%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : DAT280^1 : TPTP v9.2.0. Released v7.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n019.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 07:47:21 PM UTC 2025 % Result : Theorem 3.51s 3.74s % Output : Proof 3.59s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : DAT280^1 : TPTP v9.2.0. Released v7.0.0. % 0.03/0.13 % Command : duper %s % 0.12/0.34 % Computer : n019.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Thu Oct 2 21:49:08 EDT 2025 % 0.12/0.34 % CPUTime : % 3.51/3.74 SZS status Theorem for theBenchmark.p % 3.51/3.74 SZS output start Proof for theBenchmark.p % 3.51/3.74 Clause #0 (by assumption #[]): Eq % 3.51/3.74 (∀ (A A0 A1 : Type) (A2 : A → A0 → A1 → A1) (A3 : «type/ind_types/list» A0) (A4 : A1), % 3.51/3.74 Eq («const/lists/ITLIST2» A A0 A1 A2 («const/ind_types/NIL» A) A3 A4) A4) % 3.51/3.74 True % 3.51/3.74 Clause #1 (by assumption #[]): Eq % 3.51/3.74 (Not % 3.51/3.74 (∀ (A A0 A1 : Type) (A2 : A → A0 → A1 → A1) (A3 : A1), % 3.51/3.74 Eq («const/lists/ITLIST2» A A0 A1 A2 («const/ind_types/NIL» A) («const/ind_types/NIL» A0) A3) A3)) % 3.51/3.74 True % 3.51/3.74 Clause #2 (by clausification #[0]): ∀ (a : Type), % 3.51/3.74 Eq % 3.51/3.74 (∀ (A0 A1 : Type) (A2 : a → A0 → A1 → A1) (A3 : «type/ind_types/list» A0) (A4 : A1), % 3.51/3.74 Eq («const/lists/ITLIST2» a A0 A1 A2 («const/ind_types/NIL» a) A3 A4) A4) % 3.51/3.74 True % 3.51/3.74 Clause #3 (by clausification #[2]): ∀ (a a_1 : Type), % 3.51/3.74 Eq % 3.51/3.74 (∀ (A1 : Type) (A2 : a → a_1 → A1 → A1) (A3 : «type/ind_types/list» a_1) (A4 : A1), % 3.51/3.74 Eq («const/lists/ITLIST2» a a_1 A1 A2 («const/ind_types/NIL» a) A3 A4) A4) % 3.51/3.74 True % 3.51/3.74 Clause #4 (by clausification #[3]): ∀ (a a_1 a_2 : Type), % 3.51/3.74 Eq % 3.51/3.74 (∀ (A2 : a → a_1 → a_2 → a_2) (A3 : «type/ind_types/list» a_1) (A4 : a_2), % 3.51/3.74 Eq («const/lists/ITLIST2» a a_1 a_2 A2 («const/ind_types/NIL» a) A3 A4) A4) % 3.51/3.74 True % 3.51/3.74 Clause #5 (by clausification #[4]): ∀ (a a_1 a_2 : Type) (a_3 : a_2 → a → a_1 → a_1), % 3.51/3.74 Eq % 3.51/3.74 (∀ (A3 : «type/ind_types/list» a) (A4 : a_1), % 3.51/3.74 Eq («const/lists/ITLIST2» a_2 a a_1 a_3 («const/ind_types/NIL» a_2) A3 A4) A4) % 3.51/3.74 True % 3.51/3.74 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Type) (a_3 : a_1 → a_2 → a → a) (a_4 : «type/ind_types/list» a_2), % 3.51/3.74 Eq (∀ (A4 : a), Eq («const/lists/ITLIST2» a_1 a_2 a a_3 («const/ind_types/NIL» a_1) a_4 A4) A4) True % 3.51/3.74 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 : Type) (a_3 : a_1 → a_2 → a → a) (a_4 : «type/ind_types/list» a_2) (a_5 : a), % 3.51/3.74 Eq (Eq («const/lists/ITLIST2» a_1 a_2 a a_3 («const/ind_types/NIL» a_1) a_4 a_5) a_5) True % 3.51/3.74 