TSTP Solution File: SYN332+1 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYN332+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n012.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 02:11:13 EDT 2023
% Result : Theorem 3.60s 3.81s
% 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 : SYN332+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.14 % Command : duper %s
% 0.15/0.35 % Computer : n012.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat Aug 26 20:44:40 EDT 2023
% 0.15/0.35 % CPUTime :
% 3.60/3.81 SZS status Theorem for theBenchmark.p
% 3.60/3.81 SZS output start Proof for theBenchmark.p
% 3.60/3.81 Clause #0 (by assumption #[]): Eq
% 3.60/3.81 (Not
% 3.60/3.81 (Exists fun X =>
% 3.60/3.81 Exists fun Y =>
% 3.60/3.81 ∀ (Z : Iota),
% 3.60/3.81 Not (Iff (And (big_f X Y) (big_f Y X)) (big_f X Z)) →
% 3.60/3.81 Iff (big_f X Z) (big_f Z X) →
% 3.60/3.81 Iff (big_f X Z) (big_f Y Z) →
% 3.60/3.81 Iff (big_f Y X → big_f X Y) (big_f Z Z) → Iff (Iff (big_f X Y) (big_f Y X)) (big_f Z Y)))
% 3.60/3.81 True
% 3.60/3.81 Clause #1 (by clausification #[0]): Eq
% 3.60/3.81 (Exists fun X =>
% 3.60/3.81 Exists fun Y =>
% 3.60/3.81 ∀ (Z : Iota),
% 3.60/3.81 Not (Iff (And (big_f X Y) (big_f Y X)) (big_f X Z)) →
% 3.60/3.81 Iff (big_f X Z) (big_f Z X) →
% 3.60/3.81 Iff (big_f X Z) (big_f Y Z) →
% 3.60/3.81 Iff (big_f Y X → big_f X Y) (big_f Z Z) → Iff (Iff (big_f X Y) (big_f Y X)) (big_f Z Y))
% 3.60/3.81 False
% 3.60/3.81 Clause #2 (by clausification #[1]): ∀ (a : Iota),
% 3.60/3.81 Eq
% 3.60/3.81 (Exists fun Y =>
% 3.60/3.81 ∀ (Z : Iota),
% 3.60/3.81 Not (Iff (And (big_f a Y) (big_f Y a)) (big_f a Z)) →
% 3.60/3.81 Iff (big_f a Z) (big_f Z a) →
% 3.60/3.81 Iff (big_f a Z) (big_f Y Z) →
% 3.60/3.81 Iff (big_f Y a → big_f a Y) (big_f Z Z) → Iff (Iff (big_f a Y) (big_f Y a)) (big_f Z Y))
% 3.60/3.81 False
% 3.60/3.81 Clause #3 (by clausification #[2]): ∀ (a a_1 : Iota),
% 3.60/3.81 Eq
% 3.60/3.81 (∀ (Z : Iota),
% 3.60/3.81 Not (Iff (And (big_f a a_1) (big_f a_1 a)) (big_f a Z)) →
% 3.60/3.81 Iff (big_f a Z) (big_f Z a) →
% 3.60/3.81 Iff (big_f a Z) (big_f a_1 Z) →
% 3.60/3.81 Iff (big_f a_1 a → big_f a a_1) (big_f Z Z) → Iff (Iff (big_f a a_1) (big_f a_1 a)) (big_f Z a_1))
% 3.60/3.81 False
% 3.60/3.81 Clause #4 (by clausification #[3]): ∀ (a a_1 a_2 : Iota),
% 3.60/3.81 Eq
% 3.60/3.81 (Not
% 3.60/3.81 (Not (Iff (And (big_f a a_1) (big_f a_1 a)) (big_f a (skS.0 0 a a_1 a_2))) →
% 3.60/3.81 Iff (big_f a (skS.0 0 a a_1 a_2)) (big_f (skS.0 0 a a_1 a_2) a) →
% 3.60/3.81 Iff (big_f a (skS.0 0 a a_1 a_2)) (big_f a_1 (skS.0 0 a a_1 a_2)) →
% 3.60/3.81 Iff (big_f a_1 a → big_f a a_1) (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) →
% 3.60/3.81 Iff (Iff (big_f a a_1) (big_f a_1 a)) (big_f (skS.0 0 a a_1 a_2) a_1)))
% 3.60/3.81 True
% 3.60/3.81 Clause #5 (by clausification #[4]): ∀ (a a_1 a_2 : Iota),
% 3.60/3.81 Eq
% 3.60/3.81 (Not (Iff (And (big_f a a_1) (big_f a_1 a)) (big_f a (skS.0 0 a a_1 a_2))) →
% 3.60/3.81 Iff (big_f a (skS.0 0 a a_1 a_2)) (big_f (skS.0 0 a a_1 a_2) a) →
% 3.60/3.81 Iff (big_f a (skS.0 0 a a_1 a_2)) (big_f a_1 (skS.0 0 a a_1 a_2)) →
% 3.60/3.81 Iff (big_f a_1 a → big_f a a_1) (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) →
% 3.60/3.81 Iff (Iff (big_f a a_1) (big_f a_1 a)) (big_f (skS.0 0 a a_1 a_2) a_1))
% 3.60/3.81 False
