TSTP Solution File: GRA003+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : GRA003+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n014.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 : Thu Aug 31 00:01:25 EDT 2023
% Result : Theorem 5.36s 5.60s
% Output : Proof 5.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA003+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.00/0.14 % Command : duper %s
% 0.17/0.35 % Computer : n014.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Sun Aug 27 03:39:16 EDT 2023
% 0.17/0.35 % CPUTime :
% 5.36/5.60 SZS status Theorem for theBenchmark.p
% 5.36/5.60 SZS output start Proof for theBenchmark.p
% 5.36/5.60 Clause #4 (by assumption #[]): Eq
% 5.36/5.60 (∀ (V1 V2 P : Iota),
% 5.36/5.60 path V1 V2 P →
% 5.36/5.60 And (And (vertex V1) (vertex V2))
% 5.36/5.60 (Exists fun E =>
% 5.36/5.60 And (And (edge E) (Eq V1 (tail_of E)))
% 5.36/5.60 (Not
% 5.36/5.60 (Iff (And (Eq V2 (head_of E)) (Eq P (path_cons E empty)))
% 5.36/5.60 (Exists fun TP => And (path (head_of E) V2 TP) (Eq P (path_cons E TP)))))))
% 5.36/5.60 True
% 5.36/5.60 Clause #5 (by assumption #[]): Eq
% 5.36/5.60 (∀ (V1 V2 P E : Iota),
% 5.36/5.60 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))
% 5.36/5.60 True
% 5.36/5.60 Clause #9 (by assumption #[]): Eq
% 5.36/5.60 (∀ (P V1 V2 : Iota),
% 5.36/5.60 path V1 V2 P →
% 5.36/5.60 ∀ (E1 E2 : Iota),
% 5.36/5.60 precedes E1 E2 P →
% 5.36/5.60 And (And (on_path E1 P) (on_path E2 P))
% 5.36/5.60 (Not (Iff (sequential E1 E2) (Exists fun E3 => And (sequential E1 E3) (precedes E3 E2 P)))))
% 5.36/5.60 True
% 5.36/5.60 Clause #10 (by assumption #[]): Eq
% 5.36/5.60 (∀ (V1 V2 SP : Iota),
% 5.36/5.60 Iff (shortest_path V1 V2 SP)
% 5.36/5.60 (And (And (path V1 V2 SP) (Ne V1 V2)) (∀ (P : Iota), path V1 V2 P → less_or_equal (length_of SP) (length_of P))))
% 5.36/5.60 True
% 5.36/5.60 Clause #11 (by assumption #[]): Eq
% 5.36/5.60 (∀ (V1 V2 E1 E2 P : Iota),
% 5.36/5.60 And (shortest_path V1 V2 P) (precedes E1 E2 P) →
% 5.36/5.60 And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of E1)) (Eq (head_of E3) (head_of E2))))
% 5.36/5.60 (Not (precedes E2 E1 P)))
% 5.36/5.60 True
% 5.36/5.60 Clause #17 (by assumption #[]): Eq
% 5.36/5.60 (Not
% 5.36/5.60 (∀ (V1 V2 E1 E2 P : Iota),
% 5.36/5.60 And (shortest_path V1 V2 P) (precedes E1 E2 P) →
% 5.36/5.60 And (And (And (And (And (And (vertex V1) (vertex V2)) (Ne V1 V2)) (edge E1)) (edge E2)) (Ne E1 E2))
% 5.36/5.60 (path V1 V2 P)))
% 5.36/5.60 True
% 5.36/5.60 Clause #101 (by clausification #[5]): ∀ (a : Iota),
% 5.36/5.60 Eq
% 5.36/5.60 (∀ (V2 P E : Iota),
% 5.36/5.60 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))
% 5.36/5.60 True
% 5.36/5.60 Clause #102 (by clausification #[101]): ∀ (a a_1 : Iota),
% 5.36/5.60 Eq
% 5.36/5.60 (∀ (P E : Iota),
% 5.36/5.60 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))
% 5.36/5.60 True
% 5.36/5.60 Clause #103 (by clausification #[102]): ∀ (a a_1 a_2 : Iota),
% 5.36/5.60 Eq
% 5.36/5.60 (∀ (E : Iota),
% 5.36/5.60 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))
% 5.36/5.60 True
% 5.36/5.60 Clause #104 (by clausification #[103]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.36/5.60 Eq
% 5.36/5.60 (And (path a a_1 a_2) (on_path a_3 a_2) →
% 5.36/5.60 And (And (edge a_3) (in_path (head_of a_3) a_2)) (in_path (tail_of a_3) a_2))
% 5.36/5.60 True
% 5.36/5.60 Clause #105 (by clausification #[104]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.36/5.60 Or (Eq (And (path a a_1 a_2) (on_path a_3 a_2)) False)
% 5.36/5.60 (Eq (And (And (edge a_3) (in_path (head_of a_3) a_2)) (in_path (tail_of a_3) a_2)) True)
% 5.36/5.60 Clause #106 (by clausification #[105]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.36/5.60 Or (Eq (And (And (edge a) (in_path (head_of a) a_1)) (in_path (tail_of a) a_1)) True)
% 5.36/5.60 (Or (Eq (path a_2 a_3 a_1) False) (Eq (on_path a a_1) False))
% 5.36/5.60 Clause #108 (by clausification #[106]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.36/5.60 Or (Eq (path a a_1 a_2) False)
