TSTP Solution File: MGT036+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : MGT036+3 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 : 300s
% DateTime : Sun Sep 18 05:22:05 EDT 2022
% Result : Theorem 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : MGT036+3 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n006.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 : 300
% 0.13/0.34 % DateTime : Fri Sep 2 02:46:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(outcompetes_type, type, (
% 0.20/0.39 outcompetes: ( $i * $i * $i ) > $o)).
% 0.20/0.39 tff(tptp_fun_T_0_type, type, (
% 0.20/0.39 tptp_fun_T_0: $i)).
% 0.20/0.39 tff(efficient_producers_type, type, (
% 0.20/0.39 efficient_producers: $i)).
% 0.20/0.39 tff(first_movers_type, type, (
% 0.20/0.39 first_movers: $i)).
% 0.20/0.39 tff(greater_type, type, (
% 0.20/0.39 greater: ( $i * $i ) > $o)).
% 0.20/0.39 tff(growth_rate_type, type, (
% 0.20/0.39 growth_rate: ( $i * $i ) > $i)).
% 0.20/0.39 tff(zero_type, type, (
% 0.20/0.39 zero: $i)).
% 0.20/0.39 tff(greater_or_equal_type, type, (
% 0.20/0.39 greater_or_equal: ( $i * $i ) > $o)).
% 0.20/0.39 tff(subpopulations_type, type, (
% 0.20/0.39 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.20/0.39 tff(tptp_fun_E_1_type, type, (
% 0.20/0.39 tptp_fun_E_1: $i)).
% 0.20/0.39 tff(environment_type, type, (
% 0.20/0.39 environment: $i > $o)).
% 0.20/0.39 tff(1,plain,
% 0.20/0.39 (?[E: $i, T: $i] : (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T))) <=> ?[E: $i, T: $i] : (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 (^[E: $i, T: $i] : trans(monotonicity(rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & greater_or_equal(growth_rate(first_movers, T), zero)) <=> (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(growth_rate(first_movers, T), zero))), ((((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & greater_or_equal(growth_rate(first_movers, T), zero)) & greater(zero, growth_rate(efficient_producers, T))) <=> ((environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(growth_rate(first_movers, T), zero)) & greater(zero, growth_rate(efficient_producers, T))))), rewrite(((environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(growth_rate(first_movers, T), zero)) & greater(zero, growth_rate(efficient_producers, T))) <=> (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T)))), ((((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & greater_or_equal(growth_rate(first_movers, T), zero)) & greater(zero, growth_rate(efficient_producers, T))) <=> (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 (?[E: $i, T: $i] : (((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & greater_or_equal(growth_rate(first_movers, T), zero)) & greater(zero, growth_rate(efficient_producers, T))) <=> ?[E: $i, T: $i] : (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.39 tff(4,axiom,(?[E: $i, T: $i] : (((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & greater_or_equal(growth_rate(first_movers, T), zero)) & greater(zero, growth_rate(efficient_producers, T)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a13_star')).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 (?[E: $i, T: $i] : (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.39 tff(6,plain,
% 0.20/0.39 (?[E: $i, T: $i] : (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & greater_or_equal(growth_rate(first_movers, T), zero) & greater(zero, growth_rate(efficient_producers, T)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.20/0.39 tff(7,plain,(
% 0.20/0.39 environment(E!1) & subpopulations(first_movers, efficient_producers, E!1, T!0) & greater_or_equal(growth_rate(first_movers, T!0), zero) & greater(zero, growth_rate(efficient_producers, T!0))),
% 0.20/0.39 inference(skolemize,[status(sab)],[6])).
