%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : PUZ031_1 : TPTP v9.2.0. Released v5.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n026.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 : Fri Oct 3 07:58:14 PM UTC 2025 % Result : Theorem 4.07s 4.24s % Output : Proof 4.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : PUZ031_1 : TPTP v9.2.0. Released v5.0.0. % 0.03/0.13 % Command : duper %s % 0.12/0.34 % Computer : n026.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Thu Oct 2 20:49:53 EDT 2025 % 0.12/0.34 % CPUTime : % 4.07/4.24 SZS status Theorem for theBenchmark.p % 4.07/4.24 SZS output start Proof for theBenchmark.p % 4.07/4.24 Clause #0 (by assumption #[]): Eq % 4.07/4.24 (∀ (X : animal), % 4.07/4.24 Or (∀ (Y : plant), eats X (plant_to_edible Y)) % 4.07/4.24 (∀ (Y1 : animal), % 4.07/4.24 And (much_smaller Y1 X) (Exists fun Z => eats Y1 (plant_to_edible Z)) → eats X (animal_to_edible Y1))) % 4.07/4.24 True % 4.07/4.24 Clause #1 (by assumption #[]): Eq (∀ (X : snail) (Y : bird), much_smaller (snail_to_animal X) (bird_to_animal Y)) True % 4.07/4.24 Clause #3 (by assumption #[]): Eq (∀ (X : bird) (Y : fox), much_smaller (bird_to_animal X) (fox_to_animal Y)) True % 4.07/4.24 Clause #4 (by assumption #[]): Eq (∀ (X : fox) (Y : wolf), much_smaller (fox_to_animal X) (wolf_to_animal Y)) True % 4.07/4.24 Clause #6 (by assumption #[]): Eq (∀ (X : wolf) (Y : grain), Not (eats (wolf_to_animal X) (plant_to_edible (grain_to_plant Y)))) True % 4.07/4.24 Clause #8 (by assumption #[]): Eq (∀ (X : bird) (Y : snail), Not (eats (bird_to_animal X) (animal_to_edible (snail_to_animal Y)))) True % 4.07/4.24 Clause #10 (by assumption #[]): Eq (∀ (X : snail), Exists fun Y => eats (snail_to_animal X) (plant_to_edible Y)) True % 4.07/4.24 Clause #11 (by assumption #[]): Eq % 4.07/4.24 (Not % 4.07/4.24 (Exists fun X => % 4.07/4.24 Exists fun Y => Exists fun Z => And (eats Y (plant_to_edible (grain_to_plant Z))) (eats X (animal_to_edible Y)))) % 4.07/4.24 True % 4.07/4.24 Clause #12 (by clausification #[4]): ∀ (a : fox), Eq (∀ (Y : wolf), much_smaller (fox_to_animal a) (wolf_to_animal Y)) True % 4.07/4.24 Clause #13 (by clausification #[12]): ∀ (a : fox) (a_1 : wolf), Eq (much_smaller (fox_to_animal a) (wolf_to_animal a_1)) True % 4.07/4.24 Clause #14 (by clausification #[3]): ∀ (a : bird), Eq (∀ (Y : fox), much_smaller (bird_to_animal a) (fox_to_animal Y)) True % 4.07/4.24 Clause #15 (by clausification #[14]): ∀ (a : bird) (a_1 : fox), Eq (much_smaller (bird_to_animal a) (fox_to_animal a_1)) True % 4.07/4.24 Clause #18 (by clausification #[1]): ∀ (a : snail), Eq (∀ (Y : bird), much_smaller (snail_to_animal a) (bird_to_animal Y)) True % 4.07/4.24 Clause #19 (by clausification #[18]): ∀ (a : snail) (a_1 : bird), Eq (much_smaller (snail_to_animal a) (bird_to_animal a_1)) True % 4.07/4.24 Clause #22 (by clausification #[0]): ∀ (a : animal), % 4.07/4.24 Eq % 4.07/4.24 (Or (∀ (Y : plant), eats a (plant_to_edible Y)) % 4.07/4.24 (∀ (Y1 : animal), % 4.07/4.24 And (much_smaller Y1 a) (Exists fun Z => eats Y1 (plant_to_edible Z)) → eats a (animal_to_edible Y1))) % 4.07/4.24 True % 4.07/4.24 Clause #23 (by clausification #[22]): ∀ (a : animal), % 4.07/4.24 Or (Eq (∀ (Y : plant), eats a (plant_to_edible Y)) True) % 4.07/4.24 (Eq % 4.07/4.24 (∀ (Y1 : animal), % 4.07/4.24 And (much_smaller Y1 a) (Exists fun Z => eats Y1 (plant_to_edible Z)) → eats a (animal_to_edible Y1)) % 4.07/4.24 True) % 4.07/4.24 Clause #24 (by clausification #[23]): ∀ (a : animal) (a_1 : plant), % 4.07/4.24 Or % 4.07/4.24 (Eq % 4.07/4.24 (∀ (Y1 : animal), % 4.07/4.24 And (much_smaller Y1 a) (Exists fun Z => eats Y1 (plant_to_edible Z)) → eats a (animal_to_edible Y1)) % 4.07/4.24 True) % 4.07/4.24 (Eq (eats a (plant_to_edible a_1)) True) % 4.07/4.24 Clause #25 (by clausification #[24]): ∀ (a : animal) (a_1 : plant) (a_2 : animal), % 4.07/4.24 Or (Eq (eats a (plant_to_edible a_1)) True) % 4.07/4.24 (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) % 4.07/4.24 Clause #26 (by clausification #[25]): ∀ (a : animal) (a_1 : plant) (a_2 : animal), % 4.07/4.24 Or (Eq (eats a (plant_to_edible a_1)) True) % 4.07/4.24 (Or (Eq (And (much_smaller a_2 a) (Exists fun Z => eats a_2 (plant_to_edible Z))) False) % 4.07/4.24 (Eq (eats a (animal_to_edible a_2)) True)) % 4.07/4.24 Clause #27 (by clausification #[26]): ∀ (a : animal) (a_1 : plant) (a_2 : animal), % 4.07/4.24 Or (Eq (eats a (plant_to_edible a_1)) True) % 4.07/4.24 (Or (Eq (eats a (animal_to_edible a_2)) True) % 4.07/4.24 (Or (Eq (much_smaller a_2 a) False) (Eq (Exists fun Z => eats a_2 (plant_to_edible Z)) False))) % 4.07/4.24 Clause #28 (by clausification #[27]): ∀ (a : animal) (a_1 : plant) (a_2 : animal) (a_3 : plant), % 4.07/4.24 Or (Eq (eats a (plant_to_edible a_1)) True) % 4.07/4.24 (Or (Eq (eats a (animal_to_edible a_2)) True) % 4.07/4.24 (Or (Eq (much_smaller a_2 a) False) (Eq (eats a_2 (plant_to_edible a_3)) False))) % 4.07/4.24 Clause #29 (by superposition #[28, 13]): ∀ (a : wolf) (a_1 : plant) (a_2 : fox) (a_3 : plant), % 4.07/4.24 Or (Eq (eats (wolf_to_animal a) (plant_to_edible a_1)) True) % 4.10/4.26 (Or (Eq (eats (wolf_to_animal a) (animal_to_edible (fox_to_animal a_2))) True) % 4.10/4.26 (Or (Eq (eats (fox_to_animal a_2) (plant_to_edible a_3)) False) (Eq False True))) % 4.10/4.26 Clause #30 (by superposition #[28, 15]): ∀ (a : fox) (a_1 : plant) (a_2 : bird) (a_3 : plant), % 4.10/4.26 Or (Eq (eats (fox_to_animal a) (plant_to_edible a_1)) True) % 4.10/4.26 (Or (Eq (eats (fox_to_animal a) (animal_to_edible (bird_to_animal a_2))) True) % 4.10/4.26 (Or (Eq (eats (bird_to_animal a_2) (plant_to_edible a_3)) False) (Eq False True))) % 4.10/4.26 Clause #32 (by superposition #[28, 19]): ∀ (a : bird) (a_1 : plant) (a_2 : snail) (a_3 : plant), % 4.10/4.26 Or (Eq (eats (bird_to_animal a) (plant_to_edible