TSTP Solution File: MGT026-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : MGT026-1 : TPTP v8.1.0. Released v2.4.0.
% 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 : Unsatisfiable 0.41s 0.97s
% Output : Refutation 0.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : MGT026-1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n028.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 08:42:47 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.41/0.97 ============================== Prover9 ===============================
% 0.41/0.97 Prover9 (32) version 2009-11A, November 2009.
% 0.41/0.97 Process 13123 was started by sandbox2 on n028.cluster.edu,
% 0.41/0.97 Thu Jun 9 08:42:48 2022
% 0.41/0.97 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_12970_n028.cluster.edu".
% 0.41/0.97 ============================== end of head ===========================
% 0.41/0.97
% 0.41/0.97 ============================== INPUT =================================
% 0.41/0.97
% 0.41/0.97 % Reading from file /tmp/Prover9_12970_n028.cluster.edu
% 0.41/0.97
% 0.41/0.97 set(prolog_style_variables).
% 0.41/0.97 set(auto2).
% 0.41/0.97 % set(auto2) -> set(auto).
% 0.41/0.97 % set(auto) -> set(auto_inference).
% 0.41/0.97 % set(auto) -> set(auto_setup).
% 0.41/0.97 % set(auto_setup) -> set(predicate_elim).
% 0.41/0.97 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.41/0.97 % set(auto) -> set(auto_limits).
% 0.41/0.97 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.41/0.97 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.41/0.97 % set(auto) -> set(auto_denials).
% 0.41/0.97 % set(auto) -> set(auto_process).
% 0.41/0.97 % set(auto2) -> assign(new_constants, 1).
% 0.41/0.97 % set(auto2) -> assign(fold_denial_max, 3).
% 0.41/0.97 % set(auto2) -> assign(max_weight, "200.000").
% 0.41/0.97 % set(auto2) -> assign(max_hours, 1).
% 0.41/0.97 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.41/0.97 % set(auto2) -> assign(max_seconds, 0).
% 0.41/0.97 % set(auto2) -> assign(max_minutes, 5).
% 0.41/0.97 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.41/0.97 % set(auto2) -> set(sort_initial_sos).
% 0.41/0.97 % set(auto2) -> assign(sos_limit, -1).
% 0.41/0.97 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.41/0.97 % set(auto2) -> assign(max_megs, 400).
% 0.41/0.97 % set(auto2) -> assign(stats, some).
% 0.41/0.97 % set(auto2) -> clear(echo_input).
% 0.41/0.97 % set(auto2) -> set(quiet).
% 0.41/0.97 % set(auto2) -> clear(print_initial_clauses).
% 0.41/0.97 % set(auto2) -> clear(print_given).
% 0.41/0.97 assign(lrs_ticks,-1).
% 0.41/0.97 assign(sos_limit,10000).
% 0.41/0.97 assign(order,kbo).
% 0.41/0.97 set(lex_order_vars).
% 0.41/0.97 clear(print_given).
% 0.41/0.97
% 0.41/0.97 % formulas(sos). % not echoed (18 formulas)
% 0.41/0.97
% 0.41/0.97 ============================== end of input ==========================
% 0.41/0.97
% 0.41/0.97 % From the command line: assign(max_seconds, 300).
% 0.41/0.97
% 0.41/0.97 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/0.97
% 0.41/0.97 % Formulas that are not ordinary clauses:
% 0.41/0.97
% 0.41/0.97 ============================== end of process non-clausal formulas ===
% 0.41/0.97
% 0.41/0.97 ============================== PROCESS INITIAL CLAUSES ===============
% 0.41/0.97
% 0.41/0.97 ============================== PREDICATE ELIMINATION =================
% 0.41/0.97 1 -environment(A) | B != critical_point(A) | -greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)) # label(d1_39) # label(hypothesis). [assumption].
% 0.41/0.97 2 environment(sk1) # label(prove_l8_42) # label(negated_conjecture). [assumption].
% 0.41/0.97 Derived: A != critical_point(sk1) | -greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)). [resolve(1,a,2,a)].
% 0.41/0.97 3 -environment(A) | greater_or_equal(critical_point(A),appear(efficient_producers,A)) # label(mp_critical_point_after_EP_34) # label(axiom). [assumption].
