%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : MGT036+2 : TPTP v9.3.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n005.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 9.36s 9.61s % Output : Proof 9.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : MGT036+2 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.04 % Command : duper %s % 0.10/0.36 % Computer : n005.cluster.edu % 0.10/0.36 % Model : x86_64 x86_64 % 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.36 % Memory : 8046.5625MB % 0.10/0.36 % OS : Linux 6.8.0-71-generic % 0.10/0.36 % CPULimit : 300 % 0.10/0.36 % WCLimit : 300 % 0.10/0.36 % DateTime : Mon Sep 7 12:41:05 UTC 2026 % 0.10/0.36 % CPUTime : % 9.36/9.61 SZS status Theorem for theBenchmark.p % 9.36/9.61 SZS output start Proof for theBenchmark.p % 9.36/9.61 Clause #0 (by assumption #[]): Eq (∀ (E S1 S2 T : Iota), And (environment E) (subpopulations S1 S2 E T) → subpopulations S2 S1 E T) True % 9.36/9.61 Clause #1 (by assumption #[]): Eq (∀ (E T : Iota), And (environment E) (subpopulations first_movers efficient_producers E T) → in_environment E T) True % 9.36/9.61 Clause #2 (by assumption #[]): Eq % 9.36/9.61 (∀ (E S1 S2 T : Iota), % 9.36/9.61 Iff (And (environment E) (subpopulations S1 S2 E T) → greater_or_equal (growth_rate S1 T) zero) % 9.36/9.61 (Not (greater zero (growth_rate S1 T)))) % 9.36/9.61 True % 9.36/9.61 Clause #3 (by assumption #[]): Eq % 9.36/9.61 (∀ (E S1 S2 T : Iota), % 9.36/9.61 And (environment E) (subpopulations S1 S2 E T) → % 9.36/9.61 Iff (And (greater_or_equal (growth_rate S2 T) zero) (greater zero (growth_rate S1 T))) (outcompetes S2 S1 T)) % 9.36/9.61 True % 9.36/9.61 Clause #4 (by assumption #[]): Eq (greater (resilience efficient_producers) (resilience first_movers)) True % 9.36/9.61 Clause #5 (by assumption #[]): Eq % 9.36/9.61 (∀ (E S1 S2 T : Iota), % 9.36/9.61 And (And (And (environment E) (in_environment E T)) (Not (greater zero (growth_rate S1 T)))) % 9.36/9.61 (greater (resilience S2) (resilience S1)) → % 9.36/9.61 Not (greater zero (growth_rate S2 T))) % 9.36/9.61 True % 9.36/9.61 Clause #6 (by assumption #[]): Eq % 9.36/9.61 (Not % 9.36/9.61 (∀ (E T : Iota), % 9.36/9.61 And (environment E) (subpopulations first_movers efficient_producers E T) → % 9.36/9.61 Not (outcompetes first_movers efficient_producers T))) % 9.36/9.61 True % 9.36/9.61 Clause #7 (by clausification #[1]): ∀ (a : Iota), % 9.36/9.61 Eq (∀ (T : Iota), And (environment a) (subpopulations first_movers efficient_producers a T) → in_environment a T) True % 9.36/9.61 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), % 9.36/9.61 Eq (And (environment a) (subpopulations first_movers efficient_producers a a_1) → in_environment a a_1) True % 9.36/9.61 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), % 9.36/9.61 Or (Eq (And (environment a) (subpopulations first_movers efficient_producers a a_1)) False) % 9.36/9.61 (Eq (in_environment a a_1) True) % 9.36/9.61 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), % 9.36/9.61 Or (Eq (in_environment a a_1) True) % 9.36/9.61 (Or (Eq (environment a) False) (Eq (subpopulations first_movers efficient_producers a a_1) False)) % 9.36/9.61 Clause #11 (by clausification #[6]): Eq % 9.36/9.61 (∀ (E T : Iota), % 9.36/9.61 And (environment E) (subpopulations