TSTP Solution File: HWV016-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HWV016-2 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 Sep 17 02:10:37 EDT 2022
% Result : Unsatisfiable 0.16s 0.41s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : HWV016-2 : TPTP v8.1.0. Released v2.5.0.
% 0.02/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n018.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Wed Aug 31 22:05:41 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.15/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.31 Usage: tptp [options] [-file:]file
% 0.15/0.31 -h, -? prints this message.
% 0.15/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.31 -m, -model generate model.
% 0.15/0.31 -p, -proof generate proof.
% 0.15/0.31 -c, -core generate unsat core of named formulas.
% 0.15/0.31 -st, -statistics display statistics.
% 0.15/0.31 -t:timeout set timeout (in second).
% 0.15/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.31 -<param>:<value> configuration parameter and value.
% 0.15/0.31 -o:<output-file> file to place output in.
% 0.16/0.41 % SZS status Unsatisfiable
% 0.16/0.41 % SZS output start Proof
% 0.16/0.41 tff(p_LES_EQU__type, type, (
% 0.16/0.41 p_LES_EQU_: ( $i * $i ) > $o)).
% 0.16/0.41 tff(fwork_DOTfifo_DOTrtl_DOTlevel__type, type, (
% 0.16/0.41 fwork_DOTfifo_DOTrtl_DOTlevel_: $i > $i)).
% 0.16/0.41 tff(t_206_type, type, (
% 0.16/0.41 t_206: $i)).
% 0.16/0.41 tff(f__length__type, type, (
% 0.16/0.41 f__length_: $i > $i)).
% 0.16/0.41 tff(f__empty__type, type, (
% 0.16/0.41 f__empty_: $i)).
% 0.16/0.41 tff(fwork_DOTfifo_DOTrtl_DOTint__level__type, type, (
% 0.16/0.41 fwork_DOTfifo_DOTrtl_DOTint__level_: $i > $i)).
% 0.16/0.41 tff(f_ADD__type, type, (
% 0.16/0.41 f_ADD_: ( $i * $i ) > $i)).
% 0.16/0.41 tff(n1_type, type, (
% 0.16/0.41 n1: $i)).
% 0.16/0.41 tff(p__pred__type, type, (
% 0.16/0.41 p__pred_: $i > $o)).
% 0.16/0.41 tff(fwork_DOTfifo_DOTrtl_DOTempty__type, type, (
% 0.16/0.41 fwork_DOTfifo_DOTrtl_DOTempty_: $i > $i)).
% 0.16/0.41 tff(n0_type, type, (
% 0.16/0.41 n0: $i)).
% 0.16/0.41 tff(fwork_DOTfifo_DOTrtl_DOTrd__type, type, (
% 0.16/0.41 fwork_DOTfifo_DOTrtl_DOTrd_: $i > $i)).
% 0.16/0.41 tff(fwork_DOTfifo_DOTrtl_DOTfifo__length__type, type, (
% 0.16/0.41 fwork_DOTfifo_DOTrtl_DOTfifo__length_: $i)).
% 0.16/0.41 tff(fwork_DOTfifo_DOTrtl_DOTwr__type, type, (
% 0.16/0.41 fwork_DOTfifo_DOTrtl_DOTwr_: $i > $i)).
% 0.16/0.41 tff(fwork_DOTfifo_DOTrtl_DOTreset__type, type, (
% 0.16/0.41 fwork_DOTfifo_DOTrtl_DOTreset_: $i > $i)).
% 0.16/0.41 tff(1,plain,
% 0.16/0.41 (p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(f_ADD_(t_206, n1))) <=> p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(f_ADD_(t_206, n1)))),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 tff(2,axiom,(p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(f_ADD_(t_206, n1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quest_4')).
% 0.16/0.41 tff(3,plain,
% 0.16/0.41 (p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(f_ADD_(t_206, n1)))),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.16/0.41 tff(4,plain,
% 0.16/0.41 (^[T_4: $i] : refl(((~p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = f__length_(f__empty_))) <=> ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = f__length_(f__empty_))))),
% 0.16/0.41 inference(bind,[status(th)],[])).
