%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ031+3 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : PUZ031+3 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 02:42:16 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(eats_type, type, (
% 0.21/0.39 eats: ( $i * $i ) > $o)).
% 0.21/0.39 tff(tptp_fun_A_7_type, type, (
% 0.21/0.39 tptp_fun_A_7: $i)).
% 0.21/0.39 tff(tptp_fun_A_4_type, type, (
% 0.21/0.39 tptp_fun_A_4: $i)).
% 0.21/0.39 tff(plant_type, type, (
% 0.21/0.39 plant: $i > $o)).
% 0.21/0.39 tff(much_smaller_type, type, (
% 0.21/0.39 much_smaller: ( $i * $i ) > $o)).
% 0.21/0.39 tff(animal_type, type, (
% 0.21/0.39 animal: $i > $o)).
% 0.21/0.39 tff(tptp_fun_A_6_type, type, (
% 0.21/0.39 tptp_fun_A_6: $i)).
% 0.21/0.39 tff(bird_type, type, (
% 0.21/0.39 bird: $i > $o)).
% 0.21/0.39 tff(snail_type, type, (
% 0.21/0.39 snail: $i > $o)).
% 0.21/0.39 tff(tptp_fun_Y_9_type, type, (
% 0.21/0.39 tptp_fun_Y_9: $i > $i)).
% 0.21/0.39 tff(tptp_fun_A_3_type, type, (
% 0.21/0.39 tptp_fun_A_3: $i)).
% 0.21/0.39 tff(tptp_fun_A_8_type, type, (
% 0.21/0.39 tptp_fun_A_8: $i)).
% 0.21/0.39 tff(grain_type, type, (
% 0.21/0.39 grain: $i > $o)).
% 0.21/0.39 tff(fox_type, type, (
% 0.21/0.39 fox: $i > $o)).
% 0.21/0.39 tff(tptp_fun_A_2_type, type, (
% 0.21/0.39 tptp_fun_A_2: $i)).
% 0.21/0.39 tff(wolf_type, type, (
% 0.21/0.39 wolf: $i > $o)).
% 0.21/0.39 tff(1,assumption,(eats(A!4, A!6)), introduced(assumption)).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 (^[X: $i, Y: $i] : refl(((~eats(X, Y)) | (~snail(Y)) | (~bird(X))) <=> ((~eats(X, Y)) | (~snail(Y)) | (~bird(X))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(3,plain,
% 0.21/0.39 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.39 tff(4,plain,
% 0.21/0.39 (^[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)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y)))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[4])).
% 0.21/0.39 tff(6,plain,
% 0.21/0.39 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y)))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 (^[X: $i, Y: $i] : rewrite(((bird(X) & snail(Y)) => (~eats(X, Y))) <=> ((~eats(X, Y)) | (~(bird(X) & snail(Y)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 (![X: $i, Y: $i] : ((bird(X) & snail(Y)) => (~eats(X, Y))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[7])).
% 0.21/0.39 tff(9,axiom,(![X: $i, Y: $i] : ((bird(X) & snail(Y)) => (~eats(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_13')).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.21/0.39 tff(11,plain,
% 0.21/0.39 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.21/0.39 tff(12,plain,(
% 0.21/0.39 ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y))))),
% 0.21/0.39 inference(skolemize,[status(sab)],[11])).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.21/0.39 tff(14,plain,
% 0.21/0.39 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[13, 3])).
% 0.21/0.39 tff(15,plain,
% 0.21/0.39 (?[A: $i] : snail(A) <=> ?[A: $i] : snail(A)),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(16,axiom,(?[A: $i] : snail(A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','snail_type')).
% 0.21/0.39 tff(17,plain,
% 0.21/0.39 (?[A: $i] : snail(A)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.21/0.39 tff(18,plain,(
% 0.21/0.39 snail(A!6)),
% 0.21/0.39 inference(skolemize,[status(sab)],[17])).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 (?[A: $i] : bird(A) <=> ?[A: $i] : bird(A)),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(20,axiom,(?[A: $i] : bird(A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bird_type')).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 (?[A: $i] : bird(A)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.21/0.39 tff(22,plain,(
% 0.21/0.39 bird(A!4)),
% 0.21/0.39 inference(skolemize,[status(sab)],[21])).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | ((~bird(A!4)) | (~snail(A!6)) | (~eats(A!4, A!6)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | (~bird(A!4)) | (~snail(A!6)) | (~eats(A!4, A!6)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(24,plain,
% 0.21/0.39 (((~eats(A!4, A!6)) | (~snail(A!6)) | (~bird(A!4))) <=> ((~bird(A!4)) | (~snail(A!6)) | (~eats(A!4, A!6)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | ((~eats(A!4, A!6)) | (~snail(A!6)) | (~bird(A!4)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | ((~bird(A!4)) | (~snail(A!6)) | (~eats(A!4, A!6))))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[24])).
% 0.21/0.39 tff(26,plain,
% 0.21/0.39 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | ((~eats(A!4, A!6)) | (~snail(A!6)) | (~bird(A!4)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | (~bird(A!4)) | (~snail(A!6)) | (~eats(A!4, A!6)))),
% 0.21/0.39 inference(transitivity,[status(thm)],[25, 23])).
% 0.21/0.39 tff(27,plain,
% 0.21/0.39 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | ((~eats(A!4, A!6)) | (~snail(A!6)) | (~bird(A!4)))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(28,plain,
% 0.21/0.39 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | (~bird(A!4)) | (~snail(A!6)) | (~eats(A!4, A!6))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.21/0.39 tff(29,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[28, 22, 18, 14, 1])).
% 0.21/0.39 tff(30,plain,(~eats(A!4, A!6)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.39 tff(31,assumption,(![Z: $i] : ((~plant(Z)) | (~eats(A!6, Z)))), introduced(assumption)).
% 0.21/0.39 tff(32,plain,
% 0.21/0.39 (^[X: $i] : refl(((~snail(X)) | (~((~plant(tptp_fun_Y_9(X))) | (~eats(X, tptp_fun_Y_9(X)))))) <=> ((~snail(X)) | (~((~plant(tptp_fun_Y_9(X))) | (~eats(X, tptp_fun_Y_9(X)))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(33,plain,
% 0.21/0.39 (![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_9(X))) | (~eats(X, tptp_fun_Y_9(X)))))) <=> ![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_9(X))) | (~eats(X, tptp_fun_Y_9(X))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.39 tff(34,plain,
% 0.21/0.39 (^[X: $i] : rewrite(((~snail(X)) | (plant(tptp_fun_Y_9(X)) & eats(X, tptp_fun_Y_9(X)))) <=> ((~snail(X)) | (~((~plant(tptp_fun_Y_9(X))) | (~eats(X, tptp_fun_Y_9(X)))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(35,plain,
% 0.21/0.39 (![X: $i] : ((~snail(X)) | (plant(tptp_fun_Y_9(X)) & eats(X, tptp_fun_Y_9(X)))) <=> ![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_9(X))) | (~eats(X, tptp_fun_Y_9(X))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[34])).
% 0.21/0.39 tff(36,plain,
% 0.21/0.39 (![X: $i] : ((~snail(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y))) <=> ![X: $i] : ((~snail(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(37,plain,
% 0.21/0.39 (^[X: $i] : rewrite((snail(X) => ?[Y: $i] : (plant(Y) & eats(X, Y))) <=> ((~snail(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(38,plain,
% 0.21/0.39 (![X: $i] : (snail(X) => ?[Y: $i] : (plant(Y) & eats(X, Y))) <=> ![X: $i] : ((~snail(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[37])).
% 0.21/0.39 tff(39,axiom,(![X: $i] : (snail(X) => ?[Y: $i] : (plant(Y) & eats(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_14a')).
% 0.21/0.39 tff(40,plain,
% 0.21/0.39 (![X: $i] : ((~snail(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.21/0.39 tff(41,plain,
% 0.21/0.39 (![X: $i] : ((~snail(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.21/0.39 tff(42,plain,(
% 0.21/0.39 ![X: $i] : ((~snail(X)) | (plant(tptp_fun_Y_9(X)) & eats(X, tptp_fun_Y_9(X))))),
% 0.21/0.39 inference(skolemize,[status(sab)],[41])).
% 0.21/0.39 tff(43,plain,
% 0.21/0.39 (![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_9(X))) | (~eats(X, tptp_fun_Y_9(X))))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.21/0.39 tff(44,plain,
% 0.21/0.39 (![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_9(X))) | (~eats(X, tptp_fun_Y_9(X))))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[43, 33])).