% 5.36/5.60 (Or (Eq (on_path a_3 a_2) False) (Eq (And (edge a_3) (in_path (head_of a_3) a_2)) True))
% 5.36/5.60 Clause #109 (by clausification #[4]): ∀ (a : Iota),
% 5.36/5.60 Eq
% 5.36/5.60 (∀ (V2 P : Iota),
% 5.36/5.60 path a V2 P →
% 5.36/5.60 And (And (vertex a) (vertex V2))
% 5.36/5.60 (Exists fun E =>
% 5.36/5.60 And (And (edge E) (Eq a (tail_of E)))
% 5.36/5.60 (Not
% 5.36/5.60 (Iff (And (Eq V2 (head_of E)) (Eq P (path_cons E empty)))
% 5.36/5.60 (Exists fun TP => And (path (head_of E) V2 TP) (Eq P (path_cons E TP)))))))
% 5.36/5.60 True
% 5.36/5.60 Clause #110 (by clausification #[109]): ∀ (a a_1 : Iota),
% 5.36/5.60 Eq
% 5.36/5.60 (∀ (P : Iota),
% 5.36/5.60 path a a_1 P →
% 5.36/5.60 And (And (vertex a) (vertex a_1))
% 5.36/5.60 (Exists fun E =>
% 5.36/5.60 And (And (edge E) (Eq a (tail_of E)))
% 5.36/5.60 (Not
% 5.36/5.60 (Iff (And (Eq a_1 (head_of E)) (Eq P (path_cons E empty)))
% 5.36/5.60 (Exists fun TP => And (path (head_of E) a_1 TP) (Eq P (path_cons E TP)))))))
% 5.36/5.60 True
% 5.36/5.60 Clause #111 (by clausification #[110]): ∀ (a a_1 a_2 : Iota),
% 5.36/5.60 Eq
% 5.36/5.60 (path a a_1 a_2 →
% 5.46/5.62 And (And (vertex a) (vertex a_1))
% 5.46/5.62 (Exists fun E =>
% 5.46/5.62 And (And (edge E) (Eq a (tail_of E)))
% 5.46/5.62 (Not
% 5.46/5.62 (Iff (And (Eq a_1 (head_of E)) (Eq a_2 (path_cons E empty)))
% 5.46/5.62 (Exists fun TP => And (path (head_of E) a_1 TP) (Eq a_2 (path_cons E TP)))))))
% 5.46/5.62 True
% 5.46/5.62 Clause #112 (by clausification #[111]): ∀ (a a_1 a_2 : Iota),
% 5.46/5.62 Or (Eq (path a a_1 a_2) False)
% 5.46/5.62 (Eq
% 5.46/5.62 (And (And (vertex a) (vertex a_1))
% 5.46/5.62 (Exists fun E =>
% 5.46/5.62 And (And (edge E) (Eq a (tail_of E)))
% 5.46/5.62 (Not
% 5.46/5.62 (Iff (And (Eq a_1 (head_of E)) (Eq a_2 (path_cons E empty)))
% 5.46/5.62 (Exists fun TP => And (path (head_of E) a_1 TP) (Eq a_2 (path_cons E TP)))))))
% 5.46/5.62 True)
% 5.46/5.62 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)
% 5.46/5.62 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)
% 5.46/5.62 Clause #128 (by clausification #[114]): ∀ (a a_1 a_2 : Iota), Or (Eq (path a a_1 a_2) False) (Eq (vertex a) True)
% 5.46/5.62 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))
% 5.46/5.62 Clause #157 (by clausification #[9]): ∀ (a : Iota),
% 5.46/5.62 Eq
% 5.46/5.62 (∀ (V1 V2 : Iota),
% 5.46/5.62 path V1 V2 a →
% 5.46/5.62 ∀ (E1 E2 : Iota),
% 5.46/5.62 precedes E1 E2 a →
% 5.46/5.62 And (And (on_path E1 a) (on_path E2 a))
% 5.46/5.62 (Not (Iff (sequential E1 E2) (Exists fun E3 => And (sequential E1 E3) (precedes E3 E2 a)))))
% 5.46/5.62 True
% 5.46/5.62 Clause #158 (by clausification #[157]): ∀ (a a_1 : Iota),
% 5.46/5.62 Eq
% 5.46/5.62 (∀ (V2 : Iota),
% 5.46/5.62 path a V2 a_1 →
% 5.46/5.62 ∀ (E1 E2 : Iota),
% 5.46/5.62 precedes E1 E2 a_1 →
% 5.46/5.62 And (And (on_path E1 a_1) (on_path E2 a_1))
% 5.46/5.62 (Not (Iff (sequential E1 E2) (Exists fun E3 => And (sequential E1 E3) (precedes E3 E2 a_1)))))
% 5.46/5.62 True
% 5.46/5.62 Clause #159 (by clausification #[158]): ∀ (a a_1 a_2 : Iota),
% 5.46/5.62 Eq
% 5.46/5.62 (path a a_1 a_2 →
% 5.46/5.62 ∀ (E1 E2 : Iota),
% 5.46/5.62 precedes E1 E2 a_2 →
% 5.46/5.62 And (And (on_path E1 a_2) (on_path E2 a_2))
% 5.46/5.62 (Not (Iff (sequential E1 E2) (Exists fun E3 => And (sequential E1 E3) (precedes E3 E2 a_2)))))
% 5.46/5.62 True
% 5.46/5.62 Clause #160 (by clausification #[159]): ∀ (a a_1 a_2 : Iota),
% 5.46/5.62 Or (Eq (path a a_1 a_2) False)
% 5.46/5.62 (Eq
% 5.46/5.62 (∀ (E1 E2 : Iota),
% 5.46/5.62 precedes E1 E2 a_2 →
% 5.46/5.62 And (And (on_path E1 a_2) (on_path E2 a_2))
% 5.46/5.62 (Not (Iff (sequential E1 E2) (Exists fun E3 => And (sequential E1 E3) (precedes E3 E2 a_2)))))
% 5.46/5.62 True)
% 5.46/5.62 Clause #161 (by clausification #[160]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.46/5.62 Or (Eq (path a a_1 a_2) False)
% 5.46/5.62 (Eq
% 5.46/5.62 (∀ (E2 : Iota),
% 5.46/5.62 precedes a_3 E2 a_2 →
% 5.46/5.62 And (And (on_path a_3 a_2) (on_path E2 a_2))
