%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : MGT020+1 : TPTP v9.3.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n007.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 06:06:15 AM UTC 2026 % Result : Theorem 4.26s 4.57s % Output : Proof 4.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT020+1 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.05 % Command : duper %s % 0.12/0.37 % Computer : n007.cluster.edu % 0.12/0.37 % Model : x86_64 x86_64 % 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.37 % Memory : 8046.5625MB % 0.12/0.37 % OS : Linux 6.8.0-71-generic % 0.12/0.37 % CPULimit : 300 % 0.12/0.37 % WCLimit : 300 % 0.12/0.37 % DateTime : Mon Sep 7 11:58:26 UTC 2026 % 0.12/0.38 % CPUTime : % 4.26/4.57 SZS status Theorem for theBenchmark.p % 4.26/4.57 SZS output start Proof for theBenchmark.p % 4.26/4.57 Clause #0 (by assumption #[]): Eq % 4.26/4.57 (∀ (E T : Iota), % 4.26/4.57 And (environment E) (subpopulations first_movers efficient_producers E T) → % 4.26/4.57 Not (decreases (difference (disbanding_rate first_movers T) (disbanding_rate efficient_producers T)))) % 4.26/4.57 True % 4.26/4.57 Clause #1 (by assumption #[]): Eq % 4.26/4.57 (∀ (E T : Iota), % 4.26/4.57 environment E → % 4.26/4.57 And (in_environment E (initial_FM_EP E) → subpopulations first_movers efficient_producers E (initial_FM_EP E)) % 4.26/4.57 (subpopulations first_movers efficient_producers E T → greater_or_equal T (initial_FM_EP E))) % 4.26/4.57 True % 4.26/4.57 Clause #2 (by assumption #[]): Eq % 4.26/4.57 (∀ (E T T1 T2 : Iota), % 4.26/4.57 And % 4.26/4.57 (And (And (And (environment E) (greater_or_equal T T1)) (greater_or_equal T2 T)) % 4.26/4.57 (subpopulations first_movers efficient_producers E T2)) % 4.26/4.57 (greater (disbanding_rate first_movers T1) (disbanding_rate efficient_producers T1)) → % 4.26/4.57 Not (decreases (difference (disbanding_rate first_movers T) (disbanding_rate efficient_producers T))) → % 4.26/4.57 greater (disbanding_rate first_movers T2) (disbanding_rate efficient_producers T2)) % 4.26/4.57 True % 4.26/4.57 Clause #3 (by assumption #[]): Eq (∀ (E T : Iota), And (environment E) (subpopulations first_movers efficient_producers E T) → in_environment E T) True % 4.26/4.57 Clause #4 (by assumption #[]): Eq (∀ (E : Iota), environment E → greater_or_equal (initial_FM_EP E) (start_time E)) True % 4.26/4.57 Clause #5 (by assumption #[]): Eq % 4.26/4.57 (∀ (E T1 T2 : Iota), % 4.26/4.57 And (And (And (environment E) (greater_or_equal T1 (start_time E))) (greater T2 T1)) (in_environment E T2) → % 4.26/4.57 in_environment E T1) % 4.26/4.57 True % 4.26/4.57 Clause #7 (by assumption #[]): Eq (∀ (X Y : Iota), greater_or_equal X Y → Or (greater X Y) (Eq X Y)) True % 4.26/4.57 Clause #8 (by assumption #[]): Eq % 4.26/4.57 (∀ (E : Iota), % 4.26/4.57 environment E → % 4.26/4.57 greater (disbanding_rate first_movers (initial_FM_EP E)) (disbanding_rate efficient_producers (initial_FM_EP E))) % 4.26/4.57 True % 4.26/4.57 Clause #10 (by assumption #[]): Eq % 4.26/4.57 (Not % 4.26/4.57 (∀ (E T : Iota), % 4.26/4.57 And (environment E) (subpopulations first_movers efficient_producers E T) → % 4.26/4.57 greater (disbanding_rate first_movers T) (disbanding_rate efficient_producers T))) % 4.26/4.57 True % 4.26/4.57 Clause #11 (by clausification #[3]): ∀ (a : Iota), % 4.26/4.57 Eq (∀ (T : Iota), And (environment a) (subpopulations first_movers efficient_producers a T) → in_environment a T) True % 4.26/4.57 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), % 4.26/4.57 Eq (And (environment a) (subpopulations first_movers efficient_producers a a_1) → in_environment a a_1) True % 4.26/4.57 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), % 4.26/4.57 Or (Eq (And (environment a) (subpopulations first_movers efficient_producers a a_1)) False) % 4.26/4.57 (Eq (in_environment a a_1) True) % 4.26/4.57 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), % 4.26/4.57 Or (Eq (in_environment a a_1) True) % 4.26/4.57 (Or (Eq (environment a) False) (Eq (subpopulations first_movers efficient_producers a a_1) False)) % 4.26/4.57 Clause #20 (by clausification #[5]): ∀ (a : Iota), % 4.26/4.57 Eq % 4.26/4.57 (∀ (T1 T2 : Iota), % 4.26/4.57 And (And (And (environment a) (greater_or_equal T1 (start_time a))) (greater T2 T1)) (in_environment a