%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HWV031-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:09:00 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : HWV031-1 : TPTP v9.0.0. Released v2.5.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 17:20:24 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.44 % SZS status Unsatisfiable
% 0.21/0.44 % SZS output start Proof
% 0.21/0.44 tff(gt_type, type, (
% 0.21/0.44 gt: ( $i * $i ) > $o)).
% 0.21/0.44 tff(wr_level_type, type, (
% 0.21/0.44 wr_level: $i > $i)).
% 0.21/0.44 tff(plus_type, type, (
% 0.21/0.44 plus: ( $i * $i ) > $i)).
% 0.21/0.44 tff(n1_type, type, (
% 0.21/0.44 n1: $i)).
% 0.21/0.44 tff(x_139_type, type, (
% 0.21/0.44 x_139: $i)).
% 0.21/0.44 tff(minus_type, type, (
% 0.21/0.44 minus: ( $i * $i ) > $i)).
% 0.21/0.44 tff(fifo_length_type, type, (
% 0.21/0.44 fifo_length: $i)).
% 0.21/0.44 tff(n0_type, type, (
% 0.21/0.44 n0: $i)).
% 0.21/0.44 tff(p_Wr_type, type, (
% 0.21/0.44 p_Wr: $i > $o)).
% 0.21/0.44 tff(p_Reset_type, type, (
% 0.21/0.44 p_Reset: $i > $o)).
% 0.21/0.44 tff(p_Rd_type, type, (
% 0.21/0.44 p_Rd: $i > $o)).
% 0.21/0.44 tff(int_level_type, type, (
% 0.21/0.44 int_level: $i > $i)).
% 0.21/0.44 tff(def_10_type, type, (
% 0.21/0.44 def_10: ( $i * $i ) > $o)).
% 0.21/0.44 tff(1,plain,
% 0.21/0.44 ((n1 = plus(n0, n1)) <=> (n1 = plus(n0, n1))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(2,axiom,(n1 = plus(n0, n1)), file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax','axiom_20')).
% 0.21/0.44 tff(3,plain,
% 0.21/0.44 (n1 = plus(n0, n1)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.21/0.44 tff(4,plain,
% 0.21/0.44 (plus(n0, n1) = n1),
% 0.21/0.44 inference(symmetry,[status(thm)],[3])).
% 0.21/0.44 tff(5,plain,
% 0.21/0.44 (plus(wr_level(x_139), plus(n0, n1)) = plus(wr_level(x_139), n1)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[4])).
% 0.21/0.44 tff(6,plain,
% 0.21/0.44 (plus(wr_level(x_139), n1) = plus(wr_level(x_139), plus(n0, n1))),
% 0.21/0.44 inference(symmetry,[status(thm)],[5])).
% 0.21/0.44 tff(7,assumption,(wr_level(plus(x_139, n1)) = wr_level(x_139)), introduced(assumption)).
% 0.21/0.44 tff(8,plain,
% 0.21/0.44 (wr_level(x_139) = wr_level(plus(x_139, n1))),
% 0.21/0.44 inference(symmetry,[status(thm)],[7])).
% 0.21/0.44 tff(9,plain,
% 0.21/0.44 (plus(wr_level(x_139), n1) = plus(wr_level(plus(x_139, n1)), n1)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[8])).
% 0.21/0.44 tff(10,plain,
% 0.21/0.44 (gt(plus(wr_level(x_139), n1), fifo_length) <=> gt(plus(wr_level(plus(x_139, n1)), n1), fifo_length)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[9])).
% 0.21/0.44 tff(11,plain,
% 0.21/0.44 (gt(plus(wr_level(plus(x_139, n1)), n1), fifo_length) <=> gt(plus(wr_level(x_139), n1), fifo_length)),
% 0.21/0.44 inference(symmetry,[status(thm)],[10])).
% 0.21/0.44 tff(12,plain,
% 0.21/0.44 (gt(plus(wr_level(plus(x_139, n1)), n1), fifo_length) <=> gt(plus(wr_level(plus(x_139, n1)), n1), fifo_length)),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(13,axiom,(gt(plus(wr_level(plus(x_139, n1)), n1), fifo_length)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quest_2')).
% 0.21/0.44 tff(14,plain,
% 0.21/0.44 (gt(plus(wr_level(plus(x_139, n1)), n1), fifo_length)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.21/0.44 tff(15,plain,
% 0.21/0.44 (gt(plus(wr_level(x_139), n1), fifo_length)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.21/0.44 tff(16,plain,
% 0.21/0.44 ((~gt(plus(wr_level(x_139), n1), fifo_length)) <=> (~gt(plus(wr_level(x_139), n1), fifo_length))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(17,axiom,(~gt(plus(wr_level(x_139), n1), fifo_length)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quest_1')).
% 0.21/0.44 tff(18,plain,
% 0.21/0.44 (~gt(plus(wr_level(x_139), n1), fifo_length)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.21/0.44 tff(19,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[18, 15])).
% 0.21/0.44 tff(20,plain,(~(wr_level(plus(x_139, n1)) = wr_level(x_139))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(21,assumption,(~gt(wr_level(plus(x_139, n1)), wr_level(plus(x_139, n1)))), introduced(assumption)).
% 0.21/0.44 tff(22,assumption,(wr_level(plus(x_139, n1)) = n0), introduced(assumption)).
% 0.21/0.44 tff(23,plain,
% 0.21/0.44 (gt(fifo_length, wr_level(plus(x_139, n1))) <=> gt(fifo_length, n0)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[22])).
% 0.21/0.44 tff(24,plain,
% 0.21/0.44 (gt(fifo_length, n0) <=> gt(fifo_length, wr_level(plus(x_139, n1)))),
% 0.21/0.44 inference(symmetry,[status(thm)],[23])).
% 0.21/0.44 tff(25,plain,
% 0.21/0.44 (gt(fifo_length, n0) <=> gt(fifo_length, n0)),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(26,axiom,(gt(fifo_length, n0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quest_3')).
% 0.21/0.44 tff(27,plain,
% 0.21/0.44 (gt(fifo_length, n0)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.21/0.44 tff(28,plain,
% 0.21/0.44 (gt(fifo_length, wr_level(plus(x_139, n1)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.21/0.44 tff(29,assumption,(gt(fifo_length, wr_level(plus(x_139, n1)))), introduced(assumption)).
% 0.21/0.44 tff(30,assumption,(gt(wr_level(plus(x_139, n1)), fifo_length)), introduced(assumption)).
% 0.21/0.45 tff(31,plain,
% 0.21/0.45 (![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20))) <=> ![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(32,plain,
% 0.21/0.45 (![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20))) <=> ![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(33,plain,
% 0.21/0.45 (^[Z_21: $i, Y_20: $i, X_19: $i] : rewrite((((~gt(Z_21, Y_20)) | gt(Z_21, X_19)) | (~gt(Y_20, X_19))) <=> ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(34,plain,
% 0.21/0.45 (![Z_21: $i, Y_20: $i, X_19: $i] : (((~gt(Z_21, Y_20)) | gt(Z_21, X_19)) | (~gt(Y_20, X_19))) <=> ![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[33])).
% 0.21/0.45 tff(35,axiom,(![Z_21: $i, Y_20: $i, X_19: $i] : (((~gt(Z_21, Y_20)) | gt(Z_21, X_19)) | (~gt(Y_20, X_19)))), file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax','axiom_13')).
% 0.21/0.45 tff(36,plain,
% 0.21/0.45 (![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.21/0.45 tff(37,plain,
% 0.21/0.45 (![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.21/0.45 tff(38,plain,(
% 0.21/0.45 ![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[37])).
% 0.21/0.45 tff(39,plain,
% 0.21/0.45 (![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.21/0.45 tff(40,plain,
% 0.21/0.45 (((~![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))) | (gt(wr_level(plus(x_139, n1)), wr_level(plus(x_139, n1))) | (~gt(wr_level(plus(x_139, n1)), fifo_length)) | (~gt(fifo_length, wr_level(plus(x_139, n1)))))) <=> ((~![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))) | gt(wr_level(plus(x_139, n1)), wr_level(plus(x_139, n1))) | (~gt(wr_level(plus(x_139, n1)), fifo_length)) | (~gt(fifo_length, wr_level(plus(x_139, n1)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(41,plain,
% 0.21/0.45 (((~gt(fifo_length, wr_level(plus(x_139, n1)))) | gt(wr_level(plus(x_139, n1)), wr_level(plus(x_139, n1))) | (~gt(wr_level(plus(x_139, n1)), fifo_length))) <=> (gt(wr_level(plus(x_139, n1)), wr_level(plus(x_139, n1))) | (~gt(wr_level(plus(x_139, n1)), fifo_length)) | (~gt(fifo_length, wr_level(plus(x_139, n1)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(42,plain,
% 0.21/0.45 (((~![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))) | ((~gt(fifo_length, wr_level(plus(x_139, n1)))) | gt(wr_level(plus(x_139, n1)), wr_level(plus(x_139, n1))) | (~gt(wr_level(plus(x_139, n1)), fifo_length)))) <=> ((~![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))) | (gt(wr_level(plus(x_139, n1)), wr_level(plus(x_139, n1))) | (~gt(wr_level(plus(x_139, n1)), fifo_length)) | (~gt(fifo_length, wr_level(plus(x_139, n1))))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[41])).
% 0.21/0.45 tff(43,plain,
% 0.21/0.45 (((~![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))) | ((~gt(fifo_length, wr_level(plus(x_139, n1)))) | gt(wr_level(plus(x_139, n1)), wr_level(plus(x_139, n1))) | (~gt(wr_level(plus(x_139, n1)), fifo_length)))) <=> ((~![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))) | gt(wr_level(plus(x_139, n1)), wr_level(plus(x_139, n1))) | (~gt(wr_level(plus(x_139, n1)), fifo_length)) | (~gt(fifo_length, wr_level(plus(x_139, n1)))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[42, 40])).
% 0.21/0.45 tff(44,plain,
% 0.21/0.45 ((~![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))) | ((~gt(fifo_length, wr_level(plus(x_139, n1)))) | gt(wr_level(plus(x_139, n1)), wr_level(plus(x_139, n1))) | (~gt(wr_level(plus(x_139, n1)), fifo_length)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(45,plain,
% 0.21/0.45 ((~![Z_21: $i, Y_20: $i, X_19: $i] : ((~gt(Y_20, X_19)) | gt(Z_21, X_19) | (~gt(Z_21, Y_20)))) | gt(wr_level(plus(x_139, n1)), wr_level(plus(x_139, n1))) | (~gt(wr_level(plus(x_139, n1)), fifo_length)) | (~gt(fifo_length, wr_level(plus(x_139, n1))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.21/0.45 tff(46,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[45, 39, 21, 30, 29])).
% 0.21/0.45 tff(47,plain,((~gt(wr_level(plus(x_139, n1)), fifo_length)) | gt(wr_level(plus(x_139, n1)), wr_level(plus(x_139, n1))) | (~gt(fifo_length, wr_level(plus(x_139, n1))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(48,plain,
% 0.21/0.45 (~gt(wr_level(plus(x_139, n1)), fifo_length)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[47, 28, 21])).
% 0.21/0.45 tff(49,plain,
% 0.21/0.45 (^[X_13: $i, Y_14: $i] : refl(((Y_14 = X_13) | (~gt(plus(X_13, n1), Y_14)) | gt(X_13, Y_14)) <=> ((Y_14 = X_13) | (~gt(plus(X_13, n1), Y_14)) | gt(X_13, Y_14)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(50,plain,
% 0.21/0.45 (![X_13: $i, Y_14: $i] : ((Y_14 = X_13) | (~gt(plus(X_13, n1), Y_14)) | gt(X_13, Y_14)) <=> ![X_13: $i, Y_14: $i] : ((Y_14 = X_13) | (~gt(plus(X_13, n1), Y_14)) | gt(X_13, Y_14))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[49])).
