%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ031_1 : TPTP v9.0.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 : Sat Jun 21 05:23:13 AM UTC 2025
% Result : Theorem 0.14s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : PUZ031_1 : TPTP v9.0.0. Released v5.0.0.
% 0.14/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n011.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 : Fri Jun 20 02:40:56 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.14/0.41 % SZS status Theorem
% 0.14/0.41 % SZS output start Proof
% 0.14/0.41 tff(eats_type, type, (
% 0.14/0.41 eats: ( animal * edible ) > $o)).
% 0.14/0.41 tff(animal_to_edible_type, type, (
% 0.14/0.41 animal_to_edible: animal > edible)).
% 0.14/0.41 tff(bird_to_animal_type, type, (
% 0.14/0.41 bird_to_animal: bird > animal)).
% 0.14/0.41 tff(elem_4_type, type, (
% 0.14/0.41 elem_4: bird)).
% 0.14/0.41 tff(fox_to_animal_type, type, (
% 0.14/0.41 fox_to_animal: fox > animal)).
% 0.14/0.41 tff(elem_43_type, type, (
% 0.14/0.41 elem_43: fox)).
% 0.14/0.41 tff(plant_to_edible_type, type, (
% 0.14/0.41 plant_to_edible: plant > edible)).
% 0.14/0.41 tff(tptp_fun_Y_1_type, type, (
% 0.14/0.41 tptp_fun_Y_1: snail > plant)).
% 0.14/0.41 tff(elem_5_type, type, (
% 0.14/0.41 elem_5: snail)).
% 0.14/0.41 tff(much_smaller_type, type, (
% 0.14/0.41 much_smaller: ( animal * animal ) > $o)).
% 0.14/0.41 tff(wolf_to_animal_type, type, (
% 0.14/0.41 wolf_to_animal: wolf > animal)).
% 0.14/0.41 tff(elem_44_type, type, (
% 0.14/0.41 elem_44: wolf)).
% 0.14/0.41 tff(grain_to_plant_type, type, (
% 0.14/0.41 grain_to_plant: grain > plant)).
% 0.14/0.41 tff(elem_45_type, type, (
% 0.14/0.41 elem_45: grain)).
% 0.14/0.41 tff(snail_to_animal_type, type, (
% 0.14/0.41 snail_to_animal: snail > animal)).
% 0.14/0.41 tff(1,assumption,(eats(fox_to_animal(elem!43), plant_to_edible(tptp_fun_Y_1(elem!5)))), introduced(assumption)).
% 0.14/0.41 tff(2,plain,
% 0.14/0.41 (^[X: fox, Y: wolf] : refl(much_smaller(fox_to_animal(X), wolf_to_animal(Y)) <=> much_smaller(fox_to_animal(X), wolf_to_animal(Y)))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(3,plain,
% 0.14/0.41 (![X: fox, Y: wolf] : much_smaller(fox_to_animal(X), wolf_to_animal(Y)) <=> ![X: fox, Y: wolf] : much_smaller(fox_to_animal(X), wolf_to_animal(Y))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.14/0.41 tff(4,plain,
% 0.14/0.41 (![X: fox, Y: wolf] : much_smaller(fox_to_animal(X), wolf_to_animal(Y)) <=> ![X: fox, Y: wolf] : much_smaller(fox_to_animal(X), wolf_to_animal(Y))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(5,axiom,(![X: fox, Y: wolf] : much_smaller(fox_to_animal(X), wolf_to_animal(Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_10')).
% 0.14/0.41 tff(6,plain,
% 0.14/0.41 (![X: fox, Y: wolf] : much_smaller(fox_to_animal(X), wolf_to_animal(Y))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.14/0.41 tff(7,plain,(
% 0.14/0.41 ![X: fox, Y: wolf] : much_smaller(fox_to_animal(X), wolf_to_animal(Y))),
% 0.14/0.41 inference(skolemize,[status(sab)],[6])).
% 0.14/0.41 tff(8,plain,
% 0.14/0.41 (![X: fox, Y: wolf] : much_smaller(fox_to_animal(X), wolf_to_animal(Y))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.14/0.41 tff(9,plain,
% 0.14/0.41 ((~![X: fox, Y: wolf] : much_smaller(fox_to_animal(X), wolf_to_animal(Y))) | much_smaller(fox_to_animal(elem!43), wolf_to_animal(elem!44))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(10,plain,
% 0.14/0.41 (much_smaller(fox_to_animal(elem!43), wolf_to_animal(elem!44))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.14/0.41 tff(11,plain,
% 0.14/0.41 (^[X: wolf, Y: grain] : refl((~eats(wolf_to_animal(X), plant_to_edible(grain_to_plant(Y)))) <=> (~eats(wolf_to_animal(X), plant_to_edible(grain_to_plant(Y)))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(12,plain,
% 0.14/0.41 (![X: wolf, Y: grain] : (~eats(wolf_to_animal(X), plant_to_edible(grain_to_plant(Y)))) <=> ![X: wolf, Y: grain] : (~eats(wolf_to_animal(X), plant_to_edible(grain_to_plant(Y))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[11])).
% 0.14/0.41 tff(13,plain,
% 0.14/0.41 (![X: wolf, Y: grain] : (~eats(wolf_to_animal(X), plant_to_edible(grain_to_plant(Y)))) <=> ![X: wolf, Y: grain] : (~eats(wolf_to_animal(X), plant_to_edible(grain_to_plant(Y))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(14,axiom,(![X: wolf, Y: grain] : (~eats(wolf_to_animal(X), plant_to_edible(grain_to_plant(Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_11a')).
% 0.14/0.41 tff(15,plain,
% 0.14/0.41 (![X: wolf, Y: grain] : (~eats(wolf_to_animal(X), plant_to_edible(grain_to_plant(Y))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.14/0.41 tff(16,plain,(
% 0.14/0.41 ![X: wolf, Y: grain] : (~eats(wolf_to_animal(X), plant_to_edible(grain_to_plant(Y))))),
% 0.14/0.41 inference(skolemize,[status(sab)],[15])).
