%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : MGT036+1 : TPTP v9.3.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n020.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 06:06:18 AM UTC 2026 % Result : Theorem 9.16s 9.45s % Output : Proof 9.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT036+1 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.05 % Command : duper %s % 0.09/0.35 % Computer : n020.cluster.edu % 0.09/0.35 % Model : x86_64 x86_64 % 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.35 % Memory : 8046.5625MB % 0.09/0.35 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Mon Sep 7 12:40:28 UTC 2026 % 0.13/0.36 % CPUTime : % 9.16/9.45 SZS status Theorem for theBenchmark.p % 9.16/9.45 SZS output start Proof for theBenchmark.p % 9.16/9.45 Clause #0 (by assumption #[]): Eq % 9.16/9.45 (∀ (E T : Iota), % 9.16/9.45 And (environment E) (subpopulations first_movers efficient_producers E T) → % 9.16/9.45 subpopulations efficient_producers first_movers E T) % 9.16/9.45 True % 9.16/9.45 Clause #1 (by assumption #[]): Eq (∀ (E T : Iota), And (environment E) (subpopulations first_movers efficient_producers E T) → in_environment E T) True % 9.16/9.45 Clause #2 (by assumption #[]): Eq % 9.16/9.45 (∀ (E S1 S2 T : Iota), % 9.16/9.45 Iff (And (environment E) (subpopulations S1 S2 E T) → greater_or_equal (growth_rate S1 T) zero) % 9.16/9.45 (Not (greater zero (growth_rate S1 T)))) % 9.16/9.45 True % 9.16/9.45 Clause #3 (by assumption #[]): Eq % 9.16/9.45 (∀ (E S1 S2 T : Iota), % 9.16/9.45 And (environment E) (subpopulations S1 S2 E T) → % 9.16/9.45 Iff (And (greater_or_equal (growth_rate S2 T) zero) (greater zero (growth_rate S1 T))) (outcompetes S2 S1 T)) % 9.16/9.45 True % 9.16/9.45 Clause #4 (by assumption #[]): Eq % 9.16/9.45 (∀ (E S1 S2 T : Iota), % 9.16/9.45 And (And (And (environment E) (in_environment E T)) (Not (greater zero (growth_rate S1 T)))) % 9.16/9.45 (greater (resilience S2) (resilience S1)) → % 9.16/9.45 Not (greater zero (growth_rate S2 T))) % 9.16/9.45 True % 9.16/9.45 Clause #5 (by assumption #[]): Eq (greater (resilience efficient_producers) (resilience first_movers)) True % 9.16/9.45 Clause #6 (by assumption #[]): Eq % 9.16/9.45 (Not % 9.16/9.45 (∀ (E T : Iota), % 9.16/9.45 And (environment E) (subpopulations first_movers efficient_producers E T) → % 9.16/9.45 Not (outcompetes first_movers efficient_producers T))) % 9.16/9.45 True % 9.16/9.45 Clause #7 (by clausification #[1]): ∀ (a : Iota), % 9.16/9.45 Eq (∀ (T : Iota), And (environment a) (subpopulations first_movers efficient_producers a T) → in_environment a T) True % 9.16/9.45 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), % 9.16/9.45 Eq (And (environment a) (subpopulations first_movers efficient_producers a a_1) → in_environment a a_1) True % 9.16/9.45 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), % 9.16/9.45 Or (Eq (And (environment a) (subpopulations first_movers efficient_producers a a_1)) False) % 9.16/9.45 (Eq (in_environment a a_1) True) % 9.16/9.45 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), % 9.16/9.45 Or (Eq (in_environment a a_1) True) % 9.16/9.45 (Or (Eq (environment