%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ031-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:23:13 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.49s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : PUZ031-1 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 02:40:54 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.49 % SZS status Unsatisfiable
% 0.20/0.49 % SZS output start Proof
% 0.20/0.49 tff(eats_type, type, (
% 0.20/0.49 eats: ( $i * $i ) > $o)).
% 0.20/0.49 tff(a_grain_type, type, (
% 0.20/0.49 a_grain: $i)).
% 0.20/0.49 tff(a_wolf_type, type, (
% 0.20/0.49 a_wolf: $i)).
% 0.20/0.49 tff(caterpillar_food_of_type, type, (
% 0.20/0.49 caterpillar_food_of: $i > $i)).
% 0.20/0.49 tff(a_caterpillar_type, type, (
% 0.20/0.49 a_caterpillar: $i)).
% 0.20/0.49 tff(a_fox_type, type, (
% 0.20/0.49 a_fox: $i)).
% 0.20/0.49 tff(a_bird_type, type, (
% 0.20/0.49 a_bird: $i)).
% 0.20/0.49 tff(a_snail_type, type, (
% 0.20/0.49 a_snail: $i)).
% 0.20/0.49 tff(snail_type, type, (
% 0.20/0.49 snail: $i > $o)).
% 0.20/0.49 tff(bird_type, type, (
% 0.20/0.49 bird: $i > $o)).
% 0.20/0.49 tff(much_smaller_type, type, (
% 0.20/0.49 much_smaller: ( $i * $i ) > $o)).
% 0.20/0.49 tff(plant_type, type, (
% 0.20/0.49 plant: $i > $o)).
% 0.20/0.49 tff(grain_type, type, (
% 0.20/0.49 grain: $i > $o)).
% 0.20/0.49 tff(snail_food_of_type, type, (
% 0.20/0.49 snail_food_of: $i > $i)).
% 0.20/0.49 tff(animal_type, type, (
% 0.20/0.49 animal: $i > $o)).
% 0.20/0.49 tff(fox_type, type, (
% 0.20/0.49 fox: $i > $o)).
% 0.20/0.49 tff(caterpillar_type, type, (
% 0.20/0.49 caterpillar: $i > $o)).
% 0.20/0.49 tff(wolf_type, type, (
% 0.20/0.49 wolf: $i > $o)).
% 0.20/0.49 tff(1,plain,
% 0.20/0.49 (^[Snail: $i, Bird: $i] : refl(((~bird(Bird)) | (~snail(Snail)) | (~eats(Bird, Snail))) <=> ((~bird(Bird)) | (~snail(Snail)) | (~eats(Bird, Snail))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(2,plain,
% 0.20/0.49 (![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | (~eats(Bird, Snail))) <=> ![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | (~eats(Bird, Snail)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.49 tff(3,plain,
% 0.20/0.49 (![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | (~eats(Bird, Snail))) <=> ![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | (~eats(Bird, Snail)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(4,plain,
% 0.20/0.49 (^[Snail: $i, Bird: $i] : rewrite((((~bird(Bird)) | (~snail(Snail))) | (~eats(Bird, Snail))) <=> ((~bird(Bird)) | (~snail(Snail)) | (~eats(Bird, Snail))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(5,plain,
% 0.20/0.49 (![Snail: $i, Bird: $i] : (((~bird(Bird)) | (~snail(Snail))) | (~eats(Bird, Snail))) <=> ![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | (~eats(Bird, Snail)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.49 tff(6,axiom,(![Snail: $i, Bird: $i] : (((~bird(Bird)) | (~snail(Snail))) | (~eats(Bird, Snail)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bird_dont_eat_snail')).
% 0.20/0.49 tff(7,plain,
% 0.20/0.49 (![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | (~eats(Bird, Snail)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.49 tff(8,plain,
% 0.20/0.49 (![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | (~eats(Bird, Snail)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.49 tff(9,plain,(
% 0.20/0.49 ![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | (~eats(Bird, Snail)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[8])).
% 0.20/0.49 tff(10,plain,
% 0.20/0.49 (![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | (~eats(Bird, Snail)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.49 tff(11,plain,
% 0.20/0.49 (snail(a_snail) <=> snail(a_snail)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(12,axiom,(snail(a_snail)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','there_is_a_snail')).
% 0.20/0.49 tff(13,plain,
% 0.20/0.49 (snail(a_snail)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.20/0.49 tff(14,plain,
% 0.20/0.49 (bird(a_bird) <=> bird(a_bird)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(15,axiom,(bird(a_bird)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','there_is_a_bird')).
% 0.20/0.49 tff(16,plain,
% 0.20/0.49 (bird(a_bird)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.49 tff(17,plain,
% 0.20/0.49 (((~![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | (~eats(Bird, Snail)))) | ((~bird(a_bird)) | (~snail(a_snail)) | (~eats(a_bird, a_snail)))) <=> ((~![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | (~eats(Bird, Snail)))) | (~bird(a_bird)) | (~snail(a_snail)) | (~eats(a_bird, a_snail)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(18,plain,
% 0.20/0.49 ((~![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | (~eats(Bird, Snail)))) | ((~bird(a_bird)) | (~snail(a_snail)) | (~eats(a_bird, a_snail)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(19,plain,
% 0.20/0.49 ((~![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | (~eats(Bird, Snail)))) | (~bird(a_bird)) | (~snail(a_snail)) | (~eats(a_bird, a_snail))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.49 tff(20,plain,
% 0.20/0.49 (~eats(a_bird, a_snail)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[19, 16, 13, 10])).
% 0.20/0.49 tff(21,plain,
% 0.20/0.49 (^[Snail: $i, Bird: $i] : refl(((~bird(Bird)) | (~snail(Snail)) | much_smaller(Snail, Bird)) <=> ((~bird(Bird)) | (~snail(Snail)) | much_smaller(Snail, Bird)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(22,plain,
% 0.20/0.49 (![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | much_smaller(Snail, Bird)) <=> ![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | much_smaller(Snail, Bird))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.49 tff(23,plain,
% 0.20/0.49 (![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | much_smaller(Snail, Bird)) <=> ![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | much_smaller(Snail, Bird))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(24,plain,
% 0.20/0.49 (^[Snail: $i, Bird: $i] : trans(monotonicity(rewrite((much_smaller(Snail, Bird) | (~snail(Snail))) <=> ((~snail(Snail)) | much_smaller(Snail, Bird))), (((much_smaller(Snail, Bird) | (~snail(Snail))) | (~bird(Bird))) <=> (((~snail(Snail)) | much_smaller(Snail, Bird)) | (~bird(Bird))))), rewrite((((~snail(Snail)) | much_smaller(Snail, Bird)) | (~bird(Bird))) <=> ((~bird(Bird)) | (~snail(Snail)) | much_smaller(Snail, Bird))), (((much_smaller(Snail, Bird) | (~snail(Snail))) | (~bird(Bird))) <=> ((~bird(Bird)) | (~snail(Snail)) | much_smaller(Snail, Bird))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(25,plain,
% 0.20/0.49 (![Snail: $i, Bird: $i] : ((much_smaller(Snail, Bird) | (~snail(Snail))) | (~bird(Bird))) <=> ![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | much_smaller(Snail, Bird))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.49 tff(26,axiom,(![Snail: $i, Bird: $i] : ((much_smaller(Snail, Bird) | (~snail(Snail))) | (~bird(Bird)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','snail_smaller_than_bird')).
% 0.20/0.49 tff(27,plain,
% 0.20/0.49 (![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | much_smaller(Snail, Bird))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.49 tff(28,plain,
% 0.20/0.49 (![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | much_smaller(Snail, Bird))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.20/0.49 tff(29,plain,(
% 0.20/0.49 ![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | much_smaller(Snail, Bird))),
% 0.20/0.49 inference(skolemize,[status(sab)],[28])).
% 0.20/0.49 tff(30,plain,
% 0.20/0.49 (![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | much_smaller(Snail, Bird))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.20/0.49 tff(31,plain,
% 0.20/0.49 (((~![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | much_smaller(Snail, Bird))) | ((~bird(a_bird)) | (~snail(a_snail)) | much_smaller(a_snail, a_bird))) <=> ((~![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | much_smaller(Snail, Bird))) | (~bird(a_bird)) | (~snail(a_snail)) | much_smaller(a_snail, a_bird))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(32,plain,
% 0.20/0.49 ((~![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | much_smaller(Snail, Bird))) | ((~bird(a_bird)) | (~snail(a_snail)) | much_smaller(a_snail, a_bird))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(33,plain,
% 0.20/0.49 ((~![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | much_smaller(Snail, Bird))) | (~bird(a_bird)) | (~snail(a_snail)) | much_smaller(a_snail, a_bird)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.49 tff(34,plain,
% 0.20/0.49 (much_smaller(a_snail, a_bird)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[33, 16, 13, 30])).
% 0.20/0.49 tff(35,plain,
% 0.20/0.49 (^[X: $i] : refl((plant(X) | (~grain(X))) <=> (plant(X) | (~grain(X))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(36,plain,
% 0.20/0.49 (![X: $i] : (plant(X) | (~grain(X))) <=> ![X: $i] : (plant(X) | (~grain(X)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.49 tff(37,plain,
% 0.20/0.49 (![X: $i] : (plant(X) | (~grain(X))) <=> ![X: $i] : (plant(X) | (~grain(X)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(38,axiom,(![X: $i] : (plant(X) | (~grain(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','grain_is_a_plant')).
% 0.20/0.49 tff(39,plain,
% 0.20/0.49 (![X: $i] : (plant(X) | (~grain(X)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.20/0.49 tff(40,plain,(
% 0.20/0.49 ![X: $i] : (plant(X) | (~grain(X)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[39])).
