%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GRA004+1 : TPTP v9.2.0. Bugfixed v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n004.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 07:48:49 PM UTC 2025 % Result : Theorem 18.81s 19.03s % Output : Proof 19.06s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GRA004+1 : TPTP v9.2.0. Bugfixed v3.2.0. % 0.11/0.13 % Command : duper %s % 0.12/0.34 % Computer : n004.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 : Thu Oct 2 16:22:38 EDT 2025 % 0.12/0.34 % CPUTime : % 18.81/19.03 SZS status Theorem for theBenchmark.p % 18.81/19.03 SZS output start Proof for theBenchmark.p % 18.81/19.03 Clause #0 (by assumption #[]): Eq (∀ (E : Iota), edge E → Ne (head_of E) (tail_of E)) True % 18.81/19.03 Clause #5 (by assumption #[]): Eq % 18.81/19.03 (∀ (V1 V2 P E : Iota), % 18.81/19.03 And (path V1 V2 P) (on_path E P) → And (And (edge E) (in_path (head_of E) P)) (in_path (tail_of E) P)) % 18.81/19.03 True % 18.81/19.03 Clause #7 (by assumption #[]): Eq % 18.81/19.03 (∀ (E1 E2 : Iota), % 18.81/19.03 Iff (sequential E1 E2) (And (And (And (edge E1) (edge E2)) (Ne E1 E2)) (Eq (head_of E1) (tail_of E2)))) % 18.81/19.03 True % 18.81/19.03 Clause #8 (by assumption #[]): Eq % 18.81/19.03 (∀ (P V1 V2 : Iota), % 18.81/19.03 path V1 V2 P → % 18.81/19.03 ∀ (E1 E2 : Iota), % 18.81/19.03 And (And (on_path E1 P) (on_path E2 P)) % 18.81/19.03 (Or (sequential E1 E2) (Exists fun E3 => And (sequential E1 E3) (precedes E3 E2 P))) → % 18.81/19.03 precedes E1 E2 P) % 18.81/19.03 True % 18.81/19.03 Clause #9 (by assumption #[]): Eq % 18.81/19.03 (∀ (P V1 V2 : Iota), % 18.81/19.03 path V1 V2 P → % 18.81/19.03 ∀ (E1 E2 : Iota), % 18.81/19.03 precedes E1 E2 P → % 18.81/19.03 And (And (on_path E1 P) (on_path E2 P)) % 18.81/19.03 (Not (Iff (sequential E1 E2) (Exists fun E3 => And (sequential E1 E3) (precedes E3 E2 P))))) % 18.81/19.03 True % 18.81/19.03 Clause #10 (by assumption #[]): Eq % 18.81/19.03 (∀ (V1 V2 SP : Iota), % 18.81/19.03 Iff (shortest_path V1 V2 SP) % 18.81/19.03 (And (And (path V1 V2 SP) (Ne V1 V2)) (∀ (P : Iota), path V1 V2 P → less_or_equal (length_of SP) (length_of P)))) % 18.81/19.03 True % 18.81/19.03 Clause #11 (by assumption #[]): Eq % 18.81/19.03 (∀ (V1 V2 E1 E2 P : Iota), % 18.81/19.03 And (shortest_path V1 V2 P) (precedes E1 E2 P) → % 18.81/19.03 And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of E1)) (Eq (head_of E3) (head_of E2)))) % 18.81/19.03 (Not (precedes E2 E1 P))) % 18.81/19.03 True % 18.81/19.03 Clause #17 (by assumption #[]): Eq % 18.81/19.03 (Not % 18.81/19.03 (∀ (V1 V2 E1 E2 P : Iota), % 18.81/19.03 And (shortest_path V1 V2 P) (precedes E1 E2 P) → % 18.81/19.03 And % 18.81/19.03 (And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of E1)) (Eq (head_of E3) (head_of E2)))) % 18.81/19.03 (Ne (head_of E2) (tail_of E1))) % 18.81/19.03 (Ne (head_of E2) (head_of E1)))) % 18.81/19.03 True % 18.81/19.03 Clause #35 (by clausification #[0]): ∀ (a : Iota), Eq (edge a → Ne (head_of a) (tail_of a)) True % 18.81/19.03 Clause #36 (by clausification #[35]): ∀ (a : Iota), Or (Eq (edge a) False) (Eq (Ne (head_of a) (tail_of a)) True) % 18.81/19.03 Clause #37 (by clausification #[36]): ∀ (a : Iota), Or (Eq (edge a) False) (Ne (head_of a) (tail_of a)) % 18.81/19.03 Clause #68 (by clausification #[8]): ∀ (a : Iota), % 18.81/19.03 Eq % 18.81/19.03 (∀ (V1 V2 : Iota), % 18.81/19.03 path V1 V2 a → % 18.81/19.03 ∀ (E1 E2 : Iota), % 18.81/19.03 And (And (on_path E1 a) (on_path E2 a)) % 18.81/19.03 (Or (sequential E1 E2) (Exists fun E3 => And (sequential E1 E3) (precedes E3 E2 a))) → % 18.81/19.03 precedes E1 E2 a) % 18.81/19.03 True % 18.81/19.03 Clause #69 (by clausification #[68]): ∀ (a a_1 : Iota), % 18.81/19.03 Eq % 18.81/19.03 (∀ (V2 : Iota), % 18.81/19.03 path a V2 a_1 → % 18.81/19.03 ∀ (E1 E2 : Iota), % 18.81/19.03 And (And (on_path E1 a_1) (on_path E2 a_1)) % 18.81/19.03 (Or (sequential E1 E2) (Exists fun E3 => And (sequential E1 E3) (precedes E3 E2 a_1))) → % 18.81/19.03 precedes E1 E2 a_1) % 18.81/19.03 True % 18.81/19.03 Clause #70 (by clausification #[69]): ∀ (a a_1 a_2 : Iota), % 18.81/19.03 Eq % 18.81/19.03 (path a a_1 a_2 → % 18.81/19.03 ∀ (E1 E2 : Iota), % 18.81/19.03 And (And (on_path E1 a_2) (on_path E2 a_2)) % 18.81/19.03 (Or (sequential E1 E2) (Exists fun E3 => And (sequential E1 E3) (precedes E3 E2 a_2))) → % 18.81/19.03 precedes E1 E2 a_2) % 18.81/19.03 True % 18.81/19.03 Clause #71 (by clausification #[70]): ∀ (a a_1 a_2 : Iota), % 18.81/19.03 Or (Eq (path a a_1 a_2) False) % 18.81/19.03 (Eq % 18.81/19.03 (∀ (E1 E2 : Iota), % 18.81/19.03 And (And (on_path E1 a_2) (on_path E2 a_2)) % 18.81/19.03 (Or (sequential E1 E2) (Exists fun E3 => And (sequential E1 E3) (precedes E3 E2 a_2))) → % 18.81/19.03 precedes E1 E2 a_2) % 18.81/19.03 True) % 18.81/19.03 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 a_3 : Iota), % 18.81/19.03 Or (Eq (path a a_1 a_2) False) % 18.81/19.03 (Eq % 18.81/19.03 (∀ (E2 : Iota), % 18.81/19.03 And (And (on_path a_3 a_2) (on_path E2 a_2)) % 18.81/19.03 (Or (sequential a_3 E2) (Exists fun E3 => And (sequential a_3 E3) (precedes E3 E2 a_2))) → % 18.81/19.03 precedes a_3 E2 a_2) % 18.81/19.03 True) % 18.81/19.03 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.81/19.03 Or (Eq (path a a_1 a_2) False) % 18.81/19.03 (Eq % 18.81/19.03 (And (And (on_path a_3 a_2) (on_path a_4 a_2)) % 18.81/19.03 (Or (sequential a_3 a_4) (Exists fun E3 => And (sequential a_3 E3) (precedes E3 a_4 a_2))) → % 18.89/19.05 precedes a_3 a_4 a_2) % 18.89/19.05 True) % 18.89/19.05 Clause #74 (by clausification #[73]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.89/19.05 Or (Eq (path a a_1 a_2) False) % 18.89/19.05 (Or % 18.89/19.05 (Eq % 18.89/19.05 (And (And (on_path a_3 a_2) (on_path a_4 a_2)) % 18.89/19.05 (Or (sequential a_3 a_4) (Exists fun E3 => And (sequential a_3 E3) (precedes E3 a_4 a_2)))) % 18.89/19.05 False) % 18.89/19.05 (Eq (precedes a_3 a_4 a_2) True)) % 18.89/19.05 Clause #75 (by clausification #[74]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.89/19.05 Or (Eq (path a a_1 a_2) False) % 18.89/19.05 (Or (Eq (precedes a_3 a_4 a_2) True) % 18.89/19.05 (Or (Eq (And (on_path a_3 a_2) (on_path a_4 a_2)) False) % 18.89/19.05 (Eq (Or (sequential a_3 a_4) (Exists fun E3 => And (sequential a_3 E3) (precedes E3 a_4 a_2))) False))) % 18.89/19.05 Clause #76 (by clausification #[75]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.89/19.05 Or (Eq (path a a_1 a_2) False) % 18.89/19.05 (Or (Eq (precedes a_3 a_4 a_2) True) % 18.89/19.05 (Or (Eq (Or (sequential a_3 a_4) (Exists fun E3 => And (sequential a_3 E3) (precedes E3 a_4 a_2))) False) % 18.89/19.05 (Or (Eq (on_path a_3 a_2) False) (Eq (on_path a_4 a_2) False)))) % 18.89/19.05 Clause #78 (by clausification #[76]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.89/19.05 Or (Eq (path a a_1 a_2) False) % 18.89/19.05 (Or (Eq (precedes a_3 a_4 a_2) True) % 18.89/19.05 (Or (Eq (on_path a_3 a_2) False) (Or (Eq (on_path a_4 a_2) False) (Eq (sequential a_3 a_4) False)))) % 18.89/19.05 Clause #101 (by clausification #[5]): ∀ (a : Iota), % 18.89/19.05 Eq % 18.89/19.05 (∀ (V2 P E : Iota), % 18.89/19.05 And (path a V2 P) (on_path E P) → And (And (edge E) (in_path (head_of E) P)) (in_path (tail_of E) P)) % 18.89/19.05 True % 18.89/19.05 Clause #102 (by clausification #[101]): ∀ (a a_1 : Iota), % 18.89/19.05 Eq % 18.89/19.05 (∀ (P E : Iota), % 18.89/19.05 And (path a a_1 P) (on_path E P) → And (And (edge E) (in_path (head_of E) P)) (in_path (tail_of E) P)) % 18.89/19.05 True % 18.89/19.05 Clause #103 (by clausification #[102]): ∀ (a a_1 a_2 : Iota), % 18.89/19.05 Eq % 18.89/19.05 (∀ (E : Iota), % 18.89/19.05 And (path a a_1 a_2) (on_path E a_2) → And (And (edge E) (in_path (head_of E) a_2)) (in_path (tail_of E) a_2)) % 18.89/19.05 True % 18.89/19.05 Clause #104 (by clausification #[103]): ∀ (a a_1 a_2 a_3 : Iota), % 18.89/19.05 Eq % 18.89/19.05 (And (path a a_1 a_2) (on_path a_3 a_2) → % 18.89/19.05 And (And (edge a_3) (in_path (head_of a_3) a_2)) (in_path (tail_of a_3) a_2)) % 18.89/19.05 True % 18.89/19.05 Clause #105 (by clausification #[104]): ∀ (a a_1 a_2 a_3 : Iota), % 18.89/19.05 Or (Eq (And (path a a_1 a_2) (on_path a_3 a_2)) False) % 18.89/19.05 (Eq (And (And (edge a_3) (in_path (head_of a_3) a_2)) (in_path (tail_of a_3) a_2)) True) % 18.89/19.05 Clause #106 (by clausification #[105]): ∀ (a a_1 a_2 a_3 : Iota), % 18.89/19.05 Or (Eq (And (And (edge a) (in_path (head_of a) a_1)) (in_path (tail_of a) a_1)) True) % 18.89/19.05 (Or (Eq (path a_2 a_3 a_1) False) (Eq (on_path a a_1) False)) % 18.89/19.05 Clause #108 (by clausification #[106]): ∀ (a a_1 a_2 a_3 : Iota), % 18.89/19.05 Or (Eq (path a a_1 a_2) False) % 18.89/19.05 (Or (Eq (on_path a_3 a_2) False) (Eq (And (edge a_3) (in_path (head_of a_3) a_2)) True)) % 18.89/19.05 Clause #130 (by clausification #[108]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (path a a_1 a_2) False) (Or (Eq (on_path a_3 a_2) False) (Eq (edge a_3) True)) % 18.89/19.05 Clause #145 (by clausification #[7]): ∀ (a : Iota), % 18.89/19.05 Eq (∀ (E2 : Iota), Iff (sequential a E2) (And (And (And (edge a) (edge E2)) (Ne a E2)) (Eq (head_of a) (tail_of E2)))) % 18.89/19.05 True % 18.89/19.05 Clause #146 (by clausification #[145]): ∀ (a a_1 : Iota), % 18.89/19.05 Eq (Iff (sequential a a_1) (And (And (And (edge a) (edge a_1)) (Ne a a_1)) (Eq (head_of a) (tail_of a_1)))) True % 18.89/19.05 Clause #147 (by clausification #[146]): ∀ (a a_1 : Iota), % 18.89/19.05 Or (Eq (sequential a a_1) True) % 18.89/19.05 (Eq (And (And (And (edge a) (edge a_1)) (Ne a a_1)) (Eq (head_of a) (tail_of a_1))) False) % 18.89/19.05 Clause #149 (by clausification #[147]): ∀ (a a_1 : Iota), % 18.89/19.05 Or (Eq (sequential a a_1) True) % 18.89/19.05 (Or (Eq (And (And (edge a) (edge a_1)) (Ne a a_1)) False) (Eq (Eq (head_of a) (tail_of a_1)) False)) % 18.89/19.05 Clause #150 (by clausification #[149]): ∀ (a a_1 : Iota), % 18.89/19.05 Or (Eq (sequential a a_1) True) % 18.89/19.05 (Or (Eq (Eq (head_of a) (tail_of a_1)) False) (Or (Eq (And (edge a) (edge a_1)) False) (Eq (Ne a a_1) False))) % 18.89/19.05 Clause #151 (by clausification #[150]): ∀ (a a_1 : Iota), % 18.89/19.05 Or (Eq (sequential a a_1) True) % 18.89/19.05 (Or (Eq (And (edge a) (edge a_1)) False) (Or (Eq (Ne a a_1) False) (Ne (head_of a) (tail_of a_1)))) % 18.91/19.08 Clause #152 (by clausification #[151]): ∀ (a a_1 : Iota), % 18.91/19.08 Or (Eq (sequential a a_1) True) % 18.91/19.08 (Or (Eq (Ne a a_1) False) (Or (Ne (head_of a) (tail_of a_1)) (Or (Eq (edge a) False) (Eq (edge a_1) False)))) % 18.91/19.08 Clause #153 (by clausification #[152]): ∀ (a a_1 : Iota), % 18.91/19.08 Or (Eq (sequential a a_1) True) % 18.91/19.08 (Or (Ne (head_of a) (tail_of a_1)) (Or (Eq (edge a) False) (Or (Eq (edge a_1) False) (Eq a a_1)))) % 18.91/19.08 Clause #157 (by clausification #[9]): ∀ (a : Iota), % 18.91/19.08 Eq % 18.91/19.08 (∀ (V1 V2 : Iota), % 18.91/19.08 path V1 V2 a → % 18.91/19.08 ∀ (E1 E2 : Iota), % 18.91/19.08 precedes E1 E2 a → % 18.91/19.08 And (And (on_path E1 a) (on_path E2 a)) % 18.91/19.08 (Not (Iff (sequential E1 E2) (Exists fun E3 => And (sequential E1 E3) (precedes E3 E2 a))))) % 18.91/19.08 True % 