first_movers efficient_producers E T) → % 9.36/9.61 Not (outcompetes first_movers efficient_producers T)) % 9.36/9.61 False % 9.36/9.61 Clause #12 (by clausification #[11]): ∀ (a : Iota), % 9.36/9.61 Eq % 9.36/9.61 (Not % 9.36/9.61 (∀ (T : Iota), % 9.36/9.61 And (environment (skS.0 0 a)) (subpopulations first_movers efficient_producers (skS.0 0 a) T) → % 9.36/9.61 Not (outcompetes first_movers efficient_producers T))) % 9.36/9.61 True % 9.36/9.61 Clause #13 (by clausification #[12]): ∀ (a : Iota), % 9.36/9.61 Eq % 9.36/9.61 (∀ (T : Iota), % 9.36/9.61 And (environment (skS.0 0 a)) (subpopulations first_movers efficient_producers (skS.0 0 a) T) → % 9.36/9.61 Not (outcompetes first_movers efficient_producers T)) % 9.36/9.61 False % 9.36/9.61 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), % 9.36/9.61 Eq % 9.36/9.61 (Not % 9.36/9.61 (And (environment (skS.0 0 a)) (subpopulations first_movers efficient_producers (skS.0 0 a) (skS.0 1 a a_1)) → % 9.36/9.61 Not (outcompetes first_movers efficient_producers (skS.0 1 a a_1)))) % 9.36/9.61 True % 9.36/9.61 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), % 9.36/9.61 Eq % 9.36/9.61 (And (environment (skS.0 0 a)) (subpopulations first_movers efficient_producers (skS.0 0 a) (skS.0 1 a a_1)) → % 9.36/9.61 Not (outcompetes first_movers efficient_producers (skS.0 1 a a_1))) % 9.36/9.61 False % 9.36/9.61 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), % 9.36/9.61 Eq (And (environment (skS.0 0 a)) (subpopulations first_movers efficient_producers (skS.0 0 a) (skS.0 1 a a_1))) True % 9.36/9.61 Clause #17 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (Not (outcompetes first_movers efficient_producers (skS.0 1 a a_1))) False % 9.36/9.61 Clause #18 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (subpopulations first_movers efficient_producers (skS.0 0 a) (skS.0 1 a a_1)) True % 9.36/9.61 Clause #19 (by clausification #[16]): ∀ (a : Iota), Eq (environment (skS.0 0 a)) True % 9.36/9.61 Clause #21 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (S1 S2 T : Iota), And (environment a) (subpopulations S1 S2 a T) → subpopulations S2 S1 a T) True % 9.36/9.65 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (∀ (S2 T : Iota), And (environment a) (subpopulations a_1 S2 a T) → subpopulations S2 a_1 a T) True % 9.36/9.65 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), % 9.36/9.65 Eq (∀ (T : Iota), And (environment a) (subpopulations a_1 a_2 a T) → subpopulations a_2 a_1 a T) True % 9.36/9.65 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 a_3 : Iota), Eq (And (environment a) (subpopulations a_1 a_2 a a_3) → subpopulations a_2 a_1 a a_3) True % 9.36/9.65 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 a_3 : Iota), % 9.36/9.65 Or (Eq (And (environment a) (subpopulations a_1 a_2 a a_3)) False) (Eq (subpopulations a_2 a_1 a a_3) True) % 9.36/9.65 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 a_3 : Iota), % 9.36/9.65 Or (Eq (subpopulations a a_1 a_2 a_3) True) % 9.36/9.65 (Or (Eq (environment a_2) False) (Eq (subpopulations a_1 a a_2 a_3) False)) % 9.36/9.65 Clause #27 (by superposition #[26, 19]): ∀ (a a_1 a_2 a_3 : Iota), % 9.36/9.65 Or (Eq (subpopulations a a_1 (skS.0 0 a_2) a_3) True) % 9.36/9.65 (Or (Eq (subpopulations a_1 a (skS.0 0 