TSTP Solution File: PUZ031-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PUZ031-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 : Sun Sep 18 14:10:58 EDT 2022
% Result : Unsatisfiable 0.21s 0.46s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PUZ031-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 18:31:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.46 % SZS status Unsatisfiable
% 0.21/0.46 % SZS output start Proof
% 0.21/0.46 tff(eats_type, type, (
% 0.21/0.46 eats: ( $i * $i ) > $o)).
% 0.21/0.46 tff(a_grain_type, type, (
% 0.21/0.46 a_grain: $i)).
% 0.21/0.46 tff(a_fox_type, type, (
% 0.21/0.46 a_fox: $i)).
% 0.21/0.46 tff(a_bird_type, type, (
% 0.21/0.46 a_bird: $i)).
% 0.21/0.46 tff(a_snail_type, type, (
% 0.21/0.46 a_snail: $i)).
% 0.21/0.46 tff(snail_type, type, (
% 0.21/0.46 snail: $i > $o)).
% 0.21/0.46 tff(bird_type, type, (
% 0.21/0.46 bird: $i > $o)).
% 0.21/0.46 tff(much_smaller_type, type, (
% 0.21/0.46 much_smaller: ( $i * $i ) > $o)).
% 0.21/0.46 tff(plant_type, type, (
% 0.21/0.46 plant: $i > $o)).
% 0.21/0.46 tff(grain_type, type, (
% 0.21/0.46 grain: $i > $o)).
% 0.21/0.46 tff(snail_food_of_type, type, (
% 0.21/0.46 snail_food_of: $i > $i)).
% 0.21/0.46 tff(animal_type, type, (
% 0.21/0.46 animal: $i > $o)).
% 0.21/0.46 tff(fox_type, type, (
% 0.21/0.46 fox: $i > $o)).
% 0.21/0.46 tff(a_wolf_type, type, (
% 0.21/0.46 a_wolf: $i)).
% 0.21/0.46 tff(wolf_type, type, (
% 0.21/0.46 wolf: $i > $o)).
% 0.21/0.46 tff(1,assumption,(eats(a_fox, a_bird)), introduced(assumption)).
% 0.21/0.46 tff(2,assumption,(eats(a_bird, a_snail)), introduced(assumption)).
% 0.21/0.46 tff(3,plain,
% 0.21/0.46 (^[Snail: $i, Bird: $i] : refl(((~bird(Bird)) | (~snail(Snail)) | (~eats(Bird, Snail))) <=> ((~bird(Bird)) | (~snail(Snail)) | (~eats(Bird, Snail))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(4,plain,
% 0.21/0.46 (![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | (~eats(Bird, Snail))) <=> ![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | (~eats(Bird, Snail)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.46 tff(5,plain,
% 0.21/0.46 (![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | (~eats(Bird, Snail))) <=> ![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | (~eats(Bird, Snail)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(6,plain,
% 0.21/0.46 (^[Snail: $i, Bird: $i] : rewrite((((~bird(Bird)) | (~snail(Snail))) | (~eats(Bird, Snail))) <=> ((~bird(Bird)) | (~snail(Snail)) | (~eats(Bird, Snail))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(7,plain,
% 0.21/0.46 (![Snail: $i, Bird: $i] : (((~bird(Bird)) | (~snail(Snail))) | (~eats(Bird, Snail))) <=> ![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | (~eats(Bird, Snail)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[6])).
% 0.21/0.46 tff(8,axiom,(![Snail: $i, Bird: $i] : (((~bird(Bird)) | (~snail(Snail))) | (~eats(Bird, Snail)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bird_dont_eat_snail')).
% 0.21/0.46 tff(9,plain,
% 0.21/0.46 (![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | (~eats(Bird, Snail)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.21/0.46 tff(10,plain,
% 0.21/0.46 (![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | (~eats(Bird, Snail)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.21/0.46 tff(11,plain,(
% 0.21/0.46 ![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | (~eats(Bird, Snail)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[10])).
% 0.21/0.46 tff(12,plain,
% 0.21/0.46 (![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | (~eats(Bird, Snail)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.21/0.46 tff(13,plain,
% 0.21/0.46 (snail(a_snail) <=> snail(a_snail)),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(14,axiom,(snail(a_snail)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','there_is_a_snail')).
% 0.21/0.46 tff(15,plain,
% 0.21/0.46 (snail(a_snail)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.21/0.46 tff(16,plain,
% 0.21/0.46 (bird(a_bird) <=> bird(a_bird)),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(17,axiom,(bird(a_bird)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','there_is_a_bird')).
% 0.21/0.46 tff(18,plain,
% 0.21/0.46 (bird(a_bird)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.21/0.46 tff(19,plain,
% 0.21/0.46 (((~![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)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(20,plain,
% 0.21/0.46 ((~![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | (~eats(Bird, Snail)))) | ((~bird(a_bird)) | (~snail(a_snail)) | (~eats(a_bird, a_snail)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(21,plain,
% 0.21/0.46 ((~![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | (~eats(Bird, Snail)))) | (~bird(a_bird)) | (~snail(a_snail)) | (~eats(a_bird, a_snail))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.21/0.46 tff(22,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[21, 18, 15, 12, 2])).
% 0.21/0.46 tff(23,plain,(~eats(a_bird, a_snail)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(24,plain,
% 0.21/0.46 (^[Snail: $i, Bird: $i] : refl(((~bird(Bird)) | (~snail(Snail)) | much_smaller(Snail, Bird)) <=> ((~bird(Bird)) | (~snail(Snail)) | much_smaller(Snail, Bird)))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(25,plain,
% 0.21/0.46 (![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | much_smaller(Snail, Bird)) <=> ![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | much_smaller(Snail, Bird))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[24])).
