%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET925+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n016.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 08:00:42 PM UTC 2025 % Result : Theorem 3.53s 3.70s % Output : Proof 3.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET925+1 : TPTP v9.2.0. Released v3.2.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n016.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 : Thu Oct 2 13:50:53 EDT 2025 % 0.13/0.34 % CPUTime : % 3.53/3.70 SZS status Theorem for theBenchmark.p % 3.53/3.70 SZS output start Proof for theBenchmark.p % 3.53/3.70 Clause #4 (by assumption #[]): Eq (Not (∀ (A B : Iota), Iff (Eq (set_difference (singleton A) B) empty_set) (in A B))) True % 3.53/3.70 Clause #5 (by assumption #[]): Eq (∀ (A B : Iota), Iff (Eq (set_difference (singleton A) B) empty_set) (in A B)) True % 3.53/3.70 Clause #14 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq (set_difference (singleton a) B) empty_set) (in a B)) True % 3.53/3.70 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Eq (Iff (Eq (set_difference (singleton a) a_1) empty_set) (in a a_1)) True % 3.53/3.70 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (Eq (set_difference (singleton a) a_1) empty_set) True) (Eq (in a a_1) False) % 3.53/3.70 Clause #17 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (Eq (set_difference (singleton a) a_1) empty_set) False) (Eq (in a a_1) True) % 3.53/3.70 Clause #18 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (set_difference (singleton a) a_1) empty_set) % 3.53/3.70 Clause #19 (by clausification #[4]): Eq (∀ (A B : Iota), Iff (Eq (set_difference (singleton A) B) empty_set) (in A B)) False % 3.53/3.70 Clause #20 (by clausification #[19]): ∀ (a : Iota), % 3.53/3.70 Eq (Not (∀ (B : Iota), Iff (Eq (set_difference (singleton (skS.0 2 a)) B) empty_set) (in (skS.0 2 a) B))) True % 3.53/3.70 Clause #21 (by clausification #[20]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (Eq (set_difference (singleton (skS.0 2 a)) B) empty_set) (in (skS.0 2 a) B)) False % 3.53/3.70 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), % 3.53/3.70 Eq % 3.53/3.70 (Not (Iff (Eq (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) empty_set) (in (skS.0 2 a) (skS.0 3 a a_1)))) % 3.53/3.70 True % 3.53/3.70 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), % 3.53/3.70 Eq (Iff (Eq (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) empty_set) (in (skS.0 2 a) (skS.0 3 a a_1))) % 3.53/3.70 False % 3.53/3.70 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), % 3.53/3.70 Or (Eq (Eq (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) empty_set) False) % 3.53/3.70 (Eq (in (skS.0 2 a) (skS.0 3 a a_1)) False) % 3.53/3.70 Clause #25 (by clausification #[23]): ∀ (a a_1 : Iota), % 3.53/3.70 Or (Eq (Eq (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) empty_set) True) % 3.53/3.70 (Eq (in (skS.0 2 a) (skS.0 3 a a_1)) True) % 3.53/3.70 Clause #26 (by clausification #[24]): ∀ (a a_1 : Iota), % 3.53/3.70 Or (Eq (in (skS.0 2 a) (skS.0 3 a a_1)) False) (Ne (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) empty_set) % 3.53/3.70 Clause #27 (by forward contextual literal cutting #[26, 18]): ∀ (a a_1 : Iota), Eq (in (skS.0 2 a) (skS.0 3 a a_1)) False % 3.53/3.70 Clause #28 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) True) (Ne (set_difference (singleton a) a_1) empty_set) % 3.53/3.70 Clause #29 (by clausification #[25]): ∀ (a a_1 : Iota), % 3.53/3.70 Or (Eq (in (skS.0 2 a) (skS.0 3 a a_1)) True) (Eq (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) empty_set) % 3.53/3.70 Clause #30 (by forward demodulation #[29, 27]): ∀ (a a_1 : Iota), Or (Eq False True) (Eq (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) empty_set) % 3.53/3.70 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (set_difference (singleton (skS.0 2 a)) (skS.0 3 a a_1)) empty_set % 3.53/3.70 Clause #32 (by superposition #[31, 28]): ∀ (a a_1 : Iota), Or (Eq (in (skS.0 2 a) (skS.0 3 a a_1)) True) (Ne empty_set empty_set) % 3.53/3.70 Clause #33 (by eliminate resolved literals #[32]): ∀ (a a_1 : Iota), Eq (in (skS.0 2 a) (skS.0 3 a a_1)) True % 3.53/3.70 Clause #34 (by superposition #[33, 27]): Eq True False % 3.53/3.70 Clause #37 (by clausification #[34]): False % 3.53/3.70 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------