%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU540^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n007.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 08:01:52 PM UTC 2025 % Result : Theorem 4.42s 4.60s % Output : Proof 4.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU540^2 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.14 % Command : duper %s % 0.14/0.35 % Computer : n007.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Fri Oct 3 05:50:38 EDT 2025 % 0.14/0.35 % CPUTime : % 4.42/4.60 SZS status Theorem for theBenchmark.p % 4.42/4.60 SZS output start Proof for theBenchmark.p % 4.42/4.60 Clause #0 (by assumption #[]): Eq % 4.42/4.60 (Eq dsetconstrI % 4.42/4.60 (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx A → Xphi Xx → in Xx (dsetconstr A fun Xy => Xphi Xy))) % 4.42/4.60 True % 4.42/4.60 Clause #1 (by assumption #[]): Eq (Eq prop2set fun Xphi => dsetconstr (powerset emptyset) fun Xx => Xphi) True % 4.42/4.60 Clause #2 (by assumption #[]): Eq (Eq powersetI (∀ (A B : Iota), (∀ (Xx : Iota), in Xx B → in Xx A) → in B (powerset A))) True % 4.42/4.60 Clause #3 (by assumption #[]): Eq (Not (dsetconstrI → powersetI → ∀ (Xphi : Prop), Xphi → in emptyset (prop2set Xphi))) True % 4.42/4.60 Clause #4 (by clausification #[3]): Eq (dsetconstrI → powersetI → ∀ (Xphi : Prop), Xphi → in emptyset (prop2set Xphi)) False % 4.42/4.60 Clause #5 (by clausification #[4]): Eq dsetconstrI True % 4.42/4.60 Clause #6 (by clausification #[4]): Eq (powersetI → ∀ (Xphi : Prop), Xphi → in emptyset (prop2set Xphi)) False % 4.42/4.60 Clause #7 (by clausification #[6]): Eq powersetI True % 4.42/4.60 Clause #8 (by clausification #[6]): Eq (∀ (Xphi : Prop), Xphi → in emptyset (prop2set Xphi)) False % 4.42/4.60 Clause #9 (by clausification #[8]): ∀ (a : Prop), Eq (Not (skS.0 0 a → in emptyset (prop2set (skS.0 0 a)))) True % 4.42/4.60 Clause #10 (by clausification #[9]): ∀ (a : Prop), Eq (skS.0 0 a → in emptyset (prop2set (skS.0 0 a))) False % 4.42/4.60 Clause #11 (by clausification #[10]): ∀ (a : Prop), Eq (skS.0 0 a) True % 4.42/4.60 Clause #12 (by clausification #[10]): ∀ (a : Prop), Eq (in emptyset (prop2set (skS.0 0 a))) False % 4.42/4.60 Clause #14 (by identity boolHoist #[11]): ∀ (a : Prop), Or (Eq (skS.0 0 False) True) (Eq a True) % 4.42/4.60 Clause #17 (by betaEtaReduce #[0]): Eq (Eq dsetconstrI (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx A → Xphi Xx → in Xx (dsetconstr A Xphi))) True % 4.42/4.60 Clause #18 (by clausification #[17]): Eq dsetconstrI (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx A → Xphi Xx → in Xx (dsetconstr A Xphi)) % 4.42/4.60 Clause #19 (by forward demodulation #[18, 5]): Eq True (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx A → Xphi Xx → in Xx (dsetconstr A Xphi)) % 4.42/4.60 Clause #20 (by clausification #[19]): ∀ (a : Iota), Eq (∀ (Xphi : Iota → Prop) (Xx : Iota), in Xx a → Xphi Xx → in Xx (dsetconstr a Xphi)) True % 4.42/4.60 Clause #21 (by clausification #[20]): ∀ (a : Iota) (a_1 : Iota → Prop), Eq (∀ (Xx : Iota), in Xx a → a_1 Xx → in Xx (dsetconstr a a_1)) True % 4.42/4.60 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Eq (in a a_1 → a_2 a → in a (dsetconstr a_1 a_2)) True % 4.42/4.60 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Or (Eq (in a a_1) False) (Eq (a_2 a → in a (dsetconstr a_1 a_2)) True) % 4.42/4.60 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), % 4.42/4.60 Or (Eq (in a a_1) False) (Or (Eq (a_2 a) False) (Eq (in a (dsetconstr a_1 a_2)) True)) % 4.42/4.60 Clause #28 (by equality factoring #[14]): Or (Ne True True) (Eq (skS.0 0 False) True) % 4.42/4.60 Clause #32 (by clausification #[28]): Or (Eq (skS.0 0 False) True) (Or (Eq True False) (Eq True False)) % 4.42/4.60 Clause #34 (by clausification #[32]): Or (Eq (skS.0 0 False) True) (Eq True False) % 4.42/4.60 Clause #35 (by clausification #[34]): Eq (skS.0 0 False) True % 4.42/4.60 Clause #37 (by identity loobHoist #[12]): ∀ (a : Prop), Or (Eq (in emptyset (prop2set True)) False) (Eq (skS.0 0 a) False) % 