TSTP Solution File: SYN409+1 by Duper---1.0
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% File : Duper---1.0
% Problem : SYN409+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 02:11:40 EDT 2023
% Result : Theorem 4.00s 4.22s
% Output : Proof 4.00s
% 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 : SYN409+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.15 % Command : duper %s
% 0.15/0.36 % Computer : n012.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 21:13:55 EDT 2023
% 0.15/0.36 % CPUTime :
% 4.00/4.22 SZS status Theorem for theBenchmark.p
% 4.00/4.22 SZS output start Proof for theBenchmark.p
% 4.00/4.22 Clause #0 (by assumption #[]): Eq (Not (Iff (∀ (X : Iota), f X) (∀ (Y Z : Iota), And (f Y) (f Z)))) True
% 4.00/4.22 Clause #1 (by clausification #[0]): Eq (Iff (∀ (X : Iota), f X) (∀ (Y Z : Iota), And (f Y) (f Z))) False
% 4.00/4.22 Clause #2 (by clausification #[1]): Or (Eq (∀ (X : Iota), f X) False) (Eq (∀ (Y Z : Iota), And (f Y) (f Z)) False)
% 4.00/4.22 Clause #3 (by clausification #[1]): Or (Eq (∀ (X : Iota), f X) True) (Eq (∀ (Y Z : Iota), And (f Y) (f Z)) True)
% 4.00/4.22 Clause #4 (by clausification #[2]): ∀ (a : Iota), Or (Eq (∀ (Y Z : Iota), And (f Y) (f Z)) False) (Eq (Not (f (skS.0 0 a))) True)
% 4.00/4.22 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), Or (Eq (Not (f (skS.0 0 a))) True) (Eq (Not (∀ (Z : Iota), And (f (skS.0 1 a_1)) (f Z))) True)
% 4.00/4.22 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), Or (Eq (Not (∀ (Z : Iota), And (f (skS.0 1 a)) (f Z))) True) (Eq (f (skS.0 0 a_1)) False)
% 4.00/4.22 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Or (Eq (f (skS.0 0 a)) False) (Eq (∀ (Z : Iota), And (f (skS.0 1 a_1)) (f Z)) False)
% 4.00/4.22 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), Or (Eq (f (skS.0 0 a)) False) (Eq (Not (And (f (skS.0 1 a_1)) (f (skS.0 2 a_1 a_2)))) True)
% 4.00/4.22 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), Or (Eq (f (skS.0 0 a)) False) (Eq (And (f (skS.0 1 a_1)) (f (skS.0 2 a_1 a_2))) False)
% 4.00/4.22 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), Or (Eq (f (skS.0 0 a)) False) (Or (Eq (f (skS.0 1 a_1)) False) (Eq (f (skS.0 2 a_1 a_2)) False))
% 4.00/4.22 Clause #11 (by clausification #[3]): ∀ (a : Iota), Or (Eq (∀ (Y Z : Iota), And (f Y) (f Z)) True) (Eq (f a) True)
% 4.00/4.22 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Or (Eq (f a) True) (Eq (∀ (Z : Iota), And (f a_1) (f Z)) True)
% 4.00/4.22 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Or (Eq (f a) True) (Eq (And (f a_1) (f a_2)) True)
% 4.00/4.22 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (f a) True) (Eq (f a_1) True)
% 4.00/4.22 Clause #16 (by equality factoring #[14]): ∀ (a : Iota), Or (Ne True True) (Eq (f a) True)
% 4.00/4.22 Clause #17 (by clausification #[16]): ∀ (a : Iota), Or (Eq (f a) True) (Or (Eq True False) (Eq True False))
% 4.00/4.22 Clause #19 (by clausification #[17]): ∀ (a : Iota), Or (Eq (f a) True) (Eq True False)
% 4.00/4.22 Clause #20 (by clausification #[19]): ∀ (a : Iota), Eq (f a) True
% 4.00/4.22 Clause #21 (by backward demodulation #[20, 10]): ∀ (a a_1 a_2 : Iota), Or (Eq (f (skS.0 0 a)) False) (Or (Eq True False) (Eq (f (skS.0 2 a_1 a_2)) False))
% 4.00/4.22 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), Or (Eq (f (skS.0 0 a)) False) (Eq (f (skS.0 2 a_1 a_2)) False)
% 4.00/4.22 Clause #23 (by superposition #[22, 20]): ∀ (a a_1 : Iota), Or (Eq (f (skS.0 2 a a_1)) False) (Eq False True)
% 4.00/4.22 Clause #27 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (f (skS.0 2 a a_1)) False
% 4.00/4.22 Clause #28 (by superposition #[27, 20]): Eq False True
% 4.00/4.22 Clause #29 (by clausification #[28]): False
% 4.00/4.22 SZS output end Proof for theBenchmark.p
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