%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU586^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n022.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 08:01:58 PM UTC 2025 % Result : Theorem 3.63s 3.81s % Output : Proof 3.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU586^2 : TPTP v9.2.0. Released v3.7.0. % 0.13/0.13 % Command : duper %s % 0.13/0.34 % Computer : n022.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Oct 3 06:32:53 EDT 2025 % 0.13/0.34 % CPUTime : % 3.63/3.81 SZS status Theorem for theBenchmark.p % 3.63/3.81 SZS output start Proof for theBenchmark.p % 3.63/3.81 Clause #0 (by assumption #[]): Eq % 3.63/3.81 (Eq binunionEcases % 3.63/3.81 (∀ (A B Xx : Iota) (Xphi : Prop), in Xx (binunion A B) → (in Xx A → Xphi) → (in Xx B → Xphi) → Xphi)) % 3.63/3.81 True % 3.63/3.81 Clause #1 (by assumption #[]): Eq (Not (binunionEcases → ∀ (A B Xx : Iota), in Xx (binunion A B) → Or (in Xx A) (in Xx B))) True % 3.63/3.81 Clause #2 (by clausification #[0]): Eq binunionEcases (∀ (A B Xx : Iota) (Xphi : Prop), in Xx (binunion A B) → (in Xx A → Xphi) → (in Xx B → Xphi) → Xphi) % 3.63/3.81 Clause #30 (by clausification #[1]): Eq (binunionEcases → ∀ (A B Xx : Iota), in Xx (binunion A B) → Or (in Xx A) (in Xx B)) False % 3.63/3.81 Clause #31 (by clausification #[30]): Eq binunionEcases True % 3.63/3.81 Clause #32 (by clausification #[30]): Eq (∀ (A B Xx : Iota), in Xx (binunion A B) → Or (in Xx A) (in Xx B)) False % 3.63/3.81 Clause #33 (by backward demodulation #[31, 2]): Eq True (∀ (A B Xx : Iota) (Xphi : Prop), in Xx (binunion A B) → (in Xx A → Xphi) → (in Xx B → Xphi) → Xphi) % 3.63/3.81 Clause #36 (by clausification #[33]): ∀ (a : Iota), Eq (∀ (B Xx : Iota) (Xphi : Prop), in Xx (binunion a B) → (in Xx a → Xphi) → (in Xx B → Xphi) → Xphi) True % 3.63/3.81 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), % 3.63/3.81 Eq (∀ (Xx : Iota) (Xphi : Prop), in Xx (binunion a a_1) → (in Xx a → Xphi) → (in Xx a_1 → Xphi) → Xphi) True % 3.63/3.81 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), Eq (∀ (Xphi : Prop), in a (binunion a_1 a_2) → (in a a_1 → Xphi) → (in a a_2 → Xphi) → Xphi) True % 3.63/3.81 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), Eq (in a (binunion a_1 a_2) → (in a a_1 → a_3) → (in a a_2 → a_3) → a_3) True % 3.63/3.81 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.63/3.81 Or (Eq (in a (binunion a_1 a_2)) False) (Eq ((in a a_1 → a_3) → (in a a_2 → a_3) → a_3) True) % 3.63/3.81 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.63/3.81 Or (Eq (in a (binunion a_1 a_2)) False) (Or (Eq (in a a_1 → a_3) False) (Eq ((in a a_2 → a_3) → a_3) True)) % 3.63/3.81 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.63/3.81 Or (Eq (in a (binunion a_1 a_2)) False) (Or (Eq ((in a a_2 → a_3) → a_3) True) (Eq (in a a_1) True)) % 3.63/3.81 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.63/3.81 Or (Eq (in a (binunion a_1 a_2)) False) (Or (Eq (in a a_1) True) (Or (Eq (in a a_2 → a_3) False) (Eq a_3 True))) % 3.63/3.81 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.63/3.81 Or (Eq (in a (binunion a_1 