TSTP Solution File: MGT027+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : MGT027+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n028.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 22:22:55 EDT 2022
% Result : Theorem 0.73s 1.00s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MGT027+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 9 11:53:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.73/0.99 ============================== Prover9 ===============================
% 0.73/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.73/0.99 Process 15945 was started by sandbox on n028.cluster.edu,
% 0.73/0.99 Thu Jun 9 11:53:33 2022
% 0.73/0.99 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_15783_n028.cluster.edu".
% 0.73/0.99 ============================== end of head ===========================
% 0.73/0.99
% 0.73/0.99 ============================== INPUT =================================
% 0.73/0.99
% 0.73/0.99 % Reading from file /tmp/Prover9_15783_n028.cluster.edu
% 0.73/0.99
% 0.73/0.99 set(prolog_style_variables).
% 0.73/0.99 set(auto2).
% 0.73/0.99 % set(auto2) -> set(auto).
% 0.73/0.99 % set(auto) -> set(auto_inference).
% 0.73/0.99 % set(auto) -> set(auto_setup).
% 0.73/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.73/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.73/0.99 % set(auto) -> set(auto_limits).
% 0.73/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.73/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.73/0.99 % set(auto) -> set(auto_denials).
% 0.73/0.99 % set(auto) -> set(auto_process).
% 0.73/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.73/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.73/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.73/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.73/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.73/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.73/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.73/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.73/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.73/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.73/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.73/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.73/0.99 % set(auto2) -> assign(stats, some).
% 0.73/0.99 % set(auto2) -> clear(echo_input).
% 0.73/0.99 % set(auto2) -> set(quiet).
% 0.73/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.73/0.99 % set(auto2) -> clear(print_given).
% 0.73/0.99 assign(lrs_ticks,-1).
% 0.73/0.99 assign(sos_limit,10000).
% 0.73/0.99 assign(order,kbo).
% 0.73/0.99 set(lex_order_vars).
% 0.73/0.99 clear(print_given).
% 0.73/0.99
% 0.73/0.99 % formulas(sos). % not echoed (9 formulas)
% 0.73/0.99
% 0.73/0.99 ============================== end of input ==========================
% 0.73/0.99
% 0.73/0.99 % From the command line: assign(max_seconds, 300).
% 0.73/0.99
% 0.73/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.73/0.99
% 0.73/0.99 % Formulas that are not ordinary clauses:
% 0.73/0.99 1 (all E all To (environment(E) & stable(E) & in_environment(E,To) & (all T (greater(cardinality_at_time(first_movers,T),zero) & greater_or_equal(T,To) -> greater(zero,growth_rate(first_movers,T)))) -> contracts_from(To,first_movers))) # label(mp_contracts_from) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 2 (all E all T (environment(E) & in_environment(E,T) & greater(cardinality_at_time(first_movers,T),zero) & greater(cardinality_at_time(efficient_producers,T),zero) -> subpopulations(first_movers,efficient_producers,E,T))) # label(mp_non_empty_fm_and_ep) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 3 (all E all T1 all T2 (environment(E) & stable(E) & in_environment(E,T1) & greater(T2,T1) -> in_environment(E,T2))) # label(mp_long_stable_environments) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 4 (all E (environment(E) & stable(E) -> in_environment(E,appear(efficient_producers,E)))) # label(mp_EP_in_stable_environments) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 5 (all X all Y all Z (greater(X,Y) & greater(Y,Z) -> greater(X,Z))) # label(mp_greater_transitivity) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 6 (all X all Y (greater_or_equal(X,Y) <-> greater(X,Y) | X = Y)) # label(mp_greater_or_equal) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 7 (all E all T (environment(E) & in_environment(E,T) & greater_or_equal(T,appear(efficient_producers,E)) -> greater(cardinality_at_time(efficient_producers,T),zero))) # label(t6) # label(hypothesis) # label(non_clause). [assumption].
