%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU177+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n008.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 08:01:03 PM UTC 2025 % Result : Theorem 13.29s 13.45s % Output : Proof 13.31s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU177+1 : TPTP v9.2.0. Released v3.3.0. % 0.03/0.13 % Command : duper %s % 0.12/0.34 % Computer : n008.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Oct 3 06:16:23 EDT 2025 % 0.12/0.34 % CPUTime : % 13.29/13.45 SZS status Theorem for theBenchmark.p % 13.29/13.45 SZS output start Proof for theBenchmark.p % 13.29/13.45 Clause #17 (by assumption #[]): Eq (Not (∀ (A B C : Iota), relation C → in (ordered_pair A B) C → And (in A (relation_dom C)) (in B (relation_rng C)))) % 13.29/13.45 True % 13.29/13.45 Clause #18 (by assumption #[]): Eq % 13.29/13.45 (∀ (A : Iota), % 13.29/13.45 relation A → % 13.29/13.45 ∀ (B : Iota), Iff (Eq B (relation_dom A)) (∀ (C : Iota), Iff (in C B) (Exists fun D => in (ordered_pair C D) A))) % 13.29/13.45 True % 13.29/13.45 Clause #19 (by assumption #[]): Eq % 13.29/13.45 (∀ (A : Iota), % 13.29/13.45 relation A → % 13.29/13.45 ∀ (B : Iota), Iff (Eq B (relation_rng A)) (∀ (C : Iota), Iff (in C B) (Exists fun D => in (ordered_pair D C) A))) % 13.29/13.45 True % 13.29/13.45 Clause #80 (by clausification #[17]): Eq (∀ (A B C : Iota), relation C → in (ordered_pair A B) C → And (in A (relation_dom C)) (in B (relation_rng C))) False % 13.29/13.45 Clause #81 (by clausification #[80]): ∀ (a : Iota), % 13.29/13.45 Eq % 13.29/13.45 (Not % 13.29/13.45 (∀ (B C : Iota), % 13.29/13.45 relation C → in (ordered_pair (skS.0 4 a) B) C → And (in (skS.0 4 a) (relation_dom C)) (in B (relation_rng C)))) % 13.29/13.45 True % 13.29/13.45 Clause #82 (by clausification #[81]): ∀ (a : Iota), % 13.29/13.45 Eq % 13.29/13.45 (∀ (B C : Iota), % 13.29/13.45 relation C → in (ordered_pair (skS.0 4 a) B) C → And (in (skS.0 4 a) (relation_dom C)) (in B (relation_rng C))) % 13.29/13.45 False % 13.29/13.45 Clause #83 (by clausification #[82]): ∀ (a a_1 : Iota), % 13.29/13.45 Eq % 13.29/13.45 (Not % 13.29/13.45 (∀ (C : Iota), % 13.29/13.45 relation C → % 13.29/13.45 in (ordered_pair (skS.0 4 a) (skS.0 5 a a_1)) C → % 13.29/13.45 And (in (skS.0 4 a) (relation_dom C)) (in (skS.0 5 a a_1) (relation_rng C)))) % 13.29/13.45 True % 13.29/13.45 Clause #84 (by clausification #[83]): ∀ (a a_1 : Iota), % 13.29/13.45 Eq % 13.29/13.45 (∀ (C : Iota), % 13.29/13.45 relation C → % 13.29/13.45 in (ordered_pair (skS.0 4 a) (skS.0 5 a a_1)) C → % 13.29/13.45 And (in (skS.0 4 a) (relation_dom C)) (in (skS.0 5 a a_1) (relation_rng C))) % 13.29/13.45 False % 13.29/13.45 Clause #85 (by clausification #[84]): ∀ (a a_1 a_2 : Iota), % 13.29/13.45 Eq % 13.29/13.45 (Not % 