TSTP Solution File: GRA010+2 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : GRA010+2 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n028.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 192.69s 192.85s
% Output : Proof 192.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA010+2 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.12/0.14 % Command : duper %s
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 03:28:38 EDT 2023
% 0.13/0.35 % CPUTime :
% 192.69/192.85 SZS status Theorem for theBenchmark.p
% 192.69/192.85 SZS output start Proof for theBenchmark.p
% 192.69/192.85 Clause #15 (by assumption #[]): Eq
% 192.69/192.85 (∀ (P V1 V2 : Iota),
% 192.69/192.85 And (path V1 V2 P)
% 192.69/192.85 (∀ (E1 E2 : Iota),
% 192.69/192.85 And (And (on_path E1 P) (on_path E2 P)) (sequential E1 E2) → Exists fun E3 => triangle E1 E2 E3) →
% 192.69/192.85 Eq (number_of_in sequential_pairs P) (number_of_in triangles P))
% 192.69/192.85 True
% 192.69/192.85 Clause #18 (by assumption #[]): Eq
% 192.69/192.85 (Not
% 192.69/192.85 (complete →
% 192.69/192.85 ∀ (P V1 V2 : Iota),
% 192.69/192.85 And (path V1 V2 P)
% 192.69/192.85 (∀ (E1 E2 : Iota),
% 192.69/192.85 And (And (on_path E1 P) (on_path E2 P)) (sequential E1 E2) → Exists fun E3 => triangle E1 E2 E3) →
% 192.69/192.85 Eq (number_of_in sequential_pairs P) (number_of_in triangles P)))
% 192.69/192.85 True
% 192.69/192.85 Clause #82 (by betaEtaReduce #[15]): Eq
% 192.69/192.85 (∀ (P V1 V2 : Iota),
% 192.69/192.85 And (path V1 V2 P)
% 192.69/192.85 (∀ (E1 E2 : Iota), And (And (on_path E1 P) (on_path E2 P)) (sequential E1 E2) → Exists (triangle E1 E2)) →
% 192.69/192.85 Eq (number_of_in sequential_pairs P) (number_of_in triangles P))
% 192.69/192.85 True
% 192.69/192.85 Clause #83 (by clausification #[82]): ∀ (a : Iota),
% 192.69/192.85 Eq
% 192.69/192.85 (∀ (V1 V2 : Iota),
% 192.69/192.85 And (path V1 V2 a)
% 192.69/192.85 (∀ (E1 E2 : Iota), And (And (on_path E1 a) (on_path E2 a)) (sequential E1 E2) → Exists (triangle E1 E2)) →
% 192.69/192.85 Eq (number_of_in sequential_pairs a) (number_of_in triangles a))
% 192.69/192.85 True
% 192.69/192.85 Clause #84 (by clausification #[83]): ∀ (a a_1 : Iota),
% 192.69/192.85 Eq
% 192.69/192.85 (∀ (V2 : Iota),
% 192.69/192.85 And (path a V2 a_1)
% 192.69/192.85 (∀ (E1 E2 : Iota), And (And (on_path E1 a_1) (on_path E2 a_1)) (sequential E1 E2) → Exists (triangle E1 E2)) →
% 192.69/192.85 Eq (number_of_in sequential_pairs a_1) (number_of_in triangles a_1))
% 192.69/192.85 True
% 192.69/192.85 Clause #85 (by clausification #[84]): ∀ (a a_1 a_2 : Iota),
% 192.69/192.85 Eq
% 192.69/192.85 (And (path a a_1 a_2)
% 192.69/192.85 (∀ (E1 E2 : Iota), And (And (on_path E1 a_2) (on_path E2 a_2)) (sequential E1 E2) → Exists (triangle E1 E2)) →
% 192.69/192.85 Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2))
% 192.69/192.85 True
% 192.69/192.85 Clause #86 (by clausification #[85]): ∀ (a a_1 a_2 : Iota),
% 192.69/192.85 Or
% 192.69/192.85 (Eq
% 192.69/192.85 (And (path a a_1 a_2)
% 192.69/192.85 (∀ (E1 E2 : Iota), And (And (on_path E1 a_2) (on_path E2 a_2)) (sequential E1 E2) → Exists (triangle E1 E2)))
% 192.69/192.85 False)
% 192.69/192.85 (Eq (Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2)) True)