a) False) (Eq (subpopulations first_movers efficient_producers a a_1) False)) % 9.16/9.45 Clause #11 (by clausification #[0]): ∀ (a : Iota), % 9.16/9.45 Eq % 9.16/9.45 (∀ (T : Iota), % 9.16/9.45 And (environment a) (subpopulations first_movers efficient_producers a T) → % 9.16/9.45 subpopulations efficient_producers first_movers a T) % 9.16/9.45 True % 9.16/9.45 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), % 9.16/9.45 Eq % 9.16/9.45 (And (environment a) (subpopulations first_movers efficient_producers a a_1) → % 9.16/9.45 subpopulations efficient_producers first_movers a a_1) % 9.16/9.45 True % 9.16/9.45 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), % 9.16/9.45 Or (Eq (And (environment a) (subpopulations first_movers efficient_producers a a_1)) False) % 9.16/9.45 (Eq (subpopulations efficient_producers first_movers a a_1) True) % 9.16/9.45 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), % 9.16/9.45 Or (Eq (subpopulations efficient_producers first_movers a a_1) True) % 9.16/9.45 (Or (Eq (environment a) False) (Eq (subpopulations first_movers efficient_producers a a_1) False)) % 9.16/9.45 Clause #15 (by clausification #[6]): Eq % 9.16/9.45 (∀ (E T : Iota), % 9.16/9.45 And (environment E) (subpopulations first_movers efficient_producers E T) → % 9.16/9.45 Not (outcompetes first_movers efficient_producers T)) % 9.16/9.45 False % 9.16/9.45 Clause #16 (by clausification #[15]): ∀ (a : Iota), % 9.16/9.45 Eq % 9.16/9.45 (Not % 9.16/9.45 (∀ (T : Iota), % 9.16/9.45 And (environment (skS.0 0 a)) (subpopulations first_movers efficient_producers (skS.0 0 a) T) → % 9.16/9.45 Not (outcompetes first_movers efficient_producers T))) % 9.16/9.45 True % 9.16/9.45 Clause #17 (by clausification #[16]): ∀ (a : Iota), % 9.16/9.45 Eq % 9.16/9.45 (∀ (T : Iota), % 9.16/9.45 And (environment (skS.0 0 a)) (subpopulations first_movers efficient_producers (skS.0 0 a) T) → % 9.16/9.45 Not (outcompetes first_movers efficient_producers T)) % 9.16/9.45 False % 9.16/9.45 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), % 9.16/9.45 Eq % 9.16/9.45 (Not % 9.16/9.45 (And (environment (skS.0 0 a)) (subpopulations first_movers efficient_producers (skS.0 0 a) (skS.0 1 a a_1)) → % 9.16/9.45 Not (outcompetes first_movers efficient_producers (skS.0 1 a a_1)))) % 9.26/9.50 True % 9.26/9.50 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), % 9.26/9.50 Eq % 9.26/9.50 (And (environment (skS.0 0 a)) (subpopulations first_movers efficient_producers (skS.0 0 a) (skS.0 1 a a_1)) → % 9.26/9.50 Not (outcompetes first_movers efficient_producers (skS.0 1 a a_1))) % 9.26/9.50 False % 9.26/9.50 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), % 9.26/9.50 Eq (And (environment (skS.0 0 a)) (subpopulations first_movers efficient_producers (skS.0 0 a) (skS.0 1 a a_1))) True % 9.26/9.50 Clause #21 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (Not (outcompetes first_movers efficient_producers (skS.0 1 a a_1))) False % 9.26/9.50 Clause #22 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (subpopulations first_movers efficient_producers (skS.0 0 a) (skS.0 1 a a_1)) True % 9.26/9.50 Clause #23 (by clausification #[20]): ∀ (a : Iota), Eq (environment (skS.0 0 a)) True % 9.26/9.50 Clause #24 (by superposition #[23, 10]): ∀ (a a_1 : Iota), % 9.26/9.50 Or (Eq (in_environment (skS.0 0 a) a_1) True) % 9.26/9.50 (Or (Eq True False) (Eq (subpopulations first_movers efficient_producers (skS.0 0 a) a_1) False)) % 9.26/9.50 Clause #25 (by superposition #[23, 14]): ∀ (a a_1 : Iota), % 9.26/9.50 Or (Eq (subpopulations efficient_producers first_movers (skS.0 0 a) a_1) True) % 9.26/9.50 (Or (Eq True False) (Eq (subpopulations first_movers efficient_producers (skS.0 0 a) a_1) False)) % 9.26/9.50 Clause #26 (by clausification #[2]): ∀ (a : Iota), % 9.26/9.50 Eq % 9.26/9.50 (∀ (S1 S2 T : Iota), % 9.26/9.50 Iff (And (environment a) (subpopulations S1 S2 a T) → greater_or_equal (growth_rate S1 T) zero) % 9.26/9.50 (Not (greater zero (growth_rate S1 T)))) % 9.26/9.50 True % 9.26/9.50 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), % 9.26/9.50 Eq % 9.26/9.50 (∀ (S2 T : Iota), % 9.26/9.50 Iff (And (environment a) (subpopulations a_1 S2 a T) → greater_or_equal (growth_rate a_1 T) zero) % 9.26/9.50 (Not (greater zero (growth_rate a_1 T)))) % 9.26/9.50 True % 9.26/9.50 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), % 9.26/9.50 Eq % 9.26/9.50 (∀ (T : Iota), % 9.26/9.50 Iff (And (environment a) (subpopulations a_1 a_2 a T) → greater_or_equal (growth_rate a_1 T) zero) % 9.26/9.50 (Not (greater zero (growth_rate a_1 T)))) % 9.26/9.50 True % 9.26/9.50 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 a_3 : Iota), % 9.26/9.50 Eq % 9.26/9.50 (Iff (And (environment a) (subpopulations a_1 a_2 a a_3) → greater_or_equal (growth_rate a_1 a_3) zero) % 9.26/9.50 (Not (greater zero (growth_rate a_1 a_3)))) % 9.26/9.50 True % 9.26/9.50 Clause #31 (by clausification #[29]): ∀ (a a_1 a_2 a_3 : Iota), % 9.26/9.50 Or (Eq (And (environment a) (subpopulations a_1 a_2 a a_3) → greater_or_equal (growth_rate a_1 a_3) zero) False) % 9.26/9.50 (Eq (Not (greater zero (growth_rate a_1 a_3))) True) % 9.26/9.50 Clause #36 (by clausification #[4]): ∀ (a : Iota), % 9.26/9.50 Eq % 9.26/9.50 (∀ (S1 S2 T : Iota), % 9.26/9.50 And (And (And (environment a) (in_environment a T)) (Not (greater zero (growth_rate S1 T)))) % 9.26/9.50 (greater (resilience S2) (resilience S1)) → % 9.26/9.50 Not (greater zero (growth_rate S2 T))) % 9.26/9.50 True % 9.26/9.50 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), % 9.26/9.50 Eq % 9.26/9.50 (∀ (S2 T : Iota), % 9.26/9.50 And (And (And (environment a) (in_environment a T)) (Not (greater zero (growth_rate a_1 T)))) % 9.26/9.50 (greater (resilience S2) (resilience a_1)) → % 9.26/9.50 Not (greater zero (growth_rate S2 T))) % 9.26/9.50 True % 9.26/9.50 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), % 9.26/9.50 Eq % 9.26/9.50 (∀ (T : Iota), % 9.26/9.50 And (And (And (environment a) (in_environment a T)) (Not (greater zero (growth_rate a_1 T)))) % 9.26/9.50 (greater (resilience a_2) (resilience a_1)) → % 9.26/9.50 Not (greater zero (growth_rate a_2 T))) % 9.26/9.50 True % 9.26/9.50 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 a_3 : Iota), % 9.26/9.50 Eq % 9.26/9.50 (And (And (And (environment a) (in_environment