a_2) a_3) False) (Eq False True)) % 9.36/9.65 Clause #28 (by clausification #[2]): ∀ (a : Iota), % 9.36/9.65 Eq % 9.36/9.65 (∀ (S1 S2 T : Iota), % 9.36/9.65 Iff (And (environment a) (subpopulations S1 S2 a T) → greater_or_equal (growth_rate S1 T) zero) % 9.36/9.65 (Not (greater zero (growth_rate S1 T)))) % 9.36/9.65 True % 9.36/9.65 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), % 9.36/9.65 Eq % 9.36/9.65 (∀ (S2 T : Iota), % 9.36/9.65 Iff (And (environment a) (subpopulations a_1 S2 a T) → greater_or_equal (growth_rate a_1 T) zero) % 9.36/9.65 (Not (greater zero (growth_rate a_1 T)))) % 9.36/9.65 True % 9.36/9.65 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), % 9.36/9.65 Eq % 9.36/9.65 (∀ (T : Iota), % 9.36/9.65 Iff (And (environment a) (subpopulations a_1 a_2 a T) → greater_or_equal (growth_rate a_1 T) zero) % 9.36/9.65 (Not (greater zero (growth_rate a_1 T)))) % 9.36/9.65 True % 9.36/9.65 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 a_3 : Iota), % 9.36/9.65 Eq % 9.36/9.65 (Iff (And (environment a) (subpopulations a_1 a_2 a a_3) → greater_or_equal (growth_rate a_1 a_3) zero) % 9.36/9.65 (Not (greater zero (growth_rate a_1 a_3)))) % 9.36/9.65 True % 9.36/9.65 Clause #33 (by clausification #[31]): ∀ (a a_1 a_2 a_3 : Iota), % 9.36/9.65 Or (Eq (And (environment a) (subpopulations a_1 a_2 a a_3) → greater_or_equal (growth_rate a_1 a_3) zero) False) % 9.36/9.65 (Eq (Not (greater zero (growth_rate a_1 a_3))) True) % 9.36/9.65 Clause #38 (by clausification #[5]): ∀ (a : Iota), % 9.36/9.65 Eq % 9.36/9.65 (∀ (S1 S2 T : Iota), % 9.36/9.65 And (And (And (environment a) (in_environment a T)) (Not (greater zero (growth_rate S1 T)))) % 9.36/9.65 (greater (resilience S2) (resilience S1)) → % 9.36/9.65 Not (greater zero (growth_rate S2 T))) % 9.36/9.65 True % 9.36/9.65 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), % 9.36/9.65 Eq % 9.36/9.65 (∀ (S2 T : Iota), % 9.36/9.65 And (And (And (environment a) (in_environment a T)) (Not (greater zero (growth_rate a_1 T)))) % 9.36/9.65 (greater (resilience S2) (resilience a_1)) → % 9.36/9.65 Not (greater zero (growth_rate S2 T))) % 9.36/9.65 True % 9.36/9.65 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), % 9.36/9.65 Eq % 9.36/9.65 (∀ (T : Iota), % 9.36/9.65 And (And (And (environment a) (in_environment a T)) (Not (greater zero (growth_rate a_1 T)))) % 9.36/9.65 (greater (resilience a_2) (resilience a_1)) → % 9.36/9.65 Not (greater zero (growth_rate a_2 T))) % 9.36/9.65 True % 9.36/9.65 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 a_3 : Iota), % 9.36/9.65 Eq % 9.36/9.65 (And (And (And (environment a) (in_environment a a_1)) (Not (greater zero (growth_rate a_2 a_1)))) % 9.36/9.65 (greater (resilience a_3) (resilience a_2)) → % 9.36/9.65 Not (greater zero (growth_rate a_3 a_1))) % 9.36/9.65 True % 9.36/9.65 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 a_3 : Iota), % 9.36/9.65 Or % 9.36/9.65 (Eq % 9.36/9.65 (And (And (And (environment a) (in_environment a a_1)) (Not (greater zero (growth_rate a_2 a_1)))) % 9.36/9.65 (greater (resilience a_3) (resilience a_2))) % 9.36/9.65 False) % 9.36/9.65 (Eq (Not (greater zero (growth_rate a_3 a_1))) True) % 9.36/9.65 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota), % 9.36/9.65 Or (Eq (Not (greater zero (growth_rate a