% 5.46/5.62 (Not (Iff (sequential a_3 E2) (Exists fun E3 => And (sequential a_3 E3) (precedes E3 E2 a_2)))))
% 5.46/5.62 True)
% 5.46/5.62 Clause #162 (by clausification #[161]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.46/5.62 Or (Eq (path a a_1 a_2) False)
% 5.46/5.62 (Eq
% 5.46/5.62 (precedes a_3 a_4 a_2 →
% 5.46/5.62 And (And (on_path a_3 a_2) (on_path a_4 a_2))
% 5.46/5.62 (Not (Iff (sequential a_3 a_4) (Exists fun E3 => And (sequential a_3 E3) (precedes E3 a_4 a_2)))))
% 5.46/5.62 True)
% 5.46/5.62 Clause #163 (by clausification #[162]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.46/5.62 Or (Eq (path a a_1 a_2) False)
% 5.46/5.62 (Or (Eq (precedes a_3 a_4 a_2) False)
% 5.46/5.62 (Eq
% 5.46/5.62 (And (And (on_path a_3 a_2) (on_path a_4 a_2))
% 5.46/5.62 (Not (Iff (sequential a_3 a_4) (Exists fun E3 => And (sequential a_3 E3) (precedes E3 a_4 a_2)))))
% 5.46/5.62 True))
% 5.46/5.62 Clause #165 (by clausification #[163]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.46/5.62 Or (Eq (path a a_1 a_2) False)
% 5.46/5.62 (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))
% 5.46/5.62 Clause #177 (by clausification #[165]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.46/5.62 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))
% 5.46/5.62 Clause #178 (by clausification #[165]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.46/5.62 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))
% 5.46/5.64 Clause #179 (by clausification #[10]): ∀ (a : Iota),
% 5.46/5.64 Eq
% 5.46/5.64 (∀ (V2 SP : Iota),
% 5.46/5.64 Iff (shortest_path a V2 SP)
% 5.46/5.64 (And (And (path a V2 SP) (Ne a V2)) (∀ (P : Iota), path a V2 P → less_or_equal (length_of SP) (length_of P))))
% 5.46/5.64 True
% 5.46/5.64 Clause #180 (by clausification #[179]): ∀ (a a_1 : Iota),
% 5.46/5.64 Eq
% 5.46/5.64 (∀ (SP : Iota),
% 5.46/5.64 Iff (shortest_path a a_1 SP)
% 5.46/5.64 (And (And (path a a_1 SP) (Ne a a_1))
% 5.46/5.64 (∀ (P : Iota), path a a_1 P → less_or_equal (length_of SP) (length_of P))))
% 5.46/5.64 True
% 5.46/5.64 Clause #181 (by clausification #[180]): ∀ (a a_1 a_2 : Iota),
% 5.46/5.64 Eq
% 5.46/5.64 (Iff (shortest_path a a_1 a_2)
% 5.46/5.64 (And (And (path a a_1 a_2) (Ne a a_1))
% 5.46/5.64 (∀ (P : Iota), path a a_1 P → less_or_equal (length_of a_2) (length_of P))))
% 5.46/5.64 True
% 5.46/5.64 Clause #183 (by clausification #[181]): ∀ (a a_1 a_2 : Iota),
% 5.46/5.64 Or (Eq (shortest_path a a_1 a_2) False)
% 5.46/5.64 (Eq
% 5.46/5.64 (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)))
% 5.46/5.64 True)
% 5.46/5.64 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)
% 5.46/5.64 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)
% 5.46/5.64 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)
% 5.46/5.64 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)
% 5.46/5.64 Clause #198 (by destructive equality resolution #[197]): ∀ (a a_1 : Iota), Eq (shortest_path a a a_1) False
% 5.46/5.64 Clause #202 (by clausification #[11]): ∀ (a : Iota),
% 5.46/5.64 Eq
% 5.46/5.64 (∀ (V2 E1 E2 P : Iota),
% 5.46/5.64 And (shortest_path a V2 P) (precedes E1 E2 P) →
% 5.46/5.64 And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of E1)) (Eq (head_of E3) (head_of E2))))
% 5.46/5.64 (Not (precedes E2 E1 P)))
% 5.46/5.64 True
% 5.46/5.64 Clause #203 (by clausification #[202]): ∀ (a a_1 : Iota),
% 5.46/5.64 Eq
% 5.46/5.64 (∀ (E1 E2 P : Iota),
% 5.46/5.64 And (shortest_path a a_1 P) (precedes E1 E2 P) →
% 5.46/5.64 And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of E1)) (Eq (head_of E3) (head_of E2))))
% 5.46/5.64 (Not (precedes E2 E1 P)))
% 5.46/5.64 True
% 5.46/5.64 Clause #204 (by clausification #[203]): ∀ (a a_1 a_2 : Iota),
% 5.46/5.64 Eq
% 5.46/5.64 (∀ (E2 P : Iota),
% 5.46/5.64 And (shortest_path a a_1 P) (precedes a_2 E2 P) →
% 5.46/5.64 And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of a_2)) (Eq (head_of E3) (head_of E2))))
% 5.46/5.64 (Not (precedes E2 a_2 P)))
% 5.46/5.64 True
% 5.46/5.64 Clause #205 (by clausification #[204]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.46/5.64 Eq