% 0.73/0.99 8 (all E (environment(E) & stable(E) -> (exists To (greater(To,appear(efficient_producers,E)) & (all T (subpopulations(first_movers,efficient_producers,E,T) & greater_or_equal(T,To) -> greater(zero,growth_rate(first_movers,T)))))))) # label(l10) # label(hypothesis) # label(non_clause). [assumption].
% 0.73/0.99 9 -(all E (environment(E) & stable(E) -> (exists To (greater(To,appear(efficient_producers,E)) & contracts_from(To,first_movers))))) # label(prove_l9) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.73/1.00
% 0.73/1.00 ============================== end of process non-clausal formulas ===
% 0.73/1.00
% 0.73/1.00 ============================== PROCESS INITIAL CLAUSES ===============
% 0.73/1.00
% 0.73/1.00 ============================== PREDICATE ELIMINATION =================
% 0.73/1.00 10 -environment(A) | -stable(A) | in_environment(A,appear(efficient_producers,A)) # label(mp_EP_in_stable_environments) # label(axiom). [clausify(4)].
% 0.73/1.00 11 environment(c1) # label(prove_l9) # label(negated_conjecture). [clausify(9)].
% 0.73/1.00 Derived: -stable(c1) | in_environment(c1,appear(efficient_producers,c1)). [resolve(10,a,11,a)].
% 0.73/1.00 12 -environment(A) | -stable(A) | greater(f2(A),appear(efficient_producers,A)) # label(l10) # label(hypothesis). [clausify(8)].
% 0.73/1.00 Derived: -stable(c1) | greater(f2(c1),appear(efficient_producers,c1)). [resolve(12,a,11,a)].
% 0.73/1.00 13 -environment(A) | -stable(A) | -in_environment(A,B) | -greater(C,B) | in_environment(A,C) # label(mp_long_stable_environments) # label(axiom). [clausify(3)].
% 0.73/1.00 Derived: -stable(c1) | -in_environment(c1,A) | -greater(B,A) | in_environment(c1,B). [resolve(13,a,11,a)].
% 0.73/1.00 14 -environment(A) | -stable(A) | -in_environment(A,B) | greater_or_equal(f1(A,B),B) | contracts_from(B,first_movers) # label(mp_contracts_from) # label(axiom). [clausify(1)].
% 0.73/1.00 Derived: -stable(c1) | -in_environment(c1,A) | greater_or_equal(f1(c1,A),A) | contracts_from(A,first_movers). [resolve(14,a,11,a)].
% 0.73/1.00 15 -environment(A) | -in_environment(A,B) | -greater_or_equal(B,appear(efficient_producers,A)) | greater(cardinality_at_time(efficient_producers,B),zero) # label(t6) # label(hypothesis). [clausify(7)].
% 0.73/1.00 Derived: -in_environment(c1,A) | -greater_or_equal(A,appear(efficient_producers,c1)) | greater(cardinality_at_time(efficient_producers,A),zero). [resolve(15,a,11,a)].
% 0.73/1.00 16 -environment(A) | -stable(A) | -in_environment(A,B) | greater(cardinality_at_time(first_movers,f1(A,B)),zero) | contracts_from(B,first_movers) # label(mp_contracts_from) # label(axiom). [clausify(1)].
% 0.73/1.00 Derived: -stable(c1) | -in_environment(c1,A) | greater(cardinality_at_time(first_movers,f1(c1,A)),zero) | contracts_from(A,first_movers). [resolve(16,a,11,a)].
% 0.73/1.00 17 -environment(A) | -stable(A) | -in_environment(A,B) | -greater(zero,growth_rate(first_movers,f1(A,B))) | contracts_from(B,first_movers) # label(mp_contracts_from) # label(axiom). [clausify(1)].
% 0.73/1.00 Derived: -stable(c1) | -in_environment(c1,A) | -greater(zero,growth_rate(first_movers,f1(c1,A))) | contracts_from(A,first_movers). [resolve(17,a,11,a)].
% 0.73/1.00 18 -environment(A) | -stable(A) | -subpopulations(first_movers,efficient_producers,A,B) | -greater_or_equal(B,f2(A)) | greater(zero,growth_rate(first_movers,B)) # label(l10) # label(hypothesis). [clausify(8)].
