%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU622^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n023.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 08:02:04 PM UTC 2025 % Result : Theorem 3.48s 3.70s % Output : Proof 3.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU622^2 : TPTP v9.2.0. Released v3.7.0. % 0.13/0.13 % Command : duper %s % 0.13/0.34 % Computer : n023.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 06:42:23 EDT 2025 % 0.13/0.34 % CPUTime : % 3.48/3.70 SZS status Theorem for theBenchmark.p % 3.48/3.70 SZS output start Proof for theBenchmark.p % 3.48/3.70 Clause #0 (by assumption #[]): Eq (Eq powersetI1 (∀ (A B : Iota), subset B A → in B (powerset A))) True % 3.48/3.70 Clause #1 (by assumption #[]): Eq (Eq singletonsubset (∀ (A Xx : Iota), in Xx A → subset (setadjoin Xx emptyset) A)) True % 3.48/3.70 Clause #2 (by assumption #[]): Eq (Not (powersetI1 → singletonsubset → ∀ (A Xx : Iota), in Xx A → in (setadjoin Xx emptyset) (powerset A))) True % 3.48/3.70 Clause #3 (by clausification #[0]): Eq powersetI1 (∀ (A B : Iota), subset B A → in B (powerset A)) % 3.48/3.70 Clause #16 (by clausification #[1]): Eq singletonsubset (∀ (A Xx : Iota), in Xx A → subset (setadjoin Xx emptyset) A) % 3.48/3.70 Clause #20 (by clausification #[2]): Eq (powersetI1 → singletonsubset → ∀ (A Xx : Iota), in Xx A → in (setadjoin Xx emptyset) (powerset A)) False % 3.48/3.70 Clause #21 (by clausification #[20]): Eq powersetI1 True % 3.48/3.70 Clause #22 (by clausification #[20]): Eq (singletonsubset → ∀ (A Xx : Iota), in Xx A → in (setadjoin Xx emptyset) (powerset A)) False % 3.48/3.70 Clause #23 (by backward demodulation #[21, 3]): Eq True (∀ (A B : Iota), subset B A → in B (powerset A)) % 3.48/3.70 Clause #26 (by clausification #[23]): ∀ (a : Iota), Eq (∀ (B : Iota), subset B a → in B (powerset a)) True % 3.48/3.70 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (subset a a_1 → in a (powerset a_1)) True % 3.48/3.70 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (in a (powerset a_1)) True) % 3.48/3.70 Clause #29 (by clausification #[22]): Eq singletonsubset True % 3.48/3.70 Clause #30 (by clausification #[22]): Eq (∀ (A Xx : Iota), in Xx A → in (setadjoin Xx emptyset) (powerset A)) False % 3.48/3.70 Clause #31 (by backward demodulation #[29, 16]): Eq True (∀ (A Xx : Iota), in Xx A → subset (setadjoin Xx emptyset) A) % 3.48/3.70 Clause #32 (by clausification #[31]): ∀ (a : Iota), Eq (∀ (Xx : Iota), in Xx a → subset (setadjoin Xx emptyset) a) True % 3.48/3.70 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Eq (in a a_1 → subset (setadjoin a emptyset) a_1) True % 3.48/3.70 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (subset (setadjoin a emptyset) a_1) True) % 3.48/3.70 Clause #35 (by clausification #[30]): ∀ (a : Iota), Eq (Not (∀ (Xx : Iota), in Xx (skS.0 2 a) → in (setadjoin Xx emptyset) (powerset (skS.0 2 a)))) True % 3.48/3.70 Clause #36 (by clausification #[35]): ∀ (a : Iota), Eq (∀ (Xx : Iota), in Xx (skS.0 2 a) → in (setadjoin Xx emptyset) (powerset (skS.0 2 a))) False % 3.48/3.70 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), % 3.48/3.70 Eq (Not (in (skS.0 3 a a_1) (skS.0 2 a) → in (setadjoin (skS.0 3 a a_1) emptyset) (powerset (skS.0 2 a)))) True % 3.48/3.70 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), % 3.48/3.70 Eq (in (skS.0 3 a a_1) (skS.0 2 a) → in (setadjoin (skS.0 3 a a_1) emptyset) (powerset (skS.0 2 a))) False % 3.48/3.70 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Eq (in (skS.0 3 a a_1) (skS.0 2 a)) True % 3.48/3.70 Clause #40 (by clausification #[38]): ∀ (a a_1 : Iota), Eq (in (setadjoin (skS.0 3 a a_1) emptyset) (powerset (skS.0 2 a))) False % 3.48/3.70 Clause #41 (by superposition #[39, 34]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (subset (setadjoin (skS.0 3 a a_1) emptyset) (skS.0 2 a)) True) % 3.48/3.70 Clause #54 (by clausification #[41]): ∀ (a a_1 : Iota), Eq (subset (setadjoin (skS.0 3 a a_1) emptyset) (skS.0 2 a)) True % 3.48/3.70 Clause #55 (by superposition #[54, 28]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (in (setadjoin (skS.0 3 a a_1) emptyset) (powerset (skS.0 2 a))) True) % 3.48/3.70 Clause #57 (by clausification #[55]): ∀ (a a_1 : Iota), Eq (in (setadjoin (skS.0 3 a a_1) emptyset) (powerset (skS.0 2 a))) True % 3.48/3.70 Clause #58 (by superposition #[57, 40]): Eq True False % 3.48/3.70 Clause #60 (by clausification #[58]): False % 3.48/3.70 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------