TSTP Solution File: GRA004+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : GRA004+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n016.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 00:01:26 EDT 2023
% Result : Theorem 25.24s 25.50s
% Output : Proof 25.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GRA004+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.00/0.11 % Command : duper %s
% 0.10/0.31 % Computer : n016.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sun Aug 27 04:24:13 EDT 2023
% 0.10/0.31 % CPUTime :
% 25.24/25.50 SZS status Theorem for theBenchmark.p
% 25.24/25.50 SZS output start Proof for theBenchmark.p
% 25.24/25.50 Clause #0 (by assumption #[]): Eq (∀ (E : Iota), edge E → Ne (head_of E) (tail_of E)) True
% 25.24/25.50 Clause #5 (by assumption #[]): Eq
% 25.24/25.50 (∀ (V1 V2 P E : Iota),
% 25.24/25.50 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))
% 25.24/25.50 True
% 25.24/25.50 Clause #7 (by assumption #[]): Eq
% 25.24/25.50 (∀ (E1 E2 : Iota),
% 25.24/25.50 Iff (sequential E1 E2) (And (And (And (edge E1) (edge E2)) (Ne E1 E2)) (Eq (head_of E1) (tail_of E2))))
% 25.24/25.50 True
% 25.24/25.50 Clause #8 (by assumption #[]): Eq
% 25.24/25.50 (∀ (P V1 V2 : Iota),
% 25.24/25.50 path V1 V2 P →
% 25.24/25.50 ∀ (E1 E2 : Iota),
% 25.24/25.50 And (And (on_path E1 P) (on_path E2 P))
% 25.24/25.50 (Or (sequential E1 E2) (Exists fun E3 => And (sequential E1 E3) (precedes E3 E2 P))) →
% 25.24/25.50 precedes E1 E2 P)
% 25.24/25.50 True
% 25.24/25.50 Clause #9 (by assumption #[]): Eq
% 25.24/25.50 (∀ (P V1 V2 : Iota),
% 25.24/25.50 path V1 V2 P →
% 25.24/25.50 ∀ (E1 E2 : Iota),
% 25.24/25.50 precedes E1 E2 P →
% 25.24/25.50 And (And (on_path E1 P) (on_path E2 P))
% 25.24/25.50 (Not (Iff (sequential E1 E2) (Exists fun E3 => And (sequential E1 E3) (precedes E3 E2 P)))))
% 25.24/25.50 True
% 25.24/25.50 Clause #10 (by assumption #[]): Eq
% 25.24/25.50 (∀ (V1 V2 SP : Iota),
% 25.24/25.50 Iff (shortest_path V1 V2 SP)
% 25.24/25.50 (And (And (path V1 V2 SP) (Ne V1 V2)) (∀ (P : Iota), path V1 V2 P → less_or_equal (length_of SP) (length_of P))))
% 25.24/25.50 True
% 25.24/25.50 Clause #11 (by assumption #[]): Eq
% 25.24/25.50 (∀ (V1 V2 E1 E2 P : Iota),
% 25.24/25.50 And (shortest_path V1 V2 P) (precedes E1 E2 P) →
% 25.24/25.50 And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of E1)) (Eq (head_of E3) (head_of E2))))
% 25.24/25.50 (Not (precedes E2 E1 P)))
% 25.24/25.50 True
% 25.24/25.50 Clause #17 (by assumption #[]): Eq
% 25.24/25.50 (Not
% 25.24/25.50 (∀ (V1 V2 E1 E2 P : Iota),
% 25.24/25.50 And (shortest_path V1 V2 P) (precedes E1 E2 P) →
% 25.24/25.50 And
% 25.24/25.50 (And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of E1)) (Eq (head_of E3) (head_of E2))))
% 25.24/25.50 (Ne (head_of E2) (tail_of E1)))
% 25.24/25.50 (Ne (head_of E2) (head_of E1))))
% 25.24/25.50 True
% 25.24/25.50 Clause #35 (by clausification #[0]): ∀ (a : Iota), Eq (edge a → Ne (head_of a) (tail_of a)) True
% 25.24/25.50 Clause #36 (by clausification #[35]): ∀ (a : Iota), Or (Eq (edge a) False) (Eq (Ne (head_of a) (tail_of a)) True)
% 25.24/25.50 Clause #37 (by clausification #[36]): ∀ (a : Iota), Or (Eq (edge a) False) (Ne (head_of a) (tail_of a))
% 25.24/25.50 Clause #68 (by clausification #[8]): ∀ (a : Iota),
% 25.24/25.50 Eq
% 25.24/25.50 (∀ (V1 V2 : Iota),
% 25.24/25.50 path V1 V2 a →
% 25.24/25.50 ∀ (E1 E2 : Iota),
% 25.24/25.50 And (And (on_path E1 a) (on_path E2 a))
% 25.24/25.50 (Or (sequential E1 E2) (Exists fun E3 => And (sequential E1 E3) (precedes E3 E2 a))) →
% 25.24/25.50 precedes E1 E2 a)
% 25.24/25.50 True
% 25.24/25.50 Clause #69 (by clausification #[68]): ∀ (a a_1 : Iota),
% 25.24/25.50 Eq
% 25.24/25.50 (∀ (V2 : Iota),
% 25.24/25.50 path a V2 a_1 →
% 25.24/25.50 ∀ (E1 E2 : Iota),
% 25.24/25.50 And (And (on_path E1 a_1) (on_path E2 a_1))
% 25.24/25.50 (Or (sequential E1 E2) (Exists fun E3 => And (sequential E1 E3) (precedes E3 E2 a_1))) →
% 25.24/25.50 precedes E1 E2 a_1)
% 25.24/25.50 True
% 25.24/25.50 Clause #70 (by clausification #[69]): ∀ (a a_1 a_2 : Iota),
% 25.24/25.50 Eq
% 25.24/25.50 (path a a_1 a_2 →
% 25.24/25.50 ∀ (E1 E2 : Iota),
% 25.24/25.50 And (And (on_path E1 a_2) (on_path E2 a_2))
% 25.24/25.50 (Or (sequential E1 E2) (Exists fun E3 => And (sequential E1 E3) (precedes E3 E2 a_2))) →
% 25.24/25.50 precedes E1 E2 a_2)
% 25.24/25.50 True
% 25.24/25.50 Clause #71 (by clausification #[70]): ∀ (a a_1 a_2 : Iota),
% 25.24/25.50 Or (Eq (path a a_1 a_2) False)
% 25.24/25.50 (Eq
% 25.24/25.50 (∀ (E1 E2 : Iota),
% 25.24/25.50 And (And (on_path E1 a_2) (on_path E2 a_2))
% 25.24/25.50 (Or (sequential E1 E2) (Exists fun E3 => And (sequential E1 E3) (precedes E3 E2 a_2))) →
% 25.24/25.50 precedes E1 E2 a_2)
% 25.24/25.50 True)
% 25.24/25.50 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 a_3 : Iota),
% 25.24/25.50 Or (Eq (path a a_1 a_2) False)
% 25.24/25.50 (Eq
% 25.24/25.50 (∀ (E2 : Iota),
% 25.24/25.50 And (And (on_path a_3 a_2) (on_path E2 a_2))
