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 v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 : Unsatisfiable 0.65s 0.97s
% Output : Refutation 0.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MGT025-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 9 10:03:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.65/0.96 ============================== Prover9 ===============================
% 0.65/0.96 Prover9 (32) version 2009-11A, November 2009.
% 0.65/0.96 Process 3114 was started by sandbox2 on n021.cluster.edu,
% 0.65/0.96 Thu Jun 9 10:03:53 2022
% 0.65/0.96 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_2961_n021.cluster.edu".
% 0.65/0.96 ============================== end of head ===========================
% 0.65/0.96
% 0.65/0.96 ============================== INPUT =================================
% 0.65/0.96
% 0.65/0.96 % Reading from file /tmp/Prover9_2961_n021.cluster.edu
% 0.65/0.96
% 0.65/0.96 set(prolog_style_variables).
% 0.65/0.96 set(auto2).
% 0.65/0.96 % set(auto2) -> set(auto).
% 0.65/0.96 % set(auto) -> set(auto_inference).
% 0.65/0.96 % set(auto) -> set(auto_setup).
% 0.65/0.96 % set(auto_setup) -> set(predicate_elim).
% 0.65/0.96 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.65/0.96 % set(auto) -> set(auto_limits).
% 0.65/0.96 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.65/0.96 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.65/0.96 % set(auto) -> set(auto_denials).
% 0.65/0.96 % set(auto) -> set(auto_process).
% 0.65/0.96 % set(auto2) -> assign(new_constants, 1).
% 0.65/0.96 % set(auto2) -> assign(fold_denial_max, 3).
% 0.65/0.96 % set(auto2) -> assign(max_weight, "200.000").
% 0.65/0.96 % set(auto2) -> assign(max_hours, 1).
% 0.65/0.96 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.65/0.96 % set(auto2) -> assign(max_seconds, 0).
% 0.65/0.96 % set(auto2) -> assign(max_minutes, 5).
% 0.65/0.96 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.65/0.96 % set(auto2) -> set(sort_initial_sos).
% 0.65/0.96 % set(auto2) -> assign(sos_limit, -1).
% 0.65/0.96 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.65/0.96 % set(auto2) -> assign(max_megs, 400).
% 0.65/0.96 % set(auto2) -> assign(stats, some).
% 0.65/0.96 % set(auto2) -> clear(echo_input).
% 0.65/0.96 % set(auto2) -> set(quiet).
% 0.65/0.96 % set(auto2) -> clear(print_initial_clauses).
% 0.65/0.96 % set(auto2) -> clear(print_given).
% 0.65/0.96 assign(lrs_ticks,-1).
% 0.65/0.96 assign(sos_limit,10000).
% 0.65/0.96 assign(order,kbo).
% 0.65/0.96 set(lex_order_vars).
% 0.65/0.96 clear(print_given).
% 0.65/0.96
% 0.65/0.96 % formulas(sos). % not echoed (26 formulas)
% 0.65/0.96
% 0.65/0.96 ============================== end of input ==========================
% 0.65/0.96
% 0.65/0.96 % From the command line: assign(max_seconds, 300).
% 0.65/0.96
% 0.65/0.96 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.65/0.96
% 0.65/0.96 % Formulas that are not ordinary clauses:
% 0.65/0.96
% 0.65/0.96 ============================== end of process non-clausal formulas ===
% 0.65/0.96
% 0.65/0.96 ============================== PROCESS INITIAL CLAUSES ===============
% 0.65/0.96
% 0.65/0.96 ============================== PREDICATE ELIMINATION =================
% 0.65/0.96 1 -environment(A) | -in_environment(A,B) | subpopulation(first_movers,A,B) # label(mp_subpopulations_30) # label(axiom). [assumption].
% 0.65/0.96 2 environment(sk1) # label(prove_l7_47) # label(negated_conjecture). [assumption].
% 0.65/0.96 Derived: -in_environment(sk1,A) | subpopulation(first_movers,sk1,A). [resolve(1,a,2,a)].
% 0.65/0.96 3 -environment(A) | -in_environment(A,B) | subpopulation(efficient_producers,A,B) # label(mp_subpopulations_31) # label(axiom). [assumption].
% 0.65/0.96 Derived: -in_environment(sk1,A) | subpopulation(efficient_producers,sk1,A). [resolve(3,a,2,a)].
