%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO031^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n014.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 08:08:27 PM UTC 2025 % Result : Theorem 4.48s 4.70s % Output : Proof 4.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO031^1 : TPTP v9.2.0. Released v3.7.0. % 0.12/0.13 % Command : duper %s % 0.13/0.34 % Computer : n014.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 14:03:38 EDT 2025 % 0.13/0.34 % CPUTime : % 4.48/4.70 SZS status Theorem for theBenchmark.p % 4.48/4.70 SZS output start Proof for theBenchmark.p % 4.48/4.70 Clause #0 (by assumption #[]): Eq (Not (Not (∀ (F : Prop → Prop), Exists fun X => Eq (F X) X))) True % 4.48/4.70 Clause #1 (by clausification #[0]): Eq (Not (∀ (F : Prop → Prop), Exists fun X => Eq (F X) X)) False % 4.48/4.70 Clause #2 (by clausification #[1]): Eq (∀ (F : Prop → Prop), Exists fun X => Eq (F X) X) True % 4.48/4.70 Clause #3 (by clausification #[2]): ∀ (a : Prop → Prop), Eq (Exists fun X => Eq (a X) X) True % 4.48/4.70 Clause #4 (by clausification #[3]): ∀ (a : Prop → Prop) (a_1 : Prop), Eq (Eq (a (skS.0 0 a a_1)) (skS.0 0 a a_1)) True % 4.48/4.70 Clause #5 (by clausification #[4]): ∀ (a : Prop → Prop) (a_1 : Prop), Eq (a (skS.0 0 a a_1)) (skS.0 0 a a_1) % 4.48/4.70 Clause #6 (by identity loobHoist #[5]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (a True) (skS.0 0 a a_1)) (Eq (skS.0 0 a a_1) False) % 4.48/4.70 Clause #7 (by identity boolHoist #[5]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (a False) (skS.0 0 a a_1)) (Eq (skS.0 0 a a_1) True) % 4.48/4.70 Clause #8 (by identity loobHoist #[6]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (skS.0 0 a a_1) False) (Or (Eq (a True) (skS.0 0 a True)) (Eq a_1 False)) % 4.48/4.70 Clause #10 (by identity loobHoist #[8]): ∀ (a : Prop → Prop) (a_1 : Prop), % 4.48/4.70 Or (Eq (a True) (skS.0 0 a True)) (Or (Eq a_1 False) (Or (Eq (skS.0 0 a True) False) (Eq a_1 False))) % 4.48/4.70 Clause #12 (by eliminate duplicate literals #[10]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (a True) (skS.0 0 a True)) (Or (Eq a_1 False) (Eq (skS.0 0 a True) False)) % 4.48/4.70 Clause #13 (by falseElim #[12]): ∀ (a : Prop → Prop), Or (Eq (a True) (skS.0 0 a True)) (Eq (skS.0 0 a True) False) % 4.48/4.70 Clause #14 (by identity loobHoist #[7]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (skS.0 0 a a_1) True) (Or (Eq (a False) (skS.0 0 a True)) (Eq a_1 False)) % 4.48/4.70 Clause #16 (by identity loobHoist #[14]): ∀ (a : Prop → Prop) (a_1 : Prop), % 4.48/4.70 Or (Eq (a False) (skS.0 0 a True)) (Or (Eq a_1 False) (Or (Eq (skS.0 0 a True) True) (Eq a_1 False))) % 4.48/4.70 Clause #18 (by eliminate duplicate literals #[16]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (a False) (skS.0 0 a True)) (Or (Eq a_1 False) (Eq (skS.0 0 a True) True)) % 4.48/4.70 Clause #19 (by falseElim #[18]): ∀ (a : Prop → Prop), Or (Eq (a False) (skS.0 0 a True)) (Eq (skS.0 0 a True) True) % 4.48/4.70 Clause #22 (by equality factoring #[19]): ∀ (a : Prop → Prop), Or (Ne (a False) True) (Eq (skS.0 0 a True) True) % 4.48/4.70 Clause #26 (by clausification #[22]): ∀ (a : Prop → Prop), Or (Eq (skS.0 0 a True) True) (Or (Eq (a False) False) (Eq True False)) % 4.48/4.70 Clause #28 (by clausification #[26]): ∀ (a : Prop → Prop), Or (Eq (skS.0 0 a True) True) (Eq (a False) False) % 4.48/4.70 Clause #30 (by neHoist #[28]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), % 4.48/4.70 Or (Eq (skS.0 0 (fun x => Ne (a_1 x) (a_2 x)) True) True) (Or (Eq True False) (Eq (a_1 False) (a_2 False))) % 4.48/4.70 Clause #277 (by clausification #[30]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), % 4.48/4.70 Or (Eq (skS.0 0 (fun x => Ne (a_1 x) (a_2 x)) True) True) (Eq (a_1 False) (a_2 False)) % 4.48/4.70 Clause #278 (by superposition #[277, 13]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), % 4.48/4.70 Or (Eq (a_1 False) (a_2 False)) (Or (Eq (Ne (a_1 True) (a_2 True)) True) (Eq True False)) % 4.48/4.70 Clause #367 (by clausification #[278]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), % 4.48/4.70 Or (Eq (a_1 False) (a_2 False)) (Or (Eq True False) (Ne (a_1 True) (a_2 True))) % 4.48/4.70 Clause #368 (by clausification #[367]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), Or (Eq (a_1 False) (a_2 False)) (Ne (a_1 True) (a_2 True)) % 4.48/4.70 Clause #369 (by equality resolution #[368]): Eq ((fun x => x) False) ((fun x => True) False) % 4.48/4.70 Clause #390 (by betaEtaReduce #[369]): Eq False True % 4.48/4.70 Clause #391 (by clausification #[390]): False % 4.48/4.70 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------