%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU533^2 : 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 08:01:51 PM UTC 2025 % Result : Theorem 3.58s 3.75s % Output : Proof 3.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU533^2 : TPTP v9.2.0. Released v3.7.0. % 0.13/0.13 % Command : duper %s % 0.14/0.34 % Computer : n002.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Oct 3 04:23:38 EDT 2025 % 0.14/0.35 % CPUTime : % 3.58/3.75 SZS status Theorem for theBenchmark.p % 3.58/3.75 SZS output start Proof for theBenchmark.p % 3.58/3.75 Clause #0 (by assumption #[]): Eq (Eq setadjoinIL (∀ (Xx Xy : Iota), in Xx (setadjoin Xx Xy))) True % 3.58/3.75 Clause #1 (by assumption #[]): Eq (Eq setadjoinIR (∀ (Xx A Xy : Iota), in Xy A → in Xy (setadjoin Xx A))) True % 3.58/3.75 Clause #2 (by assumption #[]): Eq (Not (setadjoinIL → setadjoinIR → ∀ (Xx Xy : Iota), in Xy (setadjoin Xx (setadjoin Xy emptyset)))) True % 3.58/3.75 Clause #3 (by clausification #[0]): Eq setadjoinIL (∀ (Xx Xy : Iota), in Xx (setadjoin Xx Xy)) % 3.58/3.75 Clause #5 (by clausify Prop equality #[3]): Or (Eq setadjoinIL False) (Eq (∀ (Xx Xy : Iota), in Xx (setadjoin Xx Xy)) True) % 3.58/3.75 Clause #7 (by clausification #[5]): ∀ (a : Iota), Or (Eq setadjoinIL False) (Eq (∀ (Xy : Iota), in a (setadjoin a Xy)) True) % 3.58/3.75 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq setadjoinIL False) (Eq (in a (setadjoin a a_1)) True) % 3.58/3.75 Clause #13 (by clausification #[2]): Eq (setadjoinIL → setadjoinIR → ∀ (Xx Xy : Iota), in Xy (setadjoin Xx (setadjoin Xy emptyset))) False % 3.58/3.75 Clause #14 (by clausification #[13]): Eq setadjoinIL True % 3.58/3.75 Clause #15 (by clausification #[13]): Eq (setadjoinIR → ∀ (Xx Xy : Iota), in Xy (setadjoin Xx (setadjoin Xy emptyset))) False % 3.58/3.75 Clause #17 (by backward demodulation #[14, 8]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (in a (setadjoin a a_1)) True) % 3.58/3.75 Clause #19 (by clausification #[1]): Eq setadjoinIR (∀ (Xx A Xy : Iota), in Xy A → in Xy (setadjoin Xx A)) % 3.58/3.75 Clause #23 (by clausification #[17]): ∀ (a a_1 : Iota), Eq (in a (setadjoin a a_1)) True % 3.58/3.75 Clause #25 (by clausification #[15]): Eq setadjoinIR True % 3.58/3.75 Clause #26 (by clausification #[15]): Eq (∀ (Xx Xy : Iota), in Xy (setadjoin Xx (setadjoin Xy emptyset))) False % 3.58/3.75 Clause #27 (by backward demodulation #[25, 19]): Eq True (∀ (Xx A Xy : Iota), in Xy A → in Xy (setadjoin Xx A)) % 3.58/3.75 Clause #28 (by clausification #[27]): ∀ (a : Iota), Eq (∀ (A Xy : Iota), in Xy A → in Xy (setadjoin a A)) True % 3.58/3.75 Clause #29 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (∀ (Xy : Iota), in Xy a → in Xy (setadjoin a_1 a)) True % 3.58/3.75 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Eq (in a a_1 → in a (setadjoin a_2 a_1)) True % 3.58/3.75 Clause #31 (by clausification #[30]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Eq (in a (setadjoin a_2 a_1)) True) % 3.58/3.75 Clause #32 (by superposition #[31, 23]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setadjoin a_1 (setadjoin a a_2))) True) (Eq False True) % 3.58/3.75 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Eq (in a (setadjoin a_1 (setadjoin a a_2))) True % 3.58/3.75 Clause #35 (by clausification #[26]): ∀ (a : Iota), Eq (Not (∀ (Xy : Iota), in Xy (setadjoin (skS.0 2 a) (setadjoin Xy emptyset)))) True % 3.58/3.75 Clause #36 (by clausification #[35]): ∀ (a : Iota), Eq (∀ (Xy : Iota), in Xy (setadjoin (skS.0 2 a) (setadjoin Xy emptyset))) False % 3.58/3.75 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Eq (Not (in (skS.0 3 a a_1) (setadjoin (skS.0 2 a) (setadjoin (skS.0 3 a a_1) emptyset)))) True % 3.58/3.75 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), Eq (in (skS.0 3 a a_1) (setadjoin (skS.0 2 a) (setadjoin (skS.0 3 a a_1) emptyset))) False % 3.58/3.75 Clause #39 (by superposition #[38, 33]): Eq False True % 3.58/3.75 Clause #40 (by clausification #[39]): False % 3.58/3.75 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------