% 0.65/0.96 4 -environment(A) | -subpopulations(first_movers,efficient_producers,A,B) | in_environment(A,B) # label(mp_time_point_occur_45) # label(axiom). [assumption].
% 0.65/0.96 Derived: -subpopulations(first_movers,efficient_producers,sk1,A) | in_environment(sk1,A). [resolve(4,a,2,a)].
% 0.65/0.96 5 -environment(A) | -subpopulations(first_movers,efficient_producers,A,B) | greater(cardinality_at_time(first_movers,B),zero) # label(mp_non_zero_producers_43) # label(axiom). [assumption].
% 0.65/0.96 Derived: -subpopulations(first_movers,efficient_producers,sk1,A) | greater(cardinality_at_time(first_movers,A),zero). [resolve(5,a,2,a)].
% 0.65/0.96 6 -environment(A) | -subpopulations(first_movers,efficient_producers,A,B) | greater(cardinality_at_time(efficient_producers,B),zero) # label(mp_non_zero_producers_44) # label(axiom). [assumption].
% 0.65/0.96 Derived: -subpopulations(first_movers,efficient_producers,sk1,A) | greater(cardinality_at_time(efficient_producers,A),zero). [resolve(6,a,2,a)].
% 0.65/0.96 7 -environment(A) | -subpopulation(B,A,C) | -greater(cardinality_at_time(B,C),zero) | B = efficient_producers | B = first_movers # label(a9_46) # label(hypothesis). [assumption].
% 0.65/0.96 Derived: -subpopulation(A,sk1,B) | -greater(cardinality_at_time(A,B),zero) | A = efficient_producers | A = first_movers. [resolve(7,a,2,a)].
% 0.65/0.97 8 -environment(A) | -subpopulation(B,A,C) | B != efficient_producers | number_of_organizations(A,C) = sum(cardinality_at_time(first_movers,C),cardinality_at_time(efficient_producers,C)) # label(mp_only_members_28) # label(axiom). [assumption].
% 0.65/0.97 Derived: -subpopulation(A,sk1,B) | A != efficient_producers | number_of_organizations(sk1,B) = sum(cardinality_at_time(first_movers,B),cardinality_at_time(efficient_producers,B)). [resolve(8,a,2,a)].
% 0.65/0.97 9 -environment(A) | -subpopulation(B,A,C) | B != first_movers | number_of_organizations(A,C) = sum(cardinality_at_time(first_movers,C),cardinality_at_time(efficient_producers,C)) # label(mp_only_members_29) # label(axiom). [assumption].
% 0.65/0.97 Derived: -subpopulation(A,sk1,B) | A != first_movers | number_of_organizations(sk1,B) = sum(cardinality_at_time(first_movers,B),cardinality_at_time(efficient_producers,B)). [resolve(9,a,2,a)].
% 0.65/0.97 10 -environment(A) | -subpopulation(B,A,C) | greater(cardinality_at_time(B,C),zero) | number_of_organizations(A,C) = sum(cardinality_at_time(first_movers,C),cardinality_at_time(efficient_producers,C)) # label(mp_only_members_27) # label(axiom). [assumption].
% 0.65/0.97 Derived: -subpopulation(A,sk1,B) | greater(cardinality_at_time(A,B),zero) | number_of_organizations(sk1,B) = sum(cardinality_at_time(first_movers,B),cardinality_at_time(efficient_producers,B)). [resolve(10,a,2,a)].
% 0.65/0.97 11 -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_40) # label(axiom). [assumption].
% 0.65/0.97 Derived: -in_environment(sk1,A) | -subpopulation(B,sk1,A) | -greater(cardinality_at_time(B,A),zero) | -constant(cardinality_at_time(B,A)) | growth_rate(B,A) = zero. [resolve(11,a,2,a)].
% 0.65/0.97 12 -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_41) # label(axiom). [assumption].
% 0.65/0.97 Derived: -in_environment(sk1,A) | -subpopulation(B,sk1,A) | -greater(cardinality_at_time(B,A),zero) | -increases(cardinality_at_time(B,A)) | greater(growth_rate(B,A),zero). [resolve(12,a,2,a)].
% 0.65/0.97 13 -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_42) # label(axiom). [assumption].
% 0.65/0.97 Derived: -in_environment(sk1,A) | -subpopulation(B,sk1,A) | -greater(cardinality_at_time(B,A),zero) | -decreases(cardinality_at_time(B,A)) | greater(zero,growth_rate(B,A)). [resolve(13,a,2,a)].
