%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO199^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n013.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 08:08:44 PM UTC 2025 % Result : Theorem 8.46s 8.64s % Output : Proof 8.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SYO199^5 : TPTP v9.2.0. Released v4.0.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n013.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 12:58:38 EDT 2025 % 0.13/0.34 % CPUTime : % 8.46/8.64 SZS status Theorem for theBenchmark.p % 8.46/8.64 SZS output start Proof for theBenchmark.p % 8.46/8.64 Clause #0 (by assumption #[]): Eq (Not (Exists fun Xp => ∀ (Xx Xy : Prop), And (Xp Xx) (Xp Xy))) True % 8.46/8.64 Clause #1 (by clausification #[0]): Eq (Exists fun Xp => ∀ (Xx Xy : Prop), And (Xp Xx) (Xp Xy)) False % 8.46/8.64 Clause #2 (by clausification #[1]): ∀ (a : Prop → Prop), Eq (∀ (Xx Xy : Prop), And (a Xx) (a Xy)) False % 8.46/8.64 Clause #3 (by clausification #[2]): ∀ (a : Prop → Prop) (a_1 : Prop), Eq (Not (∀ (Xy : Prop), And (a (skS.0 0 a a_1)) (a Xy))) True % 8.46/8.64 Clause #4 (by clausification #[3]): ∀ (a : Prop → Prop) (a_1 : Prop), Eq (∀ (Xy : Prop), And (a (skS.0 0 a a_1)) (a Xy)) False % 8.46/8.64 Clause #5 (by clausification #[4]): ∀ (a : Prop → Prop) (a_1 a_2 : Prop), Eq (Not (And (a (skS.0 0 a a_1)) (a (skS.0 1 a a_1 a_2)))) True % 8.46/8.64 Clause #6 (by clausification #[5]): ∀ (a : Prop → Prop) (a_1 a_2 : Prop), Eq (And (a (skS.0 0 a a_1)) (a (skS.0 1 a a_1 a_2))) False % 8.46/8.64 Clause #7 (by clausification #[6]): ∀ (a : Prop → Prop) (a_1 a_2 : Prop), Or (Eq (a (skS.0 0 a a_1)) False) (Eq (a (skS.0 1 a a_1 a_2)) False) % 8.46/8.64 Clause #8 (by identity loobHoist #[7]): ∀ (a : Prop → Prop) (a_1 a_2 : Prop), % 8.46/8.64 Or (Eq (a (skS.0 1 a a_1 a_2)) False) (Or (Eq (a True) False) (Eq (skS.0 0 a a_1) False)) % 8.46/8.64 Clause #9 (by identity boolHoist #[7]): ∀ (a : Prop → Prop) (a_1 a_2 : Prop), % 8.46/8.64 Or (Eq (a (skS.0 1 a a_1 a_2)) False) (Or (Eq (a False) False) (Eq (skS.0 0 a a_1) True)) % 8.46/8.64 Clause #10 (by identity loobHoist #[8]): ∀ (a : Prop → Prop) (a_1 a_2 : Prop), % 8.46/8.64 Or (Eq (a True) False) (Or (Eq (skS.0 0 a a_1) False) (Or (Eq (a True) False) (Eq (skS.0 1 a a_1 a_2) False))) % 8.46/8.64 Clause #11 (by identity boolHoist #[8]): ∀ (a : Prop → Prop) (a_1 a_2 : Prop), % 8.46/8.64 Or (Eq (a True) False) (Or (Eq (skS.0 0 a a_1) False) (Or (Eq (a False) False) (Eq (skS.0 1 a a_1 a_2) True))) % 8.46/8.64 Clause #12 (by eliminate duplicate literals #[10]): ∀ (a : Prop → Prop) (a_1 a_2 : Prop), % 8.46/8.64 Or (Eq (a True) False) (Or (Eq (skS.0 0 a a_1) False) (Eq (skS.0 1 a a_1 a_2) False)) % 8.46/8.64 Clause #13 (by identity loobHoist #[12]): ∀ (a : Prop → Prop) (a_1 a_2 : Prop), % 8.46/8.64 Or (Eq (a True) False) (Or (Eq (skS.0 1 a a_1 a_2) False) (Or (Eq (skS.0 0 a True) False) (Eq a_1 False))) % 8.46/8.64 Clause #15 (by identity loobHoist #[13]): ∀ (a : Prop → Prop) (a_1 a_2 : Prop), % 8.46/8.64 Or (Eq (a True) False) % 8.46/8.64 (Or (Eq (skS.0 0 a True) False) (Or (Eq a_1 False) (Or (Eq (skS.0 1 a a_1 True) False) (Eq a_2 False)))) % 8.46/8.64 Clause #17 (by identity loobHoist #[15]): ∀ (a : Prop → Prop) (a_1 a_2 : Prop), % 8.46/8.64 Or (Eq (a True) False) % 8.46/8.64 (Or (Eq (skS.0 0 a True) False) % 8.46/8.64 (Or (Eq a_1 False) (Or (Eq a_2 False) (Or (Eq (skS.0 1 a True True) False) (Eq a_1 False))))) % 8.46/8.64 Clause #19 (by eliminate duplicate literals #[17]): ∀ (a : Prop → Prop) (a_1 a_2 : Prop), % 8.46/8.64 Or (Eq (a True) False) % 8.46/8.64 (Or (Eq (skS.0 0 a True) False) (Or (Eq a_1 False) (Or (Eq a_2 False) (Eq (skS.0 1 a True True) False)))) % 8.46/8.64 Clause #22 (by existsHoist #[19]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 : (x : Prop) → a x → Prop) (a_2 a_3 : Prop) (a_4 : a True), % 8.46/8.64 Or (Eq (skS.0 0 (fun x => Exists (a_1 x)) True) False) % 8.46/8.64 (Or (Eq a_2 False) % 8.46/8.64 (Or (Eq a_3 False) % 8.46/8.64 (Or (Eq (skS.0 1 (fun x => Exists (a_1 x)) True True) False) % 8.46/8.64 (Or (Eq True False) (Eq ((fun x => a_1 True x) a_4) False))))) % 8.46/8.64 Clause #26 (by identity loobHoist #[9]): ∀ (a : Prop → Prop) (a_1 a_2 : Prop), % 8.46/8.64 Or (Eq (a False) False) (Or (Eq (skS.0 0 a a_1) True) (Or (Eq (a True) False) (Eq (skS.0 1 a a_1 a_2) False))) % 8.46/8.64 Clause #27 (by identity boolHoist #[9]): ∀ (a : Prop → Prop) (a_1 a_2 : Prop), % 8.46/8.64 Or (Eq (a False) False) (Or (Eq (skS.0 0 a a_1) True) (Or (Eq (a False) False) (Eq (skS.0 1 a a_1 a_2) True))) % 8.46/8.64 Clause #28 (by identity loobHoist #[26]): ∀ (a : Prop → Prop) (a_1 a_2 : Prop), % 8.46/8.64 Or (Eq (a False) False) % 8.46/8.64 (Or (Eq (a True) False) (Or (Eq (skS.0 1 a a_1 a_2) False) (Or (Eq (skS.0 0 a True) True) (Eq a_1 False)))) % 8.46/8.64 Clause #30 (by identity loobHoist #[28]): ∀ (a : Prop → Prop) (a_1 a_2 : Prop), % 8.46/8.64 Or (Eq (a False) False) % 8.46/8.64 (Or (Eq (a True) False) % 8.46/8.64 (Or (Eq (skS.0 0 a True) True) (Or (Eq a_1 False) (Or (Eq (skS.0 1 a a_1 True) False) (Eq a_2 False))))) % 8.46/8.67 Clause #32 (by identity loobHoist #[30]): ∀ (a : Prop → Prop) (a_1 a_2 : Prop), % 8.46/8.67 Or (Eq (a False) False) % 8.46/8.67 (Or (Eq (a True) False) % 8.46/8.67 (Or (Eq (skS.0 0 a True) True) % 8.46/8.67 (Or (Eq a_1 False) (Or (Eq a_2 False) (Or (Eq (skS.0 1 a True True) False) (Eq a_1 False)))))) % 8.46/8.67 Clause #34 (by eliminate duplicate literals #[32]): ∀ (a : Prop → Prop) (a_1 a_2 : Prop), % 8.46/8.67 Or (Eq (a False) False) % 8.46/8.67 (Or (Eq (a True) False) % 8.46/8.67 (Or (Eq (skS.0 0 a True) True) (Or (Eq a_1 False) (Or (Eq a_2 False) (Eq (skS.0 1 a True True) False))))) % 8.46/8.67 Clause #37 (by existsHoist #[34]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 : (x : Prop) → a x → Prop) (a_2 a_3 : Prop) (a_4 : a False), % 8.46/8.67 Or (Eq ((fun x => Exists (a_1 x)) True) False) % 8.46/8.67 (Or (Eq (skS.0 0 (fun x => Exists (a_1 x)) True) True) % 8.46/8.67 (Or (Eq a_2 False) % 8.46/8.67 (Or (Eq a_3 False) % 8.46/8.67 (Or (Eq (skS.0 1 (fun x => Exists (a_1 x)) True True) False) % 8.46/8.67 (Or (Eq True False) (Eq ((fun x => a_1 False x) a_4) False)))))) % 8.46/8.67 Clause #45 (by identity loobHoist #[11]): ∀ (a : Prop → Prop) (a_1 a_2 : Prop), % 8.46/8.67 Or (Eq (a True) False) % 8.46/8.67 (Or (Eq (a False) False) (Or (Eq (skS.0 1 a a_1 a_2) True) (Or (Eq (skS.0 0 a True) False) (Eq a_1 False)))) % 8.46/8.67 Clause #47 (by identity loobHoist #[45]): ∀ (a : Prop → Prop) (a_1 a_2 : Prop), % 8.46/8.67 Or (Eq (a True) False) % 8.46/8.67 (Or (Eq (a False) False) % 8.46/8.67 (Or (Eq (skS.0 0 a True) False) (Or (Eq a_1 False) (Or (Eq (skS.0 1 a a_1 True) True) (Eq a_2 False))))) % 8.46/8.67 Clause #49 (by identity loobHoist #[47]): ∀ (a : Prop → Prop) (a_1 a_2 : Prop), % 8.46/8.67 Or (Eq (a True) False) % 8.46/8.67 (Or (Eq (a False) False) % 8.46/8.67 (Or (Eq (skS.0 0 a True) False) % 8.46/8.67 (Or (Eq a_1 False) (Or (Eq a_2 False) (Or (Eq (skS.0 1 a True True) True) (Eq a_1 False)))))) % 8.46/8.67 Clause #51 (by eliminate duplicate literals #[49]): ∀ (a : Prop → Prop) (a_1 a_2 : Prop), % 8.46/8.67 Or (Eq (a True) False) % 8.46/8.67 (Or (Eq (a False) False) % 8.46/8.67 (Or (Eq (skS.0 0 a True) False) (Or (Eq a_1 False) (Or (Eq a_2 False) (Eq (skS.0 1 a True True) True))))) % 8.46/8.67 Clause #54 (by existsHoist #[51]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 : (x : Prop) → a x → Prop) (a_2 a_3 : Prop) (a_4 : a True), % 8.46/8.67 Or (Eq ((fun x => Exists (a_1 x)) False) False) % 8.46/8.67 (Or (Eq (skS.0 0 (fun x => Exists (a_1 x)) True) False) % 8.46/8.67 (Or (Eq a_2 False) % 8.46/8.67 (Or (Eq a_3 False) % 8.46/8.67 (Or (Eq (skS.0 1 (fun x => Exists (a_1 x)) True True) True) % 8.46/8.67 (Or (Eq True False) (Eq ((fun x => a_1 True x) a_4) False)))))) % 8.46/8.67 Clause #58 (by eliminate duplicate literals #[27]): ∀ (a : Prop → Prop) (a_1 a_2 : Prop), % 8.46/8.67 Or (Eq (a False) False) (Or (Eq (skS.0 0 a a_1) True) (Eq (skS.0 1 a a_1 a_2) True)) % 8.46/8.67 Clause #59 (by identity loobHoist #[58]): ∀ (a : Prop → Prop) (a_1 a_2 : Prop), % 8.46/8.67 Or (Eq (a False) False) (Or (Eq (skS.0 1 a a_1 a_2) True) (Or (Eq (skS.0 0 a