%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET958+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n009.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 08:00:44 PM UTC 2025 % Result : Theorem 92.97s 93.16s % Output : Proof 93.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SET958+1 : TPTP v9.2.0. Released v3.2.0. % 0.07/0.14 % Command : duper %s % 0.14/0.36 % Computer : n009.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Thu Oct 2 14:57:53 EDT 2025 % 0.14/0.36 % CPUTime : % 92.97/93.16 SZS status Theorem for theBenchmark.p % 92.97/93.16 SZS output start Proof for theBenchmark.p % 92.97/93.16 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset A B) (∀ (C : Iota), in C A → in C B)) True % 92.97/93.16 Clause #8 (by assumption #[]): Eq % 92.97/93.16 (Not % 92.97/93.16 (∀ (A B : Iota), % 92.97/93.16 And (∀ (C : Iota), Not (And (in C A) (∀ (D E : Iota), Ne C (ordered_pair D E)))) % 92.97/93.16 (∀ (C D : Iota), in (ordered_pair C D) A → in (ordered_pair C D) B) → % 92.97/93.16 subset A B)) % 92.97/93.16 True % 92.97/93.16 Clause #15 (by clausification #[8]): Eq % 92.97/93.16 (∀ (A B : Iota), % 92.97/93.16 And (∀ (C : Iota), Not (And (in C A) (∀ (D E : Iota), Ne C (ordered_pair D E)))) % 92.97/93.16 (∀ (C D : Iota), in (ordered_pair C D) A → in (ordered_pair C D) B) → % 92.97/93.16 subset A B) % 92.97/93.16 False % 92.97/93.16 Clause #16 (by clausification #[15]): ∀ (a : Iota), % 92.97/93.16 Eq % 92.97/93.16 (Not % 92.97/93.16 (∀ (B : Iota), % 92.97/93.16 And (∀ (C : Iota), Not (And (in C (skS.0 2 a)) (∀ (D E : Iota), Ne C (ordered_pair D E)))) % 92.97/93.16 (∀ (C D : Iota), in (ordered_pair C D) (skS.0 2 a) → in (ordered_pair C D) B) → % 92.97/93.16 subset (skS.0 2 a) B)) % 92.97/93.16 True % 92.97/93.16 Clause #17 (by clausification #[16]): ∀ (a : Iota), % 92.97/93.16 Eq % 92.97/93.16 (∀ (B : Iota), % 92.97/93.16 And (∀ (C : Iota), Not (And (in C (skS.0 2 a)) (∀ (D E : Iota), Ne C (ordered_pair D E)))) % 92.97/93.16 (∀ (C D : Iota), in (ordered_pair C D) (skS.0 2 a) → in (ordered_pair C D) B) → % 92.97/93.16 subset (skS.0 2 a) B) % 92.97/93.16 False % 92.97/93.16 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), % 92.97/93.16 Eq % 92.97/93.16 (Not % 92.97/93.16 (And (∀ (C : Iota), Not (And (in C (skS.0 2 a)) (∀ (D E : Iota), Ne C (ordered_pair D E)))) % 92.97/93.16 (∀ (C D : Iota), in (ordered_pair C D) (skS.0 2 a) → in (ordered_pair C D) (skS.0 3 a a_1)) → % 92.97/93.16 subset (skS.0 2 a) (skS.0 3 a a_1))) % 92.97/93.16 True % 92.97/93.16 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), % 92.97/93.16 Eq % 92.97/93.16 (And (∀ (C : Iota), Not (And (in C (skS.0 2 a)) (∀ (D E : Iota), Ne C (ordered_pair D E)))) % 92.97/93.16 (∀ (C D : Iota), in (ordered_pair C D) (skS.0 2 a) → in (ordered_pair C D) (skS.0 3 a a_1)) → % 92.97/93.16 subset (skS.0 2 a) (skS.0 3 a a_1)) % 92.97/93.16 False % 92.97/93.16 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), % 92.97/93.16 Eq % 92.97/93.16 (And (∀ (C : Iota), Not (And (in C (skS.0 2 a)) (∀ (D E : Iota), Ne C (ordered_pair D E)))) % 92.97/93.16 (∀ (C D : Iota), in (ordered_pair C D) (skS.0 2 a) → in (ordered_pair C D) (skS.0 3 a a_1))) % 92.97/93.16 True % 92.97/93.16 Clause #21 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (subset (skS.0 2 a) (skS.0 3 a a_1)) False % 92.97/93.16 Clause #22 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (∀ (C D : Iota), in (ordered_pair C D) (skS.0 2 a) → in (ordered_pair C D) (skS.0 3 a a_1)) True % 92.97/93.16 Clause #23 (by clausification #[20]): ∀ (a : Iota), Eq (∀ (C : Iota), Not (And (in C (skS.0 2 a)) (∀ (D E : Iota), Ne C (ordered_pair D E)))) True % 92.97/93.16 Clause #24 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), % 92.97/93.16 Eq (∀ (D : Iota), in (ordered_pair a D) (skS.0 2 a_1) → in (ordered_pair a D) (skS.0 3 a_1 a_2)) True % 92.97/93.16 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (ordered_pair a a_1) (skS.0 2 a_2) → in (ordered_pair a a_1) (skS.0 3 a_2 a_3)) True % 92.97/93.16 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 a_3 : Iota), % 92.97/93.16 Or (Eq (in (ordered_pair a a_1) (skS.0 2 a_2)) False) (Eq (in (ordered_pair a a_1) (skS.0 3 a_2 a_3)) True) % 92.97/93.16 Clause #37 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset a B) (∀ (C : Iota), in C a → in C B)) True % 92.97/93.16 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (C : Iota), in C a → in C a_1)) True % 92.97/93.16 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Eq (∀ (C : Iota), in C a → in C a_1) False) % 92.97/93.16 Clause #41 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), % 92.97/93.16 Or (Eq (subset a a_1) True) (Eq (Not (in (skS.0 4 a a_1 a_2) a → in (skS.0 4 a a_1 a_2) a_1)) True) % 92.97/93.16 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 4 a a_1 a_2) a → in (skS.0 4 a a_1 a_2) a_1) False) % 92.97/93.16 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 4 a a_1 a_2) a) True) % 92.97/93.16 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 4 a a_1 a_2) a_1) False) % 93.09/93.33 Clause #66 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (Not (And (in a (skS.0 2 a_1)) (∀ (D E : Iota), Ne a (ordered_pair D E)))) True % 93.09/93.33 Clause #67 (by clausification #[66]): ∀ (a a_1 : Iota), Eq (And (in a (skS.0 2 a_1)) (∀ (D E : Iota), Ne a (ordered_pair D E))) False % 93.09/93.33 Clause #68 (by clausification #[67]): ∀ (a a_1 : Iota), Or (Eq (in a (skS.0 2 a_1)) False) (Eq (∀ (D E : Iota), Ne a (ordered_pair D E)) False) % 93.09/93.33 Clause #69 (by clausification #[68]): ∀ (a a_1 a_2 : Iota), % 93.09/93.33 Or (Eq (in a (skS.0 2 a_1)) False) (Eq (Not (∀ (E : Iota), Ne a (ordered_pair (skS.0 5 a a_2) E))) True) % 93.09/93.33 Clause #70 (by clausification #[69]): ∀ (a a_1 a_2 : Iota), % 93.09/93.33 Or (Eq (in a (skS.0 2 a_1)) False) (Eq (∀ (E : Iota), Ne a (ordered_pair (skS.0 5 a a_2) E)) False) % 93.09/93.33 Clause #71 (by clausification #[70]): ∀ (a a_1 a_2 a_3 : Iota), % 93.09/93.33 