% 3.60/3.81 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Iota), Eq (Not (Iff (And (big_f a a_1) (big_f a_1 a)) (big_f a (skS.0 0 a a_1 a_2)))) True
% 3.60/3.81 Clause #7 (by clausification #[5]): ∀ (a a_1 a_2 : Iota),
% 3.60/3.81 Eq
% 3.60/3.81 (Iff (big_f a (skS.0 0 a a_1 a_2)) (big_f (skS.0 0 a a_1 a_2) a) →
% 3.60/3.81 Iff (big_f a (skS.0 0 a a_1 a_2)) (big_f a_1 (skS.0 0 a a_1 a_2)) →
% 3.60/3.81 Iff (big_f a_1 a → big_f a a_1) (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) →
% 3.60/3.81 Iff (Iff (big_f a a_1) (big_f a_1 a)) (big_f (skS.0 0 a a_1 a_2) a_1))
% 3.60/3.81 False
% 3.60/3.81 Clause #8 (by clausification #[6]): ∀ (a a_1 a_2 : Iota), Eq (Iff (And (big_f a a_1) (big_f a_1 a)) (big_f a (skS.0 0 a a_1 a_2))) False
% 3.60/3.81 Clause #10 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (big_f a a_1) (big_f a_1 a)) True) (Eq (big_f a (skS.0 0 a a_1 a_2)) True)
% 3.60/3.81 Clause #13 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a (skS.0 0 a a_1 a_2)) True) (Eq (big_f a a_1) True)
% 3.60/3.81 Clause #18 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), Eq (Iff (big_f a (skS.0 0 a a_1 a_2)) (big_f (skS.0 0 a a_1 a_2) a)) True
% 3.60/3.81 Clause #19 (by clausification #[7]): ∀ (a a_1 a_2 : Iota),
% 3.60/3.81 Eq
% 3.60/3.81 (Iff (big_f a (skS.0 0 a a_1 a_2)) (big_f a_1 (skS.0 0 a a_1 a_2)) →
% 3.60/3.81 Iff (big_f a_1 a → big_f a a_1) (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) →
% 3.60/3.81 Iff (Iff (big_f a a_1) (big_f a_1 a)) (big_f (skS.0 0 a a_1 a_2) a_1))
% 3.60/3.81 False
% 3.60/3.81 Clause #21 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a (skS.0 0 a a_1 a_2)) False) (Eq (big_f (skS.0 0 a a_1 a_2) a) True)
% 3.67/3.83 Clause #22 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), Eq (Iff (big_f a (skS.0 0 a a_1 a_2)) (big_f a_1 (skS.0 0 a a_1 a_2))) True
% 3.67/3.83 Clause #23 (by clausification #[19]): ∀ (a a_1 a_2 : Iota),
% 3.67/3.83 Eq
% 3.67/3.83 (Iff (big_f a a_1 → big_f a_1 a) (big_f (skS.0 0 a_1 a a_2) (skS.0 0 a_1 a a_2)) →
% 3.67/3.83 Iff (Iff (big_f a_1 a) (big_f a a_1)) (big_f (skS.0 0 a_1 a a_2) a))
% 3.67/3.83 False
% 3.67/3.83 Clause #25 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a (skS.0 0 a a_1 a_2)) False) (Eq (big_f a_1 (skS.0 0 a a_1 a_2)) True)
% 3.67/3.83 Clause #28 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Eq (Iff (big_f a a_1 → big_f a_1 a) (big_f (skS.0 0 a_1 a a_2) (skS.0 0 a_1 a a_2))) True
% 3.67/3.83 Clause #29 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Eq (Iff (Iff (big_f a a_1) (big_f a_1 a)) (big_f (skS.0 0 a a_1 a_2) a_1)) False
% 3.67/3.83 Clause #30 (by clausification #[28]): ∀ (a a_1 a_2 : Iota),
% 3.67/3.83 Or (Eq (big_f a a_1 → big_f a_1 a) True) (Eq (big_f (skS.0 0 a_1 a a_2) (skS.0 0 a_1 a a_2)) False)
% 3.67/3.83 Clause #32 (by clausification #[30]): ∀ (a a_1 a_2 : Iota),
% 3.67/3.83 Or (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) False) (Or (Eq (big_f a_1 a) False) (Eq (big_f a a_1) True))
% 3.67/3.83 Clause #33 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Or (Eq (Iff (big_f a a_1) (big_f a_1 a)) False) (Eq (big_f (skS.0 0 a a_1 a_2) a_1) False)
% 3.67/3.83 Clause #35 (by clausification #[33]): ∀ (a a_1 a_2 : Iota),
% 3.67/3.83 Or (Eq (big_f (skS.0 0 a a_1 a_2) a_1) False) (Or (Eq (big_f a a_1) False) (Eq (big_f a_1 a) False))
