%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : DAT319^1 : TPTP v9.2.0. Released v7.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n031.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 07:47:23 PM UTC 2025 % Result : Theorem 3.56s 3.77s % Output : Proof 3.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : DAT319^1 : TPTP v9.2.0. Released v7.0.0. % 0.08/0.14 % Command : duper %s % 0.14/0.35 % Computer : n031.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 : Thu Oct 2 21:34:38 EDT 2025 % 0.14/0.35 % CPUTime : % 3.56/3.77 SZS status Theorem for theBenchmark.p % 3.56/3.77 SZS output start Proof for theBenchmark.p % 3.56/3.77 Clause #0 (by assumption #[]): Eq (∀ (A : Type) (A0 : «type/ind_types/list» A), Eq («const/lists/APPEND» A («const/ind_types/NIL» A) A0) A0) True % 3.56/3.77 Clause #1 (by assumption #[]): Eq % 3.56/3.77 (∀ (A : Type) (A0 : A) (A1 A2 : «type/ind_types/list» A), % 3.56/3.77 Eq («const/lists/APPEND» A («const/ind_types/CONS» A A0 A1) A2) % 3.56/3.77 («const/ind_types/CONS» A A0 («const/lists/APPEND» A A1 A2))) % 3.56/3.77 True % 3.56/3.77 Clause #2 (by assumption #[]): Eq % 3.56/3.77 (Not % 3.56/3.77 (∀ (A : Type) (A0 : A) (A1 : «type/ind_types/list» A), % 3.56/3.77 Eq («const/lists/APPEND» A («const/ind_types/CONS» A A0 («const/ind_types/NIL» A)) A1) % 3.56/3.77 («const/ind_types/CONS» A A0 A1))) % 3.56/3.77 True % 3.56/3.77 Clause #3 (by clausification #[0]): ∀ (a : Type), Eq (∀ (A0 : «type/ind_types/list» a), Eq («const/lists/APPEND» a («const/ind_types/NIL» a) A0) A0) True % 3.56/3.77 Clause #4 (by clausification #[3]): ∀ (a : Type) (a_1 : «type/ind_types/list» a), Eq (Eq («const/lists/APPEND» a («const/ind_types/NIL» a) a_1) a_1) True % 3.56/3.77 Clause #5 (by clausification #[4]): ∀ (a : Type) (a_1 : «type/ind_types/list» a), Eq («const/lists/APPEND» a («const/ind_types/NIL» a) a_1) a_1 % 3.56/3.77 Clause #6 (by clausification #[2]): Eq % 3.56/3.77 (∀ (A : Type) (A0 : A) (A1 : «type/ind_types/list» A), % 3.56/3.77 Eq («const/lists/APPEND» A («const/ind_types/CONS» A A0 («const/ind_types/NIL» A)) A1) % 3.56/3.77 («const/ind_types/CONS» A A0 A1)) % 3.56/3.77 False % 3.56/3.77 Clause #7 (by clausification #[6]): ∀ (a : Type), % 3.56/3.77 Eq % 3.56/3.77 (Not % 3.56/3.77 (∀ (A0 : skS.0 0 a) (A1 : «type/ind_types/list» (skS.0 0 a)), % 3.56/3.77 Eq % 3.56/3.77 («const/lists/APPEND» (skS.0 0 a) («const/ind_types/CONS» (skS.0 0 a) A0 («const/ind_types/NIL» (skS.0 0 a))) % 3.56/3.77 A1) % 3.56/3.77 («const/ind_types/CONS» (skS.0 0 a) A0 A1))) % 3.56/3.77 True % 3.56/3.77 Clause #8 (by clausification #[7]): ∀ (a : Type), % 3.56/3.77 Eq % 3.56/3.77 (∀ (A0 : skS.0 0 a) (A1 : «type/ind_types/list» (skS.0 0 a)), % 3.56/3.77 Eq % 3.56/3.77 («const/lists/APPEND» (skS.0 0 a) («const/ind_types/CONS» (skS.0 0 a) A0 («const/ind_types/NIL» (skS.0 0 a))) % 3.56/3.77 A1) % 3.56/3.77 («const/ind_types/CONS» (skS.0 0 a) A0 A1)) % 3.56/3.77 False % 3.56/3.77 Clause #9 (by clausification #[8]): ∀ (a : Type) (a_1 : skS.0 0 a), % 3.56/3.77 Eq % 3.56/3.77 (Not % 3.56/3.77 (∀ (A1 : «type/ind_types/list» (skS.0 0 a)), % 3.56/3.77 Eq % 3.56/3.77 («const/lists/APPEND» (skS.0 0 a) % 3.56/3.77 («const/ind_types/CONS» (skS.0 0 a) (skS.0 1 a a_1) («const/ind_types/NIL» (skS.0 0 a))) A1) % 3.56/3.77 («const/ind_types/CONS» (skS.0 0 a) (skS.0 1 a a_1) A1))) % 3.56/3.77 True % 3.56/3.77 Clause #10 (by clausification #[9]): ∀ (a : Type) (a_1 : skS.0 0 a), % 3.56/3.77 Eq % 3.56/3.77 (∀ (A1 : «type/ind_types/list» (skS.0 0 a)), % 3.56/3.77 Eq % 3.56/3.77 («const/lists/APPEND» (skS.0 0 a) % 3.56/3.77 («const/ind_types/CONS» (skS.0 0 a) (skS.0 1 a a_1) («const/ind_types/NIL» (skS.0 0 a))) A1) % 3.56/3.77 («const/ind_types/CONS» (skS.0 0 