% 0.21/0.45 tff(51,plain,
% 0.21/0.45 (![X_13: $i, Y_14: $i] : ((Y_14 = X_13) | (~gt(plus(X_13, n1), Y_14)) | gt(X_13, Y_14)) <=> ![X_13: $i, Y_14: $i] : ((Y_14 = X_13) | (~gt(plus(X_13, n1), Y_14)) | gt(X_13, Y_14))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(52,plain,
% 0.21/0.45 (^[X_13: $i, Y_14: $i] : trans(monotonicity(rewrite((gt(X_13, Y_14) | (~gt(plus(X_13, n1), Y_14))) <=> ((~gt(plus(X_13, n1), Y_14)) | gt(X_13, Y_14))), (((gt(X_13, Y_14) | (~gt(plus(X_13, n1), Y_14))) | (Y_14 = X_13)) <=> (((~gt(plus(X_13, n1), Y_14)) | gt(X_13, Y_14)) | (Y_14 = X_13)))), rewrite((((~gt(plus(X_13, n1), Y_14)) | gt(X_13, Y_14)) | (Y_14 = X_13)) <=> ((Y_14 = X_13) | (~gt(plus(X_13, n1), Y_14)) | gt(X_13, Y_14))), (((gt(X_13, Y_14) | (~gt(plus(X_13, n1), Y_14))) | (Y_14 = X_13)) <=> ((Y_14 = X_13) | (~gt(plus(X_13, n1), Y_14)) | gt(X_13, Y_14))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(53,plain,
% 0.21/0.45 (![X_13: $i, Y_14: $i] : ((gt(X_13, Y_14) | (~gt(plus(X_13, n1), Y_14))) | (Y_14 = X_13)) <=> ![X_13: $i, Y_14: $i] : ((Y_14 = X_13) | (~gt(plus(X_13, n1), Y_14)) | gt(X_13, Y_14))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[52])).
% 0.21/0.45 tff(54,axiom,(![X_13: $i, Y_14: $i] : ((gt(X_13, Y_14) | (~gt(plus(X_13, n1), Y_14))) | (Y_14 = X_13))), file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax','axiom_10')).
% 0.21/0.45 tff(55,plain,
% 0.21/0.45 (![X_13: $i, Y_14: $i] : ((Y_14 = X_13) | (~gt(plus(X_13, n1), Y_14)) | gt(X_13, Y_14))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.21/0.45 tff(56,plain,
% 0.21/0.45 (![X_13: $i, Y_14: $i] : ((Y_14 = X_13) | (~gt(plus(X_13, n1), Y_14)) | gt(X_13, Y_14))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.21/0.45 tff(57,plain,(
% 0.21/0.45 ![X_13: $i, Y_14: $i] : ((Y_14 = X_13) | (~gt(plus(X_13, n1), Y_14)) | gt(X_13, Y_14))),
% 0.21/0.45 inference(skolemize,[status(sab)],[56])).
% 0.21/0.45 tff(58,plain,
% 0.21/0.45 (![X_13: $i, Y_14: $i] : ((Y_14 = X_13) | (~gt(plus(X_13, n1), Y_14)) | gt(X_13, Y_14))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.21/0.45 tff(59,plain,
% 0.21/0.45 (((~![X_13: $i, Y_14: $i] : ((Y_14 = X_13) | (~gt(plus(X_13, n1), Y_14)) | gt(X_13, Y_14))) | ((fifo_length = wr_level(plus(x_139, n1))) | (~gt(plus(wr_level(plus(x_139, n1)), n1), fifo_length)) | gt(wr_level(plus(x_139, n1)), fifo_length))) <=> ((~![X_13: $i, Y_14: $i] : ((Y_14 = X_13) | (~gt(plus(X_13, n1), Y_14)) | gt(X_13, Y_14))) | (fifo_length = wr_level(plus(x_139, n1))) | (~gt(plus(wr_level(plus(x_139, n1)), n1), fifo_length)) | gt(wr_level(plus(x_139, n1)), fifo_length))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(60,plain,
% 0.21/0.45 ((~![X_13: $i, Y_14: $i] : ((Y_14 = X_13) | (~gt(plus(X_13, n1), Y_14)) | gt(X_13, Y_14))) | ((fifo_length = wr_level(plus(x_139, n1))) | (~gt(plus(wr_level(plus(x_139, n1)), n1), fifo_length)) | gt(wr_level(plus(x_139, n1)), fifo_length))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(61,plain,
% 0.21/0.45 ((~![X_13: $i, Y_14: $i] : ((Y_14 = X_13) | (~gt(plus(X_13, n1), Y_14)) | gt(X_13, Y_14))) | (fifo_length = wr_level(plus(x_139, n1))) | (~gt(plus(wr_level(plus(x_139, n1)), n1), fifo_length)) | gt(wr_level(plus(x_139, n1)), fifo_length)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.21/0.45 tff(62,plain,
% 0.21/0.45 ((fifo_length = wr_level(plus(x_139, n1))) | gt(wr_level(plus(x_139, n1)), fifo_length)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[61, 58, 14])).
% 0.21/0.45 tff(63,plain,
% 0.21/0.45 (fifo_length = wr_level(plus(x_139, n1))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[62, 48])).
% 0.21/0.45 tff(64,plain,
% 0.21/0.45 (fifo_length = n0),
% 0.21/0.45 inference(transitivity,[status(thm)],[63, 22])).
% 0.21/0.45 tff(65,plain,
% 0.21/0.45 (gt(plus(wr_level(x_139), n1), fifo_length) <=> gt(plus(wr_level(x_139), n1), n0)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[64])).
% 0.21/0.45 tff(66,plain,
% 0.21/0.45 (gt(plus(wr_level(x_139), n1), n0) <=> gt(plus(wr_level(x_139), n1), fifo_length)),
% 0.21/0.45 inference(symmetry,[status(thm)],[65])).
% 0.21/0.45 tff(67,plain,
% 0.21/0.45 (^[X_1: $i] : refl(gt(plus(X_1, n1), n0) <=> gt(plus(X_1, n1), n0))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(68,plain,
% 0.21/0.45 (![X_1: $i] : gt(plus(X_1, n1), n0) <=> ![X_1: $i] : gt(plus(X_1, n1), n0)),
% 0.21/0.45 inference(quant_intro,[status(thm)],[67])).
% 0.21/0.45 tff(69,plain,
% 0.21/0.45 (![X_1: $i] : gt(plus(X_1, n1), n0) <=> ![X_1: $i] : gt(plus(X_1, n1), n0)),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(70,axiom,(![X_1: $i] : gt(plus(X_1, n1), n0)), file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax','axiom_2')).
% 0.21/0.45 tff(71,plain,
% 0.21/0.45 (![X_1: $i] : gt(plus(X_1, n1), n0)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.21/0.45 tff(72,plain,(
% 0.21/0.45 ![X_1: $i] : gt(plus(X_1, n1), n0)),
% 0.21/0.45 inference(skolemize,[status(sab)],[71])).
% 0.21/0.45 tff(73,plain,
% 0.21/0.45 (![X_1: $i] : gt(plus(X_1, n1), n0)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.21/0.45 tff(74,plain,
% 0.21/0.45 ((~![X_1: $i] : gt(plus(X_1, n1), n0)) | gt(plus(wr_level(x_139), n1), n0)),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(75,plain,
% 0.21/0.45 (gt(plus(wr_level(x_139), n1), n0)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.21/0.45 tff(76,plain,
% 0.21/0.45 (gt(plus(wr_level(x_139), n1), fifo_length)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[75, 66])).
% 0.21/0.45 tff(77,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[18, 76])).
% 0.21/0.45 tff(78,plain,((~(wr_level(plus(x_139, n1)) = n0)) | gt(wr_level(plus(x_139, n1)), wr_level(plus(x_139, n1)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(79,plain,
% 0.21/0.45 (~(wr_level(plus(x_139, n1)) = n0)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[78, 21])).
% 0.21/0.45 tff(80,assumption,(~(wr_level(plus(x_139, n1)) = n0)), introduced(assumption)).
% 0.21/0.45 tff(81,plain,
% 0.21/0.45 (^[X_t_37: $i] : refl(((~p_Reset(X_t_37)) | (wr_level(plus(X_t_37, n1)) = n0)) <=> ((~p_Reset(X_t_37)) | (wr_level(plus(X_t_37, n1)) = n0)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(82,plain,
% 0.21/0.45 (![X_t_37: $i] : ((~p_Reset(X_t_37)) | (wr_level(plus(X_t_37, n1)) = n0)) <=> ![X_t_37: $i] : ((~p_Reset(X_t_37)) | (wr_level(plus(X_t_37, n1)) = n0))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[81])).
% 0.21/0.45 tff(83,plain,
% 0.21/0.45 (![X_t_37: $i] : ((~p_Reset(X_t_37)) | (wr_level(plus(X_t_37, n1)) = n0)) <=> ![X_t_37: $i] : ((~p_Reset(X_t_37)) | (wr_level(plus(X_t_37, n1)) = n0))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(84,axiom,(![X_t_37: $i] : ((~p_Reset(X_t_37)) | (wr_level(plus(X_t_37, n1)) = n0))), file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax','axiom_27')).
% 0.21/0.45 tff(85,plain,
% 0.21/0.45 (![X_t_37: $i] : ((~p_Reset(X_t_37)) | (wr_level(plus(X_t_37, n1)) = n0))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.21/0.45 tff(86,plain,(
% 0.21/0.45 ![X_t_37: $i] : ((~p_Reset(X_t_37)) | (wr_level(plus(X_t_37, n1)) = n0))),
% 0.21/0.45 inference(skolemize,[status(sab)],[85])).
% 0.21/0.45 tff(87,plain,
% 0.21/0.45 (![X_t_37: $i] : ((~p_Reset(X_t_37)) | (wr_level(plus(X_t_37, n1)) = n0))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.21/0.45 tff(88,plain,
% 0.21/0.45 (((~![X_t_37: $i] : ((~p_Reset(X_t_37)) | (wr_level(plus(X_t_37, n1)) = n0))) | ((~p_Reset(x_139)) | (wr_level(plus(x_139, n1)) = n0))) <=> ((~![X_t_37: $i] : ((~p_Reset(X_t_37)) | (wr_level(plus(X_t_37, n1)) = n0))) | (~p_Reset(x_139)) | (wr_level(plus(x_139, n1)) = n0))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(89,plain,
% 0.21/0.45 ((~![X_t_37: $i] : ((~p_Reset(X_t_37)) | (wr_level(plus(X_t_37, n1)) = n0))) | ((~p_Reset(x_139)) | (wr_level(plus(x_139, n1)) = n0))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(90,plain,
% 0.21/0.45 ((~![X_t_37: $i] : ((~p_Reset(X_t_37)) | (wr_level(plus(X_t_37, n1)) = n0))) | (~p_Reset(x_139)) | (wr_level(plus(x_139, n1)) = n0)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.21/0.45 tff(91,plain,
% 0.21/0.45 ((~p_Reset(x_139)) | (wr_level(plus(x_139, n1)) = n0)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[90, 87])).
% 0.21/0.45 tff(92,plain,
% 0.21/0.45 (~p_Reset(x_139)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[91, 80])).
% 0.21/0.45 tff(93,assumption,(~(wr_level(plus(x_139, n1)) = wr_level(x_139))), introduced(assumption)).
% 0.21/0.45 tff(94,plain,
% 0.21/0.45 (^[X_t_42: $i] : refl((p_Reset(X_t_42) | p_Wr(X_t_42) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42))) <=> (p_Reset(X_t_42) | p_Wr(X_t_42) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(95,plain,
% 0.21/0.45 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Wr(X_t_42) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42))) <=> ![X_t_42: $i] : (p_Reset(X_t_42) | p_Wr(X_t_42) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[94])).