% 25.24/25.50 (Or (sequential a_3 E2) (Exists fun E3 => And (sequential a_3 E3) (precedes E3 E2 a_2))) →
% 25.24/25.50 precedes a_3 E2 a_2)
% 25.24/25.50 True)
% 25.24/25.50 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.24/25.50 Or (Eq (path a a_1 a_2) False)
% 25.24/25.50 (Eq
% 25.24/25.50 (And (And (on_path a_3 a_2) (on_path a_4 a_2))
% 25.24/25.50 (Or (sequential a_3 a_4) (Exists fun E3 => And (sequential a_3 E3) (precedes E3 a_4 a_2))) →
% 25.24/25.53 precedes a_3 a_4 a_2)
% 25.24/25.53 True)
% 25.24/25.53 Clause #74 (by clausification #[73]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.24/25.53 Or (Eq (path a a_1 a_2) False)
% 25.24/25.53 (Or
% 25.24/25.53 (Eq
% 25.24/25.53 (And (And (on_path a_3 a_2) (on_path a_4 a_2))
% 25.24/25.53 (Or (sequential a_3 a_4) (Exists fun E3 => And (sequential a_3 E3) (precedes E3 a_4 a_2))))
% 25.24/25.53 False)
% 25.24/25.53 (Eq (precedes a_3 a_4 a_2) True))
% 25.24/25.53 Clause #75 (by clausification #[74]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.24/25.53 Or (Eq (path a a_1 a_2) False)
% 25.24/25.53 (Or (Eq (precedes a_3 a_4 a_2) True)
% 25.24/25.53 (Or (Eq (And (on_path a_3 a_2) (on_path a_4 a_2)) False)
% 25.24/25.53 (Eq (Or (sequential a_3 a_4) (Exists fun E3 => And (sequential a_3 E3) (precedes E3 a_4 a_2))) False)))
% 25.24/25.53 Clause #76 (by clausification #[75]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.24/25.53 Or (Eq (path a a_1 a_2) False)
% 25.24/25.53 (Or (Eq (precedes a_3 a_4 a_2) True)
% 25.24/25.53 (Or (Eq (Or (sequential a_3 a_4) (Exists fun E3 => And (sequential a_3 E3) (precedes E3 a_4 a_2))) False)
% 25.24/25.53 (Or (Eq (on_path a_3 a_2) False) (Eq (on_path a_4 a_2) False))))
% 25.24/25.53 Clause #78 (by clausification #[76]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.24/25.53 Or (Eq (path a a_1 a_2) False)
% 25.24/25.53 (Or (Eq (precedes a_3 a_4 a_2) True)
% 25.24/25.53 (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))))
% 25.24/25.53 Clause #101 (by clausification #[5]): ∀ (a : Iota),
% 25.24/25.53 Eq
% 25.24/25.53 (∀ (V2 P E : Iota),
% 25.24/25.53 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))
% 25.24/25.53 True
% 25.24/25.53 Clause #102 (by clausification #[101]): ∀ (a a_1 : Iota),
% 25.24/25.53 Eq
% 25.24/25.53 (∀ (P E : Iota),
% 25.24/25.53 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))
% 25.24/25.53 True
% 25.24/25.53 Clause #103 (by clausification #[102]): ∀ (a a_1 a_2 : Iota),
% 25.24/25.53 Eq
% 25.24/25.53 (∀ (E : Iota),
% 25.24/25.53 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))
% 25.24/25.53 True
% 25.24/25.53 Clause #104 (by clausification #[103]): ∀ (a a_1 a_2 a_3 : Iota),
% 25.24/25.53 Eq
% 25.24/25.53 (And (path a a_1 a_2) (on_path a_3 a_2) →
% 25.24/25.53 And (And (edge a_3) (in_path (head_of a_3) a_2)) (in_path (tail_of a_3) a_2))
% 25.24/25.53 True
% 25.24/25.53 Clause #105 (by clausification #[104]): ∀ (a a_1 a_2 a_3 : Iota),
% 25.24/25.53 Or (Eq (And (path a a_1 a_2) (on_path a_3 a_2)) False)
% 25.24/25.53 (Eq (And (And (edge a_3) (in_path (head_of a_3) a_2)) (in_path (tail_of a_3) a_2)) True)
% 25.24/25.53 Clause #106 (by clausification #[105]): ∀ (a a_1 a_2 a_3 : Iota),
% 25.24/25.53 Or (Eq (And (And (edge a) (in_path (head_of a) a_1)) (in_path (tail_of a) a_1)) True)
% 25.24/25.53 (Or (Eq (path a_2 a_3 a_1) False) (Eq (on_path a a_1) False))
% 25.24/25.53 Clause #108 (by clausification #[106]): ∀ (a a_1 a_2 a_3 : Iota),
% 25.24/25.53 Or (Eq (path a a_1 a_2) False)
% 25.24/25.53 (Or (Eq (on_path a_3 a_2) False) (Eq (And (edge a_3) (in_path (head_of a_3) a_2)) True))
% 25.24/25.53 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))
% 25.24/25.53 Clause #145 (by clausification #[7]): ∀ (a : Iota),
% 25.24/25.53 Eq (∀ (E2 : Iota), Iff (sequential a E2) (And (And (And (edge a) (edge E2)) (Ne a E2)) (Eq (head_of a) (tail_of E2))))
% 25.24/25.53 True
% 25.24/25.53 Clause #146 (by clausification #[145]): ∀ (a a_1 : Iota),
% 25.24/25.53 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
% 25.24/25.53 Clause #147 (by clausification #[146]): ∀ (a a_1 : Iota),
% 25.24/25.53 Or (Eq (sequential a a_1) True)
% 25.24/25.53 (Eq (And (And (And (edge a) (edge a_1)) (Ne a a_1)) (Eq (head_of a) (tail_of a_1))) False)
% 25.24/25.53 Clause #149 (by clausification #[147]): ∀ (a a_1 : Iota),
% 25.24/25.53 Or (Eq (sequential a a_1) True)
% 25.24/25.53 (Or (Eq (And (And (edge a) (edge a_1)) (Ne a a_1)) False) (Eq (Eq (head_of a) (tail_of a_1)) False))
% 25.24/25.53 Clause #150 (by clausification #[149]): ∀ (a a_1 : Iota),
% 25.24/25.53 Or (Eq (sequential a a_1) True)
% 25.24/25.53 (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)))
% 25.24/25.53 Clause #151 (by clausification #[150]): ∀ (a a_1 : Iota),
% 25.24/25.53 Or (Eq (sequential a a_1) True)
% 25.24/25.53 (Or (Eq (And (edge a) (edge a_1)) False) (Or (Eq (Ne a a_1) False) (Ne (head_of a) (tail_of a_1))))
% 25.33/25.55 Clause #152 (by clausification #[151]): ∀ (a a_1 : Iota),