% 0.16/0.41 tff(5,plain,
% 0.16/0.41 (![T_4: $i] : ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = f__length_(f__empty_))) <=> ![T_4: $i] : ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = f__length_(f__empty_)))),
% 0.16/0.41 inference(quant_intro,[status(thm)],[4])).
% 0.16/0.41 tff(6,plain,
% 0.16/0.41 (^[T_4: $i] : rewrite(((~p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = n0)) <=> ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = f__length_(f__empty_))))),
% 0.16/0.41 inference(bind,[status(th)],[])).
% 0.16/0.41 tff(7,plain,
% 0.16/0.41 (![T_4: $i] : ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = n0)) <=> ![T_4: $i] : ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = f__length_(f__empty_)))),
% 0.16/0.41 inference(quant_intro,[status(thm)],[6])).
% 0.16/0.41 tff(8,plain,
% 0.16/0.41 (![T_4: $i] : ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = n0)) <=> ![T_4: $i] : ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = n0))),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 tff(9,axiom,(![T_4: $i] : ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = n0))), file('/export/starexec/sandbox/benchmark/Axioms/HWV004-0.ax','axiom_9')).
% 0.16/0.41 tff(10,plain,
% 0.16/0.41 (![T_4: $i] : ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = n0))),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.16/0.41 tff(11,plain,
% 0.16/0.41 (![T_4: $i] : ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = f__length_(f__empty_)))),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[10, 7])).
% 0.16/0.41 tff(12,plain,(
% 0.16/0.41 ![T_4: $i] : ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = f__length_(f__empty_)))),
% 0.16/0.41 inference(skolemize,[status(sab)],[11])).
% 0.16/0.41 tff(13,plain,
% 0.16/0.41 (![T_4: $i] : ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = f__length_(f__empty_)))),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.16/0.42 tff(14,plain,
% 0.16/0.42 (((~![T_4: $i] : ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = f__length_(f__empty_)))) | ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(f_ADD_(t_206, n1)))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f__length_(f__empty_)))) <=> ((~![T_4: $i] : ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = f__length_(f__empty_)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(f_ADD_(t_206, n1)))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f__length_(f__empty_)))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(15,plain,
% 0.16/0.42 ((~![T_4: $i] : ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = f__length_(f__empty_)))) | ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(f_ADD_(t_206, n1)))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f__length_(f__empty_)))),
% 0.16/0.42 inference(quant_inst,[status(thm)],[])).
% 0.16/0.42 tff(16,plain,
% 0.16/0.42 ((~![T_4: $i] : ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_4))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(T_4) = f__length_(f__empty_)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(f_ADD_(t_206, n1)))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f__length_(f__empty_))),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.16/0.42 tff(17,plain,
% 0.16/0.42 (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f__length_(f__empty_)),
% 0.16/0.42 inference(unit_resolution,[status(thm)],[16, 13, 3])).
% 0.16/0.42 tff(18,assumption,(~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))), introduced(assumption)).
% 0.16/0.42 tff(19,plain,
% 0.16/0.42 ((f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1))) <=> (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))),
% 0.16/0.42 inference(commutativity,[status(thm)],[])).
% 0.16/0.42 tff(20,plain,
% 0.16/0.42 (f__length_(f__empty_) = fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1))),
% 0.16/0.42 inference(symmetry,[status(thm)],[17])).
% 0.16/0.42 tff(21,plain,
% 0.16/0.42 ((f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = f__length_(f__empty_)) <=> (f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)))),
% 0.16/0.42 inference(monotonicity,[status(thm)],[20])).
% 0.16/0.42 tff(22,plain,
% 0.16/0.42 ((f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = f__length_(f__empty_)) <=> (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))),
% 0.16/0.42 inference(transitivity,[status(thm)],[21, 19])).
% 0.16/0.42 tff(23,plain,
% 0.16/0.42 ((~(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = f__length_(f__empty_))) <=> (~(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)))),
% 0.16/0.42 inference(monotonicity,[status(thm)],[22])).
