TSTP Solution File: GRA010+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : GRA010+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n017.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 00:01:28 EDT 2023
% Result : Theorem 212.92s 213.27s
% Output : Proof 213.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRA010+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.07/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 02:44:56 EDT 2023
% 0.14/0.35 % CPUTime :
% 212.92/213.27 SZS status Theorem for theBenchmark.p
% 212.92/213.27 SZS output start Proof for theBenchmark.p
% 212.92/213.27 Clause #15 (by assumption #[]): Eq
% 212.92/213.27 (∀ (P V1 V2 : Iota),
% 212.92/213.27 And (path V1 V2 P)
% 212.92/213.27 (∀ (E1 E2 : Iota),
% 212.92/213.27 And (And (on_path E1 P) (on_path E2 P)) (sequential E1 E2) → Exists fun E3 => triangle E1 E2 E3) →
% 212.92/213.27 Eq (number_of_in sequential_pairs P) (number_of_in triangles P))
% 212.92/213.27 True
% 212.92/213.27 Clause #17 (by assumption #[]): Eq
% 212.92/213.27 (Not
% 212.92/213.27 (complete →
% 212.92/213.27 ∀ (P V1 V2 : Iota),
% 212.92/213.27 And (path V1 V2 P)
% 212.92/213.27 (∀ (E1 E2 : Iota),
% 212.92/213.27 And (And (on_path E1 P) (on_path E2 P)) (sequential E1 E2) → Exists fun E3 => triangle E1 E2 E3) →
% 212.92/213.27 Eq (number_of_in sequential_pairs P) (number_of_in triangles P)))
% 212.92/213.27 True
% 212.92/213.27 Clause #81 (by betaEtaReduce #[15]): Eq
% 212.92/213.27 (∀ (P V1 V2 : Iota),
% 212.92/213.27 And (path V1 V2 P)
% 212.92/213.27 (∀ (E1 E2 : Iota), And (And (on_path E1 P) (on_path E2 P)) (sequential E1 E2) → Exists (triangle E1 E2)) →
% 212.92/213.27 Eq (number_of_in sequential_pairs P) (number_of_in triangles P))
% 212.92/213.27 True
% 212.92/213.27 Clause #82 (by clausification #[81]): ∀ (a : Iota),
% 212.92/213.27 Eq
% 212.92/213.27 (∀ (V1 V2 : Iota),
% 212.92/213.27 And (path V1 V2 a)
% 212.92/213.27 (∀ (E1 E2 : Iota), And (And (on_path E1 a) (on_path E2 a)) (sequential E1 E2) → Exists (triangle E1 E2)) →
% 212.92/213.27 Eq (number_of_in sequential_pairs a) (number_of_in triangles a))
% 212.92/213.27 True
% 212.92/213.27 Clause #83 (by clausification #[82]): ∀ (a a_1 : Iota),
% 212.92/213.27 Eq
% 212.92/213.27 (∀ (V2 : Iota),
% 212.92/213.27 And (path a V2 a_1)
% 212.92/213.27 (∀ (E1 E2 : Iota), And (And (on_path E1 a_1) (on_path E2 a_1)) (sequential E1 E2) → Exists (triangle E1 E2)) →
% 212.92/213.27 Eq (number_of_in sequential_pairs a_1) (number_of_in triangles a_1))
% 212.92/213.27 True
% 212.92/213.27 Clause #84 (by clausification #[83]): ∀ (a a_1 a_2 : Iota),
% 212.92/213.27 Eq
% 212.92/213.27 (And (path a a_1 a_2)
% 212.92/213.27 (∀ (E1 E2 : Iota), And (And (on_path E1 a_2) (on_path E2 a_2)) (sequential E1 E2) → Exists (triangle E1 E2)) →
% 212.92/213.27 Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2))
% 212.92/213.27 True