% 25.33/25.55 Or (Eq (sequential a a_1) True)
% 25.33/25.55 (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))))
% 25.33/25.55 Clause #153 (by clausification #[152]): ∀ (a a_1 : Iota),
% 25.33/25.55 Or (Eq (sequential a a_1) True)
% 25.33/25.55 (Or (Ne (head_of a) (tail_of a_1)) (Or (Eq (edge a) False) (Or (Eq (edge a_1) False) (Eq a a_1))))
% 25.33/25.55 Clause #157 (by clausification #[9]): ∀ (a : Iota),
% 25.33/25.55 Eq
% 25.33/25.55 (∀ (V1 V2 : Iota),
% 25.33/25.55 path V1 V2 a →
% 25.33/25.55 ∀ (E1 E2 : Iota),
% 25.33/25.55 precedes E1 E2 a →
% 25.33/25.55 And (And (on_path E1 a) (on_path E2 a))
% 25.33/25.55 (Not (Iff (sequential E1 E2) (Exists fun E3 => And (sequential E1 E3) (precedes E3 E2 a)))))
% 25.33/25.55 True
% 25.33/25.55 Clause #158 (by clausification #[157]): ∀ (a a_1 : Iota),
% 25.33/25.55 Eq
% 25.33/25.55 (∀ (V2 : Iota),
% 25.33/25.55 path a V2 a_1 →
% 25.33/25.55 ∀ (E1 E2 : Iota),
% 25.33/25.55 precedes E1 E2 a_1 →
% 25.33/25.55 And (And (on_path E1 a_1) (on_path E2 a_1))
% 25.33/25.55 (Not (Iff (sequential E1 E2) (Exists fun E3 => And (sequential E1 E3) (precedes E3 E2 a_1)))))
% 25.33/25.55 True
% 25.33/25.55 Clause #159 (by clausification #[158]): ∀ (a a_1 a_2 : Iota),
% 25.33/25.55 Eq
% 25.33/25.55 (path a a_1 a_2 →
% 25.33/25.55 ∀ (E1 E2 : Iota),
% 25.33/25.55 precedes E1 E2 a_2 →
% 25.33/25.55 And (And (on_path E1 a_2) (on_path E2 a_2))
% 25.33/25.55 (Not (Iff (sequential E1 E2) (Exists fun E3 => And (sequential E1 E3) (precedes E3 E2 a_2)))))
% 25.33/25.55 True
% 25.33/25.55 Clause #160 (by clausification #[159]): ∀ (a a_1 a_2 : Iota),
% 25.33/25.55 Or (Eq (path a a_1 a_2) False)
% 25.33/25.55 (Eq
% 25.33/25.55 (∀ (E1 E2 : Iota),
% 25.33/25.55 precedes E1 E2 a_2 →
% 25.33/25.55 And (And (on_path E1 a_2) (on_path E2 a_2))
% 25.33/25.55 (Not (Iff (sequential E1 E2) (Exists fun E3 => And (sequential E1 E3) (precedes E3 E2 a_2)))))
% 25.33/25.55 True)
% 25.33/25.55 Clause #161 (by clausification #[160]): ∀ (a a_1 a_2 a_3 : Iota),
% 25.33/25.55 Or (Eq (path a a_1 a_2) False)
% 25.33/25.55 (Eq
% 25.33/25.55 (∀ (E2 : Iota),
% 25.33/25.55 precedes a_3 E2 a_2 →
% 25.33/25.55 And (And (on_path a_3 a_2) (on_path E2 a_2))
% 25.33/25.55 (Not (Iff (sequential a_3 E2) (Exists fun E3 => And (sequential a_3 E3) (precedes E3 E2 a_2)))))
% 25.33/25.55 True)
% 25.33/25.55 Clause #162 (by clausification #[161]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.33/25.55 Or (Eq (path a a_1 a_2) False)
% 25.33/25.55 (Eq
% 25.33/25.55 (precedes a_3 a_4 a_2 →
% 25.33/25.55 And (And (on_path a_3 a_2) (on_path a_4 a_2))
% 25.33/25.55 (Not (Iff (sequential a_3 a_4) (Exists fun E3 => And (sequential a_3 E3) (precedes E3 a_4 a_2)))))
% 25.33/25.55 True)
% 25.33/25.55 Clause #163 (by clausification #[162]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.33/25.55 Or (Eq (path a a_1 a_2) False)
% 25.33/25.55 (Or (Eq (precedes a_3 a_4 a_2) False)
% 25.33/25.55 (Eq
% 25.33/25.55 (And (And (on_path a_3 a_2) (on_path a_4 a_2))
% 25.33/25.55 (Not (Iff (sequential a_3 a_4) (Exists fun E3 => And (sequential a_3 E3) (precedes E3 a_4 a_2)))))
% 25.33/25.55 True))
% 25.33/25.55 Clause #165 (by clausification #[163]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.33/25.55 Or (Eq (path a a_1 a_2) False)
% 25.33/25.55 (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))
% 25.33/25.55 Clause #177 (by clausification #[165]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.33/25.55 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))
% 25.33/25.55 Clause #178 (by clausification #[165]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.33/25.55 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))
% 25.33/25.55 Clause #179 (by clausification #[10]): ∀ (a : Iota),
% 25.33/25.55 Eq
% 25.33/25.55 (∀ (V2 SP : Iota),
% 25.33/25.55 Iff (shortest_path a V2 SP)
% 25.33/25.55 (And (And (path a V2 SP) (Ne a V2)) (∀ (P : Iota), path a V2 P → less_or_equal (length_of SP) (length_of P))))
% 25.33/25.55 True
% 25.33/25.55 Clause #180 (by clausification #[179]): ∀ (a a_1 : Iota),
% 25.33/25.55 Eq
% 25.33/25.55 (∀ (SP : Iota),
% 25.33/25.55 Iff (shortest_path a a_1 SP)
% 25.33/25.55 (And (And (path a a_1 SP) (Ne a a_1))
% 25.33/25.55 (∀ (P : Iota), path a a_1 P → less_or_equal (length_of SP) (length_of P))))
% 25.33/25.55 True
% 25.33/25.55 Clause #181 (by clausification #[180]): ∀ (a a_1 a_2 : Iota),
% 25.33/25.55 Eq
% 25.33/25.55 (Iff (shortest_path a a_1 a_2)
% 25.33/25.55 (And (And (path a a_1 a_2) (Ne a a_1))
% 25.33/25.55 (∀ (P : Iota), path a a_1 P → less_or_equal (length_of a_2) (length_of P))))
% 25.33/25.55 True
% 25.33/25.55 Clause #183 (by clausification #[181]): ∀ (a a_1 a_2 : Iota),
% 25.33/25.58 Or (Eq (shortest_path a a_1 a_2) False)
% 25.33/25.58 (Eq
% 25.33/25.58 (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)))
% 25.33/25.58 True)
% 25.33/25.58 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)
% 25.33/25.58 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)