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 : Type) (a_3 : a_1 → a_2 → a → a) (a_4 : «type/ind_types/list» a_2) (a_5 : a), % 3.51/3.74 Eq («const/lists/ITLIST2» a_1 a_2 a a_3 («const/ind_types/NIL» a_1) a_4 a_5) a_5 % 3.51/3.74 Clause #9 (by clausification #[1]): Eq % 3.51/3.74 (∀ (A A0 A1 : Type) (A2 : A → A0 → A1 → A1) (A3 : A1), % 3.51/3.74 Eq («const/lists/ITLIST2» A A0 A1 A2 («const/ind_types/NIL» A) («const/ind_types/NIL» A0) A3) A3) % 3.51/3.74 False % 3.51/3.74 Clause #10 (by clausification #[9]): ∀ (a : Type), % 3.51/3.74 Eq % 3.51/3.74 (Not % 3.51/3.74 (∀ (A0 A1 : Type) (A2 : skS.0 0 a → A0 → A1 → A1) (A3 : A1), % 3.51/3.74 Eq % 3.51/3.74 («const/lists/ITLIST2» (skS.0 0 a) A0 A1 A2 («const/ind_types/NIL» (skS.0 0 a)) («const/ind_types/NIL» A0) A3) % 3.51/3.74 A3)) % 3.51/3.74 True % 3.51/3.74 Clause #11 (by clausification #[10]): ∀ (a : Type), % 3.51/3.74 Eq % 3.51/3.74 (∀ (A0 A1 : Type) (A2 : skS.0 0 a → A0 → A1 → A1) (A3 : A1), % 3.51/3.74 Eq («const/lists/ITLIST2» (skS.0 0 a) A0 A1 A2 («const/ind_types/NIL» (skS.0 0 a)) («const/ind_types/NIL» A0) A3) % 3.51/3.74 A3) % 3.51/3.74 False % 3.51/3.74 Clause #12 (by clausification #[11]): ∀ (a a_1 : Type), % 3.51/3.74 Eq % 3.51/3.74 (Not % 3.51/3.74 (∀ (A1 : Type) (A2 : skS.0 0 a → skS.0 1 a a_1 → A1 → A1) (A3 : A1), % 3.51/3.74 Eq % 3.51/3.74 («const/lists/ITLIST2» (skS.0 0 a) (skS.0 1 a a_1) A1 A2 («const/ind_types/NIL» (skS.0 0 a)) % 3.51/3.74 («const/ind_types/NIL» (skS.0 1 a a_1)) A3) % 3.51/3.74 A3)) % 3.51/3.74 True % 3.51/3.74 Clause #13 (by clausification #[12]): ∀ (a a_1 : Type), % 3.51/3.74 Eq % 3.51/3.74 (∀ (A1 : Type) (A2 : skS.0 0 a → skS.0 1 a a_1 → A1 → A1) (A3 : A1), % 3.51/3.74 Eq % 3.51/3.74 («const/lists/ITLIST2» (skS.0 0 a) (skS.0 1 a a_1) A1 A2 («const/ind_types/NIL» (skS.0 0 a)) % 3.51/3.74 («const/ind_types/NIL» (skS.0 1 a a_1)) A3) % 3.51/3.74 A3) % 3.51/3.74 False % 3.51/3.74 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 : Type), % 3.51/3.74 Eq % 3.51/3.74 (Not % 3.51/3.74 (∀ (A2 : skS.0 0 a → skS.0 1 a a_1 → skS.0 2 a a_1 a_2 → skS.0 2 a a_1 a_2) (A3 : skS.0 2 a a_1 a_2), % 3.51/3.74 Eq % 3.51/3.74 («const/lists/ITLIST2» (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) A2 («const/ind_types/NIL» (skS.0 0 a)) % 3.51/3.74 («const/ind_types/NIL» (skS.0 1 a a_1)) A3) % 3.59/3.76 A3)) % 3.59/3.76 True % 3.59/3.76 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Type), % 3.59/3.76 Eq % 3.59/3.76 (∀ (A2 : skS.0 0 a → skS.0 1 a a_1 → skS.0 2 a a_1 a_2 → skS.0 2 a a_1 a_2) (A3 : skS.0 2 a a_1 a_2), % 3.59/3.76 Eq % 3.59/3.76 («const/lists/ITLIST2» (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) A2 («const/ind_types/NIL» (skS.0 0 a)) % 3.59/3.76 («const/ind_types/NIL» (skS.0 1 a a_1)) A3) % 3.59/3.76 A3) % 