% 0.20/0.49 tff(41,plain,
% 0.20/0.49 (![X: $i] : (plant(X) | (~grain(X)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.20/0.49 tff(42,plain,
% 0.20/0.49 (grain(a_grain) <=> grain(a_grain)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(43,axiom,(grain(a_grain)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','there_is_a_grain')).
% 0.20/0.49 tff(44,plain,
% 0.20/0.49 (grain(a_grain)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.49 tff(45,plain,
% 0.20/0.49 (((~![X: $i] : (plant(X) | (~grain(X)))) | (plant(a_grain) | (~grain(a_grain)))) <=> ((~![X: $i] : (plant(X) | (~grain(X)))) | plant(a_grain) | (~grain(a_grain)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(46,plain,
% 0.20/0.49 ((~![X: $i] : (plant(X) | (~grain(X)))) | (plant(a_grain) | (~grain(a_grain)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(47,plain,
% 0.20/0.49 ((~![X: $i] : (plant(X) | (~grain(X)))) | plant(a_grain) | (~grain(a_grain))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.49 tff(48,plain,
% 0.20/0.49 (plant(a_grain)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[47, 44, 41])).
% 0.20/0.49 tff(49,plain,
% 0.20/0.49 (^[Snail: $i] : refl(((~snail(Snail)) | plant(snail_food_of(Snail))) <=> ((~snail(Snail)) | plant(snail_food_of(Snail))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(50,plain,
% 0.20/0.49 (![Snail: $i] : ((~snail(Snail)) | plant(snail_food_of(Snail))) <=> ![Snail: $i] : ((~snail(Snail)) | plant(snail_food_of(Snail)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.49 tff(51,plain,
% 0.20/0.49 (![Snail: $i] : ((~snail(Snail)) | plant(snail_food_of(Snail))) <=> ![Snail: $i] : ((~snail(Snail)) | plant(snail_food_of(Snail)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(52,plain,
% 0.20/0.49 (^[Snail: $i] : rewrite((plant(snail_food_of(Snail)) | (~snail(Snail))) <=> ((~snail(Snail)) | plant(snail_food_of(Snail))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(53,plain,
% 0.20/0.49 (![Snail: $i] : (plant(snail_food_of(Snail)) | (~snail(Snail))) <=> ![Snail: $i] : ((~snail(Snail)) | plant(snail_food_of(Snail)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.49 tff(54,axiom,(![Snail: $i] : (plant(snail_food_of(Snail)) | (~snail(Snail)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','snail_food_is_a_plant')).
% 0.20/0.49 tff(55,plain,
% 0.20/0.49 (![Snail: $i] : ((~snail(Snail)) | plant(snail_food_of(Snail)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.49 tff(56,plain,
% 0.20/0.49 (![Snail: $i] : ((~snail(Snail)) | plant(snail_food_of(Snail)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.20/0.49 tff(57,plain,(
% 0.20/0.49 ![Snail: $i] : ((~snail(Snail)) | plant(snail_food_of(Snail)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[56])).
% 0.20/0.49 tff(58,plain,
% 0.20/0.49 (![Snail: $i] : ((~snail(Snail)) | plant(snail_food_of(Snail)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.20/0.49 tff(59,plain,
% 0.20/0.49 (((~![Snail: $i] : ((~snail(Snail)) | plant(snail_food_of(Snail)))) | ((~snail(a_snail)) | plant(snail_food_of(a_snail)))) <=> ((~![Snail: $i] : ((~snail(Snail)) | plant(snail_food_of(Snail)))) | (~snail(a_snail)) | plant(snail_food_of(a_snail)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(60,plain,
% 0.20/0.49 ((~![Snail: $i] : ((~snail(Snail)) | plant(snail_food_of(Snail)))) | ((~snail(a_snail)) | plant(snail_food_of(a_snail)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(61,plain,
% 0.20/0.49 ((~![Snail: $i] : ((~snail(Snail)) | plant(snail_food_of(Snail)))) | (~snail(a_snail)) | plant(snail_food_of(a_snail))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.49 tff(62,plain,
% 0.20/0.49 (plant(snail_food_of(a_snail))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[61, 13, 58])).
% 0.20/0.49 tff(63,plain,
% 0.20/0.49 (^[X: $i] : refl((animal(X) | (~snail(X))) <=> (animal(X) | (~snail(X))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(64,plain,
% 0.20/0.49 (![X: $i] : (animal(X) | (~snail(X))) <=> ![X: $i] : (animal(X) | (~snail(X)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[63])).
% 0.20/0.49 tff(65,plain,
% 0.20/0.49 (![X: $i] : (animal(X) | (~snail(X))) <=> ![X: $i] : (animal(X) | (~snail(X)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(66,axiom,(![X: $i] : (animal(X) | (~snail(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','snail_is_an_animal')).
% 0.20/0.49 tff(67,plain,
% 0.20/0.49 (![X: $i] : (animal(X) | (~snail(X)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.20/0.49 tff(68,plain,(
% 0.20/0.49 ![X: $i] : (animal(X) | (~snail(X)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[67])).
% 0.20/0.49 tff(69,plain,
% 0.20/0.49 (![X: $i] : (animal(X) | (~snail(X)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.20/0.49 tff(70,plain,
% 0.20/0.49 (((~![X: $i] : (animal(X) | (~snail(X)))) | (animal(a_snail) | (~snail(a_snail)))) <=> ((~![X: $i] : (animal(X) | (~snail(X)))) | animal(a_snail) | (~snail(a_snail)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(71,plain,
% 0.20/0.49 ((~![X: $i] : (animal(X) | (~snail(X)))) | (animal(a_snail) | (~snail(a_snail)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(72,plain,
% 0.20/0.49 ((~![X: $i] : (animal(X) | (~snail(X)))) | animal(a_snail) | (~snail(a_snail))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.49 tff(73,plain,
% 0.20/0.49 (animal(a_snail)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[72, 69, 13])).
% 0.20/0.49 tff(74,plain,
% 0.20/0.49 (^[Snail: $i] : refl(((~snail(Snail)) | eats(Snail, snail_food_of(Snail))) <=> ((~snail(Snail)) | eats(Snail, snail_food_of(Snail))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(75,plain,
% 0.20/0.49 (![Snail: $i] : ((~snail(Snail)) | eats(Snail, snail_food_of(Snail))) <=> ![Snail: $i] : ((~snail(Snail)) | eats(Snail, snail_food_of(Snail)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[74])).
% 0.20/0.49 tff(76,plain,
% 0.20/0.49 (![Snail: $i] : ((~snail(Snail)) | eats(Snail, snail_food_of(Snail))) <=> ![Snail: $i] : ((~snail(Snail)) | eats(Snail, snail_food_of(Snail)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(77,plain,
% 0.20/0.49 (^[Snail: $i] : rewrite((eats(Snail, snail_food_of(Snail)) | (~snail(Snail))) <=> ((~snail(Snail)) | eats(Snail, snail_food_of(Snail))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(78,plain,
% 0.20/0.49 (![Snail: $i] : (eats(Snail, snail_food_of(Snail)) | (~snail(Snail))) <=> ![Snail: $i] : ((~snail(Snail)) | eats(Snail, snail_food_of(Snail)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.49 tff(79,axiom,(![Snail: $i] : (eats(Snail, snail_food_of(Snail)) | (~snail(Snail)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','snail_eats_snail_food')).
% 0.20/0.49 tff(80,plain,
% 0.20/0.49 (![Snail: $i] : ((~snail(Snail)) | eats(Snail, snail_food_of(Snail)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.49 tff(81,plain,
% 0.20/0.49 (![Snail: $i] : ((~snail(Snail)) | eats(Snail, snail_food_of(Snail)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.20/0.49 tff(82,plain,(
% 0.20/0.49 ![Snail: $i] : ((~snail(Snail)) | eats(Snail, snail_food_of(Snail)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[81])).
% 0.20/0.49 tff(83,plain,
% 0.20/0.49 (![Snail: $i] : ((~snail(Snail)) | eats(Snail, snail_food_of(Snail)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.20/0.49 tff(84,plain,
% 0.20/0.49 (((~![Snail: $i] : ((~snail(Snail)) | eats(Snail, snail_food_of(Snail)))) | ((~snail(a_snail)) | eats(a_snail, snail_food_of(a_snail)))) <=> ((~![Snail: $i] : ((~snail(Snail)) | eats(Snail, snail_food_of(Snail)))) | (~snail(a_snail)) | eats(a_snail, snail_food_of(a_snail)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(85,plain,
% 0.20/0.49 ((~![Snail: $i] : ((~snail(Snail)) | eats(Snail, snail_food_of(Snail)))) | ((~snail(a_snail)) | eats(a_snail, snail_food_of(a_snail)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(86,plain,
% 0.20/0.49 ((~![Snail: $i] : ((~snail(Snail)) | eats(Snail, snail_food_of(Snail)))) | (~snail(a_snail)) | eats(a_snail, snail_food_of(a_snail))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.49 tff(87,plain,
% 0.20/0.49 (eats(a_snail, snail_food_of(a_snail))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[86, 13, 83])).
% 0.20/0.49 tff(88,plain,
% 0.20/0.49 (^[X: $i] : refl((animal(X) | (~bird(X))) <=> (animal(X) | (~bird(X))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(89,plain,
% 0.20/0.49 (![X: $i] : (animal(X) | (~bird(X))) <=> ![X: $i] : (animal(X) | (~bird(X)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[88])).
% 0.20/0.49 tff(90,plain,
% 0.20/0.49 (![X: $i] : (animal(X) | (~bird(X))) <=> ![X: $i] : (animal(X) | (~bird(X)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(91,axiom,(![X: $i] : (animal(X) | (~bird(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bird_is_an_animal')).
% 0.20/0.49 tff(92,plain,
% 0.20/0.49 (![X: $i] : (animal(X) | (~bird(X)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.20/0.49 tff(93,plain,(
% 0.20/0.49 ![X: $i] : (animal(X) | (~bird(X)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[92])).