% 5.46/5.64 (∀ (P : Iota),
% 5.46/5.64 And (shortest_path a a_1 P) (precedes a_2 a_3 P) →
% 5.46/5.64 And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of a_2)) (Eq (head_of E3) (head_of a_3))))
% 5.46/5.64 (Not (precedes a_3 a_2 P)))
% 5.46/5.64 True
% 5.46/5.64 Clause #206 (by clausification #[205]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.46/5.64 Eq
% 5.46/5.64 (And (shortest_path a a_1 a_2) (precedes a_3 a_4 a_2) →
% 5.46/5.64 And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of a_3)) (Eq (head_of E3) (head_of a_4))))
% 5.46/5.64 (Not (precedes a_4 a_3 a_2)))
% 5.46/5.64 True
% 5.46/5.64 Clause #207 (by clausification #[206]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.46/5.64 Or (Eq (And (shortest_path a a_1 a_2) (precedes a_3 a_4 a_2)) False)
% 5.46/5.64 (Eq
% 5.46/5.64 (And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of a_3)) (Eq (head_of E3) (head_of a_4))))
% 5.46/5.64 (Not (precedes a_4 a_3 a_2)))
% 5.46/5.64 True)
% 5.46/5.64 Clause #208 (by clausification #[207]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.46/5.64 Or
% 5.46/5.64 (Eq
% 5.46/5.64 (And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of a)) (Eq (head_of E3) (head_of a_1))))
% 5.46/5.64 (Not (precedes a_1 a a_2)))
% 5.46/5.64 True)
% 5.46/5.64 (Or (Eq (shortest_path a_3 a_4 a_2) False) (Eq (precedes a a_1 a_2) False))
% 5.46/5.64 Clause #210 (by clausification #[208]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.46/5.64 Or (Eq (shortest_path a a_1 a_2) False)
% 5.46/5.64 (Or (Eq (precedes a_3 a_4 a_2) False)
% 5.46/5.64 (Eq (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of a_3)) (Eq (head_of E3) (head_of a_4)))) True))
% 5.46/5.64 Clause #212 (by clausification #[210]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.46/5.66 Or (Eq (shortest_path a a_1 a_2) False)
% 5.46/5.66 (Or (Eq (precedes a_3 a_4 a_2) False)
% 5.46/5.66 (Eq (Exists fun E3 => And (Eq (tail_of E3) (tail_of a_3)) (Eq (head_of E3) (head_of a_4))) False))
% 5.46/5.66 Clause #213 (by clausification #[212]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 5.46/5.66 Or (Eq (shortest_path a a_1 a_2) False)
% 5.46/5.66 (Or (Eq (precedes a_3 a_4 a_2) False)
% 5.46/5.66 (Eq (And (Eq (tail_of a_5) (tail_of a_3)) (Eq (head_of a_5) (head_of a_4))) False))
% 5.46/5.66 Clause #214 (by clausification #[213]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 5.46/5.66 Or (Eq (shortest_path a a_1 a_2) False)
% 5.46/5.66 (Or (Eq (precedes a_3 a_4 a_2) False)
% 5.46/5.66 (Or (Eq (Eq (tail_of a_5) (tail_of a_3)) False) (Eq (Eq (head_of a_5) (head_of a_4)) False)))
% 5.46/5.66 Clause #215 (by clausification #[214]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 5.46/5.66 Or (Eq (shortest_path a a_1 a_2) False)
% 5.46/5.66 (Or (Eq (precedes a_3 a_4 a_2) False)
% 5.46/5.66 (Or (Eq (Eq (head_of a_5) (head_of a_4)) False) (Ne (tail_of a_5) (tail_of a_3))))
% 5.46/5.66 Clause #216 (by clausification #[215]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 5.46/5.66 Or (Eq (shortest_path a a_1 a_2) False)
% 5.46/5.66 (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))))
% 5.46/5.66 Clause #231 (by clausification #[17]): Eq
% 5.46/5.66 (∀ (V1 V2 E1 E2 P : Iota),
% 5.46/5.66 And (shortest_path V1 V2 P) (precedes E1 E2 P) →
% 5.46/5.66 And (And (And (And (And (And (vertex V1) (vertex V2)) (Ne V1 V2)) (edge E1)) (edge E2)) (Ne E1 E2))
% 5.46/5.66 (path V1 V2 P))
% 5.46/5.66 False
% 5.46/5.66 Clause #232 (by clausification #[231]): ∀ (a : Iota),
% 5.46/5.66 Eq
% 5.46/5.66 (Not
% 5.46/5.66 (∀ (V2 E1 E2 P : Iota),
% 5.46/5.66 And (shortest_path (skS.0 7 a) V2 P) (precedes E1 E2 P) →
% 5.46/5.66 And
% 5.46/5.66 (And (And (And (And (And (vertex (skS.0 7 a)) (vertex V2)) (Ne (skS.0 7 a) V2)) (edge E1)) (edge E2))
% 5.46/5.66 (Ne E1 E2))
% 5.46/5.66 (path (skS.0 7 a) V2 P)))
% 5.46/5.66 True
% 5.46/5.66 Clause #233 (by clausification #[232]): ∀ (a : Iota),
% 5.46/5.66 Eq
% 5.46/5.66 (∀ (V2 E1 E2 P : Iota),
% 5.46/5.66 And (shortest_path (skS.0 7 a) V2 P) (precedes E1 E2 P) →
