%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU509^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n023.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 08:01:47 PM UTC 2025 % Result : Theorem 6.24s 6.45s % Output : Proof 6.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.09 % Problem : SEU509^2 : TPTP v9.2.0. Released v3.7.0. % 0.04/0.10 % Command : duper %s % 0.09/0.30 % Computer : n023.cluster.edu % 0.09/0.30 % Model : x86_64 x86_64 % 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.30 % Memory : 8042.1875MB % 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.30 % CPULimit : 300 % 0.09/0.30 % WCLimit : 300 % 0.09/0.30 % DateTime : Fri Oct 3 05:44:23 EDT 2025 % 0.09/0.30 % CPUTime : % 6.24/6.45 SZS status Theorem for theBenchmark.p % 6.24/6.45 SZS output start Proof for theBenchmark.p % 6.24/6.45 Clause #0 (by assumption #[]): Eq (Eq emptysetE (∀ (Xx : Iota), in Xx emptyset → ∀ (Xphi : Prop), Xphi)) True % 6.24/6.45 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 % 6.24/6.45 Clause #2 (by assumption #[]): Eq (Eq nonempty fun Xx => Ne Xx emptyset) True % 6.24/6.45 Clause #3 (by assumption #[]): Eq (Not (emptysetE → setext → ∀ (A : Iota), nonempty A → Exists fun Xx => in Xx A)) True % 6.24/6.45 Clause #4 (by clausification #[0]): Eq emptysetE (∀ (Xx : Iota), in Xx emptyset → ∀ (Xphi : Prop), Xphi) % 6.24/6.45 Clause #19 (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) % 6.24/6.45 Clause #23 (by clausification #[2]): Eq nonempty fun Xx => Ne Xx emptyset % 6.24/6.45 Clause #24 (by argument congruence #[23]): ∀ (a : Iota), Eq (nonempty a) ((fun Xx => Ne Xx emptyset) a) % 6.24/6.45 Clause #25 (by betaEtaReduce #[24]): ∀ (a : Iota), Eq (nonempty a) (Ne a emptyset) % 6.24/6.45 Clause #27 (by clausify Prop equality #[25]): ∀ (a : Iota), Or (Eq (nonempty a) False) (Eq (Ne a emptyset) True) % 6.24/6.45 Clause #32 (by clausification #[27]): ∀ (a : Iota), Or (Eq (nonempty a) False) (Ne a emptyset) % 6.24/6.45 Clause #33 (by destructive equality resolution #[32]): Eq (nonempty emptyset) False % 6.24/6.45 Clause #35 (by clausification #[3]): Eq (emptysetE → setext → ∀ (A : Iota), nonempty A → Exists fun Xx => in Xx A) False % 6.24/6.45 Clause #36 (by clausification #[35]): Eq emptysetE True % 6.24/6.45 Clause #37 (by clausification #[35]): Eq (setext → ∀ (A : Iota), nonempty A → Exists fun Xx => in Xx A) False % 6.24/6.45 Clause #38 (by backward demodulation #[36, 4]): Eq True (∀ (Xx : Iota), in Xx emptyset → ∀ (Xphi : Prop), Xphi) % 6.24/6.45 Clause #42 (by clausification #[38]): ∀ (a : Iota), Eq (in a emptyset → ∀ (Xphi : Prop), Xphi) True % 6.24/6.45 Clause #43 (by clausification #[42]): ∀ (a : Iota), Or (Eq (in a emptyset) False) (Eq (∀ (Xphi : Prop), Xphi) True) % 6.24/6.45 Clause #44 (by clausification #[43]): ∀ (a : Iota) (a_1 : Prop), Or (Eq (in a emptyset) False) (Eq a_1 True) % 6.24/6.45 Clause #76 (by clausification #[37]): Eq setext True % 6.24/6.45 Clause #77 (by clausification #[37]): Eq (∀ (A : Iota), nonempty A → Exists fun Xx => in Xx A) False % 6.24/6.45 Clause #78 (by backward demodulation #[76, 19]): Eq True (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → (∀ (Xx : Iota), in Xx B → in Xx A) → Eq A B) % 6.24/6.45 Clause #80 (by clausification #[78]): ∀ (a : Iota), Eq (∀ (B : Iota), (∀ (Xx : Iota), in Xx a → in Xx B) → (∀ (Xx : Iota), in Xx B → in Xx a) → Eq a B) True % 6.24/6.45 Clause #81 (by clausification #[80]): ∀ (a a_1 : Iota), Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → (∀ (Xx : Iota), in Xx a_1 → in Xx a) → Eq a a_1) True % 6.24/6.45 Clause #82 (by clausification #[81]): ∀ (a a_1 : Iota), % 6.24/6.45 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) % 6.24/6.45 Clause #83 (by clausification #[82]): ∀ (a a_1 a_2 : Iota), % 6.24/6.45 Or (Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → Eq a_1 a) True) % 6.24/6.45 (Eq (Not (in (skS.0 4 a_1 a a_2) a_1 → in (skS.0 4 a_1 a a_2) a)) True) % 6.24/6.45 Clause #84 (by clausification #[83]): ∀ (a a_1 a_2 : Iota), % 6.24/6.45 Or (Eq (Not (in (skS.0 4 a a_1 a_2) a → in (skS.0 4 a a_1 a_2) a_1)) True) % 6.24/6.45 (Or (Eq (∀ (Xx : Iota), in Xx a_1 → in Xx a) False) (Eq (Eq a a_1) True)) % 6.24/6.45 Clause #85 (by clausification #[84]): ∀ (a a_1 a_2 : Iota), % 6.24/6.45 Or (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) % 6.24/6.45 (Or (Eq (Eq a_1 a) True) (Eq (in (skS.0 4 a_1 a a_2) a_1 → in (skS.0 4 a_1 a a_2) a) False)) % 6.24/6.45 Clause #86 (by clausification #[85]): ∀ (a a_1 a_2 a_3 : Iota), % 6.24/6.45 Or (Eq (Eq a a_1) True) % 6.24/6.45 (Or (Eq (in (skS.0 4 a a_1 a_2) a → in (skS.0 4 a a_1 a_2) a_1) False) % 6.24/6.45 (Eq (Not (in (skS.0 5 a_1 a a_3) a_1 → in (skS.0 5 a_1 a a_3) a)) True)) % 6.24/6.45 Clause #87 (by clausification #[86]): ∀ (a a_1 a_2 a_3 : Iota), % 6.24/6.45 Or (Eq (in (skS.0 4 a a_1 a_2) a → in (skS.0 4 a a_1 a_2) a_1) False) % 6.24/6.45 (Or (Eq (Not (in (skS.0 5 a_1 a a_3) a_1 → in (skS.0 5 a_1 a a_3) a)) True) (Eq a a_1)) % 6.30/6.48 Clause #88 (by clausification #[87]): ∀ (a a_1 a_2 a_3 : Iota), % 6.30/6.48 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) % 6.30/6.48 (Or (Eq a_1 a) (Eq (in (skS.0 4 a_1 a a_3) a_1) True)) % 6.30/6.48 Clause #90 (by clausification #[88]): ∀ (a a_1 a_2 a_3 : Iota), % 6.30/6.48 Or (Eq a a_1) % 6.30/6.48 (Or (Eq (in (skS.0 4 a a_1 a_2) a) True) (Eq (in (skS.0 5 a_1 a a_3) a_1 → in (skS.0 5 a_1 a a_3) a) False)) % 6.30/6.48 Clause #91 (by clausification #[90]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq a a_1) (Or (Eq (in (skS.0 4 a a_1 a_2) a) True) (Eq (in (skS.0 5 a_1 a a_3) a_1) True)) % 6.30/6.48 Clause #107 (by superposition #[91, 44]): ∀ (a a_1 : Iota) (a_2 : Prop), % 6.30/6.48 Or (Eq a emptyset) (Or (Eq (in (skS.0 4 a emptyset a_1) a) True) (Or (Eq True False) (Eq a_2 True))) % 6.30/6.48 Clause #156 (by clausification #[77]): ∀ (a : Iota), Eq (Not (nonempty (skS.0 8 a) → Exists fun Xx => in Xx (skS.0 8 a))) True % 6.30/6.48 Clause #157 (by clausification #[156]): ∀ (a : Iota), Eq (nonempty (skS.0 8 a) → Exists fun Xx => in Xx (skS.0 8 a)) False % 6.30/6.48 Clause #158 (by clausification #[157]): ∀ (a : Iota), Eq (nonempty (skS.0 8 a)) True % 6.30/6.48 Clause #159 (by clausification #[157]): ∀ (a : Iota), Eq (Exists fun Xx => in Xx (skS.0 8 a)) False % 6.30/6.48 Clause #170 (by clausification #[159]): ∀ (a a_1 : Iota), Eq (in a (skS.0 8 a_1)) False % 6.30/6.48 Clause #190 (by clausification #[107]): ∀ (a a_1 : Iota) (a_2 : Prop), Or (Eq a emptyset) (Or (Eq (in (skS.0 4 a emptyset a_1) a) True) (Eq a_2 True)) % 6.30/6.48 Clause #197 (by superposition #[190, 170]): ∀ (a : Iota) (a_1 : Prop), Or (Eq (skS.0 8 a) emptyset) (Or (Eq a_1 True) (Eq True False)) % 6.30/6.48 Clause #219 (by clausification #[197]): ∀ (a : Iota) (a_1 : Prop), Or (Eq (skS.0 8 a) emptyset) (Eq a_1 True) % 6.30/6.48 Clause #220 (by superposition #[219, 158]): ∀ (a : Prop), Or (Eq a True) (Eq (nonempty emptyset) True) % 6.30/6.48 Clause #228 (by superposition #[220, 33]): ∀ (a : Prop), Or (Eq a True) (Eq True False) % 6.30/6.48 Clause #239 (by clausification #[228]): ∀ (a : Prop), Eq a True % 6.30/6.48 Clause #241 (by falseElim #[239]): False % 6.30/6.48 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------