% 0.21/0.45 tff(96,plain,
% 0.21/0.45 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Wr(X_t_42) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42))) <=> ![X_t_42: $i] : (p_Reset(X_t_42) | p_Wr(X_t_42) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(97,plain,
% 0.21/0.45 (^[X_t_42: $i] : rewrite(((p_Reset(X_t_42) | p_Wr(X_t_42)) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42))) <=> (p_Reset(X_t_42) | p_Wr(X_t_42) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(98,plain,
% 0.21/0.45 (![X_t_42: $i] : ((p_Reset(X_t_42) | p_Wr(X_t_42)) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42))) <=> ![X_t_42: $i] : (p_Reset(X_t_42) | p_Wr(X_t_42) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[97])).
% 0.21/0.45 tff(99,axiom,(![X_t_42: $i] : ((p_Reset(X_t_42) | p_Wr(X_t_42)) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42)))), file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax','axiom_69')).
% 0.21/0.45 tff(100,plain,
% 0.21/0.45 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Wr(X_t_42) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.21/0.45 tff(101,plain,
% 0.21/0.45 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Wr(X_t_42) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.21/0.45 tff(102,plain,(
% 0.21/0.45 ![X_t_42: $i] : (p_Reset(X_t_42) | p_Wr(X_t_42) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[101])).
% 0.21/0.45 tff(103,plain,
% 0.21/0.45 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Wr(X_t_42) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.21/0.45 tff(104,plain,
% 0.21/0.45 (((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Wr(X_t_42) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42)))) | (p_Reset(x_139) | p_Wr(x_139) | (wr_level(plus(x_139, n1)) = wr_level(x_139)))) <=> ((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Wr(X_t_42) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42)))) | p_Reset(x_139) | p_Wr(x_139) | (wr_level(plus(x_139, n1)) = wr_level(x_139)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(105,plain,
% 0.21/0.45 ((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Wr(X_t_42) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42)))) | (p_Reset(x_139) | p_Wr(x_139) | (wr_level(plus(x_139, n1)) = wr_level(x_139)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(106,plain,
% 0.21/0.45 ((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Wr(X_t_42) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42)))) | p_Reset(x_139) | p_Wr(x_139) | (wr_level(plus(x_139, n1)) = wr_level(x_139))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.21/0.45 tff(107,plain,
% 0.21/0.46 (p_Reset(x_139) | p_Wr(x_139) | (wr_level(plus(x_139, n1)) = wr_level(x_139))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[106, 103])).
% 0.21/0.46 tff(108,plain,
% 0.21/0.46 (p_Wr(x_139)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[107, 93, 92])).
% 0.21/0.46 tff(109,assumption,(~(wr_level(plus(x_139, n1)) = plus(wr_level(x_139), n1))), introduced(assumption)).
% 0.21/0.46 tff(110,assumption,(gt(minus(fifo_length, n1), wr_level(x_139))), introduced(assumption)).
% 0.21/0.46 tff(111,assumption,(~p_Reset(x_139)), introduced(assumption)).
% 0.21/0.46 tff(112,plain,
% 0.21/0.46 (p_Wr(x_139)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[107, 93, 111])).
% 0.21/0.46 tff(113,plain,
% 0.21/0.46 (![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))) <=> ![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(114,plain,
% 0.21/0.46 (^[X_t_42: $i] : refl((p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))) <=> (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(115,plain,
% 0.21/0.46 (![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))) <=> ![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[114])).
% 0.21/0.46 tff(116,plain,
% 0.21/0.46 (![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))) <=> ![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(117,plain,
% 0.21/0.46 (^[X_t_42: $i] : trans(monotonicity(trans(monotonicity(rewrite(((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | (~p_Rd(X_t_42))) <=> (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)))), ((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | (~p_Rd(X_t_42))) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))) <=> ((p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42))) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))))), rewrite(((p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42))) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))) <=> (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))), ((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | (~p_Rd(X_t_42))) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))) <=> (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))))), (((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | (~p_Rd(X_t_42))) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1))) <=> ((p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1))))), rewrite(((p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1))) <=> (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))), (((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | (~p_Rd(X_t_42))) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1))) <=> (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(118,plain,
% 0.21/0.46 (![X_t_42: $i] : ((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | (~p_Rd(X_t_42))) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1))) <=> ![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[117])).
% 0.21/0.46 tff(119,axiom,(![X_t_42: $i] : ((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | (~p_Rd(X_t_42))) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)))), file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax','axiom_67')).
% 0.21/0.46 tff(120,plain,
% 0.21/0.46 (![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.21/0.46 tff(121,plain,
% 0.21/0.46 (![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.21/0.46 tff(122,plain,(
% 0.21/0.46 ![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))),
% 0.21/0.46 inference(skolemize,[status(sab)],[121])).
% 0.21/0.46 tff(123,plain,
% 0.21/0.46 (![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[122, 115])).
% 0.21/0.46 tff(124,plain,
% 0.21/0.46 (![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[123, 113])).
% 0.21/0.46 tff(125,plain,
% 0.21/0.46 (((~![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))) | (p_Reset(x_139) | (~p_Rd(x_139)) | (~p_Wr(x_139)) | (wr_level(plus(x_139, n1)) = plus(wr_level(x_139), n1)) | (~gt(minus(fifo_length, n1), wr_level(x_139))))) <=> ((~![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))) | p_Reset(x_139) | (~p_Rd(x_139)) | (~p_Wr(x_139)) | (wr_level(plus(x_139, n1)) = plus(wr_level(x_139), n1)) | (~gt(minus(fifo_length, n1), wr_level(x_139))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(126,plain,
% 0.21/0.46 ((~![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))) | (p_Reset(x_139) | (~p_Rd(x_139)) | (~p_Wr(x_139)) | (wr_level(plus(x_139, n1)) = plus(wr_level(x_139), n1)) | (~gt(minus(fifo_length, n1), wr_level(x_139))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(127,plain,
% 0.21/0.46 ((~![X_t_42: $i] : (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))) | p_Reset(x_139) | (~p_Rd(x_139)) | (~p_Wr(x_139)) | (wr_level(plus(x_139, n1)) = plus(wr_level(x_139), n1)) | (~gt(minus(fifo_length, n1), wr_level(x_139)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.21/0.46 tff(128,plain,
% 0.21/0.46 (p_Reset(x_139) | (~p_Rd(x_139)) | (~p_Wr(x_139)) | (wr_level(plus(x_139, n1)) = plus(wr_level(x_139), n1)) | (~gt(minus(fifo_length, n1), wr_level(x_139)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[127, 124])).
% 0.21/0.46 tff(129,plain,
% 0.21/0.46 (~p_Rd(x_139)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[128, 109, 111, 112, 110])).
% 0.21/0.46 tff(130,plain,
% 0.21/0.46 (^[X_t_42: $i] : refl((p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42)) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42))) <=> (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42)) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(131,plain,
% 0.21/0.46 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42)) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42))) <=> ![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42)) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[130])).
% 0.21/0.46 tff(132,plain,
% 0.21/0.46 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42)) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42))) <=> ![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42)) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(133,plain,
% 0.21/0.46 (^[X_t_42: $i] : trans(monotonicity(trans(monotonicity(rewrite(((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) <=> (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)))), ((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | gt(fifo_length, int_level(X_t_42))) <=> ((p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42))) | gt(fifo_length, int_level(X_t_42))))), rewrite(((p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42))) | gt(fifo_length, int_level(X_t_42))) <=> (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42)))), ((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | gt(fifo_length, int_level(X_t_42))) <=> (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42))))), (((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | gt(fifo_length, int_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42))) <=> ((p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42))))), rewrite(((p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42))) <=> (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42)) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42)))), (((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | gt(fifo_length, int_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42))) <=> (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42)) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(134,plain,
% 0.21/0.46 (![X_t_42: $i] : ((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | gt(fifo_length, int_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42))) <=> ![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42)) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[133])).
% 0.21/0.46 tff(135,axiom,(![X_t_42: $i] : ((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | gt(fifo_length, int_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42)))), file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax','axiom_43')).
% 0.21/0.46 tff(136,plain,
% 0.21/0.46 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42)) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.21/0.46 tff(137,plain,
% 0.21/0.46 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42)) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.21/0.46 tff(138,plain,(
% 0.21/0.46 ![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42)) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[137])).
% 0.21/0.46 tff(139,plain,
% 0.21/0.46 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42)) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[138, 131])).
% 0.21/0.46 tff(140,plain,
% 0.21/0.46 (((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42)) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42)))) | (p_Reset(x_139) | p_Rd(x_139) | (wr_level(plus(x_139, n1)) = wr_level(x_139)) | (~p_Wr(x_139)) | gt(fifo_length, int_level(x_139)))) <=> ((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42)) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42)))) | p_Reset(x_139) | p_Rd(x_139) | (wr_level(plus(x_139, n1)) = wr_level(x_139)) | (~p_Wr(x_139)) | gt(fifo_length, int_level(x_139)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(141,plain,
% 0.21/0.46 ((p_Reset(x_139) | p_Rd(x_139) | (~p_Wr(x_139)) | gt(fifo_length, int_level(x_139)) | (wr_level(plus(x_139, n1)) = wr_level(x_139))) <=> (p_Reset(x_139) | p_Rd(x_139) | (wr_level(plus(x_139, n1)) = wr_level(x_139)) | (~p_Wr(x_139)) | gt(fifo_length, int_level(x_139)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(142,plain,
% 0.21/0.46 (((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42)) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42)))) | (p_Reset(x_139) | p_Rd(x_139) | (~p_Wr(x_139)) | gt(fifo_length, int_level(x_139)) | (wr_level(plus(x_139, n1)) = wr_level(x_139)))) <=> ((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42)) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42)))) | (p_Reset(x_139) | p_Rd(x_139) | (wr_level(plus(x_139, n1)) = wr_level(x_139)) | (~p_Wr(x_139)) | gt(fifo_length, int_level(x_139))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[141])).
% 0.21/0.46 tff(143,plain,
% 0.21/0.46 (((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42)) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42)))) | (p_Reset(x_139) | p_Rd(x_139) | (~p_Wr(x_139)) | gt(fifo_length, int_level(x_139)) | (wr_level(plus(x_139, n1)) = wr_level(x_139)))) <=> ((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42)) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42)))) | p_Reset(x_139) | p_Rd(x_139) | (wr_level(plus(x_139, n1)) = wr_level(x_139)) | (~p_Wr(x_139)) | gt(fifo_length, int_level(x_139)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[142, 140])).
% 0.21/0.46 tff(144,plain,
% 0.21/0.46 ((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42)) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42)))) | (p_Reset(x_139) | p_Rd(x_139) | (~p_Wr(x_139)) | gt(fifo_length, int_level(x_139)) | (wr_level(plus(x_139, n1)) = wr_level(x_139)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(145,plain,
% 0.21/0.46 ((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | gt(fifo_length, int_level(X_t_42)) | (wr_level(plus(X_t_42, n1)) = wr_level(X_t_42)))) | p_Reset(x_139) | p_Rd(x_139) | (wr_level(plus(x_139, n1)) = wr_level(x_139)) | (~p_Wr(x_139)) | gt(fifo_length, int_level(x_139))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.21/0.46 tff(146,plain,
% 0.21/0.46 (p_Reset(x_139) | p_Rd(x_139) | (wr_level(plus(x_139, n1)) = wr_level(x_139)) | (~p_Wr(x_139)) | gt(fifo_length, int_level(x_139))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[145, 139])).
% 0.21/0.46 tff(147,plain,
% 0.21/0.46 (gt(fifo_length, int_level(x_139))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[146, 129, 111, 93, 112])).