% 0.21/0.46 tff(26,plain,
% 0.21/0.46 (![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | much_smaller(Snail, Bird)) <=> ![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | much_smaller(Snail, Bird))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(27,plain,
% 0.21/0.46 (^[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))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(28,plain,
% 0.21/0.46 (![Snail: $i, Bird: $i] : ((much_smaller(Snail, Bird) | (~snail(Snail))) | (~bird(Bird))) <=> ![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | much_smaller(Snail, Bird))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[27])).
% 0.21/0.46 tff(29,axiom,(![Snail: $i, Bird: $i] : ((much_smaller(Snail, Bird) | (~snail(Snail))) | (~bird(Bird)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','snail_smaller_than_bird')).
% 0.21/0.46 tff(30,plain,
% 0.21/0.46 (![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | much_smaller(Snail, Bird))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.21/0.46 tff(31,plain,
% 0.21/0.46 (![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | much_smaller(Snail, Bird))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.21/0.46 tff(32,plain,(
% 0.21/0.46 ![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | much_smaller(Snail, Bird))),
% 0.21/0.46 inference(skolemize,[status(sab)],[31])).
% 0.21/0.46 tff(33,plain,
% 0.21/0.46 (![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | much_smaller(Snail, Bird))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.21/0.46 tff(34,plain,
% 0.21/0.46 (((~![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))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(35,plain,
% 0.21/0.46 ((~![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | much_smaller(Snail, Bird))) | ((~bird(a_bird)) | (~snail(a_snail)) | much_smaller(a_snail, a_bird))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(36,plain,
% 0.21/0.46 ((~![Snail: $i, Bird: $i] : ((~bird(Bird)) | (~snail(Snail)) | much_smaller(Snail, Bird))) | (~bird(a_bird)) | (~snail(a_snail)) | much_smaller(a_snail, a_bird)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.21/0.46 tff(37,plain,
% 0.21/0.46 (much_smaller(a_snail, a_bird)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[36, 18, 15, 33])).
% 0.21/0.46 tff(38,plain,
% 0.21/0.46 (^[X: $i] : refl((plant(X) | (~grain(X))) <=> (plant(X) | (~grain(X))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(39,plain,
% 0.21/0.46 (![X: $i] : (plant(X) | (~grain(X))) <=> ![X: $i] : (plant(X) | (~grain(X)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[38])).
% 0.21/0.46 tff(40,plain,
% 0.21/0.46 (![X: $i] : (plant(X) | (~grain(X))) <=> ![X: $i] : (plant(X) | (~grain(X)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(41,axiom,(![X: $i] : (plant(X) | (~grain(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','grain_is_a_plant')).
% 0.21/0.46 tff(42,plain,
% 0.21/0.46 (![X: $i] : (plant(X) | (~grain(X)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.21/0.46 tff(43,plain,(
% 0.21/0.46 ![X: $i] : (plant(X) | (~grain(X)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[42])).
% 0.21/0.46 tff(44,plain,
% 0.21/0.46 (![X: $i] : (plant(X) | (~grain(X)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.21/0.46 tff(45,plain,
% 0.21/0.46 (grain(a_grain) <=> grain(a_grain)),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(46,axiom,(grain(a_grain)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','there_is_a_grain')).
% 0.21/0.46 tff(47,plain,
% 0.21/0.46 (grain(a_grain)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.46 tff(48,plain,
% 0.21/0.46 (((~![X: $i] : (plant(X) | (~grain(X)))) | (plant(a_grain) | (~grain(a_grain)))) <=> ((~![X: $i] : (plant(X) | (~grain(X)))) | plant(a_grain) | (~grain(a_grain)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(49,plain,
% 0.21/0.46 ((~![X: $i] : (plant(X) | (~grain(X)))) | (plant(a_grain) | (~grain(a_grain)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(50,plain,
% 0.21/0.46 ((~![X: $i] : (plant(X) | (~grain(X)))) | plant(a_grain) | (~grain(a_grain))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.21/0.46 tff(51,plain,
% 0.21/0.46 (plant(a_grain)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[50, 47, 44])).
% 0.21/0.46 tff(52,plain,
% 0.21/0.46 (^[Snail: $i] : refl(((~snail(Snail)) | plant(snail_food_of(Snail))) <=> ((~snail(Snail)) | plant(snail_food_of(Snail))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(53,plain,
% 0.21/0.46 (![Snail: $i] : ((~snail(Snail)) | plant(snail_food_of(Snail))) <=> ![Snail: $i] : ((~snail(Snail)) | plant(snail_food_of(Snail)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[52])).
% 0.21/0.46 tff(54,plain,
% 0.21/0.46 (![Snail: $i] : ((~snail(Snail)) | plant(snail_food_of(Snail))) <=> ![Snail: $i] : ((~snail(Snail)) | plant(snail_food_of(Snail)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(55,plain,
% 0.21/0.46 (^[Snail: $i] : rewrite((plant(snail_food_of(Snail)) | (~snail(Snail))) <=> ((~snail(Snail)) | plant(snail_food_of(Snail))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(56,plain,
% 0.21/0.46 (![Snail: $i] : (plant(snail_food_of(Snail)) | (~snail(Snail))) <=> ![Snail: $i] : ((~snail(Snail)) | plant(snail_food_of(Snail)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[55])).
% 0.21/0.46 tff(57,axiom,(![Snail: $i] : (plant(snail_food_of(Snail)) | (~snail(Snail)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','snail_food_is_a_plant')).
% 0.21/0.46 tff(58,plain,
% 0.21/0.46 (![Snail: $i] : ((~snail(Snail)) | plant(snail_food_of(Snail)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.21/0.46 tff(59,plain,
% 0.21/0.46 (![Snail: $i] : ((~snail(Snail)) | plant(snail_food_of(Snail)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.21/0.46 tff(60,plain,(
% 0.21/0.46 ![Snail: $i] : ((~snail(Snail)) | plant(snail_food_of(Snail)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[59])).
