%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV485^1 : TPTP v9.2.0. Released v7.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n002.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 08:03:13 PM UTC 2025 % Result : Theorem 3.85s 4.04s % Output : Proof 3.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEV485^1 : TPTP v9.2.0. Released v7.0.0. % 0.07/0.13 % Command : duper %s % 0.14/0.35 % Computer : n002.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 : Fri Oct 3 01:41:53 EDT 2025 % 0.14/0.35 % CPUTime : % 3.85/4.04 SZS status Theorem for theBenchmark.p % 3.85/4.04 SZS output start Proof for theBenchmark.p % 3.85/4.04 Clause #0 (by assumption #[]): Eq % 3.85/4.04 (∀ (A : Type) (A0 : A → Prop) (A1 : «type/nums/num»), % 3.85/4.04 Eq («const/sets/HAS_SIZE» A A0 A1) (And («const/sets/FINITE» A A0) (Eq («const/sets/CARD» A A0) A1))) % 3.85/4.04 True % 3.85/4.04 Clause #1 (by assumption #[]): Eq % 3.85/4.04 («const/sets/HAS_SIZE» Prop («const/sets/UNIV» Prop) % 3.85/4.04 («const/nums/NUMERAL» («const/nums/BIT0» («const/nums/BIT1» «const/nums/_0»)))) % 3.85/4.04 True % 3.85/4.04 Clause #2 (by assumption #[]): Eq (Not («const/sets/FINITE» Prop («const/sets/UNIV» Prop))) True % 3.85/4.04 Clause #3 (by clausification #[2]): Eq («const/sets/FINITE» Prop («const/sets/UNIV» Prop)) False % 3.85/4.04 Clause #4 (by clausification #[0]): ∀ (a : Type), % 3.85/4.04 Eq % 3.85/4.04 (∀ (A0 : a → Prop) (A1 : «type/nums/num»), % 3.85/4.04 Eq («const/sets/HAS_SIZE» a A0 A1) (And («const/sets/FINITE» a A0) (Eq («const/sets/CARD» a A0) A1))) % 3.85/4.04 True % 3.85/4.04 Clause #5 (by clausification #[4]): ∀ (a : Type) (a_1 : a → Prop), % 3.85/4.04 Eq % 3.85/4.04 (∀ (A1 : «type/nums/num»), % 3.85/4.04 Eq («const/sets/HAS_SIZE» a a_1 A1) (And («const/sets/FINITE» a a_1) (Eq («const/sets/CARD» a a_1) A1))) % 3.85/4.04 True % 3.85/4.04 Clause #6 (by clausification #[5]): ∀ (a : Type) (a_1 : a → Prop) (a_2 : «type/nums/num»), % 3.85/4.04 Eq (Eq («const/sets/HAS_SIZE» a a_1 a_2) (And («const/sets/FINITE» a a_1) (Eq («const/sets/CARD» a a_1) a_2))) True % 3.85/4.04 Clause #7 (by clausification #[6]): ∀ (a : Type) (a_1 : a → Prop) (a_2 : «type/nums/num»), % 3.85/4.04 Eq («const/sets/HAS_SIZE» a a_1 a_2) (And («const/sets/FINITE» a a_1) (Eq («const/sets/CARD» a a_1) a_2)) % 3.85/4.04 Clause #8 (by identity loobHoist #[7]): ∀ (a : Type) (a_1 : a → Prop) (a_2 : «type/nums/num»), % 3.85/4.04 Or (Eq («const/sets/HAS_SIZE» a a_1 a_2) (And («const/sets/FINITE» a a_1) True)) % 3.85/4.04 (Eq (Eq («const/sets/CARD» a a_1) a_2) False) % 3.85/4.04 Clause #9 (by identity boolHoist #[7]): ∀ (a : Type) (a_1 : a → Prop) (a_2 : «type/nums/num»), % 3.85/4.04 Or (Eq («const/sets/HAS_SIZE» a a_1 a_2) (And («const/sets/FINITE» a a_1) False)) % 3.85/4.04 (Eq (Eq («const/sets/CARD» a a_1) a_2) True) % 3.85/4.04 Clause #10 (by clausification #[8]): ∀ (a : Type) (a_1 : a → Prop) (a_2 : «type/nums/num»), % 3.85/4.04 Or (Eq («const/sets/HAS_SIZE» a a_1 a_2) (And («const/sets/FINITE» a a_1) True)) (Ne («const/sets/CARD» a a_1) a_2) % 3.85/4.04 Clause #11 (by bool simp #[10]): ∀ (a : Type) (a_1 : a → Prop) (a_2 : «type/nums/num»), % 3.85/4.04 Or (Eq («const/sets/HAS_SIZE» a a_1 a_2) («const/sets/FINITE» a a_1)) (Ne («const/sets/CARD» a a_1) a_2) % 3.85/4.04 Clause #12 (by destructive equality resolution #[11]): ∀ (a : Type) (a_1 : a → Prop), Eq («const/sets/HAS_SIZE» a a_1 («const/sets/CARD» a a_1)) («const/sets/FINITE» a a_1) % 3.85/4.04 Clause #17 (by clausification #[9]): ∀ (a : Type) (a_1 : a → Prop) (a_2 : «type/nums/num»), % 3.85/4.04 Or (Eq («const/sets/HAS_SIZE» a a_1 a_2) (And («const/sets/FINITE» a a_1) False)) (Eq («const/sets/CARD» a a_1) a_2) % 3.85/4.04 Clause #18 (by bool simp #[17]): ∀ (a : Type) (a_1 : a → Prop) (a_2 : «type/nums/num»), % 3.85/4.04 Or (Eq («const/sets/HAS_SIZE» a a_1 a_2) False) (Eq («const/sets/CARD» a a_1) a_2) % 3.85/4.04 Clause #19 (by superposition #[18, 1]): Or % 3.85/4.04 (Eq («const/sets/CARD» Prop fun x => «const/sets/UNIV» Prop x) % 3.85/4.04 («const/nums/NUMERAL» («const/nums/BIT0» («const/nums/BIT1» «const/nums/_0»)))) % 3.85/4.04 (Eq False True) % 3.85/4.04 Clause #21 (by betaEtaReduce #[19]): Or % 3.85/4.04 (Eq («const/sets/CARD» Prop («const/sets/UNIV» Prop)) % 3.85/4.04 («const/nums/NUMERAL» («const/nums/BIT0» («const/nums/BIT1» «const/nums/_0»)))) % 3.85/4.04 (Eq False True) % 3.85/4.04 Clause #22 (by clausification #[21]): Eq («const/sets/CARD» Prop («const/sets/UNIV» Prop)) % 3.85/4.04 («const/nums/NUMERAL» («const/nums/BIT0» («const/nums/BIT1» «const/nums/_0»))) % 3.85/4.04 Clause #23 (by superposition #[22, 12]): Eq % 3.85/4.04 («const/sets/HAS_SIZE» Prop («const/sets/UNIV» Prop) % 3.85/4.04 («const/nums/NUMERAL» («const/nums/BIT0» («const/nums/BIT1» «const/nums/_0»)))) % 3.85/4.04 («const/sets/FINITE» Prop («const/sets/UNIV» Prop)) % 3.85/4.04 Clause #25 (by forward demodulation #[23, 3]): Eq % 3.85/4.04 («const/sets/HAS_SIZE» Prop («const/sets/UNIV» Prop) % 3.85/4.04 («const/nums/NUMERAL» («const/nums/BIT0» («const/nums/BIT1» «const/nums/_0»)))) % 3.85/4.04 False % 3.85/4.04 Clause #26 (by superposition #[25, 1]): Eq False True % 3.85/4.04 Clause #27 (by clausification #[26]): False % 3.85/4.04 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------