TSTP Solution File: SYN966+1 by Duper---1.0
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- Process Solution
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% File : Duper---1.0
% Problem : SYN966+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n015.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 02:13:28 EDT 2023
% Result : Theorem 3.94s 4.19s
% Output : Proof 4.03s
% 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 : SYN966+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 19:00:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 3.94/4.19 SZS status Theorem for theBenchmark.p
% 3.94/4.19 SZS output start Proof for theBenchmark.p
% 3.94/4.19 Clause #0 (by assumption #[]): Eq
% 3.94/4.19 (Not
% 3.94/4.19 ((∀ (X Y : Iota), Iff (eq X Y) (∀ (Z : Iota), Iff (a_member_of Z X) (a_member_of Z Y))) →
% 3.94/4.19 ∀ (A B : Iota), eq A B → eq B A))
% 3.94/4.19 True
% 3.94/4.19 Clause #1 (by clausification #[0]): Eq
% 3.94/4.19 ((∀ (X Y : Iota), Iff (eq X Y) (∀ (Z : Iota), Iff (a_member_of Z X) (a_member_of Z Y))) →
% 3.94/4.19 ∀ (A B : Iota), eq A B → eq B A)
% 3.94/4.19 False
% 3.94/4.19 Clause #2 (by clausification #[1]): Eq (∀ (X Y : Iota), Iff (eq X Y) (∀ (Z : Iota), Iff (a_member_of Z X) (a_member_of Z Y))) True
% 3.94/4.19 Clause #3 (by clausification #[1]): Eq (∀ (A B : Iota), eq A B → eq B A) False
% 3.94/4.19 Clause #4 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (eq a Y) (∀ (Z : Iota), Iff (a_member_of Z a) (a_member_of Z Y))) True
% 3.94/4.19 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), Eq (Iff (eq a a_1) (∀ (Z : Iota), Iff (a_member_of Z a) (a_member_of Z a_1))) True
% 3.94/4.19 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), Or (Eq (eq a a_1) True) (Eq (∀ (Z : Iota), Iff (a_member_of Z a) (a_member_of Z a_1)) False)
% 3.94/4.19 Clause #7 (by clausification #[5]): ∀ (a a_1 : Iota), Or (Eq (eq a a_1) False) (Eq (∀ (Z : Iota), Iff (a_member_of Z a) (a_member_of Z a_1)) True)
% 3.94/4.19 Clause #8 (by clausification #[6]): ∀ (a a_1 a_2 : Iota),
% 3.94/4.19 Or (Eq (eq a a_1) True)
% 3.94/4.19 (Eq (Not (Iff (a_member_of (skS.0 0 a a_1 a_2) a) (a_member_of (skS.0 0 a a_1 a_2) a_1))) True)
% 3.94/4.19 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota),
% 3.94/4.19 Or (Eq (eq a a_1) True) (Eq (Iff (a_member_of (skS.0 0 a a_1 a_2) a) (a_member_of (skS.0 0 a a_1 a_2) a_1)) False)
% 3.94/4.19 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota),
% 3.94/4.19 Or (Eq (eq a a_1) True)
% 3.94/4.19 (Or (Eq (a_member_of (skS.0 0 a a_1 a_2) a) False) (Eq (a_member_of (skS.0 0 a a_1 a_2) a_1) False))
% 3.94/4.19 Clause #11 (by clausification #[9]): ∀ (a a_1 a_2 : Iota),
% 3.94/4.19 Or (Eq (eq a a_1) True)
% 3.94/4.19 (Or (Eq (a_member_of (skS.0 0 a a_1 a_2) a) True) (Eq (a_member_of (skS.0 0 a a_1 a_2) a_1) True))
% 3.94/4.19 Clause #12 (by clausification #[3]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), eq (skS.0 1 a) B → eq B (skS.0 1 a))) True
% 3.94/4.19 Clause #13 (by clausification #[12]): ∀ (a : Iota), Eq (∀ (B : Iota), eq (skS.0 1 a) B → eq B (skS.0 1 a)) False
% 3.94/4.19 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Eq (Not (eq (skS.0 1 a) (skS.0 2 a a_1) → eq (skS.0 2 a a_1) (skS.0 1 a))) True
% 3.94/4.19 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Eq (eq (skS.0 1 a) (skS.0 2 a a_1) → eq (skS.0 2 a a_1) (skS.0 1 a)) False
% 3.94/4.19 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (eq (skS.0 1 a) (skS.0 2 a a_1)) True
% 3.94/4.19 Clause #17 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (eq (skS.0 2 a a_1) (skS.0 1 a)) False
% 3.94/4.19 Clause #18 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), Or (Eq (eq a a_1) False) (Eq (Iff (a_member_of a_2 a) (a_member_of a_2 a_1)) True)
% 3.94/4.19 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), Or (Eq (eq a a_1) False) (Or (Eq (a_member_of a_2 a) True) (Eq (a_member_of a_2 a_1) False))
% 3.94/4.19 Clause #20 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), Or (Eq (eq a a_1) False) (Or (Eq (a_member_of a_2 a) False) (Eq (a_member_of a_2 a_1) True))
