%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO371^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n021.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 08:08:57 PM UTC 2025 % Result : Theorem 3.76s 3.99s % Output : Proof 3.76s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SYO371^5 : TPTP v9.2.0. Released v4.0.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n021.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 13:27:08 EDT 2025 % 0.13/0.34 % CPUTime : % 3.76/3.99 SZS status Theorem for theBenchmark.p % 3.76/3.99 SZS output start Proof for theBenchmark.p % 3.76/3.99 Clause #0 (by assumption #[]): Eq (Not ((∀ (R : Prop → Prop), R cP → R cQ) → Iff cP cQ)) True % 3.76/3.99 Clause #1 (by clausification #[0]): Eq ((∀ (R : Prop → Prop), R cP → R cQ) → Iff cP cQ) False % 3.76/3.99 Clause #2 (by clausification #[1]): Eq (∀ (R : Prop → Prop), R cP → R cQ) True % 3.76/3.99 Clause #3 (by clausification #[1]): Eq (Iff cP cQ) False % 3.76/3.99 Clause #4 (by clausification #[2]): ∀ (a : Prop → Prop), Eq (a cP → a cQ) True % 3.76/3.99 Clause #5 (by clausification #[4]): ∀ (a : Prop → Prop), Or (Eq (a cP) False) (Eq (a cQ) True) % 3.76/3.99 Clause #6 (by identity loobHoist #[5]): ∀ (a : Prop → Prop), Or (Eq (a cQ) True) (Or (Eq (a True) False) (Eq cP False)) % 3.76/3.99 Clause #7 (by identity boolHoist #[5]): ∀ (a : Prop → Prop), Or (Eq (a cQ) True) (Or (Eq (a False) False) (Eq cP True)) % 3.76/3.99 Clause #9 (by identity boolHoist #[6]): ∀ (a : Prop → Prop), Or (Eq (a True) False) (Or (Eq cP False) (Or (Eq (a False) True) (Eq cQ True))) % 3.76/3.99 Clause #10 (by clausification #[3]): Or (Eq cP False) (Eq cQ False) % 3.76/3.99 Clause #11 (by clausification #[3]): Or (Eq cP True) (Eq cQ True) % 3.76/3.99 Clause #12 (by identity loobHoist #[7]): ∀ (a : Prop → Prop), Or (Eq (a False) False) (Or (Eq cP True) (Or (Eq (a True) True) (Eq cQ False))) % 3.76/3.99 Clause #16 (by neHoist #[12]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), % 3.76/3.99 Or (Eq cP True) % 3.76/3.99 (Or (Eq ((fun x => Ne (a_1 x) (a_2 x)) True) True) % 3.76/3.99 (Or (Eq cQ False) (Or (Eq True False) (Eq (a_1 False) (a_2 False))))) % 3.76/3.99 Clause #22 (by neHoist #[9]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), % 3.76/3.99 Or (Eq cP False) % 3.76/3.99 (Or (Eq ((fun x => Ne (a_1 x) (a_2 x)) False) True) % 3.76/3.99 (Or (Eq cQ True) (Or (Eq True False) (Eq (a_1 True) (a_2 True))))) % 3.76/3.99 Clause #52 (by betaEtaReduce #[16]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), % 3.76/3.99 Or (Eq cP True) % 3.76/3.99 (Or (Eq (Ne (a_1 True) (a_2 True)) True) (Or (Eq cQ False) (Or (Eq True False) (Eq (a_1 False) (a_2 False))))) % 3.76/3.99 Clause #53 (by clausification #[52]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), % 3.76/3.99 Or (Eq cP True) (Or (Eq cQ False) (Or (Eq True False) (Or (Eq (a_1 False) (a_2 False)) (Ne (a_1 True) (a_2 True))))) % 3.76/3.99 Clause #54 (by clausification #[53]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), % 3.76/3.99 Or (Eq cP True) (Or (Eq cQ False) (Or (Eq (a_1 False) (a_2 False)) (Ne (a_1 True) (a_2 True)))) % 3.76/3.99 Clause #55 (by superposition #[54, 11]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), % 3.76/3.99 Or (Eq cP True) (Or (Eq (a_1 False) (a_2 False)) (Or (Ne (a_1 True) (a_2 True)) (Or (Eq cP True) (Eq False True)))) % 3.76/3.99 Clause #60 (by clausification #[55]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), % 3.76/3.99 Or (Eq cP True) (Or (Eq (a_1 False) (a_2 False)) (Or (Ne (a_1 True) (a_2 True)) (Eq cP True))) % 3.76/3.99 Clause #61 (by eliminate duplicate literals #[60]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), % 3.76/3.99 Or (Eq cP True) (Or (Eq (a_1 False) (a_2 False)) (Ne (a_1 True) (a_2 True))) % 3.76/3.99 Clause #62 (by equality resolution #[61]): Or (Eq cP True) (Eq ((fun x => x) False) ((fun x => True) False)) % 3.76/3.99 Clause #69 (by betaEtaReduce #[62]): Or (Eq cP True) (Eq False True) % 3.76/3.99 Clause #70 (by clausification #[69]): Eq cP True % 3.76/3.99 Clause #71 (by backward demodulation #[70, 10]): Or (Eq True False) (Eq cQ False) % 3.76/3.99 Clause #85 (by clausification #[71]): Eq cQ False % 3.76/3.99 Clause #112 (by betaEtaReduce #[22]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), % 3.76/3.99 Or (Eq cP False) % 3.76/3.99 (Or (Eq (Ne (a_1 False) (a_2 False)) True) (Or (Eq cQ True) (Or (Eq True False) (Eq (a_1 True) (a_2 True))))) % 3.76/3.99 Clause #113 (by clausification #[112]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), % 3.76/3.99 Or (Eq cP False) (Or (Eq cQ True) (Or (Eq True False) (Or (Eq (a_1 True) (a_2 True)) (Ne (a_1 False) (a_2 False))))) % 3.76/3.99 Clause #114 (by clausification #[113]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), % 3.76/3.99 Or (Eq cP False) (Or (Eq cQ True) (Or (Eq (a_1 True) (a_2 True)) (Ne (a_1 False) (a_2 False)))) % 3.76/4.00 Clause #115 (by forward demodulation #[114, 70]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), % 3.76/4.00 Or (Eq True False) (Or (Eq cQ True) (Or (Eq (a_1 True) (a_2 True)) (Ne (a_1 False) (a_2 False)))) % 3.76/4.00 Clause #116 (by clausification #[115]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), % 3.76/4.00 Or (Eq cQ True) (Or (Eq (a_1 True) (a_2 True)) (Ne (a_1 False) (a_2 False))) % 3.76/4.00 Clause #117 (by equality resolution #[116]): Or (Eq cQ True) (Eq ((fun x => x) True) ((fun x => False) True)) % 3.76/4.00 Clause #124 (by betaEtaReduce #[117]): Or (Eq cQ True) (Eq True False) % 3.76/4.00 Clause #125 (by clausification #[124]): Eq cQ True % 3.76/4.00 Clause #126 (by superposition #[125, 85]): Eq True False % 3.76/4.00 Clause #129 (by clausification #[126]): False % 3.76/4.00 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------