%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET788+1 : TPTP v9.2.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n004.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 08:00:30 PM UTC 2025 % Result : Theorem 4.88s 5.04s % Output : Proof 4.88s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET788+1 : TPTP v9.2.0. Released v3.1.0. % 0.11/0.13 % Command : duper %s % 0.12/0.34 % Computer : n004.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Thu Oct 2 13:55:08 EDT 2025 % 0.12/0.34 % CPUTime : % 4.88/5.04 SZS status Theorem for theBenchmark.p % 4.88/5.04 SZS output start Proof for theBenchmark.p % 4.88/5.04 Clause #0 (by assumption #[]): Eq % 4.88/5.04 (Not % 4.88/5.04 ((∀ (X Y : Iota), Iff (equalish X Y) (∀ (Z : Iota), Iff (a_member_of Z X) (a_member_of Z Y))) → % 4.88/5.04 ∀ (X Y : Iota), Iff (equalish X Y) (equalish Y X))) % 4.88/5.04 True % 4.88/5.04 Clause #1 (by clausification #[0]): Eq % 4.88/5.04 ((∀ (X Y : Iota), Iff (equalish X Y) (∀ (Z : Iota), Iff (a_member_of Z X) (a_member_of Z Y))) → % 4.88/5.04 ∀ (X Y : Iota), Iff (equalish X Y) (equalish Y X)) % 4.88/5.04 False % 4.88/5.04 Clause #2 (by clausification #[1]): Eq (∀ (X Y : Iota), Iff (equalish X Y) (∀ (Z : Iota), Iff (a_member_of Z X) (a_member_of Z Y))) True % 4.88/5.04 Clause #3 (by clausification #[1]): Eq (∀ (X Y : Iota), Iff (equalish X Y) (equalish Y X)) False % 4.88/5.04 Clause #4 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (equalish a Y) (∀ (Z : Iota), Iff (a_member_of Z a) (a_member_of Z Y))) True % 4.88/5.04 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), Eq (Iff (equalish a a_1) (∀ (Z : Iota), Iff (a_member_of Z a) (a_member_of Z a_1))) True % 4.88/5.04 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), Or (Eq (equalish a a_1) True) (Eq (∀ (Z : Iota), Iff (a_member_of Z a) (a_member_of Z a_1)) False) % 4.88/5.04 Clause #7 (by clausification #[5]): ∀ (a a_1 : Iota), Or (Eq (equalish a a_1) False) (Eq (∀ (Z : Iota), Iff (a_member_of Z a) (a_member_of Z a_1)) True) % 4.88/5.04 Clause #8 (by clausification #[6]): ∀ (a a_1 a_2 : Iota), % 4.88/5.04 Or (Eq (equalish a a_1) True) % 4.88/5.04 (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) % 4.88/5.04 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), % 4.88/5.04 Or (Eq (equalish a a_1) True) % 4.88/5.04 (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) % 4.88/5.04 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 4.88/5.04 Or (Eq (equalish a a_1) True) % 4.88/5.04 (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)) % 4.88/5.04 Clause #11 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 4.88/5.04 Or (Eq (equalish a a_1) True) % 4.88/5.04 (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)) % 4.88/5.04 Clause #12 (by clausification #[3]): ∀ (a : Iota), Eq (Not (∀ (Y : Iota), Iff (equalish (skS.0 1 a) Y) (equalish Y (skS.0 1 a)))) True % 4.88/5.04 Clause #13 (by clausification #[12]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (equalish (skS.0 1 a) Y) (equalish Y (skS.0 1 a))) False % 4.88/5.04 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Eq (Not (Iff (equalish (skS.0 1 a) (skS.0 2 a a_1)) (equalish (skS.0 2 a a_1) (skS.0 1 a)))) True % 4.88/5.04 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Eq (Iff (equalish (skS.0 1 a) (skS.0 2 a a_1)) (equalish (skS.0 2 a a_1) (skS.0 