% 0.20/0.39 tff(8,plain,
% 0.20/0.39 (greater(zero, growth_rate(efficient_producers, T!0))),
% 0.20/0.39 inference(and_elim,[status(thm)],[7])).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 (greater_or_equal(growth_rate(first_movers, T!0), zero)),
% 0.20/0.39 inference(and_elim,[status(thm)],[7])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 ((~((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))) | (~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(11,plain,
% 0.20/0.39 (~((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[10, 9, 8])).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 (^[E: $i, T: $i] : refl(((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 (![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 (^[E: $i, T: $i] : trans(monotonicity(rewrite((environment(E) & subpopulations(first_movers, efficient_producers, E, T) & outcompetes(first_movers, efficient_producers, T)) <=> (~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T))))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & outcompetes(first_movers, efficient_producers, T))) <=> (~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T))))))), rewrite((~(~((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T))))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T)))), ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & outcompetes(first_movers, efficient_producers, T))) <=> ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(15,plain,
% 0.20/0.39 (![E: $i, T: $i] : (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & outcompetes(first_movers, efficient_producers, T))) <=> ![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.39 tff(16,plain,
% 0.20/0.39 ((~?[E: $i, T: $i] : (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & outcompetes(first_movers, efficient_producers, T))) <=> (~?[E: $i, T: $i] : (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & outcompetes(first_movers, efficient_producers, T)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 ((~?[E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & outcompetes(first_movers, efficient_producers, T))) <=> (~?[E: $i, T: $i] : (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & outcompetes(first_movers, efficient_producers, T)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(18,axiom,(~?[E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) & outcompetes(first_movers, efficient_producers, T))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_t5_star')).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 (~?[E: $i, T: $i] : (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & outcompetes(first_movers, efficient_producers, T))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 (~?[E: $i, T: $i] : (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & outcompetes(first_movers, efficient_producers, T))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[19, 16])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 (~?[E: $i, T: $i] : (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & outcompetes(first_movers, efficient_producers, T))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 (~?[E: $i, T: $i] : (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & outcompetes(first_movers, efficient_producers, T))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[21, 16])).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 (~?[E: $i, T: $i] : (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & outcompetes(first_movers, efficient_producers, T))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[22, 16])).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 (~?[E: $i, T: $i] : (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & outcompetes(first_movers, efficient_producers, T))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 (~?[E: $i, T: $i] : (environment(E) & subpopulations(first_movers, efficient_producers, E, T) & outcompetes(first_movers, efficient_producers, T))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[24, 16])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 (^[E: $i, T: $i] : refl($oeq((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & outcompetes(first_movers, efficient_producers, T))), (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & outcompetes(first_movers, efficient_producers, T)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(27,plain,(
% 0.20/0.39 ![E: $i, T: $i] : (~(environment(E) & subpopulations(first_movers, efficient_producers, E, T) & outcompetes(first_movers, efficient_producers, T)))),
% 0.20/0.39 inference(nnf-neg,[status(sab)],[25, 26])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 (![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[27, 15])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 (![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[28, 13])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 (subpopulations(first_movers, efficient_producers, E!1, T!0)),
% 0.20/0.39 inference(and_elim,[status(thm)],[7])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 (environment(E!1)),
% 0.20/0.39 inference(and_elim,[status(thm)],[7])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 (((~![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~outcompetes(first_movers, efficient_producers, T!0)))) <=> ((~![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~outcompetes(first_movers, efficient_producers, T!0)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 ((~![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~outcompetes(first_movers, efficient_producers, T!0)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 ((~![E: $i, T: $i] : ((~environment(E)) | (~subpopulations(first_movers, efficient_producers, E, T)) | (~outcompetes(first_movers, efficient_producers, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~outcompetes(first_movers, efficient_producers, T!0))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 (~outcompetes(first_movers, efficient_producers, T!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[34, 31, 30, 29])).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 ((~((~((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))) <=> outcompetes(first_movers, efficient_producers, T!0))) | ((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0)))) | outcompetes(first_movers, efficient_producers, T!0)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(37,plain,
% 0.20/0.39 (~((~((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))) <=> outcompetes(first_movers, efficient_producers, T!0))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[36, 35, 11])).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 (^[E: $i, S1: $i, S2: $i, T: $i] : refl((subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T))) <=> (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 (![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 (^[E: $i, S1: $i, S2: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(S1, S2, E, T)) <=> (~((~environment(E)) | (~subpopulations(S1, S2, E, T))))), ((~(environment(E) & subpopulations(S1, S2, E, T))) <=> (~(~((~environment(E)) | (~subpopulations(S1, S2, E, T))))))), rewrite((~(~((~environment(E)) | (~subpopulations(S1, S2, E, T))))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)))), ((~(environment(E) & subpopulations(S1, S2, E, T))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T))))), (((~(environment(E) & subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T)) <=> (((~environment(E)) | (~subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T)))), rewrite((((~environment(E)) | (~subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T)) <=> (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))), (((~(environment(E) & subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T)) <=> (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T)) <=> ![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T)) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 (^[E: $i, S1: $i, S2: $i, T: $i] : rewrite(((environment(E) & subpopulations(S1, S2, E, T)) => subpopulations(S2, S1, E, T)) <=> ((~(environment(E) & subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 (![E: $i, S1: $i, S2: $i, T: $i] : ((environment(E) & subpopulations(S1, S2, E, T)) => subpopulations(S2, S1, E, T)) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[43])).