% 0.65/0.97
% 0.65/0.97 ============================== end predicate elimination =============
% 0.65/0.97
% 0.65/0.97 Auto_denials: (non-Horn, no changes).
% 0.65/0.97
% 0.65/0.97 Term ordering decisions:
% 0.65/0.97 Function symbol KB weights: sk1=1. efficient_producers=1. first_movers=1. zero=1. sk2=1. cardinality_at_time=1. sum=1. number_of_organizations=1. growth_rate=1.
% 0.65/0.97
% 0.65/0.97 ============================== end of process initial clauses ========
% 0.65/0.97
% 0.65/0.97 ============================== CLAUSES FOR SEARCH ====================
% 0.65/0.97
% 0.65/0.97 ============================== end of clauses for search =============
% 0.65/0.97
% 0.65/0.97 ============================== SEARCH ================================
% 0.65/0.97
% 0.65/0.97 % Starting search at 0.01 seconds.
% 0.65/0.97
% 0.65/0.97 ============================== PROOF =================================
% 0.65/0.97 % SZS status Unsatisfiable
% 0.65/0.97 % SZS output start Refutation
% 0.65/0.97
% 0.65/0.97 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.65/0.97 % Length of proof is 100.
% 0.65/0.97 % Level of proof is 21.
% 0.65/0.97 % Maximum clause weight is 21.000.
% 0.65/0.97 % Given clauses 88.
% 0.65/0.97
% 0.65/0.97 1 -environment(A) | -in_environment(A,B) | subpopulation(first_movers,A,B) # label(mp_subpopulations_30) # label(axiom). [assumption].
% 0.65/0.97 2 environment(sk1) # label(prove_l7_47) # label(negated_conjecture). [assumption].
% 0.65/0.97 3 -environment(A) | -in_environment(A,B) | subpopulation(efficient_producers,A,B) # label(mp_subpopulations_31) # label(axiom). [assumption].
% 0.65/0.97 4 -environment(A) | -subpopulations(first_movers,efficient_producers,A,B) | in_environment(A,B) # label(mp_time_point_occur_45) # label(axiom). [assumption].
% 0.65/0.97 5 -environment(A) | -subpopulations(first_movers,efficient_producers,A,B) | greater(cardinality_at_time(first_movers,B),zero) # label(mp_non_zero_producers_43) # label(axiom). [assumption].
% 0.65/0.97 6 -environment(A) | -subpopulations(first_movers,efficient_producers,A,B) | greater(cardinality_at_time(efficient_producers,B),zero) # label(mp_non_zero_producers_44) # label(axiom). [assumption].
% 0.65/0.97 8 -environment(A) | -subpopulation(B,A,C) | B != efficient_producers | number_of_organizations(A,C) = sum(cardinality_at_time(first_movers,C),cardinality_at_time(efficient_producers,C)) # label(mp_only_members_28) # label(axiom). [assumption].
% 0.65/0.97 11 -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_40) # label(axiom). [assumption].
% 0.65/0.97 12 -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_41) # label(axiom). [assumption].
% 0.65/0.97 13 -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_42) # label(axiom). [assumption].
% 0.65/0.97 14 constant(number_of_organizations(sk1,sk2)) # label(prove_l7_49) # label(negated_conjecture). [assumption].
% 0.65/0.97 15 subpopulations(first_movers,efficient_producers,sk1,sk2) # label(prove_l7_48) # label(negated_conjecture). [assumption].
% 0.65/0.97 16 growth_rate(first_movers,sk2) != zero | growth_rate(efficient_producers,sk2) != zero # label(prove_l7_50) # label(negated_conjecture). [assumption].
% 0.65/0.97 17 -greater(growth_rate(first_movers,sk2),zero) | -greater(zero,growth_rate(efficient_producers,sk2)) # label(prove_l7_51) # label(negated_conjecture). [assumption].
% 0.65/0.97 18 -greater(growth_rate(efficient_producers,sk2),zero) | -greater(zero,growth_rate(first_movers,sk2)) # label(prove_l7_52) # label(negated_conjecture). [assumption].
% 0.65/0.97 19 A != sum(B,C) | -constant(A) | constant(B) | increases(B) | decreases(B) # label(mp_abc_sum_increase_32) # label(axiom). [assumption].
% 0.65/0.97 20 sum(A,B) != C | -constant(C) | constant(A) | increases(A) | decreases(A). [copy(19),flip(a)].