% 25.33/25.58 Clause #202 (by clausification #[11]): ∀ (a : Iota),
% 25.33/25.58 Eq
% 25.33/25.58 (∀ (V2 E1 E2 P : Iota),
% 25.33/25.58 And (shortest_path a V2 P) (precedes E1 E2 P) →
% 25.33/25.58 And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of E1)) (Eq (head_of E3) (head_of E2))))
% 25.33/25.58 (Not (precedes E2 E1 P)))
% 25.33/25.58 True
% 25.33/25.58 Clause #203 (by clausification #[202]): ∀ (a a_1 : Iota),
% 25.33/25.58 Eq
% 25.33/25.58 (∀ (E1 E2 P : Iota),
% 25.33/25.58 And (shortest_path a a_1 P) (precedes E1 E2 P) →
% 25.33/25.58 And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of E1)) (Eq (head_of E3) (head_of E2))))
% 25.33/25.58 (Not (precedes E2 E1 P)))
% 25.33/25.58 True
% 25.33/25.58 Clause #204 (by clausification #[203]): ∀ (a a_1 a_2 : Iota),
% 25.33/25.58 Eq
% 25.33/25.58 (∀ (E2 P : Iota),
% 25.33/25.58 And (shortest_path a a_1 P) (precedes a_2 E2 P) →
% 25.33/25.58 And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of a_2)) (Eq (head_of E3) (head_of E2))))
% 25.33/25.58 (Not (precedes E2 a_2 P)))
% 25.33/25.58 True
% 25.33/25.58 Clause #205 (by clausification #[204]): ∀ (a a_1 a_2 a_3 : Iota),
% 25.33/25.58 Eq
% 25.33/25.58 (∀ (P : Iota),
% 25.33/25.58 And (shortest_path a a_1 P) (precedes a_2 a_3 P) →
% 25.33/25.58 And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of a_2)) (Eq (head_of E3) (head_of a_3))))
% 25.33/25.58 (Not (precedes a_3 a_2 P)))
% 25.33/25.58 True
% 25.33/25.58 Clause #206 (by clausification #[205]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.33/25.58 Eq
% 25.33/25.58 (And (shortest_path a a_1 a_2) (precedes a_3 a_4 a_2) →
% 25.33/25.58 And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of a_3)) (Eq (head_of E3) (head_of a_4))))
% 25.33/25.58 (Not (precedes a_4 a_3 a_2)))
% 25.33/25.58 True
% 25.33/25.58 Clause #207 (by clausification #[206]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.33/25.58 Or (Eq (And (shortest_path a a_1 a_2) (precedes a_3 a_4 a_2)) False)
% 25.33/25.58 (Eq
% 25.33/25.58 (And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of a_3)) (Eq (head_of E3) (head_of a_4))))
% 25.33/25.58 (Not (precedes a_4 a_3 a_2)))
% 25.33/25.58 True)
% 25.33/25.58 Clause #208 (by clausification #[207]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.33/25.58 Or
% 25.33/25.58 (Eq
% 25.33/25.58 (And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of a)) (Eq (head_of E3) (head_of a_1))))
% 25.33/25.58 (Not (precedes a_1 a a_2)))
% 25.33/25.58 True)
% 25.33/25.58 (Or (Eq (shortest_path a_3 a_4 a_2) False) (Eq (precedes a a_1 a_2) False))
% 25.33/25.58 Clause #209 (by clausification #[208]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.33/25.58 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))
% 25.33/25.58 Clause #210 (by clausification #[208]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.33/25.58 Or (Eq (shortest_path a a_1 a_2) False)
% 25.33/25.58 (Or (Eq (precedes a_3 a_4 a_2) False)
% 25.33/25.58 (Eq (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of a_3)) (Eq (head_of E3) (head_of a_4)))) True))
% 25.33/25.58 Clause #211 (by clausification #[209]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.33/25.58 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))
% 25.33/25.58 Clause #212 (by clausification #[210]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.33/25.58 Or (Eq (shortest_path a a_1 a_2) False)
% 25.33/25.58 (Or (Eq (precedes a_3 a_4 a_2) False)
% 25.33/25.58 (Eq (Exists fun E3 => And (Eq (tail_of E3) (tail_of a_3)) (Eq (head_of E3) (head_of a_4))) False))
% 25.33/25.58 Clause #213 (by clausification #[212]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 25.33/25.58 Or (Eq (shortest_path a a_1 a_2) False)
% 25.33/25.58 (Or (Eq (precedes a_3 a_4 a_2) False)
% 25.33/25.58 (Eq (And (Eq (tail_of a_5) (tail_of a_3)) (Eq (head_of a_5) (head_of a_4))) False))
% 25.33/25.58 Clause #214 (by clausification #[213]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 25.33/25.58 Or (Eq (shortest_path a a_1 a_2) False)
% 25.33/25.58 (Or (Eq (precedes a_3 a_4 a_2) False)
% 25.33/25.58 (Or (Eq (Eq (tail_of a_5) (tail_of a_3)) False) (Eq (Eq (head_of a_5) (head_of a_4)) False)))
% 25.33/25.58 Clause #215 (by clausification #[214]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 25.36/25.60 Or (Eq (shortest_path a a_1 a_2) False)
% 25.36/25.60 (Or (Eq (precedes a_3 a_4 a_2) False)
% 25.36/25.60 (Or (Eq (Eq (head_of a_5) (head_of a_4)) False) (Ne (tail_of a_5) (tail_of a_3))))
% 25.36/25.60 Clause #216 (by clausification #[215]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 25.36/25.60 Or (Eq (shortest_path a a_1 a_2) False)
% 25.36/25.60 (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))))
% 25.36/25.60 Clause #231 (by clausification #[17]): Eq
% 25.36/25.60 (∀ (V1 V2 E1 E2 P : Iota),
% 25.36/25.60 And (shortest_path V1 V2 P) (precedes E1 E2 P) →
% 25.36/25.60 And
% 25.36/25.60 (And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of E1)) (Eq (head_of E3) (head_of E2))))