% 0.20/0.39 tff(45,axiom,(![E: $i, S1: $i, S2: $i, T: $i] : ((environment(E) & subpopulations(S1, S2, E, T)) => subpopulations(S2, S1, E, T))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_symmetry_of_subpopulations')).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.20/0.40 tff(48,plain,(
% 0.20/0.40 ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | subpopulations(S2, S1, E, T))),
% 0.20/0.40 inference(skolemize,[status(sab)],[47])).
% 0.20/0.40 tff(49,plain,
% 0.20/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.20/0.40 tff(50,plain,
% 0.20/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[49, 39])).
% 0.20/0.40 tff(51,plain,
% 0.20/0.40 (((~![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(52,plain,
% 0.20/0.40 ((subpopulations(efficient_producers, first_movers, E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0))) <=> ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(53,plain,
% 0.20/0.40 (((~![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))) | (subpopulations(efficient_producers, first_movers, E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[52])).
% 0.20/0.40 tff(54,plain,
% 0.20/0.40 (((~![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))) | (subpopulations(efficient_producers, first_movers, E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0))),
% 0.20/0.40 inference(transitivity,[status(thm)],[53, 51])).
% 0.20/0.40 tff(55,plain,
% 0.20/0.40 ((~![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))) | (subpopulations(efficient_producers, first_movers, E!1, T!0) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(56,plain,
% 0.20/0.40 ((~![E: $i, S1: $i, S2: $i, T: $i] : (subpopulations(S2, S1, E, T) | (~environment(E)) | (~subpopulations(S1, S2, E, T)))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | subpopulations(efficient_producers, first_movers, E!1, T!0)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.20/0.40 tff(57,plain,
% 0.20/0.40 (subpopulations(efficient_producers, first_movers, E!1, T!0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[56, 50, 31, 30])).
% 0.20/0.40 tff(58,plain,
% 0.20/0.40 (^[E: $i, S1: $i, S2: $i, T: $i] : refl(((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.40 tff(60,plain,
% 0.20/0.40 (^[E: $i, S1: $i, S2: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(S1, S2, E, T)) <=> (~((~environment(E)) | (~subpopulations(S1, S2, E, T))))), ((~(environment(E) & subpopulations(S1, S2, E, T))) <=> (~(~((~environment(E)) | (~subpopulations(S1, S2, E, T))))))), rewrite((~(~((~environment(E)) | (~subpopulations(S1, S2, E, T))))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)))), ((~(environment(E) & subpopulations(S1, S2, E, T))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T))))), rewrite(((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)) <=> ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T))), (((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))) <=> (((~environment(E)) | (~subpopulations(S1, S2, E, T))) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T))))), rewrite((((~environment(E)) | (~subpopulations(S1, S2, E, T))) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))), (((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[60])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(63,plain,
% 0.20/0.40 (^[E: $i, S1: $i, S2: $i, T: $i] : rewrite(((environment(E) & subpopulations(S1, S2, E, T)) => ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))) <=> ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((environment(E) & subpopulations(S1, S2, E, T)) => ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[63])).
% 0.20/0.40 tff(65,axiom,(![E: $i, S1: $i, S2: $i, T: $i] : ((environment(E) & subpopulations(S1, S2, E, T)) => ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2')).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.20/0.40 tff(68,plain,(
% 0.20/0.40 ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T))) | ((greater_or_equal(growth_rate(S2, T), zero) & greater(zero, growth_rate(S1, T))) <=> outcompetes(S2, S1, T)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[67])).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[69, 59])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 (((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))) | ((~environment(E!1)) | (~subpopulations(efficient_producers, first_movers, E!1, T!0)) | ((~((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))) <=> outcompetes(first_movers, efficient_producers, T!0)))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))) | (~environment(E!1)) | (~subpopulations(efficient_producers, first_movers, E!1, T!0)) | ((~((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))) <=> outcompetes(first_movers, efficient_producers, T!0)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))) | ((~environment(E!1)) | (~subpopulations(efficient_producers, first_movers, E!1, T!0)) | ((~((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))) <=> outcompetes(first_movers, efficient_producers, T!0)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | ((~((~greater_or_equal(growth_rate(S2, T), zero)) | (~greater(zero, growth_rate(S1, T))))) <=> outcompetes(S2, S1, T)))) | (~environment(E!1)) | (~subpopulations(efficient_producers, first_movers, E!1, T!0)) | ((~((~greater_or_equal(growth_rate(first_movers, T!0), zero)) | (~greater(zero, growth_rate(efficient_producers, T!0))))) <=> outcompetes(first_movers, efficient_producers, T!0))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[73, 70, 31, 57, 37])).
% 0.20/0.40 % SZS output end Proof
%------------------------------------------------------------------------------