%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : LCL579^2 : TPTP v9.3.1. Released v5.1.0. % 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 : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:36:07 AM UTC 2026 % Result : Theorem 8.67s 8.91s % Output : Proof 8.67s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL579^2 : TPTP v9.3.1. Released v5.1.0. % 0.00/0.04 % Command : duper %s % 0.10/0.37 % Computer : n003.cluster.edu % 0.10/0.37 % Model : x86_64 x86_64 % 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.37 % Memory : 8046.5625MB % 0.10/0.37 % OS : Linux 6.8.0-71-generic % 0.10/0.37 % CPULimit : 300 % 0.10/0.37 % WCLimit : 300 % 0.10/0.37 % DateTime : Sun Sep 6 00:15:06 UTC 2026 % 0.15/0.37 % CPUTime : % 8.67/8.91 SZS status Theorem for theBenchmark.p % 8.67/8.91 SZS output start Proof for theBenchmark.p % 8.67/8.91 Clause #0 (by assumption #[]): Eq (Not ((∀ (P : Iota → Prop), P cY → P cX) → ∀ (R : Iota → Prop), R cX → R cY)) True % 8.67/8.91 Clause #1 (by clausification #[0]): Eq ((∀ (P : Iota → Prop), P cY → P cX) → ∀ (R : Iota → Prop), R cX → R cY) False % 8.67/8.91 Clause #2 (by clausification #[1]): Eq (∀ (P : Iota → Prop), P cY → P cX) True % 8.67/8.91 Clause #3 (by clausification #[1]): Eq (∀ (R : Iota → Prop), R cX → R cY) False % 8.67/8.91 Clause #4 (by clausification #[2]): ∀ (a : Iota → Prop), Eq (a cY → a cX) True % 8.67/8.91 Clause #5 (by clausification #[4]): ∀ (a : Iota → Prop), Or (Eq (a cY) False) (Eq (a cX) True) % 8.67/8.91 Clause #7 (by neHoist #[5]): ∀ (a : Iota → Sort _abstMVar.0) (a_1 a_2 : (x : Iota) → a x), % 8.67/8.91 Or (Eq ((fun x => Ne (a_1 x) (a_2 x)) cX) True) (Or (Eq True False) (Eq (a_1 cY) (a_2 cY))) % 8.67/8.91 Clause #14 (by clausification #[3]): ∀ (a : Iota → Prop), Eq (Not (skS.0 0 a cX → skS.0 0 a cY)) True % 8.67/8.91 Clause #15 (by clausification #[14]): ∀ (a : Iota → Prop), Eq (skS.0 0 a cX → skS.0 0 a cY) False % 8.67/8.91 Clause #16 (by clausification #[15]): ∀ (a : Iota → Prop), Eq (skS.0 0 a cX) True % 8.67/8.91 Clause #17 (by clausification #[15]): ∀ (a : Iota → Prop), Eq (skS.0 0 a cY) False % 8.67/8.91 Clause #30 (by betaEtaReduce #[7]): ∀ (a : Iota → Sort _abstMVar.0) (a_1 a_2 : (x : Iota) → a x), % 8.67/8.91 Or (Eq (Ne (a_1 cX) (a_2 cX)) True) (Or (Eq True False) (Eq (a_1 cY) (a_2 cY))) % 8.67/8.91 Clause #31 (by clausification #[30]): ∀ (a : Iota → Sort _abstMVar.0) (a_1 a_2 : (x : Iota) → a x), % 8.67/8.91 Or (Eq True False) (Or (Eq (a_1 cY) (a_2 cY)) (Ne (a_1 cX) (a_2 cX))) % 8.67/8.91 Clause #32 (by clausification #[31]): ∀ (a : Iota → Sort _abstMVar.0) (a_1 a_2 : (x : Iota) → a x), Or (Eq (a_1 cY) (a_2 cY)) (Ne (a_1 cX) (a_2 cX)) % 8.67/8.91 Clause #33 (by equality resolution #[32]): Eq ((fun x => x) cY) ((fun x => cX) cY) % 8.67/8.91 Clause #40 (by betaEtaReduce #[33]): Eq cY cX % 8.67/8.91 Clause #43 (by backward demodulation #[40, 17]): ∀ (a : Iota → Prop), Eq (skS.0 0 a cX) False % 8.67/8.91 Clause #67 (by superposition #[43, 16]): Eq False True % 8.67/8.91 Clause #68 (by clausification #[67]): False % 8.67/8.91 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------