%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT022+2 : TPTP v9.3.0. Released v2.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 8 06:23:59 AM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT022+2 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.07/0.34 % Computer : n002.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 7 12:07:53 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(constant_type, type, (
% 0.13/0.39 constant: $i > $o)).
% 0.13/0.39 tff(difference_type, type, (
% 0.13/0.39 difference: ( $i * $i ) > $i)).
% 0.13/0.39 tff(disbanding_rate_type, type, (
% 0.13/0.39 disbanding_rate: ( $i * $i ) > $i)).
% 0.13/0.39 tff(tptp_fun_T_0_type, type, (
% 0.13/0.39 tptp_fun_T_0: $i)).
% 0.13/0.39 tff(efficient_producers_type, type, (
% 0.13/0.39 efficient_producers: $i)).
% 0.13/0.39 tff(first_movers_type, type, (
% 0.13/0.39 first_movers: $i)).
% 0.13/0.39 tff(resources_type, type, (
% 0.13/0.39 resources: ( $i * $i ) > $i)).
% 0.13/0.39 tff(tptp_fun_E_1_type, type, (
% 0.13/0.39 tptp_fun_E_1: $i)).
% 0.13/0.39 tff(decreases_type, type, (
% 0.13/0.39 decreases: $i > $o)).
% 0.13/0.39 tff(increases_type, type, (
% 0.13/0.39 increases: $i > $o)).
% 0.13/0.39 tff(subpopulations_type, type, (
% 0.13/0.39 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.13/0.39 tff(environment_type, type, (
% 0.13/0.39 environment: $i > $o)).
% 0.13/0.39 tff(greater_type, type, (
% 0.13/0.39 greater: ( $i * $i ) > $o)).
% 0.13/0.39 tff(resilience_type, type, (
% 0.13/0.39 resilience: $i > $i)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 ((~![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | ((increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T)))) & ((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))) <=> (~![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | ((increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T)))) & ((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 ((~![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => ((decreases(resources(E, T)) => increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) & (constant(resources(E, T)) => (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))) <=> (~![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | ((increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T)))) & ((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(3,axiom,(~![E: $i, T: $i] : ((environment(E) & subpopulations(first_movers, efficient_producers, E, T)) => ((decreases(resources(E, T)) => increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))) & (constant(resources(E, T)) => (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_l4')).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (~![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | ((increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T)))) & ((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (~![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | ((increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T)))) & ((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (~![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | ((increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T)))) & ((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 (~![E: $i, T: $i] : ((~(environment(E) & subpopulations(first_movers, efficient_producers, E, T))) | ((increases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T))) | (~decreases(resources(E, T)))) & ((~constant(resources(E, T))) | (~decreases(difference(disbanding_rate(first_movers, T), disbanding_rate(efficient_producers, T)))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.13/0.40 tff(8,plain,(
% 0.13/0.40 ~((~(environment(E!1) & subpopulations(first_movers, efficient_producers, E!1, T!0))) | ((increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~decreases(resources(E!1, T!0)))) & ((~constant(resources(E!1, T!0))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[7])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (environment(E!1) & subpopulations(first_movers, efficient_producers, E!1, T!0)),
% 0.13/0.40 inference(or_elim,[status(thm)],[8])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 (subpopulations(first_movers, efficient_producers, E!1, T!0)),
% 0.13/0.40 inference(and_elim,[status(thm)],[9])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 (environment(E!1)),
% 0.13/0.40 inference(and_elim,[status(thm)],[9])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (greater(resilience(efficient_producers), resilience(first_movers)) <=> greater(resilience(efficient_producers), resilience(first_movers))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(13,axiom,(greater(resilience(efficient_producers), resilience(first_movers))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a2')).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 (greater(resilience(efficient_producers), resilience(first_movers))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (^[E: $i, S1: $i, S2: $i, T: $i] : refl(((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(resilience(S2), resilience(S1))) | (~((~(increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~decreases(resources(E, T))))) | (~(constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~constant(resources(E, T)))))))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(resilience(S2), resilience(S1))) | (~((~(increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~decreases(resources(E, T))))) | (~(constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~constant(resources(E, T)))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(resilience(S2), resilience(S1))) | (~((~(increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~decreases(resources(E, T))))) | (~(constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~constant(resources(E, T)))))))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(resilience(S2), resilience(S1))) | (~((~(increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~decreases(resources(E, T))))) | (~(constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~constant(resources(E, T))))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[15])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 (^[E: $i, S1: $i, S2: $i, T: $i] : trans(monotonicity(trans(monotonicity(rewrite((environment(E) & subpopulations(S1, S2, E, T) & greater(resilience(S2), resilience(S1))) <=> (~((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(resilience(S2), resilience(S1)))))), ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(resilience(S2), resilience(S1)))) <=> (~(~((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(resilience(S2), resilience(S1)))))))), rewrite((~(~((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(resilience(S2), resilience(S1)))))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(resilience(S2), resilience(S1))))), ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(resilience(S2), resilience(S1)))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(resilience(S2), resilience(S1)))))), rewrite(((increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~decreases(resources(E, T)))) & (constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~constant(resources(E, T))))) <=> (~((~(increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~decreases(resources(E, T))))) | (~(constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~constant(resources(E, T)))))))), (((~(environment(E) & subpopulations(S1, S2, E, T) & greater(resilience(S2), resilience(S1)))) | ((increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~decreases(resources(E, T)))) & (constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~constant(resources(E, T)))))) <=> (((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(resilience(S2), resilience(S1)))) | (~((~(increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~decreases(resources(E, T))))) | (~(constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~constant(resources(E, T)))))))))), rewrite((((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(resilience(S2), resilience(S1)))) | (~((~(increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~decreases(resources(E, T))))) | (~(constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~constant(resources(E, T)))))))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(resilience(S2), resilience(S1))) | (~((~(increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~decreases(resources(E, T))))) | (~(constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~constant(resources(E, T))))))))), (((~(environment(E) & subpopulations(S1, S2, E, T) & greater(resilience(S2), resilience(S1)))) | ((increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~decreases(resources(E, T)))) & (constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~constant(resources(E, T)))))) <=> ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(resilience(S2), resilience(S1))) | (~((~(increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~decreases(resources(E, T))))) | (~(constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~constant(resources(E, T))))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(resilience(S2), resilience(S1)))) | ((increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~decreases(resources(E, T)))) & (constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~constant(resources(E, T)))))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(resilience(S2), resilience(S1))) | (~((~(increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~decreases(resources(E, T))))) | (~(constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~constant(resources(E, T))))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[17])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(resilience(S2), resilience(S1)))) | ((increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~decreases(resources(E, T)))) & (constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~constant(resources(E, T)))))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(resilience(S2), resilience(S1)))) | ((increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~decreases(resources(E, T)))) & (constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~constant(resources(E, T))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 (^[E: $i, S1: $i, S2: $i, T: $i] : trans(monotonicity(rewrite(((environment(E) & subpopulations(S1, S2, E, T)) & greater(resilience(S2), resilience(S1))) <=> (environment(E) & subpopulations(S1, S2, E, T) & greater(resilience(S2), resilience(S1)))), rewrite(((decreases(resources(E, T)) => increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T)))) & (constant(resources(E, T)) => constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))))) <=> ((increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~decreases(resources(E, T)))) & (constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~constant(resources(E, T)))))), ((((environment(E) & subpopulations(S1, S2, E, T)) & greater(resilience(S2), resilience(S1))) => ((decreases(resources(E, T)) => increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T)))) & (constant(resources(E, T)) => constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T)))))) <=> ((environment(E) & subpopulations(S1, S2, E, T) & greater(resilience(S2), resilience(S1))) => ((increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~decreases(resources(E, T)))) & (constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~constant(resources(E, T)))))))), rewrite(((environment(E) & subpopulations(S1, S2, E, T) & greater(resilience(S2), resilience(S1))) => ((increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~decreases(resources(E, T)))) & (constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~constant(resources(E, T)))))) <=> ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(resilience(S2), resilience(S1)))) | ((increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~decreases(resources(E, T)))) & (constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~constant(resources(E, T))))))), ((((environment(E) & subpopulations(S1, S2, E, T)) & greater(resilience(S2), resilience(S1))) => ((decreases(resources(E, T)) => increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T)))) & (constant(resources(E, T)) => constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T)))))) <=> ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(resilience(S2), resilience(S1)))) | ((increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~decreases(resources(E, T)))) & (constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~constant(resources(E, T))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : (((environment(E) & subpopulations(S1, S2, E, T)) & greater(resilience(S2), resilience(S1))) => ((decreases(resources(E, T)) => increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T)))) & (constant(resources(E, T)) => constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T)))))) <=> ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(resilience(S2), resilience(S1)))) | ((increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~decreases(resources(E, T)))) & (constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~constant(resources(E, T))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[20])).