% 212.92/213.27 Clause #85 (by clausification #[84]): ∀ (a a_1 a_2 : Iota),
% 212.92/213.27 Or
% 212.92/213.27 (Eq
% 212.92/213.27 (And (path a a_1 a_2)
% 212.92/213.27 (∀ (E1 E2 : Iota), And (And (on_path E1 a_2) (on_path E2 a_2)) (sequential E1 E2) → Exists (triangle E1 E2)))
% 212.92/213.27 False)
% 212.92/213.27 (Eq (Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2)) True)
% 212.92/213.27 Clause #86 (by clausification #[85]): ∀ (a a_1 a_2 : Iota),
% 212.92/213.27 Or (Eq (Eq (number_of_in sequential_pairs a) (number_of_in triangles a)) True)
% 212.92/213.27 (Or (Eq (path a_1 a_2 a) False)
% 212.92/213.27 (Eq (∀ (E1 E2 : Iota), And (And (on_path E1 a) (on_path E2 a)) (sequential E1 E2) → Exists (triangle E1 E2))
% 212.92/213.27 False))
% 212.92/213.27 Clause #87 (by clausification #[86]): ∀ (a a_1 a_2 : Iota),
% 212.92/213.27 Or (Eq (path a a_1 a_2) False)
% 212.92/213.27 (Or
% 212.92/213.27 (Eq (∀ (E1 E2 : Iota), And (And (on_path E1 a_2) (on_path E2 a_2)) (sequential E1 E2) → Exists (triangle E1 E2))
% 212.92/213.27 False)
% 212.92/213.27 (Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2)))
% 212.92/213.27 Clause #88 (by clausification #[87]): ∀ (a a_1 a_2 a_3 : Iota),
% 212.92/213.27 Or (Eq (path a a_1 a_2) False)
% 212.92/213.27 (Or (Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2))
% 212.92/213.27 (Eq
% 212.92/213.27 (Not
% 212.92/213.27 (∀ (E2 : Iota),
% 212.92/213.27 And (And (on_path (skS.0 1 a_2 a_3) a_2) (on_path E2 a_2)) (sequential (skS.0 1 a_2 a_3) E2) →
% 212.92/213.27 Exists (triangle (skS.0 1 a_2 a_3) E2)))
% 212.92/213.27 True))
% 212.92/213.27 Clause #89 (by clausification #[88]): ∀ (a a_1 a_2 a_3 : Iota),
% 212.92/213.27 Or (Eq (path a a_1 a_2) False)
% 212.92/213.27 (Or (Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2))
% 212.92/213.27 (Eq
% 212.92/213.27 (∀ (E2 : Iota),
% 212.92/213.27 And (And (on_path (skS.0 1 a_2 a_3) a_2) (on_path E2 a_2)) (sequential (skS.0 1 a_2 a_3) E2) →
% 212.92/213.27 Exists (triangle (skS.0 1 a_2 a_3) E2))
% 212.92/213.27 False))
% 212.92/213.27 Clause #90 (by clausification #[89]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 212.92/213.27 Or (Eq (path a a_1 a_2) False)
% 212.92/213.27 (Or (Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2))
% 212.92/213.27 (Eq
% 212.92/213.27 (Not
% 212.92/213.27 (And (And (on_path (skS.0 1 a_2 a_3) a_2) (on_path (skS.0 2 a_2 a_3 a_4) a_2))
% 212.92/213.27 (sequential (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_4)) →
% 212.92/213.27 Exists (triangle (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_4))))
% 212.99/213.32 True))
% 212.99/213.32 Clause #91 (by clausification #[90]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 212.99/213.32 Or (Eq (path a a_1 a_2) False)
% 212.99/213.32 (Or (Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2))
% 212.99/213.32 (Eq
% 212.99/213.32 (And (And (on_path (skS.0 1 a_2 a_3) a_2) (on_path (skS.0 2 a_2 a_3 a_4) a_2))
