TSTP Solution File: PUZ031+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PUZ031+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 14:10:58 EDT 2022
% Result : Theorem 0.22s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : PUZ031+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.35 % Computer : n022.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri Sep 2 18:24:10 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.35 Usage: tptp [options] [-file:]file
% 0.15/0.35 -h, -? prints this message.
% 0.15/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.35 -m, -model generate model.
% 0.15/0.35 -p, -proof generate proof.
% 0.15/0.35 -c, -core generate unsat core of named formulas.
% 0.15/0.35 -st, -statistics display statistics.
% 0.15/0.35 -t:timeout set timeout (in second).
% 0.15/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.35 -<param>:<value> configuration parameter and value.
% 0.15/0.35 -o:<output-file> file to place output in.
% 0.22/0.41 % SZS status Theorem
% 0.22/0.41 % SZS output start Proof
% 0.22/0.41 tff(eats_type, type, (
% 0.22/0.41 eats: ( $i * $i ) > $o)).
% 0.22/0.41 tff(tptp_fun_X1_2_type, type, (
% 0.22/0.41 tptp_fun_X1_2: $i)).
% 0.22/0.41 tff(tptp_fun_X1_1_type, type, (
% 0.22/0.41 tptp_fun_X1_1: $i)).
% 0.22/0.41 tff(grain_type, type, (
% 0.22/0.41 grain: $i > $o)).
% 0.22/0.41 tff(animal_type, type, (
% 0.22/0.41 animal: $i > $o)).
% 0.22/0.41 tff(bird_type, type, (
% 0.22/0.41 bird: $i > $o)).
% 0.22/0.41 tff(fox_type, type, (
% 0.22/0.41 fox: $i > $o)).
% 0.22/0.41 tff(tptp_fun_X_5_type, type, (
% 0.22/0.41 tptp_fun_X_5: $i)).
% 0.22/0.41 tff(plant_type, type, (
% 0.22/0.41 plant: $i > $o)).
% 0.22/0.41 tff(much_smaller_type, type, (
% 0.22/0.41 much_smaller: ( $i * $i ) > $o)).
% 0.22/0.41 tff(tptp_fun_X1_4_type, type, (
% 0.22/0.41 tptp_fun_X1_4: $i)).
% 0.22/0.41 tff(snail_type, type, (
% 0.22/0.41 snail: $i > $o)).
% 0.22/0.41 tff(caterpillar_type, type, (
% 0.22/0.41 caterpillar: $i > $o)).
% 0.22/0.41 tff(tptp_fun_Y_6_type, type, (
% 0.22/0.41 tptp_fun_Y_6: $i > $i)).
% 0.22/0.41 tff(tptp_fun_X1_3_type, type, (
% 0.22/0.41 tptp_fun_X1_3: $i)).
% 0.22/0.41 tff(tptp_fun_X1_0_type, type, (
% 0.22/0.41 tptp_fun_X1_0: $i)).
% 0.22/0.41 tff(wolf_type, type, (
% 0.22/0.41 wolf: $i > $o)).
% 0.22/0.41 tff(1,plain,
% 0.22/0.41 (?[X1: $i] : bird(X1) <=> ?[X1: $i] : bird(X1)),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(2,axiom,(?[X1: $i] : bird(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_3_2')).
% 0.22/0.41 tff(3,plain,
% 0.22/0.41 (?[X1: $i] : bird(X1)),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.22/0.41 tff(4,plain,(
% 0.22/0.41 bird(X1!2)),
% 0.22/0.41 inference(skolemize,[status(sab)],[3])).
% 0.22/0.41 tff(5,plain,
% 0.22/0.41 (^[X: $i] : refl((animal(X) | (~bird(X))) <=> (animal(X) | (~bird(X))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(6,plain,
% 0.22/0.41 (![X: $i] : (animal(X) | (~bird(X))) <=> ![X: $i] : (animal(X) | (~bird(X)))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[5])).
% 0.22/0.41 tff(7,plain,
% 0.22/0.41 (![X: $i] : (animal(X) | (~bird(X))) <=> ![X: $i] : (animal(X) | (~bird(X)))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(8,plain,
% 0.22/0.41 (^[X: $i] : rewrite((bird(X) => animal(X)) <=> (animal(X) | (~bird(X))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(9,plain,
% 0.22/0.41 (![X: $i] : (bird(X) => animal(X)) <=> ![X: $i] : (animal(X) | (~bird(X)))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[8])).
% 0.22/0.41 tff(10,axiom,(![X: $i] : (bird(X) => animal(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_3_1')).
% 0.22/0.41 tff(11,plain,
% 0.22/0.41 (![X: $i] : (animal(X) | (~bird(X)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.22/0.41 tff(12,plain,
% 0.22/0.41 (![X: $i] : (animal(X) | (~bird(X)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.22/0.41 tff(13,plain,(
% 0.22/0.41 ![X: $i] : (animal(X) | (~bird(X)))),
% 0.22/0.41 inference(skolemize,[status(sab)],[12])).
% 0.22/0.41 tff(14,plain,
% 0.22/0.41 (![X: $i] : (animal(X) | (~bird(X)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.22/0.41 tff(15,plain,
% 0.22/0.41 (((~![X: $i] : (animal(X) | (~bird(X)))) | (animal(X1!2) | (~bird(X1!2)))) <=> ((~![X: $i] : (animal(X) | (~bird(X)))) | animal(X1!2) | (~bird(X1!2)))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(16,plain,
% 0.22/0.41 ((~![X: $i] : (animal(X) | (~bird(X)))) | (animal(X1!2) | (~bird(X1!2)))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(17,plain,
% 0.22/0.41 ((~![X: $i] : (animal(X) | (~bird(X)))) | animal(X1!2) | (~bird(X1!2))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.22/0.41 tff(18,plain,
% 0.22/0.41 (animal(X1!2)),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[17, 14, 4])).
% 0.22/0.41 tff(19,plain,
% 0.22/0.41 (?[X1: $i] : fox(X1) <=> ?[X1: $i] : fox(X1)),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(20,axiom,(?[X1: $i] : fox(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_2_2')).
% 0.22/0.41 tff(21,plain,
% 0.22/0.41 (?[X1: $i] : fox(X1)),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.22/0.41 tff(22,plain,(
% 0.22/0.41 fox(X1!1)),
% 0.22/0.41 inference(skolemize,[status(sab)],[21])).
% 0.22/0.41 tff(23,plain,
% 0.22/0.41 (^[X: $i] : refl((animal(X) | (~fox(X))) <=> (animal(X) | (~fox(X))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(24,plain,
% 0.22/0.41 (![X: $i] : (animal(X) | (~fox(X))) <=> ![X: $i] : (animal(X) | (~fox(X)))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[23])).
% 0.22/0.41 tff(25,plain,
% 0.22/0.41 (![X: $i] : (animal(X) | (~fox(X))) <=> ![X: $i] : (animal(X) | (~fox(X)))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(26,plain,
% 0.22/0.41 (^[X: $i] : rewrite((fox(X) => animal(X)) <=> (animal(X) | (~fox(X))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(27,plain,
% 0.22/0.41 (![X: $i] : (fox(X) => animal(X)) <=> ![X: $i] : (animal(X) | (~fox(X)))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[26])).
% 0.22/0.42 tff(28,axiom,(![X: $i] : (fox(X) => animal(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_2_1')).
% 0.22/0.42 tff(29,plain,
% 0.22/0.42 (![X: $i] : (animal(X) | (~fox(X)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.22/0.42 tff(30,plain,
% 0.22/0.42 (![X: $i] : (animal(X) | (~fox(X)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.22/0.42 tff(31,plain,(
% 0.22/0.42 ![X: $i] : (animal(X) | (~fox(X)))),
% 0.22/0.42 inference(skolemize,[status(sab)],[30])).
% 0.22/0.42 tff(32,plain,
% 0.22/0.42 (![X: $i] : (animal(X) | (~fox(X)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.22/0.42 tff(33,plain,
% 0.22/0.42 (((~![X: $i] : (animal(X) | (~fox(X)))) | (animal(X1!1) | (~fox(X1!1)))) <=> ((~![X: $i] : (animal(X) | (~fox(X)))) | animal(X1!1) | (~fox(X1!1)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(34,plain,
% 0.22/0.42 ((~![X: $i] : (animal(X) | (~fox(X)))) | (animal(X1!1) | (~fox(X1!1)))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(35,plain,
% 0.22/0.42 ((~![X: $i] : (animal(X) | (~fox(X)))) | animal(X1!1) | (~fox(X1!1))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.22/0.42 tff(36,plain,
% 0.22/0.42 (animal(X1!1)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[35, 32, 22])).
% 0.22/0.42 tff(37,plain,
% 0.22/0.42 (^[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)))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(38,plain,
% 0.22/0.42 (![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))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[37])).
% 0.22/0.42 tff(39,plain,
% 0.22/0.42 (^[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)))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(40,plain,
% 0.22/0.42 (![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))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[39])).
% 0.22/0.42 tff(41,plain,
% 0.22/0.42 (![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))))),
% 0.22/0.42 inference(transitivity,[status(thm)],[40, 38])).
% 0.22/0.42 tff(42,plain,
% 0.22/0.42 (^[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)))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(43,plain,
% 0.22/0.42 (![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))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[42])).
% 0.22/0.42 tff(44,plain,
% 0.22/0.42 (^[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)))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(45,plain,
% 0.22/0.42 (![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))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[44])).
% 0.22/0.42 tff(46,plain,
% 0.22/0.42 ((~?[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))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(47,plain,
% 0.22/0.42 ((~?[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))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(48,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')).
% 0.22/0.42 tff(49,plain,
% 0.22/0.42 (~?[X: $i, Y: $i] : (animal(X) & animal(Y) & ?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.22/0.42 tff(50,plain,
% 0.22/0.42 (~?[X: $i, Y: $i] : (animal(X) & animal(Y) & ?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[49, 46])).
% 0.22/0.42 tff(51,plain,
% 0.22/0.42 (~?[X: $i, Y: $i] : (animal(X) & animal(Y) & ?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.22/0.42 tff(52,plain,
% 0.22/0.42 (~?[X: $i, Y: $i] : (animal(X) & animal(Y) & ?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[51, 46])).