% 0.16/0.42 tff(24,assumption,(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = f__length_(f__empty_)), introduced(assumption)).
% 0.16/0.42 tff(25,plain,
% 0.16/0.42 (^[X_80: $i] : refl((~(f_ADD_(X_80, n1) = f__length_(f__empty_))) <=> (~(f_ADD_(X_80, n1) = f__length_(f__empty_))))),
% 0.16/0.42 inference(bind,[status(th)],[])).
% 0.16/0.42 tff(26,plain,
% 0.16/0.42 (![X_80: $i] : (~(f_ADD_(X_80, n1) = f__length_(f__empty_))) <=> ![X_80: $i] : (~(f_ADD_(X_80, n1) = f__length_(f__empty_)))),
% 0.16/0.42 inference(quant_intro,[status(thm)],[25])).
% 0.16/0.42 tff(27,plain,
% 0.16/0.42 (^[X_80: $i] : rewrite((~(f_ADD_(X_80, n1) = n0)) <=> (~(f_ADD_(X_80, n1) = f__length_(f__empty_))))),
% 0.16/0.42 inference(bind,[status(th)],[])).
% 0.16/0.42 tff(28,plain,
% 0.16/0.42 (![X_80: $i] : (~(f_ADD_(X_80, n1) = n0)) <=> ![X_80: $i] : (~(f_ADD_(X_80, n1) = f__length_(f__empty_)))),
% 0.16/0.42 inference(quant_intro,[status(thm)],[27])).
% 0.16/0.42 tff(29,plain,
% 0.16/0.42 (![X_80: $i] : (~(f_ADD_(X_80, n1) = n0)) <=> ![X_80: $i] : (~(f_ADD_(X_80, n1) = n0))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(30,axiom,(![X_80: $i] : (~(f_ADD_(X_80, n1) = n0))), file('/export/starexec/sandbox/benchmark/Axioms/HWV004-0.ax','axiom_59')).
% 0.16/0.42 tff(31,plain,
% 0.16/0.42 (![X_80: $i] : (~(f_ADD_(X_80, n1) = n0))),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.16/0.42 tff(32,plain,
% 0.16/0.42 (![X_80: $i] : (~(f_ADD_(X_80, n1) = f__length_(f__empty_)))),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[31, 28])).
% 0.16/0.42 tff(33,plain,(
% 0.16/0.42 ![X_80: $i] : (~(f_ADD_(X_80, n1) = f__length_(f__empty_)))),
% 0.16/0.42 inference(skolemize,[status(sab)],[32])).
% 0.16/0.42 tff(34,plain,
% 0.16/0.42 (![X_80: $i] : (~(f_ADD_(X_80, n1) = f__length_(f__empty_)))),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.16/0.42 tff(35,plain,
% 0.16/0.42 ((~![X_80: $i] : (~(f_ADD_(X_80, n1) = f__length_(f__empty_)))) | (~(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = f__length_(f__empty_)))),
% 0.16/0.42 inference(quant_inst,[status(thm)],[])).
% 0.16/0.42 tff(36,plain,
% 0.16/0.42 ($false),
% 0.16/0.42 inference(unit_resolution,[status(thm)],[35, 34, 24])).
% 0.16/0.42 tff(37,plain,(~(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = f__length_(f__empty_))), inference(lemma,lemma(discharge,[]))).
% 0.16/0.42 tff(38,plain,
% 0.16/0.42 (~(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[37, 23])).
% 0.16/0.42 tff(39,plain,
% 0.16/0.42 (p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)) <=> p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(40,axiom,(p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quest_3')).
% 0.16/0.42 tff(41,plain,
% 0.16/0.42 (p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.16/0.42 tff(42,plain,
% 0.16/0.42 ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))) <=> (~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(43,axiom,(~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quest_2')).
% 0.16/0.42 tff(44,plain,
% 0.16/0.42 (~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.16/0.42 tff(45,plain,
% 0.16/0.42 (^[T_13: $i] : refl((p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1))) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1))))),
% 0.16/0.42 inference(bind,[status(th)],[])).