% 0.21/0.46 tff(61,plain,
% 0.21/0.46 (![Snail: $i] : ((~snail(Snail)) | plant(snail_food_of(Snail)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.21/0.46 tff(62,plain,
% 0.21/0.46 (((~![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)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(63,plain,
% 0.21/0.46 ((~![Snail: $i] : ((~snail(Snail)) | plant(snail_food_of(Snail)))) | ((~snail(a_snail)) | plant(snail_food_of(a_snail)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(64,plain,
% 0.21/0.46 ((~![Snail: $i] : ((~snail(Snail)) | plant(snail_food_of(Snail)))) | (~snail(a_snail)) | plant(snail_food_of(a_snail))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.21/0.46 tff(65,plain,
% 0.21/0.46 (plant(snail_food_of(a_snail))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[64, 15, 61])).
% 0.21/0.46 tff(66,plain,
% 0.21/0.46 (^[X: $i] : refl((animal(X) | (~snail(X))) <=> (animal(X) | (~snail(X))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(67,plain,
% 0.21/0.46 (![X: $i] : (animal(X) | (~snail(X))) <=> ![X: $i] : (animal(X) | (~snail(X)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[66])).
% 0.21/0.46 tff(68,plain,
% 0.21/0.46 (![X: $i] : (animal(X) | (~snail(X))) <=> ![X: $i] : (animal(X) | (~snail(X)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(69,axiom,(![X: $i] : (animal(X) | (~snail(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','snail_is_an_animal')).
% 0.21/0.46 tff(70,plain,
% 0.21/0.46 (![X: $i] : (animal(X) | (~snail(X)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.21/0.46 tff(71,plain,(
% 0.21/0.46 ![X: $i] : (animal(X) | (~snail(X)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[70])).
% 0.21/0.46 tff(72,plain,
% 0.21/0.46 (![X: $i] : (animal(X) | (~snail(X)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.21/0.46 tff(73,plain,
% 0.21/0.46 (((~![X: $i] : (animal(X) | (~snail(X)))) | (animal(a_snail) | (~snail(a_snail)))) <=> ((~![X: $i] : (animal(X) | (~snail(X)))) | animal(a_snail) | (~snail(a_snail)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(74,plain,
% 0.21/0.46 ((~![X: $i] : (animal(X) | (~snail(X)))) | (animal(a_snail) | (~snail(a_snail)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(75,plain,
% 0.21/0.46 ((~![X: $i] : (animal(X) | (~snail(X)))) | animal(a_snail) | (~snail(a_snail))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.21/0.46 tff(76,plain,
% 0.21/0.46 (animal(a_snail)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[75, 72, 15])).
% 0.21/0.46 tff(77,plain,
% 0.21/0.46 (^[Snail: $i] : refl(((~snail(Snail)) | eats(Snail, snail_food_of(Snail))) <=> ((~snail(Snail)) | eats(Snail, snail_food_of(Snail))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(78,plain,
% 0.21/0.46 (![Snail: $i] : ((~snail(Snail)) | eats(Snail, snail_food_of(Snail))) <=> ![Snail: $i] : ((~snail(Snail)) | eats(Snail, snail_food_of(Snail)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[77])).
% 0.21/0.46 tff(79,plain,
% 0.21/0.46 (![Snail: $i] : ((~snail(Snail)) | eats(Snail, snail_food_of(Snail))) <=> ![Snail: $i] : ((~snail(Snail)) | eats(Snail, snail_food_of(Snail)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(80,plain,
% 0.21/0.46 (^[Snail: $i] : rewrite((eats(Snail, snail_food_of(Snail)) | (~snail(Snail))) <=> ((~snail(Snail)) | eats(Snail, snail_food_of(Snail))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(81,plain,
% 0.21/0.46 (![Snail: $i] : (eats(Snail, snail_food_of(Snail)) | (~snail(Snail))) <=> ![Snail: $i] : ((~snail(Snail)) | eats(Snail, snail_food_of(Snail)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[80])).
% 0.21/0.46 tff(82,axiom,(![Snail: $i] : (eats(Snail, snail_food_of(Snail)) | (~snail(Snail)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','snail_eats_snail_food')).
% 0.21/0.46 tff(83,plain,
% 0.21/0.46 (![Snail: $i] : ((~snail(Snail)) | eats(Snail, snail_food_of(Snail)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.21/0.46 tff(84,plain,
% 0.21/0.46 (![Snail: $i] : ((~snail(Snail)) | eats(Snail, snail_food_of(Snail)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.21/0.46 tff(85,plain,(
% 0.21/0.46 ![Snail: $i] : ((~snail(Snail)) | eats(Snail, snail_food_of(Snail)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[84])).
% 0.21/0.46 tff(86,plain,
% 0.21/0.46 (![Snail: $i] : ((~snail(Snail)) | eats(Snail, snail_food_of(Snail)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.21/0.46 tff(87,plain,
% 0.21/0.46 (((~![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)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(88,plain,
% 0.21/0.46 ((~![Snail: $i] : ((~snail(Snail)) | eats(Snail, snail_food_of(Snail)))) | ((~snail(a_snail)) | eats(a_snail, snail_food_of(a_snail)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(89,plain,
% 0.21/0.46 ((~![Snail: $i] : ((~snail(Snail)) | eats(Snail, snail_food_of(Snail)))) | (~snail(a_snail)) | eats(a_snail, snail_food_of(a_snail))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.21/0.46 tff(90,plain,
% 0.21/0.46 (eats(a_snail, snail_food_of(a_snail))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[89, 15, 86])).
% 0.21/0.46 tff(91,plain,
% 0.21/0.46 (^[X: $i] : refl((animal(X) | (~bird(X))) <=> (animal(X) | (~bird(X))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(92,plain,
% 0.21/0.46 (![X: $i] : (animal(X) | (~bird(X))) <=> ![X: $i] : (animal(X) | (~bird(X)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[91])).
% 0.21/0.46 tff(93,plain,
% 0.21/0.46 (![X: $i] : (animal(X) | (~bird(X))) <=> ![X: $i] : (animal(X) | (~bird(X)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(94,axiom,(![X: $i] : (animal(X) | (~bird(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bird_is_an_animal')).