4.42/4.60 Clause #40 (by identity boolHoist #[37]): ∀ (a : Prop), Or (Eq (in emptyset (prop2set True)) False) (Or (Eq (skS.0 0 False) False) (Eq a True)) % 4.42/4.60 Clause #41 (by clausification #[2]): Eq powersetI (∀ (A B : Iota), (∀ (Xx : Iota), in Xx B → in Xx A) → in B (powerset A)) % 4.42/4.60 Clause #42 (by forward demodulation #[41, 7]): Eq True (∀ (A B : Iota), (∀ (Xx : Iota), in Xx B → in Xx A) → in B (powerset A)) % 4.42/4.60 Clause #43 (by clausification #[42]): ∀ (a : Iota), Eq (∀ (B : Iota), (∀ (Xx : Iota), in Xx B → in Xx a) → in B (powerset a)) True % 4.42/4.60 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota), Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → in a (powerset a_1)) True % 4.42/4.60 Clause #45 (by clausification #[44]): ∀ (a a_1 : Iota), Or (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) (Eq (in a (powerset a_1)) True) % 4.46/4.62 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 : Iota), % 4.46/4.62 Or (Eq (in a (powerset a_1)) True) (Eq (Not (in (skS.0 1 a a_1 a_2) a → in (skS.0 1 a a_1 a_2) a_1)) True) % 4.46/4.62 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 : Iota), % 4.46/4.62 Or (Eq (in a (powerset a_1)) True) (Eq (in (skS.0 1 a a_1 a_2) a → in (skS.0 1 a a_1 a_2) a_1) False) % 4.46/4.62 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (powerset a_1)) True) (Eq (in (skS.0 1 a a_1 a_2) a) True) % 4.46/4.62 Clause #49 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (powerset a_1)) True) (Eq (in (skS.0 1 a a_1 a_2) a_1) False) % 4.46/4.62 Clause #52 (by clausification #[1]): Eq prop2set fun Xphi => dsetconstr (powerset emptyset) fun Xx => Xphi % 4.46/4.62 Clause #53 (by argument congruence #[52]): ∀ (a : Prop), Eq (prop2set a) ((fun Xphi => dsetconstr (powerset emptyset) fun Xx => Xphi) a) % 4.46/4.62 Clause #65 (by betaEtaReduce #[53]): ∀ (a : Prop), Eq (prop2set a) (dsetconstr (powerset emptyset) fun Xx => a) % 4.46/4.62 Clause #66 (by identity loobHoist #[65]): ∀ (a : Prop), Or (Eq (prop2set True) (dsetconstr (powerset emptyset) fun Xx => a)) (Eq a False) % 4.46/4.62 Clause #69 (by superposition #[66, 7]): Or (Eq (prop2set True) (dsetconstr (powerset emptyset) fun Xx => powersetI)) (Eq False True) % 4.46/4.62 Clause #81 (by clausification #[69]): Eq (prop2set True) (dsetconstr (powerset emptyset) fun Xx => powersetI) % 4.46/4.62 Clause #276 (by superposition #[49, 48]): ∀ (a : Iota), Or (Eq (in a (powerset a)) True) (Or (Eq (in a (powerset a)) True) (Eq False True)) % 4.46/4.62 Clause #282 (by clausification #[276]): ∀ (a : Iota), Or (Eq (in a (powerset a)) True) (Eq (in a (powerset a)) True) % 4.46/4.62 Clause #283 (by eliminate duplicate literals #[282]): ∀ (a : Iota), Eq (in a (powerset a)) True % 4.46/4.62 Clause #284 (by superposition #[283, 24]): ∀ (a : Iota → Prop) (a_1 : Iota), % 4.46/4.62 Or (Eq True False) (Or (Eq (a a_1) False) (Eq (in a_1 (dsetconstr (powerset a_1) a)) True)) % 4.46/4.62 Clause #296 (by clausification #[284]): ∀ (a : Iota → Prop) (a_1 : Iota), Or (Eq (a a_1) False) (Eq (in a_1 (dsetconstr (powerset a_1) a)) True) % 4.46/4.62 Clause #298 (by superposition #[296, 7]): ∀ (a : Iota), Or (Eq (in a (dsetconstr (powerset a) fun x => powersetI)) True) (Eq False True) % 4.46/4.62 Clause #331 (by clausification #[298]): ∀ (a : Iota), Eq (in a (dsetconstr (powerset a) fun x => powersetI)) True % 4.46/4.62 Clause #335 (by superposition #[331, 81]): Eq (in emptyset (prop2set True)) True % 4.46/4.62 Clause #348 (by backward demodulation #[335, 40]): ∀ (a : Prop), Or (Eq True False) (Or (Eq (skS.0 0 False) False) (Eq a True)) % 4.46/4.62 Clause #467 (by clausification #[348]): ∀ (a : Prop), Or (Eq (skS.0 0 False) False) (Eq a True) % 4.46/4.62 Clause #468 (by superposition #[467, 35]): ∀ (a : Prop), Or (Eq a True) (Eq False True) % 4.46/4.62 Clause #511 (by clausification #[468]): ∀ (a : Prop), Eq a True % 4.46/4.62 Clause #512 (by falseElim #[511]): False % 4.46/4.62 SZS output end Proof for theBenchmark.p 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