% 0.21/0.39 tff(45,plain,
% 0.21/0.39 (((~![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_9(X))) | (~eats(X, tptp_fun_Y_9(X))))))) | ((~snail(A!6)) | (~((~plant(tptp_fun_Y_9(A!6))) | (~eats(A!6, tptp_fun_Y_9(A!6))))))) <=> ((~![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_9(X))) | (~eats(X, tptp_fun_Y_9(X))))))) | (~snail(A!6)) | (~((~plant(tptp_fun_Y_9(A!6))) | (~eats(A!6, tptp_fun_Y_9(A!6))))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(46,plain,
% 0.21/0.39 ((~![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_9(X))) | (~eats(X, tptp_fun_Y_9(X))))))) | ((~snail(A!6)) | (~((~plant(tptp_fun_Y_9(A!6))) | (~eats(A!6, tptp_fun_Y_9(A!6))))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(47,plain,
% 0.21/0.39 ((~![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_9(X))) | (~eats(X, tptp_fun_Y_9(X))))))) | (~snail(A!6)) | (~((~plant(tptp_fun_Y_9(A!6))) | (~eats(A!6, tptp_fun_Y_9(A!6)))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.39 tff(48,plain,
% 0.21/0.39 (~((~plant(tptp_fun_Y_9(A!6))) | (~eats(A!6, tptp_fun_Y_9(A!6))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[47, 18, 44])).
% 0.21/0.39 tff(49,plain,
% 0.21/0.39 (((~plant(tptp_fun_Y_9(A!6))) | (~eats(A!6, tptp_fun_Y_9(A!6)))) | eats(A!6, tptp_fun_Y_9(A!6))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(50,plain,
% 0.21/0.39 (eats(A!6, tptp_fun_Y_9(A!6))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.21/0.39 tff(51,plain,
% 0.21/0.39 (((~plant(tptp_fun_Y_9(A!6))) | (~eats(A!6, tptp_fun_Y_9(A!6)))) | plant(tptp_fun_Y_9(A!6))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(52,plain,
% 0.21/0.39 (plant(tptp_fun_Y_9(A!6))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[51, 48])).
% 0.21/0.39 tff(53,plain,
% 0.21/0.39 (((~![Z: $i] : ((~plant(Z)) | (~eats(A!6, Z)))) | ((~plant(tptp_fun_Y_9(A!6))) | (~eats(A!6, tptp_fun_Y_9(A!6))))) <=> ((~![Z: $i] : ((~plant(Z)) | (~eats(A!6, Z)))) | (~plant(tptp_fun_Y_9(A!6))) | (~eats(A!6, tptp_fun_Y_9(A!6))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(54,plain,
% 0.21/0.39 ((~![Z: $i] : ((~plant(Z)) | (~eats(A!6, Z)))) | ((~plant(tptp_fun_Y_9(A!6))) | (~eats(A!6, tptp_fun_Y_9(A!6))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(55,plain,
% 0.21/0.39 ((~![Z: $i] : ((~plant(Z)) | (~eats(A!6, Z)))) | (~plant(tptp_fun_Y_9(A!6))) | (~eats(A!6, tptp_fun_Y_9(A!6)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.21/0.39 tff(56,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[55, 52, 50, 31])).
% 0.21/0.39 tff(57,plain,(~![Z: $i] : ((~plant(Z)) | (~eats(A!6, Z)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.39 tff(58,assumption,(~eats(A!4, A!6)), introduced(assumption)).
% 0.21/0.39 tff(59,assumption,(~much_smaller(A!6, A!4)), introduced(assumption)).
% 0.21/0.39 tff(60,plain,
% 0.21/0.39 (^[Y: $i, X: $i] : refl((much_smaller(X, Y) | (~snail(X)) | (~bird(Y))) <=> (much_smaller(X, Y) | (~snail(X)) | (~bird(Y))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(61,plain,
% 0.21/0.39 (![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y))) <=> ![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[60])).
% 0.21/0.39 tff(62,plain,
% 0.21/0.39 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((bird(Y) & snail(X)) <=> (~((~bird(Y)) | (~snail(X))))), ((~(bird(Y) & snail(X))) <=> (~(~((~bird(Y)) | (~snail(X))))))), rewrite((~(~((~bird(Y)) | (~snail(X))))) <=> ((~bird(Y)) | (~snail(X)))), ((~(bird(Y) & snail(X))) <=> ((~bird(Y)) | (~snail(X))))), (((~(bird(Y) & snail(X))) | much_smaller(X, Y)) <=> (((~bird(Y)) | (~snail(X))) | much_smaller(X, Y)))), rewrite((((~bird(Y)) | (~snail(X))) | much_smaller(X, Y)) <=> (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))), (((~(bird(Y) & snail(X))) | much_smaller(X, Y)) <=> (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(63,plain,
% 0.21/0.39 (![Y: $i, X: $i] : ((~(bird(Y) & snail(X))) | much_smaller(X, Y)) <=> ![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[62])).
% 0.21/0.39 tff(64,plain,
% 0.21/0.39 (![Y: $i, X: $i] : ((~(bird(Y) & snail(X))) | much_smaller(X, Y)) <=> ![Y: $i, X: $i] : ((~(bird(Y) & snail(X))) | much_smaller(X, Y))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(65,plain,
% 0.21/0.40 (^[Y: $i, X: $i] : rewrite(((bird(Y) & snail(X)) => much_smaller(X, Y)) <=> ((~(bird(Y) & snail(X))) | much_smaller(X, Y)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(66,plain,
% 0.21/0.40 (![Y: $i, X: $i] : ((bird(Y) & snail(X)) => much_smaller(X, Y)) <=> ![Y: $i, X: $i] : ((~(bird(Y) & snail(X))) | much_smaller(X, Y))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[65])).
% 0.21/0.40 tff(67,axiom,(![Y: $i, X: $i] : ((bird(Y) & snail(X)) => much_smaller(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_8')).
% 0.21/0.40 tff(68,plain,
% 0.21/0.40 (![Y: $i, X: $i] : ((~(bird(Y) & snail(X))) | much_smaller(X, Y))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.21/0.40 tff(69,plain,
% 0.21/0.40 (![Y: $i, X: $i] : ((~(bird(Y) & snail(X))) | much_smaller(X, Y))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.21/0.40 tff(70,plain,(
% 0.21/0.40 ![Y: $i, X: $i] : ((~(bird(Y) & snail(X))) | much_smaller(X, Y))),
% 0.21/0.40 inference(skolemize,[status(sab)],[69])).
% 0.21/0.40 tff(71,plain,
% 0.21/0.40 (![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.21/0.40 tff(72,plain,
% 0.21/0.40 (![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[71, 61])).
% 0.21/0.40 tff(73,plain,
% 0.21/0.40 (((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | ((~bird(A!4)) | (~snail(A!6)) | much_smaller(A!6, A!4))) <=> ((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | (~bird(A!4)) | (~snail(A!6)) | much_smaller(A!6, A!4))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(74,plain,
% 0.21/0.40 ((much_smaller(A!6, A!4) | (~snail(A!6)) | (~bird(A!4))) <=> ((~bird(A!4)) | (~snail(A!6)) | much_smaller(A!6, A!4))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(75,plain,
% 0.21/0.40 (((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | (much_smaller(A!6, A!4) | (~snail(A!6)) | (~bird(A!4)))) <=> ((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | ((~bird(A!4)) | (~snail(A!6)) | much_smaller(A!6, A!4)))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[74])).
% 0.21/0.40 tff(76,plain,
% 0.21/0.40 (((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | (much_smaller(A!6, A!4) | (~snail(A!6)) | (~bird(A!4)))) <=> ((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | (~bird(A!4)) | (~snail(A!6)) | much_smaller(A!6, A!4))),
% 0.21/0.40 inference(transitivity,[status(thm)],[75, 73])).
% 0.21/0.40 tff(77,plain,
% 0.21/0.40 ((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | (much_smaller(A!6, A!4) | (~snail(A!6)) | (~bird(A!4)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(78,plain,
% 0.21/0.40 ((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | (~bird(A!4)) | (~snail(A!6)) | much_smaller(A!6, A!4)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.21/0.40 tff(79,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[78, 22, 18, 72, 59])).
% 0.21/0.40 tff(80,plain,(much_smaller(A!6, A!4)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(81,assumption,(~![Z: $i] : ((~plant(Z)) | (~eats(A!6, Z)))), introduced(assumption)).
% 0.21/0.40 tff(82,assumption,(![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4)))), introduced(assumption)).
% 0.21/0.40 tff(83,plain,
% 0.21/0.40 (^[A: $i] : refl((animal(A) | (~snail(A))) <=> (animal(A) | (~snail(A))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(84,plain,
% 0.21/0.40 (![A: $i] : (animal(A) | (~snail(A))) <=> ![A: $i] : (animal(A) | (~snail(A)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[83])).
% 0.21/0.40 tff(85,plain,
% 0.21/0.40 (![A: $i] : (animal(A) | (~snail(A))) <=> ![A: $i] : (animal(A) | (~snail(A)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(86,plain,
% 0.21/0.40 (^[A: $i] : rewrite((snail(A) => animal(A)) <=> (animal(A) | (~snail(A))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(87,plain,
% 0.21/0.40 (![A: $i] : (snail(A) => animal(A)) <=> ![A: $i] : (animal(A) | (~snail(A)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[86])).
% 0.21/0.40 tff(88,axiom,(![A: $i] : (snail(A) => animal(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','snail_is_animal')).
% 0.21/0.40 tff(89,plain,
% 0.21/0.40 (![A: $i] : (animal(A) | (~snail(A)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.21/0.40 tff(90,plain,
% 0.21/0.40 (![A: $i] : (animal(A) | (~snail(A)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.21/0.40 tff(91,plain,(
% 0.21/0.40 ![A: $i] : (animal(A) | (~snail(A)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[90])).