% 0.65/0.97 21 A != sum(B,C) | -constant(A) | constant(B) | increases(B) | increases(C) # label(mp_abc_sum_increase_33) # label(axiom). [assumption].
% 0.65/0.97 22 sum(A,B) != C | -constant(C) | constant(A) | increases(A) | increases(B). [copy(21),flip(a)].
% 0.65/0.97 23 A != sum(B,C) | -constant(A) | constant(B) | decreases(C) | decreases(B) # label(mp_abc_sum_increase_34) # label(axiom). [assumption].
% 0.65/0.97 24 sum(A,B) != C | -constant(C) | constant(A) | decreases(B) | decreases(A). [copy(23),flip(a)].
% 0.65/0.97 25 A != sum(B,C) | -constant(A) | constant(B) | decreases(C) | increases(C) # label(mp_abc_sum_increase_35) # label(axiom). [assumption].
% 0.65/0.97 26 sum(A,B) != C | -constant(C) | constant(A) | decreases(B) | increases(B). [copy(25),flip(a)].
% 0.65/0.97 27 A != sum(B,C) | -constant(A) | constant(C) | increases(B) | decreases(B) # label(mp_abc_sum_increase_36) # label(axiom). [assumption].
% 0.65/0.97 28 sum(A,B) != C | -constant(C) | constant(B) | increases(A) | decreases(A). [copy(27),flip(a)].
% 0.65/0.97 31 A != sum(B,C) | -constant(A) | constant(C) | decreases(C) | decreases(B) # label(mp_abc_sum_increase_38) # label(axiom). [assumption].
% 0.65/0.97 32 sum(A,B) != C | -constant(C) | constant(B) | decreases(B) | decreases(A). [copy(31),flip(a)].
% 0.65/0.97 33 A != sum(B,C) | -constant(A) | constant(C) | decreases(C) | increases(C) # label(mp_abc_sum_increase_39) # label(axiom). [assumption].
% 0.65/0.97 34 sum(A,B) != C | -constant(C) | constant(B) | decreases(B) | increases(B). [copy(33),flip(a)].
% 0.65/0.97 35 -in_environment(sk1,A) | subpopulation(first_movers,sk1,A). [resolve(1,a,2,a)].
% 0.65/0.97 36 -in_environment(sk1,A) | subpopulation(efficient_producers,sk1,A). [resolve(3,a,2,a)].
% 0.65/0.97 37 -subpopulations(first_movers,efficient_producers,sk1,A) | in_environment(sk1,A). [resolve(4,a,2,a)].
% 0.65/0.97 38 -subpopulations(first_movers,efficient_producers,sk1,A) | greater(cardinality_at_time(first_movers,A),zero). [resolve(5,a,2,a)].
% 0.65/0.97 39 -subpopulations(first_movers,efficient_producers,sk1,A) | greater(cardinality_at_time(efficient_producers,A),zero). [resolve(6,a,2,a)].
% 0.65/0.97 42 -subpopulation(A,sk1,B) | A != efficient_producers | number_of_organizations(sk1,B) = sum(cardinality_at_time(first_movers,B),cardinality_at_time(efficient_producers,B)). [resolve(8,a,2,a)].
% 0.65/0.97 43 -subpopulation(A,sk1,B) | efficient_producers != A | sum(cardinality_at_time(first_movers,B),cardinality_at_time(efficient_producers,B)) = number_of_organizations(sk1,B). [copy(42),flip(b),flip(c)].
% 0.65/0.97 48 -in_environment(sk1,A) | -subpopulation(B,sk1,A) | -greater(cardinality_at_time(B,A),zero) | -constant(cardinality_at_time(B,A)) | growth_rate(B,A) = zero. [resolve(11,a,2,a)].
% 0.65/0.97 49 -in_environment(sk1,A) | -subpopulation(B,sk1,A) | -greater(cardinality_at_time(B,A),zero) | -increases(cardinality_at_time(B,A)) | greater(growth_rate(B,A),zero). [resolve(12,a,2,a)].
% 0.65/0.97 50 -in_environment(sk1,A) | -subpopulation(B,sk1,A) | -greater(cardinality_at_time(B,A),zero) | -decreases(cardinality_at_time(B,A)) | greater(zero,growth_rate(B,A)). [resolve(13,a,2,a)].
