TSTP Solution File: PUZ031+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PUZ031+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 14:10:59 EDT 2022
% Result : Theorem 0.12s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : PUZ031+2 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 18:21:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(eats_type, type, (
% 0.12/0.40 eats: ( $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_A_4_type, type, (
% 0.12/0.40 tptp_fun_A_4: $i)).
% 0.12/0.40 tff(tptp_fun_A_2_type, type, (
% 0.12/0.40 tptp_fun_A_2: $i)).
% 0.12/0.40 tff(plant_type, type, (
% 0.12/0.40 plant: $i > $o)).
% 0.12/0.40 tff(tptp_fun_Y_6_type, type, (
% 0.12/0.40 tptp_fun_Y_6: $i > $i)).
% 0.12/0.40 tff(snail_type, type, (
% 0.12/0.40 snail: $i > $o)).
% 0.12/0.40 tff(much_smaller_type, type, (
% 0.12/0.40 much_smaller: ( $i * $i ) > $o)).
% 0.12/0.40 tff(bird_type, type, (
% 0.12/0.40 bird: $i > $o)).
% 0.12/0.40 tff(animal_type, type, (
% 0.12/0.40 animal: $i > $o)).
% 0.12/0.40 tff(tptp_fun_A_1_type, type, (
% 0.12/0.40 tptp_fun_A_1: $i)).
% 0.12/0.40 tff(tptp_fun_A_3_type, type, (
% 0.12/0.40 tptp_fun_A_3: $i)).
% 0.12/0.40 tff(tptp_fun_A_0_type, type, (
% 0.12/0.40 tptp_fun_A_0: $i)).
% 0.12/0.40 tff(tptp_fun_A_5_type, type, (
% 0.12/0.40 tptp_fun_A_5: $i)).
% 0.12/0.40 tff(wolf_type, type, (
% 0.12/0.40 wolf: $i > $o)).
% 0.12/0.40 tff(grain_type, type, (
% 0.12/0.40 grain: $i > $o)).
% 0.12/0.40 tff(fox_type, type, (
% 0.12/0.40 fox: $i > $o)).
% 0.12/0.40 tff(caterpillar_type, type, (
% 0.12/0.40 caterpillar: $i > $o)).
% 0.12/0.40 tff(1,assumption,(![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z)))), introduced(assumption)).
% 0.12/0.40 tff(2,plain,
% 0.12/0.40 (^[X: $i] : refl(((~snail(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X)))))) <=> ((~snail(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X)))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(3,plain,
% 0.12/0.40 (![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X)))))) <=> ![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.40 tff(4,plain,
% 0.12/0.40 (^[X: $i] : rewrite(((~snail(X)) | (plant(tptp_fun_Y_6(X)) & eats(X, tptp_fun_Y_6(X)))) <=> ((~snail(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X)))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(5,plain,
% 0.12/0.40 (![X: $i] : ((~snail(X)) | (plant(tptp_fun_Y_6(X)) & eats(X, tptp_fun_Y_6(X)))) <=> ![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[4])).
% 0.12/0.40 tff(6,plain,
% 0.12/0.40 (![X: $i] : ((~snail(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y))) <=> ![X: $i] : ((~snail(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(7,plain,
% 0.12/0.40 (^[X: $i] : rewrite((snail(X) => ?[Y: $i] : (plant(Y) & eats(X, Y))) <=> ((~snail(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(8,plain,
% 0.12/0.40 (![X: $i] : (snail(X) => ?[Y: $i] : (plant(Y) & eats(X, Y))) <=> ![X: $i] : ((~snail(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[7])).
% 0.12/0.40 tff(9,axiom,(![X: $i] : (snail(X) => ?[Y: $i] : (plant(Y) & eats(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_14a')).
% 0.12/0.40 tff(10,plain,
% 0.12/0.40 (![X: $i] : ((~snail(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.12/0.40 tff(11,plain,
% 0.12/0.40 (![X: $i] : ((~snail(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.12/0.40 tff(12,plain,(
% 0.12/0.40 ![X: $i] : ((~snail(X)) | (plant(tptp_fun_Y_6(X)) & eats(X, tptp_fun_Y_6(X))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[11])).
% 0.12/0.40 tff(13,plain,
% 0.12/0.40 (![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.12/0.40 tff(14,plain,
% 0.12/0.40 (![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[13, 3])).
% 0.12/0.40 tff(15,plain,
% 0.12/0.40 (?[A: $i] : snail(A) <=> ?[A: $i] : snail(A)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(16,axiom,(?[A: $i] : snail(A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','snail_type')).
% 0.12/0.40 tff(17,plain,
% 0.12/0.40 (?[A: $i] : snail(A)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.12/0.40 tff(18,plain,(
% 0.12/0.40 snail(A!4)),
% 0.12/0.40 inference(skolemize,[status(sab)],[17])).
% 0.12/0.40 tff(19,plain,
% 0.12/0.40 (((~![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | ((~snail(A!4)) | (~((~plant(tptp_fun_Y_6(A!4))) | (~eats(A!4, tptp_fun_Y_6(A!4))))))) <=> ((~![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | (~snail(A!4)) | (~((~plant(tptp_fun_Y_6(A!4))) | (~eats(A!4, tptp_fun_Y_6(A!4))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(20,plain,
% 0.12/0.40 ((~![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | ((~snail(A!4)) | (~((~plant(tptp_fun_Y_6(A!4))) | (~eats(A!4, tptp_fun_Y_6(A!4))))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(21,plain,
% 0.12/0.40 ((~![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | (~snail(A!4)) | (~((~plant(tptp_fun_Y_6(A!4))) | (~eats(A!4, tptp_fun_Y_6(A!4)))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.12/0.40 tff(22,plain,
% 0.12/0.40 (~((~plant(tptp_fun_Y_6(A!4))) | (~eats(A!4, tptp_fun_Y_6(A!4))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[21, 18, 14])).
% 0.12/0.40 tff(23,plain,
% 0.12/0.40 (((~plant(tptp_fun_Y_6(A!4))) | (~eats(A!4, tptp_fun_Y_6(A!4)))) | eats(A!4, tptp_fun_Y_6(A!4))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(24,plain,
% 0.12/0.40 (eats(A!4, tptp_fun_Y_6(A!4))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.12/0.40 tff(25,plain,
% 0.12/0.40 (((~plant(tptp_fun_Y_6(A!4))) | (~eats(A!4, tptp_fun_Y_6(A!4)))) | plant(tptp_fun_Y_6(A!4))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(26,plain,
% 0.12/0.40 (plant(tptp_fun_Y_6(A!4))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[25, 22])).
% 0.12/0.40 tff(27,plain,
% 0.12/0.40 (((~![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z)))) | ((~plant(tptp_fun_Y_6(A!4))) | (~eats(A!4, tptp_fun_Y_6(A!4))))) <=> ((~![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z)))) | (~plant(tptp_fun_Y_6(A!4))) | (~eats(A!4, tptp_fun_Y_6(A!4))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(28,plain,
% 0.12/0.40 ((~![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z)))) | ((~plant(tptp_fun_Y_6(A!4))) | (~eats(A!4, tptp_fun_Y_6(A!4))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(29,plain,
% 0.12/0.40 ((~![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z)))) | (~plant(tptp_fun_Y_6(A!4))) | (~eats(A!4, tptp_fun_Y_6(A!4)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.12/0.40 tff(30,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[29, 26, 24, 1])).
% 0.12/0.40 tff(31,plain,(~![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z)))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.40 tff(32,assumption,(~much_smaller(A!4, A!2)), introduced(assumption)).
% 0.12/0.40 tff(33,plain,
% 0.12/0.40 (^[Y: $i, X: $i] : refl((much_smaller(X, Y) | (~snail(X)) | (~bird(Y))) <=> (much_smaller(X, Y) | (~snail(X)) | (~bird(Y))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(34,plain,
% 0.12/0.40 (![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y))) <=> ![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[33])).
% 0.12/0.40 tff(35,plain,
% 0.12/0.40 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((bird(Y) & snail(X)) <=> (~((~bird(Y)) | (~snail(X))))), ((~(bird(Y) & snail(X))) <=> (~(~((~bird(Y)) | (~snail(X))))))), rewrite((~(~((~bird(Y)) | (~snail(X))))) <=> ((~bird(Y)) | (~snail(X)))), ((~(bird(Y) & snail(X))) <=> ((~bird(Y)) | (~snail(X))))), (((~(bird(Y) & snail(X))) | much_smaller(X, Y)) <=> (((~bird(Y)) | (~snail(X))) | much_smaller(X, Y)))), rewrite((((~bird(Y)) | (~snail(X))) | much_smaller(X, Y)) <=> (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))), (((~(bird(Y) & snail(X))) | much_smaller(X, Y)) <=> (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(36,plain,
% 0.12/0.40 (![Y: $i, X: $i] : ((~(bird(Y) & snail(X))) | much_smaller(X, Y)) <=> ![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[35])).
% 0.12/0.40 tff(37,plain,
% 0.12/0.40 (![Y: $i, X: $i] : ((~(bird(Y) & snail(X))) | much_smaller(X, Y)) <=> ![Y: $i, X: $i] : ((~(bird(Y) & snail(X))) | much_smaller(X, Y))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(38,plain,
% 0.12/0.40 (^[Y: $i, X: $i] : rewrite(((bird(Y) & snail(X)) => much_smaller(X, Y)) <=> ((~(bird(Y) & snail(X))) | much_smaller(X, Y)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(39,plain,
% 0.12/0.40 (![Y: $i, X: $i] : ((bird(Y) & snail(X)) => much_smaller(X, Y)) <=> ![Y: $i, X: $i] : ((~(bird(Y) & snail(X))) | much_smaller(X, Y))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[38])).
