%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU580^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n002.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 08:01:58 PM UTC 2025 % Result : Theorem 4.27s 4.49s % Output : Proof 4.27s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU580^2 : TPTP v9.2.0. Released v3.7.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n002.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 04:39:08 EDT 2025 % 0.13/0.34 % CPUTime : % 4.27/4.49 SZS status Theorem for theBenchmark.p % 4.27/4.49 SZS output start Proof for theBenchmark.p % 4.27/4.49 Clause #0 (by assumption #[]): Eq (Eq dsetconstrEL (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A fun Xy => Xphi Xy) → in Xx A)) % 4.27/4.49 True % 4.27/4.49 Clause #1 (by assumption #[]): Eq (Eq powersetI (∀ (A B : Iota), (∀ (Xx : Iota), in Xx B → in Xx A) → in B (powerset A))) True % 4.27/4.49 Clause #2 (by assumption #[]): Eq % 4.27/4.49 (Not (dsetconstrEL → powersetI → ∀ (A : Iota) (Xphi : Iota → Prop), in (dsetconstr A fun Xx => Xphi Xx) (powerset A))) % 4.27/4.49 True % 4.27/4.49 Clause #3 (by clausification #[1]): Eq powersetI (∀ (A B : Iota), (∀ (Xx : Iota), in Xx B → in Xx A) → in B (powerset A)) % 4.27/4.49 Clause #5 (by clausify Prop equality #[3]): Or (Eq powersetI False) (Eq (∀ (A B : Iota), (∀ (Xx : Iota), in Xx B → in Xx A) → in B (powerset A)) True) % 4.27/4.49 Clause #7 (by clausification #[5]): ∀ (a : Iota), Or (Eq powersetI False) (Eq (∀ (B : Iota), (∀ (Xx : Iota), in Xx B → in Xx a) → in B (powerset a)) True) % 4.27/4.49 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq powersetI False) (Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → in a (powerset a_1)) True) % 4.27/4.49 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), % 4.27/4.49 Or (Eq powersetI False) (Or (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) (Eq (in a (powerset a_1)) True)) % 4.27/4.49 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 4.27/4.49 Or (Eq powersetI False) % 4.27/4.49 (Or (Eq (in a (powerset a_1)) True) (Eq (Not (in (skS.0 0 a a_1 a_2) a → in (skS.0 0 a a_1 a_2) a_1)) True)) % 4.27/4.49 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), % 4.27/4.49 Or (Eq powersetI False) % 4.27/4.49 (Or (Eq (in a (powerset a_1)) True) (Eq (in (skS.0 0 a a_1 a_2) a → in (skS.0 0 a a_1 a_2) a_1) False)) % 4.27/4.49 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Or (Eq powersetI False) (Or (Eq (in a (powerset a_1)) True) (Eq (in (skS.0 0 a a_1 a_2) a) True)) % 4.27/4.49 Clause #13 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), % 4.27/4.49 Or (Eq powersetI False) (Or (Eq (in a (powerset a_1)) True) (Eq (in (skS.0 0 a a_1 a_2) a_1) False)) % 4.27/4.49 Clause #22 (by betaEtaReduce #[0]): Eq (Eq dsetconstrEL (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → in Xx A)) True % 4.27/4.49 Clause #23 (by clausification #[22]): Eq dsetconstrEL (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → in Xx A) % 4.27/4.49 Clause #31 (by betaEtaReduce #[2]): Eq (Not (dsetconstrEL → powersetI → ∀ (A : Iota) (Xphi : Iota → Prop), in (dsetconstr A Xphi) (powerset A))) True % 4.27/4.49 Clause #32 (by clausification #[31]): Eq (dsetconstrEL → powersetI → ∀ (A : Iota) (Xphi : Iota → Prop), in (dsetconstr A Xphi) (powerset A)) False % 4.27/4.49 Clause #33 (by clausification #[32]): Eq dsetconstrEL True % 4.27/4.49 Clause #34 (by clausification #[32]): Eq (powersetI → ∀ (A : Iota) (Xphi : Iota → Prop), in (dsetconstr A Xphi) (powerset A)) False % 4.27/4.49 Clause #35 (by backward demodulation #[33, 23]): Eq True (∀ (A : Iota) (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr A Xphi) → in Xx A) % 4.27/4.49 Clause #37 (by clausification #[35]): ∀ (a : Iota), Eq (∀ (Xphi : Iota → Prop) (Xx : Iota), in Xx (dsetconstr a Xphi) → in Xx a) True % 4.27/4.49 Clause #38 (by clausification #[37]): ∀ (a : Iota) (a_1 : Iota → Prop), Eq (∀ (Xx : Iota), in Xx (dsetconstr a a_1) → in Xx a) True % 4.27/4.49 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Eq (in a (dsetconstr a_1 a_2) → in a a_1) True % 4.27/4.49 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota) (a_2 : Iota → Prop), Or (Eq (in a (dsetconstr a_1 a_2)) False) (Eq (in a a_1) True) % 4.27/4.49 Clause #41 (by clausification #[34]): Eq powersetI True % 4.27/4.49 Clause #42 (by clausification #[34]): Eq (∀ (A : Iota) (Xphi : Iota → Prop), in (dsetconstr A Xphi) (powerset A)) False % 4.27/4.49 Clause #44 (by backward demodulation #[41, 12]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (in a (powerset a_1)) True) (Eq (in (skS.0 0 a a_1 a_2) a) True)) % 4.27/4.49 Clause #54 (by clausification #[42]): ∀ (a : Iota), Eq (Not (∀ (Xphi : Iota → Prop), in (dsetconstr (skS.0 4 a) Xphi) (powerset (skS.0 4 a)))) True % 4.27/4.49 Clause #55 (by clausification #[54]): ∀ (a : Iota), Eq (∀ (Xphi : Iota → Prop), in (dsetconstr (skS.0 4 a) Xphi) (powerset (skS.0 4 a))) False % 4.27/4.51 Clause #56 (by clausification #[55]): ∀ (a : Iota) (a_1 : Iota → Prop), Eq (Not (in (dsetconstr (skS.0 4 a) (skS.0 5 a a_1)) (powerset (skS.0 4 a)))) True % 4.27/4.51 Clause #57 (by clausification #[56]): ∀ (a : Iota) (a_1 : Iota → Prop), Eq (in (dsetconstr (skS.0 4 a) (skS.0 5 a a_1)) (powerset (skS.0 4 a))) False % 4.27/4.51 Clause #71 (by forward demodulation #[13, 41]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (in a (powerset a_1)) True) (Eq (in (skS.0 0 a a_1 a_2) a_1) False)) % 4.27/4.51 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (powerset a_1)) True) (Eq (in (skS.0 0 a a_1 a_2) a_1) False) % 4.27/4.51 Clause #73 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (powerset a_1)) True) (Eq (in (skS.0 0 a a_1 a_2) a) True) % 4.27/4.51 Clause #74 (by superposition #[73, 40]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 a_3 : Iota), % 4.27/4.51 Or (Eq (in (dsetconstr a a_1) (powerset a_2)) True) % 4.27/4.51 (Or (Eq True False) (Eq (in (skS.0 0 (dsetconstr a a_1) a_2 a_3) a) True)) % 4.27/4.51 Clause #77 (by clausification #[74]): ∀ (a : Iota) (a_1 : Iota → Prop) (a_2 a_3 : Iota), % 4.27/4.51 Or (Eq (in (dsetconstr a a_1) (powerset a_2)) True) (Eq (in (skS.0 0 (dsetconstr a a_1) a_2 a_3) a) True) % 4.27/4.51 Clause #79 (by superposition #[77, 72]): ∀ (a : Iota) (a_1 : Iota → Prop), % 4.27/4.51 Or (Eq (in (dsetconstr a a_1) (powerset a)) True) (Or (Eq (in (dsetconstr a a_1) (powerset a)) True) (Eq True False)) % 4.27/4.51 Clause #82 (by clausification #[79]): ∀ (a : Iota) (a_1 : Iota → Prop), % 4.27/4.51 Or (Eq (in (dsetconstr a a_1) (powerset a)) True) (Eq (in (dsetconstr a a_1) (powerset a)) True) % 4.27/4.51 Clause #83 (by eliminate duplicate literals #[82]): ∀ (a : Iota) (a_1 : Iota → Prop), Eq (in (dsetconstr a a_1) (powerset a)) True % 4.27/4.51 Clause #84 (by superposition #[83, 57]): Eq True False % 4.27/4.51 Clause #85 (by clausification #[84]): False % 4.27/4.51 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------