%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU531^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n001.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 08:01:50 PM UTC 2025 % Result : Theorem 3.62s 3.87s % Output : Proof 3.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SEU531^2 : TPTP v9.2.0. Released v3.7.0. % 0.08/0.13 % Command : duper %s % 0.13/0.35 % Computer : n001.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 : Fri Oct 3 06:27:08 EDT 2025 % 0.13/0.35 % CPUTime : % 3.62/3.87 SZS status Theorem for theBenchmark.p % 3.62/3.87 SZS output start Proof for theBenchmark.p % 3.62/3.87 Clause #0 (by assumption #[]): Eq % 3.62/3.87 (Eq setadjoinE % 3.62/3.87 (∀ (Xx A Xy : Iota), in Xy (setadjoin Xx A) → ∀ (Xphi : Prop), (Eq Xy Xx → Xphi) → (in Xy A → Xphi) → Xphi)) % 3.62/3.87 True % 3.62/3.87 Clause #1 (by assumption #[]): Eq (Eq uniqinunit (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy)) True % 3.62/3.87 Clause #2 (by assumption #[]): Eq % 3.62/3.87 (Not % 3.62/3.87 (setadjoinE → % 3.62/3.87 uniqinunit → ∀ (Xx Xy Xz : Iota), in Xz (setadjoin Xx (setadjoin Xy emptyset)) → Or (Eq Xz Xx) (Eq Xz Xy))) % 3.62/3.87 True % 3.62/3.87 Clause #3 (by clausification #[1]): Eq uniqinunit (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy) % 3.62/3.87 Clause #17 (by clausification #[0]): Eq setadjoinE % 3.62/3.87 (∀ (Xx A Xy : Iota), in Xy (setadjoin Xx A) → ∀ (Xphi : Prop), (Eq Xy Xx → Xphi) → (in Xy A → Xphi) → Xphi) % 3.62/3.87 Clause #21 (by clausification #[2]): Eq % 3.62/3.87 (setadjoinE → % 3.62/3.87 uniqinunit → ∀ (Xx Xy Xz : Iota), in Xz (setadjoin Xx (setadjoin Xy emptyset)) → Or (Eq Xz Xx) (Eq Xz Xy)) % 3.62/3.87 False % 3.62/3.87 Clause #22 (by clausification #[21]): Eq setadjoinE True % 3.62/3.87 Clause #23 (by clausification #[21]): Eq (uniqinunit → ∀ (Xx Xy Xz : Iota), in Xz (setadjoin Xx (setadjoin Xy emptyset)) → Or (Eq Xz Xx) (Eq Xz Xy)) False % 3.62/3.87 Clause #24 (by backward demodulation #[22, 17]): Eq True (∀ (Xx A Xy : Iota), in Xy (setadjoin Xx A) → ∀ (Xphi : Prop), (Eq Xy Xx → Xphi) → (in Xy A → Xphi) → Xphi) % 3.62/3.87 Clause #25 (by clausification #[24]): ∀ (a : Iota), % 3.62/3.87 Eq (∀ (A Xy : Iota), in Xy (setadjoin a A) → ∀ (Xphi : Prop), (Eq Xy a → Xphi) → (in Xy A → Xphi) → Xphi) True % 3.62/3.87 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), % 3.62/3.87 Eq (∀ (Xy : Iota), in Xy (setadjoin a a_1) → ∀ (Xphi : Prop), (Eq Xy a → Xphi) → (in Xy a_1 → Xphi) → Xphi) True % 3.62/3.87 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Eq (in a (setadjoin a_1 a_2) → ∀ (Xphi : Prop), (Eq a a_1 → Xphi) → (in a a_2 → Xphi) → Xphi) True % 3.62/3.87 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), % 3.62/3.87 Or (Eq (in a (setadjoin a_1 a_2)) False) (Eq (∀ (Xphi : Prop), (Eq a a_1 → Xphi) → (in a a_2 → Xphi) → Xphi) True) % 3.62/3.87 