% 0.21/0.40 tff(92,plain,
% 0.21/0.40 (![A: $i] : (animal(A) | (~snail(A)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.21/0.40 tff(93,plain,
% 0.21/0.40 (((~![A: $i] : (animal(A) | (~snail(A)))) | (animal(A!6) | (~snail(A!6)))) <=> ((~![A: $i] : (animal(A) | (~snail(A)))) | animal(A!6) | (~snail(A!6)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(94,plain,
% 0.21/0.40 ((~![A: $i] : (animal(A) | (~snail(A)))) | (animal(A!6) | (~snail(A!6)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(95,plain,
% 0.21/0.40 ((~![A: $i] : (animal(A) | (~snail(A)))) | animal(A!6) | (~snail(A!6))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.21/0.40 tff(96,plain,
% 0.21/0.40 (animal(A!6)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[95, 18, 92])).
% 0.21/0.40 tff(97,plain,
% 0.21/0.40 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4)))) | ((~animal(A!6)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!6, Z))) | (~much_smaller(A!6, A!4)) | eats(A!4, A!6))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4)))) | (~animal(A!6)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!6, Z))) | (~much_smaller(A!6, A!4)) | eats(A!4, A!6))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(98,plain,
% 0.21/0.40 (((~animal(A!6)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!6, Z))) | eats(A!4, A!6) | (~much_smaller(A!6, A!4))) <=> ((~animal(A!6)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!6, Z))) | (~much_smaller(A!6, A!4)) | eats(A!4, A!6))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(99,plain,
% 0.21/0.40 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4)))) | ((~animal(A!6)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!6, Z))) | eats(A!4, A!6) | (~much_smaller(A!6, A!4)))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4)))) | ((~animal(A!6)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!6, Z))) | (~much_smaller(A!6, A!4)) | eats(A!4, A!6)))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[98])).
% 0.21/0.40 tff(100,plain,
% 0.21/0.40 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4)))) | ((~animal(A!6)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!6, Z))) | eats(A!4, A!6) | (~much_smaller(A!6, A!4)))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4)))) | (~animal(A!6)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!6, Z))) | (~much_smaller(A!6, A!4)) | eats(A!4, A!6))),
% 0.21/0.40 inference(transitivity,[status(thm)],[99, 97])).
% 0.21/0.40 tff(101,plain,
% 0.21/0.40 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4)))) | ((~animal(A!6)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!6, Z))) | eats(A!4, A!6) | (~much_smaller(A!6, A!4)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(102,plain,
% 0.21/0.40 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4)))) | (~animal(A!6)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!6, Z))) | (~much_smaller(A!6, A!4)) | eats(A!4, A!6)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.21/0.40 tff(103,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[102, 96, 82, 81, 80, 58])).
% 0.21/0.40 tff(104,plain,((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4)))) | ![Z: $i] : ((~plant(Z)) | (~eats(A!6, Z))) | eats(A!4, A!6)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(105,plain,
% 0.21/0.40 (~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[104, 57, 30])).
% 0.21/0.40 tff(106,plain,
% 0.21/0.40 (^[A: $i] : refl((animal(A) | (~bird(A))) <=> (animal(A) | (~bird(A))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(107,plain,
% 0.21/0.40 (![A: $i] : (animal(A) | (~bird(A))) <=> ![A: $i] : (animal(A) | (~bird(A)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[106])).
% 0.21/0.40 tff(108,plain,
% 0.21/0.40 (![A: $i] : (animal(A) | (~bird(A))) <=> ![A: $i] : (animal(A) | (~bird(A)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(109,plain,
% 0.21/0.40 (^[A: $i] : rewrite((bird(A) => animal(A)) <=> (animal(A) | (~bird(A))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(110,plain,
% 0.21/0.40 (![A: $i] : (bird(A) => animal(A)) <=> ![A: $i] : (animal(A) | (~bird(A)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[109])).
% 0.21/0.40 tff(111,axiom,(![A: $i] : (bird(A) => animal(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bird_is_animal')).
% 0.21/0.40 tff(112,plain,
% 0.21/0.40 (![A: $i] : (animal(A) | (~bird(A)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.21/0.40 tff(113,plain,
% 0.21/0.40 (![A: $i] : (animal(A) | (~bird(A)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.21/0.40 tff(114,plain,(
% 0.21/0.40 ![A: $i] : (animal(A) | (~bird(A)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[113])).
% 0.21/0.40 tff(115,plain,
% 0.21/0.40 (![A: $i] : (animal(A) | (~bird(A)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.21/0.40 tff(116,plain,
% 0.21/0.40 (((~![A: $i] : (animal(A) | (~bird(A)))) | (animal(A!4) | (~bird(A!4)))) <=> ((~![A: $i] : (animal(A) | (~bird(A)))) | animal(A!4) | (~bird(A!4)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(117,plain,
% 0.21/0.40 ((~![A: $i] : (animal(A) | (~bird(A)))) | (animal(A!4) | (~bird(A!4)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(118,plain,
% 0.21/0.40 ((~![A: $i] : (animal(A) | (~bird(A)))) | animal(A!4) | (~bird(A!4))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.21/0.40 tff(119,plain,
% 0.21/0.40 (animal(A!4)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[118, 22, 115])).
% 0.21/0.40 tff(120,plain,
% 0.21/0.40 (^[X: $i] : refl(((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(121,plain,
% 0.21/0.40 (![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))))) <=> ![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)))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[120])).
% 0.21/0.40 tff(122,plain,
% 0.21/0.40 (^[X: $i] : rewrite(((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(123,plain,
% 0.21/0.40 (![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))))) <=> ![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)))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[122])).
% 0.21/0.40 tff(124,plain,
% 0.21/0.40 (![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))))) <=> ![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)))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[123, 121])).
% 0.21/0.40 tff(125,plain,
% 0.21/0.40 (^[X: $i] : rewrite(((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z))))) <=> ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(126,plain,
% 0.21/0.40 (![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))))) <=> ![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)))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[125])).
% 0.21/0.40 tff(127,plain,
% 0.21/0.40 (^[X: $i] : rewrite(((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | ((~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))))) <=> ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(128,plain,
% 0.21/0.40 (![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)))))) <=> ![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)))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[127])).
% 0.21/0.40 tff(129,plain,
% 0.21/0.40 (![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)))))) <=> ![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))))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(130,plain,
% 0.21/0.40 (^[X: $i] : trans(monotonicity(rewrite((![Y: $i] : (plant(Y) => eats(X, Y)) | ![Y1: $i] : (animal(Y1) => ((much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z))) => eats(X, Y1)))) <=> (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~(much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z))))))), ((animal(X) => (![Y: $i] : (plant(Y) => eats(X, Y)) | ![Y1: $i] : (animal(Y1) => ((much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z))) => eats(X, Y1))))) <=> (animal(X) => (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~(much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z))))))))), rewrite((animal(X) => (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~(much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z))))))) <=> ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~(much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z))))))), ((animal(X) => (![Y: $i] : (plant(Y) => eats(X, Y)) | ![Y1: $i] : (animal(Y1) => ((much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z))) => eats(X, Y1))))) <=> ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~(much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(131,plain,
% 0.21/0.40 (![X: $i] : (animal(X) => (![Y: $i] : (plant(Y) => eats(X, Y)) | ![Y1: $i] : (animal(Y1) => ((much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z))) => eats(X, Y1))))) <=> ![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~(much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[130])).
% 0.21/0.40 tff(132,axiom,(![X: $i] : (animal(X) => (![Y: $i] : (plant(Y) => eats(X, Y)) | ![Y1: $i] : (animal(Y1) => ((much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z))) => eats(X, Y1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_7')).
% 0.21/0.41 tff(133,plain,
% 0.21/0.41 (![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~(much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.21/0.41 tff(134,plain,
% 0.21/0.41 (![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~(much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.21/0.41 tff(135,plain,(
% 0.21/0.41 ![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | ((~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z))))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[134])).
% 0.21/0.41 tff(136,plain,
% 0.21/0.41 (![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[135, 128])).
% 0.21/0.41 tff(137,plain,
% 0.21/0.41 (![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[136, 126])).
% 0.21/0.41 tff(138,plain,
% 0.21/0.41 (![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[137, 124])).
% 0.21/0.41 tff(139,plain,
% 0.21/0.41 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!4)) | ![Y: $i] : ((~plant(Y)) | eats(A!4, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(A!4)) | ![Y: $i] : ((~plant(Y)) | eats(A!4, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(140,plain,
% 0.21/0.41 (((~animal(A!4)) | ![Y: $i] : ((~plant(Y)) | eats(A!4, Y)) | ![Y1: $i] : (eats(A!4, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> ((~animal(A!4)) | ![Y: $i] : ((~plant(Y)) | eats(A!4, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(141,plain,
% 0.21/0.41 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!4)) | ![Y: $i] : ((~plant(Y)) | eats(A!4, Y)) | ![Y1: $i] : (eats(A!4, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!4)) | ![Y: $i] : ((~plant(Y)) | eats(A!4, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4)))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[140])).