% 0.13/0.40 tff(22,axiom,(![E: $i, S1: $i, S2: $i, T: $i] : (((environment(E) & subpopulations(S1, S2, E, T)) & greater(resilience(S2), resilience(S1))) => ((decreases(resources(E, T)) => increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T)))) & (constant(resources(E, T)) => constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a6')).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(resilience(S2), resilience(S1)))) | ((increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~decreases(resources(E, T)))) & (constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~constant(resources(E, T))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(resilience(S2), resilience(S1)))) | ((increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~decreases(resources(E, T)))) & (constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~constant(resources(E, T))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.13/0.40 tff(25,plain,(
% 0.13/0.40 ![E: $i, S1: $i, S2: $i, T: $i] : ((~(environment(E) & subpopulations(S1, S2, E, T) & greater(resilience(S2), resilience(S1)))) | ((increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~decreases(resources(E, T)))) & (constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~constant(resources(E, T))))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[24])).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(resilience(S2), resilience(S1))) | (~((~(increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~decreases(resources(E, T))))) | (~(constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~constant(resources(E, T))))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.13/0.40 tff(27,plain,
% 0.13/0.40 (![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(resilience(S2), resilience(S1))) | (~((~(increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~decreases(resources(E, T))))) | (~(constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~constant(resources(E, T))))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 (((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(resilience(S2), resilience(S1))) | (~((~(increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~decreases(resources(E, T))))) | (~(constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~constant(resources(E, T))))))))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~greater(resilience(efficient_producers), resilience(first_movers))) | (~((~(increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~decreases(resources(E!1, T!0))))) | (~(constant(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~constant(resources(E!1, T!0))))))))) <=> ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(resilience(S2), resilience(S1))) | (~((~(increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~decreases(resources(E, T))))) | (~(constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~constant(resources(E, T))))))))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~greater(resilience(efficient_producers), resilience(first_movers))) | (~((~(increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~decreases(resources(E!1, T!0))))) | (~(constant(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~constant(resources(E!1, T!0))))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(resilience(S2), resilience(S1))) | (~((~(increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~decreases(resources(E, T))))) | (~(constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~constant(resources(E, T))))))))) | ((~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~greater(resilience(efficient_producers), resilience(first_movers))) | (~((~(increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~decreases(resources(E!1, T!0))))) | (~(constant(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~constant(resources(E!1, T!0))))))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 ((~![E: $i, S1: $i, S2: $i, T: $i] : ((~environment(E)) | (~subpopulations(S1, S2, E, T)) | (~greater(resilience(S2), resilience(S1))) | (~((~(increases(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~decreases(resources(E, T))))) | (~(constant(difference(disbanding_rate(S1, T), disbanding_rate(S2, T))) | (~constant(resources(E, T))))))))) | (~environment(E!1)) | (~subpopulations(first_movers, efficient_producers, E!1, T!0)) | (~greater(resilience(efficient_producers), resilience(first_movers))) | (~((~(increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~decreases(resources(E!1, T!0))))) | (~(constant(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~constant(resources(E!1, T!0)))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 (~((~(increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~decreases(resources(E!1, T!0))))) | (~(constant(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~constant(resources(E!1, T!0))))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[30, 27, 14, 11, 10])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 (((~(increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~decreases(resources(E!1, T!0))))) | (~(constant(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~constant(resources(E!1, T!0)))))) | (constant(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~constant(resources(E!1, T!0))))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 (constant(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~constant(resources(E!1, T!0)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.13/0.40 tff(34,plain,
% 0.13/0.40 (((~(increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~decreases(resources(E!1, T!0))))) | (~(constant(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~constant(resources(E!1, T!0)))))) | (increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~decreases(resources(E!1, T!0))))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 (increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~decreases(resources(E!1, T!0)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[34, 31])).
% 0.13/0.40 tff(36,plain,
% 0.13/0.40 ((~(~((~(increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~decreases(resources(E!1, T!0))))) | (~((~constant(resources(E!1, T!0))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))))))))) <=> ((~(increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~decreases(resources(E!1, T!0))))) | (~((~constant(resources(E!1, T!0))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 (((increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~decreases(resources(E!1, T!0)))) & ((~constant(resources(E!1, T!0))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))))) <=> (~((~(increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~decreases(resources(E!1, T!0))))) | (~((~constant(resources(E!1, T!0))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(38,plain,
% 0.13/0.40 ((~((increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~decreases(resources(E!1, T!0)))) & ((~constant(resources(E!1, T!0))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))))))) <=> (~(~((~(increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~decreases(resources(E!1, T!0))))) | (~((~constant(resources(E!1, T!0))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))))))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[37])).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 ((~((increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~decreases(resources(E!1, T!0)))) & ((~constant(resources(E!1, T!0))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))))))) <=> ((~(increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~decreases(resources(E!1, T!0))))) | (~((~constant(resources(E!1, T!0))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[38, 36])).