% 0.12/0.40 tff(40,axiom,(![Y: $i, X: $i] : ((bird(Y) & snail(X)) => much_smaller(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_8')).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 (![Y: $i, X: $i] : ((~(bird(Y) & snail(X))) | much_smaller(X, Y))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 (![Y: $i, X: $i] : ((~(bird(Y) & snail(X))) | much_smaller(X, Y))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.19/0.40 tff(43,plain,(
% 0.19/0.40 ![Y: $i, X: $i] : ((~(bird(Y) & snail(X))) | much_smaller(X, Y))),
% 0.19/0.40 inference(skolemize,[status(sab)],[42])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 (![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 (![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[44, 34])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (?[A: $i] : bird(A) <=> ?[A: $i] : bird(A)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(47,axiom,(?[A: $i] : bird(A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bird_type')).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (?[A: $i] : bird(A)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.19/0.40 tff(49,plain,(
% 0.19/0.40 bird(A!2)),
% 0.19/0.40 inference(skolemize,[status(sab)],[48])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | ((~bird(A!2)) | (~snail(A!4)) | much_smaller(A!4, A!2))) <=> ((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | (~bird(A!2)) | (~snail(A!4)) | much_smaller(A!4, A!2))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 ((much_smaller(A!4, A!2) | (~snail(A!4)) | (~bird(A!2))) <=> ((~bird(A!2)) | (~snail(A!4)) | much_smaller(A!4, A!2))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | (much_smaller(A!4, A!2) | (~snail(A!4)) | (~bird(A!2)))) <=> ((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | ((~bird(A!2)) | (~snail(A!4)) | much_smaller(A!4, A!2)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[51])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | (much_smaller(A!4, A!2) | (~snail(A!4)) | (~bird(A!2)))) <=> ((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | (~bird(A!2)) | (~snail(A!4)) | much_smaller(A!4, A!2))),
% 0.19/0.40 inference(transitivity,[status(thm)],[52, 50])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 ((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | (much_smaller(A!4, A!2) | (~snail(A!4)) | (~bird(A!2)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 ((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | (~bird(A!2)) | (~snail(A!4)) | much_smaller(A!4, A!2)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[55, 49, 18, 45, 32])).
% 0.19/0.40 tff(57,plain,(much_smaller(A!4, A!2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(58,assumption,(eats(A!0, A!5)), introduced(assumption)).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 (^[X: $i, Y: $i] : refl(((~eats(X, Y)) | (~grain(Y)) | (~wolf(X))) <=> ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[59])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((wolf(X) & grain(Y)) <=> (~((~grain(Y)) | (~wolf(X))))), ((~(wolf(X) & grain(Y))) <=> (~(~((~grain(Y)) | (~wolf(X))))))), rewrite((~(~((~grain(Y)) | (~wolf(X))))) <=> ((~grain(Y)) | (~wolf(X)))), ((~(wolf(X) & grain(Y))) <=> ((~grain(Y)) | (~wolf(X))))), (((~eats(X, Y)) | (~(wolf(X) & grain(Y)))) <=> ((~eats(X, Y)) | ((~grain(Y)) | (~wolf(X)))))), rewrite(((~eats(X, Y)) | ((~grain(Y)) | (~wolf(X)))) <=> ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))), (((~eats(X, Y)) | (~(wolf(X) & grain(Y)))) <=> ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & grain(Y)))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & grain(Y)))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & grain(Y))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (^[X: $i, Y: $i] : rewrite(((wolf(X) & grain(Y)) => (~eats(X, Y))) <=> ((~eats(X, Y)) | (~(wolf(X) & grain(Y)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((wolf(X) & grain(Y)) => (~eats(X, Y))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & grain(Y))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[64])).
% 0.19/0.41 tff(66,axiom,(![X: $i, Y: $i] : ((wolf(X) & grain(Y)) => (~eats(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_11a')).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & grain(Y))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & grain(Y))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.19/0.41 tff(69,plain,(
% 0.19/0.41 ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & grain(Y))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[68])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[70, 60])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 (?[A: $i] : grain(A) <=> ?[A: $i] : grain(A)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(73,axiom,(?[A: $i] : grain(A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','grain_type')).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (?[A: $i] : grain(A)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.19/0.41 tff(75,plain,(
% 0.19/0.41 grain(A!5)),
% 0.19/0.41 inference(skolemize,[status(sab)],[74])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 (?[A: $i] : wolf(A) <=> ?[A: $i] : wolf(A)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(77,axiom,(?[A: $i] : wolf(A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','wolf_type')).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 (?[A: $i] : wolf(A)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.19/0.41 tff(79,plain,(
% 0.19/0.41 wolf(A!0)),
% 0.19/0.41 inference(skolemize,[status(sab)],[78])).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | ((~wolf(A!0)) | (~grain(A!5)) | (~eats(A!0, A!5)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | (~wolf(A!0)) | (~grain(A!5)) | (~eats(A!0, A!5)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 (((~eats(A!0, A!5)) | (~grain(A!5)) | (~wolf(A!0))) <=> ((~wolf(A!0)) | (~grain(A!5)) | (~eats(A!0, A!5)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | ((~eats(A!0, A!5)) | (~grain(A!5)) | (~wolf(A!0)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | ((~wolf(A!0)) | (~grain(A!5)) | (~eats(A!0, A!5))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[81])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | ((~eats(A!0, A!5)) | (~grain(A!5)) | (~wolf(A!0)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | (~wolf(A!0)) | (~grain(A!5)) | (~eats(A!0, A!5)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[82, 80])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | ((~eats(A!0, A!5)) | (~grain(A!5)) | (~wolf(A!0)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | (~wolf(A!0)) | (~grain(A!5)) | (~eats(A!0, A!5))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[85, 79, 75, 71, 58])).
% 0.19/0.41 tff(87,plain,(~eats(A!0, A!5)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(88,assumption,(![Y: $i] : ((~plant(Y)) | eats(A!0, Y))), introduced(assumption)).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 (^[X: $i] : refl((plant(X) | (~grain(X))) <=> (plant(X) | (~grain(X))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 (![X: $i] : (plant(X) | (~grain(X))) <=> ![X: $i] : (plant(X) | (~grain(X)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[89])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 (![X: $i] : (plant(X) | (~grain(X))) <=> ![X: $i] : (plant(X) | (~grain(X)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 (^[X: $i] : rewrite((grain(X) => plant(X)) <=> (plant(X) | (~grain(X))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 (![X: $i] : (grain(X) => plant(X)) <=> ![X: $i] : (plant(X) | (~grain(X)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[92])).
% 0.19/0.41 tff(94,axiom,(![X: $i] : (grain(X) => plant(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_6_2')).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 (![X: $i] : (plant(X) | (~grain(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 (![X: $i] : (plant(X) | (~grain(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.19/0.41 tff(97,plain,(
% 0.19/0.41 ![X: $i] : (plant(X) | (~grain(X)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[96])).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 (![X: $i] : (plant(X) | (~grain(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 (((~![X: $i] : (plant(X) | (~grain(X)))) | (plant(A!5) | (~grain(A!5)))) <=> ((~![X: $i] : (plant(X) | (~grain(X)))) | plant(A!5) | (~grain(A!5)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 ((~![X: $i] : (plant(X) | (~grain(X)))) | (plant(A!5) | (~grain(A!5)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(101,plain,
% 0.19/0.41 ((~![X: $i] : (plant(X) | (~grain(X)))) | plant(A!5) | (~grain(A!5))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 (plant(A!5)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[101, 75, 98])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 (((~![Y: $i] : ((~plant(Y)) | eats(A!0, Y))) | ((~plant(A!5)) | eats(A!0, A!5))) <=> ((~![Y: $i] : ((~plant(Y)) | eats(A!0, Y))) | (~plant(A!5)) | eats(A!0, A!5))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 ((~![Y: $i] : ((~plant(Y)) | eats(A!0, Y))) | ((~plant(A!5)) | eats(A!0, A!5))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(105,plain,
% 0.19/0.41 ((~![Y: $i] : ((~plant(Y)) | eats(A!0, Y))) | (~plant(A!5)) | eats(A!0, A!5)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[105, 102, 88, 87])).
% 0.19/0.41 tff(107,plain,(~![Y: $i] : ((~plant(Y)) | eats(A!0, Y))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 (^[X: $i] : refl((animal(X) | (~wolf(X))) <=> (animal(X) | (~wolf(X))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 (![X: $i] : (animal(X) | (~wolf(X))) <=> ![X: $i] : (animal(X) | (~wolf(X)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[108])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 (![X: $i] : (animal(X) | (~wolf(X))) <=> ![X: $i] : (animal(X) | (~wolf(X)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 (^[X: $i] : rewrite((wolf(X) => animal(X)) <=> (animal(X) | (~wolf(X))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(112,plain,
% 0.19/0.41 (![X: $i] : (wolf(X) => animal(X)) <=> ![X: $i] : (animal(X) | (~wolf(X)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[111])).
% 0.19/0.41 tff(113,axiom,(![X: $i] : (wolf(X) => animal(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_1_1')).
% 0.19/0.41 tff(114,plain,
% 0.19/0.41 (![X: $i] : (animal(X) | (~wolf(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 (![X: $i] : (animal(X) | (~wolf(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.19/0.41 tff(116,plain,(
% 0.19/0.41 ![X: $i] : (animal(X) | (~wolf(X)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[115])).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 (![X: $i] : (animal(X) | (~wolf(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[116, 109])).
