%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET047+1 : TPTP v9.2.0. 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 Oct 3 07:59:29 PM UTC 2025 % Result : Theorem 4.95s 5.17s % Output : Proof 5.03s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SET047+1 : TPTP v9.2.0. Released v2.0.0. % 0.06/0.14 % Command : duper %s % 0.13/0.35 % Computer : n028.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 : Thu Oct 2 14:07:08 EDT 2025 % 0.13/0.35 % CPUTime : % 4.95/5.17 SZS status Theorem for theBenchmark.p % 4.95/5.17 SZS output start Proof for theBenchmark.p % 4.95/5.17 Clause #0 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (set_equal X Y) (∀ (Z : Iota), Iff (element Z X) (element Z Y))) True % 4.95/5.17 Clause #1 (by assumption #[]): Eq (Not (∀ (X Y : Iota), Iff (set_equal X Y) (set_equal Y X))) True % 4.95/5.17 Clause #2 (by clausification #[1]): Eq (∀ (X Y : Iota), Iff (set_equal X Y) (set_equal Y X)) False % 4.95/5.17 Clause #3 (by clausification #[2]): ∀ (a : Iota), Eq (Not (∀ (Y : Iota), Iff (set_equal (skS.0 0 a) Y) (set_equal Y (skS.0 0 a)))) True % 4.95/5.17 Clause #4 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (set_equal (skS.0 0 a) Y) (set_equal Y (skS.0 0 a))) False % 4.95/5.17 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), Eq (Not (Iff (set_equal (skS.0 0 a) (skS.0 1 a a_1)) (set_equal (skS.0 1 a a_1) (skS.0 0 a)))) True % 4.95/5.17 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), Eq (Iff (set_equal (skS.0 0 a) (skS.0 1 a a_1)) (set_equal (skS.0 1 a a_1) (skS.0 0 a))) False % 4.95/5.17 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), % 4.95/5.17 Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) False) (Eq (set_equal (skS.0 1 a a_1) (skS.0 0 a)) False) % 4.95/5.17 Clause #8 (by clausification #[6]): ∀ (a a_1 : Iota), Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq (set_equal (skS.0 1 a a_1) (skS.0 0 a)) True) % 4.95/5.17 Clause #9 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (set_equal a Y) (∀ (Z : Iota), Iff (element Z a) (element Z Y))) True % 4.95/5.17 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (Iff (set_equal a a_1) (∀ (Z : Iota), Iff (element Z a) (element Z a_1))) True % 4.95/5.17 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Or (Eq (set_equal a a_1) True) (Eq (∀ (Z : Iota), Iff (element Z a) (element Z a_1)) False) % 4.95/5.17 Clause #12 (by clausification #[10]): ∀ (a a_1 : Iota), Or (Eq (set_equal a a_1) False) (Eq (∀ (Z : Iota), Iff (element Z a) (element Z a_1)) True) % 4.95/5.17 Clause #13 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), % 4.95/5.17 Or (Eq (set_equal a a_1) True) (Eq (Not (Iff (element (skS.0 2 a a_1 a_2) a) (element (skS.0 2 a a_1 a_2) a_1))) True) % 4.95/5.17 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 : Iota), % 4.95/5.17 Or (Eq (set_equal a a_1) True) (Eq (Iff (element (skS.0 2 a a_1 a_2) a) (element (skS.0 2 a a_1 a_2) a_1)) False) % 4.95/5.17 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), % 4.95/5.17 Or (Eq (set_equal a a_1) True) % 4.95/5.17 (Or (Eq (element (skS.0 2 a a_1 a_2) a) False) (Eq (element (skS.0 2 a a_1 a_2) a_1) False)) % 4.95/5.17 Clause #16 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), % 4.95/5.17 Or (Eq (set_equal a a_1) True) % 4.95/5.17 (Or (Eq (element (skS.0 2 a a_1 a_2) a) True) (Eq (element (skS.0 2 a a_1 a_2) a_1) True)) % 4.95/5.17 Clause #17 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Or (Eq (set_equal a a_1) False) (Eq (Iff (element a_2 a) (element a_2 a_1)) True) % 4.95/5.17 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), Or (Eq (set_equal a a_1) False) (Or (Eq (element a_2 a) True) (Eq (element a_2 a_1) False)) % 4.95/5.17 Clause #19 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), Or (Eq (set_equal a a_1) False) (Or (Eq (element a_2 a) False) (Eq (element a_2 a_1) True)) % 4.95/5.17 Clause #22 (by superposition #[8, 18]): ∀ (a a_1 a_2 : Iota), % 4.95/5.17 Or (Eq (element a (skS.0 1 a_1 a_2)) True) % 4.95/5.17 (Or (Eq (element a (skS.0 0 a_1)) False) (Or (Eq (set_equal (skS.0 0 a_1) (skS.0 1 a_1 a_2)) True) (Eq False True))) % 4.95/5.17 Clause #23 (by superposition #[8, 19]): ∀ (a a_1 a_2 : Iota), % 4.95/5.17 Or (Eq (element a (skS.0 1 a_1 a_2)) False) % 4.95/5.17 (Or (Eq (element a (skS.0 0 a_1)) True) (Or (Eq (set_equal (skS.0 0 a_1) (skS.0 1 a_1 a_2)) True) (Eq False True))) % 4.95/5.17 Clause #38 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), % 4.95/5.17 Or (Eq (element a (skS.0 1 a_1 a_2)) False) % 4.95/5.17 (Or (Eq (element a (skS.0 0 a_1)) True) (Eq (set_equal (skS.0 0 a_1) (skS.0 1 a_1 a_2)) True)) % 4.95/5.17 Clause #41 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), % 4.95/5.17 Or (Eq (element a (skS.0 1 a_1 a_2)) True) % 4.95/5.17 (Or (Eq (element a (skS.0 0 a_1)) False) (Eq (set_equal (skS.0 0 a_1) (skS.0 1 a_1 a_2)) True)) % 4.95/5.17 Clause #42 (by superposition #[41, 16]): ∀ (a a_1 a_2 a_3 : Iota), % 4.95/5.17 Or (Eq (element (skS.0 2 (skS.0 0 a) a_1 a_2) (skS.0 1 a a_3)) True) % 5.03/5.20 (Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_3)) True) % 5.03/5.20 (Or (Eq (set_equal (skS.0 0 a) a_1) True) % 5.03/5.20 (Or (Eq False True) (Eq (element (skS.0 2 (skS.0 0 a) a_1 a_2) a_1) True)))) % 5.03/5.20 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota), % 5.03/5.20 Or (Eq (element (skS.0 2 (skS.0 0 a) a_1 a_2) (skS.0 1 a a_3)) True) % 5.03/5.20 (Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_3)) True) % 5.03/5.20 (Or (Eq (set_equal (skS.0 0 a) a_1) True) (Eq (element (skS.0 2 (skS.0 0 a) a_1 a_2) a_1) True))) % 5.03/5.20 Clause #48 (by equality factoring #[44]): ∀ (a a_1 a_2 : Iota), % 5.03/5.20 Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True) % 5.03/5.20 (Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True) % 5.03/5.20 (Or (Ne True True) (Eq (element (skS.0 2 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 1 a a_1)) True))) % 5.03/5.20 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 : Iota), % 5.03/5.20 Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True) % 5.03/5.20 (Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True) % 5.03/5.20 (Or (Eq (element (skS.0 2 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 1 a a_1)) True) % 5.03/5.20 (Or (Eq True False) (Eq True False)))) % 5.03/5.20 Clause #51 (by clausification #[49]): ∀ (a a_1 a_2 : Iota), % 5.03/5.20 Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True) % 5.03/5.20 (Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True) % 5.03/5.20 (Or (Eq (element (skS.0 2 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 1 a a_1)) True) (Eq True False))) % 5.03/5.20 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), % 5.03/5.20 Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True) % 5.03/5.20 (Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True) % 5.03/5.20 (Eq (element (skS.0 2 