% 0.41/0.97 Derived: greater_or_equal(critical_point(sk1),appear(efficient_producers,sk1)). [resolve(3,a,2,a)].
% 0.41/0.97 4 -environment(A) | -in_environment(A,B) | subpopulation(first_movers,A,B) # label(mp_subpopulations_32) # label(axiom). [assumption].
% 0.41/0.97 Derived: -in_environment(sk1,A) | subpopulation(first_movers,sk1,A). [resolve(4,a,2,a)].
% 0.41/0.97 5 -environment(A) | -in_environment(A,B) | subpopulation(efficient_producers,A,B) # label(mp_subpopulations_33) # label(axiom). [assumption].
% 0.41/0.97 Derived: -in_environment(sk1,A) | subpopulation(efficient_producers,sk1,A). [resolve(5,a,2,a)].
% 0.41/0.97 6 -environment(A) | -in_environment(A,B) | greater_or_equal(cardinality_at_time(first_movers,B),zero) # label(mp_first_movers_exist_31) # label(axiom). [assumption].
% 0.41/0.97 Derived: -in_environment(sk1,A) | greater_or_equal(cardinality_at_time(first_movers,A),zero). [resolve(6,a,2,a)].
% 0.41/0.97 7 -environment(A) | -in_environment(A,B) | -greater_or_equal(B,appear(efficient_producers,A)) | greater(cardinality_at_time(efficient_producers,B),zero) # label(t6_41) # label(hypothesis). [assumption].
% 0.41/0.97 Derived: -in_environment(sk1,A) | -greater_or_equal(A,appear(efficient_producers,sk1)) | greater(cardinality_at_time(efficient_producers,A),zero). [resolve(7,a,2,a)].
% 0.41/0.97 8 -environment(A) | -subpopulations(B,C,A,D) | -greater(growth_rate(C,D),growth_rate(B,D)) | selection_favors(C,B,D) # label(mp1_high_growth_rates_28) # label(axiom). [assumption].
% 0.41/0.97 Derived: -subpopulations(A,B,sk1,C) | -greater(growth_rate(B,C),growth_rate(A,C)) | selection_favors(B,A,C). [resolve(8,a,2,a)].
% 0.41/0.97 9 -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_30) # label(axiom). [assumption].
% 0.41/0.97 Derived: -in_environment(sk1,A) | -greater(cardinality_at_time(first_movers,A),zero) | -greater(cardinality_at_time(efficient_producers,A),zero) | subpopulations(first_movers,efficient_producers,sk1,A). [resolve(9,a,2,a)].
% 0.41/0.97 10 -environment(A) | B != critical_point(A) | -subpopulations(first_movers,efficient_producers,A,C) | -greater(C,B) | greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C)) # label(d1_40) # label(hypothesis). [assumption].
% 0.41/0.97 Derived: A != critical_point(sk1) | -subpopulations(first_movers,efficient_producers,sk1,B) | -greater(B,A) | greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)). [resolve(10,a,2,a)].
% 0.41/0.97 11 -environment(A) | -subpopulation(B,A,C) | -subpopulation(D,A,C) | -greater(cardinality_at_time(B,C),zero) | cardinality_at_time(D,C) != zero | selection_favors(B,D,C) # label(mp2_favour_members_29) # label(axiom). [assumption].
% 0.41/0.97 Derived: -subpopulation(A,sk1,B) | -subpopulation(C,sk1,B) | -greater(cardinality_at_time(A,B),zero) | cardinality_at_time(C,B) != zero | selection_favors(A,C,B). [resolve(11,a,2,a)].
% 0.41/0.97
% 0.41/0.97 ============================== end predicate elimination =============
% 0.41/0.97
% 0.41/0.97 Auto_denials: (non-Horn, no changes).
% 0.41/0.97
% 0.41/0.97 Term ordering decisions:
% 0.41/0.97
% 0.41/0.97 % Assigning unary symbol critical_point kb_weight 0 and highest precedence (16).
% 0.41/0.97 Function symbol KB weights: sk1=1. efficient_producers=1. first_movers=1. zero=1. sk2=1. cardinality_at_time=1. growth_rate=1. appear=1. critical_point=0.
