TSTP Solution File: PUZ031+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PUZ031+3 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 0.18s 0.40s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : PUZ031+3 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n008.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 18:26:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.18/0.40 % SZS status Theorem
% 0.18/0.40 % SZS output start Proof
% 0.18/0.40 tff(eats_type, type, (
% 0.18/0.40 eats: ( $i * $i ) > $o)).
% 0.18/0.40 tff(tptp_fun_A_7_type, type, (
% 0.18/0.40 tptp_fun_A_7: $i)).
% 0.18/0.40 tff(tptp_fun_A_4_type, type, (
% 0.18/0.40 tptp_fun_A_4: $i)).
% 0.18/0.40 tff(plant_type, type, (
% 0.18/0.40 plant: $i > $o)).
% 0.18/0.40 tff(much_smaller_type, type, (
% 0.18/0.40 much_smaller: ( $i * $i ) > $o)).
% 0.18/0.40 tff(animal_type, type, (
% 0.18/0.40 animal: $i > $o)).
% 0.18/0.40 tff(tptp_fun_A_6_type, type, (
% 0.18/0.40 tptp_fun_A_6: $i)).
% 0.18/0.40 tff(bird_type, type, (
% 0.18/0.40 bird: $i > $o)).
% 0.18/0.40 tff(snail_type, type, (
% 0.18/0.40 snail: $i > $o)).
% 0.18/0.40 tff(tptp_fun_Y_9_type, type, (
% 0.18/0.40 tptp_fun_Y_9: $i > $i)).
% 0.18/0.40 tff(tptp_fun_A_3_type, type, (
% 0.18/0.40 tptp_fun_A_3: $i)).
% 0.18/0.40 tff(tptp_fun_A_8_type, type, (
% 0.18/0.40 tptp_fun_A_8: $i)).
% 0.18/0.40 tff(grain_type, type, (
% 0.18/0.40 grain: $i > $o)).
% 0.18/0.40 tff(fox_type, type, (
% 0.18/0.40 fox: $i > $o)).
% 0.18/0.40 tff(tptp_fun_A_2_type, type, (
% 0.18/0.40 tptp_fun_A_2: $i)).
% 0.18/0.40 tff(wolf_type, type, (
% 0.18/0.40 wolf: $i > $o)).
% 0.18/0.40 tff(1,assumption,(eats(A!4, A!6)), introduced(assumption)).
% 0.18/0.40 tff(2,plain,
% 0.18/0.40 (^[X: $i, Y: $i] : refl(((~eats(X, Y)) | (~snail(Y)) | (~bird(X))) <=> ((~eats(X, Y)) | (~snail(Y)) | (~bird(X))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(3,plain,
% 0.18/0.40 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.18/0.40 tff(4,plain,
% 0.18/0.40 (^[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)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(5,plain,
% 0.18/0.40 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y)))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[4])).
% 0.18/0.40 tff(6,plain,
% 0.18/0.40 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y)))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(7,plain,
% 0.18/0.40 (^[X: $i, Y: $i] : rewrite(((bird(X) & snail(Y)) => (~eats(X, Y))) <=> ((~eats(X, Y)) | (~(bird(X) & snail(Y)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(8,plain,
% 0.18/0.40 (![X: $i, Y: $i] : ((bird(X) & snail(Y)) => (~eats(X, Y))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[7])).
% 0.18/0.40 tff(9,axiom,(![X: $i, Y: $i] : ((bird(X) & snail(Y)) => (~eats(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_13')).
% 0.18/0.40 tff(10,plain,
% 0.18/0.40 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.18/0.40 tff(11,plain,
% 0.18/0.40 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.18/0.40 tff(12,plain,(
% 0.18/0.40 ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[11])).
% 0.18/0.40 tff(13,plain,
% 0.18/0.40 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.18/0.40 tff(14,plain,
% 0.18/0.40 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[13, 3])).
% 0.18/0.40 tff(15,plain,
% 0.18/0.40 (?[A: $i] : snail(A) <=> ?[A: $i] : snail(A)),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(16,axiom,(?[A: $i] : snail(A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','snail_type')).
% 0.18/0.40 tff(17,plain,
% 0.18/0.40 (?[A: $i] : snail(A)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.18/0.40 tff(18,plain,(
% 0.18/0.40 snail(A!6)),
% 0.18/0.40 inference(skolemize,[status(sab)],[17])).
% 0.18/0.40 tff(19,plain,
% 0.18/0.40 (?[A: $i] : bird(A) <=> ?[A: $i] : bird(A)),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(20,axiom,(?[A: $i] : bird(A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bird_type')).
% 0.18/0.40 tff(21,plain,
% 0.18/0.40 (?[A: $i] : bird(A)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.18/0.40 tff(22,plain,(
% 0.18/0.40 bird(A!4)),
% 0.18/0.40 inference(skolemize,[status(sab)],[21])).
% 0.18/0.40 tff(23,plain,
% 0.18/0.40 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | ((~bird(A!4)) | (~snail(A!6)) | (~eats(A!4, A!6)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | (~bird(A!4)) | (~snail(A!6)) | (~eats(A!4, A!6)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(24,plain,
% 0.18/0.40 (((~eats(A!4, A!6)) | (~snail(A!6)) | (~bird(A!4))) <=> ((~bird(A!4)) | (~snail(A!6)) | (~eats(A!4, A!6)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(25,plain,
% 0.18/0.40 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | ((~eats(A!4, A!6)) | (~snail(A!6)) | (~bird(A!4)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | ((~bird(A!4)) | (~snail(A!6)) | (~eats(A!4, A!6))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[24])).
% 0.18/0.40 tff(26,plain,
% 0.18/0.40 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | ((~eats(A!4, A!6)) | (~snail(A!6)) | (~bird(A!4)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | (~bird(A!4)) | (~snail(A!6)) | (~eats(A!4, A!6)))),
% 0.18/0.40 inference(transitivity,[status(thm)],[25, 23])).
% 0.18/0.40 tff(27,plain,
% 0.18/0.40 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | ((~eats(A!4, A!6)) | (~snail(A!6)) | (~bird(A!4)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(28,plain,
% 0.18/0.40 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | (~bird(A!4)) | (~snail(A!6)) | (~eats(A!4, A!6))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.18/0.40 tff(29,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[28, 22, 18, 14, 1])).
% 0.18/0.40 tff(30,plain,(~eats(A!4, A!6)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.40 tff(31,assumption,(![Z: $i] : ((~plant(Z)) | (~eats(A!6, Z)))), introduced(assumption)).
% 0.18/0.40 tff(32,plain,
% 0.18/0.40 (^[X: $i] : refl(((~snail(X)) | (~((~plant(tptp_fun_Y_9(X))) | (~eats(X, tptp_fun_Y_9(X)))))) <=> ((~snail(X)) | (~((~plant(tptp_fun_Y_9(X))) | (~eats(X, tptp_fun_Y_9(X)))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(33,plain,
% 0.18/0.40 (![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_9(X))) | (~eats(X, tptp_fun_Y_9(X)))))) <=> ![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_9(X))) | (~eats(X, tptp_fun_Y_9(X))))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[32])).
% 0.18/0.40 tff(34,plain,
% 0.18/0.40 (^[X: $i] : rewrite(((~snail(X)) | (plant(tptp_fun_Y_9(X)) & eats(X, tptp_fun_Y_9(X)))) <=> ((~snail(X)) | (~((~plant(tptp_fun_Y_9(X))) | (~eats(X, tptp_fun_Y_9(X)))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(35,plain,
% 0.18/0.40 (![X: $i] : ((~snail(X)) | (plant(tptp_fun_Y_9(X)) & eats(X, tptp_fun_Y_9(X)))) <=> ![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_9(X))) | (~eats(X, tptp_fun_Y_9(X))))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[34])).
% 0.18/0.40 tff(36,plain,
% 0.18/0.40 (![X: $i] : ((~snail(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y))) <=> ![X: $i] : ((~snail(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(37,plain,
% 0.18/0.40 (^[X: $i] : rewrite((snail(X) => ?[Y: $i] : (plant(Y) & eats(X, Y))) <=> ((~snail(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(38,plain,
% 0.18/0.40 (![X: $i] : (snail(X) => ?[Y: $i] : (plant(Y) & eats(X, Y))) <=> ![X: $i] : ((~snail(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[37])).
% 0.18/0.40 tff(39,axiom,(![X: $i] : (snail(X) => ?[Y: $i] : (plant(Y) & eats(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_14a')).
