%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU816^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n006.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 08:02:30 PM UTC 2025 % Result : Theorem 4.68s 4.87s % Output : Proof 4.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU816^2 : TPTP v9.2.0. Released v3.7.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n006.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 05:40:53 EDT 2025 % 0.13/0.34 % CPUTime : % 4.68/4.87 SZS status Theorem for theBenchmark.p % 4.68/4.87 SZS output start Proof for theBenchmark.p % 4.68/4.87 Clause #2 (by assumption #[]): Eq % 4.68/4.87 (Eq binintTransitive % 4.68/4.87 (∀ (X : Iota), transitiveset X → ∀ (Y : Iota), transitiveset Y → transitiveset (binintersect X Y))) % 4.68/4.87 True % 4.68/4.87 Clause #5 (by assumption #[]): Eq (Eq ordinal fun Xx => And (transitiveset Xx) (wellorderedByIn Xx)) True % 4.68/4.87 Clause #6 (by assumption #[]): Eq (Not (binintTransitive → ∀ (X : Iota), ordinal X → ∀ (Y : Iota), ordinal Y → transitiveset (binintersect X Y))) True % 4.68/4.87 Clause #34 (by clausification #[2]): Eq binintTransitive (∀ (X : Iota), transitiveset X → ∀ (Y : Iota), transitiveset Y → transitiveset (binintersect X Y)) % 4.68/4.87 Clause #61 (by clausification #[5]): Eq ordinal fun Xx => And (transitiveset Xx) (wellorderedByIn Xx) % 4.68/4.87 Clause #62 (by argument congruence #[61]): ∀ (a : Iota), Eq (ordinal a) ((fun Xx => And (transitiveset Xx) (wellorderedByIn Xx)) a) % 4.68/4.87 Clause #63 (by betaEtaReduce #[62]): ∀ (a : Iota), Eq (ordinal a) (And (transitiveset a) (wellorderedByIn a)) % 4.68/4.87 Clause #64 (by identity loobHoist #[63]): ∀ (a : Iota), Or (Eq (ordinal a) (And (transitiveset a) True)) (Eq (wellorderedByIn a) False) % 4.68/4.87 Clause #65 (by identity boolHoist #[63]): ∀ (a : Iota), Or (Eq (ordinal a) (And (transitiveset a) False)) (Eq (wellorderedByIn a) True) % 4.68/4.87 Clause #66 (by bool simp #[64]): ∀ (a : Iota), Or (Eq (ordinal a) (transitiveset a)) (Eq (wellorderedByIn a) False) % 4.68/4.87 Clause #67 (by clausification #[6]): Eq (binintTransitive → ∀ (X : Iota), ordinal X → ∀ (Y : Iota), ordinal Y → transitiveset (binintersect X Y)) False % 4.68/4.87 Clause #68 (by clausification #[67]): Eq binintTransitive True % 4.68/4.87 Clause #69 (by clausification #[67]): Eq (∀ (X : Iota), ordinal X → ∀ (Y : Iota), ordinal Y → transitiveset (binintersect X Y)) False % 4.68/4.87 Clause #70 (by backward demodulation #[68, 34]): Eq True (∀ (X : Iota), transitiveset X → ∀ (Y : Iota), transitiveset Y → transitiveset (binintersect X Y)) % 4.68/4.87 Clause #72 (by clausification #[70]): ∀ (a : Iota), Eq (transitiveset a → ∀ (Y : Iota), transitiveset Y → transitiveset (binintersect a Y)) True % 4.68/4.87 Clause #73 (by clausification #[72]): ∀ (a : Iota), % 4.68/4.87 Or (Eq (transitiveset a) False) (Eq (∀ (Y : Iota), transitiveset Y → transitiveset (binintersect a Y)) True) % 4.68/4.87 Clause #74 (by clausification #[73]): ∀ (a a_1 : Iota), Or (Eq (transitiveset a) False) (Eq (transitiveset a_1 → transitiveset (binintersect a a_1)) True) % 4.68/4.87 Clause #75 (by clausification #[74]): ∀ (a a_1 : Iota), % 4.68/4.87 Or (Eq (transitiveset a) False) (Or (Eq (transitiveset a_1) False) (Eq (transitiveset (binintersect a a_1)) True)) % 4.68/4.87 Clause #76 (by