1 a))) False % 4.88/5.04 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (equalish (skS.0 1 a) (skS.0 2 a a_1)) False) (Eq (equalish (skS.0 2 a a_1) (skS.0 1 a)) False) % 4.88/5.04 Clause #17 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (equalish (skS.0 1 a) (skS.0 2 a a_1)) True) (Eq (equalish (skS.0 2 a a_1) (skS.0 1 a)) True) % 4.88/5.04 Clause #18 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), Or (Eq (equalish a a_1) False) (Eq (Iff (a_member_of a_2 a) (a_member_of a_2 a_1)) True) % 4.88/5.04 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), Or (Eq (equalish a a_1) False) (Or (Eq (a_member_of a_2 a) True) (Eq (a_member_of a_2 a_1) False)) % 4.88/5.04 Clause #20 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), Or (Eq (equalish a a_1) False) (Or (Eq (a_member_of a_2 a) False) (Eq (a_member_of a_2 a_1) True)) % 4.88/5.04 Clause #23 (by superposition #[17, 19]): ∀ (a a_1 a_2 : Iota), % 4.88/5.04 Or (Eq (a_member_of a (skS.0 2 a_1 a_2)) True) % 4.88/5.04 (Or (Eq (a_member_of a (skS.0 1 a_1)) False) % 4.88/5.04 (Or (Eq (equalish (skS.0 1 a_1) (skS.0 2 a_1 a_2)) True) (Eq False True))) % 4.88/5.04 Clause #24 (by superposition #[17, 20]): ∀ (a a_1 a_2 : Iota), % 4.88/5.04 Or (Eq (a_member_of a (skS.0 2 a_1 a_2)) False) % 4.88/5.04 (Or (Eq (a_member_of a (skS.0 1 a_1)) True) % 4.88/5.04 (Or (Eq (equalish (skS.0 1 a_1) (skS.0 2 a_1 a_2)) True) (Eq False True))) % 4.88/5.04 Clause #39 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), % 4.88/5.04 Or (Eq (a_member_of a (skS.0 2 a_1 a_2)) False) % 4.88/5.07 (Or (Eq (a_member_of a (skS.0 1 a_1)) True) (Eq (equalish (skS.0 1 a_1) (skS.0 2 a_1 a_2)) True)) % 4.88/5.07 Clause #42 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), % 4.88/5.07 Or (Eq (a_member_of a (skS.0 2 a_1 a_2)) True) % 4.88/5.07 (Or (Eq (a_member_of a (skS.0 1 a_1)) False) (Eq (equalish (skS.0 1 a_1) (skS.0 2 a_1 a_2)) True)) % 4.88/5.07 Clause #43 (by superposition #[42, 11]): ∀ (a a_1 a_2 a_3 : Iota), % 4.88/5.07 Or (Eq (a_member_of (skS.0 0 (skS.0 1 a) a_1 a_2) (skS.0 2 a a_3)) True) % 4.88/5.07 (Or (Eq (equalish (skS.0 1 a) (skS.0 2 a a_3)) True) % 4.88/5.07 (Or (Eq (equalish (skS.0 1 a) a_1) True) % 4.88/5.07 (Or (Eq False True) (Eq (a_member_of (skS.0 0 (skS.0 1 a) a_1 a_2) a_1) True)))) % 4.88/5.07 Clause #45 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota), % 4.88/5.07 Or (Eq (a_member_of (skS.0 0 (skS.0 1 a) a_1 a_2) (skS.0 2 a a_3)) True) % 4.88/5.07 (Or (Eq (equalish (skS.0 1 a) (skS.0 2 a a_3)) True) % 4.88/5.07 (Or (Eq (equalish (skS.0 1 a) a_1) True) (Eq (a_member_of (skS.0 0 (skS.0 1 a) a_1 a_2) a_1) True))) % 4.88/5.07 Clause #49 (by equality factoring #[45]): ∀ (a a_1 a_2 : Iota), % 4.88/5.07 Or (Eq (equalish (skS.0 1 a) (skS.0 2 a a_1)) True) % 4.88/5.07 (Or (Eq (equalish (skS.0 1 a) (skS.0 2 a a_1)) True) % 4.88/5.07 (Or (Ne True True) (Eq (a_member_of (skS.0 0 (skS.0 1 a) (skS.0 2 a a_1) a_2) (skS.0 2 a a_1)) True))) % 4.88/5.07 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), % 4.88/5.07 Or (Eq (equalish (skS.0 1 a) (skS.0 2 a a_1)) True) % 4.88/5.07 (Or (Eq (equalish (skS.0 1 a) (skS.0 2 a a_1)) True) % 4.88/5.07 (Or (Eq (a_member_of (skS.0 0 (skS.0 1 a) (skS.0 2 a a_1) a_2) (skS.0 2 a a_1)) True) % 4.88/5.07 (Or (Eq True False) (Eq True False)))) % 4.88/5.07 Clause #52 