%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ031+2 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:23:13 AM UTC 2025
% Result : Theorem 0.17s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : PUZ031+2 : TPTP v9.0.0. Released v4.1.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.10/0.32 % Computer : n010.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Fri Jun 20 02:42:26 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.17/0.37 % SZS status Theorem
% 0.17/0.37 % SZS output start Proof
% 0.17/0.37 tff(eats_type, type, (
% 0.17/0.37 eats: ( $i * $i ) > $o)).
% 0.17/0.37 tff(tptp_fun_A_4_type, type, (
% 0.17/0.37 tptp_fun_A_4: $i)).
% 0.17/0.37 tff(plant_type, type, (
% 0.17/0.37 plant: $i > $o)).
% 0.17/0.37 tff(tptp_fun_A_2_type, type, (
% 0.17/0.37 tptp_fun_A_2: $i)).
% 0.17/0.37 tff(bird_type, type, (
% 0.17/0.37 bird: $i > $o)).
% 0.17/0.37 tff(snail_type, type, (
% 0.17/0.37 snail: $i > $o)).
% 0.17/0.37 tff(much_smaller_type, type, (
% 0.17/0.37 much_smaller: ( $i * $i ) > $o)).
% 0.17/0.37 tff(animal_type, type, (
% 0.17/0.37 animal: $i > $o)).
% 0.17/0.37 tff(tptp_fun_A_1_type, type, (
% 0.17/0.37 tptp_fun_A_1: $i)).
% 0.17/0.37 tff(tptp_fun_Y_6_type, type, (
% 0.17/0.37 tptp_fun_Y_6: $i > $i)).
% 0.17/0.37 tff(tptp_fun_A_3_type, type, (
% 0.17/0.37 tptp_fun_A_3: $i)).
% 0.17/0.37 tff(tptp_fun_A_0_type, type, (
% 0.17/0.37 tptp_fun_A_0: $i)).
% 0.17/0.37 tff(tptp_fun_A_5_type, type, (
% 0.17/0.37 tptp_fun_A_5: $i)).
% 0.17/0.37 tff(wolf_type, type, (
% 0.17/0.37 wolf: $i > $o)).
% 0.17/0.37 tff(grain_type, type, (
% 0.17/0.37 grain: $i > $o)).
% 0.17/0.37 tff(fox_type, type, (
% 0.17/0.37 fox: $i > $o)).
% 0.17/0.37 tff(caterpillar_type, type, (
% 0.17/0.37 caterpillar: $i > $o)).
% 0.17/0.37 tff(1,assumption,(eats(A!2, A!4)), introduced(assumption)).
% 0.17/0.37 tff(2,plain,
% 0.17/0.37 (^[X: $i, Y: $i] : refl(((~eats(X, Y)) | (~snail(Y)) | (~bird(X))) <=> ((~eats(X, Y)) | (~snail(Y)) | (~bird(X))))),
% 0.17/0.37 inference(bind,[status(th)],[])).
% 0.17/0.37 tff(3,plain,
% 0.17/0.37 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))),
% 0.17/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.17/0.37 tff(4,plain,
% 0.17/0.37 (^[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)))))),
% 0.17/0.37 inference(bind,[status(th)],[])).
% 0.17/0.37 tff(5,plain,
% 0.17/0.37 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y)))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))),
% 0.17/0.37 inference(quant_intro,[status(thm)],[4])).
% 0.17/0.37 tff(6,plain,
% 0.17/0.37 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y)))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y))))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(7,plain,
% 0.17/0.37 (^[X: $i, Y: $i] : rewrite(((bird(X) & snail(Y)) => (~eats(X, Y))) <=> ((~eats(X, Y)) | (~(bird(X) & snail(Y)))))),
% 0.17/0.37 inference(bind,[status(th)],[])).
% 0.17/0.37 tff(8,plain,
% 0.17/0.37 (![X: $i, Y: $i] : ((bird(X) & snail(Y)) => (~eats(X, Y))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y))))),
% 0.17/0.37 inference(quant_intro,[status(thm)],[7])).
% 0.17/0.37 tff(9,axiom,(![X: $i, Y: $i] : ((bird(X) & snail(Y)) => (~eats(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_13')).
% 0.17/0.37 tff(10,plain,
% 0.17/0.37 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y))))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.17/0.37 tff(11,plain,
% 0.17/0.37 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y))))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.17/0.37 tff(12,plain,(
% 0.17/0.37 ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y))))),
% 0.17/0.37 inference(skolemize,[status(sab)],[11])).
% 0.17/0.37 tff(13,plain,
% 0.17/0.37 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.17/0.37 tff(14,plain,
% 0.17/0.37 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[13, 3])).
% 0.17/0.37 tff(15,plain,
% 0.17/0.37 (?[A: $i] : snail(A) <=> ?[A: $i] : snail(A)),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(16,axiom,(?[A: $i] : snail(A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','snail_type')).
% 0.17/0.37 tff(17,plain,
% 0.17/0.37 (?[A: $i] : snail(A)),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.17/0.37 tff(18,plain,(
% 0.17/0.37 snail(A!4)),
% 0.17/0.37 inference(skolemize,[status(sab)],[17])).
% 0.17/0.37 tff(19,plain,
% 0.17/0.37 (?[A: $i] : bird(A) <=> ?[A: $i] : bird(A)),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(20,axiom,(?[A: $i] : bird(A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bird_type')).
% 0.17/0.38 tff(21,plain,
% 0.17/0.38 (?[A: $i] : bird(A)),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.17/0.38 tff(22,plain,(
% 0.17/0.38 bird(A!2)),
% 0.17/0.38 inference(skolemize,[status(sab)],[21])).
% 0.17/0.38 tff(23,plain,
% 0.17/0.38 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | ((~bird(A!2)) | (~snail(A!4)) | (~eats(A!2, A!4)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | (~bird(A!2)) | (~snail(A!4)) | (~eats(A!2, A!4)))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(24,plain,
% 0.17/0.38 (((~eats(A!2, A!4)) | (~snail(A!4)) | (~bird(A!2))) <=> ((~bird(A!2)) | (~snail(A!4)) | (~eats(A!2, A!4)))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(25,plain,
% 0.17/0.38 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | ((~eats(A!2, A!4)) | (~snail(A!4)) | (~bird(A!2)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | ((~bird(A!2)) | (~snail(A!4)) | (~eats(A!2, A!4))))),
% 0.17/0.38 inference(monotonicity,[status(thm)],[24])).
% 0.17/0.38 tff(26,plain,
% 0.17/0.38 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | ((~eats(A!2, A!4)) | (~snail(A!4)) | (~bird(A!2)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | (~bird(A!2)) | (~snail(A!4)) | (~eats(A!2, A!4)))),
% 0.17/0.38 inference(transitivity,[status(thm)],[25, 23])).
% 0.17/0.38 tff(27,plain,
% 0.17/0.38 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | ((~eats(A!2, A!4)) | (~snail(A!4)) | (~bird(A!2)))),
% 0.17/0.38 inference(quant_inst,[status(thm)],[])).
% 0.17/0.38 tff(28,plain,
% 0.17/0.38 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | (~bird(A!2)) | (~snail(A!4)) | (~eats(A!2, A!4))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.17/0.38 tff(29,plain,
% 0.17/0.38 ($false),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[28, 22, 18, 14, 1])).
% 0.17/0.38 tff(30,plain,(~eats(A!2, A!4)), inference(lemma,lemma(discharge,[]))).
% 0.17/0.38 tff(31,assumption,(~much_smaller(A!4, A!2)), introduced(assumption)).
% 0.17/0.38 tff(32,plain,
% 0.17/0.38 (^[Y: $i, X: $i] : refl((much_smaller(X, Y) | (~snail(X)) | (~bird(Y))) <=> (much_smaller(X, Y) | (~snail(X)) | (~bird(Y))))),
% 0.17/0.38 inference(bind,[status(th)],[])).
% 0.17/0.38 tff(33,plain,
% 0.17/0.38 (![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y))) <=> ![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[32])).
% 0.17/0.38 tff(34,plain,
% 0.17/0.38 (^[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)))))),
% 0.17/0.38 inference(bind,[status(th)],[])).
% 0.17/0.38 tff(35,plain,
% 0.17/0.38 (![Y: $i, X: $i] : ((~(bird(Y) & snail(X))) | much_smaller(X, Y)) <=> ![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[34])).
% 0.17/0.38 tff(36,plain,
% 0.17/0.38 (![Y: $i, X: $i] : ((~(bird(Y) & snail(X))) | much_smaller(X, Y)) <=> ![Y: $i, X: $i] : ((~(bird(Y) & snail(X))) | much_smaller(X, Y))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(37,plain,
% 0.17/0.38 (^[Y: $i, X: $i] : rewrite(((bird(Y) & snail(X)) => much_smaller(X, Y)) <=> ((~(bird(Y) & snail(X))) | much_smaller(X, Y)))),
% 0.17/0.38 inference(bind,[status(th)],[])).
% 0.17/0.38 tff(38,plain,
% 0.17/0.38 (![Y: $i, X: $i] : ((bird(Y) & snail(X)) => much_smaller(X, Y)) <=> ![Y: $i, X: $i] : ((~(bird(Y) & snail(X))) | much_smaller(X, Y))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[37])).
% 0.17/0.38 tff(39,axiom,(![Y: $i, X: $i] : ((bird(Y) & snail(X)) => much_smaller(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_8')).
% 0.17/0.38 tff(40,plain,
% 0.17/0.38 (![Y: $i, X: $i] : ((~(bird(Y) & snail(X))) | much_smaller(X, Y))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.17/0.38 tff(41,plain,
% 0.17/0.38 (![Y: $i, X: $i] : ((~(bird(Y) & snail(X))) | much_smaller(X, Y))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.17/0.38 tff(42,plain,(
% 0.17/0.38 ![Y: $i, X: $i] : ((~(bird(Y) & snail(X))) | much_smaller(X, Y))),
% 0.17/0.38 inference(skolemize,[status(sab)],[41])).
% 0.17/0.38 tff(43,plain,
% 0.17/0.38 (![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.17/0.38 tff(44,plain,
% 0.17/0.38 (![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[43, 33])).
% 0.17/0.38 tff(45,plain,
% 0.17/0.38 (((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | ((~bird(A!2)) | (~snail(A!4)) | much_smaller(A!4, A!2))) <=> ((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | (~bird(A!2)) | (~snail(A!4)) | much_smaller(A!4, A!2))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(46,plain,
% 0.17/0.38 ((much_smaller(A!4, A!2) | (~snail(A!4)) | (~bird(A!2))) <=> ((~bird(A!2)) | (~snail(A!4)) | much_smaller(A!4, A!2))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(47,plain,
% 0.17/0.38 (((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | (much_smaller(A!4, A!2) | (~snail(A!4)) | (~bird(A!2)))) <=> ((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | ((~bird(A!2)) | (~snail(A!4)) | much_smaller(A!4, A!2)))),
% 0.17/0.38 inference(monotonicity,[status(thm)],[46])).
% 0.17/0.38 tff(48,plain,
% 0.17/0.38 (((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | (much_smaller(A!4, A!2) | (~snail(A!4)) | (~bird(A!2)))) <=> ((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | (~bird(A!2)) | (~snail(A!4)) | much_smaller(A!4, A!2))),
% 0.17/0.38 inference(transitivity,[status(thm)],[47, 45])).
