a,59),unit_del(b,61)].
% 0.75/1.05 68 sum(cardinality_at_time(first_movers,c2),cardinality_at_time(efficient_producers,c2)) = number_of_organizations(c1,c2). [resolve(62,a,41,a),xx(a)].
% 0.75/1.05 69 -decreases(cardinality_at_time(first_movers,c2)) | greater(zero,growth_rate(first_movers,c2)). [resolve(63,a,46,b),unit_del(a,59),unit_del(b,60)].
% 0.75/1.05 70 -increases(cardinality_at_time(first_movers,c2)) | greater(growth_rate(first_movers,c2),zero). [resolve(63,a,45,b),unit_del(a,59),unit_del(b,60)].
% 0.75/1.05 71 -constant(cardinality_at_time(first_movers,c2)) | growth_rate(first_movers,c2) = zero. [resolve(63,a,44,b),unit_del(a,59),unit_del(b,60)].
% 0.75/1.05 72 constant(cardinality_at_time(first_movers,c2)) | decreases(cardinality_at_time(efficient_producers,c2)) | decreases(cardinality_at_time(first_movers,c2)). [resolve(68,a,52,a)].
% 0.75/1.05 73 constant(cardinality_at_time(first_movers,c2)) | increases(cardinality_at_time(first_movers,c2)) | increases(cardinality_at_time(efficient_producers,c2)). [resolve(68,a,50,a)].
% 0.75/1.05 74 constant(cardinality_at_time(first_movers,c2)) | increases(cardinality_at_time(first_movers,c2)) | decreases(cardinality_at_time(first_movers,c2)). [resolve(68,a,49,a)].
% 0.75/1.05 75 constant(cardinality_at_time(first_movers,c2)) | decreases(cardinality_at_time(efficient_producers,c2)) | greater(zero,growth_rate(first_movers,c2)). [resolve(72,c,69,a)].
% 0.75/1.05 76 constant(cardinality_at_time(first_movers,c2)) | increases(cardinality_at_time(efficient_producers,c2)) | greater(growth_rate(first_movers,c2),zero). [resolve(73,b,70,a)].
% 0.75/1.05 77 constant(cardinality_at_time(first_movers,c2)) | decreases(cardinality_at_time(first_movers,c2)) | greater(growth_rate(first_movers,c2),zero). [resolve(74,b,70,a)].
% 0.75/1.05 78 constant(cardinality_at_time(first_movers,c2)) | decreases(cardinality_at_time(efficient_producers,c2)) | increases(cardinality_at_time(efficient_producers,c2)). [resolve(54,a,68,a)].
% 0.75/1.05 79 constant(cardinality_at_time(first_movers,c2)) | decreases(cardinality_at_time(efficient_producers,c2)) | greater(growth_rate(efficient_producers,c2),zero). [resolve(78,c,65,a)].
% 0.75/1.05 80 constant(cardinality_at_time(efficient_producers,c2)) | increases(cardinality_at_time(first_movers,c2)) | decreases(cardinality_at_time(first_movers,c2)). [resolve(55,a,68,a)].
% 0.75/1.05 81 constant(cardinality_at_time(efficient_producers,c2)) | decreases(cardinality_at_time(first_movers,c2)) | greater(growth_rate(first_movers,c2),zero). [resolve(80,b,70,a)].
% 0.75/1.05 83 constant(cardinality_at_time(efficient_producers,c2)) | decreases(cardinality_at_time(efficient_producers,c2)) | decreases(cardinality_at_time(first_movers,c2)). [resolve(57,a,68,a)].
% 0.75/1.05 85 constant(cardinality_at_time(efficient_producers,c2)) | decreases(cardinality_at_time(efficient_producers,c2)) | greater(zero,growth_rate(first_movers,c2)). [resolve(83,c,69,a)].
% 0.75/1.05 86 constant(cardinality_at_time(efficient_producers,c2)) | decreases(cardinality_at_time(efficient_producers,c2)) | increases(cardinality_at_time(efficient_producers,c2)). [resolve(58,a,68,a)].
% 0.75/1.05 87 constant(cardinality_at_time(efficient_producers,c2)) | decreases(cardinality_at_time(efficient_producers,c2)) | greater(growth_rate(efficient_producers,c2),zero). [resolve(86,c,65,a)].
% 0.75/1.05 88 constant(cardinality_at_time(first_movers,c2)) | increases(cardinality_at_time(efficient_producers,c2)) | -greater(zero,growth_rate(efficient_producers,c2)). [resolve(76,c,25,a)].
% 0.75/1.05 89 constant(cardinality_at_time(first_movers,c2)) | decreases(cardinality_at_time(first_movers,c2)) | -greater(zero,growth_rate(efficient_producers,c2)). [resolve(77,c,25,a)].
% 0.75/1.05 90 constant(cardinality_at_time(first_movers,c2)) | decreases(cardinality_at_time(efficient_producers,c2)) | -greater(zero,growth_rate(first_movers,c2)). [resolve(79,c,26,a)].
% 0.75/1.05 91 constant(cardinality_at_time(efficient_producers,c2)) | decreases(cardinality_at_time(first_movers,c2)) | -greater(zero,growth_rate(efficient_producers,c2)). [resolve(81,c,25,a)].