a a_1)) (Not (greater zero (growth_rate a_2 a_1)))) % 9.26/9.50 (greater (resilience a_3) (resilience a_2)) → % 9.26/9.50 Not (greater zero (growth_rate a_3 a_1))) % 9.26/9.50 True % 9.26/9.50 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 a_3 : Iota), % 9.26/9.50 Or % 9.26/9.50 (Eq % 9.26/9.50 (And (And (And (environment a) (in_environment a a_1)) (Not (greater zero (growth_rate a_2 a_1)))) % 9.26/9.50 (greater (resilience a_3) (resilience a_2))) % 9.26/9.50 False) % 9.26/9.50 (Eq (Not (greater zero (growth_rate a_3 a_1))) True) % 9.26/9.50 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 a_3 : Iota), % 9.26/9.55 Or (Eq (Not (greater zero (growth_rate a a_1))) True) % 9.26/9.55 (Or (Eq (And (And (environment a_2) (in_environment a_2 a_1)) (Not (greater zero (growth_rate a_3 a_1)))) False) % 9.26/9.55 (Eq (greater (resilience a) (resilience a_3)) False)) % 9.26/9.55 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 a_3 : Iota), % 9.26/9.55 Or (Eq (And (And (environment a) (in_environment a a_1)) (Not (greater zero (growth_rate a_2 a_1)))) False) % 9.26/9.55 (Or (Eq (greater (resilience a_3) (resilience a_2)) False) (Eq (greater zero (growth_rate a_3 a_1)) False)) % 9.26/9.55 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota), % 9.26/9.55 Or (Eq (greater (resilience a) (resilience a_1)) False) % 9.26/9.55 (Or (Eq (greater zero (growth_rate a a_2)) False) % 9.26/9.55 (Or (Eq (And (environment a_3) (in_environment a_3 a_2)) False) % 9.26/9.55 (Eq (Not (greater zero (growth_rate a_1 a_2))) False))) % 9.26/9.55 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota), % 9.26/9.55 Or (Eq (greater (resilience a) (resilience a_1)) False) % 9.26/9.55 (Or (Eq (greater zero (growth_rate a a_2)) False) % 9.26/9.55 (Or (Eq (Not (greater zero (growth_rate a_1 a_2))) False) % 9.26/9.55 (Or (Eq (environment a_3) False) (Eq (in_environment a_3 a_2) False)))) % 9.26/9.55 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota), % 9.26/9.55 Or (Eq (greater (resilience a) (resilience a_1)) False) % 9.26/9.55 (Or (Eq (greater zero (growth_rate a a_2)) False) % 9.26/9.55 (Or (Eq (environment a_3) False) % 9.26/9.55 (Or (Eq (in_environment a_3 a_2) False) (Eq (greater zero (growth_rate a_1 a_2)) True)))) % 9.26/9.55 Clause #46 (by superposition #[45, 5]): ∀ (a a_1 : Iota), % 9.26/9.55 Or (Eq (greater zero (growth_rate efficient_producers a)) False) % 9.26/9.55 (Or (Eq (environment a_1) False) % 9.26/9.55 (Or (Eq (in_environment a_1 a) False) (Or (Eq (greater zero (growth_rate first_movers a)) True) (Eq False True)))) % 9.26/9.55 Clause #47 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (outcompetes first_movers efficient_producers (skS.0 1 a a_1)) True % 9.26/9.55 Clause #48 (by clausification #[31]): ∀ (a a_1 a_2 a_3 : Iota), % 9.26/9.55 Or (Eq (Not (greater zero (growth_rate a a_1))) True) (Eq (And (environment a_2) (subpopulations a a_3 a_2 a_1)) True) % 9.26/9.55 Clause #49 (by clausification #[31]): ∀ (a a_1 : Iota), % 9.26/9.55 Or (Eq (Not (greater zero (growth_rate a a_1))) True) (Eq (greater_or_equal (growth_rate a a_1) zero) False) % 9.26/9.55 Clause #50 (by clausification #[48]): ∀ (a a_1 a_2 a_3 : Iota), % 9.26/9.55 Or (Eq (And (environment a) (subpopulations a_1 a_2 a a_3)) True) (Eq (greater zero (growth_rate a_1 a_3)) False) % 9.26/9.55 Clause #52 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), Or (Eq (greater zero (growth_rate a a_1)) False) (Eq (environment a_2) True) % 9.26/9.55 Clause #53 (by clausification #[49]): ∀ (a a_1 : Iota), % 9.26/9.55 Or (Eq (greater_or_equal (growth_rate a a_1) zero) False) (Eq (greater zero (growth_rate a a_1)) False) % 9.26/9.55 Clause #54 (by clausification #[3]): ∀ (a : Iota), % 9.26/9.55 Eq % 9.26/9.55 (∀ (S1 S2 T : Iota), % 9.26/9.55 And (environment a) (subpopulations S1 S2 a T) → % 9.26/9.55 Iff (And (greater_or_equal (growth_rate S2 T) zero) (greater zero (growth_rate S1 T))) (outcompetes S2 S1 T)) % 9.26/9.55 True % 9.26/9.55 Clause #55 (by clausification #[54]): ∀ (a a_1 : Iota), % 9.26/9.55 Eq % 9.26/9.55 (∀ (S2 T : Iota), % 9.26/9.55 And (environment a) (subpopulations a_1 S2 a T) → % 9.26/9.55 Iff (And (greater_or_equal (growth_rate S2 T) zero) (greater zero (growth_rate a_1 T))) (outcompetes S2 a_1 T)) % 9.26/9.55 True % 9.26/9.55 Clause #56 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), % 9.26/9.55 Eq % 9.26/9.55 (∀ (T : Iota), % 9.26/9.55 And (environment a) (subpopulations a_1 a_2 a T) → % 9.26/9.55 Iff (And (greater_or_equal (growth_rate a_2 T) zero) (greater zero (growth_rate a_1 T))) % 9.26/9.55 (outcompetes a_2 a_1 T)) % 9.26/9.55 True % 9.26/9.55 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 a_3 : Iota), % 9.26/9.55 Eq % 9.26/9.55 (And (environment a) (subpopulations a_1 a_2 a a_3) → % 9.26/9.55 Iff (And (greater_or_equal (growth_rate a_2 a_3) zero) (greater zero (growth_rate a_1 a_3))) % 9.26/9.55 (outcompetes a_2 a_1 a_3)) % 9.26/9.55 True % 9.26/9.55 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 a_3 : Iota), % 9.26/9.55 Or (Eq (And (environment a) (subpopulations a_1 a_2 a a_3)) False) % 9.26/9.55 (Eq % 9.26/9.55 (Iff (And (greater_or_equal (growth_rate a_2 a_3) zero) (greater zero (growth_rate a_1 a_3))) % 9.26/9.55 (outcompetes a_2 a_1 a_3)) % 9.36/9.60 True) % 9.36/9.60 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 a_3 : Iota), % 9.36/9.60 Or % 9.36/9.60 (Eq % 9.36/9.60 (Iff (And (greater_or_equal (growth_rate a a_1) zero) (greater zero (growth_rate a_2 a_1))) % 9.36/9.60 (outcompetes a a_2 a_1)) % 9.36/9.60 True) % 9.36/9.60 (Or (Eq (environment a_3) False) (Eq (subpopulations a_2 a a_3 a_1) False)) % 9.36/9.60 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 a_3 : Iota), % 9.36/9.60 Or (Eq (environment a) False) % 9.36/9.60 (Or (Eq (subpopulations a_1 a_2 a a_3) False) % 9.36/9.60 (Or (Eq (And (greater_or_equal (growth_rate a_2 a_3) zero) (greater zero (growth_rate a_1 a_3))) True) % 9.36/9.60 (Eq (outcompetes a_2 a_1 a_3) False))) % 9.36/9.60 Clause #62 (by clausification #[60]): ∀ (a a_1 a_2 a_3 : Iota), % 9.36/9.60 Or (Eq (environment a) False) % 9.36/9.60 (Or (Eq (subpopulations a_1 a_2 a a_3) False) % 9.36/9.60 (Or (Eq (outcompetes a_2 a_1 a_3) False) (Eq (greater zero (growth_rate a_1 a_3)) True))) % 9.36/9.60 Clause #63 (by clausification #[60]): ∀ (a a_1 a_2 a_3 : Iota), % 9.36/9.60 Or (Eq (environment a) False) % 9.36/9.60 (Or (Eq (subpopulations a_1 a_2 a a_3) False) % 9.36/9.60 (Or (Eq (outcompetes a_2 a_1 a_3) False) (Eq (greater_or_equal (growth_rate a_2 a_3) zero) True))) % 9.36/9.60 Clause #64 (by superposition #[62, 23]): ∀ (a a_1 a_2 a_3 : Iota), % 9.36/9.60 Or (Eq (subpopulations a a_1 (skS.0 0 a_2) a_3) False) % 9.36/9.60 (Or (Eq (outcompetes a_1 a a_3) False) (Or (Eq (greater zero (growth_rate a a_3)) True) (Eq False True))) % 9.36/9.60 Clause #65 (by superposition #[63, 23]): ∀ (a a_1 a_2 a_3 : Iota), % 9.36/9.60 Or (Eq (subpopulations a a_1 (skS.0 0 a_2) a_3) False) % 9.36/9.60 (Or (Eq (outcompetes a_1 a a_3) False) (Or (Eq (greater_or_equal (growth_rate a_1 a_3) zero) True) (Eq False True))) % 9.36/9.60 Clause #66 (by clausification #[46]): ∀ (a a_1 : Iota), % 9.36/9.60 Or (Eq (greater zero (growth_rate efficient_producers a)) False) % 9.36/9.60 (Or (Eq (environment a_1) False) % 9.36/9.60 (Or (Eq (in_environment a_1 a) False) (Eq (greater zero (growth_rate first_movers a)) True))) % 9.36/9.60 Clause #67 (by clausification #[24]): ∀ (a a_1 : Iota), % 9.36/9.60 Or (Eq (in_environment (skS.0 0 a) a_1) True) % 9.36/9.60 (Eq (subpopulations first_movers efficient_producers (skS.0 0 a) a_1) False) % 9.36/9.60 Clause #68 (by superposition #[67, 22]): ∀ (a a_1 : Iota), Or (Eq (in_environment (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq False True) % 9.36/9.60 Clause #69 (by clausification #[68]): ∀ (a a_1 : Iota), Eq (in_environment (skS.0 0 a) (skS.0 1 a a_1)) True % 9.36/9.60 Clause #70 (by clausification #[65]): ∀ (a a_1 a_2 a_3 : Iota), % 9.36/9.60 Or (Eq (subpopulations a a_1 (skS.0 0 a_2) a_3) False) % 9.36/9.60 (Or (Eq (outcompetes a_1 a a_3) False) (Eq (greater_or_equal (growth_rate a_1 a_3) zero) True)) % 9.36/9.60 Clause #72 (by clausification #[25]): ∀ (a a_1 : Iota), % 9.36/9.60 Or (Eq (subpopulations efficient_producers first_movers (skS.0 0 a) a_1) True) % 9.36/9.60 (Eq (subpopulations first_movers efficient_producers (skS.0 0 a) a_1) False) % 9.36/9.60 Clause #73 (by superposition #[72, 22]): ∀ (a a_1 : Iota), % 9.36/9.60 Or (Eq (subpopulations efficient_producers first_movers (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq False True) % 9.36/9.60 Clause #74 (by clausification #[73]): ∀ (a a_1 : Iota), Eq (subpopulations efficient_producers first_movers (skS.0 0 a) (skS.0 1 a a_1)) True % 9.36/9.60 Clause #75 (by superposition #[74, 70]): ∀ (a a_1 : Iota), % 9.36/9.60 Or (Eq True False) % 9.36/9.60 (Or (Eq (outcompetes first_movers efficient_producers (skS.0 1 a a_1)) False) % 9.36/9.60 (Eq (greater_or_equal (growth_rate first_movers (skS.0 1 a a_1)) zero) True)) % 9.36/9.60 Clause #76 (by clausification #[64]): ∀ (a a_1 a_2 a_3 : Iota), % 9.36/9.60 Or (Eq (subpopulations a a_1 (skS.0 0 a_2) a_3) False) % 9.36/9.60 (Or (Eq (outcompetes a_1 a a_3) False) (Eq (greater zero (growth_rate a a_3)) True)) % 9.36/9.60 Clause #78 (by superposition #[76, 74]): ∀ (a a_1 : Iota), % 9.36/9.60 Or (Eq (outcompetes first_movers efficient_producers (skS.0 1 a a_1)) False) % 9.36/9.60 (Or (Eq (greater zero (growth_rate efficient_producers (skS.0 