0.08/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.08/0.14 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.yCx369zmyw 0.14/0.36 % Computer : n016.cluster.edu 0.14/0.36 % Model : x86_64 x86_64 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.36 % Memory : 8042.1875MB 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.36 % CPULimit : 960 0.14/0.36 % DateTime : Thu Jul 2 06:40:05 EDT 2020 0.14/0.36 % CPUTime : 0.14/0.36 % Running portfolio for 120 s 0.14/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.14/0.36 % Number of cores: 8 0.14/0.37 % Python version: Python 3.6.8 0.14/0.37 % Running in FO mode 0.35/0.54 % Running /export/starexec/sandbox2/solver/bin/fo/fo7.sh for 25 0.35/0.54 % Solved by: fo/fo7.sh 0.35/0.54 To remain in the chosen logic fragment, unification with booleans has been disabled. 0.35/0.54 % done 80 iterations in 0.054s 0.35/0.54 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 0.35/0.54 % SZS output start Refutation 0.35/0.54 tff(prove_t6, conjecture, 0.35/0.54 (![E,T]: 0.35/0.54 ((environment(E) & greater_or_equal(T,appear(efficient_producers,E)) & 0.35/0.54 in_environment(E,T)) => 0.35/0.54 greater(cardinality_at_time(efficient_producers,T),zero)))). 0.35/0.54 tff(zf_stmt_0, negated_conjecture, 0.35/0.54 (~ 0.35/0.54 (![E,T]: 0.35/0.54 ((environment(E) & 0.35/0.54 greater_or_equal(T,appear(efficient_producers,E)) & 0.35/0.54 in_environment(E,T)) => 0.35/0.54 greater(cardinality_at_time(efficient_producers,T),zero))))). 0.35/0.54 tff('0', plain, greater_or_equal(sk_T, appear(efficient_producers, sk_E)), 0.35/0.54 inference('cnf', [status(esa)], [zf_stmt_0])). 0.35/0.54 tff(mp_previous_negative_growth, axiom, 0.35/0.54 (![E,T]: 0.35/0.54 ((environment(E) & greater_or_equal(T,appear(efficient_producers,E)) & 0.35/0.54 (cardinality_at_time(efficient_producers,T) = zero)) => 0.35/0.54 (?[To]: 0.35/0.54 (greater(To,appear(efficient_producers,E)) & in_environment(E,To) & 0.35/0.54 greater(T,To) & greater(zero,growth_rate(efficient_producers,To))))))). 0.35/0.54 tff('1', plain, 0.35/0.54 ![X11, X12]: 0.35/0.54 (~ environment(X11) 0.35/0.54 | ~ greater_or_equal(X12, appear(efficient_producers, X11)) 0.35/0.54 | cardinality_at_time(efficient_producers, X12) != zero 0.35/0.54 | in_environment(X11, sk_To(X12, X11))), 0.35/0.54 inference('cnf', [status(esa)], [mp_previous_negative_growth])). 0.35/0.54 tff('2', plain, 0.35/0.54 ( in_environment(sk_E, sk_To(sk_T, sk_E)) 0.35/0.54 | cardinality_at_time(efficient_producers, sk_T) != zero 0.35/0.54 | ~ environment(sk_E)), 0.35/0.54 inference('sup-', [status(thm)], ['0', '1'])). 0.35/0.54 tff('3', plain, in_environment(sk_E, sk_T), 0.35/0.54 inference('cnf', [status(esa)], [zf_stmt_0])). 0.35/0.54 tff(mp_efficient_producers_exist, axiom, 0.35/0.54 (![E,T]: 0.35/0.54 ((in_environment(E,T) & environment(E)) => 0.35/0.54 ((cardinality_at_time(efficient_producers,T) = zero) | 0.35/0.54 greater(cardinality_at_time(efficient_producers,T),zero))))). 0.35/0.54 tff('4', plain, 0.35/0.54 ![X18, X19]: 0.35/0.54 (~ environment(X18) 0.35/0.54 | ~ in_environment(X18, X19) 0.35/0.54 | cardinality_at_time(efficient_producers, X19) = zero 0.35/0.54 | greater(cardinality_at_time(efficient_producers, X19), zero)), 0.35/0.54 inference('cnf', [status(esa)], [mp_efficient_producers_exist])). 0.35/0.54 tff('5', plain, 0.35/0.54 ( greater(cardinality_at_time(efficient_producers, sk_T), zero) 0.35/0.54 | cardinality_at_time(efficient_producers, sk_T) = zero 0.35/0.54 | ~ environment(sk_E)), 0.35/0.54 inference('sup-', [status(thm)], ['3', '4'])). 0.35/0.54 tff('6', plain, environment(sk_E), 0.35/0.54 inference('cnf', [status(esa)], [zf_stmt_0])). 