TSTP Solution File: MGT032+2 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : MGT032+2 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n027.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 22:22:57 EDT 2022

% Result   : Theorem 0.41s 0.97s
% Output   : Refutation 0.41s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : MGT032+2 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.12  % Command  : tptp2X_and_run_prover9 %d %s
% 0.12/0.33  % Computer : n027.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 12:16:27 EDT 2022
% 0.18/0.33  % CPUTime  : 
% 0.41/0.96  ============================== Prover9 ===============================
% 0.41/0.96  Prover9 (32) version 2009-11A, November 2009.
% 0.41/0.96  Process 10221 was started by sandbox2 on n027.cluster.edu,
% 0.41/0.96  Thu Jun  9 12:16:28 2022
% 0.41/0.96  The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_10067_n027.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_10067_n027.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).
% 0.41/0.97      % 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 (3 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  1 (all E all S1 all S2 all T (environment(E) & subpopulations(S1,S2,E,T) & greater(growth_rate(S2,T),growth_rate(S1,T)) -> selection_favors(S2,S1,T))) # label(mp1_high_growth_rates) # label(axiom) # label(non_clause).  [assumption].
% 0.41/0.97  2 (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].
% 0.41/0.97  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) -> selection_favors(efficient_producers,first_movers,T))))))) # label(prove_t1) # label(negated_conjecture) # label(non_clause).  [assumption].
% 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  4 -environment(A) | -stable(A) | in_environment(A,f1(A)) # label(l1) # label(hypothesis).  [clausify(2)].
% 0.41/0.97  5 environment(c1) # label(prove_t1) # label(negated_conjecture).  [clausify(3)].
% 0.41/0.97  Derived: -stable(c1) | in_environment(c1,f1(c1)).  [resolve(4,a,5,a)].
% 0.41/0.97  6 -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) # label(axiom).  [clausify(1)].
% 0.41/0.97  Derived: -subpopulations(A,B,c1,C) | -greater(growth_rate(B,C),growth_rate(A,C)) | selection_favors(B,A,C).  [resolve(6,a,5,a)].
% 0.41/0.97  7 -environment(A) | -stable(A) | -subpopulations(first_movers,efficient_producers,A,B) | -greater_or_equal(B,f1(A)) | greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)) # label(l1) # label(hypothesis).  [clausify(2)].
% 0.41/0.97  Derived: -stable(c1) | -subpopulations(first_movers,efficient_producers,c1,A) | -greater_or_equal(A,f1(c1)) | greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)).  [resolve(7,a,5,a)].
% 0.41/0.97  8 -stable(c1) | in_environment(c1,f1(c1)).  [resolve(4,a,5,a)].
% 0.41/0.97  9 stable(c1) # label(prove_t1) # label(negated_conjecture).  [clausify(3)].
% 0.41/0.97  Derived: in_environment(c1,f1(c1)).  [resolve(8,a,9,a)].
% 0.41/0.97  10 -stable(c1) | -subpopulations(first_movers,efficient_producers,c1,A) | -greater_or_equal(A,f1(c1)) | greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)).  [resolve(7,a,5,a)].
% 0.41/0.97  Derived: -subpopulations(first_movers,efficient_producers,c1,A) | -greater_or_equal(A,f1(c1)) | greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)).  [resolve(10,a,9,a)].
% 0.41/0.97  11 in_environment(c1,f1(c1)).  [resolve(8,a,9,a)].
% 0.41/0.97  12 -in_environment(c1,A) | -selection_favors(efficient_producers,first_movers,f2(A)) # label(prove_t1) # label(negated_conjecture).  [clausify(3)].
% 0.41/0.97  13 -in_environment(c1,A) | greater_or_equal(f2(A),A) # label(prove_t1) # label(negated_conjecture).  [clausify(3)].
% 0.41/0.97  14 -in_environment(c1,A) | subpopulations(first_movers,efficient_producers,c1,f2(A)) # label(prove_t1) # label(negated_conjecture).  [clausify(3)].
% 0.41/0.97  Derived: -selection_favors(efficient_producers,first_movers,f2(f1(c1))).  [resolve(11,a,12,a)].
% 0.41/0.97  Derived: greater_or_equal(f2(f1(c1)),f1(c1)).  [resolve(11,a,13,a)].