% 0.41/0.97
% 0.41/0.97 ============================== end of process initial clauses ========
% 0.41/0.97
% 0.41/0.97 ============================== CLAUSES FOR SEARCH ====================
% 0.41/0.97
% 0.41/0.97 ============================== end of clauses for search =============
% 0.41/0.97
% 0.41/0.97 ============================== SEARCH ================================
% 0.41/0.97
% 0.41/0.97 % Starting search at 0.01 seconds.
% 0.41/0.97
% 0.41/0.97 ============================== PROOF =================================
% 0.41/0.97 % SZS status Unsatisfiable
% 0.41/0.97 % SZS output start Refutation
% 0.41/0.97
% 0.41/0.97 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.41/0.97 % Length of proof is 56.
% 0.41/0.97 % Level of proof is 16.
% 0.41/0.97 % Maximum clause weight is 25.000.
% 0.41/0.97 % Given clauses 69.
% 0.41/0.97
% 0.41/0.97 2 environment(sk1) # label(prove_l8_42) # label(negated_conjecture). [assumption].
% 0.41/0.97 3 -environment(A) | greater_or_equal(critical_point(A),appear(efficient_producers,A)) # label(mp_critical_point_after_EP_34) # label(axiom). [assumption].
% 0.41/0.97 4 -environment(A) | -in_environment(A,B) | subpopulation(first_movers,A,B) # label(mp_subpopulations_32) # label(axiom). [assumption].
% 0.41/0.97 5 -environment(A) | -in_environment(A,B) | subpopulation(efficient_producers,A,B) # label(mp_subpopulations_33) # label(axiom). [assumption].
% 0.41/0.97 6 -environment(A) | -in_environment(A,B) | greater_or_equal(cardinality_at_time(first_movers,B),zero) # label(mp_first_movers_exist_31) # label(axiom). [assumption].
% 0.41/0.97 7 -environment(A) | -in_environment(A,B) | -greater_or_equal(B,appear(efficient_producers,A)) | greater(cardinality_at_time(efficient_producers,B),zero) # label(t6_41) # label(hypothesis). [assumption].
% 0.41/0.97 8 -environment(A) | -subpopulations(B,C,A,D) | -greater(growth_rate(C,D),growth_rate(B,D)) | selection_favors(C,B,D) # label(mp1_high_growth_rates_28) # label(axiom). [assumption].
% 0.41/0.97 9 -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_30) # label(axiom). [assumption].
% 0.41/0.97 10 -environment(A) | B != critical_point(A) | -subpopulations(first_movers,efficient_producers,A,C) | -greater(C,B) | greater(growth_rate(efficient_producers,C),growth_rate(first_movers,C)) # label(d1_40) # label(hypothesis). [assumption].
% 0.41/0.97 11 -environment(A) | -subpopulation(B,A,C) | -subpopulation(D,A,C) | -greater(cardinality_at_time(B,C),zero) | cardinality_at_time(D,C) != zero | selection_favors(B,D,C) # label(mp2_favour_members_29) # label(axiom). [assumption].
% 0.41/0.97 12 in_environment(sk1,sk2) # label(prove_l8_43) # label(negated_conjecture). [assumption].
% 0.41/0.97 13 greater(sk2,critical_point(sk1)) # label(prove_l8_44) # label(negated_conjecture). [assumption].
% 0.41/0.97 14 -selection_favors(efficient_producers,first_movers,sk2) # label(prove_l8_45) # label(negated_conjecture). [assumption].
% 0.41/0.97 15 -greater(A,B) | greater_or_equal(A,B) # label(mp_greater_or_equal_37) # label(axiom). [assumption].
% 0.41/0.97 17 -greater(A,B) | -greater(B,C) | greater(A,C) # label(mp_greater_transitivity_35) # label(axiom). [assumption].
% 0.41/0.97 18 -greater_or_equal(A,B) | greater(A,B) | A = B # label(mp_greater_or_equal_36) # label(axiom). [assumption].
% 0.41/0.97 21 greater_or_equal(critical_point(sk1),appear(efficient_producers,sk1)). [resolve(3,a,2,a)].
% 0.41/0.97 22 -in_environment(sk1,A) | subpopulation(first_movers,sk1,A). [resolve(4,a,2,a)].