% 212.99/213.32 (sequential (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_4)) →
% 212.99/213.32 Exists (triangle (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_4)))
% 212.99/213.32 False))
% 212.99/213.32 Clause #92 (by clausification #[91]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 212.99/213.32 Or (Eq (path a a_1 a_2) False)
% 212.99/213.32 (Or (Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2))
% 212.99/213.32 (Eq
% 212.99/213.32 (And (And (on_path (skS.0 1 a_2 a_3) a_2) (on_path (skS.0 2 a_2 a_3 a_4) a_2))
% 212.99/213.32 (sequential (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_4)))
% 212.99/213.32 True))
% 212.99/213.32 Clause #93 (by clausification #[91]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 212.99/213.32 Or (Eq (path a a_1 a_2) False)
% 212.99/213.32 (Or (Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2))
% 212.99/213.32 (Eq (Exists (triangle (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_4))) False))
% 212.99/213.32 Clause #94 (by clausification #[92]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 212.99/213.32 Or (Eq (path a a_1 a_2) False)
% 212.99/213.32 (Or (Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2))
% 212.99/213.32 (Eq (sequential (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_4)) True))
% 212.99/213.32 Clause #95 (by clausification #[92]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 212.99/213.32 Or (Eq (path a a_1 a_2) False)
% 212.99/213.32 (Or (Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2))
% 212.99/213.32 (Eq (And (on_path (skS.0 1 a_2 a_3) a_2) (on_path (skS.0 2 a_2 a_3 a_4) a_2)) True))
% 212.99/213.32 Clause #101 (by betaEtaReduce #[17]): Eq
% 212.99/213.32 (Not
% 212.99/213.32 (complete →
% 212.99/213.32 ∀ (P V1 V2 : Iota),
% 212.99/213.32 And (path V1 V2 P)
% 212.99/213.32 (∀ (E1 E2 : Iota), And (And (on_path E1 P) (on_path E2 P)) (sequential E1 E2) → Exists (triangle E1 E2)) →
% 212.99/213.32 Eq (number_of_in sequential_pairs P) (number_of_in triangles P)))
% 212.99/213.32 True
% 212.99/213.32 Clause #102 (by clausification #[101]): Eq
% 212.99/213.32 (complete →
% 212.99/213.32 ∀ (P V1 V2 : Iota),
% 212.99/213.32 And (path V1 V2 P)
% 212.99/213.32 (∀ (E1 E2 : Iota), And (And (on_path E1 P) (on_path E2 P)) (sequential E1 E2) → Exists (triangle E1 E2)) →
% 212.99/213.32 Eq (number_of_in sequential_pairs P) (number_of_in triangles P))
% 212.99/213.32 False
% 212.99/213.32 Clause #104 (by clausification #[102]): Eq
% 212.99/213.32 (∀ (P V1 V2 : Iota),
% 212.99/213.32 And (path V1 V2 P)
% 212.99/213.32 (∀ (E1 E2 : Iota), And (And (on_path E1 P) (on_path E2 P)) (sequential E1 E2) → Exists (triangle E1 E2)) →
% 212.99/213.32 Eq (number_of_in sequential_pairs P) (number_of_in triangles P))
% 212.99/213.32 False
% 212.99/213.32 Clause #126 (by clausification #[104]): ∀ (a : Iota),
