TSTP Solution File: PUZ031_1 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : PUZ031_1 : TPTP v8.1.2. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n031.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 13:14:27 EDT 2023
% Result : Theorem 3.78s 4.13s
% Output : Proof 3.89s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : PUZ031_1 : TPTP v8.1.2. Released v5.0.0.
% 0.14/0.15 % Command : duper %s
% 0.14/0.36 % Computer : n031.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 22:30:23 EDT 2023
% 0.14/0.37 % CPUTime :
% 3.78/4.13 SZS status Theorem for theBenchmark.p
% 3.78/4.13 SZS output start Proof for theBenchmark.p
% 3.78/4.13 Clause #0 (by assumption #[]): Eq
% 3.78/4.13 (∀ (X : animal),
% 3.78/4.13 Or (∀ (Y : plant), eats X (plant_to_edible Y))
% 3.78/4.13 (∀ (Y1 : animal),
% 3.78/4.13 And (much_smaller Y1 X) (Exists fun Z => eats Y1 (plant_to_edible Z)) → eats X (animal_to_edible Y1)))
% 3.78/4.13 True
% 3.78/4.13 Clause #1 (by assumption #[]): Eq (∀ (X : snail) (Y : bird), much_smaller (snail_to_animal X) (bird_to_animal Y)) True
% 3.78/4.13 Clause #3 (by assumption #[]): Eq (∀ (X : bird) (Y : fox), much_smaller (bird_to_animal X) (fox_to_animal Y)) True
% 3.78/4.13 Clause #4 (by assumption #[]): Eq (∀ (X : fox) (Y : wolf), much_smaller (fox_to_animal X) (wolf_to_animal Y)) True
% 3.78/4.13 Clause #6 (by assumption #[]): Eq (∀ (X : wolf) (Y : grain), Not (eats (wolf_to_animal X) (plant_to_edible (grain_to_plant Y)))) True
% 3.78/4.13 Clause #8 (by assumption #[]): Eq (∀ (X : bird) (Y : snail), Not (eats (bird_to_animal X) (animal_to_edible (snail_to_animal Y)))) True
% 3.78/4.13 Clause #10 (by assumption #[]): Eq (∀ (X : snail), Exists fun Y => eats (snail_to_animal X) (plant_to_edible Y)) True
% 3.78/4.13 Clause #11 (by assumption #[]): Eq
% 3.78/4.13 (Not
% 3.78/4.13 (Exists fun X =>
% 3.78/4.13 Exists fun Y => Exists fun Z => And (eats Y (plant_to_edible (grain_to_plant Z))) (eats X (animal_to_edible Y))))
% 3.78/4.13 True
% 3.78/4.13 Clause #12 (by clausification #[4]): ∀ (a : fox), Eq (∀ (Y : wolf), much_smaller (fox_to_animal a) (wolf_to_animal Y)) True
% 3.78/4.13 Clause #13 (by clausification #[12]): ∀ (a : fox) (a_1 : wolf), Eq (much_smaller (fox_to_animal a) (wolf_to_animal a_1)) True
% 3.78/4.13 Clause #14 (by clausification #[3]): ∀ (a : bird), Eq (∀ (Y : fox), much_smaller (bird_to_animal a) (fox_to_animal Y)) True
% 3.78/4.13 Clause #15 (by clausification #[14]): ∀ (a : bird) (a_1 : fox), Eq (much_smaller (bird_to_animal a) (fox_to_animal a_1)) True
% 3.78/4.13 Clause #18 (by clausification #[1]): ∀ (a : snail), Eq (∀ (Y : bird), much_smaller (snail_to_animal a) (bird_to_animal Y)) True
% 3.78/4.13 Clause #19 (by clausification #[18]): ∀ (a : snail) (a_1 : bird), Eq (much_smaller (snail_to_animal a) (bird_to_animal a_1)) True
% 3.78/4.13 Clause #22 (by clausification #[0]): ∀ (a : animal),
% 3.78/4.13 Eq
% 3.78/4.13 (Or (∀ (Y : plant), eats a (plant_to_edible Y))
% 3.78/4.13 (∀ (Y1 : animal),
% 3.78/4.13 And (much_smaller Y1 a) (Exists fun Z => eats Y1 (plant_to_edible Z)) → eats a (animal_to_edible Y1)))
% 3.78/4.13 True
% 3.78/4.13 Clause #23 (by clausification #[22]): ∀ (a : animal),
