TSTP Solution File: MGT023+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : MGT023+2 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 0.41s 0.98s
% Output : Refutation 0.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.11 % Problem : MGT023+2 : TPTP v8.1.0. Released v2.0.0.
% 0.01/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n029.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 10:25:51 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.41/0.96 ============================== Prover9 ===============================
% 0.41/0.96 Prover9 (32) version 2009-11A, November 2009.
% 0.41/0.96 Process 3837 was started by sandbox on n029.cluster.edu,
% 0.41/0.96 Thu Jun 9 10:25:52 2022
% 0.41/0.96 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_3684_n029.cluster.edu".
% 0.41/0.96 ============================== end of head ===========================
% 0.41/0.96
% 0.41/0.96 ============================== INPUT =================================
% 0.41/0.96
% 0.41/0.96 % Reading from file /tmp/Prover9_3684_n029.cluster.edu
% 0.41/0.96
% 0.41/0.96 set(prolog_style_variables).
% 0.41/0.96 set(auto2).
% 0.41/0.96 % set(auto2) -> set(auto).
% 0.41/0.96 % set(auto) -> set(auto_inference).
% 0.41/0.96 % set(auto) -> set(auto_setup).
% 0.41/0.96 % set(auto_setup) -> set(predicate_elim).
% 0.41/0.96 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.41/0.96 % set(auto) -> set(auto_limits).
% 0.41/0.96 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.41/0.96 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.41/0.96 % set(auto) -> set(auto_denials).
% 0.41/0.96 % set(auto) -> set(auto_process).
% 0.41/0.96 % set(auto2) -> assign(new_constants, 1).
% 0.41/0.96 % set(auto2) -> assign(fold_denial_max, 3).
% 0.41/0.96 % set(auto2) -> assign(max_weight, "200.000").
% 0.41/0.96 % set(auto2) -> assign(max_hours, 1).
% 0.41/0.96 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.41/0.96 % set(auto2) -> assign(max_seconds, 0).
% 0.41/0.96 % set(auto2) -> assign(max_minutes, 5).
% 0.41/0.96 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.41/0.96 % set(auto2) -> set(sort_initial_sos).
% 0.41/0.96 % set(auto2) -> assign(sos_limit, -1).
% 0.41/0.96 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.41/0.96 % set(auto2) -> assign(max_megs, 400).
% 0.41/0.96 % set(auto2) -> assign(stats, some).
% 0.41/0.96 % set(auto2) -> clear(echo_input).
% 0.41/0.96 % set(auto2) -> set(quiet).
% 0.41/0.96 % set(auto2) -> clear(print_initial_clauses).
% 0.41/0.96 % set(auto2) -> clear(print_given).
% 0.41/0.96 assign(lrs_ticks,-1).
% 0.41/0.96 assign(sos_limit,10000).
% 0.41/0.96 assign(order,kbo).
% 0.41/0.96 set(lex_order_vars).
% 0.41/0.96 clear(print_given).
% 0.41/0.96
% 0.41/0.96 % formulas(sos). % not echoed (4 formulas)
% 0.41/0.96
% 0.41/0.96 ============================== end of input ==========================
% 0.41/0.96
% 0.41/0.96 % From the command line: assign(max_seconds, 300).
% 0.41/0.96
% 0.41/0.96 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/0.96
% 0.41/0.96 % Formulas that are not ordinary clauses:
% 0.41/0.96 1 (all E (environment(E) & (exists To (in_environment(E,To) & (all T (subpopulations(first_movers,efficient_producers,E,T) & greater_or_equal(T,To) -> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)))))) -> (exists To (in_environment(E,To) & -greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To)) & (all T (subpopulations(first_movers,efficient_producers,E,T) & greater(T,To) -> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)))))))) # label(mp_earliest_time_growth_rate_exceeds) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.96 2 (all E all To (environment(E) & -greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To)) & in_environment(E,To) & (all T (subpopulations(first_movers,efficient_producers,E,T) & greater(T,To) -> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)))) -> To = critical_point(E))) # label(d1) # label(hypothesis) # label(non_clause). [assumption].
% 0.41/0.96 3 (all E (environment(E) & stable(E) -> (exists To (in_environment(E,To) & (all T (subpopulations(first_movers,efficient_producers,E,T) & greater_or_equal(T,To) -> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)))))))) # label(l1) # label(hypothesis) # label(non_clause). [assumption].
