%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : MGT036+3 : TPTP v9.3.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n016.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 8.80s 9.07s % Output : Proof 8.90s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : MGT036+3 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.04 % Command : duper %s % 0.08/0.36 % Computer : n016.cluster.edu % 0.08/0.36 % Model : x86_64 x86_64 % 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.36 % Memory : 8046.5625MB % 0.08/0.36 % OS : Linux 6.8.0-71-generic % 0.08/0.36 % CPULimit : 300 % 0.08/0.36 % WCLimit : 300 % 0.08/0.36 % DateTime : Mon Sep 7 12:46:32 UTC 2026 % 0.08/0.36 % CPUTime : % 8.80/9.07 SZS status Theorem for theBenchmark.p % 8.80/9.07 SZS output start Proof for theBenchmark.p % 8.80/9.07 Clause #0 (by assumption #[]): Eq (∀ (E S1 S2 T : Iota), And (environment E) (subpopulations S1 S2 E T) → subpopulations S2 S1 E T) True % 8.80/9.07 Clause #1 (by assumption #[]): Eq % 8.80/9.07 (∀ (E S1 S2 T : Iota), % 8.80/9.07 And (environment E) (subpopulations S1 S2 E T) → % 8.80/9.07 Iff (And (greater_or_equal (growth_rate S2 T) zero) (greater zero (growth_rate S1 T))) (outcompetes S2 S1 T)) % 8.80/9.07 True % 8.80/9.07 Clause #2 (by assumption #[]): Eq % 8.80/9.07 (Exists fun E => % 8.80/9.07 Exists fun T => % 8.80/9.07 And % 8.80/9.07 (And (And (environment E) (subpopulations first_movers efficient_producers E T)) % 8.80/9.07 (greater_or_equal (growth_rate first_movers T) zero)) % 8.80/9.07 (greater zero (growth_rate efficient_producers T))) % 8.80/9.07 True % 8.80/9.07 Clause #3 (by assumption #[]): Eq % 8.80/9.07 (Not % 8.80/9.07 (Exists fun E => % 8.80/9.07 Exists fun T => % 8.80/9.07 And (And (environment E) (subpopulations first_movers efficient_producers E T)) % 8.80/9.07 (outcompetes first_movers efficient_producers T))) % 8.80/9.07 True % 8.80/9.07 Clause #4 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (S1 S2 T : Iota), And (environment a) (subpopulations S1 S2 a T) → subpopulations S2 S1 a T) True % 8.80/9.07 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), Eq (∀ (S2 T : Iota), And (environment a) (subpopulations a_1 S2 a T) → subpopulations S2 a_1 a T) True % 8.80/9.07 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Iota), % 8.80/9.07 Eq (∀ (T : Iota), And (environment a) (subpopulations a_1 a_2 a T) → subpopulations a_2 a_1 a T) True % 8.80/9.07 Clause #7 (by clausification #[6]): ∀ (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 % 8.80/9.07 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 a_3 : Iota), % 8.80/9.07 Or (Eq (And (environment a) (subpopulations a_1 a_2 a a_3)) False) (Eq (subpopulations a_2 a_1 a a_3) True) % 8.80/9.07 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 a_3 : Iota), % 8.80/9.07 Or (Eq (subpopulations a a_1 a_2 a_3) True) % 8.80/9.07 (Or (Eq (environment a_2) False) (Eq (subpopulations a_1 a a_2 a_3) False)) % 8.80/9.07 Clause #10 (by clausification #[3]): Eq % 8.80/9.07 (Exists fun E => % 8.80/9.07 Exists fun T => % 8.80/9.07 And (And (environment E) (subpopulations first_movers efficient_producers E T)) % 8.80/9.07 (outcompetes