T2) → % 4.26/4.57 in_environment a T1) % 4.26/4.57 True % 4.26/4.57 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), % 4.26/4.57 Eq % 4.26/4.57 (∀ (T2 : Iota), % 4.26/4.57 And (And (And (environment a) (greater_or_equal a_1 (start_time a))) (greater T2 a_1)) (in_environment a T2) → % 4.26/4.57 in_environment a a_1) % 4.26/4.57 True % 4.26/4.57 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), % 4.26/4.57 Eq % 4.26/4.57 (And (And (And (environment a) (greater_or_equal a_1 (start_time a))) (greater a_2 a_1)) (in_environment a a_2) → % 4.26/4.57 in_environment a a_1) % 4.26/4.57 True % 4.26/4.57 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), % 4.26/4.57 Or % 4.26/4.57 (Eq (And (And (And (environment a) (greater_or_equal a_1 (start_time a))) (greater a_2 a_1)) (in_environment a a_2)) % 4.26/4.57 False) % 4.26/4.57 (Eq (in_environment a a_1) True) % 4.26/4.57 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), % 4.26/4.57 Or (Eq (in_environment a a_1) True) % 4.26/4.57 (Or (Eq (And (And (environment a) (greater_or_equal a_1 (start_time a))) (greater a_2 a_1)) False) % 4.26/4.58 (Eq (in_environment a a_2) False)) % 4.26/4.58 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), % 4.26/4.58 Or (Eq (in_environment a a_1) True) % 4.26/4.58 (Or (Eq (in_environment a a_2) False) % 4.26/4.58 (Or (Eq (And (environment a) (greater_or_equal a_1 (start_time a))) False) (Eq (greater a_2 a_1) False))) % 4.26/4.58 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), % 4.26/4.58 Or (Eq (in_environment a a_1) True) % 4.26/4.58 (Or (Eq (in_environment a a_2) False) % 4.26/4.58 (Or (Eq (greater a_2 a_1) False) % 4.26/4.58 (Or (Eq (environment a) False) (Eq (greater_or_equal a_1 (start_time a)) False)))) % 4.26/4.58 Clause #27 (by clausification #[4]): ∀ (a : Iota), Eq (environment a → greater_or_equal (initial_FM_EP a) (start_time a)) True % 4.26/4.58 Clause #28 (by clausification #[27]): ∀ (a : Iota), Or (Eq (environment a) False) (Eq (greater_or_equal (initial_FM_EP a) (start_time a)) True) % 4.26/4.58 Clause #38 (by clausification #[0]): ∀ (a : Iota), % 4.26/4.58 Eq % 4.26/4.58 (∀ (T : Iota), % 4.26/4.58 And (environment a) (subpopulations first_movers efficient_producers a T) → % 4.26/4.58 Not (decreases (difference (disbanding_rate first_movers T) (disbanding_rate efficient_producers T)))) % 4.26/4.58 True % 4.26/4.58 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), % 4.26/4.58 Eq % 4.26/4.58 (And (environment a) (subpopulations first_movers efficient_producers a a_1) → % 4.26/4.58 Not (decreases (difference (disbanding_rate first_movers a_1) (disbanding_rate efficient_producers a_1)))) % 4.26/4.58 True % 4.26/4.58 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), % 4.26/4.58 Or (Eq (And (environment a) (subpopulations first_movers efficient_producers a a_1)) False) % 4.26/4.58 (Eq (Not (decreases (difference (disbanding_rate first_movers a_1) (disbanding_rate efficient_producers a_1)))) % 4.26/4.58 True) % 4.26/4.58 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), % 4.26/4.58 Or (Eq (Not (decreases (difference (disbanding_rate first_movers a) (disbanding_rate efficient_producers a)))) True) % 4.26/4.58 (Or (Eq (environment a_1) False) (Eq (subpopulations first_movers efficient_producers a_1 a) False)) % 4.26/4.58 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), % 4.26/4.58 Or (Eq (environment a) False) % 4.26/4.58 (Or (Eq (subpopulations first_movers efficient_producers a a_1) False) % 4.26/4.58 (Eq (decreases (difference (disbanding_rate first_movers a_1) (disbanding_rate efficient_producers a_1))) False)) % 4.26/4.58 Clause #43 (by clausification #[8]): ∀ (a : Iota), % 4.26/4.58 Eq % 4.26/4.58 (environment a → % 4.26/4.58 greater (disbanding_rate first_movers (initial_FM_EP a)) (disbanding_rate efficient_producers (initial_FM_EP a))) % 4.26/4.58 True % 4.26/4.58 Clause #44 (by clausification #[43]): ∀ (a : Iota), % 4.26/4.58 Or (Eq (environment a) False) % 4.26/4.58 (Eq % 4.26/4.58 (greater (disbanding_rate first_movers (initial_FM_EP a)) (disbanding_rate efficient_producers (initial_FM_EP a))) % 4.26/4.58 True) % 4.26/4.58 Clause #45 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (Y : Iota), greater_or_equal a Y → Or (greater a Y) (Eq a Y)) True % 4.26/4.58 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), Eq (greater_or_equal a a_1 → Or (greater a a_1) (Eq a a_1)) True % 4.26/4.58 Clause #47 (by clausification #[46]): ∀ (a a_1 : Iota), Or (Eq (greater_or_equal a a_1) False) (Eq (Or (greater a a_1) (Eq a a_1)) True) % 4.26/4.58 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota), Or (Eq (greater_or_equal a a_1) False) (Or (Eq (greater a a_1) True) (Eq (Eq a a_1) True)) % 4.26/4.58 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota), Or (Eq (greater_or_equal a a_1) False) (Or (Eq (greater a a_1) True) (Eq a a_1)) % 4.26/4.58 Clause #50 (by clausification #[10]): Eq % 4.26/4.58 (∀ (E T : Iota), % 4.26/4.58 And (environment E) (subpopulations first_movers efficient_producers E T) → % 4.26/4.58 greater (disbanding_rate first_movers T) (disbanding_rate efficient_producers T)) % 4.26/4.58 False % 4.26/4.58 Clause #51 (by clausification #[50]): ∀ (a : Iota), % 4.26/4.58 Eq % 4.26/4.58 (Not % 4.26/4.58 (∀ (T : Iota), % 4.26/4.58 And (environment (skS.0 0 a)) (subpopulations first_movers efficient_producers (skS.0 0 a) T) → % 4.26/4.58 greater (disbanding_rate first_movers T) (disbanding_rate efficient_producers T))) % 4.26/4.58 True % 4.26/4.58 Clause #52 (by clausification #[51]): ∀ (a : Iota), % 4.26/4.58 Eq % 4.26/4.58 (∀ (T : Iota), % 4.26/4.58 And (environment (skS.0 0 a)) (subpopulations first_movers efficient_producers (skS.0 0 a) T) → % 4.26/4.58 greater (disbanding_rate first_movers T) (disbanding_rate efficient_producers T)) % 4.36/4.60 False % 4.36/4.60 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), % 4.36/4.60 Eq % 4.36/4.60 (Not % 4.36/4.60 (And (environment (skS.0 0 a)) (subpopulations first_movers efficient_producers (skS.0 0 a) (skS.0 1 a a_1)) → % 4.36/4.60 greater (disbanding_rate first_movers (skS.0 1 a a_1)) (disbanding_rate efficient_producers (skS.0 1 a a_1)))) % 4.36/4.60 True % 4.36/4.60 Clause #54 (by clausification #[53]): ∀ (a a_1 : Iota), % 4.36/4.60 Eq % 4.36/4.60 (And (environment (skS.0 0 a)) (subpopulations first_movers efficient_producers (skS.0 0 a) (skS.0 1 a a_1)) → % 4.36/4.60 greater (disbanding_rate first_movers (skS.0 1 a a_1)) (disbanding_rate efficient_producers (skS.0 1 a a_1))) % 4.36/4.60 False % 4.36/4.60 Clause #55 (by clausification #[54]): ∀ (a a_1 : Iota), % 4.36/4.60 Eq (And (environment (skS.0 0 a)) (subpopulations first_movers efficient_producers (skS.0 0 a) (skS.0 1 a a_1))) True % 4.36/4.60 Clause #56 (by clausification #[54]): ∀ (a a_1 : Iota), % 4.36/4.60 Eq (greater (disbanding_rate first_movers (skS.0 1 a a_1)) (disbanding_rate efficient_producers (skS.0 1 a a_1))) % 4.36/4.60 False % 4.36/4.60 Clause #57 (by clausification #[55]): ∀ (a a_1 : Iota), Eq (subpopulations first_movers efficient_producers (skS.0 0 a) (skS.0 1 a a_1)) True % 4.36/4.60 Clause #58 (by clausification #[55]): ∀ (a : Iota), Eq (environment (skS.0 0 a)) True % 4.36/4.60 Clause #59 (by superposition #[58, 14]): ∀ (a a_1 : Iota), % 4.36/4.60 Or (Eq (in_environment (skS.0 0 a) a_1) True) % 4.36/4.60 (Or (Eq True False) (Eq (subpopulations first_movers efficient_producers (skS.0 0 a) a_1) False)) % 4.36/4.60 Clause #60 (by superposition #[58, 28]): ∀ (a : Iota), Or (Eq True False) (Eq (greater_or_equal (initial_FM_EP (skS.0 0 a)) (start_time (skS.0 0 a))) True) % 4.36/4.60 Clause #61 (by superposition #[58, 42]): ∀ (a a_1 : Iota), % 4.36/4.60 Or (Eq True False) % 4.36/4.60 (Or (Eq (subpopulations first_movers efficient_producers (skS.0 0 a) a_1) False) % 4.36/4.60 (Eq (decreases (difference (disbanding_rate first_movers a_1) (disbanding_rate efficient_producers a_1))) False)) % 4.36/4.60 Clause #62 (by superposition #[58, 44]): ∀ (a : Iota), % 4.36/4.60 Or (Eq True False) % 4.36/4.60 (Eq % 4.36/4.60 (greater (disbanding_rate first_movers (initial_FM_EP (skS.0 0 a))) % 4.36/4.60 (disbanding_rate efficient_producers (initial_FM_EP (skS.0 0 a)))) % 4.36/4.60 True) % 4.36/4.60 Clause #63 (by clausification #[2]): ∀ (a : Iota), % 4.36/4.60 Eq % 4.36/4.60 (∀ (T T1 T2 : Iota), % 4.36/4.60 And % 4.36/4.60 (And (And (And (environment a) (greater_or_equal T T1)) (greater_or_equal T2 T)) % 4.36/4.60 (subpopulations first_movers efficient_producers a T2)) % 4.36/4.60 (greater (disbanding_rate first_movers T1) (disbanding_rate efficient_producers T1)) → % 4.36/4.60 Not (decreases (difference (disbanding_rate first_movers T) (disbanding_rate efficient_producers T))) → % 4.36/4.60 greater (disbanding_rate first_movers T2) (disbanding_rate efficient_producers T2)) % 4.36/4.60 True % 4.36/4.60 Clause #64 (by clausification #[63]): ∀ (a a_1 : Iota), % 4.36/4.60 Eq % 4.36/4.60 (∀ (T1 T2 : Iota), % 4.36/4.60 And % 4.36/4.60 (And (And (And (environment a) (greater_or_equal a_1 T1)) (greater_or_equal T2 a_1)) % 4.36/4.60 (subpopulations first_movers efficient_producers a T2)) % 4.36/4.60 (greater (disbanding_rate first_movers T1) (disbanding_rate efficient_producers T1)) → % 4.36/4.60 Not (decreases (difference (disbanding_rate first_movers a_1) (disbanding_rate efficient_producers a_1))) → % 4.36/4.60 greater (disbanding_rate first_movers T2) (disbanding_rate efficient_producers T2)) % 4.36/4.60 True % 4.36/4.60 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota), % 4.36/4.60 Eq % 4.36/4.60 (∀ (T2 : Iota), % 4.36/4.60 And % 4.36/4.60 (And (And (And (environment a) (greater_or_equal a_1 a_2)) (greater_or_equal T2 a_1)) % 4.36/4.60 (subpopulations first_movers efficient_producers a T2)) % 4.36/4.60 (greater (disbanding_rate first_movers a_2) (disbanding_rate efficient_producers a_2)) → % 4.36/4.60 Not (decreases (difference (disbanding_rate first_movers a_1) (disbanding_rate efficient_producers a_1))) → % 4.36/4.60 greater (disbanding_rate first_movers T2) (disbanding_rate efficient_producers T2)) % 4.36/4.60 True % 4.36/4.60 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 a_3 : Iota), % 4.36/4.60 Eq % 4.36/4.60 (And % 4.36/4.60 (And (And (And (environment a) (greater_or_equal a_1 a_2)) (greater_or_equal a_3 a_1)) % 4.36/4.62 (subpopulations first_movers efficient_producers a a_3)) % 4.36/4.62 (greater (disbanding_rate first_movers a_2) (disbanding_rate efficient_producers a_2)) → % 4.36/4.62 Not (decreases (difference (disbanding_rate first_movers a_1) (disbanding_rate efficient_producers a_1))) → % 4.36/4.62 greater (disbanding_rate first_movers a_3) (disbanding_rate efficient_producers a_3)) % 4.36/4.62 True % 4.36/4.62 Clause #67 (by clausification #[66]): ∀ (a a_1 a_2 a_3 : Iota), % 4.36/4.62 Or % 4.36/4.62 (Eq % 4.36/4.62 (And % 4.36/4.62 (And (And (And (environment a) (greater_or_equal a_1 a_2)) (greater_or_equal a_3 a_1)) % 4.36/4.62 (subpopulations first_movers efficient_producers a a_3)) % 4.36/4.62 (greater (disbanding_rate first_movers a_2) (disbanding_rate efficient_producers a_2))) % 4.36/4.62 False) % 4.36/4.62 (Eq % 4.36/4.62 (Not (decreases (difference (disbanding_rate first_movers a_1) (disbanding_rate efficient_producers a_1))) → % 4.36/4.62 greater (disbanding_rate first_movers a_3) (disbanding_rate efficient_producers a_3)) % 4.36/4.62 True) % 4.36/4.62 Clause #68 (by clausification #[67]): ∀ (a a_1 a_2 a_3 : Iota), % 4.36/4.62 Or % 4.36/4.62 (Eq % 4.36/4.62 (Not (decreases (difference (disbanding_rate first_movers a) (disbanding_rate efficient_producers a))) → % 4.36/4.62 greater (disbanding_rate first_movers a_1) (disbanding_rate efficient_producers a_1)) % 4.36/4.62 True) % 4.36/4.62 (Or % 4.36/4.62 (Eq % 4.36/4.62 (And (And (And (environment a_2) (greater_or_equal a a_3)) (greater_or_equal a_1 a)) % 4.36/4.62 (subpopulations first_movers efficient_producers a_2 a_1)) % 4.36/4.62 False) % 4.36/4.62 (Eq (greater (disbanding_rate first_movers a_3) (disbanding_rate efficient_producers a_3)) False)) % 4.36/4.62 Clause #69 (by clausification #[68]): ∀ (a a_1 a_2 a_3 : Iota), % 4.36/4.62 Or % 4.36/4.62 (Eq % 4.36/4.62 (And (And (And (environment a) (greater_or_equal a_1 a_2)) (greater_or_equal a_3 a_1)) % 4.36/4.62 (subpopulations first_movers efficient_producers a a_3)) % 4.36/4.62 False) % 4.36/4.62 (Or (Eq (greater (disbanding_rate first_movers a_2) (disbanding_rate efficient_producers a_2)) False) % 4.36/4.62 (Or % 4.36/4.62 (Eq (Not (decreases (difference (disbanding_rate first_movers a_1) (disbanding_rate efficient_producers a_1)))) % 4.36/4.62 False) % 4.36/4.62 (Eq (greater (disbanding_rate first_movers a_3) (disbanding_rate efficient_producers a_3)) True))) % 4.36/4.62 Clause #70 (by clausification #[69]): ∀ (a a_1 a_2 a_3 : Iota), % 4.36/4.62 Or (Eq (greater (disbanding_rate first_movers a) (disbanding_rate efficient_producers a)) False) % 4.36/4.62 (Or % 4.36/4.62 (Eq (Not (decreases (difference (disbanding_rate