Or (Eq (in a (skS.0 2 a_1)) False) (Eq (Not (Ne a (ordered_pair (skS.0 5 a a_2) (skS.0 6 a a_2 a_3)))) True) % 93.09/93.33 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 a_3 : Iota), % 93.09/93.33 Or (Eq (in a (skS.0 2 a_1)) False) (Eq (Ne a (ordered_pair (skS.0 5 a a_2) (skS.0 6 a a_2 a_3))) False) % 93.09/93.33 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in a (skS.0 2 a_1)) False) (Eq a (ordered_pair (skS.0 5 a a_2) (skS.0 6 a a_2 a_3))) % 93.09/93.33 Clause #74 (by superposition #[73, 43]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 93.09/93.33 Or % 93.09/93.33 (Eq (skS.0 4 (skS.0 2 a) a_1 a_2) % 93.09/93.33 (ordered_pair (skS.0 5 (skS.0 4 (skS.0 2 a) a_1 a_2) a_3) (skS.0 6 (skS.0 4 (skS.0 2 a) a_1 a_2) a_3 a_4))) % 93.09/93.33 (Or (Eq (subset (skS.0 2 a) a_1) True) (Eq False True)) % 93.09/93.33 Clause #142 (by clausification #[74]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 93.09/93.33 Or % 93.09/93.33 (Eq (skS.0 4 (skS.0 2 a) a_1 a_2) % 93.09/93.33 (ordered_pair (skS.0 5 (skS.0 4 (skS.0 2 a) a_1 a_2) a_3) (skS.0 6 (skS.0 4 (skS.0 2 a) a_1 a_2) a_3 a_4))) % 93.09/93.33 (Eq (subset (skS.0 2 a) a_1) True) % 93.09/93.33 Clause #143 (by superposition #[142, 26]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 93.09/93.33 Or (Eq (subset (skS.0 2 a) a_1) True) % 93.09/93.33 (Or (Eq (in (skS.0 4 (skS.0 2 a) a_1 a_2) (skS.0 2 a_3)) False) % 93.09/93.33 (Eq (in (skS.0 4 (skS.0 2 a) a_1 a_2) (skS.0 3 a_3 a_4)) True)) % 93.09/93.33 Clause #2667 (by superposition #[143, 43]): ∀ (a a_1 a_2 a_3 : Iota), % 93.09/93.33 Or (Eq (subset (skS.0 2 a) a_1) True) % 93.09/93.33 (Or (Eq (in (skS.0 4 (skS.0 2 a) a_1 a_2) (skS.0 3 a a_3)) True) % 93.09/93.33 (Or (Eq (subset (skS.0 2 a) a_1) True) (Eq False True))) % 93.09/93.33 Clause #11742 (by clausification #[2667]): ∀ (a a_1 a_2 a_3 : Iota), % 93.09/93.33 Or (Eq (subset (skS.0 2 a) a_1) True) % 93.09/93.33 (Or (Eq (in (skS.0 4 (skS.0 2 a) a_1 a_2) (skS.0 3 a a_3)) True) (Eq (subset (skS.0 2 a) a_1) True)) % 93.09/93.33 Clause #11743 (by eliminate duplicate literals #[11742]): ∀ (a a_1 a_2 a_3 : Iota), % 93.09/93.33 Or (Eq (subset (skS.0 2 a) a_1) True) (Eq (in (skS.0 4 (skS.0 2 a) a_1 a_2) (skS.0 3 a a_3)) True) % 93.09/93.33 Clause #11744 (by superposition #[11743, 44]): ∀ (a a_1 : Iota), % 93.09/93.33 Or (Eq (subset (skS.0 2 a) (skS.0 3 a a_1)) True) (Or (Eq (subset (skS.0 2 a) (skS.0 3 a a_1)) True) (Eq True False)) % 93.09/93.33 Clause #11746 (by clausification #[11744]): ∀ (a a_1 : Iota), Or (Eq (subset (skS.0 2 a) (skS.0 3 a a_1)) True) (Eq (subset (skS.0 2 a) (skS.0 3 a a_1)) True) % 93.09/93.33 Clause #11747 (by eliminate duplicate literals #[11746]): ∀ (a a_1 : Iota), Eq (subset (skS.0 2 a) (skS.0 3 a a_1)) True % 93.09/93.33 Clause #11748 (by superposition #[11747, 21]): Eq True False % 93.09/93.33 Clause #11750 (by clausification #[11748]): False % 93.09/93.33 SZS output end Proof for theBenchmark.p 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