13.29/13.45 (relation (skS.0 6 a a_1 a_2) → % 13.29/13.45 in (ordered_pair (skS.0 4 a) (skS.0 5 a a_1)) (skS.0 6 a a_1 a_2) → % 13.29/13.45 And (in (skS.0 4 a) (relation_dom (skS.0 6 a a_1 a_2))) % 13.29/13.45 (in (skS.0 5 a a_1) (relation_rng (skS.0 6 a a_1 a_2))))) % 13.29/13.45 True % 13.29/13.45 Clause #86 (by clausification #[85]): ∀ (a a_1 a_2 : Iota), % 13.29/13.45 Eq % 13.29/13.45 (relation (skS.0 6 a a_1 a_2) → % 13.29/13.45 in (ordered_pair (skS.0 4 a) (skS.0 5 a a_1)) (skS.0 6 a a_1 a_2) → % 13.29/13.45 And (in (skS.0 4 a) (relation_dom (skS.0 6 a a_1 a_2))) (in (skS.0 5 a a_1) (relation_rng (skS.0 6 a a_1 a_2)))) % 13.29/13.45 False % 13.29/13.45 Clause #87 (by clausification #[86]): ∀ (a a_1 a_2 : Iota), Eq (relation (skS.0 6 a a_1 a_2)) True % 13.29/13.45 Clause #88 (by clausification #[86]): ∀ (a a_1 a_2 : Iota), % 13.29/13.45 Eq % 13.29/13.45 (in (ordered_pair (skS.0 4 a) (skS.0 5 a a_1)) (skS.0 6 a a_1 a_2) → % 13.29/13.45 And (in (skS.0 4 a) (relation_dom (skS.0 6 a a_1 a_2))) (in (skS.0 5 a a_1) (relation_rng (skS.0 6 a a_1 a_2)))) % 13.29/13.45 False % 13.29/13.45 Clause #98 (by clausification #[18]): ∀ (a : Iota), % 13.29/13.45 Eq % 13.29/13.45 (relation a → % 13.29/13.45 ∀ (B : Iota), Iff (Eq B (relation_dom a)) (∀ (C : Iota), Iff (in C B) (Exists fun D => in (ordered_pair C D) a))) % 13.29/13.45 True % 13.29/13.45 Clause #99 (by clausification #[98]): ∀ (a : Iota), % 13.29/13.45 Or (Eq (relation a) False) % 13.29/13.45 (Eq % 13.29/13.45 (∀ (B : Iota), Iff (Eq B (relation_dom a)) (∀ (C : Iota), Iff (in C B) (Exists fun D => in (ordered_pair C D) a))) % 13.29/13.45 True) % 13.29/13.45 Clause #100 (by clausification #[99]): ∀ (a a_1 : Iota), % 13.29/13.45 Or (Eq (relation a) False) % 13.29/13.45 (Eq (Iff (Eq a_1 (relation_dom a)) (∀ (C : Iota), Iff (in C a_1) (Exists fun D => in (ordered_pair C D) a))) True) % 13.29/13.45 Clause #102 (by clausification #[100]): ∀ (a a_1 : Iota), % 13.29/13.45 Or (Eq (relation a) False) % 13.29/13.45 (Or (Eq (Eq a_1 (relation_dom a)) False) % 13.29/13.45 (Eq (∀ (C : Iota), Iff (in C a_1) (Exists fun D => in (ordered_pair C D) a)) True)) % 13.29/13.45 Clause #125 (by clausification #[19]): ∀ (a : Iota), % 13.29/13.45 Eq % 13.29/13.45 (relation a → % 13.29/13.45 ∀ (B : Iota), Iff (Eq B (relation_rng a)) (∀ (C : Iota), Iff (in C B) (Exists fun D => in (ordered_pair D C) a))) % 13.29/13.45 True % 13.29/13.45 Clause #126 (by clausification #[125]): ∀ (a : Iota), % 13.29/13.45 Or (Eq (relation a) False) % 13.29/13.45 (Eq % 13.29/13.45 (∀ (B : Iota), Iff (Eq B (relation_rng a)) (∀ (C : Iota), Iff (in C B) (Exists fun D => in (ordered_pair D C) a))) % 13.31/13.48 True) % 13.31/13.48 Clause #127 (by clausification #[126]): ∀ (a a_1 : Iota), % 13.31/13.48 Or (Eq (relation a) False) % 13.31/13.48 (Eq (Iff (Eq a_1 (relation_rng a)) (∀ (C : Iota), Iff (in C a_1) (Exists fun D => in (ordered_pair D C) a))) True) % 13.31/13.48 Clause #129 (by clausification #[127]): ∀ (a a_1 : Iota), % 13.31/13.48 Or (Eq (relation a) False) % 13.31/13.48 (Or (Eq (Eq a_1 (relation_rng a)) False) % 13.31/13.48 (Eq (∀ (C : Iota), Iff (in C a_1) (Exists fun D => in (ordered_pair D C) a)) True)) % 13.31/13.48 Clause #173 (by clausification #[88]): ∀ (a a_1 a_2 : Iota), Eq (in (ordered_pair (skS.0 4 a) (skS.0 5 a a_1)) (skS.0 6 a a_1 a_2)) True % 13.31/13.48 Clause #174 (by clausification #[88]): ∀ (a a_1 a_2 : Iota), % 13.31/13.48 Eq (And (in (skS.0 4 a) (relation_dom (skS.0 6 a a_1 a_2))) (in (skS.0 5 a a_1) (relation_rng (skS.0 6 a a_1 a_2)))) % 13.31/13.48 False % 13.31/13.48 Clause #202 (by clausification #[102]): ∀ (a a_1 : Iota), % 13.31/13.48 Or (Eq (relation a) False) % 13.31/13.48 (Or (Eq (∀ (C : Iota), Iff (in C a_1) (Exists fun D => in (ordered_pair C D) a)) True) (Ne a_1 (relation_dom a))) % 13.31/13.48 Clause #203 (by clausification #[202]): ∀ (a a_1 a_2 : Iota), % 13.31/13.48 Or (Eq (relation a) False) % 13.31/13.48 (Or (Ne a_1 (relation_dom a)) (Eq (Iff (in a_2 a_1) (Exists fun D => in (ordered_pair a_2 D) a)) True)) % 13.31/13.48 Clause #204 (by clausification #[203]): ∀ (a a_1 a_2 : Iota), % 13.31/13.48 Or (Eq (relation a) False) % 13.31/13.48 (Or (Ne a_1 (relation_dom a)) (Or (Eq (in a_2 a_1) True) (Eq (Exists fun D => in (ordered_pair a_2 D) a) False))) % 13.31/13.48 Clause #206 (by clausification #[204]): ∀ (a a_1 a_2 a_3 : Iota), % 13.31/13.48 Or (Eq (relation a) False) % 13.31/13.48 (Or (Ne a_1 (relation_dom a)) (Or (Eq (in a_2 a_1) True) (Eq (in (ordered_pair a_2 a_3) a) False))) % 13.31/13.48 Clause #207 (by destructive equality resolution #[206]): ∀ (a a_1 a_2 : Iota), % 13.31/13.48 Or (Eq (relation a) False) (Or (Eq (in a_1 (relation_dom a)) True) (Eq (in (ordered_pair a_1 a_2) a) False)) % 13.31/13.48 Clause #209 (by superposition #[207, 87]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 13.31/13.48 Or (Eq (in a (relation_dom (skS.0 6 a_1 a_2 a_3))) True) % 13.31/13.48 (Or (Eq (in (ordered_pair a a_4) (skS.0 6 a_1 a_2 a_3)) False) (Eq False True)) % 13.31/13.48 Clause #340 (by clausification #[129]): ∀ (a a_1 : Iota), % 13.31/13.48 Or (Eq (relation a) False) % 13.31/13.48 (Or (Eq (∀ (C : Iota), Iff (in C a_1) (Exists fun D => in (ordered_pair D C) a)) True) (Ne a_1 (relation_rng a))) % 13.31/13.48 Clause #341 (by clausification #[340]): ∀ (a a_1 a_2 : Iota), % 13.31/13.48 Or (Eq (relation a) False) % 13.31/13.48 (Or (Ne a_1 (relation_rng a)) (Eq (Iff (in a_2 a_1) (Exists fun D => in (ordered_pair D a_2) a)) True)) % 13.31/13.48 Clause #342 (by clausification #[341]): ∀ (a a_1 a_2 : Iota), % 13.31/13.48 Or (Eq (relation