first_movers a_1) (disbanding_rate efficient_producers a_1)))) % 4.36/4.62 False) % 4.36/4.62 (Or (Eq (greater (disbanding_rate first_movers a_2) (disbanding_rate efficient_producers a_2)) True) % 4.36/4.62 (Or (Eq (And (And (environment a_3) (greater_or_equal a_1 a)) (greater_or_equal a_2 a_1)) False) % 4.36/4.62 (Eq (subpopulations first_movers efficient_producers a_3 a_2) False)))) % 4.36/4.62 Clause #71 (by clausification #[70]): ∀ (a a_1 a_2 a_3 : Iota), % 4.36/4.62 Or (Eq (greater (disbanding_rate first_movers a) (disbanding_rate efficient_producers a)) False) % 4.36/4.62 (Or (Eq (greater (disbanding_rate first_movers a_1) (disbanding_rate efficient_producers a_1)) True) % 4.36/4.62 (Or (Eq (And (And (environment a_2) (greater_or_equal a_3 a)) (greater_or_equal a_1 a_3)) False) % 4.36/4.62 (Or (Eq (subpopulations first_movers efficient_producers a_2 a_1) False) % 4.36/4.62 (Eq (decreases (difference (disbanding_rate first_movers a_3) (disbanding_rate efficient_producers a_3))) % 4.36/4.62 True)))) % 4.36/4.62 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 a_3 : Iota), % 4.36/4.62 Or (Eq (greater (disbanding_rate first_movers a) (disbanding_rate efficient_producers a)) False) % 4.36/4.62 (Or (Eq (greater (disbanding_rate first_movers a_1) (disbanding_rate efficient_producers a_1)) True) % 4.36/4.62 (Or (Eq (subpopulations first_movers efficient_producers a_2 a_1) False) % 4.36/4.62 (Or % 4.36/4.62 (Eq (decreases (difference (disbanding_rate first_movers a_3) (disbanding_rate efficient_producers a_3))) % 4.36/4.62 True) % 4.36/4.62 (Or (Eq (And (environment a_2) (greater_or_equal a_3 a)) False) (Eq (greater_or_equal a_1 a_3) False))))) % 4.36/4.62 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 a_3 : Iota), % 4.36/4.62 Or (Eq (greater (disbanding_rate first_movers a) (disbanding_rate efficient_producers a)) False) % 4.36/4.63 (Or (Eq (greater (disbanding_rate first_movers a_1) (disbanding_rate efficient_producers a_1)) True) % 4.36/4.63 (Or (Eq (subpopulations first_movers efficient_producers a_2 a_1) False) % 4.36/4.63 (Or % 4.36/4.63 (Eq (decreases (difference (disbanding_rate first_movers a_3) (disbanding_rate efficient_producers a_3))) % 4.36/4.63 True) % 4.36/4.63 (Or (Eq (greater_or_equal a_1 a_3) False) % 4.36/4.63 (Or (Eq (environment a_2) False) (Eq (greater_or_equal a_3 a) False)))))) % 4.36/4.63 Clause #74 (by clausification #[1]): ∀ (a : Iota), % 4.36/4.63 Eq % 4.36/4.63 (∀ (T : Iota), % 4.36/4.63 environment a → % 4.36/4.63 And (in_environment a (initial_FM_EP a) → subpopulations first_movers efficient_producers a (initial_FM_EP a)) % 4.36/4.63 (subpopulations first_movers efficient_producers a T → greater_or_equal T (initial_FM_EP a))) % 4.36/4.63 True % 4.36/4.63 Clause #75 (by clausification #[74]): ∀ (a a_1 : Iota), % 4.36/4.63 Eq % 4.36/4.63 (environment a → % 4.36/4.63 And (in_environment a (initial_FM_EP a) → subpopulations first_movers efficient_producers a (initial_FM_EP a)) % 4.36/4.63 (subpopulations first_movers efficient_producers a a_1 → greater_or_equal a_1 (initial_FM_EP a))) % 4.36/4.63 True % 4.36/4.63 Clause #76 (by clausification #[75]): ∀ (a a_1 : Iota), % 4.36/4.63 Or (Eq (environment a) False) % 4.36/4.63 (Eq % 4.36/4.63 (And (in_environment a (initial_FM_EP a) → subpopulations first_movers efficient_producers a (initial_FM_EP a)) % 4.36/4.63 (subpopulations first_movers efficient_producers a a_1 → greater_or_equal a_1 (initial_FM_EP a))) % 4.36/4.63 True) % 4.36/4.63 Clause #77 (by clausification #[76]): ∀ (a a_1 : Iota), % 4.36/4.63 Or (Eq (environment a) False) % 4.36/4.63 (Eq (subpopulations first_movers efficient_producers a a_1 → greater_or_equal a_1 (initial_FM_EP a)) True) % 4.36/4.63 Clause #78 (by clausification #[76]): ∀ (a : Iota), % 4.36/4.63 Or (Eq (environment a) False) % 4.36/4.63 (Eq (in_environment a (initial_FM_EP a) → subpopulations first_movers efficient_producers a (initial_FM_EP a)) True) % 4.36/4.63 Clause #79 (by clausification #[77]): ∀ (a a_1 : Iota), % 4.36/4.63 Or (Eq (environment a) False) % 4.36/4.63 (Or (Eq (subpopulations first_movers efficient_producers a a_1) False) % 4.36/4.63 (Eq (greater_or_equal a_1 (initial_FM_EP a)) True)) % 4.36/4.63 Clause #80 (by superposition #[79, 58]): ∀ (a a_1 : Iota), % 4.36/4.63 Or (Eq (subpopulations first_movers