TSTP Solution File: MGT036+3 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : MGT036+3 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 09:10:05 EDT 2023
% Result : Theorem 3.68s 3.89s
% Output : Proof 3.68s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : MGT036+3 : TPTP v8.1.2. Released v2.0.0.
% 0.11/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 05:37:27 EDT 2023
% 0.14/0.35 % CPUTime :
% 3.68/3.89 SZS status Theorem for theBenchmark.p
% 3.68/3.89 SZS output start Proof for theBenchmark.p
% 3.68/3.89 Clause #0 (by assumption #[]): Eq (∀ (E S1 S2 T : Iota), And (environment E) (subpopulations S1 S2 E T) → subpopulations S2 S1 E T) True
% 3.68/3.89 Clause #1 (by assumption #[]): Eq
% 3.68/3.89 (∀ (E S1 S2 T : Iota),
% 3.68/3.89 And (environment E) (subpopulations S1 S2 E T) →
% 3.68/3.89 Iff (And (greater_or_equal (growth_rate S2 T) zero) (greater zero (growth_rate S1 T))) (outcompetes S2 S1 T))
% 3.68/3.89 True
% 3.68/3.89 Clause #2 (by assumption #[]): Eq
% 3.68/3.89 (Exists fun E =>
% 3.68/3.89 Exists fun T =>
% 3.68/3.89 And
% 3.68/3.89 (And (And (environment E) (subpopulations first_movers efficient_producers E T))
% 3.68/3.89 (greater_or_equal (growth_rate first_movers T) zero))
% 3.68/3.89 (greater zero (growth_rate efficient_producers T)))
% 3.68/3.89 True
% 3.68/3.89 Clause #3 (by assumption #[]): Eq
% 3.68/3.89 (Not
% 3.68/3.89 (Exists fun E =>
% 3.68/3.89 Exists fun T =>
% 3.68/3.89 And (And (environment E) (subpopulations first_movers efficient_producers E T))
% 3.68/3.89 (outcompetes first_movers efficient_producers T)))
% 3.68/3.89 True
% 3.68/3.89 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
% 3.68/3.89 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
% 3.68/3.89 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Iota),
% 3.68/3.89 Eq (∀ (T : Iota), And (environment a) (subpopulations a_1 a_2 a T) → subpopulations a_2 a_1 a T) True
% 3.68/3.89 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
% 3.68/3.89 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.68/3.89 Or (Eq (And (environment a) (subpopulations a_1 a_2 a a_3)) False) (Eq (subpopulations a_2 a_1 a a_3) True)
% 3.68/3.89 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.68/3.89 Or (Eq (subpopulations a a_1 a_2 a_3) True)
% 3.68/3.89 (Or (Eq (environment a_2) False) (Eq (subpopulations a_1 a a_2 a_3) False))
% 3.68/3.89 Clause #10 (by clausification #[3]): Eq
% 3.68/3.89 (Exists fun E =>
% 3.68/3.89 Exists fun T =>
% 3.68/3.89 And (And (environment E) (subpopulations first_movers efficient_producers E T))
% 3.68/3.89 (outcompetes first_movers efficient_producers T))
% 3.68/3.89 False
% 3.68/3.89 Clause #11 (by clausification #[10]): ∀ (a : Iota),
% 3.68/3.89 Eq
% 3.68/3.89 (Exists fun T =>
% 3.68/3.89 And (And (environment a) (subpopulations first_movers efficient_producers a T))
% 3.68/3.89 (outcompetes first_movers efficient_producers T))
% 3.68/3.89 False
% 3.68/3.89 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota),
% 3.68/3.89 Eq
% 3.68/3.89 (And (And (environment a) (subpopulations first_movers efficient_producers a a_1))
% 3.68/3.89 (outcompetes first_movers efficient_producers a_1))
% 3.68/3.89 False
% 3.68/3.89 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota),
% 3.68/3.89 Or (Eq (And (environment a) (subpopulations first_movers efficient_producers a a_1)) False)
% 3.68/3.89 (Eq (outcompetes first_movers efficient_producers a_1) False)
% 3.68/3.89 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota),
% 3.68/3.89 Or (Eq (outcompetes first_movers efficient_producers a) False)
% 3.68/3.89 (Or (Eq (environment a_1) False) (Eq (subpopulations first_movers efficient_producers a_1 a) False))
% 3.68/3.89 Clause #15 (by clausification #[1]): ∀ (a : Iota),
% 3.68/3.89 Eq
% 3.68/3.89 (∀ (S1 S2 T : Iota),
% 3.68/3.89 And (environment a) (subpopulations S1 S2 a T) →