% 0.65/0.97 53 sum(A,B) != number_of_organizations(sk1,sk2) | constant(A) | increases(A) | decreases(A). [resolve(20,b,14,a)].
% 0.65/0.97 54 sum(A,B) != number_of_organizations(sk1,sk2) | constant(A) | increases(A) | increases(B). [resolve(22,b,14,a)].
% 0.65/0.97 56 sum(A,B) != number_of_organizations(sk1,sk2) | constant(A) | decreases(B) | decreases(A). [resolve(24,b,14,a)].
% 0.65/0.97 58 sum(A,B) != number_of_organizations(sk1,sk2) | constant(A) | decreases(B) | increases(B). [resolve(26,b,14,a)].
% 0.65/0.97 59 sum(A,B) != number_of_organizations(sk1,sk2) | constant(B) | increases(A) | decreases(A). [resolve(28,b,14,a)].
% 0.65/0.97 61 sum(A,B) != number_of_organizations(sk1,sk2) | constant(B) | decreases(B) | decreases(A). [resolve(32,b,14,a)].
% 0.65/0.97 62 sum(A,B) != number_of_organizations(sk1,sk2) | constant(B) | decreases(B) | increases(B). [resolve(34,b,14,a)].
% 0.65/0.97 63 in_environment(sk1,sk2). [resolve(37,a,15,a)].
% 0.65/0.97 64 greater(cardinality_at_time(first_movers,sk2),zero). [resolve(38,a,15,a)].
% 0.65/0.97 65 greater(cardinality_at_time(efficient_producers,sk2),zero). [resolve(39,a,15,a)].
% 0.65/0.97 66 subpopulation(efficient_producers,sk1,sk2). [resolve(63,a,36,a)].
% 0.65/0.97 67 subpopulation(first_movers,sk1,sk2). [resolve(63,a,35,a)].
% 0.65/0.97 68 -decreases(cardinality_at_time(efficient_producers,sk2)) | greater(zero,growth_rate(efficient_producers,sk2)). [resolve(66,a,50,b),unit_del(a,63),unit_del(b,65)].
% 0.65/0.97 69 -increases(cardinality_at_time(efficient_producers,sk2)) | greater(growth_rate(efficient_producers,sk2),zero). [resolve(66,a,49,b),unit_del(a,63),unit_del(b,65)].
% 0.65/0.97 70 -constant(cardinality_at_time(efficient_producers,sk2)) | growth_rate(efficient_producers,sk2) = zero. [resolve(66,a,48,b),unit_del(a,63),unit_del(b,65)].
% 0.65/0.97 72 sum(cardinality_at_time(first_movers,sk2),cardinality_at_time(efficient_producers,sk2)) = number_of_organizations(sk1,sk2). [resolve(66,a,43,a),xx(a)].
% 0.65/0.97 73 -decreases(cardinality_at_time(first_movers,sk2)) | greater(zero,growth_rate(first_movers,sk2)). [resolve(67,a,50,b),unit_del(a,63),unit_del(b,64)].
% 0.65/0.97 74 -increases(cardinality_at_time(first_movers,sk2)) | greater(growth_rate(first_movers,sk2),zero). [resolve(67,a,49,b),unit_del(a,63),unit_del(b,64)].
% 0.65/0.97 75 -constant(cardinality_at_time(first_movers,sk2)) | growth_rate(first_movers,sk2) = zero. [resolve(67,a,48,b),unit_del(a,63),unit_del(b,64)].
% 0.65/0.97 76 constant(cardinality_at_time(first_movers,sk2)) | decreases(cardinality_at_time(efficient_producers,sk2)) | decreases(cardinality_at_time(first_movers,sk2)). [resolve(72,a,56,a)].
% 0.65/0.97 77 constant(cardinality_at_time(first_movers,sk2)) | increases(cardinality_at_time(first_movers,sk2)) | increases(cardinality_at_time(efficient_producers,sk2)). [resolve(72,a,54,a)].
% 0.65/0.97 78 constant(cardinality_at_time(first_movers,sk2)) | increases(cardinality_at_time(first_movers,sk2)) | decreases(cardinality_at_time(first_movers,sk2)). [resolve(72,a,53,a)].
% 0.65/0.97 79 constant(cardinality_at_time(first_movers,sk2)) | decreases(cardinality_at_time(efficient_producers,sk2)) | greater(zero,growth_rate(first_movers,sk2)). [resolve(76,c,73,a)].
