%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO300^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n003.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 08:08:52 PM UTC 2025 % Result : Theorem 5.08s 5.29s % Output : Proof 5.08s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.11 % Problem : SYO300^5 : TPTP v9.2.0. Released v4.0.0. % 0.04/0.13 % Command : duper %s % 0.12/0.34 % Computer : n003.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Oct 3 13:33:38 EDT 2025 % 0.12/0.34 % CPUTime : % 5.08/5.29 SZS status Theorem for theBenchmark.p % 5.08/5.29 SZS output start Proof for theBenchmark.p % 5.08/5.29 Clause #0 (by assumption #[]): Eq % 5.08/5.29 (Not % 5.08/5.29 (∀ (P : ((Iota → Iota) → Iota) → ((Iota → Iota) → Iota) → Prop), % 5.08/5.29 Exists fun X => (∀ (Xz : (Iota → Iota) → Iota), P Xz Xz) → P (fun U => U (X fun V => V)) X)) % 5.08/5.29 True % 5.08/5.29 Clause #1 (by clausification #[0]): Eq % 5.08/5.29 (∀ (P : ((Iota → Iota) → Iota) → ((Iota → Iota) → Iota) → Prop), % 5.08/5.29 Exists fun X => (∀ (Xz : (Iota → Iota) → Iota), P Xz Xz) → P (fun U => U (X fun V => V)) X) % 5.08/5.29 False % 5.08/5.29 Clause #2 (by clausification #[1]): ∀ (a : ((Iota → Iota) → Iota) → ((Iota → Iota) → Iota) → Prop), % 5.08/5.29 Eq (Not (Exists fun X => (∀ (Xz : (Iota → Iota) → Iota), skS.0 0 a Xz Xz) → skS.0 0 a (fun U => U (X fun V => V)) X)) % 5.08/5.29 True % 5.08/5.29 Clause #3 (by clausification #[2]): ∀ (a : ((Iota → Iota) → Iota) → ((Iota → Iota) → Iota) → Prop), % 5.08/5.29 Eq (Exists fun X => (∀ (Xz : (Iota → Iota) → Iota), skS.0 0 a Xz Xz) → skS.0 0 a (fun U => U (X fun V => V)) X) False % 5.08/5.29 Clause #4 (by clausification #[3]): ∀ (a : ((Iota → Iota) → Iota) → ((Iota → Iota) → Iota) → Prop) (a_1 : (Iota → Iota) → Iota), % 5.08/5.29 Eq ((∀ (Xz : (Iota → Iota) → Iota), skS.0 0 a Xz Xz) → skS.0 0 a (fun U => U (a_1 fun V => V)) a_1) False % 5.08/5.29 Clause #5 (by clausification #[4]): ∀ (a : ((Iota → Iota) → Iota) → ((Iota → Iota) → Iota) → Prop), Eq (∀ (Xz : (Iota → Iota) → Iota), skS.0 0 a Xz Xz) True % 5.08/5.29 Clause #6 (by clausification #[4]): ∀ (a : ((Iota → Iota) → Iota) → ((Iota → Iota) → Iota) → Prop) (a_1 : (Iota → Iota) → Iota), % 5.08/5.29 Eq (skS.0 0 a (fun U => U (a_1 fun V => V)) a_1) False % 5.08/5.29 Clause #7 (by clausification #[5]): ∀ (a : ((Iota → Iota) → Iota) → ((Iota → Iota) → Iota) → Prop) (a_1 : (Iota → Iota) → Iota), Eq (skS.0 0 a a_1 a_1) True % 5.08/5.29 Clause #8 (by fluidSup #[6, 7]): ∀ (a : ((Iota → Iota) → Iota) → ((Iota → Iota) → Iota) → Prop) (a_1 : Prop → (Iota → Iota) → Iota) % 5.08/5.29 (a_2 : ((Iota → Iota) → Iota) → ((Iota → Iota) → Iota) → Prop) (a_3 : (Iota → Iota) → Iota), % 5.08/5.29 Eq (skS.0 0 a (fun U => U ((fun x => a_1 (skS.0 0 a_2 a_3 a_3) x) fun V => V)) (a_1 True)) False % 5.08/5.29 Clause #9 (by betaEtaReduce #[8]): ∀ (a : ((Iota → Iota) → Iota) → ((Iota → Iota) → Iota) → Prop) (a_1 : Prop → (Iota → Iota) → Iota) % 5.08/5.29 (a_2 : ((Iota → Iota) → Iota) → ((Iota → Iota) → Iota) → Prop) (a_3 : (Iota → Iota) → Iota), % 5.08/5.29 Eq (skS.0 0 a (fun U => U (a_1 (skS.0 0 a_2 a_3 a_3) fun V => V)) (a_1 True)) False % 5.08/5.29 Clause #10 (by superposition #[9, 7]): Eq False True % 5.08/5.29 Clause #12 (by clausification #[10]): False % 5.08/5.29 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------