TSTP Solution File: SYN321+1 by Duper---1.0
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% File : Duper---1.0
% Problem : SYN321+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n028.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 02:11:09 EDT 2023
% Result : Theorem 3.41s 3.60s
% Output : Proof 3.41s
% 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 : SYN321+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.14 % Command : duper %s
% 0.15/0.35 % Computer : n028.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 20:37:53 EDT 2023
% 0.15/0.35 % CPUTime :
% 3.41/3.60 SZS status Theorem for theBenchmark.p
% 3.41/3.60 SZS output start Proof for theBenchmark.p
% 3.41/3.60 Clause #0 (by assumption #[]): Eq
% 3.41/3.60 (Not
% 3.41/3.60 (Exists fun X =>
% 3.41/3.60 Exists fun Y =>
% 3.41/3.60 ((Exists fun Z => big_f X Z) → ∀ (Z : Iota), big_g X Z) →
% 3.41/3.60 (∀ (Z : Iota), big_g Z Z → big_f Z Y) → Iff (big_f X Y) (∀ (Z : Iota), big_g X Z)))
% 3.41/3.60 True
% 3.41/3.60 Clause #1 (by betaEtaReduce #[0]): Eq
% 3.41/3.60 (Not
% 3.41/3.60 (Exists fun X =>
% 3.41/3.60 Exists fun Y =>
% 3.41/3.60 (Exists (big_f X) → ∀ (Z : Iota), big_g X Z) →
% 3.41/3.60 (∀ (Z : Iota), big_g Z Z → big_f Z Y) → Iff (big_f X Y) (∀ (Z : Iota), big_g X Z)))
% 3.41/3.60 True
% 3.41/3.60 Clause #2 (by clausification #[1]): Eq
% 3.41/3.60 (Exists fun X =>
% 3.41/3.60 Exists fun Y =>
% 3.41/3.60 (Exists (big_f X) → ∀ (Z : Iota), big_g X Z) →
% 3.41/3.60 (∀ (Z : Iota), big_g Z Z → big_f Z Y) → Iff (big_f X Y) (∀ (Z : Iota), big_g X Z))
% 3.41/3.60 False
% 3.41/3.60 Clause #3 (by clausification #[2]): ∀ (a : Iota),
% 3.41/3.60 Eq
% 3.41/3.60 (Exists fun Y =>
% 3.41/3.60 (Exists (big_f a) → ∀ (Z : Iota), big_g a Z) →
% 3.41/3.60 (∀ (Z : Iota), big_g Z Z → big_f Z Y) → Iff (big_f a Y) (∀ (Z : Iota), big_g a Z))
% 3.41/3.60 False
% 3.41/3.60 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota),
% 3.41/3.60 Eq
% 3.41/3.60 ((Exists (big_f a) → ∀ (Z : Iota), big_g a Z) →
% 3.41/3.60 (∀ (Z : Iota), big_g Z Z → big_f Z a_1) → Iff (big_f a a_1) (∀ (Z : Iota), big_g a Z))
% 3.41/3.60 False
% 3.41/3.60 Clause #5 (by clausification #[4]): ∀ (a : Iota), Eq (Exists (big_f a) → ∀ (Z : Iota), big_g a Z) True
% 3.41/3.60 Clause #6 (by clausification #[4]): ∀ (a a_1 : Iota), Eq ((∀ (Z : Iota), big_g Z Z → big_f Z a) → Iff (big_f a_1 a) (∀ (Z : Iota), big_g a_1 Z)) False
% 3.41/3.60 Clause #7 (by clausification #[5]): ∀ (a : Iota), Or (Eq (Exists (big_f a)) False) (Eq (∀ (Z : Iota), big_g a Z) True)
% 3.41/3.60 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (∀ (Z : Iota), big_g a Z) True) (Eq (big_f a a_1) False)
% 3.41/3.60 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a a_1) False) (Eq (big_g a a_2) True)
% 3.41/3.60 Clause #10 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (Z : Iota), big_g Z Z → big_f Z a) True
% 3.41/3.60 Clause #11 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (Iff (big_f a a_1) (∀ (Z : Iota), big_g a Z)) False
% 3.41/3.60 Clause #12 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (big_g a a → big_f a a_1) True
% 3.41/3.60 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Or (Eq (big_g a a) False) (Eq (big_f a a_1) True)
% 3.41/3.60 Clause #14 (by clausification #[11]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1) False) (Eq (∀ (Z : Iota), big_g a Z) False)
% 3.41/3.60 Clause #15 (by clausification #[11]): ∀ (a a_1 : Iota), Or (Eq (big_f a a_1) True) (Eq (∀ (Z : Iota), big_g a Z) True)
% 3.41/3.60 Clause #16 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a a_1) False) (Eq (Not (big_g a (skS.0 0 a a_2))) True)
% 3.41/3.60 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a a_1) False) (Eq (big_g a (skS.0 0 a a_2)) False)
% 3.41/3.60 Clause #18 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a a_1) True) (Eq (big_g a a_2) True)
% 3.41/3.60 Clause #19 (by superposition #[18, 9]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_g a a_1) True) (Or (Eq True False) (Eq (big_g a a_2) True))
% 3.41/3.60 Clause #26 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_g a a_1) True) (Eq (big_g a a_2) True)
% 3.41/3.60 Clause #28 (by equality factoring #[26]): ∀ (a a_1 : Iota), Or (Ne True True) (Eq (big_g a a_1) True)
% 3.41/3.60 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Or (Eq (big_g a a_1) True) (Or (Eq True False) (Eq True False))
% 3.41/3.60 Clause #31 (by clausification #[29]): ∀ (a a_1 : Iota), Or (Eq (big_g a a_1) True) (Eq True False)
% 3.41/3.60 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Eq (big_g a a_1) True
% 3.41/3.60 Clause #33 (by superposition #[32, 13]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (big_f a a_1) True)
% 3.41/3.60 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Eq (big_f a a_1) True
% 3.41/3.60 Clause #35 (by superposition #[34, 17]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (big_g a (skS.0 0 a a_1)) False)
% 3.41/3.60 Clause #41 (by clausification #[35]): ∀ (a a_1 : Iota), Eq (big_g a (skS.0 0 a a_1)) False
% 3.41/3.60 Clause #42 (by superposition #[41, 32]): Eq False True
% 3.41/3.60 Clause #43 (by clausification #[42]): False
% 3.41/3.60 SZS output end Proof for theBenchmark.p
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