%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : GRA003+1 : TPTP v9.2.0. Bugfixed v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n003.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 5.91s 6.12s % Output : Proof 6.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GRA003+1 : TPTP v9.2.0. Bugfixed v3.2.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n003.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 : Thu Oct 2 16:14:38 EDT 2025 % 0.13/0.34 % CPUTime : % 5.91/6.12 SZS status Theorem for theBenchmark.p % 5.91/6.12 SZS output start Proof for theBenchmark.p % 5.91/6.12 Clause #4 (by assumption #[]): Eq % 5.91/6.12 (∀ (V1 V2 P : Iota), % 5.91/6.12 path V1 V2 P → % 5.91/6.12 And (And (vertex V1) (vertex V2)) % 5.91/6.12 (Exists fun E => % 5.91/6.12 And (And (edge E) (Eq V1 (tail_of E))) % 5.91/6.12 (Not % 5.91/6.12 (Iff (And (Eq V2 (head_of E)) (Eq P (path_cons E empty))) % 5.91/6.12 (Exists fun TP => And (path (head_of E) V2 TP) (Eq P (path_cons E TP))))))) % 5.91/6.12 True % 5.91/6.12 Clause #5 (by assumption #[]): Eq % 5.91/6.12 (∀ (V1 V2 P E : Iota), % 5.91/6.12 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)) % 5.91/6.12 True % 5.91/6.12 Clause #9 (by assumption #[]): Eq % 5.91/6.12 (∀ (P V1 V2 : Iota), % 5.91/6.12 path V1 V2 P → % 5.91/6.12 ∀ (E1 E2 : Iota), % 5.91/6.12 precedes E1 E2 P → % 5.91/6.12 And (And (on_path E1 P) (on_path E2 P)) % 5.91/6.12 (Not (Iff (sequential E1 E2) (Exists fun E3 => And (sequential E1 E3) (precedes E3 E2 P))))) % 5.91/6.12 True % 5.91/6.12 Clause #10 (by assumption #[]): Eq % 5.91/6.12 (∀ (V1 V2 SP : Iota), % 5.91/6.12 Iff (shortest_path V1 V2 SP) % 5.91/6.12 (And (And (path V1 V2 SP) (Ne V1 V2)) (∀ (P : Iota), path V1 V2 P → less_or_equal (length_of SP) (length_of P)))) % 5.91/6.12 True % 5.91/6.12 Clause #11 (by assumption #[]): Eq % 5.91/6.12 (∀ (V1 V2 E1 E2 P : Iota), % 5.91/6.12 And (shortest_path V1 V2 P) (precedes E1 E2 P) → % 5.91/6.12 And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of E1)) (Eq (head_of E3) (head_of E2)))) % 5.91/6.12 (Not (precedes E2 E1 P))) % 5.91/6.12 True % 5.91/6.12 Clause #17 (by assumption #[]): Eq % 5.91/6.12 (Not % 5.91/6.12 (∀ (V1 V2 E1 E2 P : Iota), % 5.91/6.12 And (shortest_path V1 V2 P) (precedes E1 E2 P) → % 5.91/6.12 And (And (And (And (And (And (vertex V1) (vertex V2)) (Ne V1 V2)) (edge E1)) (edge E2)) (Ne E1 E2)) % 5.91/6.12 (path V1 V2 P))) % 5.91/6.12 True % 5.91/6.12 Clause #101 (by clausification #[5]): ∀ (a : Iota), % 5.91/6.12 Eq % 5.91/6.12 (∀ (V2 P E : Iota), % 5.91/6.12 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)) % 5.91/6.12 True % 5.91/6.12 Clause #102 (by clausification #[101]): ∀ (a a_1 : Iota), % 5.91/6.12 Eq % 5.91/6.12 (∀ (P E : Iota), % 5.91/6.12 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)) % 5.91/6.12 True % 5.91/6.12 Clause #103 (by clausification #[102]): ∀ (a a_1 a_2 : Iota), % 5.91/6.12 Eq % 5.91/6.12 (∀ (E : Iota), % 5.91/6.12 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)) % 5.91/6.12 True % 5.91/6.12 Clause #104 (by clausification #[103]): ∀ (a a_1 a_2 a_3 : Iota), % 5.91/6.12 Eq % 5.91/6.12 (And (path a a_1 a_2) (on_path a_3 a_2) → % 5.91/6.12 And (And (edge a_3) (in_path (head_of a_3) a_2)) (in_path (tail_of a_3) a_2)) % 5.91/6.12 True % 5.91/6.12 Clause #105 (by clausification #[104]): ∀ (a a_1 a_2 a_3 : Iota), % 5.91/6.12 Or (Eq (And (path a a_1 a_2) (on_path a_3 a_2)) False) % 5.91/6.12 (Eq (And (And (edge a_3) (in_path (head_of a_3) a_2)) (in_path (tail_of a_3) a_2)) True) % 5.91/6.12 Clause #106 (by clausification #[105]): ∀ (a a_1 a_2 a_3 : Iota), % 5.91/6.12 Or (Eq (And (And (edge a) (in_path (head_of a) a_1)) (in_path (tail_of a) a_1)) True) % 5.91/6.12 (Or (Eq (path a_2 a_3 a_1) False) (Eq (on_path a a_1) False)) % 5.91/6.12 Clause #108 (by clausification #[106]): ∀ (a a_1 a_2 a_3 : Iota), % 5.91/6.12 Or (Eq (path a a_1 a_2) False) % 5.91/6.12 (Or (Eq (on_path a_3 a_2) False) (Eq (And (edge a_3) (in_path (head_of a_3) a_2)) True)) % 5.91/6.12 Clause #109 (by clausification #[4]): ∀ (a : Iota), % 5.91/6.12 Eq % 5.91/6.12 (∀ (V2 P : Iota), % 5.91/6.12 path a V2 P → % 5.91/6.12 And (And (vertex a) (vertex V2)) % 5.91/6.12 (Exists fun E => % 5.91/6.12 And (And (edge E) (Eq a (tail_of E))) % 5.91/6.12 (Not % 