%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU280+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n019.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 08:01:17 PM UTC 2025 % Result : Theorem 211.39s 211.58s % Output : Proof 211.90s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU280+1 : TPTP v9.2.0. Released v3.3.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n019.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 06:18:38 EDT 2025 % 0.13/0.34 % CPUTime : % 211.39/211.58 SZS status Theorem for theBenchmark.p % 211.39/211.58 SZS output start Proof for theBenchmark.p % 211.39/211.58 Clause #0 (by assumption #[]): Eq (Not (∀ (A : Iota), Exists fun B => ∀ (C : Iota), Iff (in C B) (And (in C A) (ordinal C)))) True % 211.39/211.58 Clause #1 (by assumption #[]): Eq (∀ (A : Iota), And (epsilon_transitive A) (epsilon_connected A) → ordinal A) True % 211.39/211.58 Clause #4 (by assumption #[]): Eq (∀ (A : Iota), ordinal A → And (epsilon_transitive A) (epsilon_connected A)) True % 211.39/211.58 Clause #5 (by assumption #[]): Eq % 211.39/211.58 (∀ (A : Iota), % 211.39/211.58 (∀ (B C D : Iota), And (And (And (Eq B C) (ordinal C)) (Eq B D)) (ordinal D) → Eq C D) → % 211.39/211.58 Exists fun B => ∀ (C : Iota), Iff (in C B) (Exists fun D => And (And (in D A) (Eq D C)) (ordinal C))) % 211.39/211.58 True % 211.39/211.58 Clause #6 (by clausification #[1]): ∀ (a : Iota), Eq (And (epsilon_transitive a) (epsilon_connected a) → ordinal a) True % 211.39/211.58 Clause #7 (by clausification #[6]): ∀ (a : Iota), Or (Eq (And (epsilon_transitive a) (epsilon_connected a)) False) (Eq (ordinal a) True) % 211.39/211.58 Clause #8 (by clausification #[7]): ∀ (a : Iota), Or (Eq (ordinal a) True) (Or (Eq (epsilon_transitive a) False) (Eq (epsilon_connected a) False)) % 211.39/211.58 Clause #13 (by clausification #[4]): ∀ (a : Iota), Eq (ordinal a → And (epsilon_transitive a) (epsilon_connected a)) True % 211.39/211.58 Clause #14 (by clausification #[13]): ∀ (a : Iota), Or (Eq (ordinal a) False) (Eq (And (epsilon_transitive a) (epsilon_connected a)) True) % 211.39/211.58 Clause #15 (by clausification #[14]): ∀ (a : Iota), Or (Eq (ordinal a) False) (Eq (epsilon_connected a) True) % 211.39/211.58 Clause #16 (by clausification #[14]): ∀ (a : Iota), Or (Eq (ordinal a) False) (Eq (epsilon_transitive a) True) % 211.39/211.58 Clause #22 (by clausification #[0]): Eq (∀ (A : Iota), Exists fun B => ∀ (C : Iota), Iff (in C B) (And (in C A) (ordinal C))) False % 211.39/211.58 Clause #23 (by clausification #[22]): ∀ (a : Iota), Eq (Not (Exists fun B => ∀ (C : Iota), Iff (in C B) (And (in C (skS.0 1 a)) (ordinal C)))) True % 211.39/211.58 Clause #24 (by clausification #[23]): ∀ (a : Iota), Eq (Exists fun B => ∀ (C : Iota), Iff (in C B) (And (in C (skS.0 1 a)) (ordinal C))) False % 211.39/211.58 Clause #25 (by clausification #[24]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), Iff (in C a) (And (in C (skS.0 1 a_1)) (ordinal C))) False % 211.39/211.58 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), % 211.39/211.58 Eq (Not (Iff (in (skS.0 2 a a_1 a_2) a) (And (in (skS.0 2 a a_1 a_2) (skS.0 1 a_1)) (ordinal (skS.0 2 a a_1 a_2))))) % 211.39/211.58 True % 211.39/211.58 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), % 211.39/211.58 Eq (Iff (in (skS.0 2 a a_1 a_2) a) (And (in (skS.0 2 a a_1 a_2) (skS.0 1 a_1)) (ordinal (skS.0 2 a a_1 a_2)))) False % 211.39/211.58 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), % 211.39/211.58 Or (Eq (in (skS.0 2 a a_1 a_2) a) False) % 211.39/211.58 (Eq (And (in (skS.0 2 a a_1 a_2) (skS.0 1 a_1)) (ordinal (skS.0 2 a a_1 a_2))) False) % 211.39/211.58 Clause #29 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), % 211.39/211.58 Or (Eq (in (skS.0 2 a a_1 a_2) a) True) % 211.39/211.58 (Eq (And (in (skS.0 2 a a_1 a_2) (skS.0 1 a_1)) (ordinal (skS.0 2 a a_1 a_2))) True) % 211.39/211.58 Clause #30 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), % 211.39/211.58 Or (Eq (in (skS.0 2 a a_1 a_2) a) False) % 211.39/211.58 (Or (Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a_1)) False) (Eq (ordinal (skS.0 2 a a_1 a_2)) False)) % 211.39/211.58 Clause #36 (by clausification #[5]): ∀ (a : Iota), % 211.39/211.58 Eq % 211.39/211.58 ((∀ (B C D : Iota), And (And (And (Eq B C) (ordinal C)) (Eq B D)) (ordinal D) → Eq C D) → % 211.39/211.58 Exists fun B => ∀ (C : Iota), Iff (in C B) (Exists fun D => And (And (in D a) (Eq D C)) (ordinal C))) % 211.39/211.58 True % 211.39/211.58 Clause #37 (by clausification #[36]): ∀ (a : Iota), % 211.39/211.58 Or (Eq (∀ (B C D : Iota), And (And (And (Eq B C) (ordinal C)) (Eq B D)) (ordinal D) → Eq C D) False) % 211.39/211.58 (Eq (Exists fun B => ∀ (C : Iota), Iff (in C B) (Exists fun D => And (And (in D a) (Eq D C)) (ordinal C))) True) % 211.39/211.58 Clause #38 (by clausification #[37]): ∀ (a a_1 : Iota), % 211.39/211.58 Or (Eq (Exists fun B => ∀ (C : Iota), Iff (in C B) (Exists fun D => And (And (in D a) (Eq D C)) (ordinal C))) True) % 211.39/211.58 (Eq % 211.39/211.58 (Not (∀ (C D : Iota), And (And (And (Eq (skS.0 3 a_1) C) (ordinal C)) (Eq (skS.0 3 a_1) D)) (ordinal D) → Eq C D)) % 211.39/211.58 True) % 211.39/211.58 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota), % 211.43/211.62 Or % 211.43/211.62 (Eq (Not (∀ (C D : Iota), And (And (And (Eq (skS.0 3 a) C) (ordinal C)) (Eq (skS.0 3 a) D)) (ordinal D) → Eq C D)) % 211.43/211.62 True) % 211.43/211.62 (Eq (∀ (C : Iota), Iff (in C (skS.0 4 a_1 a_2)) (Exists fun D => And (And (in D a_1) (Eq D C)) (ordinal C))) True) % 211.43/211.62 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota), % 211.43/211.62 Or (Eq (∀ (C : Iota), Iff (in C (skS.0 4 a a_1)) (Exists fun D => And (And (in D a) (Eq D C)) (ordinal C))) True) % 211.43/211.62 (Eq (∀ (C D : Iota), And (And (And (Eq (skS.0 3 a_2) C) (ordinal C)) (Eq (skS.0 3 a_2) D)) (ordinal D) → Eq C D) % 211.43/211.62 False) % 211.43/211.62 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 a_3 : Iota), % 211.43/211.62 Or (Eq (∀ (C D : Iota), And (And (And (Eq (skS.0 3 a) C) (ordinal C)) (Eq (skS.0 3 a) D)) (ordinal D) → Eq C D) False) % 211.43/211.62 (Eq (Iff (in a_1 (skS.0 4 a_2 a_3)) (Exists fun D => And (And (in D a_2) (Eq D a_1)) (ordinal a_1))) True) % 211.43/211.62 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 211.43/211.62 Or (Eq (Iff (in a (skS.0 4 a_1 a_2)) (Exists fun D => And (And (in D a_1) (Eq D a)) (ordinal a))) True) % 211.43/211.62 (Eq % 211.43/211.62 (Not % 211.43/211.62 (∀ (D : Iota), % 211.43/211.62 And (And (And (Eq (skS.0 3 a_3) (skS.0 5 a_3 a_4)) (ordinal (skS.0 5 a_3 a_4))) (Eq (skS.0 3 a_3) D)) % 211.43/211.62 (ordinal D) → % 211.43/211.62 Eq (skS.0 5 a_3 a_4) D)) % 211.43/211.62 True) % 211.43/211.62 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 211.43/211.62 Or % 211.43/211.62 (Eq % 211.43/211.62 (Not % 211.43/211.62 (∀ (D : Iota), % 211.43/211.62 And (And (And (Eq (skS.0 3 a) (skS.0 5 a a_1)) (ordinal (skS.0 5 a a_1))) (Eq (skS.0 3 a) D)) (ordinal D) → % 211.43/211.62 Eq (skS.0 5 a a_1) D)) % 211.43/211.62 True) % 211.43/211.62 (Or (Eq (in a_2 (skS.0 4 a_3 a_4)) True) (Eq (Exists fun D => And (And (in D a_3) (Eq D a_2)) (ordinal a_2)) False)) % 211.43/211.62 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 211.43/211.62 Or % 211.43/211.62 (Eq % 211.43/211.62 (Not % 211.43/211.62 (∀ (D : Iota), % 211.43/211.62 And (And (And (Eq (skS.0 3 a) (skS.0 5 a a_1)) (ordinal (skS.0 5 a a_1))) (Eq (skS.0 3 a) D)) (ordinal D) → % 211.43/211.62 Eq (skS.0 5 a a_1) D)) % 211.43/211.62 True) % 211.43/211.62 (Or (Eq (in a_2 (skS.0 4 a_3 a_4)) False) (Eq (Exists fun D => And (And (in D a_3) (Eq D a_2)) (ordinal a_2)) True)) % 211.43/211.62 Clause #45 (by clausification #[43]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 211.43/211.62 Or (Eq (in a (skS.0 4 a_1 a_2)) True) % 211.43/211.62 (Or (Eq (Exists fun D => And (And (in D a_1) (Eq D a)) (ordinal a)) False) % 211.43/211.62 (Eq % 211.43/211.62 (∀ (D : Iota), % 211.43/211.62 And (And (And (Eq (skS.0 3 a_3) (skS.0 5 a_3 a_4)) (ordinal (skS.0 5 a_3 a_4))) (Eq (skS.0 3 a_3) D)) % 211.43/211.62 (ordinal D) → % 211.43/211.62 Eq (skS.0 5 a_3 a_4) D) % 211.43/211.62 False)) % 211.43/211.62 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 211.43/211.62 Or (Eq (in a (skS.0 4 a_1 a_2)) True) % 211.43/211.62 (Or % 211.43/211.62 (Eq % 211.43/211.62 (∀ (D : Iota), % 211.43/211.62 And (And (And (Eq (skS.0 3 a_3) (skS.0 5 a_3 a_4)) (ordinal (skS.0 5 a_3 a_4))) (Eq (skS.0 3 a_3) D)) % 211.43/211.62 (ordinal D) → % 211.43/211.62 Eq (skS.0 5 a_3 a_4) D) % 211.43/211.62 False) % 211.43/211.62 (Eq (And (And (in a_5 a_1) (Eq a_5 a)) (ordinal a)) False)) % 211.43/211.62 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.43/211.62 Or (Eq (in a (skS.0 4 a_1 a_2)) True) % 211.43/211.62 (Or (Eq (And (And (in a_3 a_1) (Eq a_3 a)) (ordinal a)) False) % 211.43/211.62 (Eq % 211.43/211.62 (Not % 211.43/211.62 (And % 211.43/211.62 (And (And (Eq (skS.0 3 a_4) (skS.0 5 a_4 a_5)) (ordinal (skS.0 5 a_4 a_5))) % 211.43/211.62 (Eq (skS.0 3 a_4) (skS.0 6 a_4 a_5 a_6))) % 211.43/211.62 (ordinal (skS.0 6 a_4 a_5 a_6)) → % 211.43/211.62 Eq (skS.0 5 a_4 a_5) (skS.0 6 a_4 a_5 a_6))) % 211.43/211.62 True)) % 211.43/211.62 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.43/211.62 Or (Eq (in a (skS.0 4 a_1 a_2)) True) % 211.43/211.62 (Or % 211.43/211.62 (Eq % 211.43/211.62 (Not % 211.43/211.62 (And % 211.43/211.62 (And (And (Eq (skS.0 3 a_3) (skS.0 5 a_3 a_4)) (ordinal (skS.0 5 a_3 a_4))) % 211.43/211.62 (Eq (skS.0 3 a_3) (skS.0 6 a_3 a_4 a_5))) % 211.43/211.62 (ordinal (skS.0 6 a_3 a_4 a_5)) → % 211.43/211.62 Eq (skS.0 5 a_3 a_4) (skS.0 6 a_3 a_4 a_5))) % 211.43/211.62 True) % 211.43/211.62 (Or (Eq (And (in a_6 a_1) (Eq a_6 a)) False) (Eq (ordinal a) False))) % 211.43/211.62 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.43/211.62 Or (Eq (in a (skS.0 4 a_1 a_2)) True) % 211.43/211.62 (Or (Eq (And (in a_3 a_1) (Eq a_3 a)) False) % 211.46/211.64 (Or (Eq (ordinal a) False) % 211.46/211.64 (Eq % 211.46/211.64 (And % 211.46/211.64 (And (And (Eq (skS.0 3 a_4) (skS.0 5 a_4 a_5)) (ordinal (skS.0 5 a_4 a_5))) % 211.46/211.64 (Eq (skS.0 3 a_4) (skS.0 6 a_4 a_5 a_6))) % 211.46/211.64 (ordinal (skS.0 6 a_4 a_5 a_6)) → % 211.46/211.64 Eq (skS.0 5 a_4 a_5) (skS.0 6 a_4 a_5 a_6)) % 211.46/211.64 False))) % 211.46/211.64 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.46/211.64 Or (Eq (in a (skS.0 4 a_1 a_2)) True) % 211.46/211.64 (Or (Eq (ordinal a) False) % 211.46/211.64 (Or % 211.46/211.64 (Eq % 211.46/211.64 (And % 211.46/211.64 (And (And (Eq (skS.0 3 a_3) (skS.0 5 a_3 a_4)) (ordinal (skS.0 5 a_3 a_4))) % 211.46/211.64 (Eq (skS.0 3 a_3) (skS.0 6 a_3 a_4 a_5))) % 211.46/211.64 (ordinal (skS.0 6 a_3 a_4 a_5)) → % 211.46/211.64 Eq (skS.0 5 a_3 a_4) (skS.0 6 a_3 a_4 a_5)) % 211.46/211.64 False) % 211.46/211.64 (Or (Eq (in a_6 a_1) False) (Eq (Eq a_6 a) False)))) % 211.46/211.64 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.46/211.64 Or (Eq (in a (skS.0 4 a_1 a_2)) True) % 211.46/211.64 (Or (Eq (ordinal a) False) % 211.46/211.64 (Or (Eq (in a_3 a_1) False) % 211.46/211.64 (Or (Eq (Eq a_3 a) False) % 211.46/211.64 (Eq % 211.46/211.64 (And % 211.46/211.64 (And (And (Eq (skS.0 3 a_4) (skS.0 5 a_4 a_5)) (ordinal (skS.0 5 a_4 a_5))) % 211.46/211.64 (Eq (skS.0 3 a_4) (skS.0 6 a_4 a_5 a_6))) % 211.46/211.64 (ordinal (skS.0 6 a_4 a_5 a_6))) % 211.46/211.64 True)))) % 211.46/211.64 Clause #52 (by clausification #[50]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.46/211.64 Or (Eq (in a (skS.0 4 a_1 a_2)) True) % 211.46/211.64 (Or (Eq (ordinal a) False) % 211.46/211.64 (Or (Eq (in a_3 a_1) False) (Or (Eq (Eq a_3 a) False) (Eq (Eq (skS.0 5 a_4 a_5) (skS.0 6 a_4 a_5 a_6)) False)))) % 211.46/211.64 Clause #53 (by clausification #[51]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.46/211.64 Or (Eq (in a (skS.0 4 a_1 a_2)) True) % 211.46/211.64 (Or (Eq (ordinal a) False) % 211.46/211.64 (Or (Eq (in a_3 a_1) False) % 211.46/211.64 (Or % 211.46/211.64 (Eq % 211.46/211.64 (And % 211.46/211.64 (And (And (Eq (skS.0 3 a_4) (skS.0 5 a_4 a_5)) (ordinal (skS.0 5 a_4 a_5))) % 211.46/211.64 (Eq (skS.0 3 a_4) (skS.0 6 a_4 a_5 a_6))) % 211.46/211.64 (ordinal (skS.0 6 a_4 a_5 a_6))) % 211.46/211.64 True) % 211.46/211.64 (Ne a_3 a)))) % 211.46/211.64 Clause #55 (by clausification #[53]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.46/211.64 Or (Eq (in a (skS.0 4 a_1 a_2)) True) % 211.46/211.64 (Or (Eq (ordinal a) False) % 211.46/211.64 (Or (Eq (in a_3 a_1) False) % 211.46/211.64 (Or (Ne a_3 a) % 211.46/211.64 (Eq % 211.46/211.64 (And (And (Eq (skS.0 3 a_4) (skS.0 5 a_4 a_5)) (ordinal (skS.0 5 a_4 a_5))) % 211.46/211.64 (Eq (skS.0 3 a_4) (skS.0 6 a_4 a_5 a_6))) % 211.46/211.64 True)))) % 211.46/211.64 Clause #58 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 2 a a_1 a_2) a) True) (Eq (ordinal (skS.0 2 a a_1 a_2)) True) % 211.46/211.64 Clause #59 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 2 a a_1 a_2) a) True) (Eq (in (skS.0 2 a a_1 a_2) (skS.0 1 a_1)) True) % 211.46/211.64 