% 0.21/0.46 tff(148,plain,
% 0.21/0.46 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))) <=> ![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(149,plain,
% 0.21/0.47 (^[X_t_42: $i] : refl((p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))) <=> (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(150,plain,
% 0.21/0.47 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))) <=> ![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[149])).
% 0.21/0.47 tff(151,plain,
% 0.21/0.47 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))) <=> ![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(152,plain,
% 0.21/0.47 (^[X_t_42: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) <=> (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)))), ((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | (~gt(fifo_length, int_level(X_t_42)))) <=> ((p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42))) | (~gt(fifo_length, int_level(X_t_42)))))), rewrite(((p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42))) | (~gt(fifo_length, int_level(X_t_42)))) <=> (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))))), ((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | (~gt(fifo_length, int_level(X_t_42)))) <=> (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42)))))), (((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | (~gt(fifo_length, int_level(X_t_42)))) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))) <=> ((p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42)))) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))))), rewrite(((p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42)))) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))) <=> (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))), (((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | (~gt(fifo_length, int_level(X_t_42)))) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))) <=> (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))))), ((((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | (~gt(fifo_length, int_level(X_t_42)))) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1))) <=> ((p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1))))), rewrite(((p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1))) <=> (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))), ((((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | (~gt(fifo_length, int_level(X_t_42)))) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1))) <=> (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(153,plain,
% 0.21/0.47 (![X_t_42: $i] : (((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | (~gt(fifo_length, int_level(X_t_42)))) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1))) <=> ![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[152])).
% 0.21/0.47 tff(154,axiom,(![X_t_42: $i] : (((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | (~gt(fifo_length, int_level(X_t_42)))) | (~gt(minus(fifo_length, n1), wr_level(X_t_42)))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)))), file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax','axiom_40')).
% 0.21/0.47 tff(155,plain,
% 0.21/0.47 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.21/0.47 tff(156,plain,
% 0.21/0.47 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.21/0.47 tff(157,plain,(
% 0.21/0.47 ![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))),
% 0.21/0.47 inference(skolemize,[status(sab)],[156])).
% 0.21/0.47 tff(158,plain,
% 0.21/0.47 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[157, 150])).
% 0.21/0.47 tff(159,plain,
% 0.21/0.47 (![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[158, 148])).
% 0.21/0.47 tff(160,plain,
% 0.21/0.47 (((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))) | (p_Reset(x_139) | p_Rd(x_139) | (~p_Wr(x_139)) | (wr_level(plus(x_139, n1)) = plus(wr_level(x_139), n1)) | (~gt(minus(fifo_length, n1), wr_level(x_139))) | (~gt(fifo_length, int_level(x_139))))) <=> ((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))) | p_Reset(x_139) | p_Rd(x_139) | (~p_Wr(x_139)) | (wr_level(plus(x_139, n1)) = plus(wr_level(x_139), n1)) | (~gt(minus(fifo_length, n1), wr_level(x_139))) | (~gt(fifo_length, int_level(x_139))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(161,plain,
% 0.21/0.47 ((p_Reset(x_139) | p_Rd(x_139) | (~p_Wr(x_139)) | (~gt(fifo_length, int_level(x_139))) | (wr_level(plus(x_139, n1)) = plus(wr_level(x_139), n1)) | (~gt(minus(fifo_length, n1), wr_level(x_139)))) <=> (p_Reset(x_139) | p_Rd(x_139) | (~p_Wr(x_139)) | (wr_level(plus(x_139, n1)) = plus(wr_level(x_139), n1)) | (~gt(minus(fifo_length, n1), wr_level(x_139))) | (~gt(fifo_length, int_level(x_139))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(162,plain,
% 0.21/0.47 (((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))) | (p_Reset(x_139) | p_Rd(x_139) | (~p_Wr(x_139)) | (~gt(fifo_length, int_level(x_139))) | (wr_level(plus(x_139, n1)) = plus(wr_level(x_139), n1)) | (~gt(minus(fifo_length, n1), wr_level(x_139))))) <=> ((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))) | (p_Reset(x_139) | p_Rd(x_139) | (~p_Wr(x_139)) | (wr_level(plus(x_139, n1)) = plus(wr_level(x_139), n1)) | (~gt(minus(fifo_length, n1), wr_level(x_139))) | (~gt(fifo_length, int_level(x_139)))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[161])).
% 0.21/0.47 tff(163,plain,
% 0.21/0.47 (((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))) | (p_Reset(x_139) | p_Rd(x_139) | (~p_Wr(x_139)) | (~gt(fifo_length, int_level(x_139))) | (wr_level(plus(x_139, n1)) = plus(wr_level(x_139), n1)) | (~gt(minus(fifo_length, n1), wr_level(x_139))))) <=> ((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))) | p_Reset(x_139) | p_Rd(x_139) | (~p_Wr(x_139)) | (wr_level(plus(x_139, n1)) = plus(wr_level(x_139), n1)) | (~gt(minus(fifo_length, n1), wr_level(x_139))) | (~gt(fifo_length, int_level(x_139))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[162, 160])).
% 0.21/0.47 tff(164,plain,
% 0.21/0.47 ((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))) | (p_Reset(x_139) | p_Rd(x_139) | (~p_Wr(x_139)) | (~gt(fifo_length, int_level(x_139))) | (wr_level(plus(x_139, n1)) = plus(wr_level(x_139), n1)) | (~gt(minus(fifo_length, n1), wr_level(x_139))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(165,plain,
% 0.21/0.47 ((~![X_t_42: $i] : (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = plus(wr_level(X_t_42), n1)) | (~gt(minus(fifo_length, n1), wr_level(X_t_42))))) | p_Reset(x_139) | p_Rd(x_139) | (~p_Wr(x_139)) | (wr_level(plus(x_139, n1)) = plus(wr_level(x_139), n1)) | (~gt(minus(fifo_length, n1), wr_level(x_139))) | (~gt(fifo_length, int_level(x_139)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.21/0.47 tff(166,plain,
% 0.21/0.47 (p_Reset(x_139) | p_Rd(x_139) | (~p_Wr(x_139)) | (wr_level(plus(x_139, n1)) = plus(wr_level(x_139), n1)) | (~gt(minus(fifo_length, n1), wr_level(x_139))) | (~gt(fifo_length, int_level(x_139)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[165, 159])).
% 0.21/0.47 tff(167,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[166, 147, 129, 111, 112, 110, 109])).
% 0.21/0.47 tff(168,plain,((wr_level(plus(x_139, n1)) = plus(wr_level(x_139), n1)) | p_Reset(x_139) | (~gt(minus(fifo_length, n1), wr_level(x_139))) | (wr_level(plus(x_139, n1)) = wr_level(x_139))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(169,plain,
% 0.21/0.47 (~gt(minus(fifo_length, n1), wr_level(x_139))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[168, 93, 92, 109])).
% 0.21/0.47 tff(170,plain,
% 0.21/0.47 (^[X_t_42: $i] : refl((p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | gt(minus(fifo_length, n1), wr_level(X_t_42))) <=> (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | gt(minus(fifo_length, n1), wr_level(X_t_42))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(171,plain,
% 0.21/0.47 (![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | gt(minus(fifo_length, n1), wr_level(X_t_42))) <=> ![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | gt(minus(fifo_length, n1), wr_level(X_t_42)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[170])).
% 0.21/0.47 tff(172,plain,
% 0.21/0.47 (![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | gt(minus(fifo_length, n1), wr_level(X_t_42))) <=> ![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | gt(minus(fifo_length, n1), wr_level(X_t_42)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(173,plain,
% 0.21/0.47 (^[X_t_42: $i] : trans(monotonicity(trans(monotonicity(rewrite(((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | (~p_Rd(X_t_42))) <=> (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)))), ((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | (~p_Rd(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42))) <=> ((p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42))))), rewrite(((p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42))) <=> (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | gt(minus(fifo_length, n1), wr_level(X_t_42)))), ((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | (~p_Rd(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42))) <=> (p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | gt(minus(fifo_length, n1), wr_level(X_t_42))))), (((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | (~p_Rd(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = n0)) <=> ((p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | gt(minus(fifo_length, n1), wr_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = n0)))), rewrite(((p_Reset(X_t_42) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | gt(minus(fifo_length, n1), wr_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = n0)) <=> (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | gt(minus(fifo_length, n1), wr_level(X_t_42)))), (((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | (~p_Rd(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = n0)) <=> (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | gt(minus(fifo_length, n1), wr_level(X_t_42)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(174,plain,
% 0.21/0.47 (![X_t_42: $i] : ((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | (~p_Rd(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = n0)) <=> ![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | gt(minus(fifo_length, n1), wr_level(X_t_42)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[173])).
% 0.21/0.47 tff(175,axiom,(![X_t_42: $i] : ((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | (~p_Rd(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = n0))), file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax','axiom_68')).
% 0.21/0.47 tff(176,plain,
% 0.21/0.47 (![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | gt(minus(fifo_length, n1), wr_level(X_t_42)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.21/0.47 tff(177,plain,
% 0.21/0.47 (![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | gt(minus(fifo_length, n1), wr_level(X_t_42)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[176, 172])).
% 0.21/0.47 tff(178,plain,(
% 0.21/0.47 ![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | gt(minus(fifo_length, n1), wr_level(X_t_42)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[177])).
% 0.21/0.47 tff(179,plain,
% 0.21/0.47 (![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | gt(minus(fifo_length, n1), wr_level(X_t_42)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[178, 171])).
% 0.21/0.47 tff(180,plain,
% 0.21/0.47 (((~![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | gt(minus(fifo_length, n1), wr_level(X_t_42)))) | (p_Reset(x_139) | (~p_Rd(x_139)) | (wr_level(plus(x_139, n1)) = n0) | (~p_Wr(x_139)) | gt(minus(fifo_length, n1), wr_level(x_139)))) <=> ((~![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | gt(minus(fifo_length, n1), wr_level(X_t_42)))) | p_Reset(x_139) | (~p_Rd(x_139)) | (wr_level(plus(x_139, n1)) = n0) | (~p_Wr(x_139)) | gt(minus(fifo_length, n1), wr_level(x_139)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(181,plain,
% 0.21/0.48 ((p_Reset(x_139) | (wr_level(plus(x_139, n1)) = n0) | (~p_Rd(x_139)) | (~p_Wr(x_139)) | gt(minus(fifo_length, n1), wr_level(x_139))) <=> (p_Reset(x_139) | (~p_Rd(x_139)) | (wr_level(plus(x_139, n1)) = n0) | (~p_Wr(x_139)) | gt(minus(fifo_length, n1), wr_level(x_139)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(182,plain,
% 0.21/0.48 (((~![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | gt(minus(fifo_length, n1), wr_level(X_t_42)))) | (p_Reset(x_139) | (wr_level(plus(x_139, n1)) = n0) | (~p_Rd(x_139)) | (~p_Wr(x_139)) | gt(minus(fifo_length, n1), wr_level(x_139)))) <=> ((~![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | gt(minus(fifo_length, n1), wr_level(X_t_42)))) | (p_Reset(x_139) | (~p_Rd(x_139)) | (wr_level(plus(x_139, n1)) = n0) | (~p_Wr(x_139)) | gt(minus(fifo_length, n1), wr_level(x_139))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[181])).
% 0.21/0.48 tff(183,plain,
% 0.21/0.48 (((~![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | gt(minus(fifo_length, n1), wr_level(X_t_42)))) | (p_Reset(x_139) | (wr_level(plus(x_139, n1)) = n0) | (~p_Rd(x_139)) | (~p_Wr(x_139)) | gt(minus(fifo_length, n1), wr_level(x_139)))) <=> ((~![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | gt(minus(fifo_length, n1), wr_level(X_t_42)))) | p_Reset(x_139) | (~p_Rd(x_139)) | (wr_level(plus(x_139, n1)) = n0) | (~p_Wr(x_139)) | gt(minus(fifo_length, n1), wr_level(x_139)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[182, 180])).