% 0.21/0.41 tff(142,plain,
% 0.21/0.41 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!4)) | ![Y: $i] : ((~plant(Y)) | eats(A!4, Y)) | ![Y1: $i] : (eats(A!4, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(A!4)) | ![Y: $i] : ((~plant(Y)) | eats(A!4, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[141, 139])).
% 0.21/0.41 tff(143,plain,
% 0.21/0.41 ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!4)) | ![Y: $i] : ((~plant(Y)) | eats(A!4, Y)) | ![Y1: $i] : (eats(A!4, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(144,plain,
% 0.21/0.41 ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(A!4)) | ![Y: $i] : ((~plant(Y)) | eats(A!4, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.21/0.41 tff(145,plain,
% 0.21/0.41 (![Y: $i] : ((~plant(Y)) | eats(A!4, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!4, Y1) | (~much_smaller(Y1, A!4)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[144, 138, 119])).
% 0.21/0.41 tff(146,plain,
% 0.21/0.41 (![Y: $i] : ((~plant(Y)) | eats(A!4, Y))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[145, 105])).
% 0.21/0.41 tff(147,plain,
% 0.21/0.41 (?[A: $i] : plant(A) <=> ?[A: $i] : plant(A)),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(148,axiom,(?[A: $i] : plant(A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','plant_type')).
% 0.21/0.41 tff(149,plain,
% 0.21/0.41 (?[A: $i] : plant(A)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.21/0.41 tff(150,plain,(
% 0.21/0.41 plant(A!7)),
% 0.21/0.41 inference(skolemize,[status(sab)],[149])).
% 0.21/0.41 tff(151,plain,
% 0.21/0.41 (((~![Y: $i] : ((~plant(Y)) | eats(A!4, Y))) | ((~plant(A!7)) | eats(A!4, A!7))) <=> ((~![Y: $i] : ((~plant(Y)) | eats(A!4, Y))) | (~plant(A!7)) | eats(A!4, A!7))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(152,plain,
% 0.21/0.41 ((~![Y: $i] : ((~plant(Y)) | eats(A!4, Y))) | ((~plant(A!7)) | eats(A!4, A!7))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(153,plain,
% 0.21/0.41 ((~![Y: $i] : ((~plant(Y)) | eats(A!4, Y))) | (~plant(A!7)) | eats(A!4, A!7)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.21/0.41 tff(154,plain,
% 0.21/0.41 (eats(A!4, A!7)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[153, 150, 146])).
% 0.21/0.41 tff(155,assumption,(~eats(A!4, A!8)), introduced(assumption)).
% 0.21/0.41 tff(156,assumption,(![Y: $i] : ((~plant(Y)) | eats(A!4, Y))), introduced(assumption)).
% 0.21/0.41 tff(157,plain,
% 0.21/0.41 (^[A: $i] : refl((plant(A) | (~grain(A))) <=> (plant(A) | (~grain(A))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(158,plain,
% 0.21/0.41 (![A: $i] : (plant(A) | (~grain(A))) <=> ![A: $i] : (plant(A) | (~grain(A)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[157])).
% 0.21/0.41 tff(159,plain,
% 0.21/0.41 (![A: $i] : (plant(A) | (~grain(A))) <=> ![A: $i] : (plant(A) | (~grain(A)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(160,plain,
% 0.21/0.41 (^[A: $i] : rewrite((grain(A) => plant(A)) <=> (plant(A) | (~grain(A))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(161,plain,
% 0.21/0.41 (![A: $i] : (grain(A) => plant(A)) <=> ![A: $i] : (plant(A) | (~grain(A)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[160])).
% 0.21/0.41 tff(162,axiom,(![A: $i] : (grain(A) => plant(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','grain_is_plant')).
% 0.21/0.41 tff(163,plain,
% 0.21/0.41 (![A: $i] : (plant(A) | (~grain(A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.21/0.41 tff(164,plain,
% 0.21/0.41 (![A: $i] : (plant(A) | (~grain(A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[163, 159])).
% 0.21/0.41 tff(165,plain,(
% 0.21/0.41 ![A: $i] : (plant(A) | (~grain(A)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[164])).
% 0.21/0.41 tff(166,plain,
% 0.21/0.41 (![A: $i] : (plant(A) | (~grain(A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[165, 158])).
% 0.21/0.41 tff(167,plain,
% 0.21/0.41 (?[A: $i] : grain(A) <=> ?[A: $i] : grain(A)),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(168,axiom,(?[A: $i] : grain(A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','grain_type')).
% 0.21/0.41 tff(169,plain,
% 0.21/0.41 (?[A: $i] : grain(A)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.21/0.41 tff(170,plain,(
% 0.21/0.41 grain(A!8)),
% 0.21/0.41 inference(skolemize,[status(sab)],[169])).
% 0.21/0.41 tff(171,plain,
% 0.21/0.41 (((~![A: $i] : (plant(A) | (~grain(A)))) | (plant(A!8) | (~grain(A!8)))) <=> ((~![A: $i] : (plant(A) | (~grain(A)))) | plant(A!8) | (~grain(A!8)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(172,plain,
% 0.21/0.41 ((~![A: $i] : (plant(A) | (~grain(A)))) | (plant(A!8) | (~grain(A!8)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(173,plain,
% 0.21/0.41 ((~![A: $i] : (plant(A) | (~grain(A)))) | plant(A!8) | (~grain(A!8))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.21/0.41 tff(174,plain,
% 0.21/0.41 (plant(A!8)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[173, 170, 166])).
% 0.21/0.41 tff(175,plain,
% 0.21/0.41 (((~![Y: $i] : ((~plant(Y)) | eats(A!4, Y))) | ((~plant(A!8)) | eats(A!4, A!8))) <=> ((~![Y: $i] : ((~plant(Y)) | eats(A!4, Y))) | (~plant(A!8)) | eats(A!4, A!8))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(176,plain,
% 0.21/0.41 ((~![Y: $i] : ((~plant(Y)) | eats(A!4, Y))) | ((~plant(A!8)) | eats(A!4, A!8))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(177,plain,
% 0.21/0.41 ((~![Y: $i] : ((~plant(Y)) | eats(A!4, Y))) | (~plant(A!8)) | eats(A!4, A!8)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.21/0.41 tff(178,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[177, 174, 156, 155])).
% 0.21/0.41 tff(179,plain,((~![Y: $i] : ((~plant(Y)) | eats(A!4, Y))) | eats(A!4, A!8)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(180,plain,
% 0.21/0.41 (eats(A!4, A!8)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[179, 146])).
% 0.21/0.41 tff(181,assumption,(eats(A!3, A!4)), introduced(assumption)).
% 0.21/0.41 tff(182,assumption,(eats(A!4, A!8)), introduced(assumption)).
% 0.21/0.41 tff(183,plain,
% 0.21/0.41 (^[A: $i] : refl((animal(A) | (~fox(A))) <=> (animal(A) | (~fox(A))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(184,plain,
% 0.21/0.41 (![A: $i] : (animal(A) | (~fox(A))) <=> ![A: $i] : (animal(A) | (~fox(A)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[183])).
% 0.21/0.41 tff(185,plain,
% 0.21/0.41 (![A: $i] : (animal(A) | (~fox(A))) <=> ![A: $i] : (animal(A) | (~fox(A)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(186,plain,
% 0.21/0.41 (^[A: $i] : rewrite((fox(A) => animal(A)) <=> (animal(A) | (~fox(A))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(187,plain,
% 0.21/0.41 (![A: $i] : (fox(A) => animal(A)) <=> ![A: $i] : (animal(A) | (~fox(A)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[186])).
% 0.21/0.41 tff(188,axiom,(![A: $i] : (fox(A) => animal(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fox_is_animal')).
% 0.21/0.41 tff(189,plain,
% 0.21/0.41 (![A: $i] : (animal(A) | (~fox(A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.21/0.41 tff(190,plain,
% 0.21/0.41 (![A: $i] : (animal(A) | (~fox(A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[189, 185])).
% 0.21/0.41 tff(191,plain,(
% 0.21/0.41 ![A: $i] : (animal(A) | (~fox(A)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[190])).
% 0.21/0.41 tff(192,plain,
% 0.21/0.41 (![A: $i] : (animal(A) | (~fox(A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[191, 184])).
% 0.21/0.41 tff(193,plain,
% 0.21/0.41 (?[A: $i] : fox(A) <=> ?[A: $i] : fox(A)),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(194,axiom,(?[A: $i] : fox(A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fox_type')).
% 0.21/0.41 tff(195,plain,
% 0.21/0.41 (?[A: $i] : fox(A)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.21/0.41 tff(196,plain,(
% 0.21/0.41 fox(A!3)),
% 0.21/0.41 inference(skolemize,[status(sab)],[195])).