% 0.16/0.42 tff(46,plain,
% 0.16/0.42 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1))) <=> ![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))),
% 0.16/0.42 inference(quant_intro,[status(thm)],[45])).
% 0.16/0.42 tff(47,plain,
% 0.16/0.42 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1))) <=> ![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(48,plain,
% 0.16/0.42 (^[T_13: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))) <=> (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))), ((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) <=> ((p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))))), rewrite(((p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))), ((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1))))), (((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) <=> ((p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))))), rewrite(((p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) <=> ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))), (((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) <=> ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1))))), ((((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))) <=> (((~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))))), rewrite((((~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))), ((((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))))),
% 0.16/0.42 inference(bind,[status(th)],[])).
% 0.16/0.42 tff(49,plain,
% 0.16/0.42 (![T_13: $i] : (((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))) <=> ![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))),
% 0.16/0.42 inference(quant_intro,[status(thm)],[48])).
% 0.16/0.42 tff(50,axiom,(![T_13: $i] : (((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)))), file('/export/starexec/sandbox/benchmark/Axioms/HWV004-0.ax','axiom_18')).
% 0.16/0.42 tff(51,plain,
% 0.16/0.42 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.16/0.42 tff(52,plain,
% 0.16/0.42 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.16/0.42 tff(53,plain,(
% 0.16/0.42 ![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))),
% 0.16/0.42 inference(skolemize,[status(sab)],[52])).
% 0.16/0.42 tff(54,plain,
% 0.16/0.42 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.16/0.42 tff(55,plain,
% 0.16/0.42 (((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))) <=> ((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(56,plain,
% 0.16/0.42 ((p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(57,plain,
% 0.16/0.42 (((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)))) <=> ((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))))),
% 0.16/0.42 inference(monotonicity,[status(thm)],[56])).
% 0.16/0.42 tff(58,plain,
% 0.16/0.42 (((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)))) <=> ((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))),
% 0.16/0.42 inference(transitivity,[status(thm)],[57, 55])).
% 0.16/0.42 tff(59,plain,
% 0.16/0.42 ((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)))),
% 0.16/0.42 inference(quant_inst,[status(thm)],[])).
% 0.16/0.42 tff(60,plain,
% 0.16/0.42 ((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.16/0.42 tff(61,plain,
% 0.16/0.42 (p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
% 0.16/0.42 inference(unit_resolution,[status(thm)],[60, 54, 44, 41])).
% 0.16/0.42 tff(62,plain,
% 0.16/0.42 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
% 0.16/0.42 inference(unit_resolution,[status(thm)],[61, 18, 38])).
% 0.16/0.42 tff(63,plain,
% 0.16/0.42 (^[T_13: $i] : refl((p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))))),
% 0.16/0.42 inference(bind,[status(th)],[])).
% 0.16/0.42 tff(64,plain,
% 0.16/0.42 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))) <=> ![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))))),
% 0.16/0.42 inference(quant_intro,[status(thm)],[63])).
% 0.16/0.42 tff(65,plain,
% 0.16/0.42 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))) <=> ![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(66,plain,
% 0.16/0.42 (^[T_13: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))) <=> ((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))))), ((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) <=> (((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))))), rewrite((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))))), ((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))))), (((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) <=> ((p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))))), rewrite(((p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) <=> ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))))), (((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) <=> ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))))), ((((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))) <=> (((~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))))), rewrite((((~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))))), ((((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))))))),
% 0.16/0.43 inference(bind,[status(th)],[])).
% 0.16/0.43 tff(67,plain,
% 0.16/0.43 (![T_13: $i] : (((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))) <=> ![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))))),
% 0.16/0.43 inference(quant_intro,[status(thm)],[66])).
% 0.16/0.43 tff(68,axiom,(![T_13: $i] : (((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)))), file('/export/starexec/sandbox/benchmark/Axioms/HWV004-0.ax','axiom_23')).
% 0.16/0.43 tff(69,plain,
% 0.16/0.43 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))))),
% 0.16/0.43 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.16/0.43 tff(70,plain,
% 0.16/0.43 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))))),
% 0.16/0.43 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.16/0.43 tff(71,plain,(
% 0.16/0.43 ![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))))),
% 0.16/0.43 inference(skolemize,[status(sab)],[70])).
