%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : LCL827_5 : TPTP v9.3.1. Released v6.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n015.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:36:45 AM UTC 2026 % Result : Theorem 9.18s 9.41s % Output : Proof 9.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL827_5 : TPTP v9.3.1. Released v6.0.0. % 0.00/0.05 % Command : duper %s % 0.08/0.35 % Computer : n015.cluster.edu % 0.08/0.35 % Model : x86_64 x86_64 % 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.35 % Memory : 8046.5625MB % 0.08/0.35 % OS : Linux 6.8.0-71-generic % 0.08/0.35 % CPULimit : 300 % 0.08/0.35 % WCLimit : 300 % 0.08/0.35 % DateTime : Sat Sep 5 22:16:28 UTC 2026 % 0.08/0.35 % CPUTime : % 9.18/9.41 SZS status Theorem for theBenchmark.p % 9.18/9.41 SZS output start Proof for theBenchmark.p % 9.18/9.41 Clause #2 (by assumption #[]): Eq % 9.18/9.41 (And % 9.18/9.41 (∀ (E1 : fun nat type) (T4 : type) (U4 : dB) (I1 : nat), % 9.18/9.41 pp % 9.18/9.41 (aa type bool % 9.18/9.41 (aa dB (fun type bool) % 9.18/9.41 (aa (fun nat type) (fun dB (fun type bool)) typing % 9.18/9.41 (aa type (fun nat type) % 9.18/9.41 (aa nat (fun type (fun nat type)) % 9.18/9.41 (aa (fun nat type) (fun nat (fun type (fun nat type))) (shift type) E1) I1) % 9.18/9.41 t)) % 9.18/9.41 a) % 9.18/9.41 T4) → % 9.18/9.41 pp (aa dB bool it U4) → % 9.18/9.41 pp (aa type bool (aa dB (fun type bool) (aa (fun nat type) (fun dB (fun type bool)) typing E1) U4) t) → % 9.18/9.41 pp (aa dB bool it (aa nat dB (aa dB (fun nat dB) (aa dB (fun dB (fun nat dB)) subst a) U4) I1))) % 9.18/9.41 (Exists fun X11 => % 9.18/9.41 pp % 9.18/9.41 (aa type bool % 9.18/9.41 (aa dB (fun type bool) % 9.18/9.41 (aa (fun nat type) (fun dB (fun type bool)) typing % 9.18/9.41 (aa type (fun nat type) % 9.18/9.41 (aa nat (fun type (fun nat type)) (aa (fun nat type) (fun nat (fun type (fun nat type))) (shift type) e) % 9.18/9.41 i) % 9.18/9.41 t)) % 9.18/9.41 a) % 9.18/9.41 X11))) % 9.18/9.41 True % 9.18/9.41 Clause #114 (by assumption #[]): Eq % 9.18/9.41 (∀ (U : type), % 9.18/9.41 pp % 9.18/9.41 (aa type bool % 9.18/9.41 (aa dB (fun type bool) % 9.18/9.41 (aa (fun nat type) (fun dB (fun type bool)) typing % 9.18/9.41 (aa type (fun nat type) % 9.18/9.41 (aa nat (fun type (fun nat type)) (aa (fun nat type) (fun nat (fun type (fun nat type))) (shift type) e) % 9.18/9.41 i) % 9.18/9.41 t)) % 9.18/9.41 a) % 9.18/9.41 U) → % 9.18/9.41 thesis) % 9.18/9.41 True % 9.18/9.41 Clause #115 (by assumption #[]): Eq (Not thesis) True % 9.18/9.41 Clause #116 (by clausification #[115]): Eq thesis False % 9.18/9.41 Clause #118 (by clausification #[114]): ∀ (a_1 : type), % 9.18/9.41 Eq % 9.18/9.41 (pp % 9.18/9.41 (aa type bool % 9.18/9.41 (aa dB (fun type bool) % 9.18/9.41 (aa (fun nat type) (fun dB (fun type bool)) typing % 9.18/9.41 (aa