%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO016^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n005.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 08:08:25 PM UTC 2025 % Result : Theorem 6.32s 6.59s % Output : Proof 6.49s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.11 % Problem : SYO016^1 : TPTP v9.2.0. Released v3.7.0. % 0.08/0.12 % Command : duper %s % 0.09/0.32 % Computer : n005.cluster.edu % 0.09/0.32 % Model : x86_64 x86_64 % 0.09/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.32 % Memory : 8042.1875MB % 0.09/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.32 % CPULimit : 300 % 0.09/0.32 % WCLimit : 300 % 0.09/0.32 % DateTime : Fri Oct 3 14:36:38 EDT 2025 % 0.09/0.32 % CPUTime : % 6.32/6.59 SZS status Theorem for theBenchmark.p % 6.32/6.59 SZS output start Proof for theBenchmark.p % 6.32/6.59 Clause #0 (by assumption #[]): Eq (Eq leibeq fun X Y => ∀ (P : Prop → Prop), P X → P Y) True % 6.32/6.59 Clause #1 (by assumption #[]): Eq (Not (leibeq (h (leibeq (h True) (h False))) (h False))) True % 6.32/6.59 Clause #2 (by clausification #[1]): Eq (leibeq (h (leibeq (h True) (h False))) (h False)) False % 6.32/6.59 Clause #3 (by identity loobHoist #[2]): Or (Eq (leibeq (h (leibeq (h True) (h False))) True) False) (Eq (h False) False) % 6.32/6.59 Clause #4 (by identity boolHoist #[2]): Or (Eq (leibeq (h (leibeq (h True) (h False))) False) False) (Eq (h False) True) % 6.32/6.59 Clause #5 (by identity loobHoist #[3]): Or (Eq (h False) False) (Or (Eq (leibeq True True) False) (Eq (h (leibeq (h True) (h False))) False)) % 6.32/6.59 Clause #6 (by identity boolHoist #[3]): Or (Eq (h False) False) (Or (Eq (leibeq False True) False) (Eq (h (leibeq (h True) (h False))) True)) % 6.32/6.59 Clause #7 (by identity loobHoist #[5]): Or (Eq (h False) False) % 6.32/6.59 (Or (Eq (leibeq True True) False) (Or (Eq (h True) False) (Eq (leibeq (h True) (h False)) False))) % 6.32/6.59 Clause #8 (by identity boolHoist #[5]): Or (Eq (h False) False) % 6.32/6.59 (Or (Eq (leibeq True True) False) (Or (Eq (h False) False) (Eq (leibeq (h True) (h False)) True))) % 6.32/6.59 Clause #9 (by identity loobHoist #[7]): Or (Eq (h False) False) % 6.32/6.59 (Or (Eq (leibeq True True) False) % 6.32/6.59 (Or (Eq (h True) False) (Or (Eq (leibeq (h True) True) False) (Eq (h False) False)))) % 6.32/6.59 Clause #11 (by eliminate duplicate literals #[9]): Or (Eq (h False) False) (Or (Eq (leibeq True True) False) (Or (Eq (h True) False) (Eq (leibeq (h True) True) False))) % 6.32/6.59 Clause #12 (by identity loobHoist #[11]): Or (Eq (h False) False) % 6.32/6.59 (Or (Eq (leibeq True True) False) (Or (Eq (h True) False) (Or (Eq (leibeq True True) False) (Eq (h True) False)))) % 6.32/6.59 Clause #14 (by eliminate duplicate literals #[12]): Or (Eq (h False) False) (Or (Eq (leibeq True True) False) (Eq (h True) False)) % 6.32/6.59 Clause #15 (by clausification #[0]): Eq leibeq fun X Y => ∀ (P : Prop → Prop), P X → P Y % 6.32/6.59 Clause #16 (by argument congruence #[15]): ∀ (a : Prop), Eq (leibeq a) ((fun X Y => ∀ (P : Prop → Prop), P X → P Y) a) % 6.32/6.59 Clause #18 (by betaEtaReduce #[16]): ∀ (a : Prop), Eq (leibeq a) fun Y => ∀ (P : Prop → Prop), P a → P Y % 6.32/6.59 Clause #19 (by identity loobHoist #[18]): ∀ (a : Prop), Or (Eq (leibeq True) fun Y => ∀ (P : Prop → Prop), P a → P Y) (Eq a False) % 6.32/6.59 Clause #20 (by identity boolHoist #[18]): ∀ (a : Prop), Or (Eq (leibeq False) fun Y => ∀ (P : Prop → Prop), P a → P Y) (Eq a True) % 6.32/6.59 Clause #21 (by falseElim #[19]): Eq (leibeq True) fun Y => ∀ (P : Prop → Prop), P True → P Y % 6.32/6.59 Clause #22 (by argument congruence #[21]): ∀ (a : Prop), Eq (leibeq True a) ((fun Y => ∀ (P : Prop → Prop), P True → P Y) a) % 6.32/6.59 Clause #23 (by argument congruence #[20]): ∀ (a a_1 : Prop), Or (Eq (leibeq False a) ((fun Y => ∀ (P : Prop → Prop), P a_1 → P Y) a)) (Eq a_1 True) % 6.32/6.59 Clause #26 (by identity loobHoist #[4]): Or (Eq (h False) True) (Or (Eq (leibeq True False) False) (Eq (h (leibeq (h True) (h False))) False)) % 6.32/6.59 Clause #27 (by identity boolHoist #[4]): Or (Eq (h False) True) (Or (Eq (leibeq False False) False) (Eq (h (leibeq (h True) (h False))) True)) % 6.32/6.59 Clause #28 (by identity loobHoist #[26]): Or (Eq (h False) True) % 6.32/6.59 (Or (Eq (leibeq True False) False) (Or (Eq (h True) False) (Eq (leibeq (h True) (h False)) False))) % 6.32/6.59 Clause #31 (by identity boolHoist #[28]): Or (Eq (h False) True) % 6.32/6.59 (Or (Eq (leibeq True False) False) % 6.32/6.59 (Or (Eq (h True) False) (Or (Eq (leibeq (h True) False) False) (Eq (h False) True)))) % 6.32/6.59 Clause #32 (by betaEtaReduce #[22]): ∀ (a : Prop), Eq (leibeq True a) (∀ (P : Prop → Prop), P True → P a) % 6.32/6.59 Clause #33 (by identity loobHoist #[32]): ∀ (a : Prop), Or (Eq (leibeq True True) (∀ (P : Prop → Prop), P True → P a)) (Eq a False) % 6.32/6.59 Clause #35 (by falseElim #[33]): Eq (leibeq True True) (∀ (P : Prop → Prop), P True → P True) % 6.32/6.59 Clause #36 (by bool simp #[35]): Eq (leibeq True True) True % 6.32/6.59 Clause #46 (by identity loobHoist #[6]): Or (Eq (h False) False) % 6.32/6.59 (Or (Eq (leibeq False True) False) (Or (Eq (h True) True) (Eq (leibeq (h True) (h False)) False))) % 6.41/6.64 Clause #48 (by identity loobHoist #[46]): Or (Eq (h False) False) % 6.41/6.64 (Or (Eq (leibeq False True) False) % 6.41/6.64 (Or (Eq (h True) True) (Or (Eq (leibeq (h True) True) False) (Eq (h False) False)))) % 6.41/6.64 Clause #50 (by eliminate duplicate literals #[48]): Or (Eq (h False) False) (Or (Eq (leibeq False True) False) (Or (Eq (h True) True) (Eq (leibeq (h True) True) False))) % 6.41/6.64 Clause #52 (by identity boolHoist #[50]): Or (Eq (h False) False) % 6.41/6.64 (Or (Eq (leibeq False True) False) (Or (Eq (h True) True) (Or (Eq (leibeq False True) False) (Eq (h True) True)))) % 6.41/6.64 Clause #59 (by betaEtaReduce #[23]): ∀ (a a_1 : Prop), Or (Eq (leibeq False a) (∀ (P : Prop → Prop), P a_1 → P a)) (Eq a_1 True) % 6.41/6.64 Clause #61 (by identity boolHoist #[59]): ∀ (a a_1 : Prop), Or (Eq a True) (Or (Eq (leibeq False False) (∀ (P : Prop → Prop), P a → P a_1)) (Eq a_1 True)) % 6.41/6.64 Clause #71 (by equality factoring #[61]): ∀ (a : Prop), Or (Eq (leibeq False False) (∀ (P : Prop → Prop), P a → P a)) (Or (Ne True True) (Eq a True)) % 6.41/6.64 Clause #75 (by eliminate duplicate literals #[8]): Or (Eq (h False) False) (Or (Eq (leibeq True True) False) (Eq (leibeq (h True) (h False)) True)) % 6.41/6.64 Clause #76 (by forward demodulation #[75, 36]): Or (Eq (h False) False) (Or (Eq True False) (Eq (leibeq (h True) (h