18.91/19.08 Clause #158 (by clausification #[157]): ∀ (a a_1 : Iota), % 18.91/19.08 Eq % 18.91/19.08 (∀ (V2 : Iota), % 18.91/19.08 path a V2 a_1 → % 18.91/19.08 ∀ (E1 E2 : Iota), % 18.91/19.08 precedes E1 E2 a_1 → % 18.91/19.08 And (And (on_path E1 a_1) (on_path E2 a_1)) % 18.91/19.08 (Not (Iff (sequential E1 E2) (Exists fun E3 => And (sequential E1 E3) (precedes E3 E2 a_1))))) % 18.91/19.08 True % 18.91/19.08 Clause #159 (by clausification #[158]): ∀ (a a_1 a_2 : Iota), % 18.91/19.08 Eq % 18.91/19.08 (path a a_1 a_2 → % 18.91/19.08 ∀ (E1 E2 : Iota), % 18.91/19.08 precedes E1 E2 a_2 → % 18.91/19.08 And (And (on_path E1 a_2) (on_path E2 a_2)) % 18.91/19.08 (Not (Iff (sequential E1 E2) (Exists fun E3 => And (sequential E1 E3) (precedes E3 E2 a_2))))) % 18.91/19.08 True % 18.91/19.08 Clause #160 (by clausification #[159]): ∀ (a a_1 a_2 : Iota), % 18.91/19.08 Or (Eq (path a a_1 a_2) False) % 18.91/19.08 (Eq % 18.91/19.08 (∀ (E1 E2 : Iota), % 18.91/19.08 precedes E1 E2 a_2 → % 18.91/19.08 And (And (on_path E1 a_2) (on_path E2 a_2)) % 18.91/19.08 (Not (Iff (sequential E1 E2) (Exists fun E3 => And (sequential E1 E3) (precedes E3 E2 a_2))))) % 18.91/19.08 True) % 18.91/19.08 Clause #161 (by clausification #[160]): ∀ (a a_1 a_2 a_3 : Iota), % 18.91/19.08 Or (Eq (path a a_1 a_2) False) % 18.91/19.08 (Eq % 18.91/19.08 (∀ (E2 : Iota), % 18.91/19.08 precedes a_3 E2 a_2 → % 18.91/19.08 And (And (on_path a_3 a_2) (on_path E2 a_2)) % 18.91/19.08 (Not (Iff (sequential a_3 E2) (Exists fun E3 => And (sequential a_3 E3) (precedes E3 E2 a_2))))) % 18.91/19.08 True) % 18.91/19.08 Clause #162 (by clausification #[161]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.91/19.08 Or (Eq (path a a_1 a_2) False) % 18.91/19.08 (Eq % 18.91/19.08 (precedes a_3 a_4 a_2 → % 18.91/19.08 And (And (on_path a_3 a_2) (on_path a_4 a_2)) % 18.91/19.08 (Not (Iff (sequential a_3 a_4) (Exists fun E3 => And (sequential a_3 E3) (precedes E3 a_4 a_2))))) % 18.91/19.08 True) % 18.91/19.08 Clause #163 (by clausification #[162]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.91/19.08 Or (Eq (path a a_1 a_2) False) % 18.91/19.08 (Or (Eq (precedes a_3 a_4 a_2) False) % 18.91/19.08 (Eq % 18.91/19.08 (And (And (on_path a_3 a_2) (on_path a_4 a_2)) % 18.91/19.08 (Not (Iff (sequential a_3 a_4) (Exists fun E3 => And (sequential a_3 E3) (precedes E3 a_4 a_2))))) % 18.91/19.08 True)) % 18.91/19.08 Clause #165 (by clausification #[163]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.91/19.08 Or (Eq (path a a_1 a_2) False) % 18.91/19.08 (Or (Eq (precedes a_3 a_4 a_2) False) (Eq (And (on_path a_3 a_2) (on_path a_4 a_2)) True)) % 18.91/19.08 Clause #177 (by clausification #[165]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.91/19.08 Or (Eq (path a a_1 a_2) False) (Or (Eq (precedes a_3 a_4 a_2) False) (Eq (on_path a_4 a_2) True)) % 18.91/19.08 Clause #178 (by clausification #[165]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.91/19.08 Or (Eq (path a a_1 a_2) False) (Or (Eq (precedes a_3 a_4 a_2) False) (Eq (on_path a_3 a_2) True)) % 18.91/19.08 Clause #179 (by clausification #[10]): ∀ (a : Iota), % 18.91/19.08 Eq % 18.91/19.08 (∀ (V2 SP : Iota), % 18.91/19.08 Iff (shortest_path a V2 SP) % 18.91/19.08 (And (And (path a V2 SP) (Ne a V2)) (∀ (P : Iota), path a V2 P → less_or_equal (length_of SP) (length_of P)))) % 18.91/19.08 True % 18.91/19.08 Clause #180 (by clausification #[179]): ∀ (a a_1 : Iota), % 18.91/19.08 Eq % 18.91/19.08 (∀ (SP : Iota), % 18.91/19.08 Iff (shortest_path a a_1 SP) % 18.91/19.08 (And (And (path a a_1 SP) (Ne a a_1)) % 18.91/19.08 (∀ (P : Iota), path a a_1 P → less_or_equal (length_of SP) (length_of P)))) % 18.91/19.08 True % 18.91/19.08 Clause #181 (by clausification #[180]): ∀ (a a_1 a_2 : Iota), % 18.91/19.08 Eq % 18.91/19.08 (Iff (shortest_path a a_1 a_2) % 18.91/19.08 (And (And (path a a_1 a_2) (Ne a a_1)) % 18.91/19.08 (∀ (P : Iota), path a a_1 P → less_or_equal (length_of a_2) (length_of P)))) % 18.91/19.08 True % 18.91/19.08 Clause #183 (by clausification #[181]): ∀ (a a_1 a_2 : Iota), % 18.91/19.10 Or (Eq (shortest_path a a_1 a_2) False) % 18.91/19.10 (Eq % 18.91/19.10 (And (And (path a a_1 a_2) (Ne a a_1)) (∀ (P : Iota), path a a_1 P → less_or_equal (length_of a_2) (length_of P))) % 18.91/19.10 True) % 18.91/19.10 Clause #192 (by clausification #[183]): ∀ (a a_1 a_2 : Iota), Or (Eq (shortest_path a a_1 a_2) False) (Eq (And (path a a_1 a_2) (Ne a a_1)) True) % 18.91/19.10 Clause #196 (by clausification #[192]): ∀ (a a_1 a_2 : Iota), Or (Eq (shortest_path a a_1 a_2) False) (Eq (path a a_1 a_2) True) % 18.91/19.10 Clause #202 (by clausification #[11]): ∀ (a : Iota), % 18.91/19.10 Eq % 18.91/19.10 (∀ (V2 E1 E2 P : Iota), % 18.91/19.10 And (shortest_path a V2 P) (precedes E1 E2 P) → % 18.91/19.10 And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of E1)) (Eq (head_of E3) (head_of E2)))) % 18.91/19.10 (Not (precedes E2 E1 P))) % 18.91/19.10 True % 18.91/19.10 Clause #203 (by clausification #[202]): ∀ (a a_1 : Iota), % 18.91/19.10 Eq % 18.91/19.10 (∀ (E1 E2 P : Iota), % 18.91/19.10 And (shortest_path a a_1 P) (precedes E1 E2 P) → % 18.91/19.10 And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of E1)) (Eq (head_of E3) (head_of E2)))) % 18.91/19.10 (Not (precedes E2 E1 P))) % 18.91/19.10 True % 18.91/19.10 Clause #204 (by clausification #[203]): ∀ (a a_1 a_2 : Iota), % 18.91/19.10 Eq % 18.91/19.10 (∀ (E2 P : Iota), % 18.91/19.10 And (shortest_path a a_1 P) (precedes a_2 E2 P) → % 18.91/19.10 And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of a_2)) (Eq (head_of E3) (head_of E2)))) % 18.91/19.10 (Not (precedes E2 a_2 P))) % 18.91/19.10 True % 18.91/19.10 Clause #205 (by clausification #[204]): ∀ (a a_1 a_2 a_3 : Iota), % 18.91/19.10 Eq % 18.91/19.10 (∀ (P : Iota), % 18.91/19.10 And (shortest_path a a_1 P) (precedes a_2 a_3 P) → % 18.91/19.10 And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of a_2)) (Eq (head_of E3) (head_of a_3)))) % 18.91/19.10 (Not (precedes a_3 a_2 P))) % 18.91/19.10 True % 18.91/19.10 Clause #206 (by clausification #[205]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.91/19.10 Eq % 18.91/19.10 (And (shortest_path a a_1 a_2) (precedes a_3 a_4 a_2) → % 18.91/19.10 And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of a_3)) (Eq (head_of E3) (head_of a_4)))) % 18.91/19.10 (Not (precedes a_4 a_3 a_2))) % 18.91/19.10 True % 18.91/19.10 Clause #207 (by clausification #[206]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.91/19.10 Or (Eq (And (shortest_path a a_1 a_2) (precedes a_3 a_4 a_2)) False) % 18.91/19.10 (Eq % 18.91/19.10 (And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of a_3)) (Eq (head_of E3) (head_of a_4)))) % 18.91/19.10 (Not (precedes a_4 a_3 a_2))) % 18.91/19.10 True) % 18.91/19.10 Clause #208 (by clausification #[207]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.91/19.10 Or % 18.91/19.10 (Eq % 18.91/19.10 (And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of a)) (Eq (head_of E3) (head_of a_1)))) % 18.91/19.10 (Not (precedes a_1 a a_2))) % 18.91/19.10 True) % 18.91/19.10 (Or (Eq (shortest_path a_3 a_4 a_2) False) (Eq (precedes a a_1 a_2) False)) % 18.91/19.10 Clause #209 (by clausification #[208]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.91/19.10 Or (Eq (shortest_path a a_1 a_2) False) (Or (Eq (precedes a_3 a_4 a_2) False) (Eq (Not (precedes a_4 a_3 a_2)) True)) % 18.91/19.10 Clause #210 (by clausification #[208]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.91/19.10 Or (Eq (shortest_path a a_1 a_2) False) % 18.91/19.10 (Or (Eq (precedes a_3 a_4 a_2) False) % 18.91/19.10 (Eq (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of a_3)) (Eq (head_of E3) (head_of a_4)))) True)) % 18.91/19.10 Clause #211 (by clausification #[209]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.91/19.10 Or (Eq (shortest_path a a_1 a_2) False) (Or (Eq (precedes a_3 a_4 a_2) False) (Eq (precedes a_4 a_3 a_2) False)) % 18.91/19.10 Clause #212 (by clausification #[210]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.91/19.10 Or (Eq (shortest_path a a_1 a_2) False) % 18.91/19.10 (Or (Eq (precedes a_3 a_4 a_2) False) % 18.91/19.10 (Eq (Exists fun E3 => And (Eq (tail_of E3) (tail_of a_3)) (Eq (head_of E3) (head_of a_4))) False)) % 18.91/19.10 Clause #213 (by clausification #[212]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 18.91/19.10 Or (Eq (shortest_path a a_1 a_2) False) % 18.91/19.10 (Or (Eq (precedes a_3 a_4 a_2) False) % 18.91/19.10 (Eq (And (Eq (tail_of a_5) (tail_of a_3)) (Eq (head_of a_5) (head_of a_4))) False)) % 18.91/19.10 Clause #214 (by clausification #[213]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 18.91/19.10 Or (Eq (shortest_path a a_1 a_2) False) % 18.91/19.10 (Or (Eq (precedes a_3 a_4 a_2) False) % 18.91/19.10 (Or (Eq (Eq (tail_of a_5) (tail_of a_3)) False) (Eq (Eq (head_of a_5) (head_of a_4)) False))) % 18.91/19.10 Clause #215 (by clausification #[214]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 18.95/19.12 Or (Eq (shortest_path a a_1 a_2) False) % 18.95/19.12 (Or (Eq (precedes a_3 a_4 a_2) False) % 18.95/19.12 (Or (Eq (Eq (head_of a_5) (head_of a_4)) False) (Ne (tail_of a_5) (tail_of a_3)))) % 18.95/19.12 Clause #216 (by clausification #[215]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 18.95/19.12 Or (Eq (shortest_path a a_1 a_2) False) % 18.95/19.12 (Or (Eq (precedes a_3 a_4 a_2) False) (Or (Ne (tail_of a_5) (tail_of a_3)) (Ne (head_of a_5) (head_of a_4)))) % 18.95/19.12 Clause #231 (by clausification #[17]): Eq % 18.95/19.12 (∀ (V1 V2 E1 E2 P : Iota), % 18.95/19.12 And (shortest_path V1 V2 P) (precedes E1 E2 P) → % 18.95/19.12 And % 18.95/19.12 (And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of E1)) (Eq (head_of E3) (head_of E2)))) % 18.95/19.12 (Ne (head_of E2) (tail_of E1))) % 18.95/19.12 (Ne (head_of E2) (head_of E1))) % 18.95/19.12 False % 18.95/19.12 Clause #232 (by clausification #[231]): ∀ (a : Iota), % 18.95/19.12 Eq % 18.95/19.12 (Not % 18.95/19.12 (∀ (V2 E1 E2 P : Iota), % 18.95/19.12 And (shortest_path (skS.0 7 a) V2 P) (precedes E1 E2 P) → % 18.95/19.12 And % 18.95/19.12 (And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of E1)) (Eq (head_of E3) (head_of E2)))) % 18.95/19.12 (Ne (head_of E2) (tail_of E1))) % 18.95/19.12 (Ne (head_of E2) (head_of E1)))) % 18.95/19.12 True % 18.95/19.12 Clause #233 (by clausification #[232]): ∀ (a : Iota), % 18.95/19.12 Eq % 18.95/19.12 (∀ (V2 E1 E2 P : Iota), % 18.95/19.12 And (shortest_path (skS.0 7 a) V2 P) (precedes E1 E2 P) → % 18.95/19.12 And % 18.95/19.12 (And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of E1)) (Eq (head_of E3) (head_of E2)))) % 18.95/19.12 (Ne (head_of E2) (tail_of E1))) % 18.95/19.12 (Ne (head_of E2) (head_of E1))) % 18.95/19.12 False % 18.95/19.12 Clause #234 (by clausification #[233]): ∀ (a a_1 : Iota), % 18.95/19.12 Eq % 18.95/19.12 (Not % 18.95/19.12 (∀ (E1 E2 P : Iota), % 18.95/19.12 And (shortest_path (skS.0 7 a) (skS.0 8 a a_1) P) (precedes E1 E2 P) → % 18.95/19.12 And % 18.95/19.12 (And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of E1)) (Eq (head_of E3) (head_of E2)))) % 18.95/19.12 (Ne (head_of E2) (tail_of E1))) % 18.95/19.12 (Ne (head_of E2) (head_of E1)))) % 