5.91/6.12 (Iff (And (Eq V2 (head_of E)) (Eq P (path_cons E empty))) % 5.91/6.12 (Exists fun TP => And (path (head_of E) V2 TP) (Eq P (path_cons E TP))))))) % 5.91/6.12 True % 5.91/6.12 Clause #110 (by clausification #[109]): ∀ (a a_1 : Iota), % 5.91/6.12 Eq % 5.91/6.12 (∀ (P : Iota), % 5.91/6.12 path a a_1 P → % 5.91/6.12 And (And (vertex a) (vertex a_1)) % 5.91/6.12 (Exists fun E => % 5.91/6.12 And (And (edge E) (Eq a (tail_of E))) % 5.91/6.12 (Not % 5.91/6.12 (Iff (And (Eq a_1 (head_of E)) (Eq P (path_cons E empty))) % 5.91/6.12 (Exists fun TP => And (path (head_of E) a_1 TP) (Eq P (path_cons E TP))))))) % 5.91/6.12 True % 5.91/6.12 Clause #111 (by clausification #[110]): ∀ (a a_1 a_2 : Iota), % 5.91/6.12 Eq % 5.91/6.12 (path a a_1 a_2 → % 5.91/6.14 And (And (vertex a) (vertex a_1)) % 5.91/6.14 (Exists fun E => % 5.91/6.14 And (And (edge E) (Eq a (tail_of E))) % 5.91/6.14 (Not % 5.91/6.14 (Iff (And (Eq a_1 (head_of E)) (Eq a_2 (path_cons E empty))) % 5.91/6.14 (Exists fun TP => And (path (head_of E) a_1 TP) (Eq a_2 (path_cons E TP))))))) % 5.91/6.14 True % 5.91/6.14 Clause #112 (by clausification #[111]): ∀ (a a_1 a_2 : Iota), % 5.91/6.14 Or (Eq (path a a_1 a_2) False) % 5.91/6.14 (Eq % 5.91/6.14 (And (And (vertex a) (vertex a_1)) % 5.91/6.14 (Exists fun E => % 5.91/6.14 And (And (edge E) (Eq a (tail_of E))) % 5.91/6.14 (Not % 5.91/6.14 (Iff (And (Eq a_1 (head_of E)) (Eq a_2 (path_cons E empty))) % 5.91/6.14 (Exists fun TP => And (path (head_of E) a_1 TP) (Eq a_2 (path_cons E TP))))))) % 5.91/6.14 True) % 5.91/6.14 Clause #114 (by clausification #[112]): ∀ (a a_1 a_2 : Iota), Or (Eq (path a a_1 a_2) False) (Eq (And (vertex a) (vertex a_1)) True) % 5.91/6.14 Clause #127 (by clausification #[114]): ∀ (a a_1 a_2 : Iota), Or (Eq (path a a_1 a_2) False) (Eq (vertex a_1) True) % 5.91/6.14 Clause #128 (by clausification #[114]): ∀ (a a_1 a_2 : Iota), Or (Eq (path a a_1 a_2) False) (Eq (vertex a) True) % 5.91/6.14 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)) % 5.91/6.14 Clause #157 (by clausification #[9]): ∀ (a : Iota), % 5.91/6.14 Eq % 5.91/6.14 (∀ (V1 V2 : Iota), % 5.91/6.14 path V1 V2 a → % 5.91/6.14 ∀ (E1 E2 : Iota), % 5.91/6.14 precedes E1 E2 a → % 5.91/6.14 And (And (on_path E1 a) (on_path E2 a)) % 5.91/6.14 (Not (Iff (sequential E1 E2) (Exists fun E3 => And (sequential E1 E3) (precedes E3 E2 a))))) % 5.91/6.14 True % 5.91/6.14 Clause #158 (by clausification #[157]): ∀ (a a_1 : Iota), % 5.91/6.14 Eq % 5.91/6.14 (∀ (V2 : Iota), % 5.91/6.14 path a V2 a_1 → % 5.91/6.14 ∀ (E1 E2 : Iota), % 5.91/6.14 precedes E1 E2 a_1 → % 5.91/6.14 And (And (on_path E1 a_1) (on_path E2 a_1)) % 5.91/6.14 (Not (Iff (sequential E1 E2) (Exists fun E3 => And (sequential E1 E3) (precedes E3 E2 a_1))))) % 5.91/6.14 True % 5.91/6.14 Clause #159 (by clausification #[158]): ∀ (a a_1 a_2 : Iota), % 5.91/6.14 Eq % 5.91/6.14 (path a a_1 a_2 → % 5.91/6.14 ∀ (E1 E2 : Iota), % 5.91/6.14 precedes E1 E2 a_2 → % 5.91/6.14 And (And (on_path E1 a_2) (on_path E2 a_2)) % 5.91/6.14 (Not (Iff (sequential E1 E2) (Exists fun E3 => And (sequential E1 E3) (precedes E3 E2 a_2))))) % 5.91/6.14 True % 5.91/6.14 Clause #160 (by clausification #[159]): ∀ (a a_1 a_2 : Iota), % 5.91/6.14 Or (Eq (path a a_1 a_2) False) % 5.91/6.14 (Eq % 5.91/6.14 (∀ (E1 E2 : Iota), % 5.91/6.14 precedes E1 E2 a_2 → % 5.91/6.14 And (And (on_path E1 a_2) (on_path E2 a_2)) % 5.91/6.14 (Not (Iff (sequential E1 E2) (Exists fun E3 => And (sequential E1 E3) (precedes E3 E2 a_2))))) % 5.91/6.14 True) % 5.91/6.14 Clause #161 (by clausification #[160]): ∀ (a a_1 a_2 a_3 : Iota), % 5.91/6.14 Or (Eq (path a a_1 a_2) False) % 5.91/6.14 (Eq % 5.91/6.14 (∀ (E2 : Iota), % 5.91/6.14 precedes a_3 E2 a_2 → % 5.91/6.14 And (And (on_path a_3 a_2) (on_path E2 a_2)) % 5.91/6.14 (Not (Iff (sequential a_3 E2) (Exists fun E3 => And (sequential a_3 E3) (precedes E3 E2 a_2))))) % 5.91/6.14 True) % 5.91/6.14 Clause #162 (by clausification #[161]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.91/6.14 Or (Eq (path a a_1 a_2) False) % 5.91/6.14 (Eq % 5.91/6.14 (precedes a_3 a_4 a_2 → % 5.91/6.14 And (And (on_path a_3 a_2) (on_path a_4 a_2)) % 5.91/6.14 (Not (Iff (sequential a_3 a_4) (Exists fun E3 => And (sequential a_3 E3) (precedes E3 a_4 a_2))))) % 5.91/6.14 True) % 5.91/6.14 