%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU230+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n012.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 08:01:11 PM UTC 2025 % Result : Theorem 4.20s 4.37s % Output : Proof 4.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SEU230+1 : TPTP v9.2.0. Released v3.3.0. % 0.04/0.13 % Command : duper %s % 0.13/0.34 % Computer : n012.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Oct 3 04:30:08 EDT 2025 % 0.13/0.34 % CPUTime : % 4.20/4.37 SZS status Theorem for theBenchmark.p % 4.20/4.37 SZS output start Proof for theBenchmark.p % 4.20/4.37 Clause #5 (by assumption #[]): Eq (∀ (A : Iota), Eq (succ A) (set_union2 A (singleton A))) True % 4.20/4.37 Clause #6 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq B (singleton A)) (∀ (C : Iota), Iff (in C B) (Eq C A))) True % 4.20/4.37 Clause #7 (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 % 4.20/4.37 Clause #27 (by assumption #[]): Eq (Not (∀ (A : Iota), in A (succ A))) True % 4.20/4.37 Clause #70 (by clausification #[27]): Eq (∀ (A : Iota), in A (succ A)) False % 4.20/4.37 Clause #71 (by clausification #[70]): ∀ (a : Iota), Eq (Not (in (skS.0 2 a) (succ (skS.0 2 a)))) True % 4.20/4.37 Clause #72 (by clausification #[71]): ∀ (a : Iota), Eq (in (skS.0 2 a) (succ (skS.0 2 a))) False % 4.20/4.37 Clause #91 (by clausification #[5]): ∀ (a : Iota), Eq (Eq (succ a) (set_union2 a (singleton a))) True % 4.20/4.37 Clause #92 (by clausification #[91]): ∀ (a : Iota), Eq (succ a) (set_union2 a (singleton a)) % 4.20/4.37 Clause #103 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq B (singleton a)) (∀ (C : Iota), Iff (in C B) (Eq C a))) True % 4.20/4.37 Clause #104 (by clausification #[103]): ∀ (a a_1 : Iota), Eq (Iff (Eq a (singleton a_1)) (∀ (C : Iota), Iff (in C a) (Eq C a_1))) True % 4.20/4.37 Clause #106 (by clausification #[104]): ∀ (a a_1 : Iota), Or (Eq (Eq a (singleton a_1)) False) (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) % 4.20/4.37 Clause #124 (by clausification #[7]): ∀ (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 % 4.20/4.37 Clause #125 (by clausification #[124]): ∀ (a a_1 : Iota), % 4.20/4.37 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 % 4.20/4.37 Clause #126 (by clausification #[125]): ∀ (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 % 4.20/4.37 Clause #128 (by clausification #[126]): ∀ (a a_1 a_2 : Iota), % 4.20/4.37 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) % 4.20/4.37 Clause #233 (by clausification #[106]): ∀ (a a_1 : Iota), Or (Eq (∀ (C : Iota), Iff (in C a) (Eq C a_1)) True) (Ne a (singleton a_1)) % 4.20/4.37 Clause #234 (by clausification #[233]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Eq (Iff (in a_2 a) (Eq a_2 a_1)) True) % 4.20/4.37 Clause #235 (by clausification #[234]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) True) (Eq (Eq a_2 a_1) False)) % 4.20/4.37 Clause #237 (by clausification #[235]): ∀ (a a_1 a_2 : Iota), Or (Ne a (singleton a_1)) (Or (Eq (in a_2 a) True) (Ne a_2 a_1)) % 4.20/4.37 Clause #238 (by destructive equality resolution #[237]): ∀ (a a_1 : Iota), Or (Eq (in a (singleton a_1)) True) (Ne a a_1) % 4.20/4.37 Clause #239 (by destructive equality resolution #[238]): ∀ (a : Iota), Eq (in a (singleton a)) True % 4.20/4.37 Clause #269 (by clausification #[128]): ∀ (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)) % 4.20/4.37 Clause #270 (by clausification #[269]): ∀ (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) % 4.20/4.37 Clause #271 (by clausification #[270]): ∀ (a a_1 a_2 a_3 : Iota), % 4.20/4.37 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)) % 4.20/4.37 Clause #273 (by clausification #[271]): ∀ (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)) % 4.20/4.37 Clause #275 (by destructive equality resolution #[273]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (set_union2 a_1 a_2)) True) (Eq (in a a_2) False) % 4.20/4.37 Clause #277 (by superposition #[275, 239]): ∀ (a a_1 : Iota), Or (Eq (in a (set_union2 a_1 (singleton a))) True) (Eq False True) % 4.20/4.37 Clause #280 (by clausification #[277]): ∀ (a a_1 : Iota), Eq (in a (set_union2 a_1 (singleton a))) True % 4.20/4.37 Clause #285 (by superposition #[280, 92]): ∀ (a : Iota), Eq (in a (succ a)) True % 4.20/4.37 Clause #289 (by superposition #[285, 72]): Eq True False % 4.20/4.37 Clause #294 (by clausification #[289]): False % 4.20/4.37 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------