% 0.73/1.00 Derived: -stable(c1) | -subpopulations(first_movers,efficient_producers,c1,A) | -greater_or_equal(A,f2(c1)) | greater(zero,growth_rate(first_movers,A)). [resolve(18,a,11,a)].
% 0.73/1.00 19 -environment(A) | -in_environment(A,B) | -greater(cardinality_at_time(first_movers,B),zero) | -greater(cardinality_at_time(efficient_producers,B),zero) | subpopulations(first_movers,efficient_producers,A,B) # label(mp_non_empty_fm_and_ep) # label(axiom). [clausify(2)].
% 0.73/1.00 Derived: -in_environment(c1,A) | -greater(cardinality_at_time(first_movers,A),zero) | -greater(cardinality_at_time(efficient_producers,A),zero) | subpopulations(first_movers,efficient_producers,c1,A). [resolve(19,a,11,a)].
% 0.73/1.00
% 0.73/1.00 ============================== end predicate elimination =============
% 0.73/1.00
% 0.73/1.00 Auto_denials: (non-Horn, no changes).
% 0.73/1.00
% 0.73/1.00 Term ordering decisions:
% 0.73/1.00
% 0.73/1.00 % Assigning unary symbol f2 kb_weight 0 and highest precedence (16).
% 0.73/1.00 Function symbol KB weights: first_movers=1. efficient_producers=1. zero=1. c1=1. cardinality_at_time=1. appear=1. growth_rate=1. f1=1. f2=0.
% 0.73/1.00
% 0.73/1.00 ============================== end of process initial clauses ========
% 0.73/1.00
% 0.73/1.00 ============================== CLAUSES FOR SEARCH ====================
% 0.73/1.00
% 0.73/1.00 ============================== end of clauses for search =============
% 0.73/1.00
% 0.73/1.00 ============================== SEARCH ================================
% 0.73/1.00
% 0.73/1.00 % Starting search at 0.01 seconds.
% 0.73/1.00
% 0.73/1.00 ============================== PROOF =================================
% 0.73/1.00 % SZS status Theorem
% 0.73/1.00 % SZS output start Refutation
% 0.73/1.00
% 0.73/1.00 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.73/1.00 % Length of proof is 64.
% 0.73/1.00 % Level of proof is 14.
% 0.73/1.00 % Maximum clause weight is 21.000.
% 0.73/1.00 % Given clauses 58.
% 0.73/1.00
% 0.73/1.00 1 (all E all To (environment(E) & stable(E) & in_environment(E,To) & (all T (greater(cardinality_at_time(first_movers,T),zero) & greater_or_equal(T,To) -> greater(zero,growth_rate(first_movers,T)))) -> contracts_from(To,first_movers))) # label(mp_contracts_from) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 2 (all E all T (environment(E) & in_environment(E,T) & greater(cardinality_at_time(first_movers,T),zero) & greater(cardinality_at_time(efficient_producers,T),zero) -> subpopulations(first_movers,efficient_producers,E,T))) # label(mp_non_empty_fm_and_ep) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 3 (all E all T1 all T2 (environment(E) & stable(E) & in_environment(E,T1) & greater(T2,T1) -> in_environment(E,T2))) # label(mp_long_stable_environments) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 4 (all E (environment(E) & stable(E) -> in_environment(E,appear(efficient_producers,E)))) # label(mp_EP_in_stable_environments) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 5 (all X all Y all Z (greater(X,Y) & greater(Y,Z) -> greater(X,Z))) # label(mp_greater_transitivity) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 6 (all X all Y (greater_or_equal(X,Y) <-> greater(X,Y) | X = Y)) # label(mp_greater_or_equal) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.00 7 (all E all T (environment(E) & in_environment(E,T) & greater_or_equal(T,appear(efficient_producers,E)) -> greater(cardinality_at_time(efficient_producers,T),zero))) # label(t6) # label(hypothesis) # label(non_clause). [assumption].