Clause #163 (by clausification #[162]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.91/6.14 Or (Eq (path a a_1 a_2) False) % 5.91/6.14 (Or (Eq (precedes a_3 a_4 a_2) False) % 5.91/6.14 (Eq % 5.91/6.14 (And (And (on_path a_3 a_2) (on_path a_4 a_2)) % 5.91/6.14 (Not (Iff (sequential a_3 a_4) (Exists fun E3 => And (sequential a_3 E3) (precedes E3 a_4 a_2))))) % 5.91/6.14 True)) % 5.91/6.14 Clause #165 (by clausification #[163]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.91/6.14 Or (Eq (path a a_1 a_2) False) % 5.91/6.14 (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)) % 5.91/6.14 Clause #177 (by clausification #[165]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.91/6.14 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)) % 5.91/6.14 Clause #178 (by clausification #[165]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 5.91/6.14 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)) % 6.00/6.17 Clause #179 (by clausification #[10]): ∀ (a : Iota), % 6.00/6.17 Eq % 6.00/6.17 (∀ (V2 SP : Iota), % 6.00/6.17 Iff (shortest_path a V2 SP) % 6.00/6.17 (And (And (path a V2 SP) (Ne a V2)) (∀ (P : Iota), path a V2 P → less_or_equal (length_of SP) (length_of P)))) % 6.00/6.17 True % 6.00/6.17 Clause #180 (by clausification #[179]): ∀ (a a_1 : Iota), % 6.00/6.17 Eq % 6.00/6.17 (∀ (SP : Iota), % 6.00/6.17 Iff (shortest_path a a_1 SP) % 6.00/6.17 (And (And (path a a_1 SP) (Ne a a_1)) % 6.00/6.17 (∀ (P : Iota), path a a_1 P → less_or_equal (length_of SP) (length_of P)))) % 6.00/6.17 True % 6.00/6.17 Clause #181 (by clausification #[180]): ∀ (a a_1 a_2 : Iota), % 6.00/6.17 Eq % 6.00/6.17 (Iff (shortest_path a a_1 a_2) % 6.00/6.17 (And (And (path a a_1 a_2) (Ne a a_1)) % 6.00/6.17 (∀ (P : Iota), path a a_1 P → less_or_equal (length_of a_2) (length_of P)))) % 6.00/6.17 True % 6.00/6.17 Clause #183 (by clausification #[181]): ∀ (a a_1 a_2 : Iota), % 6.00/6.17 Or (Eq (shortest_path a a_1 a_2) False) % 6.00/6.17 (Eq % 6.00/6.17 (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))) % 6.00/6.17 True) % 6.00/6.17 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) % 6.00/6.17 Clause #195 (by clausification #[192]): ∀ (a a_1 a_2 : Iota), Or (Eq (shortest_path a a_1 a_2) False) (Eq (Ne a a_1) True) % 6.00/6.17 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) % 6.00/6.17 Clause #197 (by clausification #[195]): ∀ (a a_1 a_2 : Iota), Or (Eq (shortest_path a a_1 a_2) False) (Ne a a_1) % 6.00/6.17 Clause #198 (by destructive equality resolution #[197]): ∀ (a a_1 : Iota), Eq (shortest_path a a a_1) False % 6.00/6.17 Clause #202 (by clausification #[11]): ∀ (a : Iota), % 6.00/6.17 Eq % 6.00/6.17 (∀ (V2 E1 E2 P : Iota), % 6.00/6.17 And (shortest_path a V2 P) (precedes E1 E2 P) → % 6.00/6.17 And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of E1)) (Eq (head_of E3) (head_of E2)))) % 6.00/6.17 (Not (precedes E2 E1 P))) % 6.00/6.17 True % 6.00/6.17 Clause #203 (by clausification #[202]): ∀ (a a_1 : Iota), % 6.00/6.17 Eq % 6.00/6.17 (∀ (E1 E2 P : Iota), % 6.00/6.17 And (shortest_path a a_1 P) (precedes E1 E2 P) → % 6.00/6.17 And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of E1)) (Eq (head_of E3) (head_of E2)))) % 6.00/6.17 (Not (precedes E2 E1 P))) % 6.00/6.17 True % 6.00/6.17 Clause #204 (by clausification #[203]): ∀ (a a_1 a_2 : Iota), % 6.00/6.17 Eq % 6.00/6.17 (∀ (E2 P : Iota), % 6.00/6.17 And (shortest_path a a_1 P) (precedes a_2 E2 P) → % 6.00/6.17 And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of a_2)) (Eq (head_of E3) (head_of E2)))) % 6.00/6.17 (Not (precedes E2 a_2 P))) % 6.00/6.17 True % 6.00/6.17 Clause #205 (by clausification #[204]): ∀ (a a_1 a_2 a_3 : Iota), % 6.00/6.17 Eq % 6.00/6.17 (∀ (P : Iota), % 6.00/6.17 And (shortest_path a a_1 P) (precedes a_2 a_3 P) → % 6.00/6.17 And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of a_2)) (Eq (head_of E3) (head_of a_3)))) % 6.00/6.17 (Not (precedes a_3 a_2 P))) % 6.00/6.17 True % 6.00/6.17 Clause #206 (by clausification #[205]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.00/6.17 Eq % 6.00/6.17 (And (shortest_path a a_1 a_2) (precedes a_3 a_4 a_2) → % 6.00/6.17 And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of a_3)) (Eq (head_of E3) (head_of a_4)))) % 6.00/6.17 (Not (precedes a_4 a_3 