%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ031+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:23:13 AM UTC 2025
% Result : Theorem 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : PUZ031+1 : TPTP v9.0.0. Released v2.0.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 02:42:41 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.38 % SZS status Theorem
% 0.18/0.38 % SZS output start Proof
% 0.18/0.38 tff(eats_type, type, (
% 0.18/0.38 eats: ( $i * $i ) > $o)).
% 0.18/0.38 tff(tptp_fun_Y_6_type, type, (
% 0.18/0.38 tptp_fun_Y_6: $i > $i)).
% 0.18/0.38 tff(tptp_fun_X1_3_type, type, (
% 0.18/0.38 tptp_fun_X1_3: $i)).
% 0.18/0.38 tff(tptp_fun_X1_2_type, type, (
% 0.18/0.38 tptp_fun_X1_2: $i)).
% 0.18/0.38 tff(plant_type, type, (
% 0.18/0.38 plant: $i > $o)).
% 0.18/0.38 tff(much_smaller_type, type, (
% 0.18/0.38 much_smaller: ( $i * $i ) > $o)).
% 0.18/0.38 tff(animal_type, type, (
% 0.18/0.38 animal: $i > $o)).
% 0.18/0.38 tff(tptp_fun_X1_4_type, type, (
% 0.18/0.38 tptp_fun_X1_4: $i)).
% 0.18/0.38 tff(bird_type, type, (
% 0.18/0.38 bird: $i > $o)).
% 0.18/0.38 tff(snail_type, type, (
% 0.18/0.38 snail: $i > $o)).
% 0.18/0.38 tff(caterpillar_type, type, (
% 0.18/0.38 caterpillar: $i > $o)).
% 0.18/0.38 tff(tptp_fun_X1_1_type, type, (
% 0.18/0.38 tptp_fun_X1_1: $i)).
% 0.18/0.38 tff(grain_type, type, (
% 0.18/0.38 grain: $i > $o)).
% 0.18/0.38 tff(fox_type, type, (
% 0.18/0.38 fox: $i > $o)).
% 0.18/0.38 tff(tptp_fun_X_5_type, type, (
% 0.18/0.38 tptp_fun_X_5: $i)).
% 0.18/0.38 tff(tptp_fun_X1_0_type, type, (
% 0.18/0.38 tptp_fun_X1_0: $i)).
% 0.18/0.38 tff(wolf_type, type, (
% 0.18/0.38 wolf: $i > $o)).
% 0.18/0.38 tff(1,assumption,(eats(X1!2, X1!4)), introduced(assumption)).
% 0.18/0.38 tff(2,plain,
% 0.18/0.38 (^[X: $i, Y: $i] : refl(((~eats(X, Y)) | (~snail(Y)) | (~bird(X))) <=> ((~eats(X, Y)) | (~snail(Y)) | (~bird(X))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(3,plain,
% 0.18/0.38 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.18/0.38 tff(4,plain,
% 0.18/0.38 (^[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)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(5,plain,
% 0.18/0.38 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y)))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[4])).
% 0.18/0.38 tff(6,plain,
% 0.18/0.38 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y)))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(7,plain,
% 0.18/0.38 (^[X: $i, Y: $i] : rewrite(((bird(X) & snail(Y)) => (~eats(X, Y))) <=> ((~eats(X, Y)) | (~(bird(X) & snail(Y)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(8,plain,
% 0.18/0.38 (![X: $i, Y: $i] : ((bird(X) & snail(Y)) => (~eats(X, Y))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[7])).
% 0.18/0.38 tff(9,axiom,(![X: $i, Y: $i] : ((bird(X) & snail(Y)) => (~eats(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_13')).
% 0.18/0.38 tff(10,plain,
% 0.18/0.38 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.18/0.38 tff(11,plain,
% 0.18/0.38 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.18/0.38 tff(12,plain,(
% 0.18/0.38 ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y))))),
% 0.18/0.38 inference(skolemize,[status(sab)],[11])).
% 0.18/0.38 tff(13,plain,
% 0.18/0.38 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.18/0.38 tff(14,plain,
% 0.18/0.38 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[13, 3])).
% 0.18/0.38 tff(15,plain,
% 0.18/0.38 (?[X1: $i] : snail(X1) <=> ?[X1: $i] : snail(X1)),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(16,axiom,(?[X1: $i] : snail(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_5_2')).
% 0.18/0.38 tff(17,plain,
% 0.18/0.38 (?[X1: $i] : snail(X1)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.18/0.38 tff(18,plain,(
% 0.18/0.38 snail(X1!4)),
% 0.18/0.38 inference(skolemize,[status(sab)],[17])).
% 0.18/0.38 tff(19,plain,
% 0.18/0.38 (?[X1: $i] : bird(X1) <=> ?[X1: $i] : bird(X1)),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(20,axiom,(?[X1: $i] : bird(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_3_2')).
% 0.18/0.38 tff(21,plain,
% 0.18/0.38 (?[X1: $i] : bird(X1)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.18/0.38 tff(22,plain,(
% 0.18/0.38 bird(X1!2)),
% 0.18/0.38 inference(skolemize,[status(sab)],[21])).
% 0.18/0.38 tff(23,plain,
% 0.18/0.38 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | ((~bird(X1!2)) | (~snail(X1!4)) | (~eats(X1!2, X1!4)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | (~bird(X1!2)) | (~snail(X1!4)) | (~eats(X1!2, X1!4)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(24,plain,
% 0.18/0.38 (((~eats(X1!2, X1!4)) | (~snail(X1!4)) | (~bird(X1!2))) <=> ((~bird(X1!2)) | (~snail(X1!4)) | (~eats(X1!2, X1!4)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(25,plain,
% 0.18/0.38 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | ((~eats(X1!2, X1!4)) | (~snail(X1!4)) | (~bird(X1!2)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | ((~bird(X1!2)) | (~snail(X1!4)) | (~eats(X1!2, X1!4))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[24])).
% 0.18/0.38 tff(26,plain,
% 0.18/0.38 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | ((~eats(X1!2, X1!4)) | (~snail(X1!4)) | (~bird(X1!2)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | (~bird(X1!2)) | (~snail(X1!4)) | (~eats(X1!2, X1!4)))),
% 0.18/0.38 inference(transitivity,[status(thm)],[25, 23])).
% 0.18/0.38 tff(27,plain,
% 0.18/0.38 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | ((~eats(X1!2, X1!4)) | (~snail(X1!4)) | (~bird(X1!2)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(28,plain,
% 0.18/0.38 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | (~bird(X1!2)) | (~snail(X1!4)) | (~eats(X1!2, X1!4))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.18/0.38 tff(29,plain,
% 0.18/0.38 ($false),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[28, 22, 18, 14, 1])).
% 0.18/0.38 tff(30,plain,(~eats(X1!2, X1!4)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.38 tff(31,assumption,(~much_smaller(X1!4, X1!2)), introduced(assumption)).
% 0.18/0.38 tff(32,plain,
% 0.18/0.38 ((caterpillar(X1!4) | snail(X1!4)) | (~snail(X1!4))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(33,plain,
% 0.18/0.38 (caterpillar(X1!4) | snail(X1!4)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[32, 18])).
% 0.18/0.38 tff(34,plain,
% 0.18/0.38 (^[X: $i, Y: $i] : refl((much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X)))) <=> (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(35,plain,
% 0.18/0.38 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X)))) <=> ![X: $i, Y: $i] : (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[34])).
% 0.18/0.38 tff(36,plain,
% 0.18/0.38 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((bird(Y) & (caterpillar(X) | snail(X))) <=> (~((~bird(Y)) | (~(caterpillar(X) | snail(X)))))), ((~(bird(Y) & (caterpillar(X) | snail(X)))) <=> (~(~((~bird(Y)) | (~(caterpillar(X) | snail(X)))))))), rewrite((~(~((~bird(Y)) | (~(caterpillar(X) | snail(X)))))) <=> ((~bird(Y)) | (~(caterpillar(X) | snail(X))))), ((~(bird(Y) & (caterpillar(X) | snail(X)))) <=> ((~bird(Y)) | (~(caterpillar(X) | snail(X)))))), (((~(bird(Y) & (caterpillar(X) | snail(X)))) | much_smaller(X, Y)) <=> (((~bird(Y)) | (~(caterpillar(X) | snail(X)))) | much_smaller(X, Y)))), rewrite((((~bird(Y)) | (~(caterpillar(X) | snail(X)))) | much_smaller(X, Y)) <=> (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X))))), (((~(bird(Y) & (caterpillar(X) | snail(X)))) | much_smaller(X, Y)) <=> (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(37,plain,
% 0.18/0.38 (![X: $i, Y: $i] : ((~(bird(Y) & (caterpillar(X) | snail(X)))) | much_smaller(X, Y)) <=> ![X: $i, Y: $i] : (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[36])).