% 0.73/1.00 8 (all E (environment(E) & stable(E) -> (exists To (greater(To,appear(efficient_producers,E)) & (all T (subpopulations(first_movers,efficient_producers,E,T) & greater_or_equal(T,To) -> greater(zero,growth_rate(first_movers,T)))))))) # label(l10) # label(hypothesis) # label(non_clause). [assumption].
% 0.73/1.00 9 -(all E (environment(E) & stable(E) -> (exists To (greater(To,appear(efficient_producers,E)) & contracts_from(To,first_movers))))) # label(prove_l9) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.73/1.00 10 -environment(A) | -stable(A) | in_environment(A,appear(efficient_producers,A)) # label(mp_EP_in_stable_environments) # label(axiom). [clausify(4)].
% 0.73/1.00 11 environment(c1) # label(prove_l9) # label(negated_conjecture). [clausify(9)].
% 0.73/1.00 12 -environment(A) | -stable(A) | greater(f2(A),appear(efficient_producers,A)) # label(l10) # label(hypothesis). [clausify(8)].
% 0.73/1.00 13 -environment(A) | -stable(A) | -in_environment(A,B) | -greater(C,B) | in_environment(A,C) # label(mp_long_stable_environments) # label(axiom). [clausify(3)].
% 0.73/1.00 14 -environment(A) | -stable(A) | -in_environment(A,B) | greater_or_equal(f1(A,B),B) | contracts_from(B,first_movers) # label(mp_contracts_from) # label(axiom). [clausify(1)].
% 0.73/1.00 15 -environment(A) | -in_environment(A,B) | -greater_or_equal(B,appear(efficient_producers,A)) | greater(cardinality_at_time(efficient_producers,B),zero) # label(t6) # label(hypothesis). [clausify(7)].
% 0.73/1.00 16 -environment(A) | -stable(A) | -in_environment(A,B) | greater(cardinality_at_time(first_movers,f1(A,B)),zero) | contracts_from(B,first_movers) # label(mp_contracts_from) # label(axiom). [clausify(1)].
% 0.73/1.00 17 -environment(A) | -stable(A) | -in_environment(A,B) | -greater(zero,growth_rate(first_movers,f1(A,B))) | contracts_from(B,first_movers) # label(mp_contracts_from) # label(axiom). [clausify(1)].
% 0.73/1.00 18 -environment(A) | -stable(A) | -subpopulations(first_movers,efficient_producers,A,B) | -greater_or_equal(B,f2(A)) | greater(zero,growth_rate(first_movers,B)) # label(l10) # label(hypothesis). [clausify(8)].
% 0.73/1.00 19 -environment(A) | -in_environment(A,B) | -greater(cardinality_at_time(first_movers,B),zero) | -greater(cardinality_at_time(efficient_producers,B),zero) | subpopulations(first_movers,efficient_producers,A,B) # label(mp_non_empty_fm_and_ep) # label(axiom). [clausify(2)].
% 0.73/1.00 20 stable(c1) # label(prove_l9) # label(negated_conjecture). [clausify(9)].
% 0.73/1.00 21 -greater(A,appear(efficient_producers,c1)) | -contracts_from(A,first_movers) # label(prove_l9) # label(negated_conjecture). [clausify(9)].
% 0.73/1.00 22 greater_or_equal(A,B) | -greater(A,B) # label(mp_greater_or_equal) # label(axiom). [clausify(6)].
% 0.73/1.00 24 -greater(A,B) | -greater(B,C) | greater(A,C) # label(mp_greater_transitivity) # label(axiom). [clausify(5)].
% 0.73/1.00 25 -greater_or_equal(A,B) | greater(A,B) | B = A # label(mp_greater_or_equal) # label(axiom). [clausify(6)].
% 0.73/1.00 26 -stable(c1) | in_environment(c1,appear(efficient_producers,c1)). [resolve(10,a,11,a)].
% 0.73/1.00 27 in_environment(c1,appear(efficient_producers,c1)). [copy(26),unit_del(a,20)].
