%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU633^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n018.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 08:02:05 PM UTC 2025 % Result : Theorem 3.93s 4.15s % Output : Proof 3.93s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU633^2 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.13 % Command : duper %s % 0.12/0.34 % Computer : n018.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 06:27:23 EDT 2025 % 0.12/0.34 % CPUTime : % 3.93/4.15 SZS status Theorem for theBenchmark.p % 3.93/4.15 SZS output start Proof for theBenchmark.p % 3.93/4.15 Clause #0 (by assumption #[]): Eq % 3.93/4.15 (Eq setunionE (∀ (A Xx : Iota), in Xx (setunion A) → ∀ (Xphi : Prop), (∀ (B : Iota), in Xx B → in B A → Xphi) → Xphi)) % 3.93/4.15 True % 3.93/4.15 Clause #1 (by assumption #[]): Eq (Not (setunionE → ∀ (A Xx : Iota), in Xx (setunion A) → Exists fun X => And (in X A) (in Xx X))) True % 3.93/4.15 Clause #2 (by clausification #[0]): Eq setunionE (∀ (A Xx : Iota), in Xx (setunion A) → ∀ (Xphi : Prop), (∀ (B : Iota), in Xx B → in B A → Xphi) → Xphi) % 3.93/4.15 Clause #33 (by clausification #[1]): Eq (setunionE → ∀ (A Xx : Iota), in Xx (setunion A) → Exists fun X => And (in X A) (in Xx X)) False % 3.93/4.15 Clause #34 (by clausification #[33]): Eq setunionE True % 3.93/4.15 Clause #35 (by clausification #[33]): Eq (∀ (A Xx : Iota), in Xx (setunion A) → Exists fun X => And (in X A) (in Xx X)) False % 3.93/4.15 Clause #36 (by backward demodulation #[34, 2]): Eq True (∀ (A Xx : Iota), in Xx (setunion A) → ∀ (Xphi : Prop), (∀ (B : Iota), in Xx B → in B A → Xphi) → Xphi) % 3.93/4.15 Clause #39 (by clausification #[36]): ∀ (a : Iota), % 3.93/4.15 Eq (∀ (Xx : Iota), in Xx (setunion a) → ∀ (Xphi : Prop), (∀ (B : Iota), in Xx B → in B a → Xphi) → Xphi) True % 3.93/4.15 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), Eq (in a (setunion a_1) → ∀ (Xphi : Prop), (∀ (B : Iota), in a B → in B a_1 → Xphi) → Xphi) True % 3.93/4.15 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), % 3.93/4.15 Or (Eq (in a (setunion a_1)) False) (Eq (∀ (Xphi : Prop), (∀ (B : Iota), in a B → in B a_1 → Xphi) → Xphi) True) % 3.93/4.15 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota) (a_2 : Prop), % 3.93/4.15 Or (Eq (in a (setunion a_1)) False) (Eq ((∀ (B : Iota), in a B → in B a_1 → a_2) → a_2) True) % 3.93/4.15 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota) (a_2 : Prop), % 3.93/4.15 Or (Eq (in a (setunion a_1)) False) (Or (Eq (∀ (B : Iota), in a B → in B a_1 → a_2) False) (Eq a_2 True)) % 3.93/4.15 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota) (a_2 : Prop) (a_3 : Iota), % 3.93/4.15 Or (Eq (in a (setunion