% 0.22/0.42 tff(53,plain,
% 0.22/0.42 (~?[X: $i, Y: $i] : (animal(X) & animal(Y) & ?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[52, 46])).
% 0.22/0.42 tff(54,plain,
% 0.22/0.42 (~?[X: $i, Y: $i] : (animal(X) & animal(Y) & ?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.22/0.42 tff(55,plain,
% 0.22/0.42 (~?[X: $i, Y: $i] : (animal(X) & animal(Y) & ?[Z: $i] : (grain(Z) & eats(Y, Z) & eats(X, Y)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[54, 46])).
% 0.22/0.42 tff(56,plain,
% 0.22/0.42 (^[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))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(57,plain,(
% 0.22/0.42 ![X: $i, Y: $i] : ((~animal(X)) | (~animal(Y)) | ![Z: $i] : (~(grain(Z) & eats(Y, Z) & eats(X, Y))))),
% 0.22/0.42 inference(nnf-neg,[status(sab)],[55, 56])).
% 0.22/0.42 tff(58,plain,
% 0.22/0.42 (![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : (~(grain(Z) & eats(Y, Z) & eats(X, Y))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[57, 45])).
% 0.22/0.42 tff(59,plain,
% 0.22/0.42 (![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[58, 43])).
% 0.22/0.42 tff(60,plain,
% 0.22/0.42 (![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[59, 41])).
% 0.22/0.42 tff(61,plain,
% 0.22/0.42 (((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | ((~animal(X1!1)) | (~animal(X1!2)) | ![Z: $i] : ((~grain(Z)) | (~eats(X1!2, Z)) | (~eats(X1!1, X1!2))))) <=> ((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | (~animal(X1!1)) | (~animal(X1!2)) | ![Z: $i] : ((~grain(Z)) | (~eats(X1!2, Z)) | (~eats(X1!1, X1!2))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(62,plain,
% 0.22/0.42 (((~animal(X1!2)) | (~animal(X1!1)) | ![Z: $i] : ((~grain(Z)) | (~eats(X1!2, Z)) | (~eats(X1!1, X1!2)))) <=> ((~animal(X1!1)) | (~animal(X1!2)) | ![Z: $i] : ((~grain(Z)) | (~eats(X1!2, Z)) | (~eats(X1!1, X1!2))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(63,plain,
% 0.22/0.42 (((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | ((~animal(X1!2)) | (~animal(X1!1)) | ![Z: $i] : ((~grain(Z)) | (~eats(X1!2, Z)) | (~eats(X1!1, X1!2))))) <=> ((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | ((~animal(X1!1)) | (~animal(X1!2)) | ![Z: $i] : ((~grain(Z)) | (~eats(X1!2, Z)) | (~eats(X1!1, X1!2)))))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[62])).
% 0.22/0.42 tff(64,plain,
% 0.22/0.42 (((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | ((~animal(X1!2)) | (~animal(X1!1)) | ![Z: $i] : ((~grain(Z)) | (~eats(X1!2, Z)) | (~eats(X1!1, X1!2))))) <=> ((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | (~animal(X1!1)) | (~animal(X1!2)) | ![Z: $i] : ((~grain(Z)) | (~eats(X1!2, Z)) | (~eats(X1!1, X1!2))))),
% 0.22/0.42 inference(transitivity,[status(thm)],[63, 61])).
% 0.22/0.42 tff(65,plain,
% 0.22/0.42 ((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | ((~animal(X1!2)) | (~animal(X1!1)) | ![Z: $i] : ((~grain(Z)) | (~eats(X1!2, Z)) | (~eats(X1!1, X1!2))))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(66,plain,
% 0.22/0.42 ((~![X: $i, Y: $i] : ((~animal(Y)) | (~animal(X)) | ![Z: $i] : ((~grain(Z)) | (~eats(Y, Z)) | (~eats(X, Y))))) | (~animal(X1!1)) | (~animal(X1!2)) | ![Z: $i] : ((~grain(Z)) | (~eats(X1!2, Z)) | (~eats(X1!1, X1!2)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.22/0.42 tff(67,plain,
% 0.22/0.42 (![Z: $i] : ((~grain(Z)) | (~eats(X1!2, Z)) | (~eats(X1!1, X1!2)))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[66, 60, 36, 18])).
% 0.22/0.42 tff(68,assumption,(eats(X1!2, X1!4)), introduced(assumption)).
% 0.22/0.42 tff(69,plain,
% 0.22/0.42 (^[X: $i, Y: $i] : refl(((~eats(X, Y)) | (~snail(Y)) | (~bird(X))) <=> ((~eats(X, Y)) | (~snail(Y)) | (~bird(X))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(70,plain,
% 0.22/0.42 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[69])).
% 0.22/0.42 tff(71,plain,
% 0.22/0.42 (^[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)))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(72,plain,
% 0.22/0.42 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y)))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[71])).
% 0.22/0.42 tff(73,plain,
% 0.22/0.42 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y)))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(74,plain,
% 0.22/0.42 (^[X: $i, Y: $i] : rewrite(((bird(X) & snail(Y)) => (~eats(X, Y))) <=> ((~eats(X, Y)) | (~(bird(X) & snail(Y)))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(75,plain,
% 0.22/0.42 (![X: $i, Y: $i] : ((bird(X) & snail(Y)) => (~eats(X, Y))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[74])).
% 0.22/0.42 tff(76,axiom,(![X: $i, Y: $i] : ((bird(X) & snail(Y)) => (~eats(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_13')).
% 0.22/0.42 tff(77,plain,
% 0.22/0.42 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.22/0.42 tff(78,plain,
% 0.22/0.42 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.22/0.42 tff(79,plain,(
% 0.22/0.42 ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(bird(X) & snail(Y))))),
% 0.22/0.42 inference(skolemize,[status(sab)],[78])).
% 0.22/0.42 tff(80,plain,
% 0.22/0.42 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.22/0.42 tff(81,plain,
% 0.22/0.42 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[80, 70])).
% 0.22/0.42 tff(82,plain,
% 0.22/0.42 (?[X1: $i] : snail(X1) <=> ?[X1: $i] : snail(X1)),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(83,axiom,(?[X1: $i] : snail(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_5_2')).
% 0.22/0.42 tff(84,plain,
% 0.22/0.42 (?[X1: $i] : snail(X1)),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.22/0.42 tff(85,plain,(
% 0.22/0.42 snail(X1!4)),
% 0.22/0.42 inference(skolemize,[status(sab)],[84])).
% 0.22/0.42 tff(86,plain,
% 0.22/0.42 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | ((~bird(X1!2)) | (~snail(X1!4)) | (~eats(X1!2, X1!4)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | (~bird(X1!2)) | (~snail(X1!4)) | (~eats(X1!2, X1!4)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(87,plain,
% 0.22/0.42 (((~eats(X1!2, X1!4)) | (~snail(X1!4)) | (~bird(X1!2))) <=> ((~bird(X1!2)) | (~snail(X1!4)) | (~eats(X1!2, X1!4)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(88,plain,
% 0.22/0.42 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | ((~eats(X1!2, X1!4)) | (~snail(X1!4)) | (~bird(X1!2)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | ((~bird(X1!2)) | (~snail(X1!4)) | (~eats(X1!2, X1!4))))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[87])).
% 0.22/0.42 tff(89,plain,
% 0.22/0.42 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | ((~eats(X1!2, X1!4)) | (~snail(X1!4)) | (~bird(X1!2)))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | (~bird(X1!2)) | (~snail(X1!4)) | (~eats(X1!2, X1!4)))),
% 0.22/0.42 inference(transitivity,[status(thm)],[88, 86])).
% 0.22/0.42 tff(90,plain,
% 0.22/0.42 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | ((~eats(X1!2, X1!4)) | (~snail(X1!4)) | (~bird(X1!2)))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(91,plain,
% 0.22/0.42 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~snail(Y)) | (~bird(X)))) | (~bird(X1!2)) | (~snail(X1!4)) | (~eats(X1!2, X1!4))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.22/0.42 tff(92,plain,
% 0.22/0.42 ($false),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[91, 4, 85, 81, 68])).
% 0.22/0.42 tff(93,plain,(~eats(X1!2, X1!4)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.42 tff(94,assumption,(~much_smaller(X1!4, X1!2)), introduced(assumption)).
% 0.22/0.42 tff(95,plain,
% 0.22/0.42 ((caterpillar(X1!4) | snail(X1!4)) | (~snail(X1!4))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(96,plain,
% 0.22/0.42 (caterpillar(X1!4) | snail(X1!4)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[95, 85])).
% 0.22/0.42 tff(97,plain,
% 0.22/0.42 (^[X: $i, Y: $i] : refl((much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X)))) <=> (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X)))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(98,plain,
% 0.22/0.42 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X)))) <=> ![X: $i, Y: $i] : (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[97])).
% 0.22/0.42 tff(99,plain,
% 0.22/0.42 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((bird(Y) & (caterpillar(X) | snail(X))) <=> (~((~bird(Y)) | (~(caterpillar(X) | snail(X)))))), ((~(bird(Y) & (caterpillar(X) | snail(X)))) <=> (~(~((~bird(Y)) | (~(caterpillar(X) | snail(X)))))))), rewrite((~(~((~bird(Y)) | (~(caterpillar(X) | snail(X)))))) <=> ((~bird(Y)) | (~(caterpillar(X) | snail(X))))), ((~(bird(Y) & (caterpillar(X) | snail(X)))) <=> ((~bird(Y)) | (~(caterpillar(X) | snail(X)))))), (((~(bird(Y) & (caterpillar(X) | snail(X)))) | much_smaller(X, Y)) <=> (((~bird(Y)) | (~(caterpillar(X) | snail(X)))) | much_smaller(X, Y)))), rewrite((((~bird(Y)) | (~(caterpillar(X) | snail(X)))) | much_smaller(X, Y)) <=> (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X))))), (((~(bird(Y) & (caterpillar(X) | snail(X)))) | much_smaller(X, Y)) <=> (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X))))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(100,plain,
% 0.22/0.42 (![X: $i, Y: $i] : ((~(bird(Y) & (caterpillar(X) | snail(X)))) | much_smaller(X, Y)) <=> ![X: $i, Y: $i] : (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[99])).
