%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV048^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n011.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 08:02:47 PM UTC 2025 % Result : Theorem 184.35s 184.55s % Output : Proof 185.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.11 % Problem : SEV048^5 : TPTP v9.2.0. Released v4.0.0. % 0.08/0.12 % Command : duper %s % 0.12/0.32 % Computer : n011.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 300 % 0.12/0.32 % DateTime : Fri Oct 3 01:26:26 EDT 2025 % 0.12/0.33 % CPUTime : % 184.35/184.55 SZS status Theorem for theBenchmark.p % 184.35/184.55 SZS output start Proof for theBenchmark.p % 184.35/184.55 Clause #0 (by assumption #[]): Eq (Not (Exists fun R => ∀ (Xx Xy Xz : Iota → Prop), And (R Xx Xy) (R Xy Xz) → R Xx Xz)) True % 184.35/184.55 Clause #1 (by clausification #[0]): Eq (Exists fun R => ∀ (Xx Xy Xz : Iota → Prop), And (R Xx Xy) (R Xy Xz) → R Xx Xz) False % 184.35/184.55 Clause #2 (by clausification #[1]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop), Eq (∀ (Xx Xy Xz : Iota → Prop), And (a Xx Xy) (a Xy Xz) → a Xx Xz) False % 184.35/184.55 Clause #3 (by clausification #[2]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop) (a_1 : Iota → Prop), % 184.35/184.55 Eq (Not (∀ (Xy Xz : Iota → Prop), And (a (skS.0 0 a a_1) Xy) (a Xy Xz) → a (skS.0 0 a a_1) Xz)) True % 184.35/184.55 Clause #4 (by clausification #[3]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop) (a_1 : Iota → Prop), % 184.35/184.55 Eq (∀ (Xy Xz : Iota → Prop), And (a (skS.0 0 a a_1) Xy) (a Xy Xz) → a (skS.0 0 a a_1) Xz) False % 184.35/184.55 Clause #5 (by clausification #[4]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop) (a_1 a_2 : Iota → Prop), % 184.35/184.55 Eq % 184.35/184.55 (Not % 184.35/184.55 (∀ (Xz : Iota → Prop), % 184.35/184.55 And (a (skS.0 0 a a_1) (skS.0 1 a a_1 a_2)) (a (skS.0 1 a a_1 a_2) Xz) → a (skS.0 0 a a_1) Xz)) % 184.35/184.55 True % 184.35/184.55 Clause #6 (by clausification #[5]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop) (a_1 a_2 : Iota → Prop), % 184.35/184.55 Eq % 184.35/184.55 (∀ (Xz : Iota → Prop), % 184.35/184.55 And (a (skS.0 0 a a_1) (skS.0 1 a a_1 a_2)) (a (skS.0 1 a a_1 a_2) Xz) → a (skS.0 0 a a_1) Xz) % 184.35/184.55 False % 184.35/184.55 Clause #7 (by clausification #[6]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop) (a_1 a_2 a_3 : Iota → Prop), % 184.35/184.55 Eq % 184.35/184.55 (Not % 184.35/184.55 (And (a (skS.0 0 a a_1) (skS.0 1 a a_1 a_2)) (a (skS.0 1 a a_1 a_2) (skS.0 2 a a_1 a_2 a_3)) → % 184.35/184.55 a (skS.0 0 a a_1) (skS.0 2 a a_1 a_2 a_3))) % 184.35/184.55 True % 184.35/184.55 Clause #8 (by clausification #[7]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop) (a_1 a_2 a_3 : Iota → Prop), % 184.35/184.55 Eq % 184.35/184.55 (And (a (skS.0 0 a a_1) (skS.0 1 a a_1 a_2)) (a (skS.0 1 a a_1 a_2) (skS.0 2 a a_1 a_2 a_3)) → % 184.35/184.55 a (skS.0 0 a a_1) (skS.0 2 a a_1 a_2 a_3)) % 184.35/184.55 False % 184.35/184.55 Clause #10 (by clausification #[8]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Prop) (a_1 a_2 a_3 : Iota → Prop), % 184.35/184.55 Eq (a (skS.0 0 a a_1) (skS.0 2 a a_1 a_2 a_3)) False % 