TSTP Solution File: SYN386+1 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYN386+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n010.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 : Fri Sep 1 02:11:33 EDT 2023
% Result : Theorem 3.67s 3.85s
% Output : Proof 3.67s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN386+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 17:03:05 EDT 2023
% 0.13/0.35 % CPUTime :
% 3.67/3.85 SZS status Theorem for theBenchmark.p
% 3.67/3.85 SZS output start Proof for theBenchmark.p
% 3.67/3.85 Clause #0 (by assumption #[]): Eq
% 3.67/3.85 (Not
% 3.67/3.85 (And
% 3.67/3.85 (And (∀ (X : Iota), Exists fun Y => big_f X Y)
% 3.67/3.85 (Exists fun X => ∀ (E : Iota), Exists fun N => ∀ (W : Iota), big_s N W → big_d W X E))
% 3.67/3.85 (∀ (E : Iota),
% 3.67/3.85 Exists fun D => ∀ (A B : Iota), big_d A B D → ∀ (Y Z : Iota), And (big_f A Y) (big_f B Z) → big_d Y Z E) →
% 3.67/3.85 Exists fun Y => ∀ (E : Iota), Exists fun M => ∀ (W : Iota), big_s M W → ∀ (Z : Iota), big_f W Z → big_d Z Y E))
% 3.67/3.85 True
% 3.67/3.85 Clause #1 (by betaEtaReduce #[0]): Eq
% 3.67/3.85 (Not
% 3.67/3.85 (And
% 3.67/3.85 (And (∀ (X : Iota), Exists (big_f X))
% 3.67/3.85 (Exists fun X => ∀ (E : Iota), Exists fun N => ∀ (W : Iota), big_s N W → big_d W X E))
% 3.67/3.85 (∀ (E : Iota),
% 3.67/3.85 Exists fun D => ∀ (A B : Iota), big_d A B D → ∀ (Y Z : Iota), And (big_f A Y) (big_f B Z) → big_d Y Z E) →
% 3.67/3.85 Exists fun Y => ∀ (E : Iota), Exists fun M => ∀ (W : Iota), big_s M W → ∀ (Z : Iota), big_f W Z → big_d Z Y E))
% 3.67/3.85 True
% 3.67/3.85 Clause #2 (by clausification #[1]): Eq
% 3.67/3.85 (And
% 3.67/3.85 (And (∀ (X : Iota), Exists (big_f X))
% 3.67/3.85 (Exists fun X => ∀ (E : Iota), Exists fun N => ∀ (W : Iota), big_s N W → big_d W X E))
% 3.67/3.85 (∀ (E : Iota),
% 3.67/3.85 Exists fun D => ∀ (A B : Iota), big_d A B D → ∀ (Y Z : Iota), And (big_f A Y) (big_f B Z) → big_d Y Z E) →
% 3.67/3.85 Exists fun Y => ∀ (E : Iota), Exists fun M => ∀ (W : Iota), big_s M W → ∀ (Z : Iota), big_f W Z → big_d Z Y E)
% 3.67/3.85 False
% 3.67/3.85 Clause #3 (by clausification #[2]): Eq
% 3.67/3.85 (And
% 3.67/3.85 (And (∀ (X : Iota), Exists (big_f X))
% 3.67/3.85 (Exists fun X => ∀ (E : Iota), Exists fun N => ∀ (W : Iota), big_s N W → big_d W X E))
% 3.67/3.85 (∀ (E : Iota),
% 3.67/3.85 Exists fun D => ∀ (A B : Iota), big_d A B D → ∀ (Y Z : Iota), And (big_f A Y) (big_f B Z) → big_d Y Z E))
% 3.67/3.85 True
% 3.67/3.85 Clause #4 (by clausification #[2]): Eq (Exists fun Y => ∀ (E : Iota), Exists fun M => ∀ (W : Iota), big_s M W → ∀ (Z : Iota), big_f W Z → big_d Z Y E) False
% 3.67/3.85 Clause #5 (by clausification #[3]): Eq
% 3.67/3.85 (∀ (E : Iota),
% 3.67/3.85 Exists fun D => ∀ (A B : Iota), big_d A B D → ∀ (Y Z : Iota), And (big_f A Y) (big_f B Z) → big_d Y Z E)
% 3.67/3.85 True
% 3.67/3.85 Clause #6 (by clausification #[3]): Eq
% 3.67/3.85 (And (∀ (X : Iota), Exists (big_f X))
% 3.67/3.85 (Exists fun X => ∀ (E : Iota), Exists fun N => ∀ (W : Iota), big_s N W → big_d W X E))
% 3.67/3.85 True
% 3.67/3.85 Clause #7 (by clausification #[5]): ∀ (a : Iota),
% 3.67/3.85 Eq (Exists fun D => ∀ (A B : Iota), big_d A B D → ∀ (Y Z : Iota), And (big_f A Y) (big_f B Z) → big_d Y Z a) True
% 3.67/3.85 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota),
% 3.67/3.85 Eq (∀ (A B : Iota), big_d A B (skS.0 0 a a_1) → ∀ (Y Z : Iota), And (big_f A Y) (big_f B Z) → big_d Y Z a) True