first_movers efficient_producers T)) % 8.80/9.07 False % 8.80/9.07 Clause #11 (by clausification #[10]): ∀ (a : Iota), % 8.80/9.07 Eq % 8.80/9.07 (Exists fun T => % 8.80/9.07 And (And (environment a) (subpopulations first_movers efficient_producers a T)) % 8.80/9.07 (outcompetes first_movers efficient_producers T)) % 8.80/9.07 False % 8.80/9.07 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), % 8.80/9.07 Eq % 8.80/9.07 (And (And (environment a) (subpopulations first_movers efficient_producers a a_1)) % 8.80/9.07 (outcompetes first_movers efficient_producers a_1)) % 8.80/9.07 False % 8.80/9.07 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), % 8.80/9.07 Or (Eq (And (environment a) (subpopulations first_movers efficient_producers a a_1)) False) % 8.80/9.07 (Eq (outcompetes first_movers efficient_producers a_1) False) % 8.80/9.07 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), % 8.80/9.07 Or (Eq (outcompetes first_movers efficient_producers a) False) % 8.80/9.07 (Or (Eq (environment a_1) False) (Eq (subpopulations first_movers efficient_producers a_1 a) False)) % 8.80/9.07 Clause #15 (by clausification #[1]): ∀ (a : Iota), % 8.80/9.07 Eq % 8.80/9.07 (∀ (S1 S2 T : Iota), % 8.80/9.07 And (environment a) (subpopulations S1 S2 a T) → % 8.80/9.07 Iff (And (greater_or_equal (growth_rate S2 T) zero) (greater zero (growth_rate S1 T))) (outcompetes S2 S1 T)) % 8.80/9.07 True % 8.80/9.07 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), % 8.80/9.07 Eq % 8.80/9.07 (∀ (S2 T : Iota), % 8.80/9.07 And (environment a) (subpopulations a_1 S2 a T) → % 8.80/9.07 Iff (And (greater_or_equal (growth_rate S2 T) zero) (greater zero (growth_rate a_1 T))) (outcompetes S2 a_1 T)) % 8.80/9.07 True % 8.80/9.07 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 : Iota), % 8.80/9.07 Eq % 8.80/9.07 (∀ (T : Iota), % 8.80/9.07 And (environment a) (subpopulations a_1 a_2 a T) → % 8.80/9.07 Iff (And (greater_or_equal (growth_rate a_2 T) zero) (greater zero (growth_rate a_1 T))) % 8.80/9.07 (outcompetes a_2 a_1 T)) % 8.80/9.07 True % 8.80/9.07 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 a_3 : Iota), % 8.80/9.07 Eq % 8.80/9.07 (And (environment a) (subpopulations a_1 a_2 a a_3) → % 8.80/9.11 Iff (And (greater_or_equal (growth_rate a_2 a_3) zero) (greater zero (growth_rate a_1 a_3))) % 8.80/9.11 (outcompetes a_2 a_1 a_3)) % 8.80/9.11 True % 8.80/9.11 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 a_3 : Iota), % 8.80/9.11 Or (Eq (And (environment a) (subpopulations a_1 a_2 a a_3)) False) % 8.80/9.11 (Eq % 8.80/9.11 (Iff (And (greater_or_equal (growth_rate a_2 a_3) zero) (greater zero (growth_rate a_1 a_3))) % 8.80/9.11 (outcompetes a_2 a_1 a_3)) % 8.80/9.11 True) % 8.80/9.11 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 a_3 : Iota), % 8.80/9.11 Or % 8.80/9.11 (Eq % 8.80/9.11 (Iff (And (greater_or_equal (growth_rate a a_1) zero) (greater zero (growth_rate a_2 a_1))) % 8.80/9.11 (outcompetes a a_2 a_1)) % 8.80/9.11 True) % 8.80/9.11 (Or (Eq (environment a_3) False) (Eq (subpopulations a_2 a a_3 a_1) False)) % 8.80/9.11 Clause #22 (by clausification #[20]): ∀ (a a_1 a_2 a_3 : Iota), % 8.80/9.11 