%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : NUM390+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n024.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 07:56:25 PM UTC 2025 % Result : Theorem 42.52s 42.75s % Output : Proof 42.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : NUM390+1 : TPTP v9.2.0. Released v3.2.0. % 0.14/0.15 % Command : duper %s % 0.14/0.36 % Computer : n024.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Fri Oct 3 08:49:38 EDT 2025 % 0.14/0.36 % CPUTime : % 42.52/42.75 SZS status Theorem for theBenchmark.p % 42.52/42.75 SZS output start Proof for theBenchmark.p % 42.52/42.75 Clause #0 (by assumption #[]): Eq (∀ (A B : Iota), in A B → Not (in B A)) True % 42.52/42.75 Clause #3 (by assumption #[]): Eq (∀ (A : Iota), ordinal A → And (epsilon_transitive A) (epsilon_connected A)) True % 42.52/42.75 Clause #7 (by assumption #[]): Eq (∀ (A : Iota), Iff (epsilon_transitive A) (∀ (B : Iota), in B A → subset B A)) True % 42.52/42.75 Clause #8 (by assumption #[]): Eq (∀ (A B : Iota), Iff (proper_subset A B) (And (subset A B) (Ne A B))) True % 42.52/42.75 Clause #27 (by assumption #[]): Eq (∀ (A B C : Iota), And (subset A B) (subset B C) → subset A C) True % 42.52/42.75 Clause #28 (by assumption #[]): Eq (∀ (A : Iota), epsilon_transitive A → ∀ (B : Iota), ordinal B → proper_subset A B → in A B) True % 42.52/42.75 Clause #29 (by assumption #[]): Eq % 42.52/42.75 (Not % 42.52/42.75 (∀ (A : Iota), % 42.52/42.75 epsilon_transitive A → ∀ (B : Iota), ordinal B → ∀ (C : Iota), ordinal C → And (subset A B) (in B C) → in A C)) % 42.52/42.75 True % 42.52/42.75 Clause #48 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (B : Iota), in a B → Not (in B a)) True % 42.52/42.75 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota), Eq (in a a_1 → Not (in a_1 a)) True % 42.52/42.75 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (Not (in a_1 a)) True) % 42.52/42.75 Clause #51 (by clausification #[50]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (in a_1 a) False) % 42.52/42.75 Clause #82 (by clausification #[3]): ∀ (a : Iota), Eq (ordinal a → And (epsilon_transitive a) (epsilon_connected a)) True % 42.52/42.75 Clause #83 (by clausification #[82]): ∀ (a : Iota), Or (Eq (ordinal a) False) (Eq (And (epsilon_transitive a) (epsilon_connected a)) True) % 42.52/42.75 Clause #85 (by clausification #[83]): ∀ (a : Iota), Or (Eq (ordinal a) False) (Eq (epsilon_transitive a) True) % 42.52/42.75 Clause #86 (by clausification #[27]): ∀ (a : Iota), Eq (∀ (B C : Iota), And (subset a B) (subset B C) → subset a C) True % 42.52/42.75 Clause #87 (by clausification #[86]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), And (subset a a_1) (subset a_1 C) → subset a C) True % 42.52/42.75 Clause #88 (by clausification #[87]): ∀ (a a_1 a_2 : Iota), Eq (And (subset a a_1) (subset a_1 a_2) → subset a a_2) True % 42.52/42.75 Clause #89 (by clausification #[88]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (subset a a_1) (subset a_1 