% 3.67/3.85 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota),
% 3.67/3.85 Eq (∀ (B : Iota), big_d a B (skS.0 0 a_1 a_2) → ∀ (Y Z : Iota), And (big_f a Y) (big_f B Z) → big_d Y Z a_1) True
% 3.67/3.85 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.67/3.85 Eq (big_d a a_1 (skS.0 0 a_2 a_3) → ∀ (Y Z : Iota), And (big_f a Y) (big_f a_1 Z) → big_d Y Z a_2) True
% 3.67/3.85 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.67/3.85 Or (Eq (big_d a a_1 (skS.0 0 a_2 a_3)) False)
% 3.67/3.85 (Eq (∀ (Y Z : Iota), And (big_f a Y) (big_f a_1 Z) → big_d Y Z a_2) True)
% 3.67/3.85 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.67/3.85 Or (Eq (big_d a a_1 (skS.0 0 a_2 a_3)) False)
% 3.67/3.85 (Eq (∀ (Z : Iota), And (big_f a a_4) (big_f a_1 Z) → big_d a_4 Z a_2) True)
% 3.67/3.85 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 3.67/3.85 Or (Eq (big_d a a_1 (skS.0 0 a_2 a_3)) False) (Eq (And (big_f a a_4) (big_f a_1 a_5) → big_d a_4 a_5 a_2) True)
% 3.67/3.85 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 3.67/3.85 Or (Eq (big_d a a_1 (skS.0 0 a_2 a_3)) False)
% 3.67/3.85 (Or (Eq (And (big_f a a_4) (big_f a_1 a_5)) False) (Eq (big_d a_4 a_5 a_2) True))
% 3.67/3.85 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 3.67/3.85 Or (Eq (big_d a a_1 (skS.0 0 a_2 a_3)) False)
% 3.67/3.85 (Or (Eq (big_d a_4 a_5 a_2) True) (Or (Eq (big_f a a_4) False) (Eq (big_f a_1 a_5) False)))
% 3.67/3.87 Clause #16 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (E : Iota), Exists fun M => ∀ (W : Iota), big_s M W → ∀ (Z : Iota), big_f W Z → big_d Z a E) False
% 3.67/3.87 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota),
% 3.67/3.87 Eq (Not (Exists fun M => ∀ (W : Iota), big_s M W → ∀ (Z : Iota), big_f W Z → big_d Z a (skS.0 1 a a_1))) True
% 3.67/3.87 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota),
% 3.67/3.87 Eq (Exists fun M => ∀ (W : Iota), big_s M W → ∀ (Z : Iota), big_f W Z → big_d Z a (skS.0 1 a a_1)) False
% 3.67/3.87 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), Eq (∀ (W : Iota), big_s a W → ∀ (Z : Iota), big_f W Z → big_d Z a_1 (skS.0 1 a_1 a_2)) False
% 3.67/3.87 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.67/3.87 Eq
% 3.67/3.87 (Not
% 3.67/3.87 (big_s a (skS.0 2 a a_1 a_2 a_3) → ∀ (Z : Iota), big_f (skS.0 2 a a_1 a_2 a_3) Z → big_d Z a_1 (skS.0 1 a_1 a_2)))
% 3.67/3.87 True
% 3.67/3.87 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.67/3.87 Eq (big_s a (skS.0 2 a a_1 a_2 a_3) → ∀ (Z : Iota), big_f (skS.0 2 a a_1 a_2 a_3) Z → big_d Z a_1 (skS.0 1 a_1 a_2))
% 3.67/3.87 False
% 3.67/3.87 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 a_3 : Iota), Eq (big_s a (skS.0 2 a a_1 a_2 a_3)) True
% 3.67/3.87 Clause #23 (by clausification #[21]): ∀ (a a_1 a_2 a_3 : Iota), Eq (∀ (Z : Iota), big_f (skS.0 2 a a_1 a_2 a_3) Z → big_d Z a_1 (skS.0 1 a_1 a_2)) False
% 3.67/3.87 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.67/3.87 Eq
% 3.67/3.87 (Not
% 3.67/3.87 (big_f (skS.0 2 a a_1 a_2 a_3) (skS.0 3 a a_1 a_2 a_3 a_4) →
% 3.67/3.87 big_d (skS.0 3 a a_1 a_2 a_3 a_4) a_1 (skS.0 1 a_1 a_2)))
% 3.67/3.87 True
% 3.67/3.87 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.67/3.87 Eq
% 3.67/3.87 (big_f (skS.0 2 a a_1 a_2 a_3) (skS.0 3 a a_1 a_2 a_3 a_4) →
% 3.67/3.87 big_d (skS.0 3 a a_1 a_2 a_3 a_4) a_1 (skS.0 1 a_1 a_2))
% 3.67/3.87 False
% 3.67/3.87 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (big_f (skS.0 2 a a_1 a_2 a_3) (skS.0 3 a a_1 a_2 a_3 a_4)) True