% 212.99/213.32 Eq
% 212.99/213.32 (Not
% 212.99/213.32 (∀ (V1 V2 : Iota),
% 212.99/213.32 And (path V1 V2 (skS.0 4 a))
% 212.99/213.32 (∀ (E1 E2 : Iota),
% 212.99/213.32 And (And (on_path E1 (skS.0 4 a)) (on_path E2 (skS.0 4 a))) (sequential E1 E2) →
% 212.99/213.32 Exists (triangle E1 E2)) →
% 212.99/213.32 Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a))))
% 212.99/213.32 True
% 212.99/213.32 Clause #127 (by clausification #[126]): ∀ (a : Iota),
% 212.99/213.32 Eq
% 212.99/213.32 (∀ (V1 V2 : Iota),
% 212.99/213.32 And (path V1 V2 (skS.0 4 a))
% 212.99/213.32 (∀ (E1 E2 : Iota),
% 212.99/213.32 And (And (on_path E1 (skS.0 4 a)) (on_path E2 (skS.0 4 a))) (sequential E1 E2) → Exists (triangle E1 E2)) →
% 212.99/213.32 Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a)))
% 212.99/213.32 False
% 212.99/213.32 Clause #128 (by clausification #[127]): ∀ (a a_1 : Iota),
% 212.99/213.32 Eq
% 212.99/213.32 (Not
% 212.99/213.32 (∀ (V2 : Iota),
% 212.99/213.32 And (path (skS.0 5 a a_1) V2 (skS.0 4 a))
% 212.99/213.32 (∀ (E1 E2 : Iota),
% 212.99/213.32 And (And (on_path E1 (skS.0 4 a)) (on_path E2 (skS.0 4 a))) (sequential E1 E2) →
% 212.99/213.32 Exists (triangle E1 E2)) →
% 212.99/213.32 Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a))))
% 212.99/213.32 True
% 212.99/213.32 Clause #129 (by clausification #[128]): ∀ (a a_1 : Iota),
% 212.99/213.32 Eq
% 212.99/213.32 (∀ (V2 : Iota),
% 212.99/213.32 And (path (skS.0 5 a a_1) V2 (skS.0 4 a))
% 212.99/213.32 (∀ (E1 E2 : Iota),
% 212.99/213.32 And (And (on_path E1 (skS.0 4 a)) (on_path E2 (skS.0 4 a))) (sequential E1 E2) → Exists (triangle E1 E2)) →
% 212.99/213.32 Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a)))
% 212.99/213.37 False
% 212.99/213.37 Clause #130 (by clausification #[129]): ∀ (a a_1 a_2 : Iota),
% 212.99/213.37 Eq
% 212.99/213.37 (Not
% 212.99/213.37 (And (path (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) (skS.0 4 a))
% 212.99/213.37 (∀ (E1 E2 : Iota),
% 212.99/213.37 And (And (on_path E1 (skS.0 4 a)) (on_path E2 (skS.0 4 a))) (sequential E1 E2) → Exists (triangle E1 E2)) →
% 212.99/213.37 Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a))))
% 212.99/213.37 True
% 212.99/213.37 Clause #131 (by clausification #[130]): ∀ (a a_1 a_2 : Iota),
% 212.99/213.37 Eq
% 212.99/213.37 (And (path (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) (skS.0 4 a))
% 212.99/213.37 (∀ (E1 E2 : Iota),
% 212.99/213.37 And (And (on_path E1 (skS.0 4 a)) (on_path E2 (skS.0 4 a))) (sequential E1 E2) → Exists (triangle E1 E2)) →
% 212.99/213.37 Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a)))
% 212.99/213.37 False
% 212.99/213.37 Clause #132 (by clausification #[131]): ∀ (a a_1 a_2 : Iota),
% 212.99/213.37 Eq
% 212.99/213.37 (And (path (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) (skS.0 4 a))
% 212.99/213.37 (∀ (E1 E2 : Iota),
