%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM405+1 : TPTP v9.2.0. Released v3.2.0. % 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 07:56:26 PM UTC 2025 % Result : Theorem 7.70s 7.90s % Output : Proof 7.70s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : NUM405+1 : TPTP v9.2.0. Released v3.2.0. % 0.06/0.13 % Command : duper %s % 0.13/0.34 % Computer : n017.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 07:28:38 EDT 2025 % 0.13/0.34 % CPUTime : % 7.70/7.90 SZS status Theorem for theBenchmark.p % 7.70/7.90 SZS output start Proof for theBenchmark.p % 7.70/7.90 Clause #25 (by assumption #[]): Eq (∀ (A : Iota), Exists fun B => ∀ (C : Iota), Iff (in C B) (And (in C A) (ordinal C))) True % 7.70/7.90 Clause #28 (by assumption #[]): Eq (∀ (A : Iota), Not (∀ (B : Iota), Iff (in B A) (ordinal B))) True % 7.70/7.90 Clause #29 (by assumption #[]): Eq (Not (∀ (A : Iota), Not (∀ (B : Iota), ordinal B → in B A))) True % 7.70/7.90 Clause #81 (by clausification #[29]): Eq (∀ (A : Iota), Not (∀ (B : Iota), ordinal B → in B A)) False % 7.70/7.90 Clause #82 (by clausification #[81]): ∀ (a : Iota), Eq (Not (Not (∀ (B : Iota), ordinal B → in B (skS.0 4 a)))) True % 7.70/7.90 Clause #83 (by clausification #[82]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), ordinal B → in B (skS.0 4 a))) False % 7.70/7.90 Clause #84 (by clausification #[83]): ∀ (a : Iota), Eq (∀ (B : Iota), ordinal B → in B (skS.0 4 a)) True % 7.70/7.90 Clause #85 (by clausification #[84]): ∀ (a a_1 : Iota), Eq (ordinal a → in a (skS.0 4 a_1)) True % 7.70/7.90 Clause #86 (by clausification #[85]): ∀ (a a_1 : Iota), Or (Eq (ordinal a) False) (Eq (in a (skS.0 4 a_1)) True) % 7.70/7.90 Clause #140 (by clausification #[28]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), Iff (in B a) (ordinal B))) True % 7.70/7.90 Clause #141 (by clausification #[140]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (in B a) (ordinal B)) False % 7.70/7.90 Clause #142 (by clausification #[141]): ∀ (a a_1 : Iota), Eq (Not (Iff (in (skS.0 9 a a_1) a) (ordinal (skS.0 9 a a_1)))) True % 7.70/7.90 Clause #143 (by clausification #[142]): ∀ (a a_1 : Iota), Eq (Iff (in (skS.0 9 a a_1) a) (ordinal (skS.0 9 a a_1))) False % 7.70/7.90 Clause #144 (by clausification #[143]): ∀ (a a_1 : Iota), Or (Eq (in (skS.0 9 a a_1) a) False) (Eq (ordinal (skS.0 9 a a_1)) False) % 7.70/7.90 Clause #145 (by clausification #[143]): ∀ (a a_1 : Iota), Or (Eq (in (skS.0 9 a a_1) a) True) (Eq (ordinal (skS.0 9 a a_1)) True) % 7.70/7.90 Clause #212 (by clausification #[25]): ∀ (a : Iota), Eq (Exists fun B => ∀ (C : Iota), Iff (in C B) (And (in C a) (ordinal C))) True % 7.70/7.90 Clause #213 (by clausification #[212]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), Iff (in C (skS.0 16 a a_1)) (And (in C a) (ordinal C))) True % 7.70/7.90 Clause #214 (by clausification #[213]): ∀ (a a_1 a_2 : Iota), Eq (Iff (in a (skS.0 16 a_1 a_2)) (And (in a a_1) (ordinal a))) True % 7.70/7.90 Clause #215 (by clausification #[214]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 16 a_1 a_2)) True) (Eq (And (in a a_1) (ordinal a)) False) % 7.70/7.90 Clause #216 (by clausification #[214]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 16 a_1 a_2)) False) (Eq (And (in a a_1) (ordinal a)) True) % 7.70/7.90 Clause #217 (by clausification #[215]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 16 a_1 a_2)) True) (Or (Eq (in a a_1) False) (Eq (ordinal a) False)) % 7.70/7.90 Clause #291 (by clausification #[216]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 16 a_1 a_2)) False) (Eq (ordinal a) True) % 7.70/7.90 Clause #294 (by superposition #[291, 145]): ∀ (a a_1 a_2 : Iota), % 7.70/7.90 Or (Eq (ordinal (skS.0 9 (skS.0 16 a a_1) a_2)) True) % 7.70/7.90 (Or (Eq False True) (Eq (ordinal (skS.0 9 (skS.0 16 a a_1) a_2)) True)) % 7.70/7.90 Clause #447 (by clausification #[294]): ∀ (a a_1 a_2 : Iota), % 7.70/7.91 Or (Eq (ordinal (skS.0 9 (skS.0 16 a a_1) a_2)) True) (Eq (ordinal (skS.0 9 (skS.0 16 a a_1) a_2)) True) % 7.70/7.91 Clause #448 (by eliminate duplicate literals #[447]): ∀ (a a_1 a_2 : Iota), Eq (ordinal (skS.0 9 (skS.0 16 a a_1) a_2)) True % 7.70/7.91 Clause #451 (by superposition #[448, 86]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq True False) (Eq (in (skS.0 9 (skS.0 16 a a_1) a_2) (skS.0 4 a_3)) True) % 7.70/7.91 Clause #460 (by clausification #[451]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 9 (skS.0 16 a a_1) a_2) (skS.0 4 a_3)) True % 7.70/7.91 Clause #463 (by superposition #[460, 217]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 7.70/7.91 Or (Eq (in (skS.0 9 (skS.0 16 a a_1) a_2) (skS.0 16 (skS.0 4 a_3) a_4)) True) % 7.70/7.91 (Or (Eq True False) (Eq (ordinal (skS.0 9 (skS.0 16 a a_1) a_2)) False)) % 7.70/7.91 Clause #634 (by clausification #[463]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 7.70/7.91 Or (Eq (in (skS.0 9 (skS.0 16 a a_1) a_2) (skS.0 16 (skS.0 4 a_3) a_4)) True) % 7.70/7.91 (Eq (ordinal (skS.0 9 (skS.0 16 a a_1) a_2)) False) % 7.70/7.91 Clause #635 (by forward demodulation #[634, 448]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 7.70/7.91 Or (Eq (in (skS.0 9 (skS.0 16 a a_1) a_2) (skS.0 16 (skS.0 4 a_3) a_4)) True) (Eq True False) % 7.70/7.91 Clause #636 (by clausification #[635]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (in (skS.0 9 (skS.0 16 a a_1) a_2) (skS.0 16 (skS.0 4 a_3) a_4)) True % 7.70/7.91 Clause #638 (by superposition #[636, 144]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (ordinal (skS.0 9 (skS.0 16 (skS.0 4 a) a_1) a_2)) False) % 7.70/7.91 Clause #642 (by clausification #[638]): ∀ (a a_1 a_2 : Iota), Eq (ordinal (skS.0 9 (skS.0 16 (skS.0 4 a) a_1) a_2)) False % 7.70/7.91 Clause #643 (by superposition #[642, 448]): Eq False True % 7.70/7.91 Clause #644 (by clausification #[643]): False % 7.70/7.91 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------