Clause #76 (by clausification #[44]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 211.46/211.64 Or (Eq (in a (skS.0 4 a_1 a_2)) False) % 211.46/211.64 (Or (Eq (Exists fun D => And (And (in D a_1) (Eq D a)) (ordinal a)) True) % 211.46/211.64 (Eq % 211.46/211.64 (∀ (D : Iota), % 211.46/211.64 And (And (And (Eq (skS.0 3 a_3) (skS.0 5 a_3 a_4)) (ordinal (skS.0 5 a_3 a_4))) (Eq (skS.0 3 a_3) D)) % 211.46/211.64 (ordinal D) → % 211.46/211.64 Eq (skS.0 5 a_3 a_4) D) % 211.46/211.64 False)) % 211.46/211.64 Clause #77 (by clausification #[76]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 211.46/211.64 Or (Eq (in a (skS.0 4 a_1 a_2)) False) % 211.46/211.64 (Or % 211.46/211.64 (Eq % 211.46/211.64 (∀ (D : Iota), % 211.46/211.64 And (And (And (Eq (skS.0 3 a_3) (skS.0 5 a_3 a_4)) (ordinal (skS.0 5 a_3 a_4))) (Eq (skS.0 3 a_3) D)) % 211.46/211.64 (ordinal D) → % 211.46/211.64 Eq (skS.0 5 a_3 a_4) D) % 211.46/211.64 False) % 211.46/211.64 (Eq (And (And (in (skS.0 7 a_1 a a_5) a_1) (Eq (skS.0 7 a_1 a a_5) a)) (ordinal a)) True)) % 211.46/211.64 Clause #78 (by clausification #[77]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.46/211.64 Or (Eq (in a (skS.0 4 a_1 a_2)) False) % 211.46/211.64 (Or (Eq (And (And (in (skS.0 7 a_1 a a_3) a_1) (Eq (skS.0 7 a_1 a a_3) a)) (ordinal a)) True) % 211.46/211.64 (Eq % 211.46/211.64 (Not % 211.46/211.64 (And % 211.46/211.64 (And (And (Eq (skS.0 3 a_4) (skS.0 5 a_4 a_5)) (ordinal (skS.0 5 a_4 a_5))) % 211.46/211.64 (Eq (skS.0 3 a_4) (skS.0 8 a_4 a_5 a_6))) % 211.46/211.64 (ordinal (skS.0 8 a_4 a_5 a_6)) → % 211.46/211.64 Eq (skS.0 5 a_4 a_5) (skS.0 8 a_4 a_5 a_6))) % 211.46/211.67 True)) % 211.46/211.67 Clause #79 (by clausification #[78]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 211.46/211.67 Or (Eq (in a (skS.0 4 a_1 a_2)) False) % 211.46/211.67 (Or % 211.46/211.67 (Eq % 211.46/211.67 (Not % 211.46/211.67 (And % 211.46/211.67 (And (And (Eq (skS.0 3 a_3) (skS.0 5 a_3 a_4)) (ordinal (skS.0 5 a_3 a_4))) % 211.46/211.67 (Eq (skS.0 3 a_3) (skS.0 8 a_3 a_4 a_5))) % 211.46/211.67 (ordinal (skS.0 8 a_3 a_4 a_5)) → % 211.46/211.67 Eq (skS.0 5 a_3 a_4) (skS.0 8 a_3 a_4 a_5))) % 211.46/211.67 True) % 211.46/211.67 (Eq (ordinal a) True)) % 211.46/211.67 Clause #80 (by clausification #[78]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.46/211.67 Or (Eq (in a (skS.0 4 a_1 a_2)) False) % 211.46/211.67 (Or % 211.46/211.67 (Eq % 211.46/211.67 (Not % 211.46/211.67 (And % 211.46/211.67 (And (And (Eq (skS.0 3 a_3) (skS.0 5 a_3 a_4)) (ordinal (skS.0 5 a_3 a_4))) % 211.46/211.67 (Eq (skS.0 3 a_3) (skS.0 8 a_3 a_4 a_5))) % 211.46/211.67 (ordinal (skS.0 8 a_3 a_4 a_5)) → % 211.46/211.67 Eq (skS.0 5 a_3 a_4) (skS.0 8 a_3 a_4 a_5))) % 211.46/211.67 True) % 211.46/211.67 (Eq (And (in (skS.0 7 a_1 a a_6) a_1) (Eq (skS.0 7 a_1 a a_6) a)) True)) % 211.46/211.67 Clause #81 (by clausification #[79]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 211.46/211.67 Or (Eq (in a (skS.0 4 a_1 a_2)) False) % 211.46/211.67 (Or (Eq (ordinal a) True) % 211.46/211.67 (Eq % 211.46/211.67 (And % 211.46/211.67 (And (And (Eq (skS.0 3 a_3) (skS.0 5 a_3 a_4)) (ordinal (skS.0 5 a_3 a_4))) % 211.46/211.67 (Eq (skS.0 3 a_3) (skS.0 8 a_3 a_4 a_5))) % 211.46/211.67 (ordinal (skS.0 8 a_3 a_4 a_5)) → % 211.46/211.67 Eq (skS.0 5 a_3 a_4) (skS.0 8 a_3 a_4 a_5)) % 211.46/211.67 False)) % 211.46/211.67 Clause #82 (by clausification #[81]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 211.46/211.67 Or (Eq (in a (skS.0 4 a_1 a_2)) False) % 211.46/211.67 (Or (Eq (ordinal a) True) % 211.46/211.67 (Eq % 211.46/211.67 (And % 211.46/211.67 (And (And (Eq (skS.0 3 a_3) (skS.0 5 a_3 a_4)) (ordinal (skS.0 5 a_3 a_4))) % 211.46/211.67 (Eq (skS.0 3 a_3) (skS.0 8 a_3 a_4 a_5))) % 211.46/211.67 (ordinal (skS.0 8 a_3 a_4 a_5))) % 211.46/211.67 True)) % 211.46/211.67 Clause #83 (by clausification #[81]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 211.46/211.67 Or (Eq (in a (skS.0 4 a_1 a_2)) False) % 211.46/211.67 (Or (Eq (ordinal a) True) (Eq (Eq (skS.0 5 a_3 a_4) (skS.0 8 a_3 a_4 a_5)) False)) % 211.46/211.67 Clause #85 (by clausification #[82]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 211.46/211.67 Or (Eq (in a (skS.0 4 a_1 a_2)) False) % 211.46/211.67 (Or (Eq (ordinal a) True) % 211.46/211.67 (Eq % 211.46/211.67 (And (And (Eq (skS.0 3 a_3) (skS.0 5 a_3 a_4)) (ordinal (skS.0 5 a_3 a_4))) % 211.46/211.67 (Eq (skS.0 3 a_3) (skS.0 8 a_3 a_4 a_5))) % 211.46/211.67 True)) % 211.46/211.67 Clause #90 (by clausification #[83]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 211.46/211.67 Or (Eq (in a (skS.0 4 a_1 a_2)) False) (Or (Eq (ordinal a) True) (Ne (skS.0 5 a_3 a_4) (skS.0 8 a_3 a_4 a_5))) % 211.46/211.67 Clause #91 (by superposition #[90, 58]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.46/211.67 Or (Eq (ordinal (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True) % 211.46/211.67 (Or (Ne (skS.0 5 a_4 a_5) (skS.0 8 a_4 a_5 a_6)) % 211.46/211.67 (Or (Eq False True) (Eq (ordinal (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True))) % 211.46/211.67 Clause #94 (by clausification #[52]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.46/211.67 Or (Eq (in a (skS.0 4 a_1 a_2)) True) % 211.46/211.67 (Or (Eq (ordinal a) False) % 211.46/211.67 (Or (Eq (in a_3 a_1) False) (Or (Eq (Eq (skS.0 5 a_4 a_5) (skS.0 6 a_4 a_5 a_6)) False) (Ne a_3 a)))) % 211.46/211.67 Clause #95 (by clausification #[94]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.46/211.67 Or (Eq (in a (skS.0 4 a_1 a_2)) True) % 211.46/211.67 (Or (Eq (ordinal a) False) % 211.46/211.67 (Or (Eq (in a_3 a_1) False) (Or (Ne a_3 a) (Ne (skS.0 5 a_4 a_5) (skS.0 6 a_4 a_5 a_6))))) % 211.46/211.67 Clause #96 (by destructive equality resolution #[95]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 211.46/211.67 Or (Eq (in a (skS.0 4 a_1 a_2)) True) % 211.46/211.67 (Or (Eq (ordinal a) False) (Or (Eq (in a a_1) False) (Ne (skS.0 5 a_3 a_4) (skS.0 6 a_3 a_4 a_5)))) % 211.46/211.67 Clause #117 (by clausification #[55]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.46/211.67 Or (Eq (in a (skS.0 4 a_1 a_2)) True) % 211.46/211.67 (Or (Eq (ordinal a) False) % 211.46/211.67 (Or (Eq (in a_3 a_1) False) (Or (Ne a_3 a) (Eq (Eq (skS.0 3 a_4) (skS.0 6 a_4 a_5 a_6)) True)))) % 211.46/211.67 Clause #118 (by clausification #[55]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 211.46/211.67 Or (Eq (in a (skS.0 4 a_1 a_2)) True) % 211.46/211.67 (Or (Eq (ordinal a) False) % 211.46/211.67 (Or (Eq (in a_3 a_1) False) % 211.46/211.67 (Or (Ne a_3 a) (Eq (And (Eq (skS.0 3 a_4) (skS.0 5 a_4 a_5)) (ordinal (skS.0 5 a_4 a_5))) True)))) % 211.46/211.67 Clause #119 (by clausification #[117]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.46/211.70 Or (Eq (in a (skS.0 4 a_1 a_2)) True) % 211.46/211.70 (Or (Eq (ordinal a) False) (Or (Eq (in a_3 a_1) False) (Or (Ne a_3 a) (Eq (skS.0 3 a_4) (skS.0 6 a_4 a_5 a_6))))) % 211.46/211.70 Clause #120 (by destructive equality resolution #[119]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 211.46/211.70 Or (Eq (in a (skS.0 4 a_1 a_2)) True) % 211.46/211.70 (Or (Eq (ordinal a) False) (Or (Eq (in a a_1) False) (Eq (skS.0 3 a_3) (skS.0 6 a_3 a_4 a_5)))) % 211.46/211.70 Clause #139 (by clausification #[80]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.46/211.70 Or (Eq (in a (skS.0 4 a_1 a_2)) False) % 211.46/211.70 (Or (Eq (And (in (skS.0 7 a_1 a a_3) a_1) (Eq (skS.0 7 a_1 a a_3) a)) True) % 211.46/211.70 (Eq % 211.46/211.70 (And % 211.46/211.70 (And (And (Eq (skS.0 3 a_4) (skS.0 5 a_4 a_5)) (ordinal (skS.0 5 a_4 a_5))) % 211.46/211.70 (Eq (skS.0 3 a_4) (skS.0 8 a_4 a_5 a_6))) % 211.46/211.70 (ordinal (skS.0 8 a_4 a_5 a_6)) → % 211.46/211.70 Eq (skS.0 5 a_4 a_5) (skS.0 8 a_4 a_5 a_6)) % 211.46/211.70 False)) % 211.46/211.70 Clause #140 (by clausification #[139]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.46/211.70 Or (Eq (in a (skS.0 4 a_1 a_2)) False) % 211.46/211.70 (Or % 211.46/211.70 (Eq % 211.46/211.70 (And % 211.46/211.70 (And (And (Eq (skS.0 3 a_3) (skS.0 5 a_3 a_4)) (ordinal (skS.0 5 a_3 a_4))) % 211.46/211.70 (Eq (skS.0 3 a_3) (skS.0 8 a_3 a_4 a_5))) % 211.46/211.70 (ordinal (skS.0 8 a_3 a_4 a_5)) → % 211.46/211.70 Eq (skS.0 5 a_3 a_4) (skS.0 8 a_3 a_4 a_5)) % 211.46/211.70 False) % 211.46/211.70 (Eq (Eq (skS.0 7 a_1 a a_6) a) True)) % 211.46/211.70 Clause #141 (by clausification #[139]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.46/211.70 Or (Eq (in a (skS.0 4 a_1 a_2)) False) % 211.46/211.70 (Or % 211.46/211.70 (Eq % 211.46/211.70 (And % 211.46/211.70 (And (And (Eq (skS.0 3 a_3) (skS.0 5 a_3 a_4)) (ordinal (skS.0 5 a_3 a_4))) % 211.46/211.70 (Eq (skS.0 3 a_3) (skS.0 8 a_3 a_4 a_5))) % 211.46/211.70 (ordinal (skS.0 8 a_3 a_4 a_5)) → % 211.46/211.70 Eq (skS.0 5 a_3 a_4) (skS.0 8 a_3 a_4 a_5)) % 211.46/211.70 False) % 211.46/211.70 (Eq (in (skS.0 7 a_1 a a_6) a_1) True)) % 211.46/211.70 Clause #142 (by clausification #[140]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.46/211.70 Or (Eq (in a (skS.0 4 a_1 a_2)) False) % 211.46/211.70 (Or (Eq (Eq (skS.0 7 a_1 a a_3) a) True) % 211.46/211.70 (Eq % 211.46/211.70 (And % 211.46/211.70 (And (And (Eq (skS.0 3 a_4) (skS.0 5 a_4 a_5)) (ordinal (skS.0 5 a_4 a_5))) % 211.46/211.70 (Eq (skS.0 3 a_4) (skS.0 8 a_4 a_5 a_6))) % 211.46/211.70 (ordinal (skS.0 8 a_4 a_5 a_6))) % 211.46/211.70 True)) % 211.46/211.70 Clause #143 (by clausification #[140]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.46/211.70 Or (Eq (in a (skS.0 4 a_1 a_2)) False) % 211.46/211.70 (Or (Eq (Eq (skS.0 7 a_1 a a_3) a) True) (Eq (Eq (skS.0 5 a_4 a_5) (skS.0 8 a_4 a_5 a_6)) False)) % 211.46/211.70 Clause #144 (by clausification #[142]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.46/211.70 Or (Eq (in a (skS.0 4 a_1 a_2)) False) % 211.46/211.70 (Or % 211.46/211.70 (Eq % 211.46/211.70 (And % 211.46/211.70 (And (And (Eq (skS.0 3 a_3) (skS.0 5 a_3 a_4)) (ordinal (skS.0 5 a_3 a_4))) % 211.46/211.70 (Eq (skS.0 3 a_3) (skS.0 8 a_3 a_4 a_5))) % 211.46/211.70 (ordinal (skS.0 8 a_3 a_4 a_5))) % 211.46/211.70 True) % 211.46/211.70 (Eq (skS.0 7 a_1 a a_6) a)) % 211.46/211.70 Clause #146 (by clausification #[144]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.46/211.70 Or (Eq (in a (skS.0 4 a_1 a_2)) False) % 211.46/211.70 (Or (Eq (skS.0 7 a_1 a a_3) a) % 211.46/211.70 (Eq % 211.46/211.70 (And (And (Eq (skS.0 3 a_4) (skS.0 5 a_4 a_5)) (ordinal (skS.0 5 a_4 a_5))) % 211.46/211.70 (Eq (skS.0 3 a_4) (skS.0 8 a_4 a_5 a_6))) % 211.46/211.70 True)) % 211.46/211.70 Clause #165 (by clausification #[85]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 211.46/211.70 Or (Eq (in a (skS.0 4 a_1 a_2)) False) (Or (Eq (ordinal a) True) (Eq (Eq (skS.0 3 a_3) (skS.0 8 a_3 a_4 a_5)) True)) % 211.46/211.70 Clause #166 (by clausification #[85]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 211.46/211.70 Or (Eq (in a (skS.0 4 a_1 a_2)) False) % 211.46/211.70 (Or (Eq (ordinal a) True) (Eq (And (Eq (skS.0 3 a_3) (skS.0 5 a_3 a_4)) (ordinal (skS.0 5 a_3 a_4))) True)) % 211.46/211.70 Clause #167 (by clausification #[165]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 211.46/211.70 Or (Eq (in a (skS.0 4 a_1 a_2)) False) (Or (Eq (ordinal a) True) (Eq (skS.0 3 a_3) (skS.0 8 a_3 a_4 a_5))) % 211.46/211.70 Clause #168 (by superposition #[167, 58]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.46/211.70 Or (Eq (ordinal (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True) % 211.46/211.70 (Or (Eq (skS.0 3 a_4) (skS.0 8 a_4 a_5 a_6)) % 211.46/211.70 (Or (Eq False True) (Eq (ordinal (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True))) % 211.46/211.70 Clause #172 (by clausification #[166]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 211.46/211.70 Or (Eq (in a (skS.0 4 a_1 a_2)) False) (Or (Eq (ordinal a) True) (Eq (Eq (skS.0 3 a_3) (skS.0 5 a_3 a_4)) True)) % 211.54/211.73 Clause #175 (by clausification #[172]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 211.54/211.73 Or (Eq (in a (skS.0 4 a_1 a_2)) False) (Or (Eq (ordinal a) True) (Eq (skS.0 3 a_3) (skS.0 5 a_3 a_4))) % 211.54/211.73 Clause #176 (by superposition #[175, 58]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 211.54/211.73 Or (Eq (ordinal (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True) % 211.54/211.73 (Or (Eq (skS.0 3 a_4) (skS.0 5 a_4 a_5)) (Or (Eq False True) (Eq (ordinal (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True))) % 211.54/211.73 Clause #183 (by clausification #[143]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.54/211.73 Or (Eq (in a (skS.0 4 a_1 a_2)) False) % 211.54/211.73 (Or (Eq (Eq (skS.0 5 a_3 a_4) (skS.0 8 a_3 a_4 a_5)) False) (Eq (skS.0 7 a_1 a a_6) a)) % 211.54/211.73 Clause #184 (by clausification #[183]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.54/211.73 Or (Eq (in a (skS.0 4 a_1 a_2)) False) (Or (Eq (skS.0 7 a_1 a a_3) a) (Ne (skS.0 5 a_4 a_5) (skS.0 8 a_4 a_5 a_6))) % 211.54/211.73 Clause #187 (by clausification #[141]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.54/211.73 Or (Eq (in a (skS.0 4 a_1 a_2)) False) % 211.54/211.73 (Or (Eq (in (skS.0 7 a_1 a a_3) a_1) True) % 211.54/211.73 (Eq % 211.54/211.73 (And % 211.54/211.73 (And (And (Eq (skS.0 3 a_4) (skS.0 5 a_4 a_5)) (ordinal (skS.0 5 a_4 a_5))) % 211.54/211.73 (Eq (skS.0 3 a_4) (skS.0 8 a_4 a_5 a_6))) % 211.54/211.73 (ordinal (skS.0 8 a_4 a_5 a_6))) % 211.54/211.73 True)) % 211.54/211.73 Clause #188 (by clausification #[141]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.54/211.73 Or (Eq (in a (skS.0 4 a_1 a_2)) False) % 211.54/211.73 (Or (Eq (in (skS.0 7 a_1 a a_3) a_1) True) (Eq (Eq (skS.0 5 a_4 a_5) (skS.0 8 a_4 a_5 a_6)) False)) % 211.54/211.73 Clause #190 (by clausification #[187]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.54/211.73 Or (Eq (in a (skS.0 4 a_1 a_2)) False) % 211.54/211.73 (Or (Eq (in (skS.0 7 a_1 a a_3) a_1) True) % 211.54/211.73 (Eq % 211.54/211.73 (And (And (Eq (skS.0 3 a_4) (skS.0 5 a_4 a_5)) (ordinal (skS.0 5 a_4 a_5))) % 211.54/211.73 (Eq (skS.0 3 a_4) (skS.0 8 a_4 a_5 a_6))) % 211.54/211.73 True)) % 211.54/211.73 Clause #193 (by clausification #[188]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.54/211.73 Or (Eq (in a (skS.0 4 a_1 a_2)) False) % 211.54/211.73 (Or (Eq (in (skS.0 7 a_1 a a_3) a_1) True) (Ne (skS.0 5 a_4 a_5) (skS.0 8 a_4 a_5 a_6))) % 211.54/211.73 Clause #196 (by clausification #[91]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.54/211.73 Or (Eq (ordinal (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True) % 211.54/211.73 (Or (Ne (skS.0 5 a_4 a_5) (skS.0 8 a_4 a_5 a_6)) (Eq (ordinal (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True)) % 211.54/211.73 Clause #197 (by eliminate duplicate literals #[196]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.54/211.73 Or (Eq (ordinal (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True) (Ne (skS.0 5 a_4 a_5) (skS.0 8 a_4 a_5 a_6)) % 211.54/211.73 Clause #199 (by clausification #[118]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 211.54/211.73 Or (Eq (in a (skS.0 4 a_1 a_2)) True) % 211.54/211.73 (Or (Eq (ordinal a) False) % 211.54/211.73 (Or (Eq (in a_3 a_1) False) (Or (Ne a_3 a) (Eq (Eq (skS.0 3 a_4) (skS.0 5 a_4 a_5)) True)))) % 211.54/211.73 Clause #209 (by clausification #[199]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 211.54/211.73 Or (Eq (in a (skS.0 4 a_1 a_2)) True) % 211.54/211.73 (Or (Eq (ordinal a) False) (Or (Eq (in a_3 a_1) False) (Or (Ne a_3 a) (Eq (skS.0 3 a_4) (skS.0 5 a_4 a_5))))) % 211.54/211.73 Clause #210 (by destructive equality resolution #[209]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 211.54/211.73 Or (Eq (in a (skS.0 4 a_1 a_2)) True) % 211.54/211.73 (Or (Eq (ordinal a) False) (Or (Eq (in a a_1) False) (Eq (skS.0 3 a_3) (skS.0 5 a_3 a_4)))) % 211.54/211.73 Clause #301 (by clausification #[176]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 211.54/211.73 Or (Eq (ordinal (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True) % 211.54/211.73 (Or (Eq (skS.0 3 a_4) (skS.0 5 a_4 a_5)) (Eq (ordinal (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True)) % 211.54/211.73 Clause #302 (by eliminate duplicate literals #[301]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 211.54/211.73 Or (Eq (ordinal (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True) (Eq (skS.0 3 a_4) (skS.0 5 a_4 a_5)) % 211.54/211.73 Clause #490 (by clausification #[146]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.54/211.73 Or (Eq (in a (skS.0 4 a_1 a_2)) False) % 211.54/211.73 (Or (Eq (skS.0 7 a_1 a a_3) a) (Eq (Eq (skS.0 3 a_4) (skS.0 8 a_4 a_5 a_6)) True)) % 211.54/211.73 Clause #491 (by clausification #[146]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 211.54/211.73 Or (Eq (in a (skS.0 4 a_1 a_2)) False) % 211.54/211.73 (Or (Eq (skS.0 7 a_1 a a_3) a) (Eq (And (Eq (skS.0 3 a_4) (skS.0 5 a_4 a_5)) (ordinal (skS.0 5 a_4 a_5))) True)) % 211.54/211.76 Clause #492 (by clausification #[490]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.54/211.76 Or (Eq (in a (skS.0 4 a_1 a_2)) False) (Or (Eq (skS.0 7 a_1 a a_3) a) (Eq (skS.0 3 a_4) (skS.0 8 a_4 a_5 a_6))) % 211.54/211.76 Clause #524 (by clausification #[491]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 211.54/211.76 Or (Eq (in a (skS.0 4 a_1 a_2)) False) (Or (Eq (skS.0 7 a_1 a a_3) a) (Eq (Eq (skS.0 3 a_4) (skS.0 5 a_4 a_5)) True)) % 211.54/211.76 Clause #528 (by clausification #[524]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 211.54/211.76 Or (Eq (in a (skS.0 4 a_1 a_2)) False) (Or (Eq (skS.0 7 a_1 a a_3) a) (Eq (skS.0 3 a_4) (skS.0 5 a_4 a_5))) % 211.54/211.76 Clause #536 (by clausification #[168]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.54/211.76 Or (Eq (ordinal (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True) % 211.54/211.76 (Or (Eq (skS.0 3 a_4) (skS.0 8 a_4 a_5 a_6)) (Eq (ordinal (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True)) % 211.54/211.76 Clause #537 (by eliminate duplicate literals #[536]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.54/211.76 Or (Eq (ordinal (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True) (Eq (skS.0 3 a_4) (skS.0 8 a_4 a_5 a_6)) % 211.54/211.76 Clause #538 (by superposition #[537, 15]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.54/211.76 Or (Eq (skS.0 3 a) (skS.0 8 a a_1 a_2)) % 211.54/211.76 (Or (Eq True False) (Eq (epsilon_connected (skS.0 2 (skS.0 4 a_3 a_4) a_5 a_6)) True)) % 211.54/211.76 Clause #539 (by superposition #[537, 16]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.54/211.76 Or (Eq (skS.0 3 a) (skS.0 8 a a_1 a_2)) % 211.54/211.76 (Or (Eq True False) (Eq (epsilon_transitive (skS.0 2 (skS.0 4 a_3 a_4) a_5 a_6)) True)) % 211.54/211.76 Clause #554 (by clausification #[539]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.54/211.76 Or (Eq (skS.0 3 a) (skS.0 8 a a_1 a_2)) (Eq (epsilon_transitive (skS.0 2 (skS.0 4 a_3 a_4) a_5 a_6)) True) % 211.54/211.76 Clause #555 (by superposition #[554, 197]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 : Iota), % 211.54/211.76 Or (Eq (epsilon_transitive (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True) % 211.54/211.76 (Or (Eq (ordinal (skS.0 2 (skS.0 4 a_4 a_5) a_6 a_7)) True) (Ne (skS.0 5 a_8 a_9) (skS.0 3 a_8))) % 211.54/211.76 Clause #565 (by clausification #[538]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.54/211.76 Or (Eq (skS.0 3 a) (skS.0 8 a a_1 a_2)) (Eq (epsilon_connected (skS.0 2 (skS.0 4 a_3 a_4) a_5 a_6)) True) % 211.54/211.76 Clause #566 (by superposition #[565, 