TSTP Solution File: GRA002+4 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : GRA002+4 : 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 3.82s 3.99s
% Output : Proof 3.82s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA002+4 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.00/0.13 % 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 03:39:31 EDT 2023
% 0.17/0.35 % CPUTime :
% 3.82/3.99 SZS status Theorem for theBenchmark.p
% 3.82/3.99 SZS output start Proof for theBenchmark.p
% 3.82/3.99 Clause #10 (by assumption #[]): Eq
% 3.82/3.99 (∀ (V1 V2 SP : Iota),
% 3.82/3.99 Iff (shortest_path V1 V2 SP)
% 3.82/3.99 (And (And (path V1 V2 SP) (Ne V1 V2)) (∀ (P : Iota), path V1 V2 P → less_or_equal (length_of SP) (length_of P))))
% 3.82/3.99 True
% 3.82/3.99 Clause #14 (by assumption #[]): Eq (∀ (V1 V2 P : Iota), path V1 V2 P → Eq (number_of_in sequential_pairs P) (minus (length_of P) n1)) True
% 3.82/3.99 Clause #16 (by assumption #[]): Eq (∀ (Things InThese : Iota), less_or_equal (number_of_in Things InThese) (number_of_in Things graph)) True
% 3.82/3.99 Clause #17 (by assumption #[]): Eq
% 3.82/3.99 (complete →
% 3.82/3.99 ∀ (P V1 V2 : Iota), shortest_path V1 V2 P → Eq (number_of_in sequential_pairs P) (number_of_in triangles P))
% 3.82/3.99 True
% 3.82/3.99 Clause #18 (by assumption #[]): Eq
% 3.82/3.99 (Not
% 3.82/3.99 (complete →
% 3.82/3.99 ∀ (P V1 V2 : Iota),
% 3.82/3.99 shortest_path V1 V2 P → less_or_equal (minus (length_of P) n1) (number_of_in triangles graph)))
% 3.82/3.99 True
% 3.82/3.99 Clause #43 (by clausification #[16]): ∀ (a : Iota), Eq (∀ (InThese : Iota), less_or_equal (number_of_in a InThese) (number_of_in a graph)) True
% 3.82/3.99 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota), Eq (less_or_equal (number_of_in a a_1) (number_of_in a graph)) True
% 3.82/3.99 Clause #97 (by clausification #[14]): ∀ (a : Iota), Eq (∀ (V2 P : Iota), path a V2 P → Eq (number_of_in sequential_pairs P) (minus (length_of P) n1)) True
% 3.82/3.99 Clause #98 (by clausification #[97]): ∀ (a a_1 : Iota), Eq (∀ (P : Iota), path a a_1 P → Eq (number_of_in sequential_pairs P) (minus (length_of P) n1)) True
% 3.82/3.99 Clause #99 (by clausification #[98]): ∀ (a a_1 a_2 : Iota), Eq (path a a_1 a_2 → Eq (number_of_in sequential_pairs a_2) (minus (length_of a_2) n1)) True
% 3.82/3.99 Clause #100 (by clausification #[99]): ∀ (a a_1 a_2 : Iota),
% 3.82/3.99 Or (Eq (path a a_1 a_2) False) (Eq (Eq (number_of_in sequential_pairs a_2) (minus (length_of a_2) n1)) True)
% 3.82/3.99 Clause #101 (by clausification #[100]): ∀ (a a_1 a_2 : Iota), Or (Eq (path a a_1 a_2) False) (Eq (number_of_in sequential_pairs a_2) (minus (length_of a_2) n1))
% 3.82/3.99 Clause #102 (by clausification #[17]): Or (Eq complete False)
% 3.82/3.99 (Eq (∀ (P V1 V2 : Iota), shortest_path V1 V2 P → Eq (number_of_in sequential_pairs P) (number_of_in triangles P))
% 3.82/3.99 True)
% 3.82/3.99 Clause #103 (by clausification #[102]): ∀ (a : Iota),
% 3.82/3.99 Or (Eq complete False)
% 3.82/3.99 (Eq (∀ (V1 V2 : Iota), shortest_path V1 V2 a → Eq (number_of_in sequential_pairs a) (number_of_in triangles a))
% 3.82/3.99 True)
% 3.82/3.99 Clause #104 (by clausification #[103]): ∀ (a a_1 : Iota),
% 3.82/3.99 Or (Eq complete False)