% 25.36/25.60 (Ne (head_of E2) (tail_of E1)))
% 25.36/25.60 (Ne (head_of E2) (head_of E1)))
% 25.36/25.60 False
% 25.36/25.60 Clause #232 (by clausification #[231]): ∀ (a : Iota),
% 25.36/25.60 Eq
% 25.36/25.60 (Not
% 25.36/25.60 (∀ (V2 E1 E2 P : Iota),
% 25.36/25.60 And (shortest_path (skS.0 7 a) V2 P) (precedes E1 E2 P) →
% 25.36/25.60 And
% 25.36/25.60 (And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of E1)) (Eq (head_of E3) (head_of E2))))
% 25.36/25.60 (Ne (head_of E2) (tail_of E1)))
% 25.36/25.60 (Ne (head_of E2) (head_of E1))))
% 25.36/25.60 True
% 25.36/25.60 Clause #233 (by clausification #[232]): ∀ (a : Iota),
% 25.36/25.60 Eq
% 25.36/25.60 (∀ (V2 E1 E2 P : Iota),
% 25.36/25.60 And (shortest_path (skS.0 7 a) V2 P) (precedes E1 E2 P) →
% 25.36/25.60 And
% 25.36/25.60 (And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of E1)) (Eq (head_of E3) (head_of E2))))
% 25.36/25.60 (Ne (head_of E2) (tail_of E1)))
% 25.36/25.60 (Ne (head_of E2) (head_of E1)))
% 25.36/25.60 False
% 25.36/25.60 Clause #234 (by clausification #[233]): ∀ (a a_1 : Iota),
% 25.36/25.60 Eq
% 25.36/25.60 (Not
% 25.36/25.60 (∀ (E1 E2 P : Iota),
% 25.36/25.60 And (shortest_path (skS.0 7 a) (skS.0 8 a a_1) P) (precedes E1 E2 P) →
% 25.36/25.60 And
% 25.36/25.60 (And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of E1)) (Eq (head_of E3) (head_of E2))))
% 25.36/25.60 (Ne (head_of E2) (tail_of E1)))
% 25.36/25.60 (Ne (head_of E2) (head_of E1))))
% 25.36/25.60 True
% 25.36/25.60 Clause #235 (by clausification #[234]): ∀ (a a_1 : Iota),
% 25.36/25.60 Eq
% 25.36/25.60 (∀ (E1 E2 P : Iota),
% 25.36/25.60 And (shortest_path (skS.0 7 a) (skS.0 8 a a_1) P) (precedes E1 E2 P) →
% 25.36/25.60 And
% 25.36/25.60 (And (Not (Exists fun E3 => And (Eq (tail_of E3) (tail_of E1)) (Eq (head_of E3) (head_of E2))))
% 25.36/25.60 (Ne (head_of E2) (tail_of E1)))
% 25.36/25.60 (Ne (head_of E2) (head_of E1)))
% 25.36/25.60 False
% 25.36/25.60 Clause #236 (by clausification #[235]): ∀ (a a_1 a_2 : Iota),
% 25.36/25.60 Eq
% 25.36/25.60 (Not
% 25.36/25.60 (∀ (E2 P : Iota),
% 25.36/25.60 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) →
% 25.36/25.60 And
% 25.36/25.60 (And
% 25.36/25.60 (Not
% 25.36/25.60 (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))))
% 25.36/25.60 (Ne (head_of E2) (tail_of (skS.0 9 a a_1 a_2))))
% 25.36/25.60 (Ne (head_of E2) (head_of (skS.0 9 a a_1 a_2)))))
% 25.36/25.60 True
% 25.36/25.60 Clause #237 (by clausification #[236]): ∀ (a a_1 a_2 : Iota),
% 25.36/25.60 Eq
% 25.36/25.60 (∀ (E2 P : Iota),
% 25.36/25.60 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) →
% 25.36/25.60 And
% 25.36/25.60 (And
% 25.36/25.60 (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))))
% 25.36/25.60 (Ne (head_of E2) (tail_of (skS.0 9 a a_1 a_2))))
% 25.36/25.60 (Ne (head_of E2) (head_of (skS.0 9 a a_1 a_2))))
% 25.36/25.60 False
% 25.36/25.60 Clause #238 (by clausification #[237]): ∀ (a a_1 a_2 a_3 : Iota),
% 25.36/25.60 Eq
% 25.36/25.60 (Not
% 25.36/25.60 (∀ (P : Iota),
% 25.36/25.60 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) →
% 25.36/25.60 And
% 25.36/25.60 (And
% 25.36/25.60 (Not
% 25.36/25.60 (Exists fun E3 =>
% 25.36/25.60 And (Eq (tail_of E3) (tail_of (skS.0 9 a a_1 a_2)))
% 25.36/25.60 (Eq (head_of E3) (head_of (skS.0 10 a a_1 a_2 a_3)))))
% 25.36/25.60 (Ne (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2))))
% 25.36/25.60 (Ne (head_of (skS.0 10 a a_1 a_2 a_3)) (head_of (skS.0 9 a a_1 a_2)))))
% 25.36/25.60 True
% 25.36/25.60 Clause #239 (by clausification #[238]): ∀ (a a_1 a_2 a_3 : Iota),
% 25.36/25.60 Eq
% 25.36/25.60 (∀ (P : Iota),
% 25.36/25.60 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) →
% 25.36/25.63 And
% 25.36/25.63 (And
% 25.36/25.63 (Not
% 25.36/25.63 (Exists fun E3 =>
% 25.36/25.63 And (Eq (tail_of E3) (tail_of (skS.0 9 a a_1 a_2)))
% 25.36/25.63 (Eq (head_of E3) (head_of (skS.0 10 a a_1 a_2 a_3)))))
% 25.36/25.63 (Ne (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2))))
% 25.36/25.63 (Ne (head_of (skS.0 10 a a_1 a_2 a_3)) (head_of (skS.0 9 a a_1 a_2))))
% 25.36/25.63 False
% 25.36/25.63 Clause #240 (by clausification #[239]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.36/25.63 Eq
% 25.36/25.63 (Not
% 25.36/25.63 (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))
% 25.36/25.63 (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)) →
% 25.36/25.63 And
% 25.36/25.63 (And
% 25.36/25.63 (Not
% 25.36/25.63 (Exists fun E3 =>
% 25.36/25.63 And (Eq (tail_of E3) (tail_of (skS.0 9 a a_1 a_2)))
% 25.36/25.63 (Eq (head_of E3) (head_of (skS.0 10 a a_1 a_2 a_3)))))
% 25.36/25.63 (Ne (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2))))
% 25.36/25.63 (Ne (head_of (skS.0 10 a a_1 a_2 a_3)) (head_of (skS.0 9 a a_1 a_2)))))
% 25.36/25.63 True
% 25.36/25.63 Clause #241 (by clausification #[240]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.36/25.63 Eq
% 25.36/25.63 (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))