% 0.22/0.42 tff(101,plain,
% 0.22/0.42 (![X: $i, Y: $i] : ((~(bird(Y) & (caterpillar(X) | snail(X)))) | much_smaller(X, Y)) <=> ![X: $i, Y: $i] : ((~(bird(Y) & (caterpillar(X) | snail(X)))) | much_smaller(X, Y))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(102,plain,
% 0.22/0.42 (^[X: $i, Y: $i] : trans(monotonicity(rewrite((bird(Y) & (snail(X) | caterpillar(X))) <=> (bird(Y) & (caterpillar(X) | snail(X)))), (((bird(Y) & (snail(X) | caterpillar(X))) => much_smaller(X, Y)) <=> ((bird(Y) & (caterpillar(X) | snail(X))) => much_smaller(X, Y)))), rewrite(((bird(Y) & (caterpillar(X) | snail(X))) => much_smaller(X, Y)) <=> ((~(bird(Y) & (caterpillar(X) | snail(X)))) | much_smaller(X, Y))), (((bird(Y) & (snail(X) | caterpillar(X))) => much_smaller(X, Y)) <=> ((~(bird(Y) & (caterpillar(X) | snail(X)))) | much_smaller(X, Y))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(103,plain,
% 0.22/0.43 (![X: $i, Y: $i] : ((bird(Y) & (snail(X) | caterpillar(X))) => much_smaller(X, Y)) <=> ![X: $i, Y: $i] : ((~(bird(Y) & (caterpillar(X) | snail(X)))) | much_smaller(X, Y))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[102])).
% 0.22/0.43 tff(104,axiom,(![X: $i, Y: $i] : ((bird(Y) & (snail(X) | caterpillar(X))) => much_smaller(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_8')).
% 0.22/0.43 tff(105,plain,
% 0.22/0.43 (![X: $i, Y: $i] : ((~(bird(Y) & (caterpillar(X) | snail(X)))) | much_smaller(X, Y))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.22/0.43 tff(106,plain,
% 0.22/0.43 (![X: $i, Y: $i] : ((~(bird(Y) & (caterpillar(X) | snail(X)))) | much_smaller(X, Y))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.22/0.43 tff(107,plain,(
% 0.22/0.43 ![X: $i, Y: $i] : ((~(bird(Y) & (caterpillar(X) | snail(X)))) | much_smaller(X, Y))),
% 0.22/0.43 inference(skolemize,[status(sab)],[106])).
% 0.22/0.43 tff(108,plain,
% 0.22/0.43 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[107, 100])).
% 0.22/0.43 tff(109,plain,
% 0.22/0.43 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[108, 98])).
% 0.22/0.43 tff(110,plain,
% 0.22/0.43 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X))))) | ((~bird(X1!2)) | (~(caterpillar(X1!4) | snail(X1!4))) | much_smaller(X1!4, X1!2))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X))))) | (~bird(X1!2)) | (~(caterpillar(X1!4) | snail(X1!4))) | much_smaller(X1!4, X1!2))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(111,plain,
% 0.22/0.43 ((much_smaller(X1!4, X1!2) | (~bird(X1!2)) | (~(caterpillar(X1!4) | snail(X1!4)))) <=> ((~bird(X1!2)) | (~(caterpillar(X1!4) | snail(X1!4))) | much_smaller(X1!4, X1!2))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(112,plain,
% 0.22/0.43 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X))))) | (much_smaller(X1!4, X1!2) | (~bird(X1!2)) | (~(caterpillar(X1!4) | snail(X1!4))))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X))))) | ((~bird(X1!2)) | (~(caterpillar(X1!4) | snail(X1!4))) | much_smaller(X1!4, X1!2)))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[111])).
% 0.22/0.43 tff(113,plain,
% 0.22/0.43 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X))))) | (much_smaller(X1!4, X1!2) | (~bird(X1!2)) | (~(caterpillar(X1!4) | snail(X1!4))))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X))))) | (~bird(X1!2)) | (~(caterpillar(X1!4) | snail(X1!4))) | much_smaller(X1!4, X1!2))),
% 0.22/0.43 inference(transitivity,[status(thm)],[112, 110])).
% 0.22/0.43 tff(114,plain,
% 0.22/0.43 ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X))))) | (much_smaller(X1!4, X1!2) | (~bird(X1!2)) | (~(caterpillar(X1!4) | snail(X1!4))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(115,plain,
% 0.22/0.43 ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~bird(Y)) | (~(caterpillar(X) | snail(X))))) | (~bird(X1!2)) | (~(caterpillar(X1!4) | snail(X1!4))) | much_smaller(X1!4, X1!2)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.22/0.43 tff(116,plain,
% 0.22/0.43 ($false),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[115, 4, 109, 96, 94])).
% 0.22/0.43 tff(117,plain,(much_smaller(X1!4, X1!2)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.43 tff(118,assumption,(![Z: $i] : ((~plant(Z)) | (~eats(X1!4, Z)))), introduced(assumption)).
% 0.22/0.43 tff(119,plain,
% 0.22/0.43 (^[X: $i] : refl(((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X)))))) <=> ((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X)))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(120,plain,
% 0.22/0.43 (![X: $i] : ((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X)))))) <=> ![X: $i] : ((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[119])).
% 0.22/0.43 tff(121,plain,
% 0.22/0.43 (^[X: $i] : rewrite(((~(caterpillar(X) | snail(X))) | (plant(tptp_fun_Y_6(X)) & eats(X, tptp_fun_Y_6(X)))) <=> ((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X)))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(122,plain,
% 0.22/0.43 (![X: $i] : ((~(caterpillar(X) | snail(X))) | (plant(tptp_fun_Y_6(X)) & eats(X, tptp_fun_Y_6(X)))) <=> ![X: $i] : ((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[121])).
% 0.22/0.43 tff(123,plain,
% 0.22/0.43 (![X: $i] : ((~(caterpillar(X) | snail(X))) | ?[Y: $i] : (plant(Y) & eats(X, Y))) <=> ![X: $i] : ((~(caterpillar(X) | snail(X))) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(124,plain,
% 0.22/0.43 (^[X: $i] : rewrite(((caterpillar(X) | snail(X)) => ?[Y: $i] : (plant(Y) & eats(X, Y))) <=> ((~(caterpillar(X) | snail(X))) | ?[Y: $i] : (plant(Y) & eats(X, Y))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(125,plain,
% 0.22/0.43 (![X: $i] : ((caterpillar(X) | snail(X)) => ?[Y: $i] : (plant(Y) & eats(X, Y))) <=> ![X: $i] : ((~(caterpillar(X) | snail(X))) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[124])).
% 0.22/0.43 tff(126,axiom,(![X: $i] : ((caterpillar(X) | snail(X)) => ?[Y: $i] : (plant(Y) & eats(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_14')).
% 0.22/0.43 tff(127,plain,
% 0.22/0.43 (![X: $i] : ((~(caterpillar(X) | snail(X))) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.22/0.43 tff(128,plain,
% 0.22/0.43 (![X: $i] : ((~(caterpillar(X) | snail(X))) | ?[Y: $i] : (plant(Y) & eats(X, Y)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.22/0.43 tff(129,plain,(
% 0.22/0.43 ![X: $i] : ((~(caterpillar(X) | snail(X))) | (plant(tptp_fun_Y_6(X)) & eats(X, tptp_fun_Y_6(X))))),
% 0.22/0.43 inference(skolemize,[status(sab)],[128])).
% 0.22/0.43 tff(130,plain,
% 0.22/0.43 (![X: $i] : ((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[129, 122])).
% 0.22/0.43 tff(131,plain,
% 0.22/0.43 (![X: $i] : ((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[130, 120])).
% 0.22/0.43 tff(132,plain,
% 0.22/0.43 (((~![X: $i] : ((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | ((~(caterpillar(X1!4) | snail(X1!4))) | (~((~plant(tptp_fun_Y_6(X1!4))) | (~eats(X1!4, tptp_fun_Y_6(X1!4))))))) <=> ((~![X: $i] : ((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | (~(caterpillar(X1!4) | snail(X1!4))) | (~((~plant(tptp_fun_Y_6(X1!4))) | (~eats(X1!4, tptp_fun_Y_6(X1!4))))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(133,plain,
% 0.22/0.43 ((~![X: $i] : ((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | ((~(caterpillar(X1!4) | snail(X1!4))) | (~((~plant(tptp_fun_Y_6(X1!4))) | (~eats(X1!4, tptp_fun_Y_6(X1!4))))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(134,plain,
% 0.22/0.43 ((~![X: $i] : ((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | (~(caterpillar(X1!4) | snail(X1!4))) | (~((~plant(tptp_fun_Y_6(X1!4))) | (~eats(X1!4, tptp_fun_Y_6(X1!4)))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.22/0.43 tff(135,plain,
% 0.22/0.43 (~((~plant(tptp_fun_Y_6(X1!4))) | (~eats(X1!4, tptp_fun_Y_6(X1!4))))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[134, 131, 96])).
% 0.22/0.43 tff(136,plain,
% 0.22/0.43 (((~plant(tptp_fun_Y_6(X1!4))) | (~eats(X1!4, tptp_fun_Y_6(X1!4)))) | eats(X1!4, tptp_fun_Y_6(X1!4))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(137,plain,
% 0.22/0.43 (eats(X1!4, tptp_fun_Y_6(X1!4))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.22/0.43 tff(138,plain,
% 0.22/0.43 (((~plant(tptp_fun_Y_6(X1!4))) | (~eats(X1!4, tptp_fun_Y_6(X1!4)))) | plant(tptp_fun_Y_6(X1!4))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(139,plain,
% 0.22/0.43 (plant(tptp_fun_Y_6(X1!4))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[138, 135])).