% 3.67/3.87 Clause #27 (by clausification #[25]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (big_d (skS.0 3 a a_1 a_2 a_3 a_4) a_1 (skS.0 1 a_1 a_2)) False
% 3.67/3.87 Clause #28 (by clausification #[6]): Eq (Exists fun X => ∀ (E : Iota), Exists fun N => ∀ (W : Iota), big_s N W → big_d W X E) True
% 3.67/3.87 Clause #29 (by clausification #[6]): Eq (∀ (X : Iota), Exists (big_f X)) True
% 3.67/3.87 Clause #30 (by clausification #[28]): ∀ (a : Iota), Eq (∀ (E : Iota), Exists fun N => ∀ (W : Iota), big_s N W → big_d W (skS.0 4 a) E) True
% 3.67/3.87 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (Exists fun N => ∀ (W : Iota), big_s N W → big_d W (skS.0 4 a) a_1) True
% 3.67/3.87 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Eq (∀ (W : Iota), big_s (skS.0 5 a a_1 a_2) W → big_d W (skS.0 4 a) a_1) True
% 3.67/3.87 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 a_3 : Iota), Eq (big_s (skS.0 5 a a_1 a_2) a_3 → big_d a_3 (skS.0 4 a) a_1) True
% 3.67/3.87 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (big_s (skS.0 5 a a_1 a_2) a_3) False) (Eq (big_d a_3 (skS.0 4 a) a_1) True)
% 3.67/3.87 Clause #35 (by superposition #[34, 22]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 3.67/3.87 Or (Eq (big_d (skS.0 2 (skS.0 5 a a_1 a_2) a_3 a_4 a_5) (skS.0 4 a) a_1) True) (Eq False True)
% 3.67/3.87 Clause #36 (by clausification #[29]): ∀ (a : Iota), Eq (Exists (big_f a)) True
% 3.67/3.87 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Eq (big_f a (skS.0 6 a a_1)) True
% 3.67/3.87 Clause #38 (by clausification #[35]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), Eq (big_d (skS.0 2 (skS.0 5 a a_1 a_2) a_3 a_4 a_5) (skS.0 4 a) a_1) True
% 3.67/3.87 Clause #39 (by superposition #[38, 15]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 3.67/3.87 Or (Eq True False)
% 3.67/3.87 (Or (Eq (big_d a a_1 a_2) True)
% 3.67/3.87 (Or (Eq (big_f (skS.0 2 (skS.0 5 a_3 (skS.0 0 a_2 a_4) a_5) a_6 a_7 a_8) a) False)
% 3.67/3.87 (Eq (big_f (skS.0 4 a_3) a_1) False)))
% 3.67/3.87 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 3.67/3.87 Or (Eq (big_d a a_1 a_2) True)
% 3.67/3.87 (Or (Eq (big_f (skS.0 2 (skS.0 5 a_3 (skS.0 0 a_2 a_4) a_5) a_6 a_7 a_8) a) False)
% 3.67/3.87 (Eq (big_f (skS.0 4 a_3) a_1) False))
% 3.67/3.87 Clause #41 (by superposition #[40, 26]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 3.67/3.88 Or (Eq (big_d (skS.0 3 (skS.0 5 a (skS.0 0 a_1 a_2) a_3) a_4 a_5 a_6 a_7) a_8 a_1) True)
% 3.67/3.88 (Or (Eq (big_f (skS.0 4 a) a_8) False) (Eq False True))
% 3.67/3.88 Clause #43 (by clausification #[41]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 3.67/3.88 Or (Eq (big_d (skS.0 3 (skS.0 5 a (skS.0 0 a_1 a_2) a_3) a_4 a_5 a_6 a_7) a_8 a_1) True)
% 3.67/3.88 (Eq (big_f (skS.0 4 a) a_8) False)
% 3.67/3.88 Clause #44 (by superposition #[43, 37]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 3.67/3.88 Or (Eq (big_d (skS.0 3 (skS.0 5 a (skS.0 0 a_1 a_2) a_3) a_4 a_5 a_6 a_7) (skS.0 6 (skS.0 4 a) a_8) a_1) True)
% 3.67/3.88 (Eq False True)
% 3.67/3.88 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 3.67/3.88 Eq (big_d (skS.0 3 (skS.0 5 a (skS.0 0 a_1 a_2) a_3) a_4 a_5 a_6 a_7) (skS.0 6 (skS.0 4 a) a_8) a_1) True
% 3.67/3.88 Clause #47 (by superposition #[45, 27]): Eq True False
% 3.67/3.88 Clause #48 (by clausification #[47]): False
% 3.67/3.88 SZS output end Proof for theBenchmark.p
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