%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU158+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n015.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 08:01:00 PM UTC 2025 % Result : Theorem 3.78s 3.93s % Output : Proof 3.78s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU158+1 : TPTP v9.2.0. Released v3.3.0. % 0.03/0.14 % Command : duper %s % 0.14/0.35 % Computer : n015.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Fri Oct 3 04:09:08 EDT 2025 % 0.14/0.35 % CPUTime : % 3.78/3.93 SZS status Theorem for theBenchmark.p % 3.78/3.93 SZS output start Proof for theBenchmark.p % 3.78/3.93 Clause #3 (by assumption #[]): Eq (Not (∀ (A B : Iota), Iff (subset (singleton A) B) (in A B))) True % 3.78/3.93 Clause #4 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset (singleton A) B) (in A B)) True % 3.78/3.93 Clause #11 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset (singleton a) B) (in a B)) True % 3.78/3.93 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Eq (Iff (subset (singleton a) a_1) (in a a_1)) True % 3.78/3.93 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Or (Eq (subset (singleton a) a_1) True) (Eq (in a a_1) False) % 3.78/3.93 Clause #14 (by clausification #[12]): ∀ (a a_1 : Iota), Or (Eq (subset (singleton a) a_1) False) (Eq (in a a_1) True) % 3.78/3.93 Clause #16 (by clausification #[3]): Eq (∀ (A B : Iota), Iff (subset (singleton A) B) (in A B)) False % 3.78/3.93 Clause #17 (by clausification #[16]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), Iff (subset (singleton (skS.0 0 a)) B) (in (skS.0 0 a) B))) True % 3.78/3.93 Clause #18 (by clausification #[17]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset (singleton (skS.0 0 a)) B) (in (skS.0 0 a) B)) False % 3.78/3.93 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Eq (Not (Iff (subset (singleton (skS.0 0 a)) (skS.0 1 a a_1)) (in (skS.0 0 a) (skS.0 1 a a_1)))) True % 3.78/3.93 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (Iff (subset (singleton (skS.0 0 a)) (skS.0 1 a a_1)) (in (skS.0 0 a) (skS.0 1 a a_1))) False % 3.78/3.93 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), % 3.78/3.93 Or (Eq (subset (singleton (skS.0 0 a)) (skS.0 1 a a_1)) False) (Eq (in (skS.0 0 a) (skS.0 1 a a_1)) False) % 3.78/3.93 Clause #22 (by clausification #[20]): ∀ (a a_1 : Iota), % 3.78/3.93 Or (Eq (subset (singleton (skS.0 0 a)) (skS.0 1 a a_1)) True) (Eq (in (skS.0 0 a) (skS.0 1 a a_1)) True) % 3.78/3.93 Clause #29 (by superposition #[22, 14]): ∀ (a a_1 : Iota), % 3.78/3.93 Or (Eq (in (skS.0 0 a) (skS.0 1 a a_1)) True) (Or (Eq True False) (Eq (in (skS.0 0 a) (skS.0 1 a a_1)) True)) % 3.78/3.93 Clause #31 (by clausification #[29]): ∀ (a a_1 : Iota), Or (Eq (in (skS.0 0 a) (skS.0 1 a a_1)) True) (Eq (in (skS.0 0 a) (skS.0 1 a a_1)) True) % 3.78/3.93 Clause #32 (by eliminate duplicate literals #[31]): ∀ (a a_1 : Iota), Eq (in (skS.0 0 a) (skS.0 1 a a_1)) True % 3.78/3.93 Clause #33 (by backward demodulation #[32, 21]): ∀ (a a_1 : Iota), Or (Eq (subset (singleton (skS.0 0 a)) (skS.0 1 a a_1)) False) (Eq True False) % 3.78/3.93 Clause #36 (by superposition #[32, 13]): ∀ (a a_1 : Iota), Or (Eq (subset (singleton (skS.0 0 a)) (skS.0 1 a a_1)) True) (Eq True False) % 3.78/3.93 Clause #38 (by clausification #[36]): ∀ (a a_1 : Iota), Eq (subset (singleton (skS.0 0 a)) (skS.0 1 a a_1)) True % 3.78/3.93 Clause #40 (by clausification #[33]): ∀ (a a_1 : Iota), Eq (subset (singleton (skS.0 0 a)) (skS.0 1 a a_1)) False % 3.78/3.93 Clause #41 (by superposition #[40, 38]): Eq False True % 3.78/3.93 Clause #42 (by clausification #[41]): False % 3.78/3.93 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------