% 0.16/0.43 tff(72,plain,
% 0.16/0.43 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))))),
% 0.16/0.43 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.16/0.43 tff(73,plain,
% 0.16/0.43 (((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))))) <=> ((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))))),
% 0.16/0.43 inference(rewrite,[status(thm)],[])).
% 0.16/0.43 tff(74,plain,
% 0.16/0.43 ((p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))))),
% 0.16/0.43 inference(rewrite,[status(thm)],[])).
% 0.16/0.43 tff(75,plain,
% 0.16/0.43 (((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))))) <=> ((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))))),
% 0.16/0.43 inference(monotonicity,[status(thm)],[74])).
% 0.16/0.43 tff(76,plain,
% 0.16/0.43 (((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))))) <=> ((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))))),
% 0.16/0.43 inference(transitivity,[status(thm)],[75, 73])).
% 0.16/0.43 tff(77,plain,
% 0.16/0.43 ((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))))),
% 0.16/0.43 inference(quant_inst,[status(thm)],[])).
% 0.16/0.43 tff(78,plain,
% 0.16/0.43 ((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))),
% 0.16/0.43 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.16/0.43 tff(79,plain,
% 0.16/0.43 (p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))),
% 0.16/0.43 inference(unit_resolution,[status(thm)],[78, 72, 44, 41])).
% 0.16/0.43 tff(80,plain,
% 0.16/0.43 (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)),
% 0.16/0.43 inference(unit_resolution,[status(thm)],[79, 62, 18])).
% 0.16/0.43 tff(81,plain,
% 0.16/0.43 (fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1))),
% 0.16/0.43 inference(symmetry,[status(thm)],[80])).
% 0.16/0.43 tff(82,plain,
% 0.16/0.43 (fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = f__length_(f__empty_)),
% 0.16/0.43 inference(transitivity,[status(thm)],[81, 17])).
% 0.16/0.43 tff(83,plain,
% 0.16/0.43 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) <=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f__length_(f__empty_))),
% 0.16/0.43 inference(monotonicity,[status(thm)],[82])).
% 0.16/0.43 tff(84,plain,
% 0.16/0.43 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f__length_(f__empty_)) <=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
% 0.16/0.43 inference(symmetry,[status(thm)],[83])).
% 0.16/0.43 tff(85,plain,
% 0.16/0.43 ((~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f__length_(f__empty_))) <=> (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))),
% 0.16/0.43 inference(monotonicity,[status(thm)],[84])).
% 0.16/0.43 tff(86,plain,
% 0.16/0.43 ((~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n0)) <=> (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f__length_(f__empty_)))),
% 0.16/0.43 inference(rewrite,[status(thm)],[])).
% 0.16/0.43 tff(87,plain,
% 0.16/0.43 ((~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n0)) <=> (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n0))),
% 0.16/0.43 inference(rewrite,[status(thm)],[])).
% 0.16/0.43 tff(88,axiom,(~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quest_5')).
% 0.16/0.43 tff(89,plain,
% 0.16/0.43 (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n0)),
% 0.16/0.43 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.16/0.43 tff(90,plain,
% 0.16/0.43 (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f__length_(f__empty_))),
% 0.16/0.43 inference(modus_ponens,[status(thm)],[89, 86])).
% 0.16/0.43 tff(91,plain,
% 0.16/0.43 (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
% 0.16/0.43 inference(modus_ponens,[status(thm)],[90, 85])).
% 0.16/0.43 tff(92,plain,
% 0.16/0.43 ($false),
% 0.16/0.43 inference(unit_resolution,[status(thm)],[62, 91])).
% 0.16/0.43 tff(93,plain,(p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))), inference(lemma,lemma(discharge,[]))).
% 0.16/0.43 tff(94,plain,
% 0.16/0.43 (^[T_13: $i] : refl((p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_)))) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_)))))),
% 0.16/0.43 inference(bind,[status(th)],[])).