% 0.21/0.46 tff(95,plain,
% 0.21/0.46 (![X: $i] : (animal(X) | (~bird(X)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.21/0.46 tff(96,plain,(
% 0.21/0.46 ![X: $i] : (animal(X) | (~bird(X)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[95])).
% 0.21/0.46 tff(97,plain,
% 0.21/0.46 (![X: $i] : (animal(X) | (~bird(X)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.21/0.46 tff(98,plain,
% 0.21/0.46 (((~![X: $i] : (animal(X) | (~bird(X)))) | (animal(a_bird) | (~bird(a_bird)))) <=> ((~![X: $i] : (animal(X) | (~bird(X)))) | animal(a_bird) | (~bird(a_bird)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(99,plain,
% 0.21/0.46 ((~![X: $i] : (animal(X) | (~bird(X)))) | (animal(a_bird) | (~bird(a_bird)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(100,plain,
% 0.21/0.46 ((~![X: $i] : (animal(X) | (~bird(X)))) | animal(a_bird) | (~bird(a_bird))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.21/0.46 tff(101,plain,
% 0.21/0.46 (animal(a_bird)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[100, 97, 18])).
% 0.21/0.46 tff(102,plain,
% 0.21/0.46 (^[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)))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(103,plain,
% 0.21/0.46 (![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))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[102])).
% 0.21/0.46 tff(104,plain,
% 0.21/0.46 (![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))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(105,plain,
% 0.21/0.46 (^[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))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(106,plain,
% 0.21/0.46 (![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))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[105])).
% 0.21/0.47 tff(107,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')).
% 0.21/0.47 tff(108,plain,
% 0.21/0.47 (![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))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.21/0.47 tff(109,plain,
% 0.21/0.47 (![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))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.21/0.47 tff(110,plain,(
% 0.21/0.47 ![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))),
% 0.21/0.47 inference(skolemize,[status(sab)],[109])).
% 0.21/0.47 tff(111,plain,
% 0.21/0.47 (![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))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.21/0.47 tff(112,plain,
% 0.21/0.47 (((~![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))) | (~animal(a_bird)) | (~animal(a_snail)) | eats(a_bird, a_snail) | (~plant(snail_food_of(a_snail))) | (~much_smaller(a_snail, a_bird)) | eats(a_bird, a_grain) | (~plant(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))) | (~animal(a_bird)) | (~animal(a_snail)) | eats(a_bird, a_snail) | (~plant(snail_food_of(a_snail))) | (~much_smaller(a_snail, a_bird)) | eats(a_bird, a_grain) | (~plant(a_grain)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(113,plain,
% 0.21/0.47 (((~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))) | (~animal(a_bird)) | (~animal(a_snail)) | eats(a_bird, a_snail) | (~plant(snail_food_of(a_snail))) | (~much_smaller(a_snail, a_bird)) | eats(a_bird, a_grain) | (~plant(a_grain)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(114,plain,
% 0.21/0.47 (((~![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))) | (~animal(a_bird)) | (~animal(a_snail)) | eats(a_bird, a_snail) | (~plant(snail_food_of(a_snail))) | (~much_smaller(a_snail, a_bird)) | eats(a_bird, a_grain) | (~plant(a_grain))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[113])).
% 0.21/0.47 tff(115,plain,
% 0.21/0.47 (((~![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))) | (~animal(a_bird)) | (~animal(a_snail)) | eats(a_bird, a_snail) | (~plant(snail_food_of(a_snail))) | (~much_smaller(a_snail, a_bird)) | eats(a_bird, a_grain) | (~plant(a_grain)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[114, 112])).
% 0.21/0.47 tff(116,plain,
% 0.21/0.47 ((~![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))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(117,plain,
% 0.21/0.47 ((~![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))) | (~animal(a_bird)) | (~animal(a_snail)) | eats(a_bird, a_snail) | (~plant(snail_food_of(a_snail))) | (~much_smaller(a_snail, a_bird)) | eats(a_bird, a_grain) | (~plant(a_grain))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.21/0.47 tff(118,plain,
% 0.21/0.47 (eats(a_bird, a_snail) | eats(a_bird, a_grain)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[117, 111, 101, 90, 76, 65, 51, 37])).
% 0.21/0.47 tff(119,plain,
% 0.21/0.47 (eats(a_bird, a_grain)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[118, 23])).
% 0.21/0.47 tff(120,plain,
% 0.21/0.47 (fox(a_fox) <=> fox(a_fox)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(121,axiom,(fox(a_fox)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','there_is_a_fox')).
% 0.21/0.47 tff(122,plain,
% 0.21/0.47 (fox(a_fox)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.21/0.47 tff(123,plain,
% 0.21/0.47 (^[X: $i] : refl((animal(X) | (~fox(X))) <=> (animal(X) | (~fox(X))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(124,plain,
% 0.21/0.47 (![X: $i] : (animal(X) | (~fox(X))) <=> ![X: $i] : (animal(X) | (~fox(X)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[123])).
% 0.21/0.47 tff(125,plain,
% 0.21/0.47 (![X: $i] : (animal(X) | (~fox(X))) <=> ![X: $i] : (animal(X) | (~fox(X)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(126,axiom,(![X: $i] : (animal(X) | (~fox(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fox_is_an_animal')).
% 0.21/0.47 tff(127,plain,
% 0.21/0.47 (![X: $i] : (animal(X) | (~fox(X)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.21/0.47 tff(128,plain,(
% 0.21/0.47 ![X: $i] : (animal(X) | (~fox(X)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[127])).
