%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU124+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n021.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 08:00:54 PM UTC 2025 % Result : Theorem 5.22s 5.38s % Output : Proof 5.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.14 % Problem : SEU124+1 : TPTP v9.2.0. Released v3.3.0. % 0.13/0.15 % Command : duper %s % 0.16/0.35 % Computer : n021.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Fri Oct 3 06:21:23 EDT 2025 % 0.16/0.36 % CPUTime : % 5.22/5.38 SZS status Theorem for theBenchmark.p % 5.22/5.38 SZS output start Proof for theBenchmark.p % 5.22/5.38 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Eq (set_union2 A B) (set_union2 B A)) True % 5.22/5.38 Clause #2 (by assumption #[]): Eq (∀ (A B C : Iota), Iff (Eq C (set_union2 A B)) (∀ (D : Iota), Iff (in D C) (Or (in D A) (in D B)))) True % 5.22/5.38 Clause #3 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset A B) (∀ (C : Iota), in C A → in C B)) True % 5.22/5.38 Clause #15 (by assumption #[]): Eq (Not (∀ (A B : Iota), subset A (set_union2 A B))) True % 5.22/5.38 Clause #42 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (set_union2 a B) (set_union2 B a)) True % 5.22/5.38 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota), Eq (Eq (set_union2 a a_1) (set_union2 a_1 a)) True % 5.22/5.38 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota), Eq (set_union2 a a_1) (set_union2 a_1 a) % 5.22/5.38 Clause #49 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B C : Iota), Iff (Eq C (set_union2 a B)) (∀ (D : Iota), Iff (in D C) (Or (in D a) (in D B)))) True % 5.22/5.38 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota), % 5.22/5.38 Eq (∀ (C : Iota), Iff (Eq C (set_union2 a a_1)) (∀ (D : Iota), Iff (in D C) (Or (in D a) (in D a_1)))) True % 5.22/5.38 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), Eq (Iff (Eq a (set_union2 a_1 a_2)) (∀ (D : Iota), Iff (in D a) (Or (in D a_1) (in D a_2)))) True % 5.22/5.38 Clause #53 (by clausification #[51]): ∀ (a a_1 a_2 : Iota), % 5.22/5.38 Or (Eq (Eq a (set_union2 a_1 a_2)) False) (Eq (∀ (D : Iota), Iff (in D a) (Or (in D a_1) (in D a_2))) True) % 5.22/5.38 Clause #68 (by clausification #[15]): Eq (∀ (A B : Iota), subset A (set_union2 A B)) False % 5.22/5.38 Clause #69 (by clausification #[68]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), subset (skS.0 3 a) (set_union2 (skS.0 3 a) B))) True % 5.22/5.38 Clause #70 (by clausification #[69]): ∀ (a : Iota), Eq (∀ (B : Iota), subset (skS.0 3 a) (set_union2 (skS.0 3 a) B)) False % 5.22/5.38 Clause #71 (by clausification #[70]): ∀ (a a_1 : Iota), Eq (Not (subset (skS.0 3 a) (set_union2 (skS.0 3 a) (skS.0 4 a a_1)))) True % 5.22/5.38 Clause #72 (by clausification #[71]): ∀ (a a_1 : Iota), Eq (subset (skS.0 3 a) (set_union2 (skS.0 3 a) (skS.0 4 a a_1))) False % 5.22/5.38 Clause #77 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset a B) (∀ (C : Iota), in C a → in C B)) True % 5.22/5.38 Clause #78 (by clausification #[77]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (C : Iota), in C a → in C a_1)) True % 5.22/5.38 Clause #79 (by clausification #[78]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Eq (∀ (C : Iota), in C a → in C a_1) False) % 5.22/5.38 Clause #81 (by clausification #[79]): ∀ (a a_1 a_2 : Iota), % 5.22/5.38 Or (Eq (subset a a_1) True) (Eq (Not (in (skS.0 5 a a_1 a_2) a → in (skS.0 5 a a_1 a_2) a_1)) True) % 5.22/5.38 Clause #82 (by clausification #[81]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 5 a a_1 a_2) a → in (skS.0 5 a a_1 a_2) a_1) False) % 5.22/5.38 Clause #83 (by clausification #[82]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 5 a a_1 a_2) a) True) % 5.22/5.38 Clause #84 (by clausification #[82]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 5 a a_1 a_2) a_1) False) % 5.22/5.38 Clause #102 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), Or (Eq (∀ (D : Iota), Iff (in D a) (Or (in D a_1) (in D a_2))) True) (Ne a (set_union2 a_1 a_2)) % 5.22/5.38 Clause #103 (by clausification #[102]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (set_union2 a_1 a_2)) (Eq (Iff (in a_3 a) (Or (in a_3 a_1) (in a_3 a_2))) True) % 5.22/5.38 Clause #104 (by clausification #[103]): ∀ (a a_1 a_2 a_3 : Iota), % 5.22/5.38 Or (Ne a (set_union2 a_1 a_2)) (Or (Eq (in a_3 a) True) (Eq (Or (in a_3 a_1) (in a_3 a_2)) False)) % 5.22/5.38 Clause #106 (by clausification #[104]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (set_union2 a_1 a_2)) (Or (Eq (in a_3 a) True) (Eq (in a_3 a_2) False)) % 5.22/5.38 Clause #108 (by destructive equality resolution #[106]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (set_union2 a_1 a_2)) True) (Eq (in a a_2) False) % 5.22/5.38 Clause #109 (by superposition #[108, 83]): ∀ (a a_1 a_2 a_3 : Iota), % 5.22/5.38 Or (Eq (in (skS.0 5 a a_1 a_2) (set_union2 a_3 a)) True) (Or (Eq (subset a a_1) True) (Eq False True)) % 5.22/5.38 Clause #162 (by clausification #[109]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in (skS.0 5 a a_1 a_2) (set_union2 a_3 a)) True) (Eq (subset a a_1) True) % 5.22/5.38 Clause #163 (by superposition #[162, 84]): ∀ (a a_1 : Iota), % 5.22/5.38 Or (Eq (subset a (set_union2 a_1 a)) True) (Or (Eq (subset a (set_union2 a_1 a)) True) (Eq True False)) % 5.22/5.38 Clause #182 (by clausification #[163]): ∀ (a a_1 : Iota), Or (Eq (subset a (set_union2 a_1 a)) True) (Eq (subset a (set_union2 a_1 a)) True) % 5.22/5.38 Clause #183 (by eliminate duplicate literals #[182]): ∀ (a a_1 : Iota), Eq (subset a (set_union2 a_1 a)) True % 5.22/5.38 Clause #185 (by superposition #[183, 44]): ∀ (a a_1 : Iota), Eq (subset a (set_union2 a a_1)) True % 5.22/5.38 Clause #187 (by superposition #[185, 72]): Eq True False % 5.22/5.38 Clause #190 (by clausification #[187]): False % 5.22/5.38 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------