0.35/0.54 tff('7', plain, 0.35/0.54 ( greater(cardinality_at_time(efficient_producers, sk_T), zero) 0.35/0.54 | cardinality_at_time(efficient_producers, sk_T) = zero), 0.35/0.54 inference('demod', [status(thm)], ['5', '6'])). 0.35/0.54 tff('8', plain, 0.35/0.54 ~ greater(cardinality_at_time(efficient_producers, sk_T), zero), 0.35/0.54 inference('cnf', [status(esa)], [zf_stmt_0])). 0.35/0.54 tff('9', plain, cardinality_at_time(efficient_producers, sk_T) = zero, 0.35/0.54 inference('clc', [status(thm)], ['7', '8'])). 0.35/0.54 tff('10', plain, environment(sk_E), 0.35/0.54 inference('cnf', [status(esa)], [zf_stmt_0])). 0.35/0.54 tff('11', plain, ( in_environment(sk_E, sk_To(sk_T, sk_E)) | zero != zero), 0.35/0.54 inference('demod', [status(thm)], ['2', '9', '10'])). 0.35/0.54 tff('12', plain, in_environment(sk_E, sk_To(sk_T, sk_E)), 0.35/0.54 inference('simplify', [status(thm)], ['11'])). 0.35/0.54 tff(mp_subpopulations, axiom, 0.35/0.54 (![E,T]: 0.35/0.54 ((in_environment(E,T) & environment(E)) => 0.35/0.54 (subpopulation(first_movers,E,T) & 0.35/0.54 subpopulation(efficient_producers,E,T))))). 0.35/0.54 tff('13', plain, 0.35/0.54 ![X0, X1]: 0.35/0.54 (~ environment(X0) 0.35/0.54 | ~ in_environment(X0, X1) 0.35/0.54 | subpopulation(first_movers, X0, X1)), 0.35/0.54 inference('cnf', [status(esa)], [mp_subpopulations])). 0.35/0.54 tff('14', plain, 0.35/0.54 ( subpopulation(first_movers, sk_E, sk_To(sk_T, sk_E)) 0.35/0.54 | ~ environment(sk_E)), 0.35/0.54 inference('sup-', [status(thm)], ['12', '13'])). 0.35/0.54 tff('15', plain, environment(sk_E), 0.35/0.54 inference('cnf', [status(esa)], [zf_stmt_0])). 0.35/0.54 tff('16', plain, subpopulation(first_movers, sk_E, sk_To(sk_T, sk_E)), 0.35/0.54 inference('demod', [status(thm)], ['14', '15'])). 0.35/0.54 tff('17', plain, in_environment(sk_E, sk_To(sk_T, sk_E)), 0.35/0.54 inference('simplify', [status(thm)], ['11'])). 0.35/0.54 tff(mp_environment_inequality, axiom, 0.35/0.54 (![E,T]: 0.35/0.54 ((environment(E) & in_environment(E,T)) => 0.35/0.54 (greater(appear(an_organisation,E),T) | 0.35/0.54 greater_or_equal(T,appear(an_organisation,E)))))). 0.35/0.54 tff('18', plain, 0.35/0.54 ![X29, X30]: 0.35/0.54 (~ environment(X29) 0.35/0.54 | ~ in_environment(X29, X30) 0.35/0.54 | greater(appear(an_organisation, X29), X30) 0.35/0.54 | greater_or_equal(X30, appear(an_organisation, X29))), 0.35/0.54 inference('cnf', [status(esa)], [mp_environment_inequality])). 0.35/0.54 tff('19', plain, 0.35/0.54 ( greater_or_equal(sk_To(sk_T, sk_E), appear(an_organisation, sk_E)) 0.35/0.54 | greater(appear(an_organisation, sk_E), sk_To(sk_T, sk_E)) 0.35/0.54 | ~ environment(sk_E)), 0.35/0.54 inference('sup-', [status(thm)], ['17', '18'])). 0.35/0.54 tff('20', plain, environment(sk_E), 0.35/0.54 inference('cnf', [status(esa)], [zf_stmt_0])). 0.35/0.54 tff('21', plain, 0.35/0.54 ( greater_or_equal(sk_To(sk_T, sk_E), appear(an_organisation, sk_E)) 0.35/0.54 | greater(appear(an_organisation, sk_E), sk_To(sk_T, sk_E))), 0.35/0.54 inference('demod', [status(thm)], ['19', '20'])). 0.35/0.54 tff(mp_start_of_organizations, axiom, 0.35/0.54 (![E,T]: 0.35/0.54 ((environment(E) & in_environment(E,T) & 0.35/0.54 greater(appear(an_organisation,E),T)) => 0.35/0.54 (zero = number_of_organizations(E,T))))). 0.35/0.54 tff('22', plain, 0.35/0.54 ![X25, X26]: 0.35/0.54 (~ environment(X25) 0.35/0.54 | ~ in_environment(X25, X26) 0.35/0.54 | ~ greater(appear(an_organisation, X25), X26) 0.35/0.54 | zero = number_of_organizations(X25, X26)), 0.35/0.54 inference('cnf', [status(esa)], [mp_start_of_organizations])). 