% 0.21/0.47 tff(129,plain,
% 0.21/0.47 (![X: $i] : (animal(X) | (~fox(X)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.21/0.47 tff(130,plain,
% 0.21/0.47 (((~![X: $i] : (animal(X) | (~fox(X)))) | (animal(a_fox) | (~fox(a_fox)))) <=> ((~![X: $i] : (animal(X) | (~fox(X)))) | animal(a_fox) | (~fox(a_fox)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(131,plain,
% 0.21/0.47 ((~![X: $i] : (animal(X) | (~fox(X)))) | (animal(a_fox) | (~fox(a_fox)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(132,plain,
% 0.21/0.47 ((~![X: $i] : (animal(X) | (~fox(X)))) | animal(a_fox) | (~fox(a_fox))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.21/0.47 tff(133,plain,
% 0.21/0.47 (animal(a_fox)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[132, 129, 122])).
% 0.21/0.47 tff(134,plain,
% 0.21/0.47 (^[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))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(135,plain,
% 0.21/0.47 (![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)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[134])).
% 0.21/0.47 tff(136,plain,
% 0.21/0.47 (![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)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(137,plain,
% 0.21/0.47 (^[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)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(138,plain,
% 0.21/0.47 (![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)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[137])).
% 0.21/0.47 tff(139,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')).
% 0.21/0.47 tff(140,plain,
% 0.21/0.47 (![Grain_eater: $i, Animal: $i, Grain: $i] : ((~grain(Grain)) | (~animal(Grain_eater)) | (~eats(Grain_eater, Grain)) | (~eats(Animal, Grain_eater)) | (~animal(Animal)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.21/0.47 tff(141,plain,
% 0.21/0.47 (![Grain_eater: $i, Animal: $i, Grain: $i] : ((~grain(Grain)) | (~animal(Grain_eater)) | (~eats(Grain_eater, Grain)) | (~eats(Animal, Grain_eater)) | (~animal(Animal)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[140, 136])).
% 0.21/0.47 tff(142,plain,(
% 0.21/0.47 ![Grain_eater: $i, Animal: $i, Grain: $i] : ((~grain(Grain)) | (~animal(Grain_eater)) | (~eats(Grain_eater, Grain)) | (~eats(Animal, Grain_eater)) | (~animal(Animal)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[141])).
% 0.21/0.47 tff(143,plain,
% 0.21/0.47 (![Grain_eater: $i, Animal: $i, Grain: $i] : ((~grain(Grain)) | (~animal(Grain_eater)) | (~eats(Grain_eater, Grain)) | (~eats(Animal, Grain_eater)) | (~animal(Animal)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[142, 135])).
% 0.21/0.47 tff(144,plain,
% 0.21/0.47 (((~![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)) | (~animal(a_bird)) | (~eats(a_bird, a_grain)) | (~eats(a_fox, a_bird)) | (~animal(a_fox)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(145,plain,
% 0.21/0.47 ((~![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)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(146,plain,
% 0.21/0.47 ((~![Grain_eater: $i, Animal: $i, Grain: $i] : ((~grain(Grain)) | (~animal(Grain_eater)) | (~eats(Grain_eater, Grain)) | (~eats(Animal, Grain_eater)) | (~animal(Animal)))) | (~grain(a_grain)) | (~animal(a_bird)) | (~eats(a_bird, a_grain)) | (~eats(a_fox, a_bird)) | (~animal(a_fox))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.21/0.47 tff(147,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[146, 47, 143, 133, 101, 119, 1])).
% 0.21/0.47 tff(148,plain,(~eats(a_fox, a_bird)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(149,plain,
% 0.21/0.47 (^[Fox: $i, Bird: $i] : refl(((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox))) <=> ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(150,plain,
% 0.21/0.47 (![Fox: $i, Bird: $i] : ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox))) <=> ![Fox: $i, Bird: $i] : ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[149])).
% 0.21/0.47 tff(151,plain,
% 0.21/0.47 (![Fox: $i, Bird: $i] : ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox))) <=> ![Fox: $i, Bird: $i] : ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(152,plain,
% 0.21/0.47 (^[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)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(153,plain,
% 0.21/0.47 (![Fox: $i, Bird: $i] : ((much_smaller(Bird, Fox) | (~bird(Bird))) | (~fox(Fox))) <=> ![Fox: $i, Bird: $i] : ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[152])).
% 0.21/0.47 tff(154,axiom,(![Fox: $i, Bird: $i] : ((much_smaller(Bird, Fox) | (~bird(Bird))) | (~fox(Fox)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bird_smaller_than_fox')).
% 0.21/0.47 tff(155,plain,
% 0.21/0.47 (![Fox: $i, Bird: $i] : ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.21/0.47 tff(156,plain,
% 0.21/0.47 (![Fox: $i, Bird: $i] : ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.21/0.47 tff(157,plain,(
% 0.21/0.47 ![Fox: $i, Bird: $i] : ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[156])).
% 0.21/0.47 tff(158,plain,
% 0.21/0.47 (![Fox: $i, Bird: $i] : ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[157, 150])).
% 0.21/0.47 tff(159,plain,
% 0.21/0.47 (((~![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))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(160,plain,
% 0.21/0.47 (((~bird(a_bird)) | much_smaller(a_bird, a_fox) | (~fox(a_fox))) <=> ((~fox(a_fox)) | (~bird(a_bird)) | much_smaller(a_bird, a_fox))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(161,plain,
% 0.21/0.47 (((~![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)))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[160])).
% 0.21/0.47 tff(162,plain,
% 0.21/0.47 (((~![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))),
% 0.21/0.47 inference(transitivity,[status(thm)],[161, 159])).
% 0.21/0.47 tff(163,plain,
% 0.21/0.47 ((~![Fox: $i, Bird: $i] : ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox)))) | ((~bird(a_bird)) | much_smaller(a_bird, a_fox) | (~fox(a_fox)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(164,plain,
% 0.21/0.47 ((~![Fox: $i, Bird: $i] : ((~bird(Bird)) | much_smaller(Bird, Fox) | (~fox(Fox)))) | (~fox(a_fox)) | (~bird(a_bird)) | much_smaller(a_bird, a_fox)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.21/0.47 tff(165,plain,
% 0.21/0.47 (much_smaller(a_bird, a_fox)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[164, 122, 18, 158])).