% 3.82/3.99 (Eq (∀ (V2 : Iota), shortest_path a V2 a_1 → Eq (number_of_in sequential_pairs a_1) (number_of_in triangles a_1))
% 3.82/3.99 True)
% 3.82/3.99 Clause #105 (by clausification #[104]): ∀ (a a_1 a_2 : Iota),
% 3.82/3.99 Or (Eq complete False)
% 3.82/3.99 (Eq (shortest_path a a_1 a_2 → Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2)) True)
% 3.82/3.99 Clause #106 (by clausification #[105]): ∀ (a a_1 a_2 : Iota),
% 3.82/3.99 Or (Eq complete False)
% 3.82/3.99 (Or (Eq (shortest_path a a_1 a_2) False)
% 3.82/3.99 (Eq (Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2)) True))
% 3.82/3.99 Clause #107 (by clausification #[106]): ∀ (a a_1 a_2 : Iota),
% 3.82/3.99 Or (Eq complete False)
% 3.82/3.99 (Or (Eq (shortest_path a a_1 a_2) False) (Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2)))
% 3.82/3.99 Clause #128 (by clausification #[18]): Eq
% 3.82/3.99 (complete →
% 3.82/3.99 ∀ (P V1 V2 : Iota), shortest_path V1 V2 P → less_or_equal (minus (length_of P) n1) (number_of_in triangles graph))
% 3.82/3.99 False
% 3.82/3.99 Clause #129 (by clausification #[128]): Eq complete True
% 3.82/3.99 Clause #130 (by clausification #[128]): Eq (∀ (P V1 V2 : Iota), shortest_path V1 V2 P → less_or_equal (minus (length_of P) n1) (number_of_in triangles graph))
% 3.82/3.99 False
% 3.82/3.99 Clause #132 (by backward demodulation #[129, 107]): ∀ (a a_1 a_2 : Iota),
% 3.82/3.99 Or (Eq True False)
% 3.82/3.99 (Or (Eq (shortest_path a a_1 a_2) False) (Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2)))
% 3.82/3.99 Clause #133 (by clausification #[132]): ∀ (a a_1 a_2 : Iota),
% 3.82/3.99 Or (Eq (shortest_path a a_1 a_2) False) (Eq (number_of_in sequential_pairs a_2) (number_of_in triangles a_2))
% 3.82/4.01 Clause #134 (by clausification #[130]): ∀ (a : Iota),
% 3.82/4.01 Eq
% 3.82/4.01 (Not
% 3.82/4.01 (∀ (V1 V2 : Iota),
% 3.82/4.01 shortest_path V1 V2 (skS.0 4 a) →
% 3.82/4.01 less_or_equal (minus (length_of (skS.0 4 a)) n1) (number_of_in triangles graph)))
% 3.82/4.01 True
% 3.82/4.01 Clause #135 (by clausification #[134]): ∀ (a : Iota),
% 3.82/4.01 Eq
% 3.82/4.01 (∀ (V1 V2 : Iota),
% 3.82/4.01 shortest_path V1 V2 (skS.0 4 a) → less_or_equal (minus (length_of (skS.0 4 a)) n1) (number_of_in triangles graph))
% 3.82/4.01 False
% 3.82/4.01 Clause #136 (by clausification #[135]): ∀ (a a_1 : Iota),
% 3.82/4.01 Eq
% 3.82/4.01 (Not
% 3.82/4.01 (∀ (V2 : Iota),
% 3.82/4.01 shortest_path (skS.0 5 a a_1) V2 (skS.0 4 a) →
% 3.82/4.01 less_or_equal (minus (length_of (skS.0 4 a)) n1) (number_of_in triangles graph)))
% 3.82/4.01 True
% 3.82/4.01 Clause #137 (by clausification #[136]): ∀ (a a_1 : Iota),
% 3.82/4.01 Eq
% 3.82/4.01 (∀ (V2 : Iota),
% 3.82/4.01 shortest_path (skS.0 5 a a_1) V2 (skS.0 4 a) →
% 3.82/4.01 less_or_equal (minus (length_of (skS.0 4 a)) n1) (number_of_in triangles graph))
% 3.82/4.01 False
% 3.82/4.01 Clause #138 (by clausification #[137]): ∀ (a a_1 a_2 : Iota),
% 3.82/4.01 Eq
% 3.82/4.01 (Not
% 3.82/4.01 (shortest_path (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) (skS.0 4 a) →
% 3.82/4.01 less_or_equal (minus (length_of (skS.0 4 a)) n1) (number_of_in triangles graph)))
% 3.82/4.01 True
% 3.82/4.01 Clause #139 (by clausification #[138]): ∀ (a a_1 a_2 : Iota),
% 3.82/4.01 Eq
% 3.82/4.01 (shortest_path (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) (skS.0 4 a) →
