%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM532+1 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n023.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 07:56:40 PM UTC 2025 % Result : Theorem 4.46s 4.67s % Output : Proof 4.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : NUM532+1 : TPTP v9.2.0. Released v4.0.0. % 0.08/0.14 % Command : duper %s % 0.15/0.36 % Computer : n023.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 300 % 0.15/0.36 % DateTime : Fri Oct 3 07:42:23 EDT 2025 % 0.15/0.36 % CPUTime : % 4.46/4.67 SZS status Theorem for theBenchmark.p % 4.46/4.67 SZS output start Proof for theBenchmark.p % 4.46/4.67 Clause #9 (by assumption #[]): Eq % 4.46/4.67 (∀ (W0 : Iota), % 4.46/4.67 aSet0 W0 → % 4.46/4.67 ∀ (W1 : Iota), Iff (aSubsetOf0 W1 W0) (And (aSet0 W1) (∀ (W2 : Iota), aElementOf0 W2 W1 → aElementOf0 W2 W0))) % 4.46/4.67 True % 4.46/4.67 Clause #11 (by assumption #[]): Eq (aSet0 xA) True % 4.46/4.67 Clause #12 (by assumption #[]): Eq (Not (aSubsetOf0 xA xA)) True % 4.46/4.67 Clause #17 (by clausification #[12]): Eq (aSubsetOf0 xA xA) False % 4.46/4.67 Clause #59 (by clausification #[9]): ∀ (a : Iota), % 4.46/4.67 Eq % 4.46/4.67 (aSet0 a → % 4.46/4.67 ∀ (W1 : Iota), Iff (aSubsetOf0 W1 a) (And (aSet0 W1) (∀ (W2 : Iota), aElementOf0 W2 W1 → aElementOf0 W2 a))) % 4.46/4.67 True % 4.46/4.67 Clause #60 (by clausification #[59]): ∀ (a : Iota), % 4.46/4.67 Or (Eq (aSet0 a) False) % 4.46/4.67 (Eq (∀ (W1 : Iota), Iff (aSubsetOf0 W1 a) (And (aSet0 W1) (∀ (W2 : Iota), aElementOf0 W2 W1 → aElementOf0 W2 a))) % 4.46/4.67 True) % 4.46/4.67 Clause #61 (by clausification #[60]): ∀ (a a_1 : Iota), % 4.46/4.67 Or (Eq (aSet0 a) False) % 4.46/4.67 (Eq (Iff (aSubsetOf0 a_1 a) (And (aSet0 a_1) (∀ (W2 : Iota), aElementOf0 W2 a_1 → aElementOf0 W2 a))) True) % 4.46/4.67 Clause #62 (by clausification #[61]): ∀ (a a_1 : Iota), % 4.46/4.67 Or (Eq (aSet0 a) False) % 4.46/4.67 (Or (Eq (aSubsetOf0 a_1 a) True) % 4.46/4.67 (Eq (And (aSet0 a_1) (∀ (W2 : Iota), aElementOf0 W2 a_1 → aElementOf0 W2 a)) False)) % 4.46/4.67 Clause #64 (by clausification #[62]): ∀ (a a_1 : Iota), % 4.46/4.67 Or (Eq (aSet0 a) False) % 4.46/4.67 (Or (Eq (aSubsetOf0 a_1 a) True) % 4.46/4.67 (Or (Eq (aSet0 a_1) False) (Eq (∀ (W2 : Iota), aElementOf0 W2 a_1 → aElementOf0 W2 a) False))) % 4.46/4.67 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota), % 4.46/4.67 Or (Eq (aSet0 a) False) % 4.46/4.67 (Or (Eq (aSubsetOf0 a_1 a) True) % 4.46/4.67 (Or (Eq (aSet0 a_1) False) % 4.46/4.67 (Eq (Not (aElementOf0 (skS.0 1 a_1 a a_2) a_1 → aElementOf0 (skS.0 1 a_1 a a_2) a)) True))) % 4.46/4.67 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 : Iota), % 4.46/4.67 Or (Eq (aSet0 a) False) % 4.46/4.67 (Or (Eq (aSubsetOf0 a_1 a) True) % 4.46/4.67 (Or (Eq (aSet0 a_1) False) (Eq (aElementOf0 (skS.0 1 a_1 a a_2) a_1 → aElementOf0 (skS.0 1 a_1 a a_2) a) False))) % 4.46/4.67 Clause #67 (by clausification #[66]): ∀ (a a_1 a_2 : Iota), % 4.46/4.67 Or (Eq (aSet0 a) False) % 4.46/4.67 (Or (Eq (aSubsetOf0 a_1 a) True) (Or (Eq (aSet0 a_1) False) (Eq (aElementOf0 (skS.0 1 a_1 a a_2) a_1) True))) % 4.46/4.67 Clause #68 (by clausification #[66]): ∀ (a a_1 a_2 : Iota), % 4.46/4.67 Or (Eq (aSet0 a) False) % 4.46/4.67 (Or (Eq (aSubsetOf0 a_1 a) True) (Or (Eq (aSet0 a_1) False) (Eq (aElementOf0 (skS.0 1 a_1 a a_2) a) False))) % 4.46/4.67 Clause #69 (by superposition #[67, 11]): ∀ (a a_1 : Iota), % 4.46/4.67 Or (Eq (aSubsetOf0 a xA) True) % 4.46/4.67 (Or (Eq (aSet0 a) False) (Or (Eq (aElementOf0 (skS.0 1 a xA a_1) a) True) (Eq False True))) % 4.46/4.67 Clause #100 (by superposition #[68, 11]): ∀ (a a_1 : Iota), % 4.46/4.67 Or (Eq (aSubsetOf0 a xA) True) % 4.46/4.67 (Or (Eq (aSet0 a) False) (Or (Eq (aElementOf0 (skS.0 1 a xA a_1) xA) False) (Eq False True))) % 4.46/4.67 Clause #104 (by clausification #[69]): ∀ (a a_1 : Iota), Or (Eq (aSubsetOf0 a xA) True) (Or (Eq (aSet0 a) False) (Eq (aElementOf0 (skS.0 1 a xA a_1) a) True)) % 4.46/4.67 Clause #105 (by superposition #[104, 11]): ∀ (a : Iota), Or (Eq (aSubsetOf0 xA xA) True) (Or (Eq (aElementOf0 (skS.0 1 xA xA a) xA) True) (Eq False True)) % 4.46/4.67 Clause #117 (by clausification #[105]): ∀ (a : Iota), Or (Eq (aSubsetOf0 xA xA) True) (Eq (aElementOf0 (skS.0 1 xA xA a) xA) True) % 4.46/4.67 Clause #118 (by forward demodulation #[117, 17]): ∀ (a : Iota), Or (Eq False True) (Eq (aElementOf0 (skS.0 1 xA xA a) xA) True) % 4.46/4.67 Clause #119 (by clausification #[118]): ∀ (a : Iota), Eq (aElementOf0 (skS.0 1 xA xA a) xA) True % 4.46/4.67 Clause #122 (by clausification #[100]): ∀ (a a_1 : Iota), % 4.46/4.67 Or (Eq (aSubsetOf0 a xA) True) (Or (Eq (aSet0 a) False) (Eq (aElementOf0 (skS.0 1 a xA a_1) xA) False)) % 4.46/4.67 Clause #123 (by superposition #[122, 11]): ∀ (a : Iota), Or (Eq (aSubsetOf0 xA xA) True) (Or (Eq (aElementOf0 (skS.0 1 xA xA a) xA) False) (Eq False True)) % 4.46/4.67 Clause #137 (by clausification #[123]): ∀ (a : Iota), Or (Eq (aSubsetOf0 xA xA) True) (Eq (aElementOf0 (skS.0 1 xA xA a) xA) False) % 4.46/4.67 Clause #138 (by forward demodulation #[137, 17]): ∀ (a : Iota), Or (Eq False True) (Eq (aElementOf0 (skS.0 1 xA xA a) xA) False) % 4.46/4.67 Clause #139 (by clausification #[138]): ∀ (a : Iota), Eq (aElementOf0 (skS.0 1 xA xA a) xA) False % 4.46/4.67 Clause #140 (by superposition #[139, 119]): Eq False True % 4.46/4.67 Clause #141 (by clausification #[140]): False % 4.46/4.67 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------