%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO212^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n020.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 08:08:45 PM UTC 2025 % Result : Theorem 3.62s 3.78s % Output : Proof 3.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SYO212^5 : TPTP v9.2.0. Released v4.0.0. % 0.14/0.14 % Command : duper %s % 0.15/0.33 % Computer : n020.cluster.edu % 0.15/0.33 % Model : x86_64 x86_64 % 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.33 % Memory : 8042.1875MB % 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.33 % CPULimit : 300 % 0.15/0.33 % WCLimit : 300 % 0.15/0.33 % DateTime : Fri Oct 3 13:20:38 EDT 2025 % 0.15/0.33 % CPUTime : % 3.62/3.78 SZS status Theorem for theBenchmark.p % 3.62/3.78 SZS output start Proof for theBenchmark.p % 3.62/3.78 Clause #0 (by assumption #[]): Eq (Not (∀ (Xp : Prop → Prop), And (Xp a) (Xp b) → Xp (And a b))) True % 3.62/3.78 Clause #1 (by clausification #[0]): Eq (∀ (Xp : Prop → Prop), And (Xp a) (Xp b) → Xp (And a b)) False % 3.62/3.78 Clause #2 (by clausification #[1]): ∀ (a_1 : Prop → Prop), Eq (Not (And (skS.0 0 a_1 a) (skS.0 0 a_1 b) → skS.0 0 a_1 (And a b))) True % 3.62/3.78 Clause #3 (by clausification #[2]): ∀ (a_1 : Prop → Prop), Eq (And (skS.0 0 a_1 a) (skS.0 0 a_1 b) → skS.0 0 a_1 (And a b)) False % 3.62/3.78 Clause #4 (by clausification #[3]): ∀ (a_1 : Prop → Prop), Eq (And (skS.0 0 a_1 a) (skS.0 0 a_1 b)) True % 3.62/3.78 Clause #5 (by clausification #[3]): ∀ (a_1 : Prop → Prop), Eq (skS.0 0 a_1 (And a b)) False % 3.62/3.78 Clause #6 (by clausification #[4]): ∀ (a : Prop → Prop), Eq (skS.0 0 a b) True % 3.62/3.78 Clause #7 (by clausification #[4]): ∀ (a_1 : Prop → Prop), Eq (skS.0 0 a_1 a) True % 3.62/3.78 Clause #8 (by identity loobHoist #[6]): ∀ (a : Prop → Prop), Or (Eq (skS.0 0 a True) True) (Eq b False) % 3.62/3.78 Clause #9 (by identity boolHoist #[6]): ∀ (a : Prop → Prop), Or (Eq (skS.0 0 a False) True) (Eq b True) % 3.62/3.78 Clause #11 (by identity boolHoist #[7]): ∀ (a_1 : Prop → Prop), Or (Eq (skS.0 0 a_1 False) True) (Eq a True) % 3.62/3.78 Clause #12 (by identity loobHoist #[5]): ∀ (a_1 : Prop → Prop), Or (Eq (skS.0 0 a_1 True) False) (Eq (And a b) False) % 3.62/3.78 Clause #13 (by identity boolHoist #[5]): ∀ (a_1 : Prop → Prop), Or (Eq (skS.0 0 a_1 False) False) (Eq (And a b) True) % 3.62/3.78 Clause #14 (by clausification #[12]): ∀ (a_1 : Prop → Prop), Or (Eq (skS.0 0 a_1 True) False) (Or (Eq a False) (Eq b False)) % 3.62/3.78 Clause #15 (by clausification #[13]): ∀ (a : Prop → Prop), Or (Eq (skS.0 0 a False) False) (Eq b True) % 3.62/3.78 Clause #16 (by clausification #[13]): ∀ (a_1 : Prop → Prop), Or (Eq (skS.0 0 a_1 False) False) (Eq a True) % 3.62/3.78 Clause #17 (by superposition #[15, 9]): Or (Eq b True) (Or (Eq False True) (Eq b True)) % 3.62/3.78 Clause #21 (by clausification #[17]): Or (Eq b True) (Eq b True) % 3.62/3.78 Clause #22 (by eliminate duplicate literals #[21]): Eq b True % 3.62/3.78 Clause #23 (by backward demodulation #[22, 8]): ∀ (a : Prop → Prop), Or (Eq (skS.0 0 a True) True) (Eq True False) % 3.62/3.78 Clause #25 (by backward demodulation #[22, 14]): ∀ (a_1 : Prop → Prop), Or (Eq (skS.0 0 a_1 True) False) (Or (Eq a False) (Eq True False)) % 3.62/3.78 Clause #27 (by clausification #[23]): ∀ (a : Prop → Prop), Eq (skS.0 0 a True) True % 3.62/3.78 Clause #28 (by superposition #[16, 11]): Or (Eq a True) (Or (Eq False True) (Eq a True)) % 3.62/3.78 Clause #30 (by clausification #[28]): Or (Eq a True) (Eq a True) % 3.62/3.78 Clause #31 (by eliminate duplicate literals #[30]): Eq a True % 3.62/3.78 Clause #32 (by clausification #[25]): ∀ (a_1 : Prop → Prop), Or (Eq (skS.0 0 a_1 True) False) (Eq a False) % 3.62/3.78 Clause #33 (by forward demodulation #[32, 31]): ∀ (a : Prop → Prop), Or (Eq (skS.0 0 a True) False) (Eq True False) % 3.62/3.78 Clause #34 (by clausification #[33]): ∀ (a : Prop → Prop), Eq (skS.0 0 a True) False % 3.62/3.78 Clause #35 (by superposition #[34, 27]): Eq False True % 3.62/3.78 Clause #36 (by clausification #[35]): False % 3.62/3.78 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------