%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : ANA068^1 : TPTP v9.2.0. Released v7.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n012.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 07:44:31 PM UTC 2025 % Result : Theorem 3.37s 3.56s % Output : Proof 3.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : ANA068^1 : TPTP v9.2.0. Released v7.0.0. % 0.12/0.13 % Command : duper %s % 0.14/0.34 % Computer : n012.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.21/0.34 % WCLimit : 300 % 0.21/0.34 % DateTime : Thu Oct 2 22:07:08 EDT 2025 % 0.21/0.34 % CPUTime : % 3.37/3.56 SZS status Theorem for theBenchmark.p % 3.37/3.56 SZS output start Proof for theBenchmark.p % 3.37/3.56 Clause #0 (by assumption #[]): Eq % 3.37/3.56 (∀ (A : «type/realax/real»), % 3.37/3.56 Not % 3.37/3.56 («const/sets/FINITE» «type/realax/real» % 3.37/3.56 («const/sets/GSPEC» «type/realax/real» fun A0 => % 3.37/3.56 Exists fun A1 => «const/sets/SETSPEC» «type/realax/real» A0 («const/realax/real_le» A A1) A1))) % 3.37/3.56 True % 3.37/3.56 Clause #1 (by assumption #[]): Eq (∀ (A : Type) (A0 : A → Prop), «const/sets/SUBSET» A A0 («const/sets/UNIV» A)) True % 3.37/3.56 Clause #2 (by assumption #[]): Eq % 3.37/3.56 (∀ (A : Type) (A0 A1 : A → Prop), % 3.37/3.56 And («const/sets/FINITE» A A1) («const/sets/SUBSET» A A0 A1) → «const/sets/FINITE» A A0) % 3.37/3.56 True % 3.37/3.56 Clause #3 (by assumption #[]): Eq (∀ (A : Type) (A0 : A → Prop), Eq («const/sets/INFINITE» A A0) (Not («const/sets/FINITE» A A0))) True % 3.37/3.56 Clause #4 (by assumption #[]): Eq (Not («const/sets/INFINITE» «type/realax/real» («const/sets/UNIV» «type/realax/real»))) True % 3.37/3.56 Clause #5 (by clausification #[4]): Eq («const/sets/INFINITE» «type/realax/real» («const/sets/UNIV» «type/realax/real»)) False % 3.37/3.56 Clause #6 (by clausification #[2]): ∀ (a : Type), % 3.37/3.56 Eq (∀ (A0 A1 : a → Prop), And («const/sets/FINITE» a A1) («const/sets/SUBSET» a A0 A1) → «const/sets/FINITE» a A0) % 3.37/3.56 True % 3.37/3.56 Clause #7 (by clausification #[6]): ∀ (a : Type) (a_1 : a → Prop), % 3.37/3.56 Eq (∀ (A1 : a → Prop), And («const/sets/FINITE» a A1) («const/sets/SUBSET» a a_1 A1) → «const/sets/FINITE» a a_1) True % 3.37/3.56 Clause #8 (by clausification #[7]): ∀ (a : Type) (a_1 a_2 : a → Prop), % 3.37/3.56 Eq (And («const/sets/FINITE» a a_1) («const/sets/SUBSET» a a_2 a_1) → «const/sets/FINITE» a a_2) True % 3.37/3.56 Clause #9 (by clausification #[8]): ∀ (a : Type) (a_1 a_2 : a → Prop), % 3.37/3.56 Or (Eq (And («const/sets/FINITE» a a_1) («const/sets/SUBSET» a a_2 a_1)) False) (Eq («const/sets/FINITE» a a_2) True) % 3.37/3.56 Clause #10 (by clausification #[9]): ∀ (a : Type) (a_1 a_2 : a → Prop), % 3.37/3.56 Or (Eq («const/sets/FINITE» a a_1) True) % 3.37/3.56 (Or (Eq («const/sets/FINITE» a a_2) False) (Eq («const/sets/SUBSET» a a_1 a_2) False)) % 3.37/3.56 Clause #11 (by clausification #[1]): ∀ (a : Type), Eq (∀ (A0 : a → Prop), «const/sets/SUBSET» a A0 («const/sets/UNIV» a)) True % 3.37/3.56 Clause #12 (by clausification #[11]): ∀ (a : Type) (a_1 : a → Prop), Eq («const/sets/SUBSET» a a_1 («const/sets/UNIV» a)) True % 3.37/3.56 Clause #13 (by clausification #[3]): ∀ (a : Type), Eq (∀ (A0 : a → Prop), Eq («const/sets/INFINITE» a A0) (Not («const/sets/FINITE» a A0))) True % 3.37/3.56 Clause #14 (by clausification #[13]): ∀ (a : Type) (a_1 : a → Prop), Eq (Eq («const/sets/INFINITE» a a_1) (Not («const/sets/FINITE» a a_1))) True % 3.37/3.56 Clause #15 (by clausification #[14]): ∀ (a : Type) (a_1 : a → Prop), Eq («const/sets/INFINITE» a a_1) (Not («const/sets/FINITE» a a_1)) % 3.37/3.56 Clause #17 (by identity boolHoist #[15]): ∀ (a : Type) (a_1 : a → Prop), Or (Eq («const/sets/INFINITE» a a_1) (Not False)) (Eq («const/sets/FINITE» a a_1) True) % 3.37/3.56 Clause #19 (by bool simp #[17]): ∀ (a : Type) (a_1 : a → Prop), Or (Eq («const/sets/INFINITE» a a_1) True) (Eq («const/sets/FINITE» a a_1) True) % 3.37/3.56 Clause #20 (by superposition #[19, 5]): Or (Eq («const/sets/FINITE» «type/realax/real» fun x => «const/sets/UNIV» «type/realax/real» x) True) (Eq True False) % 3.37/3.56 Clause #22 (by clausification #[0]): ∀ (a : «type/realax/real»), % 3.37/3.56 Eq % 3.37/3.56 (Not % 3.37/3.56 («const/sets/FINITE» «type/realax/real» % 3.37/3.56 («const/sets/GSPEC» «type/realax/real» fun A0 => % 3.37/3.56 Exists fun A1 => «const/sets/SETSPEC» «type/realax/real» A0 («const/realax/real_le» a A1) A1))) % 3.37/3.56 True % 3.37/3.56 Clause #23 (by clausification #[22]): ∀ (a : «type/realax/real»), % 3.37/3.56 Eq % 3.37/3.56 («const/sets/FINITE» «type/realax/real» % 3.37/3.56 («const/sets/GSPEC» «type/realax/real» fun A0 => % 3.37/3.56 Exists fun A1 => «const/sets/SETSPEC» «type/realax/real» A0 («const/realax/real_le» a A1) A1)) % 3.37/3.56 False % 3.37/3.56 Clause #24 (by betaEtaReduce #[20]): Or (Eq («const/sets/FINITE» «type/realax/real» («const/sets/UNIV» «type/realax/real»)) True) (Eq True False) % 3.37/3.56 Clause #25 (by clausification #[24]): Eq («const/sets/FINITE» «type/realax/real» («const/sets/UNIV» «type/realax/real»)) True % 3.37/3.56 Clause #26 (by superposition #[25, 10]): ∀ (a : «type/realax/real» → Prop), % 3.37/3.56 Or (Eq («const/sets/FINITE» «type/realax/real» a) True) % 3.37/3.56 (Or (Eq True False) (Eq («const/sets/SUBSET» «type/realax/real» a («const/sets/UNIV» «type/realax/real»)) False)) % 3.37/3.56 Clause #29 (by clausification #[26]): ∀ (a : «type/realax/real» → Prop), % 3.37/3.56 Or (Eq («const/sets/FINITE» «type/realax/real» a) True) % 3.37/3.56 (Eq («const/sets/SUBSET» «type/realax/real» a («const/sets/UNIV» «type/realax/real»)) False) % 3.37/3.56 Clause #30 (by superposition #[29, 12]): ∀ (a : «type/realax/real» → Prop), Or (Eq («const/sets/FINITE» «type/realax/real» fun x => a x) True) (Eq False True) % 3.37/3.56 Clause #31 (by betaEtaReduce #[30]): ∀ (a : «type/realax/real» → Prop), Or (Eq («const/sets/FINITE» «type/realax/real» a) True) (Eq False True) % 3.37/3.56 Clause #32 (by clausification #[31]): ∀ (a : «type/realax/real» → Prop), Eq («const/sets/FINITE» «type/realax/real» a) True % 3.37/3.56 Clause #34 (by superposition #[32, 23]): Eq True False % 3.37/3.56 Clause #36 (by clausification #[34]): False % 3.37/3.56 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------