0.35/0.54 tff('23', plain, 0.35/0.54 ( greater_or_equal(sk_To(sk_T, sk_E), appear(an_organisation, sk_E)) 0.35/0.54 | zero = number_of_organizations(sk_E, sk_To(sk_T, sk_E)) 0.35/0.54 | ~ in_environment(sk_E, sk_To(sk_T, sk_E)) 0.35/0.54 | ~ environment(sk_E)), 0.35/0.54 inference('sup-', [status(thm)], ['21', '22'])). 0.35/0.54 tff('24', plain, in_environment(sk_E, sk_To(sk_T, sk_E)), 0.35/0.54 inference('simplify', [status(thm)], ['11'])). 0.35/0.54 tff('25', plain, environment(sk_E), 0.35/0.54 inference('cnf', [status(esa)], [zf_stmt_0])). 0.35/0.54 tff('26', plain, 0.35/0.54 ( greater_or_equal(sk_To(sk_T, sk_E), appear(an_organisation, sk_E)) 0.35/0.54 | zero = number_of_organizations(sk_E, sk_To(sk_T, sk_E))), 0.35/0.54 inference('demod', [status(thm)], ['23', '24', '25'])). 0.35/0.54 tff(a1, axiom, 0.35/0.54 (![E,T]: 0.35/0.54 ((environment(E) & in_environment(E,T) & 0.35/0.54 greater_or_equal(T,appear(an_organisation,E))) => 0.35/0.54 greater(number_of_organizations(E,T),zero)))). 0.35/0.54 tff('27', plain, 0.35/0.54 ![X23, X24]: 0.35/0.54 (~ environment(X23) 0.35/0.54 | ~ in_environment(X23, X24) 0.35/0.54 | ~ greater_or_equal(X24, appear(an_organisation, X23)) 0.35/0.54 | greater(number_of_organizations(X23, X24), zero)), 0.35/0.54 inference('cnf', [status(esa)], [a1])). 0.35/0.54 tff('28', plain, 0.35/0.54 (zero = number_of_organizations(sk_E, sk_To(sk_T, sk_E)) 0.35/0.54 | greater(number_of_organizations(sk_E, sk_To(sk_T, sk_E)), zero) 0.35/0.54 | ~ in_environment(sk_E, sk_To(sk_T, sk_E)) 0.35/0.54 | ~ environment(sk_E)), 0.35/0.54 inference('sup-', [status(thm)], ['26', '27'])). 0.35/0.54 tff('29', plain, in_environment(sk_E, sk_To(sk_T, sk_E)), 0.35/0.54 inference('simplify', [status(thm)], ['11'])). 0.35/0.54 tff('30', plain, environment(sk_E), 0.35/0.54 inference('cnf', [status(esa)], [zf_stmt_0])). 0.35/0.54 tff('31', plain, 0.35/0.54 (zero = number_of_organizations(sk_E, sk_To(sk_T, sk_E)) 0.35/0.54 | greater(number_of_organizations(sk_E, sk_To(sk_T, sk_E)), zero)), 0.35/0.54 inference('demod', [status(thm)], ['28', '29', '30'])). 0.35/0.54 tff(a3, axiom, 0.35/0.54 (![E,T]: 0.35/0.54 ((environment(E) & in_environment(E,T) & 0.35/0.54 greater(number_of_organizations(E,T),zero)) => 0.35/0.54 ((greater(equilibrium(E),T) => decreases(resources(E,T))) & 0.35/0.54 ((~greater(equilibrium(E),T)) => constant(resources(E,T))))))). 0.35/0.54 tff('32', plain, 0.35/0.54 ![X15, X16]: 0.35/0.54 (~ environment(X15) 0.35/0.54 | ~ in_environment(X15, X16) 0.35/0.54 | ~ greater(number_of_organizations(X15, X16), zero) 0.35/0.54 | constant(resources(X15, X16)) 0.35/0.54 | greater(equilibrium(X15), X16)), 0.35/0.54 inference('cnf', [status(esa)], [a3])). 0.35/0.54 tff('33', plain, 0.35/0.54 (zero = number_of_organizations(sk_E, sk_To(sk_T, sk_E)) 0.35/0.54 | greater(equilibrium(sk_E), sk_To(sk_T, sk_E)) 0.35/0.54 | constant(resources(sk_E, sk_To(sk_T, sk_E))) 0.35/0.54 | ~ in_environment(sk_E, sk_To(sk_T, sk_E)) 0.35/0.54 | ~ environment(sk_E)), 0.35/0.54 inference('sup-', [status(thm)], ['31', '32'])). 0.35/0.54 tff('34', plain, in_environment(sk_E, sk_To(sk_T, sk_E)), 0.35/0.54 inference('simplify', [status(thm)], ['11'])). 0.35/0.54 tff('35', plain, environment(sk_E), 0.35/0.54 inference('cnf', [status(esa)], [zf_stmt_0])). 0.35/0.54 tff('36', plain, 0.35/0.54 (zero = number_of_organizations(sk_E, sk_To(sk_T, sk_E)) 0.35/0.54 | greater(equilibrium(sk_E), sk_To(sk_T, sk_E)) 0.35/0.54 | constant(resources(sk_E, sk_To(sk_T, sk_E)))), 0.35/0.54 inference('demod', [status(thm)], ['33', '34', '35'])). 0.35/0.54 tff('37', plain, 0.35/0.54 (zero = number_of_organizations(sk_E, sk_To(sk_T, sk_E)) 0.35/0.54 | greater(number_of_organizations(sk_E, sk_To(sk_T, sk_E)), zero)), 0.35/0.54 inference('demod', [status(thm)], ['28', '29', '30'])). 