% 3.94/4.19 Clause #21 (by superposition #[19, 16]): ∀ (a a_1 a_2 : Iota),
% 3.94/4.19 Or (Eq (a_member_of a (skS.0 1 a_1)) True) (Or (Eq (a_member_of a (skS.0 2 a_1 a_2)) False) (Eq False True))
% 3.94/4.19 Clause #22 (by superposition #[20, 16]): ∀ (a a_1 a_2 : Iota),
% 3.94/4.19 Or (Eq (a_member_of a (skS.0 1 a_1)) False) (Or (Eq (a_member_of a (skS.0 2 a_1 a_2)) True) (Eq False True))
% 3.94/4.19 Clause #38 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), Or (Eq (a_member_of a (skS.0 1 a_1)) True) (Eq (a_member_of a (skS.0 2 a_1 a_2)) False)
% 3.94/4.19 Clause #41 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), Or (Eq (a_member_of a (skS.0 1 a_1)) False) (Eq (a_member_of a (skS.0 2 a_1 a_2)) True)
% 3.94/4.19 Clause #43 (by superposition #[41, 11]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.94/4.19 Or (Eq (a_member_of (skS.0 0 a (skS.0 1 a_1) a_2) (skS.0 2 a_1 a_3)) True)
% 3.94/4.19 (Or (Eq (eq a (skS.0 1 a_1)) True) (Or (Eq (a_member_of (skS.0 0 a (skS.0 1 a_1) a_2) a) True) (Eq False True)))
% 4.03/4.21 Clause #45 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.03/4.21 Or (Eq (a_member_of (skS.0 0 a (skS.0 1 a_1) a_2) (skS.0 2 a_1 a_3)) True)
% 4.03/4.21 (Or (Eq (eq a (skS.0 1 a_1)) True) (Eq (a_member_of (skS.0 0 a (skS.0 1 a_1) a_2) a) True))
% 4.03/4.21 Clause #50 (by equality factoring #[45]): ∀ (a a_1 a_2 : Iota),
% 4.03/4.21 Or (Eq (eq (skS.0 2 a a_1) (skS.0 1 a)) True)
% 4.03/4.21 (Or (Ne True True) (Eq (a_member_of (skS.0 0 (skS.0 2 a a_1) (skS.0 1 a) a_2) (skS.0 2 a a_1)) True))
% 4.03/4.21 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota),
% 4.03/4.21 Or (Eq (eq (skS.0 2 a a_1) (skS.0 1 a)) True)
% 4.03/4.21 (Or (Eq (a_member_of (skS.0 0 (skS.0 2 a a_1) (skS.0 1 a) a_2) (skS.0 2 a a_1)) True)
% 4.03/4.21 (Or (Eq True False) (Eq True False)))
% 4.03/4.21 Clause #53 (by clausification #[51]): ∀ (a a_1 a_2 : Iota),
% 4.03/4.21 Or (Eq (eq (skS.0 2 a a_1) (skS.0 1 a)) True)
% 4.03/4.21 (Or (Eq (a_member_of (skS.0 0 (skS.0 2 a a_1) (skS.0 1 a) a_2) (skS.0 2 a a_1)) True) (Eq True False))
% 4.03/4.21 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 : Iota),
% 4.03/4.21 Or (Eq (eq (skS.0 2 a a_1) (skS.0 1 a)) True)
% 4.03/4.21 (Eq (a_member_of (skS.0 0 (skS.0 2 a a_1) (skS.0 1 a) a_2) (skS.0 2 a a_1)) True)
% 4.03/4.21 Clause #55 (by forward demodulation #[54, 17]): ∀ (a a_1 a_2 : Iota),
% 4.03/4.21 Or (Eq False True) (Eq (a_member_of (skS.0 0 (skS.0 2 a a_1) (skS.0 1 a) a_2) (skS.0 2 a a_1)) True)
% 4.03/4.21 Clause #56 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), Eq (a_member_of (skS.0 0 (skS.0 2 a a_1) (skS.0 1 a) a_2) (skS.0 2 a a_1)) True
% 4.03/4.21 Clause #57 (by superposition #[56, 38]): ∀ (a a_1 a_2 : Iota), Or (Eq (a_member_of (skS.0 0 (skS.0 2 a a_1) (skS.0 1 a) a_2) (skS.0 1 a)) True) (Eq True False)
% 4.03/4.21 Clause #58 (by superposition #[56, 10]): ∀ (a a_1 a_2 : Iota),
% 4.03/4.21 Or (Eq (eq (skS.0 2 a a_1) (skS.0 1 a)) True)
% 4.03/4.21 (Or (Eq True False) (Eq (a_member_of (skS.0 0 (skS.0 2 a a_1) (skS.0 1 a) a_2) (skS.0 1 a)) False))
% 4.03/4.21 Clause #65 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), Eq (a_member_of (skS.0 0 (skS.0 2 a a_1) (skS.0 1 a) a_2) (skS.0 1 a)) True
% 4.03/4.21 Clause #73 (by clausification #[58]): ∀ (a a_1 a_2 : Iota),
% 4.03/4.21 Or (Eq (eq (skS.0 2 a a_1) (skS.0 1 a)) True)
% 4.03/4.21 (Eq (a_member_of (skS.0 0 (skS.0 2 a a_1) (skS.0 1 a) a_2) (skS.0 1 a)) False)
% 4.03/4.21 Clause #74 (by forward demodulation #[73, 17]): ∀ (a a_1 a_2 : Iota), Or (Eq False True) (Eq (a_member_of (skS.0 0 (skS.0 2 a a_1) (skS.0 1 a) a_2) (skS.0 1 a)) False)
% 4.03/4.21 Clause #75 (by clausification #[74]): ∀ (a a_1 a_2 : Iota), Eq (a_member_of (skS.0 0 (skS.0 2 a a_1) (skS.0 1 a) a_2) (skS.0 1 a)) False
% 4.03/4.21 Clause #76 (by superposition #[75, 65]): Eq False True
% 4.03/4.21 Clause #77 (by clausification #[76]): False
% 4.03/4.21 SZS output end Proof for theBenchmark.p
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