% 0.14/0.41 tff(17,plain,
% 0.14/0.41 (![X: wolf, Y: grain] : (~eats(wolf_to_animal(X), plant_to_edible(grain_to_plant(Y))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.14/0.41 tff(18,plain,
% 0.14/0.41 ((~![X: wolf, Y: grain] : (~eats(wolf_to_animal(X), plant_to_edible(grain_to_plant(Y))))) | (~eats(wolf_to_animal(elem!44), plant_to_edible(grain_to_plant(elem!45))))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(19,plain,
% 0.14/0.41 (~eats(wolf_to_animal(elem!44), plant_to_edible(grain_to_plant(elem!45)))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.14/0.41 tff(20,plain,
% 0.14/0.41 (^[X: wolf, Y: fox] : refl((~eats(wolf_to_animal(X), animal_to_edible(fox_to_animal(Y)))) <=> (~eats(wolf_to_animal(X), animal_to_edible(fox_to_animal(Y)))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(21,plain,
% 0.14/0.41 (![X: wolf, Y: fox] : (~eats(wolf_to_animal(X), animal_to_edible(fox_to_animal(Y)))) <=> ![X: wolf, Y: fox] : (~eats(wolf_to_animal(X), animal_to_edible(fox_to_animal(Y))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[20])).
% 0.14/0.41 tff(22,plain,
% 0.14/0.41 (![X: wolf, Y: fox] : (~eats(wolf_to_animal(X), animal_to_edible(fox_to_animal(Y)))) <=> ![X: wolf, Y: fox] : (~eats(wolf_to_animal(X), animal_to_edible(fox_to_animal(Y))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(23,axiom,(![X: wolf, Y: fox] : (~eats(wolf_to_animal(X), animal_to_edible(fox_to_animal(Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_11')).
% 0.14/0.41 tff(24,plain,
% 0.14/0.41 (![X: wolf, Y: fox] : (~eats(wolf_to_animal(X), animal_to_edible(fox_to_animal(Y))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.14/0.41 tff(25,plain,(
% 0.14/0.41 ![X: wolf, Y: fox] : (~eats(wolf_to_animal(X), animal_to_edible(fox_to_animal(Y))))),
% 0.14/0.41 inference(skolemize,[status(sab)],[24])).
% 0.14/0.41 tff(26,plain,
% 0.14/0.41 (![X: wolf, Y: fox] : (~eats(wolf_to_animal(X), animal_to_edible(fox_to_animal(Y))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.14/0.41 tff(27,plain,
% 0.14/0.41 ((~![X: wolf, Y: fox] : (~eats(wolf_to_animal(X), animal_to_edible(fox_to_animal(Y))))) | (~eats(wolf_to_animal(elem!44), animal_to_edible(fox_to_animal(elem!43))))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(28,plain,
% 0.14/0.41 (~eats(wolf_to_animal(elem!44), animal_to_edible(fox_to_animal(elem!43)))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.14/0.41 tff(29,plain,
% 0.14/0.41 (^[X: animal, Y1: animal, Z: plant, Y: plant] : trans(monotonicity(rewrite((eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z)))) <=> (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))), ((eats(X, plant_to_edible(Y)) | (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) <=> (eats(X, plant_to_edible(Y)) | (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))))), rewrite((eats(X, plant_to_edible(Y)) | (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) <=> (eats(X, plant_to_edible(Y)) | eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))), ((eats(X, plant_to_edible(Y)) | (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) <=> (eats(X, plant_to_edible(Y)) | eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(30,plain,
% 0.14/0.41 (![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) <=> ![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[29])).
% 0.14/0.41 tff(31,plain,
% 0.14/0.41 (^[X: animal, Y1: animal, Z: plant, Y: plant] : refl((eats(X, plant_to_edible(Y)) | (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) <=> (eats(X, plant_to_edible(Y)) | (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(32,plain,
% 0.14/0.41 (![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) <=> ![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z)))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[31])).
% 0.14/0.42 tff(33,plain,
% 0.14/0.42 (![X: animal] : ![Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) <=> ![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z)))))),
% 0.14/0.42 inference(pull_quant,[status(thm)],[])).
% 0.14/0.42 tff(34,plain,
% 0.14/0.42 (^[X: animal] : trans(monotonicity(trans(quant_intro(proof_bind(^[Y1: animal] : pull_quant((eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | ![Z: plant] : (~eats(Y1, plant_to_edible(Z)))) <=> ![Z: plant] : (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z)))))), (![Y1: animal] : (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | ![Z: plant] : (~eats(Y1, plant_to_edible(Z)))) <=> ![Y1: animal] : ![Z: plant] : (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z)))))), pull_quant(![Y1: animal] : ![Z: plant] : (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z)))) <=> ![Y1: animal, Z: plant] : (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))), (![Y1: animal] : (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | ![Z: plant] : (~eats(Y1, plant_to_edible(Z)))) <=> ![Y1: animal, Z: plant] : (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z)))))), ((![Y: plant] : eats(X, plant_to_edible(Y)) | ![Y1: animal] : (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | ![Z: plant] : (~eats(Y1, plant_to_edible(Z))))) <=> (![Y: plant] : eats(X, plant_to_edible(Y)) | ![Y1: animal, Z: plant] : (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))))), pull_quant((![Y: plant] : eats(X, plant_to_edible(Y)) | ![Y1: animal, Z: plant] : (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) <=> ![Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z)))))), ((![Y: plant] : eats(X, plant_to_edible(Y)) | ![Y1: animal] : (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | ![Z: plant] : (~eats(Y1, plant_to_edible(Z))))) <=> ![Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z)))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(35,plain,
% 0.14/0.42 (![X: animal] : (![Y: plant] : eats(X, plant_to_edible(Y)) | ![Y1: animal] : (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | ![Z: plant] : (~eats(Y1, plant_to_edible(Z))))) <=> ![X: animal] : ![Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z)))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[34])).
% 0.14/0.42 tff(36,plain,
% 0.14/0.42 (![X: animal] : (![Y: plant] : eats(X, plant_to_edible(Y)) | ![Y1: animal] : (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | ![Z: plant] : (~eats(Y1, plant_to_edible(Z))))) <=> ![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z)))))),
% 0.14/0.42 inference(transitivity,[status(thm)],[35, 33])).