% 212.99/213.37 And (And (on_path E1 (skS.0 4 a)) (on_path E2 (skS.0 4 a))) (sequential E1 E2) → Exists (triangle E1 E2)))
% 212.99/213.37 True
% 212.99/213.37 Clause #133 (by clausification #[131]): ∀ (a : Iota), Eq (Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a))) False
% 212.99/213.37 Clause #134 (by clausification #[132]): ∀ (a : Iota),
% 212.99/213.37 Eq
% 212.99/213.37 (∀ (E1 E2 : Iota),
% 212.99/213.37 And (And (on_path E1 (skS.0 4 a)) (on_path E2 (skS.0 4 a))) (sequential E1 E2) → Exists (triangle E1 E2))
% 212.99/213.37 True
% 212.99/213.37 Clause #135 (by clausification #[132]): ∀ (a a_1 a_2 : Iota), Eq (path (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) (skS.0 4 a)) True
% 212.99/213.37 Clause #136 (by clausification #[134]): ∀ (a a_1 : Iota),
% 212.99/213.37 Eq
% 212.99/213.37 (∀ (E2 : Iota),
% 212.99/213.37 And (And (on_path a (skS.0 4 a_1)) (on_path E2 (skS.0 4 a_1))) (sequential a E2) → Exists (triangle a E2))
% 212.99/213.37 True
% 212.99/213.37 Clause #137 (by clausification #[136]): ∀ (a a_1 a_2 : Iota),
% 212.99/213.37 Eq (And (And (on_path a (skS.0 4 a_1)) (on_path a_2 (skS.0 4 a_1))) (sequential a a_2) → Exists (triangle a a_2)) True
% 212.99/213.37 Clause #138 (by clausification #[137]): ∀ (a a_1 a_2 : Iota),
% 212.99/213.37 Or (Eq (And (And (on_path a (skS.0 4 a_1)) (on_path a_2 (skS.0 4 a_1))) (sequential a a_2)) False)
% 212.99/213.37 (Eq (Exists (triangle a a_2)) True)
% 212.99/213.37 Clause #139 (by clausification #[138]): ∀ (a a_1 a_2 : Iota),
% 212.99/213.37 Or (Eq (Exists (triangle a a_1)) True)
% 212.99/213.37 (Or (Eq (And (on_path a (skS.0 4 a_2)) (on_path a_1 (skS.0 4 a_2))) False) (Eq (sequential a a_1) False))
% 212.99/213.37 Clause #140 (by clausification #[139]): ∀ (a a_1 a_2 a_3 : Iota),
% 212.99/213.37 Or (Eq (And (on_path a (skS.0 4 a_1)) (on_path a_2 (skS.0 4 a_1))) False)
% 212.99/213.37 (Or (Eq (sequential a a_2) False) (Eq (triangle a a_2 (skS.0 7 a a_2 a_3)) True))
% 212.99/213.37 Clause #141 (by clausification #[140]): ∀ (a a_1 a_2 a_3 : Iota),
% 212.99/213.37 Or (Eq (sequential a a_1) False)
% 212.99/213.37 (Or (Eq (triangle a a_1 (skS.0 7 a a_1 a_2)) True)
% 212.99/213.37 (Or (Eq (on_path a (skS.0 4 a_3)) False) (Eq (on_path a_1 (skS.0 4 a_3)) False)))
% 212.99/213.37 Clause #166 (by clausification #[133]): ∀ (a : Iota), Ne (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a))
% 212.99/213.37 Clause #238 (by superposition #[135, 94]): ∀ (a a_1 a_2 : Iota),
% 212.99/213.37 Or (Eq True False)
% 212.99/213.37 (Or (Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a)))
% 212.99/213.37 (Eq (sequential (skS.0 1 (skS.0 4 a) a_1) (skS.0 2 (skS.0 4 a) a_1 a_2)) True))
% 212.99/213.37 Clause #305 (by clausification #[93]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 212.99/213.37 Or (Eq (path a a_1 a_2) False)
% 212.99/213.37 (Or (Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2))
