%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU806^2 : 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 08:02:29 PM UTC 2025 % Result : Theorem 3.62s 3.78s % Output : Proof 3.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU806^2 : TPTP v9.2.0. Released v3.7.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n007.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 04:19:53 EDT 2025 % 0.13/0.34 % CPUTime : % 3.62/3.78 SZS status Theorem for theBenchmark.p % 3.62/3.78 SZS output start Proof for theBenchmark.p % 3.62/3.78 Clause #0 (by assumption #[]): Eq % 3.62/3.78 (Eq foundationAx % 3.62/3.78 (∀ (A : Iota), % 3.62/3.78 (Exists fun Xx => in Xx A) → Exists fun B => And (in B A) (Not (Exists fun Xx => And (in Xx B) (in Xx A))))) % 3.62/3.78 True % 3.62/3.78 Clause #1 (by assumption #[]): Eq (Eq setadjoinIL (∀ (Xx Xy : Iota), in Xx (setadjoin Xx Xy))) True % 3.62/3.78 Clause #2 (by assumption #[]): Eq (Eq uniqinunit (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy)) True % 3.62/3.78 Clause #4 (by assumption #[]): Eq (Not (foundationAx → setadjoinIL → uniqinunit → in__Cong → ∀ (A : Iota), Not (in A A))) True % 3.62/3.78 Clause #5 (by clausification #[4]): Eq (foundationAx → setadjoinIL → uniqinunit → in__Cong → ∀ (A : Iota), Not (in A A)) False % 3.62/3.78 Clause #6 (by clausification #[5]): Eq foundationAx True % 3.62/3.78 Clause #7 (by clausification #[5]): Eq (setadjoinIL → uniqinunit → in__Cong → ∀ (A : Iota), Not (in A A)) False % 3.62/3.78 Clause #8 (by clausification #[7]): Eq setadjoinIL True % 3.62/3.78 Clause #9 (by clausification #[7]): Eq (uniqinunit → in__Cong → ∀ (A : Iota), Not (in A A)) False % 3.62/3.78 Clause #10 (by clausification #[9]): Eq uniqinunit True % 3.62/3.78 Clause #11 (by clausification #[9]): Eq (in__Cong → ∀ (A : Iota), Not (in A A)) False % 3.62/3.78 Clause #13 (by clausification #[11]): Eq (∀ (A : Iota), Not (in A A)) False % 3.62/3.78 Clause #14 (by clausification #[13]): ∀ (a : Iota), Eq (Not (Not (in (skS.0 0 a) (skS.0 0 a)))) True % 3.62/3.78 Clause #15 (by clausification #[14]): ∀ (a : Iota), Eq (Not (in (skS.0 0 a) (skS.0 0 a))) False % 3.62/3.78 Clause #16 (by clausification #[15]): ∀ (a : Iota), Eq (in (skS.0 0 a) (skS.0 0 a)) True % 3.62/3.78 Clause #17 (by clausification #[0]): Eq foundationAx % 3.62/3.78 (∀ (A : Iota), % 3.62/3.78 (Exists fun Xx => in Xx A) → Exists fun B => And (in B A) (Not (Exists fun Xx => And (in Xx B) (in Xx A)))) % 3.62/3.78 Clause #18 (by forward demodulation #[17, 6]): Eq True % 3.62/3.78 (∀ (A : Iota), % 3.62/3.78 (Exists fun Xx => in Xx A) → Exists fun B => And (in B A) (Not (Exists fun Xx => And (in Xx B) (in Xx A)))) % 3.62/3.78 Clause #19 (by clausification #[18]): ∀ (a : Iota), % 3.62/3.78 Eq ((Exists fun Xx => in Xx a) → Exists fun B => And (in B a) (Not (Exists fun Xx => And (in Xx B) (in Xx a)))) True % 3.62/3.78 Clause #20 (by clausification #[19]): ∀ (a : Iota), % 3.62/3.78 Or (Eq (Exists fun Xx => in Xx a) False) % 3.62/3.78 (Eq (Exists fun B => And (in B a) (Not (Exists fun Xx => And (in Xx B) (in Xx a)))) True) % 3.62/3.78 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), % 3.62/3.78 Or (Eq (Exists fun B => And (in B a) (Not (Exists fun Xx => And (in Xx B) (in Xx a)))) True) (Eq (in a_1 a) False) % 3.62/3.78 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), % 3.62/3.78 Or (Eq (in a a_1) False) % 3.62/3.78 (Eq (And (in (skS.0 1 a_1 a_2) a_1) (Not (Exists fun Xx => And (in Xx (skS.0 1 a_1 a_2)) (in Xx a_1)))) True) % 