% 5.46/5.66 And
% 5.46/5.66 (And (And (And (And (And (vertex (skS.0 7 a)) (vertex V2)) (Ne (skS.0 7 a) V2)) (edge E1)) (edge E2))
% 5.46/5.66 (Ne E1 E2))
% 5.46/5.66 (path (skS.0 7 a) V2 P))
% 5.46/5.66 False
% 5.46/5.66 Clause #234 (by clausification #[233]): ∀ (a a_1 : Iota),
% 5.46/5.66 Eq
% 5.46/5.66 (Not
% 5.46/5.66 (∀ (E1 E2 P : Iota),
% 5.46/5.66 And (shortest_path (skS.0 7 a) (skS.0 8 a a_1) P) (precedes E1 E2 P) →
% 5.46/5.66 And
% 5.46/5.66 (And
% 5.46/5.66 (And
% 5.46/5.66 (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)))
% 5.46/5.66 (edge E1))
% 5.46/5.66 (edge E2))
% 5.46/5.66 (Ne E1 E2))
% 5.46/5.66 (path (skS.0 7 a) (skS.0 8 a a_1) P)))
% 5.46/5.66 True
% 5.46/5.66 Clause #235 (by clausification #[234]): ∀ (a a_1 : Iota),
% 5.46/5.66 Eq
% 5.46/5.66 (∀ (E1 E2 P : Iota),
% 5.46/5.66 And (shortest_path (skS.0 7 a) (skS.0 8 a a_1) P) (precedes E1 E2 P) →
% 5.46/5.66 And
% 5.46/5.66 (And
% 5.46/5.66 (And
% 5.46/5.66 (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))
% 5.46/5.66 (edge E2))
% 5.46/5.66 (Ne E1 E2))
% 5.46/5.66 (path (skS.0 7 a) (skS.0 8 a a_1) P))
% 5.46/5.66 False
% 5.46/5.66 Clause #236 (by clausification #[235]): ∀ (a a_1 a_2 : Iota),
% 5.46/5.66 Eq
% 5.46/5.66 (Not
% 5.46/5.66 (∀ (E2 P : Iota),
% 5.46/5.66 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) →
% 5.46/5.66 And
% 5.46/5.66 (And
% 5.46/5.66 (And
% 5.46/5.66 (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)))
% 5.46/5.66 (edge (skS.0 9 a a_1 a_2)))
% 5.46/5.66 (edge E2))
% 5.46/5.66 (Ne (skS.0 9 a a_1 a_2) E2))
% 5.46/5.66 (path (skS.0 7 a) (skS.0 8 a a_1) P)))
% 5.46/5.66 True
% 5.46/5.66 Clause #237 (by clausification #[236]): ∀ (a a_1 a_2 : Iota),
% 5.46/5.66 Eq
% 5.46/5.66 (∀ (E2 P : Iota),
% 5.46/5.66 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) →
% 5.46/5.66 And
% 5.46/5.66 (And
% 5.46/5.66 (And
% 5.46/5.66 (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)))
% 5.46/5.66 (edge (skS.0 9 a a_1 a_2)))
% 5.46/5.66 (edge E2))
% 5.46/5.66 (Ne (skS.0 9 a a_1 a_2) E2))
% 5.46/5.69 (path (skS.0 7 a) (skS.0 8 a a_1) P))
% 5.46/5.69 False
% 5.46/5.69 Clause #238 (by clausification #[237]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.46/5.69 Eq
% 5.46/5.69 (Not
% 5.46/5.69 (∀ (P : Iota),
% 5.46/5.69 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) →
% 5.46/5.69 And
% 5.46/5.69 (And
% 5.46/5.69 (And
% 5.46/5.69 (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)))
% 5.46/5.69 (edge (skS.0 9 a a_1 a_2)))
% 5.46/5.69 (edge (skS.0 10 a a_1 a_2 a_3)))
% 5.46/5.69 (Ne (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3)))
% 5.46/5.69 (path (skS.0 7 a) (skS.0 8 a a_1) P)))
% 5.46/5.69 True
% 5.46/5.69 Clause #239 (by clausification #[238]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.46/5.69 Eq
% 5.46/5.69 (∀ (P : Iota),
% 5.46/5.69 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) →
% 5.46/5.69 And
% 5.46/5.69 (And
% 5.46/5.69 (And
% 5.46/5.69 (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)))
% 5.46/5.69 (edge (skS.0 9 a a_1 a_2)))
% 5.46/5.69 (edge (skS.0 10 a a_1 a_2 a_3)))
% 5.46/5.69 (Ne (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3)))
% 5.46/5.69 (path (skS.0 7 a) (skS.0 8 a a_1) P))
% 5.46/5.69 False
% 5.46/5.69 Clause #240 (by clausification #[239]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.46/5.69 Eq
% 5.46/5.69 (Not
% 5.46/5.69 (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))
% 5.46/5.69 (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)) →
% 5.46/5.69 And
% 5.46/5.69 (And
% 5.46/5.69 (And
% 5.46/5.69 (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)))
% 5.46/5.69 (edge (skS.0 9 a a_1 a_2)))
% 5.46/5.69 (edge (skS.0 10 a a_1 a_2 a_3)))
% 5.46/5.69 (Ne (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3)))
% 5.46/5.69 (path (skS.0 7 a) (skS.0 8 a a_1) (skS.0 11 a a_1 a_2 a_3 a_4))))
% 5.46/5.69 True
% 5.46/5.69 Clause #241 (by clausification #[240]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.46/5.69 Eq
% 5.46/5.69 (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))