% 0.73/1.00 28 -stable(c1) | greater(f2(c1),appear(efficient_producers,c1)). [resolve(12,a,11,a)].
% 0.73/1.00 29 greater(f2(c1),appear(efficient_producers,c1)). [copy(28),unit_del(a,20)].
% 0.73/1.00 30 -stable(c1) | -in_environment(c1,A) | -greater(B,A) | in_environment(c1,B). [resolve(13,a,11,a)].
% 0.73/1.00 31 -in_environment(c1,A) | -greater(B,A) | in_environment(c1,B). [copy(30),unit_del(a,20)].
% 0.73/1.00 32 -stable(c1) | -in_environment(c1,A) | greater_or_equal(f1(c1,A),A) | contracts_from(A,first_movers). [resolve(14,a,11,a)].
% 0.73/1.00 33 -in_environment(c1,A) | greater_or_equal(f1(c1,A),A) | contracts_from(A,first_movers). [copy(32),unit_del(a,20)].
% 0.73/1.00 34 -in_environment(c1,A) | -greater_or_equal(A,appear(efficient_producers,c1)) | greater(cardinality_at_time(efficient_producers,A),zero). [resolve(15,a,11,a)].
% 0.73/1.00 35 -stable(c1) | -in_environment(c1,A) | greater(cardinality_at_time(first_movers,f1(c1,A)),zero) | contracts_from(A,first_movers). [resolve(16,a,11,a)].
% 0.73/1.00 36 -in_environment(c1,A) | greater(cardinality_at_time(first_movers,f1(c1,A)),zero) | contracts_from(A,first_movers). [copy(35),unit_del(a,20)].
% 0.73/1.00 37 -stable(c1) | -in_environment(c1,A) | -greater(zero,growth_rate(first_movers,f1(c1,A))) | contracts_from(A,first_movers). [resolve(17,a,11,a)].
% 0.73/1.00 38 -in_environment(c1,A) | -greater(zero,growth_rate(first_movers,f1(c1,A))) | contracts_from(A,first_movers). [copy(37),unit_del(a,20)].
% 0.73/1.00 39 -stable(c1) | -subpopulations(first_movers,efficient_producers,c1,A) | -greater_or_equal(A,f2(c1)) | greater(zero,growth_rate(first_movers,A)). [resolve(18,a,11,a)].
% 0.73/1.00 40 -subpopulations(first_movers,efficient_producers,c1,A) | -greater_or_equal(A,f2(c1)) | greater(zero,growth_rate(first_movers,A)). [copy(39),unit_del(a,20)].
% 0.73/1.00 41 -in_environment(c1,A) | -greater(cardinality_at_time(first_movers,A),zero) | -greater(cardinality_at_time(efficient_producers,A),zero) | subpopulations(first_movers,efficient_producers,c1,A). [resolve(19,a,11,a)].
% 0.73/1.00 43 -greater(A,f2(c1)) | greater(A,appear(efficient_producers,c1)). [resolve(29,a,24,b)].
% 0.73/1.00 45 greater_or_equal(f2(c1),appear(efficient_producers,c1)). [resolve(29,a,22,b)].
% 0.73/1.00 46 -contracts_from(f2(c1),first_movers). [ur(21,a,29,a)].
% 0.73/1.00 47 -greater(A,appear(efficient_producers,c1)) | in_environment(c1,A). [resolve(31,a,27,a)].
% 0.73/1.00 54 -in_environment(c1,f2(c1)) | greater(cardinality_at_time(efficient_producers,f2(c1)),zero). [resolve(45,a,34,b)].
% 0.73/1.00 58 in_environment(c1,f2(c1)). [resolve(47,a,29,a)].
% 0.73/1.00 59 greater(cardinality_at_time(efficient_producers,f2(c1)),zero). [back_unit_del(54),unit_del(a,58)].
% 0.73/1.00 60 -greater(cardinality_at_time(first_movers,f2(c1)),zero) | subpopulations(first_movers,efficient_producers,c1,f2(c1)). [resolve(58,a,41,a),unit_del(b,59)].