a_2)) False) (Or (Eq (in a a_1) True) (Or (Eq a_3 True) (Eq (in a a_2) True))) % 3.63/3.81 Clause #50 (by clausification #[32]): ∀ (a : Iota), Eq (Not (∀ (B Xx : Iota), in Xx (binunion (skS.0 4 a) B) → Or (in Xx (skS.0 4 a)) (in Xx B))) True % 3.63/3.81 Clause #51 (by clausification #[50]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (binunion (skS.0 4 a) B) → Or (in Xx (skS.0 4 a)) (in Xx B)) False % 3.63/3.81 Clause #52 (by clausification #[51]): ∀ (a a_1 : Iota), % 3.63/3.81 Eq % 3.63/3.81 (Not (∀ (Xx : Iota), in Xx (binunion (skS.0 4 a) (skS.0 5 a a_1)) → Or (in Xx (skS.0 4 a)) (in Xx (skS.0 5 a a_1)))) % 3.63/3.81 True % 3.63/3.81 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), % 3.63/3.81 Eq (∀ (Xx : Iota), in Xx (binunion (skS.0 4 a) (skS.0 5 a a_1)) → Or (in Xx (skS.0 4 a)) (in Xx (skS.0 5 a a_1))) % 3.63/3.81 False % 3.63/3.81 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), % 3.63/3.81 Eq % 3.63/3.81 (Not % 3.63/3.81 (in (skS.0 6 a a_1 a_2) (binunion (skS.0 4 a) (skS.0 5 a a_1)) → % 3.63/3.81 Or (in (skS.0 6 a a_1 a_2) (skS.0 4 a)) (in (skS.0 6 a a_1 a_2) (skS.0 5 a a_1)))) % 3.63/3.81 True % 3.63/3.81 Clause #55 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), % 3.63/3.81 Eq % 3.63/3.81 (in (skS.0 6 a a_1 a_2) (binunion (skS.0 4 a) (skS.0 5 a a_1)) → % 3.63/3.81 Or (in (skS.0 6 a a_1 a_2) (skS.0 4 a)) (in (skS.0 6 a a_1 a_2) (skS.0 5 a a_1))) % 3.63/3.81 False % 3.63/3.81 Clause #56 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 6 a a_1 a_2) (binunion (skS.0 4 a) (skS.0 5 a a_1))) True % 3.63/3.81 Clause #57 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), Eq (Or (in (skS.0 6 a a_1 a_2) (skS.0 4 a)) (in (skS.0 6 a a_1 a_2) (skS.0 5 a a_1))) False % 3.63/3.82 Clause #58 (by superposition #[56, 45]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.63/3.82 Or (Eq True False) % 3.63/3.82 (Or (Eq (in (skS.0 6 a a_1 a_2) (skS.0 4 a)) True) % 3.63/3.82 (Or (Eq a_3 True) (Eq (in (skS.0 6 a a_1 a_2) (skS.0 5 a a_1)) True))) % 3.63/3.82 Clause #68 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 6 a a_1 a_2) (skS.0 5 a a_1)) False % 3.63/3.82 Clause #69 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 6 a a_1 a_2) (skS.0 4 a)) False % 3.63/3.82 Clause #70 (by clausification #[58]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.63/3.82 Or (Eq (in (skS.0 6 a a_1 a_2) (skS.0 4 a)) True) % 3.63/3.82 (Or (Eq a_3 True) (Eq (in (skS.0 6 a a_1 a_2) (skS.0 5 a a_1)) True)) % 3.63/3.82 Clause #71 (by forward demodulation #[70, 69]): ∀ (a : Prop) (a_1 a_2 a_3 : Iota), % 3.63/3.82 Or (Eq False True) (Or (Eq a True) (Eq (in (skS.0 6 a_1 a_2 a_3) (skS.0 5 a_1 a_2)) True)) % 3.63/3.82 Clause #72 (by clausification #[71]): ∀ (a : Prop) (a_1 a_2 a_3 : Iota), Or (Eq a True) (Eq (in (skS.0 6 a_1 a_2 a_3) (skS.0 5 a_1 a_2)) True) % 3.63/3.82 Clause #75 (by superposition #[72, 68]): ∀ (a : Prop), Or (Eq a True) (Eq True False) % 3.63/3.82 Clause #78 (by clausification #[75]): ∀ (a : Prop), Eq a True % 3.63/3.82 Clause #80 (by falseElim #[78]): False % 3.63/3.82 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------