% 0.18/0.38 tff(38,plain,
% 0.18/0.38 (![X: $i, Y: $i] : ((~(bird(Y) & (caterpillar(X) | snail(X)))) | much_smaller(X, Y)) <=> ![X: $i, Y: $i] : ((~(bird(Y) & (caterpillar(X) | snail(X)))) | much_smaller(X, Y))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(39,plain,
% 0.18/0.38 (^[X: $i, Y: $i] : trans(monotonicity(rewrite((bird(Y) & (snail(X) | caterpillar(X))) <=> (bird(Y) & (caterpillar(X) | snail(X)))), (((bird(Y) & (snail(X) | caterpillar(X))) => much_smaller(X, Y)) <=> ((bird(Y) & (caterpillar(X) | snail(X))) => much_smaller(X, Y)))), rewrite(((bird(Y) & (caterpillar(X) | snail(X))) => much_smaller(X, Y)) <=> ((~(bird(Y) & (caterpillar(X) | snail(X)))) | much_smaller(X, Y))), (((bird(Y) & (snail(X) | caterpillar(X))) => much_smaller(X, Y)) <=> ((~(bird(Y) & (caterpillar(X) | snail(X)))) | much_smaller(X, Y))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(40,plain,
% 0.18/0.38 (![X: $i, Y: $i] : ((bird(Y) & (snail(X) | caterpillar(X))) => much_smaller(X, Y)) <=> ![X: $i, Y: $i] : ((~(bird(Y) & (caterpillar(X) | snail(X)))) | much_smaller(X, Y))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[39])).
% 0.18/0.38 tff(41,axiom,(![X: $i, Y: $i] : ((bird(Y) & (snail(X) | caterpillar(X))) => much_smaller(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_8')).
% 0.18/0.38 tff(42,plain,
% 0.18/0.38 (![X: $i, Y: $i] : ((~(bird(Y) & (caterpillar(X) | snail(X)))) | much_smaller(X, Y))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.18/0.38 tff(43,plain,
% 0.18/0.38 (![X: $i, Y: $i] : ((~(bird(Y) & (caterpillar(X) | snail(X)))) | much_smaller(X, Y))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.18/0.38 tff(44,plain,(
% 0.18/0.38 ![X: $i, Y: $i] : ((~(bird(Y) & (caterpillar(X) | snail(X)))) | much_smaller(X, Y))),
% 0.18/0.38 inference(skolemize,[status(sab)],[43])).
% 0.18/0.38 tff(45,plain,
% 0.18/0.38 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.18/0.38 tff(46,plain,
% 0.18/0.38 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[45, 35])).
% 0.18/0.38 tff(47,plain,
% 0.18/0.38 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X))))) | ((~bird(X1!2)) | (~(caterpillar(X1!4) | snail(X1!4))) | much_smaller(X1!4, X1!2))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X))))) | (~bird(X1!2)) | (~(caterpillar(X1!4) | snail(X1!4))) | much_smaller(X1!4, X1!2))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(48,plain,
% 0.18/0.38 ((much_smaller(X1!4, X1!2) | (~bird(X1!2)) | (~(caterpillar(X1!4) | snail(X1!4)))) <=> ((~bird(X1!2)) | (~(caterpillar(X1!4) | snail(X1!4))) | much_smaller(X1!4, X1!2))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(49,plain,
% 0.18/0.38 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X))))) | (much_smaller(X1!4, X1!2) | (~bird(X1!2)) | (~(caterpillar(X1!4) | snail(X1!4))))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X))))) | ((~bird(X1!2)) | (~(caterpillar(X1!4) | snail(X1!4))) | much_smaller(X1!4, X1!2)))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[48])).
% 0.18/0.38 tff(50,plain,
% 0.18/0.38 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X))))) | (much_smaller(X1!4, X1!2) | (~bird(X1!2)) | (~(caterpillar(X1!4) | snail(X1!4))))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X))))) | (~bird(X1!2)) | (~(caterpillar(X1!4) | snail(X1!4))) | much_smaller(X1!4, X1!2))),
% 0.18/0.38 inference(transitivity,[status(thm)],[49, 47])).
% 0.18/0.38 tff(51,plain,
% 0.18/0.38 ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X))))) | (much_smaller(X1!4, X1!2) | (~bird(X1!2)) | (~(caterpillar(X1!4) | snail(X1!4))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(52,plain,
% 0.18/0.38 ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X))))) | (~bird(X1!2)) | (~(caterpillar(X1!4) | snail(X1!4))) | much_smaller(X1!4, X1!2)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.18/0.38 tff(53,plain,
% 0.18/0.38 ($false),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[52, 22, 46, 33, 31])).
% 0.18/0.38 tff(54,plain,(much_smaller(X1!4, X1!2)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.38 tff(55,assumption,(![Z: $i] : ((~plant(Z)) | (~eats(X1!4, Z)))), introduced(assumption)).
% 0.18/0.38 tff(56,plain,
% 0.18/0.38 (^[X: $i] : refl(((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X)))))) <=> ((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X)))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(57,plain,
% 0.18/0.38 (![X: $i] : ((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X)))))) <=> ![X: $i] : ((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[56])).
% 0.18/0.38 tff(58,plain,
% 0.18/0.38 (^[X: $i] : rewrite(((~(caterpillar(X) | snail(X))) | (plant(tptp_fun_Y_6(X)) & eats(X, tptp_fun_Y_6(X)))) <=> ((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X)))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(59,plain,
% 0.18/0.38 (![X: $i] : ((~(caterpillar(X) | snail(X))) | (plant(tptp_fun_Y_6(X)) & eats(X, tptp_fun_Y_6(X)))) <=> ![X: $i] : ((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[58])).
% 0.18/0.38 tff(60,plain,
% 0.18/0.38 (![X: $i] : ((~(caterpillar(X) | snail(X))) | ?[Y: $i] : (plant(Y) & eats(X, Y))) <=> ![X: $i] : ((~(caterpillar(X) | snail(X))) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(61,plain,
% 0.18/0.38 (^[X: $i] : rewrite(((caterpillar(X) | snail(X)) => ?[Y: $i] : (plant(Y) & eats(X, Y))) <=> ((~(caterpillar(X) | snail(X))) | ?[Y: $i] : (plant(Y) & eats(X, Y))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(62,plain,
% 0.18/0.38 (![X: $i] : ((caterpillar(X) | snail(X)) => ?[Y: $i] : (plant(Y) & eats(X, Y))) <=> ![X: $i] : ((~(caterpillar(X) | snail(X))) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[61])).
% 0.18/0.38 tff(63,axiom,(![X: $i] : ((caterpillar(X) | snail(X)) => ?[Y: $i] : (plant(Y) & eats(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_14')).
% 0.18/0.38 tff(64,plain,
% 0.18/0.38 (![X: $i] : ((~(caterpillar(X) | snail(X))) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.18/0.38 tff(65,plain,
% 0.18/0.38 (![X: $i] : ((~(caterpillar(X) | snail(X))) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.18/0.38 tff(66,plain,(
% 0.18/0.38 ![X: $i] : ((~(caterpillar(X) | snail(X))) | (plant(tptp_fun_Y_6(X)) & eats(X, tptp_fun_Y_6(X))))),
% 0.18/0.38 inference(skolemize,[status(sab)],[65])).
% 0.18/0.38 tff(67,plain,
% 0.18/0.38 (![X: $i] : ((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.18/0.38 tff(68,plain,
% 0.18/0.38 (![X: $i] : ((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[67, 57])).
% 0.18/0.38 tff(69,plain,
% 0.18/0.38 (((~![X: $i] : ((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | ((~(caterpillar(X1!4) | snail(X1!4))) | (~((~plant(tptp_fun_Y_6(X1!4))) | (~eats(X1!4, tptp_fun_Y_6(X1!4))))))) <=> ((~![X: $i] : ((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | (~(caterpillar(X1!4) | snail(X1!4))) | (~((~plant(tptp_fun_Y_6(X1!4))) | (~eats(X1!4, tptp_fun_Y_6(X1!4))))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(70,plain,
% 0.18/0.38 ((~![X: $i] : ((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | ((~(caterpillar(X1!4) | snail(X1!4))) | (~((~plant(tptp_fun_Y_6(X1!4))) | (~eats(X1!4, tptp_fun_Y_6(X1!4))))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(71,plain,
% 0.18/0.38 ((~![X: $i] : ((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | (~(caterpillar(X1!4) | snail(X1!4))) | (~((~plant(tptp_fun_Y_6(X1!4))) | (~eats(X1!4, tptp_fun_Y_6(X1!4)))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.18/0.38 tff(72,plain,
% 0.18/0.38 (~((~plant(tptp_fun_Y_6(X1!4))) | (~eats(X1!4, tptp_fun_Y_6(X1!4))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[71, 68, 33])).
% 0.18/0.38 tff(73,plain,
% 0.18/0.38 (((~plant(tptp_fun_Y_6(X1!4))) | (~eats(X1!4, tptp_fun_Y_6(X1!4)))) | eats(X1!4, tptp_fun_Y_6(X1!4))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(74,plain,
% 0.18/0.39 (eats(X1!4, tptp_fun_Y_6(X1!4))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.18/0.39 tff(75,plain,
% 0.18/0.39 (((~plant(tptp_fun_Y_6(X1!4))) | (~eats(X1!4, tptp_fun_Y_6(X1!4)))) | plant(tptp_fun_Y_6(X1!4))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(76,plain,
% 0.18/0.39 (plant(tptp_fun_Y_6(X1!4))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[75, 72])).
% 0.18/0.39 tff(77,plain,
% 0.18/0.39 (((~![Z: $i] : ((~plant(Z)) | (~eats(X1!4, Z)))) | ((~plant(tptp_fun_Y_6(X1!4))) | (~eats(X1!4, tptp_fun_Y_6(X1!4))))) <=> ((~![Z: $i] : ((~plant(Z)) | (~eats(X1!4, Z)))) | (~plant(tptp_fun_Y_6(X1!4))) | (~eats(X1!4, tptp_fun_Y_6(X1!4))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(78,plain,
% 0.18/0.39 ((~![Z: $i] : ((~plant(Z)) | (~eats(X1!4, Z)))) | ((~plant(tptp_fun_Y_6(X1!4))) | (~eats(X1!4, tptp_fun_Y_6(X1!4))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(79,plain,
% 0.18/0.39 ((~![Z: $i] : ((~plant(Z)) | (~eats(X1!4, Z)))) | (~plant(tptp_fun_Y_6(X1!4))) | (~eats(X1!4, tptp_fun_Y_6(X1!4)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.18/0.39 tff(80,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[79, 76, 74, 55])).