% 0.21/0.48 tff(184,plain,
% 0.21/0.48 ((~![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | gt(minus(fifo_length, n1), wr_level(X_t_42)))) | (p_Reset(x_139) | (wr_level(plus(x_139, n1)) = n0) | (~p_Rd(x_139)) | (~p_Wr(x_139)) | gt(minus(fifo_length, n1), wr_level(x_139)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(185,plain,
% 0.21/0.48 ((~![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | (~p_Rd(X_t_42)) | (~p_Wr(X_t_42)) | gt(minus(fifo_length, n1), wr_level(X_t_42)))) | p_Reset(x_139) | (~p_Rd(x_139)) | (wr_level(plus(x_139, n1)) = n0) | (~p_Wr(x_139)) | gt(minus(fifo_length, n1), wr_level(x_139))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.21/0.48 tff(186,plain,
% 0.21/0.48 (p_Reset(x_139) | (~p_Rd(x_139)) | (wr_level(plus(x_139, n1)) = n0) | (~p_Wr(x_139)) | gt(minus(fifo_length, n1), wr_level(x_139))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[185, 179])).
% 0.21/0.48 tff(187,plain,
% 0.21/0.48 (~p_Rd(x_139)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[186, 108, 92, 80, 169])).
% 0.21/0.48 tff(188,plain,
% 0.21/0.48 (gt(fifo_length, int_level(x_139))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[146, 187, 92, 93, 108])).
% 0.21/0.48 tff(189,plain,
% 0.21/0.48 (^[X_t_42: $i] : refl((p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42))) <=> (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(190,plain,
% 0.21/0.48 (![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42))) <=> ![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[189])).
% 0.21/0.48 tff(191,plain,
% 0.21/0.48 (![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42))) <=> ![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(192,plain,
% 0.21/0.48 (^[X_t_42: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) <=> (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)))), ((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | (~gt(fifo_length, int_level(X_t_42)))) <=> ((p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42))) | (~gt(fifo_length, int_level(X_t_42)))))), rewrite(((p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42))) | (~gt(fifo_length, int_level(X_t_42)))) <=> (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))))), ((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | (~gt(fifo_length, int_level(X_t_42)))) <=> (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42)))))), (((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | (~gt(fifo_length, int_level(X_t_42)))) | gt(minus(fifo_length, n1), wr_level(X_t_42))) <=> ((p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42)))) | gt(minus(fifo_length, n1), wr_level(X_t_42))))), rewrite(((p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42)))) | gt(minus(fifo_length, n1), wr_level(X_t_42))) <=> (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42)))), (((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | (~gt(fifo_length, int_level(X_t_42)))) | gt(minus(fifo_length, n1), wr_level(X_t_42))) <=> (p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42))))), ((((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | (~gt(fifo_length, int_level(X_t_42)))) | gt(minus(fifo_length, n1), wr_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = n0)) <=> ((p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = n0)))), rewrite(((p_Reset(X_t_42) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = n0)) <=> (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42)))), ((((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | (~gt(fifo_length, int_level(X_t_42)))) | gt(minus(fifo_length, n1), wr_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = n0)) <=> (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(193,plain,
% 0.21/0.48 (![X_t_42: $i] : (((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | (~gt(fifo_length, int_level(X_t_42)))) | gt(minus(fifo_length, n1), wr_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = n0)) <=> ![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[192])).
% 0.21/0.48 tff(194,axiom,(![X_t_42: $i] : (((((p_Reset(X_t_42) | (~p_Wr(X_t_42))) | p_Rd(X_t_42)) | (~gt(fifo_length, int_level(X_t_42)))) | gt(minus(fifo_length, n1), wr_level(X_t_42))) | (wr_level(plus(X_t_42, n1)) = n0))), file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax','axiom_41')).
% 0.21/0.48 tff(195,plain,
% 0.21/0.48 (![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.21/0.48 tff(196,plain,
% 0.21/0.48 (![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[195, 191])).
% 0.21/0.48 tff(197,plain,(
% 0.21/0.48 ![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42)))),
% 0.21/0.48 inference(skolemize,[status(sab)],[196])).
% 0.21/0.48 tff(198,plain,
% 0.21/0.48 (![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[197, 190])).
% 0.21/0.48 tff(199,plain,
% 0.21/0.48 (((~![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42)))) | (p_Reset(x_139) | p_Rd(x_139) | (wr_level(plus(x_139, n1)) = n0) | (~p_Wr(x_139)) | gt(minus(fifo_length, n1), wr_level(x_139)) | (~gt(fifo_length, int_level(x_139))))) <=> ((~![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42)))) | p_Reset(x_139) | p_Rd(x_139) | (wr_level(plus(x_139, n1)) = n0) | (~p_Wr(x_139)) | gt(minus(fifo_length, n1), wr_level(x_139)) | (~gt(fifo_length, int_level(x_139))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(200,plain,
% 0.21/0.48 ((p_Reset(x_139) | (wr_level(plus(x_139, n1)) = n0) | p_Rd(x_139) | (~p_Wr(x_139)) | (~gt(fifo_length, int_level(x_139))) | gt(minus(fifo_length, n1), wr_level(x_139))) <=> (p_Reset(x_139) | p_Rd(x_139) | (wr_level(plus(x_139, n1)) = n0) | (~p_Wr(x_139)) | gt(minus(fifo_length, n1), wr_level(x_139)) | (~gt(fifo_length, int_level(x_139))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(201,plain,
% 0.21/0.48 (((~![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42)))) | (p_Reset(x_139) | (wr_level(plus(x_139, n1)) = n0) | p_Rd(x_139) | (~p_Wr(x_139)) | (~gt(fifo_length, int_level(x_139))) | gt(minus(fifo_length, n1), wr_level(x_139)))) <=> ((~![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42)))) | (p_Reset(x_139) | p_Rd(x_139) | (wr_level(plus(x_139, n1)) = n0) | (~p_Wr(x_139)) | gt(minus(fifo_length, n1), wr_level(x_139)) | (~gt(fifo_length, int_level(x_139)))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[200])).
% 0.21/0.48 tff(202,plain,
% 0.21/0.48 (((~![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42)))) | (p_Reset(x_139) | (wr_level(plus(x_139, n1)) = n0) | p_Rd(x_139) | (~p_Wr(x_139)) | (~gt(fifo_length, int_level(x_139))) | gt(minus(fifo_length, n1), wr_level(x_139)))) <=> ((~![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42)))) | p_Reset(x_139) | p_Rd(x_139) | (wr_level(plus(x_139, n1)) = n0) | (~p_Wr(x_139)) | gt(minus(fifo_length, n1), wr_level(x_139)) | (~gt(fifo_length, int_level(x_139))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[201, 199])).
% 0.21/0.48 tff(203,plain,
% 0.21/0.48 ((~![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42)))) | (p_Reset(x_139) | (wr_level(plus(x_139, n1)) = n0) | p_Rd(x_139) | (~p_Wr(x_139)) | (~gt(fifo_length, int_level(x_139))) | gt(minus(fifo_length, n1), wr_level(x_139)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(204,plain,
% 0.21/0.48 ((~![X_t_42: $i] : (p_Reset(X_t_42) | (wr_level(plus(X_t_42, n1)) = n0) | p_Rd(X_t_42) | (~p_Wr(X_t_42)) | (~gt(fifo_length, int_level(X_t_42))) | gt(minus(fifo_length, n1), wr_level(X_t_42)))) | p_Reset(x_139) | p_Rd(x_139) | (wr_level(plus(x_139, n1)) = n0) | (~p_Wr(x_139)) | gt(minus(fifo_length, n1), wr_level(x_139)) | (~gt(fifo_length, int_level(x_139)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.21/0.48 tff(205,plain,
% 0.21/0.48 (p_Reset(x_139) | p_Rd(x_139) | (wr_level(plus(x_139, n1)) = n0) | (~p_Wr(x_139)) | gt(minus(fifo_length, n1), wr_level(x_139)) | (~gt(fifo_length, int_level(x_139)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[204, 198])).
% 0.21/0.48 tff(206,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[205, 188, 187, 92, 80, 169, 108])).
% 0.21/0.48 tff(207,plain,((wr_level(plus(x_139, n1)) = wr_level(x_139)) | (wr_level(plus(x_139, n1)) = n0) | (wr_level(plus(x_139, n1)) = plus(wr_level(x_139), n1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(208,plain,
% 0.21/0.48 (wr_level(plus(x_139, n1)) = plus(wr_level(x_139), n1)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[207, 79, 20])).
% 0.21/0.48 tff(209,plain,
% 0.21/0.48 (gt(wr_level(plus(x_139, n1)), fifo_length) <=> gt(plus(wr_level(x_139), n1), fifo_length)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[208])).
% 0.21/0.48 tff(210,plain,
% 0.21/0.48 (gt(plus(wr_level(x_139), n1), fifo_length) <=> gt(wr_level(plus(x_139, n1)), fifo_length)),
% 0.21/0.48 inference(symmetry,[status(thm)],[209])).
% 0.21/0.48 tff(211,plain,
% 0.21/0.48 ((~gt(plus(wr_level(x_139), n1), fifo_length)) <=> (~gt(wr_level(plus(x_139, n1)), fifo_length))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[210])).
% 0.21/0.48 tff(212,plain,
% 0.21/0.48 (~gt(wr_level(plus(x_139, n1)), fifo_length)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[18, 211])).
% 0.21/0.48 tff(213,plain,
% 0.21/0.48 (fifo_length = wr_level(plus(x_139, n1))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[62, 212])).
% 0.21/0.48 tff(214,plain,
% 0.21/0.48 (fifo_length = plus(wr_level(x_139), plus(n0, n1))),
% 0.21/0.48 inference(transitivity,[status(thm)],[213, 208, 6])).
% 0.21/0.48 tff(215,plain,
% 0.21/0.48 (minus(fifo_length, n1) = minus(plus(wr_level(x_139), plus(n0, n1)), plus(n0, n1))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[214, 3])).
% 0.21/0.48 tff(216,plain,
% 0.21/0.48 (minus(plus(wr_level(x_139), plus(n0, n1)), plus(n0, n1)) = minus(fifo_length, n1)),
% 0.21/0.48 inference(symmetry,[status(thm)],[215])).
% 0.21/0.48 tff(217,plain,
% 0.21/0.48 (plus(wr_level(x_139), n1) = wr_level(plus(x_139, n1))),
% 0.21/0.48 inference(symmetry,[status(thm)],[208])).
% 0.21/0.48 tff(218,plain,
% 0.21/0.48 (plus(plus(wr_level(x_139), n1), n1) = plus(wr_level(plus(x_139, n1)), n1)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[217])).
% 0.21/0.48 tff(219,plain,
% 0.21/0.48 (gt(plus(plus(wr_level(x_139), n1), n1), plus(n0, n1)) <=> gt(plus(wr_level(plus(x_139, n1)), n1), plus(n0, n1))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[218])).
% 0.21/0.48 tff(220,plain,
% 0.21/0.48 (gt(plus(wr_level(plus(x_139, n1)), n1), plus(n0, n1)) <=> gt(plus(plus(wr_level(x_139), n1), n1), plus(n0, n1))),
% 0.21/0.48 inference(symmetry,[status(thm)],[219])).
% 0.21/0.48 tff(221,plain,
% 0.21/0.48 ((~![X_1: $i] : gt(plus(X_1, n1), n0)) | gt(plus(wr_level(plus(x_139, n1)), n1), n0)),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(222,plain,
% 0.21/0.48 (gt(plus(wr_level(plus(x_139, n1)), n1), n0)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[221, 73])).