% 0.73/1.00 61 -greater(zero,growth_rate(first_movers,f1(c1,f2(c1)))). [resolve(58,a,38,a),unit_del(b,46)].
% 0.73/1.00 62 greater(cardinality_at_time(first_movers,f1(c1,f2(c1))),zero). [resolve(58,a,36,a),unit_del(b,46)].
% 0.73/1.00 63 greater_or_equal(f1(c1,f2(c1)),f2(c1)). [resolve(58,a,33,a),unit_del(b,46)].
% 0.73/1.00 64 -greater(A,f2(c1)) | in_environment(c1,A). [resolve(58,a,31,a)].
% 0.73/1.00 68 greater(f1(c1,f2(c1)),f2(c1)) | f1(c1,f2(c1)) = f2(c1). [resolve(63,a,25,a),flip(b)].
% 0.73/1.00 69 -subpopulations(first_movers,efficient_producers,c1,f1(c1,f2(c1))). [ur(40,b,63,a,c,61,a)].
% 0.73/1.00 75 f1(c1,f2(c1)) = f2(c1) | in_environment(c1,f1(c1,f2(c1))). [resolve(68,a,64,a)].
% 0.73/1.00 76 f1(c1,f2(c1)) = f2(c1) | greater(f1(c1,f2(c1)),appear(efficient_producers,c1)). [resolve(68,a,43,a)].
% 0.73/1.00 79 f1(c1,f2(c1)) = f2(c1) | -greater(cardinality_at_time(efficient_producers,f1(c1,f2(c1))),zero). [resolve(75,b,41,a),unit_del(b,62),unit_del(d,69)].
% 0.73/1.00 86 f1(c1,f2(c1)) = f2(c1) | greater_or_equal(f1(c1,f2(c1)),appear(efficient_producers,c1)). [resolve(76,b,22,b)].
% 0.73/1.00 87 f1(c1,f2(c1)) = f2(c1) | -in_environment(c1,f1(c1,f2(c1))) | greater(cardinality_at_time(efficient_producers,f1(c1,f2(c1))),zero). [resolve(86,b,34,b)].
% 0.73/1.00 88 f1(c1,f2(c1)) = f2(c1) | greater(cardinality_at_time(efficient_producers,f1(c1,f2(c1))),zero). [resolve(87,b,75,b),merge(c)].
% 0.73/1.00 89 f1(c1,f2(c1)) = f2(c1). [resolve(88,b,79,b),merge(b)].
% 0.73/1.00 93 -subpopulations(first_movers,efficient_producers,c1,f2(c1)). [back_rewrite(69),rewrite([89(7)])].
% 0.73/1.00 94 greater(cardinality_at_time(first_movers,f2(c1)),zero). [back_rewrite(62),rewrite([89(5)])].
% 0.73/1.00 96 $F. [back_unit_del(60),unit_del(a,94),unit_del(b,93)].
% 0.73/1.00
% 0.73/1.00 % SZS output end Refutation
% 0.73/1.00 ============================== end of proof ==========================
% 0.73/1.00
% 0.73/1.00 ============================== STATISTICS ============================
% 0.73/1.00
% 0.73/1.00 Given=58. Generated=85. Kept=69. proofs=1.
% 0.73/1.00 Usable=37. Sos=4. Demods=1. Limbo=3, Disabled=50. Hints=0.
% 0.73/1.00 Megabytes=0.13.
% 0.73/1.00 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.73/1.00
% 0.73/1.00 ============================== end of statistics =====================
% 0.73/1.00
% 0.73/1.00 ============================== end of search =========================
% 0.73/1.00
% 0.73/1.00 THEOREM PROVED
% 0.73/1.00 % SZS status Theorem
% 0.73/1.00
% 0.73/1.00 Exiting with 1 proof.
% 0.73/1.00
% 0.73/1.00 Process 15945 exit (max_proofs) Thu Jun 9 11:53:33 2022
% 0.73/1.00 Prover9 interrupted
%------------------------------------------------------------------------------