% 0.19/0.41 tff(118,plain,
% 0.19/0.41 (((~![X: $i] : (animal(X) | (~wolf(X)))) | (animal(A!0) | (~wolf(A!0)))) <=> ((~![X: $i] : (animal(X) | (~wolf(X)))) | animal(A!0) | (~wolf(A!0)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(119,plain,
% 0.19/0.41 ((~![X: $i] : (animal(X) | (~wolf(X)))) | (animal(A!0) | (~wolf(A!0)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(120,plain,
% 0.19/0.41 ((~![X: $i] : (animal(X) | (~wolf(X)))) | animal(A!0) | (~wolf(A!0))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.19/0.41 tff(121,plain,
% 0.19/0.41 (animal(A!0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[120, 79, 117])).
% 0.19/0.41 tff(122,plain,
% 0.19/0.41 (^[X: $i] : rewrite((![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(123,plain,
% 0.19/0.41 (![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> ![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[122])).
% 0.19/0.41 tff(124,plain,
% 0.19/0.41 (^[X: $i] : refl((![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(125,plain,
% 0.19/0.41 (![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> ![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[124])).
% 0.19/0.41 tff(126,plain,
% 0.19/0.41 (^[X: $i] : rewrite((![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(127,plain,
% 0.19/0.41 (![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> ![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[126])).
% 0.19/0.41 tff(128,plain,
% 0.19/0.41 (![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> ![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[127, 125])).
% 0.19/0.41 tff(129,plain,
% 0.19/0.41 (^[X: $i] : trans(monotonicity(quant_intro(proof_bind(^[Y1: $i] : trans(monotonicity(quant_intro(proof_bind(^[Z: $i] : trans(monotonicity(rewrite((plant(Z) & eats(Y1, Z)) <=> (~((~plant(Z)) | (~eats(Y1, Z))))), ((~(plant(Z) & eats(Y1, Z))) <=> (~(~((~plant(Z)) | (~eats(Y1, Z))))))), rewrite((~(~((~plant(Z)) | (~eats(Y1, Z))))) <=> ((~plant(Z)) | (~eats(Y1, Z)))), ((~(plant(Z) & eats(Y1, Z))) <=> ((~plant(Z)) | (~eats(Y1, Z)))))), (![Z: $i] : (~(plant(Z) & eats(Y1, Z))) <=> ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))), ((eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))) <=> (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))), rewrite((eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))) <=> (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))), ((eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))) <=> (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))))), (![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))) <=> ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))), ((![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z))))) <=> (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))))), rewrite((![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))), ((![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z))))) <=> (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(130,plain,
% 0.19/0.41 (![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z))))) <=> ![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[129])).
% 0.19/0.41 tff(131,plain,
% 0.19/0.41 (^[X: $i] : trans(monotonicity(quant_intro(proof_bind(^[Y1: $i] : trans(monotonicity(rewrite(((~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))) <=> ((~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z))))), ((((~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))) | eats(X, Y1)) <=> (((~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))) | eats(X, Y1)))), rewrite((((~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))) | eats(X, Y1)) <=> (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z))))), ((((~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))) | eats(X, Y1)) <=> (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z))))))), (![Y1: $i] : (((~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))) | eats(X, Y1)) <=> ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))))), ((![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (((~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))) | eats(X, Y1))) <=> (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z))))))), rewrite((![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z))))) <=> (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))))), ((![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (((~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))) | eats(X, Y1))) <=> (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(132,plain,
% 0.19/0.41 (![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (((~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))) | eats(X, Y1))) <=> ![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[131])).
% 0.19/0.41 tff(133,plain,
% 0.19/0.41 (![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : ((~(animal(Y1) & much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z)))) | eats(X, Y1))) <=> ![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : ((~(animal(Y1) & much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z)))) | eats(X, Y1)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(134,plain,
% 0.19/0.41 (^[X: $i] : trans(monotonicity(rewrite((![Y: $i] : (plant(Y) => eats(X, Y)) | ![Y1: $i] : (((animal(Y1) & much_smaller(Y1, X)) & ?[Z: $i] : (plant(Z) & eats(Y1, Z))) => eats(X, Y1))) <=> (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : ((~(animal(Y1) & much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z)))) | eats(X, Y1)))), ((animal(X) => (![Y: $i] : (plant(Y) => eats(X, Y)) | ![Y1: $i] : (((animal(Y1) & much_smaller(Y1, X)) & ?[Z: $i] : (plant(Z) & eats(Y1, Z))) => eats(X, Y1)))) <=> (animal(X) => (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : ((~(animal(Y1) & much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z)))) | eats(X, Y1)))))), rewrite((animal(X) => (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : ((~(animal(Y1) & much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z)))) | eats(X, Y1)))) <=> (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : ((~(animal(Y1) & much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z)))) | eats(X, Y1)))), ((animal(X) => (![Y: $i] : (plant(Y) => eats(X, Y)) | ![Y1: $i] : (((animal(Y1) & much_smaller(Y1, X)) & ?[Z: $i] : (plant(Z) & eats(Y1, Z))) => eats(X, Y1)))) <=> (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : ((~(animal(Y1) & much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z)))) | eats(X, Y1)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(135,plain,
% 0.19/0.41 (![X: $i] : (animal(X) => (![Y: $i] : (plant(Y) => eats(X, Y)) | ![Y1: $i] : (((animal(Y1) & much_smaller(Y1, X)) & ?[Z: $i] : (plant(Z) & eats(Y1, Z))) => eats(X, Y1)))) <=> ![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : ((~(animal(Y1) & much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z)))) | eats(X, Y1)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[134])).
% 0.19/0.41 tff(136,axiom,(![X: $i] : (animal(X) => (![Y: $i] : (plant(Y) => eats(X, Y)) | ![Y1: $i] : (((animal(Y1) & much_smaller(Y1, X)) & ?[Z: $i] : (plant(Z) & eats(Y1, Z))) => eats(X, Y1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_7')).
% 0.19/0.41 tff(137,plain,
% 0.19/0.41 (![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : ((~(animal(Y1) & much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z)))) | eats(X, Y1)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.19/0.41 tff(138,plain,
% 0.19/0.41 (![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : ((~(animal(Y1) & much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z)))) | eats(X, Y1)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.19/0.41 tff(139,plain,(
% 0.19/0.41 ![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (((~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))) | eats(X, Y1)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[138])).
% 0.19/0.41 tff(140,plain,
% 0.19/0.41 (![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[139, 132])).
% 0.19/0.41 tff(141,plain,
% 0.19/0.41 (![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[140, 130])).
% 0.19/0.42 tff(142,plain,
% 0.19/0.42 (![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[141, 128])).
% 0.19/0.42 tff(143,plain,
% 0.19/0.42 (![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[142, 123])).
% 0.19/0.42 tff(144,plain,
% 0.19/0.42 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!0)) | ![Y: $i] : ((~plant(Y)) | eats(A!0, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(A!0)) | ![Y: $i] : ((~plant(Y)) | eats(A!0, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(145,plain,
% 0.19/0.42 (((~animal(A!0)) | ![Y: $i] : ((~plant(Y)) | eats(A!0, Y)) | ![Y1: $i] : (eats(A!0, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!0)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> ((~animal(A!0)) | ![Y: $i] : ((~plant(Y)) | eats(A!0, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(146,plain,
% 0.19/0.42 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!0)) | ![Y: $i] : ((~plant(Y)) | eats(A!0, Y)) | ![Y1: $i] : (eats(A!0, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!0)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!0)) | ![Y: $i] : ((~plant(Y)) | eats(A!0, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0)))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[145])).
% 0.19/0.42 tff(147,plain,
% 0.19/0.42 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!0)) | ![Y: $i] : ((~plant(Y)) | eats(A!0, Y)) | ![Y1: $i] : (eats(A!0, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!0)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(A!0)) | ![Y: $i] : ((~plant(Y)) | eats(A!0, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[146, 144])).
% 0.19/0.42 tff(148,plain,
% 0.19/0.42 ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!0)) | ![Y: $i] : ((~plant(Y)) | eats(A!0, Y)) | ![Y1: $i] : (eats(A!0, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!0)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(149,plain,
% 0.19/0.42 ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(A!0)) | ![Y: $i] : ((~plant(Y)) | eats(A!0, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.19/0.42 tff(150,plain,
% 0.19/0.42 (![Y: $i] : ((~plant(Y)) | eats(A!0, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[149, 143, 121])).
% 0.19/0.42 tff(151,plain,
% 0.19/0.42 (![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[150, 107])).
% 0.19/0.42 tff(152,assumption,(eats(A!0, A!1)), introduced(assumption)).
% 0.19/0.42 tff(153,plain,
% 0.19/0.42 (^[X: $i, Y: $i] : refl(((~eats(X, Y)) | (~fox(Y)) | (~wolf(X))) <=> ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(154,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[153])).
% 0.19/0.42 tff(155,plain,
% 0.19/0.42 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((wolf(X) & fox(Y)) <=> (~((~fox(Y)) | (~wolf(X))))), ((~(wolf(X) & fox(Y))) <=> (~(~((~fox(Y)) | (~wolf(X))))))), rewrite((~(~((~fox(Y)) | (~wolf(X))))) <=> ((~fox(Y)) | (~wolf(X)))), ((~(wolf(X) & fox(Y))) <=> ((~fox(Y)) | (~wolf(X))))), (((~eats(X, Y)) | (~(wolf(X) & fox(Y)))) <=> ((~eats(X, Y)) | ((~fox(Y)) | (~wolf(X)))))), rewrite(((~eats(X, Y)) | ((~fox(Y)) | (~wolf(X)))) <=> ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))), (((~eats(X, Y)) | (~(wolf(X) & fox(Y)))) <=> ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(156,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & fox(Y)))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[155])).