18.95/19.12 True % 18.95/19.12 Clause #235 (by clausification #[234]): ∀ (a a_1 : Iota), % 18.95/19.12 Eq % 18.95/19.12 (∀ (E1 E2 P : Iota), % 18.95/19.12 And (shortest_path (skS.0 7 a) (skS.0 8 a a_1) P) (precedes E1 E2 P) → % 18.95/19.12 And % 18.95/19.12 (And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of E1)) (Eq (head_of E3) (head_of E2)))) % 18.95/19.12 (Ne (head_of E2) (tail_of E1))) % 18.95/19.12 (Ne (head_of E2) (head_of E1))) % 18.95/19.12 False % 18.95/19.12 Clause #236 (by clausification #[235]): ∀ (a a_1 a_2 : Iota), % 18.95/19.12 Eq % 18.95/19.12 (Not % 18.95/19.12 (∀ (E2 P : Iota), % 18.95/19.12 And (shortest_path (skS.0 7 a) (skS.0 8 a a_1) P) (precedes (skS.0 9 a a_1 a_2) E2 P) → % 18.95/19.12 And % 18.95/19.12 (And % 18.95/19.12 (Not % 18.95/19.12 (Exists fun E3 => And (Eq (tail_of E3) (tail_of (skS.0 9 a a_1 a_2))) (Eq (head_of E3) (head_of E2)))) % 18.95/19.12 (Ne (head_of E2) (tail_of (skS.0 9 a a_1 a_2)))) % 18.95/19.12 (Ne (head_of E2) (head_of (skS.0 9 a a_1 a_2))))) % 18.95/19.12 True % 18.95/19.12 Clause #237 (by clausification #[236]): ∀ (a a_1 a_2 : Iota), % 18.95/19.12 Eq % 18.95/19.12 (∀ (E2 P : Iota), % 18.95/19.12 And (shortest_path (skS.0 7 a) (skS.0 8 a a_1) P) (precedes (skS.0 9 a a_1 a_2) E2 P) → % 18.95/19.12 And % 18.95/19.12 (And % 18.95/19.12 (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of (skS.0 9 a a_1 a_2))) (Eq (head_of E3) (head_of E2)))) % 18.95/19.12 (Ne (head_of E2) (tail_of (skS.0 9 a a_1 a_2)))) % 18.95/19.12 (Ne (head_of E2) (head_of (skS.0 9 a a_1 a_2)))) % 18.95/19.12 False % 18.95/19.12 Clause #238 (by clausification #[237]): ∀ (a a_1 a_2 a_3 : Iota), % 18.95/19.12 Eq % 18.95/19.12 (Not % 18.95/19.12 (∀ (P : Iota), % 18.95/19.12 And (shortest_path (skS.0 7 a) (skS.0 8 a a_1) P) (precedes (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3) P) → % 18.95/19.12 And % 18.95/19.12 (And % 18.95/19.12 (Not % 18.95/19.12 (Exists fun E3 => % 18.95/19.12 And (Eq (tail_of E3) (tail_of (skS.0 9 a a_1 a_2))) % 18.95/19.12 (Eq (head_of E3) (head_of (skS.0 10 a a_1 a_2 a_3))))) % 18.95/19.12 (Ne (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2)))) % 18.95/19.12 (Ne (head_of (skS.0 10 a a_1 a_2 a_3)) (head_of (skS.0 9 a a_1 a_2))))) % 18.95/19.12 True % 18.95/19.12 Clause #239 (by clausification #[238]): ∀ (a a_1 a_2 a_3 : Iota), % 18.95/19.12 Eq % 18.95/19.12 (∀ (P : Iota), % 18.95/19.12 And (shortest_path (skS.0 7 a) (skS.0 8 a a_1) P) (precedes (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3) P) → % 18.98/19.15 And % 18.98/19.15 (And % 18.98/19.15 (Not % 18.98/19.15 (Exists fun E3 => % 18.98/19.15 And (Eq (tail_of E3) (tail_of (skS.0 9 a a_1 a_2))) % 18.98/19.15 (Eq (head_of E3) (head_of (skS.0 10 a a_1 a_2 a_3))))) % 18.98/19.15 (Ne (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2)))) % 18.98/19.15 (Ne (head_of (skS.0 10 a a_1 a_2 a_3)) (head_of (skS.0 9 a a_1 a_2)))) % 18.98/19.15 False % 18.98/19.15 Clause #240 (by clausification #[239]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.98/19.15 Eq % 18.98/19.15 (Not % 18.98/19.15 (And (shortest_path (skS.0 7 a) (skS.0 8 a a_1) (skS.0 11 a a_1 a_2 a_3 a_4)) % 18.98/19.15 (precedes (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3) (skS.0 11 a a_1 a_2 a_3 a_4)) → % 18.98/19.15 And % 18.98/19.15 (And % 18.98/19.15 (Not % 18.98/19.15 (Exists fun E3 => % 18.98/19.15 And (Eq (tail_of E3) (tail_of (skS.0 9 a a_1 a_2))) % 18.98/19.15 (Eq (head_of E3) (head_of (skS.0 10 a a_1 a_2 a_3))))) % 18.98/19.15 (Ne (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2)))) % 18.98/19.15 (Ne (head_of (skS.0 10 a a_1 a_2 a_3)) (head_of (skS.0 9 a a_1 a_2))))) % 18.98/19.15 True % 18.98/19.15 Clause #241 (by clausification #[240]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.98/19.15 Eq % 18.98/19.15 (And (shortest_path (skS.0 7 a) (skS.0 8 a a_1) (skS.0 11 a a_1 a_2 a_3 a_4)) % 18.98/19.15 (precedes (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3) (skS.0 11 a a_1 a_2 a_3 a_4)) → % 18.98/19.15 And % 18.98/19.15 (And % 18.98/19.15 (Not % 18.98/19.15 (Exists fun E3 => % 18.98/19.15 And (Eq (tail_of E3) (tail_of (skS.0 9 a a_1 a_2))) (Eq (head_of E3) (head_of (skS.0 10 a a_1 a_2 a_3))))) % 18.98/19.15 (Ne (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2)))) % 18.98/19.15 (Ne (head_of (skS.0 10 a a_1 a_2 a_3)) (head_of (skS.0 9 a a_1 a_2)))) % 18.98/19.15 False % 18.98/19.15 Clause #242 (by clausification #[241]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.98/19.15 Eq % 18.98/19.15 (And (shortest_path (skS.0 7 a) (skS.0 8 a a_1) (skS.0 11 a a_1 a_2 a_3 a_4)) % 18.98/19.15 (precedes (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3) (skS.0 11 a a_1 a_2 a_3 a_4))) % 18.98/19.15 True % 18.98/19.15 Clause #243 (by clausification #[241]): ∀ (a a_1 a_2 a_3 : Iota), % 18.98/19.15 Eq % 18.98/19.15 (And % 18.98/19.15 (And % 18.98/19.15 (Not % 18.98/19.15 (Exists fun E3 => % 18.98/19.15 And (Eq (tail_of E3) (tail_of (skS.0 9 a a_1 a_2))) (Eq (head_of E3) (head_of (skS.0 10 a a_1 a_2 a_3))))) % 18.98/19.15 (Ne (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2)))) % 18.98/19.15 (Ne (head_of (skS.0 10 a a_1 a_2 a_3)) (head_of (skS.0 9 a a_1 a_2)))) % 18.98/19.15 False % 18.98/19.15 Clause #244 (by clausification #[242]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.98/19.15 Eq (precedes (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3) (skS.0 11 a a_1 a_2 a_3 a_4)) True % 18.98/19.15 Clause #245 (by clausification #[242]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (shortest_path (skS.0 7 a) (skS.0 8 a a_1) (skS.0 11 a a_1 a_2 a_3 