%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN966+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n005.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 Oct 3 08:08:19 PM UTC 2025 % Result : Theorem 4.06s 4.25s % Output : Proof 4.06s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYN966+1 : TPTP v9.2.0. Released v3.1.0. % 0.07/0.14 % Command : duper %s % 0.15/0.35 % Computer : n005.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 : Thu Oct 2 15:37:53 EDT 2025 % 0.15/0.35 % CPUTime : % 4.06/4.25 SZS status Theorem for theBenchmark.p % 4.06/4.25 SZS output start Proof for theBenchmark.p % 4.06/4.25 Clause #0 (by assumption #[]): Eq % 4.06/4.25 (Not % 4.06/4.25 ((∀ (X Y : Iota), Iff (eq X Y) (∀ (Z : Iota), Iff (a_member_of Z X) (a_member_of Z Y))) → % 4.06/4.25 ∀ (A B : Iota), eq A B → eq B A)) % 4.06/4.25 True % 4.06/4.25 Clause #1 (by clausification #[0]): Eq % 4.06/4.25 ((∀ (X Y : Iota), Iff (eq X Y) (∀ (Z : Iota), Iff (a_member_of Z X) (a_member_of Z Y))) → % 4.06/4.25 ∀ (A B : Iota), eq A B → eq B A) % 4.06/4.25 False % 4.06/4.25 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 % 4.06/4.25 Clause #3 (by clausification #[1]): Eq (∀ (A B : Iota), eq A B → eq B A) False % 4.06/4.25 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 % 4.06/4.25 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 % 4.06/4.25 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) % 4.06/4.25 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) % 4.06/4.25 Clause #8 (by clausification #[6]): ∀ (a a_1 a_2 : Iota), % 4.06/4.25 Or (Eq (eq a a_1) True) % 4.06/4.25 (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) % 4.06/4.25 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), % 4.06/4.25 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) % 4.06/4.25 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 4.06/4.25 Or (Eq (eq a a_1) True) % 4.06/4.25 (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)) % 4.06/4.25 Clause #11 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 4.06/4.25 Or (Eq (eq a a_1) True) % 4.06/4.25 (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)) % 4.06/4.25 Clause #12 (by clausification #[3]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), eq (skS.0 1 a) B → eq B (skS.0 1 a))) True % 4.06/4.26 Clause #13 (by clausification #[12]): ∀ (a : Iota), Eq (∀ (B : Iota), eq (skS.0 1 a) B → eq B (skS.0 1 a)) False % 4.06/4.26 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 % 4.06/4.26 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 % 4.06/4.26 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (eq (skS.0 1 a) (skS.0 2 a a_1)) True % 4.06/4.26 Clause #17 (by clausification #[15]): ∀ (a a_1 : Iota), Eq (eq (skS.0 2 a a_1) (skS.0 1 a)) False % 4.06/4.26 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) % 4.06/4.26 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)) % 4.06/4.26 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)) % 4.06/4.26 Clause #21 (by superposition #[19, 16]): ∀ (a a_1 a_2 : Iota), % 4.06/4.26 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)) % 4.06/4.26 Clause #22 (by superposition #[20, 16]): ∀ (a a_1 a_2 : Iota), % 4.06/4.26 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)) % 4.06/4.26 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) % 4.06/4.26 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) % 4.06/4.26 Clause #43 (by superposition #[41, 11]): ∀ (a a_1 a_2 a_3 : Iota), % 4.06/4.26 Or (Eq (a_member_of (skS.0 0 a (skS.0 1 a_1) a_2) (skS.0 2 a_1 a_3)) True) % 4.06/4.26 (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))) % 4.06/4.27 Clause #45 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota), % 4.06/4.27 Or (Eq (a_member_of (skS.0 0 a (skS.0 1 a_1) a_2) (skS.0 2 a_1 a_3)) True) % 4.06/4.27 (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)) % 4.06/4.27 Clause #50 (by equality factoring #[45]): ∀ (a a_1 a_2 : Iota), % 4.06/4.27 Or (Eq (eq (skS.0 2 a a_1) (skS.0 1 a)) True) % 4.06/4.27 (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)) % 4.06/4.27 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), % 4.06/4.27 Or (Eq (eq (skS.0 2 a a_1) (skS.0 1 a)) True) % 4.06/4.27 (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) % 4.06/4.27 (Or (Eq True False) (Eq True False))) % 4.06/4.27 Clause #53 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), % 4.06/4.27 Or (Eq (eq (skS.0 2 a a_1) (skS.0 1 a)) True) % 4.06/4.27 (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)) % 4.06/4.27 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), % 4.06/4.27 Or (Eq (eq (skS.0 2 a a_1) (skS.0 1 a)) True) % 4.06/4.27 (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) % 4.06/4.27 Clause #55 (by forward demodulation #[54, 17]): ∀ (a a_1 a_2 : Iota), % 4.06/4.27 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) % 4.06/4.27 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 % 4.06/4.27 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) % 4.06/4.27 Clause #58 (by superposition #[56, 10]): ∀ (a a_1 a_2 : Iota), % 4.06/4.27 Or (Eq (eq (skS.0 2 a a_1) (skS.0 1 a)) True) % 4.06/4.27 (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)) % 4.06/4.27 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 % 4.06/4.27 Clause #73 (by clausification #[58]): ∀ (a a_1 a_2 : Iota), % 4.06/4.27 Or (Eq (eq (skS.0 2 a a_1) (skS.0 1 a)) True) % 4.06/4.27 (Eq (a_member_of (skS.0 0 (skS.0 2 a a_1) (skS.0 1 a) a_2) (skS.0 1 a)) False) % 4.06/4.27 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) % 4.06/4.27 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 % 4.06/4.27 Clause #76 (by superposition #[75, 65]): Eq False True % 4.06/4.27 Clause #77 (by clausification #[76]): False % 4.06/4.27 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------