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