% 0.18/0.40 tff(40,plain,
% 0.18/0.40 (![X: $i] : ((~snail(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.18/0.40 tff(41,plain,
% 0.18/0.40 (![X: $i] : ((~snail(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.18/0.40 tff(42,plain,(
% 0.18/0.40 ![X: $i] : ((~snail(X)) | (plant(tptp_fun_Y_9(X)) & eats(X, tptp_fun_Y_9(X))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[41])).
% 0.18/0.40 tff(43,plain,
% 0.18/0.40 (![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_9(X))) | (~eats(X, tptp_fun_Y_9(X))))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.18/0.40 tff(44,plain,
% 0.18/0.40 (![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_9(X))) | (~eats(X, tptp_fun_Y_9(X))))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[43, 33])).
% 0.18/0.40 tff(45,plain,
% 0.18/0.40 (((~![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_9(X))) | (~eats(X, tptp_fun_Y_9(X))))))) | ((~snail(A!6)) | (~((~plant(tptp_fun_Y_9(A!6))) | (~eats(A!6, tptp_fun_Y_9(A!6))))))) <=> ((~![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_9(X))) | (~eats(X, tptp_fun_Y_9(X))))))) | (~snail(A!6)) | (~((~plant(tptp_fun_Y_9(A!6))) | (~eats(A!6, tptp_fun_Y_9(A!6))))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(46,plain,
% 0.18/0.40 ((~![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_9(X))) | (~eats(X, tptp_fun_Y_9(X))))))) | ((~snail(A!6)) | (~((~plant(tptp_fun_Y_9(A!6))) | (~eats(A!6, tptp_fun_Y_9(A!6))))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(47,plain,
% 0.18/0.40 ((~![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_9(X))) | (~eats(X, tptp_fun_Y_9(X))))))) | (~snail(A!6)) | (~((~plant(tptp_fun_Y_9(A!6))) | (~eats(A!6, tptp_fun_Y_9(A!6)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.18/0.40 tff(48,plain,
% 0.18/0.40 (~((~plant(tptp_fun_Y_9(A!6))) | (~eats(A!6, tptp_fun_Y_9(A!6))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[47, 18, 44])).
% 0.18/0.40 tff(49,plain,
% 0.18/0.40 (((~plant(tptp_fun_Y_9(A!6))) | (~eats(A!6, tptp_fun_Y_9(A!6)))) | eats(A!6, tptp_fun_Y_9(A!6))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(50,plain,
% 0.18/0.40 (eats(A!6, tptp_fun_Y_9(A!6))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.18/0.40 tff(51,plain,
% 0.18/0.40 (((~plant(tptp_fun_Y_9(A!6))) | (~eats(A!6, tptp_fun_Y_9(A!6)))) | plant(tptp_fun_Y_9(A!6))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(52,plain,
% 0.18/0.40 (plant(tptp_fun_Y_9(A!6))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[51, 48])).
% 0.18/0.40 tff(53,plain,
% 0.18/0.40 (((~![Z: $i] : ((~plant(Z)) | (~eats(A!6, Z)))) | ((~plant(tptp_fun_Y_9(A!6))) | (~eats(A!6, tptp_fun_Y_9(A!6))))) <=> ((~![Z: $i] : ((~plant(Z)) | (~eats(A!6, Z)))) | (~plant(tptp_fun_Y_9(A!6))) | (~eats(A!6, tptp_fun_Y_9(A!6))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(54,plain,
% 0.18/0.40 ((~![Z: $i] : ((~plant(Z)) | (~eats(A!6, Z)))) | ((~plant(tptp_fun_Y_9(A!6))) | (~eats(A!6, tptp_fun_Y_9(A!6))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(55,plain,
% 0.18/0.40 ((~![Z: $i] : ((~plant(Z)) | (~eats(A!6, Z)))) | (~plant(tptp_fun_Y_9(A!6))) | (~eats(A!6, tptp_fun_Y_9(A!6)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.18/0.40 tff(56,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[55, 52, 50, 31])).
% 0.18/0.40 tff(57,plain,(~![Z: $i] : ((~plant(Z)) | (~eats(A!6, Z)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.40 tff(58,assumption,(~eats(A!4, A!6)), introduced(assumption)).
% 0.18/0.40 tff(59,assumption,(~much_smaller(A!6, A!4)), introduced(assumption)).
% 0.18/0.40 tff(60,plain,
% 0.18/0.40 (^[Y: $i, X: $i] : refl((much_smaller(X, Y) | (~snail(X)) | (~bird(Y))) <=> (much_smaller(X, Y) | (~snail(X)) | (~bird(Y))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(61,plain,
% 0.18/0.40 (![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y))) <=> ![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[60])).
% 0.18/0.40 tff(62,plain,
% 0.18/0.40 (^[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)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(63,plain,
% 0.18/0.40 (![Y: $i, X: $i] : ((~(bird(Y) & snail(X))) | much_smaller(X, Y)) <=> ![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[62])).
% 0.18/0.40 tff(64,plain,
% 0.18/0.40 (![Y: $i, X: $i] : ((~(bird(Y) & snail(X))) | much_smaller(X, Y)) <=> ![Y: $i, X: $i] : ((~(bird(Y) & snail(X))) | much_smaller(X, Y))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(65,plain,
% 0.18/0.40 (^[Y: $i, X: $i] : rewrite(((bird(Y) & snail(X)) => much_smaller(X, Y)) <=> ((~(bird(Y) & snail(X))) | much_smaller(X, Y)))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(66,plain,
% 0.18/0.40 (![Y: $i, X: $i] : ((bird(Y) & snail(X)) => much_smaller(X, Y)) <=> ![Y: $i, X: $i] : ((~(bird(Y) & snail(X))) | much_smaller(X, Y))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[65])).
% 0.18/0.40 tff(67,axiom,(![Y: $i, X: $i] : ((bird(Y) & snail(X)) => much_smaller(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_8')).
% 0.18/0.40 tff(68,plain,
% 0.18/0.40 (![Y: $i, X: $i] : ((~(bird(Y) & snail(X))) | much_smaller(X, Y))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.18/0.40 tff(69,plain,
% 0.18/0.40 (![Y: $i, X: $i] : ((~(bird(Y) & snail(X))) | much_smaller(X, Y))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.18/0.40 tff(70,plain,(
% 0.18/0.40 ![Y: $i, X: $i] : ((~(bird(Y) & snail(X))) | much_smaller(X, Y))),
% 0.18/0.40 inference(skolemize,[status(sab)],[69])).
% 0.18/0.40 tff(71,plain,
% 0.18/0.40 (![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.18/0.40 tff(72,plain,
% 0.18/0.40 (![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[71, 61])).
% 0.18/0.40 tff(73,plain,
% 0.18/0.40 (((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | ((~bird(A!4)) | (~snail(A!6)) | much_smaller(A!6, A!4))) <=> ((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | (~bird(A!4)) | (~snail(A!6)) | much_smaller(A!6, A!4))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(74,plain,
% 0.18/0.40 ((much_smaller(A!6, A!4) | (~snail(A!6)) | (~bird(A!4))) <=> ((~bird(A!4)) | (~snail(A!6)) | much_smaller(A!6, A!4))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(75,plain,
% 0.18/0.40 (((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | (much_smaller(A!6, A!4) | (~snail(A!6)) | (~bird(A!4)))) <=> ((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | ((~bird(A!4)) | (~snail(A!6)) | much_smaller(A!6, A!4)))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[74])).
% 0.18/0.40 tff(76,plain,
% 0.18/0.40 (((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | (much_smaller(A!6, A!4) | (~snail(A!6)) | (~bird(A!4)))) <=> ((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | (~bird(A!4)) | (~snail(A!6)) | much_smaller(A!6, A!4))),
% 0.18/0.40 inference(transitivity,[status(thm)],[75, 73])).
% 0.18/0.40 tff(77,plain,
% 0.18/0.40 ((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | (much_smaller(A!6, A!4) | (~snail(A!6)) | (~bird(A!4)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(78,plain,
% 0.18/0.40 ((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | (~bird(A!4)) | (~snail(A!6)) | much_smaller(A!6, A!4)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.18/0.40 tff(79,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[78, 22, 18, 72, 59])).
% 0.18/0.40 tff(80,plain,(much_smaller(A!6, A!4)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.40 tff(81,assumption,(~![Z: $i] : ((~plant(Z)) | (~eats(A!6, Z)))), introduced(assumption)).
% 0.18/0.40 tff(82,assumption,(![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4)))), introduced(assumption)).