% 0.17/0.38 tff(49,plain,
% 0.17/0.38 ((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | (much_smaller(A!4, A!2) | (~snail(A!4)) | (~bird(A!2)))),
% 0.17/0.38 inference(quant_inst,[status(thm)],[])).
% 0.17/0.38 tff(50,plain,
% 0.17/0.38 ((~![Y: $i, X: $i] : (much_smaller(X, Y) | (~snail(X)) | (~bird(Y)))) | (~bird(A!2)) | (~snail(A!4)) | much_smaller(A!4, A!2)),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.17/0.38 tff(51,plain,
% 0.17/0.38 ($false),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[50, 22, 18, 44, 31])).
% 0.17/0.38 tff(52,plain,(much_smaller(A!4, A!2)), inference(lemma,lemma(discharge,[]))).
% 0.17/0.38 tff(53,assumption,(eats(A!0, A!5)), introduced(assumption)).
% 0.17/0.38 tff(54,plain,
% 0.17/0.38 (^[X: $i, Y: $i] : refl(((~eats(X, Y)) | (~grain(Y)) | (~wolf(X))) <=> ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X))))),
% 0.17/0.38 inference(bind,[status(th)],[])).
% 0.17/0.38 tff(55,plain,
% 0.17/0.38 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[54])).
% 0.17/0.38 tff(56,plain,
% 0.17/0.38 (^[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)))))),
% 0.17/0.38 inference(bind,[status(th)],[])).
% 0.17/0.38 tff(57,plain,
% 0.17/0.38 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & grain(Y)))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[56])).
% 0.17/0.38 tff(58,plain,
% 0.17/0.38 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & grain(Y)))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & grain(Y))))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(59,plain,
% 0.17/0.38 (^[X: $i, Y: $i] : rewrite(((wolf(X) & grain(Y)) => (~eats(X, Y))) <=> ((~eats(X, Y)) | (~(wolf(X) & grain(Y)))))),
% 0.17/0.38 inference(bind,[status(th)],[])).
% 0.17/0.38 tff(60,plain,
% 0.17/0.38 (![X: $i, Y: $i] : ((wolf(X) & grain(Y)) => (~eats(X, Y))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & grain(Y))))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[59])).
% 0.17/0.38 tff(61,axiom,(![X: $i, Y: $i] : ((wolf(X) & grain(Y)) => (~eats(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_11a')).
% 0.17/0.38 tff(62,plain,
% 0.17/0.38 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & grain(Y))))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.17/0.38 tff(63,plain,
% 0.17/0.38 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & grain(Y))))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.17/0.38 tff(64,plain,(
% 0.17/0.38 ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & grain(Y))))),
% 0.17/0.38 inference(skolemize,[status(sab)],[63])).
% 0.17/0.38 tff(65,plain,
% 0.17/0.38 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.17/0.38 tff(66,plain,
% 0.17/0.38 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[65, 55])).
% 0.17/0.38 tff(67,plain,
% 0.17/0.38 (?[A: $i] : grain(A) <=> ?[A: $i] : grain(A)),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(68,axiom,(?[A: $i] : grain(A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','grain_type')).
% 0.17/0.38 tff(69,plain,
% 0.17/0.38 (?[A: $i] : grain(A)),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.17/0.38 tff(70,plain,(
% 0.17/0.38 grain(A!5)),
% 0.17/0.38 inference(skolemize,[status(sab)],[69])).
% 0.17/0.38 tff(71,plain,
% 0.17/0.38 (?[A: $i] : wolf(A) <=> ?[A: $i] : wolf(A)),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(72,axiom,(?[A: $i] : wolf(A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','wolf_type')).
% 0.17/0.38 tff(73,plain,
% 0.17/0.38 (?[A: $i] : wolf(A)),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.17/0.38 tff(74,plain,(
% 0.17/0.38 wolf(A!0)),
% 0.17/0.38 inference(skolemize,[status(sab)],[73])).
% 0.17/0.38 tff(75,plain,
% 0.17/0.38 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | ((~wolf(A!0)) | (~grain(A!5)) | (~eats(A!0, A!5)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | (~wolf(A!0)) | (~grain(A!5)) | (~eats(A!0, A!5)))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(76,plain,
% 0.17/0.38 (((~eats(A!0, A!5)) | (~grain(A!5)) | (~wolf(A!0))) <=> ((~wolf(A!0)) | (~grain(A!5)) | (~eats(A!0, A!5)))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(77,plain,
% 0.17/0.38 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | ((~eats(A!0, A!5)) | (~grain(A!5)) | (~wolf(A!0)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | ((~wolf(A!0)) | (~grain(A!5)) | (~eats(A!0, A!5))))),
% 0.17/0.38 inference(monotonicity,[status(thm)],[76])).
% 0.17/0.38 tff(78,plain,
% 0.17/0.38 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | ((~eats(A!0, A!5)) | (~grain(A!5)) | (~wolf(A!0)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | (~wolf(A!0)) | (~grain(A!5)) | (~eats(A!0, A!5)))),
% 0.17/0.38 inference(transitivity,[status(thm)],[77, 75])).
% 0.17/0.38 tff(79,plain,
% 0.17/0.38 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | ((~eats(A!0, A!5)) | (~grain(A!5)) | (~wolf(A!0)))),
% 0.17/0.38 inference(quant_inst,[status(thm)],[])).
% 0.17/0.38 tff(80,plain,
% 0.17/0.38 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~grain(Y)) | (~wolf(X)))) | (~wolf(A!0)) | (~grain(A!5)) | (~eats(A!0, A!5))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.17/0.38 tff(81,plain,
% 0.17/0.38 ($false),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[80, 74, 70, 66, 53])).
% 0.17/0.38 tff(82,plain,(~eats(A!0, A!5)), inference(lemma,lemma(discharge,[]))).
% 0.17/0.38 tff(83,assumption,(![Y: $i] : ((~plant(Y)) | eats(A!0, Y))), introduced(assumption)).
% 0.17/0.38 tff(84,plain,
% 0.17/0.38 (^[X: $i] : refl((plant(X) | (~grain(X))) <=> (plant(X) | (~grain(X))))),
% 0.17/0.38 inference(bind,[status(th)],[])).
% 0.17/0.38 tff(85,plain,
% 0.17/0.38 (![X: $i] : (plant(X) | (~grain(X))) <=> ![X: $i] : (plant(X) | (~grain(X)))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[84])).
% 0.17/0.38 tff(86,plain,
% 0.17/0.38 (![X: $i] : (plant(X) | (~grain(X))) <=> ![X: $i] : (plant(X) | (~grain(X)))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(87,plain,
% 0.17/0.38 (^[X: $i] : rewrite((grain(X) => plant(X)) <=> (plant(X) | (~grain(X))))),
% 0.17/0.38 inference(bind,[status(th)],[])).
% 0.17/0.38 tff(88,plain,
% 0.17/0.38 (![X: $i] : (grain(X) => plant(X)) <=> ![X: $i] : (plant(X) | (~grain(X)))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[87])).
% 0.17/0.38 tff(89,axiom,(![X: $i] : (grain(X) => plant(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_6_2')).
% 0.17/0.38 tff(90,plain,
% 0.17/0.38 (![X: $i] : (plant(X) | (~grain(X)))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.17/0.38 tff(91,plain,
% 0.17/0.38 (![X: $i] : (plant(X) | (~grain(X)))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.17/0.38 tff(92,plain,(
% 0.17/0.38 ![X: $i] : (plant(X) | (~grain(X)))),
% 0.17/0.38 inference(skolemize,[status(sab)],[91])).
% 0.17/0.38 tff(93,plain,
% 0.17/0.38 (![X: $i] : (plant(X) | (~grain(X)))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.17/0.38 tff(94,plain,
% 0.17/0.38 (((~![X: $i] : (plant(X) | (~grain(X)))) | (plant(A!5) | (~grain(A!5)))) <=> ((~![X: $i] : (plant(X) | (~grain(X)))) | plant(A!5) | (~grain(A!5)))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(95,plain,
% 0.17/0.38 ((~![X: $i] : (plant(X) | (~grain(X)))) | (plant(A!5) | (~grain(A!5)))),
% 0.17/0.38 inference(quant_inst,[status(thm)],[])).
% 0.17/0.38 tff(96,plain,
% 0.17/0.38 ((~![X: $i] : (plant(X) | (~grain(X)))) | plant(A!5) | (~grain(A!5))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.17/0.38 tff(97,plain,
% 0.17/0.38 (plant(A!5)),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[96, 70, 93])).
% 0.17/0.38 tff(98,plain,
% 0.17/0.38 (((~![Y: $i] : ((~plant(Y)) | eats(A!0, Y))) | ((~plant(A!5)) | eats(A!0, A!5))) <=> ((~![Y: $i] : ((~plant(Y)) | eats(A!0, Y))) | (~plant(A!5)) | eats(A!0, A!5))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(99,plain,
% 0.17/0.38 ((~![Y: $i] : ((~plant(Y)) | eats(A!0, Y))) | ((~plant(A!5)) | eats(A!0, A!5))),
% 0.17/0.38 inference(quant_inst,[status(thm)],[])).
% 0.17/0.38 tff(100,plain,
% 0.17/0.38 ((~![Y: $i] : ((~plant(Y)) | eats(A!0, Y))) | (~plant(A!5)) | eats(A!0, A!5)),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.17/0.38 tff(101,plain,
% 0.17/0.38 ($false),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[100, 97, 83, 82])).
% 0.17/0.38 tff(102,plain,(~![Y: $i] : ((~plant(Y)) | eats(A!0, Y))), inference(lemma,lemma(discharge,[]))).
% 0.17/0.38 tff(103,plain,
% 0.17/0.38 (^[X: $i] : refl((animal(X) | (~wolf(X))) <=> (animal(X) | (~wolf(X))))),
% 0.17/0.38 inference(bind,[status(th)],[])).
% 0.17/0.38 tff(104,plain,
% 0.17/0.38 (![X: $i] : (animal(X) | (~wolf(X))) <=> ![X: $i] : (animal(X) | (~wolf(X)))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[103])).
% 0.17/0.38 tff(105,plain,
% 0.17/0.38 (![X: $i] : (animal(X) | (~wolf(X))) <=> ![X: $i] : (animal(X) | (~wolf(X)))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(106,plain,
% 0.17/0.38 (^[X: $i] : rewrite((wolf(X) => animal(X)) <=> (animal(X) | (~wolf(X))))),
% 0.17/0.38 inference(bind,[status(th)],[])).
% 0.17/0.38 tff(107,plain,
% 0.17/0.38 (![X: $i] : (wolf(X) => animal(X)) <=> ![X: $i] : (animal(X) | (~wolf(X)))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[106])).
% 0.17/0.38 tff(108,axiom,(![X: $i] : (wolf(X) => animal(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_1_1')).
% 0.17/0.38 tff(109,plain,
% 0.17/0.38 (![X: $i] : (animal(X) | (~wolf(X)))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.17/0.38 tff(110,plain,
% 0.17/0.38 (![X: $i] : (animal(X) | (~wolf(X)))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.17/0.38 tff(111,plain,(
% 0.17/0.38 ![X: $i] : (animal(X) | (~wolf(X)))),
% 0.17/0.38 inference(skolemize,[status(sab)],[110])).