a) (skS.0 1 a a_1) A1)) % 3.56/3.77 False % 3.56/3.77 Clause #11 (by clausification #[10]): ∀ (a : Type) (a_1 : skS.0 0 a) (a_2 : «type/ind_types/list» (skS.0 0 a)), % 3.56/3.77 Eq % 3.56/3.77 (Not % 3.56/3.77 (Eq % 3.56/3.77 («const/lists/APPEND» (skS.0 0 a) % 3.56/3.77 («const/ind_types/CONS» (skS.0 0 a) (skS.0 1 a a_1) («const/ind_types/NIL» (skS.0 0 a))) (skS.0 2 a a_1 a_2)) % 3.56/3.77 («const/ind_types/CONS» (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))) % 3.56/3.77 True % 3.56/3.77 Clause #12 (by clausification #[11]): ∀ (a : Type) (a_1 : skS.0 0 a) (a_2 : «type/ind_types/list» (skS.0 0 a)), % 3.56/3.77 Eq % 3.56/3.77 (Eq % 3.56/3.77 («const/lists/APPEND» (skS.0 0 a) % 3.56/3.77 («const/ind_types/CONS» (skS.0 0 a) (skS.0 1 a a_1) («const/ind_types/NIL» (skS.0 0 a))) (skS.0 2 a a_1 a_2)) % 3.56/3.77 («const/ind_types/CONS» (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))) % 3.56/3.77 False % 3.56/3.77 Clause #13 (by clausification #[12]): ∀ (a : Type) (a_1 : skS.0 0 a) (a_2 : «type/ind_types/list» (skS.0 0 a)), % 3.56/3.77 Ne % 3.56/3.77 («const/lists/APPEND» (skS.0 0 a) % 3.56/3.77 («const/ind_types/CONS» (skS.0 0 a) (skS.0 1 a a_1) («const/ind_types/NIL» (skS.0 0 a))) (skS.0 2 a a_1 a_2)) % 3.56/3.77 («const/ind_types/CONS» (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) % 3.56/3.77 Clause #14 (by clausification #[1]): ∀ (a : Type), % 3.56/3.78 Eq % 3.56/3.78 (∀ (A0 : a) (A1 A2 : «type/ind_types/list» a), % 3.56/3.78 Eq («const/lists/APPEND» a («const/ind_types/CONS» a A0 A1) A2) % 3.56/3.78 («const/ind_types/CONS» a A0 («const/lists/APPEND» a A1 A2))) % 3.56/3.78 True % 3.56/3.78 Clause #15 (by clausification #[14]): ∀ (a : Type) (a_1 : a), % 3.56/3.78 Eq % 3.56/3.78 (∀ (A1 A2 : «type/ind_types/list» a), % 3.56/3.78 Eq («const/lists/APPEND» a («const/ind_types/CONS» a a_1 A1) A2) % 3.56/3.78 («const/ind_types/CONS» a a_1 («const/lists/APPEND» a A1 A2))) % 3.56/3.78 True % 3.56/3.78 Clause #16 (by clausification #[15]): ∀ (a : Type) (a_1 : a) (a_2 : «type/ind_types/list» a), % 3.56/3.78 Eq % 3.56/3.78 (∀ (A2 : «type/ind_types/list» a), % 3.56/3.78 Eq («const/lists/APPEND» a («const/ind_types/CONS» a a_1 a_2) A2) % 3.56/3.78 («const/ind_types/CONS» a a_1 («const/lists/APPEND» a a_2 A2))) % 3.56/3.78 True % 3.56/3.78 Clause #17 (by clausification #[16]): ∀ (a : Type) (a_1 : a) (a_2 a_3 : «type/ind_types/list» a), % 3.56/3.78 Eq % 3.56/3.78 (Eq («const/lists/APPEND» a («const/ind_types/CONS» a a_1 a_2) a_3) % 3.56/3.78 («const/ind_types/CONS» a a_1 («const/lists/APPEND» a a_2 a_3))) % 3.56/3.78 True % 3.56/3.78 Clause #18 (by clausification #[17]): ∀ (a : Type) (a_1 : a) (a_2 a_3 : «type/ind_types/list» a), % 3.56/3.78 Eq («const/lists/APPEND» a («const/ind_types/CONS» a a_1 a_2) a_3) % 3.56/3.78 («const/ind_types/CONS» a a_1 («const/lists/APPEND» a a_2 a_3)) % 3.56/3.78 Clause #19 (by backward demodulation #[18, 13]): ∀ (a : Type) (a_1 : skS.0 0 a) (a_2 : «type/ind_types/list» (skS.0 0 a)), % 3.56/3.78 Ne % 3.56/3.78 («const/ind_types/CONS» (skS.0 0 a) (skS.0 1 a a_1) % 3.56/3.78 («const/lists/APPEND» (skS.0 0 a) («const/ind_types/NIL» (skS.0 0 a)) (skS.0 2 a a_1 a_2))) % 3.56/3.78 («const/ind_types/CONS» (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) % 3.56/3.78 Clause #20 (by forward demodulation #[19, 5]): ∀ (a : Type) (a_1 : skS.0 0 a) (a_2 : «type/ind_types/list» (skS.0 0 a)), % 3.56/3.78 Ne («const/ind_types/CONS» (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) % 3.56/3.78 («const/ind_types/CONS» (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)) % 3.56/3.78 Clause #21 (by eliminate resolved literals #[20]): False % 3.56/3.78 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------