% 0.14/0.42 tff(37,plain,
% 0.14/0.42 (![X: animal] : (![Y: plant] : eats(X, plant_to_edible(Y)) | ![Y1: animal] : (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | ![Z: plant] : (~eats(Y1, plant_to_edible(Z))))) <=> ![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z)))))),
% 0.14/0.42 inference(transitivity,[status(thm)],[36, 32])).
% 0.14/0.42 tff(38,plain,
% 0.14/0.42 (^[X: animal] : rewrite((![Y: plant] : eats(X, plant_to_edible(Y)) | ![Y1: animal] : (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | ![Z: plant] : (~eats(Y1, plant_to_edible(Z))))) <=> (![Y: plant] : eats(X, plant_to_edible(Y)) | ![Y1: animal] : (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | ![Z: plant] : (~eats(Y1, plant_to_edible(Z))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(39,plain,
% 0.14/0.42 (![X: animal] : (![Y: plant] : eats(X, plant_to_edible(Y)) | ![Y1: animal] : (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | ![Z: plant] : (~eats(Y1, plant_to_edible(Z))))) <=> ![X: animal] : (![Y: plant] : eats(X, plant_to_edible(Y)) | ![Y1: animal] : (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | ![Z: plant] : (~eats(Y1, plant_to_edible(Z)))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[38])).
% 0.14/0.42 tff(40,plain,
% 0.14/0.42 (![X: animal] : (![Y: plant] : eats(X, plant_to_edible(Y)) | ![Y1: animal] : (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | ![Z: plant] : (~eats(Y1, plant_to_edible(Z))))) <=> ![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z)))))),
% 0.14/0.42 inference(transitivity,[status(thm)],[39, 37])).
% 0.14/0.42 tff(41,plain,
% 0.14/0.42 (^[X: animal] : rewrite((![Y: plant] : eats(X, plant_to_edible(Y)) | ![Y1: animal] : (((~much_smaller(Y1, X)) | ![Z: plant] : (~eats(Y1, plant_to_edible(Z)))) | eats(X, animal_to_edible(Y1)))) <=> (![Y: plant] : eats(X, plant_to_edible(Y)) | ![Y1: animal] : (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | ![Z: plant] : (~eats(Y1, plant_to_edible(Z))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(42,plain,
% 0.14/0.42 (![X: animal] : (![Y: plant] : eats(X, plant_to_edible(Y)) | ![Y1: animal] : (((~much_smaller(Y1, X)) | ![Z: plant] : (~eats(Y1, plant_to_edible(Z)))) | eats(X, animal_to_edible(Y1)))) <=> ![X: animal] : (![Y: plant] : eats(X, plant_to_edible(Y)) | ![Y1: animal] : (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | ![Z: plant] : (~eats(Y1, plant_to_edible(Z)))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[41])).
% 0.14/0.42 tff(43,plain,
% 0.14/0.42 (![X: animal] : (![Y: plant] : eats(X, plant_to_edible(Y)) | ![Y1: animal] : ((~(much_smaller(Y1, X) & ?[Z: plant] : eats(Y1, plant_to_edible(Z)))) | eats(X, animal_to_edible(Y1)))) <=> ![X: animal] : (![Y: plant] : eats(X, plant_to_edible(Y)) | ![Y1: animal] : ((~(much_smaller(Y1, X) & ?[Z: plant] : eats(Y1, plant_to_edible(Z)))) | eats(X, animal_to_edible(Y1))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(44,plain,
% 0.14/0.42 (^[X: animal] : rewrite((![Y: plant] : eats(X, plant_to_edible(Y)) | ![Y1: animal] : ((much_smaller(Y1, X) & ?[Z: plant] : eats(Y1, plant_to_edible(Z))) => eats(X, animal_to_edible(Y1)))) <=> (![Y: plant] : eats(X, plant_to_edible(Y)) | ![Y1: animal] : ((~(much_smaller(Y1, X) & ?[Z: plant] : eats(Y1, plant_to_edible(Z)))) | eats(X, animal_to_edible(Y1)))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(45,plain,
% 0.14/0.42 (![X: animal] : (![Y: plant] : eats(X, plant_to_edible(Y)) | ![Y1: animal] : ((much_smaller(Y1, X) & ?[Z: plant] : eats(Y1, plant_to_edible(Z))) => eats(X, animal_to_edible(Y1)))) <=> ![X: animal] : (![Y: plant] : eats(X, plant_to_edible(Y)) | ![Y1: animal] : ((~(much_smaller(Y1, X) & ?[Z: plant] : eats(Y1, plant_to_edible(Z)))) | eats(X, animal_to_edible(Y1))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[44])).
% 0.14/0.42 tff(46,axiom,(![X: animal] : (![Y: plant] : eats(X, plant_to_edible(Y)) | ![Y1: animal] : ((much_smaller(Y1, X) & ?[Z: plant] : eats(Y1, plant_to_edible(Z))) => eats(X, animal_to_edible(Y1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_7')).
% 0.14/0.42 tff(47,plain,
% 0.14/0.42 (![X: animal] : (![Y: plant] : eats(X, plant_to_edible(Y)) | ![Y1: animal] : ((~(much_smaller(Y1, X) & ?[Z: plant] : eats(Y1, plant_to_edible(Z)))) | eats(X, animal_to_edible(Y1))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.14/0.42 tff(48,plain,
% 0.14/0.42 (![X: animal] : (![Y: plant] : eats(X, plant_to_edible(Y)) | ![Y1: animal] : ((~(much_smaller(Y1, X) & ?[Z: plant] : eats(Y1, plant_to_edible(Z)))) | eats(X, animal_to_edible(Y1))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.14/0.42 tff(49,plain,(
% 0.14/0.42 ![X: animal] : (![Y: plant] : eats(X, plant_to_edible(Y)) | ![Y1: animal] : (((~much_smaller(Y1, X)) | ![Z: plant] : (~eats(Y1, plant_to_edible(Z)))) | eats(X, animal_to_edible(Y1))))),
% 0.14/0.42 inference(skolemize,[status(sab)],[48])).