% 3.68/3.89 Iff (And (greater_or_equal (growth_rate S2 T) zero) (greater zero (growth_rate S1 T))) (outcompetes S2 S1 T))
% 3.68/3.89 True
% 3.68/3.89 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota),
% 3.68/3.89 Eq
% 3.68/3.89 (∀ (S2 T : Iota),
% 3.68/3.89 And (environment a) (subpopulations a_1 S2 a T) →
% 3.68/3.89 Iff (And (greater_or_equal (growth_rate S2 T) zero) (greater zero (growth_rate a_1 T))) (outcompetes S2 a_1 T))
% 3.68/3.89 True
% 3.68/3.89 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 : Iota),
% 3.68/3.89 Eq
% 3.68/3.89 (∀ (T : Iota),
% 3.68/3.89 And (environment a) (subpopulations a_1 a_2 a T) →
% 3.68/3.89 Iff (And (greater_or_equal (growth_rate a_2 T) zero) (greater zero (growth_rate a_1 T)))
% 3.68/3.89 (outcompetes a_2 a_1 T))
% 3.68/3.89 True
% 3.68/3.89 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.68/3.89 Eq
% 3.68/3.89 (And (environment a) (subpopulations a_1 a_2 a a_3) →
% 3.68/3.91 Iff (And (greater_or_equal (growth_rate a_2 a_3) zero) (greater zero (growth_rate a_1 a_3)))
% 3.68/3.91 (outcompetes a_2 a_1 a_3))
% 3.68/3.91 True
% 3.68/3.91 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.68/3.91 Or (Eq (And (environment a) (subpopulations a_1 a_2 a a_3)) False)
% 3.68/3.91 (Eq
% 3.68/3.91 (Iff (And (greater_or_equal (growth_rate a_2 a_3) zero) (greater zero (growth_rate a_1 a_3)))
% 3.68/3.91 (outcompetes a_2 a_1 a_3))
% 3.68/3.91 True)
% 3.68/3.91 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.68/3.91 Or
% 3.68/3.91 (Eq
% 3.68/3.91 (Iff (And (greater_or_equal (growth_rate a a_1) zero) (greater zero (growth_rate a_2 a_1)))
% 3.68/3.91 (outcompetes a a_2 a_1))
% 3.68/3.91 True)
% 3.68/3.91 (Or (Eq (environment a_3) False) (Eq (subpopulations a_2 a a_3 a_1) False))
% 3.68/3.91 Clause #22 (by clausification #[20]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.68/3.91 Or (Eq (environment a) False)
% 3.68/3.91 (Or (Eq (subpopulations a_1 a_2 a a_3) False)
% 3.68/3.91 (Or (Eq (And (greater_or_equal (growth_rate a_2 a_3) zero) (greater zero (growth_rate a_1 a_3))) False)
% 3.68/3.91 (Eq (outcompetes a_2 a_1 a_3) True)))
% 3.68/3.91 Clause #25 (by clausification #[22]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.68/3.91 Or (Eq (environment a) False)
% 3.68/3.91 (Or (Eq (subpopulations a_1 a_2 a a_3) False)
% 3.68/3.91 (Or (Eq (outcompetes a_2 a_1 a_3) True)
% 3.68/3.91 (Or (Eq (greater_or_equal (growth_rate a_2 a_3) zero) False) (Eq (greater zero (growth_rate a_1 a_3)) False))))
% 3.68/3.91 Clause #26 (by clausification #[2]): ∀ (a : Iota),
% 3.68/3.91 Eq
% 3.68/3.91 (Exists fun T =>
% 3.68/3.91 And
% 3.68/3.91 (And (And (environment (skS.0 0 a)) (subpopulations first_movers efficient_producers (skS.0 0 a) T))
% 3.68/3.91 (greater_or_equal (growth_rate first_movers T) zero))
% 3.68/3.91 (greater zero (growth_rate efficient_producers T)))
% 3.68/3.91 True
% 3.68/3.91 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota),
% 3.68/3.91 Eq
% 3.68/3.91 (And
% 3.68/3.91 (And (And (environment (skS.0 0 a)) (subpopulations first_movers efficient_producers (skS.0 0 a) (skS.0 1 a a_1)))
% 3.68/3.91 (greater_or_equal (growth_rate first_movers (skS.0 1 a a_1)) zero))
% 3.68/3.91 (greater zero (growth_rate efficient_producers (skS.0 1 a a_1))))
% 3.68/3.91 True
% 3.68/3.91 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (greater zero (growth_rate efficient_producers (skS.0 1 a a_1))) True
% 3.68/3.91 Clause #29 (by clausification #[27]): ∀ (a a_1 : Iota),
% 3.68/3.91 Eq
% 3.68/3.91 (And (And (environment (skS.0 0 a)) (subpopulations first_movers efficient_producers (skS.0 0 a) (skS.0 1 a a_1)))
% 3.68/3.91 (greater_or_equal (growth_rate first_movers (skS.0 1 a a_1)) zero))
% 3.68/3.91 True
% 3.68/3.91 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
% 3.68/3.91 Clause #31 (by clausification #[29]): ∀ (a a_1 : Iota),
% 3.68/3.91 Eq (And (environment (skS.0 0 a)) (subpopulations first_movers efficient_producers (skS.0 0 a) (skS.0 1 a a_1))) True
