%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU574^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n019.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 08:01:57 PM UTC 2025 % Result : Theorem 40.16s 40.33s % Output : Proof 40.25s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SEU574^2 : TPTP v9.2.0. Released v3.7.0. % 0.08/0.14 % Command : duper %s % 0.13/0.35 % Computer : n019.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 05:42:38 EDT 2025 % 0.13/0.35 % CPUTime : % 40.16/40.33 SZS status Theorem for theBenchmark.p % 40.16/40.33 SZS output start Proof for theBenchmark.p % 40.16/40.33 Clause #0 (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 % 40.16/40.33 Clause #1 (by assumption #[]): Eq (Eq subsetE (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B)) True % 40.16/40.33 Clause #2 (by assumption #[]): Eq (Not (setext → subsetE → ∀ (A B : Iota), subset A B → subset B A → Eq A B)) True % 40.16/40.33 Clause #3 (by clausification #[2]): Eq (setext → subsetE → ∀ (A B : Iota), subset A B → subset B A → Eq A B) False % 40.16/40.33 Clause #4 (by clausification #[3]): Eq setext True % 40.16/40.33 Clause #5 (by clausification #[3]): Eq (subsetE → ∀ (A B : Iota), subset A B → subset B A → Eq A B) False % 40.16/40.33 Clause #6 (by clausification #[5]): Eq subsetE True % 40.16/40.33 Clause #7 (by clausification #[5]): Eq (∀ (A B : Iota), subset A B → subset B A → Eq A B) False % 40.16/40.33 Clause #8 (by clausification #[7]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), subset (skS.0 0 a) B → subset B (skS.0 0 a) → Eq (skS.0 0 a) B)) True % 40.16/40.33 Clause #9 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (B : Iota), subset (skS.0 0 a) B → subset B (skS.0 0 a) → Eq (skS.0 0 a) B) False % 40.16/40.33 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), % 40.16/40.33 Eq (Not (subset (skS.0 0 a) (skS.0 1 a a_1) → subset (skS.0 1 a a_1) (skS.0 0 a) → Eq (skS.0 0 a) (skS.0 1 a a_1))) % 40.16/40.33 True % 40.16/40.33 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), % 40.16/40.33 Eq (subset (skS.0 0 a) (skS.0 1 a a_1) → subset (skS.0 1 a a_1) (skS.0 0 a) → Eq (skS.0 0 a) (skS.0 1 a a_1)) False % 40.16/40.33 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (subset (skS.0 0 a) (skS.0 1 a a_1)) True % 40.16/40.33 Clause #13 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (subset (skS.0 1 a a_1) (skS.0 0 a) → Eq (skS.0 0 a) (skS.0 1 a a_1)) False % 40.16/40.33 Clause #14 (by clausification #[1]): Eq subsetE (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B) % 40.16/40.33 Clause #15 (by forward demodulation #[14, 6]): Eq True (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B) % 40.16/40.33 Clause #16 (by clausification #[15]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), subset a B → in Xx a → in Xx B) True % 40.16/40.33 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), subset a a_1 → in Xx a → in Xx a_1) True % 40.16/40.33 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), Eq (subset a a_1 → in a_2 a → in a_2 a_1) True % 40.16/40.33 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (in a_2 a → in a_2 a_1) True) % 40.16/40.33 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Or (Eq (in a_2 a) False) (Eq (in a_2 a_1) True)) % 40.16/40.33 Clause #21 (by superposition #[20, 12]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 0 a_1)) False) (Or (Eq (in a (skS.0 1 a_1 a_2)) True) (Eq False True)) % 40.16/40.33 Clause #22 (by clausification #[0]): Eq setext (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → (∀ (Xx : Iota), in Xx B → in Xx A) → Eq A B) % 40.16/40.33 Clause #23 (by forward demodulation #[22, 4]): Eq True (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → (∀ (Xx : Iota), in Xx B → in Xx A) → Eq A B) % 40.16/40.33 Clause #24 (by clausification #[23]): ∀ (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 % 40.16/40.33 Clause #25 (by clausification #[24]): ∀ (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 % 40.16/40.33 Clause #26 (by clausification #[25]): ∀ (a a_1 : Iota), % 40.16/40.33 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) % 40.16/40.33 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), % 40.16/40.33 Or (Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → Eq a_1 a) True) % 40.16/40.33 (Eq (Not (in (skS.0 2 a_1 a a_2) a_1 → in (skS.0 2 a_1 a a_2) a)) True) % 40.16/40.33 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), % 40.16/40.33 Or (Eq (Not (in (skS.0 2 a a_1 a_2) a → in (skS.0 2 a a_1 a_2) a_1)) True) % 40.16/40.33 (Or (Eq (∀ (Xx : Iota), in Xx a_1 → in Xx a) False) (Eq (Eq a a_1) True)) % 40.16/40.36 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), % 40.16/40.36 Or (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) % 40.16/40.36 (Or (Eq (Eq a_1 a) True) (Eq (in (skS.0 2 a_1 a a_2) a_1 → in (skS.0 2 a_1 a a_2) a) False)) % 40.16/40.36 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 a_3 : Iota), % 40.16/40.36 Or (Eq (Eq a a_1) True) % 40.16/40.36 (Or (Eq (in (skS.0 2 a a_1 a_2) a → in (skS.0 2 a a_1 a_2) a_1) False) % 40.16/40.36 (Eq (Not (in (skS.0 3 a_1 a a_3) a_1 → in (skS.0 3 a_1 a a_3) a)) True)) % 40.16/40.36 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 a_3 : Iota), % 40.16/40.36 Or (Eq (in (skS.0 2 a a_1 a_2) a → in (skS.0 2 a a_1 a_2) a_1) False) % 40.16/40.36 (Or (Eq (Not (in (skS.0 3 a_1 a a_3) a_1 → in (skS.0 3 a_1 a a_3) a)) True) (Eq a a_1)) % 40.16/40.36 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 a_3 : Iota), % 40.16/40.36 Or (Eq (Not (in (skS.0 3 a a_1 a_2) a → in (skS.0 3 a a_1 a_2) a_1)) True) % 40.16/40.36 (Or (Eq a_1 a) (Eq (in (skS.0 2 a_1 a a_3) a_1) True)) % 40.16/40.36 Clause #33 (by clausification #[31]): ∀ (a a_1 a_2 a_3 : Iota), % 40.16/40.36 Or (Eq (Not (in (skS.0 3 a a_1 a_2) a → in (skS.0 3 a a_1 a_2) a_1)) True) % 40.16/40.36 (Or (Eq a_1 a) (Eq (in (skS.0 2 a_1 a a_3) a) False)) % 40.16/40.36 Clause #34 (by clausification #[32]): ∀ (a a_1 a_2 a_3 : Iota), % 40.16/40.36 Or (Eq a a_1) % 40.16/40.36 (Or (Eq (in (skS.0 2 a a_1 a_2) a) True) (Eq (in (skS.0 3 a_1 a a_3) a_1 → in (skS.0 3 a_1 a a_3) a) False)) % 40.16/40.36 Clause #35 (by clausification #[34]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq a a_1) (Or (Eq (in (skS.0 2 a a_1 a_2) a) True) (Eq (in (skS.0 3 a_1 a a_3) a_1) True)) % 40.16/40.36 Clause #36 (by clausification #[34]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq a a_1) (Or (Eq (in (skS.0 2 a a_1 a_2) a) True) (Eq (in (skS.0 3 a_1 a a_3) a) False)) % 40.16/40.36 Clause #45 (by clausification #[13]): ∀ (a a_1 : Iota), Eq (subset (skS.0 1 a a_1) (skS.0 0 a)) True % 40.16/40.36 Clause #46 (by clausification #[13]): ∀ (a a_1 : Iota), Eq (Eq (skS.0 0 a) (skS.0 1 a a_1)) False % 40.16/40.36 Clause #47 (by superposition #[45, 20]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (in a (skS.0 1 a_1 a_2)) False) (Eq (in a (skS.0 0 a_1)) True)) % 40.16/40.36 Clause #52 (by clausification #[46]): ∀ (a a_1 : Iota), Ne (skS.0 0 a) (skS.0 1 a a_1) % 40.16/40.36 Clause #55 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 0 a_1)) False) (Eq (in a (skS.0 1 a_1 a_2)) True) % 40.16/40.36 Clause #60 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 1 a_1 a_2)) False) (Eq (in a (skS.0 0 a_1)) True) % 40.16/40.36 Clause #61 (by superposition #[60, 35]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 40.16/40.36 Or (Eq (in (skS.0 2 (skS.0 1 a a_1) a_2 a_3) (skS.0 0 a)) True) % 40.16/40.36 (Or (Eq (skS.0 1 a a_1) a_2) (Or (Eq False True) (Eq (in (skS.0 3 a_2 (skS.0 1 a a_1) a_4) a_2) True))) % 40.16/40.36 Clause #67 (by clausification #[33]): ∀ (a a_1 a_2 a_3 : Iota), % 40.16/40.36 Or (Eq a a_1) % 40.16/40.36 (Or (Eq (in (skS.0 2 a a_1 a_2) a_1) False) (Eq (in (skS.0 3 a_1 a a_3) a_1 → in (skS.0 3 a_1 a a_3) a) False)) % 40.16/40.36 Clause #68 (by clausification #[67]): ∀ (a a_1 a_2 a_3 : Iota), % 40.16/40.36 Or (Eq a a_1) (Or (Eq (in (skS.0 2 a a_1 a_2) a_1) False) (Eq (in (skS.0 3 a_1 a a_3) a_1) True)) % 40.16/40.36 Clause #69 (by clausification #[67]): ∀ (a a_1 a_2 a_3 : Iota), % 40.16/40.36 Or (Eq a a_1) (Or (Eq (in (skS.0 2 a a_1 a_2) a_1) False) (Eq (in (skS.0 3 a_1 a a_3) a) False)) % 40.16/40.36 Clause #1477 (by clausification #[61]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 40.16/40.36 Or (Eq (in (skS.0 2 (skS.0 1 a a_1) a_2 a_3) (skS.0 0 a)) True) % 40.16/40.36 (Or (Eq (skS.0 1 a a_1) a_2) (Eq (in (skS.0 3 a_2 (skS.0 1 a a_1) a_4) a_2) True)) % 40.16/40.36 Clause #1483 (by superposition #[1477, 52]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 40.16/40.36 Or (Eq (in (skS.0 2 (skS.0 1 a a_1) a_2 a_3) (skS.0 0 a)) True) % 40.16/40.36 (Or (Eq (in (skS.0 3 a_2 (skS.0 1 a a_1) a_4) a_2) True) (Ne (skS.0 0 a) a_2)) % 40.16/40.36 Clause #1559 (by destructive equality resolution #[1483]): ∀ (a a_1 a_2 a_3 : Iota), % 40.16/40.36 Or (Eq (in (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) True) % 40.16/40.36 (Eq (in (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) a_3) (skS.0 0 a)) True) % 40.16/40.36 Clause #1561 (by superposition #[1559, 68]): ∀ (a a_1 a_2 a_3 : Iota), % 40.16/40.36 Or (Eq (in (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 0 a)) True) % 40.16/40.36 (Or (Eq (skS.0 1 a a_1) (skS.0 0 a)) % 40.16/40.36 (Or (Eq True False) (Eq (in (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) a_3) (skS.0 0 a)) True))) % 40.25/40.49 Clause #7699 (by clausification #[1561]): ∀ (a a_1 a_2 a_3 : Iota), % 40.25/40.49 Or (Eq (in (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 0 a)) True) % 40.25/40.49 (Or (Eq (skS.0 1 a a_1) (skS.0 0 a)) (Eq (in (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) a_3) (skS.0 0 a)) True)) % 40.25/40.49 Clause #7700 (by forward contextual literal cutting #[7699, 52]): ∀ (a a_1 a_2 a_3 : Iota), % 40.25/40.49 Or (Eq (in (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 0 a)) True) % 40.25/40.49 (Eq (in (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) a_3) (skS.0 0 a)) True) % 40.25/40.49 Clause #7794 (by equality factoring #[7700]): ∀ (a a_1 a_2 : Iota), Or (Ne True True) (Eq (in (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 0 a)) True) % 40.25/40.49 Clause #7795 (by clausification #[7794]): ∀ (a a_1 a_2 : Iota), % 40.25/40.49 Or (Eq (in (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 0 a)) True) (Or (Eq True False) (Eq True False)) % 40.25/40.49 Clause #7797 (by clausification #[7795]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 0 a)) True) (Eq True False) % 40.25/40.49 Clause #7798 (by clausification #[7797]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 0 a)) True % 40.25/40.49 Clause #7799 (by superposition #[7798, 55]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq True False) (Eq (in (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 1 a a_3)) True) % 40.25/40.49 Clause #8059 (by clausification #[7799]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 1 a a_3)) True % 40.25/40.49 Clause #8065 (by superposition #[8059, 36]): ∀ (a a_1 a_2 : Iota), % 40.25/40.49 Or (Eq (skS.0 1 a a_1) (skS.0 0 a)) % 40.25/40.49 (Or (Eq (in (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 1 a a_1)) True) (Eq True False)) % 40.25/40.49 Clause #8162 (by clausification #[8065]): ∀ (a a_1 a_2 : Iota), % 40.25/40.49 Or (Eq (skS.0 1 a a_1) (skS.0 0 a)) (Eq (in (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 1 a a_1)) True) % 40.25/40.49 Clause #8163 (by forward contextual literal cutting #[8162, 52]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 1 a a_1)) True % 40.25/40.49 Clause #8164 (by superposition #[8163, 60]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (in (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) True) % 40.25/40.49 Clause #8243 (by clausification #[8164]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 (skS.0 1 a a_1) (skS.0 0 a) a_2) (skS.0 0 a)) True % 40.25/40.49 Clause #8246 (by superposition #[8243, 69]): ∀ (a a_1 a_2 : Iota), % 40.25/40.49 Or (Eq (skS.0 1 a a_1) (skS.0 0 a)) % 40.25/40.49 (Or (Eq True False) (Eq (in (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 1 a a_1)) False)) % 40.25/40.49 Clause #8606 (by clausification #[8246]): ∀ (a a_1 a_2 : Iota), % 40.25/40.49 Or (Eq (skS.0 1 a a_1) (skS.0 0 a)) (Eq (in (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 1 a a_1)) False) % 40.25/40.49 Clause #8607 (by forward contextual literal cutting #[8606, 52]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 3 (skS.0 0 a) (skS.0 1 a a_1) a_2) (skS.0 1 a a_1)) False % 40.25/40.49 Clause #8611 (by superposition #[8607, 8059]): Eq False True % 40.25/40.49 Clause #8672 (by clausification #[8611]): False % 40.25/40.49 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------