% 0.14/0.42 tff(50,plain,
% 0.14/0.42 (![X: animal] : (![Y: plant] : eats(X, plant_to_edible(Y)) | ![Y1: animal] : (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | ![Z: plant] : (~eats(Y1, plant_to_edible(Z)))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.14/0.42 tff(51,plain,
% 0.14/0.42 (![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | (eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z)))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[50, 40])).
% 0.14/0.42 tff(52,plain,
% 0.14/0.42 (![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[51, 30])).
% 0.14/0.42 tff(53,plain,
% 0.14/0.42 (((~![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) | (eats(wolf_to_animal(elem!44), animal_to_edible(fox_to_animal(elem!43))) | eats(wolf_to_animal(elem!44), plant_to_edible(grain_to_plant(elem!45))) | (~much_smaller(fox_to_animal(elem!43), wolf_to_animal(elem!44))) | (~eats(fox_to_animal(elem!43), plant_to_edible(tptp_fun_Y_1(elem!5)))))) <=> ((~![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) | eats(wolf_to_animal(elem!44), animal_to_edible(fox_to_animal(elem!43))) | eats(wolf_to_animal(elem!44), plant_to_edible(grain_to_plant(elem!45))) | (~much_smaller(fox_to_animal(elem!43), wolf_to_animal(elem!44))) | (~eats(fox_to_animal(elem!43), plant_to_edible(tptp_fun_Y_1(elem!5)))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(54,plain,
% 0.14/0.42 ((eats(wolf_to_animal(elem!44), plant_to_edible(grain_to_plant(elem!45))) | eats(wolf_to_animal(elem!44), animal_to_edible(fox_to_animal(elem!43))) | (~much_smaller(fox_to_animal(elem!43), wolf_to_animal(elem!44))) | (~eats(fox_to_animal(elem!43), plant_to_edible(tptp_fun_Y_1(elem!5))))) <=> (eats(wolf_to_animal(elem!44), animal_to_edible(fox_to_animal(elem!43))) | eats(wolf_to_animal(elem!44), plant_to_edible(grain_to_plant(elem!45))) | (~much_smaller(fox_to_animal(elem!43), wolf_to_animal(elem!44))) | (~eats(fox_to_animal(elem!43), plant_to_edible(tptp_fun_Y_1(elem!5)))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(55,plain,
% 0.14/0.42 (((~![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) | (eats(wolf_to_animal(elem!44), plant_to_edible(grain_to_plant(elem!45))) | eats(wolf_to_animal(elem!44), animal_to_edible(fox_to_animal(elem!43))) | (~much_smaller(fox_to_animal(elem!43), wolf_to_animal(elem!44))) | (~eats(fox_to_animal(elem!43), plant_to_edible(tptp_fun_Y_1(elem!5)))))) <=> ((~![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) | (eats(wolf_to_animal(elem!44), animal_to_edible(fox_to_animal(elem!43))) | eats(wolf_to_animal(elem!44), plant_to_edible(grain_to_plant(elem!45))) | (~much_smaller(fox_to_animal(elem!43), wolf_to_animal(elem!44))) | (~eats(fox_to_animal(elem!43), plant_to_edible(tptp_fun_Y_1(elem!5))))))),
% 0.14/0.42 inference(monotonicity,[status(thm)],[54])).
% 0.14/0.42 tff(56,plain,
% 0.14/0.42 (((~![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) | (eats(wolf_to_animal(elem!44), plant_to_edible(grain_to_plant(elem!45))) | eats(wolf_to_animal(elem!44), animal_to_edible(fox_to_animal(elem!43))) | (~much_smaller(fox_to_animal(elem!43), wolf_to_animal(elem!44))) | (~eats(fox_to_animal(elem!43), plant_to_edible(tptp_fun_Y_1(elem!5)))))) <=> ((~![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) | eats(wolf_to_animal(elem!44), animal_to_edible(fox_to_animal(elem!43))) | eats(wolf_to_animal(elem!44), plant_to_edible(grain_to_plant(elem!45))) | (~much_smaller(fox_to_animal(elem!43), wolf_to_animal(elem!44))) | (~eats(fox_to_animal(elem!43), plant_to_edible(tptp_fun_Y_1(elem!5)))))),
% 0.14/0.42 inference(transitivity,[status(thm)],[55, 53])).
% 0.14/0.42 tff(57,plain,
% 0.14/0.42 ((~![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) | (eats(wolf_to_animal(elem!44), plant_to_edible(grain_to_plant(elem!45))) | eats(wolf_to_animal(elem!44), animal_to_edible(fox_to_animal(elem!43))) | (~much_smaller(fox_to_animal(elem!43), wolf_to_animal(elem!44))) | (~eats(fox_to_animal(elem!43), plant_to_edible(tptp_fun_Y_1(elem!5)))))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(58,plain,
% 0.14/0.42 ((~![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) | eats(wolf_to_animal(elem!44), animal_to_edible(fox_to_animal(elem!43))) | eats(wolf_to_animal(elem!44), plant_to_edible(grain_to_plant(elem!45))) | (~much_smaller(fox_to_animal(elem!43), wolf_to_animal(elem!44))) | (~eats(fox_to_animal(elem!43), plant_to_edible(tptp_fun_Y_1(elem!5))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.14/0.42 tff(59,plain,
% 0.14/0.42 ($false),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[58, 52, 28, 19, 10, 1])).
% 0.14/0.42 tff(60,plain,(~eats(fox_to_animal(elem!43), plant_to_edible(tptp_fun_Y_1(elem!5)))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.42 tff(61,plain,
% 0.14/0.42 (^[X: bird, Y: fox] : refl(much_smaller(bird_to_animal(X), fox_to_animal(Y)) <=> much_smaller(bird_to_animal(X), fox_to_animal(Y)))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(62,plain,
% 0.14/0.42 (![X: bird, Y: fox] : much_smaller(bird_to_animal(X), fox_to_animal(Y)) <=> ![X: bird, Y: fox] : much_smaller(bird_to_animal(X), fox_to_animal(Y))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[61])).
% 0.14/0.42 tff(63,plain,
% 0.14/0.42 (![X: bird, Y: fox] : much_smaller(bird_to_animal(X), fox_to_animal(Y)) <=> ![X: bird, Y: fox] : much_smaller(bird_to_animal(X), fox_to_animal(Y))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(64,axiom,(![X: bird, Y: fox] : much_smaller(bird_to_animal(X), fox_to_animal(Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_9')).