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.62/3.87 Or (Eq (in a (setadjoin a_1 a_2)) False) (Eq ((Eq a a_1 → a_3) → (in a a_2 → a_3) → a_3) True) % 3.62/3.87 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.62/3.87 Or (Eq (in a (setadjoin a_1 a_2)) False) (Or (Eq (Eq a a_1 → a_3) False) (Eq ((in a a_2 → a_3) → a_3) True)) % 3.62/3.87 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.62/3.87 Or (Eq (in a (setadjoin a_1 a_2)) False) (Or (Eq ((in a a_2 → a_3) → a_3) True) (Eq (Eq a a_1) True)) % 3.62/3.87 Clause #33 (by clausification #[31]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.62/3.87 Or (Eq (in a (setadjoin a_1 a_2)) False) (Or (Eq (Eq a a_1) True) (Or (Eq (in a a_2 → a_3) False) (Eq a_3 True))) % 3.62/3.87 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.62/3.87 Or (Eq (in a (setadjoin a_1 a_2)) False) (Or (Eq (in a a_2 → a_3) False) (Or (Eq a_3 True) (Eq a a_1))) % 3.62/3.87 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.62/3.87 Or (Eq (in a (setadjoin a_1 a_2)) False) (Or (Eq a_3 True) (Or (Eq a a_1) (Eq (in a a_2) True))) % 3.62/3.87 Clause #74 (by clausification #[23]): Eq uniqinunit True % 3.62/3.87 Clause #75 (by clausification #[23]): Eq (∀ (Xx Xy Xz : Iota), in Xz (setadjoin Xx (setadjoin Xy emptyset)) → Or (Eq Xz Xx) (Eq Xz Xy)) False % 3.62/3.87 Clause #76 (by backward demodulation #[74, 3]): Eq True (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy) % 3.62/3.87 Clause #80 (by clausification #[76]): ∀ (a : Iota), Eq (∀ (Xy : Iota), in a (setadjoin Xy emptyset) → Eq a Xy) True % 3.62/3.87 Clause #81 (by clausification #[80]): ∀ (a a_1 : Iota), Eq (in a (setadjoin a_1 emptyset) → Eq a a_1) True % 3.62/3.87 Clause #82 (by clausification #[81]): ∀ (a a_1 : Iota), Or (Eq (in a (setadjoin a_1 emptyset)) False) (Eq (Eq a a_1) True) % 3.62/3.87 Clause #83 (by clausification #[82]): ∀ (a a_1 : Iota), Or (Eq (in a (setadjoin a_1 emptyset)) False) (Eq a a_1) % 3.62/3.87 Clause #84 (by clausification #[75]): ∀ (a : Iota), % 3.72/3.89 Eq (Not (∀ (Xy Xz : Iota), in Xz (setadjoin (skS.0 6 a) (setadjoin Xy emptyset)) → Or (Eq Xz (skS.0 6 a)) (Eq Xz Xy))) % 3.72/3.89 True % 3.72/3.89 Clause #85 (by clausification #[84]): ∀ (a : Iota), % 3.72/3.89 Eq (∀ (Xy Xz : Iota), in Xz (setadjoin (skS.0 6 a) (setadjoin Xy emptyset)) → Or (Eq Xz (skS.0 6 a)) (Eq Xz Xy)) False % 3.72/3.89 Clause #86 (by clausification #[85]): ∀ (a a_1 : Iota), % 3.72/3.89 Eq % 3.72/3.89 (Not % 3.72/3.89 (∀ (Xz : Iota), % 3.72/3.89 in Xz (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset)) → % 3.72/3.89 Or (Eq Xz (skS.0 6 a)) (Eq Xz (skS.0 7 a a_1)))) % 3.72/3.89 True % 3.72/3.89 Clause #87 (by clausification #[86]): ∀ (a a_1 : Iota), % 3.72/3.89 Eq % 3.72/3.89 (∀ (Xz : Iota), % 3.72/3.89 in Xz (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset)) → % 3.72/3.89 Or (Eq