0.35/0.54 tff('38', plain, 0.35/0.54 ![X15, X16]: 0.35/0.54 (~ environment(X15) 0.35/0.54 | ~ in_environment(X15, X16) 0.35/0.54 | ~ greater(number_of_organizations(X15, X16), zero) 0.35/0.54 | decreases(resources(X15, X16)) 0.35/0.54 | ~ greater(equilibrium(X15), X16)), 0.35/0.54 inference('cnf', [status(esa)], [a3])). 0.35/0.54 tff('39', plain, 0.35/0.54 (zero = number_of_organizations(sk_E, sk_To(sk_T, sk_E)) 0.35/0.54 | ~ greater(equilibrium(sk_E), sk_To(sk_T, sk_E)) 0.35/0.54 | decreases(resources(sk_E, sk_To(sk_T, sk_E))) 0.35/0.54 | ~ in_environment(sk_E, sk_To(sk_T, sk_E)) 0.35/0.54 | ~ environment(sk_E)), 0.35/0.54 inference('sup-', [status(thm)], ['37', '38'])). 0.35/0.54 tff('40', plain, in_environment(sk_E, sk_To(sk_T, sk_E)), 0.35/0.54 inference('simplify', [status(thm)], ['11'])). 0.35/0.54 tff('41', plain, environment(sk_E), 0.35/0.54 inference('cnf', [status(esa)], [zf_stmt_0])). 0.35/0.54 tff('42', plain, 0.35/0.54 (zero = number_of_organizations(sk_E, sk_To(sk_T, sk_E)) 0.35/0.54 | ~ greater(equilibrium(sk_E), sk_To(sk_T, sk_E)) 0.35/0.54 | decreases(resources(sk_E, sk_To(sk_T, sk_E)))), 0.35/0.54 inference('demod', [status(thm)], ['39', '40', '41'])). 0.35/0.54 tff('43', plain, 0.35/0.54 ( constant(resources(sk_E, sk_To(sk_T, sk_E))) 0.35/0.54 | zero = number_of_organizations(sk_E, sk_To(sk_T, sk_E)) 0.35/0.54 | decreases(resources(sk_E, sk_To(sk_T, sk_E))) 0.35/0.54 | zero = number_of_organizations(sk_E, sk_To(sk_T, sk_E))), 0.35/0.54 inference('sup-', [status(thm)], ['36', '42'])). 0.35/0.54 tff('44', plain, 0.35/0.54 ( decreases(resources(sk_E, sk_To(sk_T, sk_E))) 0.35/0.54 | zero = number_of_organizations(sk_E, sk_To(sk_T, sk_E)) 0.35/0.54 | constant(resources(sk_E, sk_To(sk_T, sk_E)))), 0.35/0.54 inference('simplify', [status(thm)], ['43'])). 0.35/0.54 tff('45', plain, in_environment(sk_E, sk_To(sk_T, sk_E)), 0.35/0.54 inference('simplify', [status(thm)], ['11'])). 0.35/0.54 tff(mp_non_decreasing, axiom, 0.35/0.54 (![E,T]: 0.35/0.54 ((environment(E) & (~decreases(number_of_organizations(E,T))) & 0.35/0.54 in_environment(E,T)) => 0.35/0.54 (?[X]: 0.35/0.54 (greater(cardinality_at_time(X,T),zero) & 0.35/0.54 (~greater(zero,growth_rate(X,T))) & subpopulation(X,E,T)))))). 0.35/0.54 tff('46', plain, 0.35/0.54 ![X27, X28]: 0.35/0.54 (~ environment(X27) 0.35/0.54 | decreases(number_of_organizations(X27, X28)) 0.35/0.54 | ~ in_environment(X27, X28) 0.35/0.54 | subpopulation(sk_X(X28, X27), X27, X28)), 0.35/0.54 inference('cnf', [status(esa)], [mp_non_decreasing])). 0.35/0.54 tff('47', plain, 0.35/0.54 ( subpopulation(sk_X(sk_To(sk_T, sk_E), sk_E), sk_E, sk_To(sk_T, sk_E)) 0.35/0.54 | decreases(number_of_organizations(sk_E, sk_To(sk_T, sk_E))) 0.35/0.54 | ~ environment(sk_E)), 0.35/0.54 inference('sup-', [status(thm)], ['45', '46'])). 0.35/0.54 tff('48', plain, environment(sk_E), 0.35/0.54 inference('cnf', [status(esa)], [zf_stmt_0])). 0.35/0.54 tff('49', plain, 0.35/0.54 ( subpopulation(sk_X(sk_To(sk_T, sk_E), sk_E), sk_E, sk_To(sk_T, sk_E)) 0.35/0.54 | decreases(number_of_organizations(sk_E, sk_To(sk_T, sk_E)))), 0.35/0.54 inference('demod', [status(thm)], ['47', '48'])). 0.35/0.54 tff('50', plain, in_environment(sk_E, sk_To(sk_T, sk_E)), 0.35/0.54 inference('simplify', [status(thm)], ['11'])). 0.35/0.54 tff('51', plain, 0.35/0.54 ![X27, X28]: 0.35/0.54 (~ environment(X27) 0.35/0.54 | decreases(number_of_organizations(X27, X28)) 0.35/0.54 | ~ in_environment(X27, X28) 0.35/0.54 | greater(cardinality_at_time(sk_X(X28, X27), X28), zero)), 0.35/0.54 inference('cnf', [status(esa)], [mp_non_decreasing])). 