% 0.22/0.43 tff(140,plain,
% 0.22/0.43 (((~![Z: $i] : ((~plant(Z)) | (~eats(X1!4, Z)))) | ((~plant(tptp_fun_Y_6(X1!4))) | (~eats(X1!4, tptp_fun_Y_6(X1!4))))) <=> ((~![Z: $i] : ((~plant(Z)) | (~eats(X1!4, Z)))) | (~plant(tptp_fun_Y_6(X1!4))) | (~eats(X1!4, tptp_fun_Y_6(X1!4))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(141,plain,
% 0.22/0.43 ((~![Z: $i] : ((~plant(Z)) | (~eats(X1!4, Z)))) | ((~plant(tptp_fun_Y_6(X1!4))) | (~eats(X1!4, tptp_fun_Y_6(X1!4))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(142,plain,
% 0.22/0.43 ((~![Z: $i] : ((~plant(Z)) | (~eats(X1!4, Z)))) | (~plant(tptp_fun_Y_6(X1!4))) | (~eats(X1!4, tptp_fun_Y_6(X1!4)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.22/0.43 tff(143,plain,
% 0.22/0.43 ($false),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[142, 139, 137, 118])).
% 0.22/0.43 tff(144,plain,(~![Z: $i] : ((~plant(Z)) | (~eats(X1!4, Z)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.43 tff(145,assumption,(![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!2, Y1) | (~much_smaller(Y1, X1!2)))), introduced(assumption)).
% 0.22/0.43 tff(146,plain,
% 0.22/0.43 (^[X: $i] : refl((animal(X) | (~snail(X))) <=> (animal(X) | (~snail(X))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(147,plain,
% 0.22/0.43 (![X: $i] : (animal(X) | (~snail(X))) <=> ![X: $i] : (animal(X) | (~snail(X)))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[146])).
% 0.22/0.43 tff(148,plain,
% 0.22/0.43 (![X: $i] : (animal(X) | (~snail(X))) <=> ![X: $i] : (animal(X) | (~snail(X)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(149,plain,
% 0.22/0.43 (^[X: $i] : rewrite((snail(X) => animal(X)) <=> (animal(X) | (~snail(X))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(150,plain,
% 0.22/0.43 (![X: $i] : (snail(X) => animal(X)) <=> ![X: $i] : (animal(X) | (~snail(X)))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[149])).
% 0.22/0.43 tff(151,axiom,(![X: $i] : (snail(X) => animal(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_5_1')).
% 0.22/0.43 tff(152,plain,
% 0.22/0.43 (![X: $i] : (animal(X) | (~snail(X)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.22/0.43 tff(153,plain,
% 0.22/0.43 (![X: $i] : (animal(X) | (~snail(X)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[152, 148])).
% 0.22/0.43 tff(154,plain,(
% 0.22/0.43 ![X: $i] : (animal(X) | (~snail(X)))),
% 0.22/0.43 inference(skolemize,[status(sab)],[153])).
% 0.22/0.43 tff(155,plain,
% 0.22/0.43 (![X: $i] : (animal(X) | (~snail(X)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[154, 147])).
% 0.22/0.43 tff(156,plain,
% 0.22/0.43 (((~![X: $i] : (animal(X) | (~snail(X)))) | (animal(X1!4) | (~snail(X1!4)))) <=> ((~![X: $i] : (animal(X) | (~snail(X)))) | animal(X1!4) | (~snail(X1!4)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(157,plain,
% 0.22/0.43 ((~![X: $i] : (animal(X) | (~snail(X)))) | (animal(X1!4) | (~snail(X1!4)))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(158,plain,
% 0.22/0.43 ((~![X: $i] : (animal(X) | (~snail(X)))) | animal(X1!4) | (~snail(X1!4))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.22/0.43 tff(159,plain,
% 0.22/0.43 (animal(X1!4)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[158, 155, 85])).
% 0.22/0.43 tff(160,plain,
% 0.22/0.43 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!2, Y1) | (~much_smaller(Y1, X1!2)))) | ((~animal(X1!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!4, Z))) | eats(X1!2, X1!4) | (~much_smaller(X1!4, X1!2)))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!2, Y1) | (~much_smaller(Y1, X1!2)))) | (~animal(X1!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!4, Z))) | eats(X1!2, X1!4) | (~much_smaller(X1!4, X1!2)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(161,plain,
% 0.22/0.43 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!2, Y1) | (~much_smaller(Y1, X1!2)))) | ((~animal(X1!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!4, Z))) | eats(X1!2, X1!4) | (~much_smaller(X1!4, X1!2)))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(162,plain,
% 0.22/0.43 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!2, Y1) | (~much_smaller(Y1, X1!2)))) | (~animal(X1!4)) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!4, Z))) | eats(X1!2, X1!4) | (~much_smaller(X1!4, X1!2))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.22/0.43 tff(163,plain,
% 0.22/0.43 ($false),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[162, 159, 145, 144, 117, 93])).
% 0.22/0.43 tff(164,plain,(~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!2, Y1) | (~much_smaller(Y1, X1!2)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.43 tff(165,plain,
% 0.22/0.43 (^[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))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(166,plain,
% 0.22/0.43 (![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)))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[165])).
% 0.22/0.43 tff(167,plain,
% 0.22/0.43 (^[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))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(168,plain,
% 0.22/0.43 (![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)))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[167])).
% 0.22/0.43 tff(169,plain,
% 0.22/0.43 (^[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))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(170,plain,
% 0.22/0.43 (![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)))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[169])).
% 0.22/0.43 tff(171,plain,
% 0.22/0.43 (![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)))))),
% 0.22/0.43 inference(transitivity,[status(thm)],[170, 168])).
% 0.22/0.43 tff(172,plain,
% 0.22/0.43 (^[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)))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(173,plain,
% 0.22/0.43 (![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)))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[172])).
% 0.22/0.43 tff(174,plain,
% 0.22/0.43 (^[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)))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(175,plain,
% 0.22/0.44 (![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)))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[174])).
% 0.22/0.44 tff(176,plain,
% 0.22/0.44 (![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)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(177,plain,
% 0.22/0.44 (^[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)))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(178,plain,
% 0.22/0.44 (![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)))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[177])).
% 0.22/0.44 tff(179,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')).
% 0.22/0.44 tff(180,plain,
% 0.22/0.44 (![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)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.22/0.44 tff(181,plain,
% 0.22/0.44 (![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)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[180, 176])).
% 0.22/0.44 tff(182,plain,(
% 0.22/0.44 ![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)))),
% 0.22/0.44 inference(skolemize,[status(sab)],[181])).
% 0.22/0.44 tff(183,plain,
% 0.22/0.44 (![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)))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[182, 175])).
% 0.22/0.44 tff(184,plain,
% 0.22/0.44 (![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)))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[183, 173])).
% 0.22/0.44 tff(185,plain,
% 0.22/0.44 (![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)))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[184, 171])).
% 0.22/0.44 tff(186,plain,
% 0.22/0.44 (![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[185, 166])).
% 0.22/0.44 tff(187,plain,
% 0.22/0.44 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(X1!2)) | ![Y: $i] : ((~plant(Y)) | eats(X1!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!2, Y1) | (~much_smaller(Y1, X1!2))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(X1!2)) | ![Y: $i] : ((~plant(Y)) | eats(X1!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!2, Y1) | (~much_smaller(Y1, X1!2))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(188,plain,
% 0.22/0.44 (((~animal(X1!2)) | ![Y: $i] : ((~plant(Y)) | eats(X1!2, Y)) | ![Y1: $i] : (eats(X1!2, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X1!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> ((~animal(X1!2)) | ![Y: $i] : ((~plant(Y)) | eats(X1!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!2, Y1) | (~much_smaller(Y1, X1!2))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(189,plain,
% 0.22/0.44 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(X1!2)) | ![Y: $i] : ((~plant(Y)) | eats(X1!2, Y)) | ![Y1: $i] : (eats(X1!2, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X1!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(X1!2)) | ![Y: $i] : ((~plant(Y)) | eats(X1!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!2, Y1) | (~much_smaller(Y1, X1!2)))))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[188])).
% 0.22/0.44 tff(190,plain,
% 0.22/0.44 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(X1!2)) | ![Y: $i] : ((~plant(Y)) | eats(X1!2, Y)) | ![Y1: $i] : (eats(X1!2, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X1!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(X1!2)) | ![Y: $i] : ((~plant(Y)) | eats(X1!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!2, Y1) | (~much_smaller(Y1, X1!2))))),
% 0.22/0.44 inference(transitivity,[status(thm)],[189, 187])).
% 0.22/0.44 tff(191,plain,
% 0.22/0.44 ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(X1!2)) | ![Y: $i] : ((~plant(Y)) | eats(X1!2, Y)) | ![Y1: $i] : (eats(X1!2, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X1!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(192,plain,
% 0.22/0.44 ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(X1!2)) | ![Y: $i] : ((~plant(Y)) | eats(X1!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!2, Y1) | (~much_smaller(Y1, X1!2)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.22/0.44 tff(193,plain,
% 0.22/0.44 (![Y: $i] : ((~plant(Y)) | eats(X1!2, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!2, Y1) | (~much_smaller(Y1, X1!2)))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[192, 186, 18])).
% 0.22/0.44 tff(194,plain,
% 0.22/0.44 (![Y: $i] : ((~plant(Y)) | eats(X1!2, Y))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[193, 164])).
% 0.22/0.44 tff(195,plain,
% 0.22/0.44 (^[X1: $i] : refl((plant(X1) | (~grain(X1))) <=> (plant(X1) | (~grain(X1))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(196,plain,
% 0.22/0.44 (![X1: $i] : (plant(X1) | (~grain(X1))) <=> ![X1: $i] : (plant(X1) | (~grain(X1)))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[195])).
% 0.22/0.44 tff(197,plain,
% 0.22/0.44 (![X1: $i] : (plant(X1) | (~grain(X1))) <=> ![X1: $i] : (plant(X1) | (~grain(X1)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(198,plain,
% 0.22/0.44 (^[X1: $i] : rewrite((grain(X1) => plant(X1)) <=> (plant(X1) | (~grain(X1))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(199,plain,
% 0.22/0.44 (![X1: $i] : (grain(X1) => plant(X1)) <=> ![X1: $i] : (plant(X1) | (~grain(X1)))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[198])).
% 0.22/0.44 tff(200,axiom,(![X1: $i] : (grain(X1) => plant(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_6_2')).