% 0.41/0.97  Derived: subpopulations(first_movers,efficient_producers,c1,f2(f1(c1))).  [resolve(11,a,14,a)].
% 0.41/0.97  15 subpopulations(first_movers,efficient_producers,c1,f2(f1(c1))).  [resolve(11,a,14,a)].
% 0.41/0.97  16 -subpopulations(A,B,c1,C) | -greater(growth_rate(B,C),growth_rate(A,C)) | selection_favors(B,A,C).  [resolve(6,a,5,a)].
% 0.41/0.97  17 -subpopulations(first_movers,efficient_producers,c1,A) | -greater_or_equal(A,f1(c1)) | greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)).  [resolve(10,a,9,a)].
% 0.41/0.97  Derived: -greater(growth_rate(efficient_producers,f2(f1(c1))),growth_rate(first_movers,f2(f1(c1)))) | selection_favors(efficient_producers,first_movers,f2(f1(c1))).  [resolve(15,a,16,a)].
% 0.41/0.97  Derived: -greater_or_equal(f2(f1(c1)),f1(c1)) | greater(growth_rate(efficient_producers,f2(f1(c1))),growth_rate(first_movers,f2(f1(c1)))).  [resolve(15,a,17,a)].
% 0.41/0.97  18 -greater(growth_rate(efficient_producers,f2(f1(c1))),growth_rate(first_movers,f2(f1(c1)))) | selection_favors(efficient_producers,first_movers,f2(f1(c1))).  [resolve(15,a,16,a)].
% 0.41/0.97  19 -selection_favors(efficient_producers,first_movers,f2(f1(c1))).  [resolve(11,a,12,a)].
% 0.41/0.97  Derived: -greater(growth_rate(efficient_producers,f2(f1(c1))),growth_rate(first_movers,f2(f1(c1)))).  [resolve(18,b,19,a)].
% 0.41/0.97  20 -greater_or_equal(f2(f1(c1)),f1(c1)) | greater(growth_rate(efficient_producers,f2(f1(c1))),growth_rate(first_movers,f2(f1(c1)))).  [resolve(15,a,17,a)].
% 0.41/0.97  21 greater_or_equal(f2(f1(c1)),f1(c1)).  [resolve(11,a,13,a)].
% 0.41/0.97  Derived: greater(growth_rate(efficient_producers,f2(f1(c1))),growth_rate(first_movers,f2(f1(c1)))).  [resolve(20,a,21,a)].
% 0.41/0.97  22 greater(growth_rate(efficient_producers,f2(f1(c1))),growth_rate(first_movers,f2(f1(c1)))).  [resolve(20,a,21,a)].
% 0.41/0.97  23 -greater(growth_rate(efficient_producers,f2(f1(c1))),growth_rate(first_movers,f2(f1(c1)))).  [resolve(18,b,19,a)].
% 0.41/0.97  Derived: $F.  [resolve(22,a,23,a)].
% 0.41/0.97  
% 0.41/0.97  ============================== end predicate elimination =============
% 0.41/0.97  
% 0.41/0.97  Auto_denials:  (no changes).
% 0.41/0.97  
% 0.41/0.97  Term ordering decisions:
% 0.41/0.97  Function symbol KB weights: 
% 0.41/0.97  
% 0.41/0.97  ============================== PROOF =================================
% 0.41/0.97  % SZS status Theorem
% 0.41/0.97  % SZS output start Refutation
% 0.41/0.97  
% 0.41/0.97  % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.41/0.97  % Length of proof is 24.
% 0.41/0.97  % Level of proof is 7.
% 0.41/0.97  % Maximum clause weight is 0.000.
% 0.41/0.97  % Given clauses 0.
% 0.41/0.97  
% 0.41/0.97  1 (all E all S1 all S2 all T (environment(E) & subpopulations(S1,S2,E,T) & greater(growth_rate(S2,T),growth_rate(S1,T)) -> selection_favors(S2,S1,T))) # label(mp1_high_growth_rates) # label(axiom) # label(non_clause).  [assumption].
% 0.41/0.97  2 (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].