% 0.14/0.42 tff(65,plain,
% 0.14/0.42 (![X: bird, Y: fox] : much_smaller(bird_to_animal(X), fox_to_animal(Y))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.14/0.42 tff(66,plain,(
% 0.14/0.42 ![X: bird, Y: fox] : much_smaller(bird_to_animal(X), fox_to_animal(Y))),
% 0.14/0.42 inference(skolemize,[status(sab)],[65])).
% 0.14/0.42 tff(67,plain,
% 0.14/0.42 (![X: bird, Y: fox] : much_smaller(bird_to_animal(X), fox_to_animal(Y))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.14/0.42 tff(68,plain,
% 0.14/0.42 ((~![X: bird, Y: fox] : much_smaller(bird_to_animal(X), fox_to_animal(Y))) | much_smaller(bird_to_animal(elem!4), fox_to_animal(elem!43))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(69,plain,
% 0.14/0.42 (much_smaller(bird_to_animal(elem!4), fox_to_animal(elem!43))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.14/0.42 tff(70,assumption,(~eats(bird_to_animal(elem!4), plant_to_edible(grain_to_plant(elem!45)))), introduced(assumption)).
% 0.14/0.42 tff(71,plain,
% 0.14/0.42 (^[X: snail, Y: bird] : refl(much_smaller(snail_to_animal(X), bird_to_animal(Y)) <=> much_smaller(snail_to_animal(X), bird_to_animal(Y)))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(72,plain,
% 0.14/0.42 (![X: snail, Y: bird] : much_smaller(snail_to_animal(X), bird_to_animal(Y)) <=> ![X: snail, Y: bird] : much_smaller(snail_to_animal(X), bird_to_animal(Y))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[71])).
% 0.14/0.42 tff(73,plain,
% 0.14/0.42 (![X: snail, Y: bird] : much_smaller(snail_to_animal(X), bird_to_animal(Y)) <=> ![X: snail, Y: bird] : much_smaller(snail_to_animal(X), bird_to_animal(Y))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(74,axiom,(![X: snail, Y: bird] : much_smaller(snail_to_animal(X), bird_to_animal(Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_8')).
% 0.14/0.42 tff(75,plain,
% 0.14/0.42 (![X: snail, Y: bird] : much_smaller(snail_to_animal(X), bird_to_animal(Y))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.14/0.42 tff(76,plain,(
% 0.14/0.42 ![X: snail, Y: bird] : much_smaller(snail_to_animal(X), bird_to_animal(Y))),
% 0.14/0.42 inference(skolemize,[status(sab)],[75])).
% 0.14/0.42 tff(77,plain,
% 0.14/0.42 (![X: snail, Y: bird] : much_smaller(snail_to_animal(X), bird_to_animal(Y))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.14/0.42 tff(78,plain,
% 0.14/0.42 ((~![X: snail, Y: bird] : much_smaller(snail_to_animal(X), bird_to_animal(Y))) | much_smaller(snail_to_animal(elem!5), bird_to_animal(elem!4))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(79,plain,
% 0.14/0.42 (much_smaller(snail_to_animal(elem!5), bird_to_animal(elem!4))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.14/0.42 tff(80,plain,
% 0.14/0.42 (^[X: bird, Y: snail] : refl((~eats(bird_to_animal(X), animal_to_edible(snail_to_animal(Y)))) <=> (~eats(bird_to_animal(X), animal_to_edible(snail_to_animal(Y)))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(81,plain,
% 0.14/0.42 (![X: bird, Y: snail] : (~eats(bird_to_animal(X), animal_to_edible(snail_to_animal(Y)))) <=> ![X: bird, Y: snail] : (~eats(bird_to_animal(X), animal_to_edible(snail_to_animal(Y))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[80])).
% 0.14/0.42 tff(82,plain,
% 0.14/0.42 (![X: bird, Y: snail] : (~eats(bird_to_animal(X), animal_to_edible(snail_to_animal(Y)))) <=> ![X: bird, Y: snail] : (~eats(bird_to_animal(X), animal_to_edible(snail_to_animal(Y))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(83,axiom,(![X: bird, Y: snail] : (~eats(bird_to_animal(X), animal_to_edible(snail_to_animal(Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_13')).
% 0.14/0.42 tff(84,plain,
% 0.14/0.42 (![X: bird, Y: snail] : (~eats(bird_to_animal(X), animal_to_edible(snail_to_animal(Y))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.14/0.42 tff(85,plain,(
% 0.14/0.42 ![X: bird, Y: snail] : (~eats(bird_to_animal(X), animal_to_edible(snail_to_animal(Y))))),
% 0.14/0.42 inference(skolemize,[status(sab)],[84])).
% 0.14/0.42 tff(86,plain,
% 0.14/0.42 (![X: bird, Y: snail] : (~eats(bird_to_animal(X), animal_to_edible(snail_to_animal(Y))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.14/0.42 tff(87,plain,
% 0.14/0.42 ((~![X: bird, Y: snail] : (~eats(bird_to_animal(X), animal_to_edible(snail_to_animal(Y))))) | (~eats(bird_to_animal(elem!4), animal_to_edible(snail_to_animal(elem!5))))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(88,plain,
% 0.14/0.42 (~eats(bird_to_animal(elem!4), animal_to_edible(snail_to_animal(elem!5)))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.14/0.42 tff(89,plain,
% 0.14/0.42 (^[X: snail] : refl(eats(snail_to_animal(X), plant_to_edible(tptp_fun_Y_1(X))) <=> eats(snail_to_animal(X), plant_to_edible(tptp_fun_Y_1(X))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(90,plain,
% 0.14/0.42 (![X: snail] : eats(snail_to_animal(X), plant_to_edible(tptp_fun_Y_1(X))) <=> ![X: snail] : eats(snail_to_animal(X), plant_to_edible(tptp_fun_Y_1(X)))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[89])).
% 0.14/0.42 tff(91,plain,
% 0.14/0.42 (![X: snail] : ?[Y: plant] : eats(snail_to_animal(X), plant_to_edible(Y)) <=> ![X: snail] : ?[Y: plant] : eats(snail_to_animal(X), plant_to_edible(Y))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(92,axiom,(![X: snail] : ?[Y: plant] : eats(snail_to_animal(X), plant_to_edible(Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_14a')).