% 0.21/0.47 tff(166,plain,
% 0.21/0.47 (((~![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_bird)) | (~plant(a_grain)) | (~eats(a_bird, a_grain)) | (~much_smaller(a_bird, a_fox)) | eats(a_fox, a_bird) | (~animal(a_fox)) | eats(a_fox, 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_bird)) | (~plant(a_grain)) | (~eats(a_bird, a_grain)) | (~much_smaller(a_bird, a_fox)) | eats(a_fox, a_bird) | (~animal(a_fox)) | eats(a_fox, a_grain))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(167,plain,
% 0.21/0.48 (((~eats(a_bird, a_grain)) | (~much_smaller(a_bird, a_fox)) | (~plant(a_grain)) | (~animal(a_bird)) | (~plant(a_grain)) | (~animal(a_fox)) | eats(a_fox, a_bird) | eats(a_fox, a_grain)) <=> ((~animal(a_bird)) | (~plant(a_grain)) | (~eats(a_bird, a_grain)) | (~much_smaller(a_bird, a_fox)) | eats(a_fox, a_bird) | (~animal(a_fox)) | eats(a_fox, a_grain))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(168,plain,
% 0.21/0.48 (((~![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, a_grain)) | (~much_smaller(a_bird, a_fox)) | (~plant(a_grain)) | (~animal(a_bird)) | (~plant(a_grain)) | (~animal(a_fox)) | eats(a_fox, a_bird) | eats(a_fox, 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_bird)) | (~plant(a_grain)) | (~eats(a_bird, a_grain)) | (~much_smaller(a_bird, a_fox)) | eats(a_fox, a_bird) | (~animal(a_fox)) | eats(a_fox, a_grain)))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[167])).
% 0.21/0.48 tff(169,plain,
% 0.21/0.48 (((~![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, a_grain)) | (~much_smaller(a_bird, a_fox)) | (~plant(a_grain)) | (~animal(a_bird)) | (~plant(a_grain)) | (~animal(a_fox)) | eats(a_fox, a_bird) | eats(a_fox, 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_bird)) | (~plant(a_grain)) | (~eats(a_bird, a_grain)) | (~much_smaller(a_bird, a_fox)) | eats(a_fox, a_bird) | (~animal(a_fox)) | eats(a_fox, a_grain))),
% 0.21/0.48 inference(transitivity,[status(thm)],[168, 166])).
% 0.21/0.48 tff(170,plain,
% 0.21/0.48 ((~![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, a_grain)) | (~much_smaller(a_bird, a_fox)) | (~plant(a_grain)) | (~animal(a_bird)) | (~plant(a_grain)) | (~animal(a_fox)) | eats(a_fox, a_bird) | eats(a_fox, a_grain))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(171,plain,
% 0.21/0.48 ((~![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_bird)) | (~plant(a_grain)) | (~eats(a_bird, a_grain)) | (~much_smaller(a_bird, a_fox)) | eats(a_fox, a_bird) | (~animal(a_fox)) | eats(a_fox, a_grain)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.21/0.48 tff(172,plain,
% 0.21/0.48 (eats(a_fox, a_bird) | eats(a_fox, a_grain)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[171, 111, 133, 101, 51, 165, 119])).
% 0.21/0.48 tff(173,plain,
% 0.21/0.48 (eats(a_fox, a_grain)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[172, 148])).
% 0.21/0.48 tff(174,assumption,(eats(a_wolf, a_fox)), introduced(assumption)).
% 0.21/0.48 tff(175,assumption,(eats(a_fox, a_grain)), introduced(assumption)).
% 0.21/0.48 tff(176,plain,
% 0.21/0.48 (wolf(a_wolf) <=> wolf(a_wolf)),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(177,axiom,(wolf(a_wolf)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','there_is_a_wolf')).
% 0.21/0.48 tff(178,plain,
% 0.21/0.48 (wolf(a_wolf)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.21/0.48 tff(179,plain,
% 0.21/0.48 (^[X: $i] : refl((animal(X) | (~wolf(X))) <=> (animal(X) | (~wolf(X))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(180,plain,
% 0.21/0.48 (![X: $i] : (animal(X) | (~wolf(X))) <=> ![X: $i] : (animal(X) | (~wolf(X)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[179])).
% 0.21/0.48 tff(181,plain,
% 0.21/0.48 (![X: $i] : (animal(X) | (~wolf(X))) <=> ![X: $i] : (animal(X) | (~wolf(X)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(182,axiom,(![X: $i] : (animal(X) | (~wolf(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','wolf_is_an_animal')).
% 0.21/0.48 tff(183,plain,
% 0.21/0.48 (![X: $i] : (animal(X) | (~wolf(X)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.21/0.48 tff(184,plain,(
% 0.21/0.48 ![X: $i] : (animal(X) | (~wolf(X)))),
% 0.21/0.48 inference(skolemize,[status(sab)],[183])).
% 0.21/0.48 tff(185,plain,
% 0.21/0.48 (![X: $i] : (animal(X) | (~wolf(X)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[184, 180])).
% 0.21/0.48 tff(186,plain,
% 0.21/0.48 (((~![X: $i] : (animal(X) | (~wolf(X)))) | (animal(a_wolf) | (~wolf(a_wolf)))) <=> ((~![X: $i] : (animal(X) | (~wolf(X)))) | animal(a_wolf) | (~wolf(a_wolf)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(187,plain,
% 0.21/0.48 ((~![X: $i] : (animal(X) | (~wolf(X)))) | (animal(a_wolf) | (~wolf(a_wolf)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(188,plain,
% 0.21/0.48 ((~![X: $i] : (animal(X) | (~wolf(X)))) | animal(a_wolf) | (~wolf(a_wolf))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.21/0.48 tff(189,plain,
% 0.21/0.48 (animal(a_wolf)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[188, 185, 178])).