% 0.20/0.49 tff(94,plain,
% 0.20/0.49 (![X: $i] : (animal(X) | (~bird(X)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.20/0.49 tff(95,plain,
% 0.20/0.49 (((~![X: $i] : (animal(X) | (~bird(X)))) | (animal(a_bird) | (~bird(a_bird)))) <=> ((~![X: $i] : (animal(X) | (~bird(X)))) | animal(a_bird) | (~bird(a_bird)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(96,plain,
% 0.20/0.49 ((~![X: $i] : (animal(X) | (~bird(X)))) | (animal(a_bird) | (~bird(a_bird)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(97,plain,
% 0.20/0.49 ((~![X: $i] : (animal(X) | (~bird(X)))) | animal(a_bird) | (~bird(a_bird))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.49 tff(98,plain,
% 0.20/0.49 (animal(a_bird)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[97, 94, 16])).
% 0.20/0.49 tff(99,plain,
% 0.20/0.49 (^[Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : refl(((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant)) <=> ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(100,plain,
% 0.20/0.49 (![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant)) <=> ![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[99])).
% 0.20/0.49 tff(101,plain,
% 0.20/0.49 (![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant)) <=> ![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(102,plain,
% 0.20/0.49 (^[Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((eats(Animal, Plant) | eats(Animal, Small_animal)) | (~animal(Animal))) <=> ((~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))), ((((eats(Animal, Plant) | eats(Animal, Small_animal)) | (~animal(Animal))) | (~plant(Plant))) <=> (((~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant)) | (~plant(Plant))))), rewrite((((~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant)) | (~plant(Plant))) <=> ((~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))), ((((eats(Animal, Plant) | eats(Animal, Small_animal)) | (~animal(Animal))) | (~plant(Plant))) <=> ((~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant)))), (((((eats(Animal, Plant) | eats(Animal, Small_animal)) | (~animal(Animal))) | (~plant(Plant))) | (~animal(Small_animal))) <=> (((~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant)) | (~animal(Small_animal))))), rewrite((((~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant)) | (~animal(Small_animal))) <=> ((~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))), (((((eats(Animal, Plant) | eats(Animal, Small_animal)) | (~animal(Animal))) | (~plant(Plant))) | (~animal(Small_animal))) <=> ((~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant)))), ((((((eats(Animal, Plant) | eats(Animal, Small_animal)) | (~animal(Animal))) | (~plant(Plant))) | (~animal(Small_animal))) | (~plant(Other_plant))) <=> (((~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant)) | (~plant(Other_plant))))), rewrite((((~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant)) | (~plant(Other_plant))) <=> ((~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))), ((((((eats(Animal, Plant) | eats(Animal, Small_animal)) | (~animal(Animal))) | (~plant(Plant))) | (~animal(Small_animal))) | (~plant(Other_plant))) <=> ((~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant)))), (((((((eats(Animal, Plant) | eats(Animal, Small_animal)) | (~animal(Animal))) | (~plant(Plant))) | (~animal(Small_animal))) | (~plant(Other_plant))) | (~much_smaller(Small_animal, Animal))) <=> (((~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant)) | (~much_smaller(Small_animal, Animal))))), rewrite((((~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant)) | (~much_smaller(Small_animal, Animal))) <=> ((~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))), (((((((eats(Animal, Plant) | eats(Animal, Small_animal)) | (~animal(Animal))) | (~plant(Plant))) | (~animal(Small_animal))) | (~plant(Other_plant))) | (~much_smaller(Small_animal, Animal))) <=> ((~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant)))), ((((((((eats(Animal, Plant) | eats(Animal, Small_animal)) | (~animal(Animal))) | (~plant(Plant))) | (~animal(Small_animal))) | (~plant(Other_plant))) | (~much_smaller(Small_animal, Animal))) | (~eats(Small_animal, Other_plant))) <=> (((~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant)) | (~eats(Small_animal, Other_plant))))), rewrite((((~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant)) | (~eats(Small_animal, Other_plant))) <=> ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))), ((((((((eats(Animal, Plant) | eats(Animal, Small_animal)) | (~animal(Animal))) | (~plant(Plant))) | (~animal(Small_animal))) | (~plant(Other_plant))) | (~much_smaller(Small_animal, Animal))) | (~eats(Small_animal, Other_plant))) <=> ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(103,plain,
% 0.20/0.49 (![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : (((((((eats(Animal, Plant) | eats(Animal, Small_animal)) | (~animal(Animal))) | (~plant(Plant))) | (~animal(Small_animal))) | (~plant(Other_plant))) | (~much_smaller(Small_animal, Animal))) | (~eats(Small_animal, Other_plant))) <=> ![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[102])).
% 0.20/0.49 tff(104,axiom,(![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : (((((((eats(Animal, Plant) | eats(Animal, Small_animal)) | (~animal(Animal))) | (~plant(Plant))) | (~animal(Small_animal))) | (~plant(Other_plant))) | (~much_smaller(Small_animal, Animal))) | (~eats(Small_animal, Other_plant)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','eating_habits')).
% 0.20/0.49 tff(105,plain,
% 0.20/0.49 (![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.20/0.49 tff(106,plain,
% 0.20/0.49 (![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.20/0.49 tff(107,plain,(
% 0.20/0.49 ![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))),
% 0.20/0.49 inference(skolemize,[status(sab)],[106])).
% 0.20/0.49 tff(108,plain,
% 0.20/0.49 (![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[107, 100])).
% 0.20/0.49 tff(109,plain,
% 0.20/0.49 (((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | ((~eats(a_snail, snail_food_of(a_snail))) | eats(a_bird, a_snail) | (~animal(a_snail)) | (~plant(snail_food_of(a_snail))) | (~much_smaller(a_snail, a_bird)) | (~animal(a_bird)) | (~plant(a_grain)) | eats(a_bird, a_grain))) <=> ((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | (~eats(a_snail, snail_food_of(a_snail))) | eats(a_bird, a_snail) | (~animal(a_snail)) | (~plant(snail_food_of(a_snail))) | (~much_smaller(a_snail, a_bird)) | (~animal(a_bird)) | (~plant(a_grain)) | eats(a_bird, a_grain))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(110,plain,
% 0.20/0.49 (((~eats(a_snail, snail_food_of(a_snail))) | (~much_smaller(a_snail, a_bird)) | (~plant(snail_food_of(a_snail))) | (~animal(a_snail)) | (~plant(a_grain)) | (~animal(a_bird)) | eats(a_bird, a_snail) | eats(a_bird, a_grain)) <=> ((~eats(a_snail, snail_food_of(a_snail))) | eats(a_bird, a_snail) | (~animal(a_snail)) | (~plant(snail_food_of(a_snail))) | (~much_smaller(a_snail, a_bird)) | (~animal(a_bird)) | (~plant(a_grain)) | eats(a_bird, a_grain))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(111,plain,
% 0.20/0.49 (((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | ((~eats(a_snail, snail_food_of(a_snail))) | (~much_smaller(a_snail, a_bird)) | (~plant(snail_food_of(a_snail))) | (~animal(a_snail)) | (~plant(a_grain)) | (~animal(a_bird)) | eats(a_bird, a_snail) | eats(a_bird, a_grain))) <=> ((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | ((~eats(a_snail, snail_food_of(a_snail))) | eats(a_bird, a_snail) | (~animal(a_snail)) | (~plant(snail_food_of(a_snail))) | (~much_smaller(a_snail, a_bird)) | (~animal(a_bird)) | (~plant(a_grain)) | eats(a_bird, a_grain)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[110])).
% 0.20/0.49 tff(112,plain,
% 0.20/0.49 (((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | ((~eats(a_snail, snail_food_of(a_snail))) | (~much_smaller(a_snail, a_bird)) | (~plant(snail_food_of(a_snail))) | (~animal(a_snail)) | (~plant(a_grain)) | (~animal(a_bird)) | eats(a_bird, a_snail) | eats(a_bird, a_grain))) <=> ((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | (~eats(a_snail, snail_food_of(a_snail))) | eats(a_bird, a_snail) | (~animal(a_snail)) | (~plant(snail_food_of(a_snail))) | (~much_smaller(a_snail, a_bird)) | (~animal(a_bird)) | (~plant(a_grain)) | eats(a_bird, a_grain))),
% 0.20/0.49 inference(transitivity,[status(thm)],[111, 109])).
% 0.20/0.49 tff(113,plain,
% 0.20/0.49 ((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | ((~eats(a_snail, snail_food_of(a_snail))) | (~much_smaller(a_snail, a_bird)) | (~plant(snail_food_of(a_snail))) | (~animal(a_snail)) | (~plant(a_grain)) | (~animal(a_bird)) | eats(a_bird, a_snail) | eats(a_bird, a_grain))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(114,plain,
% 0.20/0.49 ((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | (~eats(a_snail, snail_food_of(a_snail))) | eats(a_bird, a_snail) | (~animal(a_snail)) | (~plant(snail_food_of(a_snail))) | (~much_smaller(a_snail, a_bird)) | (~animal(a_bird)) | (~plant(a_grain)) | eats(a_bird, a_grain)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.20/0.49 tff(115,plain,
% 0.20/0.49 (eats(a_bird, a_snail) | eats(a_bird, a_grain)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[114, 108, 98, 87, 73, 62, 48, 34])).
% 0.20/0.49 tff(116,plain,
% 0.20/0.49 (eats(a_bird, a_grain)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[115, 20])).
% 0.20/0.49 tff(117,assumption,(eats(a_fox, a_bird)), introduced(assumption)).
% 0.20/0.49 tff(118,plain,
% 0.20/0.49 (fox(a_fox) <=> fox(a_fox)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(119,axiom,(fox(a_fox)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','there_is_a_fox')).