efficient_producers (skS.0 0 a) a_1) False) % 4.36/4.63 (Or (Eq (greater_or_equal a_1 (initial_FM_EP (skS.0 0 a))) True) (Eq False True)) % 4.36/4.63 Clause #81 (by clausification #[78]): ∀ (a : Iota), % 4.36/4.63 Or (Eq (environment a) False) % 4.36/4.63 (Or (Eq (in_environment a (initial_FM_EP a)) False) % 4.36/4.63 (Eq (subpopulations first_movers efficient_producers a (initial_FM_EP a)) True)) % 4.36/4.63 Clause #82 (by superposition #[81, 58]): ∀ (a : Iota), % 4.36/4.63 Or (Eq (in_environment (skS.0 0 a) (initial_FM_EP (skS.0 0 a))) False) % 4.36/4.63 (Or (Eq (subpopulations first_movers efficient_producers (skS.0 0 a) (initial_FM_EP (skS.0 0 a))) True) % 4.36/4.63 (Eq False True)) % 4.36/4.63 Clause #83 (by clausification #[60]): ∀ (a : Iota), Eq (greater_or_equal (initial_FM_EP (skS.0 0 a)) (start_time (skS.0 0 a))) True % 4.36/4.63 Clause #86 (by clausification #[62]): ∀ (a : Iota), % 4.36/4.63 Eq % 4.36/4.63 (greater (disbanding_rate first_movers (initial_FM_EP (skS.0 0 a))) % 4.36/4.63 (disbanding_rate efficient_producers (initial_FM_EP (skS.0 0 a)))) % 4.36/4.63 True % 4.36/4.63 Clause #87 (by superposition #[86, 73]): ∀ (a a_1 a_2 a_3 : Iota), % 4.36/4.63 Or (Eq True False) % 4.36/4.63 (Or (Eq (greater (disbanding_rate first_movers a) (disbanding_rate efficient_producers a)) True) % 4.36/4.63 (Or (Eq (subpopulations first_movers efficient_producers a_1 a) False) % 4.36/4.63 (Or % 4.36/4.63 (Eq (decreases (difference (disbanding_rate first_movers a_2) (disbanding_rate efficient_producers a_2))) % 4.36/4.63 True) % 4.36/4.63 (Or (Eq (greater_or_equal a a_2) False) % 4.36/4.63 (Or (Eq (environment a_1) False) (Eq (greater_or_equal a_2 (initial_FM_EP (skS.0 0 a_3))) False)))))) % 4.36/4.63 Clause #89 (by clausification #[59]): ∀ (a a_1 : Iota), % 4.36/4.63 Or (Eq (in_environment (skS.0 0 a) a_1) True) % 4.36/4.63 (Eq (subpopulations first_movers efficient_producers (skS.0 0 a) a_1) False) % 4.36/4.63 Clause #90 (by superposition #[89, 57]): ∀ (a a_1 : Iota), Or (Eq (in_environment (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq False True) % 4.36/4.65 Clause #91 (by clausification #[61]): ∀ (a a_1 : Iota), % 4.36/4.65 Or (Eq (subpopulations first_movers efficient_producers (skS.0 0 a) a_1) False) % 4.36/4.65 (Eq (decreases (difference (disbanding_rate first_movers a_1) (disbanding_rate efficient_producers a_1))) False) % 4.36/4.65 Clause #93 (by clausification #[90]): ∀ (a a_1 : Iota), Eq (in_environment (skS.0 0 a) (skS.0 1 a a_1)) True % 4.36/4.65 Clause #94 (by superposition #[93, 26]): ∀ (a a_1 a_2 : Iota), % 4.36/4.65 Or (Eq (in_environment (skS.0 0 a) a_1) True) % 4.36/4.65 (Or (Eq True False) % 4.36/4.65 (Or (Eq (greater (skS.0 1 a a_2) a_1) False) % 4.36/4.65 (Or (Eq (environment (skS.0 0 a)) False) (Eq (greater_or_equal a_1 (start_time (skS.0 0 a))) False)))) % 4.36/4.65 Clause #95 (by clausification #[80]): ∀ (a a_1 : Iota), % 4.36/4.65 Or (Eq (subpopulations first_movers efficient_producers (skS.0 0 a) a_1) False) % 4.36/4.65 (Eq (greater_or_equal a_1 (initial_FM_EP (skS.0 0 a))) True) % 4.36/4.65 Clause #96 (by superposition #[95, 57]): ∀ (a a_1 : Iota), Or (Eq (greater_or_equal (skS.0 1 a a_1) (initial_FM_EP (skS.0 0 a))) True) (Eq False True) % 4.36/4.65 Clause #97 (by clausification #[96]): ∀ (a a_1 : Iota), Eq (greater_or_equal (skS.0 1 a a_1) (initial_FM_EP (skS.0 0 a))) True % 4.36/4.65 Clause #99 (by superposition #[97, 49]): ∀ (a a_1 : Iota), % 4.36/4.65 Or (Eq True False) % 4.36/4.65 (Or (Eq (greater (skS.0 1 a a_1) (initial_FM_EP (skS.0 0 a))) True) % 4.36/4.65 (Eq (skS.0 1 a a_1) (initial_FM_EP (skS.0 0 a)))) % 4.36/4.65 Clause #102 (by clausification #[82]): ∀ (a : Iota), % 4.36/4.65 Or (Eq (in_environment (skS.0 0 a) (initial_FM_EP (skS.0 0 a))) False) % 4.36/4.65 (Eq (subpopulations first_movers efficient_producers (skS.0 0 a) (initial_FM_EP (skS.0 0 a))) True) % 4.36/4.65 Clause #105 (by clausification #[99]): ∀ (a a_1 : Iota), % 4.36/4.65 Or (Eq (greater (skS.0 1 a a_1) (initial_FM_EP (skS.0 0 a))) True) (Eq (skS.0 1 a a_1) (initial_FM_EP (skS.0 0 a))) % 4.36/4.65 Clause #110 (by clausification #[94]): ∀ (a a_1 a_2 : Iota), % 4.36/4.65 Or (Eq (in_environment (skS.0 0 a) a_1) True) % 4.36/4.65 (Or (Eq (greater (skS.0 1 a a_2) a_1) False) % 4.36/4.65 (Or (Eq (environment (skS.0 0 a)) False) (Eq (greater_or_equal