% 0.16/0.43 tff(95,plain,
% 0.16/0.43 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_)))) <=> ![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_))))),
% 0.16/0.43 inference(quant_intro,[status(thm)],[94])).
% 0.16/0.43 tff(96,plain,
% 0.16/0.43 (^[T_13: $i] : trans(monotonicity(rewrite((~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) <=> (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_)))), ((p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_)))))), rewrite((p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_)))) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_))))), ((p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_))))))),
% 0.16/0.43 inference(bind,[status(th)],[])).
% 0.16/0.43 tff(97,plain,
% 0.16/0.43 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) <=> ![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_))))),
% 0.16/0.43 inference(quant_intro,[status(thm)],[96])).
% 0.16/0.43 tff(98,plain,
% 0.16/0.43 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) <=> ![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)))),
% 0.16/0.43 inference(rewrite,[status(thm)],[])).
% 0.16/0.43 tff(99,plain,
% 0.16/0.43 (^[T_13: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) <=> ((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)))), ((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) <=> (((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))))), rewrite((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) <=> ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)))), ((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) <=> ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))))), (((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) <=> (((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))))), rewrite((((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) <=> ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)))), (((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) <=> ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))))), ((((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))) <=> (((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))))), rewrite((((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)))), ((((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)))))),
% 0.16/0.43 inference(bind,[status(th)],[])).
% 0.16/0.43 tff(100,plain,
% 0.16/0.43 (![T_13: $i] : (((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))) <=> ![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)))),
% 0.16/0.43 inference(quant_intro,[status(thm)],[99])).
% 0.16/0.43 tff(101,axiom,(![T_13: $i] : (((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)))), file('/export/starexec/sandbox/benchmark/Axioms/HWV004-0.ax','axiom_36')).
% 0.16/0.43 tff(102,plain,
% 0.16/0.43 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)))),
% 0.16/0.43 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.16/0.43 tff(103,plain,
% 0.16/0.43 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)))),
% 0.16/0.43 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.16/0.43 tff(104,plain,
% 0.16/0.43 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_))))),
% 0.16/0.43 inference(modus_ponens,[status(thm)],[103, 97])).
% 0.16/0.43 tff(105,plain,(
% 0.16/0.43 ![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_))))),
% 0.16/0.43 inference(skolemize,[status(sab)],[104])).
% 0.16/0.43 tff(106,plain,
% 0.16/0.43 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_))))),
% 0.16/0.43 inference(modus_ponens,[status(thm)],[105, 95])).
% 0.16/0.43 tff(107,plain,
% 0.16/0.43 (((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_))))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)))) <=> ((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_))))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)))),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(108,plain,
% 0.16/0.44 ((p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_)))) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)))),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(109,plain,
% 0.16/0.44 (((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_))))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))))) <=> ((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_))))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))))),
% 0.16/0.44 inference(monotonicity,[status(thm)],[108])).
% 0.16/0.44 tff(110,plain,
% 0.16/0.44 (((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_))))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))))) <=> ((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_))))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)))),
% 0.16/0.44 inference(transitivity,[status(thm)],[109, 107])).
% 0.16/0.44 tff(111,plain,
% 0.16/0.44 ((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_))))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))))),
% 0.16/0.44 inference(quant_inst,[status(thm)],[])).
% 0.16/0.44 tff(112,plain,
% 0.16/0.44 ((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_))))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.16/0.44 tff(113,plain,
% 0.16/0.44 ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))),
% 0.16/0.44 inference(unit_resolution,[status(thm)],[112, 106, 44, 41])).
% 0.16/0.44 tff(114,plain,
% 0.16/0.44 (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))),
% 0.16/0.44 inference(unit_resolution,[status(thm)],[113, 93, 38])).
% 0.16/0.44 tff(115,plain,
% 0.16/0.44 (^[T_13: $i] : refl((p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_))) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_))))),
% 0.16/0.44 inference(bind,[status(th)],[])).
% 0.16/0.44 tff(116,plain,
% 0.16/0.44 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_))) <=> ![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_)))),
% 0.16/0.44 inference(quant_intro,[status(thm)],[115])).
