TSTP Solution File: SYN069+1 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYN069+1 : TPTP v8.1.2. 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 : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 02:10:27 EDT 2023
% Result : Theorem 4.03s 4.27s
% Output : Proof 4.03s
% 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 : SYN069+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 18:52:57 EDT 2023
% 0.13/0.35 % CPUTime :
% 4.03/4.27 SZS status Theorem for theBenchmark.p
% 4.03/4.27 SZS output start Proof for theBenchmark.p
% 4.03/4.27 Clause #0 (by assumption #[]): Eq
% 4.03/4.27 (∀ (X : Iota),
% 4.03/4.27 And (big_f X) (∀ (Y : Iota), And (big_g Y) (big_h X Y) → big_j X Y) →
% 4.03/4.27 ∀ (Y1 : Iota), And (And (big_g Y1) (big_h X Y1)) (big_k Y1))
% 4.03/4.27 True
% 4.03/4.27 Clause #1 (by assumption #[]): Eq (Not (Exists fun Y => And (big_l Y) (big_k Y))) True
% 4.03/4.27 Clause #2 (by assumption #[]): Eq
% 4.03/4.27 (Exists fun X =>
% 4.03/4.27 And (And (big_f X) (∀ (Y : Iota), big_h X Y → big_l Y)) (∀ (Y1 : Iota), And (big_g Y1) (big_h X Y1) → big_j X Y1))
% 4.03/4.27 True
% 4.03/4.27 Clause #3 (by assumption #[]): Eq (Not (Exists fun X => And (big_f X) (Not (Exists fun Y => And (big_g Y) (big_h X Y))))) True
% 4.03/4.27 Clause #4 (by clausification #[1]): Eq (Exists fun Y => And (big_l Y) (big_k Y)) False
% 4.03/4.27 Clause #5 (by clausification #[4]): ∀ (a : Iota), Eq (And (big_l a) (big_k a)) False
% 4.03/4.27 Clause #6 (by clausification #[5]): ∀ (a : Iota), Or (Eq (big_l a) False) (Eq (big_k a) False)
% 4.03/4.27 Clause #7 (by clausification #[0]): ∀ (a : Iota),
% 4.03/4.27 Eq
% 4.03/4.27 (And (big_f a) (∀ (Y : Iota), And (big_g Y) (big_h a Y) → big_j a Y) →
% 4.03/4.27 ∀ (Y1 : Iota), And (And (big_g Y1) (big_h a Y1)) (big_k Y1))
% 4.03/4.27 True
% 4.03/4.27 Clause #8 (by clausification #[7]): ∀ (a : Iota),
% 4.03/4.27 Or (Eq (And (big_f a) (∀ (Y : Iota), And (big_g Y) (big_h a Y) → big_j a Y)) False)
% 4.03/4.27 (Eq (∀ (Y1 : Iota), And (And (big_g Y1) (big_h a Y1)) (big_k Y1)) True)
% 4.03/4.27 Clause #9 (by clausification #[8]): ∀ (a : Iota),
% 4.03/4.27 Or (Eq (∀ (Y1 : Iota), And (And (big_g Y1) (big_h a Y1)) (big_k Y1)) True)
% 4.03/4.27 (Or (Eq (big_f a) False) (Eq (∀ (Y : Iota), And (big_g Y) (big_h a Y) → big_j a Y) False))
% 4.03/4.27 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota),
% 4.03/4.27 Or (Eq (big_f a) False)
% 4.03/4.27 (Or (Eq (∀ (Y : Iota), And (big_g Y) (big_h a Y) → big_j a Y) False)
% 4.03/4.27 (Eq (And (And (big_g a_1) (big_h a a_1)) (big_k a_1)) True))
% 4.03/4.27 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota),
% 4.03/4.27 Or (Eq (big_f a) False)
% 4.03/4.27 (Or (Eq (And (And (big_g a_1) (big_h a a_1)) (big_k a_1)) True)
% 4.03/4.27 (Eq (Not (And (big_g (skS.0 0 a a_2)) (big_h a (skS.0 0 a a_2)) → big_j a (skS.0 0 a a_2))) True))
% 4.03/4.27 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota),
% 4.03/4.27 Or (Eq (big_f a) False)
% 4.03/4.27 (Or (Eq (Not (And (big_g (skS.0 0 a a_1)) (big_h a (skS.0 0 a a_1)) → big_j a (skS.0 0 a a_1))) True)
% 4.03/4.27 (Eq (big_k a_2) True))
% 4.03/4.27 Clause #14 (by clausification #[12]): ∀ (a a_1 a_2 : Iota),
% 4.03/4.27 Or (Eq (big_f a) False)
% 4.03/4.27 (Or (Eq (big_k a_1) True)
% 4.03/4.27 (Eq (And (big_g (skS.0 0 a a_2)) (big_h a (skS.0 0 a a_2)) → big_j a (skS.0 0 a a_2)) False))