% 0.18/0.39 tff(81,plain,(~![Z: $i] : ((~plant(Z)) | (~eats(X1!4, Z)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(82,assumption,(![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!2, Y1) | (~much_smaller(Y1, X1!2)))), introduced(assumption)).
% 0.18/0.39 tff(83,plain,
% 0.18/0.39 (^[X: $i] : refl((animal(X) | (~snail(X))) <=> (animal(X) | (~snail(X))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(84,plain,
% 0.18/0.39 (![X: $i] : (animal(X) | (~snail(X))) <=> ![X: $i] : (animal(X) | (~snail(X)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[83])).
% 0.18/0.39 tff(85,plain,
% 0.18/0.39 (![X: $i] : (animal(X) | (~snail(X))) <=> ![X: $i] : (animal(X) | (~snail(X)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(86,plain,
% 0.18/0.39 (^[X: $i] : rewrite((snail(X) => animal(X)) <=> (animal(X) | (~snail(X))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(87,plain,
% 0.18/0.39 (![X: $i] : (snail(X) => animal(X)) <=> ![X: $i] : (animal(X) | (~snail(X)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[86])).
% 0.18/0.39 tff(88,axiom,(![X: $i] : (snail(X) => animal(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_5_1')).
% 0.18/0.39 tff(89,plain,
% 0.18/0.39 (![X: $i] : (animal(X) | (~snail(X)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.18/0.39 tff(90,plain,
% 0.18/0.39 (![X: $i] : (animal(X) | (~snail(X)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.18/0.39 tff(91,plain,(
% 0.18/0.39 ![X: $i] : (animal(X) | (~snail(X)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[90])).
% 0.18/0.39 tff(92,plain,
% 0.18/0.39 (![X: $i] : (animal(X) | (~snail(X)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.18/0.39 tff(93,plain,
% 0.18/0.39 (((~![X: $i] : (animal(X) | (~snail(X)))) | (animal(X1!4) | (~snail(X1!4)))) <=> ((~![X: $i] : (animal(X) | (~snail(X)))) | animal(X1!4) | (~snail(X1!4)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(94,plain,
% 0.18/0.39 ((~![X: $i] : (animal(X) | (~snail(X)))) | (animal(X1!4) | (~snail(X1!4)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(95,plain,
% 0.18/0.39 ((~![X: $i] : (animal(X) | (~snail(X)))) | animal(X1!4) | (~snail(X1!4))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.18/0.39 tff(96,plain,
% 0.18/0.39 (animal(X1!4)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[95, 92, 18])).
% 0.18/0.39 tff(97,plain,
% 0.18/0.39 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!2, Y1) | (~much_smaller(Y1, X1!2)))) | ((~animal(X1!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!4, Z))) | eats(X1!2, X1!4) | (~much_smaller(X1!4, X1!2)))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!2, Y1) | (~much_smaller(Y1, X1!2)))) | (~animal(X1!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!4, Z))) | eats(X1!2, X1!4) | (~much_smaller(X1!4, X1!2)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(98,plain,
% 0.18/0.39 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!2, Y1) | (~much_smaller(Y1, X1!2)))) | ((~animal(X1!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!4, Z))) | eats(X1!2, X1!4) | (~much_smaller(X1!4, X1!2)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(99,plain,
% 0.18/0.39 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!2, Y1) | (~much_smaller(Y1, X1!2)))) | (~animal(X1!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!4, Z))) | eats(X1!2, X1!4) | (~much_smaller(X1!4, X1!2))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.18/0.39 tff(100,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[99, 96, 82, 81, 54, 30])).
% 0.18/0.39 tff(101,plain,(~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!2, Y1) | (~much_smaller(Y1, X1!2)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(102,plain,
% 0.18/0.39 (^[X: $i] : refl((animal(X) | (~bird(X))) <=> (animal(X) | (~bird(X))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(103,plain,
% 0.18/0.39 (![X: $i] : (animal(X) | (~bird(X))) <=> ![X: $i] : (animal(X) | (~bird(X)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[102])).
% 0.18/0.39 tff(104,plain,
% 0.18/0.39 (![X: $i] : (animal(X) | (~bird(X))) <=> ![X: $i] : (animal(X) | (~bird(X)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(105,plain,
% 0.18/0.39 (^[X: $i] : rewrite((bird(X) => animal(X)) <=> (animal(X) | (~bird(X))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(106,plain,
% 0.18/0.39 (![X: $i] : (bird(X) => animal(X)) <=> ![X: $i] : (animal(X) | (~bird(X)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[105])).
% 0.18/0.39 tff(107,axiom,(![X: $i] : (bird(X) => animal(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_3_1')).
% 0.18/0.39 tff(108,plain,
% 0.18/0.39 (![X: $i] : (animal(X) | (~bird(X)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.18/0.39 tff(109,plain,
% 0.18/0.39 (![X: $i] : (animal(X) | (~bird(X)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.18/0.39 tff(110,plain,(
% 0.18/0.39 ![X: $i] : (animal(X) | (~bird(X)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[109])).
% 0.18/0.39 tff(111,plain,
% 0.18/0.39 (![X: $i] : (animal(X) | (~bird(X)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.18/0.39 tff(112,plain,
% 0.18/0.39 (((~![X: $i] : (animal(X) | (~bird(X)))) | (animal(X1!2) | (~bird(X1!2)))) <=> ((~![X: $i] : (animal(X) | (~bird(X)))) | animal(X1!2) | (~bird(X1!2)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(113,plain,
% 0.18/0.39 ((~![X: $i] : (animal(X) | (~bird(X)))) | (animal(X1!2) | (~bird(X1!2)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(114,plain,
% 0.18/0.39 ((~![X: $i] : (animal(X) | (~bird(X)))) | animal(X1!2) | (~bird(X1!2))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.18/0.39 tff(115,plain,
% 0.18/0.39 (animal(X1!2)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[114, 111, 22])).
% 0.18/0.39 tff(116,plain,
% 0.18/0.39 (^[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))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(117,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[116])).
% 0.18/0.39 tff(118,plain,
% 0.18/0.39 (^[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))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(119,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[118])).
% 0.18/0.39 tff(120,plain,
% 0.18/0.39 (^[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))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(121,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[120])).
% 0.18/0.39 tff(122,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[121, 119])).
% 0.18/0.39 tff(123,plain,
% 0.18/0.39 (^[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)))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(124,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[123])).
% 0.18/0.39 tff(125,plain,
% 0.18/0.39 (^[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)))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(126,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[125])).
% 0.18/0.39 tff(127,plain,
% 0.18/0.39 (![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)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(128,plain,
% 0.18/0.39 (^[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)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(129,plain,
% 0.18/0.39 (![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)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[128])).
% 0.18/0.39 tff(130,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/sandbox/benchmark/theBenchmark.p','pel47_7')).
% 0.18/0.39 tff(131,plain,
% 0.18/0.39 (![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)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.18/0.39 tff(132,plain,
% 0.18/0.39 (![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)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.18/0.39 tff(133,plain,(
% 0.18/0.39 ![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)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[132])).
% 0.18/0.39 tff(134,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[133, 126])).
% 0.18/0.39 tff(135,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[134, 124])).
% 0.18/0.39 tff(136,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[135, 122])).
% 0.18/0.39 tff(137,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[136, 117])).
% 0.18/0.39 tff(138,plain,
% 0.18/0.39 (((~![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(X1!2)) | ![Y: $i] : ((~plant(Y)) | eats(X1!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!2, Y1) | (~much_smaller(Y1, X1!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(X1!2)) | ![Y: $i] : ((~plant(Y)) | eats(X1!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!2, Y1) | (~much_smaller(Y1, X1!2))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(139,plain,
% 0.18/0.39 (((~animal(X1!2)) | ![Y: $i] : ((~plant(Y)) | eats(X1!2, Y)) | ![Y1: $i] : (eats(X1!2, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X1!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> ((~animal(X1!2)) | ![Y: $i] : ((~plant(Y)) | eats(X1!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!2, Y1) | (~much_smaller(Y1, X1!2))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(140,plain,
% 0.18/0.40 (((~![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(X1!2)) | ![Y: $i] : ((~plant(Y)) | eats(X1!2, Y)) | ![Y1: $i] : (eats(X1!2, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X1!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(X1!2)) | ![Y: $i] : ((~plant(Y)) | eats(X1!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!2, Y1) | (~much_smaller(Y1, X1!2)))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[139])).
% 0.18/0.40 tff(141,plain,
% 0.18/0.40 (((~![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(X1!2)) | ![Y: $i] : ((~plant(Y)) | eats(X1!2, Y)) | ![Y1: $i] : (eats(X1!2, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X1!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(X1!2)) | ![Y: $i] : ((~plant(Y)) | eats(X1!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!2, Y1) | (~much_smaller(Y1, X1!2))))),
% 0.18/0.40 inference(transitivity,[status(thm)],[140, 138])).