a_1)) False) % 3.93/4.15 (Or (Eq a_2 True) (Eq (Not (in a (skS.0 4 a a_1 a_2 a_3) → in (skS.0 4 a a_1 a_2 a_3) a_1 → a_2)) True)) % 3.93/4.15 Clause #45 (by clausification #[44]): ∀ (a a_1 : Iota) (a_2 : Prop) (a_3 : Iota), % 3.93/4.15 Or (Eq (in a (setunion a_1)) False) % 3.93/4.15 (Or (Eq a_2 True) (Eq (in a (skS.0 4 a a_1 a_2 a_3) → in (skS.0 4 a a_1 a_2 a_3) a_1 → a_2) False)) % 3.93/4.15 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota) (a_2 : Prop) (a_3 : Iota), % 3.93/4.15 Or (Eq (in a (setunion a_1)) False) (Or (Eq a_2 True) (Eq (in a (skS.0 4 a a_1 a_2 a_3)) True)) % 3.93/4.15 Clause #47 (by clausification #[45]): ∀ (a a_1 : Iota) (a_2 : Prop) (a_3 : Iota), % 3.93/4.15 Or (Eq (in a (setunion a_1)) False) (Or (Eq a_2 True) (Eq (in (skS.0 4 a a_1 a_2 a_3) a_1 → a_2) False)) % 3.93/4.15 Clause #49 (by identity boolHoist #[46]): ∀ (a a_1 : Iota) (a_2 : Prop) (a_3 : Iota), % 3.93/4.15 Or (Eq (in a (setunion a_1)) False) (Or (Eq a_2 True) (Or (Eq (in a (skS.0 4 a a_1 False a_3)) True) (Eq a_2 True))) % 3.93/4.15 Clause #50 (by clausification #[47]): ∀ (a a_1 : Iota) (a_2 : Prop) (a_3 : Iota), % 3.93/4.15 Or (Eq (in a (setunion a_1)) False) (Or (Eq a_2 True) (Eq (in (skS.0 4 a a_1 a_2 a_3) a_1) True)) % 3.93/4.15 Clause #53 (by identity boolHoist #[50]): ∀ (a a_1 : Iota) (a_2 : Prop) (a_3 : Iota), % 3.93/4.15 Or (Eq (in a (setunion a_1)) False) (Or (Eq a_2 True) (Or (Eq (in (skS.0 4 a a_1 False a_3) a_1) True) (Eq a_2 True))) % 3.93/4.15 Clause #64 (by clausification #[35]): ∀ (a : Iota), % 3.93/4.15 Eq (Not (∀ (Xx : Iota), in Xx (setunion (skS.0 5 a)) → Exists fun X => And (in X (skS.0 5 a)) (in Xx X))) True % 3.93/4.15 Clause #65 (by clausification #[64]): ∀ (a : Iota), Eq (∀ (Xx : Iota), in Xx (setunion (skS.0 5 a)) → Exists fun X => And (in X (skS.0 5 a)) (in Xx X)) False % 3.93/4.15 Clause #66 (by clausification #[65]): ∀ (a a_1 : Iota), % 3.93/4.15 Eq (Not (in (skS.0 6 a a_1) (setunion (skS.0 5 a)) → Exists fun X => And (in X (skS.0 5 a)) (in (skS.0 6 a a_1) X))) % 3.93/4.15 True % 3.93/4.15 Clause #67 (by clausification #[66]): ∀ (a a_1 : Iota), % 3.93/4.15 Eq (in (skS.0 6 a a_1) (setunion (skS.0 5 a)) → Exists fun X => And (in X (skS.0 5 a)) (in (skS.0 6 a a_1) X)) False % 3.93/4.16 Clause #68 (by clausification #[67]): ∀ (a a_1 : Iota), Eq (in (skS.0 6 a a_1) (setunion (skS.0 5 a))) True % 3.93/4.16 Clause #69 (by clausification #[67]): ∀ (a a_1 : Iota), Eq (Exists fun X => And (in X (skS.0 5 a)) (in (skS.0 6 a a_1) X)) False % 3.93/4.16 Clause #71 (by clausification #[69]): ∀ (a a_1 a_2 : Iota), Eq (And (in a (skS.0 5 a_1)) (in (skS.0 6 a_1 a_2) a)) False % 3.93/4.16 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 5 a_1)) False) (Eq (in (skS.0 6 a_1 a_2) a) False) % 3.93/4.16 Clause #73 (by eliminate duplicate literals #[53]): ∀ (a a_1 : Iota) (a_2 : Prop) (a_3 : Iota), % 3.93/4.16 Or (Eq (in a (setunion a_1)) False) (Or (Eq a_2 True) (Eq (in (skS.0 4 a a_1 False a_3) a_1) True)) % 3.93/4.16 Clause #74 (by superposition #[73, 68]): ∀ (a : Prop) (a_1 a_2 a_3 : Iota), % 3.93/4.16 Or (Eq a True) (Or (Eq (in (skS.0 4 (skS.0 6 a_1 a_2) (skS.0 5 a_1) False a_3) (skS.0 5 a_1)) True) (Eq False True)) % 3.93/4.16 Clause #78 (by eliminate duplicate literals #[49]): ∀ (a a_1 : Iota) (a_2 : Prop) (a_3 : Iota), % 3.93/4.16 Or (Eq (in a (setunion a_1)) False) (Or (Eq a_2 True) (Eq (in a (skS.0 4 a a_1 False a_3)) True)) % 3.93/4.16 Clause #79 (by superposition #[78, 68]): ∀ (a : Prop) (a_1 a_2 a_3 : Iota), % 3.93/4.16 Or (Eq a True) % 3.93/4.16 (Or (Eq (in (skS.0 6 a_1 a_2) (skS.0 4 (skS.0 6 a_1 a_2) (skS.0 5 a_1) False a_3)) True) (Eq False True)) % 3.93/4.16 Clause #83 (by clausification #[74]): ∀ (a : Prop) (a_1 a_2 a_3 : Iota), % 3.93/4.16 Or (Eq a True) (Eq (in (skS.0 4 (skS.0 6 a_1 a_2) (skS.0 5 a_1) False a_3) (skS.0 5 a_1)) True) % 3.93/4.16 Clause #91 (by equality factoring #[83]): ∀ (a a_1 a_2 : Iota), Or (Ne True True) (Eq (in (skS.0 4 (skS.0 6 a a_1) (skS.0 5 a) False a_2) (skS.0 5 a)) True) % 3.93/4.16 Clause #100 (by clausification #[91]): ∀ (a a_1 a_2 : Iota), % 3.93/4.16 Or (Eq (in (skS.0 4 (skS.0 6 a a_1) (skS.0 5 a) False a_2) (skS.0 5 a)) True) (Or (Eq True False) (Eq True False)) % 3.93/4.16 Clause #102 (by clausification #[100]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 4 (skS.0 6 a a_1) (skS.0 5 a) False a_2) (skS.0 5 a)) True) (Eq True False) % 3.93/4.16 Clause #103 (by clausification #[102]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 4 (skS.0 6 a a_1) (skS.0 5 a) False a_2) (skS.0 5 a)) True % 3.93/4.16 Clause #104 (by superposition #[103, 72]): ∀ (a a_1 a_2 a_3 : Iota), % 3.93/4.16 Or (Eq True False) (Eq (in (skS.0 6 a a_1) (skS.0 4 (skS.0 6 a a_2) (skS.0 5 a) False a_3)) False) % 3.93/4.16 Clause #105 (by clausification #[104]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 6 a a_1) (skS.0 4 (skS.0 6 a a_2) (skS.0 5 a) False a_3)) False % 3.93/4.16 Clause #120 (by clausification #[79]): ∀ (a : Prop) (a_1 a_2 a_3 : Iota), % 3.93/4.16 Or (Eq a True) (Eq (in (skS.0 6 a_1 a_2) (skS.0 4 (skS.0 6 a_1 a_2) (skS.0 5 a_1) False a_3)) True) % 3.93/4.16 Clause #127 (by superposition #[120, 105]): ∀ (a : Prop), Or (Eq a True) (Eq True False) % 3.93/4.16 Clause #130 (by clausification #[127]): ∀ (a : Prop), Eq a True % 3.93/4.16 Clause #133 (by falseElim #[130]): False % 3.93/4.16 SZS output end Proof for theBenchmark.p 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