a_1))) True) % 9.36/9.65 (Or (Eq (And (And (environment a_2) (in_environment a_2 a_1)) (Not (greater zero (growth_rate a_3 a_1)))) False) % 9.36/9.65 (Eq (greater (resilience a) (resilience a_3)) False)) % 9.46/9.71 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota), % 9.46/9.71 Or (Eq (And (And (environment a) (in_environment a a_1)) (Not (greater zero (growth_rate a_2 a_1)))) False) % 9.46/9.71 (Or (Eq (greater (resilience a_3) (resilience a_2)) False) (Eq (greater zero (growth_rate a_3 a_1)) False)) % 9.46/9.71 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota), % 9.46/9.71 Or (Eq (greater (resilience a) (resilience a_1)) False) % 9.46/9.71 (Or (Eq (greater zero (growth_rate a a_2)) False) % 9.46/9.71 (Or (Eq (And (environment a_3) (in_environment a_3 a_2)) False) % 9.46/9.71 (Eq (Not (greater zero (growth_rate a_1 a_2))) False))) % 9.46/9.71 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 a_3 : Iota), % 9.46/9.71 Or (Eq (greater (resilience a) (resilience a_1)) False) % 9.46/9.71 (Or (Eq (greater zero (growth_rate a a_2)) False) % 9.46/9.71 (Or (Eq (Not (greater zero (growth_rate a_1 a_2))) False) % 9.46/9.71 (Or (Eq (environment a_3) False) (Eq (in_environment a_3 a_2) False)))) % 9.46/9.71 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 a_3 : Iota), % 9.46/9.71 Or (Eq (greater (resilience a) (resilience a_1)) False) % 9.46/9.71 (Or (Eq (greater zero (growth_rate a a_2)) False) % 9.46/9.71 (Or (Eq (environment a_3) False) % 9.46/9.71 (Or (Eq (in_environment a_3 a_2) False) (Eq (greater zero (growth_rate a_1 a_2)) True)))) % 9.46/9.71 Clause #48 (by superposition #[47, 4]): ∀ (a a_1 : Iota), % 9.46/9.71 Or (Eq (greater zero (growth_rate efficient_producers a)) False) % 9.46/9.71 (Or (Eq (environment a_1) False) % 9.46/9.71 (Or (Eq (in_environment a_1 a) False) (Or (Eq (greater zero (growth_rate first_movers a)) True) (Eq False True)))) % 9.46/9.71 Clause #49 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (outcompetes first_movers efficient_producers (skS.0 1 a a_1)) True % 9.46/9.71 Clause #50 (by clausification #[33]): ∀ (a a_1 a_2 a_3 : Iota), % 9.46/9.71 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) % 9.46/9.71 Clause #51 (by clausification #[33]): ∀ (a a_1 : Iota), % 9.46/9.71 Or (Eq (Not (greater zero (growth_rate a a_1))) True) (Eq (greater_or_equal (growth_rate a a_1) zero) False) % 9.46/9.71 Clause #52 (by clausification #[50]): ∀ (a a_1 a_2 a_3 : Iota), % 9.46/9.71 Or (Eq (And (environment a) (subpopulations a_1 a_2 a a_3)) True) (Eq (greater zero (growth_rate a_1 a_3)) False) % 9.46/9.71 Clause #53 (by clausification #[52]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (greater zero (growth_rate a a_1)) False) (Eq (subpopulations a a_2 a_3 a_1) True) % 9.46/9.71 Clause #54 (by clausification #[52]): ∀ (a a_1 a_2 : Iota), Or (Eq (greater zero (growth_rate a a_1)) False) (Eq (environment a_2) True) % 9.46/9.71 Clause #55 (by clausification #[51]): ∀ (a a_1 : Iota), % 9.46/9.71 Or (Eq (greater_or_equal (growth_rate a a_1) zero) False) (Eq (greater zero (growth_rate a a_1)) False) % 9.46/9.71 Clause #56 (by clausification #[3]): ∀ (a : Iota), % 9.46/9.71 Eq % 9.46/9.71 (∀ (S1 S2 T : Iota), % 9.46/9.71 And (environment a) (subpopulations S1 S2 a T) → % 9.46/9.71 Iff (And (greater_or_equal (growth_rate S2 T) zero) (greater zero (growth_rate S1 T))) (outcompetes S2 S1 T)) % 9.46/9.71 True % 9.46/9.71 Clause #57 (by clausification #[56]): ∀ (a a_1 : Iota), % 9.46/9.71 Eq % 9.46/9.71 (∀ (S2 T : Iota), % 9.46/9.71 And (environment a) (subpopulations a_1 S2 a T) → % 9.46/9.71 Iff (And (greater_or_equal (growth_rate S2 T) zero) (greater zero (growth_rate a_1 T))) (outcompetes S2 a_1 T)) % 9.46/9.71 True % 9.46/9.71 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), % 9.46/9.71 Eq % 9.46/9.71 (∀ (T : Iota), % 9.46/9.71 And (environment a) (subpopulations a_1 a_2 a T) → % 9.46/9.71 Iff (And (greater_or_equal (growth_rate a_2 T) zero) (greater zero (growth_rate a_1 T))) % 9.46/9.71 (outcompetes a_2 a_1 T)) % 9.46/9.71 True % 9.46/9.71 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 a_3 : Iota), % 9.46/9.71 Eq % 9.46/9.71 (And (environment a) (subpopulations a_1 a_2 a a_3) → % 9.46/9.71 Iff (And (greater_or_equal (growth_rate a_2 a_3) zero) (greater zero (growth_rate a_1 a_3))) % 9.46/9.71 (outcompetes a_2 a_1 a_3)) % 9.46/9.71 True % 9.46/9.71 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 a_3 : Iota), % 9.46/9.71 Or (Eq (And (environment a) (subpopulations a_1 a_2 a a_3)) False) % 9.46/9.71 (Eq % 9.46/9.71 (Iff (And (greater_or_equal (growth_rate a_2 a_3) zero) (greater zero (growth_rate a_1 a_3))) % 9.46/9.71 (outcompetes a_2 a_1 a_3)) % 9.46/9.71 True) % 9.46/9.71 Clause #61 (by clausification #[60]): ∀ (a a_1 a_2 a_3 : Iota), % 9.46/9.76 Or % 9.46/9.76 (Eq % 9.46/9.76 (Iff (And (greater_or_equal (growth_rate a a_1) zero) (greater zero (growth_rate a_2 a_1))) % 9.46/9.76 (outcompetes a a_2 a_1)) % 9.46/9.76 True) % 9.46/9.76 (Or (Eq (environment a_3) False) (Eq (subpopulations a_2 a a_3 a_1) False)) % 9.46/9.76 Clause #62 (by clausification #[61]): ∀ (a a_1 a_2 a_3 : Iota), % 9.46/9.76 Or (Eq (environment a) False) % 9.46/9.76 (Or (Eq (subpopulations a_1 a_2 a a_3) False) % 9.46/9.76 (Or (Eq (And (greater_or_equal (growth_rate a_2 a_3) zero) (greater zero (growth_rate a_1 a_3))) True) % 9.46/9.76 (Eq (outcompetes a_2 a_1 a_3) False))) % 9.46/9.76 Clause #64 (by clausification #[62]): ∀ (a a_1 a_2 a_3 : Iota), % 9.46/9.76 Or (Eq (environment a) False) % 9.46/9.76 (Or (Eq (subpopulations a_1 a_2 a a_3) False) % 9.46/9.76 (Or (Eq (outcompetes a_2 a_1 a_3) False) (Eq (greater zero (growth_rate a_1 a_3)) True))) % 9.46/9.76 Clause #65 (by clausification #[62]): ∀ (a a_1 a_2 a_3 : Iota), % 9.46/9.76 Or (Eq (environment a) False) % 9.46/9.76 (Or (Eq (subpopulations a_1 a_2 a a_3) False) % 9.46/9.76 (Or (Eq (outcompetes a_2 a_1 a_3) False) (Eq (greater_or_equal (growth_rate a_2 a_3) zero) True))) % 9.46/9.76 Clause #66 (by superposition #[64, 19]): ∀ (a a_1 a_2 a_3 : Iota), % 9.46/9.76 Or (Eq (subpopulations a a_1 (skS.0 0 a_2) a_3) False) % 9.46/9.76 (Or (Eq (outcompetes a_1 a a_3) False) (Or (Eq (greater zero (growth_rate a a_3)) True) (Eq False True))) % 9.46/9.76 Clause #67 (by superposition #[65, 19]): ∀ (a a_1 a_2 a_3 : Iota), % 9.46/9.76 Or (Eq (subpopulations a a_1 (skS.0 0 a_2) a_3) False) % 9.46/9.76 (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))) % 9.46/9.76 Clause #68 (by clausification #[48]): ∀ (a a_1 : Iota), % 9.46/9.76 Or (Eq (greater zero (growth_rate efficient_producers a)) False) % 