% 5.46/5.69 (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)) →
% 5.46/5.69 And
% 5.46/5.69 (And
% 5.46/5.69 (And
% 5.46/5.69 (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)))
% 5.46/5.69 (edge (skS.0 9 a a_1 a_2)))
% 5.46/5.69 (edge (skS.0 10 a a_1 a_2 a_3)))
% 5.46/5.69 (Ne (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3)))
% 5.46/5.69 (path (skS.0 7 a) (skS.0 8 a a_1) (skS.0 11 a a_1 a_2 a_3 a_4)))
% 5.46/5.69 False
% 5.46/5.69 Clause #242 (by clausification #[241]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.46/5.69 Eq
% 5.46/5.69 (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))
% 5.46/5.69 (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)))
% 5.46/5.69 True
% 5.46/5.69 Clause #243 (by clausification #[241]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.46/5.69 Eq
% 5.46/5.69 (And
% 5.46/5.69 (And
% 5.46/5.69 (And
% 5.46/5.69 (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)))
% 5.46/5.69 (edge (skS.0 9 a a_1 a_2)))
% 5.46/5.69 (edge (skS.0 10 a a_1 a_2 a_3)))
% 5.46/5.69 (Ne (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3)))
% 5.46/5.69 (path (skS.0 7 a) (skS.0 8 a a_1) (skS.0 11 a a_1 a_2 a_3 a_4)))
% 5.46/5.69 False
% 5.46/5.69 Clause #244 (by clausification #[242]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.46/5.69 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
% 5.46/5.69 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
% 5.46/5.69 Clause #253 (by superposition #[245, 196]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.46/5.69 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)
% 5.46/5.69 Clause #255 (by superposition #[245, 216]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 5.46/5.69 Or (Eq True False)
% 5.46/5.69 (Or (Eq (precedes a a_1 (skS.0 11 a_2 a_3 a_4 a_5 a_6)) False)
% 5.46/5.69 (Or (Ne (tail_of a_7) (tail_of a)) (Ne (head_of a_7) (head_of a_1))))
% 5.46/5.69 Clause #263 (by clausification #[255]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 5.53/5.71 Or (Eq (precedes a a_1 (skS.0 11 a_2 a_3 a_4 a_5 a_6)) False)
% 5.53/5.71 (Or (Ne (tail_of a_7) (tail_of a)) (Ne (head_of a_7) (head_of a_1)))
% 5.53/5.71 Clause #264 (by superposition #[263, 244]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.53/5.71 Or (Ne (tail_of a) (tail_of (skS.0 9 a_1 a_2 a_3)))
% 5.53/5.71 (Or (Ne (head_of a) (head_of (skS.0 10 a_1 a_2 a_3 a_4))) (Eq False True))
% 5.53/5.71 Clause #265 (by clausification #[264]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.53/5.71 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)))
% 5.53/5.71 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))
% 5.53/5.71 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
% 5.53/5.71 Clause #274 (by superposition #[267, 127]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (vertex (skS.0 8 a a_1)) True)
% 5.53/5.71 Clause #275 (by superposition #[267, 128]): ∀ (a : Iota), Or (Eq True False) (Eq (vertex (skS.0 7 a)) True)
% 5.53/5.71 Clause #277 (by superposition #[267, 130]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 5.53/5.71 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))
% 5.53/5.71 Clause #283 (by superposition #[267, 177]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 5.53/5.71 Or (Eq True False)
% 5.53/5.71 (Or (Eq (precedes a a_1 (skS.0 11 a_2 a_3 a_4 a_5 a_6)) False)
% 5.53/5.71 (Eq (on_path a_1 (skS.0 11 a_2 a_3 a_4 a_5 a_6)) True))
% 5.53/5.71 Clause #284 (by superposition #[267, 178]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 5.53/5.71 Or (Eq True False)
% 5.53/5.71 (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))
% 5.53/5.71 Clause #289 (by clausification #[275]): ∀ (a : Iota), Eq (vertex (skS.0 7 a)) True
% 5.53/5.71 Clause #296 (by clausification #[274]): ∀ (a a_1 : Iota), Eq (vertex (skS.0 8 a a_1)) True
% 5.53/5.71 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)
% 5.53/5.71 Clause #321 (by clausification #[284]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 5.53/5.71 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)