% 0.22/0.44 tff(201,plain,
% 0.22/0.44 (![X1: $i] : (plant(X1) | (~grain(X1)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.22/0.44 tff(202,plain,
% 0.22/0.44 (![X1: $i] : (plant(X1) | (~grain(X1)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[201, 197])).
% 0.22/0.44 tff(203,plain,(
% 0.22/0.44 ![X1: $i] : (plant(X1) | (~grain(X1)))),
% 0.22/0.44 inference(skolemize,[status(sab)],[202])).
% 0.22/0.44 tff(204,plain,
% 0.22/0.44 (![X1: $i] : (plant(X1) | (~grain(X1)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[203, 196])).
% 0.22/0.44 tff(205,plain,
% 0.22/0.44 (?[X: $i] : grain(X) <=> ?[X: $i] : grain(X)),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(206,axiom,(?[X: $i] : grain(X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_6_1')).
% 0.22/0.44 tff(207,plain,
% 0.22/0.44 (?[X: $i] : grain(X)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.22/0.44 tff(208,plain,(
% 0.22/0.44 grain(X!5)),
% 0.22/0.44 inference(skolemize,[status(sab)],[207])).
% 0.22/0.44 tff(209,plain,
% 0.22/0.44 (((~![X1: $i] : (plant(X1) | (~grain(X1)))) | (plant(X!5) | (~grain(X!5)))) <=> ((~![X1: $i] : (plant(X1) | (~grain(X1)))) | plant(X!5) | (~grain(X!5)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(210,plain,
% 0.22/0.44 ((~![X1: $i] : (plant(X1) | (~grain(X1)))) | (plant(X!5) | (~grain(X!5)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(211,plain,
% 0.22/0.44 ((~![X1: $i] : (plant(X1) | (~grain(X1)))) | plant(X!5) | (~grain(X!5))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.22/0.44 tff(212,plain,
% 0.22/0.44 (plant(X!5)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[211, 208, 204])).
% 0.22/0.44 tff(213,plain,
% 0.22/0.44 (((~![Y: $i] : ((~plant(Y)) | eats(X1!2, Y))) | ((~plant(X!5)) | eats(X1!2, X!5))) <=> ((~![Y: $i] : ((~plant(Y)) | eats(X1!2, Y))) | (~plant(X!5)) | eats(X1!2, X!5))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(214,plain,
% 0.22/0.44 ((~![Y: $i] : ((~plant(Y)) | eats(X1!2, Y))) | ((~plant(X!5)) | eats(X1!2, X!5))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(215,plain,
% 0.22/0.44 ((~![Y: $i] : ((~plant(Y)) | eats(X1!2, Y))) | (~plant(X!5)) | eats(X1!2, X!5)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.22/0.44 tff(216,plain,
% 0.22/0.44 (eats(X1!2, X!5)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[215, 212, 194])).
% 0.22/0.44 tff(217,assumption,(~eats(X1!2, tptp_fun_Y_6(X1!3))), introduced(assumption)).
% 0.22/0.44 tff(218,assumption,(![Y: $i] : ((~plant(Y)) | eats(X1!2, Y))), introduced(assumption)).
% 0.22/0.44 tff(219,plain,
% 0.22/0.44 (?[X1: $i] : caterpillar(X1) <=> ?[X1: $i] : caterpillar(X1)),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(220,axiom,(?[X1: $i] : caterpillar(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_4_2')).
% 0.22/0.44 tff(221,plain,
% 0.22/0.44 (?[X1: $i] : caterpillar(X1)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.22/0.44 tff(222,plain,(
% 0.22/0.44 caterpillar(X1!3)),
% 0.22/0.44 inference(skolemize,[status(sab)],[221])).
% 0.22/0.44 tff(223,plain,
% 0.22/0.44 ((caterpillar(X1!3) | snail(X1!3)) | (~caterpillar(X1!3))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(224,plain,
% 0.22/0.44 (caterpillar(X1!3) | snail(X1!3)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[223, 222])).
% 0.22/0.44 tff(225,plain,
% 0.22/0.44 (((~![X: $i] : ((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | ((~(caterpillar(X1!3) | snail(X1!3))) | (~((~plant(tptp_fun_Y_6(X1!3))) | (~eats(X1!3, tptp_fun_Y_6(X1!3))))))) <=> ((~![X: $i] : ((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | (~(caterpillar(X1!3) | snail(X1!3))) | (~((~plant(tptp_fun_Y_6(X1!3))) | (~eats(X1!3, tptp_fun_Y_6(X1!3))))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(226,plain,
% 0.22/0.44 ((~![X: $i] : ((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | ((~(caterpillar(X1!3) | snail(X1!3))) | (~((~plant(tptp_fun_Y_6(X1!3))) | (~eats(X1!3, tptp_fun_Y_6(X1!3))))))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(227,plain,
% 0.22/0.44 ((~![X: $i] : ((~(caterpillar(X) | snail(X))) | (~((~plant(tptp_fun_Y_6(X))) | (~eats(X, tptp_fun_Y_6(X))))))) | (~(caterpillar(X1!3) | snail(X1!3))) | (~((~plant(tptp_fun_Y_6(X1!3))) | (~eats(X1!3, tptp_fun_Y_6(X1!3)))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.22/0.44 tff(228,plain,
% 0.22/0.44 (~((~plant(tptp_fun_Y_6(X1!3))) | (~eats(X1!3, tptp_fun_Y_6(X1!3))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[227, 131, 224])).
% 0.22/0.44 tff(229,plain,
% 0.22/0.44 (((~plant(tptp_fun_Y_6(X1!3))) | (~eats(X1!3, tptp_fun_Y_6(X1!3)))) | plant(tptp_fun_Y_6(X1!3))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(230,plain,
% 0.22/0.44 (plant(tptp_fun_Y_6(X1!3))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[229, 228])).
% 0.22/0.44 tff(231,plain,
% 0.22/0.44 (((~![Y: $i] : ((~plant(Y)) | eats(X1!2, Y))) | ((~plant(tptp_fun_Y_6(X1!3))) | eats(X1!2, tptp_fun_Y_6(X1!3)))) <=> ((~![Y: $i] : ((~plant(Y)) | eats(X1!2, Y))) | (~plant(tptp_fun_Y_6(X1!3))) | eats(X1!2, tptp_fun_Y_6(X1!3)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(232,plain,
% 0.22/0.44 ((~![Y: $i] : ((~plant(Y)) | eats(X1!2, Y))) | ((~plant(tptp_fun_Y_6(X1!3))) | eats(X1!2, tptp_fun_Y_6(X1!3)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(233,plain,
% 0.22/0.44 ((~![Y: $i] : ((~plant(Y)) | eats(X1!2, Y))) | (~plant(tptp_fun_Y_6(X1!3))) | eats(X1!2, tptp_fun_Y_6(X1!3))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.22/0.44 tff(234,plain,
% 0.22/0.44 ($false),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[233, 230, 218, 217])).
% 0.22/0.44 tff(235,plain,((~![Y: $i] : ((~plant(Y)) | eats(X1!2, Y))) | eats(X1!2, tptp_fun_Y_6(X1!3))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.44 tff(236,plain,
% 0.22/0.44 (eats(X1!2, tptp_fun_Y_6(X1!3))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[235, 194])).
% 0.22/0.44 tff(237,assumption,(![Z: $i] : ((~plant(Z)) | (~eats(X1!2, Z)))), introduced(assumption)).
% 0.22/0.44 tff(238,plain,
% 0.22/0.44 (((~![Z: $i] : ((~plant(Z)) | (~eats(X1!2, Z)))) | ((~plant(tptp_fun_Y_6(X1!3))) | (~eats(X1!2, tptp_fun_Y_6(X1!3))))) <=> ((~![Z: $i] : ((~plant(Z)) | (~eats(X1!2, Z)))) | (~plant(tptp_fun_Y_6(X1!3))) | (~eats(X1!2, tptp_fun_Y_6(X1!3))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(239,plain,
% 0.22/0.44 ((~![Z: $i] : ((~plant(Z)) | (~eats(X1!2, Z)))) | ((~plant(tptp_fun_Y_6(X1!3))) | (~eats(X1!2, tptp_fun_Y_6(X1!3))))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(240,plain,
% 0.22/0.44 ((~![Z: $i] : ((~plant(Z)) | (~eats(X1!2, Z)))) | (~plant(tptp_fun_Y_6(X1!3))) | (~eats(X1!2, tptp_fun_Y_6(X1!3)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.22/0.44 tff(241,plain,
% 0.22/0.44 ($false),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[240, 230, 237, 236])).
% 0.22/0.45 tff(242,plain,(~![Z: $i] : ((~plant(Z)) | (~eats(X1!2, Z)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.45 tff(243,assumption,(~much_smaller(X1!2, X1!1)), introduced(assumption)).
% 0.22/0.45 tff(244,plain,
% 0.22/0.45 (^[X: $i, Y: $i] : refl((much_smaller(X, Y) | (~fox(Y)) | (~bird(X))) <=> (much_smaller(X, Y) | (~fox(Y)) | (~bird(X))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(245,plain,
% 0.22/0.45 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X))) <=> ![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[244])).
% 0.22/0.45 tff(246,plain,
% 0.22/0.45 (^[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)))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(247,plain,
% 0.22/0.45 (![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y)) <=> ![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[246])).
% 0.22/0.45 tff(248,plain,
% 0.22/0.45 (![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y)) <=> ![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(249,plain,
% 0.22/0.45 (^[X: $i, Y: $i] : rewrite(((bird(X) & fox(Y)) => much_smaller(X, Y)) <=> ((~(bird(X) & fox(Y))) | much_smaller(X, Y)))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(250,plain,
% 0.22/0.45 (![X: $i, Y: $i] : ((bird(X) & fox(Y)) => much_smaller(X, Y)) <=> ![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[249])).
% 0.22/0.45 tff(251,axiom,(![X: $i, Y: $i] : ((bird(X) & fox(Y)) => much_smaller(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_9')).
% 0.22/0.45 tff(252,plain,
% 0.22/0.45 (![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.22/0.45 tff(253,plain,
% 0.22/0.45 (![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[252, 248])).