% 0.18/0.40 tff(142,plain,
% 0.18/0.40 ((~![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(X1!2)) | ![Y: $i] : ((~plant(Y)) | eats(X1!2, Y)) | ![Y1: $i] : (eats(X1!2, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X1!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(143,plain,
% 0.18/0.40 ((~![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(X1!2)) | ![Y: $i] : ((~plant(Y)) | eats(X1!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!2, Y1) | (~much_smaller(Y1, X1!2)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.18/0.40 tff(144,plain,
% 0.18/0.40 (![Y: $i] : ((~plant(Y)) | eats(X1!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!2, Y1) | (~much_smaller(Y1, X1!2)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[143, 137, 115])).
% 0.18/0.40 tff(145,plain,
% 0.18/0.40 (![Y: $i] : ((~plant(Y)) | eats(X1!2, Y))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[144, 101])).
% 0.18/0.40 tff(146,plain,
% 0.18/0.40 (?[X1: $i] : caterpillar(X1) <=> ?[X1: $i] : caterpillar(X1)),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(147,axiom,(?[X1: $i] : caterpillar(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_4_2')).
% 0.18/0.40 tff(148,plain,
% 0.18/0.40 (?[X1: $i] : caterpillar(X1)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.18/0.40 tff(149,plain,(
% 0.18/0.40 caterpillar(X1!3)),
% 0.18/0.40 inference(skolemize,[status(sab)],[148])).
% 0.18/0.40 tff(150,plain,
% 0.18/0.40 ((caterpillar(X1!3) | snail(X1!3)) | (~caterpillar(X1!3))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(151,plain,
% 0.18/0.40 (caterpillar(X1!3) | snail(X1!3)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.18/0.40 tff(152,plain,
% 0.18/0.40 (((~![X: $i] : ((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | ((~(caterpillar(X1!3) | snail(X1!3))) | (~((~plant(tptp_fun_Y_6(X1!3))) | (~eats(X1!3, tptp_fun_Y_6(X1!3))))))) <=> ((~![X: $i] : ((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | (~(caterpillar(X1!3) | snail(X1!3))) | (~((~plant(tptp_fun_Y_6(X1!3))) | (~eats(X1!3, tptp_fun_Y_6(X1!3))))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(153,plain,
% 0.18/0.40 ((~![X: $i] : ((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | ((~(caterpillar(X1!3) | snail(X1!3))) | (~((~plant(tptp_fun_Y_6(X1!3))) | (~eats(X1!3, tptp_fun_Y_6(X1!3))))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(154,plain,
% 0.18/0.40 ((~![X: $i] : ((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | (~(caterpillar(X1!3) | snail(X1!3))) | (~((~plant(tptp_fun_Y_6(X1!3))) | (~eats(X1!3, tptp_fun_Y_6(X1!3)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.18/0.40 tff(155,plain,
% 0.18/0.40 (~((~plant(tptp_fun_Y_6(X1!3))) | (~eats(X1!3, tptp_fun_Y_6(X1!3))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[154, 68, 151])).
% 0.18/0.40 tff(156,plain,
% 0.18/0.40 (((~plant(tptp_fun_Y_6(X1!3))) | (~eats(X1!3, tptp_fun_Y_6(X1!3)))) | plant(tptp_fun_Y_6(X1!3))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(157,plain,
% 0.18/0.40 (plant(tptp_fun_Y_6(X1!3))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.18/0.40 tff(158,plain,
% 0.18/0.40 (((~![Y: $i] : ((~plant(Y)) | eats(X1!2, Y))) | ((~plant(tptp_fun_Y_6(X1!3))) | eats(X1!2, tptp_fun_Y_6(X1!3)))) <=> ((~![Y: $i] : ((~plant(Y)) | eats(X1!2, Y))) | (~plant(tptp_fun_Y_6(X1!3))) | eats(X1!2, tptp_fun_Y_6(X1!3)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(159,plain,
% 0.18/0.40 ((~![Y: $i] : ((~plant(Y)) | eats(X1!2, Y))) | ((~plant(tptp_fun_Y_6(X1!3))) | eats(X1!2, tptp_fun_Y_6(X1!3)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(160,plain,
% 0.18/0.40 ((~![Y: $i] : ((~plant(Y)) | eats(X1!2, Y))) | (~plant(tptp_fun_Y_6(X1!3))) | eats(X1!2, tptp_fun_Y_6(X1!3))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.18/0.40 tff(161,plain,
% 0.18/0.40 (eats(X1!2, tptp_fun_Y_6(X1!3))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[160, 157, 145])).
% 0.18/0.40 tff(162,plain,
% 0.18/0.40 (?[X1: $i] : fox(X1) <=> ?[X1: $i] : fox(X1)),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(163,axiom,(?[X1: $i] : fox(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_2_2')).
% 0.18/0.40 tff(164,plain,
% 0.18/0.40 (?[X1: $i] : fox(X1)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.18/0.40 tff(165,plain,(
% 0.18/0.40 fox(X1!1)),
% 0.18/0.40 inference(skolemize,[status(sab)],[164])).
% 0.18/0.40 tff(166,plain,
% 0.18/0.40 (^[X: $i] : refl((animal(X) | (~fox(X))) <=> (animal(X) | (~fox(X))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(167,plain,
% 0.18/0.40 (![X: $i] : (animal(X) | (~fox(X))) <=> ![X: $i] : (animal(X) | (~fox(X)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[166])).
% 0.18/0.40 tff(168,plain,
% 0.18/0.40 (![X: $i] : (animal(X) | (~fox(X))) <=> ![X: $i] : (animal(X) | (~fox(X)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(169,plain,
% 0.18/0.40 (^[X: $i] : rewrite((fox(X) => animal(X)) <=> (animal(X) | (~fox(X))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(170,plain,
% 0.18/0.40 (![X: $i] : (fox(X) => animal(X)) <=> ![X: $i] : (animal(X) | (~fox(X)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[169])).
% 0.18/0.40 tff(171,axiom,(![X: $i] : (fox(X) => animal(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_2_1')).
% 0.18/0.40 tff(172,plain,
% 0.18/0.40 (![X: $i] : (animal(X) | (~fox(X)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.18/0.40 tff(173,plain,
% 0.18/0.40 (![X: $i] : (animal(X) | (~fox(X)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[172, 168])).
% 0.18/0.40 tff(174,plain,(
% 0.18/0.40 ![X: $i] : (animal(X) | (~fox(X)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[173])).
% 0.18/0.40 tff(175,plain,
% 0.18/0.40 (![X: $i] : (animal(X) | (~fox(X)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[174, 167])).
% 0.18/0.40 tff(176,plain,
% 0.18/0.40 (((~![X: $i] : (animal(X) | (~fox(X)))) | (animal(X1!1) | (~fox(X1!1)))) <=> ((~![X: $i] : (animal(X) | (~fox(X)))) | animal(X1!1) | (~fox(X1!1)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(177,plain,
% 0.18/0.40 ((~![X: $i] : (animal(X) | (~fox(X)))) | (animal(X1!1) | (~fox(X1!1)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(178,plain,
% 0.18/0.40 ((~![X: $i] : (animal(X) | (~fox(X)))) | animal(X1!1) | (~fox(X1!1))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.18/0.40 tff(179,plain,
% 0.18/0.40 (animal(X1!1)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[178, 175, 165])).
% 0.18/0.40 tff(180,plain,
% 0.18/0.40 (^[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)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(181,plain,
% 0.18/0.40 (![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))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[180])).
% 0.18/0.40 tff(182,plain,
% 0.18/0.40 (^[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)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(183,plain,
% 0.18/0.40 (![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))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[182])).
% 0.18/0.40 tff(184,plain,
% 0.18/0.40 (![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))))),
% 0.18/0.40 inference(transitivity,[status(thm)],[183, 181])).
% 0.18/0.40 tff(185,plain,
% 0.18/0.40 (^[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)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(186,plain,
% 0.18/0.40 (![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))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[185])).
% 0.18/0.40 tff(187,plain,
% 0.18/0.40 (^[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)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(188,plain,
% 0.18/0.40 (![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))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[187])).
% 0.18/0.40 tff(189,plain,
% 0.18/0.40 ((~?[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))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(190,plain,
% 0.18/0.40 ((~?[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))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(191,axiom,(~?[X: $i, Y: $i] : ((animal(X) & animal(Y)) & ?[Z: $i] : ((grain(Z) & eats(Y, Z)) & eats(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47')).
% 0.18/0.40 tff(192,plain,
% 0.18/0.40 (~?[X: $i, Y: $i] : (animal(X) & animal(Y) & ?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.18/0.40 tff(193,plain,
% 0.18/0.40 (~?[X: $i, Y: $i] : (animal(X) & animal(Y) & ?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[192, 189])).
% 0.18/0.40 tff(194,plain,
% 0.18/0.40 (~?[X: $i, Y: $i] : (animal(X) & animal(Y) & ?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[193, 189])).
% 0.18/0.40 tff(195,plain,
% 0.18/0.40 (~?[X: $i, Y: $i] : (animal(X) & animal(Y) & ?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[194, 189])).
% 0.18/0.40 tff(196,plain,
% 0.18/0.40 (^[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))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(197,plain,(
% 0.18/0.40 ![X: $i, Y: $i] : ((~animal(X)) | (~animal(Y)) | ![Z: $i] : (~(grain(Z) & eats(Y, Z) & eats(X, Y))))),
% 0.18/0.40 inference(nnf-neg,[status(sab)],[195, 196])).
% 0.18/0.40 tff(198,plain,
% 0.18/0.40 (![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : (~(grain(Z) & eats(Y, Z) & eats(X, Y))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[197, 188])).
% 0.18/0.40 tff(199,plain,
% 0.18/0.40 (![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[198, 186])).