Xz (skS.0 6 a)) (Eq Xz (skS.0 7 a a_1))) % 3.72/3.89 False % 3.72/3.89 Clause #88 (by clausification #[87]): ∀ (a a_1 a_2 : Iota), % 3.72/3.89 Eq % 3.72/3.89 (Not % 3.72/3.89 (in (skS.0 8 a a_1 a_2) (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset)) → % 3.72/3.89 Or (Eq (skS.0 8 a a_1 a_2) (skS.0 6 a)) (Eq (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)))) % 3.72/3.89 True % 3.72/3.89 Clause #89 (by clausification #[88]): ∀ (a a_1 a_2 : Iota), % 3.72/3.89 Eq % 3.72/3.89 (in (skS.0 8 a a_1 a_2) (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset)) → % 3.72/3.89 Or (Eq (skS.0 8 a a_1 a_2) (skS.0 6 a)) (Eq (skS.0 8 a a_1 a_2) (skS.0 7 a a_1))) % 3.72/3.89 False % 3.72/3.89 Clause #90 (by clausification #[89]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 8 a a_1 a_2) (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset))) True % 3.72/3.89 Clause #91 (by clausification #[89]): ∀ (a a_1 a_2 : Iota), Eq (Or (Eq (skS.0 8 a a_1 a_2) (skS.0 6 a)) (Eq (skS.0 8 a a_1 a_2) (skS.0 7 a a_1))) False % 3.72/3.89 Clause #92 (by superposition #[90, 35]): ∀ (a : Prop) (a_1 a_2 a_3 : Iota), % 3.72/3.89 Or (Eq True False) % 3.72/3.89 (Or (Eq a True) % 3.72/3.89 (Or (Eq (skS.0 8 a_1 a_2 a_3) (skS.0 6 a_1)) % 3.72/3.89 (Eq (in (skS.0 8 a_1 a_2 a_3) (setadjoin (skS.0 7 a_1 a_2) emptyset)) True))) % 3.72/3.89 Clause #100 (by clausification #[91]): ∀ (a a_1 a_2 : Iota), Eq (Eq (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) False % 3.72/3.89 Clause #101 (by clausification #[91]): ∀ (a a_1 a_2 : Iota), Eq (Eq (skS.0 8 a a_1 a_2) (skS.0 6 a)) False % 3.72/3.89 Clause #102 (by clausification #[100]): ∀ (a a_1 a_2 : Iota), Ne (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) % 3.72/3.89 Clause #103 (by clausification #[101]): ∀ (a a_1 a_2 : Iota), Ne (skS.0 8 a a_1 a_2) (skS.0 6 a) % 3.72/3.89 Clause #104 (by clausification #[92]): ∀ (a : Prop) (a_1 a_2 a_3 : Iota), % 3.72/3.89 Or (Eq a True) % 3.72/3.89 (Or (Eq (skS.0 8 a_1 a_2 a_3) (skS.0 6 a_1)) % 3.72/3.89 (Eq (in (skS.0 8 a_1 a_2 a_3) (setadjoin (skS.0 7 a_1 a_2) emptyset)) True)) % 3.72/3.89 Clause #105 (by forward contextual literal cutting #[104, 103]): ∀ (a : Prop) (a_1 a_2 a_3 : Iota), % 3.72/3.89 Or (Eq a True) (Eq (in (skS.0 8 a_1 a_2 a_3) (setadjoin (skS.0 7 a_1 a_2) emptyset)) True) % 3.72/3.89 Clause #109 (by superposition #[105, 83]): ∀ (a : Prop) (a_1 a_2 a_3 : Iota), Or (Eq a True) (Or (Eq True False) (Eq (skS.0 8 a_1 a_2 a_3) (skS.0 7 a_1 a_2))) % 3.72/3.89 Clause #112 (by clausification #[109]): ∀ (a : Prop) (a_1 a_2 a_3 : Iota), Or (Eq a True) (Eq (skS.0 8 a_1 a_2 a_3) (skS.0 7 a_1 a_2)) % 3.72/3.89 Clause #113 (by forward contextual literal cutting #[112, 102]): ∀ (a : Prop), Eq a True % 3.72/3.89 Clause #115 (by falseElim #[113]): False % 3.72/3.89 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------