Or (Eq (environment a) False) % 8.80/9.11 (Or (Eq (subpopulations a_1 a_2 a a_3) False) % 8.80/9.11 (Or (Eq (And (greater_or_equal (growth_rate a_2 a_3) zero) (greater zero (growth_rate a_1 a_3))) False) % 8.80/9.11 (Eq (outcompetes a_2 a_1 a_3) True))) % 8.80/9.12 Clause #25 (by clausification #[22]): ∀ (a a_1 a_2 a_3 : Iota), % 8.80/9.12 Or (Eq (environment a) False) % 8.80/9.12 (Or (Eq (subpopulations a_1 a_2 a a_3) False) % 8.80/9.12 (Or (Eq (outcompetes a_2 a_1 a_3) True) % 8.80/9.12 (Or (Eq (greater_or_equal (growth_rate a_2 a_3) zero) False) (Eq (greater zero (growth_rate a_1 a_3)) False)))) % 8.80/9.12 Clause #26 (by clausification #[2]): ∀ (a : Iota), % 8.80/9.12 Eq % 8.80/9.12 (Exists fun T => % 8.80/9.12 And % 8.80/9.12 (And (And (environment (skS.0 0 a)) (subpopulations first_movers efficient_producers (skS.0 0 a) T)) % 8.80/9.12 (greater_or_equal (growth_rate first_movers T) zero)) % 8.80/9.12 (greater zero (growth_rate efficient_producers T))) % 8.80/9.12 True % 8.80/9.12 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), % 8.80/9.12 Eq % 8.80/9.12 (And % 8.80/9.12 (And (And (environment (skS.0 0 a)) (subpopulations first_movers efficient_producers (skS.0 0 a) (skS.0 1 a a_1))) % 8.80/9.12 (greater_or_equal (growth_rate first_movers (skS.0 1 a a_1)) zero)) % 8.80/9.12 (greater zero (growth_rate efficient_producers (skS.0 1 a a_1)))) % 8.80/9.12 True % 8.80/9.12 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (greater zero (growth_rate efficient_producers (skS.0 1 a a_1))) True % 8.80/9.12 Clause #29 (by clausification #[27]): ∀ (a a_1 : Iota), % 8.80/9.12 Eq % 8.80/9.12 (And (And (environment (skS.0 0 a)) (subpopulations first_movers efficient_producers (skS.0 0 a) (skS.0 1 a a_1))) % 8.80/9.12 (greater_or_equal (growth_rate first_movers (skS.0 1 a a_1)) zero)) % 8.80/9.12 True % 8.80/9.12 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Eq (greater_or_equal (growth_rate first_movers (skS.0 1 a a_1)) zero) True % 8.80/9.12 Clause #31 (by clausification #[29]): ∀ (a a_1 : Iota), % 8.80/9.12 Eq (And (environment (skS.0 0 a)) (subpopulations first_movers efficient_producers (skS.0 0 a) (skS.0 1 a a_1))) True % 8.80/9.12 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Eq (subpopulations first_movers efficient_producers (skS.0 0 a) (skS.0 1 a a_1)) True % 8.80/9.12 Clause #33 (by clausification #[31]): ∀ (a : Iota), Eq (environment (skS.0 0 a)) True % 8.80/9.12 Clause #34 (by superposition #[33, 9]): ∀ (a a_1 a_2 a_3 : Iota), % 8.80/9.12 Or (Eq (subpopulations a a_1 (skS.0 0 a_2) a_3) True) % 8.80/9.12 (Or (Eq True False) (Eq (subpopulations a_1 a (skS.0 0 a_2) a_3) False)) % 8.80/9.12 Clause #37 (by superposition #[33, 25]): ∀ (a a_1 a_2 a_3 : Iota), % 8.80/9.12 Or (Eq True False) % 8.80/9.12 (Or (Eq (subpopulations a a_1 (skS.0 0 a_2) a_3) False) % 8.80/9.12 (Or (Eq (outcompetes a_1 a a_3) True) % 8.80/9.12 (Or (Eq (greater_or_equal (growth_rate a_1 a_3) zero) False) (Eq (greater zero (growth_rate a a_3)) False)))) % 8.80/9.12 Clause #38 (by clausification #[34]): ∀ (a a_1 a_2 a_3 : Iota), % 8.80/9.12 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) % 8.80/9.12 Clause #39 (by superposition #[38, 32]): ∀ (a a_1 : Iota), % 8.80/9.12 Or (Eq (subpopulations efficient_producers first_movers (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq False True) % 8.80/9.12 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), Eq (subpopulations efficient_producers first_movers (skS.0 0 a) (skS.0 1 a a_1)) True % 8.80/9.12 Clause #51 (by clausification #[37]): ∀ (a a_1 a_2 a_3 : Iota), % 8.80/9.12 Or (Eq (subpopulations a a_1 (skS.0 0 a_2) a_3) False) % 8.90/9.14 (Or (Eq (outcompetes a_1 a a_3) True) % 8.90/9.14 (Or (Eq (greater_or_equal (growth_rate a_1 a_3) zero) False) (Eq (greater zero (growth_rate a a_3)) False))) % 8.90/9.14 Clause #53 (by superposition #[51, 40]): ∀ (a a_1 : Iota), % 8.90/9.14 Or (Eq (outcompetes first_movers efficient_producers (skS.0 1 a a_1)) True) % 8.90/9.14 (Or (Eq (greater_or_equal (growth_rate first_movers (skS.0 1 a a_1)) zero) False) % 8.90/9.14 (Or (Eq (greater zero (growth_rate efficient_producers (skS.0 1 a a_1))) False) (Eq False True))) % 8.90/9.14 Clause #55 (by clausification #[53]): ∀ (a a_1 : Iota), % 8.90/9.14 Or (Eq (outcompetes first_movers efficient_producers (skS.0 1 a a_1)) True) % 8.90/9.14 (Or (Eq (greater_or_equal (growth_rate first_movers (skS.0 1 a a_1)) zero) False) % 8.90/9.14 (Eq (greater zero (growth_rate efficient_producers (skS.0 1 a a_1))) False)) % 8.90/9.14 Clause #56 (by forward demodulation #[55, 28]): ∀ (a a_1 : Iota), % 8.90/9.14 Or (Eq (outcompetes first_movers efficient_producers (skS.0 1 a a_1)) True) % 8.90/9.14 (Or (Eq (greater_or_equal (growth_rate first_movers (skS.0 1 a a_1)) zero) False) (Eq True False)) % 8.90/9.14 Clause #57 (by clausification #[56]): ∀ (a a_1 : Iota), % 8.90/9.14 Or (Eq (outcompetes first_movers efficient_producers (skS.0 1 a a_1)) True) % 8.90/9.14 (Eq (greater_or_equal (growth_rate first_movers (skS.0 1 a a_1)) zero) False) % 8.90/9.14 Clause #58 (by superposition #[57, 30]): ∀ (a a_1 : Iota), Or (Eq (outcompetes first_movers efficient_producers (skS.0 1 a a_1)) True) (Eq False True) % 8.90/9.14 Clause #59 (by clausification #[58]): ∀ (a a_1 : Iota), Eq (outcompetes first_movers efficient_producers (skS.0 1 a a_1)) True % 8.90/9.14 Clause #61 (by superposition #[59, 14]): ∀ (a a_1 a_2 : Iota), % 8.90/9.14 Or (Eq True False) % 8.90/9.14 (Or (Eq (environment a) False) (Eq (subpopulations first_movers efficient_producers a (skS.0 1 a_1 a_2)) False)) % 8.90/9.14 Clause #62 (by clausification #[61]): ∀ (a a_1 a_2 : Iota), % 8.90/9.14 Or (Eq (environment a) False) (Eq (subpopulations first_movers efficient_producers a (skS.0 1 a_1 a_2)) False) % 8.90/9.14 Clause #63 (by superposition #[62, 33]): ∀ (a a_1 a_2 : Iota), % 8.90/9.14 Or (Eq (subpopulations first_movers efficient_producers (skS.0 0 a) (skS.0 1 a_1 a_2)) False) (Eq False True) % 8.90/9.14 Clause #65 (by clausification #[63]): ∀ (a a_1 a_2 : Iota), Eq (subpopulations first_movers efficient_producers (skS.0 0 a) (skS.0 1 a_1 a_2)) False % 8.90/9.14 Clause #66 (by superposition #[65, 32]): Eq False True % 8.90/9.14 Clause #67 (by clausification #[66]): False % 8.90/9.14 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------