% 0.19/0.42 tff(157,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & fox(Y)))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & fox(Y))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(158,plain,
% 0.19/0.42 (^[X: $i, Y: $i] : rewrite(((wolf(X) & fox(Y)) => (~eats(X, Y))) <=> ((~eats(X, Y)) | (~(wolf(X) & fox(Y)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(159,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((wolf(X) & fox(Y)) => (~eats(X, Y))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & fox(Y))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[158])).
% 0.19/0.42 tff(160,axiom,(![X: $i, Y: $i] : ((wolf(X) & fox(Y)) => (~eats(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_11')).
% 0.19/0.42 tff(161,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & fox(Y))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.19/0.42 tff(162,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & fox(Y))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[161, 157])).
% 0.19/0.42 tff(163,plain,(
% 0.19/0.42 ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & fox(Y))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[162])).
% 0.19/0.42 tff(164,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[163, 156])).
% 0.19/0.42 tff(165,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[164, 154])).
% 0.19/0.42 tff(166,plain,
% 0.19/0.42 (?[A: $i] : fox(A) <=> ?[A: $i] : fox(A)),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(167,axiom,(?[A: $i] : fox(A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fox_type')).
% 0.19/0.42 tff(168,plain,
% 0.19/0.42 (?[A: $i] : fox(A)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.19/0.42 tff(169,plain,(
% 0.19/0.42 fox(A!1)),
% 0.19/0.42 inference(skolemize,[status(sab)],[168])).
% 0.19/0.42 tff(170,plain,
% 0.19/0.42 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))) | ((~wolf(A!0)) | (~fox(A!1)) | (~eats(A!0, A!1)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))) | (~wolf(A!0)) | (~fox(A!1)) | (~eats(A!0, A!1)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(171,plain,
% 0.19/0.42 (((~eats(A!0, A!1)) | (~fox(A!1)) | (~wolf(A!0))) <=> ((~wolf(A!0)) | (~fox(A!1)) | (~eats(A!0, A!1)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(172,plain,
% 0.19/0.42 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))) | ((~eats(A!0, A!1)) | (~fox(A!1)) | (~wolf(A!0)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))) | ((~wolf(A!0)) | (~fox(A!1)) | (~eats(A!0, A!1))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[171])).
% 0.19/0.42 tff(173,plain,
% 0.19/0.42 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))) | ((~eats(A!0, A!1)) | (~fox(A!1)) | (~wolf(A!0)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))) | (~wolf(A!0)) | (~fox(A!1)) | (~eats(A!0, A!1)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[172, 170])).
% 0.19/0.42 tff(174,plain,
% 0.19/0.42 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))) | ((~eats(A!0, A!1)) | (~fox(A!1)) | (~wolf(A!0)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(175,plain,
% 0.19/0.42 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))) | (~wolf(A!0)) | (~fox(A!1)) | (~eats(A!0, A!1))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.19/0.42 tff(176,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[175, 79, 169, 165, 152])).
% 0.19/0.42 tff(177,plain,(~eats(A!0, A!1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(178,assumption,(~![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z)))), introduced(assumption)).
% 0.19/0.42 tff(179,assumption,(~much_smaller(A!1, A!0)), introduced(assumption)).
% 0.19/0.42 tff(180,plain,
% 0.19/0.42 (^[X: $i, Y: $i] : refl((much_smaller(X, Y) | (~wolf(Y)) | (~fox(X))) <=> (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(181,plain,
% 0.19/0.42 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X))) <=> ![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[180])).
% 0.19/0.42 tff(182,plain,
% 0.19/0.42 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((fox(X) & wolf(Y)) <=> (~((~fox(X)) | (~wolf(Y))))), ((~(fox(X) & wolf(Y))) <=> (~(~((~fox(X)) | (~wolf(Y))))))), rewrite((~(~((~fox(X)) | (~wolf(Y))))) <=> ((~fox(X)) | (~wolf(Y)))), ((~(fox(X) & wolf(Y))) <=> ((~fox(X)) | (~wolf(Y))))), (((~(fox(X) & wolf(Y))) | much_smaller(X, Y)) <=> (((~fox(X)) | (~wolf(Y))) | much_smaller(X, Y)))), rewrite((((~fox(X)) | (~wolf(Y))) | much_smaller(X, Y)) <=> (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))), (((~(fox(X) & wolf(Y))) | much_smaller(X, Y)) <=> (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(183,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y)) <=> ![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[182])).
% 0.19/0.42 tff(184,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y)) <=> ![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(185,plain,
% 0.19/0.42 (^[X: $i, Y: $i] : rewrite(((fox(X) & wolf(Y)) => much_smaller(X, Y)) <=> ((~(fox(X) & wolf(Y))) | much_smaller(X, Y)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(186,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((fox(X) & wolf(Y)) => much_smaller(X, Y)) <=> ![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[185])).
% 0.19/0.42 tff(187,axiom,(![X: $i, Y: $i] : ((fox(X) & wolf(Y)) => much_smaller(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_10')).
% 0.19/0.42 tff(188,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.19/0.42 tff(189,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[188, 184])).
% 0.19/0.42 tff(190,plain,(
% 0.19/0.42 ![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y))),
% 0.19/0.42 inference(skolemize,[status(sab)],[189])).
% 0.19/0.42 tff(191,plain,
% 0.19/0.42 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[190, 183])).
% 0.19/0.42 tff(192,plain,
% 0.19/0.42 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[191, 181])).
% 0.19/0.42 tff(193,plain,
% 0.19/0.42 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | ((~wolf(A!0)) | (~fox(A!1)) | much_smaller(A!1, A!0))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (~wolf(A!0)) | (~fox(A!1)) | much_smaller(A!1, A!0))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(194,plain,
% 0.19/0.42 ((much_smaller(A!1, A!0) | (~wolf(A!0)) | (~fox(A!1))) <=> ((~wolf(A!0)) | (~fox(A!1)) | much_smaller(A!1, A!0))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(195,plain,
% 0.19/0.42 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (much_smaller(A!1, A!0) | (~wolf(A!0)) | (~fox(A!1)))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | ((~wolf(A!0)) | (~fox(A!1)) | much_smaller(A!1, A!0)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[194])).
% 0.19/0.42 tff(196,plain,
% 0.19/0.42 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (much_smaller(A!1, A!0) | (~wolf(A!0)) | (~fox(A!1)))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (~wolf(A!0)) | (~fox(A!1)) | much_smaller(A!1, A!0))),
% 0.19/0.42 inference(transitivity,[status(thm)],[195, 193])).
% 0.19/0.42 tff(197,plain,
% 0.19/0.42 ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (much_smaller(A!1, A!0) | (~wolf(A!0)) | (~fox(A!1)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(198,plain,
% 0.19/0.42 ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (~wolf(A!0)) | (~fox(A!1)) | much_smaller(A!1, A!0)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.19/0.42 tff(199,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[198, 79, 169, 192, 179])).
% 0.19/0.42 tff(200,plain,(much_smaller(A!1, A!0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(201,assumption,(![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0)))), introduced(assumption)).
% 0.19/0.42 tff(202,plain,
% 0.19/0.42 (^[X: $i] : refl((animal(X) | (~fox(X))) <=> (animal(X) | (~fox(X))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(203,plain,
% 0.19/0.42 (![X: $i] : (animal(X) | (~fox(X))) <=> ![X: $i] : (animal(X) | (~fox(X)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[202])).
% 0.19/0.42 tff(204,plain,
% 0.19/0.42 (![X: $i] : (animal(X) | (~fox(X))) <=> ![X: $i] : (animal(X) | (~fox(X)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(205,plain,
% 0.19/0.42 (^[X: $i] : rewrite((fox(X) => animal(X)) <=> (animal(X) | (~fox(X))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(206,plain,
% 0.19/0.42 (![X: $i] : (fox(X) => animal(X)) <=> ![X: $i] : (animal(X) | (~fox(X)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[205])).
% 0.19/0.42 tff(207,axiom,(![X: $i] : (fox(X) => animal(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_2_1')).
% 0.19/0.42 tff(208,plain,
% 0.19/0.42 (![X: $i] : (animal(X) | (~fox(X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.19/0.42 tff(209,plain,
% 0.19/0.42 (![X: $i] : (animal(X) | (~fox(X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[208, 204])).
% 0.19/0.42 tff(210,plain,(
% 0.19/0.42 ![X: $i] : (animal(X) | (~fox(X)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[209])).
% 0.19/0.42 tff(211,plain,
% 0.19/0.42 (![X: $i] : (animal(X) | (~fox(X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[210, 203])).
% 0.19/0.42 tff(212,plain,
% 0.19/0.42 (((~![X: $i] : (animal(X) | (~fox(X)))) | (animal(A!1) | (~fox(A!1)))) <=> ((~![X: $i] : (animal(X) | (~fox(X)))) | animal(A!1) | (~fox(A!1)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(213,plain,
% 0.19/0.42 ((~![X: $i] : (animal(X) | (~fox(X)))) | (animal(A!1) | (~fox(A!1)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(214,plain,
% 0.19/0.42 ((~![X: $i] : (animal(X) | (~fox(X)))) | animal(A!1) | (~fox(A!1))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.19/0.42 tff(215,plain,
% 0.19/0.42 (animal(A!1)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[214, 169, 211])).