% 0.41/0.97 23 -in_environment(sk1,A) | subpopulation(efficient_producers,sk1,A). [resolve(5,a,2,a)].
% 0.41/0.97 24 -in_environment(sk1,A) | greater_or_equal(cardinality_at_time(first_movers,A),zero). [resolve(6,a,2,a)].
% 0.41/0.97 25 -in_environment(sk1,A) | -greater_or_equal(A,appear(efficient_producers,sk1)) | greater(cardinality_at_time(efficient_producers,A),zero). [resolve(7,a,2,a)].
% 0.41/0.97 26 -subpopulations(A,B,sk1,C) | -greater(growth_rate(B,C),growth_rate(A,C)) | selection_favors(B,A,C). [resolve(8,a,2,a)].
% 0.41/0.97 27 -in_environment(sk1,A) | -greater(cardinality_at_time(first_movers,A),zero) | -greater(cardinality_at_time(efficient_producers,A),zero) | subpopulations(first_movers,efficient_producers,sk1,A). [resolve(9,a,2,a)].
% 0.41/0.97 28 A != critical_point(sk1) | -subpopulations(first_movers,efficient_producers,sk1,B) | -greater(B,A) | greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)). [resolve(10,a,2,a)].
% 0.41/0.97 29 critical_point(sk1) != A | -subpopulations(first_movers,efficient_producers,sk1,B) | -greater(B,A) | greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)). [copy(28),flip(a)].
% 0.41/0.97 30 -subpopulation(A,sk1,B) | -subpopulation(C,sk1,B) | -greater(cardinality_at_time(A,B),zero) | cardinality_at_time(C,B) != zero | selection_favors(A,C,B). [resolve(11,a,2,a)].
% 0.41/0.97 32 greater_or_equal(sk2,critical_point(sk1)). [resolve(15,a,13,a)].
% 0.41/0.97 34 -greater(critical_point(sk1),A) | greater(sk2,A). [resolve(17,a,13,a)].
% 0.41/0.97 37 greater(critical_point(sk1),appear(efficient_producers,sk1)) | appear(efficient_producers,sk1) = critical_point(sk1). [resolve(21,a,18,a),flip(b)].
% 0.41/0.97 38 subpopulation(first_movers,sk1,sk2). [resolve(22,a,12,a)].
% 0.41/0.97 39 subpopulation(efficient_producers,sk1,sk2). [resolve(23,a,12,a)].
% 0.41/0.97 40 greater_or_equal(cardinality_at_time(first_movers,sk2),zero). [resolve(24,a,12,a)].
% 0.41/0.97 41 -greater_or_equal(sk2,appear(efficient_producers,sk1)) | greater(cardinality_at_time(efficient_producers,sk2),zero). [resolve(25,a,12,a)].
% 0.41/0.97 42 -greater(cardinality_at_time(first_movers,sk2),zero) | -greater(cardinality_at_time(efficient_producers,sk2),zero) | subpopulations(first_movers,efficient_producers,sk1,sk2). [resolve(27,a,12,a)].
% 0.41/0.97 44 -subpopulation(A,sk1,sk2) | -greater(cardinality_at_time(A,sk2),zero) | cardinality_at_time(first_movers,sk2) != zero | selection_favors(A,first_movers,sk2). [resolve(38,a,30,b)].
% 0.41/0.97 49 greater(cardinality_at_time(first_movers,sk2),zero) | cardinality_at_time(first_movers,sk2) = zero. [resolve(40,a,18,a)].
% 0.41/0.97 52 appear(efficient_producers,sk1) = critical_point(sk1) | greater(sk2,appear(efficient_producers,sk1)). [resolve(37,a,34,a)].
% 0.41/0.97 55 -greater(cardinality_at_time(efficient_producers,sk2),zero) | subpopulations(first_movers,efficient_producers,sk1,sk2) | cardinality_at_time(first_movers,sk2) = zero. [resolve(42,a,49,a)].
% 0.41/0.97 58 appear(efficient_producers,sk1) = critical_point(sk1) | greater_or_equal(sk2,appear(efficient_producers,sk1)). [resolve(52,b,15,a)].
% 0.41/0.97 59 appear(efficient_producers,sk1) = critical_point(sk1) | greater(cardinality_at_time(efficient_producers,sk2),zero). [resolve(58,b,41,a)].