% 0.20/0.49 tff(120,plain,
% 0.20/0.49 (fox(a_fox)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.20/0.49 tff(121,plain,
% 0.20/0.49 (^[X: $i] : refl((animal(X) | (~fox(X))) <=> (animal(X) | (~fox(X))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(122,plain,
% 0.20/0.49 (![X: $i] : (animal(X) | (~fox(X))) <=> ![X: $i] : (animal(X) | (~fox(X)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[121])).
% 0.20/0.49 tff(123,plain,
% 0.20/0.49 (![X: $i] : (animal(X) | (~fox(X))) <=> ![X: $i] : (animal(X) | (~fox(X)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(124,axiom,(![X: $i] : (animal(X) | (~fox(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fox_is_an_animal')).
% 0.20/0.49 tff(125,plain,
% 0.20/0.49 (![X: $i] : (animal(X) | (~fox(X)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.20/0.49 tff(126,plain,(
% 0.20/0.49 ![X: $i] : (animal(X) | (~fox(X)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[125])).
% 0.20/0.49 tff(127,plain,
% 0.20/0.49 (![X: $i] : (animal(X) | (~fox(X)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.20/0.49 tff(128,plain,
% 0.20/0.49 (((~![X: $i] : (animal(X) | (~fox(X)))) | (animal(a_fox) | (~fox(a_fox)))) <=> ((~![X: $i] : (animal(X) | (~fox(X)))) | animal(a_fox) | (~fox(a_fox)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(129,plain,
% 0.20/0.49 ((~![X: $i] : (animal(X) | (~fox(X)))) | (animal(a_fox) | (~fox(a_fox)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(130,plain,
% 0.20/0.49 ((~![X: $i] : (animal(X) | (~fox(X)))) | animal(a_fox) | (~fox(a_fox))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.20/0.49 tff(131,plain,
% 0.20/0.49 (animal(a_fox)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[130, 127, 120])).
% 0.20/0.49 tff(132,plain,
% 0.20/0.49 (^[Grain_eater: $i, Animal: $i, Grain: $i] : refl(((~grain(Grain)) | (~animal(Grain_eater)) | (~eats(Grain_eater, Grain)) | (~eats(Animal, Grain_eater)) | (~animal(Animal))) <=> ((~grain(Grain)) | (~animal(Grain_eater)) | (~eats(Grain_eater, Grain)) | (~eats(Animal, Grain_eater)) | (~animal(Animal))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(133,plain,
% 0.20/0.49 (![Grain_eater: $i, Animal: $i, Grain: $i] : ((~grain(Grain)) | (~animal(Grain_eater)) | (~eats(Grain_eater, Grain)) | (~eats(Animal, Grain_eater)) | (~animal(Animal))) <=> ![Grain_eater: $i, Animal: $i, Grain: $i] : ((~grain(Grain)) | (~animal(Grain_eater)) | (~eats(Grain_eater, Grain)) | (~eats(Animal, Grain_eater)) | (~animal(Animal)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[132])).
% 0.20/0.49 tff(134,plain,
% 0.20/0.49 (![Grain_eater: $i, Animal: $i, Grain: $i] : ((~grain(Grain)) | (~animal(Grain_eater)) | (~eats(Grain_eater, Grain)) | (~eats(Animal, Grain_eater)) | (~animal(Animal))) <=> ![Grain_eater: $i, Animal: $i, Grain: $i] : ((~grain(Grain)) | (~animal(Grain_eater)) | (~eats(Grain_eater, Grain)) | (~eats(Animal, Grain_eater)) | (~animal(Animal)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(135,plain,
% 0.20/0.49 (^[Grain_eater: $i, Animal: $i, Grain: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~animal(Animal)) | (~animal(Grain_eater))) | (~grain(Grain))) <=> ((~grain(Grain)) | (~animal(Grain_eater)) | (~animal(Animal)))), (((((~animal(Animal)) | (~animal(Grain_eater))) | (~grain(Grain))) | (~eats(Animal, Grain_eater))) <=> (((~grain(Grain)) | (~animal(Grain_eater)) | (~animal(Animal))) | (~eats(Animal, Grain_eater))))), rewrite((((~grain(Grain)) | (~animal(Grain_eater)) | (~animal(Animal))) | (~eats(Animal, Grain_eater))) <=> ((~grain(Grain)) | (~animal(Grain_eater)) | (~eats(Animal, Grain_eater)) | (~animal(Animal)))), (((((~animal(Animal)) | (~animal(Grain_eater))) | (~grain(Grain))) | (~eats(Animal, Grain_eater))) <=> ((~grain(Grain)) | (~animal(Grain_eater)) | (~eats(Animal, Grain_eater)) | (~animal(Animal))))), ((((((~animal(Animal)) | (~animal(Grain_eater))) | (~grain(Grain))) | (~eats(Animal, Grain_eater))) | (~eats(Grain_eater, Grain))) <=> (((~grain(Grain)) | (~animal(Grain_eater)) | (~eats(Animal, Grain_eater)) | (~animal(Animal))) | (~eats(Grain_eater, Grain))))), rewrite((((~grain(Grain)) | (~animal(Grain_eater)) | (~eats(Animal, Grain_eater)) | (~animal(Animal))) | (~eats(Grain_eater, Grain))) <=> ((~grain(Grain)) | (~animal(Grain_eater)) | (~eats(Grain_eater, Grain)) | (~eats(Animal, Grain_eater)) | (~animal(Animal)))), ((((((~animal(Animal)) | (~animal(Grain_eater))) | (~grain(Grain))) | (~eats(Animal, Grain_eater))) | (~eats(Grain_eater, Grain))) <=> ((~grain(Grain)) | (~animal(Grain_eater)) | (~eats(Grain_eater, Grain)) | (~eats(Animal, Grain_eater)) | (~animal(Animal)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(136,plain,
% 0.20/0.49 (![Grain_eater: $i, Animal: $i, Grain: $i] : (((((~animal(Animal)) | (~animal(Grain_eater))) | (~grain(Grain))) | (~eats(Animal, Grain_eater))) | (~eats(Grain_eater, Grain))) <=> ![Grain_eater: $i, Animal: $i, Grain: $i] : ((~grain(Grain)) | (~animal(Grain_eater)) | (~eats(Grain_eater, Grain)) | (~eats(Animal, Grain_eater)) | (~animal(Animal)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[135])).
% 0.20/0.49 tff(137,axiom,(![Grain_eater: $i, Animal: $i, Grain: $i] : (((((~animal(Animal)) | (~animal(Grain_eater))) | (~grain(Grain))) | (~eats(Animal, Grain_eater))) | (~eats(Grain_eater, Grain)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_the_animal_exists')).
% 0.20/0.49 tff(138,plain,
% 0.20/0.49 (![Grain_eater: $i, Animal: $i, Grain: $i] : ((~grain(Grain)) | (~animal(Grain_eater)) | (~eats(Grain_eater, Grain)) | (~eats(Animal, Grain_eater)) | (~animal(Animal)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.20/0.49 tff(139,plain,
% 0.20/0.49 (![Grain_eater: $i, Animal: $i, Grain: $i] : ((~grain(Grain)) | (~animal(Grain_eater)) | (~eats(Grain_eater, Grain)) | (~eats(Animal, Grain_eater)) | (~animal(Animal)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[138, 134])).
% 0.20/0.49 tff(140,plain,(
% 0.20/0.49 ![Grain_eater: $i, Animal: $i, Grain: $i] : ((~grain(Grain)) | (~animal(Grain_eater)) | (~eats(Grain_eater, Grain)) | (~eats(Animal, Grain_eater)) | (~animal(Animal)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[139])).
% 0.20/0.49 tff(141,plain,
% 0.20/0.49 (![Grain_eater: $i, Animal: $i, Grain: $i] : ((~grain(Grain)) | (~animal(Grain_eater)) | (~eats(Grain_eater, Grain)) | (~eats(Animal, Grain_eater)) | (~animal(Animal)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[140, 133])).
% 0.20/0.49 tff(142,plain,
% 0.20/0.49 (((~![Grain_eater: $i, Animal: $i, Grain: $i] : ((~grain(Grain)) | (~animal(Grain_eater)) | (~eats(Grain_eater, Grain)) | (~eats(Animal, Grain_eater)) | (~animal(Animal)))) | ((~grain(a_grain)) | (~eats(a_fox, a_bird)) | (~animal(a_bird)) | (~animal(a_fox)) | (~eats(a_bird, a_grain)))) <=> ((~![Grain_eater: $i, Animal: $i, Grain: $i] : ((~grain(Grain)) | (~animal(Grain_eater)) | (~eats(Grain_eater, Grain)) | (~eats(Animal, Grain_eater)) | (~animal(Animal)))) | (~grain(a_grain)) | (~eats(a_fox, a_bird)) | (~animal(a_bird)) | (~animal(a_fox)) | (~eats(a_bird, a_grain)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(143,plain,
% 0.20/0.49 (((~grain(a_grain)) | (~animal(a_bird)) | (~eats(a_bird, a_grain)) | (~eats(a_fox, a_bird)) | (~animal(a_fox))) <=> ((~grain(a_grain)) | (~eats(a_fox, a_bird)) | (~animal(a_bird)) | (~animal(a_fox)) | (~eats(a_bird, a_grain)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(144,plain,
% 0.20/0.49 (((~![Grain_eater: $i, Animal: $i, Grain: $i] : ((~grain(Grain)) | (~animal(Grain_eater)) | (~eats(Grain_eater, Grain)) | (~eats(Animal, Grain_eater)) | (~animal(Animal)))) | ((~grain(a_grain)) | (~animal(a_bird)) | (~eats(a_bird, a_grain)) | (~eats(a_fox, a_bird)) | (~animal(a_fox)))) <=> ((~![Grain_eater: $i, Animal: $i, Grain: $i] : ((~grain(Grain)) | (~animal(Grain_eater)) | (~eats(Grain_eater, Grain)) | (~eats(Animal, Grain_eater)) | (~animal(Animal)))) | ((~grain(a_grain)) | (~eats(a_fox, a_bird)) | (~animal(a_bird)) | (~animal(a_fox)) | (~eats(a_bird, a_grain))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[143])).