% 3.78/4.13 Or (Eq (∀ (Y : plant), eats a (plant_to_edible Y)) True)
% 3.78/4.13 (Eq
% 3.78/4.13 (∀ (Y1 : animal),
% 3.78/4.13 And (much_smaller Y1 a) (Exists fun Z => eats Y1 (plant_to_edible Z)) → eats a (animal_to_edible Y1))
% 3.78/4.13 True)
% 3.78/4.13 Clause #24 (by clausification #[23]): ∀ (a : animal) (a_1 : plant),
% 3.78/4.13 Or
% 3.78/4.13 (Eq
% 3.78/4.13 (∀ (Y1 : animal),
% 3.78/4.13 And (much_smaller Y1 a) (Exists fun Z => eats Y1 (plant_to_edible Z)) → eats a (animal_to_edible Y1))
% 3.78/4.13 True)
% 3.78/4.13 (Eq (eats a (plant_to_edible a_1)) True)
% 3.78/4.13 Clause #25 (by clausification #[24]): ∀ (a : animal) (a_1 : plant) (a_2 : animal),
% 3.78/4.13 Or (Eq (eats a (plant_to_edible a_1)) True)
% 3.78/4.13 (Eq (And (much_smaller a_2 a) (Exists fun Z => eats a_2 (plant_to_edible Z)) → eats a (animal_to_edible a_2)) True)
% 3.78/4.13 Clause #26 (by clausification #[25]): ∀ (a : animal) (a_1 : plant) (a_2 : animal),
% 3.78/4.13 Or (Eq (eats a (plant_to_edible a_1)) True)
% 3.78/4.13 (Or (Eq (And (much_smaller a_2 a) (Exists fun Z => eats a_2 (plant_to_edible Z))) False)
% 3.78/4.13 (Eq (eats a (animal_to_edible a_2)) True))
% 3.78/4.13 Clause #27 (by clausification #[26]): ∀ (a : animal) (a_1 : plant) (a_2 : animal),
% 3.78/4.13 Or (Eq (eats a (plant_to_edible a_1)) True)
% 3.78/4.13 (Or (Eq (eats a (animal_to_edible a_2)) True)
% 3.78/4.13 (Or (Eq (much_smaller a_2 a) False) (Eq (Exists fun Z => eats a_2 (plant_to_edible Z)) False)))
% 3.78/4.13 Clause #28 (by clausification #[27]): ∀ (a : animal) (a_1 : plant) (a_2 : animal) (a_3 : plant),
% 3.78/4.13 Or (Eq (eats a (plant_to_edible a_1)) True)
% 3.78/4.13 (Or (Eq (eats a (animal_to_edible a_2)) True)
% 3.78/4.13 (Or (Eq (much_smaller a_2 a) False) (Eq (eats a_2 (plant_to_edible a_3)) False)))
% 3.78/4.13 Clause #29 (by superposition #[28, 13]): ∀ (a : wolf) (a_1 : plant) (a_2 : fox) (a_3 : plant),
% 3.78/4.13 Or (Eq (eats (wolf_to_animal a) (plant_to_edible a_1)) True)
% 3.89/4.15 (Or (Eq (eats (wolf_to_animal a) (animal_to_edible (fox_to_animal a_2))) True)
% 3.89/4.15 (Or (Eq (eats (fox_to_animal a_2) (plant_to_edible a_3)) False) (Eq False True)))
% 3.89/4.15 Clause #30 (by superposition #[28, 15]): ∀ (a : fox) (a_1 : plant) (a_2 : bird) (a_3 : plant),
% 3.89/4.15 Or (Eq (eats (fox_to_animal a) (plant_to_edible a_1)) True)
% 3.89/4.15 (Or (Eq (eats (fox_to_animal a) (animal_to_edible (bird_to_animal a_2))) True)
% 3.89/4.15 (Or (Eq (eats (bird_to_animal a_2) (plant_to_edible a_3)) False) (Eq False True)))
% 3.89/4.15 Clause #32 (by superposition #[28, 19]): ∀ (a : bird) (a_1 : plant) (a_2 : snail) (a_3 : plant),
% 3.89/4.15 Or (Eq (eats (bird_to_animal a) (plant_to_edible a_1)) True)
% 3.89/4.15 (Or (Eq (eats (bird_to_animal a) (animal_to_edible (snail_to_animal a_2))) True)
% 3.89/4.15 (Or (Eq (eats (snail_to_animal a_2) (plant_to_edible a_3)) False) (Eq False True)))
% 3.89/4.15 Clause #33 (by clausification #[6]): ∀ (a : wolf), Eq (∀ (Y : grain), Not (eats (wolf_to_animal a) (plant_to_edible (grain_to_plant Y)))) True
% 3.89/4.15 Clause #34 (by clausification #[33]): ∀ (a : wolf) (a_1 : grain), Eq (Not (eats (wolf_to_animal a) (plant_to_edible (grain_to_plant a_1)))) True