a) False) % 13.31/13.48 (Or (Ne a_1 (relation_rng a)) (Or (Eq (in a_2 a_1) True) (Eq (Exists fun D => in (ordered_pair D a_2) a) False))) % 13.31/13.48 Clause #344 (by clausification #[342]): ∀ (a a_1 a_2 a_3 : Iota), % 13.31/13.48 Or (Eq (relation a) False) % 13.31/13.48 (Or (Ne a_1 (relation_rng a)) (Or (Eq (in a_2 a_1) True) (Eq (in (ordered_pair a_3 a_2) a) False))) % 13.31/13.48 Clause #345 (by destructive equality resolution #[344]): ∀ (a a_1 a_2 : Iota), % 13.31/13.48 Or (Eq (relation a) False) (Or (Eq (in a_1 (relation_rng a)) True) (Eq (in (ordered_pair a_2 a_1) a) False)) % 13.31/13.48 Clause #347 (by superposition #[345, 87]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 13.31/13.48 Or (Eq (in a (relation_rng (skS.0 6 a_1 a_2 a_3))) True) % 13.31/13.48 (Or (Eq (in (ordered_pair a_4 a) (skS.0 6 a_1 a_2 a_3)) False) (Eq False True)) % 13.31/13.48 Clause #1293 (by clausification #[174]): ∀ (a a_1 a_2 : Iota), % 13.31/13.48 Or (Eq (in (skS.0 4 a) (relation_dom (skS.0 6 a a_1 a_2))) False) % 13.31/13.48 (Eq (in (skS.0 5 a a_1) (relation_rng (skS.0 6 a a_1 a_2))) False) % 13.31/13.48 Clause #1964 (by clausification #[209]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 13.31/13.48 Or (Eq (in a (relation_dom (skS.0 6 a_1 a_2 a_3))) True) (Eq (in (ordered_pair a a_4) (skS.0 6 a_1 a_2 a_3)) False) % 13.31/13.48 Clause #1965 (by superposition #[1964, 173]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 4 a) (relation_dom (skS.0 6 a a_1 a_2))) True) (Eq False True) % 13.31/13.48 Clause #1966 (by clausification #[1965]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 4 a) (relation_dom (skS.0 6 a a_1 a_2))) True % 13.31/13.48 Clause #1967 (by backward demodulation #[1966, 1293]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (in (skS.0 5 a a_1) (relation_rng (skS.0 6 a a_1 a_2))) False) % 13.31/13.50 Clause #2071 (by clausification #[1967]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 5 a a_1) (relation_rng (skS.0 6 a a_1 a_2))) False % 13.31/13.50 Clause #2116 (by clausification #[347]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 13.31/13.50 Or (Eq (in a (relation_rng (skS.0 6 a_1 a_2 a_3))) True) (Eq (in (ordered_pair a_4 a) (skS.0 6 a_1 a_2 a_3)) False) % 13.31/13.50 Clause #2117 (by superposition #[2116, 173]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 5 a a_1) (relation_rng (skS.0 6 a a_1 a_2))) True) (Eq False True) % 13.31/13.50 Clause #2118 (by clausification #[2117]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 5 a a_1) (relation_rng (skS.0 6 a a_1 a_2))) True % 13.31/13.50 Clause #2119 (by superposition #[2118, 2071]): Eq True False % 13.31/13.50 Clause #2225 (by clausification #[2119]): False % 13.31/13.50 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------