TSTP Solution File: SYN082+1 by Duper---1.0
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% File : Duper---1.0
% Problem : SYN082+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n027.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 02:10:32 EDT 2023
% Result : Theorem 3.56s 3.75s
% Output : Proof 3.56s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYN082+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.14 % Command : duper %s
% 0.15/0.36 % Computer : n027.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Aug 26 19:10:35 EDT 2023
% 0.15/0.36 % CPUTime :
% 3.56/3.75 SZS status Theorem for theBenchmark.p
% 3.56/3.75 SZS output start Proof for theBenchmark.p
% 3.56/3.75 Clause #0 (by assumption #[]): Eq (Not (∀ (X : Iota), Iff (big_f X (f X)) (Exists fun Y => And (∀ (Z : Iota), big_f Z Y → big_f Z (f X)) (big_f X Y))))
% 3.56/3.75 True
% 3.56/3.75 Clause #1 (by clausification #[0]): Eq (∀ (X : Iota), Iff (big_f X (f X)) (Exists fun Y => And (∀ (Z : Iota), big_f Z Y → big_f Z (f X)) (big_f X Y))) False
% 3.56/3.75 Clause #2 (by clausification #[1]): ∀ (a : Iota),
% 3.56/3.75 Eq
% 3.56/3.75 (Not
% 3.56/3.75 (Iff (big_f (skS.0 0 a) (f (skS.0 0 a)))
% 3.56/3.75 (Exists fun Y => And (∀ (Z : Iota), big_f Z Y → big_f Z (f (skS.0 0 a))) (big_f (skS.0 0 a) Y))))
% 3.56/3.75 True
% 3.56/3.75 Clause #3 (by clausification #[2]): ∀ (a : Iota),
% 3.56/3.75 Eq
% 3.56/3.75 (Iff (big_f (skS.0 0 a) (f (skS.0 0 a)))
% 3.56/3.75 (Exists fun Y => And (∀ (Z : Iota), big_f Z Y → big_f Z (f (skS.0 0 a))) (big_f (skS.0 0 a) Y)))
% 3.56/3.75 False
% 3.56/3.75 Clause #4 (by clausification #[3]): ∀ (a : Iota),
% 3.56/3.75 Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) False)
% 3.56/3.75 (Eq (Exists fun Y => And (∀ (Z : Iota), big_f Z Y → big_f Z (f (skS.0 0 a))) (big_f (skS.0 0 a) Y)) False)
% 3.56/3.75 Clause #5 (by clausification #[3]): ∀ (a : Iota),
% 3.56/3.75 Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) True)
% 3.56/3.75 (Eq (Exists fun Y => And (∀ (Z : Iota), big_f Z Y → big_f Z (f (skS.0 0 a))) (big_f (skS.0 0 a) Y)) True)
% 3.56/3.75 Clause #6 (by clausification #[4]): ∀ (a a_1 : Iota),
% 3.56/3.75 Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) False)
% 3.56/3.75 (Eq (And (∀ (Z : Iota), big_f Z a_1 → big_f Z (f (skS.0 0 a))) (big_f (skS.0 0 a) a_1)) False)
% 3.56/3.75 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota),
% 3.56/3.75 Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) False)
% 3.56/3.75 (Or (Eq (∀ (Z : Iota), big_f Z a_1 → big_f Z (f (skS.0 0 a))) False) (Eq (big_f (skS.0 0 a) a_1) False))
% 3.56/3.75 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 : Iota),
% 3.56/3.75 Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) False)
% 3.56/3.75 (Or (Eq (big_f (skS.0 0 a) a_1) False)
% 3.56/3.75 (Eq (Not (big_f (skS.0 1 a_1 a a_2) a_1 → big_f (skS.0 1 a_1 a a_2) (f (skS.0 0 a)))) True))
% 3.56/3.75 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota),
% 3.56/3.75 Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) False)
% 3.56/3.75 (Or (Eq (big_f (skS.0 0 a) a_1) False)
% 3.56/3.75 (Eq (big_f (skS.0 1 a_1 a a_2) a_1 → big_f (skS.0 1 a_1 a a_2) (f (skS.0 0 a))) False))
% 3.56/3.75 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota),
% 3.56/3.75 Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) False)
% 3.56/3.75 (Or (Eq (big_f (skS.0 0 a) a_1) False) (Eq (big_f (skS.0 1 a_1 a a_2) a_1) True))
% 3.56/3.75 Clause #11 (by clausification #[9]): ∀ (a a_1 a_2 : Iota),