% 3.67/3.83 Clause #36 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f (skS.0 0 a a_1 a_2) a_1) False) (Or (Eq (big_f a a_1) True) (Eq (big_f a_1 a) True))
% 3.67/3.83 Clause #38 (by superposition #[21, 13]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f (skS.0 0 a a_1 a_2) a) True) (Or (Eq False True) (Eq (big_f a a_1) True))
% 3.67/3.83 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f (skS.0 0 a a_1 a_2) a) True) (Eq (big_f a a_1) True)
% 3.67/3.83 Clause #42 (by superposition #[39, 36]): ∀ (a : Iota), Or (Eq (big_f a a) True) (Or (Eq True False) (Or (Eq (big_f a a) True) (Eq (big_f a a) True)))
% 3.67/3.83 Clause #43 (by clausification #[42]): ∀ (a : Iota), Or (Eq (big_f a a) True) (Or (Eq (big_f a a) True) (Eq (big_f a a) True))
% 3.67/3.83 Clause #44 (by eliminate duplicate literals #[43]): ∀ (a : Iota), Eq (big_f a a) True
% 3.67/3.83 Clause #45 (by superposition #[44, 32]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (big_f a a_1) False) (Eq (big_f a_1 a) True))
% 3.67/3.83 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1) False) (Eq (big_f a_1 a) True)
% 3.67/3.83 Clause #51 (by superposition #[25, 13]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a (skS.0 0 a_1 a a_2)) True) (Or (Eq False True) (Eq (big_f a_1 a) True))
% 3.67/3.83 Clause #55 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a (skS.0 0 a_1 a a_2)) True) (Eq (big_f a_1 a) True)
% 3.67/3.83 Clause #56 (by superposition #[55, 46]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a a_1) True) (Or (Eq True False) (Eq (big_f (skS.0 0 a a_1 a_2) a_1) True))
% 3.67/3.83 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a a_1) True) (Eq (big_f (skS.0 0 a a_1 a_2) a_1) True)
% 3.67/3.83 Clause #58 (by superposition #[57, 36]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1) True) (Or (Eq True False) (Or (Eq (big_f a a_1) True) (Eq (big_f a_1 a) True)))
% 3.67/3.83 Clause #60 (by clausification #[58]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1) True) (Or (Eq (big_f a a_1) True) (Eq (big_f a_1 a) True))
% 3.67/3.83 Clause #61 (by eliminate duplicate literals #[60]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1) True) (Eq (big_f a_1 a) True)
% 3.67/3.83 Clause #63 (by superposition #[61, 46]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1) True) (Or (Eq True False) (Eq (big_f a a_1) True))
% 3.67/3.83 Clause #70 (by clausification #[63]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1) True) (Eq (big_f a a_1) True)
% 3.67/3.83 Clause #71 (by eliminate duplicate literals #[70]): ∀ (a a_1 : Iota), Eq (big_f a a_1) True
% 3.67/3.83 Clause #75 (by backward demodulation #[71, 35]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f (skS.0 0 a a_1 a_2) a_1) False) (Or (Eq True False) (Eq (big_f a_1 a) False))
% 3.67/3.83 Clause #84 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f (skS.0 0 a a_1 a_2) a_1) False) (Eq (big_f a_1 a) False)
% 3.67/3.83 Clause #85 (by forward demodulation #[84, 71]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f (skS.0 0 a a_1 a_2) a_1) False) (Eq True False)
% 3.67/3.83 Clause #86 (by clausification #[85]): ∀ (a a_1 a_2 : Iota), Eq (big_f (skS.0 0 a a_1 a_2) a_1) False
% 3.67/3.83 Clause #87 (by superposition #[86, 71]): Eq False True
% 3.67/3.83 Clause #88 (by clausification #[87]): False
% 3.67/3.83 SZS output end Proof for theBenchmark.p
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