% 0.14/0.42 tff(93,plain,
% 0.14/0.42 (![X: snail] : ?[Y: plant] : eats(snail_to_animal(X), plant_to_edible(Y))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.14/0.42 tff(94,plain,(
% 0.14/0.42 ![X: snail] : eats(snail_to_animal(X), plant_to_edible(tptp_fun_Y_1(X)))),
% 0.14/0.42 inference(skolemize,[status(sab)],[93])).
% 0.14/0.42 tff(95,plain,
% 0.14/0.42 (![X: snail] : eats(snail_to_animal(X), plant_to_edible(tptp_fun_Y_1(X)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.14/0.42 tff(96,plain,
% 0.14/0.42 ((~![X: snail] : eats(snail_to_animal(X), plant_to_edible(tptp_fun_Y_1(X)))) | eats(snail_to_animal(elem!5), plant_to_edible(tptp_fun_Y_1(elem!5)))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.43 tff(97,plain,
% 0.14/0.43 (eats(snail_to_animal(elem!5), plant_to_edible(tptp_fun_Y_1(elem!5)))),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.14/0.43 tff(98,plain,
% 0.14/0.43 (((~![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) | (eats(bird_to_animal(elem!4), animal_to_edible(snail_to_animal(elem!5))) | (~much_smaller(snail_to_animal(elem!5), bird_to_animal(elem!4))) | (~eats(snail_to_animal(elem!5), plant_to_edible(tptp_fun_Y_1(elem!5)))) | eats(bird_to_animal(elem!4), plant_to_edible(grain_to_plant(elem!45))))) <=> ((~![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) | eats(bird_to_animal(elem!4), animal_to_edible(snail_to_animal(elem!5))) | (~much_smaller(snail_to_animal(elem!5), bird_to_animal(elem!4))) | (~eats(snail_to_animal(elem!5), plant_to_edible(tptp_fun_Y_1(elem!5)))) | eats(bird_to_animal(elem!4), plant_to_edible(grain_to_plant(elem!45))))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(99,plain,
% 0.14/0.43 ((eats(bird_to_animal(elem!4), plant_to_edible(grain_to_plant(elem!45))) | eats(bird_to_animal(elem!4), animal_to_edible(snail_to_animal(elem!5))) | (~much_smaller(snail_to_animal(elem!5), bird_to_animal(elem!4))) | (~eats(snail_to_animal(elem!5), plant_to_edible(tptp_fun_Y_1(elem!5))))) <=> (eats(bird_to_animal(elem!4), animal_to_edible(snail_to_animal(elem!5))) | (~much_smaller(snail_to_animal(elem!5), bird_to_animal(elem!4))) | (~eats(snail_to_animal(elem!5), plant_to_edible(tptp_fun_Y_1(elem!5)))) | eats(bird_to_animal(elem!4), plant_to_edible(grain_to_plant(elem!45))))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(100,plain,
% 0.14/0.43 (((~![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) | (eats(bird_to_animal(elem!4), plant_to_edible(grain_to_plant(elem!45))) | eats(bird_to_animal(elem!4), animal_to_edible(snail_to_animal(elem!5))) | (~much_smaller(snail_to_animal(elem!5), bird_to_animal(elem!4))) | (~eats(snail_to_animal(elem!5), plant_to_edible(tptp_fun_Y_1(elem!5)))))) <=> ((~![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) | (eats(bird_to_animal(elem!4), animal_to_edible(snail_to_animal(elem!5))) | (~much_smaller(snail_to_animal(elem!5), bird_to_animal(elem!4))) | (~eats(snail_to_animal(elem!5), plant_to_edible(tptp_fun_Y_1(elem!5)))) | eats(bird_to_animal(elem!4), plant_to_edible(grain_to_plant(elem!45)))))),
% 0.14/0.43 inference(monotonicity,[status(thm)],[99])).
% 0.14/0.43 tff(101,plain,
% 0.14/0.43 (((~![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) | (eats(bird_to_animal(elem!4), plant_to_edible(grain_to_plant(elem!45))) | eats(bird_to_animal(elem!4), animal_to_edible(snail_to_animal(elem!5))) | (~much_smaller(snail_to_animal(elem!5), bird_to_animal(elem!4))) | (~eats(snail_to_animal(elem!5), plant_to_edible(tptp_fun_Y_1(elem!5)))))) <=> ((~![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) | eats(bird_to_animal(elem!4), animal_to_edible(snail_to_animal(elem!5))) | (~much_smaller(snail_to_animal(elem!5), bird_to_animal(elem!4))) | (~eats(snail_to_animal(elem!5), plant_to_edible(tptp_fun_Y_1(elem!5)))) | eats(bird_to_animal(elem!4), plant_to_edible(grain_to_plant(elem!45))))),
% 0.14/0.43 inference(transitivity,[status(thm)],[100, 98])).
% 0.14/0.43 tff(102,plain,
% 0.14/0.43 ((~![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) | (eats(bird_to_animal(elem!4), plant_to_edible(grain_to_plant(elem!45))) | eats(bird_to_animal(elem!4), animal_to_edible(snail_to_animal(elem!5))) | (~much_smaller(snail_to_animal(elem!5), bird_to_animal(elem!4))) | (~eats(snail_to_animal(elem!5), plant_to_edible(tptp_fun_Y_1(elem!5)))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(103,plain,
% 0.21/0.43 ((~![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) | eats(bird_to_animal(elem!4), animal_to_edible(snail_to_animal(elem!5))) | (~much_smaller(snail_to_animal(elem!5), bird_to_animal(elem!4))) | (~eats(snail_to_animal(elem!5), plant_to_edible(tptp_fun_Y_1(elem!5)))) | eats(bird_to_animal(elem!4), plant_to_edible(grain_to_plant(elem!45)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.21/0.43 tff(104,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[103, 52, 97, 88, 79, 70])).