% 192.69/192.85 Clause #87 (by clausification #[86]): ∀ (a a_1 a_2 : Iota),
% 192.69/192.85 Or (Eq (Eq (number_of_in sequential_pairs a) (number_of_in triangles a)) True)
% 192.69/192.85 (Or (Eq (path a_1 a_2 a) False)
% 192.69/192.85 (Eq (∀ (E1 E2 : Iota), And (And (on_path E1 a) (on_path E2 a)) (sequential E1 E2) → Exists (triangle E1 E2))
% 192.69/192.85 False))
% 192.69/192.85 Clause #88 (by clausification #[87]): ∀ (a a_1 a_2 : Iota),
% 192.69/192.85 Or (Eq (path a a_1 a_2) False)
% 192.69/192.85 (Or
% 192.69/192.85 (Eq (∀ (E1 E2 : Iota), And (And (on_path E1 a_2) (on_path E2 a_2)) (sequential E1 E2) → Exists (triangle E1 E2))
% 192.69/192.85 False)
% 192.69/192.85 (Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2)))
% 192.69/192.85 Clause #89 (by clausification #[88]): ∀ (a a_1 a_2 a_3 : Iota),
% 192.69/192.85 Or (Eq (path a a_1 a_2) False)
% 192.69/192.85 (Or (Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2))
% 192.69/192.85 (Eq
% 192.69/192.85 (Not
% 192.69/192.85 (∀ (E2 : Iota),
% 192.69/192.85 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) →
% 192.69/192.85 Exists (triangle (skS.0 1 a_2 a_3) E2)))
% 192.69/192.85 True))
% 192.69/192.85 Clause #90 (by clausification #[89]): ∀ (a a_1 a_2 a_3 : Iota),
% 192.69/192.85 Or (Eq (path a a_1 a_2) False)
% 192.69/192.85 (Or (Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2))
% 192.69/192.85 (Eq
% 192.69/192.85 (∀ (E2 : Iota),
% 192.69/192.85 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) →
% 192.69/192.85 Exists (triangle (skS.0 1 a_2 a_3) E2))
% 192.69/192.85 False))
% 192.69/192.85 Clause #91 (by clausification #[90]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 192.69/192.85 Or (Eq (path a a_1 a_2) False)
% 192.69/192.85 (Or (Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2))
% 192.69/192.85 (Eq
% 192.69/192.85 (Not
% 192.69/192.85 (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))
% 192.69/192.85 (sequential (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_4)) →
% 192.69/192.85 Exists (triangle (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_4))))
% 192.72/192.88 True))
% 192.72/192.88 Clause #92 (by clausification #[91]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 192.72/192.88 Or (Eq (path a a_1 a_2) False)
% 192.72/192.88 (Or (Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2))
% 192.72/192.88 (Eq
% 192.72/192.88 (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))
% 192.72/192.88 (sequential (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_4)) →
% 192.72/192.88 Exists (triangle (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_4)))
% 192.72/192.88 False))
% 192.72/192.88 Clause #93 (by clausification #[92]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 192.72/192.88 Or (Eq (path a a_1 a_2) False)
% 192.72/192.88 (Or (Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2))
% 192.72/192.88 (Eq
% 192.72/192.88 (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))
% 192.72/192.88 (sequential (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_4)))
% 192.72/192.88 True))
% 192.72/192.88 Clause #94 (by clausification #[92]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 192.72/192.88 Or (Eq (path a a_1 a_2) False)