% 3.68/3.91 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
% 3.68/3.91 Clause #33 (by clausification #[31]): ∀ (a : Iota), Eq (environment (skS.0 0 a)) True
% 3.68/3.91 Clause #34 (by superposition #[33, 9]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.68/3.91 Or (Eq (subpopulations a a_1 (skS.0 0 a_2) a_3) True)
% 3.68/3.91 (Or (Eq True False) (Eq (subpopulations a_1 a (skS.0 0 a_2) a_3) False))
% 3.68/3.91 Clause #37 (by superposition #[33, 25]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.68/3.91 Or (Eq True False)
% 3.68/3.91 (Or (Eq (subpopulations a a_1 (skS.0 0 a_2) a_3) False)
% 3.68/3.91 (Or (Eq (outcompetes a_1 a a_3) True)
% 3.68/3.91 (Or (Eq (greater_or_equal (growth_rate a_1 a_3) zero) False) (Eq (greater zero (growth_rate a a_3)) False))))
% 3.68/3.91 Clause #38 (by clausification #[34]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.68/3.91 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)
% 3.68/3.91 Clause #39 (by superposition #[38, 32]): ∀ (a a_1 : Iota),
% 3.68/3.91 Or (Eq (subpopulations efficient_producers first_movers (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq False True)
% 3.68/3.91 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
% 3.68/3.91 Clause #51 (by clausification #[37]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.68/3.91 Or (Eq (subpopulations a a_1 (skS.0 0 a_2) a_3) False)
% 3.68/3.92 (Or (Eq (outcompetes a_1 a a_3) True)
% 3.68/3.92 (Or (Eq (greater_or_equal (growth_rate a_1 a_3) zero) False) (Eq (greater zero (growth_rate a a_3)) False)))
% 3.68/3.92 Clause #53 (by superposition #[51, 40]): ∀ (a a_1 : Iota),
% 3.68/3.92 Or (Eq (outcompetes first_movers efficient_producers (skS.0 1 a a_1)) True)
% 3.68/3.92 (Or (Eq (greater_or_equal (growth_rate first_movers (skS.0 1 a a_1)) zero) False)
% 3.68/3.92 (Or (Eq (greater zero (growth_rate efficient_producers (skS.0 1 a a_1))) False) (Eq False True)))
% 3.68/3.92 Clause #55 (by clausification #[53]): ∀ (a a_1 : Iota),
% 3.68/3.92 Or (Eq (outcompetes first_movers efficient_producers (skS.0 1 a a_1)) True)
% 3.68/3.92 (Or (Eq (greater_or_equal (growth_rate first_movers (skS.0 1 a a_1)) zero) False)
% 3.68/3.92 (Eq (greater zero (growth_rate efficient_producers (skS.0 1 a a_1))) False))
% 3.68/3.92 Clause #56 (by forward demodulation #[55, 28]): ∀ (a a_1 : Iota),
% 3.68/3.92 Or (Eq (outcompetes first_movers efficient_producers (skS.0 1 a a_1)) True)
% 3.68/3.92 (Or (Eq (greater_or_equal (growth_rate first_movers (skS.0 1 a a_1)) zero) False) (Eq True False))
% 3.68/3.92 Clause #57 (by clausification #[56]): ∀ (a a_1 : Iota),
% 3.68/3.92 Or (Eq (outcompetes first_movers efficient_producers (skS.0 1 a a_1)) True)
% 3.68/3.92 (Eq (greater_or_equal (growth_rate first_movers (skS.0 1 a a_1)) zero) False)
% 3.68/3.92 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)
% 3.68/3.92 Clause #59 (by clausification #[58]): ∀ (a a_1 : Iota), Eq (outcompetes first_movers efficient_producers (skS.0 1 a a_1)) True
% 3.68/3.92 Clause #61 (by superposition #[59, 14]): ∀ (a a_1 a_2 : Iota),
% 3.68/3.92 Or (Eq True False)
% 3.68/3.92 (Or (Eq (environment a) False) (Eq (subpopulations first_movers efficient_producers a (skS.0 1 a_1 a_2)) False))
% 3.68/3.92 Clause #62 (by clausification #[61]): ∀ (a a_1 a_2 : Iota),
% 3.68/3.92 Or (Eq (environment a) False) (Eq (subpopulations first_movers efficient_producers a (skS.0 1 a_1 a_2)) False)
% 3.68/3.92 Clause #63 (by superposition #[62, 33]): ∀ (a a_1 a_2 : Iota),
% 3.68/3.92 Or (Eq (subpopulations first_movers efficient_producers (skS.0 0 a) (skS.0 1 a_1 a_2)) False) (Eq False True)
% 3.68/3.92 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
% 3.68/3.92 Clause #66 (by superposition #[65, 32]): Eq False True
% 3.68/3.92 Clause #67 (by clausification #[66]): False
% 3.68/3.92 SZS output end Proof for theBenchmark.p
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