% 0.20/0.49 tff(145,plain,
% 0.20/0.49 (((~![Grain_eater: $i, Animal: $i, Grain: $i] : ((~grain(Grain)) | (~animal(Grain_eater)) | (~eats(Grain_eater, Grain)) | (~eats(Animal, Grain_eater)) | (~animal(Animal)))) | ((~grain(a_grain)) | (~animal(a_bird)) | (~eats(a_bird, a_grain)) | (~eats(a_fox, a_bird)) | (~animal(a_fox)))) <=> ((~![Grain_eater: $i, Animal: $i, Grain: $i] : ((~grain(Grain)) | (~animal(Grain_eater)) | (~eats(Grain_eater, Grain)) | (~eats(Animal, Grain_eater)) | (~animal(Animal)))) | (~grain(a_grain)) | (~eats(a_fox, a_bird)) | (~animal(a_bird)) | (~animal(a_fox)) | (~eats(a_bird, a_grain)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[144, 142])).
% 0.20/0.49 tff(146,plain,
% 0.20/0.49 ((~![Grain_eater: $i, Animal: $i, Grain: $i] : ((~grain(Grain)) | (~animal(Grain_eater)) | (~eats(Grain_eater, Grain)) | (~eats(Animal, Grain_eater)) | (~animal(Animal)))) | ((~grain(a_grain)) | (~animal(a_bird)) | (~eats(a_bird, a_grain)) | (~eats(a_fox, a_bird)) | (~animal(a_fox)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(147,plain,
% 0.20/0.50 ((~![Grain_eater: $i, Animal: $i, Grain: $i] : ((~grain(Grain)) | (~animal(Grain_eater)) | (~eats(Grain_eater, Grain)) | (~eats(Animal, Grain_eater)) | (~animal(Animal)))) | (~grain(a_grain)) | (~eats(a_fox, a_bird)) | (~animal(a_bird)) | (~animal(a_fox)) | (~eats(a_bird, a_grain))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.20/0.50 tff(148,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[147, 44, 141, 131, 98, 117, 116])).
% 0.20/0.50 tff(149,plain,(~eats(a_fox, a_bird)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(150,plain,
% 0.20/0.50 (^[Fox: $i, Bird: $i] : refl(((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox))) <=> ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(151,plain,
% 0.20/0.50 (![Fox: $i, Bird: $i] : ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox))) <=> ![Fox: $i, Bird: $i] : ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[150])).
% 0.20/0.50 tff(152,plain,
% 0.20/0.50 (![Fox: $i, Bird: $i] : ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox))) <=> ![Fox: $i, Bird: $i] : ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(153,plain,
% 0.20/0.50 (^[Fox: $i, Bird: $i] : trans(monotonicity(rewrite((much_smaller(Bird, Fox) | (~bird(Bird))) <=> ((~bird(Bird)) | much_smaller(Bird, Fox))), (((much_smaller(Bird, Fox) | (~bird(Bird))) | (~fox(Fox))) <=> (((~bird(Bird)) | much_smaller(Bird, Fox)) | (~fox(Fox))))), rewrite((((~bird(Bird)) | much_smaller(Bird, Fox)) | (~fox(Fox))) <=> ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox)))), (((much_smaller(Bird, Fox) | (~bird(Bird))) | (~fox(Fox))) <=> ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(154,plain,
% 0.20/0.50 (![Fox: $i, Bird: $i] : ((much_smaller(Bird, Fox) | (~bird(Bird))) | (~fox(Fox))) <=> ![Fox: $i, Bird: $i] : ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[153])).
% 0.20/0.50 tff(155,axiom,(![Fox: $i, Bird: $i] : ((much_smaller(Bird, Fox) | (~bird(Bird))) | (~fox(Fox)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bird_smaller_than_fox')).
% 0.20/0.50 tff(156,plain,
% 0.20/0.50 (![Fox: $i, Bird: $i] : ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.20/0.50 tff(157,plain,
% 0.20/0.50 (![Fox: $i, Bird: $i] : ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[156, 152])).
% 0.20/0.50 tff(158,plain,(
% 0.20/0.50 ![Fox: $i, Bird: $i] : ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[157])).
% 0.20/0.50 tff(159,plain,
% 0.20/0.50 (![Fox: $i, Bird: $i] : ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[158, 151])).
% 0.20/0.50 tff(160,plain,
% 0.20/0.50 (((~![Fox: $i, Bird: $i] : ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox)))) | ((~fox(a_fox)) | (~bird(a_bird)) | much_smaller(a_bird, a_fox))) <=> ((~![Fox: $i, Bird: $i] : ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox)))) | (~fox(a_fox)) | (~bird(a_bird)) | much_smaller(a_bird, a_fox))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(161,plain,
% 0.20/0.50 (((~bird(a_bird)) | much_smaller(a_bird, a_fox) | (~fox(a_fox))) <=> ((~fox(a_fox)) | (~bird(a_bird)) | much_smaller(a_bird, a_fox))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(162,plain,
% 0.20/0.50 (((~![Fox: $i, Bird: $i] : ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox)))) | ((~bird(a_bird)) | much_smaller(a_bird, a_fox) | (~fox(a_fox)))) <=> ((~![Fox: $i, Bird: $i] : ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox)))) | ((~fox(a_fox)) | (~bird(a_bird)) | much_smaller(a_bird, a_fox)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[161])).
% 0.20/0.50 tff(163,plain,
% 0.20/0.50 (((~![Fox: $i, Bird: $i] : ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox)))) | ((~bird(a_bird)) | much_smaller(a_bird, a_fox) | (~fox(a_fox)))) <=> ((~![Fox: $i, Bird: $i] : ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox)))) | (~fox(a_fox)) | (~bird(a_bird)) | much_smaller(a_bird, a_fox))),
% 0.20/0.50 inference(transitivity,[status(thm)],[162, 160])).
% 0.20/0.50 tff(164,plain,
% 0.20/0.50 ((~![Fox: $i, Bird: $i] : ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox)))) | ((~bird(a_bird)) | much_smaller(a_bird, a_fox) | (~fox(a_fox)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(165,plain,
% 0.20/0.50 ((~![Fox: $i, Bird: $i] : ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox)))) | (~fox(a_fox)) | (~bird(a_bird)) | much_smaller(a_bird, a_fox)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.20/0.50 tff(166,plain,
% 0.20/0.50 (much_smaller(a_bird, a_fox)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[165, 120, 16, 159])).
% 0.20/0.50 tff(167,plain,
% 0.20/0.50 (^[Catapillar: $i] : refl(((~caterpillar(Catapillar)) | plant(caterpillar_food_of(Catapillar))) <=> ((~caterpillar(Catapillar)) | plant(caterpillar_food_of(Catapillar))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(168,plain,
% 0.20/0.50 (![Catapillar: $i] : ((~caterpillar(Catapillar)) | plant(caterpillar_food_of(Catapillar))) <=> ![Catapillar: $i] : ((~caterpillar(Catapillar)) | plant(caterpillar_food_of(Catapillar)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[167])).
% 0.20/0.50 tff(169,plain,
% 0.20/0.50 (![Catapillar: $i] : ((~caterpillar(Catapillar)) | plant(caterpillar_food_of(Catapillar))) <=> ![Catapillar: $i] : ((~caterpillar(Catapillar)) | plant(caterpillar_food_of(Catapillar)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(170,plain,
% 0.20/0.50 (^[Catapillar: $i] : rewrite((plant(caterpillar_food_of(Catapillar)) | (~caterpillar(Catapillar))) <=> ((~caterpillar(Catapillar)) | plant(caterpillar_food_of(Catapillar))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(171,plain,
% 0.20/0.50 (![Catapillar: $i] : (plant(caterpillar_food_of(Catapillar)) | (~caterpillar(Catapillar))) <=> ![Catapillar: $i] : ((~caterpillar(Catapillar)) | plant(caterpillar_food_of(Catapillar)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[170])).
% 0.20/0.50 tff(172,axiom,(![Catapillar: $i] : (plant(caterpillar_food_of(Catapillar)) | (~caterpillar(Catapillar)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','caterpillar_food_is_a_plant')).
% 0.20/0.50 tff(173,plain,
% 0.20/0.50 (![Catapillar: $i] : ((~caterpillar(Catapillar)) | plant(caterpillar_food_of(Catapillar)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.20/0.50 tff(174,plain,
% 0.20/0.50 (![Catapillar: $i] : ((~caterpillar(Catapillar)) | plant(caterpillar_food_of(Catapillar)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[173, 169])).
% 0.20/0.50 tff(175,plain,(
% 0.20/0.50 ![Catapillar: $i] : ((~caterpillar(Catapillar)) | plant(caterpillar_food_of(Catapillar)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[174])).
% 0.20/0.50 tff(176,plain,
% 0.20/0.50 (![Catapillar: $i] : ((~caterpillar(Catapillar)) | plant(caterpillar_food_of(Catapillar)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[175, 168])).
% 0.20/0.50 tff(177,plain,
% 0.20/0.50 (caterpillar(a_caterpillar) <=> caterpillar(a_caterpillar)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(178,axiom,(caterpillar(a_caterpillar)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','there_is_a_caterpillar')).