% 4.03/4.27 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota),
% 4.03/4.27 Or (Eq (big_f a) False) (Or (Eq (big_k a_1) True) (Eq (And (big_g (skS.0 0 a a_2)) (big_h a (skS.0 0 a a_2))) True))
% 4.03/4.27 Clause #16 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a) False) (Or (Eq (big_k a_1) True) (Eq (big_j a (skS.0 0 a a_2)) False))
% 4.03/4.27 Clause #17 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a) False) (Or (Eq (big_k a_1) True) (Eq (big_h a (skS.0 0 a a_2)) True))
% 4.03/4.27 Clause #18 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a) False) (Or (Eq (big_k a_1) True) (Eq (big_g (skS.0 0 a a_2)) True))
% 4.03/4.27 Clause #19 (by clausification #[2]): ∀ (a : Iota),
% 4.03/4.27 Eq
% 4.03/4.27 (And (And (big_f (skS.0 1 a)) (∀ (Y : Iota), big_h (skS.0 1 a) Y → big_l Y))
% 4.03/4.27 (∀ (Y1 : Iota), And (big_g Y1) (big_h (skS.0 1 a) Y1) → big_j (skS.0 1 a) Y1))
% 4.03/4.27 True
% 4.03/4.27 Clause #20 (by clausification #[19]): ∀ (a : Iota), Eq (∀ (Y1 : Iota), And (big_g Y1) (big_h (skS.0 1 a) Y1) → big_j (skS.0 1 a) Y1) True
% 4.03/4.27 Clause #21 (by clausification #[19]): ∀ (a : Iota), Eq (And (big_f (skS.0 1 a)) (∀ (Y : Iota), big_h (skS.0 1 a) Y → big_l Y)) True
% 4.03/4.27 Clause #22 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (And (big_g a) (big_h (skS.0 1 a_1) a) → big_j (skS.0 1 a_1) a) True
% 4.03/4.27 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Or (Eq (And (big_g a) (big_h (skS.0 1 a_1) a)) False) (Eq (big_j (skS.0 1 a_1) a) True)
% 4.03/4.27 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (big_j (skS.0 1 a) a_1) True) (Or (Eq (big_g a_1) False) (Eq (big_h (skS.0 1 a) a_1) False))
% 4.03/4.30 Clause #25 (by clausification #[21]): ∀ (a : Iota), Eq (∀ (Y : Iota), big_h (skS.0 1 a) Y → big_l Y) True
% 4.03/4.30 Clause #26 (by clausification #[21]): ∀ (a : Iota), Eq (big_f (skS.0 1 a)) True
% 4.03/4.30 Clause #27 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (big_h (skS.0 1 a) a_1 → big_l a_1) True
% 4.03/4.30 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq (big_h (skS.0 1 a) a_1) False) (Eq (big_l a_1) True)
% 4.03/4.30 Clause #29 (by clausification #[3]): Eq (Exists fun X => And (big_f X) (Not (Exists fun Y => And (big_g Y) (big_h X Y)))) False
% 4.03/4.30 Clause #30 (by clausification #[29]): ∀ (a : Iota), Eq (And (big_f a) (Not (Exists fun Y => And (big_g Y) (big_h a Y)))) False
% 4.03/4.30 Clause #31 (by clausification #[30]): ∀ (a : Iota), Or (Eq (big_f a) False) (Eq (Not (Exists fun Y => And (big_g Y) (big_h a Y))) False)
% 4.03/4.30 Clause #32 (by clausification #[31]): ∀ (a : Iota), Or (Eq (big_f a) False) (Eq (Exists fun Y => And (big_g Y) (big_h a Y)) True)
% 4.03/4.30 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Or (Eq (big_f a) False) (Eq (And (big_g (skS.0 2 a a_1)) (big_h a (skS.0 2 a a_1))) True)
% 4.03/4.30 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Or (Eq (big_f a) False) (Eq (big_h a (skS.0 2 a a_1)) True)
% 4.03/4.30 Clause #36 (by superposition #[26, 17]): ∀ (a a_1 a_2 : Iota),
% 4.03/4.30 Or (Eq True False) (Or (Eq (big_k a) True) (Eq (big_h (skS.0 1 a_1) (skS.0 0 (skS.0 1 a_1) a_2)) True))
% 4.03/4.30 Clause #37 (by superposition #[26, 18]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (big_k a) True) (Eq (big_g (skS.0 0 (skS.0 1 a_1) a_2)) True))