a_2))) % 6.00/6.17 True % 6.00/6.17 Clause #207 (by clausification #[206]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.00/6.17 Or (Eq (And (shortest_path a a_1 a_2) (precedes a_3 a_4 a_2)) False) % 6.00/6.17 (Eq % 6.00/6.17 (And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of a_3)) (Eq (head_of E3) (head_of a_4)))) % 6.00/6.17 (Not (precedes a_4 a_3 a_2))) % 6.00/6.17 True) % 6.00/6.17 Clause #208 (by clausification #[207]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.00/6.17 Or % 6.00/6.17 (Eq % 6.00/6.17 (And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of a)) (Eq (head_of E3) (head_of a_1)))) % 6.00/6.17 (Not (precedes a_1 a a_2))) % 6.00/6.17 True) % 6.00/6.17 (Or (Eq (shortest_path a_3 a_4 a_2) False) (Eq (precedes a a_1 a_2) False)) % 6.00/6.17 Clause #210 (by clausification #[208]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.00/6.17 Or (Eq (shortest_path a a_1 a_2) False) % 6.00/6.17 (Or (Eq (precedes a_3 a_4 a_2) False) % 6.00/6.17 (Eq (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of a_3)) (Eq (head_of E3) (head_of a_4)))) True)) % 6.00/6.17 Clause #212 (by clausification #[210]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.00/6.20 Or (Eq (shortest_path a a_1 a_2) False) % 6.00/6.20 (Or (Eq (precedes a_3 a_4 a_2) False) % 6.00/6.20 (Eq (Exists fun E3 => And (Eq (tail_of E3) (tail_of a_3)) (Eq (head_of E3) (head_of a_4))) False)) % 6.00/6.20 Clause #213 (by clausification #[212]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 6.00/6.20 Or (Eq (shortest_path a a_1 a_2) False) % 6.00/6.20 (Or (Eq (precedes a_3 a_4 a_2) False) % 6.00/6.20 (Eq (And (Eq (tail_of a_5) (tail_of a_3)) (Eq (head_of a_5) (head_of a_4))) False)) % 6.00/6.20 Clause #214 (by clausification #[213]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 6.00/6.20 Or (Eq (shortest_path a a_1 a_2) False) % 6.00/6.20 (Or (Eq (precedes a_3 a_4 a_2) False) % 6.00/6.20 (Or (Eq (Eq (tail_of a_5) (tail_of a_3)) False) (Eq (Eq (head_of a_5) (head_of a_4)) False))) % 6.00/6.20 Clause #215 (by clausification #[214]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 6.00/6.20 Or (Eq (shortest_path a a_1 a_2) False) % 6.00/6.20 (Or (Eq (precedes a_3 a_4 a_2) False) % 6.00/6.20 (Or (Eq (Eq (head_of a_5) (head_of a_4)) False) (Ne (tail_of a_5) (tail_of a_3)))) % 6.00/6.20 Clause #216 (by clausification #[215]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 6.00/6.20 Or (Eq (shortest_path a a_1 a_2) False) % 6.00/6.20 (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)))) % 6.00/6.20 Clause #231 (by clausification #[17]): Eq % 6.00/6.20 (∀ (V1 V2 E1 E2 P : Iota), % 6.00/6.20 And (shortest_path V1 V2 P) (precedes E1 E2 P) → % 6.00/6.20 And (And (And (And (And (And (vertex V1) (vertex V2)) (Ne V1 V2)) (edge E1)) (edge E2)) (Ne E1 E2)) % 6.00/6.20 (path V1 V2 P)) % 6.00/6.20 False % 6.00/6.20 Clause #232 (by clausification #[231]): ∀ (a : Iota), % 6.00/6.20 Eq % 6.00/6.20 (Not % 6.00/6.20 (∀ (V2 E1 E2 P : Iota), % 6.00/6.20 And (shortest_path (skS.0 7 a) V2 P) (precedes E1 E2 P) → % 6.00/6.20 And % 6.00/6.20 (And (And (And (And (And (vertex (skS.0 7 a)) (vertex V2)) (Ne (skS.0 7 a) V2)) (edge E1)) (edge E2)) % 6.00/6.20 (Ne E1 E2)) % 6.00/6.20 (path (skS.0 7 a) V2 P))) % 6.00/6.20 True % 6.00/6.20 Clause #233 (by clausification #[232]): ∀ (a : Iota), % 6.00/6.20 Eq % 6.00/6.20 (∀ (V2 E1 E2 P : Iota), % 6.00/6.20 And (shortest_path (skS.0 7 a) V2 P) (precedes E1 E2 P) → % 6.00/6.20 And % 6.00/6.20 (And (And (And (And (And (vertex (skS.0 7 a)) (vertex V2)) (Ne (skS.0 7 a) V2)) (edge E1)) (edge E2)) % 6.00/6.20 (Ne E1 E2)) % 6.00/6.20 (path (skS.0 7 a) V2 P)) % 6.00/6.20 False % 6.00/6.20 Clause #234 (by clausification #[233]): ∀ (a a_1 : Iota), % 6.00/6.20 Eq % 6.00/6.20 (Not % 6.00/6.20 (∀ (E1 E2 P : Iota), % 6.00/6.20 And (shortest_path (skS.0 7 a) (skS.0 8 a a_1) P) (precedes E1 E2 P) → % 6.00/6.20 And % 6.00/6.20 (And % 6.00/6.20 (And % 6.00/6.20 (And (And (And (vertex (skS.0 7 a)) (vertex (skS.0 8 a a_1))) (Ne (skS.0 7 a) (skS.0 8 a a_1))) % 6.00/6.20 (edge E1)) % 6.00/6.20 (edge E2)) % 6.00/6.20 (Ne E1 E2)) % 6.00/6.20 (path (skS.0 7 a) (skS.0 8 a a_1) P))) % 6.00/6.20 True % 6.00/6.20 Clause #235 (by clausification #[234]): ∀ (a a_1 : Iota), % 6.00/6.20 Eq % 6.00/6.20 (∀ (E1 E2 P : Iota), % 6.00/6.20 And (shortest_path (skS.0 7 a) (skS.0 8 a a_1) P) (precedes E1 E2 P) → % 6.00/6.20 And % 6.00/6.20 (And % 6.00/6.20 (And % 6.00/6.20 (And (And (And (vertex (skS.0 7 a)) (vertex (skS.0 8 a a_1))) (Ne (skS.0 7 a) (skS.0 8 a a_1))) (edge E1)) % 6.00/6.20 (edge E2)) % 6.00/6.20 (Ne E1 E2)) % 6.00/6.20 (path (skS.0 7 a) (skS.0 8 a a_1) P)) % 6.00/6.20 False % 6.00/6.20 Clause #236 (by clausification #[235]): ∀ (a a_1 a_2 : Iota), % 6.00/6.20 Eq % 6.00/6.20 (Not % 6.00/6.20 (∀ (E2 P : Iota), % 6.00/6.20 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) → % 6.00/6.20 And % 6.00/6.20 (And % 6.00/6.20 (And % 6.00/6.20 (And (And (And (vertex (skS.0 7 a)) (vertex (skS.0 8 a a_1))) (Ne (skS.0 7 a) (skS.0 8 a a_1))) % 6.00/6.20 (edge (skS.0 9 a a_1 a_2))) % 6.00/6.20 (edge E2)) % 6.00/6.20 (Ne (skS.0 9 a a_1 a_2) E2)) % 6.00/6.20 (path (skS.0 7 a) (skS.0 8 a a_1) P))) % 6.00/6.20 True % 6.00/6.20 Clause #237 (by clausification #[236]): ∀ (a a_1 a_2 : Iota), % 6.00/6.20 Eq % 6.00/6.20 (∀ (E2 P : Iota), % 6.00/6.20 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) → % 6.00/6.20 And % 6.00/6.20 (And % 6.00/6.20 (And % 6.00/6.20 (And (And (And (vertex (skS.0 7 a)) (vertex (skS.0 8 a a_1))) (Ne (skS.0 7 a) (skS.0 8 a a_1))) % 6.00/6.20 (edge (skS.0 9 a a_1 a_2))) % 6.00/6.20 (edge E2)) % 6.00/6.20 (Ne (skS.0 9 a a_1 a_2) E2)) % 6.05/6.23 (path (skS.0 7 a) (skS.0 8 a a_1) P)) % 6.05/6.23 False % 6.05/6.23 Clause #238 (by clausification #[237]): ∀ (a a_1 a_2 a_3 : Iota), % 6.05/6.23 Eq % 6.05/6.23 (Not % 6.05/6.23 (∀ (P : Iota), % 6.05/6.23 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) → % 6.05/6.23 And % 6.05/6.23 (And % 6.05/6.23 (And % 6.05/6.23 (And (And (And (vertex (skS.0 7 a)) (vertex (skS.0 8 a a_1))) (Ne (skS.0 7 a) (skS.0 8 a a_1))) % 6.05/6.23 (edge (skS.0 9 a a_1 a_2))) % 6.05/6.23 (edge (skS.0 10 a a_1 a_2 a_3))) % 6.05/6.23 (Ne (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3))) % 6.05/6.23 (path (skS.0 7 a) (skS.0 8 a a_1) P))) % 6.05/6.23 True % 6.05/6.23 Clause #239 (by clausification #[238]): ∀ (a a_1 a_2 a_3 : Iota), % 6.05/6.23 Eq % 6.05/6.23 (∀ (P : Iota), % 6.05/6.23 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) → % 6.05/6.23 And % 6.05/6.23 (And % 6.05/6.23 (And % 6.05/6.23 (And (And (And (vertex (skS.0 7 a)) (vertex (skS.0 8 a a_1))) (Ne (skS.0 7 a) (skS.0 8 a a_1))) % 6.05/6.23 (edge (skS.0 9 a a_1 a_2))) % 6.05/6.23 (edge (skS.0 10 a a_1 a_2 a_3))) % 6.05/6.23 (Ne (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3))) % 6.05/6.23 (path (skS.0 7 a) (skS.0 8 a a_1) P)) % 6.05/6.23 False % 6.05/6.23 Clause #240 (by clausification #[239]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.05/6.23 Eq % 6.05/6.23 (Not % 6.05/6.23 (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)) % 6.05/6.23 (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)) → % 6.05/6.23 And % 6.05/6.23 (And % 6.05/6.23 (And % 6.05/6.23 (And (And (And (vertex (skS.0 7 a)) (vertex (skS.0 8 a a_1))) (Ne (skS.0 7 a) (skS.0 8 a a_1))) % 6.05/6.23 (edge (skS.0 9 a a_1 a_2))) % 6.05/6.23 (edge (skS.0 10 a a_1 a_2 a_3))) % 6.05/6.23 (Ne (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3))) % 6.05/6.23 (path (skS.0 7 a) (skS.0 8 a a_1) (skS.0 11 a a_1 a_2 a_3 a_4)))) % 6.05/6.23 True % 6.05/6.23 Clause #241 (by clausification #[240]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.05/6.23 Eq % 6.05/6.23 (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)) % 6.05/6.23 (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)) → % 6.05/6.23 And % 6.05/6.23 (And % 6.05/6.23 (And % 6.05/6.23 (And (And (And (vertex (skS.0 7 a)) (vertex (skS.0 8 a a_1))) (Ne (skS.0 7 a) (skS.0 8 a a_1))) % 6.05/6.23 (edge (skS.0 9 a a_1 a_2))) % 6.05/6.23 (edge (skS.0 10 a a_1 a_2 a_3))) % 6.05/6.23 (Ne (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3))) % 6.05/6.23 (path (skS.0 7 a) (skS.0 8 a a_1) (skS.0 11 a a_1 a_2 a_3 a_4))) % 6.05/6.23 False % 6.05/6.23 Clause #242 (by clausification #[241]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.05/6.23 Eq % 6.05/6.23 (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)) % 6.05/6.23 (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))) % 6.05/6.23 True % 6.05/6.23 Clause #243 (by clausification #[241]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.05/6.23 Eq % 6.05/6.23 (And % 6.05/6.23 (And % 6.05/6.23 (And % 6.05/6.23 (And (And (And (vertex (skS.0 7 a)) (vertex (skS.0 8 a a_1))) (Ne (skS.0 7 a) (skS.0 8 a a_1))) % 6.05/6.23 (edge (skS.0 9 a a_1 a_2))) % 6.05/6.23 (edge (skS.0 10 a a_1 a_2 a_3))) % 6.05/6.23 (Ne (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3))) % 6.05/6.23 (path (skS.0 7 a) (skS.0 8 a a_1) (skS.0 11 a a_1 a_2 a_3 a_4))) % 6.05/6.23 False % 6.05/6.23 Clause #244 (by clausification #[242]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.05/6.23 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 % 6.05/6.23 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 % 6.05/6.23 Clause #253 (by superposition #[245, 196]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.05/6.23 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) % 6.05/6.23 Clause #255 (by superposition #[245, 216]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 6.05/6.23 Or (Eq True False) % 6.05/6.23 (Or (Eq (precedes a a_1 (skS.0 11 a_2 a_3 a_4 a_5 a_6)) False) % 6.05/6.23 (Or (Ne (tail_of a_7) (tail_of a)) (Ne (head_of a_7) (head_of a_1)))) % 6.05/6.23 Clause #263 (by clausification #[255]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota), % 6.10/6.25 Or (Eq (precedes a a_1 (skS.0 11 a_2 a_3 a_4 a_5 a_6)) False) % 6.10/6.25 (Or (Ne (tail_of a_7) (tail_of a)) (Ne (head_of a_7) (head_of a_1))) % 6.10/6.25 Clause #264 (by superposition #[263, 244]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.10/6.25 Or (Ne (tail_of a) (tail_of (skS.0 9 a_1 a_2 a_3))) % 6.10/6.25 (Or (Ne (head_of a) (head_of (skS.0 10 a_1 a_2 a_3 a_4))) (Eq False True)) % 6.10/6.25 Clause #265 (by clausification #[264]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.10/6.25 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))) % 6.10/6.25 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)) % 6.10/6.25 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 % 6.10/6.25 Clause #274 (by superposition #[267, 127]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (vertex (skS.0 8 a a_1)) True) % 6.10/6.25 Clause #275 (by superposition #[267, 128]): ∀ (a : Iota), Or (Eq True False) (Eq (vertex (skS.0 7 a)) True) % 6.10/6.25 Clause #277 (by superposition #[267, 130]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), % 6.10/6.25 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)) % 6.10/6.25 Clause #283 (by superposition #[267, 177]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 6.10/6.25 Or (Eq True False) % 6.10/6.25 (Or (Eq (precedes a a_1 (skS.0 11 a_2 a_3 a_4 a_5 a_6)) False) % 6.10/6.25 (Eq (on_path a_1 (skS.0 11 a_2 a_3 a_4 a_5 a_6)) True)) % 6.10/6.25 Clause #284 (by superposition #[267, 178]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 6.10/6.25 Or (Eq True False) % 6.10/6.25 (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)) % 6.10/6.25 Clause #289 (by clausification #[275]): ∀ (a : Iota), Eq (vertex (skS.0 7 a)) True % 6.10/6.25 Clause #296 (by clausification #[274]): ∀ (a a_1 : Iota), Eq (vertex (skS.0 8 a a_1)) True % 6.10/6.25 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) % 6.10/6.25 Clause #321 (by clausification #[284]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 6.10/6.25 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) % 6.10/6.25 Clause #322 (by superposition #[321, 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) % 6.10/6.25 Clause #323 (by clausification #[322]): ∀ (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 % 6.10/6.25 Clause #324 (by superposition #[323, 298]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (edge (skS.0 9 a a_1 a_2)) True) % 6.10/6.25 Clause #325 (by clausification #[324]): ∀ (a a_1 a_2 : Iota), Eq (edge (skS.0 9 a a_1 a_2)) True % 6.10/6.25 Clause #333 (by clausification #[243]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.10/6.25 Or % 6.10/6.25 (Eq % 6.10/6.25 (And % 6.10/6.25 (And % 6.10/6.25 (And (And (And (vertex (skS.0 7 a)) (vertex (skS.0 8 a a_1))) (Ne (skS.0 7 a) (skS.0 8 a a_1))) % 6.10/6.25 (edge (skS.0 9 a a_1 a_2))) % 6.10/6.25 (edge (skS.0 10 a a_1 a_2 a_3))) % 6.10/6.25 (Ne (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3))) % 6.10/6.25 False) % 