a_1 (start_time (skS.0 0 a))) False))) % 4.36/4.65 Clause #111 (by forward demodulation #[110, 58]): ∀ (a a_1 a_2 : Iota), % 4.36/4.65 Or (Eq (in_environment (skS.0 0 a) a_1) True) % 4.36/4.65 (Or (Eq (greater (skS.0 1 a a_2) a_1) False) % 4.36/4.65 (Or (Eq True False) (Eq (greater_or_equal a_1 (start_time (skS.0 0 a))) False))) % 4.36/4.65 Clause #112 (by clausification #[111]): ∀ (a a_1 a_2 : Iota), % 4.36/4.65 Or (Eq (in_environment (skS.0 0 a) a_1) True) % 4.36/4.65 (Or (Eq (greater (skS.0 1 a a_2) a_1) False) (Eq (greater_or_equal a_1 (start_time (skS.0 0 a))) False)) % 4.36/4.65 Clause #113 (by superposition #[112, 105]): ∀ (a a_1 : Iota), % 4.36/4.65 Or (Eq (in_environment (skS.0 0 a) (initial_FM_EP (skS.0 0 a))) True) % 4.36/4.65 (Or (Eq (greater_or_equal (initial_FM_EP (skS.0 0 a)) (start_time (skS.0 0 a))) False) % 4.36/4.65 (Or (Eq False True) (Eq (skS.0 1 a a_1) (initial_FM_EP (skS.0 0 a))))) % 4.36/4.65 Clause #115 (by clausification #[87]): ∀ (a a_1 a_2 a_3 : Iota), % 4.36/4.65 Or (Eq (greater (disbanding_rate first_movers a) (disbanding_rate efficient_producers a)) True) % 4.36/4.65 (Or (Eq (subpopulations first_movers efficient_producers a_1 a) False) % 4.36/4.65 (Or % 4.36/4.65 (Eq (decreases (difference (disbanding_rate first_movers a_2) (disbanding_rate efficient_producers a_2))) True) % 4.36/4.65 (Or (Eq (greater_or_equal a a_2) False) % 4.36/4.65 (Or (Eq (environment a_1) False) (Eq (greater_or_equal a_2 (initial_FM_EP (skS.0 0 a_3))) False))))) % 4.36/4.65 Clause #116 (by superposition #[115, 57]): ∀ (a a_1 a_2 a_3 : Iota), % 4.36/4.65 Or % 4.36/4.65 (Eq (greater (disbanding_rate first_movers (skS.0 1 a a_1)) (disbanding_rate efficient_producers (skS.0 1 a a_1))) % 4.36/4.65 True) % 4.36/4.65 (Or (Eq (decreases (difference (disbanding_rate first_movers a_2) (disbanding_rate efficient_producers a_2))) True) % 4.36/4.65 (Or (Eq (greater_or_equal (skS.0 1 a a_1) a_2) False) % 4.36/4.65 (Or (Eq (environment (skS.0 0 a)) False) % 4.36/4.65 (Or (Eq (greater_or_equal a_2 (initial_FM_EP (skS.0 0 a_3))) False) (Eq False True))))) % 4.36/4.65 Clause #124 (by clausification #[113]): ∀ (a a_1 : Iota), % 4.36/4.65 Or (Eq (in_environment (skS.0 0 a) (initial_FM_EP (skS.0 0 a))) True) % 4.36/4.65 (Or (Eq (greater_or_equal (initial_FM_EP (skS.0 0 a)) (start_time (skS.0 0 a))) False) % 4.36/4.67 (Eq (skS.0 1 a a_1) (initial_FM_EP (skS.0 0 a)))) % 4.36/4.67 Clause #125 (by superposition #[124, 83]): ∀ (a a_1 : Iota), % 4.36/4.67 Or (Eq (in_environment (skS.0 0 a) (initial_FM_EP (skS.0 0 a))) True) % 4.36/4.67 (Or (Eq (skS.0 1 a a_1) (initial_FM_EP (skS.0 0 a))) (Eq False True)) % 4.36/4.67 Clause #129 (by clausification #[125]): ∀ (a a_1 : Iota), % 4.36/4.67 Or (Eq (in_environment (skS.0 0 a) (initial_FM_EP (skS.0 0 a))) True) (Eq (skS.0 1 a a_1) (initial_FM_EP (skS.0 0 a))) % 4.36/4.67 Clause #134 (by superposition #[129, 93]): ∀ (a : Iota), % 4.36/4.67 Or (Eq (in_environment (skS.0 0 a) (initial_FM_EP (skS.0 0 a))) True) % 4.36/4.67 (Eq (in_environment (skS.0 0 a) (initial_FM_EP (skS.0 0 a))) True) % 4.36/4.67 Clause #139 (by eliminate duplicate literals #[134]): ∀ (a : Iota), Eq (in_environment (skS.0 0 a) (initial_FM_EP (skS.0 0 a))) True % 4.36/4.67 Clause #140 (by backward demodulation #[139, 102]): ∀ (a : Iota), % 4.36/4.67 Or (Eq True False) (Eq (subpopulations first_movers efficient_producers (skS.0 0 a) (initial_FM_EP (skS.0 0 a))) True) % 4.36/4.67 Clause #142 (by clausification #[140]): ∀ (a : Iota), Eq (subpopulations first_movers efficient_producers (skS.0 0 a) (initial_FM_EP (skS.0 0 a))) True % 4.36/4.67 Clause #145 (by superposition #[142, 91]): ∀ (a : Iota), % 4.36/4.67 Or (Eq True False) % 4.36/4.67 (Eq % 4.36/4.67 (decreases % 4.36/4.67 (difference (disbanding_rate first_movers (initial_FM_EP (skS.0 0 a))) % 4.36/4.67 (disbanding_rate efficient_producers (initial_FM_EP (skS.0 0 a))))) % 4.36/4.67 False) % 4.36/4.67 Clause #146 (by superposition #[142, 95]): ∀ (a : Iota), Or (Eq True False) (Eq (greater_or_equal (initial_FM_EP (skS.0 0 a)) (initial_FM_EP (skS.0 0 a))) True) % 4.36/4.67 Clause #148 (by clausification #[146]): ∀ (a : Iota), Eq (greater_or_equal (initial_FM_EP (skS.0 0 a)) (initial_FM_EP (skS.0 0 a))) True % 4.36/4.67 Clause #151 (by clausification #[116]): ∀ (a a_1 a_2 a_3 : Iota), % 4.36/4.67 Or % 4.36/4.67 (Eq (greater (disbanding_rate first_movers (skS.0 1 a a_1)) (disbanding_rate efficient_producers (skS.0 1 a a_1))) % 4.36/4.67 True) % 4.36/4.67 (Or (Eq (decreases (difference (disbanding_rate first_movers a_2) (disbanding_rate efficient_producers a_2))) True) % 4.36/4.67 (Or (Eq (greater_or_equal (skS.0 1 a a_1) a_2) False) % 4.36/4.67 (Or (Eq (environment (skS.0 0 a)) False) (Eq (greater_or_equal a_2 (initial_FM_EP (skS.0 0 a_3))) False)))) % 4.36/4.67 Clause #152 (by forward demodulation #[151, 58]): ∀ (a a_1 a_2 a_3 : Iota), % 4.36/4.67 Or % 4.36/4.67 (Eq (greater (disbanding_rate first_movers (skS.0 1 a a_1)) (disbanding_rate efficient_producers (skS.0 1 a a_1))) % 4.36/4.67 True) % 4.36/4.67 (Or (Eq (decreases (difference (disbanding_rate first_movers a_2) (disbanding_rate efficient_producers a_2))) True) % 4.36/4.67 (Or (Eq (greater_or_equal (skS.0 1 a a_1) a_2) False) % 4.36/4.67 (Or (Eq True False) (Eq (greater_or_equal a_2 (initial_FM_EP (skS.0 0 a_3))) False)))) % 4.36/4.67 Clause #153 (by clausification #[152]): ∀ (a a_1 a_2 a_3 : Iota), % 4.36/4.67 Or % 4.36/4.67 (Eq (greater (disbanding_rate first_movers (skS.0 1 a a_1)) (disbanding_rate efficient_producers (skS.0 1 a a_1))) % 4.36/4.67 True) % 4.36/4.67 (Or (Eq (decreases (difference (disbanding_rate first_movers a_2) (disbanding_rate efficient_producers a_2))) True) % 4.36/4.67 (Or (Eq (greater_or_equal (skS.0 1 a a_1) a_2) False) % 4.36/4.67 (Eq (greater_or_equal a_2 (initial_FM_EP (skS.0 0 a_3))) False))) % 4.36/4.67 Clause #154 (by superposition #[153, 97]): ∀ (a a_1 a_2 : Iota), % 4.36/4.67 Or % 4.36/4.67 (Eq (greater (disbanding_rate first_movers (skS.0 1 a a_1)) (disbanding_rate efficient_producers (skS.0 1 a a_1))) % 4.36/4.67 True) % 4.36/4.67 (Or % 4.36/4.67 (Eq % 4.36/4.67 (decreases % 4.36/4.67 (difference (disbanding_rate first_movers (initial_FM_EP (skS.0 0 a))) % 4.36/4.67 (disbanding_rate efficient_producers (initial_FM_EP (skS.0 0 a))))) % 4.36/4.67 True) % 4.36/4.67 (Or (Eq (greater_or_equal (initial_FM_EP (skS.0 0 a)) (initial_FM_EP (skS.0 0 a_2))) False) (Eq False True))) % 4.36/4.67 Clause #155 (by clausification #[145]): ∀ (a : Iota), % 4.36/4.67 Eq % 4.36/4.67 (decreases % 4.36/4.67 (difference (disbanding_rate first_movers (initial_FM_EP (skS.0 0 a))) % 4.36/4.67 (disbanding_rate efficient_producers (initial_FM_EP (skS.0 0 a))))) % 4.36/4.67 False % 4.36/4.67 Clause #176 (by clausification #[154]): ∀ (a a_1 a_2 : Iota), % 4.36/4.67 Or % 4.36/4.67 (Eq (greater (disbanding_rate first_movers (skS.0 1 a a_1)) (disbanding_rate efficient_producers (skS.0 1 a a_1))) % 4.36/4.68 True) % 4.36/4.68 (Or % 4.36/4.68 (Eq % 4.36/4.68 (decreases % 4.36/4.68 (difference (disbanding_rate first_movers (initial_FM_EP (skS.0 0 a))) % 4.36/4.68 (disbanding_rate efficient_producers (initial_FM_EP (skS.0 0 a))))) % 4.36/4.68 True) % 4.36/4.68 (Eq (greater_or_equal (initial_FM_EP (skS.0 0 a)) (initial_FM_EP (skS.0 0 a_2))) False)) % 4.36/4.68 Clause #177 (by forward demodulation #[176, 155]): ∀ (a a_1 a_2 : Iota), % 4.36/4.68 Or % 4.36/4.68 (Eq (greater (disbanding_rate first_movers (skS.0 1 a a_1)) (disbanding_rate efficient_producers (skS.0 1 a a_1))) % 4.36/4.68 True) % 4.36/4.68 (Or (Eq False True) (Eq (greater_or_equal (initial_FM_EP (skS.0 0 a)) (initial_FM_EP (skS.0 0 a_2))) False)) % 4.36/4.68 Clause #178 (by clausification #[177]): ∀ (a a_1 a_2 : Iota), % 4.36/4.68 Or % 4.36/4.68 (Eq (greater (disbanding_rate first_movers (skS.0 1 a a_1)) (disbanding_rate efficient_producers (skS.0 1 a a_1))) % 4.36/4.68 True) % 4.36/4.68 (Eq (greater_or_equal (initial_FM_EP (skS.0 0 a)) (initial_FM_EP (skS.0 0 a_2))) False) % 4.36/4.68 Clause #179 (by superposition #[178, 148]): ∀ (a a_1 : Iota), % 4.36/4.68 Or % 4.36/4.68 (Eq (greater (disbanding_rate first_movers (skS.0 1 a a_1)) (disbanding_rate efficient_producers (skS.0 1 a a_1))) % 4.36/4.68 True) % 4.36/4.68 (Eq False True) % 4.36/4.68 Clause #180 (by clausification #[179]): ∀ (a a_1 : Iota), % 4.36/4.68 Eq (greater (disbanding_rate first_movers (skS.0 1 a a_1)) (disbanding_rate efficient_producers (skS.0 1 a a_1))) True % 4.36/4.68 Clause #182 (by superposition #[180, 56]): Eq True False % 4.36/4.68 Clause #184 (by clausification #[182]): False % 4.36/4.68 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------