% 0.65/0.97 80 constant(cardinality_at_time(first_movers,sk2)) | increases(cardinality_at_time(efficient_producers,sk2)) | greater(growth_rate(first_movers,sk2),zero). [resolve(77,b,74,a)].
% 0.65/0.97 81 constant(cardinality_at_time(first_movers,sk2)) | decreases(cardinality_at_time(first_movers,sk2)) | greater(growth_rate(first_movers,sk2),zero). [resolve(78,b,74,a)].
% 0.65/0.97 82 constant(cardinality_at_time(first_movers,sk2)) | decreases(cardinality_at_time(efficient_producers,sk2)) | increases(cardinality_at_time(efficient_producers,sk2)). [resolve(58,a,72,a)].
% 0.65/0.97 83 constant(cardinality_at_time(first_movers,sk2)) | decreases(cardinality_at_time(efficient_producers,sk2)) | greater(growth_rate(efficient_producers,sk2),zero). [resolve(82,c,69,a)].
% 0.65/0.97 84 constant(cardinality_at_time(efficient_producers,sk2)) | increases(cardinality_at_time(first_movers,sk2)) | decreases(cardinality_at_time(first_movers,sk2)). [resolve(59,a,72,a)].
% 0.65/0.97 85 constant(cardinality_at_time(efficient_producers,sk2)) | decreases(cardinality_at_time(first_movers,sk2)) | greater(growth_rate(first_movers,sk2),zero). [resolve(84,b,74,a)].
% 0.65/0.97 87 constant(cardinality_at_time(efficient_producers,sk2)) | decreases(cardinality_at_time(efficient_producers,sk2)) | decreases(cardinality_at_time(first_movers,sk2)). [resolve(61,a,72,a)].
% 0.65/0.97 89 constant(cardinality_at_time(efficient_producers,sk2)) | decreases(cardinality_at_time(efficient_producers,sk2)) | greater(zero,growth_rate(first_movers,sk2)). [resolve(87,c,73,a)].
% 0.65/0.97 90 constant(cardinality_at_time(efficient_producers,sk2)) | decreases(cardinality_at_time(efficient_producers,sk2)) | increases(cardinality_at_time(efficient_producers,sk2)). [resolve(62,a,72,a)].
% 0.65/0.97 91 constant(cardinality_at_time(efficient_producers,sk2)) | decreases(cardinality_at_time(efficient_producers,sk2)) | greater(growth_rate(efficient_producers,sk2),zero). [resolve(90,c,69,a)].
% 0.65/0.97 92 constant(cardinality_at_time(first_movers,sk2)) | increases(cardinality_at_time(efficient_producers,sk2)) | -greater(zero,growth_rate(efficient_producers,sk2)). [resolve(80,c,17,a)].
% 0.65/0.97 93 constant(cardinality_at_time(first_movers,sk2)) | decreases(cardinality_at_time(first_movers,sk2)) | -greater(zero,growth_rate(efficient_producers,sk2)). [resolve(81,c,17,a)].
% 0.65/0.97 94 constant(cardinality_at_time(first_movers,sk2)) | decreases(cardinality_at_time(efficient_producers,sk2)) | -greater(zero,growth_rate(first_movers,sk2)). [resolve(83,c,18,a)].
% 0.65/0.97 95 constant(cardinality_at_time(efficient_producers,sk2)) | decreases(cardinality_at_time(first_movers,sk2)) | -greater(zero,growth_rate(efficient_producers,sk2)). [resolve(85,c,17,a)].
% 0.65/0.97 97 constant(cardinality_at_time(efficient_producers,sk2)) | decreases(cardinality_at_time(efficient_producers,sk2)) | -greater(zero,growth_rate(first_movers,sk2)). [resolve(91,c,18,a)].
% 0.65/0.97 99 constant(cardinality_at_time(first_movers,sk2)) | decreases(cardinality_at_time(efficient_producers,sk2)). [resolve(94,c,79,c),merge(c),merge(d)].
% 0.65/0.97 100 constant(cardinality_at_time(first_movers,sk2)) | greater(zero,growth_rate(efficient_producers,sk2)). [resolve(99,b,68,a)].
% 0.65/0.97 101 constant(cardinality_at_time(first_movers,sk2)) | decreases(cardinality_at_time(first_movers,sk2)). [resolve(100,b,93,c),merge(b)].