% 0.75/1.05 93 constant(cardinality_at_time(efficient_producers,c2)) | decreases(cardinality_at_time(efficient_producers,c2)) | -greater(zero,growth_rate(first_movers,c2)). [resolve(87,c,26,a)].
% 0.75/1.05 95 constant(cardinality_at_time(first_movers,c2)) | decreases(cardinality_at_time(efficient_producers,c2)). [resolve(90,c,75,c),merge(c),merge(d)].
% 0.75/1.05 96 constant(cardinality_at_time(first_movers,c2)) | greater(zero,growth_rate(efficient_producers,c2)). [resolve(95,b,64,a)].
% 0.75/1.05 97 constant(cardinality_at_time(first_movers,c2)) | decreases(cardinality_at_time(first_movers,c2)). [resolve(96,b,89,c),merge(b)].
% 0.75/1.05 98 constant(cardinality_at_time(first_movers,c2)) | increases(cardinality_at_time(efficient_producers,c2)). [resolve(96,b,88,c),merge(b)].
% 0.75/1.05 99 constant(cardinality_at_time(first_movers,c2)) | greater(zero,growth_rate(first_movers,c2)). [resolve(97,b,69,a)].
% 0.75/1.05 100 constant(cardinality_at_time(first_movers,c2)) | greater(growth_rate(efficient_producers,c2),zero). [resolve(98,b,65,a)].
% 0.75/1.05 101 constant(cardinality_at_time(first_movers,c2)) | -greater(zero,growth_rate(first_movers,c2)). [resolve(100,b,26,a)].
% 0.75/1.05 102 constant(cardinality_at_time(first_movers,c2)). [resolve(101,b,99,b),merge(b)].
% 0.75/1.05 103 growth_rate(first_movers,c2) = zero. [back_unit_del(71),unit_del(a,102)].
% 0.75/1.05 104 constant(cardinality_at_time(efficient_producers,c2)) | decreases(cardinality_at_time(efficient_producers,c2)) | -greater(zero,zero). [back_rewrite(93),rewrite([103(12)])].
% 0.75/1.05 105 constant(cardinality_at_time(efficient_producers,c2)) | decreases(cardinality_at_time(efficient_producers,c2)) | greater(zero,zero). [back_rewrite(85),rewrite([103(12)])].
% 0.75/1.05 109 -decreases(cardinality_at_time(first_movers,c2)) | greater(zero,zero). [back_rewrite(69),rewrite([103(8)])].
% 0.75/1.05 111 -greater(zero,zero) | -greater(zero,growth_rate(efficient_producers,c2)). [back_rewrite(25),rewrite([103(3)])].
% 0.75/1.05 112 growth_rate(efficient_producers,c2) != zero. [back_rewrite(24),rewrite([103(3)]),xx(a)].
% 0.75/1.05 113 -constant(cardinality_at_time(efficient_producers,c2)). [back_unit_del(66),unit_del(b,112)].
% 0.75/1.05 116 decreases(cardinality_at_time(efficient_producers,c2)) | greater(zero,zero). [back_unit_del(105),unit_del(a,113)].
% 0.75/1.05 117 decreases(cardinality_at_time(efficient_producers,c2)) | -greater(zero,zero). [back_unit_del(104),unit_del(a,113)].
% 0.75/1.05 119 decreases(cardinality_at_time(first_movers,c2)) | -greater(zero,growth_rate(efficient_producers,c2)). [back_unit_del(91),unit_del(a,113)].
% 0.75/1.05 135 decreases(cardinality_at_time(efficient_producers,c2)). [resolve(117,b,116,b),merge(b)].
% 0.75/1.05 136 greater(zero,growth_rate(efficient_producers,c2)). [back_unit_del(64),unit_del(a,135)].
% 0.75/1.05 137 decreases(cardinality_at_time(first_movers,c2)). [back_unit_del(119),unit_del(b,136)].
% 0.75/1.05 139 -greater(zero,zero). [back_unit_del(111),unit_del(b,136)].
% 0.75/1.05 140 $F. [back_unit_del(109),unit_del(a,137),unit_del(b,139)].
% 0.75/1.05
% 0.75/1.05 % SZS output end Refutation
% 0.75/1.05 ============================== end of proof ==========================
% 0.75/1.05
% 0.75/1.05 ============================== STATISTICS ============================
% 0.75/1.05
% 0.75/1.05 Given=88. Generated=150. Kept=118. proofs=1.
% 0.75/1.05 Usable=48. Sos=13. Demods=2. Limbo=3, Disabled=92. Hints=0.
% 0.75/1.05 Megabytes=0.15.
% 0.75/1.05 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.75/1.05
% 0.75/1.05 ============================== end of statistics =====================
% 0.75/1.05
% 0.75/1.05 ============================== end of search =========================
% 0.75/1.05
% 0.75/1.05 THEOREM PROVED
% 0.75/1.05 % SZS status Theorem
% 0.75/1.05
% 0.75/1.05 Exiting with 1 proof.
% 0.75/1.05
% 0.75/1.05 Process 30240 exit (max_proofs) Thu Jun 9 08:54:25 2022
% 0.75/1.05 Prover9 interrupted
%------------------------------------------------------------------------------