%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO513^1 : TPTP v9.2.0. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n007.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 08:09:13 PM UTC 2025 % Result : Theorem 3.65s 3.90s % Output : Proof 3.73s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SYO513^1 : TPTP v9.2.0. Released v4.1.0. % 0.08/0.13 % Command : duper %s % 0.13/0.34 % Computer : n007.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 : Fri Oct 3 13:38:23 EDT 2025 % 0.13/0.35 % CPUTime : % 3.65/3.90 SZS status Theorem for theBenchmark.p % 3.65/3.90 SZS output start Proof for theBenchmark.p % 3.65/3.90 Clause #0 (by assumption #[]): Eq (Not (Exists fun C => ∀ (P : Prop → Prop), (Exists fun X => P X) → P (C P))) True % 3.65/3.90 Clause #1 (by betaEtaReduce #[0]): Eq (Not (Exists fun C => ∀ (P : Prop → Prop), Exists P → P (C P))) True % 3.65/3.90 Clause #2 (by clausification #[1]): Eq (Exists fun C => ∀ (P : Prop → Prop), Exists P → P (C P)) False % 3.65/3.90 Clause #3 (by clausification #[2]): ∀ (a : (Prop → Prop) → Prop), Eq (∀ (P : Prop → Prop), Exists P → P (a P)) False % 3.65/3.90 Clause #4 (by clausification #[3]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop), % 3.65/3.90 Eq (Not (Exists (skS.0 0 a a_1) → skS.0 0 a a_1 (a (skS.0 0 a a_1)))) True % 3.65/3.90 Clause #5 (by clausification #[4]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop), Eq (Exists (skS.0 0 a a_1) → skS.0 0 a a_1 (a (skS.0 0 a a_1))) False % 3.65/3.90 Clause #6 (by clausification #[5]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop), Eq (Exists (skS.0 0 a a_1)) True % 3.65/3.90 Clause #7 (by clausification #[5]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop), Eq (skS.0 0 a a_1 (a (skS.0 0 a a_1))) False % 3.65/3.90 Clause #8 (by clausification #[6]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop) (a_2 : Prop), Eq (skS.0 0 a a_1 (skS.0 1 a a_1 a_2)) True % 3.65/3.90 Clause #9 (by identity loobHoist #[8]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop) (a_2 : Prop), % 3.65/3.90 Or (Eq (skS.0 0 a a_1 True) True) (Eq (skS.0 1 a a_1 a_2) False) % 3.65/3.90 Clause #10 (by identity boolHoist #[8]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop) (a_2 : Prop), % 3.65/3.90 Or (Eq (skS.0 0 a a_1 False) True) (Eq (skS.0 1 a a_1 a_2) True) % 3.65/3.90 Clause #12 (by identity boolHoist #[9]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop) (a_2 : Prop), % 3.65/3.90 Or (Eq (skS.0 0 a a_1 True) True) (Or (Eq (skS.0 1 a a_1 False) False) (Eq a_2 True)) % 3.65/3.90 Clause #13 (by identity loobHoist #[7]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop), Or (Eq (skS.0 0 a a_1 True) False) (Eq (a (skS.0 0 a a_1)) False) % 3.65/3.90 Clause #14 (by identity boolHoist #[7]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop), Or (Eq (skS.0 0 a a_1 False) False) (Eq (a (skS.0 0 a a_1)) True) % 3.65/3.90 Clause #16 (by identity boolHoist #[10]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop) (a_2 : Prop), % 3.65/3.90 Or (Eq (skS.0 0 a a_1 False) True) (Or (Eq (skS.0 1 a a_1 False) True) (Eq a_2 True)) % 3.65/3.90 Clause #29 (by equality factoring #[16]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop), % 3.65/3.90 Or (Eq (skS.0 0 a a_1 False) True) (Or (Ne True True) (Eq (skS.0 1 a a_1 False) True)) % 3.65/3.90 Clause #39 (by clausification #[29]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop), % 3.65/3.90 Or (Eq (skS.0 0 a a_1 False) True) (Or (Eq (skS.0 1 a a_1 False) True) (Or (Eq True False) (Eq True False))) % 3.65/3.90 Clause #41 (by clausification #[39]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop), % 3.65/3.90 Or (Eq (skS.0 0 a a_1 False) True) (Or (Eq (skS.0 1 a a_1 False) True) (Eq True False)) % 3.65/3.90 Clause #42 (by clausification #[41]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop), Or (Eq (skS.0 0 a a_1 False) True) (Eq (skS.0 1 a a_1 False) True) % 3.65/3.90 Clause #43 (by superposition #[42, 12]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop) (a_2 : Prop), % 3.65/3.90 Or (Eq (skS.0 0 (fun x => a x) (fun x => a_1 x) False) True) % 3.65/3.90 (Or (Eq (skS.0 0 a a_1 True) True) (Or (Eq True False) (Eq a_2 True))) % 3.65/3.90 Clause #48 (by betaEtaReduce #[43]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop) (a_2 : Prop), % 3.65/3.90 Or (Eq (skS.0 0 a a_1 False) True) (Or (Eq (skS.0 0 a a_1 True) True) (Or (Eq True False) (Eq a_2 True))) % 3.65/3.90 Clause #49 (by clausification #[48]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop) (a_2 : Prop), % 3.65/3.90 Or (Eq (skS.0 0 a a_1 False) True) (Or (Eq (skS.0 0 a a_1 True) True) (Eq a_2 True)) % 3.65/3.90 Clause #55 (by equality factoring #[49]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop), % 3.65/3.90 Or (Eq (skS.0 0 a a_1 True) True) (Or (Ne True True) (Eq (skS.0 0 a a_1 False) True)) % 3.65/3.90 Clause #66 (by clausification #[55]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop), % 3.65/3.90 Or (Eq (skS.0 0 a a_1 True) True) (Or (Eq (skS.0 0 a a_1 False) True) (Or (Eq True False) (Eq True False))) % 3.73/3.91 Clause #68 (by clausification #[66]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop), % 3.73/3.91 Or (Eq (skS.0 0 a a_1 True) True) (Or (Eq (skS.0 0 a a_1 False) True) (Eq True False)) % 3.73/3.91 Clause #69 (by clausification #[68]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop), Or (Eq (skS.0 0 a a_1 True) True) (Eq (skS.0 0 a a_1 False) True) % 3.73/3.91 Clause #70 (by superposition #[69, 14]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop), % 3.73/3.91 Or (Eq (skS.0 0 (fun x => a x) (fun x => a_1 x) True) True) (Or (Eq True False) (Eq (a (skS.0 0 a a_1)) True)) % 3.73/3.91 Clause #77 (by betaEtaReduce #[70]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop), % 3.73/3.91 Or (Eq (skS.0 0 a a_1 True) True) (Or (Eq True False) (Eq (a (skS.0 0 a a_1)) True)) % 3.73/3.91 Clause #78 (by clausification #[77]): ∀ (a : (Prop → Prop) → Prop) (a_1 : Prop → Prop), Or (Eq (skS.0 0 a a_1 True) True) (Eq (a (skS.0 0 a a_1)) True) % 3.73/3.91 Clause #82 (by equality factoring #[78]): ∀ (a : Prop → Prop), Or (Ne True True) (Eq (skS.0 0 (fun x => x True) a True) True) % 3.73/3.91 Clause #118 (by clausification #[82]): ∀ (a : Prop → Prop), Or (Eq (skS.0 0 (fun x => x True) a True) True) (Or (Eq True False) (Eq True False)) % 3.73/3.91 Clause #120 (by clausification #[118]): ∀ (a : Prop → Prop), Or (Eq (skS.0 0 (fun x => x True) a True) True) (Eq True False) % 3.73/3.91 Clause #121 (by clausification #[120]): ∀ (a : Prop → Prop), Eq (skS.0 0 (fun x => x True) a True) True % 3.73/3.91 Clause #122 (by superposition #[121, 13]): Or (Eq True False) (Eq True False) % 3.73/3.91 Clause #132 (by clausification #[122]): Eq True False % 3.73/3.91 Clause #133 (by clausification #[132]): False % 3.73/3.91 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------