% 0.21/0.48 tff(223,plain,
% 0.21/0.48 (^[Y_16: $i, X_15: $i] : refl((gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, n1), Y_16))) <=> (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, n1), Y_16))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(224,plain,
% 0.21/0.48 (![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, n1), Y_16))) <=> ![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, n1), Y_16)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[223])).
% 0.21/0.48 tff(225,plain,
% 0.21/0.48 (![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, n1), Y_16))) <=> ![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, n1), Y_16)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(226,plain,
% 0.21/0.48 (^[Y_16: $i, X_15: $i] : rewrite((((~gt(plus(X_15, n1), Y_16)) | gt(X_15, Y_16)) | (X_15 = Y_16)) <=> (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, n1), Y_16))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(227,plain,
% 0.21/0.49 (![Y_16: $i, X_15: $i] : (((~gt(plus(X_15, n1), Y_16)) | gt(X_15, Y_16)) | (X_15 = Y_16)) <=> ![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, n1), Y_16)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[226])).
% 0.21/0.49 tff(228,axiom,(![Y_16: $i, X_15: $i] : (((~gt(plus(X_15, n1), Y_16)) | gt(X_15, Y_16)) | (X_15 = Y_16))), file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax','axiom_11')).
% 0.21/0.49 tff(229,plain,
% 0.21/0.49 (![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, n1), Y_16)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.21/0.49 tff(230,plain,
% 0.21/0.49 (![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, n1), Y_16)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[229, 225])).
% 0.21/0.49 tff(231,plain,(
% 0.21/0.49 ![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, n1), Y_16)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[230])).
% 0.21/0.49 tff(232,plain,
% 0.21/0.49 (![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, n1), Y_16)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[231, 224])).
% 0.21/0.49 tff(233,plain,
% 0.21/0.49 (((~![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, n1), Y_16)))) | ((wr_level(plus(x_139, n1)) = n0) | gt(wr_level(plus(x_139, n1)), n0) | (~gt(plus(wr_level(plus(x_139, n1)), n1), n0)))) <=> ((~![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, n1), Y_16)))) | (wr_level(plus(x_139, n1)) = n0) | gt(wr_level(plus(x_139, n1)), n0) | (~gt(plus(wr_level(plus(x_139, n1)), n1), n0)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(234,plain,
% 0.21/0.49 ((gt(wr_level(plus(x_139, n1)), n0) | (wr_level(plus(x_139, n1)) = n0) | (~gt(plus(wr_level(plus(x_139, n1)), n1), n0))) <=> ((wr_level(plus(x_139, n1)) = n0) | gt(wr_level(plus(x_139, n1)), n0) | (~gt(plus(wr_level(plus(x_139, n1)), n1), n0)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(235,plain,
% 0.21/0.49 (((~![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, n1), Y_16)))) | (gt(wr_level(plus(x_139, n1)), n0) | (wr_level(plus(x_139, n1)) = n0) | (~gt(plus(wr_level(plus(x_139, n1)), n1), n0)))) <=> ((~![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, n1), Y_16)))) | ((wr_level(plus(x_139, n1)) = n0) | gt(wr_level(plus(x_139, n1)), n0) | (~gt(plus(wr_level(plus(x_139, n1)), n1), n0))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[234])).
% 0.21/0.49 tff(236,plain,
% 0.21/0.49 (((~![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, n1), Y_16)))) | (gt(wr_level(plus(x_139, n1)), n0) | (wr_level(plus(x_139, n1)) = n0) | (~gt(plus(wr_level(plus(x_139, n1)), n1), n0)))) <=> ((~![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, n1), Y_16)))) | (wr_level(plus(x_139, n1)) = n0) | gt(wr_level(plus(x_139, n1)), n0) | (~gt(plus(wr_level(plus(x_139, n1)), n1), n0)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[235, 233])).
% 0.21/0.49 tff(237,plain,
% 0.21/0.49 ((~![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, n1), Y_16)))) | (gt(wr_level(plus(x_139, n1)), n0) | (wr_level(plus(x_139, n1)) = n0) | (~gt(plus(wr_level(plus(x_139, n1)), n1), n0)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(238,plain,
% 0.21/0.49 ((~![Y_16: $i, X_15: $i] : (gt(X_15, Y_16) | (X_15 = Y_16) | (~gt(plus(X_15, n1), Y_16)))) | (wr_level(plus(x_139, n1)) = n0) | gt(wr_level(plus(x_139, n1)), n0) | (~gt(plus(wr_level(plus(x_139, n1)), n1), n0))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.21/0.49 tff(239,plain,
% 0.21/0.49 ((wr_level(plus(x_139, n1)) = n0) | gt(wr_level(plus(x_139, n1)), n0)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[238, 232, 222])).
% 0.21/0.49 tff(240,plain,
% 0.21/0.49 (gt(wr_level(plus(x_139, n1)), n0)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[239, 79])).
% 0.21/0.49 tff(241,plain,
% 0.21/0.49 (^[X_11: $i, Y_12: $i] : refl(((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1))) <=> ((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(242,plain,
% 0.21/0.49 (![X_11: $i, Y_12: $i] : ((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1))) <=> ![X_11: $i, Y_12: $i] : ((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[241])).
% 0.21/0.49 tff(243,plain,
% 0.21/0.49 (![X_11: $i, Y_12: $i] : ((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1))) <=> ![X_11: $i, Y_12: $i] : ((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(244,axiom,(![X_11: $i, Y_12: $i] : ((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1)))), file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax','axiom_8')).
% 0.21/0.49 tff(245,plain,
% 0.21/0.49 (![X_11: $i, Y_12: $i] : ((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.21/0.49 tff(246,plain,(
% 0.21/0.49 ![X_11: $i, Y_12: $i] : ((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[245])).
% 0.21/0.49 tff(247,plain,
% 0.21/0.49 (![X_11: $i, Y_12: $i] : ((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[246, 242])).
% 0.21/0.49 tff(248,plain,
% 0.21/0.49 (((~![X_11: $i, Y_12: $i] : ((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1)))) | ((~gt(wr_level(plus(x_139, n1)), n0)) | gt(plus(wr_level(plus(x_139, n1)), n1), plus(n0, n1)))) <=> ((~![X_11: $i, Y_12: $i] : ((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1)))) | (~gt(wr_level(plus(x_139, n1)), n0)) | gt(plus(wr_level(plus(x_139, n1)), n1), plus(n0, n1)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(249,plain,
% 0.21/0.49 ((~![X_11: $i, Y_12: $i] : ((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1)))) | ((~gt(wr_level(plus(x_139, n1)), n0)) | gt(plus(wr_level(plus(x_139, n1)), n1), plus(n0, n1)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(250,plain,
% 0.21/0.49 ((~![X_11: $i, Y_12: $i] : ((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1)))) | (~gt(wr_level(plus(x_139, n1)), n0)) | gt(plus(wr_level(plus(x_139, n1)), n1), plus(n0, n1))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.21/0.49 tff(251,plain,
% 0.21/0.49 ((~gt(wr_level(plus(x_139, n1)), n0)) | gt(plus(wr_level(plus(x_139, n1)), n1), plus(n0, n1))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[250, 247])).
% 0.21/0.49 tff(252,plain,
% 0.21/0.49 (gt(plus(wr_level(plus(x_139, n1)), n1), plus(n0, n1))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[251, 240])).
% 0.21/0.49 tff(253,plain,
% 0.21/0.49 (gt(plus(plus(wr_level(x_139), n1), n1), plus(n0, n1))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[252, 220])).
% 0.21/0.49 tff(254,assumption,(gt(plus(plus(wr_level(x_139), n1), n1), plus(n0, n1))), introduced(assumption)).
% 0.21/0.49 tff(255,plain,
% 0.21/0.49 (def_10(plus(n0, n1), plus(wr_level(x_139), n1)) <=> def_10(plus(n0, n1), plus(wr_level(x_139), plus(n0, n1)))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[6])).
% 0.21/0.49 tff(256,plain,
% 0.21/0.49 (def_10(plus(n0, n1), plus(wr_level(x_139), plus(n0, n1))) <=> def_10(plus(n0, n1), plus(wr_level(x_139), n1))),
% 0.21/0.49 inference(symmetry,[status(thm)],[255])).
% 0.21/0.49 tff(257,assumption,(def_10(plus(n0, n1), plus(wr_level(x_139), plus(n0, n1)))), introduced(assumption)).
% 0.21/0.49 tff(258,plain,
% 0.21/0.49 (def_10(plus(n0, n1), plus(wr_level(x_139), n1))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.21/0.49 tff(259,plain,
% 0.21/0.49 (^[Y_4: $i, X_3: $i] : refl(((~def_10(Y_4, X_3)) | (~gt(X_3, Y_4))) <=> ((~def_10(Y_4, X_3)) | (~gt(X_3, Y_4))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(260,plain,
% 0.21/0.49 (![Y_4: $i, X_3: $i] : ((~def_10(Y_4, X_3)) | (~gt(X_3, Y_4))) <=> ![Y_4: $i, X_3: $i] : ((~def_10(Y_4, X_3)) | (~gt(X_3, Y_4)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[259])).
% 0.21/0.49 tff(261,plain,
% 0.21/0.49 (![Y_4: $i, X_3: $i] : ((~def_10(Y_4, X_3)) | (~gt(X_3, Y_4))) <=> ![Y_4: $i, X_3: $i] : ((~def_10(Y_4, X_3)) | (~gt(X_3, Y_4)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(262,axiom,(![Y_4: $i, X_3: $i] : ((~def_10(Y_4, X_3)) | (~gt(X_3, Y_4)))), file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax','axiom_6')).
% 0.21/0.49 tff(263,plain,
% 0.21/0.49 (![Y_4: $i, X_3: $i] : ((~def_10(Y_4, X_3)) | (~gt(X_3, Y_4)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.21/0.49 tff(264,plain,(
% 0.21/0.49 ![Y_4: $i, X_3: $i] : ((~def_10(Y_4, X_3)) | (~gt(X_3, Y_4)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[263])).
% 0.21/0.49 tff(265,plain,
% 0.21/0.49 (![Y_4: $i, X_3: $i] : ((~def_10(Y_4, X_3)) | (~gt(X_3, Y_4)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[264, 260])).
% 0.21/0.49 tff(266,plain,
% 0.21/0.49 (((~![Y_4: $i, X_3: $i] : ((~def_10(Y_4, X_3)) | (~gt(X_3, Y_4)))) | ((~def_10(plus(n0, n1), plus(wr_level(x_139), n1))) | (~gt(plus(wr_level(x_139), n1), plus(n0, n1))))) <=> ((~![Y_4: $i, X_3: $i] : ((~def_10(Y_4, X_3)) | (~gt(X_3, Y_4)))) | (~def_10(plus(n0, n1), plus(wr_level(x_139), n1))) | (~gt(plus(wr_level(x_139), n1), plus(n0, n1))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(267,plain,
% 0.21/0.49 ((~![Y_4: $i, X_3: $i] : ((~def_10(Y_4, X_3)) | (~gt(X_3, Y_4)))) | ((~def_10(plus(n0, n1), plus(wr_level(x_139), n1))) | (~gt(plus(wr_level(x_139), n1), plus(n0, n1))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(268,plain,
% 0.21/0.49 ((~![Y_4: $i, X_3: $i] : ((~def_10(Y_4, X_3)) | (~gt(X_3, Y_4)))) | (~def_10(plus(n0, n1), plus(wr_level(x_139), n1))) | (~gt(plus(wr_level(x_139), n1), plus(n0, n1)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.21/0.49 tff(269,plain,
% 0.21/0.49 (~gt(plus(wr_level(x_139), n1), plus(n0, n1))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[268, 265, 258])).