% 0.21/0.43 tff(105,plain,(eats(bird_to_animal(elem!4), plant_to_edible(grain_to_plant(elem!45)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(106,plain,
% 0.21/0.43 (((~![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) | ((~eats(bird_to_animal(elem!4), plant_to_edible(grain_to_plant(elem!45)))) | eats(fox_to_animal(elem!43), plant_to_edible(tptp_fun_Y_1(elem!5))) | eats(fox_to_animal(elem!43), animal_to_edible(bird_to_animal(elem!4))) | (~much_smaller(bird_to_animal(elem!4), fox_to_animal(elem!43))))) <=> ((~![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) | (~eats(bird_to_animal(elem!4), plant_to_edible(grain_to_plant(elem!45)))) | eats(fox_to_animal(elem!43), plant_to_edible(tptp_fun_Y_1(elem!5))) | eats(fox_to_animal(elem!43), animal_to_edible(bird_to_animal(elem!4))) | (~much_smaller(bird_to_animal(elem!4), fox_to_animal(elem!43))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(107,plain,
% 0.21/0.43 ((eats(fox_to_animal(elem!43), plant_to_edible(tptp_fun_Y_1(elem!5))) | eats(fox_to_animal(elem!43), animal_to_edible(bird_to_animal(elem!4))) | (~much_smaller(bird_to_animal(elem!4), fox_to_animal(elem!43))) | (~eats(bird_to_animal(elem!4), plant_to_edible(grain_to_plant(elem!45))))) <=> ((~eats(bird_to_animal(elem!4), plant_to_edible(grain_to_plant(elem!45)))) | eats(fox_to_animal(elem!43), plant_to_edible(tptp_fun_Y_1(elem!5))) | eats(fox_to_animal(elem!43), animal_to_edible(bird_to_animal(elem!4))) | (~much_smaller(bird_to_animal(elem!4), fox_to_animal(elem!43))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(108,plain,
% 0.21/0.43 (((~![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) | (eats(fox_to_animal(elem!43), plant_to_edible(tptp_fun_Y_1(elem!5))) | eats(fox_to_animal(elem!43), animal_to_edible(bird_to_animal(elem!4))) | (~much_smaller(bird_to_animal(elem!4), fox_to_animal(elem!43))) | (~eats(bird_to_animal(elem!4), plant_to_edible(grain_to_plant(elem!45)))))) <=> ((~![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) | ((~eats(bird_to_animal(elem!4), plant_to_edible(grain_to_plant(elem!45)))) | eats(fox_to_animal(elem!43), plant_to_edible(tptp_fun_Y_1(elem!5))) | eats(fox_to_animal(elem!43), animal_to_edible(bird_to_animal(elem!4))) | (~much_smaller(bird_to_animal(elem!4), fox_to_animal(elem!43)))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[107])).
% 0.21/0.43 tff(109,plain,
% 0.21/0.43 (((~![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) | (eats(fox_to_animal(elem!43), plant_to_edible(tptp_fun_Y_1(elem!5))) | eats(fox_to_animal(elem!43), animal_to_edible(bird_to_animal(elem!4))) | (~much_smaller(bird_to_animal(elem!4), fox_to_animal(elem!43))) | (~eats(bird_to_animal(elem!4), plant_to_edible(grain_to_plant(elem!45)))))) <=> ((~![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) | (~eats(bird_to_animal(elem!4), plant_to_edible(grain_to_plant(elem!45)))) | eats(fox_to_animal(elem!43), plant_to_edible(tptp_fun_Y_1(elem!5))) | eats(fox_to_animal(elem!43), animal_to_edible(bird_to_animal(elem!4))) | (~much_smaller(bird_to_animal(elem!4), fox_to_animal(elem!43))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[108, 106])).
% 0.21/0.43 tff(110,plain,
% 0.21/0.43 ((~![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) | (eats(fox_to_animal(elem!43), plant_to_edible(tptp_fun_Y_1(elem!5))) | eats(fox_to_animal(elem!43), animal_to_edible(bird_to_animal(elem!4))) | (~much_smaller(bird_to_animal(elem!4), fox_to_animal(elem!43))) | (~eats(bird_to_animal(elem!4), plant_to_edible(grain_to_plant(elem!45)))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(111,plain,
% 0.21/0.43 ((~![X: animal, Y1: animal, Z: plant, Y: plant] : (eats(X, plant_to_edible(Y)) | eats(X, animal_to_edible(Y1)) | (~much_smaller(Y1, X)) | (~eats(Y1, plant_to_edible(Z))))) | (~eats(bird_to_animal(elem!4), plant_to_edible(grain_to_plant(elem!45)))) | eats(fox_to_animal(elem!43), plant_to_edible(tptp_fun_Y_1(elem!5))) | eats(fox_to_animal(elem!43), animal_to_edible(bird_to_animal(elem!4))) | (~much_smaller(bird_to_animal(elem!4), fox_to_animal(elem!43)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.21/0.43 tff(112,plain,
% 0.21/0.43 (eats(fox_to_animal(elem!43), plant_to_edible(tptp_fun_Y_1(elem!5))) | eats(fox_to_animal(elem!43), animal_to_edible(bird_to_animal(elem!4)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[111, 52, 105, 69])).
% 0.21/0.43 tff(113,plain,
% 0.21/0.43 (eats(fox_to_animal(elem!43), animal_to_edible(bird_to_animal(elem!4)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[112, 60])).
% 0.21/0.43 tff(114,plain,
% 0.21/0.43 (^[X: animal, Y: animal, Z: grain] : refl(((~eats(Y, plant_to_edible(grain_to_plant(Z)))) | (~eats(X, animal_to_edible(Y)))) <=> ((~eats(Y, plant_to_edible(grain_to_plant(Z)))) | (~eats(X, animal_to_edible(Y)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(115,plain,
% 0.21/0.43 (![X: animal, Y: animal, Z: grain] : ((~eats(Y, plant_to_edible(grain_to_plant(Z)))) | (~eats(X, animal_to_edible(Y)))) <=> ![X: animal, Y: animal, Z: grain] : ((~eats(Y, plant_to_edible(grain_to_plant(Z)))) | (~eats(X, animal_to_edible(Y))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[114])).