True) True) (Eq a_1 False))) % 8.46/8.67 Clause #61 (by identity loobHoist #[59]): ∀ (a : Prop → Prop) (a_1 a_2 : Prop), % 8.46/8.67 Or (Eq (a False) False) % 8.46/8.67 (Or (Eq (skS.0 0 a True) True) (Or (Eq a_1 False) (Or (Eq (skS.0 1 a a_1 True) True) (Eq a_2 False)))) % 8.46/8.67 Clause #63 (by identity loobHoist #[61]): ∀ (a : Prop → Prop) (a_1 a_2 : Prop), % 8.46/8.67 Or (Eq (a False) False) % 8.46/8.67 (Or (Eq (skS.0 0 a True) True) % 8.46/8.67 (Or (Eq a_1 False) (Or (Eq a_2 False) (Or (Eq (skS.0 1 a True True) True) (Eq a_1 False))))) % 8.46/8.67 Clause #65 (by eliminate duplicate literals #[63]): ∀ (a : Prop → Prop) (a_1 a_2 : Prop), % 8.46/8.67 Or (Eq (a False) False) % 8.46/8.67 (Or (Eq (skS.0 0 a True) True) (Or (Eq a_1 False) (Or (Eq a_2 False) (Eq (skS.0 1 a True True) True)))) % 8.46/8.67 Clause #70 (by fluidLoobHoist #[65]): ∀ (a : Prop → Prop) (a_1 a_2 : Prop), % 8.46/8.67 Or (Eq (skS.0 0 a True) True) % 8.46/8.67 (Or (Eq a_1 False) % 8.46/8.67 (Or (Eq a_2 False) (Or (Eq (skS.0 1 a True True) True) (Or (Eq True False) (Eq (a False) False))))) % 8.46/8.67 Clause #133 (by clausification #[70]): ∀ (a : Prop → Prop) (a_1 a_2 : Prop), % 8.46/8.67 Or (Eq (skS.0 0 a True) True) % 8.46/8.67 (Or (Eq a_1 False) (Or (Eq a_2 False) (Or (Eq (skS.0 1 a True True) True) (Eq (a False) False)))) % 8.46/8.67 Clause #134 (by falseElim #[133]): ∀ (a : Prop → Prop) (a_1 : Prop), % 8.46/8.67 Or (Eq (skS.0 0 a True) True) (Or (Eq a_1 False) (Or (Eq (skS.0 1 a True True) True) (Eq (a False) False))) % 8.53/8.69 Clause #140 (by falseElim #[134]): ∀ (a : Prop → Prop), Or (Eq (skS.0 0 a True) True) (Or (Eq (skS.0 1 a True True) True) (Eq (a False) False)) % 8.53/8.69 Clause #156 (by existsHoist #[140]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 : (x : Prop) → a x → Prop) (a_2 : a False), % 8.53/8.69 Or (Eq (skS.0 0 (fun x => Exists (a_1 x)) True) True) % 8.53/8.69 (Or (Eq (skS.0 1 (fun x => Exists (a_1 x)) True True) True) % 8.53/8.69 (Or (Eq True False) (Eq ((fun x => a_1 False x) a_2) False))) % 8.53/8.69 Clause #172 (by betaEtaReduce #[22]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 : (x : Prop) → a x → Prop) (a_2 a_3 : Prop) (a_4 : a True), % 8.53/8.69 Or (Eq (skS.0 0 (fun x => Exists (a_1 x)) True) False) % 8.53/8.69 (Or (Eq a_2 False) % 8.53/8.69 (Or (Eq a_3 False) % 8.53/8.69 (Or (Eq (skS.0 1 (fun x => Exists (a_1 x)) True True) False) (Or (Eq True False) (Eq (a_1 True a_4) False))))) % 8.53/8.69 Clause #173 (by clausification #[172]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 : (x : Prop) → a x → Prop) (a_2 a_3 : Prop) (a_4 : a True), % 8.53/8.69 Or (Eq (skS.0 0 (fun x => Exists (a_1 x)) True) False) % 8.53/8.69 (Or (Eq a_2 False) % 8.53/8.69 (Or (Eq a_3 