a_4)) True % 18.98/19.15 Clause #253 (by superposition #[245, 196]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.98/19.15 Or (Eq True False) (Eq (path (skS.0 7 a) (skS.0 8 a a_1) (skS.0 11 a a_1 a_2 a_3 a_4)) True) % 18.98/19.15 Clause #254 (by superposition #[245, 211]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 18.98/19.15 Or (Eq True False) % 18.98/19.15 (Or (Eq (precedes a a_1 (skS.0 11 a_2 a_3 a_4 a_5 a_6)) False) % 18.98/19.15 (Eq (precedes a_1 a (skS.0 11 a_2 a_3 a_4 a_5 a_6)) False)) % 18.98/19.15 Clause #255 (by superposition #[245, 216]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 18.98/19.15 Or (Eq True False) % 18.98/19.15 (Or (Eq (precedes a a_1 (skS.0 11 a_2 a_3 a_4 a_5 a_6)) False) % 18.98/19.15 (Or (Ne (tail_of a_7) (tail_of a)) (Ne (head_of a_7) (head_of a_1)))) % 18.98/19.15 Clause #263 (by clausification #[255]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 18.98/19.15 Or (Eq (precedes a a_1 (skS.0 11 a_2 a_3 a_4 a_5 a_6)) False) % 18.98/19.15 (Or (Ne (tail_of a_7) (tail_of a)) (Ne (head_of a_7) (head_of a_1))) % 18.98/19.15 Clause #264 (by superposition #[263, 244]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.98/19.15 Or (Ne (tail_of a) (tail_of (skS.0 9 a_1 a_2 a_3))) % 18.98/19.15 (Or (Ne (head_of a) (head_of (skS.0 10 a_1 a_2 a_3 a_4))) (Eq False True)) % 18.98/19.15 Clause #265 (by clausification #[264]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.98/19.15 Or (Ne (tail_of a) (tail_of (skS.0 9 a_1 a_2 a_3))) (Ne (head_of a) (head_of (skS.0 10 a_1 a_2 a_3 a_4))) % 18.98/19.15 Clause #266 (by equality resolution #[265]): ∀ (a a_1 a_2 a_3 : Iota), Ne (head_of (skS.0 9 a a_1 a_2)) (head_of (skS.0 10 a a_1 a_2 a_3)) % 18.98/19.17 Clause #267 (by clausification #[253]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (path (skS.0 7 a) (skS.0 8 a a_1) (skS.0 11 a a_1 a_2 a_3 a_4)) True % 18.98/19.17 Clause #277 (by superposition #[267, 130]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 18.98/19.17 Or (Eq True False) (Or (Eq (on_path a (skS.0 11 a_1 a_2 a_3 a_4 a_5)) False) (Eq (edge a) True)) % 18.98/19.17 Clause #278 (by superposition #[267, 78]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 18.98/19.17 Or (Eq True False) % 18.98/19.17 (Or (Eq (precedes a a_1 (skS.0 11 a_2 a_3 a_4 a_5 a_6)) True) % 18.98/19.17 (Or (Eq (on_path a (skS.0 11 a_2 a_3 a_4 a_5 a_6)) False) % 18.98/19.17 (Or (Eq (on_path a_1 (skS.0 11 a_2 a_3 a_4 a_5 a_6)) False) (Eq (sequential a a_1) False)))) % 18.98/19.17 Clause #283 (by superposition #[267, 177]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 18.98/19.17 Or (Eq True False) % 18.98/19.17 (Or (Eq (precedes a a_1 (skS.0 11 a_2 a_3 a_4 a_5 a_6)) False) % 18.98/19.17 (Eq (on_path a_1 (skS.0 11 a_2 a_3 a_4 a_5 a_6)) True)) % 18.98/19.17 Clause #284 (by superposition #[267, 178]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 18.98/19.17 Or (Eq True False) % 18.98/19.17 (Or (Eq (precedes a a_1 (skS.0 11 a_2 a_3 a_4 a_5 a_6)) False) (Eq (on_path a (skS.0 11 a_2 a_3 a_4 a_5 a_6)) True)) % 18.98/19.17 Clause #298 (by clausification #[277]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), Or (Eq (on_path a (skS.0 11 a_1 a_2 a_3 a_4 a_5)) False) (Eq (edge a) True) % 18.98/19.17 Clause #322 (by clausification #[284]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 18.98/19.17 Or (Eq (precedes a a_1 (skS.0 11 a_2 a_3 a_4 a_5 a_6)) False) (Eq (on_path a (skS.0 11 a_2 a_3 a_4 a_5 a_6)) True) % 18.98/19.17 Clause #323 (by superposition #[322, 244]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq (on_path (skS.0 9 a a_1 a_2) (skS.0 11 a a_1 a_2 a_3 a_4)) True) (Eq False True) % 18.98/19.17 Clause #324 (by clausification #[323]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (on_path (skS.0 9 a a_1 a_2) (skS.0 11 a a_1 a_2 a_3 a_4)) True % 18.98/19.17 Clause #325 (by superposition #[324, 298]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (edge (skS.0 9 a a_1 a_2)) True) % 18.98/19.17 Clause #327 (by clausification #[325]): ∀ (a a_1 a_2 : Iota), Eq (edge (skS.0 9 a a_1 a_2)) True % 18.98/19.17 Clause #334 (by clausification #[243]): ∀ (a a_1 a_2 a_3 : Iota), % 18.98/19.17 Or % 18.98/19.17 (Eq % 18.98/19.17 (And % 18.98/19.17 (Not % 18.98/19.17 (Exists fun E3 => % 18.98/19.17 And (Eq (tail_of E3) (tail_of (skS.0 9 a a_1 a_2))) (Eq (head_of E3) (head_of (skS.0 10 a a_1 a_2 a_3))))) % 18.98/19.17 (Ne (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2)))) % 18.98/19.17 False) % 18.98/19.17 (Eq (Ne (head_of (skS.0 10 a a_1 a_2 a_3)) (head_of (skS.0 9 a a_1 a_2))) False) % 18.98/19.17 Clause #335 (by clausification #[334]): ∀ (a a_1 a_2 a_3 : Iota), % 18.98/19.17 Or (Eq (Ne (head_of (skS.0 10 a a_1 a_2 a_3)) (head_of (skS.0 9 a a_1 a_2))) False) % 18.98/19.17 (Or % 18.98/19.17 (Eq % 18.98/19.17 (Not % 18.98/19.17 (Exists fun E3 => % 18.98/19.17 And (Eq (tail_of E3) (tail_of (skS.0 9 a a_1 a_2))) (Eq (head_of E3) (head_of (skS.0 10 a a_1 a_2 a_3))))) % 18.98/19.17 False) % 18.98/19.17 (Eq (Ne (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2))) False)) % 18.98/19.17 Clause #336 (by clausification #[335]): ∀ (a a_1 a_2 a_3 : Iota), % 18.98/19.17 Or % 18.98/19.17 (Eq % 18.98/19.17 (Not % 18.98/19.17 (Exists fun E3 => % 18.98/19.17 And (Eq (tail_of E3) (tail_of (skS.0 9 a a_1 a_2))) (Eq (head_of E3) (head_of (skS.0 10 a a_1 a_2 a_3))))) % 18.98/19.17 False) % 18.98/19.17 (Or (Eq (Ne (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2))) False) % 18.98/19.17 (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (head_of (skS.0 9 a a_1 a_2)))) % 18.98/19.17 Clause #337 (by