% 3.89/4.15 Clause #35 (by clausification #[34]): ∀ (a : wolf) (a_1 : grain), Eq (eats (wolf_to_animal a) (plant_to_edible (grain_to_plant a_1))) False
% 3.89/4.15 Clause #39 (by clausification #[10]): ∀ (a : snail), Eq (Exists fun Y => eats (snail_to_animal a) (plant_to_edible Y)) True
% 3.89/4.15 Clause #40 (by clausification #[39]): ∀ (a : snail) (a_1 : plant), Eq (eats (snail_to_animal a) (plant_to_edible (skS.0 0 a a_1))) True
% 3.89/4.15 Clause #43 (by clausification #[8]): ∀ (a : bird), Eq (∀ (Y : snail), Not (eats (bird_to_animal a) (animal_to_edible (snail_to_animal Y)))) True
% 3.89/4.15 Clause #44 (by clausification #[43]): ∀ (a : bird) (a_1 : snail), Eq (Not (eats (bird_to_animal a) (animal_to_edible (snail_to_animal a_1)))) True
% 3.89/4.15 Clause #45 (by clausification #[44]): ∀ (a : bird) (a_1 : snail), Eq (eats (bird_to_animal a) (animal_to_edible (snail_to_animal a_1))) False
% 3.89/4.15 Clause #46 (by clausification #[11]): Eq
% 3.89/4.15 (Exists fun X =>
% 3.89/4.15 Exists fun Y => Exists fun Z => And (eats Y (plant_to_edible (grain_to_plant Z))) (eats X (animal_to_edible Y)))
% 3.89/4.15 False
% 3.89/4.15 Clause #47 (by clausification #[46]): ∀ (a : animal),
% 3.89/4.15 Eq (Exists fun Y => Exists fun Z => And (eats Y (plant_to_edible (grain_to_plant Z))) (eats a (animal_to_edible Y)))
% 3.89/4.15 False
% 3.89/4.15 Clause #48 (by clausification #[47]): ∀ (a a_1 : animal),
% 3.89/4.15 Eq (Exists fun Z => And (eats a (plant_to_edible (grain_to_plant Z))) (eats a_1 (animal_to_edible a))) False
% 3.89/4.15 Clause #49 (by clausification #[48]): ∀ (a : animal) (a_1 : grain) (a_2 : animal),
% 3.89/4.15 Eq (And (eats a (plant_to_edible (grain_to_plant a_1))) (eats a_2 (animal_to_edible a))) False
% 3.89/4.15 Clause #50 (by clausification #[49]): ∀ (a : animal) (a_1 : grain) (a_2 : animal),
% 3.89/4.15 Or (Eq (eats a (plant_to_edible (grain_to_plant a_1))) False) (Eq (eats a_2 (animal_to_edible a)) False)
% 3.89/4.15 Clause #51 (by clausification #[32]): ∀ (a : bird) (a_1 : plant) (a_2 : snail) (a_3 : plant),
% 3.89/4.15 Or (Eq (eats (bird_to_animal a) (plant_to_edible a_1)) True)
% 3.89/4.15 (Or (Eq (eats (bird_to_animal a) (animal_to_edible (snail_to_animal a_2))) True)
% 3.89/4.15 (Eq (eats (snail_to_animal a_2) (plant_to_edible a_3)) False))
% 3.89/4.15 Clause #52 (by superposition #[51, 40]): ∀ (a : bird) (a_1 : plant) (a_2 : snail),
% 3.89/4.15 Or (Eq (eats (bird_to_animal a) (plant_to_edible a_1)) True)
% 3.89/4.15 (Or (Eq (eats (bird_to_animal a) (animal_to_edible (snail_to_animal a_2))) True) (Eq False True))
% 3.89/4.15 Clause #53 (by clausification #[52]): ∀ (a : bird) (a_1 : plant) (a_2 : snail),
% 3.89/4.15 Or (Eq (eats (bird_to_animal a) (plant_to_edible a_1)) True)
% 3.89/4.15 (Eq (eats (bird_to_animal a) (animal_to_edible (snail_to_animal a_2))) True)
% 3.89/4.15 Clause #55 (by superposition #[53, 45]): ∀ (a : bird) (a_1 : plant), Or (Eq (eats (bird_to_animal a) (plant_to_edible a_1)) True) (Eq True False)
% 3.89/4.15 Clause #56 (by clausification #[55]): ∀ (a : bird) (a_1 : plant), Eq (eats (bird_to_animal a) (plant_to_edible a_1)) True