% 0.18/0.40 tff(83,plain,
% 0.18/0.40 (^[A: $i] : refl((animal(A) | (~snail(A))) <=> (animal(A) | (~snail(A))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(84,plain,
% 0.18/0.40 (![A: $i] : (animal(A) | (~snail(A))) <=> ![A: $i] : (animal(A) | (~snail(A)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[83])).
% 0.18/0.40 tff(85,plain,
% 0.18/0.40 (![A: $i] : (animal(A) | (~snail(A))) <=> ![A: $i] : (animal(A) | (~snail(A)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(86,plain,
% 0.18/0.40 (^[A: $i] : rewrite((snail(A) => animal(A)) <=> (animal(A) | (~snail(A))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(87,plain,
% 0.18/0.40 (![A: $i] : (snail(A) => animal(A)) <=> ![A: $i] : (animal(A) | (~snail(A)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[86])).
% 0.18/0.40 tff(88,axiom,(![A: $i] : (snail(A) => animal(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','snail_is_animal')).
% 0.18/0.40 tff(89,plain,
% 0.18/0.40 (![A: $i] : (animal(A) | (~snail(A)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.18/0.40 tff(90,plain,
% 0.18/0.40 (![A: $i] : (animal(A) | (~snail(A)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.18/0.40 tff(91,plain,(
% 0.18/0.40 ![A: $i] : (animal(A) | (~snail(A)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[90])).
% 0.18/0.40 tff(92,plain,
% 0.18/0.40 (![A: $i] : (animal(A) | (~snail(A)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.18/0.40 tff(93,plain,
% 0.18/0.40 (((~![A: $i] : (animal(A) | (~snail(A)))) | (animal(A!6) | (~snail(A!6)))) <=> ((~![A: $i] : (animal(A) | (~snail(A)))) | animal(A!6) | (~snail(A!6)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(94,plain,
% 0.18/0.40 ((~![A: $i] : (animal(A) | (~snail(A)))) | (animal(A!6) | (~snail(A!6)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(95,plain,
% 0.18/0.40 ((~![A: $i] : (animal(A) | (~snail(A)))) | animal(A!6) | (~snail(A!6))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.18/0.40 tff(96,plain,
% 0.18/0.40 (animal(A!6)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[95, 18, 92])).
% 0.18/0.40 tff(97,plain,
% 0.18/0.40 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4)))) | ((~animal(A!6)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!6, Z))) | eats(A!4, A!6) | (~much_smaller(A!6, A!4)))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4)))) | (~animal(A!6)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!6, Z))) | eats(A!4, A!6) | (~much_smaller(A!6, A!4)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(98,plain,
% 0.18/0.40 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4)))) | ((~animal(A!6)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!6, Z))) | eats(A!4, A!6) | (~much_smaller(A!6, A!4)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(99,plain,
% 0.18/0.40 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4)))) | (~animal(A!6)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!6, Z))) | eats(A!4, A!6) | (~much_smaller(A!6, A!4))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.18/0.40 tff(100,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[99, 96, 82, 81, 80, 58])).
% 0.18/0.40 tff(101,plain,((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4)))) | ![Z: $i] : ((~plant(Z)) | (~eats(A!6, Z))) | eats(A!4, A!6)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.40 tff(102,plain,
% 0.18/0.40 (~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[101, 57, 30])).
% 0.18/0.40 tff(103,plain,
% 0.18/0.40 (^[A: $i] : refl((animal(A) | (~bird(A))) <=> (animal(A) | (~bird(A))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(104,plain,
% 0.18/0.40 (![A: $i] : (animal(A) | (~bird(A))) <=> ![A: $i] : (animal(A) | (~bird(A)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[103])).
% 0.18/0.40 tff(105,plain,
% 0.18/0.40 (![A: $i] : (animal(A) | (~bird(A))) <=> ![A: $i] : (animal(A) | (~bird(A)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(106,plain,
% 0.18/0.40 (^[A: $i] : rewrite((bird(A) => animal(A)) <=> (animal(A) | (~bird(A))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(107,plain,
% 0.18/0.40 (![A: $i] : (bird(A) => animal(A)) <=> ![A: $i] : (animal(A) | (~bird(A)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[106])).
% 0.18/0.40 tff(108,axiom,(![A: $i] : (bird(A) => animal(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bird_is_animal')).
% 0.18/0.40 tff(109,plain,
% 0.18/0.40 (![A: $i] : (animal(A) | (~bird(A)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.18/0.40 tff(110,plain,
% 0.18/0.40 (![A: $i] : (animal(A) | (~bird(A)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.18/0.40 tff(111,plain,(
% 0.18/0.40 ![A: $i] : (animal(A) | (~bird(A)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[110])).
% 0.18/0.40 tff(112,plain,
% 0.18/0.40 (![A: $i] : (animal(A) | (~bird(A)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.18/0.40 tff(113,plain,
% 0.18/0.40 (((~![A: $i] : (animal(A) | (~bird(A)))) | (animal(A!4) | (~bird(A!4)))) <=> ((~![A: $i] : (animal(A) | (~bird(A)))) | animal(A!4) | (~bird(A!4)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(114,plain,
% 0.18/0.41 ((~![A: $i] : (animal(A) | (~bird(A)))) | (animal(A!4) | (~bird(A!4)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(115,plain,
% 0.18/0.41 ((~![A: $i] : (animal(A) | (~bird(A)))) | animal(A!4) | (~bird(A!4))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.18/0.41 tff(116,plain,
% 0.18/0.41 (animal(A!4)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[115, 22, 112])).
% 0.18/0.41 tff(117,plain,
% 0.18/0.41 (^[X: $i] : refl(((~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(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))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(118,plain,
% 0.18/0.41 (![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))))) <=> ![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)))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[117])).
% 0.18/0.41 tff(119,plain,
% 0.18/0.41 (^[X: $i] : rewrite(((~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(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))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(120,plain,
% 0.18/0.41 (![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))))) <=> ![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)))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[119])).
% 0.18/0.41 tff(121,plain,
% 0.18/0.41 (![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))))) <=> ![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)))))),
% 0.18/0.41 inference(transitivity,[status(thm)],[120, 118])).
% 0.18/0.41 tff(122,plain,
% 0.18/0.41 (^[X: $i] : rewrite(((~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(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))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(123,plain,
% 0.18/0.41 (![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))))) <=> ![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)))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[122])).
% 0.18/0.41 tff(124,plain,
% 0.18/0.41 (^[X: $i] : rewrite(((~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(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))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(125,plain,
% 0.18/0.41 (![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)))))) <=> ![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)))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[124])).
% 0.18/0.41 tff(126,plain,
% 0.18/0.41 (![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)))))) <=> ![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))))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(127,plain,
% 0.18/0.41 (^[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] : (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] : (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] : (eats(X, Y1) | (~animal(Y1)) | (~(much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z))))))))), rewrite((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(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(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] : (eats(X, Y1) | (~animal(Y1)) | (~(much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z))))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(128,plain,
% 0.18/0.41 (![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] : ((~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))))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[127])).
% 0.18/0.41 tff(129,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')).
% 0.18/0.41 tff(130,plain,
% 0.18/0.41 (![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))))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.18/0.41 tff(131,plain,
% 0.18/0.41 (![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))))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.18/0.41 tff(132,plain,(
% 0.18/0.41 ![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))))))),
% 0.18/0.41 inference(skolemize,[status(sab)],[131])).
% 0.18/0.41 tff(133,plain,
% 0.18/0.41 (![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)))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[132, 125])).
% 0.18/0.41 tff(134,plain,
% 0.18/0.41 (![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)))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[133, 123])).
% 0.18/0.41 tff(135,plain,
% 0.18/0.41 (![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)))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[134, 121])).
% 0.18/0.41 tff(136,plain,
% 0.18/0.41 (((~![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!4)) | ![Y: $i] : ((~plant(Y)) | eats(A!4, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4))))) <=> ((~![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!4)) | ![Y: $i] : ((~plant(Y)) | eats(A!4, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(137,plain,
% 0.18/0.41 (((~animal(A!4)) | ![Y: $i] : ((~plant(Y)) | eats(A!4, Y)) | ![Y1: $i] : (eats(A!4, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> ((~animal(A!4)) | ![Y: $i] : ((~plant(Y)) | eats(A!4, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(138,plain,
% 0.18/0.41 (((~![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!4)) | ![Y: $i] : ((~plant(Y)) | eats(A!4, Y)) | ![Y1: $i] : (eats(A!4, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!4)) | ![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!4)) | ![Y: $i] : ((~plant(Y)) | eats(A!4, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4)))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[137])).
