%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU519^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n022.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 08:01:48 PM UTC 2025 % Result : Theorem 3.57s 3.78s % Output : Proof 3.57s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU519^2 : TPTP v9.2.0. Released v3.7.0. % 0.11/0.14 % Command : duper %s % 0.14/0.35 % Computer : n022.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 06:32:23 EDT 2025 % 0.14/0.35 % CPUTime : % 3.57/3.78 SZS status Theorem for theBenchmark.p % 3.57/3.78 SZS output start Proof for theBenchmark.p % 3.57/3.78 Clause #0 (by assumption #[]): Eq (Eq emptysetE (∀ (Xx : Iota), in Xx emptyset → ∀ (Xphi : Prop), Xphi)) True % 3.57/3.78 Clause #1 (by assumption #[]): Eq (Eq powersetI (∀ (A B : Iota), (∀ (Xx : Iota), in Xx B → in Xx A) → in B (powerset A))) True % 3.57/3.78 Clause #2 (by assumption #[]): Eq (Not (emptysetE → powersetI → ∀ (A : Iota), in emptyset (powerset A))) True % 3.57/3.78 Clause #3 (by clausification #[0]): Eq emptysetE (∀ (Xx : Iota), in Xx emptyset → ∀ (Xphi : Prop), Xphi) % 3.57/3.78 Clause #18 (by clausification #[1]): Eq powersetI (∀ (A B : Iota), (∀ (Xx : Iota), in Xx B → in Xx A) → in B (powerset A)) % 3.57/3.78 Clause #22 (by clausification #[2]): Eq (emptysetE → powersetI → ∀ (A : Iota), in emptyset (powerset A)) False % 3.57/3.78 Clause #23 (by clausification #[22]): Eq emptysetE True % 3.57/3.78 Clause #24 (by clausification #[22]): Eq (powersetI → ∀ (A : Iota), in emptyset (powerset A)) False % 3.57/3.78 Clause #25 (by backward demodulation #[23, 3]): Eq True (∀ (Xx : Iota), in Xx emptyset → ∀ (Xphi : Prop), Xphi) % 3.57/3.78 Clause #29 (by clausification #[25]): ∀ (a : Iota), Eq (in a emptyset → ∀ (Xphi : Prop), Xphi) True % 3.57/3.78 Clause #30 (by clausification #[29]): ∀ (a : Iota), Or (Eq (in a emptyset) False) (Eq (∀ (Xphi : Prop), Xphi) True) % 3.57/3.78 Clause #31 (by clausification #[30]): ∀ (a : Iota) (a_1 : Prop), Or (Eq (in a emptyset) False) (Eq a_1 True) % 3.57/3.78 Clause #32 (by clausification #[24]): Eq powersetI True % 3.57/3.78 Clause #33 (by clausification #[24]): Eq (∀ (A : Iota), in emptyset (powerset A)) False % 3.57/3.78 Clause #34 (by backward demodulation #[32, 18]): Eq True (∀ (A B : Iota), (∀ (Xx : Iota), in Xx B → in Xx A) → in B (powerset A)) % 3.57/3.78 Clause #35 (by clausification #[33]): ∀ (a : Iota), Eq (Not (in emptyset (powerset (skS.0 2 a)))) True % 3.57/3.78 Clause #36 (by clausification #[35]): ∀ (a : Iota), Eq (in emptyset (powerset (skS.0 2 a))) False % 3.57/3.78 Clause #37 (by clausification #[34]): ∀ (a : Iota), Eq (∀ (B : Iota), (∀ (Xx : Iota), in Xx B → in Xx a) → in B (powerset a)) True % 3.57/3.78 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → in a (powerset a_1)) True % 3.57/3.78 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Or (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) (Eq (in a (powerset a_1)) True) % 3.57/3.78 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), % 3.57/3.78 Or (Eq (in a (powerset a_1)) True) (Eq (Not (in (skS.0 3 a a_1 a_2) a → in (skS.0 3 a a_1 a_2) a_1)) True) % 3.57/3.78 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), % 3.57/3.78 Or (Eq (in a (powerset a_1)) True) (Eq (in (skS.0 3 a a_1 a_2) a → in (skS.0 3 a a_1 a_2) a_1) False) % 3.57/3.78 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (powerset a_1)) True) (Eq (in (skS.0 3 a a_1 a_2) a) True) % 3.57/3.78 Clause #44 (by superposition #[42, 31]): ∀ (a : Iota) (a_1 : Prop), Or (Eq (in emptyset (powerset a)) True) (Or (Eq True False) (Eq a_1 True)) % 3.57/3.78 Clause #46 (by clausification #[44]): ∀ (a : Iota) (a_1 : Prop), Or (Eq (in emptyset (powerset a)) True) (Eq a_1 True) % 3.57/3.78 Clause #47 (by superposition #[46, 36]): ∀ (a : Prop), Or (Eq a True) (Eq True False) % 3.57/3.78 Clause #51 (by clausification #[47]): ∀ (a : Prop), Eq a True % 3.57/3.78 Clause #53 (by falseElim #[51]): False % 3.57/3.78 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------