type (fun nat type) % 9.18/9.41 (aa nat (fun type (fun nat type)) (aa (fun nat type) (fun nat (fun type (fun nat type))) (shift type) e) % 9.18/9.41 i) % 9.18/9.41 t)) % 9.18/9.41 a) % 9.18/9.41 a_1) → % 9.18/9.41 thesis) % 9.18/9.41 True % 9.18/9.41 Clause #119 (by clausification #[118]): ∀ (a_1 : type), % 9.18/9.41 Or % 9.18/9.41 (Eq % 9.18/9.41 (pp % 9.18/9.41 (aa type bool % 9.18/9.41 (aa dB (fun type bool) % 9.18/9.41 (aa (fun nat type) (fun dB (fun type bool)) typing % 9.18/9.41 (aa type (fun nat type) % 9.18/9.41 (aa nat (fun type (fun nat type)) (aa (fun nat type) (fun nat (fun type (fun nat type))) (shift type) e) % 9.18/9.41 i) % 9.18/9.41 t)) % 9.18/9.41 a) % 9.18/9.41 a_1)) % 9.18/9.41 False) % 9.18/9.41 (Eq thesis True) % 9.18/9.41 Clause #120 (by forward demodulation #[119, 116]): ∀ (a_1 : type), % 9.18/9.41 Or % 9.18/9.41 (Eq % 9.18/9.41 (pp % 9.18/9.41 (aa type bool % 9.18/9.41 (aa dB (fun type bool) % 9.18/9.41 (aa (fun nat type) (fun dB (fun type bool)) typing % 9.18/9.41 (aa type (fun nat type) % 9.18/9.41 (aa nat (fun type (fun nat type)) (aa (fun nat type) (fun nat (fun type (fun nat type))) (shift type) e) % 9.18/9.41 i) % 9.18/9.41 t)) % 9.18/9.41 a) % 9.18/9.41 a_1)) % 9.18/9.41 False) % 9.18/9.41 (Eq False True) % 9.18/9.41 Clause #121 (by clausification #[120]): ∀ (a_1 : type), % 9.18/9.41 Eq % 9.18/9.41 (pp % 9.18/9.41 (aa type bool % 9.18/9.41 (aa dB (fun type bool) % 9.18/9.41 (aa (fun nat type) (fun dB (fun type bool)) typing % 9.18/9.41 (aa type (fun nat type) % 9.18/9.41 (aa nat (fun type (fun nat type)) (aa (fun nat type) (fun nat (fun type (fun nat type))) (shift type) e) % 9.18/9.41 i) % 9.18/9.41 t)) % 9.18/9.41 a) % 9.18/9.41 a_1)) % 9.18/9.41 False % 9.18/9.41 Clause #142 (by clausification #[2]): Eq % 9.18/9.41 (Exists fun X11 => % 9.18/9.41 pp % 9.18/9.41 (aa type bool % 9.18/9.41 (aa dB (fun type bool) % 9.18/9.41 (aa (fun nat type) (fun dB (fun type bool)) typing % 9.18/9.41 (aa type (fun nat type) % 9.18/9.41 (aa nat (fun type (fun nat type)) (aa (fun nat type) (fun nat (fun type (fun nat type))) (shift type) e) % 9.18/9.41 i) % 9.18/9.41 t)) % 9.18/9.41 a) % 9.18/9.41 X11)) % 9.18/9.41 True % 9.18/9.41 Clause #143 (by clausification #[142]): ∀ (a_1 : type), % 9.18/9.41 Eq % 9.18/9.41 (pp % 9.18/9.41 (aa type bool % 9.18/9.41 (aa dB (fun type bool) % 9.18/9.41 (aa (fun nat type) (fun dB (fun type bool)) typing % 9.18/9.41 (aa type (fun nat type) % 9.18/9.41 (aa nat (fun type (fun nat type)) (aa (fun nat type) (fun nat (fun type (fun nat type))) (shift type) e) % 9.18/9.41 i) % 9.18/9.41 t)) % 9.18/9.41 a) % 9.18/9.41 (skS.0 0 a_1))) % 9.18/9.41 True % 9.18/9.41 Clause #144 (by superposition #[143, 121]): Eq True False % 9.18/9.41 Clause #145 (by clausification #[144]): False % 9.18/9.41 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------