197]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 a_9 : Iota), % 211.54/211.76 Or (Eq (epsilon_connected (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True) % 211.54/211.76 (Or (Eq (ordinal (skS.0 2 (skS.0 4 a_4 a_5) a_6 a_7)) True) (Ne (skS.0 5 a_8 a_9) (skS.0 3 a_8))) % 211.54/211.76 Clause #575 (by forward contextual literal cutting #[566, 302]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 211.54/211.76 Or (Eq (epsilon_connected (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True) % 211.54/211.76 (Eq (ordinal (skS.0 2 (skS.0 4 a_4 a_5) a_6 a_7)) True) % 211.54/211.76 Clause #576 (by superposition #[575, 15]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 211.54/211.76 Or (Eq (epsilon_connected (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True) % 211.54/211.76 (Or (Eq True False) (Eq (epsilon_connected (skS.0 2 (skS.0 4 a_4 a_5) a_6 a_7)) True)) % 211.54/211.76 Clause #589 (by clausification #[576]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 211.54/211.76 Or (Eq (epsilon_connected (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True) % 211.54/211.76 (Eq (epsilon_connected (skS.0 2 (skS.0 4 a_4 a_5) a_6 a_7)) True) % 211.54/211.76 Clause #590 (by equality factoring #[589]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne True True) (Eq (epsilon_connected (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True) % 211.54/211.76 Clause #591 (by clausification #[590]): ∀ (a a_1 a_2 a_3 : Iota), % 211.54/211.76 Or (Eq (epsilon_connected (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True) (Or (Eq True False) (Eq True False)) % 211.54/211.76 Clause #593 (by clausification #[591]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (epsilon_connected (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True) (Eq True False) % 211.54/211.76 Clause #594 (by clausification #[593]): ∀ (a a_1 a_2 a_3 : Iota), Eq (epsilon_connected (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True % 211.54/211.76 Clause #595 (by forward contextual literal cutting #[555, 302]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 211.54/211.76 Or (Eq (epsilon_transitive (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True) % 211.54/211.76 (Eq (ordinal (skS.0 2 (skS.0 4 a_4 a_5) a_6 a_7)) True) % 211.54/211.76 Clause #598 (by superposition #[595, 16]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 211.54/211.76 Or (Eq (epsilon_transitive (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True) % 211.54/211.76 (Or (Eq True False) (Eq (epsilon_transitive (skS.0 2 (skS.0 4 a_4 a_5) a_6 a_7)) True)) % 211.61/211.79 Clause #604 (by clausification #[598]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 211.61/211.79 Or (Eq (epsilon_transitive (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True) % 211.61/211.79 (Eq (epsilon_transitive (skS.0 2 (skS.0 4 a_4 a_5) a_6 a_7)) True) % 211.61/211.79 Clause #606 (by equality factoring #[604]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne True True) (Eq (epsilon_transitive (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True) % 211.61/211.79 Clause #610 (by clausification #[606]): ∀ (a a_1 a_2 a_3 : Iota), % 211.61/211.79 Or (Eq (epsilon_transitive (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True) (Or (Eq True False) (Eq True False)) % 211.61/211.79 Clause #612 (by clausification #[610]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (epsilon_transitive (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True) (Eq True False) % 211.61/211.79 Clause #613 (by clausification #[612]): ∀ (a a_1 a_2 a_3 : Iota), Eq (epsilon_transitive (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True % 211.61/211.79 Clause #614 (by superposition #[613, 8]): ∀ (a a_1 a_2 a_3 : Iota), % 211.61/211.79 Or (Eq (ordinal (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True) % 211.61/211.79 (Or (Eq True False) (Eq (epsilon_connected (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) False)) % 211.61/211.79 Clause #615 (by clausification #[614]): ∀ (a a_1 a_2 a_3 : Iota), % 211.61/211.79 Or (Eq (ordinal (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True) % 211.61/211.79 (Eq (epsilon_connected (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) False) % 211.61/211.79 Clause #616 (by superposition #[615, 594]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (ordinal (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True) (Eq False True) % 211.61/211.79 Clause #617 (by clausification #[616]): ∀ (a a_1 a_2 a_3 : Iota), Eq (ordinal (skS.0 2 (skS.0 4 a a_1) a_2 a_3)) True % 211.61/211.79 Clause #625 (by superposition #[617, 210]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 211.61/211.79 Or (Eq (in (skS.0 2 (skS.0 4 a a_1) a_2 a_3) (skS.0 4 a_4 a_5)) True) % 211.61/211.79 (Or (Eq True False) (Or (Eq (in (skS.0 2 (skS.0 4 a a_1) a_2 a_3) a_4) False) (Eq (skS.0 3 a_6) (skS.0 5 a_6 a_7)))) % 211.61/211.79 Clause #670 (by clausification #[190]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.61/211.79 Or (Eq (in a (skS.0 4 a_1 a_2)) False) % 211.61/211.79 (Or (Eq (in (skS.0 7 a_1 a a_3) a_1) True) (Eq (Eq (skS.0 3 a_4) (skS.0 8 a_4 a_5 a_6)) True)) % 211.61/211.79 Clause #671 (by clausification #[190]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 211.61/211.79 Or (Eq (in a (skS.0 4 a_1 a_2)) False) % 211.61/211.79 (Or (Eq (in (skS.0 7 a_1 a a_3) a_1) True) % 211.61/211.79 (Eq (And (Eq (skS.0 3 a_4) (skS.0 5 a_4 a_5)) (ordinal (skS.0 5 a_4 a_5))) True)) % 211.61/211.79 Clause #672 (by clausification #[670]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.61/211.79 Or (Eq (in a (skS.0 4 a_1 a_2)) False) % 211.61/211.79 (Or (Eq (in (skS.0 7 a_1 a a_3) a_1) True) (Eq (skS.0 3 a_4) (skS.0 8 a_4 a_5 a_6))) % 211.61/211.79 Clause #676 (by clausification #[671]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 211.61/211.79 Or (Eq (in a (skS.0 4 a_1 a_2)) False) % 211.61/211.79 (Or (Eq (in (skS.0 7 a_1 a a_3) a_1) True) (Eq (Eq (skS.0 3 a_4) (skS.0 5 a_4 a_5)) True)) % 211.61/211.79 Clause #679 (by clausification #[676]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 211.61/211.79 Or (Eq (in a (skS.0 4 a_1 a_2)) False) % 211.61/211.79 (Or (Eq (in (skS.0 7 a_1 a a_3) a_1) True) (Eq (skS.0 3 a_4) (skS.0 5 a_4 a_5))) % 211.61/211.79 Clause #720 (by clausification #[625]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 211.61/211.79 Or (Eq (in (skS.0 2 (skS.0 4 a a_1) a_2 a_3) (skS.0 4 a_4 a_5)) True) % 211.61/211.79 (Or (Eq (in (skS.0 2 (skS.0 4 a a_1) a_2 a_3) a_4) False) (Eq (skS.0 3 a_6) (skS.0 5 a_6 a_7))) % 211.61/211.79 Clause #721 (by superposition #[720, 59]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.61/211.79 Or (Eq (in (skS.0 2 (skS.0 4 a a_1) a_2 a_3) (skS.0 4 (skS.0 1 a_2) a_4)) True) % 211.61/211.79 (Or (Eq (skS.0 3 a_5) (skS.0 5 a_5 a_6)) % 211.61/211.79 (Or (Eq (in (skS.0 2 (skS.0 4 a a_1) a_2 a_3) (skS.0 4 a a_1)) True) (Eq False True))) % 211.61/211.79 Clause #5406 (by clausification #[721]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.61/211.79 Or (Eq (in (skS.0 2 (skS.0 4 a a_1) a_2 a_3) (skS.0 4 (skS.0 1 a_2) a_4)) True) % 211.61/211.79 (Or (Eq (skS.0 3 a_5) (skS.0 5 a_5 a_6)) (Eq (in (skS.0 2 (skS.0 4 a a_1) a_2 a_3) (skS.0 4 a a_1)) True)) % 211.61/211.79 Clause #5472 (by equality factoring #[5406]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 211.61/211.79 Or (Eq (skS.0 3 a) (skS.0 5 a a_1)) % 211.61/211.79 (Or (Ne True True) (Eq (in (skS.0 2 (skS.0 4 (skS.0 1 a_2) a_3) a_2 a_4) (skS.0 4 (skS.0 1 a_2) a_3)) True)) % 211.61/211.79 Clause #5473 (by clausification #[5472]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 211.61/211.82 Or (Eq (skS.0 3 a) (skS.0 5 a a_1)) % 211.61/211.82 (Or (Eq (in (skS.0 2 (skS.0 4 (skS.0 1 a_2) a_3) a_2 a_4) (skS.0 4 (skS.0 1 a_2) a_3)) True) % 211.61/211.82 (Or (Eq True False) (Eq True False))) % 211.61/211.82 Clause #5475 (by clausification #[5473]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 211.61/211.82 Or (Eq (skS.0 3 a) (skS.0 5 a a_1)) % 211.61/211.82 (Or (Eq (in (skS.0 2 (skS.0 4 (skS.0 1 a_2) a_3) a_2 a_4) (skS.0 4 (skS.0 1 a_2) a_3)) True) (Eq True False)) % 211.61/211.82 Clause #5476 (by clausification #[5475]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 211.61/211.82 Or (Eq (skS.0 3 a) (skS.0 5 a a_1)) % 211.61/211.82 (Eq (in (skS.0 2 (skS.0 4 (skS.0 1 a_2) a_3) a_2 a_4) (skS.0 4 (skS.0 1 a_2) a_3)) True) % 211.61/211.82 Clause #5510 (by superposition #[5476, 528]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 211.61/211.82 Or (Eq (skS.0 3 a) (skS.0 5 a a_1)) % 211.61/211.82 (Or (Eq True False) % 211.61/211.82 (Or % 211.61/211.82 (Eq (skS.0 7 (skS.0 1 a_2) (skS.0 2 (skS.0 4 (skS.0 1 a_2) a_3) a_2 a_4) a_5) % 211.61/211.82 (skS.0 2 (skS.0 4 (skS.0 1 a_2) a_3) a_2 a_4)) % 211.61/211.82 (Eq (skS.0 3 a_6) (skS.0 5 a_6 a_7)))) % 211.61/211.82 Clause #5513 (by superposition #[5476, 679]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 211.61/211.82 Or (Eq (skS.0 3 a) (skS.0 5 a a_1)) % 211.61/211.82 (Or (Eq True False) % 211.61/211.82 (Or (Eq (in (skS.0 7 (skS.0 1 a_2) (skS.0 2 (skS.0 4 (skS.0 1 a_2) a_3) a_2 a_4) a_5) (skS.0 1 a_2)) True) % 211.61/211.82 (Eq (skS.0 3 a_6) (skS.0 5 a_6 a_7)))) % 211.61/211.82 Clause #5514 (by superposition #[5476, 30]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 211.61/211.82 Or (Eq (skS.0 3 a) (skS.0 5 a a_1)) % 211.61/211.82 (Or (Eq True False) % 211.61/211.82 (Or (Eq (in (skS.0 2 (skS.0 4 (skS.0 1 a_2) a_3) a_2 a_4) (skS.0 1 a_2)) False) % 211.61/211.82 (Eq (ordinal (skS.0 2 (skS.0 4 (skS.0 1 a_2) a_3) a_2 a_4)) False))) % 211.61/211.82 Clause #5608 (by clausification #[5514]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 211.61/211.82 Or (Eq (skS.0 3 a) (skS.0 5 a a_1)) % 211.61/211.82 (Or (Eq (in (skS.0 2 (skS.0 4 (skS.0 1 a_2) a_3) a_2 a_4) (skS.0 1 a_2)) False) % 211.61/211.82 (Eq (ordinal (skS.0 2 (skS.0 4 (skS.0 1 a_2) a_3) a_2 a_4)) False)) % 211.61/211.82 Clause #5609 (by forward demodulation #[5608, 617]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 211.61/211.82 Or (Eq (skS.0 3 a) (skS.0 5 a a_1)) % 211.61/211.82 (Or (Eq (in (skS.0 2 (skS.0 4 (skS.0 1 a_2) a_3) a_2 a_4) (skS.0 1 a_2)) False) (Eq True False)) % 211.61/211.82 Clause #5610 (by clausification #[5609]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 211.61/211.82 Or (Eq (skS.0 3 a) (skS.0 5 a a_1)) (Eq (in (skS.0 2 (skS.0 4 (skS.0 1 a_2) a_3) a_2 a_4) (skS.0 1 a_2)) False) % 211.61/211.82 Clause #5903 (by clausification #[5513]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 211.61/211.82 Or (Eq (skS.0 3 a) (skS.0 5 a a_1)) % 211.61/211.82 (Or (Eq (in (skS.0 7 (skS.0 1 a_2) (skS.0 2 (skS.0 4 (skS.0 1 a_2) a_3) a_2 a_4) a_5) (skS.0 1 a_2)) True) % 211.61/211.82 (Eq (skS.0 3 a_6) (skS.0 5 a_6 a_7))) % 211.61/211.82 Clause #5961 (by equality factoring #[5903]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 211.61/211.82 Or (Eq (in (skS.0 7 (skS.0 1 a) (skS.0 2 (skS.0 4 (skS.0 1 a) a_1) a a_2) a_3) (skS.0 1 a)) True) % 211.61/211.82 (Or (Ne (skS.0 3 a_4) (skS.0 3 a_4)) (Eq (skS.0 3 a_4) (skS.0 5 a_4 a_5))) % 211.61/211.82 Clause #5962 (by eliminate resolved literals #[5961]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 211.61/211.82 Or (Eq (in (skS.0 7 (skS.0 1 a) (skS.0 2 (skS.0 4 (skS.0 1 a) a_1) a a_2) a_3) (skS.0 1 a)) True) % 211.61/211.82 (Eq (skS.0 3 a_4) (skS.0 5 a_4 a_5)) % 211.61/211.82 Clause #15805 (by clausification #[5510]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 211.61/211.82 Or (Eq (skS.0 3 a) (skS.0 5 a a_1)) % 211.61/211.82 (Or % 211.61/211.82 (Eq (skS.0 7 (skS.0 1 a_2) (skS.0 2 (skS.0 4 (skS.0 1 a_2) a_3) a_2 a_4) a_5) % 211.61/211.82 (skS.0 2 (skS.0 4 (skS.0 1 a_2) a_3) a_2 a_4)) % 211.61/211.82 (Eq (skS.0 3 a_6) (skS.0 5 a_6 a_7))) % 211.61/211.82 Clause #15823 (by superposition #[15805, 5962]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota), % 211.61/211.82 Or (Eq (skS.0 3 a) (skS.0 5 a a_1)) % 211.61/211.82 (Or (Eq (skS.0 3 a_2) (skS.0 5 a_2 a_3)) % 211.61/211.82 (Or (Eq (in (skS.0 2 (skS.0 4 (skS.0 1 a_4) a_5) a_4 a_6) (skS.0 1 a_4)) True) % 211.61/211.82 (Eq (skS.0 3 a_7) (skS.0 5 a_7 a_8)))) % 211.61/211.82 Clause #15847 (by superposition #[15823, 5610]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 211.61/211.82 Or (Eq (skS.0 3 a) (skS.0 5 a a_1)) % 211.61/211.82 (Or (Eq (skS.0 3 a_2) (skS.0 5 a_2 a_3)) % 211.61/211.82 (Or (Eq (skS.0 3 a_4) (skS.0 5 a_4 a_5)) (Or (Eq (skS.0 3 a_6) (skS.0 5 a_6 a_7)) (Eq True False)))) % 211.61/211.82 Clause #15867 (by clausification #[15847]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 211.61/211.82 Or (Eq (skS.0 3 a) (skS.0 5 a a_1)) % 211.61/211.82 (Or (Eq (skS.0 3 a_2) (skS.0 5 a_2 a_3)) % 211.61/211.84 (Or (Eq (skS.0 3 a_4) (skS.0 5 a_4 a_5)) (Eq (skS.0 3 a_6) (skS.0 5 a_6 a_7)))) % 211.61/211.84 Clause #15875 (by equality factoring #[15867]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 211.61/211.84 Or (Eq (skS.0 3 a) (skS.0 5 a a_1)) % 211.61/211.84 (Or (Eq (skS.0 3 a_2) (skS.0 5 a_2 a_3)) (Or (Ne (skS.0 3 a_4) (skS.0 