% 192.72/192.88 (Or (Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2))
% 192.72/192.88 (Eq (Exists (triangle (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_4))) False))
% 192.72/192.88 Clause #95 (by clausification #[93]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 192.72/192.88 Or (Eq (path a a_1 a_2) False)
% 192.72/192.88 (Or (Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2))
% 192.72/192.88 (Eq (sequential (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_4)) True))
% 192.72/192.88 Clause #96 (by clausification #[93]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 192.72/192.88 Or (Eq (path a a_1 a_2) False)
% 192.72/192.88 (Or (Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2))
% 192.72/192.88 (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))
% 192.72/192.88 Clause #102 (by betaEtaReduce #[18]): Eq
% 192.72/192.88 (Not
% 192.72/192.88 (complete →
% 192.72/192.88 ∀ (P V1 V2 : Iota),
% 192.72/192.88 And (path V1 V2 P)
% 192.72/192.88 (∀ (E1 E2 : Iota), And (And (on_path E1 P) (on_path E2 P)) (sequential E1 E2) → Exists (triangle E1 E2)) →
% 192.72/192.88 Eq (number_of_in sequential_pairs P) (number_of_in triangles P)))
% 192.72/192.88 True
% 192.72/192.88 Clause #103 (by clausification #[102]): Eq
% 192.72/192.88 (complete →
% 192.72/192.88 ∀ (P V1 V2 : Iota),
% 192.72/192.88 And (path V1 V2 P)
% 192.72/192.88 (∀ (E1 E2 : Iota), And (And (on_path E1 P) (on_path E2 P)) (sequential E1 E2) → Exists (triangle E1 E2)) →
% 192.72/192.88 Eq (number_of_in sequential_pairs P) (number_of_in triangles P))
% 192.72/192.88 False
% 192.72/192.88 Clause #105 (by clausification #[103]): Eq
% 192.72/192.88 (∀ (P V1 V2 : Iota),
% 192.72/192.88 And (path V1 V2 P)
% 192.72/192.88 (∀ (E1 E2 : Iota), And (And (on_path E1 P) (on_path E2 P)) (sequential E1 E2) → Exists (triangle E1 E2)) →
% 192.72/192.88 Eq (number_of_in sequential_pairs P) (number_of_in triangles P))
% 192.72/192.88 False
% 192.72/192.88 Clause #127 (by clausification #[105]): ∀ (a : Iota),
% 192.72/192.88 Eq
% 192.72/192.88 (Not
% 192.72/192.88 (∀ (V1 V2 : Iota),
% 192.72/192.88 And (path V1 V2 (skS.0 4 a))
% 192.72/192.88 (∀ (E1 E2 : Iota),
% 192.72/192.88 And (And (on_path E1 (skS.0 4 a)) (on_path E2 (skS.0 4 a))) (sequential E1 E2) →
% 192.72/192.88 Exists (triangle E1 E2)) →
% 192.72/192.88 Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a))))
% 192.72/192.88 True
% 192.72/192.88 Clause #128 (by clausification #[127]): ∀ (a : Iota),
% 192.72/192.88 Eq
% 192.72/192.88 (∀ (V1 V2 : Iota),
% 192.72/192.88 And (path V1 V2 (skS.0 4 a))
% 192.72/192.88 (∀ (E1 E2 : Iota),
% 192.72/192.88 And (And (on_path E1 (skS.0 4 a)) (on_path E2 (skS.0 4 a))) (sequential E1 E2) → Exists (triangle E1 E2)) →
% 192.72/192.88 Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a)))
% 192.72/192.88 False
% 192.72/192.88 Clause #129 (by clausification #[128]): ∀ (a a_1 : Iota),
% 192.72/192.88 Eq
% 192.72/192.88 (Not
% 192.72/192.88 (∀ (V2 : Iota),
% 192.72/192.88 And (path (skS.0 5 a a_1) V2 (skS.0 4 a))
% 192.72/192.88 (∀ (E1 E2 : Iota),
% 192.72/192.88 And (And (on_path E1 (skS.0 4 a)) (on_path E2 (skS.0 4 a))) (sequential E1 E2) →
% 192.72/192.88 Exists (triangle E1 E2)) →
% 192.72/192.88 Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a))))