% 0.13/0.40 tff(40,plain,
% 0.13/0.40 (~((increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~decreases(resources(E!1, T!0)))) & ((~constant(resources(E!1, T!0))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))))))),
% 0.13/0.40 inference(or_elim,[status(thm)],[8])).
% 0.13/0.40 tff(41,plain,
% 0.13/0.40 ((~(increases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~decreases(resources(E!1, T!0))))) | (~((~constant(resources(E!1, T!0))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.13/0.40 tff(42,plain,
% 0.13/0.40 (~((~constant(resources(E!1, T!0))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[41, 35])).
% 0.13/0.40 tff(43,plain,
% 0.13/0.40 (((~constant(resources(E!1, T!0))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))))) | constant(resources(E!1, T!0))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(44,plain,
% 0.13/0.40 (constant(resources(E!1, T!0))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.13/0.40 tff(45,plain,
% 0.13/0.40 ((~(constant(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~constant(resources(E!1, T!0))))) | constant(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))) | (~constant(resources(E!1, T!0)))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(46,plain,
% 0.13/0.40 (constant(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[45, 44, 33])).
% 0.13/0.40 tff(47,plain,
% 0.13/0.40 (((~constant(resources(E!1, T!0))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))))) | decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(48,plain,
% 0.13/0.40 (decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[47, 42])).
% 0.13/0.40 tff(49,plain,
% 0.13/0.40 (^[X: $i] : refl(((~constant(X)) | (~decreases(X))) <=> ((~constant(X)) | (~decreases(X))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(50,plain,
% 0.13/0.40 (![X: $i] : ((~constant(X)) | (~decreases(X))) <=> ![X: $i] : ((~constant(X)) | (~decreases(X)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[49])).
% 0.13/0.40 tff(51,plain,
% 0.13/0.40 (![X: $i] : ((~constant(X)) | (~decreases(X))) <=> ![X: $i] : ((~constant(X)) | (~decreases(X)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(52,plain,
% 0.13/0.41 (^[X: $i] : rewrite((constant(X) => (~decreases(X))) <=> ((~constant(X)) | (~decreases(X))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(53,plain,
% 0.13/0.41 (![X: $i] : (constant(X) => (~decreases(X))) <=> ![X: $i] : ((~constant(X)) | (~decreases(X)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[52])).
% 0.13/0.41 tff(54,axiom,(![X: $i] : (constant(X) => (~decreases(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mp_constant_not_decrease')).
% 0.13/0.41 tff(55,plain,
% 0.13/0.41 (![X: $i] : ((~constant(X)) | (~decreases(X)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.13/0.41 tff(56,plain,
% 0.13/0.41 (![X: $i] : ((~constant(X)) | (~decreases(X)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.13/0.41 tff(57,plain,(
% 0.13/0.41 ![X: $i] : ((~constant(X)) | (~decreases(X)))),
% 0.13/0.41 inference(skolemize,[status(sab)],[56])).
% 0.13/0.41 tff(58,plain,
% 0.13/0.41 (![X: $i] : ((~constant(X)) | (~decreases(X)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.13/0.41 tff(59,plain,
% 0.13/0.41 (((~![X: $i] : ((~constant(X)) | (~decreases(X)))) | ((~constant(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))))) <=> ((~![X: $i] : ((~constant(X)) | (~decreases(X)))) | (~constant(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(60,plain,
% 0.13/0.41 ((~![X: $i] : ((~constant(X)) | (~decreases(X)))) | ((~constant(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(61,plain,
% 0.13/0.41 ((~![X: $i] : ((~constant(X)) | (~decreases(X)))) | (~constant(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0)))) | (~decreases(difference(disbanding_rate(first_movers, T!0), disbanding_rate(efficient_producers, T!0))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.13/0.41 tff(62,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[61, 58, 48, 46])).
% 0.13/0.41 % SZS output end Proof
% 0.13/0.41 % E exiting
%------------------------------------------------------------------------------