% 5.53/5.71 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)
% 5.53/5.71 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
% 5.53/5.71 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)
% 5.53/5.71 Clause #325 (by clausification #[324]): ∀ (a a_1 a_2 : Iota), Eq (edge (skS.0 9 a a_1 a_2)) True
% 5.53/5.71 Clause #333 (by clausification #[243]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.53/5.71 Or
% 5.53/5.71 (Eq
% 5.53/5.71 (And
% 5.53/5.71 (And
% 5.53/5.71 (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)))
% 5.53/5.71 (edge (skS.0 9 a a_1 a_2)))
% 5.53/5.71 (edge (skS.0 10 a a_1 a_2 a_3)))
% 5.53/5.71 (Ne (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3)))
% 5.53/5.71 False)
% 5.53/5.71 (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)
% 5.53/5.71 Clause #334 (by clausification #[333]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.53/5.71 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)
% 5.53/5.71 (Or
% 5.53/5.71 (Eq
% 5.53/5.71 (And
% 5.53/5.71 (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)))
% 5.53/5.71 (edge (skS.0 9 a a_1 a_2)))
% 5.53/5.71 (edge (skS.0 10 a a_1 a_2 a_3)))
% 5.53/5.71 False)
% 5.53/5.71 (Eq (Ne (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3)) False))
% 5.53/5.71 Clause #335 (by clausification #[334]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.53/5.71 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)
% 5.53/5.71 (Or (Eq (Ne (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3)) False)
% 5.53/5.71 (Or
% 5.53/5.71 (Eq
% 5.53/5.71 (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)))
% 5.53/5.71 (edge (skS.0 9 a a_1 a_2)))
% 5.53/5.71 False)
% 5.53/5.71 (Eq (edge (skS.0 10 a a_1 a_2 a_3)) False)))
% 5.53/5.74 Clause #336 (by clausification #[335]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.53/5.74 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)
% 5.53/5.74 (Or
% 5.53/5.74 (Eq
% 5.53/5.74 (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)))
% 5.53/5.74 (edge (skS.0 9 a a_1 a_2)))
% 5.53/5.74 False)
% 5.53/5.74 (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))))
% 5.53/5.74 Clause #337 (by clausification #[336]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.53/5.74 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)
% 5.53/5.74 (Or (Eq (edge (skS.0 10 a a_1 a_2 a_3)) False)
% 5.53/5.74 (Or (Eq (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3))
% 5.53/5.74 (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)
% 5.53/5.74 (Eq (edge (skS.0 9 a a_1 a_2)) False))))
% 5.53/5.74 Clause #338 (by clausification #[337]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.53/5.74 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)
% 5.53/5.74 (Or (Eq (edge (skS.0 10 a a_1 a_2 a_3)) False)
% 5.53/5.74 (Or (Eq (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3))
% 5.53/5.74 (Or (Eq (edge (skS.0 9 a a_1 a_2)) False)
% 5.53/5.74 (Or (Eq (And (vertex (skS.0 7 a)) (vertex (skS.0 8 a a_1))) False)
% 5.53/5.74 (Eq (Ne (skS.0 7 a) (skS.0 8 a a_1)) False)))))
% 5.53/5.74 Clause #339 (by clausification #[338]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.53/5.74 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)
% 5.53/5.74 (Or (Eq (edge (skS.0 10 a a_1 a_2 a_3)) False)
% 5.53/5.74 (Or (Eq (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3))
% 5.53/5.74 (Or (Eq (edge (skS.0 9 a a_1 a_2)) False)
% 5.53/5.74 (Or (Eq (Ne (skS.0 7 a) (skS.0 8 a a_1)) False)
% 5.53/5.74 (Or (Eq (vertex (skS.0 7 a)) False) (Eq (vertex (skS.0 8 a a_1)) False))))))
% 5.53/5.74 Clause #340 (by clausification #[339]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.53/5.74 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)
% 5.53/5.74 (Or (Eq (edge (skS.0 10 a a_1 a_2 a_3)) False)
% 5.53/5.74 (Or (Eq (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3))
% 5.53/5.74 (Or (Eq (edge (skS.0 9 a a_1 a_2)) False)
% 5.53/5.74 (Or (Eq (vertex (skS.0 7 a)) False)