% 192.72/192.88 True
% 192.72/192.88 Clause #130 (by clausification #[129]): ∀ (a a_1 : Iota),
% 192.72/192.88 Eq
% 192.72/192.88 (∀ (V2 : Iota),
% 192.72/192.88 And (path (skS.0 5 a a_1) V2 (skS.0 4 a))
% 192.72/192.88 (∀ (E1 E2 : Iota),
% 192.72/192.88 And (And (on_path E1 (skS.0 4 a)) (on_path E2 (skS.0 4 a))) (sequential E1 E2) → Exists (triangle E1 E2)) →
% 192.72/192.88 Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a)))
% 192.72/192.90 False
% 192.72/192.90 Clause #131 (by clausification #[130]): ∀ (a a_1 a_2 : Iota),
% 192.72/192.90 Eq
% 192.72/192.90 (Not
% 192.72/192.90 (And (path (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) (skS.0 4 a))
% 192.72/192.90 (∀ (E1 E2 : Iota),
% 192.72/192.90 And (And (on_path E1 (skS.0 4 a)) (on_path E2 (skS.0 4 a))) (sequential E1 E2) → Exists (triangle E1 E2)) →
% 192.72/192.90 Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a))))
% 192.72/192.90 True
% 192.72/192.90 Clause #132 (by clausification #[131]): ∀ (a a_1 a_2 : Iota),
% 192.72/192.90 Eq
% 192.72/192.90 (And (path (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) (skS.0 4 a))
% 192.72/192.90 (∀ (E1 E2 : Iota),
% 192.72/192.90 And (And (on_path E1 (skS.0 4 a)) (on_path E2 (skS.0 4 a))) (sequential E1 E2) → Exists (triangle E1 E2)) →
% 192.72/192.90 Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a)))
% 192.72/192.90 False
% 192.72/192.90 Clause #133 (by clausification #[132]): ∀ (a a_1 a_2 : Iota),
% 192.72/192.90 Eq
% 192.72/192.90 (And (path (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) (skS.0 4 a))
% 192.72/192.90 (∀ (E1 E2 : Iota),
% 192.72/192.90 And (And (on_path E1 (skS.0 4 a)) (on_path E2 (skS.0 4 a))) (sequential E1 E2) → Exists (triangle E1 E2)))
% 192.72/192.90 True
% 192.72/192.90 Clause #134 (by clausification #[132]): ∀ (a : Iota), Eq (Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a))) False
% 192.72/192.90 Clause #135 (by clausification #[133]): ∀ (a : Iota),
% 192.72/192.90 Eq
% 192.72/192.90 (∀ (E1 E2 : Iota),
% 192.72/192.90 And (And (on_path E1 (skS.0 4 a)) (on_path E2 (skS.0 4 a))) (sequential E1 E2) → Exists (triangle E1 E2))
% 192.72/192.90 True
% 192.72/192.90 Clause #136 (by clausification #[133]): ∀ (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
% 192.72/192.90 Clause #137 (by clausification #[135]): ∀ (a a_1 : Iota),
% 192.72/192.90 Eq
% 192.72/192.90 (∀ (E2 : Iota),
% 192.72/192.90 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))
% 192.72/192.90 True
% 192.72/192.90 Clause #138 (by clausification #[137]): ∀ (a a_1 a_2 : Iota),
% 192.72/192.90 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
% 192.72/192.90 Clause #139 (by clausification #[138]): ∀ (a a_1 a_2 : Iota),
% 192.72/192.90 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)
% 192.72/192.90 (Eq (Exists (triangle a a_2)) True)
% 192.72/192.90 Clause #140 (by clausification #[139]): ∀ (a a_1 a_2 : Iota),
% 192.72/192.90 Or (Eq (Exists (triangle a a_1)) True)
% 192.72/192.90 (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))
% 192.72/192.90 Clause #141 (by clausification #[140]): ∀ (a a_1 a_2 a_3 : Iota),
% 192.72/192.90 Or (Eq (And (on_path a (skS.0 4 a_1)) (on_path a_2 (skS.0 4 a_1))) False)