% 0.21/0.48 tff(190,plain,
% 0.21/0.48 (((~![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_grain)) | (~eats(a_wolf, a_fox)) | (~animal(a_fox)) | (~animal(a_wolf)))) <=> ((~![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_grain)) | (~eats(a_wolf, a_fox)) | (~animal(a_fox)) | (~animal(a_wolf)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(191,plain,
% 0.21/0.48 (((~grain(a_grain)) | (~animal(a_fox)) | (~eats(a_fox, a_grain)) | (~eats(a_wolf, a_fox)) | (~animal(a_wolf))) <=> ((~grain(a_grain)) | (~eats(a_fox, a_grain)) | (~eats(a_wolf, a_fox)) | (~animal(a_fox)) | (~animal(a_wolf)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(192,plain,
% 0.21/0.48 (((~![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_fox)) | (~eats(a_fox, a_grain)) | (~eats(a_wolf, a_fox)) | (~animal(a_wolf)))) <=> ((~![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_grain)) | (~eats(a_wolf, a_fox)) | (~animal(a_fox)) | (~animal(a_wolf))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[191])).
% 0.21/0.48 tff(193,plain,
% 0.21/0.48 (((~![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_fox)) | (~eats(a_fox, a_grain)) | (~eats(a_wolf, a_fox)) | (~animal(a_wolf)))) <=> ((~![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_grain)) | (~eats(a_wolf, a_fox)) | (~animal(a_fox)) | (~animal(a_wolf)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[192, 190])).
% 0.21/0.48 tff(194,plain,
% 0.21/0.48 ((~![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_fox)) | (~eats(a_fox, a_grain)) | (~eats(a_wolf, a_fox)) | (~animal(a_wolf)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(195,plain,
% 0.21/0.48 ((~![Grain_eater: $i, Animal: $i, Grain: $i] : ((~grain(Grain)) | (~animal(Grain_eater)) | (~eats(Grain_eater, Grain)) | (~eats(Animal, Grain_eater)) | (~animal(Animal)))) | (~grain(a_grain)) | (~eats(a_fox, a_grain)) | (~eats(a_wolf, a_fox)) | (~animal(a_fox)) | (~animal(a_wolf))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.21/0.48 tff(196,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[195, 47, 143, 189, 133, 175, 174])).
% 0.21/0.48 tff(197,plain,((~eats(a_wolf, a_fox)) | (~eats(a_fox, a_grain))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(198,plain,
% 0.21/0.48 (~eats(a_wolf, a_fox)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[197, 173])).
% 0.21/0.48 tff(199,assumption,(eats(a_wolf, a_grain)), introduced(assumption)).
% 0.21/0.48 tff(200,plain,
% 0.21/0.48 (^[Wolf: $i, Grain: $i] : refl(((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf))) <=> ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(201,plain,
% 0.21/0.48 (![Wolf: $i, Grain: $i] : ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf))) <=> ![Wolf: $i, Grain: $i] : ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[200])).
% 0.21/0.48 tff(202,plain,
% 0.21/0.48 (![Wolf: $i, Grain: $i] : ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf))) <=> ![Wolf: $i, Grain: $i] : ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(203,plain,
% 0.21/0.48 (^[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)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(204,plain,
% 0.21/0.48 (![Wolf: $i, Grain: $i] : (((~wolf(Wolf)) | (~grain(Grain))) | (~eats(Wolf, Grain))) <=> ![Wolf: $i, Grain: $i] : ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[203])).
% 0.21/0.48 tff(205,axiom,(![Wolf: $i, Grain: $i] : (((~wolf(Wolf)) | (~grain(Grain))) | (~eats(Wolf, Grain)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','wolf_dont_eat_grain')).
% 0.21/0.48 tff(206,plain,
% 0.21/0.48 (![Wolf: $i, Grain: $i] : ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.21/0.48 tff(207,plain,
% 0.21/0.48 (![Wolf: $i, Grain: $i] : ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[206, 202])).
% 0.21/0.48 tff(208,plain,(
% 0.21/0.48 ![Wolf: $i, Grain: $i] : ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf)))),
% 0.21/0.48 inference(skolemize,[status(sab)],[207])).
% 0.21/0.48 tff(209,plain,
% 0.21/0.48 (![Wolf: $i, Grain: $i] : ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[208, 201])).
% 0.21/0.48 tff(210,plain,
% 0.21/0.48 (((~![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)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(211,plain,
% 0.21/0.48 (((~grain(a_grain)) | (~eats(a_wolf, a_grain)) | (~wolf(a_wolf))) <=> ((~wolf(a_wolf)) | (~grain(a_grain)) | (~eats(a_wolf, a_grain)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(212,plain,
% 0.21/0.48 (((~![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))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[211])).
% 0.21/0.48 tff(213,plain,
% 0.21/0.48 (((~![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)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[212, 210])).
% 0.21/0.48 tff(214,plain,
% 0.21/0.48 ((~![Wolf: $i, Grain: $i] : ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf)))) | ((~grain(a_grain)) | (~eats(a_wolf, a_grain)) | (~wolf(a_wolf)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(215,plain,
% 0.21/0.48 ((~![Wolf: $i, Grain: $i] : ((~grain(Grain)) | (~eats(Wolf, Grain)) | (~wolf(Wolf)))) | (~wolf(a_wolf)) | (~grain(a_grain)) | (~eats(a_wolf, a_grain))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.21/0.48 tff(216,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[215, 178, 47, 209, 199])).
% 0.21/0.48 tff(217,plain,(~eats(a_wolf, a_grain)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(218,plain,
% 0.21/0.48 (^[Fox: $i, Wolf: $i] : refl(((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox))) <=> ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(219,plain,
% 0.21/0.48 (![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox))) <=> ![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[218])).