False)) True)) % 6.41/6.64 Clause #77 (by clausification #[76]): Or (Eq (h False) False) (Eq (leibeq (h True) (h False)) True) % 6.41/6.64 Clause #78 (by identity loobHoist #[77]): Or (Eq (h False) False) (Or (Eq (leibeq (h True) True) True) (Eq (h False) False)) % 6.41/6.64 Clause #80 (by eliminate duplicate literals #[78]): Or (Eq (h False) False) (Eq (leibeq (h True) True) True) % 6.41/6.64 Clause #82 (by identity boolHoist #[80]): Or (Eq (h False) False) (Or (Eq (leibeq False True) True) (Eq (h True) True)) % 6.41/6.64 Clause #143 (by clausification #[71]): ∀ (a : Prop), % 6.41/6.64 Or (Eq (leibeq False False) (∀ (P : Prop → Prop), P a → P a)) (Or (Eq a True) (Or (Eq True False) (Eq True False))) % 6.41/6.64 Clause #145 (by clausification #[143]): ∀ (a : Prop), Or (Eq (leibeq False False) (∀ (P : Prop → Prop), P a → P a)) (Or (Eq a True) (Eq True False)) % 6.41/6.64 Clause #146 (by clausification #[145]): ∀ (a : Prop), Or (Eq (leibeq False False) (∀ (P : Prop → Prop), P a → P a)) (Eq a True) % 6.41/6.64 Clause #147 (by bool simp #[146]): ∀ (a : Prop), Or (Eq (leibeq False False) True) (Eq a True) % 6.41/6.64 Clause #148 (by equality factoring #[147]): Or (Ne True True) (Eq (leibeq False False) True) % 6.41/6.64 Clause #150 (by clausification #[148]): Or (Eq (leibeq False False) True) (Or (Eq True False) (Eq True False)) % 6.41/6.64 Clause #152 (by clausification #[150]): Or (Eq (leibeq False False) True) (Eq True False) % 6.41/6.64 Clause #153 (by clausification #[152]): Eq (leibeq False False) True % 6.41/6.64 Clause #156 (by forward demodulation #[27, 153]): Or (Eq (h False) True) (Or (Eq True False) (Eq (h (leibeq (h True) (h False))) True)) % 6.41/6.64 Clause #157 (by clausification #[156]): Or (Eq (h False) True) (Eq (h (leibeq (h True) (h False))) True) % 6.41/6.64 Clause #158 (by identity loobHoist #[157]): Or (Eq (h False) True) (Or (Eq (h True) True) (Eq (leibeq (h True) (h False)) False)) % 6.41/6.64 Clause #159 (by identity boolHoist #[157]): Or (Eq (h False) True) (Or (Eq (h False) True) (Eq (leibeq (h True) (h False)) True)) % 6.41/6.64 Clause #161 (by identity boolHoist #[158]): Or (Eq (h False) True) (Or (Eq (h True) True) (Or (Eq (leibeq (h True) False) False) (Eq (h False) True))) % 6.41/6.64 Clause #178 (by eliminate duplicate literals #[159]): Or (Eq (h False) True) (Eq (leibeq (h True) (h False)) True) % 6.41/6.64 Clause #180 (by identity boolHoist #[178]): Or (Eq (h False) True) (Or (Eq (leibeq (h True) False) True) (Eq (h False) True)) % 6.41/6.64 Clause #181 (by eliminate duplicate literals #[31]): Or (Eq (h False) True) (Or (Eq (leibeq True False) False) (Or (Eq (h True) False) (Eq (leibeq (h True) False) False))) % 6.41/6.64 Clause #182 (by identity loobHoist #[181]): Or (Eq (h False) True) % 6.41/6.64 (Or (Eq (leibeq True False) False) (Or (Eq (h True) False) (Or (Eq (leibeq True False) False) (Eq (h True) False)))) % 6.41/6.64 Clause #184 (by eliminate duplicate literals #[182]): Or (Eq (h False) True) (Or (Eq (leibeq True False) False) (Eq (h True) False)) % 6.41/6.64 Clause #185 (by eliminate duplicate literals #[180]): Or (Eq (h False) True) (Eq (leibeq (h True) False) True) % 6.49/6.68 Clause #186 (by identity loobHoist #[185]): Or (Eq (h False) True) (Or (Eq (leibeq True False) True) (Eq (h True) False)) % 6.49/6.68 