% 0.41/0.96 4 -(all E (environment(E) & stable(E) -> in_environment(E,critical_point(E)))) # label(prove_l5) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.41/0.96
% 0.41/0.96 ============================== end of process non-clausal formulas ===
% 0.41/0.96
% 0.41/0.96 ============================== PROCESS INITIAL CLAUSES ===============
% 0.41/0.96
% 0.41/0.96 ============================== PREDICATE ELIMINATION =================
% 0.41/0.96 5 -environment(A) | -in_environment(A,B) | -greater(growth_rate(efficient_producers,f1(A,B)),growth_rate(first_movers,f1(A,B))) | -greater(growth_rate(efficient_producers,f2(A)),growth_rate(first_movers,f2(A))) # label(mp_earliest_time_growth_rate_exceeds) # label(axiom). [clausify(1)].
% 0.41/0.96 6 environment(c1) # label(prove_l5) # label(negated_conjecture). [clausify(4)].
% 0.41/0.96 Derived: -in_environment(c1,A) | -greater(growth_rate(efficient_producers,f1(c1,A)),growth_rate(first_movers,f1(c1,A))) | -greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))). [resolve(5,a,6,a)].
% 0.41/0.96 7 -environment(A) | -stable(A) | in_environment(A,f4(A)) # label(l1) # label(hypothesis). [clausify(3)].
% 0.41/0.96 Derived: -stable(c1) | in_environment(c1,f4(c1)). [resolve(7,a,6,a)].
% 0.41/0.96 8 -environment(A) | -in_environment(A,B) | greater_or_equal(f1(A,B),B) | in_environment(A,f2(A)) # label(mp_earliest_time_growth_rate_exceeds) # label(axiom). [clausify(1)].
% 0.41/0.96 Derived: -in_environment(c1,A) | greater_or_equal(f1(c1,A),A) | in_environment(c1,f2(c1)). [resolve(8,a,6,a)].
% 0.41/0.96 9 -environment(A) | -in_environment(A,B) | subpopulations(first_movers,efficient_producers,A,f1(A,B)) | in_environment(A,f2(A)) # label(mp_earliest_time_growth_rate_exceeds) # label(axiom). [clausify(1)].
% 0.41/0.96 Derived: -in_environment(c1,A) | subpopulations(first_movers,efficient_producers,c1,f1(c1,A)) | in_environment(c1,f2(c1)). [resolve(9,a,6,a)].
% 0.41/0.96 10 -environment(A) | -in_environment(A,B) | greater_or_equal(f1(A,B),B) | -greater(growth_rate(efficient_producers,f2(A)),growth_rate(first_movers,f2(A))) # label(mp_earliest_time_growth_rate_exceeds) # label(axiom). [clausify(1)].
% 0.41/0.96 Derived: -in_environment(c1,A) | greater_or_equal(f1(c1,A),A) | -greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))). [resolve(10,a,6,a)].
% 0.41/0.96 11 -environment(A) | -in_environment(A,B) | -greater(growth_rate(efficient_producers,f1(A,B)),growth_rate(first_movers,f1(A,B))) | in_environment(A,f2(A)) # label(mp_earliest_time_growth_rate_exceeds) # label(axiom). [clausify(1)].
% 0.41/0.96 Derived: -in_environment(c1,A) | -greater(growth_rate(efficient_producers,f1(c1,A)),growth_rate(first_movers,f1(c1,A))) | in_environment(c1,f2(c1)). [resolve(11,a,6,a)].
% 0.41/0.96 12 -environment(A) | -stable(A) | -subpopulations(first_movers,efficient_producers,A,B) | -greater_or_equal(B,f4(A)) | greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)) # label(l1) # label(hypothesis). [clausify(3)].
% 0.41/0.96 Derived: -stable(c1) | -subpopulations(first_movers,efficient_producers,c1,A) | -greater_or_equal(A,f4(c1)) | greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)). [resolve(12,a,6,a)].
% 0.41/0.96 13 -environment(A) | -in_environment(A,B) | subpopulations(first_movers,efficient_producers,A,f1(A,B)) | -greater(growth_rate(efficient_producers,f2(A)),growth_rate(first_movers,f2(A))) # label(mp_earliest_time_growth_rate_exceeds) # label(axiom). [clausify(1)].
% 0.41/0.96 Derived: -in_environment(c1,A) | subpopulations(first_movers,efficient_producers,c1,f1(c1,A)) | -greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))). [resolve(13,a,6,a)].
% 0.41/0.96 14 -environment(A) | greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)) | -in_environment(A,B) | greater(f3(A,B),B) | critical_point(A) = B # label(d1) # label(hypothesis). [clausify(2)].
% 0.41/0.96 Derived: greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)) | -in_environment(c1,A) | greater(f3(c1,A),A) | critical_point(c1) = A. [resolve(14,a,6,a)].