% 0.21/0.41 tff(197,plain,
% 0.21/0.41 (((~![A: $i] : (animal(A) | (~fox(A)))) | (animal(A!3) | (~fox(A!3)))) <=> ((~![A: $i] : (animal(A) | (~fox(A)))) | animal(A!3) | (~fox(A!3)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(198,plain,
% 0.21/0.41 ((~![A: $i] : (animal(A) | (~fox(A)))) | (animal(A!3) | (~fox(A!3)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(199,plain,
% 0.21/0.41 ((~![A: $i] : (animal(A) | (~fox(A)))) | animal(A!3) | (~fox(A!3))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.21/0.41 tff(200,plain,
% 0.21/0.41 (animal(A!3)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[199, 196, 192])).
% 0.21/0.41 tff(201,plain,
% 0.21/0.41 (^[X: $i, Y: $i, Z: $i] : refl(((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y))) <=> ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(202,plain,
% 0.21/0.41 (![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[201])).
% 0.21/0.41 tff(203,plain,
% 0.21/0.41 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((animal(X) & animal(Y) & grain(Z) & eats(Y, Z) & eats(X, Y)) <=> (~((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y))))), ((~(animal(X) & animal(Y) & grain(Z) & eats(Y, Z) & eats(X, Y))) <=> (~(~((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y))))))), rewrite((~(~((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y))))) <=> ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))), ((~(animal(X) & animal(Y) & grain(Z) & eats(Y, Z) & eats(X, Y))) <=> ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(204,plain,
% 0.21/0.41 (![X: $i, Y: $i, Z: $i] : (~(animal(X) & animal(Y) & grain(Z) & eats(Y, Z) & eats(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[203])).
% 0.21/0.41 tff(205,plain,
% 0.21/0.41 ((~?[X: $i, Y: $i, Z: $i] : (animal(X) & animal(Y) & grain(Z) & eats(Y, Z) & eats(X, Y))) <=> (~?[X: $i, Y: $i, Z: $i] : (animal(X) & animal(Y) & grain(Z) & eats(Y, Z) & eats(X, Y)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(206,plain,
% 0.21/0.41 ((~?[X: $i, Y: $i, Z: $i] : ((((animal(X) & animal(Y)) & grain(Z)) & eats(Y, Z)) & eats(X, Y))) <=> (~?[X: $i, Y: $i, Z: $i] : (animal(X) & animal(Y) & grain(Z) & eats(Y, Z) & eats(X, Y)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(207,axiom,(~?[X: $i, Y: $i, Z: $i] : ((((animal(X) & animal(Y)) & grain(Z)) & eats(Y, Z)) & eats(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47')).
% 0.21/0.41 tff(208,plain,
% 0.21/0.41 (~?[X: $i, Y: $i, Z: $i] : (animal(X) & animal(Y) & grain(Z) & eats(Y, Z) & eats(X, Y))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.21/0.41 tff(209,plain,
% 0.21/0.41 (~?[X: $i, Y: $i, Z: $i] : (animal(X) & animal(Y) & grain(Z) & eats(Y, Z) & eats(X, Y))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[208, 205])).
% 0.21/0.41 tff(210,plain,
% 0.21/0.41 (~?[X: $i, Y: $i, Z: $i] : (animal(X) & animal(Y) & grain(Z) & eats(Y, Z) & eats(X, Y))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[209, 205])).
% 0.21/0.41 tff(211,plain,
% 0.21/0.41 (~?[X: $i, Y: $i, Z: $i] : (animal(X) & animal(Y) & grain(Z) & eats(Y, Z) & eats(X, Y))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[210, 205])).
% 0.21/0.41 tff(212,plain,
% 0.21/0.41 (^[X: $i, Y: $i, Z: $i] : refl($oeq((~(animal(X) & animal(Y) & grain(Z) & eats(Y, Z) & eats(X, Y))), (~(animal(X) & animal(Y) & grain(Z) & eats(Y, Z) & eats(X, Y)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(213,plain,(
% 0.21/0.41 ![X: $i, Y: $i, Z: $i] : (~(animal(X) & animal(Y) & grain(Z) & eats(Y, Z) & eats(X, Y)))),
% 0.21/0.41 inference(nnf-neg,[status(sab)],[211, 212])).
% 0.21/0.41 tff(214,plain,
% 0.21/0.41 (![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[213, 204])).
% 0.21/0.41 tff(215,plain,
% 0.21/0.41 (![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[214, 202])).
% 0.21/0.41 tff(216,plain,
% 0.21/0.41 (((~![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))) | ((~grain(A!8)) | (~animal(A!3)) | (~animal(A!4)) | (~eats(A!4, A!8)) | (~eats(A!3, A!4)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))) | (~grain(A!8)) | (~animal(A!3)) | (~animal(A!4)) | (~eats(A!4, A!8)) | (~eats(A!3, A!4)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(217,plain,
% 0.21/0.41 (((~eats(A!4, A!8)) | (~grain(A!8)) | (~animal(A!3)) | (~animal(A!4)) | (~eats(A!3, A!4))) <=> ((~grain(A!8)) | (~animal(A!3)) | (~animal(A!4)) | (~eats(A!4, A!8)) | (~eats(A!3, A!4)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(218,plain,
% 0.21/0.42 (((~![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))) | ((~eats(A!4, A!8)) | (~grain(A!8)) | (~animal(A!3)) | (~animal(A!4)) | (~eats(A!3, A!4)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))) | ((~grain(A!8)) | (~animal(A!3)) | (~animal(A!4)) | (~eats(A!4, A!8)) | (~eats(A!3, A!4))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[217])).
% 0.21/0.42 tff(219,plain,
% 0.21/0.42 (((~![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))) | ((~eats(A!4, A!8)) | (~grain(A!8)) | (~animal(A!3)) | (~animal(A!4)) | (~eats(A!3, A!4)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))) | (~grain(A!8)) | (~animal(A!3)) | (~animal(A!4)) | (~eats(A!4, A!8)) | (~eats(A!3, A!4)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[218, 216])).
% 0.21/0.42 tff(220,plain,
% 0.21/0.42 ((~![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))) | ((~eats(A!4, A!8)) | (~grain(A!8)) | (~animal(A!3)) | (~animal(A!4)) | (~eats(A!3, A!4)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(221,plain,
% 0.21/0.42 ((~![X: $i, Y: $i, Z: $i] : ((~eats(Y, Z)) | (~grain(Z)) | (~animal(X)) | (~animal(Y)) | (~eats(X, Y)))) | (~grain(A!8)) | (~animal(A!3)) | (~animal(A!4)) | (~eats(A!4, A!8)) | (~eats(A!3, A!4))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.21/0.42 tff(222,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[221, 170, 215, 200, 119, 182, 181])).
% 0.21/0.42 tff(223,plain,((~eats(A!3, A!4)) | (~eats(A!4, A!8))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(224,plain,
% 0.21/0.42 (~eats(A!3, A!4)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[223, 180])).
% 0.21/0.42 tff(225,assumption,(eats(A!2, A!3)), introduced(assumption)).
% 0.21/0.42 tff(226,plain,
% 0.21/0.42 (^[X: $i, Y: $i] : refl(((~eats(X, Y)) | (~fox(Y)) | (~wolf(X))) <=> ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(227,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[226])).
% 0.21/0.42 tff(228,plain,
% 0.21/0.42 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((wolf(X) & fox(Y)) <=> (~((~fox(Y)) | (~wolf(X))))), ((~(wolf(X) & fox(Y))) <=> (~(~((~fox(Y)) | (~wolf(X))))))), rewrite((~(~((~fox(Y)) | (~wolf(X))))) <=> ((~fox(Y)) | (~wolf(X)))), ((~(wolf(X) & fox(Y))) <=> ((~fox(Y)) | (~wolf(X))))), (((~eats(X, Y)) | (~(wolf(X) & fox(Y)))) <=> ((~eats(X, Y)) | ((~fox(Y)) | (~wolf(X)))))), rewrite(((~eats(X, Y)) | ((~fox(Y)) | (~wolf(X)))) <=> ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))), (((~eats(X, Y)) | (~(wolf(X) & fox(Y)))) <=> ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(229,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & fox(Y)))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[228])).
% 0.21/0.42 tff(230,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & fox(Y)))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & fox(Y))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(231,plain,
% 0.21/0.42 (^[X: $i, Y: $i] : rewrite(((wolf(X) & fox(Y)) => (~eats(X, Y))) <=> ((~eats(X, Y)) | (~(wolf(X) & fox(Y)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(232,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((wolf(X) & fox(Y)) => (~eats(X, Y))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & fox(Y))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[231])).
% 0.21/0.42 tff(233,axiom,(![X: $i, Y: $i] : ((wolf(X) & fox(Y)) => (~eats(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_11')).
% 0.21/0.42 tff(234,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & fox(Y))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.21/0.42 tff(235,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & fox(Y))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[234, 230])).
% 0.21/0.42 tff(236,plain,(
% 0.21/0.42 ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & fox(Y))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[235])).
% 0.21/0.42 tff(237,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[236, 229])).
% 0.21/0.42 tff(238,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[237, 227])).
% 0.21/0.42 tff(239,plain,
% 0.21/0.42 (?[A: $i] : wolf(A) <=> ?[A: $i] : wolf(A)),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(240,axiom,(?[A: $i] : wolf(A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','wolf_type')).