% 3.89/4.15 Clause #57 (by superposition #[56, 50]): ∀ (a : animal) (a_1 : bird), Or (Eq True False) (Eq (eats a (animal_to_edible (bird_to_animal a_1))) False)
% 3.89/4.17 Clause #58 (by clausification #[57]): ∀ (a : animal) (a_1 : bird), Eq (eats a (animal_to_edible (bird_to_animal a_1))) False
% 3.89/4.17 Clause #60 (by clausification #[29]): ∀ (a : wolf) (a_1 : plant) (a_2 : fox) (a_3 : plant),
% 3.89/4.17 Or (Eq (eats (wolf_to_animal a) (plant_to_edible a_1)) True)
% 3.89/4.17 (Or (Eq (eats (wolf_to_animal a) (animal_to_edible (fox_to_animal a_2))) True)
% 3.89/4.17 (Eq (eats (fox_to_animal a_2) (plant_to_edible a_3)) False))
% 3.89/4.17 Clause #62 (by clausification #[30]): ∀ (a : fox) (a_1 : plant) (a_2 : bird) (a_3 : plant),
% 3.89/4.17 Or (Eq (eats (fox_to_animal a) (plant_to_edible a_1)) True)
% 3.89/4.17 (Or (Eq (eats (fox_to_animal a) (animal_to_edible (bird_to_animal a_2))) True)
% 3.89/4.17 (Eq (eats (bird_to_animal a_2) (plant_to_edible a_3)) False))
% 3.89/4.17 Clause #63 (by superposition #[62, 56]): ∀ (a : fox) (a_1 : plant) (a_2 : bird),
% 3.89/4.17 Or (Eq (eats (fox_to_animal a) (plant_to_edible a_1)) True)
% 3.89/4.17 (Or (Eq (eats (fox_to_animal a) (animal_to_edible (bird_to_animal a_2))) True) (Eq False True))
% 3.89/4.17 Clause #64 (by clausification #[63]): ∀ (a : fox) (a_1 : plant) (a_2 : bird),
% 3.89/4.17 Or (Eq (eats (fox_to_animal a) (plant_to_edible a_1)) True)
% 3.89/4.17 (Eq (eats (fox_to_animal a) (animal_to_edible (bird_to_animal a_2))) True)
% 3.89/4.17 Clause #67 (by superposition #[64, 58]): ∀ (a : fox) (a_1 : plant), Or (Eq (eats (fox_to_animal a) (plant_to_edible a_1)) True) (Eq True False)
% 3.89/4.17 Clause #68 (by clausification #[67]): ∀ (a : fox) (a_1 : plant), Eq (eats (fox_to_animal a) (plant_to_edible a_1)) True
% 3.89/4.17 Clause #69 (by superposition #[68, 60]): ∀ (a : wolf) (a_1 : plant) (a_2 : fox),
% 3.89/4.17 Or (Eq (eats (wolf_to_animal a) (plant_to_edible a_1)) True)
% 3.89/4.17 (Or (Eq (eats (wolf_to_animal a) (animal_to_edible (fox_to_animal a_2))) True) (Eq True False))
% 3.89/4.17 Clause #70 (by superposition #[68, 50]): ∀ (a : animal) (a_1 : fox), Or (Eq True False) (Eq (eats a (animal_to_edible (fox_to_animal a_1))) False)
% 3.89/4.17 Clause #71 (by clausification #[70]): ∀ (a : animal) (a_1 : fox), Eq (eats a (animal_to_edible (fox_to_animal a_1))) False
% 3.89/4.17 Clause #77 (by clausification #[69]): ∀ (a : wolf) (a_1 : plant) (a_2 : fox),
% 3.89/4.17 Or (Eq (eats (wolf_to_animal a) (plant_to_edible a_1)) True)
% 3.89/4.17 (Eq (eats (wolf_to_animal a) (animal_to_edible (fox_to_animal a_2))) True)
% 3.89/4.17 Clause #80 (by superposition #[77, 71]): ∀ (a : wolf) (a_1 : plant), Or (Eq (eats (wolf_to_animal a) (plant_to_edible a_1)) True) (Eq True False)
% 3.89/4.17 Clause #81 (by clausification #[80]): ∀ (a : wolf) (a_1 : plant), Eq (eats (wolf_to_animal a) (plant_to_edible a_1)) True
% 3.89/4.17 Clause #82 (by superposition #[81, 35]): Eq True False
% 3.89/4.17 Clause #84 (by clausification #[82]): False
% 3.89/4.17 SZS output end Proof for theBenchmark.p
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