% 0.18/0.41 tff(139,plain,
% 0.18/0.41 (((~![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!4)) | ![Y: $i] : ((~plant(Y)) | eats(A!4, Y)) | ![Y1: $i] : (eats(A!4, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!4)) | ![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!4)) | ![Y: $i] : ((~plant(Y)) | eats(A!4, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4))))),
% 0.18/0.41 inference(transitivity,[status(thm)],[138, 136])).
% 0.18/0.41 tff(140,plain,
% 0.18/0.41 ((~![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!4)) | ![Y: $i] : ((~plant(Y)) | eats(A!4, Y)) | ![Y1: $i] : (eats(A!4, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(141,plain,
% 0.18/0.41 ((~![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!4)) | ![Y: $i] : ((~plant(Y)) | eats(A!4, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.18/0.41 tff(142,plain,
% 0.18/0.41 (![Y: $i] : ((~plant(Y)) | eats(A!4, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[141, 135, 116])).
% 0.18/0.41 tff(143,plain,
% 0.18/0.41 (![Y: $i] : ((~plant(Y)) | eats(A!4, Y))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[142, 102])).
% 0.18/0.41 tff(144,plain,
% 0.18/0.41 (?[A: $i] : plant(A) <=> ?[A: $i] : plant(A)),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(145,axiom,(?[A: $i] : plant(A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','plant_type')).
% 0.18/0.41 tff(146,plain,
% 0.18/0.41 (?[A: $i] : plant(A)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.18/0.41 tff(147,plain,(
% 0.18/0.41 plant(A!7)),
% 0.18/0.41 inference(skolemize,[status(sab)],[146])).
% 0.18/0.41 tff(148,plain,
% 0.18/0.41 (((~![Y: $i] : ((~plant(Y)) | eats(A!4, Y))) | ((~plant(A!7)) | eats(A!4, A!7))) <=> ((~![Y: $i] : ((~plant(Y)) | eats(A!4, Y))) | (~plant(A!7)) | eats(A!4, A!7))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(149,plain,
% 0.18/0.41 ((~![Y: $i] : ((~plant(Y)) | eats(A!4, Y))) | ((~plant(A!7)) | eats(A!4, A!7))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(150,plain,
% 0.18/0.41 ((~![Y: $i] : ((~plant(Y)) | eats(A!4, Y))) | (~plant(A!7)) | eats(A!4, A!7)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.18/0.41 tff(151,plain,
% 0.18/0.41 (eats(A!4, A!7)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[150, 147, 143])).
% 0.18/0.41 tff(152,assumption,(~eats(A!4, A!8)), introduced(assumption)).
% 0.18/0.41 tff(153,assumption,(![Y: $i] : ((~plant(Y)) | eats(A!4, Y))), introduced(assumption)).
% 0.18/0.41 tff(154,plain,
% 0.18/0.41 (^[A: $i] : refl((plant(A) | (~grain(A))) <=> (plant(A) | (~grain(A))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(155,plain,
% 0.18/0.41 (![A: $i] : (plant(A) | (~grain(A))) <=> ![A: $i] : (plant(A) | (~grain(A)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[154])).
% 0.18/0.41 tff(156,plain,
% 0.18/0.41 (![A: $i] : (plant(A) | (~grain(A))) <=> ![A: $i] : (plant(A) | (~grain(A)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(157,plain,
% 0.18/0.41 (^[A: $i] : rewrite((grain(A) => plant(A)) <=> (plant(A) | (~grain(A))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(158,plain,
% 0.18/0.41 (![A: $i] : (grain(A) => plant(A)) <=> ![A: $i] : (plant(A) | (~grain(A)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[157])).
% 0.18/0.41 tff(159,axiom,(![A: $i] : (grain(A) => plant(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','grain_is_plant')).
% 0.18/0.41 tff(160,plain,
% 0.18/0.41 (![A: $i] : (plant(A) | (~grain(A)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.18/0.41 tff(161,plain,
% 0.18/0.41 (![A: $i] : (plant(A) | (~grain(A)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[160, 156])).
% 0.18/0.41 tff(162,plain,(
% 0.18/0.41 ![A: $i] : (plant(A) | (~grain(A)))),
% 0.18/0.41 inference(skolemize,[status(sab)],[161])).
% 0.18/0.41 tff(163,plain,
% 0.18/0.41 (![A: $i] : (plant(A) | (~grain(A)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[162, 155])).
% 0.18/0.41 tff(164,plain,
% 0.18/0.41 (?[A: $i] : grain(A) <=> ?[A: $i] : grain(A)),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(165,axiom,(?[A: $i] : grain(A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','grain_type')).
% 0.18/0.41 tff(166,plain,
% 0.18/0.41 (?[A: $i] : grain(A)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.18/0.41 tff(167,plain,(
% 0.18/0.41 grain(A!8)),
% 0.18/0.41 inference(skolemize,[status(sab)],[166])).
% 0.18/0.41 tff(168,plain,
% 0.18/0.41 (((~![A: $i] : (plant(A) | (~grain(A)))) | (plant(A!8) | (~grain(A!8)))) <=> ((~![A: $i] : (plant(A) | (~grain(A)))) | plant(A!8) | (~grain(A!8)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(169,plain,
% 0.18/0.41 ((~![A: $i] : (plant(A) | (~grain(A)))) | (plant(A!8) | (~grain(A!8)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(170,plain,
% 0.18/0.41 ((~![A: $i] : (plant(A) | (~grain(A)))) | plant(A!8) | (~grain(A!8))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.18/0.41 tff(171,plain,
% 0.18/0.41 (plant(A!8)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[170, 167, 163])).
% 0.18/0.41 tff(172,plain,
% 0.18/0.41 (((~![Y: $i] : ((~plant(Y)) | eats(A!4, Y))) | ((~plant(A!8)) | eats(A!4, A!8))) <=> ((~![Y: $i] : ((~plant(Y)) | eats(A!4, Y))) | (~plant(A!8)) | eats(A!4, A!8))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(173,plain,
% 0.18/0.41 ((~![Y: $i] : ((~plant(Y)) | eats(A!4, Y))) | ((~plant(A!8)) | eats(A!4, A!8))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(174,plain,
% 0.18/0.41 ((~![Y: $i] : ((~plant(Y)) | eats(A!4, Y))) | (~plant(A!8)) | eats(A!4, A!8)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.18/0.41 tff(175,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[174, 171, 153, 152])).
% 0.18/0.42 tff(176,plain,((~![Y: $i] : ((~plant(Y)) | eats(A!4, Y))) | eats(A!4, A!8)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.42 tff(177,plain,
% 0.18/0.42 (eats(A!4, A!8)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[176, 143])).
% 0.18/0.42 tff(178,assumption,(eats(A!3, A!4)), introduced(assumption)).
% 0.18/0.42 tff(179,assumption,(eats(A!4, A!8)), introduced(assumption)).
% 0.18/0.42 tff(180,plain,
% 0.18/0.42 (^[A: $i] : refl((animal(A) | (~fox(A))) <=> (animal(A) | (~fox(A))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(181,plain,
% 0.18/0.42 (![A: $i] : (animal(A) | (~fox(A))) <=> ![A: $i] : (animal(A) | (~fox(A)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[180])).
% 0.18/0.42 tff(182,plain,
% 0.18/0.42 (![A: $i] : (animal(A) | (~fox(A))) <=> ![A: $i] : (animal(A) | (~fox(A)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(183,plain,
% 0.18/0.42 (^[A: $i] : rewrite((fox(A) => animal(A)) <=> (animal(A) | (~fox(A))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(184,plain,
% 0.18/0.42 (![A: $i] : (fox(A) => animal(A)) <=> ![A: $i] : (animal(A) | (~fox(A)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[183])).
% 0.18/0.42 tff(185,axiom,(![A: $i] : (fox(A) => animal(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fox_is_animal')).
% 0.18/0.42 tff(186,plain,
% 0.18/0.42 (![A: $i] : (animal(A) | (~fox(A)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.18/0.42 tff(187,plain,
% 0.18/0.42 (![A: $i] : (animal(A) | (~fox(A)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[186, 182])).
% 0.18/0.42 tff(188,plain,(
% 0.18/0.42 ![A: $i] : (animal(A) | (~fox(A)))),
% 0.18/0.42 inference(skolemize,[status(sab)],[187])).
% 0.18/0.42 tff(189,plain,
% 0.18/0.42 (![A: $i] : (animal(A) | (~fox(A)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[188, 181])).