% 0.22/0.45 tff(254,plain,(
% 0.22/0.45 ![X: $i, Y: $i] : ((~(bird(X) & fox(Y))) | much_smaller(X, Y))),
% 0.22/0.45 inference(skolemize,[status(sab)],[253])).
% 0.22/0.45 tff(255,plain,
% 0.22/0.45 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[254, 247])).
% 0.22/0.45 tff(256,plain,
% 0.22/0.45 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[255, 245])).
% 0.22/0.45 tff(257,plain,
% 0.22/0.45 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | ((~fox(X1!1)) | (~bird(X1!2)) | much_smaller(X1!2, X1!1))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (~fox(X1!1)) | (~bird(X1!2)) | much_smaller(X1!2, X1!1))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(258,plain,
% 0.22/0.45 ((much_smaller(X1!2, X1!1) | (~fox(X1!1)) | (~bird(X1!2))) <=> ((~fox(X1!1)) | (~bird(X1!2)) | much_smaller(X1!2, X1!1))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(259,plain,
% 0.22/0.45 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (much_smaller(X1!2, X1!1) | (~fox(X1!1)) | (~bird(X1!2)))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | ((~fox(X1!1)) | (~bird(X1!2)) | much_smaller(X1!2, X1!1)))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[258])).
% 0.22/0.45 tff(260,plain,
% 0.22/0.45 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (much_smaller(X1!2, X1!1) | (~fox(X1!1)) | (~bird(X1!2)))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (~fox(X1!1)) | (~bird(X1!2)) | much_smaller(X1!2, X1!1))),
% 0.22/0.45 inference(transitivity,[status(thm)],[259, 257])).
% 0.22/0.45 tff(261,plain,
% 0.22/0.45 ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (much_smaller(X1!2, X1!1) | (~fox(X1!1)) | (~bird(X1!2)))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(262,plain,
% 0.22/0.45 ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~fox(Y)) | (~bird(X)))) | (~fox(X1!1)) | (~bird(X1!2)) | much_smaller(X1!2, X1!1)),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.22/0.45 tff(263,plain,
% 0.22/0.45 ($false),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[262, 22, 4, 256, 243])).
% 0.22/0.45 tff(264,plain,(much_smaller(X1!2, X1!1)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.45 tff(265,plain,
% 0.22/0.45 ((fox(X1!1) | grain(X1!1)) | (~fox(X1!1))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(266,plain,
% 0.22/0.45 (fox(X1!1) | grain(X1!1)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[265, 22])).
% 0.22/0.45 tff(267,assumption,(eats(X1!0, X1!1)), introduced(assumption)).
% 0.22/0.45 tff(268,plain,
% 0.22/0.45 (^[X: $i, Y: $i] : refl(((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y)))) <=> ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y)))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(269,plain,
% 0.22/0.45 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y)))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[268])).
% 0.22/0.45 tff(270,plain,
% 0.22/0.45 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((wolf(X) & (fox(Y) | grain(Y))) <=> (~((~wolf(X)) | (~(fox(Y) | grain(Y)))))), ((~(wolf(X) & (fox(Y) | grain(Y)))) <=> (~(~((~wolf(X)) | (~(fox(Y) | grain(Y)))))))), rewrite((~(~((~wolf(X)) | (~(fox(Y) | grain(Y)))))) <=> ((~wolf(X)) | (~(fox(Y) | grain(Y))))), ((~(wolf(X) & (fox(Y) | grain(Y)))) <=> ((~wolf(X)) | (~(fox(Y) | grain(Y)))))), (((~eats(X, Y)) | (~(wolf(X) & (fox(Y) | grain(Y))))) <=> ((~eats(X, Y)) | ((~wolf(X)) | (~(fox(Y) | grain(Y))))))), rewrite(((~eats(X, Y)) | ((~wolf(X)) | (~(fox(Y) | grain(Y))))) <=> ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))), (((~eats(X, Y)) | (~(wolf(X) & (fox(Y) | grain(Y))))) <=> ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(271,plain,
% 0.22/0.45 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & (fox(Y) | grain(Y))))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[270])).
% 0.22/0.45 tff(272,plain,
% 0.22/0.45 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & (fox(Y) | grain(Y))))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & (fox(Y) | grain(Y)))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(273,plain,
% 0.22/0.45 (^[X: $i, Y: $i] : rewrite(((wolf(X) & (fox(Y) | grain(Y))) => (~eats(X, Y))) <=> ((~eats(X, Y)) | (~(wolf(X) & (fox(Y) | grain(Y))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(274,plain,
% 0.22/0.45 (![X: $i, Y: $i] : ((wolf(X) & (fox(Y) | grain(Y))) => (~eats(X, Y))) <=> ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & (fox(Y) | grain(Y)))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[273])).
% 0.22/0.45 tff(275,axiom,(![X: $i, Y: $i] : ((wolf(X) & (fox(Y) | grain(Y))) => (~eats(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_11')).
% 0.22/0.45 tff(276,plain,
% 0.22/0.45 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & (fox(Y) | grain(Y)))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.22/0.45 tff(277,plain,
% 0.22/0.45 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & (fox(Y) | grain(Y)))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[276, 272])).
% 0.22/0.45 tff(278,plain,(
% 0.22/0.45 ![X: $i, Y: $i] : ((~eats(X, Y)) | (~(wolf(X) & (fox(Y) | grain(Y)))))),
% 0.22/0.45 inference(skolemize,[status(sab)],[277])).
% 0.22/0.45 tff(279,plain,
% 0.22/0.45 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[278, 271])).
% 0.22/0.45 tff(280,plain,
% 0.22/0.45 (![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[279, 269])).
% 0.22/0.45 tff(281,plain,
% 0.22/0.45 (?[X1: $i] : wolf(X1) <=> ?[X1: $i] : wolf(X1)),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(282,axiom,(?[X1: $i] : wolf(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_1_2')).
% 0.22/0.45 tff(283,plain,
% 0.22/0.45 (?[X1: $i] : wolf(X1)),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.22/0.45 tff(284,plain,(
% 0.22/0.45 wolf(X1!0)),
% 0.22/0.45 inference(skolemize,[status(sab)],[283])).
% 0.22/0.45 tff(285,plain,
% 0.22/0.45 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | ((~wolf(X1!0)) | (~eats(X1!0, X1!1)) | (~(fox(X1!1) | grain(X1!1))))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | (~wolf(X1!0)) | (~eats(X1!0, X1!1)) | (~(fox(X1!1) | grain(X1!1))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(286,plain,
% 0.22/0.45 (((~eats(X1!0, X1!1)) | (~wolf(X1!0)) | (~(fox(X1!1) | grain(X1!1)))) <=> ((~wolf(X1!0)) | (~eats(X1!0, X1!1)) | (~(fox(X1!1) | grain(X1!1))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(287,plain,
% 0.22/0.45 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | ((~eats(X1!0, X1!1)) | (~wolf(X1!0)) | (~(fox(X1!1) | grain(X1!1))))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | ((~wolf(X1!0)) | (~eats(X1!0, X1!1)) | (~(fox(X1!1) | grain(X1!1)))))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[286])).
% 0.22/0.45 tff(288,plain,
% 0.22/0.45 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | ((~eats(X1!0, X1!1)) | (~wolf(X1!0)) | (~(fox(X1!1) | grain(X1!1))))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | (~wolf(X1!0)) | (~eats(X1!0, X1!1)) | (~(fox(X1!1) | grain(X1!1))))),
% 0.22/0.45 inference(transitivity,[status(thm)],[287, 285])).
% 0.22/0.45 tff(289,plain,
% 0.22/0.45 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | ((~eats(X1!0, X1!1)) | (~wolf(X1!0)) | (~(fox(X1!1) | grain(X1!1))))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(290,plain,
% 0.22/0.45 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | (~wolf(X1!0)) | (~eats(X1!0, X1!1)) | (~(fox(X1!1) | grain(X1!1)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.22/0.45 tff(291,plain,
% 0.22/0.45 ($false),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[290, 284, 280, 267, 266])).
% 0.22/0.45 tff(292,plain,(~eats(X1!0, X1!1)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.45 tff(293,assumption,(~much_smaller(X1!1, X1!0)), introduced(assumption)).
% 0.22/0.45 tff(294,plain,
% 0.22/0.45 (^[X: $i, Y: $i] : refl((much_smaller(X, Y) | (~wolf(Y)) | (~fox(X))) <=> (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(295,plain,
% 0.22/0.45 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X))) <=> ![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[294])).
% 0.22/0.45 tff(296,plain,
% 0.22/0.45 (^[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)))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(297,plain,
% 0.22/0.45 (![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y)) <=> ![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[296])).
% 0.22/0.45 tff(298,plain,
% 0.22/0.45 (![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y)) <=> ![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(299,plain,
% 0.22/0.45 (^[X: $i, Y: $i] : rewrite(((fox(X) & wolf(Y)) => much_smaller(X, Y)) <=> ((~(fox(X) & wolf(Y))) | much_smaller(X, Y)))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(300,plain,
% 0.22/0.45 (![X: $i, Y: $i] : ((fox(X) & wolf(Y)) => much_smaller(X, Y)) <=> ![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[299])).
% 0.22/0.45 tff(301,axiom,(![X: $i, Y: $i] : ((fox(X) & wolf(Y)) => much_smaller(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_10')).
% 0.22/0.45 tff(302,plain,
% 0.22/0.45 (![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.22/0.45 tff(303,plain,
% 0.22/0.45 (![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[302, 298])).
% 0.22/0.45 tff(304,plain,(
% 0.22/0.45 ![X: $i, Y: $i] : ((~(fox(X) & wolf(Y))) | much_smaller(X, Y))),
% 0.22/0.45 inference(skolemize,[status(sab)],[303])).
% 0.22/0.45 tff(305,plain,
% 0.22/0.45 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[304, 297])).
% 0.22/0.45 tff(306,plain,
% 0.22/0.45 (![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[305, 295])).