3 a_4)) (Eq (skS.0 3 a_4) (skS.0 5 a_4 a_5)))) % 211.61/211.84 Clause #15877 (by eliminate resolved literals #[15875]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 211.61/211.84 Or (Eq (skS.0 3 a) (skS.0 5 a a_1)) (Or (Eq (skS.0 3 a_2) (skS.0 5 a_2 a_3)) (Eq (skS.0 3 a_4) (skS.0 5 a_4 a_5))) % 211.61/211.84 Clause #15885 (by equality factoring #[15877]): ∀ (a a_1 a_2 a_3 : Iota), % 211.61/211.84 Or (Eq (skS.0 3 a) (skS.0 5 a a_1)) (Or (Ne (skS.0 3 a_2) (skS.0 3 a_2)) (Eq (skS.0 3 a_2) (skS.0 5 a_2 a_3))) % 211.61/211.84 Clause #15887 (by eliminate resolved literals #[15885]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (skS.0 3 a) (skS.0 5 a a_1)) (Eq (skS.0 3 a_2) (skS.0 5 a_2 a_3)) % 211.61/211.84 Clause #15895 (by equality factoring #[15887]): ∀ (a a_1 : Iota), Or (Ne (skS.0 3 a) (skS.0 3 a)) (Eq (skS.0 3 a) (skS.0 5 a a_1)) % 211.61/211.84 Clause #15896 (by eliminate resolved literals #[15895]): ∀ (a a_1 : Iota), Eq (skS.0 3 a) (skS.0 5 a a_1) % 211.61/211.84 Clause #15898 (by backward demodulation #[15896, 96]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 211.61/211.84 Or (Eq (in a (skS.0 4 a_1 a_2)) True) % 211.61/211.84 (Or (Eq (ordinal a) False) (Or (Eq (in a a_1) False) (Ne (skS.0 3 a_3) (skS.0 6 a_3 a_4 a_5)))) % 211.61/211.84 Clause #15900 (by backward demodulation #[15896, 184]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.61/211.84 Or (Eq (in a (skS.0 4 a_1 a_2)) False) (Or (Eq (skS.0 7 a_1 a a_3) a) (Ne (skS.0 3 a_4) (skS.0 8 a_4 a_5 a_6))) % 211.61/211.84 Clause #15901 (by backward demodulation #[15896, 193]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 211.61/211.84 Or (Eq (in a (skS.0 4 a_1 a_2)) False) % 211.61/211.84 (Or (Eq (in (skS.0 7 a_1 a a_3) a_1) True) (Ne (skS.0 3 a_4) (skS.0 8 a_4 a_5 a_6))) % 211.61/211.84 Clause #15944 (by forward contextual literal cutting #[15898, 120]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 4 a_1 a_2)) True) (Or (Eq (ordinal a) False) (Eq (in a a_1) False)) % 211.61/211.84 Clause #15946 (by superposition #[15944, 617]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 211.61/211.84 Or (Eq (in (skS.0 2 (skS.0 4 a a_1) a_2 a_3) (skS.0 4 a_4 a_5)) True) % 211.61/211.84 (Or (Eq (in (skS.0 2 (skS.0 4 a a_1) a_2 a_3) a_4) False) (Eq False True)) % 211.61/211.84 Clause #15968 (by forward contextual literal cutting #[15900, 492]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in a (skS.0 4 a_1 a_2)) False) (Eq (skS.0 7 a_1 a a_3) a) % 211.61/211.84 Clause #16003 (by forward contextual literal cutting #[15901, 672]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in a (skS.0 4 a_1 a_2)) False) (Eq (in (skS.0 7 a_1 a a_3) a_1) True) % 211.61/211.84 Clause #16041 (by clausification #[15946]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 211.61/211.84 Or (Eq (in (skS.0 2 (skS.0 4 a a_1) a_2 a_3) (skS.0 4 a_4 a_5)) True) % 211.61/211.84 (Eq (in (skS.0 2 (skS.0 4 a a_1) a_2 a_3) a_4) False) % 211.61/211.84 Clause #16042 (by superposition #[16041, 59]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 211.61/211.84 Or (Eq (in (skS.0 2 (skS.0 4 a a_1) a_2 a_3) (skS.0 4 (skS.0 1 a_2) a_4)) True) % 211.61/211.84 (Or (Eq (in (skS.0 2 (skS.0 4 a a_1) a_2 a_3) (skS.0 4 a a_1)) True) (Eq False True)) % 211.61/211.84 Clause #16153 (by clausification #[16042]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 211.61/211.84 Or (Eq (in (skS.0 2 (skS.0 4 a a_1) a_2 a_3) (skS.0 4 (skS.0 1 a_2) a_4)) True) % 211.61/211.84 (Eq (in (skS.0 2 (skS.0 4 a a_1) a_2 a_3) (skS.0 4 a a_1)) True) % 211.61/211.84 Clause #16165 (by equality factoring #[16153]): ∀ (a a_1 a_2 : Iota), % 211.61/211.84 Or (Ne True True) (Eq (in (skS.0 2 (skS.0 4 (skS.0 1 a) a_1) a a_2) (skS.0 4 (skS.0 1 a) a_1)) True) % 211.61/211.84 Clause #16167 (by clausification #[16165]): ∀ (a a_1 a_2 : Iota), % 211.61/211.84 Or (Eq (in (skS.0 2 (skS.0 4 (skS.0 1 a) a_1) a a_2) (skS.0 4 (skS.0 1 a) a_1)) True) % 211.61/211.84 (Or (Eq True False) (Eq True False)) % 211.61/211.84 Clause #16169 (by clausification #[16167]): ∀ (a a_1 a_2 : Iota), % 211.61/211.84 Or (Eq (in (skS.0 2 (skS.0 4 (skS.0 1 a) a_1) a a_2) (skS.0 4 (skS.0 1 a) a_1)) True) (Eq True False) % 211.61/211.84 Clause #16170 (by clausification #[16169]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 (skS.0 4 (skS.0 1 a) a_1) a a_2) (skS.0 4 (skS.0 1 a) a_1)) True % 211.61/211.84 Clause #16172 (by superposition #[16170, 15968]): ∀ (a a_1 a_2 a_3 : Iota), % 211.61/211.84 Or (Eq True False) % 211.61/211.84 (Eq (skS.0 7 (skS.0 1 a) (skS.0 2 (skS.0 4 (skS.0 1 a) a_1) a a_2) a_3) (skS.0 2 (skS.0 4 (skS.0 1 a) a_1) a a_2)) % 211.90/212.10 Clause #16173 (by superposition #[16170, 16003]): ∀ (a a_1 a_2 a_3 : Iota), % 211.90/212.10 Or (Eq True False) (Eq (in (skS.0 7 (skS.0 1 a) (skS.0 2 (skS.0 4 (skS.0 1 a) a_1) a a_2) a_3) (skS.0 1 a)) True) % 211.90/212.10 Clause #16174 (by superposition #[16170, 30]): ∀ (a a_1 a_2 : Iota), % 211.90/212.10 Or (Eq True False) % 211.90/212.10 (Or (Eq (in (skS.0 2 (skS.0 4 (skS.0 1 a) a_1) a a_2) (skS.0 1 a)) False) % 211.90/212.10 (Eq (ordinal (skS.0 2 (skS.0 4 (skS.0 1 a) a_1) a a_2)) False)) % 211.90/212.10 Clause #16179 (by clausification #[16173]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 7 (skS.0 1 a) (skS.0 2 (skS.0 4 (skS.0 1 a) a_1) a a_2) a_3) (skS.0 1 a)) True % 211.90/212.10 Clause #16203 (by clausification #[16174]): ∀ (a a_1 a_2 : Iota), % 211.90/212.10 Or (Eq (in (skS.0 2 (skS.0 4 (skS.0 1 a) a_1) a a_2) (skS.0 1 a)) False) % 211.90/212.10 (Eq (ordinal (skS.0 2 (skS.0 4 (skS.0 1 a) a_1) a a_2)) False) % 211.90/212.10 Clause #16204 (by forward demodulation #[16203, 617]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 2 (skS.0 4 (skS.0 1 a) a_1) a a_2) (skS.0 1 a)) False) (Eq True False) % 211.90/212.10 Clause #16205 (by clausification #[16204]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 (skS.0 4 (skS.0 1 a) a_1) a a_2) (skS.0 1 a)) False % 211.90/212.10 Clause #16214 (by clausification #[16172]): ∀ (a a_1 a_2 a_3 : Iota), % 211.90/212.10 Eq (skS.0 7 (skS.0 1 a) (skS.0 2 (skS.0 4 (skS.0 1 a) a_1) a a_2) a_3) (skS.0 2 (skS.0 4 (skS.0 1 a) a_1) a a_2) % 211.90/212.10 Clause #16215 (by backward demodulation #[16214, 16179]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 2 (skS.0 4 (skS.0 1 a) a_1) a a_2) (skS.0 1 a)) True % 211.90/212.10 Clause #16219 (by superposition #[16215, 16205]): Eq True False % 211.90/212.10 Clause #16222 (by clausification #[16219]): False % 211.90/212.10 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------