% 0.17/0.38 tff(112,plain,
% 0.17/0.38 (![X: $i] : (animal(X) | (~wolf(X)))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.17/0.38 tff(113,plain,
% 0.17/0.38 (((~![X: $i] : (animal(X) | (~wolf(X)))) | (animal(A!0) | (~wolf(A!0)))) <=> ((~![X: $i] : (animal(X) | (~wolf(X)))) | animal(A!0) | (~wolf(A!0)))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(114,plain,
% 0.17/0.38 ((~![X: $i] : (animal(X) | (~wolf(X)))) | (animal(A!0) | (~wolf(A!0)))),
% 0.17/0.38 inference(quant_inst,[status(thm)],[])).
% 0.17/0.38 tff(115,plain,
% 0.17/0.38 ((~![X: $i] : (animal(X) | (~wolf(X)))) | animal(A!0) | (~wolf(A!0))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.17/0.38 tff(116,plain,
% 0.17/0.38 (animal(A!0)),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[115, 74, 112])).
% 0.17/0.38 tff(117,plain,
% 0.17/0.38 (^[X: $i] : rewrite((![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))))),
% 0.17/0.38 inference(bind,[status(th)],[])).
% 0.17/0.38 tff(118,plain,
% 0.17/0.38 (![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> ![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[117])).
% 0.17/0.38 tff(119,plain,
% 0.17/0.38 (^[X: $i] : refl((![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))))),
% 0.17/0.38 inference(bind,[status(th)],[])).
% 0.17/0.38 tff(120,plain,
% 0.17/0.38 (![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> ![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[119])).
% 0.17/0.38 tff(121,plain,
% 0.17/0.38 (^[X: $i] : rewrite((![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))))),
% 0.17/0.38 inference(bind,[status(th)],[])).
% 0.17/0.38 tff(122,plain,
% 0.17/0.38 (![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> ![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[121])).
% 0.17/0.38 tff(123,plain,
% 0.17/0.38 (![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> ![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.17/0.38 inference(transitivity,[status(thm)],[122, 120])).
% 0.17/0.38 tff(124,plain,
% 0.17/0.38 (^[X: $i] : trans(monotonicity(quant_intro(proof_bind(^[Y1: $i] : trans(monotonicity(quant_intro(proof_bind(^[Z: $i] : trans(monotonicity(rewrite((plant(Z) & eats(Y1, Z)) <=> (~((~plant(Z)) | (~eats(Y1, Z))))), ((~(plant(Z) & eats(Y1, Z))) <=> (~(~((~plant(Z)) | (~eats(Y1, Z))))))), rewrite((~(~((~plant(Z)) | (~eats(Y1, Z))))) <=> ((~plant(Z)) | (~eats(Y1, Z)))), ((~(plant(Z) & eats(Y1, Z))) <=> ((~plant(Z)) | (~eats(Y1, Z)))))), (![Z: $i] : (~(plant(Z) & eats(Y1, Z))) <=> ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))), ((eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))) <=> (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))), rewrite((eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))) <=> (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))), ((eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))) <=> (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))))), (![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))) <=> ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))), ((![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z))))) <=> (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))))), rewrite((![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))), ((![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z))))) <=> (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))))),
% 0.17/0.39 inference(bind,[status(th)],[])).
% 0.17/0.39 tff(125,plain,
% 0.17/0.39 (![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z))))) <=> ![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.17/0.39 inference(quant_intro,[status(thm)],[124])).
% 0.17/0.39 tff(126,plain,
% 0.17/0.39 (^[X: $i] : trans(monotonicity(quant_intro(proof_bind(^[Y1: $i] : trans(monotonicity(rewrite(((~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))) <=> ((~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z))))), ((((~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))) | eats(X, Y1)) <=> (((~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))) | eats(X, Y1)))), rewrite((((~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))) | eats(X, Y1)) <=> (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z))))), ((((~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))) | eats(X, Y1)) <=> (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z))))))), (![Y1: $i] : (((~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))) | eats(X, Y1)) <=> ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))))), ((![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (((~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))) | eats(X, Y1))) <=> (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z))))))), rewrite((![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z))))) <=> (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))))), ((![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (((~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))) | eats(X, Y1))) <=> (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))))))),
% 0.17/0.39 inference(bind,[status(th)],[])).
% 0.17/0.39 tff(127,plain,
% 0.17/0.39 (![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (((~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))) | eats(X, Y1))) <=> ![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))))),
% 0.17/0.39 inference(quant_intro,[status(thm)],[126])).
% 0.17/0.39 tff(128,plain,
% 0.17/0.39 (![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : ((~(animal(Y1) & much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z)))) | eats(X, Y1))) <=> ![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : ((~(animal(Y1) & much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z)))) | eats(X, Y1)))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(129,plain,
% 0.17/0.39 (^[X: $i] : trans(monotonicity(rewrite((![Y: $i] : (plant(Y) => eats(X, Y)) | ![Y1: $i] : (((animal(Y1) & much_smaller(Y1, X)) & ?[Z: $i] : (plant(Z) & eats(Y1, Z))) => eats(X, Y1))) <=> (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : ((~(animal(Y1) & much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z)))) | eats(X, Y1)))), ((animal(X) => (![Y: $i] : (plant(Y) => eats(X, Y)) | ![Y1: $i] : (((animal(Y1) & much_smaller(Y1, X)) & ?[Z: $i] : (plant(Z) & eats(Y1, Z))) => eats(X, Y1)))) <=> (animal(X) => (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : ((~(animal(Y1) & much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z)))) | eats(X, Y1)))))), rewrite((animal(X) => (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : ((~(animal(Y1) & much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z)))) | eats(X, Y1)))) <=> (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : ((~(animal(Y1) & much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z)))) | eats(X, Y1)))), ((animal(X) => (![Y: $i] : (plant(Y) => eats(X, Y)) | ![Y1: $i] : (((animal(Y1) & much_smaller(Y1, X)) & ?[Z: $i] : (plant(Z) & eats(Y1, Z))) => eats(X, Y1)))) <=> (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : ((~(animal(Y1) & much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z)))) | eats(X, Y1)))))),
% 0.17/0.39 inference(bind,[status(th)],[])).
% 0.17/0.39 tff(130,plain,
% 0.17/0.39 (![X: $i] : (animal(X) => (![Y: $i] : (plant(Y) => eats(X, Y)) | ![Y1: $i] : (((animal(Y1) & much_smaller(Y1, X)) & ?[Z: $i] : (plant(Z) & eats(Y1, Z))) => eats(X, Y1)))) <=> ![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : ((~(animal(Y1) & much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z)))) | eats(X, Y1)))),
% 0.17/0.39 inference(quant_intro,[status(thm)],[129])).
% 0.17/0.39 tff(131,axiom,(![X: $i] : (animal(X) => (![Y: $i] : (plant(Y) => eats(X, Y)) | ![Y1: $i] : (((animal(Y1) & much_smaller(Y1, X)) & ?[Z: $i] : (plant(Z) & eats(Y1, Z))) => eats(X, Y1))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_7')).
% 0.17/0.39 tff(132,plain,
% 0.17/0.39 (![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : ((~(animal(Y1) & much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z)))) | eats(X, Y1)))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.17/0.39 tff(133,plain,
% 0.17/0.39 (![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : ((~(animal(Y1) & much_smaller(Y1, X) & ?[Z: $i] : (plant(Z) & eats(Y1, Z)))) | eats(X, Y1)))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.17/0.39 tff(134,plain,(
% 0.17/0.39 ![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (((~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))) | eats(X, Y1)))),
% 0.17/0.39 inference(skolemize,[status(sab)],[133])).
% 0.17/0.39 tff(135,plain,
% 0.17/0.39 (![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : (~(plant(Z) & eats(Y1, Z)))))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[134, 127])).
% 0.17/0.39 tff(136,plain,
% 0.17/0.39 (![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[135, 125])).
% 0.17/0.39 tff(137,plain,
% 0.17/0.39 (![X: $i] : (![Y: $i] : ((~plant(Y)) | eats(X, Y)) | (~animal(X)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[136, 123])).
% 0.17/0.39 tff(138,plain,
% 0.17/0.39 (![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[137, 118])).
% 0.17/0.39 tff(139,plain,
% 0.17/0.39 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!0)) | ![Y: $i] : ((~plant(Y)) | eats(A!0, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(A!0)) | ![Y: $i] : ((~plant(Y)) | eats(A!0, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0))))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(140,plain,
% 0.17/0.39 (((~animal(A!0)) | ![Y: $i] : ((~plant(Y)) | eats(A!0, Y)) | ![Y1: $i] : (eats(A!0, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!0)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> ((~animal(A!0)) | ![Y: $i] : ((~plant(Y)) | eats(A!0, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0))))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(141,plain,
% 0.17/0.39 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!0)) | ![Y: $i] : ((~plant(Y)) | eats(A!0, Y)) | ![Y1: $i] : (eats(A!0, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!0)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!0)) | ![Y: $i] : ((~plant(Y)) | eats(A!0, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0)))))),
% 0.17/0.39 inference(monotonicity,[status(thm)],[140])).
% 0.17/0.39 tff(142,plain,
% 0.17/0.39 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!0)) | ![Y: $i] : ((~plant(Y)) | eats(A!0, Y)) | ![Y1: $i] : (eats(A!0, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!0)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(A!0)) | ![Y: $i] : ((~plant(Y)) | eats(A!0, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0))))),
% 0.17/0.39 inference(transitivity,[status(thm)],[141, 139])).
% 0.17/0.39 tff(143,plain,
% 0.17/0.39 ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!0)) | ![Y: $i] : ((~plant(Y)) | eats(A!0, Y)) | ![Y1: $i] : (eats(A!0, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!0)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.17/0.39 inference(quant_inst,[status(thm)],[])).
% 0.17/0.39 tff(144,plain,
% 0.17/0.39 ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(A!0)) | ![Y: $i] : ((~plant(Y)) | eats(A!0, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0)))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.17/0.39 tff(145,plain,
% 0.17/0.39 (![Y: $i] : ((~plant(Y)) | eats(A!0, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0)))),
% 0.17/0.39 inference(unit_resolution,[status(thm)],[144, 138, 116])).
% 0.17/0.39 tff(146,plain,
% 0.17/0.39 (![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0)))),
% 0.17/0.39 inference(unit_resolution,[status(thm)],[145, 102])).
% 0.17/0.39 tff(147,assumption,(eats(A!0, A!1)), introduced(assumption)).
% 0.17/0.39 tff(148,plain,
% 0.17/0.39 (^[X: $i, Y: $i] : refl(((~eats(X, Y)) | (~fox(Y)) | (~wolf(X))) <=> ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X))))),
% 0.17/0.39 inference(bind,[status(th)],[])).
% 0.17/0.39 tff(149,plain,
% 0.17/0.39 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))),
% 0.17/0.39 inference(quant_intro,[status(thm)],[148])).
% 0.17/0.39 tff(150,plain,
% 0.17/0.39 (^[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)))))),
% 0.17/0.39 inference(bind,[status(th)],[])).