% 0.21/0.49 tff(270,plain,
% 0.21/0.49 (((~![X_13: $i, Y_14: $i] : ((Y_14 = X_13) | (~gt(plus(X_13, n1), Y_14)) | gt(X_13, Y_14))) | (gt(plus(wr_level(x_139), n1), plus(n0, n1)) | (plus(n0, n1) = plus(wr_level(x_139), n1)) | (~gt(plus(plus(wr_level(x_139), n1), n1), plus(n0, n1))))) <=> ((~![X_13: $i, Y_14: $i] : ((Y_14 = X_13) | (~gt(plus(X_13, n1), Y_14)) | gt(X_13, Y_14))) | gt(plus(wr_level(x_139), n1), plus(n0, n1)) | (plus(n0, n1) = plus(wr_level(x_139), n1)) | (~gt(plus(plus(wr_level(x_139), n1), n1), plus(n0, n1))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(271,plain,
% 0.21/0.49 (((plus(n0, n1) = plus(wr_level(x_139), n1)) | (~gt(plus(plus(wr_level(x_139), n1), n1), plus(n0, n1))) | gt(plus(wr_level(x_139), n1), plus(n0, n1))) <=> (gt(plus(wr_level(x_139), n1), plus(n0, n1)) | (plus(n0, n1) = plus(wr_level(x_139), n1)) | (~gt(plus(plus(wr_level(x_139), n1), n1), plus(n0, n1))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(272,plain,
% 0.21/0.49 (((~![X_13: $i, Y_14: $i] : ((Y_14 = X_13) | (~gt(plus(X_13, n1), Y_14)) | gt(X_13, Y_14))) | ((plus(n0, n1) = plus(wr_level(x_139), n1)) | (~gt(plus(plus(wr_level(x_139), n1), n1), plus(n0, n1))) | gt(plus(wr_level(x_139), n1), plus(n0, n1)))) <=> ((~![X_13: $i, Y_14: $i] : ((Y_14 = X_13) | (~gt(plus(X_13, n1), Y_14)) | gt(X_13, Y_14))) | (gt(plus(wr_level(x_139), n1), plus(n0, n1)) | (plus(n0, n1) = plus(wr_level(x_139), n1)) | (~gt(plus(plus(wr_level(x_139), n1), n1), plus(n0, n1)))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[271])).
% 0.21/0.49 tff(273,plain,
% 0.21/0.49 (((~![X_13: $i, Y_14: $i] : ((Y_14 = X_13) | (~gt(plus(X_13, n1), Y_14)) | gt(X_13, Y_14))) | ((plus(n0, n1) = plus(wr_level(x_139), n1)) | (~gt(plus(plus(wr_level(x_139), n1), n1), plus(n0, n1))) | gt(plus(wr_level(x_139), n1), plus(n0, n1)))) <=> ((~![X_13: $i, Y_14: $i] : ((Y_14 = X_13) | (~gt(plus(X_13, n1), Y_14)) | gt(X_13, Y_14))) | gt(plus(wr_level(x_139), n1), plus(n0, n1)) | (plus(n0, n1) = plus(wr_level(x_139), n1)) | (~gt(plus(plus(wr_level(x_139), n1), n1), plus(n0, n1))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[272, 270])).
% 0.21/0.49 tff(274,plain,
% 0.21/0.49 ((~![X_13: $i, Y_14: $i] : ((Y_14 = X_13) | (~gt(plus(X_13, n1), Y_14)) | gt(X_13, Y_14))) | ((plus(n0, n1) = plus(wr_level(x_139), n1)) | (~gt(plus(plus(wr_level(x_139), n1), n1), plus(n0, n1))) | gt(plus(wr_level(x_139), n1), plus(n0, n1)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(275,plain,
% 0.21/0.49 ((~![X_13: $i, Y_14: $i] : ((Y_14 = X_13) | (~gt(plus(X_13, n1), Y_14)) | gt(X_13, Y_14))) | gt(plus(wr_level(x_139), n1), plus(n0, n1)) | (plus(n0, n1) = plus(wr_level(x_139), n1)) | (~gt(plus(plus(wr_level(x_139), n1), n1), plus(n0, n1)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.21/0.49 tff(276,plain,
% 0.21/0.49 (gt(plus(wr_level(x_139), n1), plus(n0, n1)) | (plus(n0, n1) = plus(wr_level(x_139), n1)) | (~gt(plus(plus(wr_level(x_139), n1), n1), plus(n0, n1)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[275, 58])).
% 0.21/0.50 tff(277,plain,
% 0.21/0.50 (plus(n0, n1) = plus(wr_level(x_139), n1)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[276, 269, 254])).
% 0.21/0.50 tff(278,plain,
% 0.21/0.50 (plus(n0, plus(n0, n1)) = plus(n0, n1)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[4])).
% 0.21/0.50 tff(279,plain,
% 0.21/0.50 (plus(n0, plus(n0, n1)) = plus(wr_level(x_139), plus(n0, n1))),
% 0.21/0.50 inference(transitivity,[status(thm)],[278, 277, 6])).
% 0.21/0.50 tff(280,plain,
% 0.21/0.50 (def_10(plus(n0, n1), plus(n0, plus(n0, n1))) <=> def_10(plus(n0, n1), plus(wr_level(x_139), plus(n0, n1)))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[279])).
% 0.21/0.50 tff(281,plain,
% 0.21/0.50 (def_10(plus(n0, n1), plus(wr_level(x_139), plus(n0, n1))) <=> def_10(plus(n0, n1), plus(n0, plus(n0, n1)))),
% 0.21/0.50 inference(symmetry,[status(thm)],[280])).
% 0.21/0.50 tff(282,plain,
% 0.21/0.50 (def_10(plus(n0, n1), plus(n0, plus(n0, n1)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[257, 281])).
% 0.21/0.50 tff(283,plain,
% 0.21/0.50 (plus(n0, n1) = plus(n0, plus(n0, n1))),
% 0.21/0.50 inference(symmetry,[status(thm)],[278])).
% 0.21/0.50 tff(284,plain,
% 0.21/0.50 (def_10(plus(n0, n1), plus(n0, n1)) <=> def_10(plus(n0, n1), plus(n0, plus(n0, n1)))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[283])).
% 0.21/0.50 tff(285,plain,
% 0.21/0.50 ((~def_10(plus(n0, n1), plus(n0, n1))) <=> (~def_10(plus(n0, n1), plus(n0, plus(n0, n1))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[284])).
% 0.21/0.50 tff(286,assumption,(def_10(plus(n0, n1), plus(n0, n1))), introduced(assumption)).
% 0.21/0.50 tff(287,plain,
% 0.21/0.50 (^[Y_4: $i] : refl((~def_10(Y_4, Y_4)) <=> (~def_10(Y_4, Y_4)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(288,plain,
% 0.21/0.50 (![Y_4: $i] : (~def_10(Y_4, Y_4)) <=> ![Y_4: $i] : (~def_10(Y_4, Y_4))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[287])).
% 0.21/0.50 tff(289,plain,
% 0.21/0.50 (![Y_4: $i] : (~def_10(Y_4, Y_4)) <=> ![Y_4: $i] : (~def_10(Y_4, Y_4))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(290,plain,
% 0.21/0.50 (![Y_4: $i, X_3: $i] : (~def_10(Y_4, Y_4)) <=> ![Y_4: $i] : (~def_10(Y_4, Y_4))),
% 0.21/0.50 inference(elim_unused_vars,[status(thm)],[])).
% 0.21/0.50 tff(291,plain,
% 0.21/0.50 (![Y_4: $i, X_3: $i] : ((~def_10(Y_4, X_3)) | (~(X_3 = Y_4))) <=> ![Y_4: $i, X_3: $i] : (~def_10(Y_4, Y_4))),
% 0.21/0.50 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.21/0.50 tff(292,plain,
% 0.21/0.50 (![Y_4: $i, X_3: $i] : ((~def_10(Y_4, X_3)) | (~(X_3 = Y_4))) <=> ![Y_4: $i] : (~def_10(Y_4, Y_4))),
% 0.21/0.50 inference(transitivity,[status(thm)],[291, 290])).
% 0.21/0.50 tff(293,axiom,(![Y_4: $i, X_3: $i] : ((~def_10(Y_4, X_3)) | (~(X_3 = Y_4)))), file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax','axiom_7')).
% 0.21/0.50 tff(294,plain,
% 0.21/0.50 (![Y_4: $i] : (~def_10(Y_4, Y_4))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[293, 292])).
% 0.21/0.50 tff(295,plain,
% 0.21/0.50 (![Y_4: $i] : (~def_10(Y_4, Y_4))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[294, 289])).
% 0.21/0.50 tff(296,plain,(
% 0.21/0.50 ![Y_4: $i] : (~def_10(Y_4, Y_4))),
% 0.21/0.50 inference(skolemize,[status(sab)],[295])).
% 0.21/0.50 tff(297,plain,
% 0.21/0.50 (![Y_4: $i] : (~def_10(Y_4, Y_4))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[296, 288])).
% 0.21/0.50 tff(298,plain,
% 0.21/0.50 ((~![Y_4: $i] : (~def_10(Y_4, Y_4))) | (~def_10(plus(n0, n1), plus(n0, n1)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(299,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[298, 297, 286])).
% 0.21/0.50 tff(300,plain,(~def_10(plus(n0, n1), plus(n0, n1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(301,plain,
% 0.21/0.50 (~def_10(plus(n0, n1), plus(n0, plus(n0, n1)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[300, 285])).
% 0.21/0.50 tff(302,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[301, 282])).
% 0.21/0.50 tff(303,plain,((~def_10(plus(n0, n1), plus(wr_level(x_139), plus(n0, n1)))) | (~gt(plus(plus(wr_level(x_139), n1), n1), plus(n0, n1)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(304,plain,
% 0.21/0.50 (~def_10(plus(n0, n1), plus(wr_level(x_139), plus(n0, n1)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[303, 253])).
% 0.21/0.50 tff(305,plain,
% 0.21/0.50 (^[Y_4: $i, Z_5: $i] : refl((def_10(Y_4, plus(Z_5, Y_4)) | (minus(plus(Z_5, Y_4), Y_4) = Z_5)) <=> (def_10(Y_4, plus(Z_5, Y_4)) | (minus(plus(Z_5, Y_4), Y_4) = Z_5)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(306,plain,
% 0.21/0.50 (![Y_4: $i, Z_5: $i] : (def_10(Y_4, plus(Z_5, Y_4)) | (minus(plus(Z_5, Y_4), Y_4) = Z_5)) <=> ![Y_4: $i, Z_5: $i] : (def_10(Y_4, plus(Z_5, Y_4)) | (minus(plus(Z_5, Y_4), Y_4) = Z_5))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[305])).
% 0.21/0.50 tff(307,plain,
% 0.21/0.50 (![Y_4: $i, Z_5: $i] : (def_10(Y_4, plus(Z_5, Y_4)) | (minus(plus(Z_5, Y_4), Y_4) = Z_5)) <=> ![Y_4: $i, Z_5: $i] : (def_10(Y_4, plus(Z_5, Y_4)) | (minus(plus(Z_5, Y_4), Y_4) = Z_5))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(308,plain,
% 0.21/0.50 (![Y_4: $i, Z_5: $i, X_3: $i] : (def_10(Y_4, plus(Z_5, Y_4)) | (minus(plus(Z_5, Y_4), Y_4) = Z_5)) <=> ![Y_4: $i, Z_5: $i] : (def_10(Y_4, plus(Z_5, Y_4)) | (minus(plus(Z_5, Y_4), Y_4) = Z_5))),
% 0.21/0.50 inference(elim_unused_vars,[status(thm)],[])).