% 0.18/0.40 tff(200,plain,
% 0.18/0.40 (![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[199, 184])).
% 0.18/0.40 tff(201,plain,
% 0.18/0.40 (((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | ((~animal(X1!1)) | (~animal(X1!2)) | ![Z: $i] : ((~grain(Z)) | (~eats(X1!2, Z)) | (~eats(X1!1, X1!2))))) <=> ((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | (~animal(X1!1)) | (~animal(X1!2)) | ![Z: $i] : ((~grain(Z)) | (~eats(X1!2, Z)) | (~eats(X1!1, X1!2))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(202,plain,
% 0.18/0.40 (((~animal(X1!2)) | (~animal(X1!1)) | ![Z: $i] : ((~grain(Z)) | (~eats(X1!2, Z)) | (~eats(X1!1, X1!2)))) <=> ((~animal(X1!1)) | (~animal(X1!2)) | ![Z: $i] : ((~grain(Z)) | (~eats(X1!2, Z)) | (~eats(X1!1, X1!2))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(203,plain,
% 0.18/0.40 (((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | ((~animal(X1!2)) | (~animal(X1!1)) | ![Z: $i] : ((~grain(Z)) | (~eats(X1!2, Z)) | (~eats(X1!1, X1!2))))) <=> ((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | ((~animal(X1!1)) | (~animal(X1!2)) | ![Z: $i] : ((~grain(Z)) | (~eats(X1!2, Z)) | (~eats(X1!1, X1!2)))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[202])).
% 0.18/0.40 tff(204,plain,
% 0.18/0.40 (((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | ((~animal(X1!2)) | (~animal(X1!1)) | ![Z: $i] : ((~grain(Z)) | (~eats(X1!2, Z)) | (~eats(X1!1, X1!2))))) <=> ((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | (~animal(X1!1)) | (~animal(X1!2)) | ![Z: $i] : ((~grain(Z)) | (~eats(X1!2, Z)) | (~eats(X1!1, X1!2))))),
% 0.18/0.40 inference(transitivity,[status(thm)],[203, 201])).
% 0.18/0.40 tff(205,plain,
% 0.18/0.40 ((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | ((~animal(X1!2)) | (~animal(X1!1)) | ![Z: $i] : ((~grain(Z)) | (~eats(X1!2, Z)) | (~eats(X1!1, X1!2))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(206,plain,
% 0.18/0.40 ((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | (~animal(X1!1)) | (~animal(X1!2)) | ![Z: $i] : ((~grain(Z)) | (~eats(X1!2, Z)) | (~eats(X1!1, X1!2)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.18/0.40 tff(207,plain,
% 0.18/0.40 (![Z: $i] : ((~grain(Z)) | (~eats(X1!2, Z)) | (~eats(X1!1, X1!2)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[206, 200, 179, 115])).
% 0.18/0.40 tff(208,assumption,(~eats(X1!2, X!5)), introduced(assumption)).
% 0.18/0.40 tff(209,assumption,(![Y: $i] : ((~plant(Y)) | eats(X1!2, Y))), introduced(assumption)).
% 0.18/0.40 tff(210,plain,
% 0.18/0.40 (^[X1: $i] : refl((plant(X1) | (~grain(X1))) <=> (plant(X1) | (~grain(X1))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(211,plain,
% 0.18/0.40 (![X1: $i] : (plant(X1) | (~grain(X1))) <=> ![X1: $i] : (plant(X1) | (~grain(X1)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[210])).
% 0.18/0.40 tff(212,plain,
% 0.18/0.40 (![X1: $i] : (plant(X1) | (~grain(X1))) <=> ![X1: $i] : (plant(X1) | (~grain(X1)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(213,plain,
% 0.18/0.41 (^[X1: $i] : rewrite((grain(X1) => plant(X1)) <=> (plant(X1) | (~grain(X1))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(214,plain,
% 0.18/0.41 (![X1: $i] : (grain(X1) => plant(X1)) <=> ![X1: $i] : (plant(X1) | (~grain(X1)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[213])).
% 0.18/0.41 tff(215,axiom,(![X1: $i] : (grain(X1) => plant(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_6_2')).
% 0.18/0.41 tff(216,plain,
% 0.18/0.41 (![X1: $i] : (plant(X1) | (~grain(X1)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.18/0.41 tff(217,plain,
% 0.18/0.41 (![X1: $i] : (plant(X1) | (~grain(X1)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[216, 212])).
% 0.18/0.41 tff(218,plain,(
% 0.18/0.41 ![X1: $i] : (plant(X1) | (~grain(X1)))),
% 0.18/0.41 inference(skolemize,[status(sab)],[217])).
% 0.18/0.41 tff(219,plain,
% 0.18/0.41 (![X1: $i] : (plant(X1) | (~grain(X1)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[218, 211])).
% 0.18/0.41 tff(220,plain,
% 0.18/0.41 (?[X: $i] : grain(X) <=> ?[X: $i] : grain(X)),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(221,axiom,(?[X: $i] : grain(X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_6_1')).
% 0.18/0.41 tff(222,plain,
% 0.18/0.41 (?[X: $i] : grain(X)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.18/0.41 tff(223,plain,(
% 0.18/0.41 grain(X!5)),
% 0.18/0.41 inference(skolemize,[status(sab)],[222])).
% 0.18/0.41 tff(224,plain,
% 0.18/0.41 (((~![X1: $i] : (plant(X1) | (~grain(X1)))) | (plant(X!5) | (~grain(X!5)))) <=> ((~![X1: $i] : (plant(X1) | (~grain(X1)))) | plant(X!5) | (~grain(X!5)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(225,plain,
% 0.18/0.41 ((~![X1: $i] : (plant(X1) | (~grain(X1)))) | (plant(X!5) | (~grain(X!5)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(226,plain,
% 0.18/0.41 ((~![X1: $i] : (plant(X1) | (~grain(X1)))) | plant(X!5) | (~grain(X!5))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.18/0.41 tff(227,plain,
% 0.18/0.41 (plant(X!5)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[226, 223, 219])).
% 0.18/0.41 tff(228,plain,
% 0.18/0.41 (((~![Y: $i] : ((~plant(Y)) | eats(X1!2, Y))) | ((~plant(X!5)) | eats(X1!2, X!5))) <=> ((~![Y: $i] : ((~plant(Y)) | eats(X1!2, Y))) | (~plant(X!5)) | eats(X1!2, X!5))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(229,plain,
% 0.18/0.41 ((~![Y: $i] : ((~plant(Y)) | eats(X1!2, Y))) | ((~plant(X!5)) | eats(X1!2, X!5))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(230,plain,
% 0.18/0.41 ((~![Y: $i] : ((~plant(Y)) | eats(X1!2, Y))) | (~plant(X!5)) | eats(X1!2, X!5)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.18/0.41 tff(231,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[230, 227, 209, 208])).
% 0.18/0.41 tff(232,plain,((~![Y: $i] : ((~plant(Y)) | eats(X1!2, Y))) | eats(X1!2, X!5)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.41 tff(233,plain,
% 0.18/0.41 (eats(X1!2, X!5)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[232, 145])).
% 0.18/0.41 tff(234,assumption,(eats(X1!1, X1!2)), introduced(assumption)).
% 0.18/0.41 tff(235,plain,
% 0.18/0.41 (((~![Z: $i] : ((~grain(Z)) | (~eats(X1!2, Z)) | (~eats(X1!1, X1!2)))) | ((~grain(X!5)) | (~eats(X1!2, X!5)) | (~eats(X1!1, X1!2)))) <=> ((~![Z: $i] : ((~grain(Z)) | (~eats(X1!2, Z)) | (~eats(X1!1, X1!2)))) | (~grain(X!5)) | (~eats(X1!2, X!5)) | (~eats(X1!1, X1!2)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(236,plain,
% 0.18/0.41 ((~![Z: $i] : ((~grain(Z)) | (~eats(X1!2, Z)) | (~eats(X1!1, X1!2)))) | ((~grain(X!5)) | (~eats(X1!2, X!5)) | (~eats(X1!1, X1!2)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(237,plain,
% 0.18/0.41 ((~![Z: $i] : ((~grain(Z)) | (~eats(X1!2, Z)) | (~eats(X1!1, X1!2)))) | (~grain(X!5)) | (~eats(X1!2, X!5)) | (~eats(X1!1, X1!2))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.18/0.41 tff(238,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[237, 223, 234, 233, 207])).
% 0.18/0.41 tff(239,plain,(~eats(X1!1, X1!2)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.41 tff(240,assumption,(~much_smaller(X1!2, X1!1)), introduced(assumption)).
% 0.18/0.41 tff(241,plain,
% 0.18/0.41 (^[X: $i, Y: $i] : refl((much_smaller(X, Y) | (~fox(Y)) | (~bird(X))) <=> (much_smaller(X, Y) | (~fox(Y)) | (~bird(X))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(242,plain,
% 0.18/0.41 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X))) <=> ![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[241])).
% 0.18/0.41 tff(243,plain,
% 0.18/0.41 (^[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)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(244,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y)) <=> ![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[243])).
% 0.18/0.41 tff(245,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y)) <=> ![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(246,plain,
% 0.18/0.41 (^[X: $i, Y: $i] : rewrite(((bird(X) & fox(Y)) => much_smaller(X, Y)) <=> ((~(bird(X) & fox(Y))) | much_smaller(X, Y)))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(247,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((bird(X) & fox(Y)) => much_smaller(X, Y)) <=> ![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[246])).