% 0.17/0.39 tff(151,plain,
% 0.17/0.39 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & fox(Y)))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))),
% 0.17/0.39 inference(quant_intro,[status(thm)],[150])).
% 0.17/0.39 tff(152,plain,
% 0.17/0.39 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & fox(Y)))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & fox(Y))))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(153,plain,
% 0.17/0.39 (^[X: $i, Y: $i] : rewrite(((wolf(X) & fox(Y)) => (~eats(X, Y))) <=> ((~eats(X, Y)) | (~(wolf(X) & fox(Y)))))),
% 0.17/0.39 inference(bind,[status(th)],[])).
% 0.17/0.39 tff(154,plain,
% 0.17/0.39 (![X: $i, Y: $i] : ((wolf(X) & fox(Y)) => (~eats(X, Y))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & fox(Y))))),
% 0.17/0.39 inference(quant_intro,[status(thm)],[153])).
% 0.17/0.39 tff(155,axiom,(![X: $i, Y: $i] : ((wolf(X) & fox(Y)) => (~eats(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_11')).
% 0.17/0.39 tff(156,plain,
% 0.17/0.39 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & fox(Y))))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.17/0.39 tff(157,plain,
% 0.17/0.39 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & fox(Y))))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[156, 152])).
% 0.17/0.39 tff(158,plain,(
% 0.17/0.39 ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & fox(Y))))),
% 0.17/0.39 inference(skolemize,[status(sab)],[157])).
% 0.17/0.39 tff(159,plain,
% 0.17/0.39 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[158, 151])).
% 0.17/0.39 tff(160,plain,
% 0.17/0.39 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[159, 149])).
% 0.17/0.39 tff(161,plain,
% 0.17/0.39 (?[A: $i] : fox(A) <=> ?[A: $i] : fox(A)),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(162,axiom,(?[A: $i] : fox(A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fox_type')).
% 0.17/0.39 tff(163,plain,
% 0.17/0.39 (?[A: $i] : fox(A)),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.17/0.39 tff(164,plain,(
% 0.17/0.39 fox(A!1)),
% 0.17/0.39 inference(skolemize,[status(sab)],[163])).
% 0.17/0.39 tff(165,plain,
% 0.17/0.39 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))) | ((~wolf(A!0)) | (~fox(A!1)) | (~eats(A!0, A!1)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))) | (~wolf(A!0)) | (~fox(A!1)) | (~eats(A!0, A!1)))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(166,plain,
% 0.17/0.39 (((~eats(A!0, A!1)) | (~fox(A!1)) | (~wolf(A!0))) <=> ((~wolf(A!0)) | (~fox(A!1)) | (~eats(A!0, A!1)))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(167,plain,
% 0.17/0.39 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))) | ((~eats(A!0, A!1)) | (~fox(A!1)) | (~wolf(A!0)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))) | ((~wolf(A!0)) | (~fox(A!1)) | (~eats(A!0, A!1))))),
% 0.17/0.39 inference(monotonicity,[status(thm)],[166])).
% 0.17/0.39 tff(168,plain,
% 0.17/0.39 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))) | ((~eats(A!0, A!1)) | (~fox(A!1)) | (~wolf(A!0)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))) | (~wolf(A!0)) | (~fox(A!1)) | (~eats(A!0, A!1)))),
% 0.17/0.39 inference(transitivity,[status(thm)],[167, 165])).
% 0.17/0.39 tff(169,plain,
% 0.17/0.39 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))) | ((~eats(A!0, A!1)) | (~fox(A!1)) | (~wolf(A!0)))),
% 0.17/0.40 inference(quant_inst,[status(thm)],[])).
% 0.17/0.40 tff(170,plain,
% 0.17/0.40 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~fox(Y)) | (~wolf(X)))) | (~wolf(A!0)) | (~fox(A!1)) | (~eats(A!0, A!1))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.17/0.40 tff(171,plain,
% 0.17/0.40 ($false),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[170, 74, 164, 160, 147])).
% 0.17/0.40 tff(172,plain,(~eats(A!0, A!1)), inference(lemma,lemma(discharge,[]))).
% 0.17/0.40 tff(173,assumption,(~![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z)))), introduced(assumption)).
% 0.17/0.40 tff(174,assumption,(~much_smaller(A!1, A!0)), introduced(assumption)).
% 0.17/0.40 tff(175,plain,
% 0.17/0.40 (^[X: $i, Y: $i] : refl((much_smaller(X, Y) | (~wolf(Y)) | (~fox(X))) <=> (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X))))),
% 0.17/0.40 inference(bind,[status(th)],[])).
% 0.17/0.40 tff(176,plain,
% 0.17/0.40 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X))) <=> ![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))),
% 0.17/0.40 inference(quant_intro,[status(thm)],[175])).
% 0.17/0.40 tff(177,plain,
% 0.17/0.40 (^[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)))))),
% 0.17/0.40 inference(bind,[status(th)],[])).
% 0.17/0.40 tff(178,plain,
% 0.17/0.40 (![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y)) <=> ![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))),
% 0.17/0.40 inference(quant_intro,[status(thm)],[177])).
% 0.17/0.40 tff(179,plain,
% 0.17/0.40 (![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y)) <=> ![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(180,plain,
% 0.17/0.40 (^[X: $i, Y: $i] : rewrite(((fox(X) & wolf(Y)) => much_smaller(X, Y)) <=> ((~(fox(X) & wolf(Y))) | much_smaller(X, Y)))),
% 0.17/0.40 inference(bind,[status(th)],[])).
% 0.17/0.40 tff(181,plain,
% 0.17/0.40 (![X: $i, Y: $i] : ((fox(X) & wolf(Y)) => much_smaller(X, Y)) <=> ![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y))),
% 0.17/0.40 inference(quant_intro,[status(thm)],[180])).
% 0.17/0.40 tff(182,axiom,(![X: $i, Y: $i] : ((fox(X) & wolf(Y)) => much_smaller(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_10')).
% 0.17/0.40 tff(183,plain,
% 0.17/0.40 (![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.17/0.40 tff(184,plain,
% 0.17/0.40 (![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[183, 179])).
% 0.17/0.40 tff(185,plain,(
% 0.17/0.40 ![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y))),
% 0.17/0.40 inference(skolemize,[status(sab)],[184])).
% 0.17/0.40 tff(186,plain,
% 0.17/0.40 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[185, 178])).
% 0.17/0.40 tff(187,plain,
% 0.17/0.40 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[186, 176])).
% 0.17/0.40 tff(188,plain,
% 0.17/0.40 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | ((~wolf(A!0)) | (~fox(A!1)) | much_smaller(A!1, A!0))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (~wolf(A!0)) | (~fox(A!1)) | much_smaller(A!1, A!0))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(189,plain,
% 0.17/0.40 ((much_smaller(A!1, A!0) | (~wolf(A!0)) | (~fox(A!1))) <=> ((~wolf(A!0)) | (~fox(A!1)) | much_smaller(A!1, A!0))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(190,plain,
% 0.17/0.40 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (much_smaller(A!1, A!0) | (~wolf(A!0)) | (~fox(A!1)))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | ((~wolf(A!0)) | (~fox(A!1)) | much_smaller(A!1, A!0)))),
% 0.17/0.40 inference(monotonicity,[status(thm)],[189])).
% 0.17/0.40 tff(191,plain,
% 0.17/0.40 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (much_smaller(A!1, A!0) | (~wolf(A!0)) | (~fox(A!1)))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (~wolf(A!0)) | (~fox(A!1)) | much_smaller(A!1, A!0))),
% 0.17/0.40 inference(transitivity,[status(thm)],[190, 188])).
% 0.17/0.40 tff(192,plain,
% 0.17/0.40 ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (much_smaller(A!1, A!0) | (~wolf(A!0)) | (~fox(A!1)))),
% 0.17/0.40 inference(quant_inst,[status(thm)],[])).
% 0.17/0.40 tff(193,plain,
% 0.17/0.40 ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (~wolf(A!0)) | (~fox(A!1)) | much_smaller(A!1, A!0)),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.17/0.40 tff(194,plain,
% 0.17/0.40 ($false),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[193, 74, 164, 187, 174])).
% 0.17/0.40 tff(195,plain,(much_smaller(A!1, A!0)), inference(lemma,lemma(discharge,[]))).
% 0.17/0.40 tff(196,assumption,(![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0)))), introduced(assumption)).
% 0.17/0.40 tff(197,plain,
% 0.17/0.40 (^[X: $i] : refl((animal(X) | (~fox(X))) <=> (animal(X) | (~fox(X))))),
% 0.17/0.40 inference(bind,[status(th)],[])).
% 0.17/0.40 tff(198,plain,
% 0.17/0.40 (![X: $i] : (animal(X) | (~fox(X))) <=> ![X: $i] : (animal(X) | (~fox(X)))),
% 0.17/0.40 inference(quant_intro,[status(thm)],[197])).
% 0.17/0.40 tff(199,plain,
% 0.17/0.40 (![X: $i] : (animal(X) | (~fox(X))) <=> ![X: $i] : (animal(X) | (~fox(X)))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(200,plain,
% 0.17/0.40 (^[X: $i] : rewrite((fox(X) => animal(X)) <=> (animal(X) | (~fox(X))))),
% 0.17/0.40 inference(bind,[status(th)],[])).
% 0.17/0.40 tff(201,plain,
% 0.17/0.40 (![X: $i] : (fox(X) => animal(X)) <=> ![X: $i] : (animal(X) | (~fox(X)))),
% 0.17/0.40 inference(quant_intro,[status(thm)],[200])).
% 0.17/0.40 tff(202,axiom,(![X: $i] : (fox(X) => animal(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_2_1')).
% 0.17/0.40 tff(203,plain,
% 0.17/0.40 (![X: $i] : (animal(X) | (~fox(X)))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.17/0.40 tff(204,plain,
% 0.17/0.40 (![X: $i] : (animal(X) | (~fox(X)))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[203, 199])).
% 0.17/0.40 tff(205,plain,(
% 0.17/0.40 ![X: $i] : (animal(X) | (~fox(X)))),
% 0.17/0.40 inference(skolemize,[status(sab)],[204])).
% 0.17/0.40 tff(206,plain,
% 0.17/0.40 (![X: $i] : (animal(X) | (~fox(X)))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[205, 198])).
% 0.17/0.40 tff(207,plain,
% 0.17/0.40 (((~![X: $i] : (animal(X) | (~fox(X)))) | (animal(A!1) | (~fox(A!1)))) <=> ((~![X: $i] : (animal(X) | (~fox(X)))) | animal(A!1) | (~fox(A!1)))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(208,plain,
% 0.17/0.40 ((~![X: $i] : (animal(X) | (~fox(X)))) | (animal(A!1) | (~fox(A!1)))),
% 0.17/0.40 inference(quant_inst,[status(thm)],[])).
% 0.17/0.40 tff(209,plain,
% 0.17/0.40 ((~![X: $i] : (animal(X) | (~fox(X)))) | animal(A!1) | (~fox(A!1))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.17/0.40 tff(210,plain,
% 0.17/0.40 (animal(A!1)),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[209, 164, 206])).