3.59/3.76 False % 3.59/3.76 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 : Type) (a_3 : skS.0 0 a → skS.0 1 a a_1 → skS.0 2 a a_1 a_2 → skS.0 2 a a_1 a_2), % 3.59/3.76 Eq % 3.59/3.76 (Not % 3.59/3.76 (∀ (A3 : skS.0 2 a a_1 a_2), % 3.59/3.76 Eq % 3.59/3.76 («const/lists/ITLIST2» (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3) % 3.59/3.76 («const/ind_types/NIL» (skS.0 0 a)) («const/ind_types/NIL» (skS.0 1 a a_1)) A3) % 3.59/3.76 A3)) % 3.59/3.76 True % 3.59/3.76 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 : Type) (a_3 : skS.0 0 a → skS.0 1 a a_1 → skS.0 2 a a_1 a_2 → skS.0 2 a a_1 a_2), % 3.59/3.76 Eq % 3.59/3.76 (∀ (A3 : skS.0 2 a a_1 a_2), % 3.59/3.76 Eq % 3.59/3.76 («const/lists/ITLIST2» (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3) % 3.59/3.76 («const/ind_types/NIL» (skS.0 0 a)) («const/ind_types/NIL» (skS.0 1 a a_1)) A3) % 3.59/3.76 A3) % 3.59/3.76 False % 3.59/3.76 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : Type) (a_3 : skS.0 0 a → skS.0 1 a a_1 → skS.0 2 a a_1 a_2 → skS.0 2 a a_1 a_2) % 3.59/3.76 (a_4 : skS.0 2 a a_1 a_2), % 3.59/3.76 Eq % 3.59/3.76 (Not % 3.59/3.76 (Eq % 3.59/3.76 («const/lists/ITLIST2» (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3) % 3.59/3.76 («const/ind_types/NIL» (skS.0 0 a)) («const/ind_types/NIL» (skS.0 1 a a_1)) (skS.0 4 a a_1 a_2 a_3 a_4)) % 3.59/3.76 (skS.0 4 a a_1 a_2 a_3 a_4))) % 3.59/3.76 True % 3.59/3.76 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Type) (a_3 : skS.0 0 a → skS.0 1 a a_1 → skS.0 2 a a_1 a_2 → skS.0 2 a a_1 a_2) % 3.59/3.76 (a_4 : skS.0 2 a a_1 a_2), % 3.59/3.76 Eq % 3.59/3.76 (Eq % 3.59/3.76 («const/lists/ITLIST2» (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3) % 3.59/3.76 («const/ind_types/NIL» (skS.0 0 a)) («const/ind_types/NIL» (skS.0 1 a a_1)) (skS.0 4 a a_1 a_2 a_3 a_4)) % 3.59/3.76 (skS.0 4 a a_1 a_2 a_3 a_4)) % 3.59/3.76 False % 3.59/3.76 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Type) (a_3 : skS.0 0 a → skS.0 1 a a_1 → skS.0 2 a a_1 a_2 → skS.0 2 a a_1 a_2) % 3.59/3.76 (a_4 : skS.0 2 a a_1 a_2), % 3.59/3.76 Ne % 3.59/3.76 («const/lists/ITLIST2» (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 3 a a_1 a_2 a_3) % 3.59/3.76 («const/ind_types/NIL» (skS.0 0 a)) («const/ind_types/NIL» (skS.0 1 a a_1)) (skS.0 4 a a_1 a_2 a_3 a_4)) % 3.59/3.76 (skS.0 4 a a_1 a_2 a_3 a_4) % 3.59/3.76 Clause #21 (by forward demodulation #[20, 8]): ∀ (a a_1 a_2 : Type) (a_3 : skS.0 0 a → skS.0 1 a a_1 → skS.0 2 a a_1 a_2 → skS.0 2 a a_1 a_2) % 3.59/3.76 (a_4 : skS.0 2 a a_1 a_2), Ne (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 4 a a_1 a_2 a_3 a_4) % 3.59/3.76 Clause #22 (by eliminate resolved literals #[21]): False % 3.59/3.76 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------