9.46/9.76 (Or (Eq (environment a_1) False) % 9.46/9.76 (Or (Eq (in_environment a_1 a) False) (Eq (greater zero (growth_rate first_movers a)) True))) % 9.46/9.76 Clause #72 (by clausification #[27]): ∀ (a a_1 a_2 a_3 : Iota), % 9.46/9.76 Or (Eq (subpopulations a a_1 (skS.0 0 a_2) a_3) True) (Eq (subpopulations a_1 a (skS.0 0 a_2) a_3) False) % 9.46/9.76 Clause #73 (by superposition #[72, 18]): ∀ (a a_1 : Iota), % 9.46/9.76 Or (Eq (subpopulations efficient_producers first_movers (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq False True) % 9.46/9.76 Clause #76 (by clausification #[73]): ∀ (a a_1 : Iota), Eq (subpopulations efficient_producers first_movers (skS.0 0 a) (skS.0 1 a a_1)) True % 9.46/9.76 Clause #79 (by clausification #[67]): ∀ (a a_1 a_2 a_3 : Iota), % 9.46/9.76 Or (Eq (subpopulations a a_1 (skS.0 0 a_2) a_3) False) % 9.46/9.76 (Or (Eq (outcompetes a_1 a a_3) False) (Eq (greater_or_equal (growth_rate a_1 a_3) zero) True)) % 9.46/9.76 Clause #81 (by superposition #[79, 76]): ∀ (a a_1 : Iota), % 9.46/9.76 Or (Eq (outcompetes first_movers efficient_producers (skS.0 1 a a_1)) False) % 9.46/9.76 (Or (Eq (greater_or_equal (growth_rate first_movers (skS.0 1 a a_1)) zero) True) (Eq False True)) % 9.46/9.76 Clause #82 (by clausification #[66]): ∀ (a a_1 a_2 a_3 : Iota), % 9.46/9.76 Or (Eq (subpopulations a a_1 (skS.0 0 a_2) a_3) False) % 9.46/9.76 (Or (Eq (outcompetes a_1 a a_3) False) (Eq (greater zero (growth_rate a a_3)) True)) % 9.46/9.76 Clause #84 (by superposition #[82, 76]): ∀ (a a_1 : Iota), % 9.46/9.76 Or (Eq (outcompetes first_movers efficient_producers (skS.0 1 a a_1)) False) % 9.46/9.76 (Or (Eq (greater zero (growth_rate efficient_producers (skS.0 1 a a_1))) True) (Eq False True)) % 9.46/9.76 Clause #89 (by clausification #[81]): ∀ (a a_1 : Iota), % 9.46/9.76 Or (Eq (outcompetes first_movers efficient_producers (skS.0 1 a a_1)) False) % 9.46/9.76 (Eq (greater_or_equal (growth_rate first_movers (skS.0 1 a a_1)) zero) True) % 9.46/9.76 Clause #90 (by forward demodulation #[89, 49]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (greater_or_equal (growth_rate first_movers (skS.0 1 a a_1)) zero) True) % 9.46/9.76 Clause #91 (by clausification #[90]): ∀ (a a_1 : Iota), Eq (greater_or_equal (growth_rate first_movers (skS.0 1 a a_1)) zero) True % 9.46/9.76 Clause #92 (by superposition #[91, 55]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (greater zero (growth_rate first_movers (skS.0 1 a a_1))) False) % 9.46/9.76 Clause #93 (by clausification #[92]): ∀ (a a_1 : Iota), Eq (greater zero (growth_rate first_movers (skS.0 1 a a_1))) False % 9.46/9.76 Clause #95 (by clausification #[84]): ∀ (a a_1 : Iota), % 9.46/9.76 Or (Eq (outcompetes first_movers efficient_producers (skS.0 1 a a_1)) False) % 9.56/9.80 (Eq (greater zero (growth_rate efficient_producers (skS.0 1 a a_1))) True) % 9.56/9.80 Clause #96 (by forward demodulation #[95, 49]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (greater zero (growth_rate efficient_producers (skS.0 1 a a_1))) True) % 9.56/9.80 Clause #97 (by clausification #[96]): ∀ (a a_1 : Iota), Eq (greater zero (growth_rate efficient_producers (skS.0 1 a a_1))) True % 9.56/9.80 Clause #98 (by superposition #[97, 53]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq True False) (Eq (subpopulations efficient_producers a a_1 (skS.0 1 a_2 a_3)) True) % 9.56/9.80 Clause #99 (by superposition #[97, 54]): ∀ (a : Iota), Or (Eq True False) (Eq (environment a) True) % 9.56/9.80 Clause #101 (by clausification #[99]): ∀ (a : Iota), Eq (environment a) True % 9.56/9.80 Clause #102 (by backward demodulation #[101, 10]): ∀ (a a_1 : Iota), % 9.56/9.80 Or (Eq (in_environment a a_1) True) % 9.56/9.80 (Or (Eq True False) (Eq (subpopulations first_movers efficient_producers a a_1) False)) % 9.56/9.80 Clause #103 (by backward demodulation #[101, 26]): ∀ (a a_1 a_2 a_3 : Iota), % 9.56/9.80 Or (Eq (subpopulations a a_1 a_2 a_3) True) (Or (Eq True False) (Eq (subpopulations a_1 a a_2 a_3) False)) % 9.56/9.80 Clause #108 (by backward demodulation #[101, 68]): ∀ (a a_1 : Iota), % 9.56/9.80 Or (Eq (greater zero (growth_rate efficient_producers a)) False) % 9.56/9.80 (Or (Eq True False) (Or (Eq (in_environment a_1 a) False) (Eq (greater zero (growth_rate first_movers a)) True))) % 9.56/9.80 Clause #112 (by clausification #[102]): ∀ (a a_1 : Iota), Or (Eq (in_environment a a_1) True) (Eq (subpopulations first_movers efficient_producers a a_1) False) % 9.56/9.80 Clause #113 (by clausification #[103]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (subpopulations a a_1 a_2 a_3) True) (Eq (subpopulations a_1 a a_2 a_3) False) % 9.56/9.80 Clause #115 (by clausification #[98]): ∀ (a a_1 a_2 a_3 : Iota), Eq (subpopulations efficient_producers a a_1 (skS.0 1 a_2 a_3)) True % 9.56/9.80 Clause #118 (by superposition #[115, 113]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (subpopulations a efficient_producers a_1 (skS.0 1 a_2 a_3)) True) (Eq True False) % 9.56/9.80 Clause #119 (by clausification #[118]): ∀ (a a_1 a_2 a_3 : Iota), Eq (subpopulations a efficient_producers a_1 (skS.0 1 a_2 a_3)) True % 9.56/9.80 Clause #123 (by superposition #[119, 112]): ∀ (a a_1 a_2 : Iota), Or (Eq (in_environment a (skS.0 1 a_1 a_2)) True) (Eq True False) % 9.56/9.80 Clause #125 (by clausification #[123]): ∀ (a a_1 a_2 : Iota), Eq (in_environment a (skS.0 1 a_1 a_2)) True % 9.56/9.80 Clause #127 (by clausification #[108]): ∀ (a a_1 : Iota), % 9.56/9.80 Or (Eq (greater zero (growth_rate efficient_producers a)) False) % 9.56/9.80 (Or (Eq (in_environment a_1 a) False) (Eq (greater zero (growth_rate first_movers a)) True)) % 9.56/9.80 Clause #128 (by superposition #[127, 97]): ∀ (a a_1 a_2 : Iota), % 9.56/9.80 Or (Eq (in_environment a (skS.0 1 a_1 a_2)) False) % 9.56/9.80 (Or (Eq (greater zero (growth_rate first_movers (skS.0 1 a_1 a_2))) True) (Eq False True)) % 9.56/9.80 Clause #144 (by clausification #[128]): ∀ (a a_1 a_2 : Iota), % 9.56/9.80 Or (Eq (in_environment a (skS.0 1 a_1 a_2)) False) % 9.56/9.80 (Eq (greater zero (growth_rate first_movers (skS.0 1 a_1 a_2))) True) % 9.56/9.80 Clause #145 (by superposition #[144, 125]): ∀ (a a_1 : Iota), Or (Eq (greater zero (growth_rate first_movers (skS.0 1 a a_1))) True) (Eq False True) % 9.56/9.80 Clause #147 (by clausification #[145]): ∀ (a a_1 : Iota), Eq (greater zero (growth_rate first_movers (skS.0 1 a a_1))) True % 9.56/9.80 Clause #149 (by superposition #[147, 93]): Eq True False % 9.56/9.80 Clause #150 (by clausification #[149]): False % 9.56/9.80 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------