% 0.17/0.40 tff(211,plain,
% 0.17/0.40 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0)))) | ((~animal(A!1)) | (~much_smaller(A!1, A!0)) | eats(A!0, A!1) | ![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z))))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0)))) | (~animal(A!1)) | (~much_smaller(A!1, A!0)) | eats(A!0, A!1) | ![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z))))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(212,plain,
% 0.17/0.40 (((~animal(A!1)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z))) | eats(A!0, A!1) | (~much_smaller(A!1, A!0))) <=> ((~animal(A!1)) | (~much_smaller(A!1, A!0)) | eats(A!0, A!1) | ![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z))))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(213,plain,
% 0.17/0.40 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0)))) | ((~animal(A!1)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z))) | eats(A!0, A!1) | (~much_smaller(A!1, A!0)))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0)))) | ((~animal(A!1)) | (~much_smaller(A!1, A!0)) | eats(A!0, A!1) | ![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z)))))),
% 0.17/0.40 inference(monotonicity,[status(thm)],[212])).
% 0.17/0.40 tff(214,plain,
% 0.17/0.40 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0)))) | ((~animal(A!1)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z))) | eats(A!0, A!1) | (~much_smaller(A!1, A!0)))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0)))) | (~animal(A!1)) | (~much_smaller(A!1, A!0)) | eats(A!0, A!1) | ![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z))))),
% 0.17/0.40 inference(transitivity,[status(thm)],[213, 211])).
% 0.17/0.40 tff(215,plain,
% 0.17/0.40 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0)))) | ((~animal(A!1)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z))) | eats(A!0, A!1) | (~much_smaller(A!1, A!0)))),
% 0.17/0.40 inference(quant_inst,[status(thm)],[])).
% 0.17/0.40 tff(216,plain,
% 0.17/0.40 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0)))) | (~animal(A!1)) | (~much_smaller(A!1, A!0)) | eats(A!0, A!1) | ![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z)))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.17/0.40 tff(217,plain,
% 0.17/0.40 ($false),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[216, 210, 196, 195, 173, 172])).
% 0.17/0.40 tff(218,plain,((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!0, Y1) | (~much_smaller(Y1, A!0)))) | ![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z)))), inference(lemma,lemma(discharge,[]))).
% 0.17/0.40 tff(219,plain,
% 0.17/0.40 (![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z)))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[218, 146])).
% 0.17/0.40 tff(220,assumption,(eats(A!1, tptp_fun_Y_6(A!3))), introduced(assumption)).
% 0.17/0.40 tff(221,assumption,(![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z)))), introduced(assumption)).
% 0.17/0.40 tff(222,plain,
% 0.17/0.40 (^[X: $i] : refl(((~caterpillar(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X)))))) <=> ((~caterpillar(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X)))))))),
% 0.17/0.40 inference(bind,[status(th)],[])).
% 0.17/0.40 tff(223,plain,
% 0.17/0.40 (![X: $i] : ((~caterpillar(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X)))))) <=> ![X: $i] : ((~caterpillar(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))),
% 0.17/0.40 inference(quant_intro,[status(thm)],[222])).
% 0.17/0.40 tff(224,plain,
% 0.17/0.40 (^[X: $i] : rewrite(((~caterpillar(X)) | (plant(tptp_fun_Y_6(X)) & eats(X, tptp_fun_Y_6(X)))) <=> ((~caterpillar(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X)))))))),
% 0.17/0.40 inference(bind,[status(th)],[])).
% 0.17/0.40 tff(225,plain,
% 0.17/0.40 (![X: $i] : ((~caterpillar(X)) | (plant(tptp_fun_Y_6(X)) & eats(X, tptp_fun_Y_6(X)))) <=> ![X: $i] : ((~caterpillar(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))),
% 0.17/0.40 inference(quant_intro,[status(thm)],[224])).
% 0.17/0.40 tff(226,plain,
% 0.17/0.40 (![X: $i] : ((~caterpillar(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y))) <=> ![X: $i] : ((~caterpillar(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(227,plain,
% 0.17/0.40 (^[X: $i] : rewrite((caterpillar(X) => ?[Y: $i] : (plant(Y) & eats(X, Y))) <=> ((~caterpillar(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y))))),
% 0.17/0.40 inference(bind,[status(th)],[])).
% 0.17/0.40 tff(228,plain,
% 0.17/0.40 (![X: $i] : (caterpillar(X) => ?[Y: $i] : (plant(Y) & eats(X, Y))) <=> ![X: $i] : ((~caterpillar(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.17/0.40 inference(quant_intro,[status(thm)],[227])).
% 0.17/0.40 tff(229,axiom,(![X: $i] : (caterpillar(X) => ?[Y: $i] : (plant(Y) & eats(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_14')).
% 0.17/0.40 tff(230,plain,
% 0.17/0.40 (![X: $i] : ((~caterpillar(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.17/0.40 tff(231,plain,
% 0.17/0.40 (![X: $i] : ((~caterpillar(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[230, 226])).
% 0.17/0.40 tff(232,plain,(
% 0.17/0.40 ![X: $i] : ((~caterpillar(X)) | (plant(tptp_fun_Y_6(X)) & eats(X, tptp_fun_Y_6(X))))),
% 0.17/0.40 inference(skolemize,[status(sab)],[231])).
% 0.17/0.40 tff(233,plain,
% 0.17/0.40 (![X: $i] : ((~caterpillar(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[232, 225])).
% 0.17/0.40 tff(234,plain,
% 0.17/0.40 (![X: $i] : ((~caterpillar(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[233, 223])).
% 0.17/0.40 tff(235,plain,
% 0.17/0.40 (?[A: $i] : caterpillar(A) <=> ?[A: $i] : caterpillar(A)),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(236,axiom,(?[A: $i] : caterpillar(A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','caterpillar_type')).
% 0.17/0.40 tff(237,plain,
% 0.17/0.40 (?[A: $i] : caterpillar(A)),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.17/0.40 tff(238,plain,(
% 0.17/0.40 caterpillar(A!3)),
% 0.17/0.40 inference(skolemize,[status(sab)],[237])).
% 0.17/0.40 tff(239,plain,
% 0.17/0.40 (((~![X: $i] : ((~caterpillar(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | ((~caterpillar(A!3)) | (~((~plant(tptp_fun_Y_6(A!3))) | (~eats(A!3, tptp_fun_Y_6(A!3))))))) <=> ((~![X: $i] : ((~caterpillar(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | (~caterpillar(A!3)) | (~((~plant(tptp_fun_Y_6(A!3))) | (~eats(A!3, tptp_fun_Y_6(A!3))))))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(240,plain,
% 0.17/0.40 ((~![X: $i] : ((~caterpillar(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | ((~caterpillar(A!3)) | (~((~plant(tptp_fun_Y_6(A!3))) | (~eats(A!3, tptp_fun_Y_6(A!3))))))),
% 0.17/0.40 inference(quant_inst,[status(thm)],[])).
% 0.17/0.40 tff(241,plain,
% 0.17/0.40 ((~![X: $i] : ((~caterpillar(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | (~caterpillar(A!3)) | (~((~plant(tptp_fun_Y_6(A!3))) | (~eats(A!3, tptp_fun_Y_6(A!3)))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.17/0.40 tff(242,plain,
% 0.17/0.40 (~((~plant(tptp_fun_Y_6(A!3))) | (~eats(A!3, tptp_fun_Y_6(A!3))))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[241, 238, 234])).
% 0.17/0.40 tff(243,plain,
% 0.17/0.40 (((~plant(tptp_fun_Y_6(A!3))) | (~eats(A!3, tptp_fun_Y_6(A!3)))) | plant(tptp_fun_Y_6(A!3))),
% 0.17/0.40 inference(tautology,[status(thm)],[])).
% 0.17/0.40 tff(244,plain,
% 0.17/0.40 (plant(tptp_fun_Y_6(A!3))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[243, 242])).
% 0.17/0.40 tff(245,plain,
% 0.17/0.40 (((~![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z)))) | ((~plant(tptp_fun_Y_6(A!3))) | (~eats(A!1, tptp_fun_Y_6(A!3))))) <=> ((~![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z)))) | (~plant(tptp_fun_Y_6(A!3))) | (~eats(A!1, tptp_fun_Y_6(A!3))))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(246,plain,
% 0.17/0.40 ((~![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z)))) | ((~plant(tptp_fun_Y_6(A!3))) | (~eats(A!1, tptp_fun_Y_6(A!3))))),
% 0.17/0.40 inference(quant_inst,[status(thm)],[])).
% 0.17/0.40 tff(247,plain,
% 0.17/0.40 ((~![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z)))) | (~plant(tptp_fun_Y_6(A!3))) | (~eats(A!1, tptp_fun_Y_6(A!3)))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.17/0.40 tff(248,plain,
% 0.17/0.40 ($false),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[247, 244, 221, 220])).
% 0.17/0.40 tff(249,plain,((~![Z: $i] : ((~plant(Z)) | (~eats(A!1, Z)))) | (~eats(A!1, tptp_fun_Y_6(A!3)))), inference(lemma,lemma(discharge,[]))).
% 0.17/0.40 tff(250,plain,
% 0.17/0.40 (~eats(A!1, tptp_fun_Y_6(A!3))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[249, 219])).
% 0.17/0.40 tff(251,assumption,(~eats(A!1, tptp_fun_Y_6(A!3))), introduced(assumption)).
% 0.17/0.40 tff(252,assumption,(![Y: $i] : ((~plant(Y)) | eats(A!1, Y))), introduced(assumption)).
% 0.17/0.40 tff(253,plain,
% 0.17/0.40 (((~![Y: $i] : ((~plant(Y)) | eats(A!1, Y))) | ((~plant(tptp_fun_Y_6(A!3))) | eats(A!1, tptp_fun_Y_6(A!3)))) <=> ((~![Y: $i] : ((~plant(Y)) | eats(A!1, Y))) | (~plant(tptp_fun_Y_6(A!3))) | eats(A!1, tptp_fun_Y_6(A!3)))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(254,plain,
% 0.17/0.40 ((~![Y: $i] : ((~plant(Y)) | eats(A!1, Y))) | ((~plant(tptp_fun_Y_6(A!3))) | eats(A!1, tptp_fun_Y_6(A!3)))),
% 0.17/0.40 inference(quant_inst,[status(thm)],[])).
% 0.17/0.40 tff(255,plain,
% 0.17/0.40 ((~![Y: $i] : ((~plant(Y)) | eats(A!1, Y))) | (~plant(tptp_fun_Y_6(A!3))) | eats(A!1, tptp_fun_Y_6(A!3))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.17/0.40 tff(256,plain,
% 0.17/0.40 ($false),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[255, 244, 252, 251])).
% 0.17/0.41 tff(257,plain,((~![Y: $i] : ((~plant(Y)) | eats(A!1, Y))) | eats(A!1, tptp_fun_Y_6(A!3))), inference(lemma,lemma(discharge,[]))).
% 0.17/0.41 tff(258,plain,
% 0.17/0.41 (~![Y: $i] : ((~plant(Y)) | eats(A!1, Y))),
% 0.17/0.41 inference(unit_resolution,[status(thm)],[257, 250])).