clausification #[336]): ∀ (a a_1 a_2 a_3 : Iota), % 18.98/19.17 Or (Eq (Ne (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2))) False) % 18.98/19.17 (Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (head_of (skS.0 9 a a_1 a_2))) % 18.98/19.17 (Eq % 18.98/19.17 (Exists fun E3 => % 18.98/19.17 And (Eq (tail_of E3) (tail_of (skS.0 9 a a_1 a_2))) (Eq (head_of E3) (head_of (skS.0 10 a a_1 a_2 a_3)))) % 18.98/19.17 True)) % 18.98/19.17 Clause #338 (by clausification #[337]): ∀ (a a_1 a_2 a_3 : Iota), % 18.98/19.17 Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (head_of (skS.0 9 a a_1 a_2))) % 18.98/19.17 (Or % 18.98/19.17 (Eq % 18.98/19.17 (Exists fun E3 => % 18.98/19.17 And (Eq (tail_of E3) (tail_of (skS.0 9 a a_1 a_2))) (Eq (head_of E3) (head_of (skS.0 10 a a_1 a_2 a_3)))) % 18.98/19.17 True) % 18.98/19.17 (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2)))) % 18.98/19.17 Clause #339 (by clausification #[338]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.98/19.20 Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (head_of (skS.0 9 a a_1 a_2))) % 18.98/19.20 (Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2))) % 18.98/19.20 (Eq % 18.98/19.20 (And (Eq (tail_of (skS.0 13 a a_1 a_2 a_3 a_4)) (tail_of (skS.0 9 a a_1 a_2))) % 18.98/19.20 (Eq (head_of (skS.0 13 a a_1 a_2 a_3 a_4)) (head_of (skS.0 10 a a_1 a_2 a_3)))) % 18.98/19.20 True)) % 18.98/19.20 Clause #340 (by clausification #[339]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.98/19.20 Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (head_of (skS.0 9 a a_1 a_2))) % 18.98/19.20 (Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2))) % 18.98/19.20 (Eq (Eq (head_of (skS.0 13 a a_1 a_2 a_3 a_4)) (head_of (skS.0 10 a a_1 a_2 a_3))) True)) % 18.98/19.20 Clause #341 (by clausification #[339]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.98/19.20 Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (head_of (skS.0 9 a a_1 a_2))) % 18.98/19.20 (Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2))) % 18.98/19.20 (Eq (Eq (tail_of (skS.0 13 a a_1 a_2 a_3 a_4)) (tail_of (skS.0 9 a a_1 a_2))) True)) % 18.98/19.20 Clause #342 (by clausification #[340]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.98/19.20 Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (head_of (skS.0 9 a a_1 a_2))) % 18.98/19.20 (Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2))) % 18.98/19.20 (Eq (head_of (skS.0 13 a a_1 a_2 a_3 a_4)) (head_of (skS.0 10 a a_1 a_2 a_3)))) % 18.98/19.20 Clause #343 (by forward contextual literal cutting #[342, 266]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.98/19.20 Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2))) % 18.98/19.20 (Eq (head_of (skS.0 13 a a_1 a_2 a_3 a_4)) (head_of (skS.0 10 a a_1 a_2 a_3))) % 18.98/19.20 Clause #348 (by clausification #[283]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 18.98/19.20 Or (Eq (precedes a a_1 (skS.0 11 a_2 a_3 a_4 a_5 a_6)) False) (Eq (on_path a_1 (skS.0 11 a_2 a_3 a_4 a_5 a_6)) True) % 18.98/19.20 Clause #349 (by superposition #[348, 244]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.98/19.20 Or (Eq (on_path (skS.0 10 a a_1 a_2 a_3) (skS.0 11 a a_1 a_2 a_3 a_4)) True) (Eq False True) % 18.98/19.20 Clause #350 (by clausification #[349]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (on_path (skS.0 10 a a_1 a_2 a_3) (skS.0 11 a a_1 a_2 a_3 a_4)) True % 18.98/19.20 Clause #351 (by superposition #[350, 298]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq True False) (Eq (edge (skS.0 10 a a_1 a_2 a_3)) True) % 18.98/19.20 Clause #355 (by clausification #[351]): ∀ (a a_1 a_2 a_3 : Iota), Eq (edge (skS.0 10 a a_1 a_2 a_3)) True % 18.98/19.20 Clause #356 (by superposition #[355, 37]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq True False) (Ne (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 10 a a_1 a_2 a_3))) % 18.98/19.20 Clause #363 (by clausification #[356]): ∀ (a a_1 a_2 a_3 : Iota), Ne (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 10 a a_1 a_2 a_3)) % 18.98/19.20 Clause #365 (by clausification #[254]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 18.98/19.20 Or (Eq (precedes a a_1 (skS.0 11 a_2 a_3 a_4 a_5 a_6)) False) % 18.98/19.20 (Eq (precedes a_1 a (skS.0 11 a_2 a_3 a_4 a_5 a_6)) False) % 18.98/19.20 Clause #366 (by superposition #[365, 244]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.98/19.20 Or (Eq (precedes (skS.0 10 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2) (skS.0 11 a a_1 a_2 a_3 a_4)) False) (Eq False True) % 18.98/19.20 Clause #378 (by clausification #[366]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.98/19.20 Eq (precedes (skS.0 10 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2) (skS.0 11 a a_1 a_2 a_3 a_4)) False % 18.98/19.20 Clause #430 (by clausification #[278]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 18.98/19.20 Or (Eq (precedes a a_1 (skS.0 11 a_2 a_3 a_4 a_5 a_6)) True) % 18.98/19.20 (Or (Eq (on_path a (skS.0 11 a_2 a_3 a_4 a_5 a_6)) False) % 18.98/19.20 (Or (Eq (on_path a_1 (skS.0 11 a_2 a_3 a_4 a_5 a_6)) False) (Eq (sequential a a_1) False))) % 18.98/19.20 Clause #432 (by superposition #[430, 350]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 18.98/19.20 Or (Eq (precedes (skS.0 10 a a_1 a_2 a_3) a_4 (skS.0 11 a a_1 a_2 a_3 a_5)) True) % 18.98/19.20 (Or (Eq (on_path a_4 (skS.0 11 a a_1 a_2 a_3 a_5)) False) % 18.98/19.20 (Or (Eq (sequential (skS.0 10 a a_1 a_2 a_3) a_4) False) (Eq False True))) % 18.98/19.20 Clause #572 (by clausification #[432]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 18.98/19.20 