% 0.21/0.48 tff(220,plain,
% 0.21/0.48 (![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox))) <=> ![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(221,plain,
% 0.21/0.48 (^[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)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(222,plain,
% 0.21/0.48 (![Fox: $i, Wolf: $i] : ((much_smaller(Fox, Wolf) | (~fox(Fox))) | (~wolf(Wolf))) <=> ![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[221])).
% 0.21/0.48 tff(223,axiom,(![Fox: $i, Wolf: $i] : ((much_smaller(Fox, Wolf) | (~fox(Fox))) | (~wolf(Wolf)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fox_smaller_than_wolf')).
% 0.21/0.48 tff(224,plain,
% 0.21/0.48 (![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.21/0.48 tff(225,plain,
% 0.21/0.48 (![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[224, 220])).
% 0.21/0.48 tff(226,plain,(
% 0.21/0.48 ![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox)))),
% 0.21/0.48 inference(skolemize,[status(sab)],[225])).
% 0.21/0.48 tff(227,plain,
% 0.21/0.48 (![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[226, 219])).
% 0.21/0.48 tff(228,plain,
% 0.21/0.48 (((~![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))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(229,plain,
% 0.21/0.48 (((~wolf(a_wolf)) | much_smaller(a_fox, a_wolf) | (~fox(a_fox))) <=> ((~wolf(a_wolf)) | (~fox(a_fox)) | much_smaller(a_fox, a_wolf))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(230,plain,
% 0.21/0.48 (((~![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)))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[229])).
% 0.21/0.48 tff(231,plain,
% 0.21/0.48 (((~![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))),
% 0.21/0.48 inference(transitivity,[status(thm)],[230, 228])).
% 0.21/0.48 tff(232,plain,
% 0.21/0.48 ((~![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox)))) | ((~wolf(a_wolf)) | much_smaller(a_fox, a_wolf) | (~fox(a_fox)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(233,plain,
% 0.21/0.48 ((~![Fox: $i, Wolf: $i] : ((~wolf(Wolf)) | much_smaller(Fox, Wolf) | (~fox(Fox)))) | (~wolf(a_wolf)) | (~fox(a_fox)) | much_smaller(a_fox, a_wolf)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.21/0.48 tff(234,plain,
% 0.21/0.48 (much_smaller(a_fox, a_wolf)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[233, 178, 122, 227])).
% 0.21/0.48 tff(235,plain,
% 0.21/0.48 (((~![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_grain)) | (~plant(a_grain)) | (~much_smaller(a_fox, a_wolf)) | (~animal(a_fox)) | eats(a_wolf, a_fox) | eats(a_wolf, a_grain) | (~animal(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))) | (~eats(a_fox, a_grain)) | (~plant(a_grain)) | (~much_smaller(a_fox, a_wolf)) | (~animal(a_fox)) | eats(a_wolf, a_fox) | eats(a_wolf, a_grain) | (~animal(a_wolf)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(236,plain,
% 0.21/0.48 (((~eats(a_fox, a_grain)) | (~much_smaller(a_fox, a_wolf)) | (~plant(a_grain)) | (~animal(a_fox)) | (~plant(a_grain)) | (~animal(a_wolf)) | eats(a_wolf, a_fox) | eats(a_wolf, a_grain)) <=> ((~eats(a_fox, a_grain)) | (~plant(a_grain)) | (~much_smaller(a_fox, a_wolf)) | (~animal(a_fox)) | eats(a_wolf, a_fox) | eats(a_wolf, a_grain) | (~animal(a_wolf)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(237,plain,
% 0.21/0.48 (((~![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_grain)) | (~much_smaller(a_fox, a_wolf)) | (~plant(a_grain)) | (~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))) | ((~eats(a_fox, a_grain)) | (~plant(a_grain)) | (~much_smaller(a_fox, a_wolf)) | (~animal(a_fox)) | eats(a_wolf, a_fox) | eats(a_wolf, a_grain) | (~animal(a_wolf))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[236])).
% 0.21/0.48 tff(238,plain,
% 0.21/0.48 (((~![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_grain)) | (~much_smaller(a_fox, a_wolf)) | (~plant(a_grain)) | (~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))) | (~eats(a_fox, a_grain)) | (~plant(a_grain)) | (~much_smaller(a_fox, a_wolf)) | (~animal(a_fox)) | eats(a_wolf, a_fox) | eats(a_wolf, a_grain) | (~animal(a_wolf)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[237, 235])).
% 0.21/0.49 tff(239,plain,
% 0.21/0.49 ((~![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_fox, a_grain)) | (~much_smaller(a_fox, a_wolf)) | (~plant(a_grain)) | (~animal(a_fox)) | (~plant(a_grain)) | (~animal(a_wolf)) | eats(a_wolf, a_fox) | eats(a_wolf, a_grain))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(240,plain,
% 0.21/0.49 ((~![Other_plant: $i, Small_animal: $i, Plant: $i, Animal: $i] : ((~eats(Small_animal, Other_plant)) | (~much_smaller(Small_animal, Animal)) | (~plant(Other_plant)) | (~animal(Small_animal)) | (~plant(Plant)) | (~animal(Animal)) | eats(Animal, Small_animal) | eats(Animal, Plant))) | (~eats(a_fox, a_grain)) | (~plant(a_grain)) | (~much_smaller(a_fox, a_wolf)) | (~animal(a_fox)) | eats(a_wolf, a_fox) | eats(a_wolf, a_grain) | (~animal(a_wolf))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.21/0.49 tff(241,plain,
% 0.21/0.49 ((~eats(a_fox, a_grain)) | eats(a_wolf, a_fox) | eats(a_wolf, a_grain)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[240, 111, 189, 133, 51, 234])).
% 0.21/0.49 tff(242,plain,
% 0.21/0.49 ((~eats(a_fox, a_grain)) | eats(a_wolf, a_fox)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[241, 217])).
% 0.21/0.49 tff(243,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[242, 198, 173])).
% 0.21/0.49 % SZS output end Proof
%------------------------------------------------------------------------------