%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU614^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n024.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 08:02:02 PM UTC 2025 % Result : Theorem 3.68s 3.84s % Output : Proof 3.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU614^2 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.13 % Command : duper %s % 0.13/0.35 % Computer : n024.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 06:30:23 EDT 2025 % 0.13/0.35 % CPUTime : % 3.68/3.84 SZS status Theorem for theBenchmark.p % 3.68/3.84 SZS output start Proof for theBenchmark.p % 3.68/3.84 Clause #0 (by assumption #[]): Eq % 3.68/3.84 (Eq symdiffE % 3.68/3.84 (∀ (A B Xx : Iota), % 3.68/3.84 in Xx (symdiff A B) → % 3.68/3.84 ∀ (Xphi : Prop), (in Xx A → Not (in Xx B) → Xphi) → (Not (in Xx A) → in Xx B → Xphi) → Xphi)) % 3.68/3.84 True % 3.68/3.84 Clause #1 (by assumption #[]): Eq (Not (symdiffE → ∀ (A B Xx : Iota), in Xx A → in Xx B → Not (in Xx (symdiff A B)))) True % 3.68/3.84 Clause #2 (by clausification #[0]): Eq symdiffE % 3.68/3.84 (∀ (A B Xx : Iota), % 3.68/3.84 in Xx (symdiff A B) → ∀ (Xphi : Prop), (in Xx A → Not (in Xx B) → Xphi) → (Not (in Xx A) → in Xx B → Xphi) → Xphi) % 3.68/3.84 Clause #35 (by clausification #[1]): Eq (symdiffE → ∀ (A B Xx : Iota), in Xx A → in Xx B → Not (in Xx (symdiff A B))) False % 3.68/3.84 Clause #36 (by clausification #[35]): Eq symdiffE True % 3.68/3.84 Clause #37 (by clausification #[35]): Eq (∀ (A B Xx : Iota), in Xx A → in Xx B → Not (in Xx (symdiff A B))) False % 3.68/3.84 Clause #38 (by backward demodulation #[36, 2]): Eq True % 3.68/3.84 (∀ (A B Xx : Iota), % 3.68/3.85 in Xx (symdiff A B) → ∀ (Xphi : Prop), (in Xx A → Not (in Xx B) → Xphi) → (Not (in Xx A) → in Xx B → Xphi) → Xphi) % 3.68/3.85 Clause #41 (by clausification #[38]): ∀ (a : Iota), % 3.68/3.85 Eq % 3.68/3.85 (∀ (B Xx : Iota), % 3.68/3.85 in Xx (symdiff a B) → ∀ (Xphi : Prop), (in Xx a → Not (in Xx B) → Xphi) → (Not (in Xx a) → in Xx B → Xphi) → Xphi) % 3.68/3.85 True % 3.68/3.85 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), % 3.68/3.85 Eq % 3.68/3.85 (∀ (Xx : Iota), % 3.68/3.85 in Xx (symdiff a a_1) → % 3.68/3.85 ∀ (Xphi : Prop), (in Xx a → Not (in Xx a_1) → Xphi) → (Not (in Xx a) → in Xx a_1 → Xphi) → Xphi) % 3.68/3.85 True % 3.68/3.85 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), % 3.68/3.85 Eq % 3.68/3.85 (in a (symdiff a_1 a_2) → % 3.68/3.85 ∀ (Xphi : Prop), (in a a_1 → Not (in a a_2) → Xphi) → (Not (in a a_1) → in a a_2 → Xphi) → Xphi) % 3.68/3.85 True % 3.68/3.85 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), % 3.68/3.85 Or (Eq (in a (symdiff a_1 a_2)) False) % 3.68/3.85 (Eq (∀ (Xphi : Prop), (in a a_1 → Not (in a a_2) → Xphi) → (Not (in a a_1) → in a a_2 → Xphi) → Xphi) True) % 3.68/3.85 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.68/3.85 Or (Eq (in a (symdiff a_1 a_2)) False) % 3.68/3.85 (Eq ((in a a_1 → Not (in a a_2) → a_3) → (Not (in a a_1) → in a a_2 → a_3) → a_3) True) % 3.68/3.85 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.68/3.85 Or (Eq (in a (symdiff a_1 a_2)) False) % 3.68/3.85 (Or (Eq (in a a_1 → Not (in a a_2) → a_3) False) (Eq ((Not (in a a_1) → in a a_2 → a_3) → a_3) True)) % 3.68/3.85 Clause #48 (by clausification #[46]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.68/3.85 Or (Eq (in a (symdiff a_1 a_2)) False) % 3.68/3.85 (Or (Eq ((Not (in a a_1) → in a a_2 → a_3) → a_3) True) (Eq (Not (in a a_2) → a_3) False)) % 3.68/3.85 Clause #53 (by clausification #[37]): ∀ (a : Iota), Eq (Not (∀ (B Xx : Iota), in Xx (skS.0 4 a) → in Xx B → Not (in Xx (symdiff (skS.0 4 a) B)))) True % 3.68/3.85 Clause #54 (by clausification #[53]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (skS.0 4 a) → in Xx B → Not (in Xx (symdiff (skS.0 4 a) B))) False % 3.68/3.85 Clause #55 (by clausification #[54]): ∀ (a a_1 : Iota), % 3.68/3.85 Eq % 3.68/3.85 (Not (∀ (Xx : Iota), in Xx (skS.0 