% 0.22/0.45 tff(307,plain,
% 0.22/0.45 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | ((~wolf(X1!0)) | (~fox(X1!1)) | much_smaller(X1!1, X1!0))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (~wolf(X1!0)) | (~fox(X1!1)) | much_smaller(X1!1, X1!0))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(308,plain,
% 0.22/0.45 ((much_smaller(X1!1, X1!0) | (~wolf(X1!0)) | (~fox(X1!1))) <=> ((~wolf(X1!0)) | (~fox(X1!1)) | much_smaller(X1!1, X1!0))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(309,plain,
% 0.22/0.45 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (much_smaller(X1!1, X1!0) | (~wolf(X1!0)) | (~fox(X1!1)))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | ((~wolf(X1!0)) | (~fox(X1!1)) | much_smaller(X1!1, X1!0)))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[308])).
% 0.22/0.45 tff(310,plain,
% 0.22/0.45 (((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (much_smaller(X1!1, X1!0) | (~wolf(X1!0)) | (~fox(X1!1)))) <=> ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (~wolf(X1!0)) | (~fox(X1!1)) | much_smaller(X1!1, X1!0))),
% 0.22/0.45 inference(transitivity,[status(thm)],[309, 307])).
% 0.22/0.45 tff(311,plain,
% 0.22/0.45 ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (much_smaller(X1!1, X1!0) | (~wolf(X1!0)) | (~fox(X1!1)))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(312,plain,
% 0.22/0.45 ((~![X: $i, Y: $i] : (much_smaller(X, Y) | (~wolf(Y)) | (~fox(X)))) | (~wolf(X1!0)) | (~fox(X1!1)) | much_smaller(X1!1, X1!0)),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[311, 310])).
% 0.22/0.45 tff(313,plain,
% 0.22/0.45 ($false),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[312, 284, 22, 306, 293])).
% 0.22/0.45 tff(314,plain,(much_smaller(X1!1, X1!0)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.45 tff(315,plain,
% 0.22/0.45 ((fox(X!5) | grain(X!5)) | (~grain(X!5))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(316,plain,
% 0.22/0.45 (fox(X!5) | grain(X!5)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[315, 208])).
% 0.22/0.45 tff(317,assumption,(eats(X1!0, X!5)), introduced(assumption)).
% 0.22/0.45 tff(318,plain,
% 0.22/0.45 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | ((~wolf(X1!0)) | (~eats(X1!0, X!5)) | (~(fox(X!5) | grain(X!5))))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | (~wolf(X1!0)) | (~eats(X1!0, X!5)) | (~(fox(X!5) | grain(X!5))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(319,plain,
% 0.22/0.45 (((~eats(X1!0, X!5)) | (~wolf(X1!0)) | (~(fox(X!5) | grain(X!5)))) <=> ((~wolf(X1!0)) | (~eats(X1!0, X!5)) | (~(fox(X!5) | grain(X!5))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(320,plain,
% 0.22/0.45 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | ((~eats(X1!0, X!5)) | (~wolf(X1!0)) | (~(fox(X!5) | grain(X!5))))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | ((~wolf(X1!0)) | (~eats(X1!0, X!5)) | (~(fox(X!5) | grain(X!5)))))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[319])).
% 0.22/0.45 tff(321,plain,
% 0.22/0.45 (((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | ((~eats(X1!0, X!5)) | (~wolf(X1!0)) | (~(fox(X!5) | grain(X!5))))) <=> ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | (~wolf(X1!0)) | (~eats(X1!0, X!5)) | (~(fox(X!5) | grain(X!5))))),
% 0.22/0.45 inference(transitivity,[status(thm)],[320, 318])).
% 0.22/0.45 tff(322,plain,
% 0.22/0.45 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | ((~eats(X1!0, X!5)) | (~wolf(X1!0)) | (~(fox(X!5) | grain(X!5))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(323,plain,
% 0.22/0.46 ((~![X: $i, Y: $i] : ((~eats(X, Y)) | (~wolf(X)) | (~(fox(Y) | grain(Y))))) | (~wolf(X1!0)) | (~eats(X1!0, X!5)) | (~(fox(X!5) | grain(X!5)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[322, 321])).
% 0.22/0.46 tff(324,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[323, 284, 280, 317, 316])).
% 0.22/0.46 tff(325,plain,(~eats(X1!0, X!5)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.46 tff(326,assumption,(![Y: $i] : ((~plant(Y)) | eats(X1!0, Y))), introduced(assumption)).
% 0.22/0.46 tff(327,plain,
% 0.22/0.46 (((~![Y: $i] : ((~plant(Y)) | eats(X1!0, Y))) | ((~plant(X!5)) | eats(X1!0, X!5))) <=> ((~![Y: $i] : ((~plant(Y)) | eats(X1!0, Y))) | (~plant(X!5)) | eats(X1!0, X!5))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(328,plain,
% 0.22/0.46 ((~![Y: $i] : ((~plant(Y)) | eats(X1!0, Y))) | ((~plant(X!5)) | eats(X1!0, X!5))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(329,plain,
% 0.22/0.46 ((~![Y: $i] : ((~plant(Y)) | eats(X1!0, Y))) | (~plant(X!5)) | eats(X1!0, X!5)),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[328, 327])).
% 0.22/0.46 tff(330,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[329, 212, 326, 325])).
% 0.22/0.46 tff(331,plain,(~![Y: $i] : ((~plant(Y)) | eats(X1!0, Y))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.46 tff(332,plain,
% 0.22/0.46 (^[X: $i] : refl((animal(X) | (~wolf(X))) <=> (animal(X) | (~wolf(X))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(333,plain,
% 0.22/0.46 (![X: $i] : (animal(X) | (~wolf(X))) <=> ![X: $i] : (animal(X) | (~wolf(X)))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[332])).
% 0.22/0.46 tff(334,plain,
% 0.22/0.46 (![X: $i] : (animal(X) | (~wolf(X))) <=> ![X: $i] : (animal(X) | (~wolf(X)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(335,plain,
% 0.22/0.46 (^[X: $i] : rewrite((wolf(X) => animal(X)) <=> (animal(X) | (~wolf(X))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(336,plain,
% 0.22/0.46 (![X: $i] : (wolf(X) => animal(X)) <=> ![X: $i] : (animal(X) | (~wolf(X)))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[335])).
% 0.22/0.46 tff(337,axiom,(![X: $i] : (wolf(X) => animal(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel47_1_1')).
% 0.22/0.46 tff(338,plain,
% 0.22/0.46 (![X: $i] : (animal(X) | (~wolf(X)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.22/0.46 tff(339,plain,
% 0.22/0.46 (![X: $i] : (animal(X) | (~wolf(X)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[338, 334])).
% 0.22/0.46 tff(340,plain,(
% 0.22/0.46 ![X: $i] : (animal(X) | (~wolf(X)))),
% 0.22/0.46 inference(skolemize,[status(sab)],[339])).
% 0.22/0.46 tff(341,plain,
% 0.22/0.46 (![X: $i] : (animal(X) | (~wolf(X)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[340, 333])).
% 0.22/0.46 tff(342,plain,
% 0.22/0.46 (((~![X: $i] : (animal(X) | (~wolf(X)))) | (animal(X1!0) | (~wolf(X1!0)))) <=> ((~![X: $i] : (animal(X) | (~wolf(X)))) | animal(X1!0) | (~wolf(X1!0)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(343,plain,
% 0.22/0.46 ((~![X: $i] : (animal(X) | (~wolf(X)))) | (animal(X1!0) | (~wolf(X1!0)))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(344,plain,
% 0.22/0.46 ((~![X: $i] : (animal(X) | (~wolf(X)))) | animal(X1!0) | (~wolf(X1!0))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[343, 342])).
% 0.22/0.46 tff(345,plain,
% 0.22/0.46 (animal(X1!0)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[344, 341, 284])).
% 0.22/0.46 tff(346,plain,
% 0.22/0.46 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(X1!0)) | ![Y: $i] : ((~plant(Y)) | eats(X1!0, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!0))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(X1!0)) | ![Y: $i] : ((~plant(Y)) | eats(X1!0, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!0))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(347,plain,
% 0.22/0.46 (((~animal(X1!0)) | ![Y: $i] : ((~plant(Y)) | eats(X1!0, Y)) | ![Y1: $i] : (eats(X1!0, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X1!0)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> ((~animal(X1!0)) | ![Y: $i] : ((~plant(Y)) | eats(X1!0, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!0))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(348,plain,
% 0.22/0.46 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(X1!0)) | ![Y: $i] : ((~plant(Y)) | eats(X1!0, Y)) | ![Y1: $i] : (eats(X1!0, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X1!0)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(X1!0)) | ![Y: $i] : ((~plant(Y)) | eats(X1!0, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!0)))))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[347])).
% 0.22/0.46 tff(349,plain,
% 0.22/0.46 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(X1!0)) | ![Y: $i] : ((~plant(Y)) | eats(X1!0, Y)) | ![Y1: $i] : (eats(X1!0, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X1!0)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(X1!0)) | ![Y: $i] : ((~plant(Y)) | eats(X1!0, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!0))))),
% 0.22/0.46 inference(transitivity,[status(thm)],[348, 346])).
% 0.22/0.46 tff(350,plain,
% 0.22/0.46 ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(X1!0)) | ![Y: $i] : ((~plant(Y)) | eats(X1!0, Y)) | ![Y1: $i] : (eats(X1!0, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X1!0)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(351,plain,
% 0.22/0.46 ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(X1!0)) | ![Y: $i] : ((~plant(Y)) | eats(X1!0, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!0)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[350, 349])).
% 0.22/0.46 tff(352,plain,
% 0.22/0.46 (![Y: $i] : ((~plant(Y)) | eats(X1!0, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!0)))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[351, 186, 345])).
% 0.22/0.46 tff(353,plain,
% 0.22/0.46 (![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!0)))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[352, 331])).
% 0.22/0.46 tff(354,plain,
% 0.22/0.46 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!0)))) | ((~animal(X1!1)) | eats(X1!0, X1!1) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z))) | (~much_smaller(X1!1, X1!0)))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!0)))) | (~animal(X1!1)) | eats(X1!0, X1!1) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z))) | (~much_smaller(X1!1, X1!0)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(355,plain,
% 0.22/0.46 (((~animal(X1!1)) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z))) | eats(X1!0, X1!1) | (~much_smaller(X1!1, X1!0))) <=> ((~animal(X1!1)) | eats(X1!0, X1!1) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z))) | (~much_smaller(X1!1, X1!0)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(356,plain,
% 0.22/0.46 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!0)))) | ((~animal(X1!1)) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z))) | eats(X1!0, X1!1) | (~much_smaller(X1!1, X1!0)))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!0)))) | ((~animal(X1!1)) | eats(X1!0, X1!1) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z))) | (~much_smaller(X1!1, X1!0))))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[355])).