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), % 4.88/5.07 Or (Eq (equalish (skS.0 1 a) (skS.0 2 a a_1)) True) % 4.88/5.07 (Or (Eq (equalish (skS.0 1 a) (skS.0 2 a a_1)) True) % 4.88/5.07 (Or (Eq (a_member_of (skS.0 0 (skS.0 1 a) (skS.0 2 a a_1) a_2) (skS.0 2 a a_1)) True) (Eq True False))) % 4.88/5.07 Clause #53 (by clausification #[52]): ∀ (a a_1 a_2 : Iota), % 4.88/5.07 Or (Eq (equalish (skS.0 1 a) (skS.0 2 a a_1)) True) % 4.88/5.07 (Or (Eq (equalish (skS.0 1 a) (skS.0 2 a a_1)) True) % 4.88/5.07 (Eq (a_member_of (skS.0 0 (skS.0 1 a) (skS.0 2 a a_1) a_2) (skS.0 2 a a_1)) True)) % 4.88/5.07 Clause #54 (by eliminate duplicate literals #[53]): ∀ (a a_1 a_2 : Iota), % 4.88/5.07 Or (Eq (equalish (skS.0 1 a) (skS.0 2 a a_1)) True) % 4.88/5.07 (Eq (a_member_of (skS.0 0 (skS.0 1 a) (skS.0 2 a a_1) a_2) (skS.0 2 a a_1)) True) % 4.88/5.07 Clause #55 (by superposition #[54, 39]): ∀ (a a_1 a_2 : Iota), % 4.88/5.07 Or (Eq (equalish (skS.0 1 a) (skS.0 2 a a_1)) True) % 4.88/5.07 (Or (Eq True False) % 4.88/5.07 (Or (Eq (a_member_of (skS.0 0 (skS.0 1 a) (skS.0 2 a a_1) a_2) (skS.0 1 a)) True) % 4.88/5.07 (Eq (equalish (skS.0 1 a) (skS.0 2 a a_1)) True))) % 4.88/5.07 Clause #66 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), % 4.88/5.07 Or (Eq (equalish (skS.0 1 a) (skS.0 2 a a_1)) True) % 4.88/5.07 (Or (Eq (a_member_of (skS.0 0 (skS.0 1 a) (skS.0 2 a a_1) a_2) (skS.0 1 a)) True) % 4.88/5.07 (Eq (equalish (skS.0 1 a) (skS.0 2 a a_1)) True)) % 4.88/5.07 Clause #67 (by eliminate duplicate literals #[66]): ∀ (a a_1 a_2 : Iota), % 4.88/5.07 Or (Eq (equalish (skS.0 1 a) (skS.0 2 a a_1)) True) % 4.88/5.07 (Eq (a_member_of (skS.0 0 (skS.0 1 a) (skS.0 2 a a_1) a_2) (skS.0 1 a)) True) % 4.88/5.07 Clause #69 (by superposition #[67, 10]): ∀ (a a_1 a_2 : Iota), % 4.88/5.07 Or (Eq (equalish (skS.0 1 a) (skS.0 2 a a_1)) True) % 4.88/5.07 (Or (Eq (equalish (skS.0 1 a) (skS.0 2 a a_1)) True) % 4.88/5.07 (Or (Eq True False) (Eq (a_member_of (skS.0 0 (skS.0 1 a) (skS.0 2 a a_1) a_2) (skS.0 2 a a_1)) False))) % 4.88/5.07 Clause #72 (by clausification #[69]): ∀ (a a_1 a_2 : Iota), % 4.88/5.07 Or (Eq (equalish (skS.0 1 a) (skS.0 2 a a_1)) True) % 4.88/5.07 (Or (Eq (equalish (skS.0 1 a) (skS.0 2 a a_1)) True) % 4.88/5.07 (Eq (a_member_of (skS.0 0 (skS.0 1 a) (skS.0 2 a a_1) a_2) (skS.0 2 a a_1)) False)) % 4.88/5.07 Clause #73 (by eliminate duplicate literals #[72]): ∀ (a a_1 a_2 : Iota), % 4.88/5.07 Or (Eq (equalish (skS.0 1 a) (skS.0 2 a a_1)) True) % 4.88/5.07 (Eq (a_member_of (skS.0 0 (skS.0 1 a) (skS.0 2 a a_1) a_2) (skS.0 2 a a_1)) False) % 4.88/5.07 Clause #74 (by superposition #[73, 54]): ∀ (a a_1 : Iota), % 4.88/5.07 Or (Eq (equalish (skS.0 1 a) (skS.0 2 a a_1)) True) % 4.88/5.07 (Or (Eq (equalish (skS.0 1 a) (skS.0 2 a a_1)) True) (Eq False True)) % 4.88/5.07 Clause #84 (by clausification #[74]): ∀ (a a_1 : Iota), Or (Eq (equalish (skS.0 1 a) (skS.0 2 a a_1)) True) (Eq (equalish (skS.0 1 a) (skS.0 2 a a_1)) True) % 4.88/5.09 Clause #85 (by eliminate duplicate literals #[84]): ∀ (a a_1 : Iota), Eq (equalish (skS.0 1 a) (skS.0 2 a a_1)) True % 4.88/5.09 Clause #86 (by backward demodulation #[85, 16]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (equalish (skS.0 2 a a_1) (skS.0 1 a)) False) % 4.88/5.09 Clause #95 (by superposition #[85, 19]): ∀ (a a_1 a_2 : Iota), % 4.88/5.09 Or (Eq True