0.35/0.54 tff('52', plain, 0.35/0.54 ( greater( 0.35/0.54 cardinality_at_time(sk_X(sk_To(sk_T, sk_E), sk_E), sk_To(sk_T, sk_E)), 0.35/0.54 zero) 0.35/0.54 | decreases(number_of_organizations(sk_E, sk_To(sk_T, sk_E))) 0.35/0.54 | ~ environment(sk_E)), 0.35/0.54 inference('sup-', [status(thm)], ['50', '51'])). 0.35/0.54 tff('53', plain, environment(sk_E), 0.35/0.54 inference('cnf', [status(esa)], [zf_stmt_0])). 0.35/0.54 tff('54', plain, 0.35/0.54 ( greater( 0.35/0.54 cardinality_at_time(sk_X(sk_To(sk_T, sk_E), sk_E), sk_To(sk_T, sk_E)), 0.35/0.54 zero) 0.35/0.54 | decreases(number_of_organizations(sk_E, sk_To(sk_T, sk_E)))), 0.35/0.54 inference('demod', [status(thm)], ['52', '53'])). 0.35/0.54 tff(a9, axiom, 0.35/0.54 (![E,X,T]: 0.35/0.54 ((environment(E) & greater(cardinality_at_time(X,T),zero) & 0.35/0.54 subpopulation(X,E,T)) => 0.35/0.54 ((first_movers = X) | (X = efficient_producers))))). 0.35/0.54 tff('55', plain, 0.35/0.54 ![X8, X9, X10]: 0.35/0.54 (X8 = efficient_producers 0.35/0.54 | first_movers = X8 0.35/0.54 | ~ environment(X9) 0.35/0.54 | ~ greater(cardinality_at_time(X8, X10), zero) 0.35/0.54 | ~ subpopulation(X8, X9, X10)), 0.35/0.54 inference('cnf', [status(esa)], [a9])). 0.35/0.54 tff('56', plain, 0.35/0.54 ![X0]: 0.35/0.54 ( decreases(number_of_organizations(sk_E, sk_To(sk_T, sk_E))) 0.35/0.54 | ~ subpopulation(sk_X(sk_To(sk_T, sk_E), sk_E), X0, 0.35/0.54 sk_To(sk_T, sk_E)) 0.35/0.54 | ~ environment(X0) 0.35/0.54 | first_movers = sk_X(sk_To(sk_T, sk_E), sk_E) 0.35/0.54 | sk_X(sk_To(sk_T, sk_E), sk_E) = efficient_producers), 0.35/0.54 inference('sup-', [status(thm)], ['54', '55'])). 0.35/0.54 tff('57', plain, 0.35/0.54 ( decreases(number_of_organizations(sk_E, sk_To(sk_T, sk_E))) 0.35/0.54 | sk_X(sk_To(sk_T, sk_E), sk_E) = efficient_producers 0.35/0.54 | first_movers = sk_X(sk_To(sk_T, sk_E), sk_E) 0.35/0.54 | ~ environment(sk_E) 0.35/0.54 | decreases(number_of_organizations(sk_E, sk_To(sk_T, sk_E)))), 0.35/0.54 inference('sup-', [status(thm)], ['49', '56'])). 0.35/0.54 tff('58', plain, environment(sk_E), 0.35/0.54 inference('cnf', [status(esa)], [zf_stmt_0])). 0.35/0.54 tff('59', plain, 0.35/0.54 ( decreases(number_of_organizations(sk_E, sk_To(sk_T, sk_E))) 0.35/0.54 | sk_X(sk_To(sk_T, sk_E), sk_E) = efficient_producers 0.35/0.54 | first_movers = sk_X(sk_To(sk_T, sk_E), sk_E) 0.35/0.54 | decreases(number_of_organizations(sk_E, sk_To(sk_T, sk_E)))), 0.35/0.54 inference('demod', [status(thm)], ['57', '58'])). 0.35/0.54 tff('60', plain, 0.35/0.54 (first_movers = sk_X(sk_To(sk_T, sk_E), sk_E) 0.35/0.54 | sk_X(sk_To(sk_T, sk_E), sk_E) = efficient_producers 0.35/0.54 | decreases(number_of_organizations(sk_E, sk_To(sk_T, sk_E)))), 0.35/0.54 inference('simplify', [status(thm)], ['59'])). 0.35/0.54 tff('61', plain, 0.35/0.54 ![X27, X28]: 0.35/0.54 (~ environment(X27) 0.35/0.54 | decreases(number_of_organizations(X27, X28)) 0.35/0.54 | ~ in_environment(X27, X28) 0.35/0.54 | ~ greater(zero, growth_rate(sk_X(X28, X27), X28))), 0.35/0.54 inference('cnf', [status(esa)], [mp_non_decreasing])). 0.35/0.54 tff('62', plain, 0.35/0.54 (~ greater(zero, growth_rate(efficient_producers, sk_To(sk_T, sk_E))) 0.35/0.54 | decreases(number_of_organizations(sk_E, sk_To(sk_T, sk_E))) 0.35/0.54 | first_movers = sk_X(sk_To(sk_T, sk_E), sk_E) 0.35/0.54 | ~ in_environment(sk_E, sk_To(sk_T, sk_E)) 0.35/0.54 | decreases(number_of_organizations(sk_E, sk_To(sk_T, sk_E))) 0.35/0.54 | ~ environment(sk_E)), 0.35/0.54 inference('sup-', [status(thm)], ['60', '61'])). 0.35/0.54 tff('63', plain, greater_or_equal(sk_T, appear(efficient_producers, sk_E)), 0.35/0.54 inference('cnf', [status(esa)], [zf_stmt_0])). 