%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU506^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n002.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 08:01:46 PM UTC 2025 % Result : Theorem 3.54s 3.75s % Output : Proof 3.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SEU506^2 : TPTP v9.2.0. Released v3.7.0. % 0.08/0.13 % Command : duper %s % 0.12/0.34 % Computer : n002.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 : Fri Oct 3 05:57:38 EDT 2025 % 0.12/0.34 % CPUTime : % 3.54/3.75 SZS status Theorem for theBenchmark.p % 3.54/3.75 SZS output start Proof for theBenchmark.p % 3.54/3.75 Clause #0 (by assumption #[]): Eq (Eq emptysetE (∀ (Xx : Iota), in Xx emptyset → ∀ (Xphi : Prop), Xphi)) True % 3.54/3.75 Clause #1 (by assumption #[]): Eq (Eq setext (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → (∀ (Xx : Iota), in Xx B → in Xx A) → Eq A B)) True % 3.54/3.75 Clause #2 (by assumption #[]): Eq (Not (emptysetE → setext → ∀ (A : Iota), (∀ (Xx : Iota), Not (in Xx A)) → Eq A emptyset)) True % 3.54/3.75 Clause #3 (by clausification #[0]): Eq emptysetE (∀ (Xx : Iota), in Xx emptyset → ∀ (Xphi : Prop), Xphi) % 3.54/3.75 Clause #18 (by clausification #[1]): Eq setext (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → (∀ (Xx : Iota), in Xx B → in Xx A) → Eq A B) % 3.54/3.75 Clause #20 (by clausify Prop equality #[18]): Or (Eq setext False) % 3.54/3.75 (Eq (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → (∀ (Xx : Iota), in Xx B → in Xx A) → Eq A B) True) % 3.54/3.75 Clause #22 (by clausification #[2]): Eq (emptysetE → setext → ∀ (A : Iota), (∀ (Xx : Iota), Not (in Xx A)) → Eq A emptyset) False % 3.54/3.75 Clause #23 (by clausification #[22]): Eq emptysetE True % 3.54/3.75 Clause #24 (by clausification #[22]): Eq (setext → ∀ (A : Iota), (∀ (Xx : Iota), Not (in Xx A)) → Eq A emptyset) False % 3.54/3.75 Clause #25 (by backward demodulation #[23, 3]): Eq True (∀ (Xx : Iota), in Xx emptyset → ∀ (Xphi : Prop), Xphi) % 3.54/3.75 Clause #29 (by clausification #[25]): ∀ (a : Iota), Eq (in a emptyset → ∀ (Xphi : Prop), Xphi) True % 3.54/3.75 Clause #30 (by clausification #[29]): ∀ (a : Iota), Or (Eq (in a emptyset) False) (Eq (∀ (Xphi : Prop), Xphi) True) % 3.54/3.75 Clause #31 (by clausification #[30]): ∀ (a : Iota) (a_1 : Prop), Or (Eq (in a emptyset) False) (Eq a_1 True) % 3.54/3.75 Clause #32 (by clausification #[24]): Eq setext True % 3.54/3.75 Clause #33 (by clausification #[24]): Eq (∀ (A : Iota), (∀ (Xx : Iota), Not (in Xx A)) → Eq A emptyset) False % 3.54/3.75 Clause #35 (by clausification #[33]): ∀ (a : Iota), Eq (Not ((∀ (Xx : Iota), Not (in Xx (skS.0 2 a))) → Eq (skS.0 2 a) emptyset)) True % 3.54/3.75 Clause #36 (by clausification #[35]): ∀ (a : Iota), Eq ((∀ (Xx : Iota), Not (in Xx (skS.0 2 a))) → Eq (skS.0 2 a) emptyset) False % 3.54/3.75 Clause #37 (by clausification #[36]): ∀ (a : Iota), Eq (∀ (Xx : Iota), Not (in Xx (skS.0 2 a))) True % 3.54/3.75 Clause #38 (by clausification #[36]): ∀ (a : Iota), Eq (Eq (skS.0 2 a) emptyset) False % 3.54/3.75 Clause #39 (by clausification #[37]): ∀ (a a_1 : Iota), Eq (Not (in a (skS.0 2 a_1))) True % 3.54/3.75 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), Eq (in a (skS.0 2 a_1)) False % 3.54/3.75 Clause #67 (by clausification #[38]): ∀ (a : Iota), Ne (skS.0 2 a) emptyset % 3.54/3.75 Clause #70 (by clausification #[20]): ∀ (a : Iota), % 3.54/3.75 Or (Eq setext False) % 3.54/3.75 (Eq (∀ (B : Iota), (∀ (Xx : Iota), in Xx a → in Xx B) → (∀ (Xx : Iota), in Xx B → in Xx a) → Eq a B) True) % 3.54/3.75 Clause #71 (by clausification #[70]): ∀ (a a_1 : Iota), % 3.54/3.75 Or (Eq setext False) % 3.54/3.75 (Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → (∀ (Xx : Iota), in Xx a_1 → in Xx a) → Eq a a_1) True) % 3.54/3.75 Clause #72 (by clausification #[71]): ∀ (a a_1 : Iota), % 3.54/3.75 Or (Eq setext False) % 3.54/3.75 (Or (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) (Eq ((∀ (Xx : Iota), in Xx a_1 → in Xx a) → Eq a a_1) True)) % 3.54/3.75 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 : Iota), % 3.54/3.75 Or (Eq setext False) % 3.54/3.75 (Or (Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → Eq a_1 a) True) % 3.54/3.75 (Eq (Not (in (skS.0 5 a_1 a a_2) a_1 → in (skS.0 5 a_1 a a_2) a)) True)) % 3.54/3.75 Clause #74 (by clausification #[73]): ∀ (a a_1 a_2 : Iota), % 3.54/3.75 Or (Eq setext False) % 3.54/3.75 (Or (Eq (Not (in (skS.0 5 a a_1 a_2) a → in (skS.0 5 a a_1 a_2) a_1)) True) % 3.54/3.75 (Or (Eq (∀ (Xx : Iota), in Xx a_1 → in Xx a) False) (Eq (Eq a a_1) True))) % 3.54/3.75 Clause #75 (by clausification #[74]): ∀ (a a_1 a_2 : Iota), % 3.54/3.75 Or (Eq setext False) % 3.54/3.75 (Or (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) % 3.54/3.75 (Or (Eq (Eq a_1 a) True) (Eq (in (skS.0 5 a_1 a a_2) a_1 → in (skS.0 5 a_1 a a_2) a) False))) % 3.54/3.75 Clause #76 (by clausification #[75]): ∀ (a a_1 a_2 a_3 : Iota), % 3.54/3.75 Or (Eq setext False) % 3.54/3.75 (Or (Eq (Eq a a_1) True) % 3.54/3.76 (Or (Eq (in (skS.0 5 a a_1 a_2) a → in (skS.0 5 a a_1 a_2) a_1) False) % 3.54/3.76 (Eq (Not (in (skS.0 6 a_1 a a_3) a_1 → in (skS.0 6 a_1 a a_3) a)) True))) % 3.54/3.76 Clause #77 (by clausification #[76]): ∀ (a a_1 a_2 a_3 : Iota), % 3.54/3.76 Or (Eq setext False) % 3.54/3.76 (Or (Eq (in (skS.0 5 a a_1 a_2) a → in (skS.0 5 a a_1 a_2) a_1) False) % 3.54/3.76 (Or (Eq (Not (in (skS.0 6 a_1 a a_3) a_1 → in (skS.0 6 a_1 a a_3) a)) True) (Eq a a_1))) % 3.54/3.76 Clause #78 (by clausification #[77]): ∀ (a a_1 a_2 a_3 : Iota), % 3.54/3.76 Or (Eq setext False) % 3.54/3.76 (Or (Eq (Not (in (skS.0 6 a a_1 a_2) a → in (skS.0 6 a a_1 a_2) a_1)) True) % 3.54/3.76 (Or (Eq a_1 a) (Eq (in (skS.0 5 a_1 a a_3) a_1) True))) % 3.54/3.76 Clause #80 (by clausification #[78]): ∀ (a a_1 a_2 a_3 : Iota), % 3.54/3.76 Or (Eq setext False) % 3.54/3.76 (Or (Eq a a_1) % 3.54/3.76 (Or (Eq (in (skS.0 5 a a_1 a_2) a) True) (Eq (in (skS.0 6 a_1 a a_3) a_1 → in (skS.0 6 a_1 a a_3) a) False))) % 3.54/3.76 Clause #81 (by clausification #[80]): ∀ (a a_1 a_2 a_3 : Iota), % 3.54/3.76 Or (Eq setext False) (Or (Eq a a_1) (Or (Eq (in (skS.0 5 a a_1 a_2) a) True) (Eq (in (skS.0 6 a_1 a a_3) a_1) True))) % 3.54/3.76 Clause #83 (by forward demodulation #[81, 32]): ∀ (a a_1 a_2 a_3 : Iota), % 3.54/3.76 Or (Eq True False) (Or (Eq a a_1) (Or (Eq (in (skS.0 5 a a_1 a_2) a) True) (Eq (in (skS.0 6 a_1 a a_3) a_1) True))) % 3.54/3.76 Clause #84 (by clausification #[83]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq a a_1) (Or (Eq (in (skS.0 5 a a_1 a_2) a) True) (Eq (in (skS.0 6 a_1 a a_3) a_1) True)) % 3.54/3.76 Clause #101 (by superposition #[84, 31]): ∀ (a a_1 : Iota) (a_2 : Prop), % 3.54/3.76 Or (Eq a emptyset) (Or (Eq (in (skS.0 5 a emptyset a_1) a) True) (Or (Eq True False) (Eq a_2 True))) % 3.54/3.76 Clause #116 (by clausification #[101]): ∀ (a a_1 : Iota) (a_2 : Prop), Or (Eq a emptyset) (Or (Eq (in (skS.0 5 a emptyset a_1) a) True) (Eq a_2 True)) % 3.54/3.76 Clause #120 (by superposition #[116, 40]): ∀ (a : Iota) (a_1 : Prop), Or (Eq (skS.0 2 a) emptyset) (Or (Eq a_1 True) (Eq True False)) % 3.54/3.76 Clause #133 (by clausification #[120]): ∀ (a : Iota) (a_1 : Prop), Or (Eq (skS.0 2 a) emptyset) (Eq a_1 True) % 3.54/3.76 Clause #134 (by forward contextual literal cutting #[133, 67]): ∀ (a : Prop), Eq a True % 3.54/3.76 Clause #136 (by falseElim #[134]): False % 3.54/3.76 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------