%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU127+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n017.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 08:00:55 PM UTC 2025 % Result : Theorem 4.00s 4.16s % Output : Proof 4.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU127+1 : TPTP v9.2.0. Released v3.3.0. % 0.03/0.13 % Command : duper %s % 0.12/0.34 % Computer : n017.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 05:28:38 EDT 2025 % 0.12/0.34 % CPUTime : % 4.00/4.16 SZS status Theorem for theBenchmark.p % 4.00/4.16 SZS output start Proof for theBenchmark.p % 4.00/4.16 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Eq (set_intersection2 A B) (set_intersection2 B A)) True % 4.00/4.16 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset A B) (∀ (C : Iota), in C A → in C B)) True % 4.00/4.16 Clause #3 (by assumption #[]): Eq (∀ (A B C : Iota), Iff (Eq C (set_intersection2 A B)) (∀ (D : Iota), Iff (in D C) (And (in D A) (in D B)))) True % 4.00/4.16 Clause #10 (by assumption #[]): Eq (Not (∀ (A B : Iota), subset (set_intersection2 A B) A)) True % 4.00/4.16 Clause #37 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (set_intersection2 a B) (set_intersection2 B a)) True % 4.00/4.16 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), Eq (Eq (set_intersection2 a a_1) (set_intersection2 a_1 a)) True % 4.00/4.16 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Eq (set_intersection2 a a_1) (set_intersection2 a_1 a) % 4.00/4.16 Clause #42 (by clausification #[10]): Eq (∀ (A B : Iota), subset (set_intersection2 A B) A) False % 4.00/4.16 Clause #43 (by clausification #[42]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), subset (set_intersection2 (skS.0 2 a) B) (skS.0 2 a))) True % 4.00/4.16 Clause #44 (by clausification #[43]): ∀ (a : Iota), Eq (∀ (B : Iota), subset (set_intersection2 (skS.0 2 a) B) (skS.0 2 a)) False % 4.00/4.16 Clause #45 (by clausification #[44]): ∀ (a a_1 : Iota), Eq (Not (subset (set_intersection2 (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 2 a))) True % 4.00/4.16 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), Eq (subset (set_intersection2 (skS.0 2 a) (skS.0 3 a a_1)) (skS.0 2 a)) False % 4.00/4.16 Clause #51 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset a B) (∀ (C : Iota), in C a → in C B)) True % 4.00/4.16 Clause #52 (by clausification #[51]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (C : Iota), in C a → in C a_1)) True % 4.00/4.16 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Eq (∀ (C : Iota), in C a → in C a_1) False) % 4.00/4.16 Clause #55 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), % 4.00/4.16 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) % 4.00/4.16 Clause #56 (by clausification #[55]): ∀ (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) % 4.00/4.16 Clause #57 (by clausification #[56]): ∀ (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) % 4.00/4.16 Clause #58 (by clausification #[56]): ∀ (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) % 4.00/4.16 Clause #61 (by clausification #[3]): ∀ (a : Iota), % 4.00/4.16 Eq (∀ (B C : Iota), Iff (Eq C (set_intersection2 a B)) (∀ (D : Iota), Iff (in D C) (And (in D a) (in D B)))) True % 4.00/4.16 Clause #62 (by clausification #[61]): ∀ (a a_1 : Iota), % 4.00/4.16 Eq (∀ (C : Iota), Iff (Eq C (set_intersection2 a a_1)) (∀ (D : Iota), Iff (in D C) (And (in D a) (in D a_1)))) True % 4.00/4.16 Clause #63 (by clausification #[62]): ∀ (a a_1 a_2 : Iota), % 4.00/4.16 Eq (Iff (Eq a (set_intersection2 a_1 a_2)) (∀ (D : Iota), Iff (in D a) (And (in D a_1) (in D a_2)))) True % 4.00/4.16 Clause #65 (by clausification #[63]): ∀ (a a_1 a_2 : Iota), % 4.00/4.16 Or (Eq (Eq a (set_intersection2 a_1 a_2)) False) (Eq (∀ (D : Iota), Iff (in D a) (And (in D a_1) (in D a_2))) True) % 4.00/4.16 Clause #95 (by clausification #[65]): ∀ (a a_1 a_2 : Iota), % 4.00/4.16 Or (Eq (∀ (D : Iota), Iff (in D a) (And (in D a_1) (in D a_2))) True) (Ne a (set_intersection2 a_1 a_2)) % 4.00/4.16 Clause #96 (by clausification #[95]): ∀ (a a_1 a_2 a_3 : Iota), % 4.00/4.16 Or (Ne a (set_intersection2 a_1 a_2)) (Eq (Iff (in a_3 a) (And (in a_3 a_1) (in a_3 a_2))) True) % 4.00/4.16 Clause #98 (by clausification #[96]): ∀ (a a_1 a_2 a_3 : Iota), % 4.00/4.16 Or (Ne a (set_intersection2 a_1 a_2)) (Or (Eq (in a_3 a) False) (Eq (And (in a_3 a_1) (in a_3 a_2)) True)) % 4.00/4.16 Clause #102 (by clausification #[98]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (set_intersection2 a_1 a_2)) (Or (Eq (in a_3 a) False) (Eq (in a_3 a_2) True)) % 4.00/4.16 Clause #104 (by destructive equality resolution #[102]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (set_intersection2 a_1 a_2)) False) (Eq (in a a_2) True) % 4.00/4.16 Clause #105 (by superposition #[104, 57]): ∀ (a a_1 a_2 a_3 : Iota), % 4.00/4.17 Or (Eq (in (skS.0 4 (set_intersection2 a a_1) a_2 a_3) a_1) True) % 4.00/4.17 (Or (Eq (subset (set_intersection2 a a_1) a_2) True) (Eq False True)) % 4.00/4.17 Clause #109 (by clausification #[105]): ∀ (a a_1 a_2 a_3 : Iota), % 4.00/4.17 Or (Eq (in (skS.0 4 (set_intersection2 a a_1) a_2 a_3) a_1) True) (Eq (subset (set_intersection2 a a_1) a_2) True) % 4.00/4.17 Clause #113 (by superposition #[109, 58]): ∀ (a a_1 : Iota), % 4.00/4.17 Or (Eq (subset (set_intersection2 a a_1) a_1) True) % 4.00/4.17 (Or (Eq (subset (set_intersection2 a a_1) a_1) True) (Eq True False)) % 4.00/4.17 Clause #149 (by clausification #[113]): ∀ (a a_1 : Iota), Or (Eq (subset (set_intersection2 a a_1) a_1) True) (Eq (subset (set_intersection2 a a_1) a_1) True) % 4.00/4.17 Clause #150 (by eliminate duplicate literals #[149]): ∀ (a a_1 : Iota), Eq (subset (set_intersection2 a a_1) a_1) True % 4.00/4.17 Clause #153 (by superposition #[150, 39]): ∀ (a a_1 : Iota), Eq (subset (set_intersection2 a a_1) a) True % 4.00/4.17 Clause #155 (by superposition #[153, 46]): Eq True False % 4.00/4.17 Clause #161 (by clausification #[155]): False % 4.00/4.17 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------