a_1)) True) % 4.10/4.26 (Or (Eq (eats (bird_to_animal a) (animal_to_edible (snail_to_animal a_2))) True) % 4.10/4.26 (Or (Eq (eats (snail_to_animal a_2) (plant_to_edible a_3)) False) (Eq False True))) % 4.10/4.26 Clause #33 (by clausification #[6]): ∀ (a : wolf), Eq (∀ (Y : grain), Not (eats (wolf_to_animal a) (plant_to_edible (grain_to_plant Y)))) True % 4.10/4.26 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 % 4.10/4.26 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 % 4.10/4.26 Clause #39 (by clausification #[10]): ∀ (a : snail), Eq (Exists fun Y => eats (snail_to_animal a) (plant_to_edible Y)) True % 4.10/4.26 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 % 4.10/4.26 Clause #43 (by clausification #[8]): ∀ (a : bird), Eq (∀ (Y : snail), Not (eats (bird_to_animal a) (animal_to_edible (snail_to_animal Y)))) True % 4.10/4.26 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 % 4.10/4.26 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 % 4.10/4.26 Clause #46 (by clausification #[11]): Eq % 4.10/4.26 (Exists fun X => % 4.10/4.26 Exists fun Y => Exists fun Z => And (eats Y (plant_to_edible (grain_to_plant Z))) (eats X (animal_to_edible Y))) % 4.10/4.26 False % 4.10/4.26 Clause #47 (by clausification #[46]): ∀ (a : animal), % 4.10/4.26 Eq (Exists fun Y => Exists fun Z => And (eats Y (plant_to_edible (grain_to_plant Z))) (eats a (animal_to_edible Y))) % 4.10/4.26 False % 4.10/4.26 Clause #48 (by clausification #[47]): ∀ (a a_1 : animal), % 4.10/4.26 Eq (Exists fun Z => And (eats a (plant_to_edible (grain_to_plant Z))) (eats a_1 (animal_to_edible a))) False % 4.10/4.26 Clause #49 (by clausification #[48]): ∀ (a : animal) (a_1 : grain) (a_2 : animal), % 4.10/4.26 Eq (And (eats a (plant_to_edible (grain_to_plant a_1))) (eats a_2 (animal_to_edible a))) False % 4.10/4.26 Clause #50 (by clausification #[49]): ∀ (a : animal) (a_1 : grain) (a_2 : animal), % 4.10/4.26 Or (Eq (eats a (plant_to_edible (grain_to_plant a_1))) False) (Eq (eats a_2 (animal_to_edible a)) False) % 4.10/4.26 Clause #51 (by clausification #[32]): ∀ (a : bird) (a_1 : plant) (a_2 : snail) (a_3 : plant), % 4.10/4.26 Or (Eq (eats (bird_to_animal a) (plant_to_edible a_1)) True) % 4.10/4.26 (Or (Eq (eats (bird_to_animal a) (animal_to_edible (snail_to_animal a_2))) True) % 4.10/4.26 (Eq (eats (snail_to_animal a_2) (plant_to_edible a_3)) False)) % 4.10/4.26 Clause #52 (by superposition #[51, 40]): ∀ (a : bird) (a_1 : plant) (a_2 : snail), % 4.10/4.26 Or (Eq (eats (bird_to_animal a) (plant_to_edible a_1)) True) % 4.10/4.26 (Or (Eq (eats (bird_to_animal a) (animal_to_edible (snail_to_animal a_2))) True) (Eq False True)) % 4.10/4.26 Clause #53 (by clausification #[52]): ∀ (a : bird) (a_1 : plant) (a_2 : snail), % 4.10/4.26 Or (Eq (eats (bird_to_animal a) (plant_to_edible a_1)) True) % 4.10/4.26 (Eq (eats (bird_to_animal a) (animal_to_edible (snail_to_animal a_2))) True) % 4.10/4.26 