% 0.41/0.97  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) -> selection_favors(efficient_producers,first_movers,T))))))) # label(prove_t1) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.41/0.97  4 -environment(A) | -stable(A) | in_environment(A,f1(A)) # label(l1) # label(hypothesis).  [clausify(2)].
% 0.41/0.97  5 environment(c1) # label(prove_t1) # label(negated_conjecture).  [clausify(3)].
% 0.41/0.97  6 -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) # label(axiom).  [clausify(1)].
% 0.41/0.97  7 -environment(A) | -stable(A) | -subpopulations(first_movers,efficient_producers,A,B) | -greater_or_equal(B,f1(A)) | greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)) # label(l1) # label(hypothesis).  [clausify(2)].
% 0.41/0.97  8 -stable(c1) | in_environment(c1,f1(c1)).  [resolve(4,a,5,a)].
% 0.41/0.97  9 stable(c1) # label(prove_t1) # label(negated_conjecture).  [clausify(3)].
% 0.41/0.97  10 -stable(c1) | -subpopulations(first_movers,efficient_producers,c1,A) | -greater_or_equal(A,f1(c1)) | greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)).  [resolve(7,a,5,a)].
% 0.41/0.97  11 in_environment(c1,f1(c1)).  [resolve(8,a,9,a)].
% 0.41/0.97  12 -in_environment(c1,A) | -selection_favors(efficient_producers,first_movers,f2(A)) # label(prove_t1) # label(negated_conjecture).  [clausify(3)].
% 0.41/0.97  13 -in_environment(c1,A) | greater_or_equal(f2(A),A) # label(prove_t1) # label(negated_conjecture).  [clausify(3)].
% 0.41/0.97  14 -in_environment(c1,A) | subpopulations(first_movers,efficient_producers,c1,f2(A)) # label(prove_t1) # label(negated_conjecture).  [clausify(3)].
% 0.41/0.97  15 subpopulations(first_movers,efficient_producers,c1,f2(f1(c1))).  [resolve(11,a,14,a)].
% 0.41/0.97  16 -subpopulations(A,B,c1,C) | -greater(growth_rate(B,C),growth_rate(A,C)) | selection_favors(B,A,C).  [resolve(6,a,5,a)].
% 0.41/0.97  17 -subpopulations(first_movers,efficient_producers,c1,A) | -greater_or_equal(A,f1(c1)) | greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A)).  [resolve(10,a,9,a)].
% 0.41/0.97  18 -greater(growth_rate(efficient_producers,f2(f1(c1))),growth_rate(first_movers,f2(f1(c1)))) | selection_favors(efficient_producers,first_movers,f2(f1(c1))).  [resolve(15,a,16,a)].
% 0.41/0.97  19 -selection_favors(efficient_producers,first_movers,f2(f1(c1))).  [resolve(11,a,12,a)].
% 0.41/0.97  20 -greater_or_equal(f2(f1(c1)),f1(c1)) | greater(growth_rate(efficient_producers,f2(f1(c1))),growth_rate(first_movers,f2(f1(c1)))).  [resolve(15,a,17,a)].
% 0.41/0.97  21 greater_or_equal(f2(f1(c1)),f1(c1)).  [resolve(11,a,13,a)].
% 0.41/0.97  22 greater(growth_rate(efficient_producers,f2(f1(c1))),growth_rate(first_movers,f2(f1(c1)))).  [resolve(20,a,21,a)].
% 0.41/0.97  23 -greater(growth_rate(efficient_producers,f2(f1(c1))),growth_rate(first_movers,f2(f1(c1)))).  [resolve(18,b,19,a)].
% 0.41/0.97  24 $F.  [resolve(22,a,23,a)].
% 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=0. Generated=1. Kept=0. proofs=1.
% 0.41/0.97  Usable=0. Sos=0. Demods=0. Limbo=0, Disabled=21. Hints=0.
% 0.41/0.97  Megabytes=0.03.
% 0.41/0.97  User_CPU=0.01, 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 Theorem
% 0.41/0.97  
% 0.41/0.97  Exiting with 1 proof.
% 0.41/0.97  
% 0.41/0.97  Process 10221 exit (max_proofs) Thu Jun  9 12:16:28 2022
% 0.41/0.97  Prover9 interrupted
%------------------------------------------------------------------------------