% 25.36/25.63 (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)) →
% 25.36/25.63 And
% 25.36/25.63 (And
% 25.36/25.63 (Not
% 25.36/25.63 (Exists fun E3 =>
% 25.36/25.63 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)))))
% 25.36/25.63 (Ne (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2))))
% 25.36/25.63 (Ne (head_of (skS.0 10 a a_1 a_2 a_3)) (head_of (skS.0 9 a a_1 a_2))))
% 25.36/25.63 False
% 25.36/25.63 Clause #242 (by clausification #[241]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.36/25.63 Eq
% 25.36/25.63 (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))
% 25.36/25.63 (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)))
% 25.36/25.63 True
% 25.36/25.63 Clause #243 (by clausification #[241]): ∀ (a a_1 a_2 a_3 : Iota),
% 25.36/25.63 Eq
% 25.36/25.63 (And
% 25.36/25.63 (And
% 25.36/25.63 (Not
% 25.36/25.63 (Exists fun E3 =>
% 25.36/25.63 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)))))
% 25.36/25.63 (Ne (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2))))
% 25.36/25.63 (Ne (head_of (skS.0 10 a a_1 a_2 a_3)) (head_of (skS.0 9 a a_1 a_2))))
% 25.36/25.63 False
% 25.36/25.63 Clause #244 (by clausification #[242]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.36/25.63 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
% 25.36/25.63 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
% 25.36/25.63 Clause #253 (by superposition #[245, 196]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.36/25.63 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)
% 25.36/25.63 Clause #254 (by superposition #[245, 211]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 25.36/25.63 Or (Eq True False)
% 25.36/25.63 (Or (Eq (precedes a a_1 (skS.0 11 a_2 a_3 a_4 a_5 a_6)) False)
% 25.36/25.63 (Eq (precedes a_1 a (skS.0 11 a_2 a_3 a_4 a_5 a_6)) False))
% 25.36/25.63 Clause #255 (by superposition #[245, 216]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 25.36/25.63 Or (Eq True False)
% 25.36/25.63 (Or (Eq (precedes a a_1 (skS.0 11 a_2 a_3 a_4 a_5 a_6)) False)
% 25.36/25.63 (Or (Ne (tail_of a_7) (tail_of a)) (Ne (head_of a_7) (head_of a_1))))
% 25.36/25.63 Clause #263 (by clausification #[255]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 25.36/25.63 Or (Eq (precedes a a_1 (skS.0 11 a_2 a_3 a_4 a_5 a_6)) False)
% 25.36/25.63 (Or (Ne (tail_of a_7) (tail_of a)) (Ne (head_of a_7) (head_of a_1)))
% 25.36/25.63 Clause #264 (by superposition #[263, 244]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.36/25.63 Or (Ne (tail_of a) (tail_of (skS.0 9 a_1 a_2 a_3)))
% 25.36/25.63 (Or (Ne (head_of a) (head_of (skS.0 10 a_1 a_2 a_3 a_4))) (Eq False True))
% 25.36/25.63 Clause #265 (by clausification #[264]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.36/25.63 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)))
% 25.36/25.63 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))
% 25.41/25.66 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
% 25.41/25.66 Clause #277 (by superposition #[267, 130]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 25.41/25.66 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))
% 25.41/25.66 Clause #278 (by superposition #[267, 78]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 25.41/25.66 Or (Eq True False)
% 25.41/25.66 (Or (Eq (precedes a a_1 (skS.0 11 a_2 a_3 a_4 a_5 a_6)) True)
% 25.41/25.66 (Or (Eq (on_path a (skS.0 11 a_2 a_3 a_4 a_5 a_6)) False)
% 25.41/25.66 (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))))
% 25.41/25.66 Clause #283 (by superposition #[267, 177]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 25.41/25.66 Or (Eq True False)
% 25.41/25.66 (Or (Eq (precedes a a_1 (skS.0 11 a_2 a_3 a_4 a_5 a_6)) False)
% 25.41/25.66 (Eq (on_path a_1 (skS.0 11 a_2 a_3 a_4 a_5 a_6)) True))
% 25.41/25.66 Clause #284 (by superposition #[267, 178]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 25.41/25.66 Or (Eq True False)
% 25.41/25.66 (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))
% 25.41/25.66 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)
% 25.41/25.66 Clause #322 (by clausification #[284]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 25.41/25.66 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)
% 25.41/25.66 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)
% 25.41/25.66 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
% 25.41/25.66 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)
% 25.41/25.66 Clause #327 (by clausification #[325]): ∀ (a a_1 a_2 : Iota), Eq (edge (skS.0 9 a a_1 a_2)) True
% 25.41/25.66 Clause #334 (by clausification #[243]): ∀ (a a_1 a_2 a_3 : Iota),
% 25.41/25.66 Or
% 25.41/25.66 (Eq
% 25.41/25.66 (And
% 25.41/25.66 (Not
% 25.41/25.66 (Exists fun E3 =>
% 25.41/25.66 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)))))
% 25.41/25.66 (Ne (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2))))
% 25.41/25.66 False)
% 25.41/25.66 (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)