0.35/0.54 tff('64', plain, 0.35/0.54 ![X11, X12]: 0.35/0.54 (~ environment(X11) 0.35/0.54 | ~ greater_or_equal(X12, appear(efficient_producers, X11)) 0.35/0.54 | cardinality_at_time(efficient_producers, X12) != zero 0.35/0.54 | greater(zero, growth_rate(efficient_producers, sk_To(X12, X11)))), 0.35/0.54 inference('cnf', [status(esa)], [mp_previous_negative_growth])). 0.35/0.54 tff('65', plain, 0.35/0.54 ( greater(zero, growth_rate(efficient_producers, sk_To(sk_T, sk_E))) 0.35/0.54 | cardinality_at_time(efficient_producers, sk_T) != zero 0.35/0.54 | ~ environment(sk_E)), 0.35/0.54 inference('sup-', [status(thm)], ['63', '64'])). 0.35/0.54 tff('66', plain, cardinality_at_time(efficient_producers, sk_T) = zero, 0.35/0.54 inference('clc', [status(thm)], ['7', '8'])). 0.35/0.54 tff('67', plain, environment(sk_E), 0.35/0.54 inference('cnf', [status(esa)], [zf_stmt_0])). 0.35/0.54 tff('68', plain, 0.35/0.54 ( greater(zero, growth_rate(efficient_producers, sk_To(sk_T, sk_E))) 0.35/0.54 | zero != zero), 0.35/0.54 inference('demod', [status(thm)], ['65', '66', '67'])). 0.35/0.54 tff('69', plain, 0.35/0.54 greater(zero, growth_rate(efficient_producers, sk_To(sk_T, sk_E))), 0.35/0.54 inference('simplify', [status(thm)], ['68'])). 0.35/0.54 tff('70', plain, in_environment(sk_E, sk_To(sk_T, sk_E)), 0.35/0.54 inference('simplify', [status(thm)], ['11'])). 0.35/0.54 tff('71', plain, environment(sk_E), 0.35/0.54 inference('cnf', [status(esa)], [zf_stmt_0])). 0.35/0.54 tff('72', plain, 0.35/0.54 ( decreases(number_of_organizations(sk_E, sk_To(sk_T, sk_E))) 0.35/0.54 | first_movers = sk_X(sk_To(sk_T, sk_E), sk_E) 0.35/0.54 | decreases(number_of_organizations(sk_E, sk_To(sk_T, sk_E)))), 0.35/0.54 inference('demod', [status(thm)], ['62', '69', '70', '71'])). 0.35/0.54 tff('73', plain, 0.35/0.54 (first_movers = sk_X(sk_To(sk_T, sk_E), sk_E) 0.35/0.54 | decreases(number_of_organizations(sk_E, sk_To(sk_T, sk_E)))), 0.35/0.54 inference('simplify', [status(thm)], ['72'])). 0.35/0.54 tff('74', plain, 0.35/0.54 ![X27, X28]: 0.35/0.54 (~ environment(X27) 0.35/0.54 | decreases(number_of_organizations(X27, X28)) 0.35/0.54 | ~ in_environment(X27, X28) 0.35/0.54 | ~ greater(zero, growth_rate(sk_X(X28, X27), X28))), 0.35/0.54 inference('cnf', [status(esa)], [mp_non_decreasing])). 0.35/0.54 tff('75', plain, 0.35/0.54 (~ greater(zero, growth_rate(first_movers, sk_To(sk_T, sk_E))) 0.35/0.54 | decreases(number_of_organizations(sk_E, sk_To(sk_T, sk_E))) 0.35/0.54 | ~ in_environment(sk_E, sk_To(sk_T, sk_E)) 0.35/0.54 | decreases(number_of_organizations(sk_E, sk_To(sk_T, sk_E))) 0.35/0.54 | ~ environment(sk_E)), 0.35/0.54 inference('sup-', [status(thm)], ['73', '74'])). 0.35/0.54 tff('76', plain, in_environment(sk_E, sk_To(sk_T, sk_E)), 0.35/0.54 inference('simplify', [status(thm)], ['11'])). 0.35/0.54 tff('77', plain, 0.35/0.54 greater(zero, growth_rate(efficient_producers, sk_To(sk_T, sk_E))), 0.35/0.54 inference('simplify', [status(thm)], ['68'])). 0.35/0.54 tff(a2, axiom, 0.35/0.54 (greater(resilience(efficient_producers),resilience(first_movers)))). 0.35/0.54 tff('78', plain, 0.35/0.54 greater(resilience(efficient_producers), resilience(first_movers)), 0.35/0.54 inference('cnf', [status(esa)], [a2])). 0.35/0.54 tff(a12, axiom, 0.35/0.54 (![E,S1,S2,T]: 0.35/0.54 ((in_environment(E,T) & (~greater(zero,growth_rate(S1,T))) & 0.35/0.54 greater(resilience(S2),resilience(S1)) & environment(E)) => 0.35/0.54 (~greater(zero,growth_rate(S2,T)))))). 0.35/0.54 tff('79', plain, 0.35/0.54 ![X2, X3, X4, X5]: 0.35/0.54 (~ environment(X2) 0.35/0.54 | ~ greater(resilience(X3), resilience(X4)) 0.35/0.54 | ~ in_environment(X2, X5) 0.35/0.54 | greater(zero, growth_rate(X4, X5)) 0.35/0.54 | ~ greater(zero, growth_rate(X3, X5))), 0.35/0.54 inference('cnf', [status(esa)], [a12])). 