%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO235^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n019.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 08:08:47 PM UTC 2025 % Result : Theorem 3.81s 3.98s % Output : Proof 3.81s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SYO235^5 : TPTP v9.2.0. Released v4.0.0. % 0.11/0.14 % Command : duper %s % 0.13/0.35 % Computer : n019.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Oct 3 14:09:08 EDT 2025 % 0.13/0.35 % CPUTime : % 3.81/3.98 SZS status Theorem for theBenchmark.p % 3.81/3.98 SZS output start Proof for theBenchmark.p % 3.81/3.98 Clause #0 (by assumption #[]): Eq (Not (Or (∀ (Q : Prop → Prop), Q cA → Q cB) (Iff cA cB) → Eq cA cB)) True % 3.81/3.98 Clause #1 (by clausification #[0]): Eq (Or (∀ (Q : Prop → Prop), Q cA → Q cB) (Iff cA cB) → Eq cA cB) False % 3.81/3.98 Clause #2 (by clausification #[1]): Eq (Or (∀ (Q : Prop → Prop), Q cA → Q cB) (Iff cA cB)) True % 3.81/3.98 Clause #3 (by clausification #[1]): Eq (Eq cA cB) False % 3.81/3.98 Clause #4 (by clausification #[2]): Or (Eq (∀ (Q : Prop → Prop), Q cA → Q cB) True) (Eq (Iff cA cB) True) % 3.81/3.98 Clause #5 (by clausification #[4]): ∀ (a : Prop → Prop), Or (Eq (Iff cA cB) True) (Eq (a cA → a cB) True) % 3.81/3.98 Clause #6 (by clausification #[5]): ∀ (a : Prop → Prop), Or (Eq (a cA → a cB) True) (Or (Eq cA True) (Eq cB False)) % 3.81/3.98 Clause #7 (by clausification #[5]): ∀ (a : Prop → Prop), Or (Eq (a cA → a cB) True) (Or (Eq cA False) (Eq cB True)) % 3.81/3.98 Clause #8 (by clausification #[6]): ∀ (a : Prop → Prop), Or (Eq cA True) (Or (Eq cB False) (Or (Eq (a cA) False) (Eq (a cB) True))) % 3.81/3.98 Clause #10 (by identity boolHoist #[8]): ∀ (a : Prop → Prop), Or (Eq cA True) (Or (Eq cB False) (Or (Eq (a cB) True) (Or (Eq (a False) False) (Eq cA True)))) % 3.81/3.98 Clause #11 (by clausification #[3]): Ne cA cB % 3.81/3.98 Clause #12 (by clausification #[11]): Or (Eq cA False) (Eq cB False) % 3.81/3.98 Clause #13 (by clausification #[11]): Or (Eq cA True) (Eq cB True) % 3.81/3.98 Clause #14 (by clausification #[7]): ∀ (a : Prop → Prop), Or (Eq cA False) (Or (Eq cB True) (Or (Eq (a cA) False) (Eq (a cB) True))) % 3.81/3.98 Clause #15 (by identity loobHoist #[14]): ∀ (a : Prop → Prop), Or (Eq cA False) (Or (Eq cB True) (Or (Eq (a cB) True) (Or (Eq (a True) False) (Eq cA False)))) % 3.81/3.98 Clause #17 (by eliminate duplicate literals #[15]): ∀ (a : Prop → Prop), Or (Eq cA False) (Or (Eq cB True) (Or (Eq (a cB) True) (Eq (a True) False))) % 3.81/3.98 Clause #19 (by identity boolHoist #[17]): ∀ (a : Prop → Prop), Or (Eq cA False) (Or (Eq cB True) (Or (Eq (a True) False) (Or (Eq (a False) True) (Eq cB True)))) % 3.81/3.98 Clause #20 (by eliminate duplicate literals #[10]): ∀ (a : Prop → Prop), Or (Eq cA True) (Or (Eq cB False) (Or (Eq (a cB) True) (Eq (a False) False))) % 3.81/3.98 Clause #21 (by identity loobHoist #[20]): ∀ (a : Prop → Prop), Or (Eq cA True) (Or (Eq cB False) (Or (Eq (a False) False) (Or (Eq (a True) True) (Eq cB False)))) % 3.81/3.98 Clause #23 (by eliminate duplicate literals #[21]): ∀ (a : Prop → Prop), Or (Eq cA True) (Or (Eq cB False) (Or (Eq (a False) False) (Eq (a True) True))) % 3.81/3.98 Clause #24 (by superposition #[23, 13]): ∀ (a : Prop → Prop), Or (Eq cA True) (Or (Eq (a False) False) (Or (Eq (a True) True) (Or (Eq cA True) (Eq False