% 0.41/0.96 15 -environment(A) | greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)) | -in_environment(A,B) | subpopulations(first_movers,efficient_producers,A,f3(A,B)) | critical_point(A) = B # label(d1) # label(hypothesis). [clausify(2)].
% 0.41/0.96 Derived: greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)) | -in_environment(c1,A) | subpopulations(first_movers,efficient_producers,c1,f3(c1,A)) | critical_point(c1) = A. [resolve(15,a,6,a)].
% 0.41/0.96 16 -environment(A) | -in_environment(A,B) | greater_or_equal(f1(A,B),B) | -subpopulations(first_movers,efficient_producers,A,C) | -greater(C,f2(A)) | greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C)) # label(mp_earliest_time_growth_rate_exceeds) # label(axiom). [clausify(1)].
% 0.41/0.96 Derived: -in_environment(c1,A) | greater_or_equal(f1(c1,A),A) | -subpopulations(first_movers,efficient_producers,c1,B) | -greater(B,f2(c1)) | greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)). [resolve(16,a,6,a)].
% 0.41/0.98 17 -environment(A) | greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)) | -in_environment(A,B) | -greater(growth_rate(efficient_producers,f3(A,B)),growth_rate(first_movers,f3(A,B))) | critical_point(A) = B # label(d1) # label(hypothesis). [clausify(2)].
% 0.41/0.98 Derived: greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)) | -in_environment(c1,A) | -greater(growth_rate(efficient_producers,f3(c1,A)),growth_rate(first_movers,f3(c1,A))) | critical_point(c1) = A. [resolve(17,a,6,a)].
% 0.41/0.98 18 -environment(A) | -in_environment(A,B) | subpopulations(first_movers,efficient_producers,A,f1(A,B)) | -subpopulations(first_movers,efficient_producers,A,C) | -greater(C,f2(A)) | greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C)) # label(mp_earliest_time_growth_rate_exceeds) # label(axiom). [clausify(1)].
% 0.41/0.98 Derived: -in_environment(c1,A) | subpopulations(first_movers,efficient_producers,c1,f1(c1,A)) | -subpopulations(first_movers,efficient_producers,c1,B) | -greater(B,f2(c1)) | greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)). [resolve(18,a,6,a)].
% 0.41/0.98 19 -environment(A) | -in_environment(A,B) | -greater(growth_rate(efficient_producers,f1(A,B)),growth_rate(first_movers,f1(A,B))) | -subpopulations(first_movers,efficient_producers,A,C) | -greater(C,f2(A)) | greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C)) # label(mp_earliest_time_growth_rate_exceeds) # label(axiom). [clausify(1)].
% 0.41/0.98 Derived: -in_environment(c1,A) | -greater(growth_rate(efficient_producers,f1(c1,A)),growth_rate(first_movers,f1(c1,A))) | -subpopulations(first_movers,efficient_producers,c1,B) | -greater(B,f2(c1)) | greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)). [resolve(19,a,6,a)].
% 0.41/0.98
% 0.41/0.98 ============================== end predicate elimination =============
% 0.41/0.98
% 0.41/0.98 Auto_denials: (non-Horn, no changes).
% 0.41/0.98
% 0.41/0.98 Term ordering decisions:
% 0.41/0.98 Function symbol KB weights: efficient_producers=1. first_movers=1. c1=1. growth_rate=1. f1=1. f3=1. critical_point=1. f2=1. f4=1.
% 0.41/0.98
% 0.41/0.98 ============================== end of process initial clauses ========
% 0.41/0.98
% 0.41/0.98 ============================== CLAUSES FOR SEARCH ====================
% 0.41/0.98
% 0.41/0.98 ============================== end of clauses for search =============
% 0.41/0.98
% 0.41/0.98 ============================== SEARCH ================================
% 0.41/0.98
% 0.41/0.98 % Starting search at 0.01 seconds.
% 0.41/0.98
% 0.41/0.98 ============================== PROOF =================================
% 0.41/0.98 % SZS status Theorem
% 0.41/0.98 % SZS output start Refutation
% 0.41/0.98
% 0.41/0.98 % Proof 1 at 0.03 (+ 0.00) seconds.
% 0.41/0.98 % Length of proof is 81.
% 0.41/0.98 % Level of proof is 32.
% 0.41/0.98 % Maximum clause weight is 57.000.
% 0.41/0.98 % Given clauses 99.