% 0.18/0.41 tff(248,axiom,(![X: $i, Y: $i] : ((bird(X) & fox(Y)) => much_smaller(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_9')).
% 0.18/0.41 tff(249,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.18/0.41 tff(250,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[249, 245])).
% 0.18/0.41 tff(251,plain,(
% 0.18/0.41 ![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y))),
% 0.18/0.41 inference(skolemize,[status(sab)],[250])).
% 0.18/0.41 tff(252,plain,
% 0.18/0.41 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[251, 244])).
% 0.18/0.41 tff(253,plain,
% 0.18/0.41 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[252, 242])).
% 0.18/0.41 tff(254,plain,
% 0.18/0.41 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | ((~fox(X1!1)) | (~bird(X1!2)) | much_smaller(X1!2, X1!1))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (~fox(X1!1)) | (~bird(X1!2)) | much_smaller(X1!2, X1!1))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(255,plain,
% 0.18/0.41 ((much_smaller(X1!2, X1!1) | (~fox(X1!1)) | (~bird(X1!2))) <=> ((~fox(X1!1)) | (~bird(X1!2)) | much_smaller(X1!2, X1!1))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(256,plain,
% 0.18/0.41 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (much_smaller(X1!2, X1!1) | (~fox(X1!1)) | (~bird(X1!2)))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | ((~fox(X1!1)) | (~bird(X1!2)) | much_smaller(X1!2, X1!1)))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[255])).
% 0.18/0.41 tff(257,plain,
% 0.18/0.41 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (much_smaller(X1!2, X1!1) | (~fox(X1!1)) | (~bird(X1!2)))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (~fox(X1!1)) | (~bird(X1!2)) | much_smaller(X1!2, X1!1))),
% 0.18/0.41 inference(transitivity,[status(thm)],[256, 254])).
% 0.18/0.41 tff(258,plain,
% 0.18/0.41 ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (much_smaller(X1!2, X1!1) | (~fox(X1!1)) | (~bird(X1!2)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(259,plain,
% 0.18/0.41 ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (~fox(X1!1)) | (~bird(X1!2)) | much_smaller(X1!2, X1!1)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.18/0.41 tff(260,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[259, 165, 22, 253, 240])).
% 0.18/0.41 tff(261,plain,(much_smaller(X1!2, X1!1)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.41 tff(262,plain,
% 0.18/0.41 ((fox(X1!1) | grain(X1!1)) | (~fox(X1!1))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(263,plain,
% 0.18/0.41 (fox(X1!1) | grain(X1!1)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[262, 165])).
% 0.18/0.41 tff(264,assumption,(eats(X1!0, X1!1)), introduced(assumption)).
% 0.18/0.41 tff(265,plain,
% 0.18/0.41 (^[X: $i, Y: $i] : refl(((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y)))) <=> ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(266,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y)))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[265])).
% 0.18/0.41 tff(267,plain,
% 0.18/0.41 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((wolf(X) & (fox(Y) | grain(Y))) <=> (~((~wolf(X)) | (~(fox(Y) | grain(Y)))))), ((~(wolf(X) & (fox(Y) | grain(Y)))) <=> (~(~((~wolf(X)) | (~(fox(Y) | grain(Y)))))))), rewrite((~(~((~wolf(X)) | (~(fox(Y) | grain(Y)))))) <=> ((~wolf(X)) | (~(fox(Y) | grain(Y))))), ((~(wolf(X) & (fox(Y) | grain(Y)))) <=> ((~wolf(X)) | (~(fox(Y) | grain(Y)))))), (((~eats(X, Y)) | (~(wolf(X) & (fox(Y) | grain(Y))))) <=> ((~eats(X, Y)) | ((~wolf(X)) | (~(fox(Y) | grain(Y))))))), rewrite(((~eats(X, Y)) | ((~wolf(X)) | (~(fox(Y) | grain(Y))))) <=> ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))), (((~eats(X, Y)) | (~(wolf(X) & (fox(Y) | grain(Y))))) <=> ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(268,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & (fox(Y) | grain(Y))))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[267])).
% 0.18/0.41 tff(269,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & (fox(Y) | grain(Y))))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & (fox(Y) | grain(Y)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(270,plain,
% 0.18/0.41 (^[X: $i, Y: $i] : rewrite(((wolf(X) & (fox(Y) | grain(Y))) => (~eats(X, Y))) <=> ((~eats(X, Y)) | (~(wolf(X) & (fox(Y) | grain(Y))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(271,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((wolf(X) & (fox(Y) | grain(Y))) => (~eats(X, Y))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & (fox(Y) | grain(Y)))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[270])).
% 0.18/0.41 tff(272,axiom,(![X: $i, Y: $i] : ((wolf(X) & (fox(Y) | grain(Y))) => (~eats(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_11')).
% 0.18/0.41 tff(273,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & (fox(Y) | grain(Y)))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.18/0.41 tff(274,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & (fox(Y) | grain(Y)))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[273, 269])).
% 0.18/0.41 tff(275,plain,(
% 0.18/0.41 ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & (fox(Y) | grain(Y)))))),
% 0.18/0.41 inference(skolemize,[status(sab)],[274])).
% 0.18/0.41 tff(276,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[275, 268])).
% 0.18/0.41 tff(277,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[276, 266])).
% 0.18/0.41 tff(278,plain,
% 0.18/0.41 (?[X1: $i] : wolf(X1) <=> ?[X1: $i] : wolf(X1)),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(279,axiom,(?[X1: $i] : wolf(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_1_2')).
% 0.18/0.41 tff(280,plain,
% 0.18/0.41 (?[X1: $i] : wolf(X1)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.18/0.41 tff(281,plain,(
% 0.18/0.41 wolf(X1!0)),
% 0.18/0.41 inference(skolemize,[status(sab)],[280])).
% 0.18/0.41 tff(282,plain,
% 0.18/0.41 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | ((~wolf(X1!0)) | (~eats(X1!0, X1!1)) | (~(fox(X1!1) | grain(X1!1))))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | (~wolf(X1!0)) | (~eats(X1!0, X1!1)) | (~(fox(X1!1) | grain(X1!1))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(283,plain,
% 0.18/0.41 (((~eats(X1!0, X1!1)) | (~wolf(X1!0)) | (~(fox(X1!1) | grain(X1!1)))) <=> ((~wolf(X1!0)) | (~eats(X1!0, X1!1)) | (~(fox(X1!1) | grain(X1!1))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(284,plain,
% 0.18/0.41 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | ((~eats(X1!0, X1!1)) | (~wolf(X1!0)) | (~(fox(X1!1) | grain(X1!1))))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | ((~wolf(X1!0)) | (~eats(X1!0, X1!1)) | (~(fox(X1!1) | grain(X1!1)))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[283])).
% 0.18/0.41 tff(285,plain,
% 0.18/0.41 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | ((~eats(X1!0, X1!1)) | (~wolf(X1!0)) | (~(fox(X1!1) | grain(X1!1))))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | (~wolf(X1!0)) | (~eats(X1!0, X1!1)) | (~(fox(X1!1) | grain(X1!1))))),
% 0.18/0.41 inference(transitivity,[status(thm)],[284, 282])).
% 0.18/0.41 tff(286,plain,
% 0.18/0.41 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | ((~eats(X1!0, X1!1)) | (~wolf(X1!0)) | (~(fox(X1!1) | grain(X1!1))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(287,plain,
% 0.18/0.41 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | (~wolf(X1!0)) | (~eats(X1!0, X1!1)) | (~(fox(X1!1) | grain(X1!1)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.18/0.41 tff(288,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[287, 281, 277, 264, 263])).
% 0.18/0.41 tff(289,plain,(~eats(X1!0, X1!1)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.41 tff(290,assumption,(~much_smaller(X1!1, X1!0)), introduced(assumption)).
% 0.18/0.41 tff(291,plain,
% 0.18/0.41 (^[X: $i, Y: $i] : refl((much_smaller(X, Y) | (~wolf(Y)) | (~fox(X))) <=> (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(292,plain,
% 0.18/0.41 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X))) <=> ![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[291])).
% 0.18/0.41 tff(293,plain,
% 0.18/0.41 (^[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)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(294,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y)) <=> ![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[293])).
% 0.18/0.41 tff(295,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y)) <=> ![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(296,plain,
% 0.18/0.41 (^[X: $i, Y: $i] : rewrite(((fox(X) & wolf(Y)) => much_smaller(X, Y)) <=> ((~(fox(X) & wolf(Y))) | much_smaller(X, Y)))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(297,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((fox(X) & wolf(Y)) => much_smaller(X, Y)) <=> ![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[296])).
% 0.18/0.41 tff(298,axiom,(![X: $i, Y: $i] : ((fox(X) & wolf(Y)) => much_smaller(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_10')).
% 0.18/0.41 tff(299,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.18/0.41 tff(300,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[299, 295])).
% 0.18/0.41 tff(301,plain,(
% 0.18/0.41 ![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y))),
% 0.18/0.41 inference(skolemize,[status(sab)],[300])).
% 0.18/0.41 tff(302,plain,
% 0.18/0.41 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[301, 294])).
% 0.18/0.41 tff(303,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)],[302, 292])).