3.62/3.78 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), % 3.62/3.78 Or (Eq (in a a_1) False) (Eq (Not (Exists fun Xx => And (in Xx (skS.0 1 a_1 a_2)) (in Xx a_1))) True) % 3.62/3.78 Clause #24 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Eq (in (skS.0 1 a_1 a_2) a_1) True) % 3.62/3.78 Clause #25 (by clausification #[23]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Eq (Exists fun Xx => And (in Xx (skS.0 1 a_1 a_2)) (in Xx a_1)) False) % 3.62/3.78 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in a a_1) False) (Eq (And (in a_2 (skS.0 1 a_1 a_3)) (in a_2 a_1)) False) % 3.62/3.78 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in a a_1) False) (Or (Eq (in a_2 (skS.0 1 a_1 a_3)) False) (Eq (in a_2 a_1) False)) % 3.62/3.78 Clause #29 (by clausification #[2]): Eq uniqinunit (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy) % 3.62/3.78 Clause #30 (by forward demodulation #[29, 10]): Eq True (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy) % 3.62/3.78 Clause #31 (by clausification #[30]): ∀ (a : Iota), Eq (∀ (Xy : Iota), in a (setadjoin Xy emptyset) → Eq a Xy) True % 3.62/3.78 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Eq (in a (setadjoin a_1 emptyset) → Eq a a_1) True % 3.62/3.78 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Or (Eq (in a (setadjoin a_1 emptyset)) False) (Eq (Eq a a_1) True) % 3.62/3.78 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Or (Eq (in a (setadjoin a_1 emptyset)) False) (Eq a a_1) % 3.62/3.79 Clause #35 (by clausification #[1]): Eq setadjoinIL (∀ (Xx Xy : Iota), in Xx (setadjoin Xx Xy)) % 3.62/3.79 Clause #36 (by forward demodulation #[35, 8]): Eq True (∀ (Xx Xy : Iota), in Xx (setadjoin Xx Xy)) % 3.62/3.79 Clause #37 (by clausification #[36]): ∀ (a : Iota), Eq (∀ (Xy : Iota), in a (setadjoin a Xy)) True % 3.62/3.79 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), Eq (in a (setadjoin a a_1)) True % 3.62/3.79 Clause #39 (by superposition #[38, 27]): ∀ (a a_1 a_2 a_3 : Iota), % 3.62/3.79 Or (Eq True False) (Or (Eq (in a (skS.0 1 (setadjoin a_1 a_2) a_3)) False) (Eq (in a (setadjoin a_1 a_2)) False)) % 3.62/3.79 Clause #41 (by superposition #[24, 38]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (in (skS.0 1 (setadjoin a a_1) a_2) (setadjoin a a_1)) True) % 3.62/3.79 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 1 (setadjoin a a_1) a_2) (setadjoin a a_1)) True % 3.62/3.79 Clause #43 (by superposition #[42, 34]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (skS.0 1 (setadjoin a emptyset) a_1) a) % 3.62/3.79 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota), Eq (skS.0 1 (setadjoin a emptyset) a_1) a % 3.62/3.79 Clause #62 (by clausification #[39]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in a (skS.0 1 (setadjoin a_1 a_2) a_3)) False) (Eq (in a (setadjoin a_1 a_2)) False) % 3.62/3.79 Clause #63 (by superposition #[62, 44]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (in a (setadjoin a_1 emptyset)) False) % 3.62/3.79 Clause #64 (by superposition #[63, 16]): ∀ (a : Iota), Or (Eq (in (skS.0 0 a) (setadjoin (skS.0 0 a) emptyset)) False) (Eq False True) % 3.62/3.79 Clause #69 (by clausification #[64]): ∀ (a : Iota), Eq (in (skS.0 0 a) (setadjoin (skS.0 0 a) emptyset)) False % 3.62/3.79 Clause #70 (by superposition #[69, 38]): Eq False True % 3.62/3.79 Clause #71 (by clausification #[70]): False % 3.62/3.79 SZS output end Proof for theBenchmark.p 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