TSTP Solution File: SYN398+1 by Duper---1.0
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% File : Duper---1.0
% Problem : SYN398+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n002.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 02:11:38 EDT 2023
% Result : Theorem 3.37s 3.56s
% Output : Proof 3.37s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN398+1 : TPTP v8.1.2. Released v2.0.0.
% 0.07/0.14 % Command : duper %s
% 0.15/0.35 % Computer : n002.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 19:07:33 EDT 2023
% 0.15/0.35 % CPUTime :
% 3.37/3.56 SZS status Theorem for theBenchmark.p
% 3.37/3.56 SZS output start Proof for theBenchmark.p
% 3.37/3.56 Clause #0 (by assumption #[]): Eq (Not (Iff (∀ (X : Iota), And p (f X)) (And p (∀ (Y : Iota), f Y)))) True
% 3.37/3.56 Clause #1 (by clausification #[0]): Eq (Iff (∀ (X : Iota), And p (f X)) (And p (∀ (Y : Iota), f Y))) False
% 3.37/3.56 Clause #2 (by clausification #[1]): Or (Eq (∀ (X : Iota), And p (f X)) False) (Eq (And p (∀ (Y : Iota), f Y)) False)
% 3.37/3.56 Clause #3 (by clausification #[1]): Or (Eq (∀ (X : Iota), And p (f X)) True) (Eq (And p (∀ (Y : Iota), f Y)) True)
% 3.37/3.56 Clause #4 (by clausification #[2]): ∀ (a : Iota), Or (Eq (And p (∀ (Y : Iota), f Y)) False) (Eq (Not (And p (f (skS.0 0 a)))) True)
% 3.37/3.56 Clause #5 (by clausification #[4]): ∀ (a : Iota), Or (Eq (Not (And p (f (skS.0 0 a)))) True) (Or (Eq p False) (Eq (∀ (Y : Iota), f Y) False))
% 3.37/3.56 Clause #6 (by clausification #[5]): ∀ (a : Iota), Or (Eq p False) (Or (Eq (∀ (Y : Iota), f Y) False) (Eq (And p (f (skS.0 0 a))) False))
% 3.37/3.56 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Or (Eq p False) (Or (Eq (And p (f (skS.0 0 a))) False) (Eq (Not (f (skS.0 1 a_1))) True))
% 3.37/3.56 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq p False) (Or (Eq (Not (f (skS.0 1 a))) True) (Or (Eq p False) (Eq (f (skS.0 0 a_1)) False)))
% 3.37/3.56 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq p False) (Or (Eq p False) (Or (Eq (f (skS.0 0 a)) False) (Eq (f (skS.0 1 a_1)) False)))
% 3.37/3.56 Clause #10 (by eliminate duplicate literals #[9]): ∀ (a a_1 : Iota), Or (Eq p False) (Or (Eq (f (skS.0 0 a)) False) (Eq (f (skS.0 1 a_1)) False))
% 3.37/3.56 Clause #11 (by clausification #[3]): ∀ (a : Iota), Or (Eq (And p (∀ (Y : Iota), f Y)) True) (Eq (And p (f a)) True)
% 3.37/3.56 Clause #12 (by clausification #[11]): ∀ (a : Iota), Or (Eq (And p (f a)) True) (Eq (∀ (Y : Iota), f Y) True)
% 3.37/3.56 Clause #13 (by clausification #[11]): ∀ (a : Iota), Or (Eq (And p (f a)) True) (Eq p True)
% 3.37/3.56 Clause #14 (by clausification #[12]): ∀ (a : Iota), Or (Eq (∀ (Y : Iota), f Y) True) (Eq (f a) True)
% 3.37/3.56 Clause #16 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (f a) True) (Eq (f a_1) True)
% 3.37/3.56 Clause #17 (by equality factoring #[16]): ∀ (a : Iota), Or (Ne True True) (Eq (f a) True)
% 3.37/3.56 Clause #18 (by clausification #[17]): ∀ (a : Iota), Or (Eq (f a) True) (Or (Eq True False) (Eq True False))
% 3.37/3.56 Clause #20 (by clausification #[18]): ∀ (a : Iota), Or (Eq (f a) True) (Eq True False)
% 3.37/3.56 Clause #21 (by clausification #[20]): ∀ (a : Iota), Eq (f a) True
% 3.37/3.56 Clause #23 (by clausification #[13]): Or (Eq p True) (Eq p True)
% 3.37/3.56 Clause #24 (by eliminate duplicate literals #[23]): Eq p True
% 3.37/3.56 Clause #25 (by backward demodulation #[24, 10]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (f (skS.0 0 a)) False) (Eq (f (skS.0 1 a_1)) False))
% 3.37/3.56 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), Or (Eq (f (skS.0 0 a)) False) (Eq (f (skS.0 1 a_1)) False)
% 3.37/3.56 Clause #27 (by superposition #[26, 21]): ∀ (a : Iota), Or (Eq (f (skS.0 1 a)) False) (Eq False True)
% 3.37/3.56 Clause #28 (by clausification #[27]): ∀ (a : Iota), Eq (f (skS.0 1 a)) False
% 3.37/3.56 Clause #29 (by superposition #[28, 21]): Eq False True
% 3.37/3.56 Clause #30 (by clausification #[29]): False
% 3.37/3.56 SZS output end Proof for theBenchmark.p
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