% 0.18/0.42 tff(190,plain,
% 0.18/0.42 (?[A: $i] : fox(A) <=> ?[A: $i] : fox(A)),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(191,axiom,(?[A: $i] : fox(A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fox_type')).
% 0.18/0.42 tff(192,plain,
% 0.18/0.42 (?[A: $i] : fox(A)),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.18/0.42 tff(193,plain,(
% 0.18/0.42 fox(A!3)),
% 0.18/0.42 inference(skolemize,[status(sab)],[192])).
% 0.18/0.42 tff(194,plain,
% 0.18/0.42 (((~![A: $i] : (animal(A) | (~fox(A)))) | (animal(A!3) | (~fox(A!3)))) <=> ((~![A: $i] : (animal(A) | (~fox(A)))) | animal(A!3) | (~fox(A!3)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(195,plain,
% 0.18/0.42 ((~![A: $i] : (animal(A) | (~fox(A)))) | (animal(A!3) | (~fox(A!3)))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(196,plain,
% 0.18/0.42 ((~![A: $i] : (animal(A) | (~fox(A)))) | animal(A!3) | (~fox(A!3))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.18/0.42 tff(197,plain,
% 0.18/0.42 (animal(A!3)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[196, 193, 189])).
% 0.18/0.42 tff(198,plain,
% 0.18/0.42 (^[X: $i, Y: $i, Z: $i] : refl(((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y))) <=> ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(199,plain,
% 0.18/0.42 (![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[198])).
% 0.18/0.42 tff(200,plain,
% 0.18/0.42 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((animal(X) & animal(Y) & grain(Z) & eats(Y, Z) & eats(X, Y)) <=> (~((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y))))), ((~(animal(X) & animal(Y) & grain(Z) & eats(Y, Z) & eats(X, Y))) <=> (~(~((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y))))))), rewrite((~(~((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y))))) <=> ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))), ((~(animal(X) & animal(Y) & grain(Z) & eats(Y, Z) & eats(X, Y))) <=> ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(201,plain,
% 0.18/0.42 (![X: $i, Y: $i, Z: $i] : (~(animal(X) & animal(Y) & grain(Z) & eats(Y, Z) & eats(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[200])).
% 0.18/0.42 tff(202,plain,
% 0.18/0.42 ((~?[X: $i, Y: $i, Z: $i] : (animal(X) & animal(Y) & grain(Z) & eats(Y, Z) & eats(X, Y))) <=> (~?[X: $i, Y: $i, Z: $i] : (animal(X) & animal(Y) & grain(Z) & eats(Y, Z) & eats(X, Y)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(203,plain,
% 0.18/0.42 ((~?[X: $i, Y: $i, Z: $i] : ((((animal(X) & animal(Y)) & grain(Z)) & eats(Y, Z)) & eats(X, Y))) <=> (~?[X: $i, Y: $i, Z: $i] : (animal(X) & animal(Y) & grain(Z) & eats(Y, Z) & eats(X, Y)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(204,axiom,(~?[X: $i, Y: $i, Z: $i] : ((((animal(X) & animal(Y)) & grain(Z)) & eats(Y, Z)) & eats(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47')).
% 0.18/0.42 tff(205,plain,
% 0.18/0.42 (~?[X: $i, Y: $i, Z: $i] : (animal(X) & animal(Y) & grain(Z) & eats(Y, Z) & eats(X, Y))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.18/0.42 tff(206,plain,
% 0.18/0.42 (~?[X: $i, Y: $i, Z: $i] : (animal(X) & animal(Y) & grain(Z) & eats(Y, Z) & eats(X, Y))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[205, 202])).
% 0.18/0.42 tff(207,plain,
% 0.18/0.42 (~?[X: $i, Y: $i, Z: $i] : (animal(X) & animal(Y) & grain(Z) & eats(Y, Z) & eats(X, Y))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[206, 202])).
% 0.18/0.42 tff(208,plain,
% 0.18/0.42 (~?[X: $i, Y: $i, Z: $i] : (animal(X) & animal(Y) & grain(Z) & eats(Y, Z) & eats(X, Y))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[207, 202])).
% 0.18/0.42 tff(209,plain,
% 0.18/0.42 (~?[X: $i, Y: $i, Z: $i] : (animal(X) & animal(Y) & grain(Z) & eats(Y, Z) & eats(X, Y))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[208, 202])).
% 0.18/0.42 tff(210,plain,
% 0.18/0.42 (~?[X: $i, Y: $i, Z: $i] : (animal(X) & animal(Y) & grain(Z) & eats(Y, Z) & eats(X, Y))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[209, 202])).
% 0.18/0.42 tff(211,plain,
% 0.18/0.42 (~?[X: $i, Y: $i, Z: $i] : (animal(X) & animal(Y) & grain(Z) & eats(Y, Z) & eats(X, Y))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[210, 202])).
% 0.18/0.42 tff(212,plain,
% 0.18/0.42 (^[X: $i, Y: $i, Z: $i] : refl($oeq((~(animal(X) & animal(Y) & grain(Z) & eats(Y, Z) & eats(X, Y))), (~(animal(X) & animal(Y) & grain(Z) & eats(Y, Z) & eats(X, Y)))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(213,plain,(
% 0.18/0.42 ![X: $i, Y: $i, Z: $i] : (~(animal(X) & animal(Y) & grain(Z) & eats(Y, Z) & eats(X, Y)))),
% 0.18/0.42 inference(nnf-neg,[status(sab)],[211, 212])).
% 0.18/0.42 tff(214,plain,
% 0.18/0.42 (![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[213, 201])).
% 0.18/0.42 tff(215,plain,
% 0.18/0.42 (![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[214, 199])).
% 0.18/0.42 tff(216,plain,
% 0.18/0.42 (((~![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))) | ((~grain(A!8)) | (~animal(A!3)) | (~animal(A!4)) | (~eats(A!4, A!8)) | (~eats(A!3, A!4)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))) | (~grain(A!8)) | (~animal(A!3)) | (~animal(A!4)) | (~eats(A!4, A!8)) | (~eats(A!3, A!4)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(217,plain,
% 0.18/0.42 (((~eats(A!4, A!8)) | (~grain(A!8)) | (~animal(A!3)) | (~animal(A!4)) | (~eats(A!3, A!4))) <=> ((~grain(A!8)) | (~animal(A!3)) | (~animal(A!4)) | (~eats(A!4, A!8)) | (~eats(A!3, A!4)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(218,plain,
% 0.18/0.42 (((~![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))) | ((~eats(A!4, A!8)) | (~grain(A!8)) | (~animal(A!3)) | (~animal(A!4)) | (~eats(A!3, A!4)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))) | ((~grain(A!8)) | (~animal(A!3)) | (~animal(A!4)) | (~eats(A!4, A!8)) | (~eats(A!3, A!4))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[217])).
% 0.18/0.42 tff(219,plain,
% 0.18/0.42 (((~![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))) | ((~eats(A!4, A!8)) | (~grain(A!8)) | (~animal(A!3)) | (~animal(A!4)) | (~eats(A!3, A!4)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))) | (~grain(A!8)) | (~animal(A!3)) | (~animal(A!4)) | (~eats(A!4, A!8)) | (~eats(A!3, A!4)))),
% 0.18/0.42 inference(transitivity,[status(thm)],[218, 216])).
% 0.18/0.42 tff(220,plain,
% 0.18/0.42 ((~![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))) | ((~eats(A!4, A!8)) | (~grain(A!8)) | (~animal(A!3)) | (~animal(A!4)) | (~eats(A!3, A!4)))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(221,plain,
% 0.18/0.42 ((~![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))) | (~grain(A!8)) | (~animal(A!3)) | (~animal(A!4)) | (~eats(A!4, A!8)) | (~eats(A!3, A!4))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.18/0.42 tff(222,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[221, 167, 215, 197, 116, 179, 178])).
% 0.18/0.42 tff(223,plain,((~eats(A!3, A!4)) | (~eats(A!4, A!8))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.42 tff(224,plain,
% 0.18/0.42 (~eats(A!3, A!4)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[223, 177])).
% 0.18/0.42 tff(225,assumption,(![Y: $i] : ((~plant(Y)) | eats(A!3, Y))), introduced(assumption)).