% 0.21/0.42 tff(241,plain,
% 0.21/0.42 (?[A: $i] : wolf(A)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.21/0.42 tff(242,plain,(
% 0.21/0.42 wolf(A!2)),
% 0.21/0.42 inference(skolemize,[status(sab)],[241])).
% 0.21/0.42 tff(243,plain,
% 0.21/0.42 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))) | ((~wolf(A!2)) | (~fox(A!3)) | (~eats(A!2, A!3)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))) | (~wolf(A!2)) | (~fox(A!3)) | (~eats(A!2, A!3)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(244,plain,
% 0.21/0.42 (((~eats(A!2, A!3)) | (~fox(A!3)) | (~wolf(A!2))) <=> ((~wolf(A!2)) | (~fox(A!3)) | (~eats(A!2, A!3)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(245,plain,
% 0.21/0.42 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))) | ((~eats(A!2, A!3)) | (~fox(A!3)) | (~wolf(A!2)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))) | ((~wolf(A!2)) | (~fox(A!3)) | (~eats(A!2, A!3))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[244])).
% 0.21/0.42 tff(246,plain,
% 0.21/0.42 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))) | ((~eats(A!2, A!3)) | (~fox(A!3)) | (~wolf(A!2)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))) | (~wolf(A!2)) | (~fox(A!3)) | (~eats(A!2, A!3)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[245, 243])).
% 0.21/0.42 tff(247,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))) | ((~eats(A!2, A!3)) | (~fox(A!3)) | (~wolf(A!2)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(248,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))) | (~wolf(A!2)) | (~fox(A!3)) | (~eats(A!2, A!3))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.21/0.42 tff(249,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[248, 242, 196, 238, 225])).
% 0.21/0.42 tff(250,plain,(~eats(A!2, A!3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(251,assumption,(~much_smaller(A!3, A!2)), introduced(assumption)).
% 0.21/0.42 tff(252,plain,
% 0.21/0.42 (^[X: $i, Y: $i] : refl((much_smaller(X, Y) | (~wolf(Y)) | (~fox(X))) <=> (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(253,plain,
% 0.21/0.42 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X))) <=> ![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[252])).
% 0.21/0.42 tff(254,plain,
% 0.21/0.42 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((fox(X) & wolf(Y)) <=> (~((~fox(X)) | (~wolf(Y))))), ((~(fox(X) & wolf(Y))) <=> (~(~((~fox(X)) | (~wolf(Y))))))), rewrite((~(~((~fox(X)) | (~wolf(Y))))) <=> ((~fox(X)) | (~wolf(Y)))), ((~(fox(X) & wolf(Y))) <=> ((~fox(X)) | (~wolf(Y))))), (((~(fox(X) & wolf(Y))) | much_smaller(X, Y)) <=> (((~fox(X)) | (~wolf(Y))) | much_smaller(X, Y)))), rewrite((((~fox(X)) | (~wolf(Y))) | much_smaller(X, Y)) <=> (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))), (((~(fox(X) & wolf(Y))) | much_smaller(X, Y)) <=> (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(255,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y)) <=> ![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[254])).
% 0.21/0.42 tff(256,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y)) <=> ![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(257,plain,
% 0.21/0.42 (^[X: $i, Y: $i] : rewrite(((fox(X) & wolf(Y)) => much_smaller(X, Y)) <=> ((~(fox(X) & wolf(Y))) | much_smaller(X, Y)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(258,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((fox(X) & wolf(Y)) => much_smaller(X, Y)) <=> ![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[257])).
% 0.21/0.42 tff(259,axiom,(![X: $i, Y: $i] : ((fox(X) & wolf(Y)) => much_smaller(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_10')).
% 0.21/0.42 tff(260,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.21/0.42 tff(261,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[260, 256])).
% 0.21/0.42 tff(262,plain,(
% 0.21/0.42 ![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y))),
% 0.21/0.42 inference(skolemize,[status(sab)],[261])).
% 0.21/0.42 tff(263,plain,
% 0.21/0.42 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[262, 255])).
% 0.21/0.42 tff(264,plain,
% 0.21/0.42 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[263, 253])).
% 0.21/0.42 tff(265,plain,
% 0.21/0.42 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | ((~wolf(A!2)) | (~fox(A!3)) | much_smaller(A!3, A!2))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (~wolf(A!2)) | (~fox(A!3)) | much_smaller(A!3, A!2))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(266,plain,
% 0.21/0.42 ((much_smaller(A!3, A!2) | (~wolf(A!2)) | (~fox(A!3))) <=> ((~wolf(A!2)) | (~fox(A!3)) | much_smaller(A!3, A!2))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(267,plain,
% 0.21/0.42 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (much_smaller(A!3, A!2) | (~wolf(A!2)) | (~fox(A!3)))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | ((~wolf(A!2)) | (~fox(A!3)) | much_smaller(A!3, A!2)))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[266])).
% 0.21/0.42 tff(268,plain,
% 0.21/0.42 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (much_smaller(A!3, A!2) | (~wolf(A!2)) | (~fox(A!3)))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (~wolf(A!2)) | (~fox(A!3)) | much_smaller(A!3, A!2))),
% 0.21/0.42 inference(transitivity,[status(thm)],[267, 265])).
% 0.21/0.42 tff(269,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (much_smaller(A!3, A!2) | (~wolf(A!2)) | (~fox(A!3)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(270,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (~wolf(A!2)) | (~fox(A!3)) | much_smaller(A!3, A!2)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.21/0.42 tff(271,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[270, 242, 196, 264, 251])).
% 0.21/0.42 tff(272,plain,(much_smaller(A!3, A!2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(273,assumption,(eats(A!2, A!8)), introduced(assumption)).
% 0.21/0.42 tff(274,plain,
% 0.21/0.42 (^[X: $i, Y: $i] : refl(((~eats(X, Y)) | (~grain(Y)) | (~wolf(X))) <=> ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(275,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[274])).
% 0.21/0.42 tff(276,plain,
% 0.21/0.42 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((wolf(X) & grain(Y)) <=> (~((~grain(Y)) | (~wolf(X))))), ((~(wolf(X) & grain(Y))) <=> (~(~((~grain(Y)) | (~wolf(X))))))), rewrite((~(~((~grain(Y)) | (~wolf(X))))) <=> ((~grain(Y)) | (~wolf(X)))), ((~(wolf(X) & grain(Y))) <=> ((~grain(Y)) | (~wolf(X))))), (((~eats(X, Y)) | (~(wolf(X) & grain(Y)))) <=> ((~eats(X, Y)) | ((~grain(Y)) | (~wolf(X)))))), rewrite(((~eats(X, Y)) | ((~grain(Y)) | (~wolf(X)))) <=> ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))), (((~eats(X, Y)) | (~(wolf(X) & grain(Y)))) <=> ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(277,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & grain(Y)))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[276])).
% 0.21/0.42 tff(278,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & grain(Y)))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & grain(Y))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(279,plain,
% 0.21/0.42 (^[X: $i, Y: $i] : rewrite(((wolf(X) & grain(Y)) => (~eats(X, Y))) <=> ((~eats(X, Y)) | (~(wolf(X) & grain(Y)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(280,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((wolf(X) & grain(Y)) => (~eats(X, Y))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & grain(Y))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[279])).
% 0.21/0.42 tff(281,axiom,(![X: $i, Y: $i] : ((wolf(X) & grain(Y)) => (~eats(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_11a')).
% 0.21/0.42 tff(282,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & grain(Y))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.21/0.42 tff(283,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & grain(Y))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[282, 278])).
% 0.21/0.42 tff(284,plain,(
% 0.21/0.42 ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & grain(Y))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[283])).
% 0.21/0.42 tff(285,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[284, 277])).
% 0.21/0.42 tff(286,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[285, 275])).
% 0.21/0.42 tff(287,plain,
% 0.21/0.42 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | ((~wolf(A!2)) | (~grain(A!8)) | (~eats(A!2, A!8)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | (~wolf(A!2)) | (~grain(A!8)) | (~eats(A!2, A!8)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(288,plain,
% 0.21/0.42 (((~eats(A!2, A!8)) | (~grain(A!8)) | (~wolf(A!2))) <=> ((~wolf(A!2)) | (~grain(A!8)) | (~eats(A!2, A!8)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(289,plain,
% 0.21/0.42 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | ((~eats(A!2, A!8)) | (~grain(A!8)) | (~wolf(A!2)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | ((~wolf(A!2)) | (~grain(A!8)) | (~eats(A!2, A!8))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[288])).
% 0.21/0.42 tff(290,plain,
% 0.21/0.42 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | ((~eats(A!2, A!8)) | (~grain(A!8)) | (~wolf(A!2)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | (~wolf(A!2)) | (~grain(A!8)) | (~eats(A!2, A!8)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[289, 287])).
% 0.21/0.42 tff(291,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | ((~eats(A!2, A!8)) | (~grain(A!8)) | (~wolf(A!2)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(292,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | (~wolf(A!2)) | (~grain(A!8)) | (~eats(A!2, A!8))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.21/0.42 tff(293,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[292, 242, 170, 286, 273])).
% 0.21/0.42 tff(294,plain,(~eats(A!2, A!8)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(295,assumption,(![Y: $i] : ((~plant(Y)) | eats(A!2, Y))), introduced(assumption)).