% 25.41/25.66 Clause #335 (by clausification #[334]): ∀ (a a_1 a_2 a_3 : Iota),
% 25.41/25.66 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)
% 25.41/25.66 (Or
% 25.41/25.66 (Eq
% 25.41/25.66 (Not
% 25.41/25.66 (Exists fun E3 =>
% 25.41/25.66 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)))))
% 25.41/25.66 False)
% 25.41/25.66 (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))
% 25.41/25.66 Clause #336 (by clausification #[335]): ∀ (a a_1 a_2 a_3 : Iota),
% 25.41/25.66 Or
% 25.41/25.66 (Eq
% 25.41/25.66 (Not
% 25.41/25.66 (Exists fun E3 =>
% 25.41/25.66 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)))))
% 25.41/25.66 False)
% 25.41/25.66 (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)
% 25.41/25.66 (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (head_of (skS.0 9 a a_1 a_2))))
% 25.41/25.66 Clause #337 (by clausification #[336]): ∀ (a a_1 a_2 a_3 : Iota),
% 25.41/25.66 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)
% 25.41/25.66 (Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (head_of (skS.0 9 a a_1 a_2)))
% 25.41/25.66 (Eq
% 25.41/25.66 (Exists fun E3 =>
% 25.41/25.66 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))))
% 25.41/25.66 True))
% 25.41/25.66 Clause #338 (by clausification #[337]): ∀ (a a_1 a_2 a_3 : Iota),
% 25.41/25.66 Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (head_of (skS.0 9 a a_1 a_2)))
% 25.41/25.66 (Or
% 25.41/25.66 (Eq
% 25.41/25.66 (Exists fun E3 =>
% 25.41/25.66 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))))
% 25.41/25.66 True)
% 25.41/25.66 (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2))))
% 25.41/25.66 Clause #339 (by clausification #[338]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.41/25.69 Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (head_of (skS.0 9 a a_1 a_2)))
% 25.41/25.69 (Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2)))
% 25.41/25.69 (Eq
% 25.41/25.69 (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)))
% 25.41/25.69 (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))))
% 25.41/25.69 True))
% 25.41/25.69 Clause #340 (by clausification #[339]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.41/25.69 Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (head_of (skS.0 9 a a_1 a_2)))
% 25.41/25.69 (Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2)))
% 25.41/25.69 (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))
% 25.41/25.69 Clause #341 (by clausification #[339]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.41/25.69 Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (head_of (skS.0 9 a a_1 a_2)))
% 25.41/25.69 (Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2)))
% 25.41/25.69 (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))
% 25.41/25.69 Clause #342 (by clausification #[340]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.41/25.69 Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (head_of (skS.0 9 a a_1 a_2)))
% 25.41/25.69 (Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2)))
% 25.41/25.69 (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))))
% 25.41/25.69 Clause #343 (by forward contextual literal cutting #[342, 266]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.41/25.69 Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2)))
% 25.41/25.69 (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)))
% 25.41/25.69 Clause #348 (by clausification #[283]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 25.41/25.69 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)
% 25.41/25.69 Clause #349 (by superposition #[348, 244]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.41/25.69 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)
% 25.41/25.69 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
% 25.41/25.69 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)
% 25.41/25.69 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
% 25.41/25.69 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)))
% 25.41/25.69 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))
% 25.41/25.69 Clause #365 (by clausification #[254]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 25.41/25.69 Or (Eq (precedes a a_1 (skS.0 11 a_2 a_3 a_4 a_5 a_6)) False)
% 25.41/25.69 (Eq (precedes a_1 a (skS.0 11 a_2 a_3 a_4 a_5 a_6)) False)
% 25.41/25.69 Clause #366 (by superposition #[365, 244]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.41/25.69 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)
% 25.41/25.69 Clause #378 (by clausification #[366]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.41/25.69 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
% 25.41/25.69 Clause #430 (by clausification #[278]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 25.41/25.69 Or (Eq (precedes a a_1 (skS.0 11 a_2 a_3 a_4 a_5 a_6)) True)
% 25.41/25.69 (Or (Eq (on_path a (skS.0 11 a_2 a_3 a_4 a_5 a_6)) False)
% 25.41/25.69 (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)))