1 a a_1))) True) (Eq False True)) % 9.36/9.60 Clause #84 (by clausification #[75]): ∀ (a a_1 : Iota), % 9.36/9.60 Or (Eq (outcompetes first_movers efficient_producers (skS.0 1 a a_1)) False) % 9.36/9.60 (Eq (greater_or_equal (growth_rate first_movers (skS.0 1 a a_1)) zero) True) % 9.36/9.60 Clause #85 (by forward demodulation #[84, 47]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (greater_or_equal (growth_rate first_movers (skS.0 1 a a_1)) zero) True) % 9.36/9.63 Clause #86 (by clausification #[85]): ∀ (a a_1 : Iota), Eq (greater_or_equal (growth_rate first_movers (skS.0 1 a a_1)) zero) True % 9.36/9.63 Clause #87 (by superposition #[86, 53]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (greater zero (growth_rate first_movers (skS.0 1 a a_1))) False) % 9.36/9.63 Clause #89 (by clausification #[87]): ∀ (a a_1 : Iota), Eq (greater zero (growth_rate first_movers (skS.0 1 a a_1))) False % 9.36/9.63 Clause #91 (by clausification #[78]): ∀ (a a_1 : Iota), % 9.36/9.63 Or (Eq (outcompetes first_movers efficient_producers (skS.0 1 a a_1)) False) % 9.36/9.63 (Eq (greater zero (growth_rate efficient_producers (skS.0 1 a a_1))) True) % 9.36/9.63 Clause #92 (by forward demodulation #[91, 47]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (greater zero (growth_rate efficient_producers (skS.0 1 a a_1))) True) % 9.36/9.63 Clause #93 (by clausification #[92]): ∀ (a a_1 : Iota), Eq (greater zero (growth_rate efficient_producers (skS.0 1 a a_1))) True % 9.36/9.63 Clause #95 (by superposition #[93, 52]): ∀ (a : Iota), Or (Eq True False) (Eq (environment a) True) % 9.36/9.63 Clause #97 (by clausification #[95]): ∀ (a : Iota), Eq (environment a) True % 9.36/9.63 Clause #104 (by backward demodulation #[97, 66]): ∀ (a a_1 : Iota), % 9.36/9.63 Or (Eq (greater zero (growth_rate efficient_producers a)) False) % 9.36/9.63 (Or (Eq True False) (Or (Eq (in_environment a_1 a) False) (Eq (greater zero (growth_rate first_movers a)) True))) % 9.36/9.63 Clause #114 (by clausification #[104]): ∀ (a a_1 : Iota), % 9.36/9.63 Or (Eq (greater zero (growth_rate efficient_producers a)) False) % 9.36/9.63 (Or (Eq (in_environment a_1 a) False) (Eq (greater zero (growth_rate first_movers a)) True)) % 9.36/9.63 Clause #115 (by superposition #[114, 93]): ∀ (a a_1 a_2 : Iota), % 9.36/9.63 Or (Eq (in_environment a (skS.0 1 a_1 a_2)) False) % 9.36/9.63 (Or (Eq (greater zero (growth_rate first_movers (skS.0 1 a_1 a_2))) True) (Eq False True)) % 9.36/9.63 Clause #128 (by clausification #[115]): ∀ (a a_1 a_2 : Iota), % 9.36/9.63 Or (Eq (in_environment a (skS.0 1 a_1 a_2)) False) % 9.36/9.63 (Eq (greater zero (growth_rate first_movers (skS.0 1 a_1 a_2))) True) % 9.36/9.63 Clause #129 (by superposition #[128, 69]): ∀ (a a_1 : Iota), Or (Eq (greater zero (growth_rate first_movers (skS.0 1 a a_1))) True) (Eq False True) % 9.36/9.63 Clause #131 (by clausification #[129]): ∀ (a a_1 : Iota), Eq (greater zero (growth_rate first_movers (skS.0 1 a a_1))) True % 9.36/9.63 Clause #133 (by superposition #[131, 89]): Eq True False % 9.36/9.63 Clause #134 (by clausification #[133]): False % 9.36/9.63 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------