% 212.99/213.37 (Eq (triangle (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_4) a_5) False))
% 212.99/213.37 Clause #306 (by superposition #[305, 135]): ∀ (a a_1 a_2 a_3 : Iota),
% 212.99/213.37 Or (Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a)))
% 212.99/213.37 (Or (Eq (triangle (skS.0 1 (skS.0 4 a) a_1) (skS.0 2 (skS.0 4 a) a_1 a_2) a_3) False) (Eq False True))
% 212.99/213.37 Clause #318 (by clausification #[95]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 212.99/213.37 Or (Eq (path a a_1 a_2) False)
% 212.99/213.37 (Or (Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2))
% 212.99/213.37 (Eq (on_path (skS.0 2 a_2 a_3 a_4) a_2) True))
% 213.10/213.42 Clause #319 (by clausification #[95]): ∀ (a a_1 a_2 a_3 : Iota),
% 213.10/213.42 Or (Eq (path a a_1 a_2) False)
% 213.10/213.42 (Or (Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2)) (Eq (on_path (skS.0 1 a_2 a_3) a_2) True))
% 213.10/213.42 Clause #320 (by superposition #[318, 135]): ∀ (a a_1 a_2 : Iota),
% 213.10/213.42 Or (Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a)))
% 213.10/213.42 (Or (Eq (on_path (skS.0 2 (skS.0 4 a) a_1 a_2) (skS.0 4 a)) True) (Eq False True))
% 213.10/213.42 Clause #321 (by superposition #[319, 135]): ∀ (a a_1 : Iota),
% 213.10/213.42 Or (Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a)))
% 213.10/213.42 (Or (Eq (on_path (skS.0 1 (skS.0 4 a) a_1) (skS.0 4 a)) True) (Eq False True))
% 213.10/213.42 Clause #362 (by clausification #[321]): ∀ (a a_1 : Iota),
% 213.10/213.42 Or (Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a)))
% 213.10/213.42 (Eq (on_path (skS.0 1 (skS.0 4 a) a_1) (skS.0 4 a)) True)
% 213.10/213.42 Clause #363 (by forward contextual literal cutting #[362, 166]): ∀ (a a_1 : Iota), Eq (on_path (skS.0 1 (skS.0 4 a) a_1) (skS.0 4 a)) True
% 213.10/213.42 Clause #411 (by clausification #[238]): ∀ (a a_1 a_2 : Iota),
% 213.10/213.42 Or (Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a)))
% 213.10/213.42 (Eq (sequential (skS.0 1 (skS.0 4 a) a_1) (skS.0 2 (skS.0 4 a) a_1 a_2)) True)
% 213.10/213.42 Clause #412 (by forward contextual literal cutting #[411, 166]): ∀ (a a_1 a_2 : Iota), Eq (sequential (skS.0 1 (skS.0 4 a) a_1) (skS.0 2 (skS.0 4 a) a_1 a_2)) True
% 213.10/213.42 Clause #413 (by superposition #[412, 141]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 213.10/213.42 Or (Eq True False)
% 213.10/213.42 (Or
% 213.10/213.42 (Eq
% 213.10/213.42 (triangle (skS.0 1 (skS.0 4 a) a_1) (skS.0 2 (skS.0 4 a) a_1 a_2)
% 213.10/213.42 (skS.0 7 (skS.0 1 (skS.0 4 a) a_1) (skS.0 2 (skS.0 4 a) a_1 a_2) a_3))
% 213.10/213.42 True)
% 213.10/213.42 (Or (Eq (on_path (skS.0 1 (skS.0 4 a) a_1) (skS.0 4 a_4)) False)
% 213.10/213.42 (Eq (on_path (skS.0 2 (skS.0 4 a) a_1 a_2) (skS.0 4 a_4)) False)))
% 213.10/213.42 Clause #530 (by clausification #[320]): ∀ (a a_1 a_2 : Iota),
% 213.10/213.42 Or (Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a)))