% 0.22/0.46 tff(357,plain,
% 0.22/0.46 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!0)))) | ((~animal(X1!1)) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z))) | eats(X1!0, X1!1) | (~much_smaller(X1!1, X1!0)))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!0)))) | (~animal(X1!1)) | eats(X1!0, X1!1) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z))) | (~much_smaller(X1!1, X1!0)))),
% 0.22/0.46 inference(transitivity,[status(thm)],[356, 354])).
% 0.22/0.46 tff(358,plain,
% 0.22/0.46 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!0)))) | ((~animal(X1!1)) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z))) | eats(X1!0, X1!1) | (~much_smaller(X1!1, X1!0)))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(359,plain,
% 0.22/0.46 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!0, Y1) | (~much_smaller(Y1, X1!0)))) | (~animal(X1!1)) | eats(X1!0, X1!1) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z))) | (~much_smaller(X1!1, X1!0))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[358, 357])).
% 0.22/0.46 tff(360,plain,
% 0.22/0.46 (eats(X1!0, X1!1) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z))) | (~much_smaller(X1!1, X1!0))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[359, 36, 353])).
% 0.22/0.46 tff(361,plain,
% 0.22/0.46 (eats(X1!0, X1!1) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z)))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[360, 314])).
% 0.22/0.46 tff(362,plain,
% 0.22/0.46 (![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z)))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[361, 292])).
% 0.22/0.46 tff(363,plain,
% 0.22/0.46 (((~![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z)))) | ((~plant(tptp_fun_Y_6(X1!3))) | (~eats(X1!1, tptp_fun_Y_6(X1!3))))) <=> ((~![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z)))) | (~plant(tptp_fun_Y_6(X1!3))) | (~eats(X1!1, tptp_fun_Y_6(X1!3))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(364,plain,
% 0.22/0.46 ((~![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z)))) | ((~plant(tptp_fun_Y_6(X1!3))) | (~eats(X1!1, tptp_fun_Y_6(X1!3))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(365,plain,
% 0.22/0.46 ((~![Z: $i] : ((~plant(Z)) | (~eats(X1!1, Z)))) | (~plant(tptp_fun_Y_6(X1!3))) | (~eats(X1!1, tptp_fun_Y_6(X1!3)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[364, 363])).
% 0.22/0.46 tff(366,plain,
% 0.22/0.46 (~eats(X1!1, tptp_fun_Y_6(X1!3))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[365, 230, 362])).
% 0.22/0.46 tff(367,assumption,(![Y: $i] : ((~plant(Y)) | eats(X1!1, Y))), introduced(assumption)).
% 0.22/0.46 tff(368,plain,
% 0.22/0.46 (((~![Y: $i] : ((~plant(Y)) | eats(X1!1, Y))) | ((~plant(tptp_fun_Y_6(X1!3))) | eats(X1!1, tptp_fun_Y_6(X1!3)))) <=> ((~![Y: $i] : ((~plant(Y)) | eats(X1!1, Y))) | (~plant(tptp_fun_Y_6(X1!3))) | eats(X1!1, tptp_fun_Y_6(X1!3)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(369,plain,
% 0.22/0.46 ((~![Y: $i] : ((~plant(Y)) | eats(X1!1, Y))) | ((~plant(tptp_fun_Y_6(X1!3))) | eats(X1!1, tptp_fun_Y_6(X1!3)))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(370,plain,
% 0.22/0.46 ((~![Y: $i] : ((~plant(Y)) | eats(X1!1, Y))) | (~plant(tptp_fun_Y_6(X1!3))) | eats(X1!1, tptp_fun_Y_6(X1!3))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[369, 368])).
% 0.22/0.46 tff(371,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[370, 230, 367, 366])).
% 0.22/0.46 tff(372,plain,(~![Y: $i] : ((~plant(Y)) | eats(X1!1, Y))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.46 tff(373,plain,
% 0.22/0.46 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(X1!1)) | ![Y: $i] : ((~plant(Y)) | eats(X1!1, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!1, Y1) | (~much_smaller(Y1, X1!1))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(X1!1)) | ![Y: $i] : ((~plant(Y)) | eats(X1!1, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!1, Y1) | (~much_smaller(Y1, X1!1))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(374,plain,
% 0.22/0.47 (((~animal(X1!1)) | ![Y: $i] : ((~plant(Y)) | eats(X1!1, Y)) | ![Y1: $i] : (eats(X1!1, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X1!1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))))) <=> ((~animal(X1!1)) | ![Y: $i] : ((~plant(Y)) | eats(X1!1, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!1, Y1) | (~much_smaller(Y1, X1!1))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(375,plain,
% 0.22/0.47 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(X1!1)) | ![Y: $i] : ((~plant(Y)) | eats(X1!1, Y)) | ![Y1: $i] : (eats(X1!1, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X1!1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(X1!1)) | ![Y: $i] : ((~plant(Y)) | eats(X1!1, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!1, Y1) | (~much_smaller(Y1, X1!1)))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[374])).
% 0.22/0.47 tff(376,plain,
% 0.22/0.47 (((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(X1!1)) | ![Y: $i] : ((~plant(Y)) | eats(X1!1, Y)) | ![Y1: $i] : (eats(X1!1, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X1!1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) <=> ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(X1!1)) | ![Y: $i] : ((~plant(Y)) | eats(X1!1, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!1, Y1) | (~much_smaller(Y1, X1!1))))),
% 0.22/0.47 inference(transitivity,[status(thm)],[375, 373])).
% 0.22/0.47 tff(377,plain,
% 0.22/0.47 ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | ((~animal(X1!1)) | ![Y: $i] : ((~plant(Y)) | eats(X1!1, Y)) | ![Y1: $i] : (eats(X1!1, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X1!1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(378,plain,
% 0.22/0.47 ((~![X: $i] : ((~animal(X)) | ![Y: $i] : ((~plant(Y)) | eats(X, Y)) | ![Y1: $i] : (eats(X, Y1) | (~animal(Y1)) | (~much_smaller(Y1, X)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z)))))) | (~animal(X1!1)) | ![Y: $i] : ((~plant(Y)) | eats(X1!1, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!1, Y1) | (~much_smaller(Y1, X1!1)))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[377, 376])).
% 0.22/0.47 tff(379,plain,
% 0.22/0.47 (![Y: $i] : ((~plant(Y)) | eats(X1!1, Y)) | ![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!1, Y1) | (~much_smaller(Y1, X1!1)))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[378, 186, 36])).
% 0.22/0.47 tff(380,plain,
% 0.22/0.47 (![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!1, Y1) | (~much_smaller(Y1, X1!1)))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[379, 372])).
% 0.22/0.47 tff(381,plain,
% 0.22/0.47 (((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!1, Y1) | (~much_smaller(Y1, X1!1)))) | ((~animal(X1!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!2, Z))) | eats(X1!1, X1!2) | (~much_smaller(X1!2, X1!1)))) <=> ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!1, Y1) | (~much_smaller(Y1, X1!1)))) | (~animal(X1!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!2, Z))) | eats(X1!1, X1!2) | (~much_smaller(X1!2, X1!1)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(382,plain,
% 0.22/0.47 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!1, Y1) | (~much_smaller(Y1, X1!1)))) | ((~animal(X1!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!2, Z))) | eats(X1!1, X1!2) | (~much_smaller(X1!2, X1!1)))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(383,plain,
% 0.22/0.47 ((~![Y1: $i] : ((~animal(Y1)) | ![Z: $i] : ((~plant(Z)) | (~eats(Y1, Z))) | eats(X1!1, Y1) | (~much_smaller(Y1, X1!1)))) | (~animal(X1!2)) | ![Z: $i] : ((~plant(Z)) | (~eats(X1!2, Z))) | eats(X1!1, X1!2) | (~much_smaller(X1!2, X1!1))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[382, 381])).
% 0.22/0.47 tff(384,plain,
% 0.22/0.47 (![Z: $i] : ((~plant(Z)) | (~eats(X1!2, Z))) | eats(X1!1, X1!2) | (~much_smaller(X1!2, X1!1))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[383, 18, 380])).
% 0.22/0.47 tff(385,plain,
% 0.22/0.47 (![Z: $i] : ((~plant(Z)) | (~eats(X1!2, Z))) | eats(X1!1, X1!2)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[384, 264])).
% 0.22/0.47 tff(386,plain,
% 0.22/0.47 (eats(X1!1, X1!2)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[385, 242])).
% 0.22/0.47 tff(387,plain,
% 0.22/0.47 (((~![Z: $i] : ((~grain(Z)) | (~eats(X1!2, Z)) | (~eats(X1!1, X1!2)))) | ((~grain(X!5)) | (~eats(X1!2, X!5)) | (~eats(X1!1, X1!2)))) <=> ((~![Z: $i] : ((~grain(Z)) | (~eats(X1!2, Z)) | (~eats(X1!1, X1!2)))) | (~grain(X!5)) | (~eats(X1!2, X!5)) | (~eats(X1!1, X1!2)))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(388,plain,
% 0.22/0.47 ((~![Z: $i] : ((~grain(Z)) | (~eats(X1!2, Z)) | (~eats(X1!1, X1!2)))) | ((~grain(X!5)) | (~eats(X1!2, X!5)) | (~eats(X1!1, X1!2)))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(389,plain,
% 0.22/0.47 ((~![Z: $i] : ((~grain(Z)) | (~eats(X1!2, Z)) | (~eats(X1!1, X1!2)))) | (~grain(X!5)) | (~eats(X1!2, X!5)) | (~eats(X1!1, X1!2))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[388, 387])).
% 0.22/0.47 tff(390,plain,
% 0.22/0.47 ($false),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[389, 208, 386, 216, 67])).
% 0.22/0.47 % SZS output end Proof
%------------------------------------------------------------------------------