% 0.65/0.97 102 constant(cardinality_at_time(first_movers,sk2)) | increases(cardinality_at_time(efficient_producers,sk2)). [resolve(100,b,92,c),merge(b)].
% 0.65/0.97 103 constant(cardinality_at_time(first_movers,sk2)) | greater(zero,growth_rate(first_movers,sk2)). [resolve(101,b,73,a)].
% 0.65/0.97 104 constant(cardinality_at_time(first_movers,sk2)) | greater(growth_rate(efficient_producers,sk2),zero). [resolve(102,b,69,a)].
% 0.65/0.97 105 constant(cardinality_at_time(first_movers,sk2)) | -greater(zero,growth_rate(first_movers,sk2)). [resolve(104,b,18,a)].
% 0.65/0.97 106 constant(cardinality_at_time(first_movers,sk2)). [resolve(105,b,103,b),merge(b)].
% 0.65/0.97 107 growth_rate(first_movers,sk2) = zero. [back_unit_del(75),unit_del(a,106)].
% 0.65/0.97 108 constant(cardinality_at_time(efficient_producers,sk2)) | decreases(cardinality_at_time(efficient_producers,sk2)) | -greater(zero,zero). [back_rewrite(97),rewrite([107(12)])].
% 0.65/0.97 109 constant(cardinality_at_time(efficient_producers,sk2)) | decreases(cardinality_at_time(efficient_producers,sk2)) | greater(zero,zero). [back_rewrite(89),rewrite([107(12)])].
% 0.65/0.97 113 -decreases(cardinality_at_time(first_movers,sk2)) | greater(zero,zero). [back_rewrite(73),rewrite([107(8)])].
% 0.65/0.97 115 -greater(zero,zero) | -greater(zero,growth_rate(efficient_producers,sk2)). [back_rewrite(17),rewrite([107(3)])].
% 0.65/0.97 116 growth_rate(efficient_producers,sk2) != zero. [back_rewrite(16),rewrite([107(3)]),xx(a)].
% 0.65/0.97 117 -constant(cardinality_at_time(efficient_producers,sk2)). [back_unit_del(70),unit_del(b,116)].
% 0.65/0.97 120 decreases(cardinality_at_time(efficient_producers,sk2)) | greater(zero,zero). [back_unit_del(109),unit_del(a,117)].
% 0.65/0.97 121 decreases(cardinality_at_time(efficient_producers,sk2)) | -greater(zero,zero). [back_unit_del(108),unit_del(a,117)].
% 0.65/0.97 123 decreases(cardinality_at_time(first_movers,sk2)) | -greater(zero,growth_rate(efficient_producers,sk2)). [back_unit_del(95),unit_del(a,117)].
% 0.65/0.97 139 decreases(cardinality_at_time(efficient_producers,sk2)). [resolve(121,b,120,b),merge(b)].
% 0.65/0.97 140 greater(zero,growth_rate(efficient_producers,sk2)). [back_unit_del(68),unit_del(a,139)].
% 0.65/0.97 141 decreases(cardinality_at_time(first_movers,sk2)). [back_unit_del(123),unit_del(b,140)].
% 0.65/0.97 143 -greater(zero,zero). [back_unit_del(115),unit_del(b,140)].
% 0.65/0.97 144 $F. [back_unit_del(113),unit_del(a,141),unit_del(b,143)].
% 0.65/0.97
% 0.65/0.97 % SZS output end Refutation
% 0.65/0.97 ============================== end of proof ==========================
% 0.65/0.97
% 0.65/0.97 ============================== STATISTICS ============================
% 0.65/0.97
% 0.65/0.97 Given=88. Generated=150. Kept=118. proofs=1.
% 0.65/0.97 Usable=48. Sos=13. Demods=2. Limbo=3, Disabled=92. Hints=0.
% 0.65/0.97 Megabytes=0.13.
% 0.65/0.97 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.65/0.97
% 0.65/0.97 ============================== end of statistics =====================
% 0.65/0.97
% 0.65/0.97 ============================== end of search =========================
% 0.65/0.97
% 0.65/0.97 THEOREM PROVED
% 0.65/0.97 % SZS status Unsatisfiable
% 0.65/0.97
% 0.65/0.97 Exiting with 1 proof.
% 0.65/0.97
% 0.65/0.97 Process 3114 exit (max_proofs) Thu Jun 9 10:03:53 2022
% 0.65/0.97 Prover9 interrupted
%------------------------------------------------------------------------------