% 0.20/0.50 tff(179,plain,
% 0.20/0.50 (caterpillar(a_caterpillar)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.20/0.50 tff(180,plain,
% 0.20/0.50 (((~![Catapillar: $i] : ((~caterpillar(Catapillar)) | plant(caterpillar_food_of(Catapillar)))) | ((~caterpillar(a_caterpillar)) | plant(caterpillar_food_of(a_caterpillar)))) <=> ((~![Catapillar: $i] : ((~caterpillar(Catapillar)) | plant(caterpillar_food_of(Catapillar)))) | (~caterpillar(a_caterpillar)) | plant(caterpillar_food_of(a_caterpillar)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(181,plain,
% 0.20/0.50 ((~![Catapillar: $i] : ((~caterpillar(Catapillar)) | plant(caterpillar_food_of(Catapillar)))) | ((~caterpillar(a_caterpillar)) | plant(caterpillar_food_of(a_caterpillar)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(182,plain,
% 0.20/0.50 ((~![Catapillar: $i] : ((~caterpillar(Catapillar)) | plant(caterpillar_food_of(Catapillar)))) | (~caterpillar(a_caterpillar)) | plant(caterpillar_food_of(a_caterpillar))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.20/0.50 tff(183,plain,
% 0.20/0.50 (plant(caterpillar_food_of(a_caterpillar))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[182, 179, 176])).
% 0.20/0.50 tff(184,plain,
% 0.20/0.50 (((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | ((~eats(a_snail, snail_food_of(a_snail))) | eats(a_bird, a_snail) | (~animal(a_snail)) | (~plant(snail_food_of(a_snail))) | (~much_smaller(a_snail, a_bird)) | (~animal(a_bird)) | (~plant(caterpillar_food_of(a_caterpillar))) | eats(a_bird, caterpillar_food_of(a_caterpillar)))) <=> ((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | (~eats(a_snail, snail_food_of(a_snail))) | eats(a_bird, a_snail) | (~animal(a_snail)) | (~plant(snail_food_of(a_snail))) | (~much_smaller(a_snail, a_bird)) | (~animal(a_bird)) | (~plant(caterpillar_food_of(a_caterpillar))) | eats(a_bird, caterpillar_food_of(a_caterpillar)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(185,plain,
% 0.20/0.50 (((~eats(a_snail, snail_food_of(a_snail))) | (~much_smaller(a_snail, a_bird)) | (~plant(snail_food_of(a_snail))) | (~animal(a_snail)) | (~plant(caterpillar_food_of(a_caterpillar))) | (~animal(a_bird)) | eats(a_bird, a_snail) | eats(a_bird, caterpillar_food_of(a_caterpillar))) <=> ((~eats(a_snail, snail_food_of(a_snail))) | eats(a_bird, a_snail) | (~animal(a_snail)) | (~plant(snail_food_of(a_snail))) | (~much_smaller(a_snail, a_bird)) | (~animal(a_bird)) | (~plant(caterpillar_food_of(a_caterpillar))) | eats(a_bird, caterpillar_food_of(a_caterpillar)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(186,plain,
% 0.20/0.50 (((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | ((~eats(a_snail, snail_food_of(a_snail))) | (~much_smaller(a_snail, a_bird)) | (~plant(snail_food_of(a_snail))) | (~animal(a_snail)) | (~plant(caterpillar_food_of(a_caterpillar))) | (~animal(a_bird)) | eats(a_bird, a_snail) | eats(a_bird, caterpillar_food_of(a_caterpillar)))) <=> ((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | ((~eats(a_snail, snail_food_of(a_snail))) | eats(a_bird, a_snail) | (~animal(a_snail)) | (~plant(snail_food_of(a_snail))) | (~much_smaller(a_snail, a_bird)) | (~animal(a_bird)) | (~plant(caterpillar_food_of(a_caterpillar))) | eats(a_bird, caterpillar_food_of(a_caterpillar))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[185])).
% 0.20/0.50 tff(187,plain,
% 0.20/0.50 (((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | ((~eats(a_snail, snail_food_of(a_snail))) | (~much_smaller(a_snail, a_bird)) | (~plant(snail_food_of(a_snail))) | (~animal(a_snail)) | (~plant(caterpillar_food_of(a_caterpillar))) | (~animal(a_bird)) | eats(a_bird, a_snail) | eats(a_bird, caterpillar_food_of(a_caterpillar)))) <=> ((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | (~eats(a_snail, snail_food_of(a_snail))) | eats(a_bird, a_snail) | (~animal(a_snail)) | (~plant(snail_food_of(a_snail))) | (~much_smaller(a_snail, a_bird)) | (~animal(a_bird)) | (~plant(caterpillar_food_of(a_caterpillar))) | eats(a_bird, caterpillar_food_of(a_caterpillar)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[186, 184])).
% 0.20/0.50 tff(188,plain,
% 0.20/0.50 ((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | ((~eats(a_snail, snail_food_of(a_snail))) | (~much_smaller(a_snail, a_bird)) | (~plant(snail_food_of(a_snail))) | (~animal(a_snail)) | (~plant(caterpillar_food_of(a_caterpillar))) | (~animal(a_bird)) | eats(a_bird, a_snail) | eats(a_bird, caterpillar_food_of(a_caterpillar)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(189,plain,
% 0.20/0.50 ((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | (~eats(a_snail, snail_food_of(a_snail))) | eats(a_bird, a_snail) | (~animal(a_snail)) | (~plant(snail_food_of(a_snail))) | (~much_smaller(a_snail, a_bird)) | (~animal(a_bird)) | (~plant(caterpillar_food_of(a_caterpillar))) | eats(a_bird, caterpillar_food_of(a_caterpillar))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.20/0.50 tff(190,plain,
% 0.20/0.50 (eats(a_bird, a_snail) | eats(a_bird, caterpillar_food_of(a_caterpillar))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[189, 108, 98, 183, 87, 73, 62, 34])).
% 0.20/0.50 tff(191,plain,
% 0.20/0.50 (eats(a_bird, caterpillar_food_of(a_caterpillar))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[190, 20])).
% 0.20/0.50 tff(192,plain,
% 0.20/0.50 (((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | (eats(a_fox, a_bird) | (~animal(a_bird)) | (~animal(a_fox)) | (~plant(caterpillar_food_of(a_caterpillar))) | (~eats(a_bird, caterpillar_food_of(a_caterpillar))) | eats(a_fox, caterpillar_food_of(a_caterpillar)) | (~much_smaller(a_bird, a_fox)))) <=> ((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | eats(a_fox, a_bird) | (~animal(a_bird)) | (~animal(a_fox)) | (~plant(caterpillar_food_of(a_caterpillar))) | (~eats(a_bird, caterpillar_food_of(a_caterpillar))) | eats(a_fox, caterpillar_food_of(a_caterpillar)) | (~much_smaller(a_bird, a_fox)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(193,plain,
% 0.20/0.50 (((~eats(a_bird, caterpillar_food_of(a_caterpillar))) | (~much_smaller(a_bird, a_fox)) | (~plant(caterpillar_food_of(a_caterpillar))) | (~animal(a_bird)) | (~plant(caterpillar_food_of(a_caterpillar))) | (~animal(a_fox)) | eats(a_fox, a_bird) | eats(a_fox, caterpillar_food_of(a_caterpillar))) <=> (eats(a_fox, a_bird) | (~animal(a_bird)) | (~animal(a_fox)) | (~plant(caterpillar_food_of(a_caterpillar))) | (~eats(a_bird, caterpillar_food_of(a_caterpillar))) | eats(a_fox, caterpillar_food_of(a_caterpillar)) | (~much_smaller(a_bird, a_fox)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(194,plain,
% 0.20/0.50 (((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | ((~eats(a_bird, caterpillar_food_of(a_caterpillar))) | (~much_smaller(a_bird, a_fox)) | (~plant(caterpillar_food_of(a_caterpillar))) | (~animal(a_bird)) | (~plant(caterpillar_food_of(a_caterpillar))) | (~animal(a_fox)) | eats(a_fox, a_bird) | eats(a_fox, caterpillar_food_of(a_caterpillar)))) <=> ((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | (eats(a_fox, a_bird) | (~animal(a_bird)) | (~animal(a_fox)) | (~plant(caterpillar_food_of(a_caterpillar))) | (~eats(a_bird, caterpillar_food_of(a_caterpillar))) | eats(a_fox, caterpillar_food_of(a_caterpillar)) | (~much_smaller(a_bird, a_fox))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[193])).
% 0.20/0.50 tff(195,plain,
% 0.20/0.50 (((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | ((~eats(a_bird, caterpillar_food_of(a_caterpillar))) | (~much_smaller(a_bird, a_fox)) | (~plant(caterpillar_food_of(a_caterpillar))) | (~animal(a_bird)) | (~plant(caterpillar_food_of(a_caterpillar))) | (~animal(a_fox)) | eats(a_fox, a_bird) | eats(a_fox, caterpillar_food_of(a_caterpillar)))) <=> ((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | eats(a_fox, a_bird) | (~animal(a_bird)) | (~animal(a_fox)) | (~plant(caterpillar_food_of(a_caterpillar))) | (~eats(a_bird, caterpillar_food_of(a_caterpillar))) | eats(a_fox, caterpillar_food_of(a_caterpillar)) | (~much_smaller(a_bird, a_fox)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[194, 192])).
% 0.20/0.50 tff(196,plain,
% 0.20/0.50 ((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | ((~eats(a_bird, caterpillar_food_of(a_caterpillar))) | (~much_smaller(a_bird, a_fox)) | (~plant(caterpillar_food_of(a_caterpillar))) | (~animal(a_bird)) | (~plant(caterpillar_food_of(a_caterpillar))) | (~animal(a_fox)) | eats(a_fox, a_bird) | eats(a_fox, caterpillar_food_of(a_caterpillar)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(197,plain,
% 0.20/0.50 ((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | eats(a_fox, a_bird) | (~animal(a_bird)) | (~animal(a_fox)) | (~plant(caterpillar_food_of(a_caterpillar))) | (~eats(a_bird, caterpillar_food_of(a_caterpillar))) | eats(a_fox, caterpillar_food_of(a_caterpillar)) | (~much_smaller(a_bird, a_fox))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.20/0.50 tff(198,plain,
% 0.20/0.50 (eats(a_fox, a_bird) | eats(a_fox, caterpillar_food_of(a_caterpillar))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[197, 108, 131, 98, 183, 191, 166])).