% 0.19/0.42 tff(216,plain,
% 0.19/0.42 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0)))) | ((~animal(A!1)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z))) | eats(A!0, A!1) | (~much_smaller(A!1, A!0)))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0)))) | (~animal(A!1)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z))) | eats(A!0, A!1) | (~much_smaller(A!1, A!0)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(217,plain,
% 0.19/0.43 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0)))) | ((~animal(A!1)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z))) | eats(A!0, A!1) | (~much_smaller(A!1, A!0)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(218,plain,
% 0.19/0.43 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0)))) | (~animal(A!1)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z))) | eats(A!0, A!1) | (~much_smaller(A!1, A!0))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.19/0.43 tff(219,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[218, 215, 201, 200, 178, 177])).
% 0.19/0.43 tff(220,plain,((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0)))) | ![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(221,plain,
% 0.19/0.43 (![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[220, 151])).
% 0.19/0.43 tff(222,assumption,(eats(A!1, tptp_fun_Y_6(A!3))), introduced(assumption)).
% 0.19/0.43 tff(223,assumption,(![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z)))), introduced(assumption)).
% 0.19/0.43 tff(224,plain,
% 0.19/0.43 (^[X: $i] : refl(((~caterpillar(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X)))))) <=> ((~caterpillar(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X)))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(225,plain,
% 0.19/0.43 (![X: $i] : ((~caterpillar(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X)))))) <=> ![X: $i] : ((~caterpillar(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[224])).
% 0.19/0.43 tff(226,plain,
% 0.19/0.43 (^[X: $i] : rewrite(((~caterpillar(X)) | (plant(tptp_fun_Y_6(X)) & eats(X, tptp_fun_Y_6(X)))) <=> ((~caterpillar(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X)))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(227,plain,
% 0.19/0.43 (![X: $i] : ((~caterpillar(X)) | (plant(tptp_fun_Y_6(X)) & eats(X, tptp_fun_Y_6(X)))) <=> ![X: $i] : ((~caterpillar(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[226])).
% 0.19/0.43 tff(228,plain,
% 0.19/0.43 (![X: $i] : ((~caterpillar(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y))) <=> ![X: $i] : ((~caterpillar(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(229,plain,
% 0.19/0.43 (^[X: $i] : rewrite((caterpillar(X) => ?[Y: $i] : (plant(Y) & eats(X, Y))) <=> ((~caterpillar(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(230,plain,
% 0.19/0.43 (![X: $i] : (caterpillar(X) => ?[Y: $i] : (plant(Y) & eats(X, Y))) <=> ![X: $i] : ((~caterpillar(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[229])).
% 0.19/0.43 tff(231,axiom,(![X: $i] : (caterpillar(X) => ?[Y: $i] : (plant(Y) & eats(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_14')).
% 0.19/0.43 tff(232,plain,
% 0.19/0.43 (![X: $i] : ((~caterpillar(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.19/0.43 tff(233,plain,
% 0.19/0.43 (![X: $i] : ((~caterpillar(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[232, 228])).
% 0.19/0.43 tff(234,plain,(
% 0.19/0.43 ![X: $i] : ((~caterpillar(X)) | (plant(tptp_fun_Y_6(X)) & eats(X, tptp_fun_Y_6(X))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[233])).
% 0.19/0.43 tff(235,plain,
% 0.19/0.43 (![X: $i] : ((~caterpillar(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[234, 227])).
% 0.19/0.43 tff(236,plain,
% 0.19/0.43 (![X: $i] : ((~caterpillar(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[235, 225])).
% 0.19/0.43 tff(237,plain,
% 0.19/0.43 (?[A: $i] : caterpillar(A) <=> ?[A: $i] : caterpillar(A)),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(238,axiom,(?[A: $i] : caterpillar(A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','caterpillar_type')).
% 0.19/0.43 tff(239,plain,
% 0.19/0.43 (?[A: $i] : caterpillar(A)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.19/0.43 tff(240,plain,(
% 0.19/0.43 caterpillar(A!3)),
% 0.19/0.43 inference(skolemize,[status(sab)],[239])).
% 0.19/0.43 tff(241,plain,
% 0.19/0.43 (((~![X: $i] : ((~caterpillar(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | ((~caterpillar(A!3)) | (~((~plant(tptp_fun_Y_6(A!3))) | (~eats(A!3, tptp_fun_Y_6(A!3))))))) <=> ((~![X: $i] : ((~caterpillar(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | (~caterpillar(A!3)) | (~((~plant(tptp_fun_Y_6(A!3))) | (~eats(A!3, tptp_fun_Y_6(A!3))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(242,plain,
% 0.19/0.43 ((~![X: $i] : ((~caterpillar(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | ((~caterpillar(A!3)) | (~((~plant(tptp_fun_Y_6(A!3))) | (~eats(A!3, tptp_fun_Y_6(A!3))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(243,plain,
% 0.19/0.43 ((~![X: $i] : ((~caterpillar(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | (~caterpillar(A!3)) | (~((~plant(tptp_fun_Y_6(A!3))) | (~eats(A!3, tptp_fun_Y_6(A!3)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.19/0.43 tff(244,plain,
% 0.19/0.43 (~((~plant(tptp_fun_Y_6(A!3))) | (~eats(A!3, tptp_fun_Y_6(A!3))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[243, 240, 236])).
% 0.19/0.43 tff(245,plain,
% 0.19/0.43 (((~plant(tptp_fun_Y_6(A!3))) | (~eats(A!3, tptp_fun_Y_6(A!3)))) | plant(tptp_fun_Y_6(A!3))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(246,plain,
% 0.19/0.43 (plant(tptp_fun_Y_6(A!3))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[245, 244])).
% 0.19/0.43 tff(247,plain,
% 0.19/0.43 (((~![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z)))) | ((~plant(tptp_fun_Y_6(A!3))) | (~eats(A!1, tptp_fun_Y_6(A!3))))) <=> ((~![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z)))) | (~plant(tptp_fun_Y_6(A!3))) | (~eats(A!1, tptp_fun_Y_6(A!3))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(248,plain,
% 0.19/0.43 ((~![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z)))) | ((~plant(tptp_fun_Y_6(A!3))) | (~eats(A!1, tptp_fun_Y_6(A!3))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(249,plain,
% 0.19/0.43 ((~![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z)))) | (~plant(tptp_fun_Y_6(A!3))) | (~eats(A!1, tptp_fun_Y_6(A!3)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.19/0.43 tff(250,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[249, 246, 223, 222])).
% 0.19/0.43 tff(251,plain,((~![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z)))) | (~eats(A!1, tptp_fun_Y_6(A!3)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(252,plain,
% 0.19/0.43 (~eats(A!1, tptp_fun_Y_6(A!3))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[251, 221])).
% 0.19/0.43 tff(253,assumption,(![Y: $i] : ((~plant(Y)) | eats(A!1, Y))), introduced(assumption)).
% 0.19/0.43 tff(254,plain,
% 0.19/0.43 (((~![Y: $i] : ((~plant(Y)) | eats(A!1, Y))) | ((~plant(tptp_fun_Y_6(A!3))) | eats(A!1, tptp_fun_Y_6(A!3)))) <=> ((~![Y: $i] : ((~plant(Y)) | eats(A!1, Y))) | (~plant(tptp_fun_Y_6(A!3))) | eats(A!1, tptp_fun_Y_6(A!3)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(255,plain,
% 0.19/0.43 ((~![Y: $i] : ((~plant(Y)) | eats(A!1, Y))) | ((~plant(tptp_fun_Y_6(A!3))) | eats(A!1, tptp_fun_Y_6(A!3)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(256,plain,
% 0.19/0.43 ((~![Y: $i] : ((~plant(Y)) | eats(A!1, Y))) | (~plant(tptp_fun_Y_6(A!3))) | eats(A!1, tptp_fun_Y_6(A!3))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.19/0.43 tff(257,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[256, 246, 253, 252])).
% 0.19/0.43 tff(258,plain,(~![Y: $i] : ((~plant(Y)) | eats(A!1, Y))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(259,plain,
% 0.19/0.43 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!1)) | ![Y: $i] : ((~plant(Y)) | eats(A!1, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(A!1)) | ![Y: $i] : ((~plant(Y)) | eats(A!1, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(260,plain,
% 0.19/0.43 (((~animal(A!1)) | ![Y: $i] : ((~plant(Y)) | eats(A!1, Y)) | ![Y1: $i] : (eats(A!1, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> ((~animal(A!1)) | ![Y: $i] : ((~plant(Y)) | eats(A!1, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(261,plain,
% 0.19/0.43 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!1)) | ![Y: $i] : ((~plant(Y)) | eats(A!1, Y)) | ![Y1: $i] : (eats(A!1, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!1)) | ![Y: $i] : ((~plant(Y)) | eats(A!1, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1)))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[260])).
% 0.19/0.43 tff(262,plain,
% 0.19/0.43 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!1)) | ![Y: $i] : ((~plant(Y)) | eats(A!1, Y)) | ![Y1: $i] : (eats(A!1, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(A!1)) | ![Y: $i] : ((~plant(Y)) | eats(A!1, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[261, 259])).
% 0.19/0.43 tff(263,plain,
% 0.19/0.43 ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!1)) | ![Y: $i] : ((~plant(Y)) | eats(A!1, Y)) | ![Y1: $i] : (eats(A!1, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(264,plain,
% 0.19/0.43 ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(A!1)) | ![Y: $i] : ((~plant(Y)) | eats(A!1, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.19/0.43 tff(265,plain,
% 0.19/0.43 (![Y: $i] : ((~plant(Y)) | eats(A!1, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[264, 143, 215])).
% 0.19/0.43 tff(266,plain,
% 0.19/0.43 (![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[265, 258])).