False) (Or (Eq (skS.0 1 (fun x => Exists (a_1 x)) True True) False) (Eq (a_1 True a_4) False)))) % 8.53/8.69 Clause #327 (by betaEtaReduce #[37]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 : (x : Prop) → a x → Prop) (a_2 a_3 : Prop) (a_4 : a False), % 8.53/8.69 Or (Eq (Exists (a_1 True)) False) % 8.53/8.69 (Or (Eq (skS.0 0 (fun x => Exists (a_1 x)) True) True) % 8.53/8.69 (Or (Eq a_2 False) % 8.53/8.69 (Or (Eq a_3 False) % 8.53/8.69 (Or (Eq (skS.0 1 (fun x => Exists (a_1 x)) True True) False) % 8.53/8.69 (Or (Eq True False) (Eq (a_1 False a_4) False)))))) % 8.53/8.69 Clause #328 (by clausification #[327]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 : (x : Prop) → a x → Prop) (a_2 a_3 : Prop) (a_4 : a False) (a_5 : a True), % 8.53/8.69 Or (Eq (skS.0 0 (fun x => Exists (a_1 x)) True) True) % 8.53/8.69 (Or (Eq a_2 False) % 8.53/8.69 (Or (Eq a_3 False) % 8.53/8.69 (Or (Eq (skS.0 1 (fun x => Exists (a_1 x)) True True) False) % 8.53/8.69 (Or (Eq True False) (Or (Eq (a_1 False a_4) False) (Eq (a_1 True a_5) False)))))) % 8.53/8.69 Clause #329 (by clausification #[328]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 : (x : Prop) → a x → Prop) (a_2 a_3 : Prop) (a_4 : a False) (a_5 : a True), % 8.53/8.69 Or (Eq (skS.0 0 (fun x => Exists (a_1 x)) True) True) % 8.53/8.69 (Or (Eq a_2 False) % 8.53/8.69 (Or (Eq a_3 False) % 8.53/8.69 (Or (Eq (skS.0 1 (fun x => Exists (a_1 x)) True True) False) % 8.53/8.69 (Or (Eq (a_1 False a_4) False) (Eq (a_1 True a_5) False))))) % 8.53/8.69 Clause #330 (by falseElim #[329]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 : (x : Prop) → a x → Prop) (a_2 : Prop) (a_3 : a False) (a_4 : a True), % 8.53/8.69 Or (Eq (skS.0 0 (fun x => Exists (a_1 x)) True) True) % 8.53/8.69 (Or (Eq a_2 False) % 8.53/8.69 (Or (Eq (skS.0 1 (fun x => Exists (a_1 x)) True True) False) % 8.53/8.69 (Or (Eq (a_1 False a_3) False) (Eq (a_1 True a_4) False)))) % 8.53/8.69 Clause #450 (by betaEtaReduce #[54]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 : (x : Prop) → a x → Prop) (a_2 a_3 : Prop) (a_4 : a True), % 8.53/8.69 Or (Eq (Exists (a_1 False)) False) % 8.53/8.69 (Or (Eq (skS.0 0 (fun x => Exists (a_1 x)) True) False) % 8.53/8.69 (Or (Eq a_2 False) % 8.53/8.69 (Or (Eq a_3 False) % 8.53/8.69 (Or (Eq (skS.0 1 (fun x => Exists (a_1 x)) True True) True) (Or (Eq True False) (Eq (a_1 True a_4) False)))))) % 8.53/8.69 Clause #451 (by clausification #[450]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 : (x : Prop) → a x → Prop) (a_2 a_3 : Prop) (a_4 : a True) (a_5 : a False), % 8.53/8.69 Or (Eq (skS.0 0 (fun x => Exists (a_1 x)) True) False) % 8.53/8.69 (Or (Eq a_2 False) % 8.53/8.69 (Or (Eq a_3 False) % 8.53/8.69 (Or (Eq (skS.0 1 (fun x => Exists (a_1 