% 4.03/4.30 Clause #38 (by superposition #[26, 34]): ∀ (a a_1 : Iota), Or (Eq (big_h (skS.0 1 a) (skS.0 2 (skS.0 1 a) a_1)) True) (Eq False True)
% 4.03/4.30 Clause #40 (by superposition #[16, 26]): ∀ (a a_1 a_2 : Iota),
% 4.03/4.30 Or (Eq True False) (Or (Eq (big_k a) True) (Eq (big_j (skS.0 1 a_1) (skS.0 0 (skS.0 1 a_1) a_2)) False))
% 4.03/4.30 Clause #43 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_k a) True) (Eq (big_g (skS.0 0 (skS.0 1 a_1) a_2)) True)
% 4.03/4.30 Clause #44 (by superposition #[43, 24]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.03/4.30 Or (Eq (big_k a) True)
% 4.03/4.30 (Or (Eq (big_j (skS.0 1 a_1) (skS.0 0 (skS.0 1 a_2) a_3)) True)
% 4.03/4.30 (Or (Eq True False) (Eq (big_h (skS.0 1 a_1) (skS.0 0 (skS.0 1 a_2) a_3)) False)))
% 4.03/4.30 Clause #62 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_k a) True) (Eq (big_h (skS.0 1 a_1) (skS.0 0 (skS.0 1 a_1) a_2)) True)
% 4.03/4.30 Clause #74 (by clausification #[38]): ∀ (a a_1 : Iota), Eq (big_h (skS.0 1 a) (skS.0 2 (skS.0 1 a) a_1)) True
% 4.03/4.30 Clause #75 (by superposition #[74, 28]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (big_l (skS.0 2 (skS.0 1 a) a_1)) True)
% 4.03/4.30 Clause #76 (by clausification #[75]): ∀ (a a_1 : Iota), Eq (big_l (skS.0 2 (skS.0 1 a) a_1)) True
% 4.03/4.30 Clause #77 (by superposition #[76, 6]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (big_k (skS.0 2 (skS.0 1 a) a_1)) False)
% 4.03/4.30 Clause #78 (by clausification #[77]): ∀ (a a_1 : Iota), Eq (big_k (skS.0 2 (skS.0 1 a) a_1)) False
% 4.03/4.30 Clause #80 (by superposition #[78, 62]): ∀ (a a_1 : Iota), Or (Eq False True) (Eq (big_h (skS.0 1 a) (skS.0 0 (skS.0 1 a) a_1)) True)
% 4.03/4.30 Clause #87 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_k a) True) (Eq (big_j (skS.0 1 a_1) (skS.0 0 (skS.0 1 a_1) a_2)) False)
% 4.03/4.30 Clause #91 (by clausification #[80]): ∀ (a a_1 : Iota), Eq (big_h (skS.0 1 a) (skS.0 0 (skS.0 1 a) a_1)) True
% 4.03/4.30 Clause #100 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.03/4.30 Or (Eq (big_k a) True)
% 4.03/4.30 (Or (Eq (big_j (skS.0 1 a_1) (skS.0 0 (skS.0 1 a_2) a_3)) True)
% 4.03/4.30 (Eq (big_h (skS.0 1 a_1) (skS.0 0 (skS.0 1 a_2) a_3)) False))
% 4.03/4.30 Clause #101 (by superposition #[100, 91]): ∀ (a a_1 a_2 : Iota),
% 4.03/4.30 Or (Eq (big_k a) True) (Or (Eq (big_j (skS.0 1 a_1) (skS.0 0 (skS.0 1 a_1) a_2)) True) (Eq False True))
% 4.03/4.30 Clause #102 (by clausification #[101]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_k a) True) (Eq (big_j (skS.0 1 a_1) (skS.0 0 (skS.0 1 a_1) a_2)) True)
% 4.03/4.30 Clause #104 (by superposition #[102, 87]): ∀ (a a_1 : Iota), Or (Eq (big_k a) True) (Or (Eq (big_k a_1) True) (Eq True False))
% 4.03/4.30 Clause #111 (by clausification #[104]): ∀ (a a_1 : Iota), Or (Eq (big_k a) True) (Eq (big_k a_1) True)
% 4.03/4.30 Clause #112 (by superposition #[111, 78]): ∀ (a : Iota), Or (Eq (big_k a) True) (Eq True False)
% 4.03/4.30 Clause #116 (by clausification #[112]): ∀ (a : Iota), Eq (big_k a) True
% 4.03/4.30 Clause #117 (by superposition #[116, 78]): Eq True False
% 4.03/4.30 Clause #119 (by clausification #[117]): False
% 4.03/4.30 SZS output end Proof for theBenchmark.p
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