%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU552^2 : TPTP v9.2.0. Bugfixed v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n013.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 08:01:53 PM UTC 2025 % Result : Theorem 4.81s 5.01s % Output : Proof 4.81s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.02/0.09 % Problem : SEU552^2 : TPTP v9.2.0. Bugfixed v4.0.0. % 0.02/0.10 % Command : duper %s % 0.10/0.30 % Computer : n013.cluster.edu % 0.10/0.30 % Model : x86_64 x86_64 % 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.30 % Memory : 8042.1875MB % 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.30 % CPULimit : 300 % 0.10/0.30 % WCLimit : 300 % 0.10/0.30 % DateTime : Fri Oct 3 04:56:38 EDT 2025 % 0.10/0.30 % CPUTime : % 4.81/5.01 SZS status Theorem for theBenchmark.p % 4.81/5.01 SZS output start Proof for theBenchmark.p % 4.81/5.01 Clause #0 (by assumption #[]): Eq (Not (∀ (Xx Xy : Iota), Eq Xx Xy → ∀ (Xz Xu : Iota), Eq Xz Xu → Eq (setadjoin Xx Xz) (setadjoin Xy Xu))) True % 4.81/5.01 Clause #1 (by clausification #[0]): Eq (∀ (Xx Xy : Iota), Eq Xx Xy → ∀ (Xz Xu : Iota), Eq Xz Xu → Eq (setadjoin Xx Xz) (setadjoin Xy Xu)) False % 4.81/5.01 Clause #2 (by clausification #[1]): ∀ (a : Iota), % 4.81/5.01 Eq % 4.81/5.01 (Not % 4.81/5.01 (∀ (Xy : Iota), Eq (skS.0 0 a) Xy → ∀ (Xz Xu : Iota), Eq Xz Xu → Eq (setadjoin (skS.0 0 a) Xz) (setadjoin Xy Xu))) % 4.81/5.01 True % 4.81/5.01 Clause #3 (by clausification #[2]): ∀ (a : Iota), % 4.81/5.01 Eq (∀ (Xy : Iota), Eq (skS.0 0 a) Xy → ∀ (Xz Xu : Iota), Eq Xz Xu → Eq (setadjoin (skS.0 0 a) Xz) (setadjoin Xy Xu)) % 4.81/5.01 False % 4.81/5.01 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota), % 4.81/5.01 Eq % 4.81/5.01 (Not % 4.81/5.01 (Eq (skS.0 0 a) (skS.0 1 a a_1) → % 4.81/5.01 ∀ (Xz Xu : Iota), Eq Xz Xu → Eq (setadjoin (skS.0 0 a) Xz) (setadjoin (skS.0 1 a a_1) Xu))) % 4.81/5.01 True % 4.81/5.01 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), % 4.81/5.01 Eq % 4.81/5.01 (Eq (skS.0 0 a) (skS.0 1 a a_1) → % 4.81/5.01 ∀ (Xz Xu : Iota), Eq Xz Xu → Eq (setadjoin (skS.0 0 a) Xz) (setadjoin (skS.0 1 a a_1) Xu)) % 4.81/5.01 False % 4.81/5.01 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), Eq (Eq (skS.0 0 a) (skS.0 1 a a_1)) True % 4.81/5.01 Clause #7 (by clausification #[5]): ∀ (a a_1 : Iota), Eq (∀ (Xz Xu : Iota), Eq Xz Xu → Eq (setadjoin (skS.0 0 a) Xz) (setadjoin (skS.0 1 a a_1) Xu)) False % 4.81/5.01 Clause #8 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (skS.0 0 a) (skS.0 1 a a_1) % 4.81/5.01 Clause #9 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), % 4.81/5.01 Eq % 4.81/5.01 (Not % 4.81/5.01 (∀ (Xu : Iota), % 4.81/5.01 Eq (skS.0 2 a a_1 a_2) Xu → Eq (setadjoin (skS.0 0 a) (skS.0 2 a a_1 a_2)) (setadjoin (skS.0 1 a a_1) Xu))) % 4.81/5.01 True % 4.81/5.01 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 4.81/5.01 Eq % 4.81/5.01 (∀ (Xu : Iota), % 4.81/5.01 Eq (skS.0 2 a a_1 a_2) Xu → Eq (setadjoin (skS.0 0 a) (skS.0 2 a a_1 a_2)) (setadjoin (skS.0 1 a a_1) Xu)) % 4.81/5.01 False % 4.81/5.01 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 a_3 : Iota), % 4.81/5.01 Eq % 4.81/5.01 (Not % 4.81/5.01 (Eq (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3) → % 4.81/5.01 Eq (setadjoin (skS.0 0 a) (skS.0 2 a a_1 a_2)) (setadjoin (skS.0 1 a a_1) (skS.0 3 a a_1 a_2 a_3)))) % 4.81/5.01 True % 4.81/5.01 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 a_3 : Iota), % 4.81/5.01 Eq % 4.81/5.01 (Eq (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3) → % 4.81/5.01 Eq (setadjoin (skS.0 0 a) (skS.0 2 a a_1 a_2)) (setadjoin (skS.0 1 a a_1) (skS.0 3 a a_1 a_2 a_3))) % 4.81/5.01 False % 4.81/5.01 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 a_3 : Iota), Eq (Eq (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3)) True % 4.81/5.01 Clause #14 (by clausification #[12]): ∀ (a a_1 a_2 a_3 : Iota), % 4.81/5.01 Eq (Eq (setadjoin (skS.0 0 a) (skS.0 2 a a_1 a_2)) (setadjoin (skS.0 1 a a_1) (skS.0 3 a a_1 a_2 a_3))) False % 4.81/5.01 Clause #15 (by clausification #[13]): ∀ (a a_1 a_2 a_3 : Iota), Eq (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3) % 4.81/5.01 Clause #16 (by clausification #[14]): ∀ (a a_1 a_2 a_3 : Iota), % 4.81/5.01 Ne (setadjoin (skS.0 0 a) (skS.0 2 a a_1 a_2)) (setadjoin (skS.0 1 a a_1) (skS.0 3 a a_1 a_2 a_3)) % 4.81/5.01 Clause #17 (by forward demodulation #[16, 15]): ∀ (a a_1 a_2 : Iota), Ne (setadjoin (skS.0 0 a) (skS.0 2 a a_1 a_2)) (setadjoin (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) % 4.81/5.01 Clause #18 (by forward demodulation #[17, 8]): ∀ (a a_1 a_2 : Iota), Ne (setadjoin (skS.0 0 a) (skS.0 2 a a_1 a_2)) (setadjoin (skS.0 0 a) (skS.0 2 a a_1 a_2)) % 4.81/5.01 Clause #19 (by eliminate resolved literals #[18]): False % 4.81/5.01 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------