% 0.20/0.50 tff(199,plain,
% 0.20/0.50 (eats(a_fox, caterpillar_food_of(a_caterpillar))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[198, 149])).
% 0.20/0.50 tff(200,assumption,(eats(a_fox, caterpillar_food_of(a_caterpillar))), introduced(assumption)).
% 0.20/0.50 tff(201,plain,
% 0.20/0.50 (^[Fox: $i, Wolf: $i] : refl(((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox))) <=> ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(202,plain,
% 0.20/0.50 (![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox))) <=> ![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[201])).
% 0.20/0.50 tff(203,plain,
% 0.20/0.50 (![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox))) <=> ![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(204,plain,
% 0.20/0.50 (^[Fox: $i, Wolf: $i] : trans(monotonicity(rewrite((much_smaller(Fox, Wolf) | (~fox(Fox))) <=> (much_smaller(Fox, Wolf) | (~fox(Fox)))), (((much_smaller(Fox, Wolf) | (~fox(Fox))) | (~wolf(Wolf))) <=> ((much_smaller(Fox, Wolf) | (~fox(Fox))) | (~wolf(Wolf))))), rewrite(((much_smaller(Fox, Wolf) | (~fox(Fox))) | (~wolf(Wolf))) <=> ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox)))), (((much_smaller(Fox, Wolf) | (~fox(Fox))) | (~wolf(Wolf))) <=> ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(205,plain,
% 0.20/0.50 (![Fox: $i, Wolf: $i] : ((much_smaller(Fox, Wolf) | (~fox(Fox))) | (~wolf(Wolf))) <=> ![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[204])).
% 0.20/0.50 tff(206,axiom,(![Fox: $i, Wolf: $i] : ((much_smaller(Fox, Wolf) | (~fox(Fox))) | (~wolf(Wolf)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fox_smaller_than_wolf')).
% 0.20/0.50 tff(207,plain,
% 0.20/0.50 (![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.20/0.50 tff(208,plain,
% 0.20/0.50 (![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[207, 203])).
% 0.20/0.50 tff(209,plain,(
% 0.20/0.50 ![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[208])).
% 0.20/0.50 tff(210,plain,
% 0.20/0.50 (![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[209, 202])).
% 0.20/0.50 tff(211,plain,
% 0.20/0.50 (wolf(a_wolf) <=> wolf(a_wolf)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(212,axiom,(wolf(a_wolf)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','there_is_a_wolf')).
% 0.20/0.50 tff(213,plain,
% 0.20/0.50 (wolf(a_wolf)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.20/0.50 tff(214,plain,
% 0.20/0.50 (((~![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox)))) | ((~wolf(a_wolf)) | (~fox(a_fox)) | much_smaller(a_fox, a_wolf))) <=> ((~![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox)))) | (~wolf(a_wolf)) | (~fox(a_fox)) | much_smaller(a_fox, a_wolf))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(215,plain,
% 0.20/0.50 (((~wolf(a_wolf)) | much_smaller(a_fox, a_wolf) | (~fox(a_fox))) <=> ((~wolf(a_wolf)) | (~fox(a_fox)) | much_smaller(a_fox, a_wolf))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(216,plain,
% 0.20/0.50 (((~![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox)))) | ((~wolf(a_wolf)) | much_smaller(a_fox, a_wolf) | (~fox(a_fox)))) <=> ((~![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox)))) | ((~wolf(a_wolf)) | (~fox(a_fox)) | much_smaller(a_fox, a_wolf)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[215])).
% 0.20/0.50 tff(217,plain,
% 0.20/0.50 (((~![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox)))) | ((~wolf(a_wolf)) | much_smaller(a_fox, a_wolf) | (~fox(a_fox)))) <=> ((~![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox)))) | (~wolf(a_wolf)) | (~fox(a_fox)) | much_smaller(a_fox, a_wolf))),
% 0.20/0.50 inference(transitivity,[status(thm)],[216, 214])).
% 0.20/0.50 tff(218,plain,
% 0.20/0.50 ((~![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox)))) | ((~wolf(a_wolf)) | much_smaller(a_fox, a_wolf) | (~fox(a_fox)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(219,plain,
% 0.20/0.50 ((~![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox)))) | (~wolf(a_wolf)) | (~fox(a_fox)) | much_smaller(a_fox, a_wolf)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.20/0.50 tff(220,plain,
% 0.20/0.50 (much_smaller(a_fox, a_wolf)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[219, 213, 120, 210])).
% 0.20/0.50 tff(221,plain,
% 0.20/0.50 (^[Fox: $i, Wolf: $i] : refl(((~wolf(Wolf)) | (~fox(Fox)) | (~eats(Wolf, Fox))) <=> ((~wolf(Wolf)) | (~fox(Fox)) | (~eats(Wolf, Fox))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(222,plain,
% 0.20/0.50 (![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | (~fox(Fox)) | (~eats(Wolf, Fox))) <=> ![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | (~fox(Fox)) | (~eats(Wolf, Fox)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[221])).
% 0.20/0.50 tff(223,plain,
% 0.20/0.50 (![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | (~fox(Fox)) | (~eats(Wolf, Fox))) <=> ![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | (~fox(Fox)) | (~eats(Wolf, Fox)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(224,plain,
% 0.20/0.50 (^[Fox: $i, Wolf: $i] : trans(monotonicity(rewrite(((~wolf(Wolf)) | (~fox(Fox))) <=> ((~wolf(Wolf)) | (~fox(Fox)))), ((((~wolf(Wolf)) | (~fox(Fox))) | (~eats(Wolf, Fox))) <=> (((~wolf(Wolf)) | (~fox(Fox))) | (~eats(Wolf, Fox))))), rewrite((((~wolf(Wolf)) | (~fox(Fox))) | (~eats(Wolf, Fox))) <=> ((~wolf(Wolf)) | (~fox(Fox)) | (~eats(Wolf, Fox)))), ((((~wolf(Wolf)) | (~fox(Fox))) | (~eats(Wolf, Fox))) <=> ((~wolf(Wolf)) | (~fox(Fox)) | (~eats(Wolf, Fox)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(225,plain,
% 0.20/0.50 (![Fox: $i, Wolf: $i] : (((~wolf(Wolf)) | (~fox(Fox))) | (~eats(Wolf, Fox))) <=> ![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | (~fox(Fox)) | (~eats(Wolf, Fox)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[224])).
% 0.20/0.50 tff(226,axiom,(![Fox: $i, Wolf: $i] : (((~wolf(Wolf)) | (~fox(Fox))) | (~eats(Wolf, Fox)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','wolf_dont_eat_fox')).
% 0.20/0.50 tff(227,plain,
% 0.20/0.50 (![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | (~fox(Fox)) | (~eats(Wolf, Fox)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.20/0.50 tff(228,plain,
% 0.20/0.50 (![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | (~fox(Fox)) | (~eats(Wolf, Fox)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[227, 223])).
% 0.20/0.50 tff(229,plain,(
% 0.20/0.50 ![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | (~fox(Fox)) | (~eats(Wolf, Fox)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[228])).
% 0.20/0.50 tff(230,plain,
% 0.20/0.50 (![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | (~fox(Fox)) | (~eats(Wolf, Fox)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[229, 222])).
% 0.20/0.50 tff(231,plain,
% 0.20/0.50 (((~![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | (~fox(Fox)) | (~eats(Wolf, Fox)))) | ((~wolf(a_wolf)) | (~fox(a_fox)) | (~eats(a_wolf, a_fox)))) <=> ((~![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | (~fox(Fox)) | (~eats(Wolf, Fox)))) | (~wolf(a_wolf)) | (~fox(a_fox)) | (~eats(a_wolf, a_fox)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(232,plain,
% 0.20/0.50 ((~![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | (~fox(Fox)) | (~eats(Wolf, Fox)))) | ((~wolf(a_wolf)) | (~fox(a_fox)) | (~eats(a_wolf, a_fox)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(233,plain,
% 0.20/0.50 ((~![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | (~fox(Fox)) | (~eats(Wolf, Fox)))) | (~wolf(a_wolf)) | (~fox(a_fox)) | (~eats(a_wolf, a_fox))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.20/0.50 tff(234,plain,
% 0.20/0.50 (~eats(a_wolf, a_fox)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[233, 213, 120, 230])).
% 0.20/0.50 tff(235,assumption,(~eats(a_wolf, a_grain)), introduced(assumption)).
% 0.20/0.50 tff(236,plain,
% 0.20/0.50 (^[X: $i] : refl((animal(X) | (~wolf(X))) <=> (animal(X) | (~wolf(X))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(237,plain,
% 0.20/0.50 (![X: $i] : (animal(X) | (~wolf(X))) <=> ![X: $i] : (animal(X) | (~wolf(X)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[236])).
% 0.20/0.50 tff(238,plain,
% 0.20/0.50 (![X: $i] : (animal(X) | (~wolf(X))) <=> ![X: $i] : (animal(X) | (~wolf(X)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(239,axiom,(![X: $i] : (animal(X) | (~wolf(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','wolf_is_an_animal')).
% 0.20/0.50 tff(240,plain,
% 0.20/0.50 (![X: $i] : (animal(X) | (~wolf(X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.20/0.50 tff(241,plain,(
% 0.20/0.50 ![X: $i] : (animal(X) | (~wolf(X)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[240])).
