%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : DAT315^1 : TPTP v9.2.0. Released v7.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n017.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 3.41s 3.58s % Output : Proof 3.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : DAT315^1 : TPTP v9.2.0. Released v7.0.0. % 0.12/0.14 % Command : duper %s % 0.15/0.34 % Computer : n017.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Thu Oct 2 21:51:53 EDT 2025 % 0.15/0.34 % CPUTime : % 3.41/3.58 SZS status Theorem for theBenchmark.p % 3.41/3.58 SZS output start Proof for theBenchmark.p % 3.41/3.58 Clause #0 (by assumption #[]): Eq % 3.41/3.58 (∀ (A : Type) (A0 : «type/nums/num») (A1 : «type/ind_types/list» A), % 3.41/3.58 Eq («const/lists/EL» A («const/nums/SUC» A0) A1) («const/lists/EL» A A0 («const/lists/TL» A A1))) % 3.41/3.58 True % 3.41/3.58 Clause #1 (by assumption #[]): Eq % 3.41/3.58 (∀ (A : «type/nums/num»), % 3.41/3.58 Eq («const/nums/SUC» A) («const/arith/+» A («const/nums/NUMERAL» («const/nums/BIT1» «const/nums/_0»)))) % 3.41/3.58 True % 3.41/3.58 Clause #2 (by assumption #[]): Eq % 3.41/3.58 (Not % 3.41/3.58 (∀ (A : Type) (A0 : «type/ind_types/list» A) (A1 : «type/nums/num»), % 3.41/3.58 Eq («const/lists/EL» A A1 («const/lists/TL» A A0)) % 3.41/3.58 («const/lists/EL» A («const/arith/+» A1 («const/nums/NUMERAL» («const/nums/BIT1» «const/nums/_0»))) A0))) % 3.41/3.58 True % 3.41/3.58 Clause #3 (by clausification #[1]): ∀ (a : «type/nums/num»), % 3.41/3.58 Eq (Eq («const/nums/SUC» a) («const/arith/+» a («const/nums/NUMERAL» («const/nums/BIT1» «const/nums/_0»)))) True % 3.41/3.58 Clause #4 (by clausification #[3]): ∀ (a : «type/nums/num»), % 3.41/3.58 Eq («const/nums/SUC» a) («const/arith/+» a («const/nums/NUMERAL» («const/nums/BIT1» «const/nums/_0»))) % 3.41/3.58 Clause #5 (by clausification #[0]): ∀ (a : Type), % 3.41/3.58 Eq % 3.41/3.58 (∀ (A0 : «type/nums/num») (A1 : «type/ind_types/list» a), % 3.41/3.58 Eq («const/lists/EL» a («const/nums/SUC» A0) A1) («const/lists/EL» a A0 («const/lists/TL» a A1))) % 3.41/3.58 True % 3.41/3.58 Clause #6 (by clausification #[5]): ∀ (a : Type) (a_1 : «type/nums/num»), % 3.41/3.58 Eq % 3.41/3.58 (∀ (A1 : «type/ind_types/list» a), % 3.41/3.58 Eq («const/lists/EL» a («const/nums/SUC» a_1) A1) («const/lists/EL» a a_1 («const/lists/TL» a A1))) % 3.41/3.58 True % 3.41/3.58 Clause #7 (by clausification #[6]): ∀ (a : Type) (a_1 : «type/nums/num») (a_2 : «type/ind_types/list» a), % 3.41/3.58 Eq (Eq («const/lists/EL» a («const/nums/SUC» a_1) a_2) («const/lists/EL» a a_1 («const/lists/TL» a a_2))) True % 3.41/3.58 Clause #8 (by clausification #[7]): ∀ (a : Type) (a_1 : «type/nums/num») (a_2 : «type/ind_types/list» a), % 3.41/3.58 Eq («const/lists/EL» a («const/nums/SUC» a_1) a_2) («const/lists/EL» a a_1 («const/lists/TL» a a_2)) % 3.41/3.58 Clause #9 (by clausification #[2]): Eq % 3.41/3.58 (∀ (A : Type) (A0 : «type/ind_types/list» A) (A1 : «type/nums/num»), % 3.41/3.58 Eq («const/lists/EL» A A1 («const/lists/TL» A A0)) % 3.41/3.58 («const/lists/EL» A («const/arith/+» A1 («const/nums/NUMERAL» («const/nums/BIT1» «const/nums/_0»))) A0)) % 3.41/3.58 False % 3.41/3.58 Clause #10 (by clausification #[9]): ∀ (a : Type), % 3.41/3.58 Eq % 3.41/3.58 (Not % 3.41/3.58 (∀ (A0 : «type/ind_types/list» (skS.0 0 a)) (A1 : «type/nums/num»), % 3.41/3.58 Eq («const/lists/EL» (skS.0 0 a) A1 («const/lists/TL» (skS.0 0 a) A0)) % 3.41/3.58 («const/lists/EL» (skS.0 0 a) («const/arith/+» A1 («const/nums/NUMERAL» («const/nums/BIT1» «const/nums/_0»))) % 3.41/3.58 