clausification #[69]): ∀ (a : Iota), Eq (Not (ordinal (skS.0 1 a) → ∀ (Y : Iota), ordinal Y → transitiveset (binintersect (skS.0 1 a) Y))) True % 4.68/4.87 Clause #77 (by clausification #[76]): ∀ (a : Iota), Eq (ordinal (skS.0 1 a) → ∀ (Y : Iota), ordinal Y → transitiveset (binintersect (skS.0 1 a) Y)) False % 4.68/4.87 Clause #78 (by clausification #[77]): ∀ (a : Iota), Eq (ordinal (skS.0 1 a)) True % 4.68/4.87 Clause #79 (by clausification #[77]): ∀ (a : Iota), Eq (∀ (Y : Iota), ordinal Y → transitiveset (binintersect (skS.0 1 a) Y)) False % 4.68/4.87 Clause #82 (by bool simp #[65]): ∀ (a : Iota), Or (Eq (ordinal a) False) (Eq (wellorderedByIn a) True) % 4.68/4.87 Clause #83 (by superposition #[82, 78]): ∀ (a : Iota), Or (Eq (wellorderedByIn (skS.0 1 a)) True) (Eq False True) % 4.68/4.87 Clause #84 (by clausification #[83]): ∀ (a : Iota), Eq (wellorderedByIn (skS.0 1 a)) True % 4.68/4.87 Clause #85 (by superposition #[84, 66]): ∀ (a : Iota), Or (Eq (ordinal (skS.0 1 a)) (transitiveset (skS.0 1 a))) (Eq True False) % 4.68/4.87 Clause #94 (by clausification #[79]): ∀ (a a_1 : Iota), Eq (Not (ordinal (skS.0 3 a a_1) → transitiveset (binintersect (skS.0 1 a) (skS.0 3 a a_1)))) True % 4.68/4.87 Clause #95 (by clausification #[94]): ∀ (a a_1 : Iota), Eq (ordinal (skS.0 3 a a_1) → transitiveset (binintersect (skS.0 1 a) (skS.0 3 a a_1))) False % 4.68/4.87 Clause #96 (by clausification #[95]): ∀ (a a_1 : Iota), Eq (ordinal (skS.0 3 a a_1)) True % 4.68/4.87 Clause #97 (by clausification #[95]): ∀ (a a_1 : Iota), Eq (transitiveset (binintersect (skS.0 1 a) (skS.0 3 a a_1))) False % 4.68/4.88 Clause #98 (by superposition #[96, 82]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (wellorderedByIn (skS.0 3 a a_1)) True) % 4.68/4.88 Clause #101 (by clausification #[98]): ∀ (a a_1 : Iota), Eq (wellorderedByIn (skS.0 3 a a_1)) True % 4.68/4.88 Clause #102 (by superposition #[101, 66]): ∀ (a a_1 : Iota), Or (Eq (ordinal (skS.0 3 a a_1)) (transitiveset (skS.0 3 a a_1))) (Eq True False) % 4.68/4.88 Clause #128 (by clausification #[85]): ∀ (a : Iota), Eq (ordinal (skS.0 1 a)) (transitiveset (skS.0 1 a)) % 4.68/4.88 Clause #131 (by superposition #[128, 78]): ∀ (a : Iota), Eq (transitiveset (skS.0 1 a)) True % 4.68/4.88 Clause #138 (by superposition #[131, 75]): ∀ (a a_1 : Iota), % 4.68/4.88 Or (Eq True False) (Or (Eq (transitiveset a) False) (Eq (transitiveset (binintersect (skS.0 1 a_1) a)) True)) % 4.68/4.88 Clause #144 (by clausification #[138]): ∀ (a a_1 : Iota), Or (Eq (transitiveset a) False) (Eq (transitiveset (binintersect (skS.0 1 a_1) a)) True) % 4.68/4.88 Clause #211 (by clausification #[102]): ∀ (a a_1 : Iota), Eq (ordinal (skS.0 3 a a_1)) (transitiveset (skS.0 3 a a_1)) % 4.68/4.88 Clause #214 (by superposition #[211, 96]): ∀ (a a_1 : Iota), Eq (transitiveset (skS.0 3 a a_1)) True % 4.68/4.88 Clause #220 (by superposition #[214, 144]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (transitiveset (binintersect (skS.0 1 a) (skS.0 3 a_1 a_2))) True) % 4.68/4.88 Clause #259 (by clausification #[220]): ∀ (a a_1 a_2 : Iota), Eq (transitiveset (binintersect (skS.0 1 a) (skS.0 3 a_1 a_2))) True % 4.68/4.88 Clause #260 (by superposition #[259, 97]): Eq True False % 4.68/4.88 Clause #271 (by clausification #[260]): False % 4.68/4.88 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------