% 0.18/0.42 tff(304,plain,
% 0.18/0.42 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | ((~wolf(X1!0)) | (~fox(X1!1)) | much_smaller(X1!1, X1!0))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (~wolf(X1!0)) | (~fox(X1!1)) | much_smaller(X1!1, X1!0))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(305,plain,
% 0.18/0.42 ((much_smaller(X1!1, X1!0) | (~wolf(X1!0)) | (~fox(X1!1))) <=> ((~wolf(X1!0)) | (~fox(X1!1)) | much_smaller(X1!1, X1!0))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(306,plain,
% 0.18/0.42 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (much_smaller(X1!1, X1!0) | (~wolf(X1!0)) | (~fox(X1!1)))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | ((~wolf(X1!0)) | (~fox(X1!1)) | much_smaller(X1!1, X1!0)))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[305])).
% 0.18/0.42 tff(307,plain,
% 0.18/0.42 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (much_smaller(X1!1, X1!0) | (~wolf(X1!0)) | (~fox(X1!1)))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (~wolf(X1!0)) | (~fox(X1!1)) | much_smaller(X1!1, X1!0))),
% 0.18/0.42 inference(transitivity,[status(thm)],[306, 304])).
% 0.18/0.42 tff(308,plain,
% 0.18/0.42 ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (much_smaller(X1!1, X1!0) | (~wolf(X1!0)) | (~fox(X1!1)))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(309,plain,
% 0.18/0.42 ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (~wolf(X1!0)) | (~fox(X1!1)) | much_smaller(X1!1, X1!0)),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[308, 307])).
% 0.18/0.42 tff(310,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[309, 281, 165, 303, 290])).
% 0.18/0.42 tff(311,plain,(much_smaller(X1!1, X1!0)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.42 tff(312,plain,
% 0.18/0.42 ((fox(X!5) | grain(X!5)) | (~grain(X!5))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(313,plain,
% 0.18/0.42 (fox(X!5) | grain(X!5)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[312, 223])).
% 0.18/0.42 tff(314,assumption,(eats(X1!0, X!5)), introduced(assumption)).
% 0.18/0.42 tff(315,plain,
% 0.18/0.42 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | ((~wolf(X1!0)) | (~eats(X1!0, X!5)) | (~(fox(X!5) | grain(X!5))))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | (~wolf(X1!0)) | (~eats(X1!0, X!5)) | (~(fox(X!5) | grain(X!5))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(316,plain,
% 0.18/0.42 (((~eats(X1!0, X!5)) | (~wolf(X1!0)) | (~(fox(X!5) | grain(X!5)))) <=> ((~wolf(X1!0)) | (~eats(X1!0, X!5)) | (~(fox(X!5) | grain(X!5))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(317,plain,
% 0.18/0.42 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | ((~eats(X1!0, X!5)) | (~wolf(X1!0)) | (~(fox(X!5) | grain(X!5))))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | ((~wolf(X1!0)) | (~eats(X1!0, X!5)) | (~(fox(X!5) | grain(X!5)))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[316])).
% 0.18/0.42 tff(318,plain,
% 0.18/0.42 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | ((~eats(X1!0, X!5)) | (~wolf(X1!0)) | (~(fox(X!5) | grain(X!5))))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | (~wolf(X1!0)) | (~eats(X1!0, X!5)) | (~(fox(X!5) | grain(X!5))))),
% 0.18/0.42 inference(transitivity,[status(thm)],[317, 315])).
% 0.18/0.42 tff(319,plain,
% 0.18/0.42 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | ((~eats(X1!0, X!5)) | (~wolf(X1!0)) | (~(fox(X!5) | grain(X!5))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(320,plain,
% 0.18/0.42 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | (~wolf(X1!0)) | (~eats(X1!0, X!5)) | (~(fox(X!5) | grain(X!5)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[319, 318])).
% 0.18/0.42 tff(321,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[320, 281, 277, 314, 313])).
% 0.18/0.42 tff(322,plain,(~eats(X1!0, X!5)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.42 tff(323,assumption,(![Y: $i] : ((~plant(Y)) | eats(X1!0, Y))), introduced(assumption)).
% 0.18/0.42 tff(324,plain,
% 0.18/0.42 (((~![Y: $i] : ((~plant(Y)) | eats(X1!0, Y))) | ((~plant(X!5)) | eats(X1!0, X!5))) <=> ((~![Y: $i] : ((~plant(Y)) | eats(X1!0, Y))) | (~plant(X!5)) | eats(X1!0, X!5))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(325,plain,
% 0.18/0.42 ((~![Y: $i] : ((~plant(Y)) | eats(X1!0, Y))) | ((~plant(X!5)) | eats(X1!0, X!5))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(326,plain,
% 0.18/0.42 ((~![Y: $i] : ((~plant(Y)) | eats(X1!0, Y))) | (~plant(X!5)) | eats(X1!0, X!5)),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[325, 324])).
% 0.18/0.42 tff(327,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[326, 227, 323, 322])).
% 0.18/0.42 tff(328,plain,(~![Y: $i] : ((~plant(Y)) | eats(X1!0, Y))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.42 tff(329,plain,
% 0.18/0.42 (^[X: $i] : refl((animal(X) | (~wolf(X))) <=> (animal(X) | (~wolf(X))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(330,plain,
% 0.18/0.42 (![X: $i] : (animal(X) | (~wolf(X))) <=> ![X: $i] : (animal(X) | (~wolf(X)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[329])).
% 0.18/0.42 tff(331,plain,
% 0.18/0.42 (![X: $i] : (animal(X) | (~wolf(X))) <=> ![X: $i] : (animal(X) | (~wolf(X)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(332,plain,
% 0.18/0.42 (^[X: $i] : rewrite((wolf(X) => animal(X)) <=> (animal(X) | (~wolf(X))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(333,plain,
% 0.18/0.42 (![X: $i] : (wolf(X) => animal(X)) <=> ![X: $i] : (animal(X) | (~wolf(X)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[332])).
% 0.18/0.42 tff(334,axiom,(![X: $i] : (wolf(X) => animal(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_1_1')).
% 0.18/0.42 tff(335,plain,
% 0.18/0.42 (![X: $i] : (animal(X) | (~wolf(X)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[334, 333])).
% 0.18/0.42 tff(336,plain,
% 0.18/0.42 (![X: $i] : (animal(X) | (~wolf(X)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[335, 331])).
% 0.18/0.42 tff(337,plain,(
% 0.18/0.42 ![X: $i] : (animal(X) | (~wolf(X)))),
% 0.18/0.42 inference(skolemize,[status(sab)],[336])).
% 0.18/0.42 tff(338,plain,
% 0.18/0.42 (![X: $i] : (animal(X) | (~wolf(X)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[337, 330])).
% 0.18/0.42 tff(339,plain,
% 0.18/0.42 (((~![X: $i] : (animal(X) | (~wolf(X)))) | (animal(X1!0) | (~wolf(X1!0)))) <=> ((~![X: $i] : (animal(X) | (~wolf(X)))) | animal(X1!0) | (~wolf(X1!0)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(340,plain,
% 0.18/0.42 ((~![X: $i] : (animal(X) | (~wolf(X)))) | (animal(X1!0) | (~wolf(X1!0)))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(341,plain,
% 0.18/0.42 ((~![X: $i] : (animal(X) | (~wolf(X)))) | animal(X1!0) | (~wolf(X1!0))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[340, 339])).
% 0.18/0.42 tff(342,plain,
% 0.18/0.42 (animal(X1!0)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[341, 338, 281])).
% 0.18/0.42 tff(343,plain,
% 0.18/0.42 (((~![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(X1!0)) | ![Y: $i] : ((~plant(Y)) | eats(X1!0, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!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(X1!0)) | ![Y: $i] : ((~plant(Y)) | eats(X1!0, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!0))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(344,plain,
% 0.18/0.42 (((~animal(X1!0)) | ![Y: $i] : ((~plant(Y)) | eats(X1!0, Y)) | ![Y1: $i] : (eats(X1!0, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X1!0)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> ((~animal(X1!0)) | ![Y: $i] : ((~plant(Y)) | eats(X1!0, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!0))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(345,plain,
% 0.18/0.42 (((~![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(X1!0)) | ![Y: $i] : ((~plant(Y)) | eats(X1!0, Y)) | ![Y1: $i] : (eats(X1!0, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X1!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(X1!0)) | ![Y: $i] : ((~plant(Y)) | eats(X1!0, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!0)))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[344])).
% 0.18/0.42 tff(346,plain,
% 0.18/0.42 (((~![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(X1!0)) | ![Y: $i] : ((~plant(Y)) | eats(X1!0, Y)) | ![Y1: $i] : (eats(X1!0, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X1!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(X1!0)) | ![Y: $i] : ((~plant(Y)) | eats(X1!0, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!0))))),
% 0.18/0.42 inference(transitivity,[status(thm)],[345, 343])).
% 0.18/0.42 tff(347,plain,
% 0.18/0.42 ((~![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(X1!0)) | ![Y: $i] : ((~plant(Y)) | eats(X1!0, Y)) | ![Y1: $i] : (eats(X1!0, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X1!0)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(348,plain,
% 0.18/0.42 ((~![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(X1!0)) | ![Y: $i] : ((~plant(Y)) | eats(X1!0, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!0)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[347, 346])).
% 0.18/0.42 tff(349,plain,
% 0.18/0.42 (![Y: $i] : ((~plant(Y)) | eats(X1!0, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!0)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[348, 137, 342])).
% 0.18/0.42 tff(350,plain,
% 0.18/0.42 (![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!0)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[349, 328])).