% 0.19/0.43 tff(267,assumption,(![Y: $i] : ((~plant(Y)) | eats(A!2, Y))), introduced(assumption)).
% 0.19/0.43 tff(268,plain,
% 0.19/0.43 (((~![Y: $i] : ((~plant(Y)) | eats(A!2, Y))) | ((~plant(tptp_fun_Y_6(A!3))) | eats(A!2, tptp_fun_Y_6(A!3)))) <=> ((~![Y: $i] : ((~plant(Y)) | eats(A!2, Y))) | (~plant(tptp_fun_Y_6(A!3))) | eats(A!2, tptp_fun_Y_6(A!3)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(269,plain,
% 0.19/0.43 ((~![Y: $i] : ((~plant(Y)) | eats(A!2, Y))) | ((~plant(tptp_fun_Y_6(A!3))) | eats(A!2, tptp_fun_Y_6(A!3)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(270,plain,
% 0.19/0.43 ((~![Y: $i] : ((~plant(Y)) | eats(A!2, Y))) | (~plant(tptp_fun_Y_6(A!3))) | eats(A!2, tptp_fun_Y_6(A!3))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.19/0.43 tff(271,plain,
% 0.19/0.43 (eats(A!2, tptp_fun_Y_6(A!3))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[270, 246, 267])).
% 0.19/0.43 tff(272,assumption,(eats(A!2, tptp_fun_Y_6(A!3))), introduced(assumption)).
% 0.19/0.43 tff(273,assumption,(![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z)))), introduced(assumption)).
% 0.19/0.43 tff(274,plain,
% 0.19/0.43 (((~![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z)))) | ((~plant(tptp_fun_Y_6(A!3))) | (~eats(A!2, tptp_fun_Y_6(A!3))))) <=> ((~![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z)))) | (~plant(tptp_fun_Y_6(A!3))) | (~eats(A!2, tptp_fun_Y_6(A!3))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(275,plain,
% 0.19/0.43 ((~![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z)))) | ((~plant(tptp_fun_Y_6(A!3))) | (~eats(A!2, tptp_fun_Y_6(A!3))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(276,plain,
% 0.19/0.43 ((~![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z)))) | (~plant(tptp_fun_Y_6(A!3))) | (~eats(A!2, tptp_fun_Y_6(A!3)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.19/0.43 tff(277,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[276, 246, 273, 272])).
% 0.19/0.43 tff(278,plain,((~![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z)))) | (~eats(A!2, tptp_fun_Y_6(A!3)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(279,plain,
% 0.19/0.43 (~![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[278, 271])).
% 0.19/0.43 tff(280,plain,
% 0.19/0.43 (((~![Y: $i] : ((~plant(Y)) | eats(A!2, Y))) | ((~plant(A!5)) | eats(A!2, A!5))) <=> ((~![Y: $i] : ((~plant(Y)) | eats(A!2, Y))) | (~plant(A!5)) | eats(A!2, A!5))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(281,plain,
% 0.19/0.43 ((~![Y: $i] : ((~plant(Y)) | eats(A!2, Y))) | ((~plant(A!5)) | eats(A!2, A!5))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(282,plain,
% 0.19/0.43 ((~![Y: $i] : ((~plant(Y)) | eats(A!2, Y))) | (~plant(A!5)) | eats(A!2, A!5)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.19/0.43 tff(283,plain,
% 0.19/0.43 (eats(A!2, A!5)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[282, 102, 267])).
% 0.19/0.43 tff(284,plain,
% 0.19/0.43 (^[X: $i] : refl((animal(X) | (~bird(X))) <=> (animal(X) | (~bird(X))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(285,plain,
% 0.19/0.43 (![X: $i] : (animal(X) | (~bird(X))) <=> ![X: $i] : (animal(X) | (~bird(X)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[284])).
% 0.19/0.43 tff(286,plain,
% 0.19/0.43 (![X: $i] : (animal(X) | (~bird(X))) <=> ![X: $i] : (animal(X) | (~bird(X)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(287,plain,
% 0.19/0.43 (^[X: $i] : rewrite((bird(X) => animal(X)) <=> (animal(X) | (~bird(X))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(288,plain,
% 0.19/0.43 (![X: $i] : (bird(X) => animal(X)) <=> ![X: $i] : (animal(X) | (~bird(X)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[287])).
% 0.19/0.43 tff(289,axiom,(![X: $i] : (bird(X) => animal(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_3_1')).
% 0.19/0.43 tff(290,plain,
% 0.19/0.43 (![X: $i] : (animal(X) | (~bird(X)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.19/0.43 tff(291,plain,
% 0.19/0.43 (![X: $i] : (animal(X) | (~bird(X)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[290, 286])).
% 0.19/0.43 tff(292,plain,(
% 0.19/0.43 ![X: $i] : (animal(X) | (~bird(X)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[291])).
% 0.19/0.43 tff(293,plain,
% 0.19/0.43 (![X: $i] : (animal(X) | (~bird(X)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[292, 285])).
% 0.19/0.43 tff(294,plain,
% 0.19/0.43 (((~![X: $i] : (animal(X) | (~bird(X)))) | (animal(A!2) | (~bird(A!2)))) <=> ((~![X: $i] : (animal(X) | (~bird(X)))) | animal(A!2) | (~bird(A!2)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(295,plain,
% 0.19/0.43 ((~![X: $i] : (animal(X) | (~bird(X)))) | (animal(A!2) | (~bird(A!2)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(296,plain,
% 0.19/0.43 ((~![X: $i] : (animal(X) | (~bird(X)))) | animal(A!2) | (~bird(A!2))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.19/0.43 tff(297,plain,
% 0.19/0.43 (animal(A!2)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[296, 49, 293])).
% 0.19/0.43 tff(298,plain,
% 0.19/0.43 (^[X: $i, Y: $i] : refl(((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y)))) <=> ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(299,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y)))) <=> ![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[298])).
% 0.19/0.44 tff(300,plain,
% 0.19/0.44 (^[X: $i, Y: $i] : rewrite(((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y)))) <=> ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(301,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y)))) <=> ![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[300])).
% 0.19/0.44 tff(302,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y)))) <=> ![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[301, 299])).
% 0.19/0.44 tff(303,plain,
% 0.19/0.44 (^[X: $i, Y: $i] : rewrite(((~animal(Y)) | (~animal(X)) | ![Z: $i] : (~(grain(Z) & eats(Y, Z) & eats(X, Y)))) <=> ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(304,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : (~(grain(Z) & eats(Y, Z) & eats(X, Y)))) <=> ![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[303])).
% 0.19/0.44 tff(305,plain,
% 0.19/0.44 (^[X: $i, Y: $i] : rewrite(((~animal(X)) | (~animal(Y)) | ![Z: $i] : (~(grain(Z) & eats(Y, Z) & eats(X, Y)))) <=> ((~animal(Y)) | (~animal(X)) | ![Z: $i] : (~(grain(Z) & eats(Y, Z) & eats(X, Y)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(306,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((~animal(X)) | (~animal(Y)) | ![Z: $i] : (~(grain(Z) & eats(Y, Z) & eats(X, Y)))) <=> ![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : (~(grain(Z) & eats(Y, Z) & eats(X, Y))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[305])).
% 0.19/0.44 tff(307,plain,
% 0.19/0.44 ((~?[X: $i, Y: $i] : (animal(X) & animal(Y) & ?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y)))) <=> (~?[X: $i, Y: $i] : (animal(X) & animal(Y) & ?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(308,plain,
% 0.19/0.44 ((~?[X: $i, Y: $i] : ((animal(X) & animal(Y)) & ?[Z: $i] : ((grain(Z) & eats(Y, Z)) & eats(X, Y)))) <=> (~?[X: $i, Y: $i] : (animal(X) & animal(Y) & ?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(309,axiom,(~?[X: $i, Y: $i] : ((animal(X) & animal(Y)) & ?[Z: $i] : ((grain(Z) & eats(Y, Z)) & eats(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47')).
% 0.19/0.44 tff(310,plain,
% 0.19/0.44 (~?[X: $i, Y: $i] : (animal(X) & animal(Y) & ?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.19/0.44 tff(311,plain,
% 0.19/0.44 (~?[X: $i, Y: $i] : (animal(X) & animal(Y) & ?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[310, 307])).
% 0.19/0.44 tff(312,plain,
% 0.19/0.44 (~?[X: $i, Y: $i] : (animal(X) & animal(Y) & ?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[311, 307])).
% 0.19/0.44 tff(313,plain,
% 0.19/0.44 (~?[X: $i, Y: $i] : (animal(X) & animal(Y) & ?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[312, 307])).
% 0.19/0.44 tff(314,plain,
% 0.19/0.44 (~?[X: $i, Y: $i] : (animal(X) & animal(Y) & ?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[313, 307])).
% 0.19/0.44 tff(315,plain,
% 0.19/0.44 (~?[X: $i, Y: $i] : (animal(X) & animal(Y) & ?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[314, 307])).
% 0.19/0.44 tff(316,plain,
% 0.19/0.44 (~?[X: $i, Y: $i] : (animal(X) & animal(Y) & ?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[315, 307])).