% 0.21/0.43 tff(116,plain,
% 0.21/0.43 (^[X: animal, Y: animal, Z: grain] : trans(monotonicity(rewrite((eats(Y, plant_to_edible(grain_to_plant(Z))) & eats(X, animal_to_edible(Y))) <=> (~((~eats(Y, plant_to_edible(grain_to_plant(Z)))) | (~eats(X, animal_to_edible(Y)))))), ((~(eats(Y, plant_to_edible(grain_to_plant(Z))) & eats(X, animal_to_edible(Y)))) <=> (~(~((~eats(Y, plant_to_edible(grain_to_plant(Z)))) | (~eats(X, animal_to_edible(Y)))))))), rewrite((~(~((~eats(Y, plant_to_edible(grain_to_plant(Z)))) | (~eats(X, animal_to_edible(Y)))))) <=> ((~eats(Y, plant_to_edible(grain_to_plant(Z)))) | (~eats(X, animal_to_edible(Y))))), ((~(eats(Y, plant_to_edible(grain_to_plant(Z))) & eats(X, animal_to_edible(Y)))) <=> ((~eats(Y, plant_to_edible(grain_to_plant(Z)))) | (~eats(X, animal_to_edible(Y))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(117,plain,
% 0.21/0.43 (![X: animal, Y: animal, Z: grain] : (~(eats(Y, plant_to_edible(grain_to_plant(Z))) & eats(X, animal_to_edible(Y)))) <=> ![X: animal, Y: animal, Z: grain] : ((~eats(Y, plant_to_edible(grain_to_plant(Z)))) | (~eats(X, animal_to_edible(Y))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[116])).
% 0.21/0.43 tff(118,plain,
% 0.21/0.43 ((~?[X: animal, Y: animal, Z: grain] : (eats(Y, plant_to_edible(grain_to_plant(Z))) & eats(X, animal_to_edible(Y)))) <=> (~?[X: animal, Y: animal, Z: grain] : (eats(Y, plant_to_edible(grain_to_plant(Z))) & eats(X, animal_to_edible(Y))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(119,axiom,(~?[X: animal, Y: animal, Z: grain] : (eats(Y, plant_to_edible(grain_to_plant(Z))) & eats(X, animal_to_edible(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47')).
% 0.21/0.43 tff(120,plain,
% 0.21/0.43 (~?[X: animal, Y: animal, Z: grain] : (eats(Y, plant_to_edible(grain_to_plant(Z))) & eats(X, animal_to_edible(Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.21/0.43 tff(121,plain,
% 0.21/0.43 (~?[X: animal, Y: animal, Z: grain] : (eats(Y, plant_to_edible(grain_to_plant(Z))) & eats(X, animal_to_edible(Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[120, 118])).
% 0.21/0.43 tff(122,plain,
% 0.21/0.43 (~?[X: animal, Y: animal, Z: grain] : (eats(Y, plant_to_edible(grain_to_plant(Z))) & eats(X, animal_to_edible(Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[121, 118])).
% 0.21/0.43 tff(123,plain,
% 0.21/0.43 (~?[X: animal, Y: animal, Z: grain] : (eats(Y, plant_to_edible(grain_to_plant(Z))) & eats(X, animal_to_edible(Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.21/0.43 tff(124,plain,
% 0.21/0.43 (^[X: animal, Y: animal, Z: grain] : refl($oeq((~(eats(Y, plant_to_edible(grain_to_plant(Z))) & eats(X, animal_to_edible(Y)))), (~(eats(Y, plant_to_edible(grain_to_plant(Z))) & eats(X, animal_to_edible(Y))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(125,plain,(
% 0.21/0.43 ![X: animal, Y: animal, Z: grain] : (~(eats(Y, plant_to_edible(grain_to_plant(Z))) & eats(X, animal_to_edible(Y))))),
% 0.21/0.43 inference(nnf-neg,[status(sab)],[123, 124])).
% 0.21/0.43 tff(126,plain,
% 0.21/0.43 (![X: animal, Y: animal, Z: grain] : ((~eats(Y, plant_to_edible(grain_to_plant(Z)))) | (~eats(X, animal_to_edible(Y))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[125, 117])).
% 0.21/0.43 tff(127,plain,
% 0.21/0.43 (![X: animal, Y: animal, Z: grain] : ((~eats(Y, plant_to_edible(grain_to_plant(Z)))) | (~eats(X, animal_to_edible(Y))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[126, 115])).
% 0.21/0.43 tff(128,plain,
% 0.21/0.43 (((~![X: animal, Y: animal, Z: grain] : ((~eats(Y, plant_to_edible(grain_to_plant(Z)))) | (~eats(X, animal_to_edible(Y))))) | ((~eats(bird_to_animal(elem!4), plant_to_edible(grain_to_plant(elem!45)))) | (~eats(fox_to_animal(elem!43), animal_to_edible(bird_to_animal(elem!4)))))) <=> ((~![X: animal, Y: animal, Z: grain] : ((~eats(Y, plant_to_edible(grain_to_plant(Z)))) | (~eats(X, animal_to_edible(Y))))) | (~eats(bird_to_animal(elem!4), plant_to_edible(grain_to_plant(elem!45)))) | (~eats(fox_to_animal(elem!43), animal_to_edible(bird_to_animal(elem!4)))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(129,plain,
% 0.21/0.43 ((~![X: animal, Y: animal, Z: grain] : ((~eats(Y, plant_to_edible(grain_to_plant(Z)))) | (~eats(X, animal_to_edible(Y))))) | ((~eats(bird_to_animal(elem!4), plant_to_edible(grain_to_plant(elem!45)))) | (~eats(fox_to_animal(elem!43), animal_to_edible(bird_to_animal(elem!4)))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(130,plain,
% 0.21/0.43 ((~![X: animal, Y: animal, Z: grain] : ((~eats(Y, plant_to_edible(grain_to_plant(Z)))) | (~eats(X, animal_to_edible(Y))))) | (~eats(bird_to_animal(elem!4), plant_to_edible(grain_to_plant(elem!45)))) | (~eats(fox_to_animal(elem!43), animal_to_edible(bird_to_animal(elem!4))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.21/0.43 tff(131,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[130, 127, 105, 113])).
% 0.21/0.43 % SZS output end Proof
% 0.21/0.44 % E exiting
%------------------------------------------------------------------------------