%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU706^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n015.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 08:02:15 PM UTC 2025 % Result : Theorem 4.95s 5.10s % Output : Proof 4.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SEU706^2 : TPTP v9.2.0. Released v3.7.0. % 0.06/0.13 % Command : duper %s % 0.14/0.35 % Computer : n015.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Fri Oct 3 04:41:38 EDT 2025 % 0.14/0.35 % CPUTime : % 4.95/5.10 SZS status Theorem for theBenchmark.p % 4.95/5.10 SZS output start Proof for theBenchmark.p % 4.95/5.10 Clause #0 (by assumption #[]): Eq (Eq uniqinunit (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy)) True % 4.95/5.10 Clause #4 (by assumption #[]): Eq (Eq setunionsingleton (∀ (Xx : Iota), Eq (setunion (setadjoin Xx emptyset)) Xx)) True % 4.95/5.10 Clause #5 (by assumption #[]): Eq (Eq singleton fun A => Exists fun Xx => And (in Xx A) (Eq A (setadjoin Xx emptyset))) True % 4.95/5.10 Clause #6 (by assumption #[]): Eq % 4.95/5.10 (Not % 4.95/5.10 (uniqinunit → % 4.95/5.10 in__Cong → % 4.95/5.10 setadjoin__Cong → % 4.95/5.10 setunion__Cong → setunionsingleton → ∀ (X : Iota), singleton X → ∀ (Xx : Iota), in Xx X → Eq (setunion X) Xx)) % 4.95/5.10 True % 4.95/5.10 Clause #7 (by clausification #[0]): Eq uniqinunit (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy) % 4.95/5.10 Clause #21 (by clausification #[4]): Eq setunionsingleton (∀ (Xx : Iota), Eq (setunion (setadjoin Xx emptyset)) Xx) % 4.95/5.10 Clause #23 (by clausify Prop equality #[21]): Or (Eq setunionsingleton False) (Eq (∀ (Xx : Iota), Eq (setunion (setadjoin Xx emptyset)) Xx) True) % 4.95/5.10 Clause #29 (by clausification #[23]): ∀ (a : Iota), Or (Eq setunionsingleton False) (Eq (Eq (setunion (setadjoin a emptyset)) a) True) % 4.95/5.10 Clause #30 (by clausification #[29]): ∀ (a : Iota), Or (Eq setunionsingleton False) (Eq (setunion (setadjoin a emptyset)) a) % 4.95/5.10 Clause #55 (by clausification #[6]): Eq % 4.95/5.10 (uniqinunit → % 4.95/5.10 in__Cong → % 4.95/5.10 setadjoin__Cong → % 4.95/5.10 setunion__Cong → setunionsingleton → ∀ (X : Iota), singleton X → ∀ (Xx : Iota), in Xx X → Eq (setunion X) Xx) % 4.95/5.10 False % 4.95/5.10 Clause #56 (by clausification #[55]): Eq uniqinunit True % 4.95/5.10 Clause #57 (by clausification #[55]): Eq % 4.95/5.10 (in__Cong → % 4.95/5.10 setadjoin__Cong → % 4.95/5.10 setunion__Cong → setunionsingleton → ∀ (X : Iota), singleton X → ∀ (Xx : Iota), in Xx X → Eq (setunion X) Xx) % 4.95/5.10 False % 4.95/5.10 Clause #58 (by backward demodulation #[56, 7]): Eq True (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy) % 4.95/5.10 Clause #61 (by clausification #[58]): ∀ (a : Iota), Eq (∀ (Xy : Iota), in a (setadjoin Xy emptyset) → Eq a Xy) True % 4.95/5.10 Clause #62 (by clausification #[61]): ∀ (a a_1 : Iota), Eq (in a (setadjoin a_1 emptyset) → Eq a a_1) True % 4.95/5.10 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota), Or (Eq (in a (setadjoin a_1 emptyset)) False) (Eq (Eq a a_1) True) % 4.95/5.10 Clause #64 (by clausification #[63]): ∀ (a a_1 : Iota), Or (Eq (in a (setadjoin a_1 emptyset)) False) (Eq a a_1) % 4.95/5.10 Clause #65 (by clausification #[5]): Eq singleton fun A => Exists fun Xx => And (in Xx A) (Eq A (setadjoin Xx emptyset)) % 4.95/5.10 Clause #66 (by argument congruence #[65]): ∀ (a : Iota), Eq (singleton a) ((fun A => Exists fun Xx => And (in Xx A) (Eq A (setadjoin Xx emptyset))) a) % 4.95/5.10 Clause #68 (by clausification #[57]): Eq % 4.95/5.10 (setadjoin__Cong → % 4.95/5.10 setunion__Cong → setunionsingleton → ∀ (X : Iota), singleton X → ∀ (Xx : Iota), in Xx X → Eq (setunion X) Xx) % 4.95/5.10 False % 4.95/5.10 Clause #71 (by clausification #[68]): Eq (setunion__Cong → setunionsingleton → ∀ (X : Iota), singleton X → ∀ (Xx : Iota), in Xx X → Eq (setunion X) Xx) False % 4.95/5.10 Clause #74 (by clausification #[71]): Eq (setunionsingleton → ∀ (X : Iota), singleton X → ∀ (Xx : Iota), in Xx X → Eq (setunion X) Xx) False % 4.95/5.10 Clause #83 (by clausification #[74]): Eq setunionsingleton True % 4.95/5.10 Clause #84 (by clausification #[74]): Eq (∀ (X : Iota), singleton X → ∀ (Xx : Iota), in Xx X → Eq (setunion X) Xx) False % 4.95/5.10 Clause #87 (by superposition #[83, 30]): ∀ (a : Iota), Or (Eq True False) (Eq (setunion (setadjoin a emptyset)) a) % 4.95/5.10 Clause #90 (by clausification #[87]): ∀ (a : Iota), Eq (setunion (setadjoin a emptyset)) a % 4.95/5.10 Clause #92 (by clausification #[84]): ∀ (a : Iota), Eq (Not (singleton (skS.0 5 a) → ∀ (Xx : Iota), in Xx (skS.0 5 a) → Eq (setunion (skS.0 5 a)) Xx)) True % 4.95/5.10 Clause #93 (by clausification #[92]): ∀ (a : Iota), Eq (singleton (skS.0 5 a) → ∀ (Xx : Iota), in Xx (skS.0 5 a) → Eq (setunion (skS.0 5 a)) Xx) False % 4.95/5.10 Clause #94 (by clausification #[93]): ∀ (a : Iota), Eq (singleton (skS.0 5 a)) True % 4.95/5.10 Clause #95 (by clausification #[93]): ∀ (a : Iota), Eq (∀ (Xx : Iota), in Xx (skS.0 5 a) → Eq (setunion (skS.0 5 a)) Xx) False % 4.95/5.13 Clause #96 (by clausification #[95]): ∀ (a a_1 : Iota), Eq (Not (in (skS.0 6 a a_1) (skS.0 5 a) → Eq (setunion (skS.0 5 a)) (skS.0 6 a a_1))) True % 4.95/5.13 Clause #97 (by clausification #[96]): ∀ (a a_1 : Iota), Eq (in (skS.0 6 a a_1) (skS.0 5 a) → Eq (setunion (skS.0 5 a)) (skS.0 6 a a_1)) False % 4.95/5.13 Clause #98 (by clausification #[97]): ∀ (a a_1 : Iota), Eq (in (skS.0 6 a a_1) (skS.0 5 a)) True % 4.95/5.13 Clause #99 (by clausification #[97]): ∀ (a a_1 : Iota), Eq (Eq (setunion (skS.0 5 a)) (skS.0 6 a a_1)) False % 4.95/5.13 Clause #166 (by betaEtaReduce #[66]): ∀ (a : Iota), Eq (singleton a) (Exists fun Xx => And (in Xx a) (Eq a (setadjoin Xx emptyset))) % 4.95/5.13 Clause #168 (by clausify Prop equality #[166]): ∀ (a : Iota), Or (Eq (singleton a) False) (Eq (Exists fun Xx => And (in Xx a) (Eq a (setadjoin Xx emptyset))) True) % 4.95/5.13 Clause #174 (by clausification #[168]): ∀ (a a_1 : Iota), % 4.95/5.13 Or (Eq (singleton a) False) (Eq (And (in (skS.0 11 a a_1) a) (Eq a (setadjoin (skS.0 11 a a_1) emptyset))) True) % 4.95/5.13 Clause #175 (by clausification #[174]): ∀ (a a_1 : Iota), Or (Eq (singleton a) False) (Eq (Eq a (setadjoin (skS.0 11 a a_1) emptyset)) True) % 4.95/5.13 Clause #177 (by clausification #[175]): ∀ (a a_1 : Iota), Or (Eq (singleton a) False) (Eq a (setadjoin (skS.0 11 a a_1) emptyset)) % 4.95/5.13 Clause #178 (by superposition #[177, 94]): ∀ (a a_1 : Iota), Or (Eq (skS.0 5 a) (setadjoin (skS.0 11 (skS.0 5 a) a_1) emptyset)) (Eq False True) % 4.95/5.13 Clause #182 (by clausification #[99]): ∀ (a a_1 : Iota), Ne (setunion (skS.0 5 a)) (skS.0 6 a a_1) % 4.95/5.13 Clause #400 (by clausification #[178]): ∀ (a a_1 : Iota), Eq (skS.0 5 a) (setadjoin (skS.0 11 (skS.0 5 a) a_1) emptyset) % 4.95/5.13 Clause #402 (by superposition #[400, 90]): ∀ (a a_1 : Iota), Eq (setunion (skS.0 5 a)) (skS.0 11 (skS.0 5 a) a_1) % 4.95/5.13 Clause #433 (by backward demodulation #[402, 400]): ∀ (a : Iota), Eq (skS.0 5 a) (setadjoin (setunion (skS.0 5 a)) emptyset) % 4.95/5.13 Clause #463 (by superposition #[433, 64]): ∀ (a a_1 : Iota), Or (Eq (in a (skS.0 5 a_1)) False) (Eq a (setunion (skS.0 5 a_1))) % 4.95/5.13 Clause #468 (by superposition #[463, 98]): ∀ (a a_1 : Iota), Or (Eq (skS.0 6 a a_1) (setunion (skS.0 5 a))) (Eq False True) % 4.95/5.13 Clause #478 (by clausification #[468]): ∀ (a a_1 : Iota), Eq (skS.0 6 a a_1) (setunion (skS.0 5 a)) % 4.95/5.13 Clause #479 (by forward contextual literal cutting #[478, 182]): False % 4.95/5.13 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------