%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU618^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n009.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 3.91s 4.15s % Output : Proof 3.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.13 % Problem : SEU618^2 : TPTP v9.2.0. Released v3.7.0. % 0.06/0.14 % Command : duper %s % 0.13/0.35 % Computer : n009.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Oct 3 04:23:38 EDT 2025 % 0.13/0.36 % CPUTime : % 3.91/4.15 SZS status Theorem for theBenchmark.p % 3.91/4.15 SZS output start Proof for theBenchmark.p % 3.91/4.15 Clause #0 (by assumption #[]): Eq (Eq setunionI (∀ (A Xx B : Iota), in Xx B → in B A → in Xx (setunion A))) True % 3.91/4.15 Clause #1 (by assumption #[]): Eq (Eq secondinupair (∀ (Xx Xy : Iota), in Xy (setadjoin Xx (setadjoin Xy emptyset)))) True % 3.91/4.15 Clause #2 (by assumption #[]): Eq % 3.91/4.15 (Not % 3.91/4.15 (setunionI → % 3.91/4.15 secondinupair → % 3.91/4.15 ∀ (Xx Xy : Iota), % 3.91/4.15 in Xy % 3.91/4.15 (setunion (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))))) % 3.91/4.15 True % 3.91/4.15 Clause #3 (by clausification #[1]): Eq secondinupair (∀ (Xx Xy : Iota), in Xy (setadjoin Xx (setadjoin Xy emptyset))) % 3.91/4.15 Clause #5 (by clausify Prop equality #[3]): Or (Eq secondinupair False) (Eq (∀ (Xx Xy : Iota), in Xy (setadjoin Xx (setadjoin Xy emptyset))) True) % 3.91/4.15 Clause #7 (by clausification #[5]): ∀ (a : Iota), Or (Eq secondinupair False) (Eq (∀ (Xy : Iota), in Xy (setadjoin a (setadjoin Xy emptyset))) True) % 3.91/4.15 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq secondinupair False) (Eq (in a (setadjoin a_1 (setadjoin a emptyset))) True) % 3.91/4.15 Clause #13 (by clausification #[0]): Eq setunionI (∀ (A Xx B : Iota), in Xx B → in B A → in Xx (setunion A)) % 3.91/4.15 Clause #22 (by clausification #[2]): Eq % 3.91/4.15 (setunionI → % 3.91/4.15 secondinupair → % 3.91/4.15 ∀ (Xx Xy : Iota), % 3.91/4.15 in Xy % 3.91/4.15 (setunion (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)))) % 3.91/4.15 False % 3.91/4.15 Clause #23 (by clausification #[22]): Eq setunionI True % 3.91/4.15 Clause #24 (by clausification #[22]): Eq % 3.91/4.15 (secondinupair → % 3.91/4.15 ∀ (Xx Xy : Iota), % 3.91/4.15 in Xy (setunion (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)))) % 3.91/4.15 False % 3.91/4.15 Clause #25 (by backward demodulation #[23, 13]): Eq True (∀ (A Xx B : Iota), in Xx B → in B A → in Xx (setunion A)) % 3.91/4.15 Clause #27 (by clausification #[25]): ∀ (a : Iota), Eq (∀ (Xx B : Iota), in Xx B → in B a → in Xx (setunion a)) True % 3.91/4.15 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (∀ (B : Iota), in a B → in B a_1 → in a (setunion a_1)) True % 3.91/4.15 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Eq (in a a_1 → in a_1 a_2 → in a (setunion a_2)) True % 3.91/4.15 Clause #30 (by clausification #[29]): ∀ (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) % 3.91/4.15 Clause #31 (by clausification #[30]): ∀ (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)) % 3.91/4.15 Clause #41 (by clausification #[24]): Eq secondinupair True % 3.91/4.15 Clause #42 (by clausification #[24]): Eq % 3.91/4.15 (∀ (Xx Xy : Iota), % 3.91/4.15 in Xy (setunion (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset)))) % 3.91/4.15 False % 3.91/4.15 Clause #44 (by backward demodulation #[41, 8]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (in a (setadjoin a_1 (setadjoin a emptyset))) True) % 3.91/4.15 Clause #46 (by clausification #[44]): ∀ (a a_1 : Iota), Eq (in a (setadjoin a_1 (setadjoin a emptyset))) True % 3.91/4.15 Clause #47 (by superposition #[46, 31]): ∀ (a a_1 a_2 : Iota), % 3.91/4.15 Or (Eq True False) (Or (Eq (in (setadjoin a (setadjoin a_1 emptyset)) a_2) False) (Eq (in a_1 (setunion a_2)) True)) % 3.91/4.15 Clause #49 (by clausification #[47]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (setadjoin a (setadjoin a_1 emptyset)) a_2) False) (Eq (in a_1 (setunion a_2)) True) % 3.91/4.15 Clause #50 (by superposition #[49, 46]): ∀ (a a_1 a_2 : Iota), % 3.91/4.15 Or (Eq (in a (setunion (setadjoin a_1 (setadjoin (setadjoin a_2 (setadjoin a emptyset)) emptyset)))) True) % 3.91/4.15 (Eq False True) % 3.91/4.15 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota), % 3.91/4.15 Eq (in a (setunion (setadjoin a_1 (setadjoin (setadjoin a_2 (setadjoin a emptyset)) emptyset)))) True % 3.91/4.15 Clause #54 (by clausification #[42]): ∀ (a : Iota), % 3.91/4.15 Eq % 3.91/4.15 (Not % 3.91/4.15 (∀ (Xy : Iota), % 3.91/4.15 in Xy % 3.91/4.15 (setunion % 3.91/4.15 (setadjoin (setadjoin (skS.0 5 a) emptyset) % 3.91/4.15 (setadjoin (setadjoin (skS.0 5 a) (setadjoin Xy emptyset)) emptyset))))) % 3.91/4.15 True % 3.91/4.15 Clause #55 (by clausification #[54]): ∀ (a : Iota), % 3.91/4.15 Eq % 3.91/4.15 (∀ (Xy : Iota), % 3.91/4.16 in Xy % 3.91/4.16 (setunion % 3.91/4.16 (setadjoin (setadjoin (skS.0 5 a) emptyset) % 3.91/4.16 (setadjoin (setadjoin (skS.0 5 a) (setadjoin Xy emptyset)) emptyset)))) % 3.91/4.16 False % 3.91/4.16 Clause #56 (by clausification #[55]): ∀ (a a_1 : Iota), % 3.91/4.16 Eq % 3.91/4.16 (Not % 3.91/4.16 (in (skS.0 6 a a_1) % 3.91/4.16 (setunion % 3.91/4.16 (setadjoin (setadjoin (skS.0 5 a) emptyset) % 3.91/4.16 (setadjoin (setadjoin (skS.0 5 a) (setadjoin (skS.0 6 a a_1) emptyset)) emptyset))))) % 3.91/4.16 True % 3.91/4.16 Clause #57 (by clausification #[56]): ∀ (a a_1 : Iota), % 3.91/4.16 Eq % 3.91/4.16 (in (skS.0 6 a a_1) % 3.91/4.16 (setunion % 3.91/4.16 (setadjoin (setadjoin (skS.0 5 a) emptyset) % 3.91/4.16 (setadjoin (setadjoin (skS.0 5 a) (setadjoin (skS.0 6 a a_1) emptyset)) emptyset)))) % 3.91/4.16 False % 3.91/4.16 Clause #58 (by superposition #[57, 51]): Eq False True % 3.91/4.16 Clause #62 (by clausification #[58]): False % 3.91/4.16 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------