%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU571^2 : 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 08:01:56 PM UTC 2025 % Result : Theorem 4.16s 4.33s % Output : Proof 4.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU571^2 : TPTP v9.2.0. Released v3.7.0. % 0.03/0.13 % 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 05:13:23 EDT 2025 % 0.13/0.35 % CPUTime : % 4.16/4.33 SZS status Theorem for theBenchmark.p % 4.16/4.33 SZS output start Proof for theBenchmark.p % 4.16/4.33 Clause #0 (by assumption #[]): Eq (Eq setadjoinIR (∀ (Xx A Xy : Iota), in Xy A → in Xy (setadjoin Xx A))) True % 4.16/4.33 Clause #1 (by assumption #[]): Eq (Eq subsetI1 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B)) True % 4.16/4.33 Clause #2 (by assumption #[]): Eq (Not (setadjoinIR → subsetI1 → ∀ (Xx A : Iota), subset A (setadjoin Xx A))) True % 4.16/4.33 Clause #3 (by clausification #[1]): Eq subsetI1 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) % 4.16/4.33 Clause #22 (by clausification #[2]): Eq (setadjoinIR → subsetI1 → ∀ (Xx A : Iota), subset A (setadjoin Xx A)) False % 4.16/4.33 Clause #23 (by clausification #[22]): Eq setadjoinIR True % 4.16/4.33 Clause #24 (by clausification #[22]): Eq (subsetI1 → ∀ (Xx A : Iota), subset A (setadjoin Xx A)) False % 4.16/4.33 Clause #25 (by clausification #[0]): Eq setadjoinIR (∀ (Xx A Xy : Iota), in Xy A → in Xy (setadjoin Xx A)) % 4.16/4.33 Clause #26 (by forward demodulation #[25, 23]): Eq True (∀ (Xx A Xy : Iota), in Xy A → in Xy (setadjoin Xx A)) % 4.16/4.33 Clause #27 (by clausification #[26]): ∀ (a : Iota), Eq (∀ (A Xy : Iota), in Xy A → in Xy (setadjoin a A)) True % 4.16/4.33 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (∀ (Xy : Iota), in Xy a → in Xy (setadjoin a_1 a)) True % 4.16/4.33 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Eq (in a a_1 → in a (setadjoin a_2 a_1)) True % 4.16/4.33 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Eq (in a (setadjoin a_2 a_1)) True) % 4.16/4.33 Clause #31 (by clausification #[24]): Eq subsetI1 True % 4.16/4.33 Clause #32 (by clausification #[24]): Eq (∀ (Xx A : Iota), subset A (setadjoin Xx A)) False % 4.16/4.33 Clause #33 (by backward demodulation #[31, 3]): Eq True (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) % 4.16/4.33 Clause #36 (by clausification #[33]): ∀ (a : Iota), Eq (∀ (B : Iota), (∀ (Xx : Iota), in Xx a → in Xx B) → subset a B) True % 4.16/4.33 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → subset a a_1) True % 4.16/4.33 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), Or (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) (Eq (subset a a_1) True) % 4.16/4.33 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), % 4.16/4.33 Or (Eq (subset a 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) % 4.16/4.33 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a 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) % 4.16/4.33 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 3 a a_1 a_2) a) True) % 4.16/4.33 Clause #42 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 3 a a_1 a_2) a_1) False) % 4.16/4.33 Clause #43 (by superposition #[41, 30]): ∀ (a a_1 a_2 a_3 : Iota), % 4.16/4.33 Or (Eq (subset a a_1) True) (Or (Eq True False) (Eq (in (skS.0 3 a a_1 a_2) (setadjoin a_3 a)) True)) % 4.16/4.33 Clause #44 (by clausification #[32]): ∀ (a : Iota), Eq (Not (∀ (A : Iota), subset A (setadjoin (skS.0 4 a) A))) True % 4.16/4.33 Clause #45 (by clausification #[44]): ∀ (a : Iota), Eq (∀ (A : Iota), subset A (setadjoin (skS.0 4 a) A)) False % 4.16/4.33 Clause #46 (by clausification #[45]): ∀ (a a_1 : Iota), Eq (Not (subset (skS.0 5 a a_1) (setadjoin (skS.0 4 a) (skS.0 5 a a_1)))) True % 4.16/4.33 Clause #47 (by clausification #[46]): ∀ (a a_1 : Iota), Eq (subset (skS.0 5 a a_1) (setadjoin (skS.0 4 a) (skS.0 5 a a_1))) False % 4.16/4.33 Clause #57 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 3 a a_1 a_2) (setadjoin a_3 a)) True) % 4.16/4.33 Clause #58 (by superposition #[57, 42]): ∀ (a a_1 : Iota), Or (Eq (subset a (setadjoin a_1 a)) True) (Or (Eq (subset a (setadjoin a_1 a)) True) (Eq True False)) % 4.16/4.33 Clause #60 (by clausification #[58]): ∀ (a a_1 : Iota), Or (Eq (subset a (setadjoin a_1 a)) True) (Eq (subset a (setadjoin a_1 a)) True) % 4.16/4.33 Clause #61 (by eliminate duplicate literals #[60]): ∀ (a a_1 : Iota), Eq (subset a (setadjoin a_1 a)) True % 4.16/4.33 Clause #62 (by superposition #[61, 47]): Eq True False % 4.16/4.33 Clause #63 (by clausification #[62]): False % 4.16/4.33 SZS output end Proof for theBenchmark.p 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