%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU530^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n008.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 08:01:50 PM UTC 2025 % Result : Theorem 3.43s 3.67s % Output : Proof 3.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SEU530^2 : TPTP v9.2.0. Released v3.7.0. % 0.06/0.13 % Command : duper %s % 0.13/0.34 % Computer : n008.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 04:49:23 EDT 2025 % 0.13/0.34 % CPUTime : % 3.43/3.67 SZS status Theorem for theBenchmark.p % 3.43/3.67 SZS output start Proof for theBenchmark.p % 3.43/3.67 Clause #0 (by assumption #[]): Eq (Eq uniqinunit (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy)) True % 3.43/3.67 Clause #1 (by assumption #[]): Eq (Eq eqinunit (∀ (Xx Xy : Iota), Eq Xx Xy → in Xx (setadjoin Xy emptyset))) True % 3.43/3.67 Clause #2 (by assumption #[]): Eq (Not (uniqinunit → eqinunit → ∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → in Xy (setadjoin Xx emptyset))) True % 3.43/3.67 Clause #3 (by clausification #[0]): Eq uniqinunit (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy) % 3.43/3.67 Clause #17 (by clausification #[1]): Eq eqinunit (∀ (Xx Xy : Iota), Eq Xx Xy → in Xx (setadjoin Xy emptyset)) % 3.43/3.67 Clause #21 (by clausification #[2]): Eq (uniqinunit → eqinunit → ∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → in Xy (setadjoin Xx emptyset)) False % 3.43/3.67 Clause #22 (by clausification #[21]): Eq uniqinunit True % 3.43/3.67 Clause #23 (by clausification #[21]): Eq (eqinunit → ∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → in Xy (setadjoin Xx emptyset)) False % 3.43/3.67 Clause #24 (by backward demodulation #[22, 3]): Eq True (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy) % 3.43/3.67 Clause #27 (by clausification #[24]): ∀ (a : Iota), Eq (∀ (Xy : Iota), in a (setadjoin Xy emptyset) → Eq a Xy) True % 3.43/3.67 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (in a (setadjoin a_1 emptyset) → Eq a a_1) True % 3.43/3.67 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Or (Eq (in a (setadjoin a_1 emptyset)) False) (Eq (Eq a a_1) True) % 3.43/3.67 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Or (Eq (in a (setadjoin a_1 emptyset)) False) (Eq a a_1) % 3.43/3.67 Clause #31 (by clausification #[23]): Eq eqinunit True % 3.43/3.67 Clause #32 (by clausification #[23]): Eq (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → in Xy (setadjoin Xx emptyset)) False % 3.43/3.67 Clause #33 (by backward demodulation #[31, 17]): Eq True (∀ (Xx Xy : Iota), Eq Xx Xy → in Xx (setadjoin Xy emptyset)) % 3.43/3.67 Clause #34 (by clausification #[33]): ∀ (a : Iota), Eq (∀ (Xy : Iota), Eq a Xy → in a (setadjoin Xy emptyset)) True % 3.43/3.67 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), Eq (Eq a a_1 → in a (setadjoin a_1 emptyset)) True % 3.43/3.67 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Or (Eq (Eq a a_1) False) (Eq (in a (setadjoin a_1 emptyset)) True) % 3.43/3.67 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (in a (setadjoin a_1 emptyset)) True) (Ne a a_1) % 3.43/3.67 Clause #38 (by destructive equality resolution #[37]): ∀ (a : Iota), Eq (in a (setadjoin a emptyset)) True % 3.43/3.67 Clause #39 (by clausification #[32]): ∀ (a : Iota), % 3.43/3.67 Eq (Not (∀ (Xy : Iota), in (skS.0 2 a) (setadjoin Xy emptyset) → in Xy (setadjoin (skS.0 2 a) emptyset))) True % 3.43/3.67 Clause #40 (by clausification #[39]): ∀ (a : Iota), Eq (∀ (Xy : Iota), in (skS.0 2 a) (setadjoin Xy emptyset) → in Xy (setadjoin (skS.0 2 a) emptyset)) False % 3.43/3.67 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), % 3.43/3.67 Eq (Not (in (skS.0 2 a) (setadjoin (skS.0 3 a a_1) emptyset) → in (skS.0 3 a a_1) (setadjoin (skS.0 2 a) emptyset))) % 3.43/3.67 True % 3.43/3.67 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), % 3.43/3.67 Eq (in (skS.0 2 a) (setadjoin (skS.0 3 a a_1) emptyset) → in (skS.0 3 a a_1) (setadjoin (skS.0 2 a) emptyset)) False % 3.43/3.67 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota), Eq (in (skS.0 2 a) (setadjoin (skS.0 3 a a_1) emptyset)) True % 3.43/3.67 Clause #44 (by clausification #[42]): ∀ (a a_1 : Iota), Eq (in (skS.0 3 a a_1) (setadjoin (skS.0 2 a) emptyset)) False % 3.43/3.67 Clause #45 (by superposition #[43, 30]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (skS.0 2 a) (skS.0 3 a a_1)) % 3.43/3.67 Clause #62 (by clausification #[45]): ∀ (a a_1 : Iota), Eq (skS.0 2 a) (skS.0 3 a a_1) % 3.43/3.67 Clause #64 (by forward demodulation #[44, 62]): ∀ (a : Iota), Eq (in (skS.0 2 a) (setadjoin (skS.0 2 a) emptyset)) False % 3.43/3.67 Clause #65 (by superposition #[64, 38]): Eq False True % 3.43/3.67 Clause #66 (by clausification #[65]): False % 3.43/3.67 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------