% 0.21/0.42 tff(296,plain,
% 0.21/0.42 (((~![Y: $i] : ((~plant(Y)) | eats(A!2, Y))) | ((~plant(A!8)) | eats(A!2, A!8))) <=> ((~![Y: $i] : ((~plant(Y)) | eats(A!2, Y))) | (~plant(A!8)) | eats(A!2, A!8))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(297,plain,
% 0.21/0.42 ((~![Y: $i] : ((~plant(Y)) | eats(A!2, Y))) | ((~plant(A!8)) | eats(A!2, A!8))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(298,plain,
% 0.21/0.42 ((~![Y: $i] : ((~plant(Y)) | eats(A!2, Y))) | (~plant(A!8)) | eats(A!2, A!8)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.21/0.42 tff(299,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[298, 174, 295, 294])).
% 0.21/0.42 tff(300,plain,(~![Y: $i] : ((~plant(Y)) | eats(A!2, Y))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(301,plain,
% 0.21/0.42 (^[A: $i] : refl((animal(A) | (~wolf(A))) <=> (animal(A) | (~wolf(A))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(302,plain,
% 0.21/0.42 (![A: $i] : (animal(A) | (~wolf(A))) <=> ![A: $i] : (animal(A) | (~wolf(A)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[301])).
% 0.21/0.42 tff(303,plain,
% 0.21/0.42 (![A: $i] : (animal(A) | (~wolf(A))) <=> ![A: $i] : (animal(A) | (~wolf(A)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(304,plain,
% 0.21/0.42 (^[A: $i] : rewrite((wolf(A) => animal(A)) <=> (animal(A) | (~wolf(A))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(305,plain,
% 0.21/0.42 (![A: $i] : (wolf(A) => animal(A)) <=> ![A: $i] : (animal(A) | (~wolf(A)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[304])).
% 0.21/0.42 tff(306,axiom,(![A: $i] : (wolf(A) => animal(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','wolf_is_animal')).
% 0.21/0.42 tff(307,plain,
% 0.21/0.42 (![A: $i] : (animal(A) | (~wolf(A)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.21/0.42 tff(308,plain,
% 0.21/0.42 (![A: $i] : (animal(A) | (~wolf(A)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[307, 303])).
% 0.21/0.42 tff(309,plain,(
% 0.21/0.42 ![A: $i] : (animal(A) | (~wolf(A)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[308])).
% 0.21/0.42 tff(310,plain,
% 0.21/0.42 (![A: $i] : (animal(A) | (~wolf(A)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[309, 302])).
% 0.21/0.42 tff(311,plain,
% 0.21/0.42 (((~![A: $i] : (animal(A) | (~wolf(A)))) | (animal(A!2) | (~wolf(A!2)))) <=> ((~![A: $i] : (animal(A) | (~wolf(A)))) | animal(A!2) | (~wolf(A!2)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(312,plain,
% 0.21/0.42 ((~![A: $i] : (animal(A) | (~wolf(A)))) | (animal(A!2) | (~wolf(A!2)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(313,plain,
% 0.21/0.42 ((~![A: $i] : (animal(A) | (~wolf(A)))) | animal(A!2) | (~wolf(A!2))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.21/0.42 tff(314,plain,
% 0.21/0.42 (animal(A!2)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[313, 242, 310])).
% 0.21/0.42 tff(315,plain,
% 0.21/0.42 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!2)) | ![Y: $i] : ((~plant(Y)) | eats(A!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(A!2)) | ![Y: $i] : ((~plant(Y)) | eats(A!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(316,plain,
% 0.21/0.42 (((~animal(A!2)) | ![Y: $i] : ((~plant(Y)) | eats(A!2, Y)) | ![Y1: $i] : (eats(A!2, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> ((~animal(A!2)) | ![Y: $i] : ((~plant(Y)) | eats(A!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(317,plain,
% 0.21/0.42 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!2)) | ![Y: $i] : ((~plant(Y)) | eats(A!2, Y)) | ![Y1: $i] : (eats(A!2, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!2)) | ![Y: $i] : ((~plant(Y)) | eats(A!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[316])).
% 0.21/0.43 tff(318,plain,
% 0.21/0.43 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!2)) | ![Y: $i] : ((~plant(Y)) | eats(A!2, Y)) | ![Y1: $i] : (eats(A!2, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(A!2)) | ![Y: $i] : ((~plant(Y)) | eats(A!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[317, 315])).
% 0.21/0.43 tff(319,plain,
% 0.21/0.43 ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!2)) | ![Y: $i] : ((~plant(Y)) | eats(A!2, Y)) | ![Y1: $i] : (eats(A!2, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(320,plain,
% 0.21/0.43 ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(A!2)) | ![Y: $i] : ((~plant(Y)) | eats(A!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[319, 318])).
% 0.21/0.43 tff(321,plain,
% 0.21/0.43 (![Y: $i] : ((~plant(Y)) | eats(A!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[320, 138, 314])).
% 0.21/0.43 tff(322,plain,
% 0.21/0.43 (![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[321, 300])).
% 0.21/0.43 tff(323,plain,
% 0.21/0.43 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))) | ((~animal(A!3)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!3, Z))) | (~much_smaller(A!3, A!2)) | eats(A!2, A!3))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))) | (~animal(A!3)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!3, Z))) | (~much_smaller(A!3, A!2)) | eats(A!2, A!3))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(324,plain,
% 0.21/0.43 (((~animal(A!3)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!3, Z))) | eats(A!2, A!3) | (~much_smaller(A!3, A!2))) <=> ((~animal(A!3)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!3, Z))) | (~much_smaller(A!3, A!2)) | eats(A!2, A!3))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(325,plain,
% 0.21/0.43 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))) | ((~animal(A!3)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!3, Z))) | eats(A!2, A!3) | (~much_smaller(A!3, A!2)))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))) | ((~animal(A!3)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!3, Z))) | (~much_smaller(A!3, A!2)) | eats(A!2, A!3)))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[324])).
% 0.21/0.43 tff(326,plain,
% 0.21/0.43 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))) | ((~animal(A!3)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!3, Z))) | eats(A!2, A!3) | (~much_smaller(A!3, A!2)))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))) | (~animal(A!3)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!3, Z))) | (~much_smaller(A!3, A!2)) | eats(A!2, A!3))),
% 0.21/0.43 inference(transitivity,[status(thm)],[325, 323])).
% 0.21/0.43 tff(327,plain,
% 0.21/0.43 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))) | ((~animal(A!3)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!3, Z))) | eats(A!2, A!3) | (~much_smaller(A!3, A!2)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(328,plain,
% 0.21/0.43 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))) | (~animal(A!3)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!3, Z))) | (~much_smaller(A!3, A!2)) | eats(A!2, A!3)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.21/0.43 tff(329,plain,
% 0.21/0.43 (![Z: $i] : ((~plant(Z)) | (~eats(A!3, Z))) | (~much_smaller(A!3, A!2)) | eats(A!2, A!3)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[328, 200, 322])).
% 0.21/0.43 tff(330,plain,
% 0.21/0.43 (![Z: $i] : ((~plant(Z)) | (~eats(A!3, Z))) | eats(A!2, A!3)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[329, 272])).
% 0.21/0.43 tff(331,plain,
% 0.21/0.43 (![Z: $i] : ((~plant(Z)) | (~eats(A!3, Z)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[330, 250])).
% 0.21/0.43 tff(332,plain,
% 0.21/0.43 (((~![Z: $i] : ((~plant(Z)) | (~eats(A!3, Z)))) | ((~plant(A!7)) | (~eats(A!3, A!7)))) <=> ((~![Z: $i] : ((~plant(Z)) | (~eats(A!3, Z)))) | (~plant(A!7)) | (~eats(A!3, A!7)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(333,plain,
% 0.21/0.43 ((~![Z: $i] : ((~plant(Z)) | (~eats(A!3, Z)))) | ((~plant(A!7)) | (~eats(A!3, A!7)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(334,plain,
% 0.21/0.43 ((~![Z: $i] : ((~plant(Z)) | (~eats(A!3, Z)))) | (~plant(A!7)) | (~eats(A!3, A!7))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[333, 332])).
% 0.21/0.43 tff(335,plain,
% 0.21/0.43 (~eats(A!3, A!7)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[334, 150, 331])).
% 0.21/0.43 tff(336,assumption,(![Y: $i] : ((~plant(Y)) | eats(A!3, Y))), introduced(assumption)).
% 0.21/0.43 tff(337,plain,
% 0.21/0.43 (((~![Y: $i] : ((~plant(Y)) | eats(A!3, Y))) | ((~plant(A!7)) | eats(A!3, A!7))) <=> ((~![Y: $i] : ((~plant(Y)) | eats(A!3, Y))) | (~plant(A!7)) | eats(A!3, A!7))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(338,plain,
% 0.21/0.43 ((~![Y: $i] : ((~plant(Y)) | eats(A!3, Y))) | ((~plant(A!7)) | eats(A!3, A!7))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(339,plain,
% 0.21/0.43 ((~![Y: $i] : ((~plant(Y)) | eats(A!3, Y))) | (~plant(A!7)) | eats(A!3, A!7)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[338, 337])).