% 0.21/0.50 tff(309,plain,
% 0.21/0.50 (![Y_4: $i, Z_5: $i, X_3: $i] : (def_10(Y_4, X_3) | (minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3))) <=> ![Y_4: $i, Z_5: $i, X_3: $i] : (def_10(Y_4, plus(Z_5, Y_4)) | (minus(plus(Z_5, Y_4), Y_4) = Z_5))),
% 0.21/0.50 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.21/0.50 tff(310,plain,
% 0.21/0.50 (![Y_4: $i, Z_5: $i, X_3: $i] : (def_10(Y_4, X_3) | (minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3))) <=> ![Y_4: $i, Z_5: $i] : (def_10(Y_4, plus(Z_5, Y_4)) | (minus(plus(Z_5, Y_4), Y_4) = Z_5))),
% 0.21/0.50 inference(transitivity,[status(thm)],[309, 308])).
% 0.21/0.50 tff(311,plain,
% 0.21/0.50 (^[Y_4: $i, Z_5: $i, X_3: $i] : trans(monotonicity(rewrite(((minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3))) <=> ((minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3)))), ((((minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3))) | def_10(Y_4, X_3)) <=> (((minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3))) | def_10(Y_4, X_3)))), rewrite((((minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3))) | def_10(Y_4, X_3)) <=> (def_10(Y_4, X_3) | (minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3)))), ((((minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3))) | def_10(Y_4, X_3)) <=> (def_10(Y_4, X_3) | (minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3)))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(312,plain,
% 0.21/0.50 (![Y_4: $i, Z_5: $i, X_3: $i] : (((minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3))) | def_10(Y_4, X_3)) <=> ![Y_4: $i, Z_5: $i, X_3: $i] : (def_10(Y_4, X_3) | (minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[311])).
% 0.21/0.50 tff(313,plain,
% 0.21/0.50 (![Y_4: $i, Z_5: $i, X_3: $i] : (((minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3))) | def_10(Y_4, X_3)) <=> ![Y_4: $i, Z_5: $i] : (def_10(Y_4, plus(Z_5, Y_4)) | (minus(plus(Z_5, Y_4), Y_4) = Z_5))),
% 0.21/0.50 inference(transitivity,[status(thm)],[312, 310])).
% 0.21/0.50 tff(314,axiom,(![Y_4: $i, Z_5: $i, X_3: $i] : (((minus(X_3, Y_4) = Z_5) | (~(plus(Z_5, Y_4) = X_3))) | def_10(Y_4, X_3))), file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax','axiom_5')).
% 0.21/0.50 tff(315,plain,
% 0.21/0.50 (![Y_4: $i, Z_5: $i] : (def_10(Y_4, plus(Z_5, Y_4)) | (minus(plus(Z_5, Y_4), Y_4) = Z_5))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[314, 313])).
% 0.21/0.50 tff(316,plain,
% 0.21/0.50 (![Y_4: $i, Z_5: $i] : (def_10(Y_4, plus(Z_5, Y_4)) | (minus(plus(Z_5, Y_4), Y_4) = Z_5))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[315, 307])).
% 0.21/0.50 tff(317,plain,(
% 0.21/0.50 ![Y_4: $i, Z_5: $i] : (def_10(Y_4, plus(Z_5, Y_4)) | (minus(plus(Z_5, Y_4), Y_4) = Z_5))),
% 0.21/0.50 inference(skolemize,[status(sab)],[316])).
% 0.21/0.50 tff(318,plain,
% 0.21/0.50 (![Y_4: $i, Z_5: $i] : (def_10(Y_4, plus(Z_5, Y_4)) | (minus(plus(Z_5, Y_4), Y_4) = Z_5))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[317, 306])).
% 0.21/0.50 tff(319,plain,
% 0.21/0.50 (((~![Y_4: $i, Z_5: $i] : (def_10(Y_4, plus(Z_5, Y_4)) | (minus(plus(Z_5, Y_4), Y_4) = Z_5))) | (def_10(plus(n0, n1), plus(wr_level(x_139), plus(n0, n1))) | (minus(plus(wr_level(x_139), plus(n0, n1)), plus(n0, n1)) = wr_level(x_139)))) <=> ((~![Y_4: $i, Z_5: $i] : (def_10(Y_4, plus(Z_5, Y_4)) | (minus(plus(Z_5, Y_4), Y_4) = Z_5))) | def_10(plus(n0, n1), plus(wr_level(x_139), plus(n0, n1))) | (minus(plus(wr_level(x_139), plus(n0, n1)), plus(n0, n1)) = wr_level(x_139)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(320,plain,
% 0.21/0.50 ((~![Y_4: $i, Z_5: $i] : (def_10(Y_4, plus(Z_5, Y_4)) | (minus(plus(Z_5, Y_4), Y_4) = Z_5))) | (def_10(plus(n0, n1), plus(wr_level(x_139), plus(n0, n1))) | (minus(plus(wr_level(x_139), plus(n0, n1)), plus(n0, n1)) = wr_level(x_139)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(321,plain,
% 0.21/0.50 ((~![Y_4: $i, Z_5: $i] : (def_10(Y_4, plus(Z_5, Y_4)) | (minus(plus(Z_5, Y_4), Y_4) = Z_5))) | def_10(plus(n0, n1), plus(wr_level(x_139), plus(n0, n1))) | (minus(plus(wr_level(x_139), plus(n0, n1)), plus(n0, n1)) = wr_level(x_139))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.21/0.50 tff(322,plain,
% 0.21/0.50 (def_10(plus(n0, n1), plus(wr_level(x_139), plus(n0, n1))) | (minus(plus(wr_level(x_139), plus(n0, n1)), plus(n0, n1)) = wr_level(x_139))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[321, 318])).
% 0.21/0.50 tff(323,plain,
% 0.21/0.50 (minus(plus(wr_level(x_139), plus(n0, n1)), plus(n0, n1)) = wr_level(x_139)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[322, 304])).
% 0.21/0.50 tff(324,plain,
% 0.21/0.50 (wr_level(x_139) = minus(plus(wr_level(x_139), plus(n0, n1)), plus(n0, n1))),
% 0.21/0.50 inference(symmetry,[status(thm)],[323])).
% 0.21/0.50 tff(325,plain,
% 0.21/0.50 (wr_level(x_139) = minus(fifo_length, n1)),
% 0.21/0.50 inference(transitivity,[status(thm)],[324, 216])).
% 0.21/0.50 tff(326,plain,
% 0.21/0.50 (gt(wr_level(x_139), wr_level(x_139)) <=> gt(minus(fifo_length, n1), wr_level(x_139))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[325])).
% 0.21/0.50 tff(327,plain,
% 0.21/0.50 (gt(minus(fifo_length, n1), wr_level(x_139)) <=> gt(wr_level(x_139), wr_level(x_139))),
% 0.21/0.50 inference(symmetry,[status(thm)],[326])).
% 0.21/0.50 tff(328,plain,
% 0.21/0.50 (p_Wr(x_139)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[107, 92, 20])).
% 0.21/0.50 tff(329,assumption,(~gt(minus(fifo_length, n1), wr_level(x_139))), introduced(assumption)).
% 0.21/0.50 tff(330,plain,
% 0.21/0.50 (~p_Rd(x_139)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[186, 329, 92, 80, 328])).
% 0.21/0.50 tff(331,plain,
% 0.21/0.50 (gt(fifo_length, int_level(x_139))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[146, 330, 92, 20, 328])).
% 0.21/0.50 tff(332,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[205, 331, 330, 92, 80, 329, 328])).
% 0.21/0.50 tff(333,plain,(gt(minus(fifo_length, n1), wr_level(x_139)) | (wr_level(plus(x_139, n1)) = n0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(334,plain,
% 0.21/0.50 (gt(minus(fifo_length, n1), wr_level(x_139))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[333, 79])).
% 0.21/0.50 tff(335,plain,
% 0.21/0.50 (gt(wr_level(x_139), wr_level(x_139))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[334, 327])).
% 0.21/0.50 tff(336,plain,
% 0.21/0.50 (gt(wr_level(plus(x_139, n1)), wr_level(plus(x_139, n1))) <=> gt(plus(wr_level(x_139), n1), plus(wr_level(x_139), n1))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[208, 208])).
% 0.21/0.50 tff(337,plain,
% 0.21/0.50 ((~gt(wr_level(plus(x_139, n1)), wr_level(plus(x_139, n1)))) <=> (~gt(plus(wr_level(x_139), n1), plus(wr_level(x_139), n1)))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[336])).
% 0.21/0.50 tff(338,plain,
% 0.21/0.50 (~gt(plus(wr_level(x_139), n1), plus(wr_level(x_139), n1))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[21, 337])).
% 0.21/0.50 tff(339,plain,
% 0.21/0.50 (((~![X_11: $i, Y_12: $i] : ((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1)))) | ((~gt(wr_level(x_139), wr_level(x_139))) | gt(plus(wr_level(x_139), n1), plus(wr_level(x_139), n1)))) <=> ((~![X_11: $i, Y_12: $i] : ((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1)))) | (~gt(wr_level(x_139), wr_level(x_139))) | gt(plus(wr_level(x_139), n1), plus(wr_level(x_139), n1)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(340,plain,
% 0.21/0.50 ((~![X_11: $i, Y_12: $i] : ((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1)))) | ((~gt(wr_level(x_139), wr_level(x_139))) | gt(plus(wr_level(x_139), n1), plus(wr_level(x_139), n1)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(341,plain,
% 0.21/0.50 ((~![X_11: $i, Y_12: $i] : ((~gt(Y_12, X_11)) | gt(plus(Y_12, n1), plus(X_11, n1)))) | (~gt(wr_level(x_139), wr_level(x_139))) | gt(plus(wr_level(x_139), n1), plus(wr_level(x_139), n1))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[340, 339])).
% 0.21/0.50 tff(342,plain,
% 0.21/0.50 ((~gt(wr_level(x_139), wr_level(x_139))) | gt(plus(wr_level(x_139), n1), plus(wr_level(x_139), n1))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[341, 247])).
% 0.21/0.50 tff(343,plain,
% 0.21/0.50 (~gt(wr_level(x_139), wr_level(x_139))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[342, 338])).
% 0.21/0.50 tff(344,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[343, 335])).
% 0.21/0.50 tff(345,plain,(gt(wr_level(plus(x_139, n1)), wr_level(plus(x_139, n1)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(346,plain,
% 0.21/0.50 (^[X_28: $i] : refl((~gt(X_28, X_28)) <=> (~gt(X_28, X_28)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(347,plain,
% 0.21/0.50 (![X_28: $i] : (~gt(X_28, X_28)) <=> ![X_28: $i] : (~gt(X_28, X_28))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[346])).
% 0.21/0.50 tff(348,plain,
% 0.21/0.50 (![X_28: $i] : (~gt(X_28, X_28)) <=> ![X_28: $i] : (~gt(X_28, X_28))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(349,axiom,(![X_28: $i] : (~gt(X_28, X_28))), file('/export/starexec/sandbox/benchmark/Axioms/HWV003-0.ax','axiom_17')).
% 0.21/0.50 tff(350,plain,
% 0.21/0.50 (![X_28: $i] : (~gt(X_28, X_28))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[349, 348])).
% 0.21/0.50 tff(351,plain,(
% 0.21/0.50 ![X_28: $i] : (~gt(X_28, X_28))),
% 0.21/0.50 inference(skolemize,[status(sab)],[350])).
% 0.21/0.50 tff(352,plain,
% 0.21/0.50 (![X_28: $i] : (~gt(X_28, X_28))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[351, 347])).
% 0.21/0.50 tff(353,plain,
% 0.21/0.50 ((~![X_28: $i] : (~gt(X_28, X_28))) | (~gt(wr_level(plus(x_139, n1)), wr_level(plus(x_139, n1))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(354,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[353, 352, 345])).
% 0.21/0.50 % SZS output end Proof
% 0.21/0.51 % E exiting
%------------------------------------------------------------------------------