%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU819^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n029.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 08:02:31 PM UTC 2025 % Result : Theorem 7.56s 7.75s % Output : Proof 7.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU819^2 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n029.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 05:33:08 EDT 2025 % 0.13/0.35 % CPUTime : % 7.56/7.75 SZS status Theorem for theBenchmark.p % 7.56/7.75 SZS output start Proof for theBenchmark.p % 7.56/7.75 Clause #2 (by assumption #[]): Eq (Eq setunionTransitive (∀ (X : Iota), (∀ (Xx : Iota), in Xx X → transitiveset Xx) → transitiveset (setunion X))) True % 7.56/7.75 Clause #5 (by assumption #[]): Eq (Eq ordinal fun Xx => And (transitiveset Xx) (wellorderedByIn Xx)) True % 7.56/7.75 Clause #6 (by assumption #[]): Eq (Not (setunionTransitive → ∀ (X : Iota), (∀ (Xx : Iota), in Xx X → ordinal Xx) → transitiveset (setunion X))) True % 7.56/7.75 Clause #7 (by clausification #[6]): Eq (setunionTransitive → ∀ (X : Iota), (∀ (Xx : Iota), in Xx X → ordinal Xx) → transitiveset (setunion X)) False % 7.56/7.75 Clause #8 (by clausification #[7]): Eq setunionTransitive True % 7.56/7.75 Clause #9 (by clausification #[7]): Eq (∀ (X : Iota), (∀ (Xx : Iota), in Xx X → ordinal Xx) → transitiveset (setunion X)) False % 7.56/7.75 Clause #10 (by clausification #[9]): ∀ (a : Iota), Eq (Not ((∀ (Xx : Iota), in Xx (skS.0 0 a) → ordinal Xx) → transitiveset (setunion (skS.0 0 a)))) True % 7.56/7.75 Clause #11 (by clausification #[10]): ∀ (a : Iota), Eq ((∀ (Xx : Iota), in Xx (skS.0 0 a) → ordinal Xx) → transitiveset (setunion (skS.0 0 a))) False % 7.56/7.75 Clause #12 (by clausification #[11]): ∀ (a : Iota), Eq (∀ (Xx : Iota), in Xx (skS.0 0 a) → ordinal Xx) True % 7.56/7.75 Clause #13 (by clausification #[11]): ∀ (a : Iota), Eq (transitiveset (setunion (skS.0 0 a))) False % 7.56/7.75 Clause #14 (by clausification #[12]): ∀ (a a_1 : Iota), Eq (in a (skS.0 0 a_1) → ordinal a) True % 7.56/7.75 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (in a (skS.0 0 a_1)) False) (Eq (ordinal a) True) % 7.56/7.75 Clause #16 (by clausification #[2]): Eq setunionTransitive (∀ (X : Iota), (∀ (Xx : Iota), in Xx X → transitiveset Xx) → transitiveset (setunion X)) % 7.56/7.75 Clause #17 (by forward demodulation #[16, 8]): Eq True (∀ (X : Iota), (∀ (Xx : Iota), in Xx X → transitiveset Xx) → transitiveset (setunion X)) % 7.56/7.75 Clause #18 (by clausification #[17]): ∀ (a : Iota), Eq ((∀ (Xx : Iota), in Xx a → transitiveset Xx) → transitiveset (setunion a)) True % 7.56/7.75 Clause #19 (by clausification #[18]): ∀ (a : Iota), Or (Eq (∀ (Xx : Iota), in Xx a → transitiveset Xx) False) (Eq (transitiveset (setunion a)) True) % 7.56/7.75 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), % 7.56/7.75 Or (Eq (transitiveset (setunion a)) True) (Eq (Not (in (skS.0 1 a a_1) a → transitiveset (skS.0 1 a a_1))) True) % 7.56/7.75 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), % 7.56/7.75 Or (Eq (transitiveset (setunion a)) True) (Eq (in (skS.0 1 a a_1) a → transitiveset (skS.0 1 a a_1)) False) % 7.56/7.75 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (transitiveset (setunion a)) True) (Eq (in (skS.0 1 a a_1) a) True) % 7.56/7.75 Clause #23 (by clausification #[21]): ∀ (a a_1 : Iota), Or (Eq (transitiveset (setunion a)) True) (Eq (transitiveset (skS.0 1 a a_1)) False) % 7.56/7.75 Clause #24 (by superposition #[22, 15]): ∀ (a a_1 : Iota), % 7.56/7.75 Or (Eq (transitiveset (setunion (skS.0 0 a))) True) (Or (Eq True False) (Eq (ordinal (skS.0 1 (skS.0 0 a) a_1)) True)) % 7.56/7.75 Clause #73 (by clausification #[5]): Eq ordinal fun Xx => And (transitiveset Xx) (wellorderedByIn Xx) % 7.56/7.75 Clause #74 (by argument congruence #[73]): ∀ (a : Iota), Eq (ordinal a) ((fun Xx => And (transitiveset Xx) (wellorderedByIn Xx)) a) % 7.56/7.75 Clause #75 (by betaEtaReduce #[74]): ∀ (a : Iota), Eq (ordinal a) (And (transitiveset a) (wellorderedByIn a)) % 7.56/7.75 Clause #76 (by identity loobHoist #[75]): ∀ (a : Iota), Or (Eq (ordinal a) (And (transitiveset a) True)) (Eq (wellorderedByIn a) False) % 7.56/7.75 Clause #77 (by identity boolHoist #[75]): ∀ (a : Iota), Or (Eq (ordinal a) (And (transitiveset a) False)) (Eq (wellorderedByIn a) True) % 7.56/7.75 Clause #78 (by bool simp #[76]): ∀ (a : Iota), Or (Eq (ordinal a) (transitiveset a)) (Eq (wellorderedByIn a) False) % 7.56/7.75 Clause #79 (by bool simp #[77]): ∀ (a : Iota), Or (Eq (ordinal a) False) (Eq (wellorderedByIn a) True) % 7.56/7.75 Clause #90 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (transitiveset (setunion (skS.0 0 a))) True) (Eq (ordinal (skS.0 1 (skS.0 0 a) a_1)) True) % 7.56/7.75 Clause #91 (by forward demodulation #[90, 13]): ∀ (a a_1 : Iota), Or (Eq False True) (Eq (ordinal (skS.0 1 (skS.0 0 a) a_1)) True) % 7.60/7.76 Clause #92 (by clausification #[91]): ∀ (a a_1 : Iota), Eq (ordinal (skS.0 1 (skS.0 0 a) a_1)) True % 7.60/7.76 Clause #93 (by superposition #[92, 79]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (wellorderedByIn (skS.0 1 (skS.0 0 a) a_1)) True) % 7.60/7.76 Clause #128 (by clausification #[93]): ∀ (a a_1 : Iota), Eq (wellorderedByIn (skS.0 1 (skS.0 0 a) a_1)) True % 7.60/7.76 Clause #129 (by superposition #[128, 78]): ∀ (a a_1 : Iota), Or (Eq (ordinal (skS.0 1 (skS.0 0 a) a_1)) (transitiveset (skS.0 1 (skS.0 0 a) a_1))) (Eq True False) % 7.60/7.76 Clause #502 (by clausification #[129]): ∀ (a a_1 : Iota), Eq (ordinal (skS.0 1 (skS.0 0 a) a_1)) (transitiveset (skS.0 1 (skS.0 0 a) a_1)) % 7.60/7.76 Clause #505 (by superposition #[502, 92]): ∀ (a a_1 : Iota), Eq (transitiveset (skS.0 1 (skS.0 0 a) a_1)) True % 7.60/7.76 Clause #512 (by superposition #[505, 23]): ∀ (a : Iota), Or (Eq (transitiveset (setunion (skS.0 0 a))) True) (Eq True False) % 7.60/7.76 Clause #521 (by clausification #[512]): ∀ (a : Iota), Eq (transitiveset (setunion (skS.0 0 a))) True % 7.60/7.76 Clause #522 (by superposition #[521, 13]): Eq True False % 7.60/7.76 Clause #532 (by clausification #[522]): False % 7.60/7.76 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------