% 3.56/3.75 Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) False)
% 3.56/3.75 (Or (Eq (big_f (skS.0 0 a) a_1) False) (Eq (big_f (skS.0 1 a_1 a a_2) (f (skS.0 0 a))) False))
% 3.56/3.75 Clause #12 (by clausification #[5]): ∀ (a a_1 : Iota),
% 3.56/3.75 Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) True)
% 3.56/3.75 (Eq (And (∀ (Z : Iota), big_f Z (skS.0 2 a a_1) → big_f Z (f (skS.0 0 a))) (big_f (skS.0 0 a) (skS.0 2 a a_1)))
% 3.56/3.75 True)
% 3.56/3.75 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) True) (Eq (big_f (skS.0 0 a) (skS.0 2 a a_1)) True)
% 3.56/3.75 Clause #14 (by clausification #[12]): ∀ (a a_1 : Iota),
% 3.56/3.75 Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) True)
% 3.56/3.75 (Eq (∀ (Z : Iota), big_f Z (skS.0 2 a a_1) → big_f Z (f (skS.0 0 a))) True)
% 3.56/3.75 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota),
% 3.56/3.75 Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) True) (Eq (big_f a_1 (skS.0 2 a a_2) → big_f a_1 (f (skS.0 0 a))) True)
% 3.56/3.75 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 : Iota),
% 3.56/3.75 Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) True)
% 3.56/3.75 (Or (Eq (big_f a_1 (skS.0 2 a a_2)) False) (Eq (big_f a_1 (f (skS.0 0 a))) True))
% 3.56/3.75 Clause #17 (by superposition #[16, 13]): ∀ (a : Iota),
% 3.56/3.75 Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) True)
% 3.56/3.75 (Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) True)
% 3.56/3.75 (Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) True) (Eq False True)))
% 3.56/3.75 Clause #18 (by clausification #[17]): ∀ (a : Iota),
% 3.56/3.75 Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) True)
% 3.56/3.75 (Or (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) True) (Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) True))
% 3.56/3.75 Clause #19 (by eliminate duplicate literals #[18]): ∀ (a : Iota), Eq (big_f (skS.0 0 a) (f (skS.0 0 a))) True
% 3.56/3.76 Clause #21 (by backward demodulation #[19, 11]): ∀ (a a_1 a_2 : Iota),
% 3.56/3.76 Or (Eq True False) (Or (Eq (big_f (skS.0 0 a) a_1) False) (Eq (big_f (skS.0 1 a_1 a a_2) (f (skS.0 0 a))) False))
% 3.56/3.76 Clause #22 (by superposition #[19, 10]): ∀ (a a_1 a_2 : Iota),
% 3.56/3.76 Or (Eq True False) (Or (Eq (big_f (skS.0 0 a) a_1) False) (Eq (big_f (skS.0 1 a_1 a a_2) a_1) True))
% 3.56/3.76 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f (skS.0 0 a) a_1) False) (Eq (big_f (skS.0 1 a_1 a a_2) a_1) True)
% 3.56/3.76 Clause #24 (by superposition #[23, 19]): ∀ (a a_1 : Iota), Or (Eq (big_f (skS.0 1 (f (skS.0 0 a)) a a_1) (f (skS.0 0 a))) True) (Eq False True)
% 3.56/3.76 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Eq (big_f (skS.0 1 (f (skS.0 0 a)) a a_1) (f (skS.0 0 a))) True
% 3.56/3.76 Clause #26 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f (skS.0 0 a) a_1) False) (Eq (big_f (skS.0 1 a_1 a a_2) (f (skS.0 0 a))) False)
% 3.56/3.76 Clause #27 (by superposition #[26, 19]): ∀ (a a_1 : Iota), Or (Eq (big_f (skS.0 1 (f (skS.0 0 a)) a a_1) (f (skS.0 0 a))) False) (Eq False True)
% 3.56/3.76 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (big_f (skS.0 1 (f (skS.0 0 a)) a a_1) (f (skS.0 0 a))) False
% 3.56/3.76 Clause #29 (by superposition #[28, 25]): Eq False True
% 3.56/3.76 Clause #30 (by clausification #[29]): False
% 3.56/3.76 SZS output end Proof for theBenchmark.p
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