% 0.41/0.98
% 0.41/0.98 1 (all E (environment(E) & (exists To (in_environment(E,To) & (all T (subpopulations(first_movers,efficient_producers,E,T) & greater_or_equal(T,To) -> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)))))) -> (exists To (in_environment(E,To) & -greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To)) & (all T (subpopulations(first_movers,efficient_producers,E,T) & greater(T,To) -> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)))))))) # label(mp_earliest_time_growth_rate_exceeds) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 2 (all E all To (environment(E) & -greater(growth_rate(efficient_producers,To),growth_rate(first_movers,To)) & in_environment(E,To) & (all T (subpopulations(first_movers,efficient_producers,E,T) & greater(T,To) -> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)))) -> To = critical_point(E))) # label(d1) # label(hypothesis) # label(non_clause). [assumption].
% 0.41/0.98 3 (all E (environment(E) & stable(E) -> (exists To (in_environment(E,To) & (all T (subpopulations(first_movers,efficient_producers,E,T) & greater_or_equal(T,To) -> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)))))))) # label(l1) # label(hypothesis) # label(non_clause). [assumption].
% 0.41/0.98 4 -(all E (environment(E) & stable(E) -> in_environment(E,critical_point(E)))) # label(prove_l5) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.41/0.98 5 -environment(A) | -in_environment(A,B) | -greater(growth_rate(efficient_producers,f1(A,B)),growth_rate(first_movers,f1(A,B))) | -greater(growth_rate(efficient_producers,f2(A)),growth_rate(first_movers,f2(A))) # label(mp_earliest_time_growth_rate_exceeds) # label(axiom). [clausify(1)].
% 0.41/0.98 6 environment(c1) # label(prove_l5) # label(negated_conjecture). [clausify(4)].
% 0.41/0.98 7 -environment(A) | -stable(A) | in_environment(A,f4(A)) # label(l1) # label(hypothesis). [clausify(3)].
% 0.41/0.98 8 -environment(A) | -in_environment(A,B) | greater_or_equal(f1(A,B),B) | in_environment(A,f2(A)) # label(mp_earliest_time_growth_rate_exceeds) # label(axiom). [clausify(1)].
% 0.41/0.98 9 -environment(A) | -in_environment(A,B) | subpopulations(first_movers,efficient_producers,A,f1(A,B)) | in_environment(A,f2(A)) # label(mp_earliest_time_growth_rate_exceeds) # label(axiom). [clausify(1)].
% 0.41/0.98 10 -environment(A) | -in_environment(A,B) | greater_or_equal(f1(A,B),B) | -greater(growth_rate(efficient_producers,f2(A)),growth_rate(first_movers,f2(A))) # label(mp_earliest_time_growth_rate_exceeds) # label(axiom). [clausify(1)].
% 0.41/0.98 11 -environment(A) | -in_environment(A,B) | -greater(growth_rate(efficient_producers,f1(A,B)),growth_rate(first_movers,f1(A,B))) | in_environment(A,f2(A)) # label(mp_earliest_time_growth_rate_exceeds) # label(axiom). [clausify(1)].
% 0.41/0.98 12 -environment(A) | -stable(A) | -subpopulations(first_movers,efficient_producers,A,B) | -greater_or_equal(B,f4(A)) | greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)) # label(l1) # label(hypothesis). [clausify(3)].
% 0.41/0.98 13 -environment(A) | -in_environment(A,B) | subpopulations(first_movers,efficient_producers,A,f1(A,B)) | -greater(growth_rate(efficient_producers,f2(A)),growth_rate(first_movers,f2(A))) # label(mp_earliest_time_growth_rate_exceeds) # label(axiom). [clausify(1)].
% 0.41/0.98 14 -environment(A) | greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)) | -in_environment(A,B) | greater(f3(A,B),B) | critical_point(A) = B # label(d1) # label(hypothesis). [clausify(2)].
% 0.41/0.98 15 -environment(A) | greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)) | -in_environment(A,B) | subpopulations(first_movers,efficient_producers,A,f3(A,B)) | critical_point(A) = B # label(d1) # label(hypothesis). [clausify(2)].
% 0.41/0.98 16 -environment(A) | -in_environment(A,B) | greater_or_equal(f1(A,B),B) | -subpopulations(first_movers,efficient_producers,A,C) | -greater(C,f2(A)) | greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C)) # label(mp_earliest_time_growth_rate_exceeds) # label(axiom). [clausify(1)].
% 0.41/0.98 17 -environment(A) | greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)) | -in_environment(A,B) | -greater(growth_rate(efficient_producers,f3(A,B)),growth_rate(first_movers,f3(A,B))) | critical_point(A) = B # label(d1) # label(hypothesis). [clausify(2)].
% 0.41/0.98 18 -environment(A) | -in_environment(A,B) | subpopulations(first_movers,efficient_producers,A,f1(A,B)) | -subpopulations(first_movers,efficient_producers,A,C) | -greater(C,f2(A)) | greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C)) # label(mp_earliest_time_growth_rate_exceeds) # label(axiom). [clausify(1)].