% 0.19/0.44 tff(317,plain,
% 0.19/0.44 (^[X: $i, Y: $i] : nnf_neg(refl($oeq((~animal(X)), (~animal(X)))), refl($oeq((~animal(Y)), (~animal(Y)))), nnf_neg(proof_bind(^[Z: $i] : refl($oeq((~(grain(Z) & eats(Y, Z) & eats(X, Y))), (~(grain(Z) & eats(Y, Z) & eats(X, Y)))))), $oeq((~?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y))), ![Z: $i] : (~(grain(Z) & eats(Y, Z) & eats(X, Y))))), $oeq((~(animal(X) & animal(Y) & ?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y)))), ((~animal(X)) | (~animal(Y)) | ![Z: $i] : (~(grain(Z) & eats(Y, Z) & eats(X, Y))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(318,plain,(
% 0.19/0.44 ![X: $i, Y: $i] : ((~animal(X)) | (~animal(Y)) | ![Z: $i] : (~(grain(Z) & eats(Y, Z) & eats(X, Y))))),
% 0.19/0.44 inference(nnf-neg,[status(sab)],[316, 317])).
% 0.19/0.44 tff(319,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : (~(grain(Z) & eats(Y, Z) & eats(X, Y))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[318, 306])).
% 0.19/0.44 tff(320,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[319, 304])).
% 0.19/0.44 tff(321,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[320, 302])).
% 0.19/0.44 tff(322,plain,
% 0.19/0.44 (((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | ((~animal(A!1)) | (~animal(A!2)) | ![Z: $i] : ((~grain(Z)) | (~eats(A!2, Z)) | (~eats(A!1, A!2))))) <=> ((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | (~animal(A!1)) | (~animal(A!2)) | ![Z: $i] : ((~grain(Z)) | (~eats(A!2, Z)) | (~eats(A!1, A!2))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(323,plain,
% 0.19/0.44 (((~animal(A!2)) | (~animal(A!1)) | ![Z: $i] : ((~grain(Z)) | (~eats(A!2, Z)) | (~eats(A!1, A!2)))) <=> ((~animal(A!1)) | (~animal(A!2)) | ![Z: $i] : ((~grain(Z)) | (~eats(A!2, Z)) | (~eats(A!1, A!2))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(324,plain,
% 0.19/0.44 (((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | ((~animal(A!2)) | (~animal(A!1)) | ![Z: $i] : ((~grain(Z)) | (~eats(A!2, Z)) | (~eats(A!1, A!2))))) <=> ((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | ((~animal(A!1)) | (~animal(A!2)) | ![Z: $i] : ((~grain(Z)) | (~eats(A!2, Z)) | (~eats(A!1, A!2)))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[323])).
% 0.19/0.44 tff(325,plain,
% 0.19/0.44 (((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | ((~animal(A!2)) | (~animal(A!1)) | ![Z: $i] : ((~grain(Z)) | (~eats(A!2, Z)) | (~eats(A!1, A!2))))) <=> ((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | (~animal(A!1)) | (~animal(A!2)) | ![Z: $i] : ((~grain(Z)) | (~eats(A!2, Z)) | (~eats(A!1, A!2))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[324, 322])).
% 0.19/0.44 tff(326,plain,
% 0.19/0.44 ((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | ((~animal(A!2)) | (~animal(A!1)) | ![Z: $i] : ((~grain(Z)) | (~eats(A!2, Z)) | (~eats(A!1, A!2))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(327,plain,
% 0.19/0.44 ((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | (~animal(A!1)) | (~animal(A!2)) | ![Z: $i] : ((~grain(Z)) | (~eats(A!2, Z)) | (~eats(A!1, A!2)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[326, 325])).
% 0.19/0.44 tff(328,plain,
% 0.19/0.44 (![Z: $i] : ((~grain(Z)) | (~eats(A!2, Z)) | (~eats(A!1, A!2)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[327, 321, 215, 297])).
% 0.19/0.44 tff(329,assumption,(eats(A!1, A!2)), introduced(assumption)).
% 0.19/0.44 tff(330,assumption,(eats(A!2, A!5)), introduced(assumption)).
% 0.19/0.44 tff(331,plain,
% 0.19/0.44 (((~![Z: $i] : ((~grain(Z)) | (~eats(A!2, Z)) | (~eats(A!1, A!2)))) | ((~grain(A!5)) | (~eats(A!2, A!5)) | (~eats(A!1, A!2)))) <=> ((~![Z: $i] : ((~grain(Z)) | (~eats(A!2, Z)) | (~eats(A!1, A!2)))) | (~grain(A!5)) | (~eats(A!2, A!5)) | (~eats(A!1, A!2)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(332,plain,
% 0.19/0.44 ((~![Z: $i] : ((~grain(Z)) | (~eats(A!2, Z)) | (~eats(A!1, A!2)))) | ((~grain(A!5)) | (~eats(A!2, A!5)) | (~eats(A!1, A!2)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(333,plain,
% 0.19/0.44 ((~![Z: $i] : ((~grain(Z)) | (~eats(A!2, Z)) | (~eats(A!1, A!2)))) | (~grain(A!5)) | (~eats(A!2, A!5)) | (~eats(A!1, A!2))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[332, 331])).
% 0.19/0.44 tff(334,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[333, 75, 330, 329, 328])).
% 0.19/0.44 tff(335,plain,((~eats(A!1, A!2)) | (~eats(A!2, A!5))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(336,plain,
% 0.19/0.44 (~eats(A!1, A!2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[335, 283])).
% 0.19/0.44 tff(337,assumption,(~eats(A!1, A!2)), introduced(assumption)).
% 0.19/0.44 tff(338,assumption,(~![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z)))), introduced(assumption)).
% 0.19/0.44 tff(339,assumption,(~much_smaller(A!2, A!1)), introduced(assumption)).
% 0.19/0.44 tff(340,plain,
% 0.19/0.44 (^[X: $i, Y: $i] : refl((much_smaller(X, Y) | (~fox(Y)) | (~bird(X))) <=> (much_smaller(X, Y) | (~fox(Y)) | (~bird(X))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(341,plain,
% 0.19/0.44 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X))) <=> ![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[340])).
% 0.19/0.44 tff(342,plain,
% 0.19/0.44 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((bird(X) & fox(Y)) <=> (~((~bird(X)) | (~fox(Y))))), ((~(bird(X) & fox(Y))) <=> (~(~((~bird(X)) | (~fox(Y))))))), rewrite((~(~((~bird(X)) | (~fox(Y))))) <=> ((~bird(X)) | (~fox(Y)))), ((~(bird(X) & fox(Y))) <=> ((~bird(X)) | (~fox(Y))))), (((~(bird(X) & fox(Y))) | much_smaller(X, Y)) <=> (((~bird(X)) | (~fox(Y))) | much_smaller(X, Y)))), rewrite((((~bird(X)) | (~fox(Y))) | much_smaller(X, Y)) <=> (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))), (((~(bird(X) & fox(Y))) | much_smaller(X, Y)) <=> (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(343,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y)) <=> ![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[342])).
% 0.19/0.44 tff(344,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y)) <=> ![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(345,plain,
% 0.19/0.44 (^[X: $i, Y: $i] : rewrite(((bird(X) & fox(Y)) => much_smaller(X, Y)) <=> ((~(bird(X) & fox(Y))) | much_smaller(X, Y)))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(346,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((bird(X) & fox(Y)) => much_smaller(X, Y)) <=> ![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[345])).
% 0.19/0.44 tff(347,axiom,(![X: $i, Y: $i] : ((bird(X) & fox(Y)) => much_smaller(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_9')).
% 0.19/0.44 tff(348,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[347, 346])).
% 0.19/0.44 tff(349,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[348, 344])).
% 0.19/0.44 tff(350,plain,(
% 0.19/0.44 ![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y))),
% 0.19/0.44 inference(skolemize,[status(sab)],[349])).
% 0.19/0.44 tff(351,plain,
% 0.19/0.44 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[350, 343])).
% 0.19/0.44 tff(352,plain,
% 0.19/0.44 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[351, 341])).
% 0.19/0.44 tff(353,plain,
% 0.19/0.44 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | ((~fox(A!1)) | (~bird(A!2)) | much_smaller(A!2, A!1))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (~fox(A!1)) | (~bird(A!2)) | much_smaller(A!2, A!1))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(354,plain,
% 0.19/0.44 ((much_smaller(A!2, A!1) | (~fox(A!1)) | (~bird(A!2))) <=> ((~fox(A!1)) | (~bird(A!2)) | much_smaller(A!2, A!1))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(355,plain,
% 0.19/0.44 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (much_smaller(A!2, A!1) | (~fox(A!1)) | (~bird(A!2)))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | ((~fox(A!1)) | (~bird(A!2)) | much_smaller(A!2, A!1)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[354])).
% 0.19/0.44 tff(356,plain,
% 0.19/0.44 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (much_smaller(A!2, A!1) | (~fox(A!1)) | (~bird(A!2)))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (~fox(A!1)) | (~bird(A!2)) | much_smaller(A!2, A!1))),
% 0.19/0.44 inference(transitivity,[status(thm)],[355, 353])).
% 0.19/0.44 tff(357,plain,
% 0.19/0.44 ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (much_smaller(A!2, A!1) | (~fox(A!1)) | (~bird(A!2)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(358,plain,
% 0.19/0.44 ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (~fox(A!1)) | (~bird(A!2)) | much_smaller(A!2, A!1)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[357, 356])).
% 0.19/0.44 tff(359,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[358, 169, 49, 352, 339])).
% 0.19/0.44 tff(360,plain,(much_smaller(A!2, A!1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(361,assumption,(![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1)))), introduced(assumption)).
% 0.19/0.44 tff(362,plain,
% 0.19/0.44 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1)))) | ((~animal(A!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z))) | eats(A!1, A!2) | (~much_smaller(A!2, A!1)))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1)))) | (~animal(A!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z))) | eats(A!1, A!2) | (~much_smaller(A!2, A!1)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(363,plain,
% 0.19/0.44 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1)))) | ((~animal(A!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z))) | eats(A!1, A!2) | (~much_smaller(A!2, A!1)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(364,plain,
% 0.19/0.44 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1)))) | (~animal(A!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z))) | eats(A!1, A!2) | (~much_smaller(A!2, A!1))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[363, 362])).