% 192.72/192.90 (Or (Eq (sequential a a_2) False) (Eq (triangle a a_2 (skS.0 7 a a_2 a_3)) True))
% 192.72/192.90 Clause #142 (by clausification #[141]): ∀ (a a_1 a_2 a_3 : Iota),
% 192.72/192.90 Or (Eq (sequential a a_1) False)
% 192.72/192.90 (Or (Eq (triangle a a_1 (skS.0 7 a a_1 a_2)) True)
% 192.72/192.90 (Or (Eq (on_path a (skS.0 4 a_3)) False) (Eq (on_path a_1 (skS.0 4 a_3)) False)))
% 192.72/192.90 Clause #180 (by clausification #[134]): ∀ (a : Iota), Ne (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a))
% 192.72/192.90 Clause #249 (by superposition #[136, 95]): ∀ (a a_1 a_2 : Iota),
% 192.72/192.90 Or (Eq True False)
% 192.72/192.90 (Or (Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a)))
% 192.72/192.90 (Eq (sequential (skS.0 1 (skS.0 4 a) a_1) (skS.0 2 (skS.0 4 a) a_1 a_2)) True))
% 192.72/192.90 Clause #315 (by clausification #[94]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 192.72/192.90 Or (Eq (path a a_1 a_2) False)
% 192.72/192.90 (Or (Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2))
% 192.72/192.90 (Eq (triangle (skS.0 1 a_2 a_3) (skS.0 2 a_2 a_3 a_4) a_5) False))
% 192.72/192.90 Clause #316 (by superposition #[315, 136]): ∀ (a a_1 a_2 a_3 : Iota),
% 192.72/192.90 Or (Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a)))
% 192.72/192.90 (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))
% 192.72/192.90 Clause #329 (by clausification #[96]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 192.72/192.90 Or (Eq (path a a_1 a_2) False)
% 192.72/192.90 (Or (Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2))
% 192.72/192.90 (Eq (on_path (skS.0 2 a_2 a_3 a_4) a_2) True))
% 192.77/192.93 Clause #330 (by clausification #[96]): ∀ (a a_1 a_2 a_3 : Iota),
% 192.77/192.93 Or (Eq (path a a_1 a_2) False)
% 192.77/192.93 (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))
% 192.77/192.93 Clause #331 (by superposition #[329, 136]): ∀ (a a_1 a_2 : Iota),
% 192.77/192.93 Or (Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a)))
% 192.77/192.93 (Or (Eq (on_path (skS.0 2 (skS.0 4 a) a_1 a_2) (skS.0 4 a)) True) (Eq False True))
% 192.77/192.93 Clause #332 (by superposition #[330, 136]): ∀ (a a_1 : Iota),
% 192.77/192.93 Or (Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a)))
% 192.77/192.93 (Or (Eq (on_path (skS.0 1 (skS.0 4 a) a_1) (skS.0 4 a)) True) (Eq False True))
% 192.77/192.93 Clause #376 (by clausification #[332]): ∀ (a a_1 : Iota),
% 192.77/192.93 Or (Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a)))
% 192.77/192.93 (Eq (on_path (skS.0 1 (skS.0 4 a) a_1) (skS.0 4 a)) True)
% 192.77/192.93 Clause #377 (by forward contextual literal cutting #[376, 180]): ∀ (a a_1 : Iota), Eq (on_path (skS.0 1 (skS.0 4 a) a_1) (skS.0 4 a)) True
% 192.77/192.93 Clause #417 (by clausification #[249]): ∀ (a a_1 a_2 : Iota),
% 192.77/192.93 Or (Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a)))
% 192.77/192.93 (Eq (sequential (skS.0 1 (skS.0 4 a) a_1) (skS.0 2 (skS.0 4 a) a_1 a_2)) True)
% 192.77/192.93 Clause #418 (by forward contextual literal cutting #[417, 180]): ∀ (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
% 192.77/192.93 Clause #419 (by superposition #[418, 142]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 192.77/192.93 Or (Eq True False)