% 0.41/0.98 19 -environment(A) | -in_environment(A,B) | -greater(growth_rate(efficient_producers,f1(A,B)),growth_rate(first_movers,f1(A,B))) | -subpopulations(first_movers,efficient_producers,A,C) | -greater(C,f2(A)) | greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C)) # label(mp_earliest_time_growth_rate_exceeds) # label(axiom). [clausify(1)].
% 0.41/0.98 20 stable(c1) # label(prove_l5) # label(negated_conjecture). [clausify(4)].
% 0.41/0.98 21 -in_environment(c1,critical_point(c1)) # label(prove_l5) # label(negated_conjecture). [clausify(4)].
% 0.41/0.98 22 -in_environment(c1,A) | -greater(growth_rate(efficient_producers,f1(c1,A)),growth_rate(first_movers,f1(c1,A))) | -greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))). [resolve(5,a,6,a)].
% 0.41/0.98 23 -stable(c1) | in_environment(c1,f4(c1)). [resolve(7,a,6,a)].
% 0.41/0.98 24 in_environment(c1,f4(c1)). [copy(23),unit_del(a,20)].
% 0.41/0.98 25 -in_environment(c1,A) | greater_or_equal(f1(c1,A),A) | in_environment(c1,f2(c1)). [resolve(8,a,6,a)].
% 0.41/0.98 26 -in_environment(c1,A) | subpopulations(first_movers,efficient_producers,c1,f1(c1,A)) | in_environment(c1,f2(c1)). [resolve(9,a,6,a)].
% 0.41/0.98 27 -in_environment(c1,A) | greater_or_equal(f1(c1,A),A) | -greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))). [resolve(10,a,6,a)].
% 0.41/0.98 28 -in_environment(c1,A) | -greater(growth_rate(efficient_producers,f1(c1,A)),growth_rate(first_movers,f1(c1,A))) | in_environment(c1,f2(c1)). [resolve(11,a,6,a)].
% 0.41/0.98 29 -stable(c1) | -subpopulations(first_movers,efficient_producers,c1,A) | -greater_or_equal(A,f4(c1)) | greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)). [resolve(12,a,6,a)].
% 0.41/0.98 30 -subpopulations(first_movers,efficient_producers,c1,A) | -greater_or_equal(A,f4(c1)) | greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)). [copy(29),unit_del(a,20)].
% 0.41/0.98 31 -in_environment(c1,A) | subpopulations(first_movers,efficient_producers,c1,f1(c1,A)) | -greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))). [resolve(13,a,6,a)].
% 0.41/0.98 32 greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)) | -in_environment(c1,A) | greater(f3(c1,A),A) | critical_point(c1) = A. [resolve(14,a,6,a)].
% 0.41/0.98 33 greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)) | -in_environment(c1,A) | subpopulations(first_movers,efficient_producers,c1,f3(c1,A)) | critical_point(c1) = A. [resolve(15,a,6,a)].
% 0.41/0.98 34 -in_environment(c1,A) | greater_or_equal(f1(c1,A),A) | -subpopulations(first_movers,efficient_producers,c1,B) | -greater(B,f2(c1)) | greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)). [resolve(16,a,6,a)].
% 0.41/0.98 35 greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)) | -in_environment(c1,A) | -greater(growth_rate(efficient_producers,f3(c1,A)),growth_rate(first_movers,f3(c1,A))) | critical_point(c1) = A. [resolve(17,a,6,a)].
% 0.41/0.98 36 -in_environment(c1,A) | subpopulations(first_movers,efficient_producers,c1,f1(c1,A)) | -subpopulations(first_movers,efficient_producers,c1,B) | -greater(B,f2(c1)) | greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)). [resolve(18,a,6,a)].
% 0.41/0.98 37 -in_environment(c1,A) | -greater(growth_rate(efficient_producers,f1(c1,A)),growth_rate(first_movers,f1(c1,A))) | -subpopulations(first_movers,efficient_producers,c1,B) | -greater(B,f2(c1)) | greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)). [resolve(19,a,6,a)].
% 0.41/0.98 38 -greater(growth_rate(efficient_producers,f1(c1,f4(c1))),growth_rate(first_movers,f1(c1,f4(c1)))) | -greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))). [resolve(24,a,22,a)].
% 0.41/0.98 39 greater_or_equal(f1(c1,f4(c1)),f4(c1)) | in_environment(c1,f2(c1)). [resolve(25,a,24,a)].