% 0.18/0.42 tff(351,plain,
% 0.18/0.42 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!0)))) | ((~animal(X1!1)) | (~much_smaller(X1!1, X1!0)) | eats(X1!0, X1!1) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z))))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!0)))) | (~animal(X1!1)) | (~much_smaller(X1!1, X1!0)) | eats(X1!0, X1!1) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(352,plain,
% 0.18/0.42 (((~animal(X1!1)) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z))) | eats(X1!0, X1!1) | (~much_smaller(X1!1, X1!0))) <=> ((~animal(X1!1)) | (~much_smaller(X1!1, X1!0)) | eats(X1!0, X1!1) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(353,plain,
% 0.18/0.42 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!0)))) | ((~animal(X1!1)) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z))) | eats(X1!0, X1!1) | (~much_smaller(X1!1, X1!0)))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!0)))) | ((~animal(X1!1)) | (~much_smaller(X1!1, X1!0)) | eats(X1!0, X1!1) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z)))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[352])).
% 0.18/0.42 tff(354,plain,
% 0.18/0.42 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!0)))) | ((~animal(X1!1)) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z))) | eats(X1!0, X1!1) | (~much_smaller(X1!1, X1!0)))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!0)))) | (~animal(X1!1)) | (~much_smaller(X1!1, X1!0)) | eats(X1!0, X1!1) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z))))),
% 0.18/0.42 inference(transitivity,[status(thm)],[353, 351])).
% 0.18/0.42 tff(355,plain,
% 0.18/0.42 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!0)))) | ((~animal(X1!1)) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z))) | eats(X1!0, X1!1) | (~much_smaller(X1!1, X1!0)))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(356,plain,
% 0.18/0.42 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!0)))) | (~animal(X1!1)) | (~much_smaller(X1!1, X1!0)) | eats(X1!0, X1!1) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[355, 354])).
% 0.18/0.42 tff(357,plain,
% 0.18/0.42 ((~much_smaller(X1!1, X1!0)) | eats(X1!0, X1!1) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[356, 179, 350])).
% 0.18/0.42 tff(358,plain,
% 0.18/0.42 (eats(X1!0, X1!1) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[357, 311])).
% 0.18/0.42 tff(359,plain,
% 0.18/0.42 (![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[358, 289])).
% 0.18/0.42 tff(360,plain,
% 0.18/0.42 (((~![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z)))) | ((~plant(tptp_fun_Y_6(X1!3))) | (~eats(X1!1, tptp_fun_Y_6(X1!3))))) <=> ((~![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z)))) | (~plant(tptp_fun_Y_6(X1!3))) | (~eats(X1!1, tptp_fun_Y_6(X1!3))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(361,plain,
% 0.18/0.42 ((~![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z)))) | ((~plant(tptp_fun_Y_6(X1!3))) | (~eats(X1!1, tptp_fun_Y_6(X1!3))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(362,plain,
% 0.18/0.42 ((~![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z)))) | (~plant(tptp_fun_Y_6(X1!3))) | (~eats(X1!1, tptp_fun_Y_6(X1!3)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[361, 360])).
% 0.18/0.42 tff(363,plain,
% 0.18/0.42 (~eats(X1!1, tptp_fun_Y_6(X1!3))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[362, 157, 359])).
% 0.18/0.42 tff(364,assumption,(![Y: $i] : ((~plant(Y)) | eats(X1!1, Y))), introduced(assumption)).
% 0.18/0.42 tff(365,plain,
% 0.18/0.42 (((~![Y: $i] : ((~plant(Y)) | eats(X1!1, Y))) | ((~plant(tptp_fun_Y_6(X1!3))) | eats(X1!1, tptp_fun_Y_6(X1!3)))) <=> ((~![Y: $i] : ((~plant(Y)) | eats(X1!1, Y))) | (~plant(tptp_fun_Y_6(X1!3))) | eats(X1!1, tptp_fun_Y_6(X1!3)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(366,plain,
% 0.18/0.42 ((~![Y: $i] : ((~plant(Y)) | eats(X1!1, Y))) | ((~plant(tptp_fun_Y_6(X1!3))) | eats(X1!1, tptp_fun_Y_6(X1!3)))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(367,plain,
% 0.18/0.42 ((~![Y: $i] : ((~plant(Y)) | eats(X1!1, Y))) | (~plant(tptp_fun_Y_6(X1!3))) | eats(X1!1, tptp_fun_Y_6(X1!3))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[366, 365])).
% 0.18/0.42 tff(368,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[367, 157, 364, 363])).
% 0.18/0.42 tff(369,plain,(~![Y: $i] : ((~plant(Y)) | eats(X1!1, Y))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.42 tff(370,plain,
% 0.18/0.42 (((~![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(X1!1)) | ![Y: $i] : ((~plant(Y)) | eats(X1!1, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!1, Y1) | (~much_smaller(Y1, X1!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(X1!1)) | ![Y: $i] : ((~plant(Y)) | eats(X1!1, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!1, Y1) | (~much_smaller(Y1, X1!1))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(371,plain,
% 0.18/0.43 (((~animal(X1!1)) | ![Y: $i] : ((~plant(Y)) | eats(X1!1, Y)) | ![Y1: $i] : (eats(X1!1, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X1!1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> ((~animal(X1!1)) | ![Y: $i] : ((~plant(Y)) | eats(X1!1, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!1, Y1) | (~much_smaller(Y1, X1!1))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(372,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(X1!1)) | ![Y: $i] : ((~plant(Y)) | eats(X1!1, Y)) | ![Y1: $i] : (eats(X1!1, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X1!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(X1!1)) | ![Y: $i] : ((~plant(Y)) | eats(X1!1, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!1, Y1) | (~much_smaller(Y1, X1!1)))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[371])).
% 0.18/0.43 tff(373,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(X1!1)) | ![Y: $i] : ((~plant(Y)) | eats(X1!1, Y)) | ![Y1: $i] : (eats(X1!1, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X1!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(X1!1)) | ![Y: $i] : ((~plant(Y)) | eats(X1!1, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!1, Y1) | (~much_smaller(Y1, X1!1))))),
% 0.18/0.43 inference(transitivity,[status(thm)],[372, 370])).
% 0.18/0.43 tff(374,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(X1!1)) | ![Y: $i] : ((~plant(Y)) | eats(X1!1, Y)) | ![Y1: $i] : (eats(X1!1, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X1!1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(375,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(X1!1)) | ![Y: $i] : ((~plant(Y)) | eats(X1!1, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!1, Y1) | (~much_smaller(Y1, X1!1)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[374, 373])).
% 0.18/0.43 tff(376,plain,
% 0.18/0.43 (![Y: $i] : ((~plant(Y)) | eats(X1!1, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!1, Y1) | (~much_smaller(Y1, X1!1)))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[375, 137, 179])).
% 0.18/0.43 tff(377,plain,
% 0.18/0.43 (![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!1, Y1) | (~much_smaller(Y1, X1!1)))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[376, 369])).
% 0.18/0.43 tff(378,plain,
% 0.18/0.43 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!1, Y1) | (~much_smaller(Y1, X1!1)))) | ((~animal(X1!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!2, Z))) | eats(X1!1, X1!2) | (~much_smaller(X1!2, X1!1)))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!1, Y1) | (~much_smaller(Y1, X1!1)))) | (~animal(X1!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!2, Z))) | eats(X1!1, X1!2) | (~much_smaller(X1!2, X1!1)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(379,plain,
% 0.18/0.43 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!1, Y1) | (~much_smaller(Y1, X1!1)))) | ((~animal(X1!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!2, Z))) | eats(X1!1, X1!2) | (~much_smaller(X1!2, X1!1)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(380,plain,
% 0.18/0.43 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!1, Y1) | (~much_smaller(Y1, X1!1)))) | (~animal(X1!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!2, Z))) | eats(X1!1, X1!2) | (~much_smaller(X1!2, X1!1))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.18/0.43 tff(381,plain,
% 0.18/0.43 (![Z: $i] : ((~plant(Z)) | (~eats(X1!2, Z))) | eats(X1!1, X1!2) | (~much_smaller(X1!2, X1!1))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[380, 115, 377])).
% 0.18/0.43 tff(382,plain,
% 0.18/0.43 (![Z: $i] : ((~plant(Z)) | (~eats(X1!2, Z))) | eats(X1!1, X1!2)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[381, 261])).
% 0.18/0.43 tff(383,plain,
% 0.18/0.43 (![Z: $i] : ((~plant(Z)) | (~eats(X1!2, Z)))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[382, 239])).
% 0.18/0.43 tff(384,plain,
% 0.18/0.43 (((~![Z: $i] : ((~plant(Z)) | (~eats(X1!2, Z)))) | ((~plant(tptp_fun_Y_6(X1!3))) | (~eats(X1!2, tptp_fun_Y_6(X1!3))))) <=> ((~![Z: $i] : ((~plant(Z)) | (~eats(X1!2, Z)))) | (~plant(tptp_fun_Y_6(X1!3))) | (~eats(X1!2, tptp_fun_Y_6(X1!3))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(385,plain,
% 0.18/0.43 ((~![Z: $i] : ((~plant(Z)) | (~eats(X1!2, Z)))) | ((~plant(tptp_fun_Y_6(X1!3))) | (~eats(X1!2, tptp_fun_Y_6(X1!3))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(386,plain,
% 0.18/0.43 ((~![Z: $i] : ((~plant(Z)) | (~eats(X1!2, Z)))) | (~plant(tptp_fun_Y_6(X1!3))) | (~eats(X1!2, tptp_fun_Y_6(X1!3)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[385, 384])).
% 0.18/0.43 tff(387,plain,
% 0.18/0.43 ($false),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[386, 157, 383, 161])).
% 0.18/0.43 % SZS output end Proof
% 0.18/0.43 % E exiting
%------------------------------------------------------------------------------