% 213.10/213.42 (Eq (on_path (skS.0 2 (skS.0 4 a) a_1 a_2) (skS.0 4 a)) True)
% 213.10/213.42 Clause #531 (by forward contextual literal cutting #[530, 166]): ∀ (a a_1 a_2 : Iota), Eq (on_path (skS.0 2 (skS.0 4 a) a_1 a_2) (skS.0 4 a)) True
% 213.10/213.42 Clause #786 (by clausification #[306]): ∀ (a a_1 a_2 a_3 : Iota),
% 213.10/213.42 Or (Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a)))
% 213.10/213.42 (Eq (triangle (skS.0 1 (skS.0 4 a) a_1) (skS.0 2 (skS.0 4 a) a_1 a_2) a_3) False)
% 213.10/213.42 Clause #787 (by forward contextual literal cutting #[786, 166]): ∀ (a a_1 a_2 a_3 : Iota), Eq (triangle (skS.0 1 (skS.0 4 a) a_1) (skS.0 2 (skS.0 4 a) a_1 a_2) a_3) False
% 213.10/213.42 Clause #3702 (by clausification #[413]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 213.10/213.42 Or
% 213.10/213.42 (Eq
% 213.10/213.42 (triangle (skS.0 1 (skS.0 4 a) a_1) (skS.0 2 (skS.0 4 a) a_1 a_2)
% 213.10/213.42 (skS.0 7 (skS.0 1 (skS.0 4 a) a_1) (skS.0 2 (skS.0 4 a) a_1 a_2) a_3))
% 213.10/213.42 True)
% 213.10/213.42 (Or (Eq (on_path (skS.0 1 (skS.0 4 a) a_1) (skS.0 4 a_4)) False)
% 213.10/213.42 (Eq (on_path (skS.0 2 (skS.0 4 a) a_1 a_2) (skS.0 4 a_4)) False))
% 213.10/213.42 Clause #3703 (by superposition #[3702, 363]): ∀ (a a_1 a_2 a_3 : Iota),
% 213.10/213.42 Or
% 213.10/213.42 (Eq
% 213.10/213.42 (triangle (skS.0 1 (skS.0 4 a) a_1) (skS.0 2 (skS.0 4 a) a_1 a_2)
% 213.10/213.42 (skS.0 7 (skS.0 1 (skS.0 4 a) a_1) (skS.0 2 (skS.0 4 a) a_1 a_2) a_3))
% 213.10/213.42 True)
% 213.10/213.42 (Or (Eq (on_path (skS.0 2 (skS.0 4 a) a_1 a_2) (skS.0 4 a)) False) (Eq False True))
% 213.10/213.42 Clause #19149 (by clausification #[3703]): ∀ (a a_1 a_2 a_3 : Iota),
% 213.10/213.42 Or
% 213.10/213.42 (Eq
% 213.10/213.42 (triangle (skS.0 1 (skS.0 4 a) a_1) (skS.0 2 (skS.0 4 a) a_1 a_2)
% 213.10/213.42 (skS.0 7 (skS.0 1 (skS.0 4 a) a_1) (skS.0 2 (skS.0 4 a) a_1 a_2) a_3))
% 213.10/213.42 True)
% 213.10/213.42 (Eq (on_path (skS.0 2 (skS.0 4 a) a_1 a_2) (skS.0 4 a)) False)
% 213.10/213.42 Clause #19150 (by forward demodulation #[19149, 531]): ∀ (a a_1 a_2 a_3 : Iota),
% 213.10/213.42 Or
% 213.10/213.42 (Eq
% 213.10/213.42 (triangle (skS.0 1 (skS.0 4 a) a_1) (skS.0 2 (skS.0 4 a) a_1 a_2)
% 213.10/213.42 (skS.0 7 (skS.0 1 (skS.0 4 a) a_1) (skS.0 2 (skS.0 4 a) a_1 a_2) a_3))
% 213.10/213.42 True)
% 213.10/213.42 (Eq True False)
% 213.10/213.42 Clause #19151 (by clausification #[19150]): ∀ (a a_1 a_2 a_3 : Iota),
% 213.10/213.42 Eq
% 213.10/213.42 (triangle (skS.0 1 (skS.0 4 a) a_1) (skS.0 2 (skS.0 4 a) a_1 a_2)
% 213.49/213.81 (skS.0 7 (skS.0 1 (skS.0 4 a) a_1) (skS.0 2 (skS.0 4 a) a_1 a_2) a_3))
% 213.49/213.81 True
% 213.49/213.81 Clause #19152 (by superposition #[19151, 787]): Eq True False
% 213.49/213.81 Clause #19157 (by clausification #[19152]): False
% 213.49/213.81 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------