% 5.53/5.74 (Or (Eq (vertex (skS.0 8 a a_1)) False) (Eq (skS.0 7 a) (skS.0 8 a a_1)))))))
% 5.53/5.74 Clause #341 (by forward demodulation #[340, 325]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.53/5.74 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)
% 5.53/5.74 (Or (Eq (edge (skS.0 10 a a_1 a_2 a_3)) False)
% 5.53/5.74 (Or (Eq (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3))
% 5.53/5.74 (Or (Eq True False)
% 5.53/5.74 (Or (Eq (vertex (skS.0 7 a)) False)
% 5.53/5.74 (Or (Eq (vertex (skS.0 8 a a_1)) False) (Eq (skS.0 7 a) (skS.0 8 a a_1)))))))
% 5.53/5.74 Clause #342 (by clausification #[341]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.53/5.74 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)
% 5.53/5.74 (Or (Eq (edge (skS.0 10 a a_1 a_2 a_3)) False)
% 5.53/5.74 (Or (Eq (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3))
% 5.53/5.74 (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))))))
% 5.53/5.74 Clause #343 (by forward demodulation #[342, 289]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.53/5.74 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)
% 5.53/5.74 (Or (Eq (edge (skS.0 10 a a_1 a_2 a_3)) False)
% 5.53/5.74 (Or (Eq (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3))
% 5.53/5.74 (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))))))
% 5.53/5.74 Clause #344 (by clausification #[343]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.53/5.74 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)
% 5.53/5.74 (Or (Eq (edge (skS.0 10 a a_1 a_2 a_3)) False)
% 5.53/5.74 (Or (Eq (skS.0 9 a a_1 a_2) (skS.0 10 a a_1 a_2 a_3))
% 5.53/5.74 (Or (Eq (vertex (skS.0 8 a a_1)) False) (Eq (skS.0 7 a) (skS.0 8 a a_1)))))
% 5.53/5.74 Clause #345 (by forward demodulation #[344, 296]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.53/5.74 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)
% 5.53/5.74 (Or (Eq (edge (skS.0 10 a a_1 a_2 a_3)) False)
% 5.53/5.74 (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)))))
% 5.53/5.76 Clause #346 (by clausification #[345]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.53/5.76 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)
% 5.53/5.76 (Or (Eq (edge (skS.0 10 a a_1 a_2 a_3)) False)
% 5.53/5.76 (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))))
% 5.53/5.76 Clause #347 (by superposition #[346, 267]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.53/5.76 Or (Eq (edge (skS.0 10 a a_1 a_2 a_3)) False)
% 5.53/5.76 (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)))
% 5.53/5.76 Clause #358 (by clausification #[283]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 5.53/5.76 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)
% 5.53/5.76 Clause #359 (by superposition #[358, 244]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.53/5.76 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)
% 5.53/5.76 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
% 5.53/5.76 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)
% 5.53/5.76 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
% 5.53/5.76 Clause #405 (by clausification #[347]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.53/5.76 Or (Eq (edge (skS.0 10 a a_1 a_2 a_3)) False)
% 5.53/5.76 (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)))
% 5.53/5.76 Clause #406 (by superposition #[405, 364]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.53/5.76 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))
% 5.53/5.76 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))
% 5.53/5.76 Clause #409 (by superposition #[407, 266]): ∀ (a a_1 a_2 : Iota),
% 5.53/5.76 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)))
% 5.53/5.76 Clause #419 (by eliminate resolved literals #[409]): ∀ (a a_1 : Iota), Eq (skS.0 7 a) (skS.0 8 a a_1)
% 5.53/5.76 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
% 5.53/5.76 Clause #437 (by superposition #[420, 198]): Eq True False
% 5.53/5.76 Clause #442 (by clausification #[437]): False
% 5.53/5.76 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------