% 0.16/0.44 tff(117,plain,
% 0.16/0.44 (^[T_13: $i] : trans(monotonicity(rewrite(p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0) <=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_))), ((p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_))))), rewrite((p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_))) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_)))), ((p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_)))))),
% 0.16/0.44 inference(bind,[status(th)],[])).
% 0.16/0.44 tff(118,plain,
% 0.16/0.44 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) <=> ![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_)))),
% 0.16/0.44 inference(quant_intro,[status(thm)],[117])).
% 0.16/0.44 tff(119,plain,
% 0.16/0.44 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) <=> ![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(120,plain,
% 0.16/0.44 (^[T_13: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) <=> ((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))), ((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) <=> (((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))))), rewrite((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) <=> ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))), ((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) <=> ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)))), (((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) <=> (((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))))), rewrite((((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) <=> ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))), (((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) <=> ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)))), ((((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))) <=> (((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))))), rewrite((((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))), ((((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))))),
% 0.16/0.44 inference(bind,[status(th)],[])).
% 0.16/0.44 tff(121,plain,
% 0.16/0.44 (![T_13: $i] : (((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))) <=> ![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))),
% 0.16/0.44 inference(quant_intro,[status(thm)],[120])).
% 0.16/0.44 tff(122,axiom,(![T_13: $i] : (((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)))), file('/export/starexec/sandbox/benchmark/Axioms/HWV004-0.ax','axiom_31')).
% 0.16/0.44 tff(123,plain,
% 0.16/0.44 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.16/0.44 tff(124,plain,
% 0.16/0.44 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.16/0.44 tff(125,plain,
% 0.16/0.44 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_)))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[124, 118])).
% 0.16/0.44 tff(126,plain,(
% 0.16/0.44 ![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_)))),
% 0.16/0.44 inference(skolemize,[status(sab)],[125])).
% 0.16/0.44 tff(127,plain,
% 0.16/0.44 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_)))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[126, 116])).
% 0.16/0.44 tff(128,plain,
% 0.16/0.44 (((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_)))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))) <=> ((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(129,plain,
% 0.16/0.44 ((p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(130,plain,
% 0.16/0.44 (((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_)))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_)))) <=> ((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_)))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))))),
% 0.16/0.44 inference(monotonicity,[status(thm)],[129])).
% 0.16/0.44 tff(131,plain,
% 0.16/0.44 (((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_)))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_)))) <=> ((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))),
% 0.16/0.44 inference(transitivity,[status(thm)],[130, 128])).
% 0.16/0.44 tff(132,plain,
% 0.16/0.44 ((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_)))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_)))),
% 0.16/0.44 inference(quant_inst,[status(thm)],[])).
% 0.16/0.44 tff(133,plain,
% 0.16/0.44 ((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), f__length_(f__empty_)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.16/0.44 tff(134,plain,
% 0.16/0.44 ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
% 0.16/0.44 inference(unit_resolution,[status(thm)],[133, 127, 44, 41])).
% 0.16/0.44 tff(135,plain,
% 0.16/0.44 (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)),
% 0.16/0.44 inference(unit_resolution,[status(thm)],[134, 114, 93])).
% 0.16/0.44 tff(136,plain,
% 0.16/0.44 (fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1))),
% 0.16/0.44 inference(symmetry,[status(thm)],[135])).
% 0.16/0.44 tff(137,plain,
% 0.16/0.44 (^[T_0: $i] : refl((fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0)) <=> (fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0)))),
% 0.16/0.44 inference(bind,[status(th)],[])).
% 0.16/0.44 tff(138,plain,
% 0.16/0.44 (![T_0: $i] : (fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0)) <=> ![T_0: $i] : (fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0))),
% 0.16/0.44 inference(quant_intro,[status(thm)],[137])).
% 0.16/0.44 tff(139,plain,
% 0.16/0.44 (![T_0: $i] : (fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0)) <=> ![T_0: $i] : (fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0))),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(140,axiom,(![T_0: $i] : (fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0))), file('/export/starexec/sandbox/benchmark/Axioms/HWV004-0.ax','axiom_5')).