a_2)) False) (Eq (subset a a_2) True) % 42.52/42.75 Clause #90 (by clausification #[89]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Or (Eq (subset a a_2) False) (Eq (subset a_2 a_1) False)) % 42.52/42.75 Clause #109 (by clausification #[28]): ∀ (a : Iota), Eq (epsilon_transitive a → ∀ (B : Iota), ordinal B → proper_subset a B → in a B) True % 42.52/42.75 Clause #110 (by clausification #[109]): ∀ (a : Iota), Or (Eq (epsilon_transitive a) False) (Eq (∀ (B : Iota), ordinal B → proper_subset a B → in a B) True) % 42.52/42.75 Clause #111 (by clausification #[110]): ∀ (a a_1 : Iota), Or (Eq (epsilon_transitive a) False) (Eq (ordinal a_1 → proper_subset a a_1 → in a a_1) True) % 42.52/42.75 Clause #112 (by clausification #[111]): ∀ (a a_1 : Iota), % 42.52/42.75 Or (Eq (epsilon_transitive a) False) (Or (Eq (ordinal a_1) False) (Eq (proper_subset a a_1 → in a a_1) True)) % 42.52/42.75 Clause #113 (by clausification #[112]): ∀ (a a_1 : Iota), % 42.52/42.75 Or (Eq (epsilon_transitive a) False) % 42.52/42.75 (Or (Eq (ordinal a_1) False) (Or (Eq (proper_subset a a_1) False) (Eq (in a a_1) True))) % 42.52/42.75 Clause #117 (by clausification #[7]): ∀ (a : Iota), Eq (Iff (epsilon_transitive a) (∀ (B : Iota), in B a → subset B a)) True % 42.52/42.75 Clause #119 (by clausification #[117]): ∀ (a : Iota), Or (Eq (epsilon_transitive a) False) (Eq (∀ (B : Iota), in B a → subset B a) True) % 42.52/42.75 Clause #131 (by clausification #[119]): ∀ (a a_1 : Iota), Or (Eq (epsilon_transitive a) False) (Eq (in a_1 a → subset a_1 a) True) % 42.52/42.75 Clause #132 (by clausification #[131]): ∀ (a a_1 : Iota), Or (Eq (epsilon_transitive a) False) (Or (Eq (in a_1 a) False) (Eq (subset a_1 a) True)) % 42.52/42.75 Clause #135 (by clausification #[8]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (proper_subset a B) (And (subset a B) (Ne a B))) True % 42.52/42.75 Clause #136 (by clausification #[135]): ∀ (a a_1 : Iota), Eq (Iff (proper_subset a a_1) (And (subset a a_1) (Ne a a_1))) True % 42.52/42.75 Clause #137 (by clausification #[136]): ∀ (a a_1 : Iota), Or (Eq (proper_subset a a_1) True) (Eq (And (subset a a_1) (Ne a a_1)) False) % 42.55/42.78 Clause #139 (by clausification #[137]): ∀ (a a_1 : Iota), Or (Eq (proper_subset a a_1) True) (Or (Eq (subset a a_1) False) (Eq (Ne a a_1) False)) % 42.55/42.78 Clause #140 (by clausification #[139]): ∀ (a a_1 : Iota), Or (Eq (proper_subset a a_1) True) (Or (Eq (subset a a_1) False) (Eq a a_1)) % 42.55/42.78 Clause #224 (by clausification #[29]): Eq % 42.55/42.78 (∀ (A : Iota), % 42.55/42.78 epsilon_transitive A → ∀ (B : Iota), ordinal B → ∀ (C : Iota), ordinal C → And (subset A B) (in B C) → in A C) % 42.55/42.78 False % 42.55/42.78 Clause #225 (by clausification #[224]): ∀ (a : Iota), % 42.55/42.78 Eq % 42.55/42.78 (Not % 42.55/42.78 (epsilon_transitive (skS.0 13 a) → % 42.55/42.78 ∀ (B : Iota), ordinal B → ∀ (C : Iota), ordinal C → And (subset (skS.0 13 a) B) (in B C) → in (skS.0 13 a) C)) % 42.55/42.78 True % 42.55/42.78 Clause #226 (by clausification #[225]): ∀ (a : Iota), % 42.55/42.78 Eq % 42.55/42.78 (epsilon_transitive (skS.0 13 a) → % 42.55/42.78 ∀ (B : Iota), ordinal B → ∀ (C : Iota), ordinal C → And (subset (skS.0 13 a) B) (in B C) → in (skS.0 13 a) C) % 42.55/42.78 False % 42.55/42.78 Clause #227 (by clausification #[226]): ∀ (a : Iota), Eq (epsilon_transitive (skS.0 13 a)) True % 42.55/42.78 Clause #228 (by clausification #[226]): ∀ (a : Iota), % 42.55/42.78 Eq (∀ (B : Iota), ordinal B → ∀ (C : Iota), ordinal C → And (subset (skS.0 13 a) B) (in B C) → in (skS.0 13 a) C) % 42.55/42.78 False % 42.55/42.78 Clause #230 (by superposition #[227, 113]): ∀ (a a_1 : Iota), % 42.55/42.78 Or (Eq True False) % 42.55/42.78 (Or (Eq (ordinal a) False) (Or (Eq (proper_subset (skS.0 13 a_1) a) False) (Eq (in (skS.0 13 a_1) a) True))) % 42.55/42.78 Clause #264 (by clausification #[228]): ∀ (a a_1 : Iota), % 42.55/42.78 Eq % 42.55/42.78 (Not % 42.55/42.78 (ordinal (skS.0 14 a a_1) → % 42.55/42.78 ∀ (C : Iota), % 42.55/42.78 ordinal C → And (subset (skS.0 13 a) (skS.0 14 a a_1)) (in (skS.0 14 a a_1) C) → in (skS.0 13 a) C)) % 42.55/42.78 True % 42.55/42.78 Clause #265 (by clausification #[264]): ∀ (a a_1 : Iota), % 42.55/42.78 Eq % 42.55/42.78 (ordinal (skS.0 14 a a_1) → % 42.55/42.78 ∀ (C : Iota), ordinal C → And (subset (skS.0 13 a) (skS.0 14 a a_1)) (in (skS.0 14 a a_1) C) → in (skS.0 13 a) C) % 42.55/42.78 False % 42.55/42.78 Clause #266 (by clausification #[265]): ∀ (a a_1 : Iota), Eq (ordinal (skS.0 14 a a_1)) True % 42.55/42.78 Clause #267 (by clausification #[265]): ∀ (a a_1 : Iota), % 42.55/42.78 Eq (∀ (C : Iota), ordinal C → And (subset (skS.0 13 a) (skS.0 14 a a_1)) (in (skS.0 14 a a_1) C) → in (skS.0 13 a) C) % 42.55/42.78 False % 42.55/42.78 Clause #279 (by clausification #[267]): ∀ (a a_1 a_2 : Iota), % 42.55/42.78 Eq % 42.55/42.78 (Not % 42.55/42.78 (ordinal (skS.0 15 a a_1 a_2) → % 42.55/42.78 And (subset (skS.0 13 a) (skS.0 14 a a_1)) (in (skS.0 14 a a_1) (skS.0 15 a a_1 a_2)) → % 42.55/42.78 in (skS.0 13 a) (skS.0 15 a a_1 a_2))) % 42.55/42.78 True % 42.55/42.78 Clause #280 (by clausification #[279]): ∀ (a a_1 a_2 : Iota), % 42.55/42.78 Eq % 42.55/42.78 (ordinal (skS.0 15 a a_1 a_2) → % 42.55/42.78 And (subset (skS.0 13 a) (skS.0 14 a a_1)) (in (skS.0 14 a a_1) (skS.0 15 a a_1 a_2)) → % 42.55/42.78 in (skS.0 13 a) (skS.0 15 a a_1 a_2)) % 42.55/42.78 False % 42.55/42.78 Clause #281 (by clausification #[280]): ∀ (a a_1 a_2 : Iota), Eq (ordinal (skS.0 15 a a_1 a_2)) True % 42.55/42.78 Clause #282 (by clausification #[280]): ∀ (a a_1 a_2 : Iota), % 42.55/42.78 Eq % 42.55/42.78 (And (subset (skS.0 13 a) (skS.0 14 a a_1)) (in (skS.0 14 a a_1) (skS.0 15 a a_1 a_2)) → % 42.55/42.78 in (skS.0 13 a) (skS.0 15 a a_1 a_2)) % 42.55/42.78 False % 42.55/42.78 Clause #284 (by superposition #[281, 85]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (epsilon_transitive (skS.0 15 a a_1 a_2)) True) % 42.55/42.78 Clause #286 (by clausification #[284]): ∀ (a a_1 a_2 : Iota), Eq (epsilon_transitive (skS.0 15 a a_1 a_2)) True % 42.55/42.78 Clause #289 (by superposition #[286, 132]): ∀ (a a_1 a_2 a_3 : Iota), % 42.55/42.78 Or (Eq True False) (Or (Eq (in a (skS.0 15 a_1 a_2 a_3)) False) (Eq (subset a (skS.0 15 a_1 a_2 a_3)) True)) % 42.55/42.78 Clause #434 (by clausification #[282]): ∀ (a a_1 a_2 : Iota), Eq (And (subset (skS.0 13 a) (skS.0 14 a a_1)) (in (skS.0 14 a a_1) (skS.0 15 a a_1 a_2))) True % 42.55/42.78 Clause #435 (by clausification #[282]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 13 a) (skS.0 15 a a_1 a_2)) False % 42.55/42.78 Clause #436 (by clausification #[434]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 14 a a_1) (skS.0 15 a a_1 a_2)) True % 42.55/42.78 Clause #437 (by clausification #[434]): ∀ (a a_1 : Iota), Eq (subset (skS.0 13 a) (skS.0 14 a a_1)) True % 42.55/42.80 Clause #446 (by superposition #[437, 90]): ∀ (a a_1 a_2 : Iota), % 42.55/42.80 Or (Eq (subset (skS.0 13 a) a_1) True) (Or (Eq True False) (Eq (subset (skS.0 14 a a_2) a_1) False)) % 42.55/42.80 Clause #447 (by superposition #[437, 140]): ∀ (a a_1 : Iota), % 42.55/42.80 Or (Eq (proper_subset (skS.0 13 a) (skS.0 14 a a_1)) True) (Or (Eq True False) (Eq (skS.0 13 a) (skS.0 14 a a_1))) % 42.55/42.80 Clause #450 (by clausification #[230]): ∀ (a a_1 : Iota), % 42.55/42.80 Or (Eq (ordinal a) False) (Or (Eq (proper_subset (skS.0 13 a_1) a) False) (Eq (in (skS.0 13 a_1) a) True)) % 42.55/42.80 Clause #452 (by superposition #[450, 266]): ∀ (a a_1 a_2 : Iota), % 42.55/42.80 Or (Eq (proper_subset (skS.0 13 a) (skS.0 14 a_1 a_2)) False) % 42.55/42.80 (Or (Eq (in (skS.0 13 a) (skS.0 14 a_1 a_2)) True) (Eq False True)) % 42.55/42.80 Clause #453 (by superposition #[450, 281]): ∀ (a a_1 a_2 a_3 : Iota), % 42.55/42.80 Or (Eq (proper_subset (skS.0 13 a) (skS.0 15 a_1 a_2 a_3)) False) % 42.55/42.80 (Or (Eq (in (skS.0 13 a) (skS.0 15 a_1 a_2 a_3)) True) (Eq False True)) % 42.55/42.80 Clause #477 (by clausification #[446]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset (skS.0 13 a) a_1) True) (Eq (subset (skS.0 14 a a_2) a_1) False) % 42.55/42.80 Clause #597 (by clausification #[289]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in a (skS.0 15 a_1 a_2 a_3)) False) (Eq (subset a (skS.0 15 a_1 a_2 a_3)) True) % 42.55/42.80 Clause #598 (by superposition #[597, 436]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset (skS.0 14 a a_1) (skS.0 15 a a_1 a_2)) True) (Eq False True) % 42.55/42.80 Clause #619 (by clausification #[598]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 14 a a_1) (skS.0 15 a a_1 a_2)) True % 42.55/42.80 Clause #620 (by superposition #[619, 477]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset (skS.0 13 a) (skS.0 15 a a_1 a_2)) True) (Eq True False) % 42.55/42.80 Clause #626 (by clausification #[620]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 13 a) (skS.0 15 a a_1 a_2)) True % 42.55/42.80 Clause #628 (by superposition #[626, 140]): ∀ (a a_1 a_2 : Iota), % 42.55/42.80 Or (Eq (proper_subset (skS.0 13 a) (skS.0 15 a a_1 