% 192.77/192.93 (Or
% 192.77/192.93 (Eq
% 192.77/192.93 (triangle (skS.0 1 (skS.0 4 a) a_1) (skS.0 2 (skS.0 4 a) a_1 a_2)
% 192.77/192.93 (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))
% 192.77/192.93 True)
% 192.77/192.93 (Or (Eq (on_path (skS.0 1 (skS.0 4 a) a_1) (skS.0 4 a_4)) False)
% 192.77/192.93 (Eq (on_path (skS.0 2 (skS.0 4 a) a_1 a_2) (skS.0 4 a_4)) False)))
% 192.77/192.93 Clause #545 (by clausification #[331]): ∀ (a a_1 a_2 : Iota),
% 192.77/192.93 Or (Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a)))
% 192.77/192.93 (Eq (on_path (skS.0 2 (skS.0 4 a) a_1 a_2) (skS.0 4 a)) True)
% 192.77/192.93 Clause #546 (by forward contextual literal cutting #[545, 180]): ∀ (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
% 192.77/192.93 Clause #721 (by clausification #[316]): ∀ (a a_1 a_2 a_3 : Iota),
% 192.77/192.93 Or (Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a)))
% 192.77/192.93 (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)
% 192.77/192.93 Clause #722 (by forward contextual literal cutting #[721, 180]): ∀ (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
% 192.77/192.93 Clause #2962 (by clausification #[419]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 192.77/192.93 Or
% 192.77/192.93 (Eq
% 192.77/192.93 (triangle (skS.0 1 (skS.0 4 a) a_1) (skS.0 2 (skS.0 4 a) a_1 a_2)
% 192.77/192.93 (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))
% 192.77/192.93 True)
% 192.77/192.93 (Or (Eq (on_path (skS.0 1 (skS.0 4 a) a_1) (skS.0 4 a_4)) False)
% 192.77/192.93 (Eq (on_path (skS.0 2 (skS.0 4 a) a_1 a_2) (skS.0 4 a_4)) False))
% 192.77/192.93 Clause #2963 (by superposition #[2962, 377]): ∀ (a a_1 a_2 a_3 : Iota),
% 192.77/192.93 Or
% 192.77/192.93 (Eq
% 192.77/192.93 (triangle (skS.0 1 (skS.0 4 a) a_1) (skS.0 2 (skS.0 4 a) a_1 a_2)
% 192.77/192.93 (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))
% 192.77/192.93 True)
% 192.77/192.93 (Or (Eq (on_path (skS.0 2 (skS.0 4 a) a_1 a_2) (skS.0 4 a)) False) (Eq False True))
% 192.77/192.93 Clause #20461 (by clausification #[2963]): ∀ (a a_1 a_2 a_3 : Iota),
% 192.77/192.93 Or
% 192.77/192.93 (Eq
% 192.77/192.93 (triangle (skS.0 1 (skS.0 4 a) a_1) (skS.0 2 (skS.0 4 a) a_1 a_2)
% 192.77/192.93 (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))
% 192.77/192.93 True)
% 192.77/192.93 (Eq (on_path (skS.0 2 (skS.0 4 a) a_1 a_2) (skS.0 4 a)) False)
% 192.77/192.93 Clause #20462 (by forward demodulation #[20461, 546]): ∀ (a a_1 a_2 a_3 : Iota),
% 192.77/192.93 Or
% 192.77/192.93 (Eq
% 192.77/192.93 (triangle (skS.0 1 (skS.0 4 a) a_1) (skS.0 2 (skS.0 4 a) a_1 a_2)
% 192.77/192.93 (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))
% 192.77/192.93 True)
% 192.77/192.93 (Eq True False)
% 192.77/192.93 Clause #20463 (by clausification #[20462]): ∀ (a a_1 a_2 a_3 : Iota),
% 192.77/192.93 Eq
% 192.77/192.93 (triangle (skS.0 1 (skS.0 4 a) a_1) (skS.0 2 (skS.0 4 a) a_1 a_2)
% 192.87/193.19 (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))
% 192.87/193.19 True
% 192.87/193.19 Clause #20464 (by superposition #[20463, 722]): Eq True False
% 192.87/193.19 Clause #20469 (by clausification #[20464]): False
% 192.87/193.19 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------