x)) True True) True) % 8.53/8.69 (Or (Eq True False) (Or (Eq (a_1 True a_4) False) (Eq (a_1 False a_5) False)))))) % 8.53/8.69 Clause #452 (by clausification #[451]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 : (x : Prop) → a x → Prop) (a_2 a_3 : Prop) (a_4 : a True) (a_5 : a False), % 8.53/8.69 Or (Eq (skS.0 0 (fun x => Exists (a_1 x)) True) False) % 8.53/8.69 (Or (Eq a_2 False) % 8.53/8.69 (Or (Eq a_3 False) % 8.53/8.69 (Or (Eq (skS.0 1 (fun x => Exists (a_1 x)) True True) True) % 8.53/8.69 (Or (Eq (a_1 True a_4) False) (Eq (a_1 False a_5) False))))) % 8.53/8.72 Clause #467 (by betaEtaReduce #[156]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 : (x : Prop) → a x → Prop) (a_2 : a False), % 8.53/8.72 Or (Eq (skS.0 0 (fun x => Exists (a_1 x)) True) True) % 8.53/8.72 (Or (Eq (skS.0 1 (fun x => Exists (a_1 x)) True True) True) (Or (Eq True False) (Eq (a_1 False a_2) False))) % 8.53/8.72 Clause #468 (by clausification #[467]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 : (x : Prop) → a x → Prop) (a_2 : a False), % 8.53/8.72 Or (Eq (skS.0 0 (fun x => Exists (a_1 x)) True) True) % 8.53/8.72 (Or (Eq (skS.0 1 (fun x => Exists (a_1 x)) True True) True) (Eq (a_1 False a_2) False)) % 8.53/8.72 Clause #476 (by neHoist #[468]): ∀ (a : Sort _abstMVar.0) (a_1 a_2 : a), % 8.53/8.72 Or (Eq (skS.0 0 (fun x => Exists ((fun x x => x) x)) True) True) % 8.53/8.72 (Or (Eq (skS.0 1 (fun x => Exists ((fun x x => x) x)) True True) True) (Or (Eq True False) (Eq a_1 a_2))) % 8.53/8.72 Clause #515 (by falseElim #[330]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 : (x : Prop) → a x → Prop) (a_2 : a False) (a_3 : a True), % 8.53/8.72 Or (Eq (skS.0 0 (fun x => Exists (a_1 x)) True) True) % 8.53/8.72 (Or (Eq (skS.0 1 (fun x => Exists (a_1 x)) True True) False) % 8.53/8.72 (Or (Eq (a_1 False a_2) False) (Eq (a_1 True a_3) False))) % 8.53/8.72 Clause #686 (by betaEtaReduce #[476]): ∀ (a : Sort _abstMVar.0) (a_1 a_2 : a), % 8.53/8.72 Or (Eq (skS.0 0 (fun x => Exists fun x => x) True) True) % 8.53/8.72 (Or (Eq (skS.0 1 (fun x => Exists fun x => x) True True) True) (Or (Eq True False) (Eq a_1 a_2))) % 8.53/8.72 Clause #687 (by clausification #[686]): ∀ (a : Sort _abstMVar.0) (a_1 a_2 : a), % 8.53/8.72 Or (Eq (skS.0 0 (fun x => Exists fun x => x) True) True) % 8.53/8.72 (Or (Eq (skS.0 1 (fun x => Exists fun x => x) True True) True) (Eq a_1 a_2)) % 8.53/8.72 Clause #758 (by equality factoring #[687]): ∀ (a : Prop), % 8.53/8.72 Or (Eq (skS.0 0 (fun x => Exists fun x => x) True) True) % 8.53/8.72 (Or (Ne a True) (Eq (skS.0 1 (fun x => Exists fun x => x) True True) True)) % 8.53/8.72 Clause #776 (by clausification #[758]): ∀ (a : Prop), % 8.53/8.72 Or (Eq (skS.0 0 (fun x => Exists fun x => x) True) True) % 8.53/8.72 (Or (Eq (skS.0 1 (fun x => Exists fun x => x) True True) True) (Or (Eq a False) (Eq True False))) % 8.53/8.72 Clause #778 (by clausification #[776]): ∀ (a : Prop), % 8.53/8.72 Or (Eq (skS.0 0 (fun x => Exists fun x => x) True) True) % 8.53/8.72 (Or (Eq (skS.0 1 (fun x => Exists fun x => x) True True) True) (Eq a False)) % 8.53/8.72 Clause #781 (by falseElim #[778]): Or (Eq (skS.0 0 (fun x => Exists fun x => x) True) True) (Eq (skS.0 1 (fun x => Exists fun x => x) True True) True) % 8.53/8.72 Clause #792 (by superposition #[781, 515]): ∀ (a : (fun x => Prop) False) (a_1 : (fun x => Prop) True), % 8.53/8.72 Or (Eq (skS.0 0 (fun x => Exists fun x => x) True) True) % 8.53/8.72 (Or (Eq (skS.0 0 (fun x => Exists fun x => x) True) True) (Or (Eq True False) (Or (Eq a False) (Eq a_1 False)))) % 8.53/8.72 Clause #850 (by clausification #[792]): ∀ (a : (fun x => Prop) False) (a_1 : (fun x => Prop) True), % 8.53/8.72 Or (Eq (skS.0 0 (fun x => Exists fun x => x) True) True) % 8.53/8.72 (Or (Eq (skS.0 0 (fun x => Exists fun x => x) True) True) (Or (Eq a False) (Eq a_1 False))) % 8.53/8.72 Clause #851 (by eliminate duplicate literals #[850]): ∀ (a : (fun x => Prop) False) (a_1 : (fun x => Prop) True), % 8.53/8.72 Or (Eq (skS.0 0 (fun x => Exists fun x => x) True) True) (Or (Eq a False) (Eq a_1 False)) % 8.53/8.72 Clause #853 (by superposition #[851, 781]): ∀ (a : (fun x => Prop) True), % 8.53/8.72 Or (Eq (skS.0 0 (fun x => Exists fun x => x) True) True) % 8.53/8.72 (Or (Eq a False) (Or (Eq (skS.0 0 (fun x => Exists fun x => x) True) True) (Eq False True))) % 8.53/8.72 Clause #863 (by clausification #[853]): ∀ (a : (fun x => Prop) True), % 8.53/8.72 Or (Eq (skS.0 0 (fun x => Exists fun x => x) True) True) % 8.53/8.72 (Or (Eq a False) (Eq (skS.0 0 (fun x => Exists fun x => x) True) True)) % 8.53/8.72 Clause #864 (by eliminate duplicate literals #[863]): ∀ (a : (fun x => Prop) True), Or (Eq (skS.0 0 (fun x => Exists fun x => x) True) True) (Eq a False) % 8.53/8.72 Clause #866 (by superposition #[864, 781]): Or (Eq (skS.0 0 (fun x => Exists fun x => x) True) True) % 8.53/8.72 (Or (Eq (skS.0 0 (fun x => Exists fun x => x) True) True) (Eq False True)) % 8.53/8.72 Clause #876 (by clausification #[866]): Or (Eq (skS.0 0 (fun x => Exists fun x => x) True) True) (Eq (skS.0 0 (fun x => Exists fun x => x) True) True) % 8.53/8.72 Clause #877 (by eliminate duplicate literals #[876]): Eq (skS.0 0 (fun x => Exists fun x => x) True) True % 8.61/8.77 Clause #879 (by superposition #[877, 173]): ∀ (a a_1 : Prop) (a_2 : (fun x => Prop) True), % 8.61/8.77 Or (Eq True False) % 8.61/8.77 (Or (Eq a False) % 8.61/8.77 (Or (Eq a_1 False) (Or (Eq (skS.0 1 (fun x => Exists fun x => x) True