% 25.41/25.69 Clause #432 (by superposition #[430, 350]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 25.41/25.69 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)
% 25.41/25.69 (Or (Eq (on_path a_4 (skS.0 11 a a_1 a_2 a_3 a_5)) False)
% 25.41/25.69 (Or (Eq (sequential (skS.0 10 a a_1 a_2 a_3) a_4) False) (Eq False True)))
% 25.41/25.69 Clause #572 (by clausification #[432]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 25.41/25.69 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)
% 25.41/25.69 (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))
% 25.41/25.72 Clause #573 (by superposition #[572, 324]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.41/25.72 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)
% 25.41/25.72 (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))
% 25.41/25.72 Clause #630 (by clausification #[341]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.41/25.72 Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (head_of (skS.0 9 a a_1 a_2)))
% 25.41/25.72 (Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2)))
% 25.41/25.72 (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))))
% 25.41/25.72 Clause #631 (by forward contextual literal cutting #[630, 266]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.41/25.72 Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2)))
% 25.41/25.72 (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)))
% 25.41/25.72 Clause #635 (by superposition #[631, 265]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 a_8 : Iota),
% 25.41/25.72 Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2)))
% 25.41/25.72 (Or (Ne (tail_of (skS.0 9 a a_1 a_2)) (tail_of (skS.0 9 a_4 a_5 a_6)))
% 25.41/25.72 (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))))
% 25.41/25.72 Clause #782 (by clausification #[573]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.41/25.72 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)
% 25.41/25.72 (Eq (sequential (skS.0 10 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2)) False)
% 25.41/25.72 Clause #1020 (by equality resolution #[635]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 25.41/25.72 Or (Eq (head_of (skS.0 10 a a_1 a_2 a_3)) (tail_of (skS.0 9 a a_1 a_2)))
% 25.41/25.72 (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)))
% 25.41/25.72 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))
% 25.41/25.72 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))
% 25.41/25.72 Clause #1042 (by superposition #[1022, 153]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.41/25.72 Or (Eq (sequential (skS.0 10 a a_1 a_2 a_3) a_4) True)
% 25.41/25.72 (Or (Ne (tail_of (skS.0 9 a a_1 a_2)) (tail_of a_4))
% 25.41/25.72 (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))))
% 25.41/25.72 Clause #1125 (by forward demodulation #[1042, 355]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.41/25.72 Or (Eq (sequential (skS.0 10 a a_1 a_2 a_3) a_4) True)
% 25.41/25.72 (Or (Ne (tail_of (skS.0 9 a a_1 a_2)) (tail_of a_4))
% 25.41/25.72 (Or (Eq True False) (Or (Eq (edge a_4) False) (Eq (skS.0 10 a a_1 a_2 a_3) a_4))))
% 25.41/25.72 Clause #1126 (by clausification #[1125]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.41/25.72 Or (Eq (sequential (skS.0 10 a a_1 a_2 a_3) a_4) True)
% 25.41/25.72 (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)))
% 25.41/25.72 Clause #1127 (by equality resolution #[1126]): ∀ (a a_1 a_2 a_3 : Iota),
% 25.41/25.72 Or (Eq (sequential (skS.0 10 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2)) True)
% 25.41/25.72 (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)))
% 25.41/25.72 Clause #1132 (by forward demodulation #[1127, 327]): ∀ (a a_1 a_2 a_3 : Iota),
% 25.41/25.72 Or (Eq (sequential (skS.0 10 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2)) True)
% 25.41/25.72 (Or (Eq True False) (Eq (skS.0 10 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2)))
% 25.41/25.72 Clause #1133 (by clausification #[1132]): ∀ (a a_1 a_2 a_3 : Iota),
% 25.41/25.72 Or (Eq (sequential (skS.0 10 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2)) True)
% 25.41/25.72 (Eq (skS.0 10 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2))
% 25.41/25.72 Clause #1134 (by superposition #[1133, 782]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.41/25.72 Or (Eq (skS.0 10 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2))
% 25.41/25.72 (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))
% 25.41/25.72 Clause #1149 (by clausification #[1134]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 25.41/25.72 Or (Eq (skS.0 10 a a_1 a_2 a_3) (skS.0 9 a a_1 a_2))
% 25.41/25.72 (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)
% 25.41/25.72 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)
% 25.41/25.72 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)
% 25.41/25.72 Clause #1202 (by backward positive simplify reflect #[1158, 1024]): False
% 25.41/25.72 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------