% 0.41/0.98 40 subpopulations(first_movers,efficient_producers,c1,f1(c1,f4(c1))) | in_environment(c1,f2(c1)). [resolve(26,a,24,a)].
% 0.41/0.98 41 greater_or_equal(f1(c1,f4(c1)),f4(c1)) | -greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))). [resolve(27,a,24,a)].
% 0.41/0.98 42 -greater(growth_rate(efficient_producers,f1(c1,f4(c1))),growth_rate(first_movers,f1(c1,f4(c1)))) | in_environment(c1,f2(c1)). [resolve(28,a,24,a)].
% 0.41/0.98 43 subpopulations(first_movers,efficient_producers,c1,f1(c1,f4(c1))) | -greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))). [resolve(31,a,24,a)].
% 0.41/0.98 47 in_environment(c1,f2(c1)) | -greater_or_equal(f1(c1,f4(c1)),f4(c1)) | greater(growth_rate(efficient_producers,f1(c1,f4(c1))),growth_rate(first_movers,f1(c1,f4(c1)))). [resolve(40,a,30,a)].
% 0.41/0.98 52 in_environment(c1,f2(c1)) | greater(growth_rate(efficient_producers,f1(c1,f4(c1))),growth_rate(first_movers,f1(c1,f4(c1)))). [resolve(47,b,39,a),merge(c)].
% 0.41/0.98 53 greater(growth_rate(efficient_producers,f1(c1,f4(c1))),growth_rate(first_movers,f1(c1,f4(c1)))) | greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))) | -greater(growth_rate(efficient_producers,f3(c1,f2(c1))),growth_rate(first_movers,f3(c1,f2(c1)))) | f2(c1) = critical_point(c1). [resolve(52,a,35,b),flip(d)].
% 0.41/0.98 54 greater(growth_rate(efficient_producers,f1(c1,f4(c1))),growth_rate(first_movers,f1(c1,f4(c1)))) | greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))) | subpopulations(first_movers,efficient_producers,c1,f3(c1,f2(c1))) | f2(c1) = critical_point(c1). [resolve(52,a,33,b),flip(d)].
% 0.41/0.98 55 greater(growth_rate(efficient_producers,f1(c1,f4(c1))),growth_rate(first_movers,f1(c1,f4(c1)))) | greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))) | greater(f3(c1,f2(c1)),f2(c1)) | f2(c1) = critical_point(c1). [resolve(52,a,32,b),flip(d)].
% 0.41/0.98 59 greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))) | greater(f3(c1,f2(c1)),f2(c1)) | f2(c1) = critical_point(c1) | in_environment(c1,f2(c1)). [resolve(55,a,42,a)].
% 0.41/0.98 65 greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))) | greater(f3(c1,f2(c1)),f2(c1)) | f2(c1) = critical_point(c1). [resolve(59,d,32,b),flip(f),merge(d),merge(e),merge(f)].
% 0.41/0.98 68 greater(f3(c1,f2(c1)),f2(c1)) | f2(c1) = critical_point(c1) | subpopulations(first_movers,efficient_producers,c1,f1(c1,f4(c1))). [resolve(65,a,43,b)].
% 0.41/0.98 69 greater(f3(c1,f2(c1)),f2(c1)) | f2(c1) = critical_point(c1) | greater_or_equal(f1(c1,f4(c1)),f4(c1)). [resolve(65,a,41,b)].
% 0.41/0.98 73 greater(f3(c1,f2(c1)),f2(c1)) | f2(c1) = critical_point(c1) | -greater_or_equal(f1(c1,f4(c1)),f4(c1)) | greater(growth_rate(efficient_producers,f1(c1,f4(c1))),growth_rate(first_movers,f1(c1,f4(c1)))). [resolve(68,c,30,a)].
% 0.41/0.98 76 greater(f3(c1,f2(c1)),f2(c1)) | f2(c1) = critical_point(c1) | greater(growth_rate(efficient_producers,f1(c1,f4(c1))),growth_rate(first_movers,f1(c1,f4(c1)))). [resolve(73,c,69,c),merge(d),merge(e)].
% 0.41/0.98 78 greater(f3(c1,f2(c1)),f2(c1)) | f2(c1) = critical_point(c1) | -greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))). [resolve(76,c,38,a)].
% 0.41/0.98 84 greater(f3(c1,f2(c1)),f2(c1)) | f2(c1) = critical_point(c1). [resolve(78,c,65,a),merge(c),merge(d)].