% 0.41/0.97 64 -greater(cardinality_at_time(efficient_producers,sk2),zero) | cardinality_at_time(first_movers,sk2) != zero. [resolve(44,a,39,a),unit_del(c,14)].
% 0.41/0.97 65 cardinality_at_time(first_movers,sk2) != zero | appear(efficient_producers,sk1) = critical_point(sk1). [resolve(64,a,59,b)].
% 0.41/0.97 68 subpopulations(first_movers,efficient_producers,sk1,sk2) | cardinality_at_time(first_movers,sk2) = zero | appear(efficient_producers,sk1) = critical_point(sk1). [resolve(55,a,59,b)].
% 0.41/0.97 69 cardinality_at_time(first_movers,sk2) = zero | appear(efficient_producers,sk1) = critical_point(sk1) | critical_point(sk1) != A | -greater(sk2,A) | greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)). [resolve(68,a,29,b)].
% 0.41/0.97 70 cardinality_at_time(first_movers,sk2) = zero | appear(efficient_producers,sk1) = critical_point(sk1) | -greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)). [resolve(68,a,26,a),unit_del(d,14)].
% 0.41/0.97 71 cardinality_at_time(first_movers,sk2) = zero | appear(efficient_producers,sk1) = critical_point(sk1) | greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)). [resolve(69,d,13,a),xx(c)].
% 0.41/0.97 72 cardinality_at_time(first_movers,sk2) = zero | appear(efficient_producers,sk1) = critical_point(sk1). [resolve(71,c,70,c),merge(c),merge(d)].
% 0.41/0.97 74 cardinality_at_time(first_movers,sk2) = zero | greater(cardinality_at_time(efficient_producers,sk2),zero). [para(72(b,1),41(a,2)),unit_del(b,32)].
% 0.41/0.97 75 cardinality_at_time(first_movers,sk2) = zero | subpopulations(first_movers,efficient_producers,sk1,sk2). [resolve(74,b,55,a),merge(c)].
% 0.41/0.97 80 cardinality_at_time(first_movers,sk2) = zero | critical_point(sk1) != A | -greater(sk2,A) | greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)). [resolve(75,b,29,b)].
% 0.41/0.97 81 cardinality_at_time(first_movers,sk2) = zero | -greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)). [resolve(75,b,26,a),unit_del(c,14)].
% 0.41/0.97 82 cardinality_at_time(first_movers,sk2) = zero | greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)). [resolve(80,c,13,a),xx(b)].
% 0.41/0.97 83 cardinality_at_time(first_movers,sk2) = zero. [resolve(82,b,81,b),merge(b)].
% 0.41/0.97 85 appear(efficient_producers,sk1) = critical_point(sk1). [back_rewrite(65),rewrite([83(3)]),xx(a)].
% 0.41/0.97 86 -greater(cardinality_at_time(efficient_producers,sk2),zero). [back_rewrite(64),rewrite([83(8)]),xx(b)].
% 0.41/0.97 90 $F. [back_rewrite(41),rewrite([85(4)]),unit_del(a,32),unit_del(b,86)].
% 0.41/0.97
% 0.41/0.97 % SZS output end Refutation
% 0.41/0.97 ============================== end of proof ==========================
% 0.41/0.97
% 0.41/0.97 ============================== STATISTICS ============================
% 0.41/0.97
% 0.41/0.97 Given=69. Generated=116. Kept=76. proofs=1.
% 0.41/0.97 Usable=28. Sos=2. Demods=2. Limbo=5, Disabled=69. Hints=0.
% 0.41/0.97 Megabytes=0.12.
% 0.41/0.97 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.41/0.97
% 0.41/0.97 ============================== end of statistics =====================
% 0.41/0.97
% 0.41/0.97 ============================== end of search =========================
% 0.41/0.97
% 0.41/0.97 THEOREM PROVED
% 0.41/0.97 % SZS status Unsatisfiable
% 0.41/0.97
% 0.41/0.97 Exiting with 1 proof.
% 0.41/0.97
% 0.41/0.97 Process 13123 exit (max_proofs) Thu Jun 9 08:42:48 2022
% 0.41/0.97 Prover9 interrupted
%------------------------------------------------------------------------------