%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : ANA109^1 : TPTP v9.2.0. Released v7.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n028.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 07:44:34 PM UTC 2025 % Result : Theorem 3.61s 3.78s % Output : Proof 3.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : ANA109^1 : TPTP v9.2.0. Released v7.0.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n028.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 : Thu Oct 2 22:10:38 EDT 2025 % 0.13/0.34 % CPUTime : % 3.61/3.78 SZS status Theorem for theBenchmark.p % 3.61/3.78 SZS output start Proof for theBenchmark.p % 3.61/3.78 Clause #0 (by assumption #[]): Eq % 3.61/3.78 (∀ (A : Type) (A0 : A → «type/realax/real») (A1 : A), % 3.61/3.78 Eq («const/iterate/sum» A («const/sets/INSERT» A A1 («const/sets/EMPTY» A)) A0) (A0 A1)) % 3.61/3.78 True % 3.61/3.78 Clause #1 (by assumption #[]): Eq % 3.61/3.78 (∀ (A : «type/nums/num»), % 3.61/3.78 Eq («const/iterate/..» A A) («const/sets/INSERT» «type/nums/num» A («const/sets/EMPTY» «type/nums/num»))) % 3.61/3.78 True % 3.61/3.78 Clause #2 (by assumption #[]): Eq % 3.61/3.78 (Not % 3.61/3.78 (∀ (A : «type/nums/num» → «type/realax/real») (A0 : «type/nums/num»), % 3.61/3.78 Eq («const/iterate/sum» «type/nums/num» («const/iterate/..» A0 A0) A) (A A0))) % 3.61/3.78 True % 3.61/3.78 Clause #3 (by clausification #[1]): ∀ (a : «type/nums/num»), % 3.61/3.78 Eq (Eq («const/iterate/..» a a) («const/sets/INSERT» «type/nums/num» a («const/sets/EMPTY» «type/nums/num»))) True % 3.61/3.78 Clause #4 (by clausification #[3]): ∀ (a : «type/nums/num»), % 3.61/3.78 Eq («const/iterate/..» a a) («const/sets/INSERT» «type/nums/num» a («const/sets/EMPTY» «type/nums/num»)) % 3.61/3.78 Clause #10 (by clausification #[0]): ∀ (a : Type), % 3.61/3.78 Eq % 3.61/3.78 (∀ (A0 : a → «type/realax/real») (A1 : a), % 3.61/3.78 Eq («const/iterate/sum» a («const/sets/INSERT» a A1 («const/sets/EMPTY» a)) A0) (A0 A1)) % 3.61/3.78 True % 3.61/3.78 Clause #11 (by clausification #[10]): ∀ (a : Type) (a_1 : a → «type/realax/real»), % 3.61/3.78 Eq (∀ (A1 : a), Eq («const/iterate/sum» a («const/sets/INSERT» a A1 («const/sets/EMPTY» a)) a_1) (a_1 A1)) True % 3.61/3.78 Clause #12 (by clausification #[11]): ∀ (a : Type) (a_1 : a) (a_2 : a → «type/realax/real»), % 3.61/3.78 Eq (Eq («const/iterate/sum» a («const/sets/INSERT» a a_1 («const/sets/EMPTY» a)) a_2) (a_2 a_1)) True % 3.61/3.78 Clause #13 (by clausification #[12]): ∀ (a : Type) (a_1 : a) (a_2 : a → «type/realax/real»), % 3.61/3.78 Eq («const/iterate/sum» a («const/sets/INSERT» a a_1 («const/sets/EMPTY» a)) a_2) (a_2 a_1) % 3.61/3.78 Clause #14 (by superposition #[13, 4]): ∀ (a : «type/nums/num») (a_1 : «type/nums/num» → «type/realax/real»), % 3.61/3.78 Eq («const/iterate/sum» «type/nums/num» («const/iterate/..» a a) a_1) (a_1 a) % 3.61/3.78 Clause #81 (by clausification #[2]): Eq % 3.61/3.78 (∀ (A : «type/nums/num» → «type/realax/real») (A0 : «type/nums/num»), % 3.61/3.78 Eq («const/iterate/sum» «type/nums/num» («const/iterate/..» A0 A0) A) (A A0)) % 3.61/3.78 False % 3.61/3.78 Clause #82 (by clausification #[81]): ∀ (a : «type/nums/num» → «type/realax/real»), % 3.61/3.78 Eq % 3.61/3.78 (Not % 3.61/3.78 (∀ (A0 : «type/nums/num»), % 3.61/3.78 Eq («const/iterate/sum» «type/nums/num» («const/iterate/..» A0 A0) (skS.0 0 a)) (skS.0 0 a A0))) % 3.61/3.78 True % 3.61/3.78 Clause #83 (by clausification #[82]): ∀ (a : «type/nums/num» → «type/realax/real»), % 3.61/3.78 Eq % 3.61/3.78 (∀ (A0 : «type/nums/num»), % 3.61/3.78 Eq («const/iterate/sum» «type/nums/num» («const/iterate/..» A0 A0) (skS.0 0 a)) (skS.0 0 a A0)) % 3.61/3.78 False % 3.61/3.78 Clause #84 (by clausification #[83]): ∀ (a : «type/nums/num» → «type/realax/real») (a_1 : «type/nums/num»), % 3.61/3.78 Eq % 3.61/3.78 (Not % 3.61/3.78 (Eq («const/iterate/sum» «type/nums/num» («const/iterate/..» (skS.0 1 a a_1) (skS.0 1 a a_1)) (skS.0 0 a)) % 3.61/3.78 (skS.0 0 a (skS.0 1 a a_1)))) % 3.61/3.78 True % 3.61/3.78 Clause #85 (by clausification #[84]): ∀ (a : «type/nums/num» → «type/realax/real») (a_1 : «type/nums/num»), % 3.61/3.78 Eq % 3.61/3.78 (Eq («const/iterate/sum» «type/nums/num» («const/iterate/..» (skS.0 1 a a_1) (skS.0 1 a a_1)) (skS.0 0 a)) % 3.61/3.78 (skS.0 0 a (skS.0 1 a a_1))) % 3.61/3.78 False % 3.61/3.78 Clause #86 (by clausification #[85]): ∀ (a : «type/nums/num» → «type/realax/real») (a_1 : «type/nums/num»), % 3.61/3.78 Ne («const/iterate/sum» «type/nums/num» («const/iterate/..» (skS.0 1 a a_1) (skS.0 1 a a_1)) (skS.0 0 a)) % 3.61/3.78 (skS.0 0 a (skS.0 1 a a_1)) % 3.61/3.78 Clause #87 (by forward demodulation #[86, 14]): ∀ (a : «type/nums/num» → «type/realax/real») (a_1 : «type/nums/num»), % 3.61/3.78 Ne (skS.0 0 a (skS.0 1 a a_1)) (skS.0 0 a (skS.0 1 a a_1)) % 3.61/3.78 Clause #88 (by eliminate resolved literals #[87]): False % 3.61/3.78 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------