% 3.82/4.01 less_or_equal (minus (length_of (skS.0 4 a)) n1) (number_of_in triangles graph))
% 3.82/4.01 False
% 3.82/4.01 Clause #140 (by clausification #[139]): ∀ (a a_1 a_2 : Iota), Eq (shortest_path (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) (skS.0 4 a)) True
% 3.82/4.01 Clause #141 (by clausification #[139]): ∀ (a : Iota), Eq (less_or_equal (minus (length_of (skS.0 4 a)) n1) (number_of_in triangles graph)) False
% 3.82/4.01 Clause #142 (by superposition #[140, 133]): ∀ (a : Iota), Or (Eq True False) (Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a)))
% 3.82/4.01 Clause #153 (by clausification #[142]): ∀ (a : Iota), Eq (number_of_in sequential_pairs (skS.0 4 a)) (number_of_in triangles (skS.0 4 a))
% 3.82/4.01 Clause #205 (by clausification #[10]): ∀ (a : Iota),
% 3.82/4.01 Eq
% 3.82/4.01 (∀ (V2 SP : Iota),
% 3.82/4.01 Iff (shortest_path a V2 SP)
% 3.82/4.01 (And (And (path a V2 SP) (Ne a V2)) (∀ (P : Iota), path a V2 P → less_or_equal (length_of SP) (length_of P))))
% 3.82/4.01 True
% 3.82/4.01 Clause #206 (by clausification #[205]): ∀ (a a_1 : Iota),
% 3.82/4.01 Eq
% 3.82/4.01 (∀ (SP : Iota),
% 3.82/4.01 Iff (shortest_path a a_1 SP)
% 3.82/4.01 (And (And (path a a_1 SP) (Ne a a_1))
% 3.82/4.01 (∀ (P : Iota), path a a_1 P → less_or_equal (length_of SP) (length_of P))))
% 3.82/4.01 True
% 3.82/4.01 Clause #207 (by clausification #[206]): ∀ (a a_1 a_2 : Iota),
% 3.82/4.01 Eq
% 3.82/4.01 (Iff (shortest_path a a_1 a_2)
% 3.82/4.01 (And (And (path a a_1 a_2) (Ne a a_1))
% 3.82/4.01 (∀ (P : Iota), path a a_1 P → less_or_equal (length_of a_2) (length_of P))))
% 3.82/4.01 True
% 3.82/4.01 Clause #209 (by clausification #[207]): ∀ (a a_1 a_2 : Iota),
% 3.82/4.01 Or (Eq (shortest_path a a_1 a_2) False)
% 3.82/4.01 (Eq
% 3.82/4.01 (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)))
% 3.82/4.01 True)
% 3.82/4.01 Clause #218 (by clausification #[209]): ∀ (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)
% 3.82/4.01 Clause #223 (by clausification #[218]): ∀ (a a_1 a_2 : Iota), Or (Eq (shortest_path a a_1 a_2) False) (Eq (path a a_1 a_2) True)
% 3.82/4.01 Clause #226 (by superposition #[223, 140]): ∀ (a a_1 a_2 : Iota), Or (Eq (path (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) (skS.0 4 a)) True) (Eq False True)
% 3.82/4.01 Clause #242 (by clausification #[226]): ∀ (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
% 3.82/4.01 Clause #246 (by superposition #[242, 101]): ∀ (a : Iota), Or (Eq True False) (Eq (number_of_in sequential_pairs (skS.0 4 a)) (minus (length_of (skS.0 4 a)) n1))
% 3.82/4.01 Clause #280 (by clausification #[246]): ∀ (a : Iota), Eq (number_of_in sequential_pairs (skS.0 4 a)) (minus (length_of (skS.0 4 a)) n1)
% 3.82/4.01 Clause #281 (by forward demodulation #[280, 153]): ∀ (a : Iota), Eq (number_of_in triangles (skS.0 4 a)) (minus (length_of (skS.0 4 a)) n1)
% 3.82/4.01 Clause #282 (by backward demodulation #[281, 141]): ∀ (a : Iota), Eq (less_or_equal (number_of_in triangles (skS.0 4 a)) (number_of_in triangles graph)) False
% 3.82/4.01 Clause #283 (by superposition #[282, 44]): Eq False True
% 3.82/4.01 Clause #291 (by clausification #[283]): False
% 3.82/4.01 SZS output end Proof for theBenchmark.p
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