4 a) → in Xx (skS.0 5 a a_1) → Not (in Xx (symdiff (skS.0 4 a) (skS.0 5 a a_1))))) % 3.68/3.85 True % 3.68/3.85 Clause #56 (by clausification #[55]): ∀ (a a_1 : Iota), % 3.68/3.85 Eq (∀ (Xx : Iota), in Xx (skS.0 4 a) → in Xx (skS.0 5 a a_1) → Not (in Xx (symdiff (skS.0 4 a) (skS.0 5 a a_1)))) % 3.68/3.85 False % 3.68/3.85 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 : Iota), % 3.68/3.85 Eq % 3.68/3.85 (Not % 3.68/3.85 (in (skS.0 6 a a_1 a_2) (skS.0 4 a) → % 3.68/3.85 in (skS.0 6 a a_1 a_2) (skS.0 5 a a_1) → Not (in (skS.0 6 a a_1 a_2) (symdiff (skS.0 4 a) (skS.0 5 a a_1))))) % 3.68/3.85 True % 3.68/3.85 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 : Iota), % 3.68/3.85 Eq % 3.68/3.85 (in (skS.0 6 a a_1 a_2) (skS.0 4 a) → % 3.68/3.85 in (skS.0 6 a a_1 a_2) (skS.0 5 a a_1) → Not (in (skS.0 6 a a_1 a_2) (symdiff (skS.0 4 a) (skS.0 5 a a_1)))) % 3.68/3.85 False % 3.68/3.85 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 6 a a_1 a_2) (skS.0 4 a)) True % 3.68/3.85 Clause #60 (by clausification #[58]): ∀ (a a_1 a_2 : Iota), % 3.68/3.86 Eq (in (skS.0 6 a a_1 a_2) (skS.0 5 a a_1) → Not (in (skS.0 6 a a_1 a_2) (symdiff (skS.0 4 a) (skS.0 5 a a_1)))) False % 3.68/3.86 Clause #61 (by clausification #[48]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.68/3.86 Or (Eq (in a (symdiff a_1 a_2)) False) % 3.68/3.86 (Or (Eq (Not (in a a_2) → a_3) False) (Or (Eq (Not (in a a_1) → in a a_2 → a_3) False) (Eq a_3 True))) % 3.68/3.86 Clause #62 (by clausification #[61]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.68/3.86 Or (Eq (in a (symdiff a_1 a_2)) False) % 3.68/3.86 (Or (Eq (Not (in a a_1) → in a a_2 → a_3) False) (Or (Eq a_3 True) (Eq (Not (in a a_2)) True))) % 3.68/3.86 Clause #64 (by clausification #[62]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.68/3.86 Or (Eq (in a (symdiff a_1 a_2)) False) (Or (Eq a_3 True) (Or (Eq (Not (in a a_2)) True) (Eq (Not (in a a_1)) True))) % 3.68/3.86 Clause #66 (by clausification #[64]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.68/3.86 Or (Eq (in a (symdiff a_1 a_2)) False) (Or (Eq a_3 True) (Or (Eq (Not (in a a_1)) True) (Eq (in a a_2) False))) % 3.68/3.86 Clause #67 (by clausification #[66]): ∀ (a a_1 a_2 : Iota) (a_3 : Prop), % 3.68/3.86 Or (Eq (in a (symdiff a_1 a_2)) False) (Or (Eq a_3 True) (Or (Eq (in a a_2) False) (Eq (in a a_1) False))) % 3.68/3.86 Clause #105 (by clausification #[60]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 6 a a_1 a_2) (skS.0 5 a a_1)) True % 3.68/3.86 Clause #106 (by clausification #[60]): ∀ (a a_1 a_2 : Iota), Eq (Not (in (skS.0 6 a a_1 a_2) (symdiff (skS.0 4 a) (skS.0 5 a a_1)))) False % 3.68/3.86 Clause #107 (by clausification #[106]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 6 a a_1 a_2) (symdiff (skS.0 4 a) (skS.0 5 a a_1))) True % 3.68/3.86 Clause #108 (by superposition #[107, 67]): ∀ (a : Prop) (a_1 a_2 a_3 : Iota), % 3.68/3.86 Or (Eq True False) % 3.68/3.86 (Or (Eq a True) % 3.68/3.86 (Or (Eq (in (skS.0 6 a_1 a_2 a_3) (skS.0 5 a_1 a_2)) False) (Eq (in (skS.0 6 a_1 a_2 a_3) (skS.0 4 a_1)) False))) % 3.68/3.86 Clause #112 (by clausification #[108]): ∀ (a : Prop) (a_1 a_2 a_3 : Iota), % 3.68/3.86 Or (Eq a True) % 3.68/3.86 (Or (Eq (in (skS.0 6 a_1 a_2 a_3) (skS.0 5 a_1 a_2)) False) (Eq (in (skS.0 6 a_1 a_2 a_3) (skS.0 4 a_1)) False)) % 3.68/3.86 Clause #113 (by forward demodulation #[112, 59]): ∀ (a : Prop) (a_1 a_2 a_3 : Iota), % 3.68/3.86 Or (Eq a True) (Or (Eq (in (skS.0 6 a_1 a_2 a_3) (skS.0 5 a_1 a_2)) False) (Eq True False)) % 3.68/3.86 Clause #114 (by clausification #[113]): ∀ (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)) False) % 3.68/3.86 Clause #115 (by superposition #[114, 105]): ∀ (a : Prop), Or (Eq a True) (Eq False True) % 3.68/3.86 Clause #116 (by clausification #[115]): ∀ (a : Prop), Eq a True % 3.68/3.86 Clause #117 (by falseElim #[116]): False % 3.68/3.86 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------