TSTP Solution File: SYN317+1 by Duper---1.0
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% File : Duper---1.0
% Problem : SYN317+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n018.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 02:11:08 EDT 2023
% Result : Theorem 3.44s 3.65s
% Output : Proof 3.44s
% 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 : SYN317+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 21:05:15 EDT 2023
% 0.13/0.35 % CPUTime :
% 3.44/3.65 SZS status Theorem for theBenchmark.p
% 3.44/3.65 SZS output start Proof for theBenchmark.p
% 3.44/3.65 Clause #0 (by assumption #[]): Eq (Not (Iff (Exists fun X => big_f X → big_g X) (Exists fun X => Exists fun Y => big_f X → big_g Y))) True
% 3.44/3.65 Clause #1 (by clausification #[0]): Eq (Iff (Exists fun X => big_f X → big_g X) (Exists fun X => Exists fun Y => big_f X → big_g Y)) False
% 3.44/3.65 Clause #2 (by clausification #[1]): Or (Eq (Exists fun X => big_f X → big_g X) False) (Eq (Exists fun X => Exists fun Y => big_f X → big_g Y) False)
% 3.44/3.65 Clause #3 (by clausification #[1]): Or (Eq (Exists fun X => big_f X → big_g X) True) (Eq (Exists fun X => Exists fun Y => big_f X → big_g Y) True)
% 3.44/3.65 Clause #4 (by clausification #[2]): ∀ (a : Iota), Or (Eq (Exists fun X => Exists fun Y => big_f X → big_g Y) False) (Eq (big_f a → big_g a) False)
% 3.44/3.65 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), Or (Eq (big_f a → big_g a) False) (Eq (Exists fun Y => big_f a_1 → big_g Y) False)
% 3.44/3.65 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), Or (Eq (Exists fun Y => big_f a → big_g Y) False) (Eq (big_f a_1) True)
% 3.44/3.65 Clause #7 (by clausification #[5]): ∀ (a a_1 : Iota), Or (Eq (Exists fun Y => big_f a → big_g Y) False) (Eq (big_g a_1) False)
% 3.44/3.65 Clause #8 (by clausification #[6]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a) True) (Eq (big_f a_1 → big_g a_2) False)
% 3.44/3.65 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq (big_f a) True) (Eq (big_f a_1) True)
% 3.44/3.65 Clause #11 (by equality factoring #[9]): ∀ (a : Iota), Or (Ne True True) (Eq (big_f a) True)
% 3.44/3.65 Clause #12 (by clausification #[11]): ∀ (a : Iota), Or (Eq (big_f a) True) (Or (Eq True False) (Eq True False))
% 3.44/3.65 Clause #14 (by clausification #[12]): ∀ (a : Iota), Or (Eq (big_f a) True) (Eq True False)
% 3.44/3.65 Clause #15 (by clausification #[14]): ∀ (a : Iota), Eq (big_f a) True
% 3.44/3.65 Clause #16 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_g a) False) (Eq (big_f a_1 → big_g a_2) False)
% 3.44/3.65 Clause #18 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (big_g a) False) (Eq (big_g a_1) False)
% 3.44/3.65 Clause #19 (by clausification #[3]): ∀ (a : Iota),
% 3.44/3.65 Or (Eq (Exists fun X => Exists fun Y => big_f X → big_g Y) True) (Eq (big_f (skS.0 0 a) → big_g (skS.0 0 a)) True)
% 3.44/3.65 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota),
% 3.44/3.65 Or (Eq (big_f (skS.0 0 a) → big_g (skS.0 0 a)) True) (Eq (Exists fun Y => big_f (skS.0 1 a_1) → big_g Y) True)
% 3.44/3.65 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota),
% 3.44/3.65 Or (Eq (Exists fun Y => big_f (skS.0 1 a) → big_g Y) True)
% 3.44/3.65 (Or (Eq (big_f (skS.0 0 a_1)) False) (Eq (big_g (skS.0 0 a_1)) True))
% 3.44/3.65 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : Iota),
% 3.44/3.65 Or (Eq (big_f (skS.0 0 a)) False)
% 3.44/3.65 (Or (Eq (big_g (skS.0 0 a)) True) (Eq (big_f (skS.0 1 a_1) → big_g (skS.0 2 a_1 a_2)) True))
% 3.44/3.65 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 : Iota),
% 3.44/3.65 Or (Eq (big_f (skS.0 0 a)) False)
% 3.44/3.65 (Or (Eq (big_g (skS.0 0 a)) True) (Or (Eq (big_f (skS.0 1 a_1)) False) (Eq (big_g (skS.0 2 a_1 a_2)) True)))
% 3.44/3.65 Clause #24 (by forward demodulation #[23, 15]): ∀ (a a_1 a_2 : Iota),
% 3.44/3.65 Or (Eq True False)
% 3.44/3.65 (Or (Eq (big_g (skS.0 0 a)) True) (Or (Eq (big_f (skS.0 1 a_1)) False) (Eq (big_g (skS.0 2 a_1 a_2)) True)))
% 3.44/3.65 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota),
% 3.44/3.65 Or (Eq (big_g (skS.0 0 a)) True) (Or (Eq (big_f (skS.0 1 a_1)) False) (Eq (big_g (skS.0 2 a_1 a_2)) True))
% 3.44/3.65 Clause #26 (by forward demodulation #[25, 15]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_g (skS.0 0 a)) True) (Or (Eq True False) (Eq (big_g (skS.0 2 a_1 a_2)) True))
% 3.44/3.65 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_g (skS.0 0 a)) True) (Eq (big_g (skS.0 2 a_1 a_2)) True)
% 3.44/3.65 Clause #29 (by superposition #[18, 27]): ∀ (a a_1 : Iota), Or (Eq (big_g (skS.0 0 a)) True) (Or (Eq True False) (Eq (big_g a_1) False))
% 3.44/3.65 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Or (Eq (big_g (skS.0 0 a)) True) (Eq (big_g a_1) False)
% 3.44/3.65 Clause #32 (by superposition #[30, 27]): ∀ (a a_1 : Iota), Or (Eq (big_g (skS.0 0 a)) True) (Or (Eq (big_g (skS.0 0 a_1)) True) (Eq False True))
% 3.44/3.65 Clause #36 (by clausification #[32]): ∀ (a a_1 : Iota), Or (Eq (big_g (skS.0 0 a)) True) (Eq (big_g (skS.0 0 a_1)) True)
% 3.44/3.65 Clause #39 (by equality factoring #[36]): ∀ (a : Iota), Or (Ne True True) (Eq (big_g (skS.0 0 a)) True)
% 3.44/3.65 Clause #40 (by clausification #[39]): ∀ (a : Iota), Or (Eq (big_g (skS.0 0 a)) True) (Or (Eq True False) (Eq True False))
% 3.44/3.65 Clause #42 (by clausification #[40]): ∀ (a : Iota), Or (Eq (big_g (skS.0 0 a)) True) (Eq True False)
% 3.44/3.65 Clause #43 (by clausification #[42]): ∀ (a : Iota), Eq (big_g (skS.0 0 a)) True
% 3.44/3.65 Clause #44 (by superposition #[43, 18]): ∀ (a : Iota), Or (Eq True False) (Eq (big_g a) False)
% 3.44/3.65 Clause #46 (by clausification #[44]): ∀ (a : Iota), Eq (big_g a) False
% 3.44/3.65 Clause #47 (by superposition #[46, 43]): Eq False True
% 3.44/3.65 Clause #48 (by clausification #[47]): False
% 3.44/3.65 SZS output end Proof for theBenchmark.p
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