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 1 a a_1)) True)) % 5.03/5.20 Clause #53 (by eliminate duplicate literals #[52]): ∀ (a a_1 a_2 : Iota), % 5.03/5.20 Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True) % 5.03/5.20 (Eq (element (skS.0 2 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 1 a a_1)) True) % 5.03/5.20 Clause #54 (by superposition #[53, 38]): ∀ (a a_1 a_2 : Iota), % 5.03/5.20 Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True) % 5.03/5.20 (Or (Eq True False) % 5.03/5.20 (Or (Eq (element (skS.0 2 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 0 a)) True) % 5.03/5.20 (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True))) % 5.03/5.20 Clause #65 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), % 5.03/5.20 Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True) % 5.03/5.20 (Or (Eq (element (skS.0 2 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 0 a)) True) % 5.03/5.20 (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True)) % 5.03/5.20 Clause #66 (by eliminate duplicate literals #[65]): ∀ (a a_1 a_2 : Iota), % 5.03/5.20 Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True) % 5.03/5.20 (Eq (element (skS.0 2 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 0 a)) True) % 5.03/5.20 Clause #68 (by superposition #[66, 15]): ∀ (a a_1 a_2 : Iota), % 5.03/5.20 Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True) % 5.03/5.20 (Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True) % 5.03/5.20 (Or (Eq True False) (Eq (element (skS.0 2 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 1 a a_1)) False))) % 5.03/5.20 Clause #71 (by clausification #[68]): ∀ (a a_1 a_2 : Iota), % 5.03/5.20 Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True) % 5.03/5.20 (Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True) % 5.03/5.20 (Eq (element (skS.0 2 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 1 a a_1)) False)) % 5.03/5.20 Clause #72 (by eliminate duplicate literals #[71]): ∀ (a a_1 a_2 : Iota), % 5.03/5.20 Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True) % 5.03/5.20 (Eq (element (skS.0 2 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 1 a a_1)) False) % 5.03/5.20 Clause #73 (by superposition #[72, 53]): ∀ (a a_1 : Iota), % 5.03/5.20 Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True) % 5.03/5.20 (Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq False True)) % 5.03/5.20 Clause #83 (by clausification #[73]): ∀ (a a_1 : Iota), Or (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True) % 5.03/5.20 Clause #84 (by eliminate duplicate literals #[83]): ∀ (a a_1 : Iota), Eq (set_equal (skS.0 0 a) (skS.0 1 a a_1)) True % 5.03/5.20 Clause #85 (by backward demodulation #[84, 7]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (set_equal (skS.0 1 a a_1) (skS.0 0 a)) False) % 5.03/5.20 Clause #94 (by superposition #[84, 18]): ∀ (a a_1 a_2 : Iota), % 5.03/5.20 Or (Eq True False) (Or (Eq (element a (skS.0 0 a_1)) True) (Eq (element a (skS.0 1 a_1 a_2)) False)) % 5.03/5.22 Clause #95 (by superposition #[84, 19]): ∀ (a a_1 a_2 : Iota), % 5.03/5.22 Or (Eq True False) (Or (Eq (element a (skS.0 0 a_1)) False) (Eq (element a (skS.0 1 a_1 a_2)) True)) % 5.03/5.22 Clause #96 (by clausification #[85]): ∀ (a a_1 : Iota), Eq (set_equal (skS.0 1 a a_1) (skS.0 0 a)) False % 5.03/5.22 Clause #97 (by clausification #[95]): ∀ (a a_1 a_2 : Iota), Or (Eq (element a (skS.0 0 a_1)) False) (Eq (element a (skS.0 1 a_1 a_2)) True) % 5.03/5.22 Clause #99 (by superposition #[97, 16]): ∀ (a a_1 a_2 a_3 : Iota), % 5.03/5.22 Or (Eq (element (skS.0 2 a (skS.0 0 a_1) a_2) (skS.0 1 a_1 a_3)) True) % 5.03/5.22 (Or (Eq (set_equal a (skS.0 0 a_1)) True) (Or (Eq (element (skS.0 2 a (skS.0 0 a_1) a_2) a) True) (Eq False True))) % 5.03/5.22 Clause #100 (by clausification #[94]): ∀ (a a_1 a_2 : Iota), Or (Eq (element a (skS.0 0 a_1)) True) (Eq (element a (skS.0 1 a_1 a_2)) False) % 5.03/5.22 Clause #108 (by clausification #[99]): ∀ (a a_1 a_2 a_3 : Iota), % 5.03/5.22 Or (Eq (element (skS.0 2 a (skS.0 0 a_1) a_2) (skS.0 1 a_1 a_3)) True) % 5.03/5.22 (Or (Eq (set_equal a (skS.0 0 a_1)) True) (Eq (element (skS.0 2 a (skS.0 0 a_1) a_2) a) True)) % 5.03/5.22 Clause #113 (by equality factoring #[108]): ∀ (a a_1 a_2 : Iota), % 5.03/5.22 Or (Eq (set_equal (skS.0 1 a a_1) (skS.0 0 a)) True) % 5.03/5.22 (Or (Ne True True) (Eq (element (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 1 a a_1)) True)) % 5.03/5.22 Clause #114 (by clausification #[113]): ∀ (a a_1 a_2 : Iota), % 5.03/5.22 Or (Eq (set_equal (skS.0 1 a a_1) (skS.0 0 a)) True) % 5.03/5.22 (Or (Eq (element (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 1 a a_1)) True) % 5.03/5.22 (Or (Eq True False) (Eq True False))) % 5.03/5.22 Clause #116 (by clausification #[114]): ∀ (a a_1 a_2 : Iota), % 5.03/5.22 Or (Eq (set_equal (skS.0 1 a a_1) (skS.0 0 a)) True) % 5.03/5.22 (Or (Eq (element (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 1 a a_1)) True) (Eq True False)) % 5.03/5.22 Clause #117 (by clausification #[116]): ∀ (a a_1 a_2 : Iota), % 5.03/5.22 Or (Eq (set_equal (skS.0 1 a a_1) (skS.0 0 a)) True) % 5.03/5.22 (Eq (element (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 1 a a_1)) True) % 5.03/5.22 Clause #118 (by forward demodulation #[117, 96]): ∀ (a a_1 a_2 : Iota), Or (Eq False True) (Eq (element (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 1 a a_1)) True) % 5.03/5.22 Clause #119 (by clausification #[118]): ∀ (a a_1 a_2 : Iota), Eq (element (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 1 a a_1)) True % 5.03/5.22 Clause #120 (by superposition #[119, 100]): ∀ (a a_1 a_2 : Iota), Or (Eq (element (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) True) (Eq True False) % 5.03/5.22 Clause #121 (by superposition #[119, 15]): ∀ (a a_1 a_2 : Iota), % 5.03/5.22 Or (Eq (set_equal (skS.0 1 a a_1) (skS.0 0 a)) True) % 5.03/5.22 (Or (Eq True False) (Eq (element (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) False)) % 5.03/5.22 Clause #122 (by clausification #[120]): ∀ (a a_1 a_2 : Iota), Eq (element (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) True % 5.03/5.22 Clause #125 (by clausification #[121]): ∀ (a a_1 a_2 : Iota), % 5.03/5.22 Or (Eq (set_equal (skS.0 1 a a_1) (skS.0 0 a)) True) % 5.03/5.22 (Eq (element (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) False) % 5.03/5.22 Clause #126 (by forward demodulation #[125, 96]): ∀ (a a_1 a_2 : Iota), Or (Eq False True) (Eq (element (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) False) % 5.03/5.22 Clause #127 (by clausification #[126]): ∀ (a a_1 a_2 : Iota), Eq (element (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) False % 5.03/5.22 Clause #128 (by superposition #[127, 122]): Eq False True % 5.03/5.22 Clause #131 (by clausification #[128]): False % 5.03/5.22 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------