True) False) (Eq a_2 False)))) % 8.61/8.77 Clause #880 (by superposition #[877, 452]): ∀ (a a_1 : Prop) (a_2 : (fun x => Prop) True) (a_3 : (fun x => Prop) False), % 8.61/8.77 Or (Eq True False) % 8.61/8.77 (Or (Eq a False) % 8.61/8.77 (Or (Eq a_1 False) % 8.61/8.77 (Or (Eq (skS.0 1 (fun x => Exists fun x => x) True True) True) (Or (Eq a_2 False) (Eq a_3 False))))) % 8.61/8.77 Clause #897 (by clausification #[879]): ∀ (a a_1 : Prop) (a_2 : (fun x => Prop) True), % 8.61/8.77 Or (Eq a False) (Or (Eq a_1 False) (Or (Eq (skS.0 1 (fun x => Exists fun x => x) True True) False) (Eq a_2 False))) % 8.61/8.77 Clause #900 (by falseElim #[897]): ∀ (a : Prop) (a_1 : (fun x => Prop) True), % 8.61/8.77 Or (Eq a False) (Or (Eq (skS.0 1 (fun x => Exists fun x => x) True True) False) (Eq a_1 False)) % 8.61/8.77 Clause #912 (by falseElim #[900]): ∀ (a : (fun x => Prop) True), Or (Eq (skS.0 1 (fun x => Exists fun x => x) True True) False) (Eq a False) % 8.61/8.77 Clause #977 (by clausification #[880]): ∀ (a a_1 : Prop) (a_2 : (fun x => Prop) True) (a_3 : (fun x => Prop) False), % 8.61/8.77 Or (Eq a False) % 8.61/8.77 (Or (Eq a_1 False) % 8.61/8.77 (Or (Eq (skS.0 1 (fun x => Exists fun x => x) True True) True) (Or (Eq a_2 False) (Eq a_3 False)))) % 8.61/8.77 Clause #980 (by falseElim #[977]): ∀ (a : Prop) (a_1 : (fun x => Prop) True) (a_2 : (fun x => Prop) False), % 8.61/8.77 Or (Eq a False) (Or (Eq (skS.0 1 (fun x => Exists fun x => x) True True) True) (Or (Eq a_1 False) (Eq a_2 False))) % 8.61/8.77 Clause #992 (by falseElim #[980]): ∀ (a : (fun x => Prop) True) (a_1 : (fun x => Prop) False), % 8.61/8.77 Or (Eq (skS.0 1 (fun x => Exists fun x => x) True True) True) (Or (Eq a False) (Eq a_1 False)) % 8.61/8.77 Clause #1003 (by superposition #[992, 877]): ∀ (a : (fun x => Prop) False), % 8.61/8.77 Or (Eq (skS.0 1 (fun x => Exists fun x => x) True True) True) (Or (Eq a False) (Eq False True)) % 8.61/8.77 Clause #1013 (by clausification #[1003]): ∀ (a : (fun x => Prop) False), Or (Eq (skS.0 1 (fun x => Exists fun x => x) True True) True) (Eq a False) % 8.61/8.77 Clause #1015 (by superposition #[1013, 877]): Or (Eq (skS.0 1 (fun x => Exists fun x => x) True True) True) (Eq False True) % 8.61/8.77 Clause #1025 (by clausification #[1015]): Eq (skS.0 1 (fun x => Exists fun x => x) True True) True % 8.61/8.77 Clause #1028 (by superposition #[1025, 912]): ∀ (a : (fun x => Prop) True), Or (Eq True False) (Eq a False) % 8.61/8.77 Clause #1035 (by clausification #[1028]): ∀ (a : (fun x => Prop) True), Eq a False % 8.61/8.77 Clause #1037 (by superposition #[1035, 877]): Eq False True % 8.61/8.77 Clause #1047 (by clausification #[1037]): False % 8.61/8.77 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------