% 0.19/0.44 tff(365,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[364, 297, 361, 360, 338, 337])).
% 0.19/0.44 tff(366,plain,((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1)))) | ![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z))) | eats(A!1, A!2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(367,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[366, 336, 279, 266])).
% 0.19/0.44 tff(368,plain,(~![Y: $i] : ((~plant(Y)) | eats(A!2, Y))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(369,plain,
% 0.19/0.44 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!2)) | ![Y: $i] : ((~plant(Y)) | eats(A!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(A!2)) | ![Y: $i] : ((~plant(Y)) | eats(A!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(370,plain,
% 0.19/0.44 (((~animal(A!2)) | ![Y: $i] : ((~plant(Y)) | eats(A!2, Y)) | ![Y1: $i] : (eats(A!2, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> ((~animal(A!2)) | ![Y: $i] : ((~plant(Y)) | eats(A!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(371,plain,
% 0.19/0.45 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!2)) | ![Y: $i] : ((~plant(Y)) | eats(A!2, Y)) | ![Y1: $i] : (eats(A!2, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!2)) | ![Y: $i] : ((~plant(Y)) | eats(A!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[370])).
% 0.19/0.45 tff(372,plain,
% 0.19/0.45 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!2)) | ![Y: $i] : ((~plant(Y)) | eats(A!2, Y)) | ![Y1: $i] : (eats(A!2, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(A!2)) | ![Y: $i] : ((~plant(Y)) | eats(A!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[371, 369])).
% 0.19/0.45 tff(373,plain,
% 0.19/0.45 ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!2)) | ![Y: $i] : ((~plant(Y)) | eats(A!2, Y)) | ![Y1: $i] : (eats(A!2, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(374,plain,
% 0.19/0.45 ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(A!2)) | ![Y: $i] : ((~plant(Y)) | eats(A!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[373, 372])).
% 0.19/0.45 tff(375,plain,
% 0.19/0.45 (![Y: $i] : ((~plant(Y)) | eats(A!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[374, 143, 297])).
% 0.19/0.45 tff(376,plain,
% 0.19/0.45 (![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[375, 368])).
% 0.19/0.45 tff(377,plain,
% 0.19/0.45 (^[X: $i] : refl((animal(X) | (~snail(X))) <=> (animal(X) | (~snail(X))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(378,plain,
% 0.19/0.45 (![X: $i] : (animal(X) | (~snail(X))) <=> ![X: $i] : (animal(X) | (~snail(X)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[377])).
% 0.19/0.45 tff(379,plain,
% 0.19/0.45 (![X: $i] : (animal(X) | (~snail(X))) <=> ![X: $i] : (animal(X) | (~snail(X)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(380,plain,
% 0.19/0.45 (^[X: $i] : rewrite((snail(X) => animal(X)) <=> (animal(X) | (~snail(X))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(381,plain,
% 0.19/0.45 (![X: $i] : (snail(X) => animal(X)) <=> ![X: $i] : (animal(X) | (~snail(X)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[380])).
% 0.19/0.45 tff(382,axiom,(![X: $i] : (snail(X) => animal(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_4_2')).
% 0.19/0.45 tff(383,plain,
% 0.19/0.45 (![X: $i] : (animal(X) | (~snail(X)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[382, 381])).
% 0.19/0.45 tff(384,plain,
% 0.19/0.45 (![X: $i] : (animal(X) | (~snail(X)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[383, 379])).
% 0.19/0.45 tff(385,plain,(
% 0.19/0.45 ![X: $i] : (animal(X) | (~snail(X)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[384])).
% 0.19/0.45 tff(386,plain,
% 0.19/0.45 (![X: $i] : (animal(X) | (~snail(X)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[385, 378])).
% 0.19/0.45 tff(387,plain,
% 0.19/0.45 (((~![X: $i] : (animal(X) | (~snail(X)))) | (animal(A!4) | (~snail(A!4)))) <=> ((~![X: $i] : (animal(X) | (~snail(X)))) | animal(A!4) | (~snail(A!4)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(388,plain,
% 0.19/0.45 ((~![X: $i] : (animal(X) | (~snail(X)))) | (animal(A!4) | (~snail(A!4)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(389,plain,
% 0.19/0.45 ((~![X: $i] : (animal(X) | (~snail(X)))) | animal(A!4) | (~snail(A!4))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[388, 387])).
% 0.19/0.45 tff(390,plain,
% 0.19/0.45 (animal(A!4)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[389, 18, 386])).
% 0.19/0.45 tff(391,plain,
% 0.19/0.45 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))) | ((~animal(A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | eats(A!2, A!4) | (~much_smaller(A!4, A!2)))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))) | (~animal(A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | eats(A!2, A!4) | (~much_smaller(A!4, A!2)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(392,plain,
% 0.19/0.45 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))) | ((~animal(A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | eats(A!2, A!4) | (~much_smaller(A!4, A!2)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(393,plain,
% 0.19/0.45 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))) | (~animal(A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | eats(A!2, A!4) | (~much_smaller(A!4, A!2))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[392, 391])).
% 0.19/0.45 tff(394,plain,
% 0.19/0.45 (![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | eats(A!2, A!4) | (~much_smaller(A!4, A!2))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[393, 390, 376])).
% 0.19/0.45 tff(395,plain,
% 0.19/0.45 (![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | eats(A!2, A!4)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[394, 57])).
% 0.19/0.45 tff(396,plain,
% 0.19/0.45 (eats(A!2, A!4)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[395, 31])).
% 0.19/0.45 tff(397,plain,
% 0.19/0.45 (^[X: $i, Y: $i] : refl(((~eats(X, Y)) | (~snail(Y)) | (~bird(X))) <=> ((~eats(X, Y)) | (~snail(Y)) | (~bird(X))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(398,plain,
% 0.19/0.45 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[397])).
% 0.19/0.45 tff(399,plain,
% 0.19/0.45 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((bird(X) & snail(Y)) <=> (~((~bird(X)) | (~snail(Y))))), ((~(bird(X) & snail(Y))) <=> (~(~((~bird(X)) | (~snail(Y))))))), rewrite((~(~((~bird(X)) | (~snail(Y))))) <=> ((~bird(X)) | (~snail(Y)))), ((~(bird(X) & snail(Y))) <=> ((~bird(X)) | (~snail(Y))))), (((~eats(X, Y)) | (~(bird(X) & snail(Y)))) <=> ((~eats(X, Y)) | ((~bird(X)) | (~snail(Y)))))), rewrite(((~eats(X, Y)) | ((~bird(X)) | (~snail(Y)))) <=> ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))), (((~eats(X, Y)) | (~(bird(X) & snail(Y)))) <=> ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(400,plain,
% 0.19/0.45 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y)))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[399])).
% 0.19/0.45 tff(401,plain,
% 0.19/0.45 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y)))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(402,plain,
% 0.19/0.45 (^[X: $i, Y: $i] : rewrite(((bird(X) & snail(Y)) => (~eats(X, Y))) <=> ((~eats(X, Y)) | (~(bird(X) & snail(Y)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(403,plain,
% 0.19/0.45 (![X: $i, Y: $i] : ((bird(X) & snail(Y)) => (~eats(X, Y))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[402])).
% 0.19/0.45 tff(404,axiom,(![X: $i, Y: $i] : ((bird(X) & snail(Y)) => (~eats(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_13')).
% 0.19/0.45 tff(405,plain,
% 0.19/0.45 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[404, 403])).
% 0.19/0.45 tff(406,plain,
% 0.19/0.45 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[405, 401])).
% 0.19/0.45 tff(407,plain,(
% 0.19/0.45 ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[406])).
% 0.19/0.45 tff(408,plain,
% 0.19/0.45 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[407, 400])).
% 0.19/0.45 tff(409,plain,
% 0.19/0.45 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[408, 398])).
% 0.19/0.45 tff(410,plain,
% 0.19/0.46 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | ((~bird(A!2)) | (~snail(A!4)) | (~eats(A!2, A!4)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | (~bird(A!2)) | (~snail(A!4)) | (~eats(A!2, A!4)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(411,plain,
% 0.19/0.46 (((~eats(A!2, A!4)) | (~snail(A!4)) | (~bird(A!2))) <=> ((~bird(A!2)) | (~snail(A!4)) | (~eats(A!2, A!4)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(412,plain,
% 0.19/0.46 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | ((~eats(A!2, A!4)) | (~snail(A!4)) | (~bird(A!2)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | ((~bird(A!2)) | (~snail(A!4)) | (~eats(A!2, A!4))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[411])).
% 0.19/0.46 tff(413,plain,
% 0.19/0.46 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | ((~eats(A!2, A!4)) | (~snail(A!4)) | (~bird(A!2)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | (~bird(A!2)) | (~snail(A!4)) | (~eats(A!2, A!4)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[412, 410])).
% 0.19/0.46 tff(414,plain,
% 0.19/0.46 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | ((~eats(A!2, A!4)) | (~snail(A!4)) | (~bird(A!2)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(415,plain,
% 0.19/0.46 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | (~bird(A!2)) | (~snail(A!4)) | (~eats(A!2, A!4))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[414, 413])).
% 0.19/0.46 tff(416,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[415, 49, 18, 409, 396])).
% 0.19/0.46 % SZS output end Proof
%------------------------------------------------------------------------------