% 0.17/0.41 tff(259,plain,
% 0.17/0.41 (((~![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!1)) | ![Y: $i] : ((~plant(Y)) | eats(A!1, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(A!1)) | ![Y: $i] : ((~plant(Y)) | eats(A!1, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1))))),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(260,plain,
% 0.17/0.41 (((~animal(A!1)) | ![Y: $i] : ((~plant(Y)) | eats(A!1, Y)) | ![Y1: $i] : (eats(A!1, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> ((~animal(A!1)) | ![Y: $i] : ((~plant(Y)) | eats(A!1, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1))))),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(261,plain,
% 0.17/0.41 (((~![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!1)) | ![Y: $i] : ((~plant(Y)) | eats(A!1, Y)) | ![Y1: $i] : (eats(A!1, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!1)) | ![Y: $i] : ((~plant(Y)) | eats(A!1, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1)))))),
% 0.17/0.41 inference(monotonicity,[status(thm)],[260])).
% 0.17/0.41 tff(262,plain,
% 0.17/0.41 (((~![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!1)) | ![Y: $i] : ((~plant(Y)) | eats(A!1, Y)) | ![Y1: $i] : (eats(A!1, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(A!1)) | ![Y: $i] : ((~plant(Y)) | eats(A!1, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1))))),
% 0.17/0.41 inference(transitivity,[status(thm)],[261, 259])).
% 0.17/0.41 tff(263,plain,
% 0.17/0.41 ((~![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!1)) | ![Y: $i] : ((~plant(Y)) | eats(A!1, Y)) | ![Y1: $i] : (eats(A!1, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.17/0.41 inference(quant_inst,[status(thm)],[])).
% 0.17/0.41 tff(264,plain,
% 0.17/0.41 ((~![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!1)) | ![Y: $i] : ((~plant(Y)) | eats(A!1, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1)))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.17/0.41 tff(265,plain,
% 0.17/0.41 (![Y: $i] : ((~plant(Y)) | eats(A!1, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[264, 138, 210])).
% 0.18/0.41 tff(266,plain,
% 0.18/0.41 (![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[265, 258])).
% 0.18/0.41 tff(267,assumption,(![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1)))), introduced(assumption)).
% 0.18/0.41 tff(268,assumption,(![Y: $i] : ((~plant(Y)) | eats(A!2, Y))), introduced(assumption)).
% 0.18/0.41 tff(269,plain,
% 0.18/0.41 (((~![Y: $i] : ((~plant(Y)) | eats(A!2, Y))) | ((~plant(tptp_fun_Y_6(A!3))) | eats(A!2, tptp_fun_Y_6(A!3)))) <=> ((~![Y: $i] : ((~plant(Y)) | eats(A!2, Y))) | (~plant(tptp_fun_Y_6(A!3))) | eats(A!2, tptp_fun_Y_6(A!3)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(270,plain,
% 0.18/0.41 ((~![Y: $i] : ((~plant(Y)) | eats(A!2, Y))) | ((~plant(tptp_fun_Y_6(A!3))) | eats(A!2, tptp_fun_Y_6(A!3)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(271,plain,
% 0.18/0.41 ((~![Y: $i] : ((~plant(Y)) | eats(A!2, Y))) | (~plant(tptp_fun_Y_6(A!3))) | eats(A!2, tptp_fun_Y_6(A!3))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.18/0.41 tff(272,plain,
% 0.18/0.41 (eats(A!2, tptp_fun_Y_6(A!3))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[271, 244, 268])).
% 0.18/0.41 tff(273,assumption,(eats(A!2, tptp_fun_Y_6(A!3))), introduced(assumption)).
% 0.18/0.41 tff(274,assumption,(![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z)))), introduced(assumption)).
% 0.18/0.41 tff(275,plain,
% 0.18/0.41 (((~![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z)))) | ((~plant(tptp_fun_Y_6(A!3))) | (~eats(A!2, tptp_fun_Y_6(A!3))))) <=> ((~![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z)))) | (~plant(tptp_fun_Y_6(A!3))) | (~eats(A!2, tptp_fun_Y_6(A!3))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(276,plain,
% 0.18/0.41 ((~![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z)))) | ((~plant(tptp_fun_Y_6(A!3))) | (~eats(A!2, tptp_fun_Y_6(A!3))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(277,plain,
% 0.18/0.41 ((~![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z)))) | (~plant(tptp_fun_Y_6(A!3))) | (~eats(A!2, tptp_fun_Y_6(A!3)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.18/0.41 tff(278,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[277, 244, 274, 273])).
% 0.18/0.41 tff(279,plain,((~![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z)))) | (~eats(A!2, tptp_fun_Y_6(A!3)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.41 tff(280,plain,
% 0.18/0.41 (~![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[279, 272])).
% 0.18/0.41 tff(281,plain,
% 0.18/0.41 (((~![Y: $i] : ((~plant(Y)) | eats(A!2, Y))) | ((~plant(A!5)) | eats(A!2, A!5))) <=> ((~![Y: $i] : ((~plant(Y)) | eats(A!2, Y))) | (~plant(A!5)) | eats(A!2, A!5))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(282,plain,
% 0.18/0.41 ((~![Y: $i] : ((~plant(Y)) | eats(A!2, Y))) | ((~plant(A!5)) | eats(A!2, A!5))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(283,plain,
% 0.18/0.41 ((~![Y: $i] : ((~plant(Y)) | eats(A!2, Y))) | (~plant(A!5)) | eats(A!2, A!5)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.18/0.41 tff(284,plain,
% 0.18/0.41 (eats(A!2, A!5)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[283, 97, 268])).
% 0.18/0.41 tff(285,plain,
% 0.18/0.41 (^[X: $i] : refl((animal(X) | (~bird(X))) <=> (animal(X) | (~bird(X))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(286,plain,
% 0.18/0.41 (![X: $i] : (animal(X) | (~bird(X))) <=> ![X: $i] : (animal(X) | (~bird(X)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[285])).
% 0.18/0.41 tff(287,plain,
% 0.18/0.41 (![X: $i] : (animal(X) | (~bird(X))) <=> ![X: $i] : (animal(X) | (~bird(X)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(288,plain,
% 0.18/0.41 (^[X: $i] : rewrite((bird(X) => animal(X)) <=> (animal(X) | (~bird(X))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(289,plain,
% 0.18/0.41 (![X: $i] : (bird(X) => animal(X)) <=> ![X: $i] : (animal(X) | (~bird(X)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[288])).
% 0.18/0.41 tff(290,axiom,(![X: $i] : (bird(X) => animal(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_3_1')).
% 0.18/0.41 tff(291,plain,
% 0.18/0.41 (![X: $i] : (animal(X) | (~bird(X)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.18/0.41 tff(292,plain,
% 0.18/0.41 (![X: $i] : (animal(X) | (~bird(X)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[291, 287])).
% 0.18/0.41 tff(293,plain,(
% 0.18/0.41 ![X: $i] : (animal(X) | (~bird(X)))),
% 0.18/0.41 inference(skolemize,[status(sab)],[292])).
% 0.18/0.41 tff(294,plain,
% 0.18/0.41 (![X: $i] : (animal(X) | (~bird(X)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[293, 286])).
% 0.18/0.41 tff(295,plain,
% 0.18/0.41 (((~![X: $i] : (animal(X) | (~bird(X)))) | (animal(A!2) | (~bird(A!2)))) <=> ((~![X: $i] : (animal(X) | (~bird(X)))) | animal(A!2) | (~bird(A!2)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(296,plain,
% 0.18/0.41 ((~![X: $i] : (animal(X) | (~bird(X)))) | (animal(A!2) | (~bird(A!2)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(297,plain,
% 0.18/0.41 ((~![X: $i] : (animal(X) | (~bird(X)))) | animal(A!2) | (~bird(A!2))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[296, 295])).
% 0.18/0.41 tff(298,plain,
% 0.18/0.41 (animal(A!2)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[297, 22, 294])).
% 0.18/0.41 tff(299,plain,
% 0.18/0.41 (^[X: $i, Y: $i] : refl(((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y)))) <=> ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(300,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y)))) <=> ![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[299])).
% 0.18/0.41 tff(301,plain,
% 0.18/0.41 (^[X: $i, Y: $i] : rewrite(((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y)))) <=> ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(302,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y)))) <=> ![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[301])).
% 0.18/0.41 tff(303,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y)))) <=> ![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))),
% 0.18/0.41 inference(transitivity,[status(thm)],[302, 300])).
% 0.18/0.41 tff(304,plain,
% 0.18/0.41 (^[X: $i, Y: $i] : rewrite(((~animal(Y)) | (~animal(X)) | ![Z: $i] : (~(grain(Z) & eats(Y, Z) & eats(X, Y)))) <=> ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(305,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : (~(grain(Z) & eats(Y, Z) & eats(X, Y)))) <=> ![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[304])).
% 0.18/0.41 tff(306,plain,
% 0.18/0.41 (^[X: $i, Y: $i] : rewrite(((~animal(X)) | (~animal(Y)) | ![Z: $i] : (~(grain(Z) & eats(Y, Z) & eats(X, Y)))) <=> ((~animal(Y)) | (~animal(X)) | ![Z: $i] : (~(grain(Z) & eats(Y, Z) & eats(X, Y)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(307,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~animal(X)) | (~animal(Y)) | ![Z: $i] : (~(grain(Z) & eats(Y, Z) & eats(X, Y)))) <=> ![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : (~(grain(Z) & eats(Y, Z) & eats(X, Y))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[306])).
% 0.18/0.41 tff(308,plain,
% 0.18/0.41 ((~?[X: $i, Y: $i] : (animal(X) & animal(Y) & ?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y)))) <=> (~?[X: $i, Y: $i] : (animal(X) & animal(Y) & ?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(309,plain,
% 0.18/0.41 ((~?[X: $i, Y: $i] : ((animal(X) & animal(Y)) & ?[Z: $i] : ((grain(Z) & eats(Y, Z)) & eats(X, Y)))) <=> (~?[X: $i, Y: $i] : (animal(X) & animal(Y) & ?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(310,axiom,(~?[X: $i, Y: $i] : ((animal(X) & animal(Y)) & ?[Z: $i] : ((grain(Z) & eats(Y, Z)) & eats(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47')).
% 0.18/0.41 tff(311,plain,
% 0.18/0.41 (~?[X: $i, Y: $i] : (animal(X) & animal(Y) & ?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.18/0.41 tff(312,plain,
% 0.18/0.41 (~?[X: $i, Y: $i] : (animal(X) & animal(Y) & ?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[311, 308])).
% 0.18/0.41 tff(313,plain,
% 0.18/0.41 (~?[X: $i, Y: $i] : (animal(X) & animal(Y) & ?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[312, 308])).
% 0.18/0.41 tff(314,plain,
% 0.18/0.41 (~?[X: $i, Y: $i] : (animal(X) & animal(Y) & ?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[313, 308])).
% 0.18/0.41 tff(315,plain,
% 0.18/0.41 (^[X: $i, Y: $i] : nnf_neg(refl($oeq((~animal(X)), (~animal(X)))), refl($oeq((~animal(Y)), (~animal(Y)))), nnf_neg(proof_bind(^[Z: $i] : refl($oeq((~(grain(Z) & eats(Y, Z) & eats(X, Y))), (~(grain(Z) & eats(Y, Z) & eats(X, Y)))))), $oeq((~?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y))), ![Z: $i] : (~(grain(Z) & eats(Y, Z) & eats(X, Y))))), $oeq((~(animal(X) & animal(Y) & ?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y)))), ((~animal(X)) | (~animal(Y)) | ![Z: $i] : (~(grain(Z) & eats(Y, Z) & eats(X, Y))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(316,plain,(
% 0.18/0.41 ![X: $i, Y: $i] : ((~animal(X)) | (~animal(Y)) | ![Z: $i] : (~(grain(Z) & eats(Y, Z) & eats(X, Y))))),
% 0.18/0.41 inference(nnf-neg,[status(sab)],[314, 315])).
