%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU617^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n025.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 08:02:03 PM UTC 2025 % Result : Theorem 3.58s 3.79s % Output : Proof 3.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU617^2 : TPTP v9.2.0. Released v3.7.0. % 0.12/0.13 % Command : duper %s % 0.14/0.34 % Computer : n025.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 06:42:23 EDT 2025 % 0.14/0.35 % CPUTime : % 3.58/3.79 SZS status Theorem for theBenchmark.p % 3.58/3.79 SZS output start Proof for theBenchmark.p % 3.58/3.79 Clause #0 (by assumption #[]): Eq (Eq setadjoinIL (∀ (Xx Xy : Iota), in Xx (setadjoin Xx Xy))) True % 3.58/3.79 Clause #1 (by assumption #[]): Eq (Eq setunionI (∀ (A Xx B : Iota), in Xx B → in B A → in Xx (setunion A))) True % 3.58/3.79 Clause #2 (by assumption #[]): Eq % 3.58/3.79 (Not % 3.58/3.79 (setadjoinIL → % 3.58/3.79 setunionI → % 3.58/3.79 ∀ (Xx Xy : Iota), % 3.58/3.79 in Xx % 3.58/3.79 (setunion (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))))) % 3.58/3.79 True % 3.58/3.79 Clause #3 (by clausification #[0]): Eq setadjoinIL (∀ (Xx Xy : Iota), in Xx (setadjoin Xx Xy)) % 3.58/3.79 Clause #5 (by clausify Prop equality #[3]): Or (Eq setadjoinIL False) (Eq (∀ (Xx Xy : Iota), in Xx (setadjoin Xx Xy)) True) % 3.58/3.79 Clause #7 (by clausification #[5]): ∀ (a : Iota), Or (Eq setadjoinIL False) (Eq (∀ (Xy : Iota), in a (setadjoin a Xy)) True) % 3.58/3.79 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq setadjoinIL False) (Eq (in a (setadjoin a a_1)) True) % 3.58/3.79 Clause #13 (by clausification #[1]): Eq setunionI (∀ (A Xx B : Iota), in Xx B → in B A → in Xx (setunion A)) % 3.58/3.79 Clause #17 (by clausification #[2]): Eq % 3.58/3.79 (setadjoinIL → % 3.58/3.79 setunionI → % 3.58/3.79 ∀ (Xx Xy : Iota), % 3.58/3.79 in Xx % 3.58/3.79 (setunion (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)))) % 3.58/3.79 False % 3.58/3.79 Clause #18 (by clausification #[17]): Eq setadjoinIL True % 3.58/3.79 Clause #19 (by clausification #[17]): Eq % 3.58/3.79 (setunionI → % 3.58/3.79 ∀ (Xx Xy : Iota), % 3.58/3.79 in Xx (setunion (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)))) % 3.58/3.79 False % 3.58/3.79 Clause #21 (by backward demodulation #[18, 8]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (in a (setadjoin a a_1)) True) % 3.58/3.79 Clause #23 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (in a (setadjoin a a_1)) True % 3.58/3.79 Clause #38 (by clausification #[19]): Eq setunionI True % 3.58/3.79 Clause #39 (by clausification #[19]): Eq % 3.58/3.79 (∀ (Xx Xy : Iota), % 3.58/3.79 in Xx (setunion (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)))) % 3.58/3.79 False % 3.58/3.79 Clause #40 (by backward demodulation #[38, 13]): Eq True (∀ (A Xx B : Iota), in Xx B → in B A → in Xx (setunion A)) % 3.58/3.79 Clause #43 (by clausification #[40]): ∀ (a : Iota), Eq (∀ (Xx B : Iota), in Xx B → in B a → in Xx (setunion a)) True % 3.58/3.79 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota), Eq (∀ (B : Iota), in a B → in B a_1 → in a (setunion a_1)) True % 3.58/3.79 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), Eq (in a a_1 → in a_1 a_2 → in a (setunion a_2)) True % 3.58/3.79 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Eq (in a_1 a_2 → in a (setunion a_2)) True) % 3.58/3.79 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Or (Eq (in a_1 a_2) False) (Eq (in a (setunion a_2)) True)) % 3.58/3.79 Clause #48 (by superposition #[47, 23]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (setadjoin a a_1) a_2) False) (Or (Eq (in a (setunion a_2)) True) (Eq False True)) % 3.58/3.79 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (setadjoin a a_1) a_2) False) (Eq (in a (setunion a_2)) True) % 3.58/3.79 Clause #50 (by superposition #[49, 23]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setunion (setadjoin (setadjoin a a_1) a_2))) True) (Eq False True) % 3.58/3.79 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), Eq (in a (setunion (setadjoin (setadjoin a a_1) a_2))) True % 3.58/3.79 Clause #65 (by clausification #[39]): ∀ (a : Iota), % 3.58/3.79 Eq % 3.58/3.79 (Not % 3.58/3.79 (∀ (Xy : Iota), % 3.58/3.79 in (skS.0 5 a) % 3.58/3.79 (setunion % 3.58/3.79 (setadjoin (setadjoin (skS.0 5 a) emptyset) % 3.58/3.79 (setadjoin (setadjoin (skS.0 5 a) (setadjoin Xy emptyset)) emptyset))))) % 3.58/3.79 True % 3.58/3.79 Clause #66 (by clausification #[65]): ∀ (a : Iota), % 3.58/3.79 Eq % 3.58/3.79 (∀ (Xy : Iota), % 3.58/3.79 in (skS.0 5 a) % 3.58/3.79 (setunion % 3.58/3.79 (setadjoin (setadjoin (skS.0 5 a) emptyset) % 3.58/3.79 (setadjoin (setadjoin (skS.0 5 a) (setadjoin Xy emptyset)) emptyset)))) % 3.58/3.79 False % 3.58/3.79 Clause #67 (by clausification #[66]): ∀ (a a_1 : Iota), % 3.58/3.79 Eq % 3.58/3.79 (Not % 3.58/3.79 (in (skS.0 5 a) % 3.58/3.79 (setunion % 3.58/3.79 (setadjoin (setadjoin (skS.0 5 a) emptyset) % 3.58/3.79 (setadjoin (setadjoin (skS.0 5 a) (setadjoin (skS.0 6 a a_1) emptyset)) emptyset))))) % 3.58/3.79 True % 3.58/3.79 Clause #68 (by clausification #[67]): ∀ (a a_1 : Iota), % 3.58/3.79 Eq % 3.58/3.79 (in (skS.0 5 a) % 3.58/3.79 (setunion % 3.58/3.79 (setadjoin (setadjoin (skS.0 5 a) emptyset) % 3.58/3.79 (setadjoin (setadjoin (skS.0 5 a) (setadjoin (skS.0 6 a a_1) emptyset)) emptyset)))) % 3.58/3.79 False % 3.58/3.79 Clause #69 (by superposition #[68, 51]): Eq False True % 3.58/3.79 Clause #70 (by clausification #[69]): False % 3.58/3.79 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------