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) % 4.10/4.26 Clause #56 (by clausification #[55]): ∀ (a : bird) (a_1 : plant), Eq (eats (bird_to_animal a) (plant_to_edible a_1)) True % 4.10/4.26 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) % 4.10/4.28 Clause #58 (by clausification #[57]): ∀ (a : animal) (a_1 : bird), Eq (eats a (animal_to_edible (bird_to_animal a_1))) False % 4.10/4.28 Clause #60 (by clausification #[29]): ∀ (a : wolf) (a_1 : plant) (a_2 : fox) (a_3 : plant), % 4.10/4.28 Or (Eq (eats (wolf_to_animal a) (plant_to_edible a_1)) True) % 4.10/4.28 (Or (Eq (eats (wolf_to_animal a) (animal_to_edible (fox_to_animal a_2))) True) % 4.10/4.28 (Eq (eats (fox_to_animal a_2) (plant_to_edible a_3)) False)) % 4.10/4.28 Clause #62 (by clausification #[30]): ∀ (a : fox) (a_1 : plant) (a_2 : bird) (a_3 : plant), % 4.10/4.28 Or (Eq (eats (fox_to_animal a) (plant_to_edible a_1)) True) % 4.10/4.28 (Or (Eq (eats (fox_to_animal a) (animal_to_edible (bird_to_animal a_2))) True) % 4.10/4.28 (Eq (eats (bird_to_animal a_2) (plant_to_edible a_3)) False)) % 4.10/4.28 Clause #63 (by superposition #[62, 56]): ∀ (a : fox) (a_1 : plant) (a_2 : bird), % 4.10/4.28 Or (Eq (eats (fox_to_animal a) (plant_to_edible a_1)) True) % 4.10/4.28 (Or (Eq (eats (fox_to_animal a) (animal_to_edible (bird_to_animal a_2))) True) (Eq False True)) % 4.10/4.28 Clause #64 (by clausification #[63]): ∀ (a : fox) (a_1 : plant) (a_2 : bird), % 4.10/4.28 Or (Eq (eats (fox_to_animal a) (plant_to_edible a_1)) True) % 4.10/4.28 (Eq (eats (fox_to_animal a) (animal_to_edible (bird_to_animal a_2))) True) % 4.10/4.28 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) % 4.10/4.28 Clause #68 (by clausification #[67]): ∀ (a : fox) (a_1 : plant), Eq (eats (fox_to_animal a) (plant_to_edible a_1)) True % 4.10/4.28 Clause #69 (by superposition #[68, 60]): ∀ (a : wolf) (a_1 : plant) (a_2 : fox), % 4.10/4.28 Or (Eq (eats (wolf_to_animal a) (plant_to_edible a_1)) True) % 4.10/4.28 (Or (Eq (eats (wolf_to_animal a) (animal_to_edible (fox_to_animal a_2))) True) (Eq True False)) % 4.10/4.28 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) % 4.10/4.28 Clause #71 (by clausification #[70]): ∀ (a : animal) (a_1 : fox), Eq (eats a (animal_to_edible (fox_to_animal a_1))) False % 4.10/4.28 Clause #77 (by clausification #[69]): ∀ (a : wolf) (a_1 : plant) (a_2 : fox), % 4.10/4.28 Or (Eq (eats (wolf_to_animal a) (plant_to_edible a_1)) True) % 4.10/4.28 (Eq (eats (wolf_to_animal a) (animal_to_edible (fox_to_animal a_2))) True) % 4.10/4.28 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) % 4.10/4.28 Clause #81 (by clausification #[80]): ∀ (a : wolf) (a_1 : plant), Eq (eats (wolf_to_animal a) (plant_to_edible a_1)) True % 4.10/4.28 Clause #82 (by superposition #[81, 35]): Eq True False % 4.10/4.28 Clause #84 (by clausification #[82]): False % 4.10/4.28 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------