False) (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)) % 4.88/5.09 Clause #96 (by superposition #[85, 20]): ∀ (a a_1 a_2 : Iota), % 4.88/5.09 Or (Eq True False) (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)) % 4.88/5.09 Clause #97 (by clausification #[86]): ∀ (a a_1 : Iota), Eq (equalish (skS.0 2 a a_1) (skS.0 1 a)) False % 4.88/5.09 Clause #98 (by clausification #[96]): ∀ (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) % 4.88/5.09 Clause #100 (by superposition #[98, 11]): ∀ (a a_1 a_2 a_3 : Iota), % 4.88/5.09 Or (Eq (a_member_of (skS.0 0 a (skS.0 1 a_1) a_2) (skS.0 2 a_1 a_3)) True) % 4.88/5.09 (Or (Eq (equalish a (skS.0 1 a_1)) True) % 4.88/5.09 (Or (Eq (a_member_of (skS.0 0 a (skS.0 1 a_1) a_2) a) True) (Eq False True))) % 4.88/5.09 Clause #101 (by clausification #[95]): ∀ (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) % 4.88/5.09 Clause #109 (by clausification #[100]): ∀ (a a_1 a_2 a_3 : Iota), % 4.88/5.09 Or (Eq (a_member_of (skS.0 0 a (skS.0 1 a_1) a_2) (skS.0 2 a_1 a_3)) True) % 4.88/5.09 (Or (Eq (equalish a (skS.0 1 a_1)) True) (Eq (a_member_of (skS.0 0 a (skS.0 1 a_1) a_2) a) True)) % 4.88/5.09 Clause #114 (by equality factoring #[109]): ∀ (a a_1 a_2 : Iota), % 4.88/5.09 Or (Eq (equalish (skS.0 2 a a_1) (skS.0 1 a)) True) % 4.88/5.09 (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)) % 4.88/5.09 Clause #115 (by clausification #[114]): ∀ (a a_1 a_2 : Iota), % 4.88/5.09 Or (Eq (equalish (skS.0 2 a a_1) (skS.0 1 a)) True) % 4.88/5.09 (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) % 4.88/5.09 (Or (Eq True False) (Eq True False))) % 4.88/5.09 Clause #117 (by clausification #[115]): ∀ (a a_1 a_2 : Iota), % 4.88/5.09 Or (Eq (equalish (skS.0 2 a a_1) (skS.0 1 a)) True) % 4.88/5.09 (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)) % 4.88/5.09 Clause #118 (by clausification #[117]): ∀ (a a_1 a_2 : Iota), % 4.88/5.09 Or (Eq (equalish (skS.0 2 a a_1) (skS.0 1 a)) True) % 4.88/5.09 (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) % 4.88/5.09 Clause #119 (by forward demodulation #[118, 97]): ∀ (a a_1 a_2 : Iota), % 4.88/5.09 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) % 4.88/5.09 Clause #120 (by clausification #[119]): ∀ (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 % 4.88/5.09 Clause #121 (by superposition #[120, 101]): ∀ (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) % 4.88/5.09 Clause #122 (by superposition #[120, 10]): ∀ (a a_1 a_2 : Iota), % 4.88/5.09 Or (Eq (equalish (skS.0 2 a a_1) (skS.0 1 a)) True) % 4.88/5.09 (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)) % 4.88/5.09 Clause #123 (by clausification #[121]): ∀ (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 % 4.88/5.09 Clause #126 (by clausification #[122]): ∀ (a a_1 a_2 : Iota), % 4.88/5.09 Or (Eq (equalish (skS.0 2 a a_1) (skS.0 1 a)) True) % 4.88/5.09 (Eq (a_member_of (skS.0 0 (skS.0 2 a a_1) (skS.0 1 a) a_2) (skS.0 1 a)) False) % 4.88/5.09 Clause #127 (by forward demodulation #[126, 97]): ∀ (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) % 4.88/5.09 Clause #128 (by clausification #[127]): ∀ (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 % 4.88/5.09 Clause #129 (by superposition #[128, 123]): Eq False True % 4.88/5.09 Clause #132 (by clausification #[129]): False % 4.88/5.09 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------