% 0.21/0.43 tff(340,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[339, 150, 336, 335])).
% 0.21/0.43 tff(341,plain,(~![Y: $i] : ((~plant(Y)) | eats(A!3, Y))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(342,plain,
% 0.21/0.43 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!3)) | ![Y: $i] : ((~plant(Y)) | eats(A!3, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(A!3)) | ![Y: $i] : ((~plant(Y)) | eats(A!3, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(343,plain,
% 0.21/0.43 (((~animal(A!3)) | ![Y: $i] : ((~plant(Y)) | eats(A!3, Y)) | ![Y1: $i] : (eats(A!3, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!3)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> ((~animal(A!3)) | ![Y: $i] : ((~plant(Y)) | eats(A!3, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(344,plain,
% 0.21/0.43 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!3)) | ![Y: $i] : ((~plant(Y)) | eats(A!3, Y)) | ![Y1: $i] : (eats(A!3, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!3)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!3)) | ![Y: $i] : ((~plant(Y)) | eats(A!3, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3)))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[343])).
% 0.21/0.43 tff(345,plain,
% 0.21/0.43 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!3)) | ![Y: $i] : ((~plant(Y)) | eats(A!3, Y)) | ![Y1: $i] : (eats(A!3, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!3)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(A!3)) | ![Y: $i] : ((~plant(Y)) | eats(A!3, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[344, 342])).
% 0.21/0.43 tff(346,plain,
% 0.21/0.43 ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!3)) | ![Y: $i] : ((~plant(Y)) | eats(A!3, Y)) | ![Y1: $i] : (eats(A!3, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!3)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(347,plain,
% 0.21/0.43 ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(A!3)) | ![Y: $i] : ((~plant(Y)) | eats(A!3, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[346, 345])).
% 0.21/0.43 tff(348,plain,
% 0.21/0.43 (![Y: $i] : ((~plant(Y)) | eats(A!3, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[347, 138, 200])).
% 0.21/0.43 tff(349,plain,
% 0.21/0.43 (![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[348, 341])).
% 0.21/0.43 tff(350,assumption,(~eats(A!3, A!4)), introduced(assumption)).
% 0.21/0.43 tff(351,assumption,(~much_smaller(A!4, A!3)), introduced(assumption)).
% 0.21/0.43 tff(352,plain,
% 0.21/0.43 (^[X: $i, Y: $i] : refl((much_smaller(X, Y) | (~fox(Y)) | (~bird(X))) <=> (much_smaller(X, Y) | (~fox(Y)) | (~bird(X))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(353,plain,
% 0.21/0.43 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X))) <=> ![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[352])).
% 0.21/0.43 tff(354,plain,
% 0.21/0.43 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((bird(X) & fox(Y)) <=> (~((~bird(X)) | (~fox(Y))))), ((~(bird(X) & fox(Y))) <=> (~(~((~bird(X)) | (~fox(Y))))))), rewrite((~(~((~bird(X)) | (~fox(Y))))) <=> ((~bird(X)) | (~fox(Y)))), ((~(bird(X) & fox(Y))) <=> ((~bird(X)) | (~fox(Y))))), (((~(bird(X) & fox(Y))) | much_smaller(X, Y)) <=> (((~bird(X)) | (~fox(Y))) | much_smaller(X, Y)))), rewrite((((~bird(X)) | (~fox(Y))) | much_smaller(X, Y)) <=> (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))), (((~(bird(X) & fox(Y))) | much_smaller(X, Y)) <=> (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(355,plain,
% 0.21/0.43 (![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y)) <=> ![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[354])).
% 0.21/0.43 tff(356,plain,
% 0.21/0.43 (![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y)) <=> ![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(357,plain,
% 0.21/0.43 (^[X: $i, Y: $i] : rewrite(((bird(X) & fox(Y)) => much_smaller(X, Y)) <=> ((~(bird(X) & fox(Y))) | much_smaller(X, Y)))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(358,plain,
% 0.21/0.43 (![X: $i, Y: $i] : ((bird(X) & fox(Y)) => much_smaller(X, Y)) <=> ![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[357])).
% 0.21/0.43 tff(359,axiom,(![X: $i, Y: $i] : ((bird(X) & fox(Y)) => much_smaller(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel47_9')).
% 0.21/0.43 tff(360,plain,
% 0.21/0.43 (![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[359, 358])).
% 0.21/0.44 tff(361,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[360, 356])).
% 0.21/0.44 tff(362,plain,(
% 0.21/0.44 ![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y))),
% 0.21/0.44 inference(skolemize,[status(sab)],[361])).
% 0.21/0.44 tff(363,plain,
% 0.21/0.44 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[362, 355])).
% 0.21/0.44 tff(364,plain,
% 0.21/0.44 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[363, 353])).
% 0.21/0.44 tff(365,plain,
% 0.21/0.44 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | ((~fox(A!3)) | (~bird(A!4)) | much_smaller(A!4, A!3))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (~fox(A!3)) | (~bird(A!4)) | much_smaller(A!4, A!3))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(366,plain,
% 0.21/0.44 ((much_smaller(A!4, A!3) | (~fox(A!3)) | (~bird(A!4))) <=> ((~fox(A!3)) | (~bird(A!4)) | much_smaller(A!4, A!3))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(367,plain,
% 0.21/0.44 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (much_smaller(A!4, A!3) | (~fox(A!3)) | (~bird(A!4)))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | ((~fox(A!3)) | (~bird(A!4)) | much_smaller(A!4, A!3)))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[366])).
% 0.21/0.44 tff(368,plain,
% 0.21/0.44 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (much_smaller(A!4, A!3) | (~fox(A!3)) | (~bird(A!4)))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (~fox(A!3)) | (~bird(A!4)) | much_smaller(A!4, A!3))),
% 0.21/0.44 inference(transitivity,[status(thm)],[367, 365])).
% 0.21/0.44 tff(369,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (much_smaller(A!4, A!3) | (~fox(A!3)) | (~bird(A!4)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(370,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (~fox(A!3)) | (~bird(A!4)) | much_smaller(A!4, A!3)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[369, 368])).
% 0.21/0.44 tff(371,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[370, 196, 22, 364, 351])).
% 0.21/0.44 tff(372,plain,(much_smaller(A!4, A!3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(373,assumption,(~![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z)))), introduced(assumption)).
% 0.21/0.44 tff(374,assumption,(![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3)))), introduced(assumption)).
% 0.21/0.44 tff(375,plain,
% 0.21/0.44 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3)))) | ((~animal(A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | (~much_smaller(A!4, A!3)) | eats(A!3, A!4))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3)))) | (~animal(A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | (~much_smaller(A!4, A!3)) | eats(A!3, A!4))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(376,plain,
% 0.21/0.44 (((~animal(A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | eats(A!3, A!4) | (~much_smaller(A!4, A!3))) <=> ((~animal(A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | (~much_smaller(A!4, A!3)) | eats(A!3, A!4))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(377,plain,
% 0.21/0.44 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3)))) | ((~animal(A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | eats(A!3, A!4) | (~much_smaller(A!4, A!3)))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3)))) | ((~animal(A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | (~much_smaller(A!4, A!3)) | eats(A!3, A!4)))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[376])).
% 0.21/0.44 tff(378,plain,
% 0.21/0.44 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3)))) | ((~animal(A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | eats(A!3, A!4) | (~much_smaller(A!4, A!3)))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3)))) | (~animal(A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | (~much_smaller(A!4, A!3)) | eats(A!3, A!4))),
% 0.21/0.44 inference(transitivity,[status(thm)],[377, 375])).
% 0.21/0.44 tff(379,plain,
% 0.21/0.44 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3)))) | ((~animal(A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | eats(A!3, A!4) | (~much_smaller(A!4, A!3)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(380,plain,
% 0.21/0.44 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3)))) | (~animal(A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | (~much_smaller(A!4, A!3)) | eats(A!3, A!4)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.21/0.44 tff(381,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[380, 119, 374, 373, 372, 350])).
% 0.21/0.44 tff(382,plain,((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!3, Y1) | (~much_smaller(Y1, A!3)))) | ![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | eats(A!3, A!4)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(383,plain,
% 0.21/0.44 (![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | eats(A!3, A!4)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[382, 349])).
% 0.21/0.44 tff(384,plain,
% 0.21/0.44 (![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[383, 224])).
% 0.21/0.44 tff(385,plain,
% 0.21/0.44 (((~![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z)))) | ((~plant(A!7)) | (~eats(A!4, A!7)))) <=> ((~![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z)))) | (~plant(A!7)) | (~eats(A!4, A!7)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(386,plain,
% 0.21/0.44 ((~![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z)))) | ((~plant(A!7)) | (~eats(A!4, A!7)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(387,plain,
% 0.21/0.44 ((~![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z)))) | (~plant(A!7)) | (~eats(A!4, A!7))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[386, 385])).
% 0.21/0.44 tff(388,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[387, 150, 384, 154])).
% 0.21/0.44 % SZS output end Proof
% 0.21/0.44 % E exiting
%------------------------------------------------------------------------------