6.10/6.25 (Eq (path (skS.0 7 a) (skS.0 8 a a_1) (skS.0 11 a a_1 a_2 a_3 a_4)) False) % 6.10/6.25 Clause #334 (by clausification #[333]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.10/6.25 Or (Eq (path (skS.0 7 a) (skS.0 8 a a_1) (skS.0 11 a a_1 a_2 a_3 a_4)) False) % 6.10/6.25 (Or % 6.10/6.25 (Eq % 6.10/6.25 (And % 6.10/6.25 (And (And (And (vertex (skS.0 7 a)) (vertex (skS.0 8 a a_1))) (Ne (skS.0 7 a) (skS.0 8 a a_1))) % 6.10/6.25 (edge (skS.0 9 a a_1 a_2))) % 6.10/6.25 (edge (skS.0 10 a a_1 a_2 a_3))) % 6.10/6.25 False) % 6.10/6.25 (Eq (Ne (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3)) False)) % 6.10/6.25 Clause #335 (by clausification #[334]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.10/6.25 Or (Eq (path (skS.0 7 a) (skS.0 8 a a_1) (skS.0 11 a a_1 a_2 a_3 a_4)) False) % 6.10/6.25 (Or (Eq (Ne (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3)) False) % 6.10/6.25 (Or % 6.10/6.25 (Eq % 6.10/6.25 (And (And (And (vertex (skS.0 7 a)) (vertex (skS.0 8 a a_1))) (Ne (skS.0 7 a) (skS.0 8 a a_1))) % 6.10/6.25 (edge (skS.0 9 a a_1 a_2))) % 6.10/6.25 False) % 6.10/6.25 (Eq (edge (skS.0 10 a a_1 a_2 a_3)) False))) % 6.10/6.29 Clause #336 (by clausification #[335]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.10/6.29 Or (Eq (path (skS.0 7 a) (skS.0 8 a a_1) (skS.0 11 a a_1 a_2 a_3 a_4)) False) % 6.10/6.29 (Or % 6.10/6.29 (Eq % 6.10/6.29 (And (And (And (vertex (skS.0 7 a)) (vertex (skS.0 8 a a_1))) (Ne (skS.0 7 a) (skS.0 8 a a_1))) % 6.10/6.29 (edge (skS.0 9 a a_1 a_2))) % 6.10/6.29 False) % 6.10/6.29 (Or (Eq (edge (skS.0 10 a a_1 a_2 a_3)) False) (Eq (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3)))) % 6.10/6.29 Clause #337 (by clausification #[336]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.10/6.29 Or (Eq (path (skS.0 7 a) (skS.0 8 a a_1) (skS.0 11 a a_1 a_2 a_3 a_4)) False) % 6.10/6.29 (Or (Eq (edge (skS.0 10 a a_1 a_2 a_3)) False) % 6.10/6.29 (Or (Eq (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3)) % 6.10/6.29 (Or (Eq (And (And (vertex (skS.0 7 a)) (vertex (skS.0 8 a a_1))) (Ne (skS.0 7 a) (skS.0 8 a a_1))) False) % 6.10/6.29 (Eq (edge (skS.0 9 a a_1 a_2)) False)))) % 6.10/6.29 Clause #338 (by clausification #[337]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.10/6.29 Or (Eq (path (skS.0 7 a) (skS.0 8 a a_1) (skS.0 11 a a_1 a_2 a_3 a_4)) False) % 6.10/6.29 (Or (Eq (edge (skS.0 10 a a_1 a_2 a_3)) False) % 6.10/6.29 (Or (Eq (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3)) % 6.10/6.29 (Or (Eq (edge (skS.0 9 a a_1 a_2)) False) % 6.10/6.29 (Or (Eq (And (vertex (skS.0 7 a)) (vertex (skS.0 8 a a_1))) False) % 6.10/6.29 (Eq (Ne (skS.0 7 a) (skS.0 8 a a_1)) False))))) % 6.10/6.29 Clause #339 (by clausification #[338]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.10/6.29 Or (Eq (path (skS.0 7 a) (skS.0 8 a a_1) (skS.0 11 a a_1 a_2 a_3 a_4)) False) % 6.10/6.29 (Or (Eq (edge (skS.0 10 a a_1 a_2 a_3)) False) % 6.10/6.29 (Or (Eq (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3)) % 6.10/6.29 (Or (Eq (edge (skS.0 9 a a_1 a_2)) False) % 6.10/6.29 (Or (Eq (Ne (skS.0 7 a) (skS.0 8 a a_1)) False) % 6.10/6.29 (Or (Eq (vertex (skS.0 7 a)) False) (Eq (vertex (skS.0 8 a a_1)) False)))))) % 6.10/6.29 Clause #340 (by clausification #[339]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.10/6.29 Or (Eq (path (skS.0 7 a) (skS.0 8 a a_1) (skS.0 11 a a_1 a_2 a_3 a_4)) False) % 6.10/6.29 (Or (Eq (edge (skS.0 10 a a_1 a_2 a_3)) False) % 6.10/6.29 (Or (Eq (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3)) % 6.10/6.29 (Or (Eq (edge (skS.0 9 a a_1 a_2)) False) % 6.10/6.29 (Or (Eq (vertex (skS.0 7 a)) False) % 6.10/6.29 (Or (Eq (vertex (skS.0 8 a a_1)) False) (Eq (skS.0 7 a) (skS.0 8 a a_1))))))) % 6.10/6.29 Clause #341 (by forward demodulation #[340, 325]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.10/6.29 Or (Eq (path (skS.0 7 a) (skS.0 8 a a_1) (skS.0 11 a a_1 a_2 a_3 a_4)) False) % 6.10/6.29 (Or (Eq (edge (skS.0 10 a a_1 a_2 a_3)) False) % 6.10/6.29 (Or (Eq (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3)) % 6.10/6.29 (Or (Eq True False) % 6.10/6.29 (Or (Eq (vertex (skS.0 7 a)) False) % 6.10/6.29 (Or (Eq (vertex (skS.0 8 a a_1)) False) (Eq (skS.0 7 a) (skS.0 8 a a_1))))))) % 6.10/6.29 Clause #342 (by clausification #[341]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.10/6.29 Or (Eq (path (skS.0 7 a) (skS.0 8 a a_1) (skS.0 11 a a_1 a_2 a_3 a_4)) False) % 6.10/6.29 (Or (Eq (edge (skS.0 10 a a_1 a_2 a_3)) False) % 6.10/6.29 (Or (Eq (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3)) % 6.10/6.29 (Or (Eq (vertex (skS.0 7 a)) False) (Or (Eq (vertex (skS.0 8 a a_1)) False) (Eq (skS.0 7 a) (skS.0 8 a a_1)))))) % 6.10/6.29 Clause #343 (by forward demodulation #[342, 289]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.10/6.29 Or (Eq (path (skS.0 7 a) (skS.0 8 a a_1) (skS.0 11 a a_1 a_2 a_3 a_4)) False) % 6.10/6.29 (Or (Eq (edge (skS.0 10 a a_1 a_2 a_3)) False) % 6.10/6.29 (Or (Eq (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3)) % 6.10/6.29 (Or (Eq True False) (Or (Eq (vertex (skS.0 8 a a_1)) False) (Eq (skS.0 7 a) (skS.0 8 a a_1)))))) % 6.10/6.29 Clause #344 (by clausification #[343]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.10/6.29 Or (Eq (path (skS.0 7 a) (skS.0 8 a a_1) (skS.0 11 a a_1 a_2 a_3 a_4)) False) % 6.10/6.29 (Or (Eq (edge (skS.0 10 a a_1 a_2 a_3)) False) % 6.10/6.29 (Or (Eq (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3)) % 6.10/6.29 (Or (Eq (vertex (skS.0 8 a a_1)) False) (Eq (skS.0 7 a) (skS.0 8 a a_1))))) % 6.10/6.29 Clause #345 (by forward demodulation #[344, 296]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.10/6.29 Or (Eq (path (skS.0 7 a) (skS.0 8 a a_1) (skS.0 11 a a_1 a_2 a_3 a_4)) False) % 6.10/6.29 (Or (Eq (edge (skS.0 10 a a_1 a_2 a_3)) False) % 6.10/6.29 (Or (Eq (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3)) (Or (Eq True False) (Eq (skS.0 7 a) (skS.0 8 a a_1))))) % 6.15/6.30 Clause #346 (by clausification #[345]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.15/6.30 Or (Eq (path (skS.0 7 a) (skS.0 8 a a_1) (skS.0 11 a a_1 a_2 a_3 a_4)) False) % 6.15/6.30 (Or (Eq (edge (skS.0 10 a a_1 a_2 a_3)) False) % 6.15/6.30 (Or (Eq (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3)) (Eq (skS.0 7 a) (skS.0 8 a a_1)))) % 6.15/6.30 Clause #347 (by superposition #[346, 267]): ∀ (a a_1 a_2 a_3 : Iota), % 6.15/6.30 Or (Eq (edge (skS.0 10 a a_1 a_2 a_3)) False) % 6.15/6.30 (Or (Eq (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3)) (Or (Eq (skS.0 7 a) (skS.0 8 a a_1)) (Eq False True))) % 6.15/6.30 Clause #358 (by clausification #[283]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota), % 6.15/6.30 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) % 6.15/6.30 Clause #359 (by superposition #[358, 244]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 6.15/6.30 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) % 6.15/6.30 Clause #360 (by clausification #[359]): ∀ (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 % 6.15/6.30 Clause #361 (by superposition #[360, 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) % 6.15/6.30 Clause #364 (by clausification #[361]): ∀ (a a_1 a_2 a_3 : Iota), Eq (edge (skS.0 10 a a_1 a_2 a_3)) True % 6.15/6.30 Clause #405 (by clausification #[347]): ∀ (a a_1 a_2 a_3 : Iota), % 6.15/6.30 Or (Eq (edge (skS.0 10 a a_1 a_2 a_3)) False) % 6.15/6.30 (Or (Eq (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3)) (Eq (skS.0 7 a) (skS.0 8 a a_1))) % 6.15/6.30 Clause #406 (by superposition #[405, 364]): ∀ (a a_1 a_2 a_3 : Iota), % 6.15/6.30 Or (Eq (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3)) (Or (Eq (skS.0 7 a) (skS.0 8 a a_1)) (Eq False True)) % 6.15/6.30 Clause #407 (by clausification #[406]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3)) (Eq (skS.0 7 a) (skS.0 8 a a_1)) % 6.15/6.30 Clause #409 (by superposition #[407, 266]): ∀ (a a_1 a_2 : Iota), % 6.15/6.30 Or (Eq (skS.0 7 a) (skS.0 8 a a_1)) (Ne (head_of (skS.0 9 a a_1 a_2)) (head_of (skS.0 9 a a_1 a_2))) % 6.15/6.30 Clause #419 (by eliminate resolved literals #[409]): ∀ (a a_1 : Iota), Eq (skS.0 7 a) (skS.0 8 a a_1) % 6.15/6.30 Clause #420 (by backward demodulation #[419, 245]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (shortest_path (skS.0 7 a) (skS.0 7 a) (skS.0 11 a a_1 a_2 a_3 a_4)) True % 6.15/6.30 Clause #437 (by superposition #[420, 198]): Eq True False % 6.15/6.30 Clause #442 (by clausification #[437]): False % 6.15/6.30 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------