% 0.41/0.98 86 greater(growth_rate(efficient_producers,f1(c1,f4(c1))),growth_rate(first_movers,f1(c1,f4(c1)))) | greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))) | f2(c1) = critical_point(c1) | -in_environment(c1,A) | subpopulations(first_movers,efficient_producers,c1,f1(c1,A)) | -greater(f3(c1,f2(c1)),f2(c1)) | greater(growth_rate(efficient_producers,f3(c1,f2(c1))),growth_rate(first_movers,f3(c1,f2(c1)))). [resolve(54,c,36,c)].
% 0.41/0.98 87 greater(growth_rate(efficient_producers,f1(c1,f4(c1))),growth_rate(first_movers,f1(c1,f4(c1)))) | greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))) | f2(c1) = critical_point(c1) | -in_environment(c1,A) | greater_or_equal(f1(c1,A),A) | -greater(f3(c1,f2(c1)),f2(c1)) | greater(growth_rate(efficient_producers,f3(c1,f2(c1))),growth_rate(first_movers,f3(c1,f2(c1)))). [resolve(54,c,34,c)].
% 0.41/0.98 90 greater(growth_rate(efficient_producers,f1(c1,f4(c1))),growth_rate(first_movers,f1(c1,f4(c1)))) | greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))) | f2(c1) = critical_point(c1) | greater_or_equal(f1(c1,f4(c1)),f4(c1)) | -greater(f3(c1,f2(c1)),f2(c1)) | greater(growth_rate(efficient_producers,f3(c1,f2(c1))),growth_rate(first_movers,f3(c1,f2(c1)))). [resolve(87,d,24,a)].
% 0.41/0.98 93 greater(growth_rate(efficient_producers,f1(c1,f4(c1))),growth_rate(first_movers,f1(c1,f4(c1)))) | greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))) | f2(c1) = critical_point(c1) | greater_or_equal(f1(c1,f4(c1)),f4(c1)) | greater(growth_rate(efficient_producers,f3(c1,f2(c1))),growth_rate(first_movers,f3(c1,f2(c1)))). [resolve(90,e,84,a),merge(f)].
% 0.41/0.98 95 greater(growth_rate(efficient_producers,f1(c1,f4(c1))),growth_rate(first_movers,f1(c1,f4(c1)))) | greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))) | f2(c1) = critical_point(c1) | subpopulations(first_movers,efficient_producers,c1,f1(c1,f4(c1))) | -greater(f3(c1,f2(c1)),f2(c1)) | greater(growth_rate(efficient_producers,f3(c1,f2(c1))),growth_rate(first_movers,f3(c1,f2(c1)))). [resolve(86,d,24,a)].
% 0.41/0.99 101 greater(growth_rate(efficient_producers,f1(c1,f4(c1))),growth_rate(first_movers,f1(c1,f4(c1)))) | greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))) | f2(c1) = critical_point(c1) | subpopulations(first_movers,efficient_producers,c1,f1(c1,f4(c1))) | greater(growth_rate(efficient_producers,f3(c1,f2(c1))),growth_rate(first_movers,f3(c1,f2(c1)))). [resolve(95,e,84,a),merge(f)].
% 0.41/0.99 105 greater(growth_rate(efficient_producers,f1(c1,f4(c1))),growth_rate(first_movers,f1(c1,f4(c1)))) | greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))) | f2(c1) = critical_point(c1) | greater(growth_rate(efficient_producers,f3(c1,f2(c1))),growth_rate(first_movers,f3(c1,f2(c1)))) | -greater_or_equal(f1(c1,f4(c1)),f4(c1)). [resolve(101,d,30,a),merge(f)].
% 0.41/0.99 106 greater(growth_rate(efficient_producers,f1(c1,f4(c1))),growth_rate(first_movers,f1(c1,f4(c1)))) | greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))) | f2(c1) = critical_point(c1) | greater(growth_rate(efficient_producers,f3(c1,f2(c1))),growth_rate(first_movers,f3(c1,f2(c1)))). [resolve(105,e,93,d),merge(e),merge(f),merge(g),merge(h)].
% 0.41/0.99 107 greater(growth_rate(efficient_producers,f1(c1,f4(c1))),growth_rate(first_movers,f1(c1,f4(c1)))) | greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))) | f2(c1) = critical_point(c1). [resolve(106,d,53,c),merge(d),merge(e),merge(f)].
% 0.41/0.99 109 greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))) | f2(c1) = critical_point(c1) | in_environment(c1,f2(c1)). [resolve(107,a,42,a)].
% 0.41/0.99 110 greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))) | f2(c1) = critical_point(c1) | -greater(growth_rate(efficient_producers,f3(c1,f2(c1))),growth_rate(first_movers,f3(c1,f2(c1)))). [resolve(109,c,35,b),flip(e),merge(c),merge(e)].