Clause #223 (by eliminate duplicate literals #[161]): Or (Eq (h False) True) (Or (Eq (h True) True) (Eq (leibeq (h True) False) False)) % 6.49/6.68 Clause #225 (by identity boolHoist #[223]): Or (Eq (h False) True) (Or (Eq (h True) True) (Or (Eq (leibeq False False) False) (Eq (h True) True))) % 6.49/6.68 Clause #226 (by eliminate duplicate literals #[52]): Or (Eq (h False) False) (Or (Eq (leibeq False True) False) (Eq (h True) True)) % 6.49/6.68 Clause #227 (by eliminate duplicate literals #[225]): Or (Eq (h False) True) (Or (Eq (h True) True) (Eq (leibeq False False) False)) % 6.49/6.68 Clause #228 (by superposition #[227, 153]): Or (Eq (h False) True) (Or (Eq (h True) True) (Eq False True)) % 6.49/6.68 Clause #229 (by clausification #[228]): Or (Eq (h False) True) (Eq (h True) True) % 6.49/6.68 Clause #231 (by superposition #[229, 82]): Or (Eq (h True) True) (Or (Eq True False) (Or (Eq (leibeq False True) True) (Eq (h True) True))) % 6.49/6.68 Clause #232 (by superposition #[229, 226]): Or (Eq (h True) True) (Or (Eq True False) (Or (Eq (leibeq False True) False) (Eq (h True) True))) % 6.49/6.68 Clause #233 (by clausification #[231]): Or (Eq (h True) True) (Or (Eq (leibeq False True) True) (Eq (h True) True)) % 6.49/6.68 Clause #234 (by eliminate duplicate literals #[233]): Or (Eq (h True) True) (Eq (leibeq False True) True) % 6.49/6.68 Clause #236 (by clausification #[232]): Or (Eq (h True) True) (Or (Eq (leibeq False True) False) (Eq (h True) True)) % 6.49/6.68 Clause #237 (by eliminate duplicate literals #[236]): Or (Eq (h True) True) (Eq (leibeq False True) False) % 6.49/6.68 Clause #238 (by superposition #[237, 234]): Or (Eq (h True) True) (Or (Eq (h True) True) (Eq False True)) % 6.49/6.68 Clause #241 (by clausification #[238]): Or (Eq (h True) True) (Eq (h True) True) % 6.49/6.68 Clause #242 (by eliminate duplicate literals #[241]): Eq (h True) True % 6.49/6.68 Clause #243 (by backward demodulation #[242, 14]): Or (Eq (h False) False) (Or (Eq (leibeq True True) False) (Eq True False)) % 6.49/6.68 Clause #244 (by backward demodulation #[242, 184]): Or (Eq (h False) True) (Or (Eq (leibeq True False) False) (Eq True False)) % 6.49/6.68 Clause #245 (by backward demodulation #[242, 186]): Or (Eq (h False) True) (Or (Eq (leibeq True False) True) (Eq True False)) % 6.49/6.68 Clause #249 (by clausification #[245]): Or (Eq (h False) True) (Eq (leibeq True False) True) % 6.49/6.68 Clause #254 (by clausification #[244]): Or (Eq (h False) True) (Eq (leibeq True False) False) % 6.49/6.68 Clause #255 (by superposition #[254, 249]): Or (Eq (h False) True) (Or (Eq (h False) True) (Eq False True)) % 6.49/6.68 Clause #256 (by clausification #[255]): Or (Eq (h False) True) (Eq (h False) True) % 6.49/6.68 Clause #257 (by eliminate duplicate literals #[256]): Eq (h False) True % 6.49/6.68 Clause #260 (by clausification #[243]): Or (Eq (h False) False) (Eq (leibeq True True) False) % 6.49/6.68 Clause #261 (by forward demodulation #[260, 257]): Or (Eq True False) (Eq (leibeq True True) False) % 6.49/6.68 Clause #262 (by clausification #[261]): Eq (leibeq True True) False % 6.49/6.68 Clause #263 (by superposition #[262, 36]): Eq False True % 6.49/6.68 Clause #264 (by clausification #[263]): False % 6.49/6.68 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------