A0))) % 3.41/3.58 True % 3.41/3.58 Clause #11 (by clausification #[10]): ∀ (a : Type), % 3.41/3.58 Eq % 3.41/3.58 (∀ (A0 : «type/ind_types/list» (skS.0 0 a)) (A1 : «type/nums/num»), % 3.41/3.58 Eq («const/lists/EL» (skS.0 0 a) A1 («const/lists/TL» (skS.0 0 a) A0)) % 3.41/3.58 («const/lists/EL» (skS.0 0 a) («const/arith/+» A1 («const/nums/NUMERAL» («const/nums/BIT1» «const/nums/_0»))) % 3.41/3.58 A0)) % 3.41/3.58 False % 3.41/3.58 Clause #12 (by clausification #[11]): ∀ (a : Type) (a_1 : «type/ind_types/list» (skS.0 0 a)), % 3.41/3.58 Eq % 3.41/3.58 (Not % 3.41/3.58 (∀ (A1 : «type/nums/num»), % 3.41/3.58 Eq («const/lists/EL» (skS.0 0 a) A1 («const/lists/TL» (skS.0 0 a) (skS.0 1 a a_1))) % 3.41/3.58 («const/lists/EL» (skS.0 0 a) («const/arith/+» A1 («const/nums/NUMERAL» («const/nums/BIT1» «const/nums/_0»))) % 3.41/3.58 (skS.0 1 a a_1)))) % 3.41/3.58 True % 3.41/3.58 Clause #13 (by clausification #[12]): ∀ (a : Type) (a_1 : «type/ind_types/list» (skS.0 0 a)), % 3.41/3.58 Eq % 3.41/3.58 (∀ (A1 : «type/nums/num»), % 3.41/3.58 Eq («const/lists/EL» (skS.0 0 a) A1 («const/lists/TL» (skS.0 0 a) (skS.0 1 a a_1))) % 3.41/3.58 («const/lists/EL» (skS.0 0 a) («const/arith/+» A1 («const/nums/NUMERAL» («const/nums/BIT1» «const/nums/_0»))) % 3.41/3.58 (skS.0 1 a a_1))) % 3.41/3.58 False % 3.41/3.58 Clause #14 (by clausification #[13]): ∀ (a : Type) (a_1 : «type/ind_types/list» (skS.0 0 a)) (a_2 : «type/nums/num»), % 3.41/3.59 Eq % 3.41/3.59 (Not % 3.41/3.59 (Eq («const/lists/EL» (skS.0 0 a) (skS.0 2 a a_1 a_2) («const/lists/TL» (skS.0 0 a) (skS.0 1 a a_1))) % 3.41/3.59 («const/lists/EL» (skS.0 0 a) % 3.41/3.59 («const/arith/+» (skS.0 2 a a_1 a_2) («const/nums/NUMERAL» («const/nums/BIT1» «const/nums/_0»))) % 3.41/3.59 (skS.0 1 a a_1)))) % 3.41/3.59 True % 3.41/3.59 Clause #15 (by clausification #[14]): ∀ (a : Type) (a_1 : «type/ind_types/list» (skS.0 0 a)) (a_2 : «type/nums/num»), % 3.41/3.59 Eq % 3.41/3.59 (Eq («const/lists/EL» (skS.0 0 a) (skS.0 2 a a_1 a_2) («const/lists/TL» (skS.0 0 a) (skS.0 1 a a_1))) % 3.41/3.59 («const/lists/EL» (skS.0 0 a) % 3.41/3.59 («const/arith/+» (skS.0 2 a a_1 a_2) («const/nums/NUMERAL» («const/nums/BIT1» «const/nums/_0»))) % 3.41/3.59 (skS.0 1 a a_1))) % 3.41/3.59 False % 3.41/3.59 Clause #16 (by clausification #[15]): ∀ (a : Type) (a_1 : «type/ind_types/list» (skS.0 0 a)) (a_2 : «type/nums/num»), % 3.41/3.59 Ne («const/lists/EL» (skS.0 0 a) (skS.0 2 a a_1 a_2) («const/lists/TL» (skS.0 0 a) (skS.0 1 a a_1))) % 3.41/3.59 («const/lists/EL» (skS.0 0 a) % 3.41/3.59 («const/arith/+» (skS.0 2 a a_1 a_2) («const/nums/NUMERAL» («const/nums/BIT1» «const/nums/_0»))) (skS.0 1 a a_1)) % 3.41/3.59 Clause #17 (by forward demodulation #[16, 8]): ∀ (a : Type) (a_1 : «type/ind_types/list» (skS.0 0 a)) (a_2 : «type/nums/num»), % 3.41/3.59 Ne («const/lists/EL» (skS.0 0 a) («const/nums/SUC» (skS.0 2 a a_1 a_2)) (skS.0 1 a a_1)) % 3.41/3.59 («const/lists/EL» (skS.0 0 a) % 3.41/3.59 («const/arith/+» (skS.0 2 a a_1 a_2) («const/nums/NUMERAL» («const/nums/BIT1» «const/nums/_0»))) (skS.0 1 a a_1)) % 3.41/3.59 Clause #18 (by forward demodulation #[17, 4]): ∀ (a : Type) (a_1 : «type/ind_types/list» (skS.0 0 a)) (a_2 : «type/nums/num»), % 3.41/3.59 Ne («const/lists/EL» (skS.0 0 a) («const/nums/SUC» (skS.0 2 a a_1 a_2)) (skS.0 1 a a_1)) % 3.41/3.59 («const/lists/EL» (skS.0 0 a) («const/nums/SUC» (skS.0 2 a a_1 a_2)) (skS.0 1 a a_1)) % 3.41/3.59 Clause #19 (by eliminate resolved literals #[18]): False % 3.41/3.59 SZS output end Proof for theBenchmark.p 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