% 0.16/0.44 tff(141,plain,
% 0.16/0.44 (![T_0: $i] : (fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.16/0.44 tff(142,plain,(
% 0.16/0.44 ![T_0: $i] : (fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0))),
% 0.16/0.44 inference(skolemize,[status(sab)],[141])).
% 0.16/0.44 tff(143,plain,
% 0.16/0.44 (![T_0: $i] : (fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0))),
% 0.16/0.44 inference(modus_ponens,[status(thm)],[142, 138])).
% 0.16/0.44 tff(144,plain,
% 0.16/0.44 ((~![T_0: $i] : (fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0))) | (fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
% 0.16/0.44 inference(quant_inst,[status(thm)],[])).
% 0.16/0.44 tff(145,plain,
% 0.16/0.44 (fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)),
% 0.16/0.45 inference(unit_resolution,[status(thm)],[144, 143])).
% 0.16/0.45 tff(146,plain,
% 0.16/0.45 (fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) = f__length_(f__empty_)),
% 0.16/0.45 inference(transitivity,[status(thm)],[145, 136, 17])).
% 0.16/0.45 tff(147,plain,
% 0.16/0.45 (p_LES_EQU_(f__length_(f__empty_), fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) <=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)), f__length_(f__empty_))),
% 0.16/0.45 inference(monotonicity,[status(thm)],[20, 146])).
% 0.16/0.45 tff(148,plain,
% 0.16/0.45 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)), f__length_(f__empty_)) <=> p_LES_EQU_(f__length_(f__empty_), fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))),
% 0.16/0.45 inference(symmetry,[status(thm)],[147])).
% 0.16/0.45 tff(149,plain,
% 0.16/0.45 ((~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)), f__length_(f__empty_))) <=> (~p_LES_EQU_(f__length_(f__empty_), fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)))),
% 0.16/0.45 inference(monotonicity,[status(thm)],[148])).
% 0.16/0.45 tff(150,plain,
% 0.16/0.45 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_)) <=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)), f__length_(f__empty_))),
% 0.16/0.45 inference(monotonicity,[status(thm)],[136])).
% 0.16/0.45 tff(151,plain,
% 0.16/0.45 ((~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) <=> (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)), f__length_(f__empty_)))),
% 0.16/0.45 inference(monotonicity,[status(thm)],[150])).
% 0.16/0.45 tff(152,plain,
% 0.16/0.45 (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)), f__length_(f__empty_))),
% 0.16/0.45 inference(modus_ponens,[status(thm)],[114, 151])).
% 0.16/0.45 tff(153,plain,
% 0.16/0.45 (~p_LES_EQU_(f__length_(f__empty_), fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))),
% 0.16/0.45 inference(modus_ponens,[status(thm)],[152, 149])).
% 0.16/0.45 tff(154,plain,
% 0.16/0.45 (p_LES_EQU_(n0, fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) <=> p_LES_EQU_(f__length_(f__empty_), fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))),
% 0.16/0.45 inference(rewrite,[status(thm)],[])).
% 0.16/0.45 tff(155,plain,
% 0.16/0.45 (p_LES_EQU_(n0, fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)) <=> p_LES_EQU_(n0, fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))),
% 0.16/0.45 inference(rewrite,[status(thm)],[])).
% 0.16/0.45 tff(156,axiom,(p_LES_EQU_(n0, fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quest_1')).
% 0.16/0.45 tff(157,plain,
% 0.16/0.45 (p_LES_EQU_(n0, fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))),
% 0.16/0.45 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.16/0.45 tff(158,plain,
% 0.16/0.45 (p_LES_EQU_(f__length_(f__empty_), fwork_DOTfifo_DOTrtl_DOTlevel_(t_206))),
% 0.16/0.45 inference(modus_ponens,[status(thm)],[157, 154])).
% 0.16/0.45 tff(159,plain,
% 0.16/0.45 ($false),
% 0.16/0.45 inference(unit_resolution,[status(thm)],[158, 153])).
% 0.16/0.45 % SZS output end Proof
%------------------------------------------------------------------------------