% 0.18/0.42 tff(226,plain,
% 0.18/0.42 (((~![Y: $i] : ((~plant(Y)) | eats(A!3, Y))) | ((~plant(A!8)) | eats(A!3, A!8))) <=> ((~![Y: $i] : ((~plant(Y)) | eats(A!3, Y))) | (~plant(A!8)) | eats(A!3, A!8))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(227,plain,
% 0.18/0.42 ((~![Y: $i] : ((~plant(Y)) | eats(A!3, Y))) | ((~plant(A!8)) | eats(A!3, A!8))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(228,plain,
% 0.18/0.42 ((~![Y: $i] : ((~plant(Y)) | eats(A!3, Y))) | (~plant(A!8)) | eats(A!3, A!8)),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.18/0.42 tff(229,plain,
% 0.18/0.42 (eats(A!3, A!8)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[228, 171, 225])).
% 0.18/0.42 tff(230,plain,
% 0.18/0.42 (((~![Y: $i] : ((~plant(Y)) | eats(A!3, Y))) | ((~plant(A!7)) | eats(A!3, A!7))) <=> ((~![Y: $i] : ((~plant(Y)) | eats(A!3, Y))) | (~plant(A!7)) | eats(A!3, A!7))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(231,plain,
% 0.18/0.42 ((~![Y: $i] : ((~plant(Y)) | eats(A!3, Y))) | ((~plant(A!7)) | eats(A!3, A!7))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(232,plain,
% 0.18/0.42 ((~![Y: $i] : ((~plant(Y)) | eats(A!3, Y))) | (~plant(A!7)) | eats(A!3, A!7)),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.18/0.42 tff(233,plain,
% 0.18/0.42 (eats(A!3, A!7)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[232, 147, 225])).
% 0.18/0.42 tff(234,assumption,(eats(A!3, A!7)), introduced(assumption)).
% 0.18/0.42 tff(235,assumption,(![Z: $i] : ((~plant(Z)) | (~eats(A!3, Z)))), introduced(assumption)).
% 0.18/0.42 tff(236,plain,
% 0.18/0.42 (((~![Z: $i] : ((~plant(Z)) | (~eats(A!3, Z)))) | ((~plant(A!7)) | (~eats(A!3, A!7)))) <=> ((~![Z: $i] : ((~plant(Z)) | (~eats(A!3, Z)))) | (~plant(A!7)) | (~eats(A!3, A!7)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(237,plain,
% 0.18/0.42 ((~![Z: $i] : ((~plant(Z)) | (~eats(A!3, Z)))) | ((~plant(A!7)) | (~eats(A!3, A!7)))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(238,plain,
% 0.18/0.42 ((~![Z: $i] : ((~plant(Z)) | (~eats(A!3, Z)))) | (~plant(A!7)) | (~eats(A!3, A!7))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.18/0.42 tff(239,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[238, 147, 235, 234])).
% 0.18/0.42 tff(240,plain,((~![Z: $i] : ((~plant(Z)) | (~eats(A!3, Z)))) | (~eats(A!3, A!7))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.42 tff(241,plain,
% 0.18/0.42 (~![Z: $i] : ((~plant(Z)) | (~eats(A!3, Z)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[240, 233])).
% 0.18/0.42 tff(242,assumption,(~much_smaller(A!3, A!2)), introduced(assumption)).
% 0.18/0.42 tff(243,plain,
% 0.18/0.42 (^[X: $i, Y: $i] : refl((much_smaller(X, Y) | (~wolf(Y)) | (~fox(X))) <=> (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(244,plain,
% 0.18/0.42 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X))) <=> ![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[243])).
% 0.18/0.42 tff(245,plain,
% 0.18/0.42 (^[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)))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(246,plain,
% 0.18/0.42 (![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y)) <=> ![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[245])).
% 0.18/0.42 tff(247,plain,
% 0.18/0.42 (![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y)) <=> ![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(248,plain,
% 0.18/0.42 (^[X: $i, Y: $i] : rewrite(((fox(X) & wolf(Y)) => much_smaller(X, Y)) <=> ((~(fox(X) & wolf(Y))) | much_smaller(X, Y)))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(249,plain,
% 0.18/0.42 (![X: $i, Y: $i] : ((fox(X) & wolf(Y)) => much_smaller(X, Y)) <=> ![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[248])).
% 0.18/0.42 tff(250,axiom,(![X: $i, Y: $i] : ((fox(X) & wolf(Y)) => much_smaller(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_10')).
% 0.18/0.42 tff(251,plain,
% 0.18/0.42 (![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.18/0.42 tff(252,plain,
% 0.18/0.42 (![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[251, 247])).
% 0.18/0.42 tff(253,plain,(
% 0.18/0.42 ![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y))),
% 0.18/0.42 inference(skolemize,[status(sab)],[252])).
% 0.18/0.42 tff(254,plain,
% 0.18/0.42 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[253, 246])).
% 0.18/0.42 tff(255,plain,
% 0.18/0.42 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[254, 244])).
% 0.18/0.42 tff(256,plain,
% 0.18/0.42 (?[A: $i] : wolf(A) <=> ?[A: $i] : wolf(A)),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(257,axiom,(?[A: $i] : wolf(A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','wolf_type')).
% 0.18/0.42 tff(258,plain,
% 0.18/0.42 (?[A: $i] : wolf(A)),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.18/0.42 tff(259,plain,(
% 0.18/0.42 wolf(A!2)),
% 0.18/0.42 inference(skolemize,[status(sab)],[258])).
% 0.18/0.42 tff(260,plain,
% 0.18/0.42 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | ((~wolf(A!2)) | (~fox(A!3)) | much_smaller(A!3, A!2))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (~wolf(A!2)) | (~fox(A!3)) | much_smaller(A!3, A!2))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(261,plain,
% 0.18/0.42 ((much_smaller(A!3, A!2) | (~wolf(A!2)) | (~fox(A!3))) <=> ((~wolf(A!2)) | (~fox(A!3)) | much_smaller(A!3, A!2))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(262,plain,
% 0.18/0.42 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (much_smaller(A!3, A!2) | (~wolf(A!2)) | (~fox(A!3)))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | ((~wolf(A!2)) | (~fox(A!3)) | much_smaller(A!3, A!2)))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[261])).
% 0.18/0.42 tff(263,plain,
% 0.18/0.42 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (much_smaller(A!3, A!2) | (~wolf(A!2)) | (~fox(A!3)))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (~wolf(A!2)) | (~fox(A!3)) | much_smaller(A!3, A!2))),
% 0.18/0.42 inference(transitivity,[status(thm)],[262, 260])).
% 0.18/0.42 tff(264,plain,
% 0.18/0.42 ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (much_smaller(A!3, A!2) | (~wolf(A!2)) | (~fox(A!3)))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(265,plain,
% 0.18/0.42 ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (~wolf(A!2)) | (~fox(A!3)) | much_smaller(A!3, A!2)),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.18/0.42 tff(266,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[265, 259, 193, 255, 242])).
% 0.18/0.42 tff(267,plain,(much_smaller(A!3, A!2)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.43 tff(268,assumption,(eats(A!2, A!8)), introduced(assumption)).
% 0.18/0.43 tff(269,plain,
% 0.18/0.43 (^[X: $i, Y: $i] : refl(((~eats(X, Y)) | (~grain(Y)) | (~wolf(X))) <=> ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(270,plain,
% 0.18/0.43 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[269])).
% 0.18/0.43 tff(271,plain,
% 0.18/0.43 (^[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)))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(272,plain,
% 0.18/0.43 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & grain(Y)))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[271])).
% 0.18/0.43 tff(273,plain,
% 0.18/0.43 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & grain(Y)))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & grain(Y))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(274,plain,
% 0.18/0.43 (^[X: $i, Y: $i] : rewrite(((wolf(X) & grain(Y)) => (~eats(X, Y))) <=> ((~eats(X, Y)) | (~(wolf(X) & grain(Y)))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(275,plain,
% 0.18/0.43 (![X: $i, Y: $i] : ((wolf(X) & grain(Y)) => (~eats(X, Y))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & grain(Y))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[274])).
% 0.18/0.43 tff(276,axiom,(![X: $i, Y: $i] : ((wolf(X) & grain(Y)) => (~eats(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_11a')).
% 0.18/0.43 tff(277,plain,
% 0.18/0.43 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & grain(Y))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.18/0.43 tff(278,plain,
% 0.18/0.43 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & grain(Y))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[277, 273])).
% 0.18/0.43 tff(279,plain,(
% 0.18/0.43 ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & grain(Y))))),
% 0.18/0.43 inference(skolemize,[status(sab)],[278])).
% 0.18/0.43 tff(280,plain,
% 0.18/0.43 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[279, 272])).
% 0.18/0.43 tff(281,plain,
% 0.18/0.43 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[280, 270])).