0.35/0.54 tff('80', plain, 0.35/0.54 ![X0, X1]: 0.35/0.54 (~ greater(zero, growth_rate(efficient_producers, X0)) 0.35/0.54 | greater(zero, growth_rate(first_movers, X0)) 0.35/0.54 | ~ in_environment(X1, X0) 0.35/0.54 | ~ environment(X1)), 0.35/0.54 inference('sup-', [status(thm)], ['78', '79'])). 0.35/0.54 tff('81', plain, 0.35/0.54 ![X0]: 0.35/0.54 (~ environment(X0) 0.35/0.54 | ~ in_environment(X0, sk_To(sk_T, sk_E)) 0.35/0.54 | greater(zero, growth_rate(first_movers, sk_To(sk_T, sk_E)))), 0.35/0.54 inference('sup-', [status(thm)], ['77', '80'])). 0.35/0.54 tff('82', plain, 0.35/0.54 ( greater(zero, growth_rate(first_movers, sk_To(sk_T, sk_E))) 0.35/0.54 | ~ environment(sk_E)), 0.35/0.54 inference('sup-', [status(thm)], ['76', '81'])). 0.35/0.54 tff('83', plain, environment(sk_E), 0.35/0.54 inference('cnf', [status(esa)], [zf_stmt_0])). 0.35/0.54 tff('84', plain, 0.35/0.54 greater(zero, growth_rate(first_movers, sk_To(sk_T, sk_E))), 0.35/0.54 inference('demod', [status(thm)], ['82', '83'])). 0.35/0.54 tff('85', plain, in_environment(sk_E, sk_To(sk_T, sk_E)), 0.35/0.54 inference('simplify', [status(thm)], ['11'])). 0.35/0.54 tff('86', plain, environment(sk_E), 0.35/0.54 inference('cnf', [status(esa)], [zf_stmt_0])). 0.35/0.54 tff('87', plain, 0.35/0.54 ( decreases(number_of_organizations(sk_E, sk_To(sk_T, sk_E))) 0.35/0.54 | decreases(number_of_organizations(sk_E, sk_To(sk_T, sk_E)))), 0.35/0.54 inference('demod', [status(thm)], ['75', '84', '85', '86'])). 0.35/0.54 tff('88', plain, 0.35/0.54 decreases(number_of_organizations(sk_E, sk_To(sk_T, sk_E))), 0.35/0.54 inference('simplify', [status(thm)], ['87'])). 0.35/0.54 tff(a6, axiom, 0.35/0.54 (![E,T]: 0.35/0.54 ((in_environment(E,T) & environment(E)) => 0.35/0.54 ((decreases(resources(E,T)) => 0.35/0.54 (~decreases(number_of_organizations(E,T)))) & 0.35/0.54 (constant(resources(E,T)) => constant(number_of_organizations(E,T))))))). 0.35/0.54 tff('89', plain, 0.35/0.54 ![X6, X7]: 0.35/0.54 (~ environment(X6) 0.35/0.54 | ~ in_environment(X6, X7) 0.35/0.54 | ~ decreases(number_of_organizations(X6, X7)) 0.35/0.54 | ~ decreases(resources(X6, X7))), 0.35/0.54 inference('cnf', [status(esa)], [a6])). 0.35/0.54 tff('90', plain, 0.35/0.54 (~ decreases(resources(sk_E, sk_To(sk_T, sk_E))) 0.35/0.54 | ~ in_environment(sk_E, sk_To(sk_T, sk_E)) 0.35/0.54 | ~ environment(sk_E)), 0.35/0.54 inference('sup-', [status(thm)], ['88', '89'])). 0.35/0.54 tff('91', plain, in_environment(sk_E, sk_To(sk_T, sk_E)), 0.35/0.54 inference('simplify', [status(thm)], ['11'])). 0.35/0.54 tff('92', plain, environment(sk_E), 0.35/0.54 inference('cnf', [status(esa)], [zf_stmt_0])). 0.35/0.54 tff('93', plain, ~ decreases(resources(sk_E, sk_To(sk_T, sk_E))), 0.35/0.54 inference('demod', [status(thm)], ['90', '91', '92'])). 0.35/0.54 tff('94', plain, 0.35/0.54 ( constant(resources(sk_E, sk_To(sk_T, sk_E))) 0.35/0.54 | zero = number_of_organizations(sk_E, sk_To(sk_T, sk_E))), 0.35/0.54 inference('sup-', [status(thm)], ['44', '93'])). 0.35/0.54 tff('95', plain, 0.35/0.54 ![X6, X7]: 0.35/0.54 (~ environment(X6) 0.35/0.54 | ~ in_environment(X6, X7) 0.35/0.54 | constant(number_of_organizations(X6, X7)) 0.35/0.54 | ~ constant(resources(X6, X7))), 0.35/0.54 inference('cnf', [status(esa)], [a6])). 0.35/0.54 tff('96', plain, 0.35/0.54 (zero = number_of_organizations(sk_E, sk_To(sk_T, sk_E)) 0.35/0.54 | constant(number_of_organizations(sk_E, sk_To(sk_T, sk_E))) 0.35/0.54 | ~ in_environment(sk_E, sk_To(sk_T, sk_E)) 0.35/0.54 | ~ environment(sk_E)), 0.35/0.54 inference('sup-', [status(thm)], ['94', '95'])). 0.35/0.54 tff('97', plain, in_environment(sk_E, sk_To(sk_T, sk_E)), 0.35/0.54 inference('simplify', [status(thm)], ['11'])). 