% 0.41/0.99 111 greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))) | f2(c1) = critical_point(c1) | subpopulations(first_movers,efficient_producers,c1,f3(c1,f2(c1))). [resolve(109,c,33,b),flip(e),merge(c),merge(e)].
% 0.41/0.99 112 greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))) | f2(c1) = critical_point(c1) | -in_environment(c1,A) | -greater(growth_rate(efficient_producers,f1(c1,A)),growth_rate(first_movers,f1(c1,A))) | -greater(f3(c1,f2(c1)),f2(c1)) | greater(growth_rate(efficient_producers,f3(c1,f2(c1))),growth_rate(first_movers,f3(c1,f2(c1)))). [resolve(111,c,37,c)].
% 0.41/0.99 119 greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))) | f2(c1) = critical_point(c1) | -greater(growth_rate(efficient_producers,f1(c1,f4(c1))),growth_rate(first_movers,f1(c1,f4(c1)))) | -greater(f3(c1,f2(c1)),f2(c1)) | greater(growth_rate(efficient_producers,f3(c1,f2(c1))),growth_rate(first_movers,f3(c1,f2(c1)))). [resolve(112,c,24,a)].
% 0.41/0.99 130 greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))) | f2(c1) = critical_point(c1) | -greater(f3(c1,f2(c1)),f2(c1)) | greater(growth_rate(efficient_producers,f3(c1,f2(c1))),growth_rate(first_movers,f3(c1,f2(c1)))). [resolve(119,c,107,a),merge(e),merge(f)].
% 0.41/0.99 131 greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))) | f2(c1) = critical_point(c1) | greater(growth_rate(efficient_producers,f3(c1,f2(c1))),growth_rate(first_movers,f3(c1,f2(c1)))). [resolve(130,c,84,a),merge(d)].
% 0.41/0.99 132 greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))) | f2(c1) = critical_point(c1). [resolve(131,c,110,c),merge(c),merge(d)].
% 0.41/0.99 135 f2(c1) = critical_point(c1) | subpopulations(first_movers,efficient_producers,c1,f1(c1,f4(c1))). [resolve(132,a,43,b)].
% 0.41/0.99 136 f2(c1) = critical_point(c1) | greater_or_equal(f1(c1,f4(c1)),f4(c1)). [resolve(132,a,41,b)].
% 0.41/0.99 140 f2(c1) = critical_point(c1) | -greater_or_equal(f1(c1,f4(c1)),f4(c1)) | greater(growth_rate(efficient_producers,f1(c1,f4(c1))),growth_rate(first_movers,f1(c1,f4(c1)))). [resolve(135,b,30,a)].
% 0.41/0.99 141 f2(c1) = critical_point(c1) | greater(growth_rate(efficient_producers,f1(c1,f4(c1))),growth_rate(first_movers,f1(c1,f4(c1)))). [resolve(140,b,136,b),merge(c)].
% 0.41/0.99 144 f2(c1) = critical_point(c1) | -greater(growth_rate(efficient_producers,f2(c1)),growth_rate(first_movers,f2(c1))). [resolve(141,b,38,a)].
% 0.41/0.99 145 f2(c1) = critical_point(c1). [resolve(144,b,132,a),merge(b)].
% 0.41/0.99 155 greater(growth_rate(efficient_producers,f1(c1,f4(c1))),growth_rate(first_movers,f1(c1,f4(c1)))). [back_rewrite(52),rewrite([145(3)]),unit_del(a,21)].
% 0.41/0.99 160 $F. [back_rewrite(42),rewrite([145(16)]),unit_del(a,155),unit_del(b,21)].
% 0.41/0.99
% 0.41/0.99 % SZS output end Refutation
% 0.41/0.99 ============================== end of proof ==========================
% 0.41/0.99
% 0.41/0.99 ============================== STATISTICS ============================
% 0.41/0.99
% 0.41/0.99 Given=99. Generated=197. Kept=138. proofs=1.
% 0.41/0.99 Usable=24. Sos=0. Demods=1. Limbo=15, Disabled=130. Hints=0.
% 0.41/0.99 Megabytes=0.26.
% 0.41/0.99 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.41/0.99
% 0.41/0.99 ============================== end of statistics =====================
% 0.41/0.99
% 0.41/0.99 ============================== end of search =========================
% 0.41/0.99
% 0.41/0.99 THEOREM PROVED
% 0.41/0.99 % SZS status Theorem
% 0.41/0.99
% 0.41/0.99 Exiting with 1 proof.
% 0.41/0.99
% 0.41/0.99 Process 3837 exit (max_proofs) Thu Jun 9 10:25:52 2022
% 0.41/0.99 Prover9 interrupted
%------------------------------------------------------------------------------