% 0.18/0.43 tff(282,plain,
% 0.18/0.43 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | ((~wolf(A!2)) | (~grain(A!8)) | (~eats(A!2, A!8)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | (~wolf(A!2)) | (~grain(A!8)) | (~eats(A!2, A!8)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(283,plain,
% 0.18/0.43 (((~eats(A!2, A!8)) | (~grain(A!8)) | (~wolf(A!2))) <=> ((~wolf(A!2)) | (~grain(A!8)) | (~eats(A!2, A!8)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(284,plain,
% 0.18/0.43 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | ((~eats(A!2, A!8)) | (~grain(A!8)) | (~wolf(A!2)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | ((~wolf(A!2)) | (~grain(A!8)) | (~eats(A!2, A!8))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[283])).
% 0.18/0.43 tff(285,plain,
% 0.18/0.43 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | ((~eats(A!2, A!8)) | (~grain(A!8)) | (~wolf(A!2)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | (~wolf(A!2)) | (~grain(A!8)) | (~eats(A!2, A!8)))),
% 0.18/0.43 inference(transitivity,[status(thm)],[284, 282])).
% 0.18/0.43 tff(286,plain,
% 0.18/0.43 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | ((~eats(A!2, A!8)) | (~grain(A!8)) | (~wolf(A!2)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(287,plain,
% 0.18/0.43 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | (~wolf(A!2)) | (~grain(A!8)) | (~eats(A!2, A!8))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.18/0.43 tff(288,plain,
% 0.18/0.43 ($false),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[287, 259, 167, 281, 268])).
% 0.18/0.43 tff(289,plain,(~eats(A!2, A!8)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.43 tff(290,assumption,(![Y: $i] : ((~plant(Y)) | eats(A!2, Y))), introduced(assumption)).
% 0.18/0.43 tff(291,plain,
% 0.18/0.43 (((~![Y: $i] : ((~plant(Y)) | eats(A!2, Y))) | ((~plant(A!8)) | eats(A!2, A!8))) <=> ((~![Y: $i] : ((~plant(Y)) | eats(A!2, Y))) | (~plant(A!8)) | eats(A!2, A!8))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(292,plain,
% 0.18/0.43 ((~![Y: $i] : ((~plant(Y)) | eats(A!2, Y))) | ((~plant(A!8)) | eats(A!2, A!8))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(293,plain,
% 0.18/0.43 ((~![Y: $i] : ((~plant(Y)) | eats(A!2, Y))) | (~plant(A!8)) | eats(A!2, A!8)),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.18/0.43 tff(294,plain,
% 0.18/0.43 ($false),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[293, 171, 290, 289])).
% 0.18/0.43 tff(295,plain,(~![Y: $i] : ((~plant(Y)) | eats(A!2, Y))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.43 tff(296,plain,
% 0.18/0.43 (^[A: $i] : refl((animal(A) | (~wolf(A))) <=> (animal(A) | (~wolf(A))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(297,plain,
% 0.18/0.43 (![A: $i] : (animal(A) | (~wolf(A))) <=> ![A: $i] : (animal(A) | (~wolf(A)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[296])).
% 0.18/0.43 tff(298,plain,
% 0.18/0.43 (![A: $i] : (animal(A) | (~wolf(A))) <=> ![A: $i] : (animal(A) | (~wolf(A)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(299,plain,
% 0.18/0.43 (^[A: $i] : rewrite((wolf(A) => animal(A)) <=> (animal(A) | (~wolf(A))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(300,plain,
% 0.18/0.43 (![A: $i] : (wolf(A) => animal(A)) <=> ![A: $i] : (animal(A) | (~wolf(A)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[299])).
% 0.18/0.43 tff(301,axiom,(![A: $i] : (wolf(A) => animal(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','wolf_is_animal')).
% 0.18/0.43 tff(302,plain,
% 0.18/0.43 (![A: $i] : (animal(A) | (~wolf(A)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.18/0.43 tff(303,plain,
% 0.18/0.43 (![A: $i] : (animal(A) | (~wolf(A)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[302, 298])).
% 0.18/0.43 tff(304,plain,(
% 0.18/0.43 ![A: $i] : (animal(A) | (~wolf(A)))),
% 0.18/0.43 inference(skolemize,[status(sab)],[303])).
% 0.18/0.43 tff(305,plain,
% 0.18/0.43 (![A: $i] : (animal(A) | (~wolf(A)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[304, 297])).
% 0.18/0.43 tff(306,plain,
% 0.18/0.43 (((~![A: $i] : (animal(A) | (~wolf(A)))) | (animal(A!2) | (~wolf(A!2)))) <=> ((~![A: $i] : (animal(A) | (~wolf(A)))) | animal(A!2) | (~wolf(A!2)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(307,plain,
% 0.18/0.43 ((~![A: $i] : (animal(A) | (~wolf(A)))) | (animal(A!2) | (~wolf(A!2)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(308,plain,
% 0.18/0.43 ((~![A: $i] : (animal(A) | (~wolf(A)))) | animal(A!2) | (~wolf(A!2))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.18/0.43 tff(309,plain,
% 0.18/0.43 (animal(A!2)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[308, 259, 305])).
% 0.18/0.43 tff(310,plain,
% 0.18/0.43 (((~![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!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))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(311,plain,
% 0.18/0.43 (((~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))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(312,plain,
% 0.18/0.43 (((~![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!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)))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[311])).
% 0.18/0.43 tff(313,plain,
% 0.18/0.43 (((~![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!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))))),
% 0.18/0.43 inference(transitivity,[status(thm)],[312, 310])).
% 0.18/0.43 tff(314,plain,
% 0.18/0.43 ((~![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!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)))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(315,plain,
% 0.18/0.43 ((~![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!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)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[314, 313])).
% 0.18/0.43 tff(316,plain,
% 0.18/0.43 (![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)))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[315, 135, 309])).
% 0.18/0.43 tff(317,plain,
% 0.18/0.43 (![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[316, 295])).
% 0.18/0.43 tff(318,plain,
% 0.18/0.43 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))) | ((~animal(A!3)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!3, Z))) | eats(A!2, A!3) | (~much_smaller(A!3, A!2)))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))) | (~animal(A!3)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!3, Z))) | eats(A!2, A!3) | (~much_smaller(A!3, A!2)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(319,plain,
% 0.18/0.43 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))) | ((~animal(A!3)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!3, Z))) | eats(A!2, A!3) | (~much_smaller(A!3, A!2)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(320,plain,
% 0.18/0.43 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))) | (~animal(A!3)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!3, Z))) | eats(A!2, A!3) | (~much_smaller(A!3, A!2))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[319, 318])).
% 0.18/0.43 tff(321,plain,
% 0.18/0.43 (![Z: $i] : ((~plant(Z)) | (~eats(A!3, Z))) | eats(A!2, A!3) | (~much_smaller(A!3, A!2))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[320, 197, 317])).
% 0.18/0.43 tff(322,plain,
% 0.18/0.43 (![Z: $i] : ((~plant(Z)) | (~eats(A!3, Z))) | eats(A!2, A!3)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[321, 267])).
% 0.18/0.43 tff(323,plain,
% 0.18/0.43 (eats(A!2, A!3)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[322, 241])).
% 0.18/0.43 tff(324,plain,
% 0.18/0.43 (((~![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))) | ((~grain(A!8)) | (~animal(A!2)) | (~animal(A!3)) | (~eats(A!3, A!8)) | (~eats(A!2, A!3)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))) | (~grain(A!8)) | (~animal(A!2)) | (~animal(A!3)) | (~eats(A!3, A!8)) | (~eats(A!2, A!3)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(325,plain,
% 0.18/0.43 (((~eats(A!3, A!8)) | (~grain(A!8)) | (~animal(A!2)) | (~animal(A!3)) | (~eats(A!2, A!3))) <=> ((~grain(A!8)) | (~animal(A!2)) | (~animal(A!3)) | (~eats(A!3, A!8)) | (~eats(A!2, A!3)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(326,plain,
% 0.18/0.43 (((~![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))) | ((~eats(A!3, A!8)) | (~grain(A!8)) | (~animal(A!2)) | (~animal(A!3)) | (~eats(A!2, A!3)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))) | ((~grain(A!8)) | (~animal(A!2)) | (~animal(A!3)) | (~eats(A!3, A!8)) | (~eats(A!2, A!3))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[325])).
% 0.18/0.43 tff(327,plain,
% 0.18/0.43 (((~![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))) | ((~eats(A!3, A!8)) | (~grain(A!8)) | (~animal(A!2)) | (~animal(A!3)) | (~eats(A!2, A!3)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))) | (~grain(A!8)) | (~animal(A!2)) | (~animal(A!3)) | (~eats(A!3, A!8)) | (~eats(A!2, A!3)))),
% 0.18/0.43 inference(transitivity,[status(thm)],[326, 324])).