0.35/0.54 tff('98', plain, environment(sk_E), 0.35/0.54 inference('cnf', [status(esa)], [zf_stmt_0])). 0.35/0.54 tff('99', plain, 0.35/0.54 (zero = number_of_organizations(sk_E, sk_To(sk_T, sk_E)) 0.35/0.54 | constant(number_of_organizations(sk_E, sk_To(sk_T, sk_E)))), 0.35/0.54 inference('demod', [status(thm)], ['96', '97', '98'])). 0.35/0.54 tff('100', plain, 0.35/0.54 decreases(number_of_organizations(sk_E, sk_To(sk_T, sk_E))), 0.35/0.54 inference('simplify', [status(thm)], ['87'])). 0.35/0.54 tff(mp_constant_not_decrease, axiom, 0.35/0.54 (![X]: (constant(X) => (~decreases(X))))). 0.35/0.54 tff('101', plain, ![X17]: (~ decreases(X17) | ~ constant(X17)), 0.35/0.54 inference('cnf', [status(esa)], [mp_constant_not_decrease])). 0.35/0.54 tff('102', plain, 0.35/0.54 ~ constant(number_of_organizations(sk_E, sk_To(sk_T, sk_E))), 0.35/0.54 inference('sup-', [status(thm)], ['100', '101'])). 0.35/0.54 tff('103', plain, zero = number_of_organizations(sk_E, sk_To(sk_T, sk_E)), 0.35/0.54 inference('clc', [status(thm)], ['99', '102'])). 0.35/0.54 tff(mp_no_members, axiom, 0.35/0.54 (![E,T,X]: 0.35/0.54 ((subpopulation(X,E,T) & (number_of_organizations(E,T) = zero) & 0.35/0.54 in_environment(E,T) & environment(E)) => 0.35/0.54 (cardinality_at_time(X,T) = zero)))). 0.35/0.54 tff('104', plain, 0.35/0.54 ![X20, X21, X22]: 0.35/0.54 (~ environment(X20) 0.35/0.54 | ~ in_environment(X20, X21) 0.35/0.54 | number_of_organizations(X20, X21) != zero 0.35/0.54 | ~ subpopulation(X22, X20, X21) 0.35/0.54 | cardinality_at_time(X22, X21) = zero), 0.35/0.54 inference('cnf', [status(esa)], [mp_no_members])). 0.35/0.54 tff('105', plain, 0.35/0.54 ![X0]: 0.35/0.54 (zero != zero 0.35/0.54 | cardinality_at_time(X0, sk_To(sk_T, sk_E)) = zero 0.35/0.54 | ~ subpopulation(X0, sk_E, sk_To(sk_T, sk_E)) 0.35/0.54 | ~ in_environment(sk_E, sk_To(sk_T, sk_E)) 0.35/0.54 | ~ environment(sk_E)), 0.35/0.54 inference('sup-', [status(thm)], ['103', '104'])). 0.35/0.54 tff('106', plain, in_environment(sk_E, sk_To(sk_T, sk_E)), 0.35/0.54 inference('simplify', [status(thm)], ['11'])). 0.35/0.54 tff('107', plain, environment(sk_E), 0.35/0.54 inference('cnf', [status(esa)], [zf_stmt_0])). 0.35/0.54 tff('108', plain, 0.35/0.54 ![X0]: 0.35/0.54 (zero != zero 0.35/0.54 | cardinality_at_time(X0, sk_To(sk_T, sk_E)) = zero 0.35/0.54 | ~ subpopulation(X0, sk_E, sk_To(sk_T, sk_E))), 0.35/0.54 inference('demod', [status(thm)], ['105', '106', '107'])). 0.35/0.54 tff('109', plain, 0.35/0.54 ![X0]: 0.35/0.54 (~ subpopulation(X0, sk_E, sk_To(sk_T, sk_E)) 0.35/0.54 | cardinality_at_time(X0, sk_To(sk_T, sk_E)) = zero), 0.35/0.54 inference('simplify', [status(thm)], ['108'])). 0.35/0.54 tff('110', plain, 0.35/0.54 cardinality_at_time(first_movers, sk_To(sk_T, sk_E)) = zero, 0.35/0.54 inference('sup-', [status(thm)], ['16', '109'])). 0.35/0.54 tff('111', plain, 0.35/0.54 greater(zero, growth_rate(first_movers, sk_To(sk_T, sk_E))), 0.35/0.54 inference('demod', [status(thm)], ['82', '83'])). 0.35/0.54 tff(mp_empty_not_decreasing, axiom, 0.35/0.54 (![S,T]: 0.35/0.54 ((cardinality_at_time(S,T) = zero) => (~greater(zero,growth_rate(S,T)))))). 0.35/0.54 tff('112', plain, 0.35/0.54 ![X13, X14]: 0.35/0.54 (~ greater(zero, growth_rate(X13, X14)) 0.35/0.54 | cardinality_at_time(X13, X14) != zero), 0.35/0.54 inference('cnf', [status(esa)], [mp_empty_not_decreasing])). 0.35/0.54 tff('113', plain, 0.35/0.54 cardinality_at_time(first_movers, sk_To(sk_T, sk_E)) != zero, 0.35/0.54 inference('sup-', [status(thm)], ['111', '112'])). 0.35/0.54 tff('114', plain, $false, 0.35/0.54 inference('simplify_reflect-', [status(thm)], ['110', '113'])). 0.35/0.54 0.35/0.54 % SZS output end Refutation 0.35/0.54 0.35/0.55 % Zipperpin 1.5 exiting 0.35/0.55 EOF