Or (Eq (precedes (skS.0 10 a a_1 a_2 a_3) a_4 (skS.0 11 a a_1 a_2 a_3 a_5)) True) % 18.98/19.20 (Or (Eq (on_path a_4 (skS.0 11 a a_1 a_2 a_3 a_5)) False) (Eq (sequential (skS.0 10 a a_1 a_2 a_3) a_4) False)) % 18.98/19.22 Clause #573 (by superposition #[572, 324]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.98/19.22 Or (Eq (precedes (skS.0 10 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2) (skS.0 11 a a_1 a_2 a_3 a_4)) True) % 18.98/19.22 (Or (Eq (sequential (skS.0 10 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2)) False) (Eq False True)) % 18.98/19.22 Clause #630 (by clausification #[341]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.98/19.22 Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (head_of (skS.0 9 a a_1 a_2))) % 18.98/19.22 (Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2))) % 18.98/19.22 (Eq (tail_of (skS.0 13 a a_1 a_2 a_3 a_4)) (tail_of (skS.0 9 a a_1 a_2)))) % 18.98/19.22 Clause #631 (by forward contextual literal cutting #[630, 266]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.98/19.22 Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2))) % 18.98/19.22 (Eq (tail_of (skS.0 13 a a_1 a_2 a_3 a_4)) (tail_of (skS.0 9 a a_1 a_2))) % 18.98/19.22 Clause #635 (by superposition #[631, 265]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota), % 18.98/19.22 Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2))) % 18.98/19.22 (Or (Ne (tail_of (skS.0 9 a a_1 a_2)) (tail_of (skS.0 9 a_4 a_5 a_6))) % 18.98/19.22 (Ne (head_of (skS.0 13 a a_1 a_2 a_3 a_7)) (head_of (skS.0 10 a_4 a_5 a_6 a_8)))) % 18.98/19.22 Clause #782 (by clausification #[573]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.98/19.22 Or (Eq (precedes (skS.0 10 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2) (skS.0 11 a a_1 a_2 a_3 a_4)) True) % 18.98/19.22 (Eq (sequential (skS.0 10 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2)) False) % 18.98/19.22 Clause #1020 (by equality resolution #[635]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 18.98/19.22 Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2))) % 18.98/19.22 (Ne (head_of (skS.0 13 a a_1 a_2 a_3 a_4)) (head_of (skS.0 10 a a_1 a_2 a_5))) % 18.98/19.22 Clause #1022 (by backward contextual literal cutting #[1020, 343]): ∀ (a a_1 a_2 a_3 : Iota), Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2)) % 18.98/19.22 Clause #1024 (by backward demodulation #[1022, 363]): ∀ (a a_1 a_2 a_3 : Iota), Ne (tail_of (skS.0 9 a a_1 a_2)) (tail_of (skS.0 10 a a_1 a_2 a_3)) % 18.98/19.22 Clause #1042 (by superposition #[1022, 153]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.98/19.22 Or (Eq (sequential (skS.0 10 a a_1 a_2 a_3) a_4) True) % 18.98/19.22 (Or (Ne (tail_of (skS.0 9 a a_1 a_2)) (tail_of a_4)) % 18.98/19.22 (Or (Eq (edge (skS.0 10 a a_1 a_2 a_3)) False) (Or (Eq (edge a_4) False) (Eq (skS.0 10 a a_1 a_2 a_3) a_4)))) % 18.98/19.22 Clause #1125 (by forward demodulation #[1042, 355]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.98/19.22 Or (Eq (sequential (skS.0 10 a a_1 a_2 a_3) a_4) True) % 18.98/19.22 (Or (Ne (tail_of (skS.0 9 a a_1 a_2)) (tail_of a_4)) % 18.98/19.22 (Or (Eq True False) (Or (Eq (edge a_4) False) (Eq (skS.0 10 a a_1 a_2 a_3) a_4)))) % 18.98/19.22 Clause #1126 (by clausification #[1125]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.98/19.22 Or (Eq (sequential (skS.0 10 a a_1 a_2 a_3) a_4) True) % 18.98/19.22 (Or (Ne (tail_of (skS.0 9 a a_1 a_2)) (tail_of a_4)) (Or (Eq (edge a_4) False) (Eq (skS.0 10 a a_1 a_2 a_3) a_4))) % 18.98/19.22 Clause #1127 (by equality resolution #[1126]): ∀ (a a_1 a_2 a_3 : Iota), % 18.98/19.22 Or (Eq (sequential (skS.0 10 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2)) True) % 18.98/19.22 (Or (Eq (edge (skS.0 9 a a_1 a_2)) False) (Eq (skS.0 10 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2))) % 18.98/19.22 Clause #1132 (by forward demodulation #[1127, 327]): ∀ (a a_1 a_2 a_3 : Iota), % 18.98/19.22 Or (Eq (sequential (skS.0 10 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2)) True) % 18.98/19.22 (Or (Eq True False) (Eq (skS.0 10 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2))) % 18.98/19.22 Clause #1133 (by clausification #[1132]): ∀ (a a_1 a_2 a_3 : Iota), % 18.98/19.22 Or (Eq (sequential (skS.0 10 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2)) True) % 18.98/19.22 (Eq (skS.0 10 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2)) % 18.98/19.22 Clause #1134 (by superposition #[1133, 782]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.98/19.22 Or (Eq (skS.0 10 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2)) % 18.98/19.22 (Or (Eq (precedes (skS.0 10 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2) (skS.0 11 a a_1 a_2 a_3 a_4)) True) (Eq True False)) % 18.98/19.22 Clause #1149 (by clausification #[1134]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 18.98/19.22 Or (Eq (skS.0 10 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2)) % 18.98/19.22 (Eq (precedes (skS.0 10 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2) (skS.0 11 a a_1 a_2 a_3 a_4)) True) % 18.98/19.22 Clause #1150 (by superposition #[1149, 378]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (skS.0 10 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2)) (Eq True False) % 19.06/19.23 Clause #1158 (by clausification #[1150]): ∀ (a a_1 a_2 a_3 : Iota), Eq (skS.0 10 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2) % 19.06/19.23 Clause #1202 (by backward positive simplify reflect #[1158, 1024]): False % 19.06/19.23 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------