a_2)) True) % 42.55/42.80 (Or (Eq True False) (Eq (skS.0 13 a) (skS.0 15 a a_1 a_2))) % 42.55/42.80 Clause #828 (by clausification #[447]): ∀ (a a_1 : Iota), Or (Eq (proper_subset (skS.0 13 a) (skS.0 14 a a_1)) True) (Eq (skS.0 13 a) (skS.0 14 a a_1)) % 42.55/42.80 Clause #839 (by clausification #[452]): ∀ (a a_1 a_2 : Iota), % 42.55/42.80 Or (Eq (proper_subset (skS.0 13 a) (skS.0 14 a_1 a_2)) False) (Eq (in (skS.0 13 a) (skS.0 14 a_1 a_2)) True) % 42.55/42.80 Clause #840 (by superposition #[839, 828]): ∀ (a a_1 : Iota), % 42.55/42.80 Or (Eq (in (skS.0 13 a) (skS.0 14 a a_1)) True) (Or (Eq False True) (Eq (skS.0 13 a) (skS.0 14 a a_1))) % 42.55/42.80 Clause #852 (by clausification #[453]): ∀ (a a_1 a_2 a_3 : Iota), % 42.55/42.80 Or (Eq (proper_subset (skS.0 13 a) (skS.0 15 a_1 a_2 a_3)) False) (Eq (in (skS.0 13 a) (skS.0 15 a_1 a_2 a_3)) True) % 42.55/42.80 Clause #1244 (by clausification #[840]): ∀ (a a_1 : Iota), Or (Eq (in (skS.0 13 a) (skS.0 14 a a_1)) True) (Eq (skS.0 13 a) (skS.0 14 a a_1)) % 42.55/42.80 Clause #1245 (by superposition #[1244, 51]): ∀ (a a_1 : Iota), % 42.55/42.80 Or (Eq (skS.0 13 a) (skS.0 14 a a_1)) (Or (Eq True False) (Eq (in (skS.0 14 a a_1) (skS.0 13 a)) False)) % 42.55/42.80 Clause #1264 (by clausification #[1245]): ∀ (a a_1 : Iota), Or (Eq (skS.0 13 a) (skS.0 14 a a_1)) (Eq (in (skS.0 14 a a_1) (skS.0 13 a)) False) % 42.55/42.80 Clause #1634 (by clausification #[628]): ∀ (a a_1 a_2 : Iota), % 42.55/42.80 Or (Eq (proper_subset (skS.0 13 a) (skS.0 15 a a_1 a_2)) True) (Eq (skS.0 13 a) (skS.0 15 a a_1 a_2)) % 42.55/42.80 Clause #1635 (by superposition #[1634, 852]): ∀ (a a_1 a_2 : Iota), % 42.55/42.80 Or (Eq (skS.0 13 a) (skS.0 15 a a_1 a_2)) (Or (Eq True False) (Eq (in (skS.0 13 a) (skS.0 15 a a_1 a_2)) True)) % 42.55/42.80 Clause #2333 (by clausification #[1635]): ∀ (a a_1 a_2 : Iota), Or (Eq (skS.0 13 a) (skS.0 15 a a_1 a_2)) (Eq (in (skS.0 13 a) (skS.0 15 a a_1 a_2)) True) % 42.55/42.80 Clause #2334 (by superposition #[2333, 435]): ∀ (a a_1 a_2 : Iota), Or (Eq (skS.0 13 a) (skS.0 15 a a_1 a_2)) (Eq True False) % 42.55/42.80 Clause #2343 (by clausification #[2334]): ∀ (a a_1 a_2 : Iota), Eq (skS.0 13 a) (skS.0 15 a a_1 a_2) % 42.55/42.80 Clause #2346 (by backward demodulation #[2343, 436]): ∀ (a a_1 : Iota), Eq (in (skS.0 14 a a_1) (skS.0 13 a)) True % 42.55/42.80 Clause #2349 (by backward demodulation #[2343, 435]): ∀ (a : Iota), Eq (in (skS.0 13 a) (skS.0 13 a)) False % 42.55/42.81 Clause #2460 (by superposition #[2346, 1264]): ∀ (a a_1 : Iota), Or (Eq (skS.0 13 a) (skS.0 14 a a_1)) (Eq True False) % 42.55/42.81 Clause #2470 (by clausification #[2460]): ∀ (a a_1 : Iota), Eq (skS.0 13 a) (skS.0 14 a a_1) % 42.55/42.81 Clause #2497 (by backward demodulation #[2470, 2346]): ∀ (a : Iota), Eq (in (skS.0 13 a) (skS.0 13 a)) True % 42.55/42.81 Clause #2505 (by superposition #[2497, 2349]): Eq True False % 42.55/42.81 Clause #2511 (by clausification #[2505]): False % 42.55/42.81 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------