% 0.18/0.41 tff(317,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : (~(grain(Z) & eats(Y, Z) & eats(X, Y))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[316, 307])).
% 0.18/0.41 tff(318,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[317, 305])).
% 0.18/0.41 tff(319,plain,
% 0.18/0.41 (![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[318, 303])).
% 0.18/0.41 tff(320,plain,
% 0.18/0.41 (((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | ((~animal(A!1)) | (~animal(A!2)) | ![Z: $i] : ((~grain(Z)) | (~eats(A!2, Z)) | (~eats(A!1, A!2))))) <=> ((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | (~animal(A!1)) | (~animal(A!2)) | ![Z: $i] : ((~grain(Z)) | (~eats(A!2, Z)) | (~eats(A!1, A!2))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(321,plain,
% 0.18/0.41 (((~animal(A!2)) | (~animal(A!1)) | ![Z: $i] : ((~grain(Z)) | (~eats(A!2, Z)) | (~eats(A!1, A!2)))) <=> ((~animal(A!1)) | (~animal(A!2)) | ![Z: $i] : ((~grain(Z)) | (~eats(A!2, Z)) | (~eats(A!1, A!2))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(322,plain,
% 0.18/0.41 (((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | ((~animal(A!2)) | (~animal(A!1)) | ![Z: $i] : ((~grain(Z)) | (~eats(A!2, Z)) | (~eats(A!1, A!2))))) <=> ((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | ((~animal(A!1)) | (~animal(A!2)) | ![Z: $i] : ((~grain(Z)) | (~eats(A!2, Z)) | (~eats(A!1, A!2)))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[321])).
% 0.18/0.41 tff(323,plain,
% 0.18/0.41 (((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | ((~animal(A!2)) | (~animal(A!1)) | ![Z: $i] : ((~grain(Z)) | (~eats(A!2, Z)) | (~eats(A!1, A!2))))) <=> ((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | (~animal(A!1)) | (~animal(A!2)) | ![Z: $i] : ((~grain(Z)) | (~eats(A!2, Z)) | (~eats(A!1, A!2))))),
% 0.18/0.41 inference(transitivity,[status(thm)],[322, 320])).
% 0.18/0.41 tff(324,plain,
% 0.18/0.41 ((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | ((~animal(A!2)) | (~animal(A!1)) | ![Z: $i] : ((~grain(Z)) | (~eats(A!2, Z)) | (~eats(A!1, A!2))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(325,plain,
% 0.18/0.41 ((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | (~animal(A!1)) | (~animal(A!2)) | ![Z: $i] : ((~grain(Z)) | (~eats(A!2, Z)) | (~eats(A!1, A!2)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[324, 323])).
% 0.18/0.42 tff(326,plain,
% 0.18/0.42 (![Z: $i] : ((~grain(Z)) | (~eats(A!2, Z)) | (~eats(A!1, A!2)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[325, 319, 210, 298])).
% 0.18/0.42 tff(327,assumption,(eats(A!1, A!2)), introduced(assumption)).
% 0.18/0.42 tff(328,assumption,(eats(A!2, A!5)), introduced(assumption)).
% 0.18/0.42 tff(329,plain,
% 0.18/0.42 (((~![Z: $i] : ((~grain(Z)) | (~eats(A!2, Z)) | (~eats(A!1, A!2)))) | ((~grain(A!5)) | (~eats(A!2, A!5)) | (~eats(A!1, A!2)))) <=> ((~![Z: $i] : ((~grain(Z)) | (~eats(A!2, Z)) | (~eats(A!1, A!2)))) | (~grain(A!5)) | (~eats(A!2, A!5)) | (~eats(A!1, A!2)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(330,plain,
% 0.18/0.42 ((~![Z: $i] : ((~grain(Z)) | (~eats(A!2, Z)) | (~eats(A!1, A!2)))) | ((~grain(A!5)) | (~eats(A!2, A!5)) | (~eats(A!1, A!2)))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(331,plain,
% 0.18/0.42 ((~![Z: $i] : ((~grain(Z)) | (~eats(A!2, Z)) | (~eats(A!1, A!2)))) | (~grain(A!5)) | (~eats(A!2, A!5)) | (~eats(A!1, A!2))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[330, 329])).
% 0.18/0.42 tff(332,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[331, 70, 328, 327, 326])).
% 0.18/0.42 tff(333,plain,((~eats(A!1, A!2)) | (~eats(A!2, A!5))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.42 tff(334,plain,
% 0.18/0.42 (~eats(A!1, A!2)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[333, 284])).
% 0.18/0.42 tff(335,assumption,(~eats(A!1, A!2)), introduced(assumption)).
% 0.18/0.42 tff(336,assumption,(~![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z)))), introduced(assumption)).
% 0.18/0.42 tff(337,assumption,(~much_smaller(A!2, A!1)), introduced(assumption)).
% 0.18/0.42 tff(338,plain,
% 0.18/0.42 (^[X: $i, Y: $i] : refl((much_smaller(X, Y) | (~fox(Y)) | (~bird(X))) <=> (much_smaller(X, Y) | (~fox(Y)) | (~bird(X))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(339,plain,
% 0.18/0.42 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X))) <=> ![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[338])).
% 0.18/0.42 tff(340,plain,
% 0.18/0.42 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((bird(X) & fox(Y)) <=> (~((~bird(X)) | (~fox(Y))))), ((~(bird(X) & fox(Y))) <=> (~(~((~bird(X)) | (~fox(Y))))))), rewrite((~(~((~bird(X)) | (~fox(Y))))) <=> ((~bird(X)) | (~fox(Y)))), ((~(bird(X) & fox(Y))) <=> ((~bird(X)) | (~fox(Y))))), (((~(bird(X) & fox(Y))) | much_smaller(X, Y)) <=> (((~bird(X)) | (~fox(Y))) | much_smaller(X, Y)))), rewrite((((~bird(X)) | (~fox(Y))) | much_smaller(X, Y)) <=> (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))), (((~(bird(X) & fox(Y))) | much_smaller(X, Y)) <=> (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(341,plain,
% 0.18/0.42 (![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y)) <=> ![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[340])).
% 0.18/0.42 tff(342,plain,
% 0.18/0.42 (![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y)) <=> ![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(343,plain,
% 0.18/0.42 (^[X: $i, Y: $i] : rewrite(((bird(X) & fox(Y)) => much_smaller(X, Y)) <=> ((~(bird(X) & fox(Y))) | much_smaller(X, Y)))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(344,plain,
% 0.18/0.42 (![X: $i, Y: $i] : ((bird(X) & fox(Y)) => much_smaller(X, Y)) <=> ![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[343])).
% 0.18/0.42 tff(345,axiom,(![X: $i, Y: $i] : ((bird(X) & fox(Y)) => much_smaller(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_9')).
% 0.18/0.42 tff(346,plain,
% 0.18/0.42 (![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.18/0.42 tff(347,plain,
% 0.18/0.42 (![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[346, 342])).
% 0.18/0.42 tff(348,plain,(
% 0.18/0.42 ![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y))),
% 0.18/0.42 inference(skolemize,[status(sab)],[347])).
% 0.18/0.42 tff(349,plain,
% 0.18/0.42 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[348, 341])).
% 0.18/0.42 tff(350,plain,
% 0.18/0.42 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[349, 339])).
% 0.18/0.42 tff(351,plain,
% 0.18/0.42 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | ((~fox(A!1)) | (~bird(A!2)) | much_smaller(A!2, A!1))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (~fox(A!1)) | (~bird(A!2)) | much_smaller(A!2, A!1))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(352,plain,
% 0.18/0.42 ((much_smaller(A!2, A!1) | (~fox(A!1)) | (~bird(A!2))) <=> ((~fox(A!1)) | (~bird(A!2)) | much_smaller(A!2, A!1))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(353,plain,
% 0.18/0.42 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (much_smaller(A!2, A!1) | (~fox(A!1)) | (~bird(A!2)))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | ((~fox(A!1)) | (~bird(A!2)) | much_smaller(A!2, A!1)))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[352])).
% 0.18/0.42 tff(354,plain,
% 0.18/0.42 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (much_smaller(A!2, A!1) | (~fox(A!1)) | (~bird(A!2)))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (~fox(A!1)) | (~bird(A!2)) | much_smaller(A!2, A!1))),
% 0.18/0.42 inference(transitivity,[status(thm)],[353, 351])).
% 0.18/0.42 tff(355,plain,
% 0.18/0.42 ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (much_smaller(A!2, A!1) | (~fox(A!1)) | (~bird(A!2)))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(356,plain,
% 0.18/0.42 ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (~fox(A!1)) | (~bird(A!2)) | much_smaller(A!2, A!1)),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[355, 354])).
% 0.18/0.42 tff(357,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[356, 164, 22, 350, 337])).
% 0.18/0.42 tff(358,plain,(much_smaller(A!2, A!1)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.42 tff(359,plain,
% 0.18/0.42 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1)))) | ((~animal(A!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z))) | (~much_smaller(A!2, A!1)) | eats(A!1, A!2))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1)))) | (~animal(A!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z))) | (~much_smaller(A!2, A!1)) | eats(A!1, A!2))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(360,plain,
% 0.18/0.42 (((~animal(A!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z))) | eats(A!1, A!2) | (~much_smaller(A!2, A!1))) <=> ((~animal(A!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z))) | (~much_smaller(A!2, A!1)) | eats(A!1, A!2))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(361,plain,
% 0.18/0.42 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1)))) | ((~animal(A!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z))) | eats(A!1, A!2) | (~much_smaller(A!2, A!1)))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1)))) | ((~animal(A!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z))) | (~much_smaller(A!2, A!1)) | eats(A!1, A!2)))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[360])).
% 0.18/0.42 tff(362,plain,
% 0.18/0.42 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1)))) | ((~animal(A!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z))) | eats(A!1, A!2) | (~much_smaller(A!2, A!1)))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1)))) | (~animal(A!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z))) | (~much_smaller(A!2, A!1)) | eats(A!1, A!2))),
% 0.18/0.42 inference(transitivity,[status(thm)],[361, 359])).
% 0.18/0.42 tff(363,plain,
% 0.18/0.42 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1)))) | ((~animal(A!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z))) | eats(A!1, A!2) | (~much_smaller(A!2, A!1)))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(364,plain,
% 0.18/0.42 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1)))) | (~animal(A!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z))) | (~much_smaller(A!2, A!1)) | eats(A!1, A!2)),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[363, 362])).
% 0.18/0.42 tff(365,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[364, 298, 267, 358, 336, 335])).
% 0.18/0.42 tff(366,plain,((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1)))) | ![Z: $i] : ((~plant(Z)) | (~eats(A!2, Z))) | eats(A!1, A!2)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.42 tff(367,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[366, 334, 280, 267])).