184.35/184.55 Clause #75 (by existsHoist #[10]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Sort _abstMVar.0) (a_1 : (x x_1 : Iota → Prop) → a x x_1 → Prop) % 184.35/184.55 (a_2 a_3 a_4 : Iota → Prop) % 184.35/184.55 (a_5 : a (skS.0 0 (fun x x_1 => Exists (a_1 x x_1)) a_2) (skS.0 2 (fun x x_1 => Exists (a_1 x x_1)) a_2 a_3 a_4)), % 184.35/184.55 Or (Eq True False) % 184.35/184.55 (Eq % 184.35/184.55 ((fun x => % 184.35/184.55 a_1 (skS.0 0 (fun x x_1 => Exists (a_1 x x_1)) a_2) (skS.0 2 (fun x x_1 => Exists (a_1 x x_1)) a_2 a_3 a_4) x) % 184.35/184.55 a_5) % 184.35/184.55 False) % 184.35/184.55 Clause #1007 (by betaEtaReduce #[75]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Sort _abstMVar.0) (a_1 : (x x_1 : Iota → Prop) → a x x_1 → Prop) % 184.35/184.55 (a_2 a_3 a_4 : Iota → Prop) % 184.35/184.55 (a_5 : a (skS.0 0 (fun x x_1 => Exists (a_1 x x_1)) a_2) (skS.0 2 (fun x x_1 => Exists (a_1 x x_1)) a_2 a_3 a_4)), % 184.35/184.55 Or (Eq True False) % 184.35/184.55 (Eq % 184.35/184.55 (a_1 (skS.0 0 (fun x x_1 => Exists (a_1 x x_1)) a_2) (skS.0 2 (fun x x_1 => Exists (a_1 x x_1)) a_2 a_3 a_4) a_5) % 184.35/184.55 False) % 184.35/184.55 Clause #1008 (by clausification #[1007]): ∀ (a : (Iota → Prop) → (Iota → Prop) → Sort _abstMVar.0) (a_1 : (x x_1 : Iota → Prop) → a x x_1 → Prop) % 184.35/184.55 (a_2 a_3 a_4 : Iota → Prop) % 184.35/184.55 (a_5 : a (skS.0 0 (fun x x_1 => Exists (a_1 x x_1)) a_2) (skS.0 2 (fun x x_1 => Exists (a_1 x x_1)) a_2 a_3 a_4)), % 184.35/184.55 Eq (a_1 (skS.0 0 (fun x x_1 => Exists (a_1 x x_1)) a_2) (skS.0 2 (fun x x_1 => Exists (a_1 x x_1)) a_2 a_3 a_4) a_5) % 184.35/184.55 False % 184.35/184.55 Clause #1075 (by fluidBoolHoist #[1008]): ∀ (a : Prop → Prop) (a_1 : Prop), Or (Eq (a False) False) (Eq a_1 True) % 184.35/184.55 Clause #1077 (by neHoist #[1075]): ∀ (a : Prop) (a_1 : Prop → Sort _abstMVar.0) (a_2 a_3 : (_ : Prop) → a_1 _), % 184.35/184.55 Or (Eq a True) (Or (Eq True False) (Eq (a_2 False) (a_3 False))) % 184.35/184.55 Clause #11452 (by clausification #[1077]): ∀ (a : Prop) (a_1 : Prop → Sort _abstMVar.0) (a_2 a_3 : (_ : Prop) → a_1 _), Or (Eq a True) (Eq (a_2 False) (a_3 False)) % 185.23/185.44 Clause #11458 (by equality factoring #[11452]): ∀ (a : (_ : Prop) → (fun _ => Prop) _) (a_1 : Prop), Or (Ne (a False) a_1) (Eq a_1 True) % 185.23/185.44 Clause #12365 (by betaEtaReduce #[11458]): ∀ (a : (_ : Prop) → (fun _ => Prop) _) (a_1 : Prop), Or (Ne (a False) a_1) (Eq a_1 True) % 185.23/185.44 Clause #12367 (by clausification #[12365]): ∀ (a : Prop) (a_1 : (_ : Prop) → (fun _ => Prop) _), Or (Eq a True) (Or (Eq (a_1 False) True) (Eq a True)) % 185.23/185.44 Clause #12693 (by eliminate duplicate literals #[12367]): ∀ (a : Prop) (a_1 : (_ : Prop) → (fun _ => Prop) _), Or (Eq a True) (Eq (a_1 False) True) % 185.23/185.44 Clause #12699 (by falseElim #[12693]): ∀ (a : (_ : Prop) → (fun _ => Prop) _), Eq (a False) True % 185.23/185.44 Clause #13537 (by fluidSup #[12699, 12699]): Eq ((fun _ => False) True) True % 185.23/185.44 Clause #13540 (by betaEtaReduce #[13537]): Eq False True % 185.23/185.44 Clause #13541 (by clausification #[13540]): False % 185.23/185.44 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------