% 0.20/0.50 tff(242,plain,
% 0.20/0.50 (![X: $i] : (animal(X) | (~wolf(X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[241, 237])).
% 0.20/0.50 tff(243,plain,
% 0.20/0.50 (((~![X: $i] : (animal(X) | (~wolf(X)))) | (animal(a_wolf) | (~wolf(a_wolf)))) <=> ((~![X: $i] : (animal(X) | (~wolf(X)))) | animal(a_wolf) | (~wolf(a_wolf)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(244,plain,
% 0.20/0.50 ((~![X: $i] : (animal(X) | (~wolf(X)))) | (animal(a_wolf) | (~wolf(a_wolf)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(245,plain,
% 0.20/0.50 ((~![X: $i] : (animal(X) | (~wolf(X)))) | animal(a_wolf) | (~wolf(a_wolf))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.20/0.50 tff(246,plain,
% 0.20/0.50 (animal(a_wolf)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[245, 242, 213])).
% 0.20/0.50 tff(247,plain,
% 0.20/0.50 (((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | ((~animal(a_wolf)) | eats(a_wolf, a_grain) | (~animal(a_fox)) | eats(a_wolf, a_fox) | (~plant(caterpillar_food_of(a_caterpillar))) | (~plant(a_grain)) | (~eats(a_fox, caterpillar_food_of(a_caterpillar))) | (~much_smaller(a_fox, a_wolf)))) <=> ((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | (~animal(a_wolf)) | eats(a_wolf, a_grain) | (~animal(a_fox)) | eats(a_wolf, a_fox) | (~plant(caterpillar_food_of(a_caterpillar))) | (~plant(a_grain)) | (~eats(a_fox, caterpillar_food_of(a_caterpillar))) | (~much_smaller(a_fox, a_wolf)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(248,plain,
% 0.20/0.50 (((~eats(a_fox, caterpillar_food_of(a_caterpillar))) | (~much_smaller(a_fox, a_wolf)) | (~plant(caterpillar_food_of(a_caterpillar))) | (~animal(a_fox)) | (~plant(a_grain)) | (~animal(a_wolf)) | eats(a_wolf, a_fox) | eats(a_wolf, a_grain)) <=> ((~animal(a_wolf)) | eats(a_wolf, a_grain) | (~animal(a_fox)) | eats(a_wolf, a_fox) | (~plant(caterpillar_food_of(a_caterpillar))) | (~plant(a_grain)) | (~eats(a_fox, caterpillar_food_of(a_caterpillar))) | (~much_smaller(a_fox, a_wolf)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(249,plain,
% 0.20/0.50 (((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | ((~eats(a_fox, caterpillar_food_of(a_caterpillar))) | (~much_smaller(a_fox, a_wolf)) | (~plant(caterpillar_food_of(a_caterpillar))) | (~animal(a_fox)) | (~plant(a_grain)) | (~animal(a_wolf)) | eats(a_wolf, a_fox) | eats(a_wolf, a_grain))) <=> ((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | ((~animal(a_wolf)) | eats(a_wolf, a_grain) | (~animal(a_fox)) | eats(a_wolf, a_fox) | (~plant(caterpillar_food_of(a_caterpillar))) | (~plant(a_grain)) | (~eats(a_fox, caterpillar_food_of(a_caterpillar))) | (~much_smaller(a_fox, a_wolf))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[248])).
% 0.20/0.50 tff(250,plain,
% 0.20/0.50 (((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | ((~eats(a_fox, caterpillar_food_of(a_caterpillar))) | (~much_smaller(a_fox, a_wolf)) | (~plant(caterpillar_food_of(a_caterpillar))) | (~animal(a_fox)) | (~plant(a_grain)) | (~animal(a_wolf)) | eats(a_wolf, a_fox) | eats(a_wolf, a_grain))) <=> ((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | (~animal(a_wolf)) | eats(a_wolf, a_grain) | (~animal(a_fox)) | eats(a_wolf, a_fox) | (~plant(caterpillar_food_of(a_caterpillar))) | (~plant(a_grain)) | (~eats(a_fox, caterpillar_food_of(a_caterpillar))) | (~much_smaller(a_fox, a_wolf)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[249, 247])).
% 0.20/0.50 tff(251,plain,
% 0.20/0.50 ((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | ((~eats(a_fox, caterpillar_food_of(a_caterpillar))) | (~much_smaller(a_fox, a_wolf)) | (~plant(caterpillar_food_of(a_caterpillar))) | (~animal(a_fox)) | (~plant(a_grain)) | (~animal(a_wolf)) | eats(a_wolf, a_fox) | eats(a_wolf, a_grain))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(252,plain,
% 0.20/0.51 ((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | (~animal(a_wolf)) | eats(a_wolf, a_grain) | (~animal(a_fox)) | eats(a_wolf, a_fox) | (~plant(caterpillar_food_of(a_caterpillar))) | (~plant(a_grain)) | (~eats(a_fox, caterpillar_food_of(a_caterpillar))) | (~much_smaller(a_fox, a_wolf))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.20/0.51 tff(253,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[252, 108, 246, 131, 183, 48, 235, 234, 220, 200])).
% 0.20/0.51 tff(254,plain,((~eats(a_fox, caterpillar_food_of(a_caterpillar))) | eats(a_wolf, a_grain)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(255,plain,
% 0.20/0.51 (eats(a_wolf, a_grain)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[254, 199])).
% 0.20/0.51 tff(256,plain,
% 0.20/0.51 (^[Wolf: $i, Grain: $i] : refl(((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf))) <=> ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(257,plain,
% 0.20/0.51 (![Wolf: $i, Grain: $i] : ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf))) <=> ![Wolf: $i, Grain: $i] : ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[256])).
% 0.20/0.51 tff(258,plain,
% 0.20/0.51 (![Wolf: $i, Grain: $i] : ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf))) <=> ![Wolf: $i, Grain: $i] : ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(259,plain,
% 0.20/0.51 (^[Wolf: $i, Grain: $i] : trans(monotonicity(rewrite(((~wolf(Wolf)) | (~grain(Grain))) <=> ((~grain(Grain)) | (~wolf(Wolf)))), ((((~wolf(Wolf)) | (~grain(Grain))) | (~eats(Wolf, Grain))) <=> (((~grain(Grain)) | (~wolf(Wolf))) | (~eats(Wolf, Grain))))), rewrite((((~grain(Grain)) | (~wolf(Wolf))) | (~eats(Wolf, Grain))) <=> ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf)))), ((((~wolf(Wolf)) | (~grain(Grain))) | (~eats(Wolf, Grain))) <=> ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf)))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(260,plain,
% 0.20/0.51 (![Wolf: $i, Grain: $i] : (((~wolf(Wolf)) | (~grain(Grain))) | (~eats(Wolf, Grain))) <=> ![Wolf: $i, Grain: $i] : ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[259])).
% 0.20/0.51 tff(261,axiom,(![Wolf: $i, Grain: $i] : (((~wolf(Wolf)) | (~grain(Grain))) | (~eats(Wolf, Grain)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','wolf_dont_eat_grain')).
% 0.20/0.51 tff(262,plain,
% 0.20/0.51 (![Wolf: $i, Grain: $i] : ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.20/0.51 tff(263,plain,
% 0.20/0.51 (![Wolf: $i, Grain: $i] : ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[262, 258])).
% 0.20/0.51 tff(264,plain,(
% 0.20/0.51 ![Wolf: $i, Grain: $i] : ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[263])).
% 0.20/0.51 tff(265,plain,
% 0.20/0.51 (![Wolf: $i, Grain: $i] : ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[264, 257])).
% 0.20/0.51 tff(266,plain,
% 0.20/0.51 (((~![Wolf: $i, Grain: $i] : ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf)))) | ((~wolf(a_wolf)) | (~grain(a_grain)) | (~eats(a_wolf, a_grain)))) <=> ((~![Wolf: $i, Grain: $i] : ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf)))) | (~wolf(a_wolf)) | (~grain(a_grain)) | (~eats(a_wolf, a_grain)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(267,plain,
% 0.20/0.51 (((~grain(a_grain)) | (~eats(a_wolf, a_grain)) | (~wolf(a_wolf))) <=> ((~wolf(a_wolf)) | (~grain(a_grain)) | (~eats(a_wolf, a_grain)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(268,plain,
% 0.20/0.51 (((~![Wolf: $i, Grain: $i] : ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf)))) | ((~grain(a_grain)) | (~eats(a_wolf, a_grain)) | (~wolf(a_wolf)))) <=> ((~![Wolf: $i, Grain: $i] : ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf)))) | ((~wolf(a_wolf)) | (~grain(a_grain)) | (~eats(a_wolf, a_grain))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[267])).
% 0.20/0.51 tff(269,plain,
% 0.20/0.51 (((~![Wolf: $i, Grain: $i] : ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf)))) | ((~grain(a_grain)) | (~eats(a_wolf, a_grain)) | (~wolf(a_wolf)))) <=> ((~![Wolf: $i, Grain: $i] : ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf)))) | (~wolf(a_wolf)) | (~grain(a_grain)) | (~eats(a_wolf, a_grain)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[268, 266])).
% 0.20/0.51 tff(270,plain,
% 0.20/0.51 ((~![Wolf: $i, Grain: $i] : ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf)))) | ((~grain(a_grain)) | (~eats(a_wolf, a_grain)) | (~wolf(a_wolf)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(271,plain,
% 0.20/0.51 ((~![Wolf: $i, Grain: $i] : ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf)))) | (~wolf(a_wolf)) | (~grain(a_grain)) | (~eats(a_wolf, a_grain))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.20/0.51 tff(272,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[271, 213, 44, 265, 255])).
% 0.20/0.51 % SZS output end Proof
% 0.20/0.51 % E exiting
%------------------------------------------------------------------------------