% 0.18/0.42 tff(368,plain,((~![Y: $i] : ((~plant(Y)) | eats(A!2, Y))) | (~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!1, Y1) | (~much_smaller(Y1, A!1))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.42 tff(369,plain,
% 0.18/0.42 (~![Y: $i] : ((~plant(Y)) | eats(A!2, Y))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[368, 266])).
% 0.18/0.42 tff(370,plain,
% 0.18/0.42 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!2)) | ![Y: $i] : ((~plant(Y)) | eats(A!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(A!2)) | ![Y: $i] : ((~plant(Y)) | eats(A!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(371,plain,
% 0.18/0.42 (((~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))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(372,plain,
% 0.18/0.42 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!2)) | ![Y: $i] : ((~plant(Y)) | eats(A!2, Y)) | ![Y1: $i] : (eats(A!2, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!2)) | ![Y: $i] : ((~plant(Y)) | eats(A!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[371])).
% 0.18/0.42 tff(373,plain,
% 0.18/0.42 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!2)) | ![Y: $i] : ((~plant(Y)) | eats(A!2, Y)) | ![Y1: $i] : (eats(A!2, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(A!2)) | ![Y: $i] : ((~plant(Y)) | eats(A!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2))))),
% 0.18/0.42 inference(transitivity,[status(thm)],[372, 370])).
% 0.18/0.42 tff(374,plain,
% 0.18/0.42 ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(A!2)) | ![Y: $i] : ((~plant(Y)) | eats(A!2, Y)) | ![Y1: $i] : (eats(A!2, Y1) | (~animal(Y1)) | (~much_smaller(Y1, A!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(375,plain,
% 0.18/0.42 ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(A!2)) | ![Y: $i] : ((~plant(Y)) | eats(A!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[374, 373])).
% 0.18/0.42 tff(376,plain,
% 0.18/0.42 (![Y: $i] : ((~plant(Y)) | eats(A!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[375, 138, 298])).
% 0.18/0.42 tff(377,plain,
% 0.18/0.42 (![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[376, 369])).
% 0.18/0.42 tff(378,plain,
% 0.18/0.42 (^[X: $i] : refl((animal(X) | (~snail(X))) <=> (animal(X) | (~snail(X))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(379,plain,
% 0.18/0.42 (![X: $i] : (animal(X) | (~snail(X))) <=> ![X: $i] : (animal(X) | (~snail(X)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[378])).
% 0.18/0.42 tff(380,plain,
% 0.18/0.42 (![X: $i] : (animal(X) | (~snail(X))) <=> ![X: $i] : (animal(X) | (~snail(X)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(381,plain,
% 0.18/0.42 (^[X: $i] : rewrite((snail(X) => animal(X)) <=> (animal(X) | (~snail(X))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(382,plain,
% 0.18/0.42 (![X: $i] : (snail(X) => animal(X)) <=> ![X: $i] : (animal(X) | (~snail(X)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[381])).
% 0.18/0.42 tff(383,axiom,(![X: $i] : (snail(X) => animal(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_4_2')).
% 0.18/0.42 tff(384,plain,
% 0.18/0.42 (![X: $i] : (animal(X) | (~snail(X)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[383, 382])).
% 0.18/0.42 tff(385,plain,
% 0.18/0.42 (![X: $i] : (animal(X) | (~snail(X)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[384, 380])).
% 0.18/0.43 tff(386,plain,(
% 0.18/0.43 ![X: $i] : (animal(X) | (~snail(X)))),
% 0.18/0.43 inference(skolemize,[status(sab)],[385])).
% 0.18/0.43 tff(387,plain,
% 0.18/0.43 (![X: $i] : (animal(X) | (~snail(X)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[386, 379])).
% 0.18/0.43 tff(388,plain,
% 0.18/0.43 (((~![X: $i] : (animal(X) | (~snail(X)))) | (animal(A!4) | (~snail(A!4)))) <=> ((~![X: $i] : (animal(X) | (~snail(X)))) | animal(A!4) | (~snail(A!4)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(389,plain,
% 0.18/0.43 ((~![X: $i] : (animal(X) | (~snail(X)))) | (animal(A!4) | (~snail(A!4)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(390,plain,
% 0.18/0.43 ((~![X: $i] : (animal(X) | (~snail(X)))) | animal(A!4) | (~snail(A!4))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[389, 388])).
% 0.18/0.43 tff(391,plain,
% 0.18/0.43 (animal(A!4)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[390, 18, 387])).
% 0.18/0.43 tff(392,plain,
% 0.18/0.43 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))) | ((~animal(A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | (~much_smaller(A!4, A!2)) | eats(A!2, A!4))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))) | (~animal(A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | (~much_smaller(A!4, A!2)) | eats(A!2, A!4))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(393,plain,
% 0.18/0.43 (((~animal(A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | eats(A!2, A!4) | (~much_smaller(A!4, A!2))) <=> ((~animal(A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | (~much_smaller(A!4, A!2)) | eats(A!2, A!4))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(394,plain,
% 0.18/0.43 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))) | ((~animal(A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | eats(A!2, A!4) | (~much_smaller(A!4, A!2)))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))) | ((~animal(A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | (~much_smaller(A!4, A!2)) | eats(A!2, A!4)))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[393])).
% 0.18/0.43 tff(395,plain,
% 0.18/0.43 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))) | ((~animal(A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | eats(A!2, A!4) | (~much_smaller(A!4, A!2)))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))) | (~animal(A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | (~much_smaller(A!4, A!2)) | eats(A!2, A!4))),
% 0.18/0.43 inference(transitivity,[status(thm)],[394, 392])).
% 0.18/0.43 tff(396,plain,
% 0.18/0.43 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))) | ((~animal(A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | eats(A!2, A!4) | (~much_smaller(A!4, A!2)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(397,plain,
% 0.18/0.43 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(A!2, Y1) | (~much_smaller(Y1, A!2)))) | (~animal(A!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | (~much_smaller(A!4, A!2)) | eats(A!2, A!4)),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[396, 395])).
% 0.18/0.43 tff(398,plain,
% 0.18/0.43 (![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z))) | eats(A!2, A!4)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[397, 391, 377, 52])).
% 0.18/0.43 tff(399,plain,
% 0.18/0.43 (![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z)))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[398, 30])).
% 0.18/0.43 tff(400,plain,
% 0.18/0.43 (^[X: $i] : refl(((~snail(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X)))))) <=> ((~snail(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X)))))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(401,plain,
% 0.18/0.43 (![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X)))))) <=> ![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[400])).
% 0.18/0.43 tff(402,plain,
% 0.18/0.43 (^[X: $i] : rewrite(((~snail(X)) | (plant(tptp_fun_Y_6(X)) & eats(X, tptp_fun_Y_6(X)))) <=> ((~snail(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X)))))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(403,plain,
% 0.18/0.43 (![X: $i] : ((~snail(X)) | (plant(tptp_fun_Y_6(X)) & eats(X, tptp_fun_Y_6(X)))) <=> ![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[402])).
% 0.18/0.43 tff(404,plain,
% 0.18/0.43 (![X: $i] : ((~snail(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y))) <=> ![X: $i] : ((~snail(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(405,plain,
% 0.18/0.43 (^[X: $i] : rewrite((snail(X) => ?[Y: $i] : (plant(Y) & eats(X, Y))) <=> ((~snail(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(406,plain,
% 0.18/0.43 (![X: $i] : (snail(X) => ?[Y: $i] : (plant(Y) & eats(X, Y))) <=> ![X: $i] : ((~snail(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[405])).
% 0.18/0.43 tff(407,axiom,(![X: $i] : (snail(X) => ?[Y: $i] : (plant(Y) & eats(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_14a')).
% 0.18/0.43 tff(408,plain,
% 0.18/0.43 (![X: $i] : ((~snail(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.18/0.43 tff(409,plain,
% 0.18/0.43 (![X: $i] : ((~snail(X)) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[408, 404])).
% 0.18/0.43 tff(410,plain,(
% 0.18/0.43 ![X: $i] : ((~snail(X)) | (plant(tptp_fun_Y_6(X)) & eats(X, tptp_fun_Y_6(X))))),
% 0.18/0.43 inference(skolemize,[status(sab)],[409])).
% 0.18/0.43 tff(411,plain,
% 0.18/0.43 (![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[410, 403])).
% 0.18/0.43 tff(412,plain,
% 0.18/0.43 (![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[411, 401])).
% 0.18/0.43 tff(413,plain,
% 0.18/0.43 (((~![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | ((~snail(A!4)) | (~((~plant(tptp_fun_Y_6(A!4))) | (~eats(A!4, tptp_fun_Y_6(A!4))))))) <=> ((~![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | (~snail(A!4)) | (~((~plant(tptp_fun_Y_6(A!4))) | (~eats(A!4, tptp_fun_Y_6(A!4))))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(414,plain,
% 0.18/0.43 ((~![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | ((~snail(A!4)) | (~((~plant(tptp_fun_Y_6(A!4))) | (~eats(A!4, tptp_fun_Y_6(A!4))))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(415,plain,
% 0.18/0.43 ((~![X: $i] : ((~snail(X)) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | (~snail(A!4)) | (~((~plant(tptp_fun_Y_6(A!4))) | (~eats(A!4, tptp_fun_Y_6(A!4)))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[414, 413])).
% 0.18/0.43 tff(416,plain,
% 0.18/0.43 (~((~plant(tptp_fun_Y_6(A!4))) | (~eats(A!4, tptp_fun_Y_6(A!4))))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[415, 18, 412])).
% 0.18/0.43 tff(417,plain,
% 0.18/0.43 (((~plant(tptp_fun_Y_6(A!4))) | (~eats(A!4, tptp_fun_Y_6(A!4)))) | eats(A!4, tptp_fun_Y_6(A!4))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(418,plain,
% 0.18/0.43 (eats(A!4, tptp_fun_Y_6(A!4))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[417, 416])).
% 0.18/0.43 tff(419,plain,
% 0.18/0.43 (((~plant(tptp_fun_Y_6(A!4))) | (~eats(A!4, tptp_fun_Y_6(A!4)))) | plant(tptp_fun_Y_6(A!4))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(420,plain,
% 0.18/0.43 (plant(tptp_fun_Y_6(A!4))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[419, 416])).
% 0.18/0.43 tff(421,plain,
% 0.18/0.43 (((~![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z)))) | ((~plant(tptp_fun_Y_6(A!4))) | (~eats(A!4, tptp_fun_Y_6(A!4))))) <=> ((~![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z)))) | (~plant(tptp_fun_Y_6(A!4))) | (~eats(A!4, tptp_fun_Y_6(A!4))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(422,plain,
% 0.18/0.43 ((~![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z)))) | ((~plant(tptp_fun_Y_6(A!4))) | (~eats(A!4, tptp_fun_Y_6(A!4))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(423,plain,
% 0.18/0.43 ((~![Z: $i] : ((~plant(Z)) | (~eats(A!4, Z)))) | (~plant(tptp_fun_Y_6(A!4))) | (~eats(A!4, tptp_fun_Y_6(A!4)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[422, 421])).
% 0.18/0.43 tff(424,plain,
% 0.18/0.43 ($false),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[423, 420, 418, 399])).
% 0.18/0.43 % SZS output end Proof
% 0.18/0.43 % E exiting
%------------------------------------------------------------------------------