% 0.18/0.43 tff(328,plain,
% 0.18/0.43 ((~![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))) | ((~eats(A!3, A!8)) | (~grain(A!8)) | (~animal(A!2)) | (~animal(A!3)) | (~eats(A!2, A!3)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(329,plain,
% 0.18/0.43 ((~![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))) | (~grain(A!8)) | (~animal(A!2)) | (~animal(A!3)) | (~eats(A!3, A!8)) | (~eats(A!2, A!3))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[328, 327])).
% 0.18/0.43 tff(330,plain,
% 0.18/0.43 ($false),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[329, 167, 215, 309, 197, 323, 229])).
% 0.18/0.43 tff(331,plain,(~![Y: $i] : ((~plant(Y)) | eats(A!3, Y))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.43 tff(332,plain,
% 0.18/0.43 (((~![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!3)) | ![Y: $i] : ((~plant(Y)) | eats(A!3, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3))))) <=> ((~![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!3)) | ![Y: $i] : ((~plant(Y)) | eats(A!3, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(333,plain,
% 0.18/0.43 (((~animal(A!3)) | ![Y: $i] : ((~plant(Y)) | eats(A!3, Y)) | ![Y1: $i] : (eats(A!3, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!3)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> ((~animal(A!3)) | ![Y: $i] : ((~plant(Y)) | eats(A!3, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(334,plain,
% 0.18/0.43 (((~![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!3)) | ![Y: $i] : ((~plant(Y)) | eats(A!3, Y)) | ![Y1: $i] : (eats(A!3, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!3)) | ![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!3)) | ![Y: $i] : ((~plant(Y)) | eats(A!3, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3)))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[333])).
% 0.18/0.43 tff(335,plain,
% 0.18/0.43 (((~![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!3)) | ![Y: $i] : ((~plant(Y)) | eats(A!3, Y)) | ![Y1: $i] : (eats(A!3, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!3)) | ![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!3)) | ![Y: $i] : ((~plant(Y)) | eats(A!3, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3))))),
% 0.18/0.43 inference(transitivity,[status(thm)],[334, 332])).
% 0.18/0.43 tff(336,plain,
% 0.18/0.43 ((~![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!3)) | ![Y: $i] : ((~plant(Y)) | eats(A!3, Y)) | ![Y1: $i] : (eats(A!3, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!3)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(337,plain,
% 0.18/0.43 ((~![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!3)) | ![Y: $i] : ((~plant(Y)) | eats(A!3, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[336, 335])).
% 0.18/0.43 tff(338,plain,
% 0.18/0.43 (![Y: $i] : ((~plant(Y)) | eats(A!3, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3)))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[337, 135, 197])).
% 0.18/0.43 tff(339,plain,
% 0.18/0.43 (![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3)))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[338, 331])).
% 0.18/0.43 tff(340,assumption,(~eats(A!3, A!4)), introduced(assumption)).
% 0.18/0.43 tff(341,assumption,(~much_smaller(A!4, A!3)), introduced(assumption)).
% 0.18/0.43 tff(342,plain,
% 0.18/0.43 (^[X: $i, Y: $i] : refl((much_smaller(X, Y) | (~fox(Y)) | (~bird(X))) <=> (much_smaller(X, Y) | (~fox(Y)) | (~bird(X))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(343,plain,
% 0.18/0.43 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X))) <=> ![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[342])).
% 0.18/0.43 tff(344,plain,
% 0.18/0.43 (^[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)))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(345,plain,
% 0.18/0.43 (![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y)) <=> ![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[344])).
% 0.18/0.44 tff(346,plain,
% 0.18/0.44 (![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y)) <=> ![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(347,plain,
% 0.18/0.44 (^[X: $i, Y: $i] : rewrite(((bird(X) & fox(Y)) => much_smaller(X, Y)) <=> ((~(bird(X) & fox(Y))) | much_smaller(X, Y)))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(348,plain,
% 0.18/0.44 (![X: $i, Y: $i] : ((bird(X) & fox(Y)) => much_smaller(X, Y)) <=> ![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[347])).
% 0.18/0.44 tff(349,axiom,(![X: $i, Y: $i] : ((bird(X) & fox(Y)) => much_smaller(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_9')).
% 0.18/0.44 tff(350,plain,
% 0.18/0.44 (![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[349, 348])).
% 0.18/0.44 tff(351,plain,
% 0.18/0.44 (![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[350, 346])).
% 0.18/0.44 tff(352,plain,(
% 0.18/0.44 ![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y))),
% 0.18/0.44 inference(skolemize,[status(sab)],[351])).
% 0.18/0.44 tff(353,plain,
% 0.18/0.44 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[352, 345])).
% 0.18/0.44 tff(354,plain,
% 0.18/0.44 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[353, 343])).
% 0.18/0.44 tff(355,plain,
% 0.18/0.44 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | ((~fox(A!3)) | (~bird(A!4)) | much_smaller(A!4, A!3))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (~fox(A!3)) | (~bird(A!4)) | much_smaller(A!4, A!3))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(356,plain,
% 0.18/0.44 ((much_smaller(A!4, A!3) | (~fox(A!3)) | (~bird(A!4))) <=> ((~fox(A!3)) | (~bird(A!4)) | much_smaller(A!4, A!3))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(357,plain,
% 0.18/0.44 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (much_smaller(A!4, A!3) | (~fox(A!3)) | (~bird(A!4)))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | ((~fox(A!3)) | (~bird(A!4)) | much_smaller(A!4, A!3)))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[356])).
% 0.18/0.44 tff(358,plain,
% 0.18/0.44 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (much_smaller(A!4, A!3) | (~fox(A!3)) | (~bird(A!4)))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (~fox(A!3)) | (~bird(A!4)) | much_smaller(A!4, A!3))),
% 0.18/0.44 inference(transitivity,[status(thm)],[357, 355])).
% 0.18/0.44 tff(359,plain,
% 0.18/0.44 ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (much_smaller(A!4, A!3) | (~fox(A!3)) | (~bird(A!4)))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(360,plain,
% 0.18/0.44 ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (~fox(A!3)) | (~bird(A!4)) | much_smaller(A!4, A!3)),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[359, 358])).
% 0.18/0.44 tff(361,plain,
% 0.18/0.44 ($false),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[360, 193, 22, 354, 341])).
% 0.18/0.44 tff(362,plain,(much_smaller(A!4, A!3)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.44 tff(363,assumption,(~![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z)))), introduced(assumption)).
% 0.18/0.44 tff(364,assumption,(![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3)))), introduced(assumption)).
% 0.18/0.44 tff(365,plain,
% 0.18/0.44 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3)))) | ((~animal(A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | eats(A!3, A!4) | (~much_smaller(A!4, A!3)))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3)))) | (~animal(A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | eats(A!3, A!4) | (~much_smaller(A!4, A!3)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(366,plain,
% 0.18/0.44 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3)))) | ((~animal(A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | eats(A!3, A!4) | (~much_smaller(A!4, A!3)))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(367,plain,
% 0.18/0.44 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3)))) | (~animal(A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | eats(A!3, A!4) | (~much_smaller(A!4, A!3))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[366, 365])).
% 0.18/0.44 tff(368,plain,
% 0.18/0.44 ($false),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[367, 116, 364, 363, 362, 340])).
% 0.18/0.44 tff(369,plain,((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3)))) | ![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | eats(A!3, A!4)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.44 tff(370,plain,
% 0.18/0.44 (![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | eats(A!3, A!4)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[369, 339])).
% 0.18/0.44 tff(371,plain,
% 0.18/0.44 (![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z)))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[370, 224])).
% 0.18/0.44 tff(372,plain,
% 0.18/0.44 (((~![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z)))) | ((~plant(A!7)) | (~eats(A!4, A!7)))) <=> ((~![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z)))) | (~plant(A!7)) | (~eats(A!4, A!7)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(373,plain,
% 0.18/0.44 ((~![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z)))) | ((~plant(A!7)) | (~eats(A!4, A!7)))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(374,plain,
% 0.18/0.44 ((~![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z)))) | (~plant(A!7)) | (~eats(A!4, A!7))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[373, 372])).
% 0.18/0.44 tff(375,plain,
% 0.18/0.44 ($false),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[374, 147, 371, 151])).
% 0.18/0.44 % SZS output end Proof
%------------------------------------------------------------------------------