True)))) % 3.81/3.98 Clause #25 (by clausification #[24]): ∀ (a : Prop → Prop), Or (Eq cA True) (Or (Eq (a False) False) (Or (Eq (a True) True) (Eq cA True))) % 3.81/3.98 Clause #26 (by eliminate duplicate literals #[25]): ∀ (a : Prop → Prop), Or (Eq cA True) (Or (Eq (a False) False) (Eq (a True) True)) % 3.81/3.98 Clause #29 (by neHoist #[26]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), % 3.81/3.98 Or (Eq cA True) (Or (Eq ((fun x => Ne (a_1 x) (a_2 x)) True) True) (Or (Eq True False) (Eq (a_1 False) (a_2 False)))) % 3.81/3.98 Clause #37 (by eliminate duplicate literals #[19]): ∀ (a : Prop → Prop), Or (Eq cA False) (Or (Eq cB True) (Or (Eq (a True) False) (Eq (a False) True))) % 3.81/3.98 Clause #58 (by betaEtaReduce #[29]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), % 3.81/3.98 Or (Eq cA True) (Or (Eq (Ne (a_1 True) (a_2 True)) True) (Or (Eq True False) (Eq (a_1 False) (a_2 False)))) % 3.81/3.98 Clause #59 (by clausification #[58]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), % 3.81/3.98 Or (Eq cA True) (Or (Eq True False) (Or (Eq (a_1 False) (a_2 False)) (Ne (a_1 True) (a_2 True)))) % 3.81/3.98 Clause #60 (by clausification #[59]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), % 3.81/3.98 Or (Eq cA True) (Or (Eq (a_1 False) (a_2 False)) (Ne (a_1 True) (a_2 True))) % 3.81/3.98 Clause #61 (by equality resolution #[60]): Or (Eq cA True) (Eq ((fun x => x) False) ((fun x => True) False)) % 3.81/3.98 Clause #68 (by betaEtaReduce #[61]): Or (Eq cA True) (Eq False True) % 3.81/3.99 Clause #69 (by clausification #[68]): Eq cA True % 3.81/3.99 Clause #70 (by backward demodulation #[69, 12]): Or (Eq True False) (Eq cB False) % 3.81/3.99 Clause #73 (by backward demodulation #[69, 37]): ∀ (a : Prop → Prop), Or (Eq True False) (Or (Eq cB True) (Or (Eq (a True) False) (Eq (a False) True))) % 3.81/3.99 Clause #79 (by clausification #[70]): Eq cB False % 3.81/3.99 Clause #81 (by clausification #[73]): ∀ (a : Prop → Prop), Or (Eq cB True) (Or (Eq (a True) False) (Eq (a False) True)) % 3.81/3.99 Clause #84 (by neHoist #[81]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), % 3.81/3.99 Or (Eq cB True) (Or (Eq ((fun x => Ne (a_1 x) (a_2 x)) False) True) (Or (Eq True False) (Eq (a_1 True) (a_2 True)))) % 3.81/3.99 Clause #140 (by betaEtaReduce #[84]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), % 3.81/3.99 Or (Eq cB True) (Or (Eq (Ne (a_1 False) (a_2 False)) True) (Or (Eq True False) (Eq (a_1 True) (a_2 True)))) % 3.81/3.99 Clause #141 (by clausification #[140]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), % 3.81/3.99 Or (Eq cB True) (Or (Eq True False) (Or (Eq (a_1 True) (a_2 True)) (Ne (a_1 False) (a_2 False)))) % 3.81/3.99 Clause #142 (by clausification #[141]): ∀ (a : Prop → Sort _abstMVar.0) (a_1 a_2 : (x : Prop) → a x), % 3.81/3.99 Or (Eq cB True) (Or (Eq (a_1 True) (a_2 True)) (Ne (a_1 False) (a_2 False))) % 3.81/3.99 Clause #143 (by equality resolution #[142]): Or (Eq cB True) (Eq ((fun x => x) True) ((fun x => False) True)) % 3.81/3.99 Clause #151 (by betaEtaReduce #[143]): Or (Eq cB True) (Eq True False) % 3.81/3.99 Clause #152 (by clausification #[151]): Eq cB True % 3.81/3.99 Clause #153 (by superposition #[152, 79]): Eq True False % 3.81/3.99 Clause #157 (by clausification #[153]): False % 3.81/3.99 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------